{"count": 113, "status":"OK", "data":[{"pols": "[169*X^4, -5733*X^4-8970*X^3-8203*X^2-3718*X-676, 81936*X^4+249216*X^3+339440*X^2+219232*X+55120, -655360*X^4-2915328*X^3-5199872*X^2-4153344*X-1224704, 2048000*X^4+9207808*X^3+14827520*X^2+10223616*X+2572288, -2097152*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 358/5.105", "degz": 5, "h3": "208", "sol": "1 4 20 112 916 11504 159536 2075840 25409428 308606224", "n_discr_factors": "3", "c3": "-128", "operator": "4 5 0 0 0 0 169 -676 -3718 -8203 -8970 -5733 55120 219232 339440 249216 81936 -1224704 -4153344 -5199872 -2915328 -655360 2572288 10223616 14827520 9207808 2048000 -2097152 -8388608 -12582912 -8388608 -2097152", "new_number": "5.104", "id": 186, "operator_tex": "13^{2} \\theta^4-13 x\\left(441\\theta^4+690\\theta^3+631\\theta^2+286\\theta+52\\right)+2^{4} x^{2}\\left(5121\\theta^4+15576\\theta^3+21215\\theta^2+13702\\theta+3445\\right)-2^{10} x^{3}\\left(640\\theta^4+2847\\theta^3+5078\\theta^2+4056\\theta+1196\\right)+2^{14} x^{4}\\left(125\\theta^4+562\\theta^3+905\\theta^2+624\\theta+157\\right)-2^{21} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "7/13 21/13", "discriminant": "5 169 -5733 81936 -655360 2048000 -2097152", "aesz": "357", "n_sing_complex": "2", "inst_int": "", "c2h": "160", "hash": "afee0651c9b3b8e98079f5c2d5bfa8a5", "dim_h": "48", "inst": " 7/13 -10/13 21/13 296/13 608/13 -1020/13 5922/13 11928 666516/13 -13020", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(128z^2-13z+1)(-13+32z)^2", "discr_factors": "-2097152, (-13/32+z)^2, z^2-13/128*z+1/128, z-1/16", "dm_basis": null, "q": "0 1 -6 35 -208 821 -3474 14797 -61472 110511", "yuk": "1 7/13 -73/13 574/13 18871/13 76007/13 -219826/13 2031253/13 79411639/13 485890738/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/32","im":"0","approx_re":"0.40625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2000*X^4+992*X^3+496*X^2-16, 1310720*X^4-587776*X^3+772096*X^2+243712*X+22528, -335609856*X^4-321650688*X^3-341639168*X^2-162791424*X-32964608, 48091889664*X^4+117121744896*X^3+131625648128*X^2+73064775680*X+16139681792, -2903397892096*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 357/5.04", "degz": 5, "h3": null, "sol": "1 16 -880 -180992 -12537584 691548416 293972347136 32854346485760 -349086840668912 -722814870658191104", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -16 0 496 992 -2000 22528 243712 772096 -587776 1310720 -32964608 -162791424 -341639168 -321650688 -335609856 16139681792 73064775680 131625648128 117121744896 48091889664 -2903397892096 -11613591568384 -17420387352576 -11613591568384 -2903397892096", "new_number": "5.105", "id": 187, "operator_tex": "\\theta^4-2^{4} x\\left(125\\theta^4-62\\theta^3-31\\theta^2+1\\right)+2^{11} x^{2}\\left(640\\theta^4-287\\theta^3+377\\theta^2+119\\theta+11\\right)-2^{16} x^{3}\\left(5121\\theta^4+4908\\theta^3+5213\\theta^2+2484\\theta+503\\right)+2^{23} 13 x^{4}\\left(441\\theta^4+1074\\theta^3+1207\\theta^2+670\\theta+148\\right)-2^{34} 13^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-336 -4761360", "discriminant": "5 1 -2000 1310720 -335609856 48091889664 -2903397892096", "aesz": "358", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "f026b6514e3be9b730646bc9410b1049", "dim_h": null, "inst": " -336 -30306 -4761360 -962369202 -225176272240 -57956090342842 -15948662788921552 -4611322641626776234 -1384954980602120752512 -428673788588552594915990", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(32768z^2-208z+1)(-1+832z)^2", "discr_factors": "-2903397892096, z-1/128, (-1/832+z)^2, z^2-13/2048*z+1/32768", "dm_basis": null, "q": "0 1 64 16672 4375552 1259439920 384225030144 122172750749184 40062339694329856 13452434268185226904", "yuk": "1 -336 -242784 -128557056 -61591871712 -28147034030336 -12518515642853376 -5470391336600092672 -2360997192574501303520 -1009632180858946157138304", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/832","im":"0","approx_re":"0.00120192307692","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4096","im":"-7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"-0.004522","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4096","im":"7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"0.004522","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 624*X^4-672*X^3-464*X^2-128*X-16, 2048*X*(37*X^3-137*X^2-10*X-1), -11862016*X^4-29884416*X^3-23134208*X^2-8650752*X-1245184, -1509949440*X^4-2516582400*X^3-1509949440*X^2-251658240*X+41943040, 26843545600*(X+1)^4]", "text": "This is operator \"5.11\" from ...", "degz": 5, "h3": "32", "sol": "1 16 656 40192 3006736 252252416 22788843776 2168291250176 214374731955472 21830665093755136", "n_discr_factors": "4", "c3": "304", "operator": "4 5 0 0 0 0 1 -16 -128 -464 -672 624 0 -2048 -20480 -280576 75776 -1245184 -8650752 -23134208 -29884416 -11862016 41943040 -251658240 -1509949440 -2516582400 -1509949440 26843545600 107374182400 161061273600 107374182400 26843545600", "new_number": "5.11", "id": 203, "operator_tex": "\\theta^4+2^{4} x\\left(39\\theta^4-42\\theta^3-29\\theta^2-8\\theta-1\\right)+2^{11} x^{2}\\theta(37\\theta^3-137\\theta^2-10\\theta-1)-2^{16} x^{3}\\left(181\\theta^4+456\\theta^3+353\\theta^2+132\\theta+19\\right)-2^{23} 5 x^{4}\\left(36\\theta^4+60\\theta^3+36\\theta^2+6\\theta-1\\right)+2^{30} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "112 378800", "discriminant": "5 1 624 75776 -11862016 -1509949440 26843545600", "aesz": "71", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "cf4de65b0566a4f6294132c167d227eb", "dim_h": "8", "inst": " 112 -4570 378800 -40565898 5098744272 -707870516690 105432934036208 -16535931080941762 2698540270299157632 -454448691741869508414", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(16z-1)(128z-1)(128z+1)(1+320z)^2", "discr_factors": "26843545600, z+1/128, z-1/16, z-1/128, (1/320+z)^2", "dm_basis": null, "q": "0 1 -64 5152 -592896 81453872 -12454109184 2036443729408 -348923423752192 61860266815790744", "yuk": "1 112 -36448 10227712 -2596253920 637343034112 -152900021413888 36163496374419456 -8466396716038436064 1967235857048096141440", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/320","im":"0","approx_re":"-0.003125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 72+540*X+1596*X^2+2112*X^3+3072*X^4, -1920+1920*X+74752*X^2+249856*X^3+331264*X^4, 454656+2912256*X+7376896*X^2+10100736*X^3+13037568*X^4, 4587520+50462720*X+165150720*X^2+229376000*X^3+122945536*X^4, -205520896*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 212/5.31", "degz": 5, "h3": "432", "sol": "1 -8 424 -36224 3778216 -440739008 55291965184 -7301041037312 1001440179848872 -141454394147037248", "n_discr_factors": "3", "c3": "-1152", "operator": "4 5 0 0 0 0 9 72 540 1596 2112 3072 -1920 1920 74752 249856 331264 454656 2912256 7376896 10100736 13037568 4587520 50462720 165150720 229376000 122945536 -205520896 -822083584 -1233125376 -822083584 -205520896", "new_number": "5.15", "id": 222, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(256\\theta^4+176\\theta^3+133\\theta^2+45\\theta+6\\right)+2^{7} x^{2}\\left(2588\\theta^4+1952\\theta^3+584\\theta^2+15\\theta-15\\right)+2^{12} x^{3}\\left(3183\\theta^4+2466\\theta^3+1801\\theta^2+711\\theta+111\\right)+2^{17} 7 x^{4}\\left(134\\theta^4+250\\theta^3+180\\theta^2+55\\theta+5\\right)-2^{22} 7^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-52/3 -17428", "discriminant": "5 9 3072 331264 13037568 122945536 -205520896", "aesz": "117", "n_sing_complex": "0", "inst_int": "", "c2h": "288", "hash": "111a4ce3248a309bf6283916fd9f11c4", "dim_h": "96", "inst": " -52/3 1348/3 -17428 884000 -163422880/3 3852894052 -900638629436/3 75278976461744/3 -2211698609231952 609674044784449696/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(256z^2-176z-1)(3+224z)^2", "discr_factors": "-205520896, z^2-11/16*z-1/256, z+1/16, (3/224+z)^2", "dm_basis": null, "q": "0 1 28 -418 20912 -1327571 102389128 -8836797806 815317139904 -78754860905978", "yuk": "1 -52/3 10732/3 -1411720/3 169738732/3 -6809286684 2496673944760/3 -102973016632200 38542836118151660/3 -4836984858391690744/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/224","im":"0","approx_re":"-0.0133928571429","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32+5/32*5^(1/2)","im":"0","approx_re":"0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -465*X^4-594*X^3-431*X^2-134*X-16, 42000*X^4+30576*X^3-15136*X^2-14144*X-2816, -1030720*X^4+231936*X^3+335424*X^2+82176*X+2304, -2222080*X^4-4788224*X^3-4386816*X^2-1992704*X-372736, 3211264*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 22/5.5", "degz": 5, "h3": "180", "sol": "1 16 1816 310336 64483576 15001950016 3756814881856 990767991264256 271513815031152376 76641403901116604416", "n_discr_factors": "3", "c3": "-900", "operator": "4 5 0 0 0 0 1 -16 -134 -431 -594 -465 -2816 -14144 -15136 30576 42000 2304 82176 335424 231936 -1030720 -372736 -1992704 -4386816 -4788224 -2222080 3211264 12845056 19267584 12845056 3211264", "new_number": "5.16", "id": 223, "operator_tex": "\\theta^4-x\\left(465\\theta^4+594\\theta^3+431\\theta^2+134\\theta+16\\right)+2^{4} x^{2}\\left(2625\\theta^4+1911\\theta^3-946\\theta^2-884\\theta-176\\right)-2^{6} x^{3}\\left(16105\\theta^4-3624\\theta^3-5241\\theta^2-1284\\theta-36\\right)-2^{11} 7 x^{4}\\left(155\\theta^4+334\\theta^3+306\\theta^2+139\\theta+26\\right)+2^{16} 7^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "55 116555", "discriminant": "5 1 -465 42000 -1030720 -2222080 3211264", "aesz": "118", "n_sing_complex": "0", "inst_int": "", "c2h": "0", "hash": "d950d38dab80e3772855675af0cdb950", "dim_h": "30", "inst": " 55 1915 116555 10661240 1227998285 162350589750 23577384844690 3667742827262750 601330335417896290 102757467277183662915", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(z-1)(1024z^2+352z-1)(-1+56z)^2", "discr_factors": "3211264, z-1, z^2+11/32*z-1/1024, (-1/56+z)^2", "dm_basis": null, "q": "0 1 -70 -595 -67760 -11713690 -1815175374 -296780681310 -51373190652480 -9283081256642125", "yuk": "1 55 15375 3147040 682334735 153499785680 35067730548360 8087043001728725 1877884328240862735 438369814519649542450", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/64-5/64*5^(1/2)","im":"0","approx_re":"-0.346568","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/64+5/64*5^(1/2)","im":"0","approx_re":"0.002818","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/56","im":"0","approx_re":"0.0178571428571","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[3721*X^4, -184769*X^4-339892*X^3-285297*X^2-115351*X-18605, 1215215*X^4+3428132*X^3+4267228*X^2+2572675*X+611586, -3188970*X^4-11354418*X^3-16751367*X^2-11517471*X-3023892, 3713526*X^4+14631030*X^3+22018716*X^2+14703201*X+3661038, -1594323*(X+1)^4]", "text": "This is operator \"5.18\" from ...", "degz": 5, "h3": "61", "sol": "1 5 69 1427 35749 1000005 30058575 950480445 31208594085 1054973524145", "n_discr_factors": "2", "c3": "-86", "operator": "4 5 0 0 0 0 3721 -18605 -115351 -285297 -339892 -184769 611586 2572675 4267228 3428132 1215215 -3023892 -11517471 -16751367 -11354418 -3188970 3661038 14703201 22018716 14631030 3713526 -1594323 -6377292 -9565938 -6377292 -1594323", "new_number": "5.18", "id": 225, "operator_tex": "61^{2} \\theta^4-61 x\\left(3029\\theta^4+5572\\theta^3+4677\\theta^2+1891\\theta+305\\right)+x^{2}\\left(1215215\\theta^4+3428132\\theta^3+4267228\\theta^2+2572675\\theta+611586\\right)-3^{4} x^{3}\\left(39370\\theta^4+140178\\theta^3+206807\\theta^2+142191\\theta+37332\\right)+3^{8} x^{4}\\left(566\\theta^4+2230\\theta^3+3356\\theta^2+2241\\theta+558\\right)-3^{13} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "163/61 4795/61", "discriminant": "5 3721 -184769 1215215 -3188970 3713526 -1594323", "aesz": "124", "n_sing_complex": "2", "inst_int": "", "c2h": "94", "hash": "394b401a3162e31c79ede5b46973791d", "dim_h": "18", "inst": " 163/61 630/61 4795/61 48422/61 599809/61 8459307/61 130721868/61 2160794564/61 37614259014/61 682135961319/61", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(243z^3-200z^2+47z-1)(-61+81z)^2", "discr_factors": "-1594323, z^3-200/243*z^2+47/243*z-1/243, (-61/81+z)^2", "dm_basis": null, "q": "0 1 -11 38 -246 -494 -20837 -319545 -6032901 -115504922", "yuk": "1 163/61 5203/61 129628/61 3104211/61 74976288/61 1827344980/61 44837600887/61 1106329920979/61 27420794950834/61", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1458*(11853908+1175148*93^(1/2))^(1/3)-11474/729/(11853908+1175148*93^(1/2))^(1/3)+200/729","im":"0","approx_re":"0.023574","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2916*(11853908+1175148*93^(1/2))^(1/3)+5737/729/(11853908+1175148*93^(1/2))^(1/3)+200/729","im":"1/2*3^(1/2)*(-1/1458*(11853908+1175148*93^(1/2))^(1/3)+11474/729/(11853908+1175148*93^(1/2))^(1/3))","approx_re":"0.399736","approx_im":"-0.121575","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2916*(11853908+1175148*93^(1/2))^(1/3)+5737/729/(11853908+1175148*93^(1/2))^(1/3)+200/729","im":"-1/2*3^(1/2)*(-1/1458*(11853908+1175148*93^(1/2))^(1/3)+11474/729/(11853908+1175148*93^(1/2))^(1/3))","approx_re":"0.399736","approx_im":"0.121575","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"61/81","im":"0","approx_re":"0.753086419753","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -765*X^4-1260*X^3-1080*X^2-450*X-75, 3186*X^4+4968*X^3+3246*X^2+930*X+90, -22842*X^4-116640*X^3-237546*X^2-204930*X-63180, 67797*X^4+332424*X^3+551610*X^2+385398*X+97686, -59049*(X+1)^4]", "text": "There is a second MUM-point at infinity, \ncorresponding to Operator AESZ 290/5.71\nA-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \\times P^2 \\times P^2$\n", "degz": 5, "h3": "90", "sol": "1 3 27 381 6219 111753 2151549 43497891 912018123 19671397617", "n_discr_factors": "3", "c3": "-90", "operator": "4 5 0 0 0 0 25 -75 -450 -1080 -1260 -765 90 930 3246 4968 3186 -63180 -204930 -237546 -116640 -22842 97686 385398 551610 332424 67797 -59049 -236196 -354294 -236196 -59049", "new_number": "5.1", "id": 227, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(51\\theta^4+84\\theta^3+72\\theta^2+30\\theta+5\\right)+2 3 x^{2}\\left(531\\theta^4+828\\theta^3+541\\theta^2+155\\theta+15\\right)-2 3^{3} x^{3}\\left(423\\theta^4+2160\\theta^3+4399\\theta^2+3795\\theta+1170\\right)+3^{5} x^{4}\\left(279\\theta^4+1368\\theta^3+2270\\theta^2+1586\\theta+402\\right)-3^{10} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "6/5 118/5", "discriminant": "5 25 -765 3186 -22842 67797 -59049", "aesz": "17", "n_sing_complex": "2", "inst_int": "", "c2h": "108", "hash": "370d10edbf5900002f79cf6163e106a5", "dim_h": "24", "inst": " 6/5 39/10 118/5 1443/10 6108/5 117827/10 609006/5 13554147/10 15889556 968968881/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z-1)(27z^2+1)(-5+9z)^2", "discr_factors": "-59049, z^2+1/27, (-5/9+z)^2, z-1/27", "dm_basis": null, "q": "0 1 -6 3 -74 105 -3744 -35310 -429666 -5527026", "yuk": "1 6/5 162/5 3192/5 46338/5 763506/5 12728664/5 208889064/5 693981594 57917434812/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"-1/9*3^(1/2)","approx_re":"0.0","approx_im":"-0.19245","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/9*3^(1/2)","approx_re":"0.0","approx_im":"0.19245","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/9","im":"0","approx_re":"0.555555555556","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[361*X^4, -13300*X^4-23522*X^3-18981*X^2-7220*X-1083, -64745*X^4-368006*X^3-609133*X^2-412756*X-102258, 172719*X^4+329346*X^3-321921*X^2-738720*X-304722, 46656*X^4+841266*X^3+1767825*X^2+1347192*X+354294, -177147*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 187/5.21", "degz": 5, "h3": "57", "sol": "1 3 51 1029 25299 687753 20045229 613654443 19490199507 636940635897", "n_discr_factors": "3", "c3": "-84", "operator": "4 5 0 0 0 0 361 -1083 -7220 -18981 -23522 -13300 -102258 -412756 -609133 -368006 -64745 -304722 -738720 -321921 329346 172719 354294 1347192 1767825 841266 46656 -177147 -708588 -1062882 -708588 -177147", "new_number": "5.20", "id": 228, "operator_tex": "19^{2} \\theta^4-19 x\\left(700\\theta^4+1238\\theta^3+999\\theta^2+380\\theta+57\\right)-x^{2}\\left(64745\\theta^4+368006\\theta^3+609133\\theta^2+412756\\theta+102258\\right)+3^{3} x^{3}\\left(6397\\theta^4+12198\\theta^3-11923\\theta^2-27360\\theta-11286\\right)+3^{6} x^{4}\\left(64\\theta^4+1154\\theta^3+2425\\theta^2+1848\\theta+486\\right)-3^{11} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "49/19 1761/19", "discriminant": "5 361 -13300 -64745 172719 46656 -177147", "aesz": "186", "n_sing_complex": "0", "inst_int": "", "c2h": "90", "hash": "b3d164f22d02de1efcd62d3aa9ab5ce4", "dim_h": "17", "inst": " 49/19 252/19 1761/19 18990/19 246159/19 3654804/19 59305344/19 1030386030/19 18850527984/19 359318138564/19", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(243z^2+35z-1)(-19+27z)^2", "discr_factors": "-177147, z+1, (-19/27+z)^2, z^2+35/243*z-1/243", "dm_basis": null, "q": "0 1 -8 -26 88 -1649 -31760 -532724 -10232000 -207545111", "yuk": "1 49/19 2065/19 47596/19 64075 30769924/19 789487276/19 20341733041/19 527558864785/19 13742034947932/19", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-35/486-13/486*13^(1/2)","im":"0","approx_re":"-0.168461","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-35/486+13/486*13^(1/2)","im":"0","approx_re":"0.024428","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"19/27","im":"0","approx_re":"0.703703703704","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -64*X^4+898*X^3+653*X^2+204*X+27, -57573*X^4-120510*X^3+91215*X^2+67428*X+14850, 5244345*X^4-8831106*X^3-8619615*X^2-3201768*X-374706, 261783900*X^4+584152074*X^3+555355845*X^2+263279808*X+51608826, -1726651809*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 186/ 5.20", "degz": 5, "h3": null, "sol": "1 -27 1971 -220941 30762099 -4844676177 825067846989 -148318424601507 27741555966933747 -5348924047337355873", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 27 204 653 898 -64 14850 67428 91215 -120510 -57573 -374706 -3201768 -8619615 -8831106 5244345 51608826 263279808 555355845 584152074 261783900 -1726651809 -6906607236 -10359910854 -6906607236 -1726651809", "new_number": "5.21", "id": 229, "operator_tex": "\\theta^4-x\\left(64\\theta^4-898\\theta^3-653\\theta^2-204\\theta-27\\right)-3^{2} x^{2}\\left(6397\\theta^4+13390\\theta^3-10135\\theta^2-7492\\theta-1650\\right)+3^{4} x^{3}\\left(64745\\theta^4-109026\\theta^3-106415\\theta^2-39528\\theta-4626\\right)+3^{9} 19 x^{4}\\left(700\\theta^4+1562\\theta^3+1485\\theta^2+704\\theta+138\\right)-3^{14} 19^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-107 -121311", "discriminant": "5 1 -64 -57573 5244345 261783900 -1726651809", "aesz": "187", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "9a367922f464a13fa56d1c2e238faa34", "dim_h": null, "inst": " -107 -7701/4 -121311 -6204874 -518204863 -144727904433/4 -3396966107796 -275029740111146 -27494665072543119 -9712148044341170273/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(243z+1)(243z^2-35z-1)(-1+171z)^2", "discr_factors": "-1726651809, (-1/171+z)^2, z+1/243, z^2-35/243*z-1/243", "dm_basis": null, "q": "0 1 96 7602 680912 62289861 6078381912 600899848960 61845403954536 6407579473697160", "yuk": "1 -107 -15509 -3275504 -397127445 -64775607982 -7815310130288 -1165159374974135 -140815227334034197 -20043610837887209255", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"35/486-13/486*13^(1/2)","im":"0","approx_re":"-0.024428","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/243","im":"0","approx_re":"-0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/171","im":"0","approx_re":"0.00584795321637","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"35/486+13/486*13^(1/2)","im":"0","approx_re":"0.168461","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -539-4067*X-11781*X^2-15428*X^3-7945*X^4, 28723*X^4+40708*X^3+13260*X^2-1337*X-896, -32126*X^4-38514*X^3-26511*X^2-10731*X-1806, 10010*X^4+19558*X^3+14784*X^2+5005*X+616, 121*(X+1)^4]", "text": "There is a second MUM-point at infinity,\n corresponding to Operator AESZ 198/5.25", "degz": 5, "h3": "21", "sol": "1 11 559 42923 3996751 416148761 46607742091 5494953548459 673006663951183 84887862132737261", "n_discr_factors": "2", "c3": "-102", "operator": "4 5 0 0 0 0 49 -539 -4067 -11781 -15428 -7945 -896 -1337 13260 40708 28723 -1806 -10731 -26511 -38514 -32126 616 5005 14784 19558 10010 121 484 726 484 121", "new_number": "5.22", "id": 230, "operator_tex": "7^{2} \\theta^4-7 x\\left(1135\\theta^4+2204\\theta^3+1683\\theta^2+581\\theta+77\\right)+x^{2}\\left(28723\\theta^4+40708\\theta^3+13260\\theta^2-1337\\theta-896\\right)-x^{3}\\left(32126\\theta^4+38514\\theta^3+26511\\theta^2+10731\\theta+1806\\right)+7 11 x^{4}\\left(130\\theta^4+254\\theta^3+192\\theta^2+65\\theta+8\\right)+11^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "129/7 41441/7", "discriminant": "5 49 -7945 28723 -32126 10010 121", "aesz": "193", "n_sing_complex": "3", "inst_int": "", "c2h": "-6", "hash": "44e6fc2823d5ff31e66059ba6b37f2ae", "dim_h": "3", "inst": " 129/7 1557/7 41441/7 1594332/7 75470601/7 4083256483/7 242408011110/7 15405866523039/7 1031525154832019/7 71972605248215250/7", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(z^3+84z^2-159z+1)(-7+11z)^2", "discr_factors": "121, z^3+84*z^2-159*z+1, (-7/11+z)^2", "dm_basis": null, "q": "0 1 -39 366 -7798 -253224 -16489617 -1110602999 -78861263877 -5835798947685", "yuk": "1 129/7 12585/7 1119036/7 102049833/7 1347689322 125997790260 83145947810859/7 7887803761845801/7 751981837873660887/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/4*(-7164+228*I*3^(1/2))^(1/3)-279/(-7164+228*I*3^(1/2))^(1/3)-28+1/2*I*3^(1/2)*(3/2*(-7164+228*I*3^(1/2))^(1/3)-558/(-7164+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"-85.852157","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/4*(-7164+228*I*3^(1/2))^(1/3)-279/(-7164+228*I*3^(1/2))^(1/3)-28-1/2*I*3^(1/2)*(3/2*(-7164+228*I*3^(1/2))^(1/3)-558/(-7164+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00631","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/11","im":"0","approx_re":"0.636363636364","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/2*(-7164+228*I*3^(1/2))^(1/3)+558/(-7164+228*I*3^(1/2))^(1/3)-28","im":"0","approx_re":"1.845846","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, -2023-13872*X-37400*X^2-47056*X^3-24905*X^4, 30600+131852*X+250034*X^2+263164*X^3+124030*X^4, -91800-402084*X-691362*X^2-589356*X^3-233550*X^4, 122472+510300*X+815022*X^2+609444*X^3+193185*X^4, -59049*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 199/5.26", "degz": 5, "h3": "34", "sol": "1 7 183 7225 345079 18406257 1055299449 63665014791 3988953598455 257341097428513", "n_discr_factors": "3", "c3": "-88", "operator": "4 5 0 0 0 0 289 -2023 -13872 -37400 -47056 -24905 30600 131852 250034 263164 124030 -91800 -402084 -691362 -589356 -233550 122472 510300 815022 609444 193185 -59049 -236196 -354294 -236196 -59049", "new_number": "5.23", "id": 231, "operator_tex": "17^{2} \\theta^4-17 x\\left(1465\\theta^4+2768\\theta^3+2200\\theta^2+816\\theta+119\\right)+2 x^{2}\\left(62015\\theta^4+131582\\theta^3+125017\\theta^2+65926\\theta+15300\\right)-2 3^{3} x^{3}\\left(4325\\theta^4+10914\\theta^3+12803\\theta^2+7446\\theta+1700\\right)+3^{6} x^{4}\\left(265\\theta^4+836\\theta^3+1118\\theta^2+700\\theta+168\\right)-3^{10} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "126/17 11700/17", "discriminant": "5 289 -24905 124030 -233550 193185 -59049", "aesz": "194", "n_sing_complex": "0", "inst_int": "", "c2h": "76", "hash": "6bf19665aa6705f30ef88df42bc4eac4", "dim_h": "12", "inst": " 126/17 848/17 11700/17 229808/17 5539258/17 152369132/17 4596841530/17 148424442312/17 5048268480098/17 178910315960992/17", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+81z)(27z-17)^2(z-1)^2", "discr_factors": "-59049, (z-17/27)^2, -1/81+z, (z-1)^2", "dm_basis": null, "q": "0 1 -20 94 -1036 -16091 -560268 -18941924 -683866732 -25690637802", "yuk": "1 126/17 6910/17 316026/17 865566 692407376/17 32912055322/17 1576716644916/17 75993329178366/17 3680187722307468/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/27","im":"0","approx_re":"0.62962962963","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 847+5929*X+16170*X^2+20482*X^3+10010*X^4, -11198-55253*X-103725*X^2-89990*X^3-32126*X^4, 1716+20625*X+63474*X^2+74184*X^3+28723*X^4, -770-4991*X-13167*X^2-16352*X^3-7945*X^4, 49*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22", "degz": 5, "h3": "132", "sol": "1 -7 199 -8359 423751 -23973757 1457477659 -93222362023 6192061490503 -423467225669257", "n_discr_factors": "2", "c3": "-408", "operator": "4 5 0 0 0 0 121 847 5929 16170 20482 10010 -11198 -55253 -103725 -89990 -32126 1716 20625 63474 74184 28723 -770 -4991 -13167 -16352 -7945 49 196 294 196 49", "new_number": "5.25", "id": 233, "operator_tex": "11^{2} \\theta^4+7 11 x\\left(130\\theta^4+266\\theta^3+210\\theta^2+77\\theta+11\\right)-x^{2}\\left(11198+55253\\theta+103725\\theta^2+89990\\theta^3+32126\\theta^4\\right)+x^{3}\\left(1716+20625\\theta+63474\\theta^2+74184\\theta^3+28723\\theta^4\\right)-7 x^{4}\\left(1135\\theta^4+2336\\theta^3+1881\\theta^2+713\\theta+110\\right)+7^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-84/11 -9052/11", "discriminant": "5 121 10010 -32126 28723 -7945 49", "aesz": "198", "n_sing_complex": "3", "inst_int": "", "c2h": "132", "hash": "a1f924763b047c2720d99cfca5ca63db", "dim_h": "33", "inst": " -84/11 639/11 -9052/11 189021/11 -4838013/11 141421066/11 -4533181206/11 155521104120/11 -510941431295 846550286988477/44", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(z^3-159z^2+84z+1)(-11+7z)^2", "discr_factors": "49, z^3-159*z^2+84*z+1, (-11/7+z)^2", "dm_basis": null, "q": "0 1 21 93 970 -23541 740418 -27416745 1047984201 -41848595538", "yuk": "1 -84/11 5028/11 -244488/11 12102372/11 -604751709/11 30546710880/11 -1554881153742/11 7238801582892 -4097239337799093/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/4*(43452+228*I*3^(1/2))^(1/3)-927/(43452+228*I*3^(1/2))^(1/3)+53+1/2*I*3^(1/2)*(3/2*(43452+228*I*3^(1/2))^(1/3)-1854/(43452+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.011648","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/4*(43452+228*I*3^(1/2))^(1/3)-927/(43452+228*I*3^(1/2))^(1/3)+53-1/2*I*3^(1/2)*(3/2*(43452+228*I*3^(1/2))^(1/3)-1854/(43452+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.541757","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/7","im":"0","approx_re":"1.57142857143","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/2*(43452+228*I*3^(1/2))^(1/3)+1854/(43452+228*I*3^(1/2))^(1/3)+53","im":"0","approx_re":"158.469891","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -15-88*X-200*X^2-224*X^3-265*X^4, 2808+16308*X+36066*X^2+38316*X^3+25950*X^4, -86832-673596*X-1842498*X^2-2096604*X^3-1116270*X^4, 2478600+14128020*X+33287598*X^2+38319156*X^3+18155745*X^4, -17065161*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to \nOperator AESZ 194/5.23.", "degz": 5, "h3": null, "sol": "1 15 567 28113 1584279 96217065 6137825625 405392060655 27477962447895 1900205271755385", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -15 -88 -200 -224 -265 2808 16308 36066 38316 25950 -86832 -673596 -1842498 -2096604 -1116270 2478600 14128020 33287598 38319156 18155745 -17065161 -68260644 -102390966 -68260644 -17065161", "new_number": "5.26", "id": 234, "operator_tex": "\\theta^4-x\\left(15+88\\theta+200\\theta^2+224\\theta^3+265\\theta^4\\right)+2 3 x^{2}\\left(4325\\theta^4+6386\\theta^3+6011\\theta^2+2718\\theta+468\\right)-2 3^{2} x^{3}\\left(62015\\theta^4+116478\\theta^3+102361\\theta^2+37422\\theta+4824\\right)+3^{6} 17 x^{4}\\left(1465\\theta^4+3092\\theta^3+2686\\theta^2+1140\\theta+200\\right)-3^{10} 17^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-2 3820/9", "discriminant": "5 1 -265 25950 -1116270 18155745 -17065161", "aesz": "199", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f7b5c9e3ad50b0885d03c98d07a051f1", "dim_h": null, "inst": " -2 28 3820/9 3924 21606 -28252/3 -621714 36924812 13821031360/9 34301740012", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(z-1)(81z-1)^2(51z-1)^2", "discr_factors": "-17065161, (z-1/51)^2, (z-1/81)^2, z-1", "dm_basis": null, "q": "0 1 -28 282 -100 -909 -119796 -1068648 393948 226538829", "yuk": "1 -2 222 11458 251358 2700748 -2022462 -213247904 18905755102 1119503551618", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/51","im":"0","approx_re":"0.0196078431373","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[361*X^4, 26030*X^4+49780*X^3+39691*X^2+14801*X+2166, 39521*X^4-3916*X^3-106779*X^2-95266*X-25384, -13192*X^4-158232*X^3-237336*X^2-140904*X-31008, -80*(X+1)*(499*X^3+1411*X^2+1378*X+456), -12800*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 203/5.28", "degz": 5, "h3": null, "sol": "1 -6 142 -4920 205326 -9555756 477712096 -25120559232 1371618200590 -77102666841156", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 361 2166 14801 39691 49780 26030 -25384 -95266 -106779 -3916 39521 -31008 -140904 -237336 -158232 -13192 -36480 -146720 -223120 -152800 -39920 -12800 -51200 -76800 -51200 -12800", "new_number": "5.27", "id": 235, "operator_tex": "19^{2} \\theta^4+19 x\\left(1370\\theta^4+2620\\theta^3+2089\\theta^2+779\\theta+114\\right)+x^{2}\\left(39521\\theta^4-3916\\theta^3-106779\\theta^2-95266\\theta-25384\\right)-2^{3} x^{3}\\left(1649\\theta^4+19779\\theta^3+29667\\theta^2+17613\\theta+3876\\right)-2^{4} 5 x^{4}(\\theta+1)(499\\theta^3+1411\\theta^2+1378\\theta+456)-2^{9} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-113/19 -8515/19", "discriminant": "5 361 26030 39521 -13192 -39920 -12800", "aesz": "202", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "3bf3c283277de7b3808ad309fac9b7a1", "dim_h": null, "inst": " -113/19 2921/76 -8515/19 146869/19 -3105422/19 299610759/76 -1981081104/19 56074672419/19 -1671866897017/19 103874712503999/38", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(32z^2+71z+1)(19+20z)^2", "discr_factors": "-12800, (19/20+z)^2, z-1, z^2+71/32*z+1/32", "dm_basis": null, "q": "0 1 17 52 447 -11351 287944 -8732823 275975113 -9085625815", "yuk": "1 -113/19 5729/19 -230018/19 9405345/19 -388177863/19 16178756810/19 -679510818785/19 28710241683873/19 -1218790968155411/19", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-71/64-17/64*17^(1/2)","im":"0","approx_re":"-2.204575","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-19/20","im":"0","approx_re":"-0.95","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-71/64+17/64*17^(1/2)","im":"0","approx_re":"-0.014175","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X*(499*X^3+86*X^2+53*X+10), -35200-176320*X-316416*X^2-210928*X^3+26384*X^4, -2529344*X^4-10368000*X^3-9094080*X^2-3298560*X-418560, -6770688-39651328*X-95295488*X^2-111288320*X^3-53309440*X^4, -23658496*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 202 /5.27", "degz": 5, "h3": null, "sol": "1 0 88 -1728 99576 -4104000 218996800 -11248204800 623355019000 -34914774384000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 0 50 265 430 2495 -35200 -176320 -316416 -210928 26384 -418560 -3298560 -9094080 -10368000 -2529344 -6770688 -39651328 -95295488 -111288320 -53309440 -23658496 -94633984 -141950976 -94633984 -23658496", "new_number": "5.28", "id": 236, "operator_tex": "5^{2} \\theta^4+5 x\\theta(499\\theta^3+86\\theta^2+53\\theta+10)+2^{4} x^{2}\\left(1649\\theta^4-13183\\theta^3-19776\\theta^2-11020\\theta-2200\\right)-2^{6} x^{3}\\left(39521\\theta^4+162000\\theta^3+142095\\theta^2+51540\\theta+6540\\right)-2^{11} 19 x^{4}\\left(1370\\theta^4+2860\\theta^3+2449\\theta^2+1019\\theta+174\\right)-2^{16} 19^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-13/5 -6729/5", "discriminant": "5 25 2495 26384 -2529344 -53309440 -23658496", "aesz": "203\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "dfab012366b4bc6f7af83dc79f28b802", "dim_h": null, "inst": " -13/5 427/5 -6729/5 173044/5 -952275 31195374 -5514062598/5 42168142346 -8475611077782/5 355803042375043/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(32z-1)(32z^2+71z+1)(5+152z)^2", "discr_factors": "-23658496, z-1/32, z^2+71/32*z+1/32, (5/152+z)^2", "dm_basis": null, "q": "0 1 2 -275 4288 -95386 2950426 -114735582 4761541376 -209360204557", "yuk": "1 -13/5 3403/5 -181696/5 11078219/5 -595171888/5 6738165128 -1891323471127/5 107950455483979/5 -6178720475884774/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-71/64-17/64*17^(1/2)","im":"0","approx_re":"-2.204575","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/152","im":"0","approx_re":"-0.0328947368421","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-71/64+17/64*17^(1/2)","im":"0","approx_re":"-0.014175","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 1876*X^4+4004*X^3+3276*X^2+1274*X+196, -7672-32900*X-54004*X^2-41064*X^3-12732*X^4, 20704*X^4+67200*X^3+82048*X^2+45192*X+9520, -8352-34416*X-54768*X^2-40704*X^3-12288*X^4, 2304*(X+1)^4]", "text": "There is a second MUM-point corresponding to Operator AESZ 117 /5.515.", "degz": 5, "h3": null, "sol": "1 -4 64 -1408 37216 -1093504 34467616 -1141889536 39261600352 -1389328714624", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 49 196 1274 3276 4004 1876 -7672 -32900 -54004 -41064 -12732 9520 45192 82048 67200 20704 -8352 -34416 -54768 -40704 -12288 2304 9216 13824 9216 2304", "new_number": "5.31", "id": 240, "operator_tex": "7^{2} \\theta^4+2 7 x\\left(134\\theta^4+286\\theta^3+234\\theta^2+91\\theta+14\\right)-2^{2} x^{2}\\left(3183\\theta^4+10266\\theta^3+13501\\theta^2+8225\\theta+1918\\right)+2^{3} x^{3}\\left(2588\\theta^4+8400\\theta^3+10256\\theta^2+5649\\theta+1190\\right)-2^{4} 3 x^{4}\\left(256\\theta^4+848\\theta^3+1141\\theta^2+717\\theta+174\\right)+2^{8} 3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-20/7 -104", "discriminant": "5 49 1876 -12732 20704 -12288 2304", "aesz": "212", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f72aa947ba945355102b3fef56e0af0f", "dim_h": null, "inst": " -20/7 57/4 -104 16385/14 -110508/7 487971/2 -28874844/7 522536803/7 -9957702452/7 112972467743/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(4z-1)(16z^2-44z-1)(6z-7)^2", "discr_factors": "2304, z^2-11/4*z-1/16, (z-7/6)^2, z-1/4", "dm_basis": null, "q": "0 1 10 1 -20 -2412 31482 -619038 12504648 -262953732", "yuk": "1 -20/7 778/7 -19676/7 75014 -1973360 368887198/7 -9904071512/7 267539368234/7 -7259165107184/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"11/8-5/8*5^(1/2)","im":"0","approx_re":"-0.022542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/6","im":"0","approx_re":"1.16666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/8+5/8*5^(1/2)","im":"0","approx_re":"2.772542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 295*X^4+572*X^3+424*X^2+138*X+17, 1686*X^4+1488*X^3-946*X^2-962*X-202, 2258*X^4-1032*X^3-1450*X^2-318*X+8, -519*X^4-1056*X^3-870*X^2-342*X-54, -9*(X+1)^4]", "text": "A-incarnation: $7 \\times 7$ linear Pfaffian in $P^7$.\nThere is a second MUM point at infinity, associated to\nthe 7 fold linear section of $G(2,7)$ AESZ 27/5.7\n", "degz": 5, "h3": null, "sol": "1 -17 1549 -215585 36505501 -6921832517 1412721479989 -303643747364513 67815981014552605 -15600719128907479517", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 1 17 138 424 572 295 -202 -962 -946 1488 1686 8 -318 -1450 -1032 2258 -54 -342 -870 -1056 -519 -9 -36 -54 -36 -9", "new_number": "5.46", "id": 256, "operator_tex": "\\theta^4+x\\left(295\\theta^4+572\\theta^3+424\\theta^2+138\\theta+17\\right)+2 x^{2}\\left(843\\theta^4+744\\theta^3-473\\theta^2-481\\theta-101\\right)+2 x^{3}\\left(1129\\theta^4-516\\theta^3-725\\theta^2-159\\theta+4\\right)-3 x^{4}\\left(173\\theta^4+352\\theta^3+290\\theta^2+114\\theta+18\\right)-3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-42 -41706", "discriminant": "5 1 295 1686 2258 -519 -9", "aesz": "243\n", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "93c30005b5a976a2b7c5206d5e679a45", "dim_h": null, "inst": " -42 875 -41706 2954224 -257813864 25738516377 -2820518451954 330947014189001 -40915701638541114 5271607385884271558", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z^3+57z^2-289z-1)(3z+1)^2", "discr_factors": "-9, (z+1/3)^2, z^3+57*z^2-289*z-1", "dm_basis": null, "q": "0 1 70 1127 47530 -3054373 361505368 -45010753732 5899877798258 -806209019396627", "yuk": "1 -42 6958 -1126104 189077294 -32226733042 5559518418328 -967437829020264 169444871453845806 -29827546494497598210", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/6*(-756+84*I*3^(1/2))^(1/3)-98/(-756+84*I*3^(1/2))^(1/3)-19+1/2*I*3^(1/2)*(7/3*(-756+84*I*3^(1/2))^(1/3)-196/(-756+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"-61.684843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/6*(-756+84*I*3^(1/2))^(1/3)-98/(-756+84*I*3^(1/2))^(1/3)-19-1/2*I*3^(1/2)*(7/3*(-756+84*I*3^(1/2))^(1/3)-196/(-756+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.003458","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"7/3*(-756+84*I*3^(1/2))^(1/3)+196/(-756+84*I*3^(1/2))^(1/3)-19","im":"0","approx_re":"4.688301","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -240*X^4-960*X^3-980*X^2-500*X-100, -8704*X^4-28672*X^3-39104*X^2-25280*X-6480, 57344*X^4+491520*X^3+1180672*X^2+1090560*X+350720, 589824*X^4+3145728*X^3+5357568*X^2+3784704*X+962560, 1048576*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 247/5.48", "degz": 5, "h3": null, "sol": "1 4 44 400 5356 59504 851696 10373696 153465580 1971364144", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -100 -500 -980 -960 -240 -6480 -25280 -39104 -28672 -8704 350720 1090560 1180672 491520 57344 962560 3784704 5357568 3145728 589824 1048576 4194304 6291456 4194304 1048576", "new_number": "5.47", "id": 257, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(12\\theta^4+48\\theta^3+49\\theta^2+25\\theta+5\\right)-2^{4} x^{2}\\left(544\\theta^4+1792\\theta^3+2444\\theta^2+1580\\theta+405\\right)+2^{9} x^{3}\\left(112\\theta^4+960\\theta^3+2306\\theta^2+2130\\theta+685\\right)+2^{12} x^{4}\\left(144\\theta^4+768\\theta^3+1308\\theta^2+924\\theta+235\\right)+2^{20} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-4/5 -108/5", "discriminant": "5 25 -240 -8704 57344 589824 1048576", "aesz": "246", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f51a0c39f9179dc6a561b9afb6f9d85f", "dim_h": null, "inst": " -4/5 22/5 -108/5 694/5 -1040 45234/5 -435788/5 4527046/5 -49614888/5 566774264/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+16z)(16z+5)^2(16z-1)^2", "discr_factors": "1048576, (z-1/16)^2, (z+5/16)^2, 1/16+z", "dm_basis": null, "q": "0 1 -4 -26 368 -1919 5544 -26382 512960 -8419180", "yuk": "1 -4/5 172/5 -584 44588/5 -650004/5 1953560 -149475288/5 463578428 -36169256272/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/16","im":"0","approx_re":"-0.3125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2304*X^4-3072*X^3-2112*X^2-576*X-80, 917504*X^4-4194304*X^3+802816*X^2+409600*X+106496, -570425344*X^4-402653184*X^3-348127232*X^2-113246208*X-22020096, -64424509440*X^4+123480309760*X^2+123480309760*X+37580963840, 27487790694400*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operaor AESZ 246/ 5.47", "degz": 5, "h3": null, "sol": "1 80 11024 1850624 343952656 68020122880 14026137862400 2980639208427520 647948081603714320 143375501435413402880", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -80 -576 -2112 -3072 2304 106496 409600 802816 -4194304 917504 -22020096 -113246208 -348127232 -402653184 -570425344 37580963840 123480309760 123480309760 0 -64424509440 27487790694400 109951162777600 164926744166400 109951162777600 27487790694400", "new_number": "5.48", "id": 258, "operator_tex": "\\theta^4+2^{4} x\\left(144\\theta^4-192\\theta^3-132\\theta^2-36\\theta-5\\right)+2^{13} x^{2}\\left(112\\theta^4-512\\theta^3+98\\theta^2+50\\theta+13\\right)-2^{20} x^{3}\\left(544\\theta^4+384\\theta^3+332\\theta^2+108\\theta+21\\right)-2^{30} 5 x^{4}\\left(12\\theta^4-23\\theta^2-23\\theta-7\\right)+2^{40} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "608 22293216", "discriminant": "5 1 2304 917504 -570425344 -64424509440 27487790694400", "aesz": "247", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "6c0503129f3500c26cf001c1908a17f7", "dim_h": null, "inst": " 608 -85544 22293216 -7629059800 3042437418016 -1338511583787272 630552444969044832 -312384713823657262168 160854766596487097431296 -85399168156054562446369592", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+256z)(1280z+1)^2(256z-1)^2", "discr_factors": "27487790694400, (z-1/256)^2, (z+1/1280)^2, 1/256+z", "dm_basis": null, "q": "0 1 -256 85856 -35256320 16388700720 -8241592643584 4371452849885696 -2409036448795197440 1366191528562010983064", "yuk": "1 608 -683744 601917440 -488260510944 380304677252608 -289118501496817664 216279488624382377984 -159940973478200778740960 117263124848839094629332224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1280","im":"0","approx_re":"-0.00078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -720*X^4-1680*X^3-1440*X^2-600*X-100, -2896*X^4-4288*X^3-1136*X^2+1120*X+560, 256*(X+1)*(37*X^3+248*X^2+375*X+165), 39936*X^4+202752*X^3+338944*X^2+237568*X+60416, 32768*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to\nOperator AESZ 71/5.11\n\nA-Incarnation: (2,0),(02),(1,1),(1,1),(1,1) intersection in $P^4 \\times P^4$", "degz": 5, "h3": "80", "sol": "1 4 44 688 13036 275504 6254576 149329856 3701367532 94438711984", "n_discr_factors": "4", "c3": "-88", "operator": "4 5 0 0 0 0 25 -100 -600 -1440 -1680 -720 560 1120 -1136 -4288 -2896 42240 138240 159488 72960 9472 60416 237568 338944 202752 39936 32768 131072 196608 131072 32768", "new_number": "5.4", "id": 260, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(36\\theta^4+84\\theta^3+72\\theta^2+30\\theta+5\\right)-2^{4} x^{2}\\left(181\\theta^4+268\\theta^3+71\\theta^2-70\\theta-35\\right)+2^{8} x^{3}(\\theta+1)(37\\theta^3+248\\theta^2+375\\theta+165)+2^{10} x^{4}\\left(39\\theta^4+198\\theta^3+331\\theta^2+232\\theta+59\\right)+2^{15} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "8/5 152/5", "discriminant": "5 25 -720 -2896 9472 39936 32768", "aesz": "21", "n_sing_complex": "0", "inst_int": "", "c2h": "104", "hash": "42a2bc0f0ee2a405ede956176c95721f", "dim_h": "22", "inst": " 8/5 57/10 152/5 253 11552/5 251603/10 294136 37079957/10 245240208/5 3383879274/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(4z+1)(32z-1)(4z-1)(8z+5)^2", "discr_factors": "32768, z-1/32, z-1/4, (z+5/8)^2, z+1/4", "dm_basis": null, "q": "0 1 -8 14 -32 -719 -2480 -75638 -856192 -13365820", "yuk": "1 8/5 236/5 4112/5 81196/5 1444008/5 27177464/5 504443248/5 9492550188/5 178780115744/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/8","im":"0","approx_re":"-0.625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 2720*X^4+4480*X^3+3940*X^2+1700*X+300, 89344*X^4+259072*X^3+350784*X^2+236800*X+63280, 1245184*X^4+4669440*X^3+7458816*X^2+5621760*X+1597440, 7602176*X^4+30932992*X^3+48431104*X^2+32964608*X+8208384, 16777216*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to the Operator AESZ 263/5.57", "degz": 5, "h3": null, "sol": "1 -12 236 -6384 217836 -8674512 381058544 -17846749632 873802015468 -44205033911952", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 300 1700 3940 4480 2720 63280 236800 350784 259072 89344 1597440 5621760 7458816 4669440 1245184 8208384 32964608 48431104 30932992 7602176 16777216 67108864 100663296 67108864 16777216", "new_number": "5.56", "id": 267, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(136\\theta^4+224\\theta^3+197\\theta^2+85\\theta+15\\right)+2^{4} x^{2}\\left(5584\\theta^4+16192\\theta^3+21924\\theta^2+14800\\theta+3955\\right)+2^{11} x^{3}\\left(608\\theta^4+2280\\theta^3+3642\\theta^2+2745\\theta+780\\right)+2^{14} x^{4}\\left(464\\theta^4+1888\\theta^3+2956\\theta^2+2012\\theta+501\\right)+2^{24} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-28/5 -1268/5", "discriminant": "5 25 2720 89344 1245184 7602176 16777216", "aesz": "262", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "4899f97226a5ec3b1ded2994470e9fdc", "dim_h": null, "inst": " -28/5 153/5 -1268/5 18598/5 -320048/5 6328003/5 -137296404/5 3185758982/5 -77892222744/5 1984455155124/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+64z)(32z+5)^2(16z+1)^2", "discr_factors": "16777216, (z+1/16)^2, 1/64+z, (z+5/32)^2", "dm_basis": null, "q": "0 1 20 230 2896 22145 310968 -432142 67997504 -1435072876", "yuk": "1 -28/5 1196/5 -34264/5 1191468/5 -40006028/5 1366815608/5 -9418533320 1631109790252/5 -11356686082928", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/32","im":"0","approx_re":"-0.15625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 7424*X^4-512*X^3+1216*X^2+1472*X+336, 19922944*X^4+4980736*X^3+14745600*X^2+4292608*X+163840, 23420993536*X^4+25769803776*X^3+28739371008*X^2+11777605632*X+1975517184, 11682311045120*X^4+27487790694400*X^3+29291676958720*X^2+15547781611520*X+3350074490880, 1759218604441600*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 262/5.56", "degz": 5, "h3": null, "sol": "1 -336 198416 -142318848 112152177936 -93351842555136 80529573836308736 -71239576786325262336 64211432766884647771408 -58719439168904679249536256", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 336 1472 1216 -512 7424 163840 4292608 14745600 4980736 19922944 1975517184 11777605632 28739371008 25769803776 23420993536 3350074490880 15547781611520 29291676958720 27487790694400 11682311045120 1759218604441600 7036874417766400 10555311626649600 7036874417766400 1759218604441600", "new_number": "5.57", "id": 268, "operator_tex": "\\theta^4+2^{4} x\\left(464\\theta^4-32\\theta^3+76\\theta^2+92\\theta+21\\right)+2^{15} x^{2}\\left(608\\theta^4+152\\theta^3+450\\theta^2+131\\theta+5\\right)+2^{22} x^{3}\\left(5584\\theta^4+6144\\theta^3+6852\\theta^2+2808\\theta+471\\right)+2^{34} 5 x^{4}\\left(136\\theta^4+320\\theta^3+341\\theta^2+181\\theta+39\\right)+2^{46} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "1312 58156704", "discriminant": "5 1 7424 19922944 23420993536 11682311045120 1759218604441600", "aesz": "263", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2157fe92de97f7b684b3cbd7b8bdf280", "dim_h": null, "inst": " 1312 -211968 58156704 -19819112104 7519377878624 -3012318999683072 1232376137934942240 -500667031433854121000 195372771916305547947776 -69064326912662753956586496", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+256z)(1024z+1)^2(2560z+1)^2", "discr_factors": "1759218604441600, (z+1/2560)^2, (z+1/1024)^2, 1/256+z", "dm_basis": null, "q": "0 1 128 -20128 10958848 -5555650000 2838355329024 -1438773593984512 715220103942373376 -343517369577114490216", "yuk": "1 1312 -1694432 1570232320 -1268424869088 939922234829312 -650660902363006976 422705015311685189632 -256341520095401734821088 142426750726986746024161024", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1024","im":"0","approx_re":"-0.0009765625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2560","im":"0","approx_re":"-0.000390625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -405*X^4-1620*X^3-1860*X^2-1050*X-225, -24786*X^4-81648*X^3-117126*X^2-80190*X-21960, 275562*X^4+2361960*X^3+5629338*X^2+5183190*X+1674270, 4782969*X^4+25509168*X^3+43341966*X^2+30587382*X+7768224, 14348907*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to\nOperator AESZ 267/5.59", "degz": 5, "h3": null, "sol": "1 9 171 3087 69579 1469259 35132301 794840769 19583956683 460583978931", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -225 -1050 -1860 -1620 -405 -21960 -80190 -117126 -81648 -24786 1674270 5183190 5629338 2361960 275562 7768224 30587382 43341966 25509168 4782969 14348907 57395628 86093442 57395628 14348907", "new_number": "5.58", "id": 269, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(27\\theta^4+108\\theta^3+124\\theta^2+70\\theta+15\\right)-2 3^{2} x^{2}\\left(1377\\theta^4+4536\\theta^3+6507\\theta^2+4455\\theta+1220\\right)+2 3^{5} x^{3}\\left(567\\theta^4+4860\\theta^3+11583\\theta^2+10665\\theta+3445\\right)+3^{8} x^{4}\\left(729\\theta^4+3888\\theta^3+6606\\theta^2+4662\\theta+1184\\right)+3^{15} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-18/5 -642/5", "discriminant": "5 25 -405 -24786 275562 4782969 14348907", "aesz": "266\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5d46913a13c5fa5fa6a547d8b5646133", "dim_h": null, "inst": " -18/5 117/10 -642/5 1197 -76788/5 2203593/10 -17643978/5 303594291/5 -1101609276 104184958419/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+27z)(27z+5)^2(27z-1)^2", "discr_factors": "14348907, (z-1/27)^2, 1/27+z, (z+5/27)^2", "dm_basis": null, "q": "0 1 -6 -81 1510 -10263 44064 -698494 20872590 -484387938", "yuk": "1 -18/5 90 -17352/5 76698 -9598518/5 47594232 -6051884472/5 155440660482/5 -4015365828372/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/27","im":"0","approx_re":"-0.185185185185","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 6561*X^4-8748*X^3-6156*X^2-1782*X-279, 7440174*X^4-34012224*X^3+5314410*X^2+2480058*X+918540, -13172296626*X^4-9298091736*X^3-11106054018*X^2-4390765542*X-1080950994, -4236443047215*X^4+5962401325710*X^2+5962401325710*X+1882863576540, 5147278302366225*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to\nOperator AESZ 266/5.58", "degz": 5, "h3": null, "sol": "1 279 124011 64869777 36848978379 21998516212629 13576417815818061 8580116213203618719 5520066684174606599883 3600982100772644288927661", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -279 -1782 -6156 -8748 6561 918540 2480058 5314410 -34012224 7440174 -1080950994 -4390765542 -11106054018 -9298091736 -13172296626 1882863576540 5962401325710 5962401325710 0 -4236443047215 5147278302366225 20589113209464900 30883669814197350 20589113209464900 5147278302366225", "new_number": "5.59", "id": 270, "operator_tex": "\\theta^4+3^{2} x\\left(729\\theta^4-972\\theta^3-684\\theta^2-198\\theta-31\\right)+2 3^{8} x^{2}\\left(567\\theta^4-2592\\theta^3+405\\theta^2+189\\theta+70\\right)-2 3^{14} x^{3}\\left(1377\\theta^4+972\\theta^3+1161\\theta^2+459\\theta+113\\right)-3^{22} 5 x^{4}\\left(27\\theta^4-38\\theta^2-38\\theta-12\\right)+3^{30} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "1818 467810538", "discriminant": "5 1 6561 7440174 -13172296626 -4236443047215 5147278302366225", "aesz": "267", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "924287a9ba8517571071ec73d860af7e", "dim_h": null, "inst": " 1818 -681336 467810538 -422903176767 446062311232740 -519402409798743174 647892884549133772434 -850164640719377212142649 1159772332620656681302786044 -1631505517025864921717367507570", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+729z)(3645z+1)^2(729z-1)^2", "discr_factors": "5147278302366225, 1/729+z, (z+1/3645)^2, (z-1/729)^2", "dm_basis": null, "q": "0 1 -666 575343 -616165062 752261852457 -996972190760160 1396191940153465410 -2033717234011998737454 3050702206815313433430558", "yuk": "1 1818 -5448870 12630886344 -27065808761958 55757788904094318 -112190920503903089928 222227259400352883946680 -435284296048348198425798246 845474030480458720682361912420", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/729","im":"0","approx_re":"-0.00137174211248","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3645","im":"0","approx_re":"-0.000274348422497","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/729","im":"0","approx_re":"0.00137174211248","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -1085*X^4-2002*X^3-1638*X^2-637*X-98, -16105*X^4-68044*X^3-102261*X^2-66094*X-15736, 21000*X^4+68712*X^3+72568*X^2+30072*X+3808, -7440*X^4-20256*X^3-23024*X^2-12896*X-2944, 512*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 118/5.16\nA-Incarnation: five (1,1) sections in ${\\bf P}^4 \\times {\\bf P}^4$.Quotient by ${\\bf Z}/2$ of this: \nthe Reye congruence Calabi-Yau threefold.", "degz": 5, "h3": "140", "sol": "1 2 34 488 9826 206252 4734304 113245568 2816649826 72001228052", "n_discr_factors": "3", "c3": "-200", "operator": "4 5 0 0 0 0 49 -98 -637 -1638 -2002 -1085 -15736 -66094 -102261 -68044 -16105 3808 30072 72568 68712 21000 -2944 -12896 -23024 -20256 -7440 512 2048 3072 2048 512", "new_number": "5.5", "id": 271, "operator_tex": "7^{2} \\theta^4-7 x\\left(155\\theta^4+286\\theta^3+234\\theta^2+91\\theta+14\\right)-x^{2}\\left(16105\\theta^4+68044\\theta^3+102261\\theta^2+66094\\theta+15736\\right)+2^{3} x^{3}\\left(2625\\theta^4+8589\\theta^3+9071\\theta^2+3759\\theta+476\\right)-2^{4} x^{4}\\left(465\\theta^4+1266\\theta^3+1439\\theta^2+806\\theta+184\\right)+2^{9} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "10/7 295/7", "discriminant": "5 49 -1085 -16105 21000 -7440 512", "aesz": "22", "n_sing_complex": "0", "inst_int": "", "c2h": "-40", "hash": "5b96eae0872756be1130d4b12ffe60a6", "dim_h": "20", "inst": " 10/7 65/7 295/7 3065/7 4245 377115/7 694590 69723305/7 1031662155/7 2296011250", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(32z-1)(z^2-11z-1)(4z-7)^2", "discr_factors": "512, z-1/32, (z-7/4)^2, z^2-11*z-1", "dm_basis": null, "q": "0 1 -5 -40 115 -645 -12846 -177350 -2574585 -44198680", "yuk": "1 10/7 530/7 7975/7 196690/7 3714385/7 11637905 1667710600/7 35698528850/7 752081718970/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"11/2-5/2*5^(1/2)","im":"0","approx_re":"-0.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/4","im":"0","approx_re":"1.75","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2+5/2*5^(1/2)","im":"0","approx_re":"11.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -6300-26700*X-39660*X^2-25920*X^3-6480*X^4, -8358480-26827200*X-34416576*X^2-20901888*X^3-6345216*X^4, 6714109440+20524907520*X+22513572864*X^2+9674588160*X^3+1128701952*X^4, 501439279104+1984258031616*X+2820142448640*X^2+1671768834048*X^3+313456656384*X^4, 15045919506432*(X+1)^4]", "text": "There is a second MUM-point at infinity, correspondint to\nOperator AESZ 269/5.61", "degz": 5, "h3": null, "sol": "1 252 87084 31502448 12121584876 4712866852752 1882522128613104 754669010404306368 307249546738094748396 125267668677349183660752", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -6300 -26700 -39660 -25920 -6480 -8358480 -26827200 -34416576 -20901888 -6345216 6714109440 20524907520 22513572864 9674588160 1128701952 501439279104 1984258031616 2820142448640 1671768834048 313456656384 15045919506432 60183678025728 90275517038592 60183678025728 15045919506432", "new_number": "5.60", "id": 272, "operator_tex": "5^{2} \\theta^4-2^{2} 3 5 x\\left(108\\theta^4+432\\theta^3+661\\theta^2+445\\theta+105\\right)-2^{4} 3^{2} x^{2}\\left(44064\\theta^4+145152\\theta^3+239004\\theta^2+186300\\theta+58045\\right)+2^{9} 3^{5} x^{3}\\left(9072\\theta^4+77760\\theta^3+180954\\theta^2+164970\\theta+53965\\right)+2^{12} 3^{8} x^{4}\\left(11664\\theta^4+62208\\theta^3+104940\\theta^2+73836\\theta+18659\\right)+2^{20} 3^{15} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-828/5 -4270932/5", "discriminant": "5 25 -6480 -6345216 1128701952 313456656384 15045919506432", "aesz": "268", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "638e2881183378c7a47b7508d9acc072", "dim_h": null, "inst": " -828/5 25533/5 -4270932/5 598304142/5 -24767201520 5516686677699 -6905915218789236/5 1839719752683668766/5 -517693573962167020632/5 30345720052057395286068", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+432z)(432z+5)^2(432z-1)^2", "discr_factors": "15045919506432, (z+5/432)^2, (z-1/432)^2, 1/432+z", "dm_basis": null, "q": "0 1 -60 -20250 2749840 -229230975 49927836888 -15561414895630 4667881532942400 -1428189403919231340", "yuk": "1 -828/5 203436/5 -115315992/5 38291668524/5 -15479500950828/5 5958021496803192/5 -2368728920044708776/5 941936513412330076716/5 -75479723083683974671344", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/432","im":"0","approx_re":"-0.0115740740741","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -112464-565056*X-1684800*X^2-2239488*X^3+1679616*X^4, 67775864832-2902376448*X+113192681472*X^2-2229025112064*X^3+487599243264*X^4, -48452876117213184-163037583771697152*X-340699801303646208*X^2-155996093442686976*X^3-220994465710473216*X^4, 505427342754305802240-2190185151935325143040*X-2190185151935325143040*X^2-18195384339155008880640*X^4, 5659492344850773962234265600*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 268/5.60", "degz": 5, "h3": null, "sol": "1 112464 16304096016 2572332025515264 423329707157060783376 71449611307953723990238464 12263730529723761243479626711296 2130368461612459022498783244821581824 373413841262786707002896614274115279822096 65911327617588382602056644419982035975857374464", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -112464 -565056 -1684800 -2239488 1679616 67775864832 -2902376448 113192681472 -2229025112064 487599243264 -48452876117213184 -163037583771697152 -340699801303646208 -155996093442686976 -220994465710473216 505427342754305802240 -2190185151935325143040 -2190185151935325143040 0 -18195384339155008880640 5659492344850773962234265600 22637969379403095848937062400 33956954069104643773405593600 22637969379403095848937062400 5659492344850773962234265600", "new_number": "5.61", "id": 273, "operator_tex": "\\theta^4+2^{4} 3^{2} x\\left(11664\\theta^4-15552\\theta^3-11700\\theta^2-3924\\theta-781\\right)+2^{13} 3^{8} x^{2}\\left(9072\\theta^4-41472\\theta^3+2106\\theta^2-54\\theta+1261\\right)-2^{20} 3^{14} x^{3}\\left(44064\\theta^4+31104\\theta^3+67932\\theta^2+32508\\theta+9661\\right)-2^{30} 3^{22} 5 x^{4}\\left(108\\theta^4+13\\theta^2+13\\theta-3\\right)+2^{40} 3^{30} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "549216 5134247872650720", "discriminant": "5 1 1679616 487599243264 -220994465710473216 -18195384339155008880640 5659492344850773962234265600", "aesz": "269", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f6285c6dd849b8edc6913a248c74c2ac", "dim_h": null, "inst": " 549216 -39437661960 5134247872650720 -893529522332436373560 182442495912657901797814560 -41262812389744861577153158690920 10019116026820060769801991618641662560 -2563084582322256940199919288251046522481080 682423086469588020265348285068230145316728864000 -187526681844608918990817759123005226960876251407732440", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+186624z)(933120z+1)^2(186624z-1)^2", "discr_factors": "5659492344850773962234265600, (z-1/186624)^2, 1/186624+z, (z+1/933120)^2", "dm_basis": null, "q": "0 1 -115200 16592726880 -3236585370777600 744468775927259638320 -188590932068932155933757440 50864734112229617807411676172800 -14333826376721778264506293828143022080 4172214184513021365268279600028021795343000", "yuk": "1 549216 -315500746464 138624692562118656 -57185889429591428654304 22805311989082237724727369216 -8912767476184889962040705216415744 3436556797199280844042083125194090807296 -1312299306148995553382415861473965410938967264 497486430036329666773438899814739914560587903974656", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/186624","im":"0","approx_re":"-5.35836762689e-06","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/933120","im":"0","approx_re":"-1.07167352538e-06","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/186624","im":"0","approx_re":"5.35836762689e-06","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -960*X^4-3840*X^3-5020*X^2-3100*X-700, -139264*X^4-458752*X^3-698624*X^2-508160*X-148240, 3670016*X^4+31457280*X^3+74235904*X^2+68075520*X+22108160, 150994944*X^4+805306368*X^3+1364197376*X^2+961544192*X+243728384, 1073741824*(X+1)^4]", "text": "There is a second MUM-point at infinity, \ncorresponding to Operator AESZ 271/ 5.63", "degz": 5, "h3": null, "sol": "1 28 1324 63856 3489004 188608528 10840129264 615372248512 36295765586668 2117009706332752", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -700 -3100 -5020 -3840 -960 -148240 -508160 -698624 -458752 -139264 22108160 68075520 74235904 31457280 3670016 243728384 961544192 1364197376 805306368 150994944 1073741824 4294967296 6442450944 4294967296 1073741824", "new_number": "5.62", "id": 274, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(48\\theta^4+192\\theta^3+251\\theta^2+155\\theta+35\\right)-2^{4} x^{2}\\left(8704\\theta^4+28672\\theta^3+43664\\theta^2+31760\\theta+9265\\right)+2^{11} x^{3}\\left(1792\\theta^4+15360\\theta^3+36248\\theta^2+33240\\theta+10795\\right)+2^{16} x^{4}\\left(2304\\theta^4+12288\\theta^3+20816\\theta^2+14672\\theta+3719\\right)+2^{30} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-76/5 -2100", "discriminant": "5 25 -960 -139264 3670016 150994944 1073741824", "aesz": "270", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "256e3b3a92e3fd332be8b01f71853ea4", "dim_h": null, "inst": " -76/5 367/5 -2100 43436 -6582256/5 221180469/5 -1648544084 330479016412/5 -13945393057272/5 614000624977324/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+64z)(64z+5)^2(64z-1)^2", "discr_factors": "1073741824, 1/64+z, (z+5/64)^2, (z-1/64)^2", "dm_basis": null, "q": "0 1 -12 -474 15440 -185343 2784504 -152938830 8375024448 -401371946988", "yuk": "1 -76/5 572 -283576/5 2780476 -822782076/5 47774700664/5 -2827253104136/5 169205270305324/5 -10166191539034864/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/64","im":"0","approx_re":"-0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","-1/4","1","5/4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 36864*X^4-49152*X^3-35584*X^2-11008*X-1936, 234881024*X^4-1073741824*X^3+120586240*X^2+45088768*X+30801920, -2336462209024*X^4-1649267441664*X^3-2649994821632*X^2-1172526071808*X-322390982656, -4222124650659840*X^4+3254554418216960*X^2+3254554418216960*X+1143492092887040, 28823037615171174400*(X+1)^4]", "text": "There is a second MUM-point at infinity, \ncorresponding to Operator AESZ 270 /5.62", "degz": 5, "h3": null, "sol": "1 1936 5433616 17299986688 58672579116304 206669099292334336 746575590027267318016 2745949421061368330162176 10236991103358250791812996368 38566284406834450611369673402624", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -1936 -11008 -35584 -49152 36864 30801920 45088768 120586240 -1073741824 234881024 -322390982656 -1172526071808 -2649994821632 -1649267441664 -2336462209024 1143492092887040 3254554418216960 3254554418216960 0 -4222124650659840 28823037615171174400 115292150460684697600 172938225691027046400 115292150460684697600 28823037615171174400", "new_number": "5.63", "id": 275, "operator_tex": "\\theta^4+2^{4} x\\left(2304\\theta^4-3072\\theta^3-2224\\theta^2-688\\theta-121\\right)+2^{17} x^{2}\\left(1792\\theta^4-8192\\theta^3+920\\theta^2+344\\theta+235\\right)-2^{28} x^{3}\\left(8704\\theta^4+6144\\theta^3+9872\\theta^2+4368\\theta+1201\\right)-2^{44} 5 x^{4}\\left(48\\theta^4-37\\theta^2-37\\theta-13\\right)+2^{60} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "10912 71557619232", "discriminant": "5 1 36864 234881024 -2336462209024 -4222124650659840 28823037615171174400", "aesz": "271", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "c20fda7ad02ecc06f9b3f74bf4327d05", "dim_h": null, "inst": " 10912 -20731504 71557619232 -326717237089712 1743820693922321120 -10286426285031347485104 65046725007339572898273696 -432911472352501135094316776368 2996380229369184777213698461434624 -21392301510610273389194136435773058000", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+4096z)(20480z+1)^2(4096z-1)^2", "discr_factors": "28823037615171174400, (z+1/20480)^2, (z-1/4096)^2, 1/4096+z", "dm_basis": null, "q": "0 1 -3264 13635168 -72297617408 442113725658672 -2950154620733945856 20858990544340177535488 -153651119276899169695825920 1166825950518608865433631799960", "yuk": "1 10912 -165841120 1932055730176 -20909903339582688 217977586740290150912 -2221868077564839166904320 22311026677517473504107888640 -221650673844480602078193529083104 2184361187210135702588788110441571072", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4096","im":"0","approx_re":"-0.000244140625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/20480","im":"0","approx_re":"-4.8828125e-05","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","approx_im":"0.0","exponents":["0","-1/4","1","5/4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, 4862*X^4+12478*X^3+11152*X^2+4913*X+867, 36990*X^4+198666*X^3+334881*X^2+236385*X+61200, -369603*X^4-1784592*X^3-3143448*X^2-2416635*X-685746, 807003*X^4+3621672*X^3+5767119*X^2+3956283*X+997272, -531441*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 280/5.69", "degz": 5, "h3": "153", "sol": "1 -3 9 51 -1431 16497 -93141 -675027 25911657 -366207267", "n_discr_factors": "2", "c3": "-126", "operator": "4 5 0 0 0 0 289 867 4913 11152 12478 4862 61200 236385 334881 198666 36990 -685746 -2416635 -3143448 -1784592 -369603 997272 3956283 5767119 3621672 807003 -531441 -2125764 -3188646 -2125764 -531441", "new_number": "5.68", "id": 280, "operator_tex": "17^{2} \\theta^4+17 x\\left(286\\theta^4+734\\theta^3+656\\theta^2+289\\theta+51\\right)+3^{2} x^{2}\\left(4110\\theta^4+22074\\theta^3+37209\\theta^2+26265\\theta+6800\\right)-3^{5} x^{3}\\left(1521\\theta^4+7344\\theta^3+12936\\theta^2+9945\\theta+2822\\right)+3^{8} x^{4}\\left(123\\theta^4+552\\theta^3+879\\theta^2+603\\theta+152\\right)-3^{12} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-10/17 10", "discriminant": "5 289 4862 36990 -369603 807003 -531441", "aesz": "279", "n_sing_complex": "2", "inst_int": "", "c2h": "90", "hash": "06f80606fbeb2b0cc9559df633f1f59d", "dim_h": "33", "inst": " -10/17 -19/17 10 -369/17 -1413/17 23517/17 -94575/17 -353339/17 8025851/17 -43298322/17", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(729z^3-189z^2-20z-1)(-17+27z)^2", "discr_factors": "-531441, z^3-7/27*z^2-20/729*z-1/729, (-17/27+z)^2", "dm_basis": null, "q": "0 1 5 30 44 108 39 -9936 -18201 148149", "yuk": "1 -10/17 -162/17 4580/17 -23778/17 -176635/17 5084100/17 -32439235/17 -10643138 5850849959/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/324*(10700+1044*29^(1/2))^(1/3)-109/81/(10700+1044*29^(1/2))^(1/3)+7/81","im":"-1/2*3^(1/2)*(1/162*(10700+1044*29^(1/2))^(1/3)-218/81/(10700+1044*29^(1/2))^(1/3))","approx_re":"-0.044921","approx_im":"-0.04372","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/324*(10700+1044*29^(1/2))^(1/3)-109/81/(10700+1044*29^(1/2))^(1/3)+7/81","im":"1/2*3^(1/2)*(1/162*(10700+1044*29^(1/2))^(1/3)-218/81/(10700+1044*29^(1/2))^(1/3))","approx_re":"-0.044921","approx_im":"0.04372","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/162*(10700+1044*29^(1/2))^(1/3)+218/81/(10700+1044*29^(1/2))^(1/3)+7/81","im":"0","approx_re":"0.349102","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/27","im":"0","approx_re":"0.62962962963","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1107*X^4+540*X^3+351*X^2+81*X+9, 369603*X^4-306180*X^3+7290*X^2-5103*X-2430, -26965710*X^4+36964674*X^3+28560033*X^2+10687869*X+1443420, -2583866142*X^4-3704143770*X^3-1535864490*X^2+316207395*X+271034910, -111964521321*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 279/5.68", "degz": 5, "h3": null, "sol": "1 -9 81 1017 -93231 3192291 -55221669 -887397849 112636210257 -4735203200001", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 1 9 81 351 540 -1107 -2430 -5103 7290 -306180 369603 1443420 10687869 28560033 36964674 -26965710 271034910 316207395 -1535864490 -3704143770 -2583866142 -111964521321 -447858085284 -671787127926 -447858085284 -111964521321", "new_number": "5.69", "id": 281, "operator_tex": "\\theta^4-3^{2} x\\left(123\\theta^4-60\\theta^3-39\\theta^2-9\\theta-1\\right)+3^{5} x^{2}\\left(1521\\theta^4-1260\\theta^3+30\\theta^2-21\\theta-10\\right)-3^{8} x^{3}\\left(4110\\theta^4-5634\\theta^3-4353\\theta^2-1629\\theta-220\\right)-3^{12} 17 x^{4}\\left(286\\theta^4+410\\theta^3+170\\theta^2-35\\theta-30\\right)-3^{18} 17^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-117 -844872", "discriminant": "5 1 -1107 369603 -26965710 -2583866142 -111964521321", "aesz": "280", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5083c4e9f432302302c564ba554e3bcd", "dim_h": null, "inst": " -117 -28899/4 -844872 -131189436 -23932952667 -4844455507473 -1054483950295746 -242170121624346954 -57955634299699381155 -57320791824608013614013/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(531441z^3+14580z^2+189z-1)(-1+459z)^2", "discr_factors": "-111964521321, (-1/459+z)^2, z^3+20/729*z^2+7/19683*z-1/531441", "dm_basis": null, "q": "0 1 45 4779 770964 153461358 34181002080 8170040350179 2050199242747677 533147528609281332", "yuk": "1 -117 -57915 -22811661 -8396181819 -2991619083492 -1046402412483627 -361687994951440995 -123991102280061822267 -42249657404480871673656", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8748*(150812+28188*29^(1/2))^(1/3)+167/2187/(150812+28188*29^(1/2))^(1/3)-20/2187","im":"-1/54*3^(1/2)*(1/162*(150812+28188*29^(1/2))^(1/3)+334/81/(150812+28188*29^(1/2))^(1/3))","approx_re":"-0.015682","approx_im":"-0.015263","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8748*(150812+28188*29^(1/2))^(1/3)+167/2187/(150812+28188*29^(1/2))^(1/3)-20/2187","im":"1/54*3^(1/2)*(1/162*(150812+28188*29^(1/2))^(1/3)+334/81/(150812+28188*29^(1/2))^(1/3))","approx_re":"-0.015682","approx_im":"0.015263","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/459","im":"0","approx_re":"0.00217864923747","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4374*(150812+28188*29^(1/2))^(1/3)-334/2187/(150812+28188*29^(1/2))^(1/3)-20/2187","im":"0","approx_re":"0.003929","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -768*X^4-960*X^3-876*X^2-396*X-72, 24832*X^4+56320*X^3+67456*X^2+40320*X+9600, -385024*X^4-1179648*X^3-1626112*X^2-1069056*X-270336, 2883584*X^4+10485760*X^3+15335424*X^2+10092544*X+2490368, -8388608*(X+1)^4]", "text": "There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9\nA-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \\times P^4$", "degz": 5, "h3": "96", "sol": "1 8 104 1664 30376 611008 13247744 304586752 7331997352 182972345408", "n_discr_factors": "3", "c3": "-32", "operator": "4 5 0 0 0 0 9 -72 -396 -876 -960 -768 9600 40320 67456 56320 24832 -270336 -1069056 -1626112 -1179648 -385024 2490368 10092544 15335424 10485760 2883584 -8388608 -33554432 -50331648 -33554432 -8388608", "new_number": "5.6", "id": 282, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(64\\theta^4+80\\theta^3+73\\theta^2+33\\theta+6\\right)+2^{7} x^{2}\\left(194\\theta^4+440\\theta^3+527\\theta^2+315\\theta+75\\right)-2^{12} x^{3}\\left(94\\theta^4+288\\theta^3+397\\theta^2+261\\theta+66\\right)+2^{17} x^{4}\\left(22\\theta^4+80\\theta^3+117\\theta^2+77\\theta+19\\right)-2^{23} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "4/3 44/3", "discriminant": "5 9 -768 24832 -385024 2883584 -8388608", "aesz": "23", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "65760d446ba9c3da587ce5bd9912745e", "dim_h": "24", "inst": " 4/3 13/3 44/3 278/3 2336/3 19855/3 61284 618890 19733168/3 217792936/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+32z)(16z-1)^2(32z-3)^2", "discr_factors": "-8388608, -1/32+z, (z-3/32)^2, (z-1/16)^2", "dm_basis": null, "q": "0 1 -12 94 -624 3117 -15528 48786 -336064 -572410", "yuk": "1 4/3 36 1192/3 17900/3 292004/3 1429992 63061240/3 950632940/3 14385480664/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32","im":"0","approx_re":"0.09375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 837*X^4-756*X^3-480*X^2-102*X-9, 205578*X^4-227448*X^3+222102*X^2+104490*X+17982, 20903346*X^4+51018336*X^3+48931938*X^2+22320522*X+4094064, 3658971285*X^4+8609344200*X^3+9039811410*X^2+4735139310*X+1004423490, 87169610025*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 17/5.1", "degz": 5, "h3": null, "sol": "1 9 -837 -32553 4787019 253184859 -43950787299 -2639149978743 498347490542283 32056927648039251", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -9 -102 -480 -756 837 17982 104490 222102 -227448 205578 4094064 22320522 48931938 51018336 20903346 1004423490 4735139310 9039811410 8609344200 3658971285 87169610025 348678440100 523017660150 348678440100 87169610025", "new_number": "5.71", "id": 284, "operator_tex": "\\theta^4+3 x\\left(279\\theta^4-252\\theta^3-160\\theta^2-34\\theta-3\\right)+2 3^{5} x^{2}\\left(423\\theta^4-468\\theta^3+457\\theta^2+215\\theta+37\\right)+2 3^{9} x^{3}\\left(531\\theta^4+1296\\theta^3+1243\\theta^2+567\\theta+104\\right)+3^{15} 5 x^{4}\\left(51\\theta^4+120\\theta^3+126\\theta^2+66\\theta+14\\right)+3^{20} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "162 751026", "discriminant": "5 1 837 205578 20903346 3658971285 87169610025", "aesz": "290", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5552195a371df176b84ac2c2d791be7e", "dim_h": null, "inst": " 162 -8829 751026 -163125009/2 10343901204 -1453521572691 218980788617178 -69355077686713017/2 5703503255639183244 -966692381759058168864", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(27z+1)(19683z^2+1)(1+405z)^2", "discr_factors": "87169610025, (1/405+z)^2, z+1/27, z^2+1/19683", "dm_basis": null, "q": "0 1 -66 9891 -1506622 243708009 -41334322464 7277240009714 -1318339725168678 244138179772480590", "yuk": "1 162 -70470 20277864 -5220070758 1292987650662 -313960639494024 75110410495692216 -17754899893018603110 4157853873360984862740", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/405","im":"0","approx_re":"-0.00246913580247","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/243*3^(1/2)","approx_re":"0.0","approx_im":"-0.007128","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/243*3^(1/2)","approx_re":"0.0","approx_im":"0.007128","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -566*X^4-34*X^3-62*X^2-45*X-9, 118110*X^4+51906*X^3+67479*X^2+25107*X+3420, -10936935*X^4-12894552*X^3-11467098*X^2-4844205*X-838998, 404089803*X^4+873015408*X^3+818451945*X^2+381944241*X+73107036, -1977491961*(X+1)^4]", "text": "There is a second MUM-point at infinity, \ncorresponding to Operator AESZ 124/5.18", "degz": 5, "h3": null, "sol": "1 9 189 3375 -159651 -33202791 -3756442689 -360595119519 -31731126659235 -2611165899213459", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 1 -9 -45 -62 -34 -566 3420 25107 67479 51906 118110 -838998 -4844205 -11467098 -12894552 -10936935 73107036 381944241 818451945 873015408 404089803 -1977491961 -7909967844 -11864951766 -7909967844 -1977491961", "new_number": "5.72", "id": 285, "operator_tex": "\\theta^4-x\\left(566\\theta^4+34\\theta^3+62\\theta^2+45\\theta+9\\right)+3 x^{2}\\left(39370\\theta^4+17302\\theta^3+22493\\theta^2+8369\\theta+1140\\right)-3^{2} x^{3}\\left(1215215\\theta^4+1432728\\theta^3+1274122\\theta^2+538245\\theta+93222\\right)+3^{7} 61 x^{4}\\left(3029\\theta^4+6544\\theta^3+6135\\theta^2+2863\\theta+548\\right)-3^{12} 61^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-28 -37768", "discriminant": "5 1 -566 118110 -10936935 404089803 -1977491961", "aesz": "291", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "cbc8242a8fecc72056e6e36b4864b868", "dim_h": null, "inst": " -28 -809 -37768 -2185213 -143204777 -30489768010/3 -762199509690 -59514316974923 -4792148905304457 -395337642872739927", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(59049z^3-11421z^2+200z-1)(-1+183z)^2", "discr_factors": "-1977491961, z^3-47/243*z^2+200/59049*z-1/59049, (-1/183+z)^2", "dm_basis": null, "q": "0 1 -9 321 22870 1995363 175451346 15725145505 1430794075599 131756626614654", "yuk": "1 -28 -6500 -1019764 -139860132 -17900597153 -2195264322956 -261434431823698 -30471330431020708 -3493476551967968917", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/183","im":"0","approx_re":"0.00546448087432","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2916*(518428+4836*93^(1/2))^(1/3)-1609/729/(518428+4836*93^(1/2))^(1/3)+47/729","im":"-1/2*3^(1/2)*(1/1458*(518428+4836*93^(1/2))^(1/3)-3218/729/(518428+4836*93^(1/2))^(1/3))","approx_re":"0.009423","approx_im":"-0.002866","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2916*(518428+4836*93^(1/2))^(1/3)-1609/729/(518428+4836*93^(1/2))^(1/3)+47/729","im":"1/2*3^(1/2)*(1/1458*(518428+4836*93^(1/2))^(1/3)-3218/729/(518428+4836*93^(1/2))^(1/3))","approx_re":"0.009423","approx_im":"0.002866","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1458*(518428+4836*93^(1/2))^(1/3)+3218/729/(518428+4836*93^(1/2))^(1/3)+47/729","im":"0","approx_re":"0.174569","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -519*X^4-1020*X^3-816*X^2-306*X-45, -2258*X^4-10064*X^3-15194*X^2-9546*X-2166, 1686*X^4+5256*X^3+4706*X^2+1350*X+12, -295*X^4-608*X^3-478*X^2-174*X-26, (X+1)^4]", "text": "A-incarnation: X(1,1,1,1,1,1,1) in G(2,7)\nThere is a second MUM point at infinity related to\nthe Pfaffian in P^7, AESZ 243/5.46", "degz": 5, "h3": "378", "sol": "1 5 109 3317 121501 4954505 216867925 9981053045 476860000285 23451310381505", "n_discr_factors": "2", "c3": "-882", "operator": "4 5 0 0 0 0 9 -45 -306 -816 -1020 -519 -2166 -9546 -15194 -10064 -2258 12 1350 4706 5256 1686 -26 -174 -478 -608 -295 1 4 6 4 1", "new_number": "5.7", "id": 293, "operator_tex": "3^{2} \\theta^4-3 x\\left(173\\theta^4+340\\theta^3+272\\theta^2+102\\theta+15\\right)-2 x^{2}\\left(1129\\theta^4+5032\\theta^3+7597\\theta^2+4773\\theta+1083\\right)+2 x^{3}\\left(843\\theta^4+2628\\theta^3+2353\\theta^2+675\\theta+6\\right)-x^{4}\\left(295\\theta^4+608\\theta^3+478\\theta^2+174\\theta+26\\right)+x^{5}\\left((\\theta+1)^4\\right)", "superseek": "14/3 910/3", "discriminant": "5 9 -519 -2258 1686 -295 1", "aesz": "27", "n_sing_complex": "3", "inst_int": "", "c2h": "-252", "hash": "3671a1760894e9030e36de89070612e8", "dim_h": "42", "inst": " 14/3 175/6 910/3 14147/3 265496/3 3801105/2 44713634 1125927236 89584714366/3 2475567318392/3", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(z^3-289z^2-57z+1)(z-3)^2", "discr_factors": "1, (z-3)^2, z^3-289*z^2-57*z+1", "dm_basis": null, "q": "0 1 -14 7 14 -8869 -165816 -4477284 -126418042 -3699502611", "yuk": "1 14/3 238 24584/3 906122/3 11062338 410527768 46010329400/3 1729425140618/3 65307256797398/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/6*(70588+84*I*3^(1/2))^(1/3)-5978/3/(70588+84*I*3^(1/2))^(1/3)+289/3+1/2*I*3^(1/2)*(7/3*(70588+84*I*3^(1/2))^(1/3)-11956/3/(70588+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.213297","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/6*(70588+84*I*3^(1/2))^(1/3)-5978/3/(70588+84*I*3^(1/2))^(1/3)+289/3-1/2*I*3^(1/2)*(7/3*(70588+84*I*3^(1/2))^(1/3)-11956/3/(70588+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.016211","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3","im":"0","approx_re":"3.0","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"7/3*(70588+84*I*3^(1/2))^(1/3)+11956/3/(70588+84*I*3^(1/2))^(1/3)+289/3","im":"0","approx_re":"289.197085","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -2365*X^4-4460*X^3-3480*X^2-1250*X-175, 3946*X^4-9272*X^3-28834*X^2-21790*X-5490, 6174*X^4+34560*X^3+20646*X^2-6210*X-5760, -6723*X^4+8424*X^3+37098*X^2+32886*X+9234, -6561*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 319/5.85\nFibre product: 53211- x 632--1(1)\n", "degz": 5, "h3": "30", "sol": "1 7 219 9961 546379 33440757 2199262269 152168119383 10933656369867 808865626688413", "n_discr_factors": "3", "c3": "-86", "operator": "4 5 0 0 0 0 25 -175 -1250 -3480 -4460 -2365 -5490 -21790 -28834 -9272 3946 -5760 -6210 20646 34560 6174 9234 32886 37098 8424 -6723 -6561 -26244 -39366 -26244 -6561", "new_number": "5.84", "id": 298, "operator_tex": "5^{2} \\theta^4-5 x\\left(473\\theta^4+892\\theta^3+696\\theta^2+250\\theta+35\\right)+2 x^{2}\\left(1973\\theta^4-4636\\theta^3-14417\\theta^2-10895\\theta-2745\\right)+2 3^{2} x^{3}\\left(343\\theta^4+1920\\theta^3+1147\\theta^2-345\\theta-320\\right)-3^{4} x^{4}\\left(83\\theta^4-104\\theta^3-458\\theta^2-406\\theta-114\\right)-3^{8} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "46/5 1126", "discriminant": "5 25 -2365 3946 6174 -6723 -6561", "aesz": "318", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3fa38f629ecd5f39b585ce0c1bd88463", "dim_h": "11", "inst": " 46/5 717/10 1126 51481/2 3609772/5 693353459/30 4058216342/5 305088059917/10 6040466014836/5 249239441393223/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(81z^2+92z-1)(-5+9z)^2", "discr_factors": "-6561, z+1, (-5/9+z)^2, z^2+92/81*z-1/81", "dm_basis": null, "q": "0 1 -22 75 -874 -37047 -1214304 -48755214 -2049708066 -89619902802", "yuk": "1 46/5 2914/5 152056/5 8239874/5 451221546/5 24960879448/5 1391968205352/5 78102551578626/5 880699944993500", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-46/81-13/81*13^(1/2)","im":"0","approx_re":"-1.14657","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-46/81+13/81*13^(1/2)","im":"0","approx_re":"0.010767","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/9","im":"0","approx_re":"0.555555555556","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 83*X^4+436*X^3+352*X^2+134*X+21, -6174*X^4+9864*X^3+45990*X^2+31482*X+7290, -319626*X^4-2029536*X^3-1835298*X^2-625482*X-55404, 15516765*X^4+32805000*X^3+28146690*X^2+11744190*X+2033910, -13286025*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding\nto Operator AESZ 318/5.84\nB-Incarnation:\nFibre product 53211- x 632--1(0)\n", "degz": 5, "h3": null, "sol": "1 -21 891 -48027 2920779 -191143071 13146142941 -937446412581 68726414815947 -5150709386794839", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 21 134 352 436 83 7290 31482 45990 9864 -6174 -55404 -625482 -1835298 -2029536 -319626 2033910 11744190 28146690 32805000 15516765 -13286025 -53144100 -79716150 -53144100 -13286025", "new_number": "5.85", "id": 299, "operator_tex": "\\theta^4+x\\left(83\\theta^4+436\\theta^3+352\\theta^2+134\\theta+21\\right)-2 3^{2} x^{2}\\left(343\\theta^4-548\\theta^3-2555\\theta^2-1749\\theta-405\\right)-2 3^{4} x^{3}\\left(1973\\theta^4+12528\\theta^3+11329\\theta^2+3861\\theta+342\\right)+3^{8} 5 x^{4}\\left(473\\theta^4+1000\\theta^3+858\\theta^2+358\\theta+62\\right)-3^{12} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-26 -14942/3", "discriminant": "5 1 83 -6174 -319626 15516765 -13286025", "aesz": "319", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "40a034330b9ad40ec865803f0a601932", "dim_h": null, "inst": " -26 -475/2 -14942/3 -244479/2 -3574404 -226112855/2 -3849559890 -274068834263/2 -15227020463156/3 -193449114452573", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(81z+1)(81z^2-92z-1)(-1+45z)^2", "discr_factors": "-13286025, z+1/81, (-1/45+z)^2, z^2-92/81*z-1/81", "dm_basis": null, "q": "0 1 50 2091 84062 3380745 137821152 5706038418 239835054246 10217160741870", "yuk": "1 -26 -1926 -134504 -7825254 -446800526 -24420324744 -1320399042296 -70161629396582 -3700165972681412", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/81","im":"0","approx_re":"-0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"46/81-13/81*13^(1/2)","im":"0","approx_re":"-0.010767","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/45","im":"0","approx_re":"0.0222222222222","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"46/81+13/81*13^(1/2)","im":"0","approx_re":"1.14657","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -352*X^4-128*X^3-144*X^2-80*X-16, 48128*X^4+45056*X^3+49664*X^2+23040*X+4096, -3178496*X^4-5505024*X^3-6078464*X^2-3194880*X-671744, 100663296*X^4+276824064*X^3+341311488*X^2+202899456*X+47185920, -1207959552*(X+1)^4]", "text": "There is a second MUM-point hiding at infinity, corresponding to Operator...", "degz": 5, "h3": "128", "sol": "1 16 464 17152 725776 33449216 1633531136 83137654784 4362766699792 234378319042816", "n_discr_factors": "3", "c3": "544", "operator": "4 5 0 0 0 0 1 -16 -80 -144 -128 -352 4096 23040 49664 45056 48128 -671744 -3194880 -6078464 -5505024 -3178496 47185920 202899456 341311488 276824064 100663296 -1207959552 -4831838208 -7247757312 -4831838208 -1207959552", "new_number": "5.9", "id": 315, "operator_tex": "\\theta^4-2^{4} x\\left(22\\theta^4+8\\theta^3+9\\theta^2+5\\theta+1\\right)+2^{9} x^{2}\\left(94\\theta^4+88\\theta^3+97\\theta^2+45\\theta+8\\right)-2^{14} x^{3}\\left(194\\theta^4+336\\theta^3+371\\theta^2+195\\theta+41\\right)+2^{19} 3 x^{4}\\left(64\\theta^4+176\\theta^3+217\\theta^2+129\\theta+30\\right)-2^{27} 3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-16 -3280", "discriminant": "5 1 -352 48128 -3178496 100663296 -1207959552", "aesz": "56", "n_sing_complex": "0", "inst_int": "", "c2h": "-64", "hash": "58a7f24bf18cb98b526885069667f9f0", "dim_h": "16", "inst": " -16 -178 -3280 -76197 -2046896 -60450314 -1908455824 -63296186075 -2180416654720 -77402940045830", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+32z)(96z-1)^2(64z-1)^2", "discr_factors": "-1207959552, -1/32+z, (z-1/64)^2, (z-1/96)^2", "dm_basis": null, "q": "0 1 -16 128 -1024 1968 -48640 781312 74416128 4319629464", "yuk": "1 -16 -1440 -88576 -4878048 -255862016 -13057357824 -654600347648 -32407652148448 -1589523741379456", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96","im":"0","approx_re":"0.0104166666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[729*X^4, -80919*X^4-131220*X^3-102060*X^2-36450*X-5103, 861975*X^4+309960*X^3-1146582*X^2-922914*X-204120, 131679*X^4+10007388*X^3+11054610*X^2+5385852*X+1142019, -20696678*X^4-53080096*X^3-84018776*X^2-59911056*X-15760116, 19663130*X^4+134877848*X^3+287380608*X^2+233423852*X+67198286, -112801028-317294820*X-258432404*X^2-11794896*X^3+29081774*X^4, 34539050+18687880*X-142675476*X^2-187765160*X^3-41895970*X^4, 1325117*X^4+114002144*X^3+209338120*X^2+141064960*X+32960772, 20650221*X^4+38200572*X^3+36049212*X^2+24370470*X+8218017, -10635381*X^4-38158776*X^3-54626886*X^2-35547498*X-8739252, 1594323*(X+1)^4]", "text": "This is operator \"11.14\" from ...", "degz": 11, "h3": null, "sol": "1 7 231 11185 654199 42703257 2995533969 221082941247 16945109109495 1337245467114193", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 729 -5103 -36450 -102060 -131220 -80919 -204120 -922914 -1146582 309960 861975 1142019 5385852 11054610 10007388 131679 -15760116 -59911056 -84018776 -53080096 -20696678 67198286 233423852 287380608 134877848 19663130 -112801028 -317294820 -258432404 -11794896 29081774 34539050 18687880 -142675476 -187765160 -41895970 32960772 141064960 209338120 114002144 1325117 8218017 24370470 36049212 38200572 20650221 -8739252 -35547498 -54626886 -38158776 -10635381 1594323 6377292 9565938 6377292 1594323", "new_number": "11.14", "id": 330, "operator_tex": "3^{6} \\theta^4-3^{6} x\\left(111\\theta^4+180\\theta^3+140\\theta^2+50\\theta+7\\right)+3^{3} x^{2}\\left(31925\\theta^4+11480\\theta^3-42466\\theta^2-34182\\theta-7560\\right)+3^{3} x^{3}\\left(4877\\theta^4+370644\\theta^3+409430\\theta^2+199476\\theta+42297\\right)-2 x^{4}\\left(10348339\\theta^4+26540048\\theta^3+42009388\\theta^2+29955528\\theta+7880058\\right)+2 x^{5}\\left(9831565\\theta^4+67438924\\theta^3+143690304\\theta^2+116711926\\theta+33599143\\right)+2 x^{6}\\left(14540887\\theta^4-5897448\\theta^3-129216202\\theta^2-158647410\\theta-56400514\\right)-2 x^{7}\\left(20947985\\theta^4+93882580\\theta^3+71337738\\theta^2-9343940\\theta-17269525\\right)+x^{8}\\left(1325117\\theta^4+114002144\\theta^3+209338120\\theta^2+141064960\\theta+32960772\\right)+3^{4} x^{9}\\left(254941\\theta^4+471612\\theta^3+445052\\theta^2+300870\\theta+101457\\right)-3^{8} x^{10}\\left(1621\\theta^4+5816\\theta^3+8326\\theta^2+5418\\theta+1332\\right)+3^{13} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "10 13958/9", "discriminant": "11 729 -80919 861975 131679 -20696678 19663130 29081774 -41895970 1325117 20650221 -10635381 1594323", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "0a4e6572e1bb29d996fd62dc404c2446", "dim_h": null, "inst": " 10 2591/27 13958/9 1037839/27 3535478/3 371146237/9 42727053718/27 1755397540159/27 25327325460920/9 3427241102571305/27", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "9", "laurent": null, "discriminant_tex": "(z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2", "discr_factors": "1594323, z-1, z^4-520/243*z^3+310/243*z^2+32/81*z-1/243, (1/3-7/3*z-143/81*z^2+z^3)^2", "dm_basis": null, "q": "0 1 -22 17 -626 -55126 -2048572 -88461351 -4055850218 -193869600674", "yuk": "1 10 20998/27 41884 66442694/27 441934780/3 240503913172/27 14655379425544/27 898763607004102/27 2051513362376404", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/243*(1298008+4374*I*150770^(1/2))^(1/3)-16594/243/(1298008+4374*I*150770^(1/2))^(1/3)+143/243+1/2*I*3^(1/2)*(2/243*(1298008+4374*I*150770^(1/2))^(1/3)-33188/243/(1298008+4374*I*150770^(1/2))^(1/3))","im":"0","approx_re":"-0.97581","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/243*(1298008+4374*I*150770^(1/2))^(1/3)-16594/243/(1298008+4374*I*150770^(1/2))^(1/3)+143/243-1/2*I*3^(1/2)*(2/243*(1298008+4374*I*150770^(1/2))^(1/3)-33188/243/(1298008+4374*I*150770^(1/2))^(1/3))","im":"0","approx_re":"0.130861","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/243*(1298008+4374*I*150770^(1/2))^(1/3)+33188/243/(1298008+4374*I*150770^(1/2))^(1/3)+143/243","im":"0","approx_re":"2.610381","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 1621*X^4+668*X^3+604*X^2+270*X+45, 86904+582486*X+1679586*X^2+1644456*X^3+764823*X^4, -11926053*X^4+978315084*X^3+1122458490*X^2+531852156*X+102987855, 41651161308+200488343616*X+370137030408*X^2+44136459360*X^3-91626486390*X^4, 6941651518422+25433811791964*X+25805218900752*X^2-68089279550472*X^3-15455247056334*X^4, 767134409632812+1983120250683420*X+93735612472572*X^2-7260948022648464*X^3+2539299813290190*X^4, 649483686026278902*X^4+932225087477673144*X^3+1536371364206564604*X^2+993929790511088280*X+234868967396672562, -23371937750856175884-97394741126052762960*X-138614145771401492760*X^2-72295788559186671264*X^3+1004131051225603173*X^4, -1597257077285565645975*X^4-5814666171405745947540*X^3-5735816456329722409308*X^2-2126840982158477544570*X-230195139000497651907, -9191195087047038173556-43986433630867968402018*X-87316353326946862648782*X^2-86659839392157788493528*X^3-36436523380793615616597*X^4, -79766443076872509863361*(X+1)^4]", "text": "This is operator \"11.15\" from ...", "degz": 11, "h3": null, "sol": "1 -45 3591 -147771 -62088201 28881797805 -8451428806575 1955276265259755 -345150678543204105 29430956340480209445", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 1 45 270 604 668 1621 86904 582486 1679586 1644456 764823 102987855 531852156 1122458490 978315084 -11926053 41651161308 200488343616 370137030408 44136459360 -91626486390 6941651518422 25433811791964 25805218900752 -68089279550472 -15455247056334 767134409632812 1983120250683420 93735612472572 -7260948022648464 2539299813290190 234868967396672562 993929790511088280 1536371364206564604 932225087477673144 649483686026278902 -23371937750856175884 -97394741126052762960 -138614145771401492760 -72295788559186671264 1004131051225603173 -230195139000497651907 -2126840982158477544570 -5735816456329722409308 -5814666171405745947540 -1597257077285565645975 -9191195087047038173556 -43986433630867968402018 -87316353326946862648782 -86659839392157788493528 -36436523380793615616597 -79766443076872509863361 -319065772307490039453444 -478598658461235059180166 -319065772307490039453444 -79766443076872509863361", "new_number": "11.15", "id": 331, "operator_tex": "\\theta^4+x\\left(1621\\theta^4+668\\theta^3+604\\theta^2+270\\theta+45\\right)+3 x^{2}\\left(254941\\theta^4+548152\\theta^3+559862\\theta^2+194162\\theta+28968\\right)-3^{2} x^{3}\\left(1325117\\theta^4-108701676\\theta^3-124717610\\theta^2-59094684\\theta-11443095\\right)-2 3^{7} x^{4}\\left(20947985\\theta^4-10090640\\theta^3-84622092\\theta^2-45836384\\theta-9522442\\right)-2 3^{12} x^{5}\\left(14540887\\theta^4+64060996\\theta^3-24278536\\theta^2-23929102\\theta-6530971\\right)+2 3^{17} x^{6}\\left(9831565\\theta^4-28112664\\theta^3+362922\\theta^2+7678170\\theta+2970162\\right)+2 3^{22} x^{7}\\left(10348339\\theta^4+14853308\\theta^3+24479278\\theta^2+15836460\\theta+3742209\\right)+3^{30} x^{8}\\left(4877\\theta^4-351136\\theta^3-673240\\theta^2-473040\\theta-113516\\right)-3^{35} x^{9}\\left(31925\\theta^4+116220\\theta^3+114644\\theta^2+42510\\theta+4601\\right)-3^{43} x^{10}\\left(111\\theta^4+264\\theta^3+266\\theta^2+134\\theta+28\\right)-3^{48} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "26 1205094", "discriminant": "11 1 1621 764823 -11926053 -91626486390 -15455247056334 2539299813290190 649483686026278902 1004131051225603173 -1597257077285565645975 -36436523380793615616597 -79766443076872509863361", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "3569012dbdb9fd87263426cf2bb6fc1e", "dim_h": null, "inst": " 26 -15173 1205094 -256830529 38564264386 -24621015178375/3 1568706159253554 -347793971847052721 75180661140829033848 -17439957415989860451459", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "9", "laurent": null, "discriminant_tex": "-(243z+1)(14348907z^4+5668704z^3-75330z^2-520z-1)(-1-429z+137781z^2+4782969z^3)^2", "discr_factors": "-79766443076872509863361, (-1/4782969-143/1594323*z+7/243*z^2+z^3)^2, z^4+32/81*z^3-310/59049*z^2-520/14348907*z-1/14348907, z+1/243", "dm_basis": null, "q": "0 1 90 13713 532414 283817322 -14472937116 10324833700441 -1514592578687994 520845182876613150", "yuk": "1 26 -121358 32537564 -16437275214 4820533048276 -1772713060426820 538066212623969048 -178070513602128268366 54806701971664398212756", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2187*(-1584+2*I*150770^(1/2))^(1/3)-146/2187/(-1584+2*I*150770^(1/2))^(1/3)-7/729+1/6*I*3^(1/2)*(2/729*(-1584+2*I*150770^(1/2))^(1/3)-292/729/(-1584+2*I*150770^(1/2))^(1/3))","im":"0","approx_re":"-0.031447","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/243","im":"0","approx_re":"-0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2187*(-1584+2*I*150770^(1/2))^(1/3)-146/2187/(-1584+2*I*150770^(1/2))^(1/3)-7/729-1/6*I*3^(1/2)*(2/729*(-1584+2*I*150770^(1/2))^(1/3)-292/729/(-1584+2*I*150770^(1/2))^(1/3))","im":"0","approx_re":"-0.001576","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"2/2187*(-1584+2*I*150770^(1/2))^(1/3)+292/2187/(-1584+2*I*150770^(1/2))^(1/3)-7/729","im":"0","approx_re":"0.004217","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1225*X^4, -6125-42875*X-117635*X^2-149520*X^3-93030*X^4, -482475-2058700*X-2927049*X^2-1102432*X^3+364211*X^4, 1107645+7584675*X+17848802*X^2+16891206*X^3+3547267*X^4, -5628891-26546780*X-46592338*X^2-38194636*X^3-16110878*X^4, -2497725-2956011*X-1361238*X^2-8096466*X^3-6058407*X^4, 16028559+68583294*X+117915543*X^2+95134392*X^3+28681623*X^4, 39522573+134643681*X+158738562*X^2+73123506*X^3+13927437*X^4, 19440729+51462378*X+35704314*X^2-4876848*X^3-7620561*X^4, 349920-6075486*X-19346931*X^2-17465382*X^3-3585951*X^4, -966654-3513780*X-4005126*X^2-982692*X^3+571536*X^4, 236196*(X+1)^4]", "text": "This is operator \"11.16\" from ...", "degz": 11, "h3": null, "sol": "1 5 129 4523 191329 9007905 455268675 24194149845 1334740804065 75797178695645", "n_discr_factors": "2", "c3": null, "operator": "4 11 0 0 0 0 1225 -6125 -42875 -117635 -149520 -93030 -482475 -2058700 -2927049 -1102432 364211 1107645 7584675 17848802 16891206 3547267 -5628891 -26546780 -46592338 -38194636 -16110878 -2497725 -2956011 -1361238 -8096466 -6058407 16028559 68583294 117915543 95134392 28681623 39522573 134643681 158738562 73123506 13927437 19440729 51462378 35704314 -4876848 -7620561 349920 -6075486 -19346931 -17465382 -3585951 -966654 -3513780 -4005126 -982692 571536 236196 944784 1417176 944784 236196", "new_number": "11.16", "id": 332, "operator_tex": "5^{2} 7^{2} \\theta^4-5 7 x\\left(2658\\theta^4+4272\\theta^3+3361\\theta^2+1225\\theta+175\\right)-x^{2}\\left(482475+2058700\\theta+2927049\\theta^2+1102432\\theta^3-364211\\theta^4\\right)+x^{3}\\left(1107645+7584675\\theta+17848802\\theta^2+16891206\\theta^3+3547267\\theta^4\\right)-x^{4}\\left(5628891+26546780\\theta+46592338\\theta^2+38194636\\theta^3+16110878\\theta^4\\right)-3 x^{5}\\left(2019469\\theta^4+2698822\\theta^3+453746\\theta^2+985337\\theta+832575\\right)+3^{2} x^{6}\\left(3186847\\theta^4+10570488\\theta^3+13101727\\theta^2+7620366\\theta+1780951\\right)+3^{3} x^{7}\\left(515831\\theta^4+2708278\\theta^3+5879206\\theta^2+4986803\\theta+1463799\\right)-3^{4} x^{8}\\left(94081\\theta^4+60208\\theta^3-440794\\theta^2-635338\\theta-240009\\right)-3^{6} x^{9}\\left(4919\\theta^4+23958\\theta^3+26539\\theta^2+8334\\theta-480\\right)+2 3^{6} x^{10}\\left(392\\theta^4-674\\theta^3-2747\\theta^2-2410\\theta-663\\right)+2^{2} 3^{10} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "211/35 19279/35", "discriminant": "11 1225 -93030 364211 3547267 -16110878 -6058407 28681623 13927437 -7620561 -3585951 571536 236196", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "dc993c4f73af62a0915341e2b6d1f81f", "dim_h": null, "inst": " 211/35 1643/35 19279/35 69901/7 7789913/35 39678242/7 5534913028/35 165311273921/35 5201243378046/35 24360698902146/5", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "9", "laurent": null, "discriminant_tex": "(1-66z-379z^2+427z^3+439z^4+81z^5)(35-174z-81z^2+54z^3)^2", "discr_factors": "236196, 1/81-22/27*z-379/81*z^2+427/81*z^3+439/81*z^4+z^5, (35/54-29/9*z-3/2*z^2+z^3)^2", "dm_basis": null, "q": "0 1 -15 -28 84 -15879 -437827 -13370542 -445627277 -15490057323", "yuk": "1 211/35 2671/7 74392/5 4476335/7 973739336/35 42853035248/35 379695033763/7 84639394629227/35 3791706423116278/35", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*(3537+6*I*1845645^(1/2))^(1/3)-143/12/(3537+6*I*1845645^(1/2))^(1/3)+1/2+1/6*I*3^(1/2)*(1/6*(3537+6*I*1845645^(1/2))^(1/3)-143/2/(3537+6*I*1845645^(1/2))^(1/3))","im":"0","approx_re":"-1.31797","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*(3537+6*I*1845645^(1/2))^(1/3)-143/12/(3537+6*I*1845645^(1/2))^(1/3)+1/2-1/6*I*3^(1/2)*(1/6*(3537+6*I*1845645^(1/2))^(1/3)-143/2/(3537+6*I*1845645^(1/2))^(1/3))","im":"0","approx_re":"0.186913","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18*(3537+6*I*1845645^(1/2))^(1/3)+143/6/(3537+6*I*1845645^(1/2))^(1/3)+1/2","im":"0","approx_re":"2.631057","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[4*X^4, 132+1012*X+3254*X^2+4484*X^3+784*X^4, 106434+603774*X+1281501*X^2+346842*X^3-398439*X^4, 8450568+36850950*X+41503428*X^2-230448564*X^3-68585049*X^4, 3223189665+13976878617*X+16717913514*X^2-12694629582*X^3+10153101573*X^4, -64479205089-202472643708*X+271749698145*X^2+1156893912900*X^3+1693621156527*X^4, 5429181592683+1383736846545*X-64198358715258*X^2-77183545593978*X^3-28977172870383*X^4, -1391107263067899-6391469517277500*X-11108778100598322*X^2-10169352375620364*X^3-6241684232979342*X^4, -61888690185902703-262710337624956189*X-362175524494225326*X^2-84795953649744042*X^3+111316997176038603*X^4, 294396358371236451+2462412186267092118*X+6521189826833817777*X^2+6505336209662529804*X^3+925775495201533419*X^4, -5022714167448962355-23874106222035024795*X-46789789224169458495*X^2-45831366004268867400*X^3-19154052018765196470*X^4, 20429547582091547025*(X+1)^4]", "text": "This is operator \"11.17\" from ...", "degz": 11, "h3": null, "sol": "1 -33 3321 -480255 82588329 -15768471933 3232989859779 -698218313550273 156880622682111465 -36361161453883871697", "n_discr_factors": "2", "c3": null, "operator": "4 11 0 0 0 0 4 132 1012 3254 4484 784 106434 603774 1281501 346842 -398439 8450568 36850950 41503428 -230448564 -68585049 3223189665 13976878617 16717913514 -12694629582 10153101573 -64479205089 -202472643708 271749698145 1156893912900 1693621156527 5429181592683 1383736846545 -64198358715258 -77183545593978 -28977172870383 -1391107263067899 -6391469517277500 -11108778100598322 -10169352375620364 -6241684232979342 -61888690185902703 -262710337624956189 -362175524494225326 -84795953649744042 111316997176038603 294396358371236451 2462412186267092118 6521189826833817777 6505336209662529804 925775495201533419 -5022714167448962355 -23874106222035024795 -46789789224169458495 -45831366004268867400 -19154052018765196470 20429547582091547025 81718190328366188100 122577285492549282150 81718190328366188100 20429547582091547025", "new_number": "11.17", "id": 333, "operator_tex": "2^{2} \\theta^4+2 x\\left(392\\theta^4+2242\\theta^3+1627\\theta^2+506\\theta+66\\right)-3^{4} x^{2}\\left(4919\\theta^4-4282\\theta^3-15821\\theta^2-7454\\theta-1314\\right)-3^{6} x^{3}\\left(94081\\theta^4+316116\\theta^3-56932\\theta^2-50550\\theta-11592\\right)+3^{9} x^{4}\\left(515831\\theta^4-644954\\theta^3+849358\\theta^2+710099\\theta+163755\\right)+3^{12} x^{5}\\left(3186847\\theta^4+2176900\\theta^3+511345\\theta^2-380988\\theta-121329\\right)-3^{15} x^{6}\\left(2019469\\theta^4+5379054\\theta^3+4474094\\theta^2-96435\\theta-378369\\right)-3^{18} x^{7}\\left(16110878\\theta^4+26248876\\theta^3+28673698\\theta^2+16497500\\theta+3590691\\right)+3^{22} x^{8}\\left(3547267\\theta^4-2702138\\theta^3-11541214\\theta^2-8371621\\theta-1972167\\right)+3^{26} x^{9}\\left(364211\\theta^4+2559276\\theta^3+2565513\\theta^2+968742\\theta+115819\\right)-3^{30} 5 7 x^{10}\\left(2658\\theta^4+6360\\theta^3+6493\\theta^2+3313\\theta+697\\right)+3^{34} 5^{2} 7^{2} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "-263/2 -218434", "discriminant": "11 4 784 -398439 -68585049 10153101573 1693621156527 -28977172870383 -6241684232979342 111316997176038603 925775495201533419 -19154052018765196470 20429547582091547025", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "8aa8ad0296efe97c979c0336a2ec2312", "dim_h": null, "inst": " -263/2 -21293/8 -218434 -32618595/2 -1709392950 -173979355415 -41961612798069/2 -4974661097568935/2 -322591278663318874 -41693240844689209325", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "9", "laurent": null, "discriminant_tex": "(43046721z^5-35075106z^4-2486619z^3+34587z^2+439z+1)(2-243z-42282z^2+688905z^3)^2", "discr_factors": "20429547582091547025, z^5-22/27*z^4-379/6561*z^3+427/531441*z^2+439/43046721*z+1/43046721, (2/688905-1/2835*z-58/945*z^2+z^3)^2", "dm_basis": null, "q": "0 1 121 11325 1129552 122171439 14561496222 1819977598050 239925687242565 32568776592743907", "yuk": "1 -263/2 -42849/2 -11795699/2 -2087632929/2 -427348237763/2 -75159093377565/2 -7196416594868965 -2547026484042927649/2 -470338084291130713991/2", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/5670*(244252+105*I*1845645^(1/2))^(1/3)-4309/5670/(244252+105*I*1845645^(1/2))^(1/3)+58/2835+1/54*I*3^(1/2)*(1/105*(244252+105*I*1845645^(1/2))^(1/3)-4309/105/(244252+105*I*1845645^(1/2))^(1/3))","im":"0","approx_re":"-0.009367","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/5670*(244252+105*I*1845645^(1/2))^(1/3)-4309/5670/(244252+105*I*1845645^(1/2))^(1/3)+58/2835-1/54*I*3^(1/2)*(1/105*(244252+105*I*1845645^(1/2))^(1/3)-4309/105/(244252+105*I*1845645^(1/2))^(1/3))","im":"0","approx_re":"0.004692","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2835*(244252+105*I*1845645^(1/2))^(1/3)+4309/2835/(244252+105*I*1845645^(1/2))^(1/3)+58/2835","im":"0","approx_re":"0.066051","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[676*X^4, 6084+43940*X+123838*X^2+159796*X^3+75452*X^4, 80262+347178*X+406119*X^2-148458*X^3-289407*X^4, 211302+628056*X+427287*X^2-23598*X^3+322974*X^4, -1727559-7082469*X-9486576*X^2-2910870*X^3+245808*X^4, 1660014+6911487*X+11660355*X^2+8369082*X^3-95580*X^4, -4024566-11979171*X-10999638*X^2-3085128*X^3-578097*X^4, 6502680+18864333*X+11193795*X^2-9590724*X^3-677241*X^4, -286497+1688364*X+6375105*X^2+6451650*X^3+2882466*X^4, -1102248-6088608*X-10945935*X^2-6574122*X^3+688905*X^4, 131220+209952*X-656100*X^2-1732104*X^3-1102248*X^4, 944784*(X+1)^4]", "text": "This is operator \"11.18\" from ...", "degz": 11, "h3": null, "sol": "1 -9 333 -18639 1264509 -95900409 7821949311 -671524215777 59886463715901 -5499795491309421", "n_discr_factors": "2", "c3": null, "operator": "4 11 0 0 0 0 676 6084 43940 123838 159796 75452 80262 347178 406119 -148458 -289407 211302 628056 427287 -23598 322974 -1727559 -7082469 -9486576 -2910870 245808 1660014 6911487 11660355 8369082 -95580 -4024566 -11979171 -10999638 -3085128 -578097 6502680 18864333 11193795 -9590724 -677241 -286497 1688364 6375105 6451650 2882466 -1102248 -6088608 -10945935 -6574122 688905 131220 209952 -656100 -1732104 -1102248 944784 3779136 5668704 3779136 944784", "new_number": "11.18", "id": 334, "operator_tex": "2^{2} 13^{2} \\theta^4+2 13 x\\left(2902\\theta^4+6146\\theta^3+4763\\theta^2+1690\\theta+234\\right)-3 x^{2}\\left(96469\\theta^4+49486\\theta^3-135373\\theta^2-115726\\theta-26754\\right)+3 x^{3}\\left(107658\\theta^4-7866\\theta^3+142429\\theta^2+209352\\theta+70434\\right)+3^{2} x^{4}\\left(27312\\theta^4-323430\\theta^3-1054064\\theta^2-786941\\theta-191951\\right)-3^{4} x^{5}\\left(1180\\theta^4-103322\\theta^3-143955\\theta^2-85327\\theta-20494\\right)-3^{5} x^{6}\\left(2379\\theta^4+12696\\theta^3+45266\\theta^2+49297\\theta+16562\\right)-3^{6} x^{7}\\left(929\\theta^4+13156\\theta^3-15355\\theta^2-25877\\theta-8920\\right)+3^{7} x^{8}\\left(1318\\theta^4+2950\\theta^3+2915\\theta^2+772\\theta-131\\right)+3^{7} x^{9}\\left(315\\theta^4-3006\\theta^3-5005\\theta^2-2784\\theta-504\\right)-2^{2} 3^{8} x^{10}\\left(42\\theta^4+66\\theta^3+25\\theta^2-8\\theta-5\\right)+2^{4} 3^{10} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "-343/26 -27836/13", "discriminant": "11 676 75452 -289407 322974 245808 -95580 -578097 -677241 2882466 688905 -1102248 944784", "aesz": null, "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "7fd9e473da9a826dea365ad9c234d2b1", "dim_h": null, "inst": " -343/26 11207/104 -27836/13 764852/13 -52338075/26 2041910283/26 -43703976857/13 2002549942971/13 -96665555874384/13 38898080991396283/104", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "9", "laurent": null, "discriminant_tex": "(1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2", "discr_factors": "944784, 1/81+116/81*z+25/27*z^2+2*z^3-4/3*z^4+z^5, (13/54-19/36*z+1/12*z^2+z^3)^2", "dm_basis": null, "q": "0 1 29 231 3742 -55558 3266496 -152207602 7845030189 -418080458403", "yuk": "1 -343/26 22071/26 -1503487/26 97923127/26 -3271129859/13 441051140055/26 -29980928124245/26 2050611239525431/26 -140938380466355359/26", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*(5959+18*72533^(1/2))^(1/3)-229/36/(5959+18*72533^(1/2))^(1/3)-1/36","im":"0","approx_re":"-0.92963","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(5959+18*72533^(1/2))^(1/3)+229/72/(5959+18*72533^(1/2))^(1/3)-1/36","im":"1/6*3^(1/2)*(-1/12*(5959+18*72533^(1/2))^(1/3)+229/12/(5959+18*72533^(1/2))^(1/3))","approx_re":"0.423148","approx_im":"-0.282683","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(5959+18*72533^(1/2))^(1/3)+229/72/(5959+18*72533^(1/2))^(1/3)-1/36","im":"-1/6*3^(1/2)*(-1/12*(5959+18*72533^(1/2))^(1/3)+229/12/(5959+18*72533^(1/2))^(1/3))","approx_re":"0.423148","approx_im":"0.282683","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -48-336*X-948*X^2-1224*X^3-504*X^4, 16092+82404*X+159381*X^2+115182*X^3+8505*X^4, 277020+1078920*X+1438317*X^2+1692738*X^3+960822*X^4, 69710625+266278185*X+323122689*X^2+61935840*X^3-6095169*X^4, -130734486-747737487*X-1266719148*X^2+187775820*X^3-140477571*X^4, -13487972580-59576130423*X-91987654131*X^2-57417948522*X^3-627100380*X^4, -172716199236-385266558627*X+127702083654*X^2+689828486994*X^3+43544149776*X^4, 1708022144745+7601132598552*X+11650953761325*X^2+6291967021686*X^3+1544774629806*X^4, -225478724598-31922673452622*X-114282458106687*X^2-130324378294710*X^3-37374067153341*X^4, 5711352848838+91200332792556*X+338782945969962*X^2+495165226354812*X^3+263084856624252*X^4, 63640788887052*(X+1)^4]", "text": "This is operator \"11.19\" from ...", "degz": 11, "h3": null, "sol": "1 3 -27 -1563 -40491 -148797 35251119 1589471019 24444499221 -991399568793", "n_discr_factors": "2", "c3": null, "operator": "4 11 0 0 0 0 16 -48 -336 -948 -1224 -504 16092 82404 159381 115182 8505 277020 1078920 1438317 1692738 960822 69710625 266278185 323122689 61935840 -6095169 -130734486 -747737487 -1266719148 187775820 -140477571 -13487972580 -59576130423 -91987654131 -57417948522 -627100380 -172716199236 -385266558627 127702083654 689828486994 43544149776 1708022144745 7601132598552 11650953761325 6291967021686 1544774629806 -225478724598 -31922673452622 -114282458106687 -130324378294710 -37374067153341 5711352848838 91200332792556 338782945969962 495165226354812 263084856624252 63640788887052 254563155548208 381844733322312 254563155548208 63640788887052", "new_number": "11.19", "id": 335, "operator_tex": "2^{4} \\theta^4-2^{2} 3 x\\left(42\\theta^4+102\\theta^3+79\\theta^2+28\\theta+4\\right)+3^{3} x^{2}\\left(315\\theta^4+4266\\theta^3+5903\\theta^2+3052\\theta+596\\right)+3^{6} x^{3}\\left(1318\\theta^4+2322\\theta^3+1973\\theta^2+1480\\theta+380\\right)-3^{8} x^{4}\\left(929\\theta^4-9440\\theta^3-49249\\theta^2-40585\\theta-10625\\right)-3^{10} x^{5}\\left(2379\\theta^4-3180\\theta^3+21452\\theta^2+12663\\theta+2214\\right)-3^{12} x^{6}\\left(1180\\theta^4+108042\\theta^3+173091\\theta^2+112103\\theta+25380\\right)+3^{13} x^{7}\\left(27312\\theta^4+432678\\theta^3+80098\\theta^2-241649\\theta-108332\\right)+3^{15} x^{8}\\left(107658\\theta^4+438498\\theta^3+811975\\theta^2+529736\\theta+119035\\right)-3^{18} x^{9}\\left(96469\\theta^4+336390\\theta^3+294983\\theta^2+82398\\theta+582\\right)+2 3^{20} 13 x^{10}\\left(2902\\theta^4+5462\\theta^3+3737\\theta^2+1006\\theta+63\\right)+2^{2} 3^{23} 13^{2} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "21/4 -1045/6", "discriminant": "11 16 -504 8505 960822 -6095169 -140477571 -627100380 43544149776 1544774629806 -37374067153341 263084856624252 63640788887052", "aesz": null, "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "acf903f94ac2a08b9f2b26dff65a52ff", "dim_h": null, "inst": " 21/4 -969/16 -1045/6 -35199/4 536619/4 33449027/24 72901461/2 -2916376749/4 -74285877749/3 -5584377170031/16", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "9", "laurent": null, "discriminant_tex": "(1-36z+1458z^2+18225z^3+761076z^4+177147z^5)(4+9z-1539z^2+18954z^3)^2", "discr_factors": "63640788887052, 1/177147-4/19683*z+2/243*z^2+25/243*z^3+116/27*z^4+z^5, (2/9477+1/2106*z-19/234*z^2+z^3)^2", "dm_basis": null, "q": "0 1 -9 216 -774 60129 -1206009 13280967 -468977283 10829533383", "yuk": "1 21/4 -1917/4 -18789/4 -2254653/4 16769349 1204144245/4 50010402267/4 -1493187150141/4 -72205873190817/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/9*RootOf(3*_Z^5+116*_Z^4+25*_Z^3+18*_Z^2-4*_Z+1,index = 3)","im":"0","approx_re":"-4.272671","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/702*(31868+117*72533^(1/2))^(1/3)-283/702/(31868+117*72533^(1/2))^(1/3)+19/702","im":"0","approx_re":"-0.039841","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9*RootOf(3*_Z^5+116*_Z^4+25*_Z^3+18*_Z^2-4*_Z+1,index = 2)","im":"0","approx_re":"-0.024843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9*RootOf(3*_Z^5+116*_Z^4+25*_Z^3+18*_Z^2-4*_Z+1,index = 4)","im":"0","approx_re":"-0.024843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9*RootOf(3*_Z^5+116*_Z^4+25*_Z^3+18*_Z^2-4*_Z+1,index = 1)","im":"0","approx_re":"0.01303","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9*RootOf(3*_Z^5+116*_Z^4+25*_Z^3+18*_Z^2-4*_Z+1,index = 5)","im":"0","approx_re":"0.01303","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1404*(31868+117*72533^(1/2))^(1/3)+283/1404/(31868+117*72533^(1/2))^(1/3)+19/702","im":"1/18*3^(1/2)*(-1/78*(31868+117*72533^(1/2))^(1/3)+283/78/(31868+117*72533^(1/2))^(1/3))","approx_re":"0.060519","approx_im":"-0.040429","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1404*(31868+117*72533^(1/2))^(1/3)+283/1404/(31868+117*72533^(1/2))^(1/3)+19/702","im":"-1/18*3^(1/2)*(-1/78*(31868+117*72533^(1/2))^(1/3)+283/78/(31868+117*72533^(1/2))^(1/3))","approx_re":"0.060519","approx_im":"0.040429","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -64-448*X-1236*X^2-1576*X^3-1112*X^4, -11952-57616*X-96951*X^2-56722*X^3-4615*X^4, 125312+565152*X+1063758*X^2+947364*X^3+258732*X^4, -1430728-5365104*X-7153953*X^2-3814866*X^3-1139565*X^4, 5371968+17505504*X+18432150*X^2+4169940*X^3-1719612*X^4, -6533224-12684960*X+3287856*X^2+17954208*X^3+5354188*X^4, -2443248-16699072*X-32798688*X^2-21784576*X^3+278080*X^4, 695872+1816448*X-1509696*X^2-7883008*X^3-6787264*X^4, 3826688+14241792*X+21052416*X^2+15393792*X^3+5002240*X^4, -1257472-5079040*X-7680000*X^2-5201920*X^3-1372160*X^4, 131072*(X+1)^4]", "text": "This is operator \"11.20\" from ...", "degz": 11, "h3": null, "sol": "1 4 116 3856 163636 7612304 381492656 20081833664 1097542901044 61738874530384", "n_discr_factors": "4", "c3": null, "operator": "4 11 0 0 0 0 16 -64 -448 -1236 -1576 -1112 -11952 -57616 -96951 -56722 -4615 125312 565152 1063758 947364 258732 -1430728 -5365104 -7153953 -3814866 -1139565 5371968 17505504 18432150 4169940 -1719612 -6533224 -12684960 3287856 17954208 5354188 -2443248 -16699072 -32798688 -21784576 278080 695872 1816448 -1509696 -7883008 -6787264 3826688 14241792 21052416 15393792 5002240 -1257472 -5079040 -7680000 -5201920 -1372160 131072 524288 786432 524288 131072", "new_number": "11.20", "id": 337, "operator_tex": "2^{4} \\theta^4-2^{2} x\\left(278\\theta^4+394\\theta^3+309\\theta^2+112\\theta+16\\right)-x^{2}\\left(11952+57616\\theta+96951\\theta^2+56722\\theta^3+4615\\theta^4\\right)+2 x^{3}\\left(129366\\theta^4+473682\\theta^3+531879\\theta^2+282576\\theta+62656\\right)-x^{4}\\left(1430728+5365104\\theta+7153953\\theta^2+3814866\\theta^3+1139565\\theta^4\\right)-2 3 x^{5}\\left(286602\\theta^4-694990\\theta^3-3072025\\theta^2-2917584\\theta-895328\\right)+2^{2} x^{6}\\left(1338547\\theta^4+4488552\\theta^3+821964\\theta^2-3171240\\theta-1633306\\right)+2^{4} x^{7}\\left(17380\\theta^4-1361536\\theta^3-2049918\\theta^2-1043692\\theta-152703\\right)-2^{6} x^{8}\\left(106051\\theta^4+123172\\theta^3+23589\\theta^2-28382\\theta-10873\\right)+2^{10} x^{9}\\left(4885\\theta^4+15033\\theta^3+20559\\theta^2+13908\\theta+3737\\right)-2^{12} x^{10}\\left(335\\theta^4+1270\\theta^3+1875\\theta^2+1240\\theta+307\\right)+2^{17} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "21/4 1285/2", "discriminant": "11 16 -1112 -4615 258732 -1139565 -1719612 5354188 278080 -6787264 5002240 -1372160 131072", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "b07e191c8c5d8b6a2c25e842f85fcaf0", "dim_h": null, "inst": " 21/4 1965/32 1285/2 103095/8 1157421/4 124986905/16 906936123/4 28397105361/4 233461836458 256357685528925/32", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "9", "laurent": null, "discriminant_tex": "(z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2", "discr_factors": "131072, z^2-z-1/16, z-1, (1/4-27/16*z-25/8*z^2+z^3)^2, z^2-71/32*z+1/32", "dm_basis": null, "q": "0 1 -12 -126 392 -19449 -615912 -20326558 -693854064 -25331702601", "yuk": "1 21/4 993/2 69411/4 1650513/2 72338823/2 3374682123/2 155539545105/2 7269660622929/2 680774715180939/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48*(26047+6*I*4895115^(1/2))^(1/3)-949/48/(26047+6*I*4895115^(1/2))^(1/3)+25/24+1/2*I*3^(1/2)*(1/24*(26047+6*I*4895115^(1/2))^(1/3)-949/24/(26047+6*I*4895115^(1/2))^(1/3))","im":"0","approx_re":"-0.573963","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*5^(1/2)","im":"0","approx_re":"-0.059017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"71/64-17/64*17^(1/2)","im":"0","approx_re":"0.014175","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(26047+6*I*4895115^(1/2))^(1/3)-949/48/(26047+6*I*4895115^(1/2))^(1/3)+25/24-1/2*I*3^(1/2)*(1/24*(26047+6*I*4895115^(1/2))^(1/3)-949/24/(26047+6*I*4895115^(1/2))^(1/3))","im":"0","approx_re":"0.121762","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*5^(1/2)","im":"0","approx_re":"1.059017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"71/64+17/64*17^(1/2)","im":"0","approx_re":"2.204575","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(26047+6*I*4895115^(1/2))^(1/3)+949/24/(26047+6*I*4895115^(1/2))^(1/3)+25/24","im":"0","approx_re":"3.577201","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 112+640*X+1200*X^2+1120*X^3+5360*X^4, 491520+3381248*X+9768960*X^2+9230336*X^3+10004480*X^4, 1571356672+8535932928*X+19030278144*X^2+19728433152*X^3+6950158336*X^4, 1845384708096+9210557366272*X+17942980853760*X^2+12004567810048*X^3+145794007040*X^4, 848370931335168+3539375174451200*X+4952537526435840*X^2-929469577560064*X^3-1437253897289728*X^4, 56221053185163264-4050600836726784*X-604091204631527424*X^2-1518478884272603136*X^3-236341673657892864*X^4, 38300018606042251264+144710789126575620096*X+179211247390744903680*X^2+52311702209210351616*X^3+80189757958819676160*X^4, -2331567570285234225152-8819849510242379366400*X-8140418456058756857856*X^2+3154825582168560893952*X^3+9321802710310585368576*X^4, -15126330140441832325120-284448793616601285918720*X-839788023955627337318400*X^2-705809321748274863931392*X^3+85131723900169580707840*X^4, -3664556390706844685828096-16471614292249322505371648*X-30034250831050943559106560*X^2-27125273077603242107469824*X^3-10502543057902090955259904*X^4, -77371252455336267181195264*(X+1)^4]", "text": "This is operator \"11.21\" from ...", "degz": 11, "h3": null, "sol": "1 -112 28304 -9202432 3381592336 -1336386336512 554301159467264 -237996533152329728 104877656438276898064 -47163818308963166148352", "n_discr_factors": "4", "c3": null, "operator": "4 11 0 0 0 0 1 112 640 1200 1120 5360 491520 3381248 9768960 9230336 10004480 1571356672 8535932928 19030278144 19728433152 6950158336 1845384708096 9210557366272 17942980853760 12004567810048 145794007040 848370931335168 3539375174451200 4952537526435840 -929469577560064 -1437253897289728 56221053185163264 -4050600836726784 -604091204631527424 -1518478884272603136 -236341673657892864 38300018606042251264 144710789126575620096 179211247390744903680 52311702209210351616 80189757958819676160 -2331567570285234225152 -8819849510242379366400 -8140418456058756857856 3154825582168560893952 9321802710310585368576 -15126330140441832325120 -284448793616601285918720 -839788023955627337318400 -705809321748274863931392 85131723900169580707840 -3664556390706844685828096 -16471614292249322505371648 -30034250831050943559106560 -27125273077603242107469824 -10502543057902090955259904 -77371252455336267181195264 -309485009821345068724781056 -464227514732017603087171584 -309485009821345068724781056 -77371252455336267181195264", "new_number": "11.21", "id": 338, "operator_tex": "\\theta^4+2^{4} x\\left(335\\theta^4+70\\theta^3+75\\theta^2+40\\theta+7\\right)+2^{11} x^{2}\\left(4885\\theta^4+4507\\theta^3+4770\\theta^2+1651\\theta+240\\right)+2^{16} x^{3}\\left(106051\\theta^4+301032\\theta^3+290379\\theta^2+130248\\theta+23977\\right)+2^{23} x^{4}\\left(17380\\theta^4+1431056\\theta^3+2138970\\theta^2+1097984\\theta+219987\\right)-2^{30} x^{5}\\left(1338547\\theta^4+865636\\theta^3-4612410\\theta^2-3296300\\theta-790107\\right)-2^{38} 3 x^{6}\\left(286602\\theta^4+1841398\\theta^3+732557\\theta^2+4912\\theta-68177\\right)+2^{46} x^{7}\\left(1139565\\theta^4+743394\\theta^3+2546745\\theta^2+2056464\\theta+544276\\right)+2^{56} x^{8}\\left(129366\\theta^4+43782\\theta^3-112971\\theta^2-122400\\theta-32357\\right)+2^{64} x^{9}\\left(4615\\theta^4-38262\\theta^3-45525\\theta^2-15420\\theta-820\\right)-2^{75} x^{10}\\left(278\\theta^4+718\\theta^3+795\\theta^2+436\\theta+97\\right)-2^{86} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "240 31333936", "discriminant": "11 1 5360 10004480 6950158336 145794007040 -1437253897289728 -236341673657892864 80189757958819676160 9321802710310585368576 85131723900169580707840 -10502543057902090955259904 -77371252455336267181195264", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "9a8c2dbc999179b3ef13a33cce17dc01", "dim_h": null, "inst": " 240 -95082 31333936 -15748488666 8901200955216 -5629093947200546 3813566167925096304 -2725633283729035119762 2028546540169498741256320 -1559269337582876885534139246", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "9", "laurent": null, "discriminant_tex": "-(512z+1)(8192z^2+1136z+1)(16384z^2-512z-1)(-1-1600z+442368z^2+33554432z^3)^2", "discr_factors": "-77371252455336267181195264, (-1/33554432-25/524288*z+27/2048*z^2+z^3)^2, z^2+71/512*z+1/8192, z^2-1/32*z-1/16384, z+1/512", "dm_basis": null, "q": "0 1 192 48672 -945152 6252866352 -3621429313536 3033481724390912 -2411315037362847744 2010029899208155053720", "yuk": "1 240 -760416 846016512 -1007904035040 1112650119402240 -1215884291750062080 1308053195598308032512 -1395524241270273885353184 1478810427783564583221873792", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-71/1024-17/1024*17^(1/2)","im":"0","approx_re":"-0.137786","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12288*(-40527+12*I*4895115^(1/2))^(1/3)-443/4096/(-40527+12*I*4895115^(1/2))^(1/3)-9/2048+1/128*I*3^(1/2)*(1/96*(-40527+12*I*4895115^(1/2))^(1/3)-443/32/(-40527+12*I*4895115^(1/2))^(1/3))","im":"0","approx_re":"-0.01604","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"0","approx_re":"-0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64-1/128*5^(1/2)","im":"0","approx_re":"-0.001844","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-71/1024+17/1024*17^(1/2)","im":"0","approx_re":"-0.000886","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12288*(-40527+12*I*4895115^(1/2))^(1/3)-443/4096/(-40527+12*I*4895115^(1/2))^(1/3)-9/2048-1/128*I*3^(1/2)*(1/96*(-40527+12*I*4895115^(1/2))^(1/3)-443/32/(-40527+12*I*4895115^(1/2))^(1/3))","im":"0","approx_re":"-0.000546","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6144*(-40527+12*I*4895115^(1/2))^(1/3)+443/2048/(-40527+12*I*4895115^(1/2))^(1/3)-9/2048","im":"0","approx_re":"0.003403","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64+1/128*5^(1/2)","im":"0","approx_re":"0.033094","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3940*X^4-8360*X^3-6380*X^2-2200*X-300, 2896*X^4+81088*X^3+164656*X^2+108000*X+25360, -110528*X^4+304512*X^3+727360*X^2+291840*X+22080, 1203712*X^4+2330624*X^3-5696000*X^2-6426624*X-1962496, -2158592*X^4-5931008*X^3-65536*X^2+7417856*X+3633152, 16154624*X^4-50036736*X^3-25853952*X^2-11894784*X-3801088, -102236160*X^4+36962304*X^3-113377280*X^2-191234048*X-73793536, 158334976*X^4-109051904*X^3-305135616*X^2-250609664*X-68157440, -96468992*X^4-100663296*X^3-356515840*X^2-553648128*X-230686720, 33554432*(X+1)*(7*X^3+31*X^2+35*X+12), -268435456*(X+1)^4]", "text": "This is operator \"11.4\" from ...", "degz": 11, "h3": null, "sol": "1 12 572 42960 3944556 405927312 44976624944 5248589511744 636470775893740 79500376972668432", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 25 -300 -2200 -6380 -8360 -3940 25360 108000 164656 81088 2896 22080 291840 727360 304512 -110528 -1962496 -6426624 -5696000 2330624 1203712 3633152 7417856 -65536 -5931008 -2158592 -3801088 -11894784 -25853952 -50036736 16154624 -73793536 -191234048 -113377280 36962304 -102236160 -68157440 -250609664 -305135616 -109051904 158334976 -230686720 -553648128 -356515840 -100663296 -96468992 402653184 1577058304 2214592512 1275068416 234881024 -268435456 -1073741824 -1610612736 -1073741824 -268435456", "new_number": "11.4", "id": 341, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(197\\theta^4+418\\theta^3+319\\theta^2+110\\theta+15\\right)+2^{4} x^{2}\\left(181\\theta^4+5068\\theta^3+10291\\theta^2+6750\\theta+1585\\right)-2^{6} x^{3}\\left(1727\\theta^4-4758\\theta^3-11365\\theta^2-4560\\theta-345\\right)+2^{9} x^{4}\\left(2351\\theta^4+4552\\theta^3-11125\\theta^2-12552\\theta-3833\\right)-2^{12} x^{5}\\left(527\\theta^4+1448\\theta^3+16\\theta^2-1811\\theta-887\\right)+2^{15} x^{6}\\left(493\\theta^4-1527\\theta^3-789\\theta^2-363\\theta-116\\right)-2^{17} x^{7}\\left(780\\theta^4-282\\theta^3+865\\theta^2+1459\\theta+563\\right)+2^{20} x^{8}\\left(151\\theta^4-104\\theta^3-291\\theta^2-239\\theta-65\\right)-2^{22} x^{9}\\left(23\\theta^4+24\\theta^3+85\\theta^2+132\\theta+55\\right)+2^{25} x^{10}(\\theta+1)(7\\theta^3+31\\theta^2+35\\theta+12)-2^{28} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "116/5 29628/5", "discriminant": "11 25 -3940 2896 -110528 1203712 -2158592 16154624 -102236160 158334976 -96468992 234881024 -268435456", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "4222cdacde3dbaf06ed32adadb70f0d6", "dim_h": null, "inst": " 116/5 1059/5 29628/5 2227181/10 51562768/5 2740127457/5 159563395868/5 19902142099427/10 130761042201704 44764725674950396/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2", "discr_factors": "-268435456, (z^3-1/2*z^2-1/16*z-5/256)^2, -1/256+39/64*z+5/8*z^2+z^3, (z-1/4)^2", "dm_basis": null, "q": "0 1 -40 502 -12096 -142623 -15843632 -963478046 -67896513280 -4927396898828", "yuk": "1 116/5 8588/5 800072/5 14255676 6445346116/5 591868339256/5 10946048956568 5094948448731692/5 476623998826011152/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(6236+708*177^(1/2))^(1/3)+23/6/(6236+708*177^(1/2))^(1/3)-5/24","im":"-1/8*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.315684","approx_im":"-0.716756","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(6236+708*177^(1/2))^(1/3)+23/6/(6236+708*177^(1/2))^(1/3)-5/24","im":"1/8*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.315684","approx_im":"0.716756","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(271+3*5721^(1/2))^(1/3)-7/12/(271+3*5721^(1/2))^(1/3)+1/6","im":"-1/8*3^(1/2)*(1/6*(271+3*5721^(1/2))^(1/3)-14/3/(271+3*5721^(1/2))^(1/3))","approx_re":"-0.072055","approx_im":"-0.158527","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(271+3*5721^(1/2))^(1/3)-7/12/(271+3*5721^(1/2))^(1/3)+1/6","im":"1/8*3^(1/2)*(1/6*(271+3*5721^(1/2))^(1/3)-14/3/(271+3*5721^(1/2))^(1/3))","approx_re":"-0.072055","approx_im":"0.158527","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(6236+708*177^(1/2))^(1/3)-23/3/(6236+708*177^(1/2))^(1/3)-5/24","im":"0","approx_re":"0.006368","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(271+3*5721^(1/2))^(1/3)+7/6/(271+3*5721^(1/2))^(1/3)+1/6","im":"0","approx_re":"0.64411","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*X*(7*X^3-10*X^2-6*X-1), 5888*X^4+17408*X^3+38656*X^2+14848*X+1792, -1236992*X^4-5799936*X^3-7593984*X^2-4694016*X-1130496, 102236160*X^4+445906944*X^3+837681152*X^2+555352064*X+135135232, -2067791872*X^4-14675869696*X^3-28311552000*X^2-22389194752*X-6199181312, 35366371328*X^4+44291850240*X^3-78248935424*X^2-26373783552*X+1275068416, -2524367028224*X^4-5209795330048*X^3+11462193971200*X^2+14978698444800*X+4946728583168, 29669634080768*X^4+200420353900544*X^3+227994043940864*X^2+51745765982208*X-11424613007360, -99505802313728*X^4+2388139255529472*X^3+2103915499749376*X^2+356241767399424*X-131391639519232, 17328303253749760*X^4+32545544182169600*X^3+21726349764853760*X^2+5453577673768960*X+263882790666240, -14073748835532800*(X+1)^4]", "text": "This is operator \"11.5\" from ...", "degz": 11, "h3": null, "sol": "1 0 -112 13824 -136944 -42624000 3262265600 33086054400 -21000227586800 1156137025075200", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 1 0 16 96 160 -112 1792 14848 38656 17408 5888 -1130496 -4694016 -7593984 -5799936 -1236992 135135232 555352064 837681152 445906944 102236160 -6199181312 -22389194752 -28311552000 -14675869696 -2067791872 1275068416 -26373783552 -78248935424 44291850240 35366371328 4946728583168 14978698444800 11462193971200 -5209795330048 -2524367028224 -11424613007360 51745765982208 227994043940864 200420353900544 29669634080768 -131391639519232 356241767399424 2103915499749376 2388139255529472 -99505802313728 263882790666240 5453577673768960 21726349764853760 32545544182169600 17328303253749760 -14073748835532800 -56294995342131200 -84442493013196800 -56294995342131200 -14073748835532800", "new_number": "11.5", "id": 342, "operator_tex": "\\theta^4-2^{4} x\\theta(7\\theta^3-10\\theta^2-6\\theta-1)+2^{8} x^{2}\\left(23\\theta^4+68\\theta^3+151\\theta^2+58\\theta+7\\right)-2^{13} x^{3}\\left(151\\theta^4+708\\theta^3+927\\theta^2+573\\theta+138\\right)+2^{17} x^{4}\\left(780\\theta^4+3402\\theta^3+6391\\theta^2+4237\\theta+1031\\right)-2^{22} x^{5}\\left(493\\theta^4+3499\\theta^3+6750\\theta^2+5338\\theta+1478\\right)+2^{26} x^{6}\\left(527\\theta^4+660\\theta^3-1166\\theta^2-393\\theta+19\\right)-2^{30} x^{7}\\left(2351\\theta^4+4852\\theta^3-10675\\theta^2-13950\\theta-4607\\right)+2^{34} x^{8}\\left(1727\\theta^4+11666\\theta^3+13271\\theta^2+3012\\theta-665\\right)-2^{39} x^{9}\\left(181\\theta^4-4344\\theta^3-3827\\theta^2-648\\theta+239\\right)+2^{44} 5 x^{10}\\left(197\\theta^4+370\\theta^3+247\\theta^2+62\\theta+3\\right)-2^{49} 5^{2} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "-32 608", "discriminant": "11 1 -112 5888 -1236992 102236160 -2067791872 35366371328 -2524367028224 29669634080768 -99505802313728 17328303253749760 -14073748835532800", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "f5f2274632f5544ebf559c6c512159d1", "dim_h": null, "inst": " -32 -616 608 -21270 -15181664 -157477192 14725008608 -891823196878 -50522477326080 2876556822580744", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2", "discr_factors": "-14073748835532800, (z-1/32)^2, -1/8192-5/512*z-39/32*z^2+z^3, (z^3+1/40*z^2+1/640*z-1/40960)^2", "dm_basis": null, "q": "0 1 16 928 -5120 -413392 15455744 235988480 -68586143744 1647378282136", "yuk": "1 -32 -4960 16384 -1366240 -1897708032 -34015062016 5050677952512 -456613478167776 -36830885970695936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/960*(2006+30*5721^(1/2))^(1/3)+13/120/(2006+30*5721^(1/2))^(1/3)-1/120","im":"-1/32*3^(1/2)*(1/30*(2006+30*5721^(1/2))^(1/3)+52/15/(2006+30*5721^(1/2))^(1/3))","approx_re":"-0.018565","approx_im":"-0.040844","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/960*(2006+30*5721^(1/2))^(1/3)+13/120/(2006+30*5721^(1/2))^(1/3)-1/120","im":"1/32*3^(1/2)*(1/30*(2006+30*5721^(1/2))^(1/3)+52/15/(2006+30*5721^(1/2))^(1/3))","approx_re":"-0.018565","approx_im":"0.040844","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(61128+177*177^(1/2))^(1/3)-517/64/(61128+177*177^(1/2))^(1/3)+13/32","im":"-1/32*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.004021","approx_im":"-0.009129","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(61128+177*177^(1/2))^(1/3)-517/64/(61128+177*177^(1/2))^(1/3)+13/32","im":"1/32*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.004021","approx_im":"0.009129","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/480*(2006+30*5721^(1/2))^(1/3)-13/60/(2006+30*5721^(1/2))^(1/3)-1/120","im":"0","approx_re":"0.012129","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(61128+177*177^(1/2))^(1/3)+517/32/(61128+177*177^(1/2))^(1/3)+13/32","im":"0","approx_re":"1.226791","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2752*X^2+1216*X+176+3072*X^3-2304*X^4, -409600*X^2+2539520*X+589824-5242880*X^3+1638400*X^4, 203423744+377487360*X-1317011456*X^2+2617245696*X^3-150994944*X^4, 15032385536*X^2-92341796864*X-16106127360-274877906944*X^3-227633266688*X^4, -68444598829056*X^2-78340203479040*X-24532853194752-65970697666560*X^3+49478023249920*X^4, 10766417859182592+42432352739131392*X+62698551062298624*X^2+40532396646334464*X^3+7599824371187712*X^4, -1945555039024054272*(X+1)^4]", "text": "This is operator \"7.18\" from ...", "degz": 7, "h3": null, "sol": "1 -176 17168 -4715264 653856016 -191557409536 30340274422016 -9057045220569088 1542586229229919504 -463281504713458547456", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 1 176 1216 2752 3072 -2304 589824 2539520 -409600 -5242880 1638400 203423744 377487360 -1317011456 2617245696 -150994944 -16106127360 -92341796864 15032385536 -274877906944 -227633266688 -24532853194752 -78340203479040 -68444598829056 -65970697666560 49478023249920 10766417859182592 42432352739131392 62698551062298624 40532396646334464 7599824371187712 -1945555039024054272 -7782220156096217088 -11673330234144325632 -7782220156096217088 -1945555039024054272", "new_number": "7.18", "id": 440, "operator_tex": "\\theta^4-2^{4} x\\left(144\\theta^4-192\\theta^3-172\\theta^2-76\\theta-11\\right)+2^{14} x^{2}\\left(100\\theta^4-320\\theta^3-25\\theta^2+155\\theta+36\\right)-2^{21} x^{3}\\left(72\\theta^4-1248\\theta^3+628\\theta^2-180\\theta-97\\right)-2^{30} x^{4}\\left(212\\theta^4+256\\theta^3-14\\theta^2+86\\theta+15\\right)+2^{36} 3 x^{5}\\left(240\\theta^4-320\\theta^3-332\\theta^2-380\\theta-119\\right)+2^{46} 3^{2} x^{6}\\left(12\\theta^4+64\\theta^3+99\\theta^2+67\\theta+17\\right)-2^{56} 3^{3} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "352 26115552", "discriminant": "7 1 -2304 1638400 -150994944 -227633266688 49478023249920 7599824371187712 -1945555039024054272", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "df2c3b4e6a3366531b24bb05809eb1a4", "dim_h": null, "inst": " 352 60664 26115552 16623590600 13165993300256 11986704764296088 12020218264693813856 12940227600404919292744 14708343012850857454009600 17451325510266418328472861992", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(256z-1)^2(256z+1)^2(768z-1)^3", "discr_factors": "-1945555039024054272, (z-1/768)^3, (z-1/256)^2, (z+1/256)^2", "dm_basis": null, "q": "0 1 512 445280 480479232 578735581744 745583606296576 1005278122520203776 1400774260891946319872 2001101029745058591951512", "yuk": "1 352 485664 705120256 1063910284064 1645749162532352 2589128229793560576 4122934864789978152960 6625396531408382588168992 10722382056368275084678118656", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/768","im":"0","approx_re":"0.00130208333333","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[27*X^4, 108-432*X^4+468*X+756*X^2+576*X^3, -99264*X^2-11520*X^4-23472-78528*X-61440*X^3, 501760*X^2-132096-34816*X+606208*X^3+217088*X^4, 16637952+589824*X^4+44793856*X+39354368*X^2+12582912*X^3, -402391040*X^2-26214400*X^4-72351744-302776320*X-188743680*X^3, 1329594368*X^2+240123904+926941184*X+805306368*X^3+150994944*X^4, -268435456*(X+1)^4]", "text": "This is operator \"7.19\" from ...", "degz": 7, "h3": null, "sol": "1 -4 68 -496 9796 -84944 1732016 -16427072 337469764 -3388418704", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 27 108 468 756 576 -432 -23472 -78528 -99264 -61440 -11520 -132096 -34816 501760 606208 217088 16637952 44793856 39354368 12582912 589824 -72351744 -302776320 -402391040 -188743680 -26214400 240123904 926941184 1329594368 805306368 150994944 -268435456 -1073741824 -1610612736 -1073741824 -268435456", "new_number": "7.19", "id": 441, "operator_tex": "3^{3} \\theta^4-2^{2} 3^{2} x\\left(12\\theta^4-16\\theta^3-21\\theta^2-13\\theta-3\\right)-2^{4} 3 x^{2}\\left(240\\theta^4+1280\\theta^3+2068\\theta^2+1636\\theta+489\\right)+2^{10} x^{3}\\left(212\\theta^4+592\\theta^3+490\\theta^2-34\\theta-129\\right)+2^{13} x^{4}\\left(72\\theta^4+1536\\theta^3+4804\\theta^2+5468\\theta+2031\\right)-2^{18} x^{5}\\left(100\\theta^4+720\\theta^3+1535\\theta^2+1155\\theta+276\\right)+2^{20} x^{6}\\left(144\\theta^4+768\\theta^3+1268\\theta^2+884\\theta+229\\right)-2^{28} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "4/3 -124/81", "discriminant": "7 27 -432 -11520 217088 589824 -26214400 150994944 -268435456", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f7f0f5d883101c38ed22cb74c80c8f5c", "dim_h": null, "inst": " 4/3 -14/9 -124/81 -4498/243 37024/729 165074/243 80629772/19683 122791610/59049 -1576000/9 -7208283828944/4782969", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(16z-1)^2(16z+1)^2(16z-3)^3", "discr_factors": "-268435456, (z+1/16)^2, (z-3/16)^3, (z-1/16)^2", "dm_basis": null, "q": "0 1 4/3 -182/3 -24976/81 544783/243 96632/3 559420178/6561 -29268772288/19683 -18960126", "yuk": "1 4/3 -100/9 -40 -290572/243 4628972/729 146680 27656038040/19683 62798695324/59049 -127656040", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16","im":"0","approx_re":"0.1875","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -14*X*(46*X^3+52*X^2+33*X+7), -25088-106680*X-170532*X^2-115392*X^3-29328*X^4, -561568-1780464*X-1927728*X^2-716160*X^3-45760*X^4, -1561088-3332608*X-379392*X^2+3031040*X^3+1141760*X^4, 3112960+17940480*X+32292864*X^2+21626880*X^3+2850816*X^4, 3670016+11010048*X+4718592*X^2-12582912*X^3-11534336*X^4, -33554432*(X+1)^4]", "text": "This is operator \"7.1\" from ...", "degz": 7, "h3": "56", "sol": "1 0 32 288 7776 144000 3552800 82320000 2087125600 52959513600", "n_discr_factors": "4", "c3": "-64", "operator": "4 7 0 0 0 0 49 0 -98 -462 -728 -644 -25088 -106680 -170532 -115392 -29328 -561568 -1780464 -1927728 -716160 -45760 -1561088 -3332608 -379392 3031040 1141760 3112960 17940480 32292864 21626880 2850816 3670016 11010048 4718592 -12582912 -11534336 -33554432 -134217728 -201326592 -134217728 -33554432", "new_number": "7.1", "id": 442, "operator_tex": "7^{2} \\theta^4-2 7 x\\theta(46\\theta^3+52\\theta^2+33\\theta+7)-2^{2} x^{2}\\left(7332\\theta^4+28848\\theta^3+42633\\theta^2+26670\\theta+6272\\right)-2^{4} x^{3}\\left(2860\\theta^4+44760\\theta^3+120483\\theta^2+111279\\theta+35098\\right)+2^{9} x^{4}\\left(2230\\theta^4+5920\\theta^3-741\\theta^2-6509\\theta-3049\\right)+2^{14} x^{5}\\left(174\\theta^4+1320\\theta^3+1971\\theta^2+1095\\theta+190\\right)-2^{19} x^{6}\\left(22\\theta^4+24\\theta^3-9\\theta^2-21\\theta-7\\right)-2^{25} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "10/7 508/7", "discriminant": "7 49 -644 -29328 -45760 1141760 2850816 -11534336 -33554432", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "08ab3cb496250adfa30bc3e24ac63c4f", "dim_h": "16", "inst": " 10/7 100/7 508/7 808 59910/7 855864/7 12382494/7 200115472/7 3327848026/7 58373507100/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(32z-1)(32z-7)^2(4z+1)^3", "discr_factors": "-33554432, (z+1/4)^3, z-1/32, z+1/16, (z-7/32)^2", "dm_basis": null, "q": "0 1 -2 -71 -236 -580 -16018 -462550 -8253320 -151220156", "yuk": "1 10/7 810/7 13726/7 362794/7 7488760/7 184881150/7 4247195452/7 102459484458/7 2426001224680/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/32","im":"0","approx_re":"0.21875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 48+304*X+816*X^2+1024*X^3+352*X^4, 40960+213504*X+483840*X^2+319488*X^3-89088*X^4, 15908864+62472192*X+83902464*X^2-49152000*X^3-36536320*X^4, 1259339776+3589799936*X+1763180544*X^2-17469276160*X^3+1499463680*X^4, 96502546432+185220464640*X+10871635968*X^2+64424509440*X^3+984084381696*X^4, 481036337152*(X+1)*(46*X^3+86*X^2+67*X+20), -1724034232352768*(X+1)^4]", "text": "This is operator \"7.2\" from ...", "degz": 7, "h3": null, "sol": "1 -48 5072 -733440 124117776 -22993813248 4514074006784 -922557199896576 194202215551290640 -41817326010225224448", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 1 48 304 816 1024 352 40960 213504 483840 319488 -89088 15908864 62472192 83902464 -49152000 -36536320 1259339776 3589799936 1763180544 -17469276160 1499463680 96502546432 185220464640 10871635968 64424509440 984084381696 9620726743040 41850161332224 73598559584256 63496796504064 22127671508992 -1724034232352768 -6896136929411072 -10344205394116608 -6896136929411072 -1724034232352768", "new_number": "7.2", "id": 445, "operator_tex": "\\theta^4+2^{4} x\\left(22\\theta^4+64\\theta^3+51\\theta^2+19\\theta+3\\right)-2^{9} x^{2}\\left(174\\theta^4-624\\theta^3-945\\theta^2-417\\theta-80\\right)-2^{14} x^{3}\\left(2230\\theta^4+3000\\theta^3-5121\\theta^2-3813\\theta-971\\right)+2^{19} x^{4}\\left(2860\\theta^4-33320\\theta^3+3363\\theta^2+6847\\theta+2402\\right)+2^{27} x^{5}\\left(7332\\theta^4+480\\theta^3+81\\theta^2+1380\\theta+719\\right)+2^{36} 7 x^{6}(\\theta+1)(46\\theta^3+86\\theta^2+67\\theta+20)-2^{45} 7^{2} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "-80 -249872", "discriminant": "7 1 352 -89088 -36536320 1499463680 984084381696 22127671508992 -1724034232352768", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "341389ebf4ab0242c5b70d9a8fd7a1d9", "dim_h": null, "inst": " -80 -4202 -249872 -22251117 -2195810928 -242075456098 -28398707449808 -3506021022953923 -449382234721506176 -59370368013868946798", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(64z+1)(32z-1)(224z-1)^2(256z+1)^3", "discr_factors": "-1724034232352768, (z-1/224)^2, (z+1/256)^3, z+1/64, z-1/32", "dm_basis": null, "q": "0 1 112 10624 1182720 141298608 18027074048 2404776557568 332011071045632 47052345138815128", "yuk": "1 -80 -33696 -6746624 -1424105184 -274476366080 -52288305297408 -9740756655284224 -1795082765176513760 -327599649111984748928", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/224","im":"0","approx_re":"0.00446428571429","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3344*X^4+16832*X^3+23536*X^2+13408*X+2928, 34560*X^4-207360*X^3-634752*X^2-480384*X-127872, -2092032*X^4-4184064*X^3+5068800*X^2+7160832*X+2405376, 9953280*X^4+99532800*X^3+56070144*X^2-8294400*X-11612160, 277364736*X^4-286654464*X^3-571981824*X^2-286654464*X-35831808, -95551488*(3*X^2+3*X+1)*(10*X^2+10*X+3), 6879707136*(X+1)^4]", "text": "Hadamard product $c \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single \nMUM-point defined over $\\Q(\\sqrt{?})$.", "degz": 8, "h3": "48", "sol": "1 12 300 10416 431964 20026512 1002175824 52995470400 2920544068572 166150997604048", "n_discr_factors": "5", "c3": "28", "operator": "4 8 0 0 0 0 1 -12 -76 -196 -240 -120 2928 13408 23536 16832 3344 -127872 -480384 -634752 -207360 34560 2405376 7160832 5068800 -4184064 -2092032 -11612160 -8294400 56070144 99532800 9953280 -35831808 -286654464 -571981824 -286654464 277364736 -286654464 -1815478272 -4682022912 -5733089280 -2866544640 6879707136 27518828544 41278242816 27518828544 6879707136", "new_number": "8.10", "id": 453, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{4} x^{2}\\left(209\\theta^4+1052\\theta^3+1471\\theta^2+838\\theta+183\\right)+2^{7} 3^{2} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-2^{10} 3^{2} x^{4}\\left(227\\theta^4+454\\theta^3-550\\theta^2-777\\theta-261\\right)+2^{12} 3^{4} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+2^{14} 3^{4} x^{6}\\left(209\\theta^4-216\\theta^3-431\\theta^2-216\\theta-27\\right)-2^{17} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{20} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 1828/3", "discriminant": "8 1 -120 3344 34560 -2092032 9953280 277364736 -2866544640 6879707136", "aesz": "123", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f0d76ab2b6b8808f4faa4ab8ecadff2c", "dim_h": "14", "inst": " 12 -47/2 1828/3 -10813/4 127948 -1853581/6 39969036 280168449/4 50657172196/3 256398596897/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2", "discr_factors": "6879707136, z-1/8, z-1/36, (-1/288+z^2)^2, z-1/4, z-1/72", "dm_basis": null, "q": "0 1 -28 572 -11744 233550 -4947920 102001240 -2228888832 46514995429", "yuk": "1 12 -176 16464 -173184 15993512 -66712640 13709379360 35861388288 12309692860092", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*2^(1/2)","im":"0","approx_re":"-0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*2^(1/2)","im":"0","approx_re":"0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(10*X^2+10*X+3), 2457*X^4+12744*X^3+17793*X^2+10098*X+2187, 21870*X^4-131220*X^3-401679*X^2-303993*X-80919, -1312200*X^4-2624400*X^3+3372354*X^2+4684554*X+1554957, 5314410*X^4+53144100*X^3+29937843*X^2-4428675*X-6200145, 145083393*X^4-172186884*X^3-336402153*X^2-172186884*X-23914845, -43046721*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3486784401*(X+1)^4]", "text": "Hadamard product $c \\ast f$. This operator has a second MUM point at infinity with the same instanton numbers. It can be\nreduced to an operator of degree 4 with a single MUM-point over\n$Q(\\sqrt{?})$", "degz": 8, "h3": null, "sol": "1 9 135 1953 5751 -1381941 -85144149 -3528575055 -113081675913 -2516451077241", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -57 -147 -180 -90 2187 10098 17793 12744 2457 -80919 -303993 -401679 -131220 21870 1554957 4684554 3372354 -2624400 -1312200 -6200145 -4428675 29937843 53144100 5314410 -23914845 -172186884 -336402153 -172186884 145083393 -129140163 -817887699 -2109289329 -2582803260 -1291401630 3486784401 13947137604 20920706406 13947137604 3486784401", "new_number": "8.11", "id": 454, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+3^{3} x^{2}\\left(91\\theta^4+472\\theta^3+659\\theta^2+374\\theta+81\\right)+3^{6} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-3^{8} x^{4}\\left(200\\theta^4+400\\theta^3-514\\theta^2-714\\theta-237\\right)+3^{11} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+3^{13} x^{6}\\left(91\\theta^4-108\\theta^3-211\\theta^2-108\\theta-15\\right)-3^{16} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+3^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "9 242/3", "discriminant": "8 1 -90 2457 21870 -1312200 5314410 145083393 -1291401630 3486784401", "aesz": "162", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "542708b59b898c35f43e00120897ff8d", "dim_h": null, "inst": " 9 -153/4 242/3 -4923 34245 -1607315/6 14322780 -52271253 1396850748 -270428230305/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2", "discr_factors": "3486784401, z^2-1/3*z+1/27, z^2-1/27*z+1/2187, (-1/243+z^2)^2", "dm_basis": null, "q": "0 1 -21 414 -6664 121290 -2200473 39153920 -756944925 14059133226", "yuk": "1 9 -297 2187 -315369 4280634 -57861459 4912713549 -26763196905 1018304197479", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27*3^(1/2)","im":"0","approx_re":"-0.06415","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"-1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"-0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*3^(1/2)","im":"0","approx_re":"0.06415","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"-1/18*3^(1/2)","approx_re":"0.166666666667","approx_im":"-0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"1/18*3^(1/2)","approx_re":"0.166666666667","approx_im":"0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(17*X^2+17*X+6), 7209*X^4+36612*X^3+51273*X^2+29322*X+6480, 110160*X^4-660960*X^3-2021112*X^2-1537704*X-419904, -10182672*X^4-20365344*X^3+24984288*X^2+35166960*X+11967264, 71383680*X^4+713836800*X^3+403527744*X^2-52488000*X-85660416, 3027087936*X^4-3265173504*X^3-6428310336*X^2-3265173504*X-408146688, -272097792*(10*X^2+10*X+3)*(17*X^2+17*X+6), 176319369216*(X+1)^4]", "text": "Hadamard product $c \\ast g$. This operator has a second MUM-point\nat infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 18 630 29016 1529766 87271668 5244963984 327192462720 20994740454438 1377396131965308", "n_discr_factors": "5", "c3": "216", "operator": "4 8 0 0 0 0 1 -18 -111 -281 -340 -170 6480 29322 51273 36612 7209 -419904 -1537704 -2021112 -660960 110160 11967264 35166960 24984288 -20365344 -10182672 -85660416 -52488000 403527744 713836800 71383680 -408146688 -3265173504 -6428310336 -3265173504 3027087936 -4897760256 -30202854912 -76459479552 -92513249280 -46256624640 176319369216 705277476864 1057916215296 705277476864 176319369216", "new_number": "8.12", "id": 455, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+3^{4} x^{2}\\left(89\\theta^4+452\\theta^3+633\\theta^2+362\\theta+80\\right)+2^{3} 3^{4} x^{3}\\left(170\\theta^4-1020\\theta^3-3119\\theta^2-2373\\theta-648\\right)-2^{4} 3^{8} x^{4}\\left(97\\theta^4+194\\theta^3-238\\theta^2-335\\theta-114\\right)+2^{6} 3^{8} x^{5}\\left(170\\theta^4+1700\\theta^3+961\\theta^2-125\\theta-204\\right)+2^{6} 3^{12} x^{6}\\left(89\\theta^4-96\\theta^3-189\\theta^2-96\\theta-12\\right)-2^{9} 3^{12} x^{7}(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+2^{12} 3^{16} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "17 1387", "discriminant": "8 1 -170 7209 110160 -10182672 71383680 3027087936 -46256624640 176319369216", "aesz": "175", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f6db11b5e593983f455489d5bb1003c5", "dim_h": "18", "inst": " 17 -299/4 1387 -47623/2 500282 -42126461/4 254375312 -12313756771/2 160380505659 -8361141516655/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2", "discr_factors": "176319369216, z-1/9, z-1/8, z-1/72, z-1/81, (-1/648+z^2)^2", "dm_basis": null, "q": "0 1 -39 1164 -32809 938661 -27510480 817408641 -24553710831 744082098363", "yuk": "1 17 -581 37466 -1524517 62535267 -2274792026 87250732033 -3152323257893 116917388662877", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/2)","im":"0","approx_re":"-0.039284","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/2)","im":"0","approx_re":"0.039284","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(3*X^2+3*X+1)^2, 3024*X^4+22464*X^3+31536*X^2+18144*X+4176, 10368*(3*X^2+3*X+1)*(3*X^2-21*X-35), -6718464*X^4-13436928*X^3+28366848*X^2+35085312*X+12192768, 8957952*(3*X^2+3*X+1)*(3*X^2+27*X-11), 2257403904*X^4-7739670528*X^3-13221937152*X^2-7739670528*X-1397440512, -7739670528*(3*X^2+3*X+1)^2, 557256278016*(X+1)^4]", "text": "Hadamard product $d \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 12 180 2352 6084 -1278288 -68988816 -2512105920 -70933293756 -1393810859472", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -72 -180 -216 -108 4176 18144 31536 22464 3024 -362880 -1306368 -1710720 -559872 93312 12192768 35085312 28366848 -13436928 -6718464 -98537472 -53747712 456855552 806215680 80621568 -1397440512 -7739670528 -13221937152 -7739670528 2257403904 -7739670528 -46438023168 -116095057920 -139314069504 -69657034752 557256278016 2229025112064 3343537668096 2229025112064 557256278016", "new_number": "8.13", "id": 456, "operator_tex": "\\theta^4-2^{2} 3 x\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{4} 3^{2} x^{2}\\left(21\\theta^4+156\\theta^3+219\\theta^2+126\\theta+29\\right)+2^{7} 3^{4} x^{3}(3\\theta^2+3\\theta+1)(3\\theta^2-21\\theta-35)-2^{10} 3^{5} x^{4}\\left(27\\theta^4+54\\theta^3-114\\theta^2-141\\theta-49\\right)+2^{12} 3^{7} x^{5}(3\\theta^2+3\\theta+1)(3\\theta^2+27\\theta-11)+2^{14} 3^{8} x^{6}\\left(21\\theta^4-72\\theta^3-123\\theta^2-72\\theta-13\\right)-2^{17} 3^{10} x^{7}\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{20} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 3020/3", "discriminant": "8 1 -108 3024 93312 -6718464 80621568 2257403904 -69657034752 557256278016", "aesz": "163", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "e21fd830a9dca03305deb8363a26fcf2", "dim_h": null, "inst": " 12 -96 3020/3 -71493/4 319584 -19126516/3 139598148 -12567360273/4 221121122720/3 -1788903000504", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2", "discr_factors": "557256278016, (-1/864+z^2)^2, z^2-1/12*z+1/432, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -24 630 -16064 426309 -11440656 310799594 -8551209216 237533688594", "yuk": "1 12 -756 27192 -1144644 39948012 -1377082728 47882164776 -1608623259588 53732432848152", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/72*6^(1/2)","im":"0","approx_re":"-0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*6^(1/2)","im":"0","approx_re":"0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(17*X^2+17*X+6), 10400*X^4+69248*X^3+97696*X^2+56896*X+13440, 470016*X^4-2820096*X^3-8607744*X^2-6607872*X-1880064, -58540032*X^4-117080064*X^3+214401024*X^2+272941056*X+98205696, 1082916864*X^4+10829168640*X^3+6157762560*X^2-615776256*X-1358954496, 55207526400*X^4-146767085568*X^3-252935405568*X^2-146767085568*X-24461180928, -48922361856*(3*X^2+3*X+1)*(17*X^2+17*X+6), 28179280429056*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "96", "sol": "1 24 840 34944 1618344 80725824 4249779456 232938823680 13169473126056 762911587628736", "n_discr_factors": "6", "c3": "472", "operator": "4 8 0 0 0 0 1 -24 -140 -344 -408 -204 13440 56896 97696 69248 10400 -1880064 -6607872 -8607744 -2820096 470016 98205696 272941056 214401024 -117080064 -58540032 -1358954496 -615776256 6157762560 10829168640 1082916864 -24461180928 -146767085568 -252935405568 -146767085568 55207526400 -293534171136 -1712282664960 -4207323119616 -4990080909312 -2495040454656 28179280429056 112717121716224 169075682574336 112717121716224 28179280429056", "new_number": "8.14", "id": 457, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{5} x^{2}\\left(325\\theta^4+2164\\theta^3+3053\\theta^2+1778\\theta+420\\right)+2^{10} 3^{2} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{14} 3^{2} x^{4}\\left(397\\theta^4+794\\theta^3-1454\\theta^2-1851\\theta-666\\right)+2^{18} 3^{4} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{21} 3^{4} x^{6}\\left(325\\theta^4-864\\theta^3-1489\\theta^2-864\\theta-144\\right)-2^{26} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{32} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "24 15448/3", "discriminant": "8 1 -204 10400 470016 -58540032 1082916864 55207526400 -2495040454656 28179280429056", "aesz": "176", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "e2a40a57f7e88dba6655d936b4abe327", "dim_h": "20", "inst": " 24 -509/2 15448/3 -128530 3746624 -718242157/6 4087498824 -292948763739/2 16349300937760/3 -208868645210788", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2", "discr_factors": "28179280429056, (z+1/48)^2, z-1/32, (z-1/48)^2, z-1/64, z-1/36, z-1/72", "dm_basis": null, "q": "0 1 -44 1814 -75664 3198717 -136975528 5934383866 -259779116352 11475414116374", "yuk": "1 24 -2012 139056 -8227932 468328024 -25856580632 1402012096656 -74994891745116 3972880128014736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(17*X^2+17*X+6), 5859*X^4+46764*X^3+65907*X^2+38286*X+9072, 297432*X^4-1784592*X^3-5447088*X^2-4181544*X-1189728, -30338064*X^4-60676128*X^3+137518560*X^2+167856624*X+59836320, 578207808*X^4+5782078080*X^3+3287848320*X^2-328784832*X-725594112, 22141957824*X^4-88159684608*X^3-148259284416*X^2-88159684608*X-15917720832, -22039921152*(3*X^2+3*X+1)*(17*X^2+17*X+6), 14281868906496*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "162", "sol": "1 18 378 6552 21546 -5570532 -361058256 -15509667456 -509913925974 -11554728615612", "n_discr_factors": "3", "c3": "702", "operator": "4 8 0 0 0 0 1 -18 -105 -258 -306 -153 9072 38286 65907 46764 5859 -1189728 -4181544 -5447088 -1784592 297432 59836320 167856624 137518560 -60676128 -30338064 -725594112 -328784832 3287848320 5782078080 578207808 -15917720832 -88159684608 -148259284416 -88159684608 22141957824 -132239526912 -771397240320 -1895433219072 -2248071957504 -1124035978752 14281868906496 57127475625984 85691213438976 57127475625984 14281868906496", "new_number": "8.15", "id": 458, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+3^{3} x^{2}\\left(217\\theta^4+1732\\theta^3+2441\\theta^2+1418\\theta+336\\right)+2^{3} 3^{6} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{4} 3^{8} x^{4}\\left(289\\theta^4+578\\theta^3-1310\\theta^2-1599\\theta-570\\right)+2^{6} 3^{11} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{6} 3^{13} x^{6}\\left(217\\theta^4-864\\theta^3-1453\\theta^2-864\\theta-156\\right)-2^{9} 3^{16} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{12} 3^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "18 9799/3", "discriminant": "8 1 -153 5859 297432 -30338064 578207808 22141957824 -1124035978752 14281868906496", "aesz": "178", "n_sing_complex": "4", "inst_int": "", "c2h": "0", "hash": "e748913f322a008ae5c350f96f1cd860", "dim_h": "27", "inst": " 18 -423/2 9799/3 -150003/2 1914237 -324455821/6 1628820972 -103046534199/2 1691501544869 -57212542607211", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2", "discr_factors": "14281868906496, z^2-1/27*z+1/2187, (-1/1944+z^2)^2, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -33 1224 -44609 1661721 -62614674 2389779914 -92178406965 3589034423679", "yuk": "1 18 -1674 88209 -4801770 239279643 -11680323039 558685593414 -26379917556714 1233104626297710", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*6^(1/2)","im":"0","approx_re":"-0.02268","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"-1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"-0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108*6^(1/2)","im":"0","approx_re":"0.02268","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[2209*X^4, -11045-72897*X-190021*X^2-234248*X^3-116983*X^4, -161022-701851*X-1135848*X^2-790072*X^3-208867*X^4, 38352+149319*X+383912*X^2+637644*X^3+370857*X^4, -1770676-5161283*X-4424049*X^2-511820*X^3+291161*X^4, 2151-260936*X-750755*X^2-749482*X^3-406192*X^4, 483678+2462238*X+4118877*X^2+2450250*X^3+143235*X^4, 21870+119556*X+287226*X^2+335340*X^3+154548*X^4, -236196*(X+1)^4]", "text": "The operator has a second MUM-point at infinity, corresponding to operator 8.17 .", "degz": 8, "h3": "47", "sol": "1 5 93 2507 81229 2932005 113625975 4630472565 195899905485 8531436911945", "n_discr_factors": "2", "c3": "-90", "operator": "4 8 0 0 0 0 2209 -11045 -72897 -190021 -234248 -116983 -161022 -701851 -1135848 -790072 -208867 38352 149319 383912 637644 370857 -1770676 -5161283 -4424049 -511820 291161 2151 -260936 -750755 -749482 -406192 483678 2462238 4118877 2450250 143235 21870 119556 287226 335340 154548 -236196 -944784 -1417176 -944784 -236196", "new_number": "8.16", "id": 459, "operator_tex": "47^{2} \\theta^4-47 x\\left(2489\\theta^4+4984\\theta^3+4043\\theta^2+1551\\theta+235\\right)-x^{2}\\left(161022+701851\\theta+1135848\\theta^2+790072\\theta^3+208867\\theta^4\\right)+x^{3}\\left(38352+149319\\theta+383912\\theta^2+637644\\theta^3+370857\\theta^4\\right)-x^{4}\\left(1770676+5161283\\theta+4424049\\theta^2+511820\\theta^3-291161\\theta^4\\right)+x^{5}\\left(2151-260936\\theta-750755\\theta^2-749482\\theta^3-406192\\theta^4\\right)+3^{3} x^{6}\\left(5305\\theta^4+90750\\theta^3+152551\\theta^2+91194\\theta+17914\\right)+2 3^{6} x^{7}\\left(106\\theta^4+230\\theta^3+197\\theta^2+82\\theta+15\\right)-2^{2} 3^{10} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "189/47 9277/47", "discriminant": "8 2209 -116983 -208867 370857 291161 -406192 143235 154548 -236196", "aesz": "196", "n_sing_complex": "2", "inst_int": "", "c2h": "86", "hash": "fdeee36c14d9c003b59c1738c024d479", "dim_h": "15", "inst": " 189/47 979/47 9277/47 124795/47 2049020/47 38377054/47 787759316/47 17303101967/47 400293853797/47 9648375461263/47", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+53z+90z^2-50z^3+81z^4)(-47-z+54z^2)^2", "discr_factors": "-236196, (-47/54-1/54*z+z^2)^2, -1/81+53/81*z+10/9*z^2-50/81*z^3+z^4", "dm_basis": null, "q": "0 1 -13 25 -160 -4327 -81024 -1923068 -47020667 -1201504338", "yuk": "1 189/47 8021/47 250668/47 7994901/47 256127689/47 8289702164/47 270201445577/47 8859196202005/47 291814219668681/47", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/108-1/108*10153^(1/2)","im":"0","approx_re":"-0.923723","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108+1/108*10153^(1/2)","im":"0","approx_re":"0.942242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[4*X^4, -12-92*X-286*X^2-388*X^3-212*X^4, 18522+111366*X+263607*X^2+208590*X^3-15915*X^4, 1299402+5552064*X+8455149*X^2+7877574*X^3+3655728*X^4, 168006069+719312319*X+832243167*X^2-1222142256*X^3-212256369*X^4, -363623742-11160320049*X-41105307978*X^2-49942699416*X^3-21898734993*X^4, 66071933766+167867862993*X+90082438146*X^2+217127660724*X^3+999004386123*X^4, 4224433012056+28023286230837*X+73290271006575*X^2+90533969551476*X^3+45321611064687*X^4, -69320760676281*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.16", "degz": 8, "h3": null, "sol": "1 3 -243 -15315 -55971 57523203 3697866999 -76965580269 -26677861488675 -1301369936124273", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 4 -12 -92 -286 -388 -212 18522 111366 263607 208590 -15915 1299402 5552064 8455149 7877574 3655728 168006069 719312319 832243167 -1222142256 -212256369 -363623742 -11160320049 -41105307978 -49942699416 -21898734993 66071933766 167867862993 90082438146 217127660724 999004386123 4224433012056 28023286230837 73290271006575 90533969551476 45321611064687 -69320760676281 -277283042705124 -415924564057686 -277283042705124 -69320760676281", "new_number": "8.17", "id": 460, "operator_tex": "2^{2} \\theta^4-2 x\\left(106\\theta^4+194\\theta^3+143\\theta^2+46\\theta+6\\right)-3 x^{2}\\left(5305\\theta^4-69530\\theta^3-87869\\theta^2-37122\\theta-6174\\right)+3^{2} x^{3}\\left(406192\\theta^4+875286\\theta^3+939461\\theta^2+616896\\theta+144378\\right)-3^{6} x^{4}\\left(291161\\theta^4+1676464\\theta^3-1141623\\theta^2-986711\\theta-230461\\right)-3^{10} x^{5}\\left(370857\\theta^4+845784\\theta^3+696122\\theta^2+189001\\theta+6158\\right)+3^{14} x^{6}\\left(208867\\theta^4+45396\\theta^3+18834\\theta^2+35097\\theta+13814\\right)+3^{18} 47 x^{7}\\left(2489\\theta^4+4972\\theta^3+4025\\theta^2+1539\\theta+232\\right)-3^{22} 47^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "19/2 -99607/18", "discriminant": "8 4 -212 -15915 3655728 -212256369 -21898734993 999004386123 45321611064687 -69320760676281", "aesz": "200", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e970fa76e74543660fe271b31c8ad485", "dim_h": null, "inst": " 19/2 -5195/8 -99607/18 -217650 23603349/2 4141965211/72 293319801/2 -1354423071148 -74334425422670/9 9657787488408155/8", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(531441z^4-347733z^3-7290z^2+50z-1)(-2+3z+11421z^2)^2", "discr_factors": "-69320760676281, z^4-53/81*z^3-10/729*z^2+50/531441*z-1/531441, (-2/11421+1/3807*z+z^2)^2", "dm_basis": null, "q": "0 1 -11 1173 7600 1081995 -21857016 770715954 -7525331409 6254857107369", "yuk": "1 19/2 -10371/2 -149401 -27869571/2 1475209322 12425741037 50304345881 -1386929252725123/2 -6021088459385671", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/7614-1/7614*10153^(1/2)","im":"0","approx_re":"-0.013365","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7614+1/7614*10153^(1/2)","im":"0","approx_re":"0.013102","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -676-4394*X-11323*X^2-13858*X^3-6929*X^4, -35152-159536*X-265720*X^2-185952*X^3-48984*X^4, 336960+1175616*X+1495936*X^2+843648*X^3+208832*X^4, -1098240-3208192*X-2512896*X^2+223232*X^3+383488*X^4, 729088+172032*X-3960832*X^2-5201920*X^3-1552384*X^4, 917504+5111808*X+8945664*X^2+5111808*X^3-294912*X^4, 262144+1835008*X+5242880*X^2+6815744*X^3+3407872*X^4, -2097152*(X+1)^4]", "text": "The operator has a second MUM-point at infinity, corresponding to operator 8.19.", "degz": 8, "h3": "52", "sol": "1 4 68 1552 43156 1331504 44101616 1535335232 55477774228 2063217683344", "n_discr_factors": "4", "c3": "-88", "operator": "4 8 0 0 0 0 169 -676 -4394 -11323 -13858 -6929 -35152 -159536 -265720 -185952 -48984 336960 1175616 1495936 843648 208832 -1098240 -3208192 -2512896 223232 383488 729088 172032 -3960832 -5201920 -1552384 917504 5111808 8945664 5111808 -294912 262144 1835008 5242880 6815744 3407872 -2097152 -8388608 -12582912 -8388608 -2097152", "new_number": "8.18", "id": 461, "operator_tex": "13^{2} \\theta^4-13^{2} x\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{3} 13 x^{2}\\left(471\\theta^4+1788\\theta^3+2555\\theta^2+1534\\theta+338\\right)+2^{6} 13 x^{3}\\left(251\\theta^4+1014\\theta^3+1798\\theta^2+1413\\theta+405\\right)+2^{9} x^{4}\\left(749\\theta^4+436\\theta^3-4908\\theta^2-6266\\theta-2145\\right)-2^{12} x^{5}\\left(379\\theta^4+1270\\theta^3+967\\theta^2-42\\theta-178\\right)-2^{15} x^{6}\\left(9\\theta^4-156\\theta^3-273\\theta^2-156\\theta-28\\right)+2^{18} x^{7}\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)-2^{21} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "3 1621/13", "discriminant": "8 169 -6929 -48984 208832 383488 -1552384 -294912 3407872 -2097152", "aesz": "197", "n_sing_complex": "0", "inst_int": "", "c2h": "-8", "hash": "4cc8bdba73e5fa6cb4089fa5296429de", "dim_h": "8", "inst": " 3 226/13 1621/13 20666/13 289056/13 4823420/13 86575842/13 1674803122/13 34027261716/13 721083596092/13", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2", "discr_factors": "-2097152, z-1, (-13/64+z^2)^2, z^2-3/4*z+1/64, z+1/8", "dm_basis": null, "q": "0 1 -10 -13 136 -3931 -40798 -970035 -20224224 -458183025", "yuk": "1 3 1847/13 43806/13 1324471/13 36132039/13 1041904334/13 29695513845/13 857500522935/13 24805873834770/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8*13^(1/2)","im":"0","approx_re":"-0.450694","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8*13^(1/2)","im":"0","approx_re":"0.450694","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-112*X-320*X^2-416*X^3-208*X^4, 5120+29184*X+63744*X^2+49152*X^3+2304*X^4, -245760-1302528*X-2330624*X^2+1007616*X^3+1552384*X^4, 31064064+122028032*X+112852992*X^2-167772160*X^3-49086464*X^4, -368050176-1976565760*X-3571449856*X^2+136314880*X^3-3421503488*X^4, 9160359936+20937965568*X+3707764736*X^2+20937965568*X^3+102726893568*X^4, 181462368256+1179505393664*X+3039494668288*X^2+3719978549248*X^3+1859989274624*X^4, -5806795784192*(X+1)^4]", "text": "This operator has a second MUM-point, corresponding to operator 8.18", "degz": 8, "h3": "32", "sol": "1 16 752 49408 3805456 322370816 29129674496 2759377375232 271039591709968 27401384461854976", "n_discr_factors": "4", "c3": "80", "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -208 5120 29184 63744 49152 2304 -245760 -1302528 -2330624 1007616 1552384 31064064 122028032 112852992 -167772160 -49086464 -368050176 -1976565760 -3571449856 136314880 -3421503488 9160359936 20937965568 3707764736 20937965568 102726893568 181462368256 1179505393664 3039494668288 3719978549248 1859989274624 -5806795784192 -23227183136768 -34840774705152 -23227183136768 -5806795784192", "new_number": "8.19", "id": 462, "operator_tex": "\\theta^4-2^{4} x\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(9\\theta^4+192\\theta^3+249\\theta^2+114\\theta+20\\right)+2^{12} x^{3}\\left(379\\theta^4+246\\theta^3-569\\theta^2-318\\theta-60\\right)-2^{16} x^{4}\\left(749\\theta^4+2560\\theta^3-1722\\theta^2-1862\\theta-474\\right)-2^{20} 13 x^{5}\\left(251\\theta^4-10\\theta^3+262\\theta^2+145\\theta+27\\right)+2^{24} 13 x^{6}\\left(471\\theta^4+96\\theta^3+17\\theta^2+96\\theta+42\\right)+2^{28} 13^{2} x^{7}\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{35} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 7584", "discriminant": "8 1 -208 2304 1552384 -49086464 -3421503488 102726893568 1859989274624 -5806795784192", "aesz": "201", "n_sing_complex": "0", "inst_int": "", "c2h": "56", "hash": "d21570c07bca6887061716b2d727fa75", "dim_h": "10", "inst": " 32 -152 7584 -160593 7055200 -213557688 10843665184 -373079787214 20257075760896 -766662378340104", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2", "discr_factors": "-5806795784192, z-1/128, z^2-3/8*z+1/256, z+1/16, (-1/3328+z^2)^2", "dm_basis": null, "q": "0 1 -48 1504 -48128 1753392 -73966080 3182293504 -149641527296 7014952908440", "yuk": "1 32 -1184 204800 -10279136 881900032 -46128257024 3719377158144 -191016861332704 14767408229897984", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/208*13^(1/2)","im":"0","approx_re":"-0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/208*13^(1/2)","im":"0","approx_re":"0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(7*X^2+7*X+2)*(11*X^2+11*X+3), -1049*X^4-4100*X^3-5689*X^2-3178*X-640, 616*X^4-3696*X^3-11360*X^2-8424*X-2016, 16656*X^4+33312*X^3-22496*X^2-39152*X-11936, 4928*X^4+49280*X^3+27392*X^2-5952*X-5120, -67136*X^4-6144*X^3+20288*X^2-6144*X-6400, -512*(7*X^2+7*X+2)*(11*X^2+11*X+3), 4096*(X+1)^4]", "text": "Hadamard product $a \\ast b$. The operator has a second MUM-point at infinity with the same instanton numbers. In fact, there is a symmetry in the operator. It can be reduced to an operator with a single MUM point of degree 4, defined over $Q(\\sqrt{2})$.", "degz": 8, "h3": "240", "sol": "1 6 190 8232 432846 25341756 1593697456 105412062720 7239272059342 511821344117796", "n_discr_factors": "3", "c3": "-720", "operator": "4 8 0 0 0 0 1 -6 -43 -120 -154 -77 -640 -3178 -5689 -4100 -1049 -2016 -8424 -11360 -3696 616 -11936 -39152 -22496 33312 16656 -5120 -5952 27392 49280 4928 -6400 -6144 20288 -6144 -67136 -3072 -22016 -61440 -78848 -39424 4096 16384 24576 16384 4096", "new_number": "8.1", "id": 463, "operator_tex": "\\theta^4-x(7\\theta^2+7\\theta+2)(11\\theta^2+11\\theta+3)-x^{2}\\left(1049\\theta^4+4100\\theta^3+5689\\theta^2+3178\\theta+640\\right)+2^{3} x^{3}\\left(77\\theta^4-462\\theta^3-1420\\theta^2-1053\\theta-252\\right)+2^{4} x^{4}\\left(1041\\theta^4+2082\\theta^3-1406\\theta^2-2447\\theta-746\\right)+2^{6} x^{5}\\left(77\\theta^4+770\\theta^3+428\\theta^2-93\\theta-80\\right)-2^{6} x^{6}\\left(1049\\theta^4+96\\theta^3-317\\theta^2+96\\theta+100\\right)-2^{9} x^{7}(7\\theta^2+7\\theta+2)(11\\theta^2+11\\theta+3)+2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 1053", "discriminant": "8 1 -77 -1049 616 16656 4928 -67136 -39424 4096", "aesz": "102", "n_sing_complex": "0", "inst_int": "", "c2h": "-96", "hash": "e928905653beb9d844e6a942f50d94ac", "dim_h": "32", "inst": " 8 153/2 1053 49101/2 670214 21215430 732865525 54287309225/2 1058581265221 86051614150163/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(64z^2+88z-1)(z^2-11z-1)(-1+8z^2)^2", "discr_factors": "4096, z^2-11*z-1, (-1/8+z^2)^2, z^2+11/8*z-1/64", "dm_basis": null, "q": "0 1 -19 -33 415 -44038 -1204843 -47847225 -1972984423 -85146953458", "yuk": "1 8 620 28439 1571852 83776758 4582561931 251372875083 13897552733452 771705742374548", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4*2^(1/2)","im":"0","approx_re":"-0.353553","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2-5/2*5^(1/2)","im":"0","approx_re":"-0.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4*2^(1/2)","im":"0","approx_re":"0.353553","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2+5/2*5^(1/2)","im":"0","approx_re":"11.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1444*X^4, -10108-67868*X-179550*X^2-223364*X^3-114532*X^4, 402002+1810054*X+3057079*X^2+2305502*X^3+689717*X^4, -1576582-6295992*X-9142457*X^2-5812350*X^3-1438808*X^4, 663471+3375833*X+6297445*X^2+5075392*X^3+1395491*X^4, 52928-604005*X-2407768*X^2-2657224*X^3-834163*X^4, -4832+148359*X+572576*X^2+692484*X^3+277543*X^4, -1958-20295*X-70345*X^2-100100*X^3-50875*X^4, -121*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.23", "degz": 8, "h3": null, "sol": "1 7 163 5767 247651 11887657 613571239 33328809031 1880385860899 109242135415357", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 1444 -10108 -67868 -179550 -223364 -114532 402002 1810054 3057079 2305502 689717 -1576582 -6295992 -9142457 -5812350 -1438808 663471 3375833 6297445 5075392 1395491 52928 -604005 -2407768 -2657224 -834163 -4832 148359 572576 692484 277543 -1958 -20295 -70345 -100100 -50875 -121 -484 -726 -484 -121", "new_number": "8.22", "id": 466, "operator_tex": "2^{2} 19^{2} \\theta^4-2 19 x\\left(3014\\theta^4+5878\\theta^3+4725\\theta^2+1786\\theta+266\\right)+x^{2}\\left(402002+1810054\\theta+3057079\\theta^2+2305502\\theta^3+689717\\theta^4\\right)-x^{3}\\left(1576582+6295992\\theta+9142457\\theta^2+5812350\\theta^3+1438808\\theta^4\\right)+x^{4}\\left(663471+3375833\\theta+6297445\\theta^2+5075392\\theta^3+1395491\\theta^4\\right)+x^{5}\\left(52928-604005\\theta-2407768\\theta^2-2657224\\theta^3-834163\\theta^4\\right)-x^{6}\\left(4832-148359\\theta-572576\\theta^2-692484\\theta^3-277543\\theta^4\\right)-11 x^{7}\\left(4625\\theta^4+9100\\theta^3+6395\\theta^2+1845\\theta+178\\right)-11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "241/38 8729/19", "discriminant": "8 1444 -114532 689717 -1438808 1395491 -834163 277543 -50875 -121", "aesz": "284\n", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "dbe506beab1f66a0b331f15c91b7fcde", "dim_h": null, "inst": " 241/38 1353/38 8729/19 150334/19 6399445/38 155385713/38 2068271169/19 117844935221/38 3536280405741/38 55282926685155/19", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+78z-374z^2+425z^3+z^4)(38-25z+11z^2)^2", "discr_factors": "-121, -1+78*z-374*z^2+425*z^3+z^4, (38/11-25/11*z+z^2)^2", "dm_basis": null, "q": "0 1 -19 118 -1282 -4296 -318375 -8340681 -272803251 -9003454197", "yuk": "1 241/38 11065/38 471607/38 19253817/38 399965433/19 33563796439/38 1418834022175/38 60336626086969/38 1288974208128398/19", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"25/22","im":"-1/22*1047^(1/2)","approx_re":"1.13636363636","approx_im":"-1.47079","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"25/22","im":"1/22*1047^(1/2)","approx_re":"1.13636363636","approx_im":"1.47079","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 50875*X^4+103400*X^3+75295*X^2+23595*X+2783, -4444-29513*X-160382*X^2-417688*X^3-277543*X^4, 834163*X^4+679428*X^3-558926*X^2-423489*X-72226, 94818+425155*X+555785*X^2-506572*X^3-1395491*X^4, 1438808*X^4-57118*X^3+338255*X^2+307104*X+49505, -33242-146466*X-278875*X^2-453366*X^3-689717*X^4, 114532*X^4+234764*X^3+196650*X^2+79268*X+12958, -1444*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.22", "degz": 8, "h3": null, "sol": "1 -23 3043 -620663 154394851 -43048195673 12925906984999 -4088463189197879 1343985011396033059 -455117797433950010573", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 121 2783 23595 75295 103400 50875 -4444 -29513 -160382 -417688 -277543 -72226 -423489 -558926 679428 834163 94818 425155 555785 -506572 -1395491 49505 307104 338255 -57118 1438808 -33242 -146466 -278875 -453366 -689717 12958 79268 196650 234764 114532 -1444 -5776 -8664 -5776 -1444", "new_number": "8.23", "id": 467, "operator_tex": "11^{2} \\theta^4+11 x\\left(4625\\theta^4+9400\\theta^3+6845\\theta^2+2145\\theta+253\\right)-x^{2}\\left(4444+29513\\theta+160382\\theta^2+417688\\theta^3+277543\\theta^4\\right)+x^{3}\\left(834163\\theta^4+679428\\theta^3-558926\\theta^2-423489\\theta-72226\\right)+x^{4}\\left(94818+425155\\theta+555785\\theta^2-506572\\theta^3-1395491\\theta^4\\right)+x^{5}\\left(1438808\\theta^4-57118\\theta^3+338255\\theta^2+307104\\theta+49505\\right)-x^{6}\\left(33242+146466\\theta+278875\\theta^2+453366\\theta^3+689717\\theta^4\\right)+2 19 x^{7}\\left(3014\\theta^4+6178\\theta^3+5175\\theta^2+2086\\theta+341\\right)-2^{2} 19^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-795/11 -1594688/11", "discriminant": "8 121 50875 -277543 834163 -1395491 1438808 -689717 114532 -1444", "aesz": "285", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "009974f32940428eb2d2d31380b138a9", "dim_h": null, "inst": " -795/11 89027/44 -1594688/11 166273857/11 -21441641455/11 3163844145211/11 -512517010405881/11 88904496382284500/11 -16250306116171779111/11 12382042641907714876515/44", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1-425z+374z^2-78z^3+z^4)(11-25z+38z^2)^2", "discr_factors": "-1444, -1-425*z+374*z^2-78*z^3+z^4, (11/38-25/38*z+z^2)^2", "dm_basis": null, "q": "0 1 103 2564 168402 -14043843 2586260473 -472475102927 91615165106231 -18509145416390999", "yuk": "1 -795/11 177259/11 -43057371/11 10641704107/11 -2680205182670/11 683390292486259/11 -175793334569217978/11 45519102158371368107/11 -11846473158689270029290/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"25/76","im":"-1/76*1047^(1/2)","approx_re":"0.328947368421","approx_im":"-0.425755","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"25/76","im":"1/76*1047^(1/2)","approx_re":"0.328947368421","approx_im":"0.425755","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -1210-9075*X-26323*X^2-34496*X^3-16687*X^4, -24266-106953*X-202166*X^2-207620*X^3-90362*X^4, -53130-217437*X-415082*X^2-507996*X^3-245714*X^4, -15226-183269*X-564786*X^2-785972*X^3-407863*X^4, -25160-279826*X-728323*X^2-790148*X^3-434831*X^4, -61152-303576*X-586744*X^2-562248*X^3-290888*X^4, -39040-172960*X-310160*X^2-274400*X^3-104560*X^4, -12800*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.27.", "degz": 8, "h3": "22", "sol": "1 10 466 32392 2727826 256793260 25999151200 2770767256960 306741044897170 34970581120268260", "n_discr_factors": "3", "c3": "-84", "operator": "4 8 0 0 0 0 121 -1210 -9075 -26323 -34496 -16687 -24266 -106953 -202166 -207620 -90362 -53130 -217437 -415082 -507996 -245714 -15226 -183269 -564786 -785972 -407863 -25160 -279826 -728323 -790148 -434831 -61152 -303576 -586744 -562248 -290888 -39040 -172960 -310160 -274400 -104560 -12800 -51200 -76800 -51200 -12800", "new_number": "8.26", "id": 470, "operator_tex": "11^{2} \\theta^4-11 x\\left(1517\\theta^4+3136\\theta^3+2393\\theta^2+825\\theta+110\\right)-x^{2}\\left(24266+106953\\theta+202166\\theta^2+207620\\theta^3+90362\\theta^4\\right)-x^{3}\\left(53130+217437\\theta+415082\\theta^2+507996\\theta^3+245714\\theta^4\\right)-x^{4}\\left(15226+183269\\theta+564786\\theta^2+785972\\theta^3+407863\\theta^4\\right)-x^{5}\\left(25160+279826\\theta+728323\\theta^2+790148\\theta^3+434831\\theta^4\\right)-2^{3} x^{6}\\left(36361\\theta^4+70281\\theta^3+73343\\theta^2+37947\\theta+7644\\right)-2^{4} 5 x^{7}\\left(1307\\theta^4+3430\\theta^3+3877\\theta^2+2162\\theta+488\\right)-2^{9} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "193/11 48570/11", "discriminant": "8 121 -16687 -90362 -245714 -407863 -434831 -290888 -104560 -12800", "aesz": "301", "n_sing_complex": "2", "inst_int": "", "c2h": "64", "hash": "a91db18876a9dfbf42b88f8d64c55d85", "dim_h": "9", "inst": " 193/11 1973/11 48570/11 1689283/11 72444183/11 3550769296/11 190951621547/11 10993183799383/11 666771302469817/11 42142859324558057/11", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2", "discr_factors": "-12800, (z+1)^2, -1/32+143/32*z+z^2, (z^2+17/20*z+11/20)^2", "dm_basis": null, "q": "0 1 -35 279 -5371 -178284 -10060533 -618825298 -39747432347 -2664472529088", "yuk": "1 193/11 15977/11 1311583/11 108130089/11 9055523068/11 766967495303/11 65496406190814/11 5628510213414185/11 486076279501808176/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-143/64-19/64*57^(1/2)","im":"0","approx_re":"-4.475732","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"-1/40*591^(1/2)","approx_re":"-0.425","approx_im":"-0.607762","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"1/40*591^(1/2)","approx_re":"-0.425","approx_im":"0.607762","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-143/64+19/64*57^(1/2)","im":"0","approx_re":"0.006982","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -400-2650*X-7145*X^2-8990*X^3-6535*X^4, 145920+693440*X+1290656*X^2+1202608*X^3+581776*X^4, -7573760-34924800*X-61879360*X^2-60747264*X^3-27829184*X^4, 38162432+450230272*X+1339490304*X^2+1731543040*X^3+835303424*X^4, 754122752-4692049920*X-23945412608*X^2-31120424960*X^3-16103112704*X^4, 4657774592+75428265984*X+254757830656*X^2+322600697856*X^3+189502849024*X^4, -43553652736-458420649984*X-1540618190848*X^2-2164395081728*X^3-1119845613568*X^4, -259845521408*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.26", "degz": 8, "h3": "20", "sol": "1 16 664 41920 3350776 307182016 30655306816 3238525410304 356430066908920 40464009003164416", "n_discr_factors": "3", "c3": "12", "operator": "4 8 0 0 0 0 25 -400 -2650 -7145 -8990 -6535 145920 693440 1290656 1202608 581776 -7573760 -34924800 -61879360 -60747264 -27829184 38162432 450230272 1339490304 1731543040 835303424 754122752 -4692049920 -23945412608 -31120424960 -16103112704 4657774592 75428265984 254757830656 322600697856 189502849024 -43553652736 -458420649984 -1540618190848 -2164395081728 -1119845613568 -259845521408 -1039382085632 -1559073128448 -1039382085632 -259845521408", "new_number": "8.27", "id": 471, "operator_tex": "5^{2} \\theta^4-5 x\\left(1307\\theta^4+1798\\theta^3+1429\\theta^2+530\\theta+80\\right)+2^{4} x^{2}\\left(36361\\theta^4+75163\\theta^3+80666\\theta^2+43340\\theta+9120\\right)-2^{6} x^{3}\\left(434831\\theta^4+949176\\theta^3+966865\\theta^2+545700\\theta+118340\\right)+2^{11} x^{4}\\left(407863\\theta^4+845480\\theta^3+654048\\theta^2+219839\\theta+18634\\right)-2^{16} x^{5}\\left(245714\\theta^4+474860\\theta^3+365378\\theta^2+71595\\theta-11507\\right)+2^{21} x^{6}\\left(90362\\theta^4+153828\\theta^3+121478\\theta^2+35967\\theta+2221\\right)-2^{26} 11 x^{7}\\left(1517\\theta^4+2932\\theta^3+2087\\theta^2+621\\theta+59\\right)-2^{31} 11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "109/5 16777/5", "discriminant": "8 25 -6535 581776 -27829184 835303424 -16103112704 189502849024 -1119845613568 -259845521408", "aesz": "302", "n_sing_complex": "2", "inst_int": "", "c2h": "44", "hash": "e18ddbe4d66a3648b349130bcf119dc7", "dim_h": "7", "inst": " 109/5 867/4 16777/5 662976/5 26339071/5 4725689263/20 11911994862 3199079453966/5 180895125715734/5 42664671283257213/20", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+143z+32z^2)(32z-1)^2(2816z^2-136z+5)^2", "discr_factors": "-259845521408, (z-1/32)^2, -1/32+143/32*z+z^2, (z^2-17/352*z+5/2816)^2", "dm_basis": null, "q": "0 1 -42 877 -19824 95014 -6976610 -379741214 -20268310336 -1319988021517", "yuk": "1 109/5 8779/5 453088/5 42439243/5 3292383984/5 51037536392 20429071188439/5 327585744573967 131872546647223174/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-143/64-19/64*57^(1/2)","im":"0","approx_re":"-4.475732","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-143/64+19/64*57^(1/2)","im":"0","approx_re":"0.006982","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/704","im":"-1/704*591^(1/2)","approx_re":"0.0241477272727","approx_im":"-0.034532","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"17/704","im":"1/704*591^(1/2)","approx_re":"0.0241477272727","approx_im":"0.034532","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -1352-9802*X-27651*X^2-35698*X^3-19565*X^4, -37024-166296*X-222964*X^2-8344*X^3+91844*X^4, -1664+86112*X+516192*X^2+899136*X^3+240768*X^4, -530688-1974144*X-2242816*X^2-795392*X^3-926848*X^4, 265216+971776*X+999680*X^2-462336*X^3-1558272*X^4, 225280+1794048*X+4510720*X^2+4159488*X^3+566272*X^4, 606208+2621440*X+4505600*X^2+3768320*X^3+1343488*X^4, 262144*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.29", "degz": 8, "h3": "52", "sol": "1 8 292 15776 1030036 75099008 5885649904 485387853056 41575046526868 3666751505766368", "n_discr_factors": "3", "c3": "-172", "operator": "4 8 0 0 0 0 169 -1352 -9802 -27651 -35698 -19565 -37024 -166296 -222964 -8344 91844 -1664 86112 516192 899136 240768 -530688 -1974144 -2242816 -795392 -926848 265216 971776 999680 -462336 -1558272 225280 1794048 4510720 4159488 566272 606208 2621440 4505600 3768320 1343488 262144 1048576 1572864 1048576 262144", "new_number": "8.28", "id": 472, "operator_tex": "13^{2} \\theta^4-13 x\\left(1505\\theta^4+2746\\theta^3+2127\\theta^2+754\\theta+104\\right)+2^{2} x^{2}\\left(22961\\theta^4-2086\\theta^3-55741\\theta^2-41574\\theta-9256\\right)+2^{5} x^{3}\\left(7524\\theta^4+28098\\theta^3+16131\\theta^2+2691\\theta-52\\right)-2^{7} x^{4}\\left(7241\\theta^4+6214\\theta^3+17522\\theta^2+15423\\theta+4146\\right)-2^{8} x^{5}\\left(6087\\theta^4+1806\\theta^3-3905\\theta^2-3796\\theta-1036\\right)+2^{10} x^{6}\\left(553\\theta^4+4062\\theta^3+4405\\theta^2+1752\\theta+220\\right)+2^{14} x^{7}\\left(82\\theta^4+230\\theta^3+275\\theta^2+160\\theta+37\\right)+2^{18} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "151/13 26293/13", "discriminant": "8 169 -19565 91844 240768 -926848 -1558272 566272 1343488 262144", "aesz": "303", "n_sing_complex": "3", "inst_int": "", "c2h": "-8", "hash": "e081c85684dd16a72eeaf5a1b139b912", "dim_h": "8", "inst": " 151/13 1436/13 26293/13 719465/13 24184128/13 927933648/13 39063063298/13 1760373069905/13 83576612574164/13 4134781753475992/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2", "discr_factors": "262144, z-1, (-13/64+11/16*z+z^2)^2, z^3+19/4*z^2+27/16*z-1/64", "dm_basis": null, "q": "0 1 -26 99 -1528 -76235 -3056142 -146660787 -7386800928 -387344930961", "yuk": "1 151/13 11639/13 710062/13 46057399/13 3023016151/13 200434389518/13 13398630711365/13 901311057848759/13 60927350567275618/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12+1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-4.362346","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32-1/32*329^(1/2)","im":"0","approx_re":"-0.910574","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12-1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.396684","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(-4537+111*I*111^(1/2))^(1/3)+70/3/(-4537+111*I*111^(1/2))^(1/3)-19/12","im":"0","approx_re":"0.009029","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32+1/32*329^(1/2)","im":"0","approx_re":"0.223074","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 82*X^4+98*X^3+77*X^2+28*X+4, -636-2916*X-4463*X^2-1850*X^3+553*X^4, -24348*X^4-90168*X^3-108796*X^2-59664*X-12544, -232704-958176*X-1354432*X^2-728000*X^3-231712*X^4, 963072*X^4+255744*X^3-2946432*X^2-3152256*X-919808, 415744+7217664*X+22600448*X^2+24046080*X^3+5878016*X^4, -20034560*X^4-43583488*X^3-38857728*X^2-17065984*X-3141632, 2768896*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.28", "degz": 8, "h3": null, "sol": "1 -4 112 -3712 155536 -7165504 355277056 -18506272768 1000758296848 -55700350533184", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 4 28 77 98 82 -636 -2916 -4463 -1850 553 -12544 -59664 -108796 -90168 -24348 -232704 -958176 -1354432 -728000 -231712 -919808 -3152256 -2946432 255744 963072 415744 7217664 22600448 24046080 5878016 -3141632 -17065984 -38857728 -43583488 -20034560 2768896 11075584 16613376 11075584 2768896", "new_number": "8.29", "id": 473, "operator_tex": "\\theta^4+x\\left(82\\theta^4+98\\theta^3+77\\theta^2+28\\theta+4\\right)-x^{2}\\left(636+2916\\theta+4463\\theta^2+1850\\theta^3-553\\theta^4\\right)-2^{2} x^{3}\\left(6087\\theta^4+22542\\theta^3+27199\\theta^2+14916\\theta+3136\\right)-2^{5} x^{4}\\left(7241\\theta^4+22750\\theta^3+42326\\theta^2+29943\\theta+7272\\right)+2^{7} x^{5}\\left(7524\\theta^4+1998\\theta^3-23019\\theta^2-24627\\theta-7186\\right)+2^{8} x^{6}\\left(22961\\theta^4+93930\\theta^3+88283\\theta^2+28194\\theta+1624\\right)-2^{10} 13 x^{7}\\left(1505\\theta^4+3274\\theta^3+2919\\theta^2+1282\\theta+236\\right)+2^{14} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-5 -641", "discriminant": "8 1 82 553 -24348 -231712 963072 5878016 -20034560 2768896", "aesz": "304", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "cf055a245b1537ed4f2609fa56cf67aa", "dim_h": null, "inst": " -5 469/8 -641 50173/4 -276231 58913297/8 -211861501 26272904923/4 -213904895800 58141299762679/8", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(64z^3-432z^2-76z-1)(-1-11z+52z^2)^2", "discr_factors": "2768896, (-1/52-11/52*z+z^2)^2, z-1/16, z^3-27/4*z^2-19/16*z-1/64", "dm_basis": null, "q": "0 1 12 -112 -192 -20336 562432 -19211008 653916160 -23597083368", "yuk": "1 -5 464 -17312 803232 -34528880 1590642176 -72668494848 3362932633376 -155936669055512", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4+1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.157556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104-1/104*329^(1/2)","im":"0","approx_re":"-0.068638","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4-1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.014327","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104+1/104*329^(1/2)","im":"0","approx_re":"0.280177","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(22005+111*I*111^(1/2))^(1/3)+131/2/(22005+111*I*111^(1/2))^(1/3)+9/4","im":"0","approx_re":"6.921883","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(7*X^2+7*X+2), -71*X^4-1148*X^3-1591*X^2-886*X-192, -5040*X^4+30240*X^3+92808*X^2+69336*X+17280, -20592*X^4-41184*X^3+163872*X^2+184464*X+59616, 362880*X^4+3628800*X^3+2026944*X^2-388800*X-393984, -368064*X^4+4478976*X^3+7397568*X^2+4478976*X+933120, 373248*(10*X^2+10*X+3)*(7*X^2+7*X+2), 26873856*(X+1)^4]", "text": "Hadamard product $a \\ast c$. This operator has a second MUM-point at infinity with the same instanton point. \nIt is reducible to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{-2})$", "degz": 8, "h3": "36", "sol": "1 6 150 5208 221094 10478556 534006096 28636761600 1594933457958 91464881448084", "n_discr_factors": "5", "c3": "-60", "operator": "4 8 0 0 0 0 1 -6 -41 -111 -140 -70 -192 -886 -1591 -1148 -71 17280 69336 92808 30240 -5040 59616 184464 163872 -41184 -20592 -393984 -388800 2026944 3628800 362880 933120 4478976 7397568 4478976 -368064 2239488 15303168 41430528 52254720 26127360 26873856 107495424 161243136 107495424 26873856", "new_number": "8.2", "id": 474, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)-x^{2}\\left(71\\theta^4+1148\\theta^3+1591\\theta^2+886\\theta+192\\right)-2^{3} 3^{2} x^{3}\\left(70\\theta^4-420\\theta^3-1289\\theta^2-963\\theta-240\\right)-2^{4} 3^{2} x^{4}\\left(143\\theta^4+286\\theta^3-1138\\theta^2-1281\\theta-414\\right)+2^{6} 3^{4} x^{5}\\left(70\\theta^4+700\\theta^3+391\\theta^2-75\\theta-76\\right)-2^{6} 3^{4} x^{6}\\left(71\\theta^4-864\\theta^3-1427\\theta^2-864\\theta-180\\right)+2^{9} 3^{6} x^{7}(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "7 1271/3", "discriminant": "8 1 -70 -71 -5040 -20592 362880 -368064 26127360 26873856", "aesz": "104", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "d6bd0d1524954c8ce0a6421d295e9795", "dim_h": "12", "inst": " 7 93/2 1271/3 18507/2 190710 9428013/2 128027760 7423428159/2 339968018663/3 3607055297185", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2", "discr_factors": "26873856, z+1/9, z-1/8, z-1/72, z+1, (1/72+z^2)^2", "dm_basis": null, "q": "0 1 -17 28 337 -25739 -225296 -10088399 -338161817 -10983844277", "yuk": "1 7 379 11446 592603 23838757 1018237222 43913521687 1900398201307 82612228546555", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -375-3000*X-9200*X^2-12400*X^3-5975*X^4, -7350-32700*X-70230*X^2-96180*X^3-51810*X^4, -76050-375300*X-642195*X^2-330210*X^3-68355*X^4, -275670-1023300*X-1343601*X^2-448794*X^3+279666*X^4, -417555-1226340*X-549585*X^2+1428030*X^3+373410*X^4, -38880+422820*X+1565163*X^2+1465290*X^3-296217*X^4, 72900+151632*X-189540*X^2-682344*X^3-472392*X^4, -104976*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.32", "degz": 8, "h3": "90", "sol": "1 15 1179 140505 20362059 3303744165 576944468325 106100672742135 20274620622792075 3990488846246692485", "n_discr_factors": "3", "c3": "-456", "operator": "4 8 0 0 0 0 25 -375 -3000 -9200 -12400 -5975 -7350 -32700 -70230 -96180 -51810 -76050 -375300 -642195 -330210 -68355 -275670 -1023300 -1343601 -448794 279666 -417555 -1226340 -549585 1428030 373410 -38880 422820 1565163 1465290 -296217 72900 151632 -189540 -682344 -472392 -104976 -419904 -629856 -419904 -104976", "new_number": "8.31", "id": 476, "operator_tex": "5^{2} \\theta^4-5^{2} x\\left(239\\theta^4+496\\theta^3+368\\theta^2+120\\theta+15\\right)-2 3 5 x^{2}\\left(1727\\theta^4+3206\\theta^3+2341\\theta^2+1090\\theta+245\\right)-3^{2} 5 x^{3}\\left(1519\\theta^4+7338\\theta^3+14271\\theta^2+8340\\theta+1690\\right)+3^{3} x^{4}\\left(10358\\theta^4-16622\\theta^3-49763\\theta^2-37900\\theta-10210\\right)+3^{4} 5 x^{5}\\left(922\\theta^4+3526\\theta^3-1357\\theta^2-3028\\theta-1031\\right)-3^{5} x^{6}\\left(1219\\theta^4-6030\\theta^3-6441\\theta^2-1740\\theta+160\\right)-2^{2} 3^{6} x^{7}\\left(162\\theta^4+234\\theta^3+65\\theta^2-52\\theta-25\\right)-2^{4} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "38 26135", "discriminant": "8 25 -5975 -51810 -68355 279666 373410 -296217 -472392 -104976", "aesz": "315", "n_sing_complex": "3", "inst_int": "", "c2h": "-252", "hash": "44be55b95bb1c725c5aaa2c9a6635e89", "dim_h": "-6", "inst": " 38 3068/5 26135 7871998/5 117518569 10026476044 939050808787 470839561711662/5 149248204793942713/15 1095604619374814176", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(81z^3+351z^2+246z-1)(-5-15z+36z^2)^2", "discr_factors": "-104976, (-5/36-5/12*z+z^2)^2, z^3+13/3*z^2+82/27*z-1/81, z+1", "dm_basis": null, "q": "0 1 -60 840 -30692 -1600482 -165376764 -17536395468 -1965039173412 -229463945992809", "yuk": "1 38 24734/5 705683 503832606/5 14689821163 10828597680479/5 322094427413979 48213971220040710 36267313764931607674/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*(-4748+428*I*107^(1/2))^(1/3)-29/3/(-4748+428*I*107^(1/2))^(1/3)-13/9+1/6*I*3^(1/2)*(1/6*(-4748+428*I*107^(1/2))^(1/3)-58/(-4748+428*I*107^(1/2))^(1/3))","im":"0","approx_re":"-3.452681","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*(-4748+428*I*107^(1/2))^(1/3)-29/3/(-4748+428*I*107^(1/2))^(1/3)-13/9-1/6*I*3^(1/2)*(1/6*(-4748+428*I*107^(1/2))^(1/3)-58/(-4748+428*I*107^(1/2))^(1/3))","im":"0","approx_re":"-0.884694","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/24-1/24*105^(1/2)","im":"0","approx_re":"-0.218623","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18*(-4748+428*I*107^(1/2))^(1/3)+58/3/(-4748+428*I*107^(1/2))^(1/3)-13/9","im":"0","approx_re":"0.004042","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/24+1/24*105^(1/2)","im":"0","approx_re":"0.63529","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -240-1536*X-4020*X^2-4968*X^3-1944*X^4, 73116+319248*X+512001*X^2+294462*X^3+32913*X^4, -2386260-7989840*X-7779645*X^2+196830*X^3+1120230*X^4, -10731609-64892664*X-136142937*X^2-126964098*X^3-22652946*X^4, -177343830-419641560*X-134926965*X^2+124199730*X^3-149492385*X^4, 30114990+1562436540*X+5464984950*X^2+6557981940*X^3+3059328690*X^4, -239148450-3348078300*X-12515435550*X^2-18334714500*X^3-9526079925*X^4, -1076168025*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.31", "degz": 8, "h3": "11", "sol": "1 15 459 19545 1019259 60504165 3910479525 267933366135 19147233606075 1412455648664085", "n_discr_factors": "3", "c3": "-88", "operator": "4 8 0 0 0 0 16 -240 -1536 -4020 -4968 -1944 73116 319248 512001 294462 32913 -2386260 -7989840 -7779645 196830 1120230 -10731609 -64892664 -136142937 -126964098 -22652946 -177343830 -419641560 -134926965 124199730 -149492385 30114990 1562436540 5464984950 6557981940 3059328690 -239148450 -3348078300 -12515435550 -18334714500 -9526079925 -1076168025 -4304672100 -6457008150 -4304672100 -1076168025", "new_number": "8.32", "id": 477, "operator_tex": "2^{4} \\theta^4-2^{2} 3 x\\left(162\\theta^4+414\\theta^3+335\\theta^2+128\\theta+20\\right)+3^{3} x^{2}\\left(1219\\theta^4+10906\\theta^3+18963\\theta^2+11824\\theta+2708\\right)+3^{5} 5 x^{3}\\left(922\\theta^4+162\\theta^3-6403\\theta^2-6576\\theta-1964\\right)-3^{7} x^{4}\\left(10358\\theta^4+58054\\theta^3+62251\\theta^2+29672\\theta+4907\\right)-3^{9} 5 x^{5}\\left(1519\\theta^4-1262\\theta^3+1371\\theta^2+4264\\theta+1802\\right)+2 3^{11} 5 x^{6}\\left(1727\\theta^4+3702\\theta^3+3085\\theta^2+882\\theta+17\\right)-3^{13} 5^{2} x^{7}\\left(239\\theta^4+460\\theta^3+314\\theta^2+84\\theta+6\\right)-3^{16} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "69/4 14365/12", "discriminant": "8 16 -1944 32913 1120230 -22652946 -149492385 3059328690 -9526079925 -1076168025", "aesz": "317", "n_sing_complex": "3", "inst_int": "", "c2h": "50", "hash": "cda8cce31025f51636125bea67a820d1", "dim_h": "6", "inst": " 69/4 -30 14365/12 3015/2 1376205/4 9897421/3 388901931/2 7471470879/2 636889759589/4 4303811481090", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2", "discr_factors": "-1076168025, z-1/27, (-4/405-1/9*z+z^2)^2, z^3+82/9*z^2-13/27*z+1/243", "dm_basis": null, "q": "0 1 -36 972 -26604 669816 -17273412 416721960 -10686110652 249004225278", "yuk": "1 69/4 -891/4 64677/2 385029/4 86012847/2 1425292821/2 266786724735/4 7650786565125/4 464292634869735/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27+1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"-9.163702","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18-1/90*105^(1/2)","im":"0","approx_re":"-0.058299","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27-1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"0.010727","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54*(-4526396+3852*I*107^(1/2))^(1/3)+13682/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27","im":"0","approx_re":"0.041864","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18+1/90*105^(1/2)","im":"0","approx_re":"0.169411","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -18-117*X-300*X^2-366*X^3+15*X^4, -5052-23736*X-41729*X^2-32600*X^3-8603*X^4, -46848-245880*X-489388*X^2-433188*X^3-133216*X^4, -276144-1356992*X-2552500*X^2-2190424*X^3-721604*X^4, -611584-3034560*X-5690672*X^2-4779920*X^3-1518944*X^4, -111424-1102656*X-3047248*X^2-3267456*X^3-1172656*X^4, -66816-330624*X-692736*X^2-724224*X^3-311424*X^4, -9216*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.34", "degz": 8, "h3": null, "sol": "1 2 46 632 16846 371252 10387504 276173312 8072876494 234674601932", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 9 -18 -117 -300 -366 15 -5052 -23736 -41729 -32600 -8603 -46848 -245880 -489388 -433188 -133216 -276144 -1356992 -2552500 -2190424 -721604 -611584 -3034560 -5690672 -4779920 -1518944 -111424 -1102656 -3047248 -3267456 -1172656 -66816 -330624 -692736 -724224 -311424 -9216 -36864 -55296 -36864 -9216", "new_number": "8.33", "id": 478, "operator_tex": "3^{2} \\theta^4+3 x\\left(5\\theta^4-122\\theta^3-100\\theta^2-39\\theta-6\\right)-x^{2}\\left(5052+23736\\theta+41729\\theta^2+32600\\theta^3+8603\\theta^4\\right)-2^{2} x^{3}\\left(33304\\theta^4+108297\\theta^3+122347\\theta^2+61470\\theta+11712\\right)-2^{2} x^{4}\\left(180401\\theta^4+547606\\theta^3+638125\\theta^2+339248\\theta+69036\\right)-2^{4} x^{5}\\left(94934\\theta^4+298745\\theta^3+355667\\theta^2+189660\\theta+38224\\right)-2^{4} x^{6}\\left(73291\\theta^4+204216\\theta^3+190453\\theta^2+68916\\theta+6964\\right)-2^{7} 3 x^{7}\\left(811\\theta^4+1886\\theta^3+1804\\theta^2+861\\theta+174\\right)-2^{10} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4/3 95/3", "discriminant": "8 9 15 -8603 -133216 -721604 -1518944 -1172656 -311424 -9216", "aesz": "322", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "a19da26bf1a7748e3b7e6151e803da30", "dim_h": null, "inst": " 4/3 18 95/3 14575/12 18158/3 187103 4924031/3 527352805/12 1590965963/3 39385718023/3", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2", "discr_factors": "-9216, (1/4+11/6*z+z^2)^2, -1/64+13/64*z+827/64*z^2+241/8*z^3+z^4", "dm_basis": null, "q": "0 1 -5 -77 461 -3514 -11817 -693433 -4229517 -222501606", "yuk": "1 4/3 436/3 2569/3 233636/3 2269754/3 121245745/3 562980879 67501392676/3 1159814189596/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/12-1/12*85^(1/2)","im":"0","approx_re":"-1.684962","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/12+1/12*85^(1/2)","im":"0","approx_re":"-0.148371","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -126-999*X-3036*X^2-4074*X^3-2433*X^4, -2424-7494*X+17551*X^2+88948*X^3+73291*X^4, -3360-41400*X-232288*X^2-647928*X^3-759472*X^4, 11328+252608*X+1243408*X^2+2783968*X^3+2886416*X^4, 307712+1081728*X+348160*X^2-3189632*X^3-4262912*X^4, -243712-938496*X-1139968*X^2+463872*X^3+2202368*X^4, 368640+1382400*X+1818624*X^2+872448*X^3+30720*X^4, -147456*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.33", "degz": 8, "h3": null, "sol": "1 14 1054 120776 16816846 2620698764 439499218096 77609164054016 14239403354079694 2690863533920253524", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 9 -126 -999 -3036 -4074 -2433 -2424 -7494 17551 88948 73291 -3360 -41400 -232288 -647928 -759472 11328 252608 1243408 2783968 2886416 307712 1081728 348160 -3189632 -4262912 -243712 -938496 -1139968 463872 2202368 368640 1382400 1818624 872448 30720 -147456 -589824 -884736 -589824 -147456", "new_number": "8.34", "id": 479, "operator_tex": "3^{2} \\theta^4-3 x\\left(811\\theta^4+1358\\theta^3+1012\\theta^2+333\\theta+42\\right)-x^{2}\\left(2424+7494\\theta-17551\\theta^2-88948\\theta^3-73291\\theta^4\\right)-2^{3} x^{3}\\left(94934\\theta^4+80991\\theta^3+29036\\theta^2+5175\\theta+420\\right)+2^{4} x^{4}\\left(180401\\theta^4+173998\\theta^3+77713\\theta^2+15788\\theta+708\\right)-2^{7} x^{5}\\left(33304\\theta^4+24919\\theta^3-2720\\theta^2-8451\\theta-2404\\right)+2^{8} x^{6}\\left(8603\\theta^4+1812\\theta^3-4453\\theta^2-3666\\theta-952\\right)+2^{11} 3 x^{7}\\left(5\\theta^4+142\\theta^3+296\\theta^2+225\\theta+60\\right)-2^{14} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "100/3 73111/3", "discriminant": "8 9 -2433 73291 -759472 2886416 -4262912 2202368 30720 -147456", "aesz": "323", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "77c03b04c3a10350b5b0ccd2d204b18f", "dim_h": null, "inst": " 100/3 1880/3 73111/3 4310384/3 314245046/3 26179411786/3 798060796981 234462287589080/3 24193920474062539/3 867261407707451140", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+241z-827z^2+104z^3+64z^4)(3-44z+48z^2)^2", "discr_factors": "-147456, -1/64+241/64*z-827/64*z^2+13/8*z^3+z^4, (1/16-11/12*z+z^2)^2", "dm_basis": null, "q": "0 1 -55 467 -19997 -1644914 -153217663 -15871202977 -1736601601115 -197946221943014", "yuk": "1 100/3 15140/3 1974097/3 275879716/3 39280630850/3 5654754934913/3 821204560093549/3 120044691521488676/3 17637368025593565028/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"11/24-1/24*85^(1/2)","im":"0","approx_re":"0.074186","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/24+1/24*85^(1/2)","im":"0","approx_re":"0.842481","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 363+2178*X+5214*X^2+6072*X^3+3729*X^4, 35244+155430*X+256840*X^2+190276*X^3+56794*X^4, -502524-1617066*X-1681833*X^2-542466*X^3-9495*X^4, -437688-2323554*X-4274391*X^2-3157842*X^3-699990*X^4, -573507-918252*X+469143*X^2+890118*X^3-115794*X^4, 101412+1323540*X+3850623*X^2+4264002*X^3+1653867*X^4, -403704-1777248*X-3225960*X^2-2897424*X^3-1081296*X^4, 139968*(X+1)^4]", "text": "This operator has a second MUM point at infinity corresponding to operator 8.38.", "degz": 8, "h3": null, "sol": "1 -3 9 141 -3879 51597 -248751 -7237107 237153177 -3634238523", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 121 363 2178 5214 6072 3729 35244 155430 256840 190276 56794 -502524 -1617066 -1681833 -542466 -9495 -437688 -2323554 -4274391 -3157842 -699990 -573507 -918252 469143 890118 -115794 101412 1323540 3850623 4264002 1653867 -403704 -1777248 -3225960 -2897424 -1081296 139968 559872 839808 559872 139968", "new_number": "8.37", "id": 482, "operator_tex": "11^{2} \\theta^4+3 11 x\\left(113\\theta^4+184\\theta^3+158\\theta^2+66\\theta+11\\right)+2 x^{2}\\left(28397\\theta^4+95138\\theta^3+128420\\theta^2+77715\\theta+17622\\right)-3 x^{3}\\left(3165\\theta^4+180822\\theta^3+560611\\theta^2+539022\\theta+167508\\right)-3 x^{4}\\left(233330\\theta^4+1052614\\theta^3+1424797\\theta^2+774518\\theta+145896\\right)-3^{2} x^{5}\\left(12866\\theta^4-98902\\theta^3-52127\\theta^2+102028\\theta+63723\\right)+3^{2} x^{6}\\left(183763\\theta^4+473778\\theta^3+427847\\theta^2+147060\\theta+11268\\right)-2^{3} 3^{3} x^{7}\\left(5006\\theta^4+13414\\theta^3+14935\\theta^2+8228\\theta+1869\\right)+2^{6} 3^{7} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/11 357/11", "discriminant": "8 121 3729 56794 -9495 -699990 -115794 1653867 -1081296 139968", "aesz": "345", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "60f282ab4e1936cd96eb5ba12983db2d", "dim_h": null, "inst": " -12/11 -28/11 357/11 -1172/11 -5250/11 124524/11 -798399/11 -2939644/11 1037816990/99 -994092416/11", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(3z-1)(81z^3-457z^2-30z-1)(-11-21z+24z^2)^2", "discr_factors": "139968, z^3-457/81*z^2-10/27*z-1/81, (-11/24-7/8*z+z^2)^2, z-1/3", "dm_basis": null, "q": "0 1 6 45 -6 -42 -144 -58063 111318 3610368", "yuk": "1 -12/11 -236/11 9627/11 -75244/11 -656262/11 26906587/11 -273850869/11 -1505172972/11 84063185817/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"7/16-1/48*1497^(1/2)","im":"0","approx_re":"-0.368564","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(804238892+2500956*93^(1/2))^(1/3)-216139/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"-1/2*3^(1/2)*(1/486*(804238892+2500956*93^(1/2))^(1/3)-432278/243/(804238892+2500956*93^(1/2))^(1/3))","approx_re":"-0.032637","approx_im":"-0.033136","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(804238892+2500956*93^(1/2))^(1/3)-216139/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"1/2*3^(1/2)*(1/486*(804238892+2500956*93^(1/2))^(1/3)-432278/243/(804238892+2500956*93^(1/2))^(1/3))","approx_re":"-0.032637","approx_im":"0.033136","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3","im":"0","approx_re":"0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/16+1/48*1497^(1/2)","im":"0","approx_re":"1.243564","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/486*(804238892+2500956*93^(1/2))^(1/3)+432278/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"0","approx_re":"5.707249","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[64*X^4, -1344-11392*X-37832*X^2-52880*X^3-40048*X^4, 55080+603504*X+2945457*X^2+7054398*X^3+4961601*X^4, -46661832-310309056*X-703721925*X^2-328850442*X^3-28137942*X^4, 1364563341+8824636854*X+19667155185*X^2+7044191406*X^3-13777903170*X^4, -54717165360-250598877786*X-177615553815*X^2+804313632978*X^3-15138096885*X^4, 409632597036+1885188099474*X+3457857004488*X^2+4765272014700*X^3+7334386417422*X^4, 11046132982368+51778748354850*X+98034430218516*X^2+92511363727332*X^3+39006657093987*X^4, 102521921742603*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.37", "degz": 8, "h3": null, "sol": "1 21 2889 636357 171536121 51864327621 16892958818961 5797180903739589 2067831094837609017 759877198757877380061", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 64 -1344 -11392 -37832 -52880 -40048 55080 603504 2945457 7054398 4961601 -46661832 -310309056 -703721925 -328850442 -28137942 1364563341 8824636854 19667155185 7044191406 -13777903170 -54717165360 -250598877786 -177615553815 804313632978 -15138096885 409632597036 1885188099474 3457857004488 4765272014700 7334386417422 11046132982368 51778748354850 98034430218516 92511363727332 39006657093987 102521921742603 410087686970412 615131530455618 410087686970412 102521921742603", "new_number": "8.38", "id": 483, "operator_tex": "2^{6} \\theta^4-2^{3} x\\left(5006\\theta^4+6610\\theta^3+4729\\theta^2+1424\\theta+168\\right)+3^{3} x^{2}\\left(183763\\theta^4+261274\\theta^3+109091\\theta^2+22352\\theta+2040\\right)-3^{7} x^{3}\\left(12866\\theta^4+150366\\theta^3+321775\\theta^2+141888\\theta+21336\\right)-3^{10} x^{4}\\left(233330\\theta^4-119294\\theta^3-333065\\theta^2-149446\\theta-23109\\right)-3^{14} x^{5}\\left(3165\\theta^4-168162\\theta^3+37135\\theta^2+52394\\theta+11440\\right)+2 3^{17} x^{6}\\left(28397\\theta^4+18450\\theta^3+13388\\theta^2+7299\\theta+1586\\right)+3^{22} 11 x^{7}\\left(113\\theta^4+268\\theta^3+284\\theta^2+150\\theta+32\\right)+3^{25} 11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "713/8 571555/2", "discriminant": "8 64 -40048 4961601 -28137942 -13777903170 -15138096885 7334386417422 39006657093987 102521921742603", "aesz": "346", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "65579ed94e039ed095e1b5b7db3674ff", "dim_h": null, "inst": " 713/8 3274 571555/2 66913005/2 20047292157/4 861703056756 651656749404791/4 65985762313595899/2 56338136746414079803/8 3133491053600280118197/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z-1)(6561z^3+2430z^2+457z-1)(-8+567z+24057z^2)^2", "discr_factors": "102521921742603, z-1/27, (-8/24057+7/297*z+z^2)^2, z^3+10/27*z^2+457/6561*z-1/6561", "dm_basis": null, "q": "0 1 -94 99 -231682 -32460303 -6790272276 -1439692483666 -324864095494510 -76384538354407158", "yuk": "1 713/8 210249/8 61728653/8 17129939529/8 5011823039963/8 1489022944012557/8 447036530091687339/8 135138841235374340681/8 5133812711016990738130", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/972*(286308+30876*93^(1/2))^(1/3)+157/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"-1/2*3^(1/2)*(1/486*(286308+30876*93^(1/2))^(1/3)+314/81/(286308+30876*93^(1/2))^(1/3))","approx_re":"-0.186267","approx_im":"-0.189115","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(286308+30876*93^(1/2))^(1/3)+157/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"1/2*3^(1/2)*(1/486*(286308+30876*93^(1/2))^(1/3)+314/81/(286308+30876*93^(1/2))^(1/3))","approx_re":"-0.186267","approx_im":"0.189115","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/594-1/1782*1497^(1/2)","im":"0","approx_re":"-0.033497","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/486*(286308+30876*93^(1/2))^(1/3)-314/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"0","approx_re":"0.002163","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/594+1/1782*1497^(1/2)","im":"0","approx_re":"0.009928","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -828*X^4-2088*X^3-1584*X^2-540*X-72, -24384*X^4-63552*X^3-59808*X^2-29664*X-6336, -436992*X^4-838656*X^3-462336*X^2-218880*X-59904, -4640768*X^4-8347648*X^3-4438016*X^2-1099776*X-36864, -34013184*X^4-52297728*X^3-53805056*X^2-25624576*X-4063232, -159907840*X^4-292552704*X^3-327680000*X^2-188743680*X-42991616, -436207616*X^4-1174405120*X^3-1392508928*X^2-805306368*X-184549376, -536870912*(X+1)^4]", "text": "This is operator \"8.41\" from ...", "degz": 8, "h3": null, "sol": "1 8 328 18944 1324456 103395008 8676937984 766283976704 70287683444392 6638749358516288", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1584 -2088 -828 -6336 -29664 -59808 -63552 -24384 -59904 -218880 -462336 -838656 -436992 -36864 -1099776 -4438016 -8347648 -4640768 -4063232 -25624576 -53805056 -52297728 -34013184 -42991616 -188743680 -327680000 -292552704 -159907840 -184549376 -805306368 -1392508928 -1174405120 -436207616 -536870912 -2147483648 -3221225472 -2147483648 -536870912", "new_number": "8.41", "id": 487, "operator_tex": "3^{2} \\theta^4-2^{2} 3^{2} x\\left(23\\theta^4+58\\theta^3+44\\theta^2+15\\theta+2\\right)-2^{5} 3 x^{2}\\left(254\\theta^4+662\\theta^3+623\\theta^2+309\\theta+66\\right)-2^{8} 3 x^{3}\\left(569\\theta^4+1092\\theta^3+602\\theta^2+285\\theta+78\\right)-2^{11} x^{4}\\left(2266\\theta^4+4076\\theta^3+2167\\theta^2+537\\theta+18\\right)-2^{16} x^{5}\\left(519\\theta^4+798\\theta^3+821\\theta^2+391\\theta+62\\right)-2^{19} x^{6}\\left(305\\theta^4+558\\theta^3+625\\theta^2+360\\theta+82\\right)-2^{24} x^{7}\\left(26\\theta^4+70\\theta^3+83\\theta^2+48\\theta+11\\right)-2^{29} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "16 7568/3", "discriminant": "8 9 -828 -24384 -436992 -4640768 -34013184 -159907840 -436207616 -536870912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "051d7068f49d14c45c3c3369d63d56b5", "dim_h": null, "inst": " 16 751/6 7568/3 229516/3 8099456/3 222405623/2 5001523248 481878066665/2 12229091481152 1940301178711292/3", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2", "discr_factors": "-536870912, (3/256+3/32*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048, z+1/4", "dm_basis": null, "q": "0 1 -28 118 -1424 -116291 -3964232 -219558630 -11723251008 -656390362154", "yuk": "1 16 3052/3 68128 14692076/3 1012432048/3 72059629240/3 1715522474080 370082369890796/3 8915007689827936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"-1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"-0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"-1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"-0.097578","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"0.097578","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)-1/8","im":"0","approx_re":"0.00843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 104*X^4+136*X^3+116*X^2+48*X+8, 4880*X^4+10592*X^3+12496*X^2+6976*X+1504, 132864*X^4+327168*X^3+394496*X^2+238848*X+54528, 2320384*X^4+5107712*X^3+3619840*X^2+648192*X-165888, 27967488*X^4+58195968*X^3+36372480*X^2-3981312*X-6291456, 199753728*X^4+278396928*X^3+126615552*X^2-25952256*X-22020096, 868220928*X^4+1283457024*X^3+301989888*X^2-339738624*X-150994944, -1207959552*(X+1)^4]", "text": "This is operator \"8.42\" from ...", "degz": 8, "h3": null, "sol": "1 -8 112 -1664 23056 -276608 3138304 -71469056 3424240912 -154371932288", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 8 48 116 136 104 1504 6976 12496 10592 4880 54528 238848 394496 327168 132864 -165888 648192 3619840 5107712 2320384 -6291456 -3981312 36372480 58195968 27967488 -22020096 -25952256 126615552 278396928 199753728 -150994944 -339738624 301989888 1283457024 868220928 -1207959552 -4831838208 -7247757312 -4831838208 -1207959552", "new_number": "8.42", "id": 488, "operator_tex": "\\theta^4+2^{2} x\\left(26\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(305\\theta^4+662\\theta^3+781\\theta^2+436\\theta+94\\right)+2^{8} x^{3}\\left(519\\theta^4+1278\\theta^3+1541\\theta^2+933\\theta+213\\right)+2^{10} x^{4}\\left(2266\\theta^4+4988\\theta^3+3535\\theta^2+633\\theta-162\\right)+2^{14} 3 x^{5}\\left(569\\theta^4+1184\\theta^3+740\\theta^2-81\\theta-128\\right)+2^{18} 3 x^{6}\\left(254\\theta^4+354\\theta^3+161\\theta^2-33\\theta-28\\right)+2^{22} 3^{2} x^{7}\\left(23\\theta^4+34\\theta^3+8\\theta^2-9\\theta-4\\right)-2^{27} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-4 140", "discriminant": "8 1 104 4880 132864 2320384 27967488 199753728 868220928 -1207959552", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "7bc3855c04953ca11620400320722844", "dim_h": null, "inst": " -4 1/2 140 1025/2 -9196 -38947/2 578972 -7110765/2 -27940512 2905266427/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2", "discr_factors": "-1207959552, (1/192+1/16*z+z^2)^2, z+1/32, z^3-7/8*z^2-3/64*z-1/1024", "dm_basis": null, "q": "0 1 16 208 1792 5360 -62464 -1070848 -8339456 19820440", "yuk": "1 -4 0 3776 32800 -1149504 -4202496 198587392 -1820323040 -20368629472", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"-1/96*39^(1/2)","approx_re":"-0.03125","approx_im":"-0.065052","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"1/96*39^(1/2)","approx_re":"-0.03125","approx_im":"0.065052","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(3554+66*33^(1/2))^(1/3)-29/12/(3554+66*33^(1/2))^(1/3)+7/24","im":"-1/16*3^(1/2)*(1/6*(3554+66*33^(1/2))^(1/3)-116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"-0.025859","approx_im":"-0.019623","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(3554+66*33^(1/2))^(1/3)-29/12/(3554+66*33^(1/2))^(1/3)+7/24","im":"1/16*3^(1/2)*(1/6*(3554+66*33^(1/2))^(1/3)-116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"-0.025859","approx_im":"0.019623","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(3554+66*33^(1/2))^(1/3)+29/6/(3554+66*33^(1/2))^(1/3)+7/24","im":"0","approx_re":"0.926719","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -6328*X^4-8960*X^3-7126*X^2-2646*X-392, 188624*X^4+312896*X^3+255852*X^2+124040*X+28000, -2471168*X^4-4829952*X^3-4988032*X^2-2776032*X-634816, 16892928*X^4+41109504*X^3+49575168*X^2+30080256*X+7218688, -64356352*X^4-192053248*X^3-259612672*X^2-168603648*X-42344448, 136839168*X^4+476577792*X^3+693960704*X^2+467927040*X+119799808, -142606336-574619648*X-864026624*X^2-578813952*X^3-150994944*X^4, 67108864*(X+1)^4]", "text": "This is operator \"8.43\" from ...", "degz": 8, "h3": null, "sol": "1 8 224 10016 547936 33563008 2211981344 153473130112 11062214390368 821152908493568", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 49 -392 -2646 -7126 -8960 -6328 28000 124040 255852 312896 188624 -634816 -2776032 -4988032 -4829952 -2471168 7218688 30080256 49575168 41109504 16892928 -42344448 -168603648 -259612672 -192053248 -64356352 119799808 467927040 693960704 476577792 136839168 -142606336 -574619648 -864026624 -578813952 -150994944 67108864 268435456 402653184 268435456 67108864", "new_number": "8.43", "id": 489, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(452\\theta^4+640\\theta^3+509\\theta^2+189\\theta+28\\right)+2^{2} x^{2}\\left(47156\\theta^4+78224\\theta^3+63963\\theta^2+31010\\theta+7000\\right)-2^{5} x^{3}\\left(77224\\theta^4+150936\\theta^3+155876\\theta^2+86751\\theta+19838\\right)+2^{8} x^{4}\\left(65988\\theta^4+160584\\theta^3+193653\\theta^2+117501\\theta+28198\\right)-2^{12} x^{5}\\left(15712\\theta^4+46888\\theta^3+63382\\theta^2+41163\\theta+10338\\right)+2^{16} x^{6}\\left(2088\\theta^4+7272\\theta^3+10589\\theta^2+7140\\theta+1828\\right)-2^{22} x^{7}\\left(36\\theta^4+138\\theta^3+206\\theta^2+137\\theta+34\\right)+2^{26} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "66/7 8716/7", "discriminant": "8 49 -6328 188624 -2471168 16892928 -64356352 136839168 -150994944 67108864", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "923554dba37f79c41bf0f67b875c36f7", "dim_h": null, "inst": " 66/7 573/7 8716/7 197852/7 5617614/7 181938998/7 6461182982/7 35092617104 9839912329042/7 410745132222403/7", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2", "discr_factors": "67108864, (z^2-11/16*z+7/128)^2, 1/256-3/8*z+z^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 -22 89 -1604 -31716 -1360006 -53763318 -2282542360 -100929896284", "yuk": "1 66/7 4650/7 235398/7 12667178/7 702201816/7 39299063550/7 2216185762892/7 125771952367914/7 1024756584015288", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32-1/32*65^(1/2)","im":"0","approx_re":"0.091804","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32+1/32*65^(1/2)","im":"0","approx_re":"0.595696","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1152*X^4-192*X^3-256*X^2-160*X-32, 534528*X^4+276480*X^3+333056*X^2+146944*X+23808, -128712704*X^4-130744320*X^3-139182080*X^2-63774720*X-11313152, 17298358272*X^4+27097300992*X^3+28266725376*X^2+13632798720*X+2556952576, -1295603728384*X^4-2650129039360*X^3-2791930068992*X^2-1360447668224*X-255869321216, 50633369452544*X^4+118541097369600*X^3+120502823682048*X^2+54619099103232*X+9540196106240, -869713697570816*X^4-2247401767174144*X^3-2503313098539008*X^2-1379612214951936*X-307863255777280, 3448068464705536*(X+1)^4]", "text": "This is operator \"8.44\" from ...", "degz": 8, "h3": null, "sol": "1 32 2096 172544 15870736 1559276032 160054348544 16950443548672 1837683501894928 202898418734838272", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -160 -256 -192 -1152 23808 146944 333056 276480 534528 -11313152 -63774720 -139182080 -130744320 -128712704 2556952576 13632798720 28266725376 27097300992 17298358272 -255869321216 -1360447668224 -2791930068992 -2650129039360 -1295603728384 9540196106240 54619099103232 120502823682048 118541097369600 50633369452544 -307863255777280 -1379612214951936 -2503313098539008 -2247401767174144 -869713697570816 3448068464705536 13792273858822144 20688410788233216 13792273858822144 3448068464705536", "new_number": "8.44", "id": 490, "operator_tex": "\\theta^4-2^{5} x\\left(36\\theta^4+6\\theta^3+8\\theta^2+5\\theta+1\\right)+2^{8} x^{2}\\left(2088\\theta^4+1080\\theta^3+1301\\theta^2+574\\theta+93\\right)-2^{13} x^{3}\\left(15712\\theta^4+15960\\theta^3+16990\\theta^2+7785\\theta+1381\\right)+2^{18} x^{4}\\left(65988\\theta^4+103368\\theta^3+107829\\theta^2+52005\\theta+9754\\right)-2^{24} x^{5}\\left(77224\\theta^4+157960\\theta^3+166412\\theta^2+81089\\theta+15251\\right)+2^{30} x^{6}\\left(47156\\theta^4+110400\\theta^3+112227\\theta^2+50868\\theta+8885\\right)-2^{38} 7 x^{7}\\left(452\\theta^4+1168\\theta^3+1301\\theta^2+717\\theta+160\\right)+2^{46} 7^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 -131904", "discriminant": "8 1 -1152 534528 -128712704 17298358272 -1295603728384 50633369452544 -869713697570816 3448068464705536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2d570a3dc1cbc5b6596272f33b48fc98", "dim_h": null, "inst": " -64 -2084 -131904 -10745878 -1015115456 -105793050452 -11816074995264 -1389140511529039 -169882887296828928 -21436003799740611660", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2", "discr_factors": "3448068464705536, (z^2-11/448*z+1/14336)^2, 1/1024-3/16*z+z^2, (z-1/128)^2", "dm_basis": null, "q": "0 1 -32 640 28672 3475888 440300544 57936946176 7820948340736 1078701695219864", "yuk": "1 -64 -16736 -3561472 -687752928 -126889432064 -22851302475776 -4052913723375616 -711239942590620896 -123844624839391849984", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"11/896-1/896*65^(1/2)","im":"0","approx_re":"0.003279","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"11/896+1/896*65^(1/2)","im":"0","approx_re":"0.021275","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 380*X^4+1720*X^3+1460*X^2+600*X+100, 11344*X^4+68032*X^3+117424*X^2+77280*X+18640, -107520*X^4-29184*X^3+843264*X^2+1013760*X+339200, -971776*X^4-6944768*X^3-11622400*X^2-7904256*X-1934336, 5386240*X^4+17539072*X^3+29487104*X^2+23527424*X+6926336, 10043392*X^4+25559040*X^3+15941632*X^2-3538944*X-4079616, -2883584-10223616*X-10485760*X^2-524288*X^3+2883584*X^4, -1048576*(X+1)^4]", "text": "This is operator \"8.45\" from ...", "degz": 8, "h3": null, "sol": "1 -4 -4 464 -4244 -64304 2188976 -10994624 -630978836 14385797456", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 600 1460 1720 380 18640 77280 117424 68032 11344 339200 1013760 843264 -29184 -107520 -1934336 -7904256 -11622400 -6944768 -971776 6926336 23527424 29487104 17539072 5386240 -4079616 -3538944 15941632 25559040 10043392 -2883584 -10223616 -10485760 -524288 2883584 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.45", "id": 491, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(19\\theta^4+86\\theta^3+73\\theta^2+30\\theta+5\\right)+2^{4} x^{2}\\left(709\\theta^4+4252\\theta^3+7339\\theta^2+4830\\theta+1165\\right)-2^{8} x^{3}\\left(420\\theta^4+114\\theta^3-3294\\theta^2-3960\\theta-1325\\right)-2^{10} x^{4}\\left(949\\theta^4+6782\\theta^3+11350\\theta^2+7719\\theta+1889\\right)+2^{12} x^{5}\\left(1315\\theta^4+4282\\theta^3+7199\\theta^2+5744\\theta+1691\\right)+2^{14} x^{6}\\left(613\\theta^4+1560\\theta^3+973\\theta^2-216\\theta-249\\right)+2^{18} x^{7}\\left(11\\theta^4-2\\theta^3-40\\theta^2-39\\theta-11\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/5 -20", "discriminant": "8 25 380 11344 -107520 -971776 5386240 10043392 2883584 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "52e4f6959f297529016ddef66a399c12", "dim_h": null, "inst": " -12/5 -83/5 -20 3941/20 -13872/5 -197789/5 173580 57625509/20 -244692056/5 -480447172", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2", "discr_factors": "-1048576, z^3-39/8*z^2-5/32*z-1/128, z+1/8, (-5/32+z+z^2)^2", "dm_basis": null, "q": "0 1 8 126 1280 12209 135664 1558810 14866944 131815364", "yuk": "1 -12/5 -676/5 -2712/5 12476 -1734012/5 -8545160 297689688/5 7376127532/5 -178380511536/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2-1/8*26^(1/2)","im":"0","approx_re":"-1.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"-1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"-0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2+1/8*26^(1/2)","im":"0","approx_re":"0.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(61128+177*177^(1/2))^(1/3)+517/8/(61128+177*177^(1/2))^(1/3)+13/8","im":"0","approx_re":"4.907166","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -352*X^4-1472*X^3-1024*X^2-288*X-32, -156928*X^4-228352*X^3+7424*X^2+16896*X+1792, -10772480*X^4-8011776*X^3-18374656*X^2-8749056*X-1466368, 248774656*X^4-782761984*X^3-865599488*X^2-411303936*X-82051072, 3523215360*X^4+13136560128*X^3-9361686528*X^2-10821304320*X-2961178624, -47580184576*X^4+95026151424*X^3+78047608832*X^2+4831838208*X-8791261184, -204010946560*X^4+107374182400*X^3+762356695040*X^2+708669603840*X+204010946560, -1717986918400*(X+1)^4]", "text": "This is operator \"8.46\" from ...", "degz": 8, "h3": null, "sol": "1 32 6224 1859072 679223056 278574418432 123145098554624 57372286737276928 27788219971629427984 13867811101033655562752", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -288 -1024 -1472 -352 1792 16896 7424 -228352 -156928 -1466368 -8749056 -18374656 -8011776 -10772480 -82051072 -411303936 -865599488 -782761984 248774656 -2961178624 -10821304320 -9361686528 13136560128 3523215360 -8791261184 4831838208 78047608832 95026151424 -47580184576 204010946560 708669603840 762356695040 107374182400 -204010946560 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.46", "id": 492, "operator_tex": "\\theta^4-2^{5} x\\left(11\\theta^4+46\\theta^3+32\\theta^2+9\\theta+1\\right)-2^{8} x^{2}\\left(613\\theta^4+892\\theta^3-29\\theta^2-66\\theta-7\\right)-2^{13} x^{3}\\left(1315\\theta^4+978\\theta^3+2243\\theta^2+1068\\theta+179\\right)+2^{18} x^{4}\\left(949\\theta^4-2986\\theta^3-3302\\theta^2-1569\\theta-313\\right)+2^{23} x^{5}\\left(420\\theta^4+1566\\theta^3-1116\\theta^2-1290\\theta-353\\right)-2^{26} x^{6}\\left(709\\theta^4-1416\\theta^3-1163\\theta^2-72\\theta+131\\right)-2^{31} 5 x^{7}\\left(19\\theta^4-10\\theta^3-71\\theta^2-66\\theta-19\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "192 616896", "discriminant": "8 1 -352 -156928 -10772480 248774656 3523215360 -47580184576 -204010946560 -1717986918400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e38642e59fc2f9e3117437fcdbfe450e", "dim_h": null, "inst": " 192 3108 616896 73692781 15330708544 3169207515476 757547413779136 190303924221409951 50710465810985333248 14050572909374827223116", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2", "discr_factors": "-1717986918400, z^3+5/32*z^2+39/1024*z-1/16384, (-1/2560-1/20*z+z^2)^2, z+1/16", "dm_basis": null, "q": "0 1 -160 9024 -1007616 -9990480 -21114321920 -3882553055232 -1270290167169024 -355955892124246888", "yuk": "1 192 25056 16656384 4716363040 1916338568192 684548840024064 259838762926243840 97435609206078257952 36967929576208324594176", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"-1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"-0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40-1/160*26^(1/2)","im":"0","approx_re":"-0.006869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(6236+708*177^(1/2))^(1/3)-23/12/(6236+708*177^(1/2))^(1/3)-5/96","im":"0","approx_re":"0.001592","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40+1/160*26^(1/2)","im":"0","approx_re":"0.056869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1539*X^4+3564*X^3+4995*X^2+2862*X+576, -13608*X^4+81648*X^3+250128*X^2+188568*X+49248, 571536*X^4+1143072*X^3+396576*X^2-174960*X-54432, 2939328*X^4+29393280*X^3+16516224*X^2-2659392*X-3359232, 71803584*X^4+120932352*X^3+165022272*X^2+120932352*X+31912704, 30233088*(3*X^2+3*X+1)*(7*X^2+7*X+2), 2176782336*(X+1)^4]", "text": "Hadamard product $a \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over$Q(\\sqrt{6})$.", "degz": 8, "h3": null, "sol": "1 6 90 1176 3114 -668844 -36760464 -1357447680 -38737262934 -767282453076", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -6 -39 -102 -126 -63 576 2862 4995 3564 1539 49248 188568 250128 81648 -13608 -54432 -174960 396576 1143072 571536 -3359232 -2659392 16516224 29393280 2939328 31912704 120932352 165022272 120932352 71803584 60466176 393030144 1027924992 1269789696 634894848 2176782336 8707129344 13060694016 8707129344 2176782336", "new_number": "8.4", "id": 496, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+3^{2} x^{2}\\left(171\\theta^4+396\\theta^3+555\\theta^2+318\\theta+64\\right)-2^{3} 3^{4} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{4} 3^{5} x^{4}\\left(147\\theta^4+294\\theta^3+102\\theta^2-45\\theta-14\\right)+2^{6} 3^{7} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{6} 3^{8} x^{6}\\left(171\\theta^4+288\\theta^3+393\\theta^2+288\\theta+76\\right)+2^{9} 3^{10} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{12} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "6 -325", "discriminant": "8 1 -63 1539 -13608 571536 2939328 71803584 634894848 2176782336", "aesz": "160", "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "8ce8667fe6e49ce6625fafe044b1641b", "dim_h": null, "inst": " 6 6 -325 -1977/2 -5421 234971/4 6144684 150590955/2 175485337/3 -76710752151/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2", "discr_factors": "2176782336, z^2+1/3*z+1/27, z^2-1/24*z+1/1728, (1/216+z^2)^2", "dm_basis": null, "q": "0 1 -15 144 529 -20487 229986 -760582 -56200827 533023983", "yuk": "1 6 54 -8769 -63210 -677619 12679713 2107626618 38551221270 42642928122", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/6","im":"-1/18*3^(1/2)","approx_re":"-0.166666666667","approx_im":"-0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"1/18*3^(1/2)","approx_re":"-0.166666666667","approx_im":"0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/36*6^(1/2)","approx_re":"0.0","approx_im":"-0.068041","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/36*6^(1/2)","approx_re":"0.0","approx_im":"0.068041","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2816*X^4-512*X^3+64*X^2+320*X+80, 2621440*X^4+1048576*X^3+2785280*X^2+917504*X+110592, 922746880*X^4+2717908992*X^3+2499805184*X^2+1459617792*X+356515840, 124554051584*X^4+1099511627776*X^3+1726576852992*X^2+1151051235328*X+301721452544, -8796093022208*X^4+123145302310912*X^3+436506116227072*X^2+385928581349376*X+120121645334528, -5629499534213120*X^4-20266198323167232*X^3+6192449487634432*X^2+27021597764222976*X+12596005207801856, -288230376151711744*X^4-4035225266123964416*X^3-8070450532247928832*X^2-6052837899185946624*X-1585267068834414592, 73786976294838206464*(X+1)^4]", "text": "This is operator \"8.52\" from ...", "degz": 8, "h3": null, "sol": "1 -80 6928 -597248 95243536 -28956980480 7986476089600 -1683104643338240 279503410283322640 -43551775862241793280", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 80 320 64 -512 2816 110592 917504 2785280 1048576 2621440 356515840 1459617792 2499805184 2717908992 922746880 301721452544 1151051235328 1726576852992 1099511627776 124554051584 120121645334528 385928581349376 436506116227072 123145302310912 -8796093022208 12596005207801856 27021597764222976 6192449487634432 -20266198323167232 -5629499534213120 -1585267068834414592 -6052837899185946624 -8070450532247928832 -4035225266123964416 -288230376151711744 73786976294838206464 295147905179352825856 442721857769029238784 295147905179352825856 73786976294838206464", "new_number": "8.52", "id": 499, "operator_tex": "\\theta^4+2^{4} x\\left(176\\theta^4-32\\theta^3+4\\theta^2+20\\theta+5\\right)+2^{12} x^{2}\\left(640\\theta^4+256\\theta^3+680\\theta^2+224\\theta+27\\right)+2^{22} x^{3}\\left(220\\theta^4+648\\theta^3+596\\theta^2+348\\theta+85\\right)+2^{30} x^{4}\\left(116\\theta^4+1024\\theta^3+1608\\theta^2+1072\\theta+281\\right)-2^{38} x^{5}\\left(32\\theta^4-448\\theta^3-1588\\theta^2-1404\\theta-437\\right)-2^{46} x^{6}\\left(80\\theta^4+288\\theta^3-88\\theta^2-384\\theta-179\\right)-2^{57} x^{7}\\left(2\\theta^4+28\\theta^3+56\\theta^2+42\\theta+11\\right)+2^{66} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "416 9734432", "discriminant": "8 1 2816 2621440 922746880 124554051584 -8796093022208 -5629499534213120 -288230376151711744 73786976294838206464", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "87729f275f24cb2daf88133571476576", "dim_h": null, "inst": " 416 -52752 9734432 -2404009688 687625871328 -217118709400784 73338593607948448 -26035652821989456984 9601842176969903024896 -3649624408522473126874544", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1+256z+65536z^2)(256z+1)^2(131072z^2-1024z-1)^2", "discr_factors": "73786976294838206464, 1/65536+1/256*z+z^2, (z^2-1/128*z-1/131072)^2, (z+1/256)^2", "dm_basis": null, "q": "0 1 0 20320 -4311040 1648867888 -592819957760 230549894795776 -92139926455320576 37832399858049845912", "yuk": "1 416 -421600 262830080 -153857041632 85953233916416 -46897640968161280 25155137607526318080 -13330254245012459017440 6999742947011059567979264", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"-1/512*3^(1/2)","approx_re":"-0.001953125","approx_im":"-0.003383","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"1/512*3^(1/2)","approx_re":"-0.001953125","approx_im":"0.003383","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256-1/512*6^(1/2)","im":"0","approx_re":"-0.000878","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256+1/512*6^(1/2)","im":"0","approx_re":"0.00869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -64*X^4+640*X^3+512*X^2+192*X+32, -20480*X^4-8192*X^3+120832*X^2+86016*X+23296, -524288*X^4-9437184*X^3+851968*X^2+4915200*X+2310144, 121634816*X^4-587202560*X^3-805306368*X^2-486539264*X-95420416, 14763950080*X^4+15569256448*X^3-1879048192*X^2-14763950080*X-6375342080, 687194767360*X^4+2473901162496*X^3+4028679323648*X^2+3143916060672*X+930934161408, 12094627905536*X^4+50577534877696*X^3+79439715106816*X^2+54150947667968*X+13537736916992, 70368744177664*(X+1)^4]", "text": "This is operator \"8.53\" from ...", "degz": 8, "h3": null, "sol": "1 -32 1168 -43520 1777936 -88044032 5065771264 -295547150336 16184017108240 -837789769974272", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 32 192 512 640 -64 23296 86016 120832 -8192 -20480 2310144 4915200 851968 -9437184 -524288 -95420416 -486539264 -805306368 -587202560 121634816 -6375342080 -14763950080 -1879048192 15569256448 14763950080 930934161408 3143916060672 4028679323648 2473901162496 687194767360 13537736916992 54150947667968 79439715106816 50577534877696 12094627905536 70368744177664 281474976710656 422212465065984 281474976710656 70368744177664", "new_number": "8.53", "id": 500, "operator_tex": "\\theta^4-2^{5} x\\left(2\\theta^4-20\\theta^3-16\\theta^2-6\\theta-1\\right)-2^{8} x^{2}\\left(80\\theta^4+32\\theta^3-472\\theta^2-336\\theta-91\\right)-2^{14} x^{3}\\left(32\\theta^4+576\\theta^3-52\\theta^2-300\\theta-141\\right)+2^{20} x^{4}\\left(116\\theta^4-560\\theta^3-768\\theta^2-464\\theta-91\\right)+2^{26} x^{5}\\left(220\\theta^4+232\\theta^3-28\\theta^2-220\\theta-95\\right)+2^{30} x^{6}\\left(640\\theta^4+2304\\theta^3+3752\\theta^2+2928\\theta+867\\right)+2^{36} x^{7}\\left(176\\theta^4+736\\theta^3+1156\\theta^2+788\\theta+197\\right)+2^{46} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 -64320", "discriminant": "8 1 -64 -20480 -524288 121634816 14763950080 687194767360 12094627905536 70368744177664", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0714a480e1c587ebada71771f7e3b555", "dim_h": null, "inst": " -64 -1604 -64320 -3255802 -191614656 -12464539636 -868855080512 -63674279873218 -4847597834984960 -380343970931855788", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2", "discr_factors": "70368744177664, (z+1/64)^2, (z^2+1/16*z-1/2048)^2, 1/4096+1/64*z+z^2", "dm_basis": null, "q": "0 1 64 4896 401408 33915696 2926147584 256722484736 22834572820480 2054278570450584", "yuk": "1 -64 -12896 -1736704 -208384224 -23951832064 -2692342310912 -298017292615680 -32601231503471840 -3533898821705772544", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32-1/64*6^(1/2)","im":"0","approx_re":"-0.069523","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"-1/128*3^(1/2)","approx_re":"-0.0078125","approx_im":"-0.013532","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"1/128*3^(1/2)","approx_re":"-0.0078125","approx_im":"0.013532","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32+1/64*6^(1/2)","im":"0","approx_re":"0.007023","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -544*X^4-704*X^3-496*X^2-144*X-16, 48128*X^4-7168*X^3-86016*X^2-50176*X-9728, -1507328*X^4+4521984*X^3+6164480*X^2+2248704*X+245760, 1835008*X^4-179568640*X^3-10092544*X^2+60817408*X+21692416, 710934528*X^4+1170210816*X^3-3142582272*X^2-2406481920*X-529530880, -6308233216*X^4+37648072704*X^3+34091302912*X^2+8858370048*X-402653184, -123480309760*X^4-214748364800*X^3-130191196160*X^2-22817013760*X+2684354560, -107374182400*(X+1)^4]", "text": "This is operator \"8.56\" from ...", "degz": 8, "h3": null, "sol": "1 16 2512 533248 138259216 40134006016 12541610112256 4127695343644672 1411736921485577488 497357749211943844096", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -144 -496 -704 -544 -9728 -50176 -86016 -7168 48128 245760 2248704 6164480 4521984 -1507328 21692416 60817408 -10092544 -179568640 1835008 -529530880 -2406481920 -3142582272 1170210816 710934528 -402653184 8858370048 34091302912 37648072704 -6308233216 2684354560 -22817013760 -130191196160 -214748364800 -123480309760 -107374182400 -429496729600 -644245094400 -429496729600 -107374182400", "new_number": "8.56", "id": 503, "operator_tex": "\\theta^4-2^{4} x\\left(34\\theta^4+44\\theta^3+31\\theta^2+9\\theta+1\\right)+2^{9} x^{2}\\left(94\\theta^4-14\\theta^3-168\\theta^2-98\\theta-19\\right)-2^{12} x^{3}\\left(368\\theta^4-1104\\theta^3-1505\\theta^2-549\\theta-60\\right)+2^{16} x^{4}\\left(28\\theta^4-2740\\theta^3-154\\theta^2+928\\theta+331\\right)+2^{20} x^{5}\\left(678\\theta^4+1116\\theta^3-2997\\theta^2-2295\\theta-505\\right)-2^{26} x^{6}\\left(94\\theta^4-561\\theta^3-508\\theta^2-132\\theta+6\\right)-2^{28} 5 x^{7}\\left(92\\theta^4+160\\theta^3+97\\theta^2+17\\theta-2\\right)-2^{32} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "80 266256", "discriminant": "8 1 -544 48128 -1507328 1835008 710934528 -6308233216 -123480309760 -107374182400", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "b561c9f1501dce5c055c95391a2176d3", "dim_h": null, "inst": " 80 3554 266256 31532007 4663446128 790195697786 147150962991056 29358316330539673 6173488610620216192 1353085059855442029590", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2", "discr_factors": "-107374182400, z+1/16, (1/1280-1/20*z+z^2)^2, z^3+19/16*z^2+27/256*z-1/4096", "dm_basis": null, "q": "0 1 -80 -2176 -130048 -33520208 -6736487936 -1401478824960 -310706478153728 -71951901097203560", "yuk": "1 80 28512 7188992 2018076960 582930766080 170682277939200 50472780305932288 15031457963254389536 4500473197142144792960", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(-4537+111*I*111^(1/2))^(1/3)-35/12/(-4537+111*I*111^(1/2))^(1/3)-19/48+1/32*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-1.090586","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(-4537+111*I*111^(1/2))^(1/3)-35/12/(-4537+111*I*111^(1/2))^(1/3)-19/48-1/32*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.099171","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(-4537+111*I*111^(1/2))^(1/3)+35/6/(-4537+111*I*111^(1/2))^(1/3)-19/48","im":"0","approx_re":"0.002257","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40","im":"-1/80","approx_re":"0.025","approx_im":"-0.0125","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40","im":"1/80","approx_re":"0.025","approx_im":"0.0125","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1840*X^4+4160*X^3+3380*X^2+1300*X+200, 6016*X^4+59968*X^3+111296*X^2+75200*X+18240, -43392*X^4-102144*X^3+145728*X^2+277440*X+105280, -7168*X^4-730112*X^3-2107904*X^2-1816576*X-516352, 376832*X^4+2637824*X^3+4111360*X^2+2378752*X+466944, -770048*X^4-3194880*X^3-3588096*X^2-1474560*X-155648, 557056*X^4+1507328*X^3+1687552*X^2+933888*X+212992, -65536*(X+1)^4]", "text": "This is operator \"8.57\" from ...", "degz": 8, "h3": null, "sol": "1 -8 172 -5696 231916 -10603808 522270064 -27095384576 1460770929388 -81118185306848", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 200 1300 3380 4160 1840 18240 75200 111296 59968 6016 105280 277440 145728 -102144 -43392 -516352 -1816576 -2107904 -730112 -7168 466944 2378752 4111360 2637824 376832 -155648 -1474560 -3588096 -3194880 -770048 212992 933888 1687552 1507328 557056 -65536 -262144 -393216 -262144 -65536", "new_number": "8.57", "id": 504, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(92\\theta^4+208\\theta^3+169\\theta^2+65\\theta+10\\right)+2^{6} x^{2}\\left(94\\theta^4+937\\theta^3+1739\\theta^2+1175\\theta+285\\right)-2^{6} x^{3}\\left(678\\theta^4+1596\\theta^3-2277\\theta^2-4335\\theta-1645\\right)-2^{8} x^{4}\\left(28\\theta^4+2852\\theta^3+8234\\theta^2+7096\\theta+2017\\right)+2^{10} x^{5}\\left(368\\theta^4+2576\\theta^3+4015\\theta^2+2323\\theta+456\\right)-2^{13} x^{6}\\left(94\\theta^4+390\\theta^3+438\\theta^2+180\\theta+19\\right)+2^{14} x^{7}\\left(34\\theta^4+92\\theta^3+103\\theta^2+57\\theta+13\\right)-2^{16} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-36/5 -380", "discriminant": "8 25 1840 6016 -43392 -7168 376832 -770048 557056 -65536", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "c2a931d298755811a60b7f8e5dd3afbe", "dim_h": null, "inst": " -36/5 132/5 -380 112043/20 -560656/5 2498656 -306618636/5 32192228607/20 -222490141128/5 6408957842744/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(64z^3-432z^2-76z-1)(5-16z+16z^2)^2", "discr_factors": "-65536, z+1/4, (5/16-z+z^2)^2, z^3-27/4*z^2-19/16*z-1/64", "dm_basis": null, "q": "0 1 20 190 2448 15601 394296 -2665254 161323584 -4122362364", "yuk": "1 -36/5 204 -51336/5 1793708/5 -70082036/5 539699640 -105170192184/5 4120607055404/5 -162195312933648/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4+1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.157556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4-1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.014327","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"-1/4","approx_re":"0.5","approx_im":"-0.25","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"1/4","approx_re":"0.5","approx_im":"0.25","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(22005+111*I*111^(1/2))^(1/3)+131/2/(22005+111*I*111^(1/2))^(1/3)+9/4","im":"0","approx_re":"6.921883","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1114*X^4-2444*X^3-1704*X^2-482*X-51, -85922*X^4-94748*X^3+21782*X^2+21164*X+3273, -1559178*X^4-369036*X^3-503208*X^2-290898*X-51111, 1705608*X^4-8265420*X^3-7577586*X^2-2760588*X-425979, 2457378*X^4+7347996*X^3-7092360*X^2-7335846*X-1878633, -1571886*X^4+5537484*X^3+5035122*X^2+1145988*X-161109, -1013310*X^4-1239300*X^3-29160*X^2+590490*X+229635, -164025*(X+1)^4]", "text": "This is operator \"8.58\" from ...", "degz": 8, "h3": null, "sol": "1 51 18267 10280301 7092708939 5496409856601 4591887095300541 4043530915373562867 3701955750151332264651 3492265673761014339609729", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -51 -482 -1704 -2444 -1114 3273 21164 21782 -94748 -85922 -51111 -290898 -503208 -369036 -1559178 -425979 -2760588 -7577586 -8265420 1705608 -1878633 -7335846 -7092360 7347996 2457378 -161109 1145988 5035122 5537484 -1571886 229635 590490 -29160 -1239300 -1013310 -164025 -656100 -984150 -656100 -164025", "new_number": "8.58", "id": 505, "operator_tex": "\\theta^4-x\\left(1114\\theta^4+2444\\theta^3+1704\\theta^2+482\\theta+51\\right)-x^{2}\\left(85922\\theta^4+94748\\theta^3-21782\\theta^2-21164\\theta-3273\\right)-3^{2} x^{3}\\left(173242\\theta^4+41004\\theta^3+55912\\theta^2+32322\\theta+5679\\right)+3^{2} x^{4}\\left(189512\\theta^4-918380\\theta^3-841954\\theta^2-306732\\theta-47331\\right)+3^{4} x^{5}\\left(30338\\theta^4+90716\\theta^3-87560\\theta^2-90566\\theta-23193\\right)-3^{4} x^{6}\\left(19406\\theta^4-68364\\theta^3-62162\\theta^2-14148\\theta+1989\\right)-3^{6} 5 x^{7}\\left(278\\theta^4+340\\theta^3+8\\theta^2-162\\theta-63\\right)-3^{8} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "286 12179050/3", "discriminant": "8 1 -1114 -85922 -1559178 1705608 2457378 -1571886 -1013310 -164025", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "870f2e78b48eb5ee8f5de2f6a438f2b8", "dim_h": null, "inst": " 286 38919/2 12179050/3 2393489451/2 439227114444 368997789338867/2 85118370209405862 84116263332158448075/2 65699383759906133335900/3 11884580150263279731514633", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(81z^3+549z^2+1187z-1)(-1-36z+45z^2)^2", "discr_factors": "-164025, z+1, z^3+61/9*z^2+1187/81*z-1/81, (-1/45-4/5*z+z^2)^2", "dm_basis": null, "q": "0 1 -278 17299 -3881210 -959658839 -507507926048 -262668733865966 -145088484205534418 -83463003176743276082", "yuk": "1 286 155962 109611736 76591818394 54903389305786 39851761358365048 29195600981826210952 21533763413109154525594 15964950253657190510235436", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/54*(98972+12*67995561^(1/2))^(1/3)-80/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"-1/2*3^(1/2)*(1/27*(98972+12*67995561^(1/2))^(1/3)-160/27/(98972+12*67995561^(1/2))^(1/3))","approx_re":"-3.38931","approx_im":"-1.781181","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(98972+12*67995561^(1/2))^(1/3)-80/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"1/2*3^(1/2)*(1/27*(98972+12*67995561^(1/2))^(1/3)-160/27/(98972+12*67995561^(1/2))^(1/3))","approx_re":"-3.38931","approx_im":"1.781181","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5-1/15*41^(1/2)","im":"0","approx_re":"-0.026875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*(98972+12*67995561^(1/2))^(1/3)+160/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"0","approx_re":"0.000842","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5+1/15*41^(1/2)","im":"0","approx_re":"0.826875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1390*X^4+3860*X^3+3280*X^2+1350*X+225, 19406*X^4+145988*X^3+259366*X^2+172540*X+41745, -273042*X^4-275724*X^3+1599120*X^2+2118150*X+725085, -1705608*X^4-15087852*X^3-27452322*X^2-19224108*X-4728051, 14032602*X^4+52809084*X^3+78760512*X^2+52606098*X+13082067, 6959682*X^4+20164140*X^3+16969986*X^2+3000564*X-1030077, 812106*X^4+1466748*X^3+769824*X^2+36450*X-41553, -6561*(X+1)^4]", "text": "This is operator \"8.59\" from ...", "degz": 8, "h3": null, "sol": "1 -9 123 -1719 17739 96741 -14036259 573808023 -17342131509 419272268589", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 225 1350 3280 3860 1390 41745 172540 259366 145988 19406 725085 2118150 1599120 -275724 -273042 -4728051 -19224108 -27452322 -15087852 -1705608 13082067 52606098 78760512 52809084 14032602 -1030077 3000564 16969986 20164140 6959682 -41553 36450 769824 1466748 812106 -6561 -26244 -39366 -26244 -6561", "new_number": "8.59", "id": 506, "operator_tex": "5^{2} \\theta^4+5 x\\left(278\\theta^4+772\\theta^3+656\\theta^2+270\\theta+45\\right)+x^{2}\\left(19406\\theta^4+145988\\theta^3+259366\\theta^2+172540\\theta+41745\\right)-3^{2} x^{3}\\left(30338\\theta^4+30636\\theta^3-177680\\theta^2-235350\\theta-80565\\right)-3^{2} x^{4}\\left(189512\\theta^4+1676428\\theta^3+3050258\\theta^2+2136012\\theta+525339\\right)+3^{4} x^{5}\\left(173242\\theta^4+651964\\theta^3+972352\\theta^2+649458\\theta+161507\\right)+3^{4} x^{6}\\left(85922\\theta^4+248940\\theta^3+209506\\theta^2+37044\\theta-12717\\right)+3^{6} x^{7}\\left(1114\\theta^4+2012\\theta^3+1056\\theta^2+50\\theta-57\\right)-3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-26/5 -234/5", "discriminant": "8 25 1390 19406 -273042 -1705608 14032602 6959682 812106 -6561", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "53885e46a1519d98ee4697de1c109214", "dim_h": null, "inst": " -26/5 -177/10 -234/5 -1837/2 -27716/5 -162179/6 -3761394/5 -7510965/2 -138687964/5 -5286369579/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2", "discr_factors": "-6561, (-5/9+4*z+z^2)^2, z^3-1187/9*z^2-61/9*z-1/9, z+1/9", "dm_basis": null, "q": "0 1 18 307 4590 68905 1012896 14546674 209303574 2977428238", "yuk": "1 -26/5 -734/5 -6344/5 -294654/5 -3464526/5 -29199272/5 -1290158168/5 -9614329854/5 -20220706420", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-2-1/3*41^(1/2)","im":"0","approx_re":"-4.134375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(1675379780+108*67995561^(1/2))^(1/3)-705308/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"-1/2*3^(1/2)*(1/27*(1675379780+108*67995561^(1/2))^(1/3)-1410616/27/(1675379780+108*67995561^(1/2))^(1/3))","approx_re":"-0.025688","approx_im":"-0.0135","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(1675379780+108*67995561^(1/2))^(1/3)-705308/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"1/2*3^(1/2)*(1/27*(1675379780+108*67995561^(1/2))^(1/3)-1410616/27/(1675379780+108*67995561^(1/2))^(1/3))","approx_re":"-0.025688","approx_im":"0.0135","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-2+1/3*41^(1/2)","im":"0","approx_re":"0.134375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*(1675379780+108*67995561^(1/2))^(1/3)+1410616/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"0","approx_re":"131.940265","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(7*X^2+7*X+2)*(17*X^2+17*X+6), 3520*X^4+7168*X^3+9920*X^2+5504*X+960, -68544*X^4+411264*X^3+1258560*X^2+953856*X+255744, 3391488*X^4+6782976*X^3+3612672*X^2+221184*X+331776, 39481344*X^4+394813440*X^3+222621696*X^2-31850496*X-46448640, 1167851520*X^4+2293235712*X^3+3163815936*X^2+2293235712*X+573308928, 191102976*(7*X^2+7*X+2)*(17*X^2+17*X+6), 110075314176*(X+1)^4]", "text": "Hadamard product $a \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 12 420 17472 828324 42238512 2264481024 125871390720 7191959038884 419977122762288", "n_discr_factors": "5", "c3": "192", "operator": "4 8 0 0 0 0 1 -12 -76 -195 -238 -119 960 5504 9920 7168 3520 255744 953856 1258560 411264 -68544 331776 221184 3612672 6782976 3391488 -46448640 -31850496 222621696 394813440 39481344 573308928 2293235712 3163815936 2293235712 1167851520 2293235712 14523826176 37265080320 45482508288 22741254144 110075314176 440301256704 660451885056 440301256704 110075314176", "new_number": "8.5", "id": 507, "operator_tex": "\\theta^4-x(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{6} x^{2}\\left(55\\theta^4+112\\theta^3+155\\theta^2+86\\theta+15\\right)-2^{6} 3^{2} x^{3}\\left(119\\theta^4-714\\theta^3-2185\\theta^2-1656\\theta-444\\right)+2^{12} 3^{2} x^{4}\\left(92\\theta^4+184\\theta^3+98\\theta^2+6\\theta+9\\right)+2^{12} 3^{4} x^{5}\\left(119\\theta^4+1190\\theta^3+671\\theta^2-96\\theta-140\\right)+2^{18} 3^{4} x^{6}\\left(55\\theta^4+108\\theta^3+149\\theta^2+108\\theta+27\\right)+2^{18} 3^{6} x^{7}(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{24} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "11 -2434/3", "discriminant": "8 1 -119 3520 -68544 3391488 39481344 1167851520 22741254144 110075314176", "aesz": "173", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "afa82ed9ee239bb5fcac960f8884db01", "dim_h": "18", "inst": " 11 229/4 -2434/3 7512 54801 -12678391/6 32879631 150774408 -30805117507/3 890194486255/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2", "discr_factors": "110075314176, z-1/72, z+1/9, z+1/8, (1/576+z^2)^2, z-1/64", "dm_basis": null, "q": "0 1 -28 334 2984 -203003 3367304 9854854 -1734288784 35967438370", "yuk": "1 11 469 -21895 481237 6850136 -456443513 11277713444 77196978133 -7485643576096", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/24","approx_re":"0.0","approx_im":"-0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/24","approx_re":"0.0","approx_im":"0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1182*X^4-2172*X^3-1519*X^2-433*X-46, 70937*X^4+62468*X^3-34151*X^2-26294*X-4528, -1127480*X^4+333744*X^3+666208*X^2+234936*X+27008, 1008336*X^4-6452064*X^3-4827744*X^2-1254576*X-94752, 1882880*X^4+5074688*X^3-5883712*X^2-5690688*X-1408768, -1121216*X^4+4675584*X^3+4283072*X^2+1056768*X-91904, -898560*X^4-1305600*X^3-450560*X^2+202240*X+117760, -102400*(X+1)^4]", "text": "This is operator \"8.60\" from ...", "degz": 8, "h3": null, "sol": "1 46 15670 8332840 5425831846 3966524531596 3125421518142736 2595460605915940480 2240735314680592704550 1993206045269010448338436", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -46 -433 -1519 -2172 -1182 -4528 -26294 -34151 62468 70937 27008 234936 666208 333744 -1127480 -94752 -1254576 -4827744 -6452064 1008336 -1408768 -5690688 -5883712 5074688 1882880 -91904 1056768 4283072 4675584 -1121216 117760 202240 -450560 -1305600 -898560 -102400 -409600 -614400 -409600 -102400", "new_number": "8.60", "id": 508, "operator_tex": "\\theta^4-x\\left(1182\\theta^4+2172\\theta^3+1519\\theta^2+433\\theta+46\\right)+x^{2}\\left(70937\\theta^4+62468\\theta^3-34151\\theta^2-26294\\theta-4528\\right)-2^{3} x^{3}\\left(140935\\theta^4-41718\\theta^3-83276\\theta^2-29367\\theta-3376\\right)+2^{4} 3 x^{4}\\left(21007\\theta^4-134418\\theta^3-100578\\theta^2-26137\\theta-1974\\right)+2^{6} x^{5}\\left(29420\\theta^4+79292\\theta^3-91933\\theta^2-88917\\theta-22012\\right)-2^{6} x^{6}\\left(17519\\theta^4-73056\\theta^3-66923\\theta^2-16512\\theta+1436\\right)-2^{9} 5 x^{7}\\left(351\\theta^4+510\\theta^3+176\\theta^2-79\\theta-46\\right)-2^{12} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "247 3584909", "discriminant": "8 1 -1182 70937 -1127480 1008336 1882880 -1121216 -898560 -102400", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "540ab51629d98ae18b7d061824bd258b", "dim_h": null, "inst": " 247 38017/2 3584909 2039721503/2 359173241174 289778276762921/2 64197103661613552 60932799164040671635/2 15237129940800217615517 7942298204883109102617333", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2", "discr_factors": "-102400, (1/40-4/5*z+z^2)^2, z+1, z^3+75/8*z^2+1119/64*z-1/64", "dm_basis": null, "q": "0 1 -249 8556 -2592215 -934458075 -430575301776 -216010977283007 -114383349378060561 -63161064256109550501", "yuk": "1 247 152315 96792790 65271240411 44896655146997 31296053987340326 22019606555933448583 15598796586059683178971 11107867726843358738504683", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/32*(-484+116*I*87^(1/2))^(1/3)-21/2/(-484+116*I*87^(1/2))^(1/3)-25/8+1/2*I*3^(1/2)*(3/16*(-484+116*I*87^(1/2))^(1/3)-21/(-484+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-6.805514","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/32*(-484+116*I*87^(1/2))^(1/3)-21/2/(-484+116*I*87^(1/2))^(1/3)-25/8-1/2*I*3^(1/2)*(3/16*(-484+116*I*87^(1/2))^(1/3)-21/(-484+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-2.570379","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16*(-484+116*I*87^(1/2))^(1/3)+21/(-484+116*I*87^(1/2))^(1/3)-25/8","im":"0","approx_re":"0.000893","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5-3/20*6^(1/2)","im":"0","approx_re":"0.032577","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5+3/20*6^(1/2)","im":"0","approx_re":"0.767423","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1755*X^4+4470*X^3+3760*X^2+1525*X+250, 17519*X^4+143132*X^3+257359*X^2+171910*X+41600, -235360*X^4-307104*X^3+1226312*X^2+1721160*X+599200, -1008336*X^4-10485408*X^3-20578464*X^2-14988624*X-3792480, 9019840*X^4+38749312*X^3+56799232*X^2+35309376*X+8023552, -4539968*X^4-14161920*X^3-13060288*X^2-3477504*X+250624, 605184*X^4+1308672*X^3+1072640*X^2+418304*X+72704, -4096*(X+1)^4]", "text": "This is operator \"8.61\" from ...", "degz": 8, "h3": null, "sol": "1 -10 190 -4888 151246 -5276260 199601200 -7993561600 333748769230 -14382842944060", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 250 1525 3760 4470 1755 41600 171910 257359 143132 17519 599200 1721160 1226312 -307104 -235360 -3792480 -14988624 -20578464 -10485408 -1008336 8023552 35309376 56799232 38749312 9019840 250624 -3477504 -13060288 -14161920 -4539968 72704 418304 1072640 1308672 605184 -4096 -16384 -24576 -16384 -4096", "new_number": "8.61", "id": 509, "operator_tex": "5^{2} \\theta^4+5 x\\left(351\\theta^4+894\\theta^3+752\\theta^2+305\\theta+50\\right)+x^{2}\\left(17519\\theta^4+143132\\theta^3+257359\\theta^2+171910\\theta+41600\\right)-2^{3} x^{3}\\left(29420\\theta^4+38388\\theta^3-153289\\theta^2-215145\\theta-74900\\right)-2^{4} 3 x^{4}\\left(21007\\theta^4+218446\\theta^3+428718\\theta^2+312263\\theta+79010\\right)+2^{6} x^{5}\\left(140935\\theta^4+605458\\theta^3+887488\\theta^2+551709\\theta+125368\\right)-2^{6} x^{6}\\left(70937\\theta^4+221280\\theta^3+204067\\theta^2+54336\\theta-3916\\right)+2^{9} x^{7}\\left(1182\\theta^4+2556\\theta^3+2095\\theta^2+817\\theta+142\\right)-2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-32/5 -863/5", "discriminant": "8 25 1755 17519 -235360 -1008336 9019840 -4539968 605184 -4096", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "9699709447380eb1373469a1cf5a9586", "dim_h": null, "inst": " -32/5 -33/10 -863/5 715/2 -83882/5 141804 -16129463/5 470935691/10 -4686251279/5 169789642113/10", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2", "discr_factors": "-4096, (5/8-4*z+z^2)^2, z^3-1119/8*z^2-75/8*z-1/8, z+1/8", "dm_basis": null, "q": "0 1 21 327 5143 74514 1108797 15375687 225733185 2975502342", "yuk": "1 -32/5 -164/5 -23333/5 114236/5 -10485282/5 30624971 -5532405841/5 120559651132/5 -3416277205724/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(1926187+116*I*87^(1/2))^(1/3)-46443/16/(1926187+116*I*87^(1/2))^(1/3)+373/8+1/2*I*3^(1/2)*(3/8*(1926187+116*I*87^(1/2))^(1/3)-46443/8/(1926187+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-0.048631","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(1926187+116*I*87^(1/2))^(1/3)-46443/16/(1926187+116*I*87^(1/2))^(1/3)+373/8-1/2*I*3^(1/2)*(3/8*(1926187+116*I*87^(1/2))^(1/3)-46443/8/(1926187+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-0.018367","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"2-3/4*6^(1/2)","im":"0","approx_re":"0.162883","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"2+3/4*6^(1/2)","im":"0","approx_re":"3.837117","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8*(1926187+116*I*87^(1/2))^(1/3)+46443/8/(1926187+116*I*87^(1/2))^(1/3)+373/8","im":"0","approx_re":"139.941998","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 578*X^4-572*X^3-359*X^2-73*X-6, 42057*X^4+17028*X^3+284409*X^2+103626*X+15552, -5951880*X^4+87025104*X^3+22952160*X^2+14469192*X+3592512, 1999897776*X^4+1243545696*X^3+12038437728*X^2+6922012464*X+1500107040, -256452168960*X^4-274410623232*X^3+219684954816*X^2+268934655168*X+78228115200, -10796806374336*X^4-76434446555136*X^3-82531239743808*X^2-39142899965952*X-7041754808064, 1776307445245440*X^4+5266439159270400*X^3+6641069041520640*X^2+4007849461885440*X+946173815055360, -28920784535654400*(X+1)^4]", "text": "This is operator \"8.62\" from ...", "degz": 8, "h3": null, "sol": "1 6 -810 -47784 3354534 538267356 -10663408944 -6600029299200 -174404179684314 79255303462908564", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -6 -73 -359 -572 578 15552 103626 284409 17028 42057 3592512 14469192 22952160 87025104 -5951880 1500107040 6922012464 12038437728 1243545696 1999897776 78228115200 268934655168 219684954816 -274410623232 -256452168960 -7041754808064 -39142899965952 -82531239743808 -76434446555136 -10796806374336 946173815055360 4007849461885440 6641069041520640 5266439159270400 1776307445245440 -28920784535654400 -115683138142617600 -173524707213926400 -115683138142617600 -28920784535654400", "new_number": "8.62", "id": 510, "operator_tex": "\\theta^4+x\\left(578\\theta^4-572\\theta^3-359\\theta^2-73\\theta-6\\right)+3^{2} x^{2}\\left(4673\\theta^4+1892\\theta^3+31601\\theta^2+11514\\theta+1728\\right)-2^{3} 3^{4} x^{3}\\left(9185\\theta^4-134298\\theta^3-35420\\theta^2-22329\\theta-5544\\right)+2^{4} 3^{8} x^{4}\\left(19051\\theta^4+11846\\theta^3+114678\\theta^2+65939\\theta+14290\\right)-2^{6} 3^{12} x^{5}\\left(7540\\theta^4+8068\\theta^3-6459\\theta^2-7907\\theta-2300\\right)-2^{6} 3^{16} x^{6}\\left(3919\\theta^4+27744\\theta^3+29957\\theta^2+14208\\theta+2556\\right)+2^{9} 3^{20} 5 x^{7}\\left(199\\theta^4+590\\theta^3+744\\theta^2+449\\theta+106\\right)-2^{12} 3^{24} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "127 1566863/3", "discriminant": "8 1 578 42057 -5951880 1999897776 -256452168960 -10796806374336 1776307445245440 -28920784535654400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4165325308c2b65daacebc1d19717e13", "dim_h": null, "inst": " 127 -14353/2 1566863/3 -106847355/2 6507370854 -1747126569829/2 124896327270384 -37542752696166551/2 8802495080253830111/3 -472867804119236671997", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(81z+1)(419904z^3-22680z^2+79z-1)(-1-288z+29160z^2)^2", "discr_factors": "-28920784535654400, z^3-35/648*z^2+79/419904*z-1/419904, (-1/29160-4/405*z+z^2)^2, z+1/81", "dm_basis": null, "q": "0 1 -49 7356 -883951 126439797 -19431562416 3153811031025 -529587874041177 91384585610935851", "yuk": "1 127 -57285 14101894 -3419172645 813421356877 -188689655497050 42839440253741839 -9610944693637809701 2139006304501694818867", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/81","im":"0","approx_re":"-0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/405-1/1620*154^(1/2)","im":"0","approx_re":"-0.002722","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7776*(313444+36*28181793^(1/2))^(1/3)-247/486/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"-1/2*3^(1/2)*(1/3888*(313444+36*28181793^(1/2))^(1/3)-247/243/(313444+36*28181793^(1/2))^(1/3))","approx_re":"0.001382","approx_im":"-0.006675","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7776*(313444+36*28181793^(1/2))^(1/3)-247/486/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"1/2*3^(1/2)*(1/3888*(313444+36*28181793^(1/2))^(1/3)-247/243/(313444+36*28181793^(1/2))^(1/3))","approx_re":"0.001382","approx_im":"0.006675","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/405+1/1620*154^(1/2)","im":"0","approx_re":"0.012599","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(313444+36*28181793^(1/2))^(1/3)+247/243/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"0","approx_re":"0.051248","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -995*X^4-1030*X^3-840*X^2-325*X-50, 3919*X^4-12068*X^3-29761*X^2-21850*X-5520, 60320*X^4+176736*X^3+116616*X^2+7560*X-11040, -304816*X^4-1029728*X^3-3095136*X^2-3265328*X-1123744, 587840*X^4+10946432*X^3+27045376*X^2+25031872*X+7990272, -2691648*X^4-9676800*X^3-31082688*X^2-37269504*X-14167296, -23970816*X^4-119605248*X^3-200102400*X^2-140299776*X-35582976, -26873856*(X+1)^4]", "text": "This is operator \"8.63\" from ...", "degz": 8, "h3": null, "sol": "1 2 30 488 9934 219252 5201904 129402240 3338871246 88609731788", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 -50 -325 -840 -1030 -995 -5520 -21850 -29761 -12068 3919 -11040 7560 116616 176736 60320 -1123744 -3265328 -3095136 -1029728 -304816 7990272 25031872 27045376 10946432 587840 -14167296 -37269504 -31082688 -9676800 -2691648 -35582976 -140299776 -200102400 -119605248 -23970816 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.63", "id": 511, "operator_tex": "5^{2} \\theta^4-5 x\\left(199\\theta^4+206\\theta^3+168\\theta^2+65\\theta+10\\right)+x^{2}\\left(3919\\theta^4-12068\\theta^3-29761\\theta^2-21850\\theta-5520\\right)+2^{3} x^{3}\\left(7540\\theta^4+22092\\theta^3+14577\\theta^2+945\\theta-1380\\right)-2^{4} x^{4}\\left(19051\\theta^4+64358\\theta^3+193446\\theta^2+204083\\theta+70234\\right)+2^{6} x^{5}\\left(9185\\theta^4+171038\\theta^3+422584\\theta^2+391123\\theta+124848\\right)-2^{6} 3^{2} x^{6}\\left(4673\\theta^4+16800\\theta^3+53963\\theta^2+64704\\theta+24596\\right)-2^{9} 3^{4} x^{7}\\left(578\\theta^4+2884\\theta^3+4825\\theta^2+3383\\theta+858\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8/5 67", "discriminant": "8 25 -995 3919 60320 -304816 587840 -2691648 -23970816 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "2c5f91dca73abc39f5d6eb00b9c4ea16", "dim_h": null, "inst": " 8/5 101/10 67 6197/10 32978/5 5114699/60 6004279/5 181646353/10 288778475 23931403561/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2", "discr_factors": "-26873856, z^3-79/648*z^2+35/648*z-1/648, z+1/8, (-5/72+4/9*z+z^2)^2", "dm_basis": null, "q": "0 1 -5 -33 -71 -1110 -13629 -270585 -4687185 -81808146", "yuk": "1 8/5 412/5 9053/5 198716/5 4122258/5 92074039/5 411893541 46501665084/5 1052597550428/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-2/9-1/36*154^(1/2)","im":"0","approx_re":"-0.566935","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1944*(1900997+2916*28181793^(1/2))^(1/3)+61799/1944/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"0","approx_re":"0.030113","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(1900997+2916*28181793^(1/2))^(1/3)-61799/3888/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"1/2*3^(1/2)*(-1/1944*(1900997+2916*28181793^(1/2))^(1/3)-61799/1944/(1900997+2916*28181793^(1/2))^(1/3))","approx_re":"0.0459","approx_im":"-0.221678","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(1900997+2916*28181793^(1/2))^(1/3)-61799/3888/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"-1/2*3^(1/2)*(-1/1944*(1900997+2916*28181793^(1/2))^(1/3)-61799/1944/(1900997+2916*28181793^(1/2))^(1/3))","approx_re":"0.0459","approx_im":"0.221678","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-2/9+1/36*154^(1/2)","im":"0","approx_re":"0.122491","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -512*X^4-256*X^3-224*X^2-96*X-16, 88064*X^4+180224*X^3+188416*X^2+77824*X+13312, -3997696*X^4-33423360*X^3-40632320*X^2-21430272*X-4456448, -461373440*X^4+1090519040*X^3+3951034368*X^2+2550136832*X+591396864, 47513075712*X^4+144955146240*X^3-44694503424*X^2-82543902720*X-26642219008, 575525617664*X^4-6597069766656*X^3-6390911336448*X^2-2113123909632*X-124554051584, -100330436034560*X^4-233646220902400*X^3-230897441832960*X^2-114074331381760*X-23364622090240, -439804651110400*(X+1)^4]", "text": "This is operator \"8.64\" from ...", "degz": 8, "h3": null, "sol": "1 16 272 -15104 -2814704 -264611584 -16376176384 -267584155648 101539591200016 18215778428313856", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -96 -224 -256 -512 13312 77824 188416 180224 88064 -4456448 -21430272 -40632320 -33423360 -3997696 591396864 2550136832 3951034368 1090519040 -461373440 -26642219008 -82543902720 -44694503424 144955146240 47513075712 -124554051584 -2113123909632 -6390911336448 -6597069766656 575525617664 -23364622090240 -114074331381760 -230897441832960 -233646220902400 -100330436034560 -439804651110400 -1759218604441600 -2638827906662400 -1759218604441600 -439804651110400", "new_number": "8.64", "id": 512, "operator_tex": "\\theta^4-2^{4} x\\left(32\\theta^4+16\\theta^3+14\\theta^2+6\\theta+1\\right)+2^{10} x^{2}\\left(86\\theta^4+176\\theta^3+184\\theta^2+76\\theta+13\\right)-2^{16} x^{3}\\left(61\\theta^4+510\\theta^3+620\\theta^2+327\\theta+68\\right)-2^{22} x^{4}\\left(110\\theta^4-260\\theta^3-942\\theta^2-608\\theta-141\\right)+2^{26} x^{5}\\left(708\\theta^4+2160\\theta^3-666\\theta^2-1230\\theta-397\\right)+2^{32} x^{6}\\left(134\\theta^4-1536\\theta^3-1488\\theta^2-492\\theta-29\\right)-2^{38} 5 x^{7}\\left(73\\theta^4+170\\theta^3+168\\theta^2+83\\theta+17\\right)-2^{44} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "0 -32768", "discriminant": "8 1 -512 88064 -3997696 -461373440 47513075712 575525617664 -100330436034560 -439804651110400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "00b5810e4a2d21fec464e4e87169df86", "dim_h": null, "inst": " 0 -1116 -32768 -2011784 -92274688 -5281675308 -281181421568 -17208628462728 -1097313761525760 -78166610255616308", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2", "discr_factors": "-439804651110400, (-1/10240+1/80*z+z^2)^2, z^3+7/32*z^2-3/1024*z+1/65536, z-1/64", "dm_basis": null, "q": "0 1 -32 1888 -22528 4272688 59175936 13148885504 494941700096 51752657480344", "yuk": "1 0 -8928 -884736 -128763104 -11534336000 -1140842760192 -96445227597824 -8810817901679840 -799941732153163776", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(3554+66*33^(1/2))^(1/3)-29/24/(3554+66*33^(1/2))^(1/3)-7/96","im":"0","approx_re":"-0.23168","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/160-1/320*14^(1/2)","im":"0","approx_re":"-0.017943","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/160+1/320*14^(1/2)","im":"0","approx_re":"0.005443","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3554+66*33^(1/2))^(1/3)+29/48/(3554+66*33^(1/2))^(1/3)-7/96","im":"1/64*3^(1/2)*(-1/6*(3554+66*33^(1/2))^(1/3)+116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"0.006465","approx_im":"-0.004906","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3554+66*33^(1/2))^(1/3)+29/48/(3554+66*33^(1/2))^(1/3)-7/96","im":"-1/64*3^(1/2)*(-1/6*(3554+66*33^(1/2))^(1/3)+116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"0.006465","approx_im":"0.004906","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1460*X^4+2440*X^3+1920*X^2+700*X+100, -2144*X^4-33152*X^3-62784*X^2-42560*X-10320, -45312*X^4-43008*X^3+185472*X^2+240000*X+82240, 112640*X^4+716800*X^3+509952*X^2-57344*X-107520, 249856*X^4-1089536*X^3-2228224*X^2-1527808*X-360448, -1409024*X^4-2752512*X^3-2818048*X^2-1769472*X-507904, 2097152*X^4+7340032*X^3+10354688*X^2+6684672*X+1638400, -1048576*(X+1)^4]", "text": "This is operator \"8.65\" from ...", "degz": 8, "h3": null, "sol": "1 -4 92 -2704 95596 -3755504 158254256 -7009022528 322174768876 -15241307862064", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 700 1920 2440 1460 -10320 -42560 -62784 -33152 -2144 82240 240000 185472 -43008 -45312 -107520 -57344 509952 716800 112640 -360448 -1527808 -2228224 -1089536 249856 -507904 -1769472 -2818048 -2752512 -1409024 1638400 6684672 10354688 7340032 2097152 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.65", "id": 513, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(73\\theta^4+122\\theta^3+96\\theta^2+35\\theta+5\\right)-2^{4} x^{2}\\left(134\\theta^4+2072\\theta^3+3924\\theta^2+2660\\theta+645\\right)-2^{6} x^{3}\\left(708\\theta^4+672\\theta^3-2898\\theta^2-3750\\theta-1285\\right)+2^{10} x^{4}\\left(110\\theta^4+700\\theta^3+498\\theta^2-56\\theta-105\\right)+2^{12} x^{5}\\left(61\\theta^4-266\\theta^3-544\\theta^2-373\\theta-88\\right)-2^{14} x^{6}\\left(86\\theta^4+168\\theta^3+172\\theta^2+108\\theta+31\\right)+2^{16} x^{7}\\left(32\\theta^4+112\\theta^3+158\\theta^2+102\\theta+25\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-24/5 -1608/5", "discriminant": "8 25 1460 -2144 -45312 112640 249856 -1409024 2097152 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5e457fa5807a784e24220c973aeceba8", "dim_h": null, "inst": " -24/5 329/10 -1608/5 48409/10 -455264/5 19503331/10 -228835848/5 5747617313/5 -152077212208/5 4192795689514/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2", "discr_factors": "-1048576, z-1/4, (-5/32-1/2*z+z^2)^2, z^3-3/4*z^2+7/32*z+1/256", "dm_basis": null, "q": "0 1 12 -34 -48 -6895 194376 -4884294 135726400 -3970197852", "yuk": "1 -24/5 1292/5 -8688 310076 -56908024/5 2106317624/5 -78490695888/5 2942781614636/5 -110864287743072/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/4-1/8*14^(1/2)","im":"0","approx_re":"-0.217707","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(189+33*33^(1/2))^(1/3)+1/4/(189+33*33^(1/2))^(1/3)+1/4","im":"0","approx_re":"-0.016861","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"-0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"-1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/8*14^(1/2)","im":"0","approx_re":"0.717707","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*X^4+96*X^3+92*X^2+44*X+8, -4096*X^4-50176*X^3-61952*X^2-28544*X-5248, 126976*X^4-122880*X^3-3571712*X^2-3280896*X-888832, -27525120*X^4-11796480*X^3+261881856*X^2+190906368*X+45416448, -809500672*X^4-8346664960*X^3-7846494208*X^2-1582301184*X+278921216, 3087007744*X^4+185623117824*X^3+156564979712*X^2+45097156608*X+1275068416, -2560874250240*X^4-4992899481600*X^3-3741990256640*X^2-1245540515840*X-150323855360, -1717986918400*(X+1)^4]", "text": "This is operator \"8.66\" from ...", "degz": 8, "h3": null, "sol": "1 -8 424 -6272 859816 2204992 2994022144 96187875328 15174775326376 906671921263552", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 8 44 92 96 -48 -5248 -28544 -61952 -50176 -4096 -888832 -3280896 -3571712 -122880 126976 45416448 190906368 261881856 -11796480 -27525120 278921216 -1582301184 -7846494208 -8346664960 -809500672 1275068416 45097156608 156564979712 185623117824 3087007744 -150323855360 -1245540515840 -3741990256640 -4992899481600 -2560874250240 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.66", "id": 514, "operator_tex": "\\theta^4-2^{2} x\\left(12\\theta^4-24\\theta^3-23\\theta^2-11\\theta-2\\right)-2^{7} x^{2}\\left(32\\theta^4+392\\theta^3+484\\theta^2+223\\theta+41\\right)+2^{12} x^{3}\\left(31\\theta^4-30\\theta^3-872\\theta^2-801\\theta-217\\right)-2^{16} 3 x^{4}\\left(140\\theta^4+60\\theta^3-1332\\theta^2-971\\theta-231\\right)-2^{20} x^{5}\\left(772\\theta^4+7960\\theta^3+7483\\theta^2+1509\\theta-266\\right)+2^{26} x^{6}\\left(46\\theta^4+2766\\theta^3+2333\\theta^2+672\\theta+19\\right)-2^{30} 5 x^{7}\\left(477\\theta^4+930\\theta^3+697\\theta^2+232\\theta+28\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 12332", "discriminant": "8 1 -48 -4096 126976 -27525120 -809500672 3087007744 -2560874250240 -1717986918400", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "d941d8e5d41f2e7285be47b4fbc81023", "dim_h": null, "inst": " 4 500 12332 358180 15491360 885685372 54935795244 3548002584068 239694499238576 16917401503904160", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2", "discr_factors": "-1717986918400, z+1/64, (1/2560-1/80*z+z^2)^2, z^3+3/2*z^2+3/256*z-1/4096", "dm_basis": null, "q": "0 1 12 -930 -52496 -1340883 -28378200 -2072239982 -209770968384 -17118246818298", "yuk": "1 4 4004 332968 22927524 1936420004 191308377320 18842977768696 1816577345970340 174737289945254872", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2+1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-1.492036","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2-1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.017379","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"-3/160","approx_re":"0.00625","approx_im":"-0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"3/160","approx_re":"0.00625","approx_im":"0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32*(-148+4*I*3^(1/2))^(1/3)+21/8/(-148+4*I*3^(1/2))^(1/3)-1/2","im":"0","approx_re":"0.009415","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 2385*X^4+4890*X^3+3845*X^2+1400*X+200, -184*X^4+10328*X^3+22756*X^2+16480*X+4160, 3088*X^4-19488*X^3-47060*X^2-29340*X-5920, 6720*X^4+24000*X^3-32256*X^2-63024*X-24576, -1984*X^4-9856*X^3+38144*X^2+46656*X+14528, 4096*X^4-33792*X^3-64000*X^2-38784*X-7424, 3072*X^4+18432*X^3+30976*X^2+21760*X+5632, -4096*(X+1)^4]", "text": "This is operator \"8.67\" from ...", "degz": 8, "h3": null, "sol": "1 -8 244 -11312 635716 -39929408 2696823424 -191699605952 14154070278916 -1076148551433248", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 200 1400 3845 4890 2385 4160 16480 22756 10328 -184 -5920 -29340 -47060 -19488 3088 -24576 -63024 -32256 24000 6720 14528 46656 38144 -9856 -1984 -7424 -38784 -64000 -33792 4096 5632 21760 30976 18432 3072 -4096 -16384 -24576 -16384 -4096", "new_number": "8.67", "id": 515, "operator_tex": "5^{2} \\theta^4+5 x\\left(477\\theta^4+978\\theta^3+769\\theta^2+280\\theta+40\\right)-2^{2} x^{2}\\left(46\\theta^4-2582\\theta^3-5689\\theta^2-4120\\theta-1040\\right)+2^{2} x^{3}\\left(772\\theta^4-4872\\theta^3-11765\\theta^2-7335\\theta-1480\\right)+2^{4} 3 x^{4}\\left(140\\theta^4+500\\theta^3-672\\theta^2-1313\\theta-512\\right)-2^{6} x^{5}\\left(31\\theta^4+154\\theta^3-596\\theta^2-729\\theta-227\\right)+2^{7} x^{6}\\left(32\\theta^4-264\\theta^3-500\\theta^2-303\\theta-58\\right)+2^{8} x^{7}\\left(12\\theta^4+72\\theta^3+121\\theta^2+85\\theta+22\\right)-2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-49/5 -5776/5", "discriminant": "8 25 2385 -184 3088 6720 -1984 4096 3072 -4096", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "807c6166f3d1991fadc5a93fdf4671e8", "dim_h": null, "inst": " -49/5 1441/20 -5776/5 26480 -748058 24136712 -4270429984/5 161744207422/5 -6453444686131/5 107320033012549/2", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(64z^3-48z^2-96z-1)(5-4z+8z^2)^2", "discr_factors": "-4096, z+1, z^3-3/4*z^2-3/2*z-1/64, (5/8-1/2*z+z^2)^2", "dm_basis": null, "q": "0 1 24 156 2084 -26214 1252560 -48593658 2064329352 -90975825645", "yuk": "1 -49/5 2833/5 -156001/5 8476433/5 -467536299/5 26067495841/5 -1464757484561/5 82813042676497/5 -940912235269100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(4+4*I*3^(1/2))^(1/3)-3/4/(4+4*I*3^(1/2))^(1/3)+1/4+1/8*I*3^(1/2)*(3/2*(4+4*I*3^(1/2))^(1/3)-6/(4+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.899067","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(4+4*I*3^(1/2))^(1/3)-3/4/(4+4*I*3^(1/2))^(1/3)+1/4-1/8*I*3^(1/2)*(3/2*(4+4*I*3^(1/2))^(1/3)-6/(4+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.010472","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"-3/4","approx_re":"0.25","approx_im":"-0.75","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"3/4","approx_re":"0.25","approx_im":"0.75","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8*(4+4*I*3^(1/2))^(1/3)+3/2/(4+4*I*3^(1/2))^(1/3)+1/4","im":"0","approx_re":"1.659539","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80*X^4-136*X^3-116*X^2-48*X-8, 2000*X^4+5792*X^3+7536*X^2+4544*X+1056, -24448*X^4-77568*X^3-109440*X^2-75264*X-19712, 196608*X^4+565248*X^3+575488*X^2+274432*X+50176, -1097728*X^4-3112960*X^3-3055616*X^2-1015808*X-24576, 3997696*X^4+9830400*X^3+11337728*X^2+6094848*X+1245184, -9961472*X^4-26214400*X^3-29360128*X^2-16252928*X-3670016, 8388608*(X+1)^4]", "text": "This is operator \"8.69\" from ...", "degz": 8, "h3": null, "sol": "1 8 128 2816 74896 2247808 73109504 2514939904 90124906768 3331662028928", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -8 -48 -116 -136 -80 1056 4544 7536 5792 2000 -19712 -75264 -109440 -77568 -24448 50176 274432 575488 565248 196608 -24576 -1015808 -3055616 -3112960 -1097728 1245184 6094848 11337728 9830400 3997696 -3670016 -16252928 -29360128 -26214400 -9961472 8388608 33554432 50331648 33554432 8388608", "new_number": "8.69", "id": 517, "operator_tex": "\\theta^4-2^{2} x\\left(20\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(125\\theta^4+362\\theta^3+471\\theta^2+284\\theta+66\\right)-2^{7} x^{3}\\left(191\\theta^4+606\\theta^3+855\\theta^2+588\\theta+154\\right)+2^{10} x^{4}\\left(192\\theta^4+552\\theta^3+562\\theta^2+268\\theta+49\\right)-2^{13} x^{5}\\left(134\\theta^4+380\\theta^3+373\\theta^2+124\\theta+3\\right)+2^{16} x^{6}\\left(61\\theta^4+150\\theta^3+173\\theta^2+93\\theta+19\\right)-2^{19} x^{7}\\left(19\\theta^4+50\\theta^3+56\\theta^2+31\\theta+7\\right)+2^{23} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 52", "discriminant": "8 1 -80 2000 -24448 196608 -1097728 3997696 -9961472 8388608", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e303d10e77a367612be2fb706f37b895", "dim_h": null, "inst": " 4 15/2 52 1563/2 7276 210627/2 1572452 97434231/4 409802336 14179335317/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2", "discr_factors": "8388608, z-1/8, z^2-3/4*z+1/64, z-1/16, (1/32-1/8*z+z^2)^2", "dm_basis": null, "q": "0 1 -16 160 -1536 10512 -79872 128512 -3670016 -65954024", "yuk": "1 4 64 1408 50080 909504 22749184 539351040 12471631648 298745904352", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"-1/16*7^(1/2)","approx_re":"0.0625","approx_im":"-0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"1/16*7^(1/2)","approx_re":"0.0625","approx_im":"0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(11*X^2+11*X+3), 1025*X^4+3992*X^3+5533*X^2+3082*X+615, -990*X^4+5940*X^3+18243*X^2+13581*X+3321, 18288*X^4+36576*X^3-24534*X^2-42822*X-12879, 8910*X^4+89100*X^3+49653*X^2-10125*X-9477, 83025*X^4+8748*X^3-23733*X^2+8748*X+8019, 729*(10*X^2+10*X+3)*(11*X^2+11*X+3), 6561*(X+1)^4]", "text": " Hadamard product $b \\ast c$.This operator has a second MUM-point at infinity with the same instanton numbers.\nIf can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 9 285 13671 799389 52360209 3691303071 274010100345 21132856450269 1678617004203261", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -63 -173 -220 -110 615 3082 5533 3992 1025 3321 13581 18243 5940 -990 -12879 -42822 -24534 36576 18288 -9477 -10125 49653 89100 8910 8019 8748 -23733 8748 83025 6561 45927 126117 160380 80190 6561 26244 39366 26244 6561", "new_number": "8.6", "id": 518, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(11\\theta^2+11\\theta+3)+x^{2}\\left(1025\\theta^4+3992\\theta^3+5533\\theta^2+3082\\theta+615\\right)-3^{2} x^{3}\\left(110\\theta^4-660\\theta^3-2027\\theta^2-1509\\theta-369\\right)+3^{2} x^{4}\\left(2032\\theta^4+4064\\theta^3-2726\\theta^2-4758\\theta-1431\\right)+3^{4} x^{5}\\left(110\\theta^4+1100\\theta^3+613\\theta^2-125\\theta-117\\right)+3^{4} x^{6}\\left(1025\\theta^4+108\\theta^3-293\\theta^2+108\\theta+99\\right)+3^{6} x^{7}(10\\theta^2+10\\theta+3)(11\\theta^2+11\\theta+3)+3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "11 1200", "discriminant": "8 1 -110 1025 -990 18288 8910 83025 80190 6561", "aesz": "113", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "3754b3cce7930e99efa8acb802e524bb", "dim_h": null, "inst": " 11 66 1200 28201 802124 78992543/3 945877209 36374793729 1473483691648 62194027520607", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2", "discr_factors": "6561, (1/9+z^2)^2, z^2+11*z-1, z^2+11/9*z-1/81", "dm_basis": null, "q": "0 1 -27 280 -4140 -5021 -1390509 -49445486 -2137442403 -96121662770", "yuk": "1 11 539 32411 1805403 100265511 5687496035 324435882698 18623896194651 1074169611243803", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/2-5/2*5^(1/2)","im":"0","approx_re":"-11.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18-5/18*5^(1/2)","im":"0","approx_re":"-1.232241","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/3","approx_re":"0.0","approx_im":"-0.333333333333","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/3","approx_re":"0.0","approx_im":"0.333333333333","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18+5/18*5^(1/2)","im":"0","approx_re":"0.010019","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/2+5/2*5^(1/2)","im":"0","approx_re":"0.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -304*X^4-416*X^3-320*X^2-112*X-16, 31232*X^4+48128*X^3+45568*X^2+24064*X+5120, -2195456*X^4-2555904*X^3-606208*X^2-294912*X-98304, 100663296*X^4+113246208*X^3+30408704*X^2-16777216*X-8912896, -3204448256*X^4-2650800128*X^3-3070230528*X^2-1140850688*X-100663296, 67108864000*X^4+74088185856*X^3+72477573120*X^2+38654705664*X+8589934592, -687194767360*X^4-1580547964928*X^3-1614907703296*X^2-824633720832*X-171798691840, 2199023255552*(X+1)^4]", "text": "This is operator \"8.70\" from ...", "degz": 8, "h3": null, "sol": "1 16 848 72448 7745296 937385216 122664279296 16939643629568 2433562089368848 360347222034278656", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -304 5120 24064 45568 48128 31232 -98304 -294912 -606208 -2555904 -2195456 -8912896 -16777216 30408704 113246208 100663296 -100663296 -1140850688 -3070230528 -2650800128 -3204448256 8589934592 38654705664 72477573120 74088185856 67108864000 -171798691840 -824633720832 -1614907703296 -1580547964928 -687194767360 2199023255552 8796093022208 13194139533312 8796093022208 2199023255552", "new_number": "8.70", "id": 519, "operator_tex": "\\theta^4-2^{4} x\\left(19\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{9} x^{2}\\left(61\\theta^4+94\\theta^3+89\\theta^2+47\\theta+10\\right)-2^{14} x^{3}\\left(134\\theta^4+156\\theta^3+37\\theta^2+18\\theta+6\\right)+2^{19} x^{4}\\left(192\\theta^4+216\\theta^3+58\\theta^2-32\\theta-17\\right)-2^{24} x^{5}\\left(191\\theta^4+158\\theta^3+183\\theta^2+68\\theta+6\\right)+2^{29} x^{6}\\left(125\\theta^4+138\\theta^3+135\\theta^2+72\\theta+16\\right)-2^{35} x^{7}\\left(20\\theta^4+46\\theta^3+47\\theta^2+24\\theta+5\\right)+2^{41} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 8608", "discriminant": "8 1 -304 31232 -2195456 100663296 -3204448256 67108864000 -687194767360 2199023255552", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "664bcad4360eb63fde0fdd3018aed2f2", "dim_h": null, "inst": " 32 504 8608 475061 28268384 1693799704 116319515424 8638470496671 670782321623808 54286844629652008", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2", "discr_factors": "2199023255552, z-1/32, z^2-3/16*z+1/1024, (1/2048-1/64*z+z^2)^2, z-1/16", "dm_basis": null, "q": "0 1 -48 704 -12288 -667984 -29815296 -2510217216 -221242556416 -18648433943400", "yuk": "1 32 4064 232448 30407968 3533548032 365860972544 39897593790464 4422896924703520 489000312463988480", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"-1/128*7^(1/2)","approx_re":"0.0078125","approx_im":"-0.02067","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"1/128*7^(1/2)","approx_re":"0.0078125","approx_im":"0.02067","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(11*X^2+11*X+3), 3856*X^4+15040*X^3+20848*X^2+11616*X+2320, -4224*X^4+25344*X^3+77696*X^2+58368*X+14976, 244736*X^4+489472*X^3-329728*X^2-574464*X-173056, 135168*X^4+1351680*X^3+757760*X^2-131072*X-151552, 3948544*X^4+393216*X^3-1163264*X^2+393216*X+376832, 131072*(3*X^2+3*X+1)*(11*X^2+11*X+3), 1048576*(X+1)^4]", "text": "Hadamard product $b\\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": "40", "sol": "1 12 380 16464 845676 48432912 2990911664 195076591680 13256109819628 929751677079312", "n_discr_factors": "3", "c3": "-30", "operator": "4 8 0 0 0 0 1 -12 -80 -212 -264 -132 2320 11616 20848 15040 3856 14976 58368 77696 25344 -4224 -173056 -574464 -329728 489472 244736 -151552 -131072 757760 1351680 135168 376832 393216 -1163264 393216 3948544 393216 2621440 6946816 8650752 4325376 1048576 4194304 6291456 4194304 1048576", "new_number": "8.7", "id": 529, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{4} x^{2}\\left(241\\theta^4+940\\theta^3+1303\\theta^2+726\\theta+145\\right)-2^{7} x^{3}\\left(33\\theta^4-198\\theta^3-607\\theta^2-456\\theta-117\\right)+2^{10} x^{4}\\left(239\\theta^4+478\\theta^3-322\\theta^2-561\\theta-169\\right)+2^{12} x^{5}\\left(33\\theta^4+330\\theta^3+185\\theta^2-32\\theta-37\\right)+2^{14} x^{6}\\left(241\\theta^4+24\\theta^3-71\\theta^2+24\\theta+23\\right)+2^{17} x^{7}(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 356", "discriminant": "8 1 -132 3856 -4224 244736 135168 3948544 4325376 1048576", "aesz": "106", "n_sing_complex": "2", "inst_int": "", "c2h": "76", "hash": "fe1c90929d18b81637eaaa93366409ed", "dim_h": "13", "inst": " 12 20 356 34561/4 161840 4245848 110102724 12708064929/4 95966999384 3019304295592", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2", "discr_factors": "1048576, z^2+11/8*z-1/64, z^2+11/4*z-1/16, (1/32+z^2)^2", "dm_basis": null, "q": "0 1 -32 638 -10784 128433 -1511040 1810202 -116066944 -8653279804", "yuk": "1 12 172 9624 553148 20230012 917112952 37765234344 1626632864060 69959942560560", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/8-5/8*5^(1/2)","im":"0","approx_re":"-2.772542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/8*2^(1/2)","approx_re":"0.0","approx_im":"-0.176777","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/8*2^(1/2)","approx_re":"0.0","approx_im":"0.176777","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/8+5/8*5^(1/2)","im":"0","approx_re":"0.022542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 1776*X^4+2976*X^3+2676*X^2+1188*X+216, 143872*X^4+394240*X^3+539008*X^2+346752*X+86400, 6897664*X^4+19955712*X^3+28913664*X^2+22007808*X+6266880, 239599616*X^4+649068544*X^3+671744000*X^2+366870528*X+78512128, 6039797760*X^4+16710107136*X^3+17632854016*X^2+5796528128*X-109051904, 107374182400*X^4+270582939648*X^3+359166640128*X^2+209379655680*X+44560285696, 1374389534720*X^4+3573412790272*X^3+4054449127424*X^2+2267742732288*X+515396075520, 8796093022208*(X+1)^4]", "text": "This is operator \"8.80\" from ...", "degz": 8, "h3": null, "sol": "1 -24 872 -37248 1740456 -86159424 4440663296 -235759116288 12803384026792 -707813470774464", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 216 1188 2676 2976 1776 86400 346752 539008 394240 143872 6266880 22007808 28913664 19955712 6897664 78512128 366870528 671744000 649068544 239599616 -109051904 5796528128 17632854016 16710107136 6039797760 44560285696 209379655680 359166640128 270582939648 107374182400 515396075520 2267742732288 4054449127424 3573412790272 1374389534720 8796093022208 35184372088832 52776558133248 35184372088832 8796093022208", "new_number": "8.80", "id": 530, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(148\\theta^4+248\\theta^3+223\\theta^2+99\\theta+18\\right)+2^{7} x^{2}\\left(1124\\theta^4+3080\\theta^3+4211\\theta^2+2709\\theta+675\\right)+2^{12} x^{3}\\left(1684\\theta^4+4872\\theta^3+7059\\theta^2+5373\\theta+1530\\right)+2^{17} x^{4}\\left(1828\\theta^4+4952\\theta^3+5125\\theta^2+2799\\theta+599\\right)+2^{23} x^{5}\\left(720\\theta^4+1992\\theta^3+2102\\theta^2+691\\theta-13\\right)+2^{29} x^{6}\\left(200\\theta^4+504\\theta^3+669\\theta^2+390\\theta+83\\right)+2^{35} x^{7}\\left(40\\theta^4+104\\theta^3+118\\theta^2+66\\theta+15\\right)+2^{43} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-28/3 2764/3", "discriminant": "8 9 1776 143872 6897664 239599616 6039797760 107374182400 1374389534720 8796093022208", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "01b1872abfd55652952ae535920a40fe", "dim_h": null, "inst": " -28/3 49/3 2764/3 13414 44384 -8885861/3 -81850300 -812021314 41589680432/3 2127578374856/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2", "discr_factors": "8796093022208, (z^2+1/64*z+3/2048)^2, z+1/16, (z+1/64)^2, z+1/32", "dm_basis": null, "q": "0 1 36 990 22224 397101 5031672 23346450 -740104128 -19032919290", "yuk": "1 -28/3 364/3 74600/3 2575852/3 16643972/3 -1919270984/3 -84223958728/3 -1247262162452/3 30318877109528/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"-1/128*23^(1/2)","approx_re":"-0.0078125","approx_im":"-0.037467","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"1/128*23^(1/2)","approx_re":"-0.0078125","approx_im":"0.037467","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 640*X^4+896*X^3+736*X^2+288*X+48, 204800*X^4+303104*X^3+365568*X^2+241664*X+59392, 47185920*X^4+58195968*X^3+29229056*X^2+27328512*X+8257536, 7667187712*X^4+9898557440*X^3+5188354048*X^2-390070272*X-834666496, 904090615808*X^4+1000727379968*X^3+1367410212864*X^2+464393338880*X+15032385536, 77240691851264*X^4+97306779058176*X^3+117853902602240*X^2+66589172957184*X+15187004358656, 3905465301860352*X^4+9077567998918656*X^3+9684498417451008*X^2+5145714417991680*X+1108307720798208, 81064793292668928*(X+1)^4]", "text": "This is operator \"8.81\" from ...", "degz": 8, "h3": null, "sol": "1 -48 4112 -470784 65066256 -10232187648 1761620390144 -323655077031936 62379658769915152 -12466167933398262528", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 48 288 736 896 640 59392 241664 365568 303104 204800 8257536 27328512 29229056 58195968 47185920 -834666496 -390070272 5188354048 9898557440 7667187712 15032385536 464393338880 1367410212864 1000727379968 904090615808 15187004358656 66589172957184 117853902602240 97306779058176 77240691851264 1108307720798208 5145714417991680 9684498417451008 9077567998918656 3905465301860352 81064793292668928 324259173170675712 486388759756013568 324259173170675712 81064793292668928", "new_number": "8.81", "id": 531, "operator_tex": "\\theta^4+2^{4} x\\left(40\\theta^4+56\\theta^3+46\\theta^2+18\\theta+3\\right)+2^{10} x^{2}\\left(200\\theta^4+296\\theta^3+357\\theta^2+236\\theta+58\\right)+2^{16} x^{3}\\left(720\\theta^4+888\\theta^3+446\\theta^2+417\\theta+126\\right)+2^{22} x^{4}\\left(1828\\theta^4+2360\\theta^3+1237\\theta^2-93\\theta-199\\right)+2^{29} x^{5}\\left(1684\\theta^4+1864\\theta^3+2547\\theta^2+865\\theta+28\\right)+2^{36} x^{6}\\left(1124\\theta^4+1416\\theta^3+1715\\theta^2+969\\theta+221\\right)+2^{43} 3 x^{7}\\left(148\\theta^4+344\\theta^3+367\\theta^2+195\\theta+42\\right)+2^{53} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 54464", "discriminant": "8 1 640 204800 47185920 7667187712 904090615808 77240691851264 3905465301860352 81064793292668928", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "3cc4cfea037192a297dc29928555ed1d", "dim_h": null, "inst": " -64 2380 54464 -1677212 -279711424 4006736476 880612121024 37648400346244 -5655979688414720 -187099219902460796", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2", "discr_factors": "81064793292668928, (z+1/64)^2, z+1/128, z+1/256, (z^2+1/384*z+1/24576)^2", "dm_basis": null, "q": "0 1 96 5088 112640 -6503376 -322993152 26322614784 2924519817216 -100541400198504", "yuk": "1 -64 18976 1470464 -107322592 -34963928064 865456568320 302049957511168 19275980869954336 -4123209192852860416", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"-1/768*23^(1/2)","approx_re":"-0.00130208333333","approx_im":"-0.006245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"1/768*23^(1/2)","approx_re":"-0.00130208333333","approx_im":"0.006245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X^2*(-1-2*X+107*X^2), 4800+20800*X+34276*X^2+23768*X^3+8696*X^4, -190080-604260*X-613836*X^2-152928*X^3+11088*X^4, -2115072-7610544*X-10054080*X^2-5688000*X^3-1016640*X^4, -13379904-41383872*X-44831232*X^2-20601216*X^3-4567104*X^4, -19968768-43390080*X-11736576*X^2+24634368*X^3+12358656*X^4, 39191040+151352064*X+204353280*X^2+106002432*X^3+12690432*X^4, -26873856*(X+1)^4]", "text": "This is operator \"8.84\" from ...", "degz": 8, "h3": null, "sol": "1 0 -12 144 324 -21600 182400 2116800 -59931900 239904000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 0 0 -5 -10 535 4800 20800 34276 23768 8696 -190080 -604260 -613836 -152928 11088 -2115072 -7610544 -10054080 -5688000 -1016640 -13379904 -41383872 -44831232 -20601216 -4567104 -19968768 -43390080 -11736576 24634368 12358656 39191040 151352064 204353280 106002432 12690432 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.84", "id": 534, "operator_tex": "5^{2} \\theta^4+5 x\\theta^2(-1-2\\theta+107\\theta^2)+2^{2} x^{2}\\left(2174\\theta^4+5942\\theta^3+8569\\theta^2+5200\\theta+1200\\right)+2^{2} 3^{2} x^{3}\\left(308\\theta^4-4248\\theta^3-17051\\theta^2-16785\\theta-5280\\right)-2^{4} 3^{2} x^{4}\\left(7060\\theta^4+39500\\theta^3+69820\\theta^2+52851\\theta+14688\\right)-2^{6} 3^{4} x^{5}\\left(881\\theta^4+3974\\theta^3+8648\\theta^2+7983\\theta+2581\\right)+2^{7} 3^{4} x^{6}\\left(1192\\theta^4+2376\\theta^3-1132\\theta^2-4185\\theta-1926\\right)+2^{8} 3^{6} x^{7}\\left(68\\theta^4+568\\theta^3+1095\\theta^2+811\\theta+210\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "1/5 224/5", "discriminant": "8 25 535 8696 11088 -1016640 -4567104 12358656 12690432 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "258fab6f0a4f132fe597fc6f30e54eea", "dim_h": null, "inst": " 1/5 -6 224/5 -448/5 -4334/5 162734/15 4944/5 -5368254/5 52756707/5 93552762/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2", "discr_factors": "-26873856, z-1/9, (-5/72-1/2*z+z^2)^2, z^3+23/36*z^2+1/36*z+1/576", "dm_basis": null, "q": "0 1 0 28 -324 1306 -6192 2566 -308712 9605779", "yuk": "1 1/5 -239/5 6049/5 -28911/5 -541749/5 11722657/5 1695793/5 -2748574959/5 38459645452/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216*(76276+3348*93^(1/2))^(1/3)-421/54/(76276+3348*93^(1/2))^(1/3)-23/108","im":"0","approx_re":"-0.597246","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4-1/12*19^(1/2)","im":"0","approx_re":"-0.113242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"-0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"-1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/12*19^(1/2)","im":"0","approx_re":"0.613242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-212*X-804*X^2-1184*X^3+272*X^4, -306176*X^3+7296+56192*X+141824*X^2-152576*X^4, -5640192-33730560*X-74170368*X^2+16588800*X^3-32477184*X^4, -2047279104*X+4164157440*X^4-6641418240*X^3-461832192-3727687680*X^2, -84085309440-283766685696*X-208854319104*X^2+465441914880*X^3+26159874048*X^4, -11817468297216*X^4-14970242727936*X^3-15263776899072*X-20585442705408*X^2-4354090205184, 3913788948480*(107*X^2+216*X+108)*(X+1)^2, -11271712171622400*(X+1)^4]", "text": "This is operator \"8.85\" from ...", "degz": 8, "h3": null, "sol": "1 24 2472 412800 83283624 18774633024 4554940413696 1163856179847168 309041211448837800 84530694901570627776", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -24 -212 -804 -1184 272 7296 56192 141824 -306176 -152576 -5640192 -33730560 -74170368 16588800 -32477184 -461832192 -2047279104 -3727687680 -6641418240 4164157440 -84085309440 -283766685696 -208854319104 465441914880 26159874048 -4354090205184 -15263776899072 -20585442705408 -14970242727936 -11817468297216 422689206435840 1690756825743360 2532221449666560 1682929247846400 418775417487360 -11271712171622400 -45086848686489600 -67630273029734400 -45086848686489600 -11271712171622400", "new_number": "8.85", "id": 535, "operator_tex": "\\theta^4+2^{2} x\\left(68\\theta^4-296\\theta^3-201\\theta^2-53\\theta-6\\right)-2^{7} x^{2}\\left(1192\\theta^4+2392\\theta^3-1108\\theta^2-439\\theta-57\\right)-2^{12} 3^{2} x^{3}\\left(881\\theta^4-450\\theta^3+2012\\theta^2+915\\theta+153\\right)+2^{16} 3^{2} x^{4}\\left(7060\\theta^4-11260\\theta^3-6320\\theta^2-3471\\theta-783\\right)+2^{20} 3^{4} x^{5}\\left(308\\theta^4+5480\\theta^3-2459\\theta^2-3341\\theta-990\\right)-2^{26} 3^{4} x^{6}\\left(2174\\theta^4+2754\\theta^3+3787\\theta^2+2808\\theta+801\\right)+2^{30} 3^{6} 5 x^{7}(107\\theta^2+216\\theta+108)(\\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "196 1986884/3", "discriminant": "8 1 272 -152576 -32477184 4164157440 26159874048 -11817468297216 418775417487360 -11271712171622400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "d959f61fe3ba327116d3bae5ae5a0ade", "dim_h": null, "inst": " 196 -5988 1986884/3 -62128884 8854857504 -1146735352140 183415180420716 -27611245050623892 14126021120260010768/3 -772678094092466100512", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2", "discr_factors": "-11271712171622400, (-1/23040-1/80*z+z^2)^2, z+1/64, z^3-1/36*z^2+23/20736*z-1/331776", "dm_basis": null, "q": "0 1 -116 10846 -1487120 215580205 -35627325272 5931431854738 -1059924964623680 189652857748496902", "yuk": "1 196 -47708 17882152 -3976296284 1106857188196 -247694818227992 62911406884305784 -14136957469895728988 3432623132223200498776", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160-1/480*19^(1/2)","im":"0","approx_re":"-0.002831","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/864*(1828+372*93^(1/2))^(1/3)+53/216/(1828+372*93^(1/2))^(1/3)+1/108","im":"0","approx_re":"0.002907","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"-0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"-1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160+1/480*19^(1/2)","im":"0","approx_re":"0.015331","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1225*X^4, -7350-50225*X-135310*X^2-170170*X^3-112805*X^4, -6440+193270*X+1217171*X^2+2477628*X^3+1818051*X^4, -1075200-5053440*X-11478624*X^2-16097136*X^3-11951280*X^4, 11346176+45483520*X+75485376*X^2+70855552*X^3+39597248*X^4, -55123968-207126528*X-299452416*X^2-213430272*X^3-79276032*X^4, 128319488+476774400*X+659849216*X^2+411893760*X^3+108888064*X^4, -1048576*(X+1)*(99+295*X+286*X^2+88*X^3), 33554432*(X+1)^4]", "text": "This is operator \"8.86\" from ...", "degz": 8, "h3": null, "sol": "1 6 146 5280 229986 11172756 583080896 32009360256 1824641280610 107082373667676", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1225 -7350 -50225 -135310 -170170 -112805 -6440 193270 1217171 2477628 1818051 -1075200 -5053440 -11478624 -16097136 -11951280 11346176 45483520 75485376 70855552 39597248 -55123968 -207126528 -299452416 -213430272 -79276032 128319488 476774400 659849216 411893760 108888064 -103809024 -413138944 -609222656 -392167424 -92274688 33554432 134217728 201326592 134217728 33554432", "new_number": "8.86", "id": 536, "operator_tex": "5^{2} 7^{2} \\theta^4-5 7 x\\left(3223\\theta^4+4862\\theta^3+3866\\theta^2+1435\\theta+210\\right)-x^{2}\\left(6440-193270\\theta-1217171\\theta^2-2477628\\theta^3-1818051\\theta^4\\right)-2^{4} 3 x^{3}\\left(248985\\theta^4+335357\\theta^3+239138\\theta^2+105280\\theta+22400\\right)+2^{6} x^{4}\\left(618707\\theta^4+1107118\\theta^3+1179459\\theta^2+710680\\theta+177284\\right)-2^{11} 3 x^{5}\\left(12903\\theta^4+34738\\theta^3+48739\\theta^2+33712\\theta+8972\\right)+2^{15} x^{6}\\left(3323\\theta^4+12570\\theta^3+20137\\theta^2+14550\\theta+3916\\right)-2^{20} x^{7}(\\theta+1)(99+295\\theta+286\\theta^2+88\\theta^3)+2^{25} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "226/35 3959/7", "discriminant": "8 1225 -112805 1818051 -11951280 39597248 -79276032 108888064 -92274688 33554432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "815127e123ce989d9ab793a009bb2e6a", "dim_h": null, "inst": " 226/35 1599/35 3959/7 51101/5 8052703/35 206397733/35 5799307242/35 34883328863/7 5526085914583/35 182437558747622/35", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(1-77z+251z^2-352z^3+512z^4)(32z-5)^2(8z-7)^2", "discr_factors": "33554432, 1/512-77/512*z+251/512*z^2-11/16*z^3+z^4, (z-5/32)^2, (z-7/8)^2", "dm_basis": null, "q": "0 1 -17 32 -441 -14093 -420462 -13144910 -441450597 -15446509960", "yuk": "1 226/35 13018/35 534691/35 22906266/35 1006588101/35 44582457811/35 1989162384232/35 89301344795546/35 4028516632265698/35", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"5/32","im":"0","approx_re":"0.15625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"7/8","im":"0","approx_re":"0.875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(11*X^2+11*X+3), 3294*X^4+12852*X^3+17820*X^2+9936*X+1989, -2673*X^4+16038*X^3+49167*X^2+36936*X+9477, 176418*X^4+352836*X^3-237654*X^2-414072*X-125145, 72171*X^4+721710*X^3+404595*X^2-69984*X-80919, 2401326*X^4+236196*X^3-708588*X^2+236196*X+229635, 59049*(3*X^2+3*X+1)*(11*X^2+11*X+3), 531441*(X+1)^4]", "text": "Hadamard product $b \\qst f$. This operator has a second MUM-point at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{\\})$", "degz": 8, "h3": null, "sol": "1 9 171 3087 11259 -3342141 -254105739 -12988702431 -513268445637 -14081616379629", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -60 -159 -198 -99 1989 9936 17820 12852 3294 9477 36936 49167 16038 -2673 -125145 -414072 -237654 352836 176418 -80919 -69984 404595 721710 72171 229635 236196 -708588 236196 2401326 177147 1180980 3129597 3897234 1948617 531441 2125764 3188646 2125764 531441", "new_number": "8.8", "id": 537, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+3^{2} x^{2}\\left(366\\theta^4+1428\\theta^3+1980\\theta^2+1104\\theta+221\\right)-3^{4} x^{3}\\left(33\\theta^4-198\\theta^3-607\\theta^2-456\\theta-117\\right)+3^{5} x^{4}\\left(726\\theta^4+1452\\theta^3-978\\theta^2-1704\\theta-515\\right)+3^{7} x^{5}\\left(33\\theta^4+330\\theta^3+185\\theta^2-32\\theta-37\\right)+3^{8} x^{6}\\left(366\\theta^4+36\\theta^3-108\\theta^2+36\\theta+35\\right)+3^{10} x^{7}(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "9 -1229/3", "discriminant": "8 1 -99 3294 -2673 176418 72171 2401326 1948617 531441", "aesz": "161", "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "641d1de9a6564241575c5db52faef694", "dim_h": null, "inst": " 9 -81/4 -1229/3 -4644 -26685 13063453/12 36204768 546978924 -2609884270 -1560871855179/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(729z^4+2673z^3+3240z^2-99z+1)(1+27z^2)^2", "discr_factors": "531441, (1/27+z^2)^2, z^4+11/3*z^3+40/9*z^2-11/81*z+1/729", "dm_basis": null, "q": "0 1 -24 486 -6104 77451 -758808 15116 -62802120 -642731841", "yuk": "1 9 -153 -11052 -297369 -3335616 235130940 12418235433 280052911719 -1902605643882", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 2)","im":"0","approx_re":"-1.848362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 3)","im":"0","approx_re":"-1.848362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/9*3^(1/2)","approx_re":"0.0","approx_im":"-0.19245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/9*3^(1/2)","approx_re":"0.0","approx_im":"0.19245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 1)","im":"0","approx_re":"0.015028","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 4)","im":"0","approx_re":"0.015028","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(11*X^2+11*X+3)*(17*X^2+17*X+6), 8711*X^4+33980*X^3+47095*X^2+26230*X+5232, -13464*X^4+80784*X^3+247392*X^2+186840*X+49248, 1244016*X^4+2488032*X^3-1677600*X^2-2921616*X-878688, 969408*X^4+9694080*X^3+5453568*X^2-844992*X-1119744, 45157824*X^4+4478976*X^3-13369536*X^2+4478976*X+4292352, 373248*(11*X^2+11*X+3)*(17*X^2+17*X+6), 26873856*(X+1)^4]", "text": "Hadamard product $ b \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "60", "sol": "1 18 798 45864 2994894 211061268 15653165424 1204397092224 95293403750862 7707665811006252", "n_discr_factors": "3", "c3": "100", "operator": "4 8 0 0 0 0 1 -18 -117 -304 -374 -187 5232 26230 47095 33980 8711 49248 186840 247392 80784 -13464 -878688 -2921616 -1677600 2488032 1244016 -1119744 -844992 5453568 9694080 969408 4292352 4478976 -13369536 4478976 45157824 6718464 43670016 113467392 139594752 69797376 26873856 107495424 161243136 107495424 26873856", "new_number": "8.9", "id": 538, "operator_tex": "\\theta^4-x(11\\theta^2+11\\theta+3)(17\\theta^2+17\\theta+6)+x^{2}\\left(8711\\theta^4+33980\\theta^3+47095\\theta^2+26230\\theta+5232\\right)-2^{3} 3^{2} x^{3}\\left(187\\theta^4-1122\\theta^3-3436\\theta^2-2595\\theta-684\\right)+2^{4} 3^{2} x^{4}\\left(8639\\theta^4+17278\\theta^3-11650\\theta^2-20289\\theta-6102\\right)+2^{6} 3^{4} x^{5}\\left(187\\theta^4+1870\\theta^3+1052\\theta^2-163\\theta-216\\right)+2^{6} 3^{4} x^{6}\\left(8711\\theta^4+864\\theta^3-2579\\theta^2+864\\theta+828\\right)+2^{9} 3^{6} x^{7}(11\\theta^2+11\\theta+3)(17\\theta^2+17\\theta+6)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "16 -13", "discriminant": "8 1 -187 8711 -13464 1244016 969408 45157824 69797376 26873856", "aesz": "174", "n_sing_complex": "2", "inst_int": "", "c2h": "84", "hash": "3f987b46d9ebf201eeead1a885b78e66", "dim_h": "17", "inst": " 16 7/2 -13 11663/2 -26414 18325639/12 8541579 887994147/2 10885529907 212926469048", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z^2+99z-1)(64z^2+88z-1)(1+72z^2)^2", "discr_factors": "26873856, z^2+11/9*z-1/81, (1/72+z^2)^2, z^2+11/8*z-1/64", "dm_basis": null, "q": "0 1 -45 1351 -31167 567874 -7815141 54690823 918281991 -49549032218", "yuk": "1 16 44 -335 373260 -3301734 329861195 2929761613 227326874892 7935551301868", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18-5/18*5^(1/2)","im":"0","approx_re":"-1.232241","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18+5/18*5^(1/2)","im":"0","approx_re":"0.010019","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -57*X^4-116*X^3-84*X^2-26*X-3, -1788*X^4-6416*X^3-9142*X^2-5542*X-1302, -14644*X^4-112736*X^3-249566*X^2-202198*X-59514, 125406*X^4-487440*X^3-2519838*X^2-2493126*X-815346, 2853954*X^4+7949016*X^3-5063310*X^2-12942666*X-5601636, 14198004*X^4+109699920*X^3+104542974*X^2+18882558*X-10143306, -70150212*X^4+306110016*X^3+547384230*X^2+322053246*X+54915570, -990074583*X^4-2066242608*X^3-1807962282*X^2-774840978*X-143489070, -3486784401*(X+1)^4]", "text": "This is operator \"9.3\" from ...", "degz": 9, "h3": null, "sol": "1 3 135 5349 258039 13868253 798329169 48299457195 3032418099447 195934418454837", "n_discr_factors": "3", "c3": null, "operator": "4 9 0 0 0 0 1 -3 -26 -84 -116 -57 -1302 -5542 -9142 -6416 -1788 -59514 -202198 -249566 -112736 -14644 -815346 -2493126 -2519838 -487440 125406 -5601636 -12942666 -5063310 7949016 2853954 -10143306 18882558 104542974 109699920 14198004 54915570 322053246 547384230 306110016 -70150212 -143489070 -774840978 -1807962282 -2066242608 -990074583 -3486784401 -13947137604 -20920706406 -13947137604 -3486784401", "new_number": "9.3", "id": 542, "operator_tex": "\\theta^4-x\\left(57\\theta^4+116\\theta^3+84\\theta^2+26\\theta+3\\right)-2 x^{2}\\left(894\\theta^4+3208\\theta^3+4571\\theta^2+2771\\theta+651\\right)-2 x^{3}\\left(7322\\theta^4+56368\\theta^3+124783\\theta^2+101099\\theta+29757\\right)+2 3^{2} x^{4}\\left(6967\\theta^4-27080\\theta^3-139991\\theta^2-138507\\theta-45297\\right)+2 3^{4} x^{5}\\left(17617\\theta^4+49068\\theta^3-31255\\theta^2-79893\\theta-34578\\right)+2 3^{8} x^{6}\\left(1082\\theta^4+8360\\theta^3+7967\\theta^2+1439\\theta-773\\right)-2 3^{11} x^{7}\\left(198\\theta^4-864\\theta^3-1545\\theta^2-909\\theta-155\\right)-3^{15} x^{8}\\left(69\\theta^4+144\\theta^3+126\\theta^2+54\\theta+10\\right)-3^{20} x^{9}\\left((\\theta+1)^4\\right)", "superseek": "10 3394/3", "discriminant": "9 1 -57 -1788 -14644 125406 2853954 14198004 -70150212 -990074583 -3486784401", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "40e3715abcc5c4cb07e700ca79f80abf", "dim_h": null, "inst": " 10 77 3394/3 24029 640402 58912007/3 659800738 23733455789 2698636083688/3 35532268316211", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3", "discr_factors": "-3486784401, -1/81+z, (-1/9+z)^2, (z^2+14/81*z+1/81)^3", "dm_basis": null, "q": "0 1 -14 -135 -458 -22038 -1292652 -48153487 -1891905026 -78912224514", "yuk": "1 10 626 30556 1538482 80050260 4241695676 226311653144 12151530902450 655768568366740", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/81","im":"-4/81*2^(1/2)","approx_re":"-0.0864197530864","approx_im":"-0.069838","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/81","im":"4/81*2^(1/2)","approx_re":"-0.0864197530864","approx_im":"0.069838","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 621*X^4+1188*X^3+972*X^2+378*X+63, 96228*X^4+804816*X^3+1086210*X^2+584658*X+131706, -42594012*X^4+158723712*X^3+418106286*X^2+246313062*X+59954418, -18724792194*X^4-22745674800*X^3+77332105674*X^2+63085235346*X+18484580862, -1799439031242*X^4-14191987353048*X^3+4377593245374*X^2+8359759311642*X+3288941671284, 459544236914196*X^4-1699598188423440*X^3-24414464375802*X^2+542955093354918*X+275839513963110, 122711114728410804*X^4+50511957740553888*X^3+42688094720957226*X^2+44335223777714418*X+18804723397977942, 8555394211928949897*X^4+16810599153263901552*X^3+11707381553165931438*X^2+3302081976533980662*X+300189270593998242, -328256967394537077627*(X+1)^4]", "text": "This is operator \"9.4\" from ...", "degz": 9, "h3": null, "sol": "1 -63 4455 34551 -114913161 30602620287 -5040143263791 399712092845625 73215019075182327 -39771176551496250777", "n_discr_factors": "3", "c3": null, "operator": "4 9 0 0 0 0 1 63 378 972 1188 621 131706 584658 1086210 804816 96228 59954418 246313062 418106286 158723712 -42594012 18484580862 63085235346 77332105674 -22745674800 -18724792194 3288941671284 8359759311642 4377593245374 -14191987353048 -1799439031242 275839513963110 542955093354918 -24414464375802 -1699598188423440 459544236914196 18804723397977942 44335223777714418 42688094720957226 50511957740553888 122711114728410804 300189270593998242 3302081976533980662 11707381553165931438 16810599153263901552 8555394211928949897 -328256967394537077627 -1313027869578148310508 -1969541804367222465762 -1313027869578148310508 -328256967394537077627", "new_number": "9.4", "id": 543, "operator_tex": "\\theta^4+3^{2} x\\left(69\\theta^4+132\\theta^3+108\\theta^2+42\\theta+7\\right)+2 3^{5} x^{2}\\left(198\\theta^4+1656\\theta^3+2235\\theta^2+1203\\theta+271\\right)-2 3^{9} x^{3}\\left(1082\\theta^4-4032\\theta^3-10621\\theta^2-6257\\theta-1523\\right)-2 3^{12} x^{4}\\left(17617\\theta^4+21400\\theta^3-72757\\theta^2-59353\\theta-17391\\right)-2 3^{17} x^{5}\\left(6967\\theta^4+54948\\theta^3-16949\\theta^2-32367\\theta-12734\\right)+2 3^{22} x^{6}\\left(7322\\theta^4-27080\\theta^3-389\\theta^2+8651\\theta+4395\\right)+2 3^{29} x^{7}\\left(894\\theta^4+368\\theta^3+311\\theta^2+323\\theta+137\\right)+3^{36} x^{8}\\left(57\\theta^4+112\\theta^3+78\\theta^2+22\\theta+2\\right)-3^{43} x^{9}\\left((\\theta+1)^4\\right)", "superseek": "-90 -413926", "discriminant": "9 1 621 96228 -42594012 -18724792194 -1799439031242 459544236914196 122711114728410804 8555394211928949897 -328256967394537077627", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e2329b2f9cd1e3f65d29644e6ce39d24", "dim_h": null, "inst": " -90 -8685/2 -413926 -38862153 -4502063682 -1160798198855/2 -78997404823794 -11316942525045753 -1684968614368188280 -516710619226734930693/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+27z)(-1+243z)^2(59049z^2+378z+1)^3", "discr_factors": "-328256967394537077627, -1/27+z, (z^2+14/2187*z+1/59049)^3, (-1/243+z)^2", "dm_basis": null, "q": "0 1 126 18873 2482170 359156970 54095097996 8455289580657 1363385621250162 225172657035540990", "yuk": "1 -90 -34830 -11176092 -2487212622 -562757960340 -125366216687172 -27096109854561432 -5794274575310638158 -1228342119874420432212", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/2187","im":"-4/2187*2^(1/2)","approx_re":"-0.00320073159579","approx_im":"-0.002587","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/2187","im":"4/2187*2^(1/2)","approx_re":"-0.00320073159579","approx_im":"0.002587","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2*X*(-2-13*X-22*X^2+88*X^3), 1024+5224*X+9460*X^2+2888*X^3+13292*X^4, 103872+535872*X+1053264*X^2+809952*X^3+619344*X^4, 5044864+25654784*X+50251104*X^2+43766720*X^3+19798624*X^4, 107344896+557360640*X+1116636672*X^2+1014655488*X^3+382440960*X^4, 732946432+4260642816*X+9610430464*X^2+9819291648*X^3+3723368448*X^4, 4596695040+21116354560*X+39535247360*X^2+36837785600*X^3+14785576960*X^4, 10276044800*(X+1)^4]", "text": "This is operator \"8.87\" from ...", "degz": 8, "h3": null, "sol": "1 0 -64 576 22716 -619200 -8224000 610579200 -1406876975 -552144348000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 0 -4 -26 -44 176 1024 5224 9460 2888 13292 103872 535872 1053264 809952 619344 5044864 25654784 50251104 43766720 19798624 107344896 557360640 1116636672 1014655488 382440960 732946432 4260642816 9610430464 9819291648 3723368448 4596695040 21116354560 39535247360 36837785600 14785576960 10276044800 41104179200 61656268800 41104179200 10276044800", "new_number": "8.87", "id": 549, "operator_tex": "\\theta^4+2 x\\theta(-2-13\\theta-22\\theta^2+88\\theta^3)+2^{2} x^{2}\\left(3323\\theta^4+722\\theta^3+2365\\theta^2+1306\\theta+256\\right)+2^{4} 3 x^{3}\\left(12903\\theta^4+16874\\theta^3+21943\\theta^2+11164\\theta+2164\\right)+2^{5} x^{4}\\left(618707\\theta^4+1367710\\theta^3+1570347\\theta^2+801712\\theta+157652\\right)+2^{9} 3 x^{5}\\left(248985\\theta^4+660583\\theta^3+726977\\theta^2+362865\\theta+69886\\right)+2^{11} x^{6}\\left(1818051\\theta^4+4794576\\theta^3+4692593\\theta^2+2080392\\theta+357884\\right)+2^{17} 5 7 x^{7}\\left(3223\\theta^4+8030\\theta^3+8618\\theta^2+4603\\theta+1002\\right)+2^{23} 5^{2} 7^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "10 18994/9", "discriminant": "8 1 176 13292 619344 19798624 382440960 3723368448 14785576960 10276044800", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "038b62cbc5b6e43ac232ededcc3b6a59", "dim_h": null, "inst": " 10 -581/4 18994/9 -274969/8 3458142/5 -632204633/36 24611861082/49 -3756728769411/256 34809504792187/81 -1289173855159147/100", "cleanlist": "True", "n_sing_real": "0", "sol_explicit": "", "n_sing_rational": "0", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+44z+2008z^2+39424z^3+32768z^4)(10z+1)^2(56z+1)^2", "discr_factors": "10276044800, (z+1/10)^2, 1/32768+11/8192*z+251/4096*z^2+77/64*z^3+z^4, (z+1/56)^2", "dm_basis": null, "q": "0 1 -4 248 -5504 134228 -3444960 98469408 -3061476864 196840604563/2", "yuk": "1 10 -1152 56992 -2200904 86453560 -3793171968 172283027584 -7513459739726 313285543186675", "gv2": null, "gv0": null, "gv1": null, 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