{"count": 18, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(3*X^2+3*X+1), -16*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "A-Incarnation: (1,1) and (2,2) intersection in $P^3 \\times P^3$", "degz": 2, "h3": "40", "sol": "1 4 108 3280 126700 5355504 243791856 11651694912 578075329260 29514351895600", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -4 -28 -76 -96 -48 -720 -3456 -5824 -4096 -1024", "new_number": "2.60", "id": 56, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)-2^{4} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "4 364", "discriminant": "2 1 -48 -1024", "aesz": "18", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "bb479f8a4185bf4a943dba2d433e13e5", "dim_h": "14", "inst": " 4 39 364 6800 662416/5 3162589 80141644 2204992496 63488383784 9551133342652/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(64z-1)", "discr_factors": "-1024, z-1/64, z+1/16", "dm_basis": ["-310145437/500000000*I", "31/3", "1", "1", "-11/3", "-20", "-1", "0", "0", "40", "0", "0", "-40", "0", "0", "0"], "q": "0 1 -12 -90 848 -14079 -313608 -8135374 -247756992 -8049920748", "yuk": "1 4 316 9832 435516 16560404 683129368 27488583896 1128956593468 46283031788368", "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":["5.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+1.240581747*I","-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874*I",".83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556+.237778168*I","-.215484184-.13439635535307517084282460136674259681093394077448747152619589977220956719817767653758542141230068337129840546697038724373576309794988610478359908883826879271070615034168564920273348519362186788154897*I","46/3","-20/3","529/180","-.83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556-.237778168*I","40","-20","26/3","-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874*I","80","-40","46/3","-10/3-256*lambda"],"monodromy_dm":["-7","-56","-3","-2","4","29","3/2","1","-112","-784","-41","-28","88","616","33","23"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","40","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0",".56859997e-1*I",".9619019e-2","11/3","1","121/360","-.56859997e-1*I","0","0","1","0","40","0","11/3","1.-.620290874*I"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"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": "[529*X^4, -21183*X^4-47058*X^3-37812*X^2-14283*X-2116, -380851*X^4-1328584*X^3-1772673*X^2-1033528*X-221168, -951722*X^4-2620344*X^3-2057582*X^2-417864*X+54464, -603364*X^4-953360*X^3-349452*X^2+113152*X+66368, 6936*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.2\" from ...", "degz": 5, "h3": "46", "sol": "1 4 84 2200 71140 2541504 97536936 3933223536 164621744100 7091115631600", "n_discr_factors": "3", "c3": "-106", "operator": "4 5 0 0 0 0 529 -2116 -14283 -37812 -47058 -21183 -221168 -1033528 -1772673 -1328584 -380851 54464 -417864 -2057582 -2620344 -951722 66368 113152 -349452 -953360 -603364 55488 235824 367608 249696 62424", "new_number": "5.2", "id": 238, "operator_tex": "23^{2} \\theta^4-23 x\\left(921\\theta^4+2046\\theta^3+1644\\theta^2+621\\theta+92\\right)-x^{2}\\left(380851\\theta^4+1328584\\theta^3+1772673\\theta^2+1033528\\theta+221168\\right)-2 x^{3}\\left(475861\\theta^4+1310172\\theta^3+1028791\\theta^2+208932\\theta-27232\\right)-2^{2} 17 x^{4}\\left(8873\\theta^4+14020\\theta^3+5139\\theta^2-1664\\theta-976\\right)+2^{3} 3 17^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "80/23 4655/23", "discriminant": "5 529 -21183 -380851 -951722 -603364 62424", "aesz": "19", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "4532f44d62f644bf66aa7b153d4f5c5a", "dim_h": "15", "inst": " 80/23 1157/46 4655/23 71184/23 1156690/23 22723282/23 477652417/23 10851707552/23 258585745581/23 12862622382465/46", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(54z-1)(z^2-11z-1)(23+34z)^2", "discr_factors": "62424, (23/34+z)^2, z-1/54, z^2-11*z-1", "dm_basis": null, "q": "0 1 -11 -37 371 -7540 -102111 -2527917 -63499383 -1687775155", "yuk": "1 80/23 4708/23 125765/23 4560484/23 144586330/23 4908359305/23 163834779111/23 5556078827108/23 188509008654314/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-23/34","im":"0","approx_re":"-0.676470588235","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":"1/54","im":"0","approx_re":"0.0185185185185","approx_im":"0.0","exponents":["0","1","1","2"],"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":["2/3","1","1","4/3"],"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": "[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": "[169*X^4, -4251*X^4-13494*X^3-11141*X^2-4394*X-676, -205568*X^4-672128*X^3-833312*X^2-456768*X-91312, -249856*X^4+3833856*X^3+12986368*X^2+11821056*X+3168256, 65536*(2*X+1)*(76*X^3+426*X^2+570*X+227), 8388608*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.80\" from ...", "degz": 5, "h3": "52", "sol": "1 4 84 1840 56980 1827504 65127216 2403800256 92748607380 3672378870160", "n_discr_factors": "2", "c3": "-144", "operator": "4 5 0 0 0 0 169 -676 -4394 -11141 -13494 -4251 -91312 -456768 -833312 -672128 -205568 3168256 11821056 12986368 3833856 -249856 14876672 67108864 102629376 60817408 9961472 25165824 117440512 192937984 134217728 33554432", "new_number": "5.80", "id": 294, "operator_tex": "13^{2} \\theta^4-13 x\\left(327\\theta^4+1038\\theta^3+857\\theta^2+338\\theta+52\\right)-2^{4} x^{2}\\left(12848\\theta^4+42008\\theta^3+52082\\theta^2+28548\\theta+5707\\right)-2^{11} x^{3}\\left(122\\theta^4-1872\\theta^3-6341\\theta^2-5772\\theta-1547\\right)+2^{16} x^{4}(2\\theta+1)(76\\theta^3+426\\theta^2+570\\theta+227)+2^{23} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "25/13 875/13", "discriminant": "5 169 -4251 -205568 -249856 9961472 33554432", "aesz": "311", "n_sing_complex": "3", "inst_int": "", "c2h": "100", "hash": "8219f3f4bd56f6c2b2cc3ab9093b65d1", "dim_h": "17", "inst": " 25/13 1359/52 875/13 36572/13 256800/13 34500709/52 104613534/13 3142545372/13 51341929900/13 1458903910460/13", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(8192z^3-896z^2-35z+1)(13+64z)^2", "discr_factors": "33554432, (13/64+z)^2, z^3-7/64*z^2-35/8192*z+1/8192", "dm_basis": null, "q": "0 1 -10 -61 1328 -19755 61538 -2237427 -17950176 -1074578897", "yuk": "1 25/13 211 23650/13 2343351/13 32100025/13 1863064654/13 35882442187/13 1608985573815/13 37428266920750/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/64","im":"0","approx_re":"-0.203125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(3698+474*I*237^(1/2))^(1/3)-203/384/(3698+474*I*237^(1/2))^(1/3)+7/192+1/2*I*3^(1/2)*(1/384*(3698+474*I*237^(1/2))^(1/3)-203/192/(3698+474*I*237^(1/2))^(1/3))","im":"0","approx_re":"-0.045147","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":"-1/768*(3698+474*I*237^(1/2))^(1/3)-203/384/(3698+474*I*237^(1/2))^(1/3)+7/192-1/2*I*3^(1/2)*(1/384*(3698+474*I*237^(1/2))^(1/3)-203/192/(3698+474*I*237^(1/2))^(1/3))","im":"0","approx_re":"0.020117","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3698+474*I*237^(1/2))^(1/3)+203/192/(3698+474*I*237^(1/2))^(1/3)+7/192","im":"0","approx_re":"0.134405","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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -1719*X^4-7758*X^3-6147*X^2-2268*X-324, -231200*X^4-794720*X^3-980288*X^2-517536*X-98208, -3392256*X^4-9179136*X^3-7076096*X^2-1783296*X-46080, -20480*(2*X+1)*(314*X^3+363*X^2+68*X-31), 1638400*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.87\" from ...", "degz": 5, "h3": "36", "sol": "1 4 132 4000 179620 8127504 412976256 21605895168 1184481569700 66548256071440", "n_discr_factors": "3", "c3": "-128", "operator": "4 5 0 0 0 0 81 -324 -2268 -6147 -7758 -1719 -98208 -517536 -980288 -794720 -231200 -46080 -1783296 -7076096 -9179136 -3392256 634880 -122880 -10219520 -21299200 -12861440 4915200 22937600 37683200 26214400 6553600", "new_number": "5.87", "id": 301, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(191\\theta^4+862\\theta^3+683\\theta^2+252\\theta+36\\right)-2^{5} x^{2}\\left(7225\\theta^4+24835\\theta^3+30634\\theta^2+16173\\theta+3069\\right)-2^{8} x^{3}\\left(13251\\theta^4+35856\\theta^3+27641\\theta^2+6966\\theta+180\\right)-2^{12} 5 x^{4}(2\\theta+1)(314\\theta^3+363\\theta^2+68\\theta-31)+2^{16} 5^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "35/9 3002/9", "discriminant": "5 81 -1719 -231200 -3392256 -12861440 6553600", "aesz": "321", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "b786027c217dd5d5c5abac7b1ecc570b", "dim_h": "13", "inst": " 35/9 261/4 3002/9 126800/9 1727129/9 14907123/2 1476084167/9 55207321888/9 1554991360055/9 232053578385767/36", "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)(9+80z)^2", "discr_factors": "6553600, z+1/32, z^2-71/32*z+1/32, (9/80+z)^2", "dm_basis": null, "q": "0 1 -12 -178 2664 -47355 -234392 -22549626 -420799504 -24839805918", "yuk": "1 35/9 4733/9 81089/9 8119933/9 71963720/3 14489809343/9 506296869316/9 9422052308863/3 1133588701561184/9", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-9/80","im":"0","approx_re":"-0.1125","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":"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":"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -15821*X^4-19162*X^3-14651*X^2-5070*X-676, -82144*X^4-1343296*X^3-2272384*X^2-1337856*X-265200, 9119488*X^4+36162048*X^3+38695360*X^2+17269824*X+2820480, -10240*(2*X+1)*(4324*X^3+10698*X^2+9903*X+3110), 4915200*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.98\" from ...", "degz": 5, "h3": null, "sol": "1 4 180 7600 433300 26523504 1760408496 122456917440 8849508138900 658069964266000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 169 -676 -5070 -14651 -19162 -15821 -265200 -1337856 -2272384 -1343296 -82144 2820480 17269824 38695360 36162048 9119488 -31846400 -165099520 -312360960 -263372800 -88555520 117964800 579993600 997785600 707788800 176947200", "new_number": "5.98", "id": 313, "operator_tex": "13^{2} \\theta^4-13 x\\left(1217\\theta^4+1474\\theta^3+1127\\theta^2+390\\theta+52\\right)-2^{4} x^{2}\\left(5134\\theta^4+83956\\theta^3+142024\\theta^2+83616\\theta+16575\\right)+2^{6} x^{3}\\left(142492\\theta^4+565032\\theta^3+604615\\theta^2+269841\\theta+44070\\right)-2^{11} 5 x^{4}(2\\theta+1)(4324\\theta^3+10698\\theta^2+9903\\theta+3110)+2^{16} 3 5^{2} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "87/13 21589/13", "discriminant": "5 169 -15821 -82144 9119488 -88555520 176947200", "aesz": "341", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "eed12a307d671fcf681b9d108c5e4c9e", "dim_h": null, "inst": " 87/13 1532/13 21589/13 589110/13 17749920/13 652121660/13 25606888578/13 1088305023982/13 48500571351604/13 2257264405232620/13", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(27z+1)(256z^2-96z+1)(-13+160z)^2", "discr_factors": "176947200, z+1/27, z^2-3/8*z+1/256, (-13/160+z)^2", "dm_basis": null, "q": "0 1 -14 -301 736 -52635 -3014442 -134862035 -6142738464 -304565522449", "yuk": "1 87/13 12343/13 582990/13 37715383/13 2218740087/13 140858873806/13 8783162782341/13 42862477691859 2719762808915562", "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":"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":"13/160","im":"0","approx_re":"0.08125","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":["1/2","2/3","4/3","3/2"],"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, -32*X^4-100*X^3-78*X^2-28*X-4, -248-856*X-876*X^4-1340*X^2-1560*X^3, -9312-17088*X^3-42560*X^2-32352*X-1840*X^4, 7808*X^4-50432*X^3+9664*X^2-58432*X-44544, 635136+1958400*X-232704*X^4+2269440*X^2+1142784*X^3, 10905600-2193408*X^3+17694720*X^2+25555968*X-113664*X^4, -2482176*X^4-2015232*X^3-2506752*X^2+41263104*X+32489472, -61734912-142245888*X+4718592*X^4-45318144*X^2+93192192*X^3, -249298944+575668224*X^3+802553856*X^2+58982400*X-11665408*X^4, -126877696*X^4+557842432*X^3+3221225472*X^2+3876585472*X+1413480448, 41943040*(X+1)*(21*X^3+63*X^2+206*X+218), 838860800*(X+2)*(X+1)*(2*X^2-12*X-27), 16777216000*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"13.15\" from ...", "degz": 13, "h3": null, "sol": "1 4 76 1936 57820 1922224 68529616 2567560384 99833328604 3995000055280", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 -4 -28 -78 -100 -32 -248 -856 -1340 -1560 -876 -9312 -32352 -42560 -17088 -1840 -44544 -58432 9664 -50432 7808 635136 1958400 2269440 1142784 -232704 10905600 25555968 17694720 -2193408 -113664 32489472 41263104 -2506752 -2015232 -2482176 -61734912 -142245888 -45318144 93192192 4718592 -249298944 58982400 802553856 575668224 -11665408 1413480448 3876585472 3221225472 557842432 -126877696 9143582720 17783848960 11282677760 3523215360 880803840 -45298483200 -88080384000 -49492787200 -5033164800 1677721600 201326592000 469762048000 385875968000 134217728000 16777216000", "new_number": "13.15", "id": 367, "operator_tex": "\\theta^4-2 x\\left(16\\theta^4+50\\theta^3+39\\theta^2+14\\theta+2\\right)-2^{2} x^{2}\\left(219\\theta^4+390\\theta^3+335\\theta^2+214\\theta+62\\right)-2^{4} x^{3}\\left(115\\theta^4+1068\\theta^3+2660\\theta^2+2022\\theta+582\\right)+2^{6} x^{4}\\left(122\\theta^4-788\\theta^3+151\\theta^2-913\\theta-696\\right)-2^{8} 3 x^{5}\\left(303\\theta^4-1488\\theta^3-2955\\theta^2-2550\\theta-827\\right)-2^{10} 3 x^{6}\\left(37\\theta^4+714\\theta^3-5760\\theta^2-8319\\theta-3550\\right)-2^{13} 3 x^{7}\\left(101\\theta^4+82\\theta^3+102\\theta^2-1679\\theta-1322\\right)+2^{15} 3 x^{8}\\left(48\\theta^4+948\\theta^3-461\\theta^2-1447\\theta-628\\right)-2^{17} x^{9}\\left(89\\theta^4-4392\\theta^3-6123\\theta^2-450\\theta+1902\\right)-2^{20} x^{10}\\left(121\\theta^4-532\\theta^3-3072\\theta^2-3697\\theta-1348\\right)+2^{23} 5 x^{11}(\\theta+1)(21\\theta^3+63\\theta^2+206\\theta+218)+2^{25} 5^{2} x^{12}(\\theta+2)(\\theta+1)(2\\theta^2-12\\theta-27)+2^{27} 5^{3} x^{13}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "6 626/3", "discriminant": "13 1 -32 -876 -1840 7808 -232704 -113664 -2482176 4718592 -11665408 -126877696 880803840 1677721600 16777216000", "aesz": null, "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "3e24fdfe8119ac950ce846460f109e44", "dim_h": null, "inst": " 6 41/4 626/3 12349/8 33062 5728907/12 9908166 1526186815/8 4159057094 364170185561/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "11", "laurent": null, "discriminant_tex": "(4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2", "discr_factors": "16777216000, z^3+3/20*z^2+3/40*z-1/640, z+1/4, (1/320+3/160*z-3/20*z^2+z^3)^2, z-1/4, z^2+1/4*z+1/16", "dm_basis": null, "q": "0 1 -12 28 -352 622 -97680 -716520 -31206656 -560990939", "yuk": "1 6 88 5640 98880 4132756 103126048 3398500944 97676055040 3031952627166", "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":"-1/8*3^(1/2)","approx_re":"-0.125","approx_im":"-0.216506","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"1/8*3^(1/2)","approx_re":"-0.125","approx_im":"0.216506","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/40*2^(1/3)+3/80*2^(2/3)-1/20","im":"-1/8*3^(1/2)*(3/5*2^(1/3)+3/10*2^(2/3))","approx_re":"-0.084967","approx_im":"-0.266773","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/40*2^(1/3)+3/80*2^(2/3)-1/20","im":"1/8*3^(1/2)*(3/5*2^(1/3)+3/10*2^(2/3))","approx_re":"-0.084967","approx_im":"0.266773","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/40*(122+10*151^(1/2))^(1/3)+3/20/(122+10*151^(1/2))^(1/3)+1/20","im":"0","approx_re":"-0.082432","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":"3/20*2^(1/3)-3/40*2^(2/3)-1/20","im":"0","approx_re":"0.019933","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/80*(122+10*151^(1/2))^(1/3)-3/40/(122+10*151^(1/2))^(1/3)+1/20","im":"1/4*3^(1/2)*(-1/20*(122+10*151^(1/2))^(1/3)-3/10/(122+10*151^(1/2))^(1/3))","approx_re":"0.116216","approx_im":"-0.156217","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/80*(122+10*151^(1/2))^(1/3)-3/40/(122+10*151^(1/2))^(1/3)+1/20","im":"-1/4*3^(1/2)*(-1/20*(122+10*151^(1/2))^(1/3)-3/10/(122+10*151^(1/2))^(1/3))","approx_re":"0.116216","approx_im":"0.156217","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -336*X^4-420*X^3-399*X^2-189*X-36, 4393*X^4+9340*X^3+10903*X^2+6360*X+1488, -23338*X^4-55440*X^3-54038*X^2-16920*X+1824, 27196*X^4-41152*X^3-328732*X^2-476672*X-210688, 56*(X+1)*(2611*X^3+15537*X^2+26998*X+14360), -3136*(X+1)*(X+2)*(83*X^2+105*X-66), -351232*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"7.6\" from ...", "degz": 7, "h3": null, "sol": "1 4 28 232 2188 22624 250936 2937232 35844748 451950352", "n_discr_factors": "6", "c3": null, "operator": "4 7 0 0 0 0 9 -36 -189 -399 -420 -336 1488 6360 10903 9340 4393 1824 -16920 -54038 -55440 -23338 -210688 -476672 -328732 -41152 27196 804160 2316048 2381960 1016288 146216 413952 -37632 -1301440 -1110144 -260288 -4214784 -9834496 -8078336 -2809856 -351232", "new_number": "7.6", "id": 449, "operator_tex": "3^{2} \\theta^4-3 x\\left(112\\theta^4+140\\theta^3+133\\theta^2+63\\theta+12\\right)+x^{2}\\left(4393\\theta^4+9340\\theta^3+10903\\theta^2+6360\\theta+1488\\right)-2 x^{3}\\left(11669\\theta^4+27720\\theta^3+27019\\theta^2+8460\\theta-912\\right)+2^{2} x^{4}\\left(6799\\theta^4-10288\\theta^3-82183\\theta^2-119168\\theta-52672\\right)+2^{3} 7 x^{5}(\\theta+1)(2611\\theta^3+15537\\theta^2+26998\\theta+14360)-2^{6} 7^{2} x^{6}(\\theta+1)(\\theta+2)(83\\theta^2+105\\theta-66)-2^{10} 7^{3} x^{7}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "1/3 5/3", "discriminant": "7 9 -336 4393 -23338 27196 146216 -260288 -351232", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "24ba77c97bc4b46c39a41c77cc1d1ef4", "dim_h": null, "inst": " 1/3 5/6 5/3 19/3 29 281/2 702 11624/3 67528/3 272197/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2", "discr_factors": "-351232, z-1/8, z+1, z+1/2, z-1/16, z-1/7, (-3/14+z)^2", "dm_basis": null, "q": "0 1 -5 10 5 -150 370 -583 -4805 -2132", "yuk": "1 1/3 7 136/3 1237/3 10876/3 30400 722359/3 5952725/3 49228048/3", "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":"-1/2","im":"0","approx_re":"-0.5","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":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/7","im":"0","approx_re":"0.142857142857","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/14","im":"0","approx_re":"0.214285714286","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","2","2","3"],"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": "[9*X^4, -36-234*X-603*X^2-738*X^3-342*X^4, -2556-12510*X-22605*X^2-17106*X^3-6135*X^4, 36288+134568*X+190200*X^2+142200*X^3+52992*X^4, -683616-2151888*X-1727864*X^2+450992*X^3+482296*X^4, -129664-3273952*X-9657264*X^2-9689728*X^3-3290416*X^4, 8114944+39123072*X+64345600*X^2+34978176*X^3-6580992*X^4, 15837184+80152064*X+166659840*X^2+171651584*X^3+74914048*X^4, -11214848*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.24\" from ...", "degz": 8, "h3": "48", "sol": "1 4 72 1696 49960 1617504 56399616 2065102848 78509001384 3071712566560", "n_discr_factors": "2", "c3": "-86", "operator": "4 8 0 0 0 0 9 -36 -234 -603 -738 -342 -2556 -12510 -22605 -17106 -6135 36288 134568 190200 142200 52992 -683616 -2151888 -1727864 450992 482296 -129664 -3273952 -9657264 -9689728 -3290416 8114944 39123072 64345600 34978176 -6580992 15837184 80152064 166659840 171651584 74914048 -168222720 -695320576 -1065410560 -717750272 -179437568", "new_number": "8.24", "id": 468, "operator_tex": "3^{2} \\theta^4-3^{2} x\\left(38\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-3 x^{2}\\left(2045\\theta^4+5702\\theta^3+7535\\theta^2+4170\\theta+852\\right)+2^{3} 3 x^{3}\\left(2208\\theta^4+5925\\theta^3+7925\\theta^2+5607\\theta+1512\\right)+2^{3} x^{4}\\left(60287\\theta^4+56374\\theta^3-215983\\theta^2-268986\\theta-85452\\right)-2^{4} x^{5}\\left(205651\\theta^4+605608\\theta^3+603579\\theta^2+204622\\theta+8104\\right)-2^{7} x^{6}\\left(51414\\theta^4-273267\\theta^3-502700\\theta^2-305649\\theta-63398\\right)+2^{8} 37 x^{7}\\left(7909\\theta^4+18122\\theta^3+17595\\theta^2+8462\\theta+1672\\right)-2^{13} 37^{2} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "3 437/3", "discriminant": "8 9 -342 -6135 52992 482296 -3290416 -6580992 74914048 -179437568", "aesz": "286", "n_sing_complex": "2", "inst_int": "", "c2h": "84", "hash": "94afcd38a40c3a3e54fc3c57b4b85459", "dim_h": "15", "inst": " 3 539/24 437/3 18531/8 90274/3 14180887/24 10711739 2751585605/12 4879799322 1342664492735/12", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2", "discr_factors": "-179437568, (-3/148-3/148*z+z^2)^2, -1/8192+5/1024*z+63/1024*z^2-193/512*z^3+z^4", "dm_basis": null, "q": "0 1 -10 -28 272 -7113 -29692 -1859356 -29643712 -862582466", "yuk": "1 3 548/3 3936 445292/3 11284259/3 382896296/3 3674126480 117401134244 3557373709674", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"3/296-1/296*1785^(1/2)","im":"0","approx_re":"-0.132599","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 3)","im":"0","approx_re":"-0.070843","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*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 1)","im":"0","approx_re":"0.020383","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/296+1/296*1785^(1/2)","im":"0","approx_re":"0.152869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 2)","im":"0","approx_re":"0.213707","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 4)","im":"0","approx_re":"0.213707","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -9909*X^4-10746*X^3-7965*X^2-2592*X-324, -86400*X^4-898992*X^3-1561248*X^2-867888*X-169344, 13910208*X^4+19715328*X^3-9327168*X^2-14961024*X-4326912, 112509952*X^4+634849280*X^3+57610240*X^2-224283648*X-80093184, -4664246272*X^4+2094891008*X^3+4194140160*X^2+1856798720*X+224215040, -74138910720*X^4-70271631360*X^3-47035842560*X^2-21172322304*X-4385669120, -359250526208*X^4-918267363328*X^3-1016095309824*X^2-545863499776*X-115091701760, -78920024064*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.47\" from ...", "degz": 8, "h3": null, "sol": "1 4 228 12640 901540 70455504 5932407936 524802634752 48205904264100 4557901439462800", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 81 -324 -2592 -7965 -10746 -9909 -169344 -867888 -1561248 -898992 -86400 -4326912 -14961024 -9327168 19715328 13910208 -80093184 -224283648 57610240 634849280 112509952 224215040 1856798720 4194140160 2094891008 -4664246272 -4385669120 -21172322304 -47035842560 -70271631360 -74138910720 -115091701760 -545863499776 -1016095309824 -918267363328 -359250526208 -631360192512 -2683280818176 -4182761275392 -2841120866304 -710280216576", "new_number": "8.47", "id": 493, "operator_tex": "3^{4} \\theta^4-3^{3} x\\left(367\\theta^4+398\\theta^3+295\\theta^2+96\\theta+12\\right)-2^{4} 3^{3} x^{2}\\left(200\\theta^4+2081\\theta^3+3614\\theta^2+2009\\theta+392\\right)+2^{6} 3 x^{3}\\left(72449\\theta^4+102684\\theta^3-48579\\theta^2-77922\\theta-22536\\right)+2^{10} x^{4}\\left(109873\\theta^4+619970\\theta^3+56260\\theta^2-219027\\theta-78216\\right)-2^{14} 7 x^{5}\\left(40669\\theta^4-18266\\theta^3-36570\\theta^2-16190\\theta-1955\\right)-2^{17} 7 x^{6}\\left(80805\\theta^4+76590\\theta^3+51265\\theta^2+23076\\theta+4780\\right)-2^{24} 7^{2} x^{7}\\left(437\\theta^4+1117\\theta^3+1236\\theta^2+664\\theta+140\\right)-2^{29} 3 7^{2} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "31/3 43174/9", "discriminant": "8 81 -9909 -86400 13910208 112509952 -4664246272 -74138910720 -359250526208 -710280216576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "b79bf25fcecf028aa40c1a6a8233efe7", "dim_h": null, "inst": " 31/3 1964/9 43174/9 1469755/9 19813517/3 315467008 148386069209/9 925792234621 492778954234601/9 10128857593326760/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2", "discr_factors": "-710280216576, z+1/27, (-9/3584+3/64*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048", "dm_basis": null, "q": "0 1 -16 -434 -4696 -227995 -13002992 -803331770 -50035732496 -3256430021246", "yuk": "1 31/3 15805/9 388597/3 94080125/9 2476689656/3 613269045055/9 50896421738780/9 4266050711213693/9 119745285879396640/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"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":"-3/128-3/896*273^(1/2)","im":"0","approx_re":"-0.078759","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":"1/48*(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":"-3/128+3/896*273^(1/2)","im":"0","approx_re":"0.031884","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -36-261*X-735*X^2-948*X^3-456*X^4, -5808-25608*X-43193*X^2-31076*X^3-8807*X^4, -105792-370584*X-470174*X^2-212640*X^3-21266*X^4, -701504-2034816*X-1737868*X^2+76576*X^3+262604*X^4, -1469760-2153840*X+2176424*X^2+5160480*X^3+1211976*X^4, 2029056+11852544*X+21318400*X^2+13432320*X^3-866816*X^4, 5708800+13959168*X+3885056*X^2-14409728*X^3-11699200*X^4, -32768*(590*X^2+1126*X+597)*(X+1)^2, -9437184*(X+1)^2*(X+2)^2]", "text": "This is operator \"9.5\" from ...", "degz": 9, "h3": null, "sol": "1 4 108 3496 137548 6004704 281273976 13848121872 707622721164 37215146789392", "n_discr_factors": "5", "c3": null, "operator": "4 9 0 0 0 0 9 -36 -261 -735 -948 -456 -5808 -25608 -43193 -31076 -8807 -105792 -370584 -470174 -212640 -21266 -701504 -2034816 -1737868 76576 262604 -1469760 -2153840 2176424 5160480 1211976 2029056 11852544 21318400 13432320 -866816 5708800 13959168 3885056 -14409728 -11699200 -19562496 -76021760 -112689152 -75563008 -19333120 -37748736 -113246208 -122683392 -56623104 -9437184", "new_number": "9.5", "id": 544, "operator_tex": "3^{2} \\theta^4-3 x\\left(152\\theta^4+316\\theta^3+245\\theta^2+87\\theta+12\\right)-x^{2}\\left(5808+25608\\theta+43193\\theta^2+31076\\theta^3+8807\\theta^4\\right)-2 x^{3}\\left(10633\\theta^4+106320\\theta^3+235087\\theta^2+185292\\theta+52896\\right)+2^{2} x^{4}\\left(65651\\theta^4+19144\\theta^3-434467\\theta^2-508704\\theta-175376\\right)+2^{3} x^{5}\\left(151497\\theta^4+645060\\theta^3+272053\\theta^2-269230\\theta-183720\\right)-2^{8} x^{6}\\left(3386\\theta^4-52470\\theta^3-83275\\theta^2-46299\\theta-7926\\right)-2^{10} x^{7}\\left(11425\\theta^4+14072\\theta^3-3794\\theta^2-13632\\theta-5575\\right)-2^{15} x^{8}(590\\theta^2+1126\\theta+597)(\\theta+1)^2-2^{20} 3^{2} x^{9}(\\theta+1)^2(\\theta+2)^2", "superseek": "17/3 4127/9", "discriminant": "9 9 -456 -8807 -21266 262604 1211976 -866816 -11699200 -19333120 -9437184", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "98a7e046a956f1c9ec13973072ab8283", "dim_h": null, "inst": " 17/3 257/6 4127/9 23827/3 496999/3 71729629/18 104658718 2945771458 785847748280/9 16183383951883/6", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(9z+1)(2z+1)(z+1)(128z^2+64z-1)(-3-2z+64z^2)^2", "discr_factors": "-9437184, z^2+1/2*z-1/128, (-3/64-1/32*z+z^2)^2, z+1/2, z+1, z+1/9", "dm_basis": null, "q": "0 1 -13 -54 173 -11862 -345054 -9839047 -305425645 -10024615764", "yuk": "1 17/3 1045/3 37160/3 1525973/3 62124892/3 2582304832/3 107693820839/3 4524706485461/3 190961002869200/3", "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":"-1/4-3/16*2^(1/2)","im":"0","approx_re":"-0.515165","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64-1/64*193^(1/2)","im":"0","approx_re":"-0.201444","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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4+3/16*2^(1/2)","im":"0","approx_re":"0.015165","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64+1/64*193^(1/2)","im":"0","approx_re":"0.232694","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","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[27*X^4, -1080*X^4-2448*X^3-1944*X^2-720*X-108, 6192*X^4+49728*X^3+69360*X^2+30048*X+2736, 419840*X^4+1034752*X^3+1820032*X^2+1866368*X+754752, -4396032*X^4+860160*X^3+26789888*X^2+17959936*X+3554304, 4685824*X^4-47063040*X^3-539981824*X^2-543836160*X-18164736, 1038209024*X^4+1100398592*X^3-1724329984*X^2-4393951232*X-2630938624, -4405100544*X^4+15843262464*X^3+3547955200*X^2+2510028800*X+2922299392, -18063097856*X^4-24164696064*X^3-250203865088*X^2-75539939328*X+15624830976, 651701518336*X^4-81321263104*X^3-94561632256*X^2+128318439424*X+226505523200, 149315125248*X^4+4151480156160*X^3+12803802923008*X^2+16455131201536*X+8119969120256, -21217440432128*X^4-70266805813248*X^3-137193184034816*X^2-135180991856640*X-54832664674304, -860067201024*X^4+18563117088768*X^3-13890326888448*X^2-110554874118144*X-92799345098752, 286583303438336*X^4+1784789765980160*X^3+5121708503597056*X^2+6995398723895296*X+3665801697558528, -8990977163264*X^4-1444558562918400*X^3-6453041796481024*X^2-10447448891719680*X-60878325131771904, -1941368167464960*X^4-15574539257774080*X^3-52954726261587968*X^2-84935160121786368*X-50239772207087616, -347647537840128*X^4+10096815277867008*X^3+70731960971952128*X^2+152715739827011584*X+105689730586247168, 7556977777442816*X^4+60106108802433024*X^3+167509943656644608*X^2+211352179540230144*X+98574395705917440, 4944435070631936*X^4+14362095759917056*X^3-10464945514741760*X^2-101598860136153088*X-95841748533641216, -21130414462599168*X^4-186492565233598464*X^3-509670368718356480*X^2-472903799397154816*X-84379545972506624, -11272193207959552*X^4-22430037206630400*X^3-6772991627100160*X^2+43844125669195776*X+51558299249672192, 25297563531870208*X^4+174197826211807232*X^3+449031752690696192*X^2+503796227846963200*X+212667539044433920, 26194765020135424*X^4+151644643702865920*X^3+296129267685654528*X^2+236614902297395200*X+66656792922292224, -37295434414161920*X^4-240661105087610880*X^3-591801138534154240*X^2-658651445502935040*X-280419445547991040, 7036874417766400*(X+2)^4]", "text": "This is operator \"24.14\" from ...", "degz": 24, "h3": null, "sol": "1 4 52 464 1412 -693765232/5625 -6731441951024/1366875 -61182688180883776/468838125 -1257035453283020332/468838125 -40668093989763282842512/1025348979375", "n_discr_factors": "1", "c3": null, "operator": "4 24 0 0 0 0 27 -108 -720 -1944 -2448 -1080 2736 30048 69360 49728 6192 754752 1866368 1820032 1034752 419840 3554304 17959936 26789888 860160 -4396032 -18164736 -543836160 -539981824 -47063040 4685824 -2630938624 -4393951232 -1724329984 1100398592 1038209024 2922299392 2510028800 3547955200 15843262464 -4405100544 15624830976 -75539939328 -250203865088 -24164696064 -18063097856 226505523200 128318439424 -94561632256 -81321263104 651701518336 8119969120256 16455131201536 12803802923008 4151480156160 149315125248 -54832664674304 -135180991856640 -137193184034816 -70266805813248 -21217440432128 -92799345098752 -110554874118144 -13890326888448 18563117088768 -860067201024 3665801697558528 6995398723895296 5121708503597056 1784789765980160 286583303438336 -60878325131771904 -10447448891719680 -6453041796481024 -1444558562918400 -8990977163264 -50239772207087616 -84935160121786368 -52954726261587968 -15574539257774080 -1941368167464960 105689730586247168 152715739827011584 70731960971952128 10096815277867008 -347647537840128 98574395705917440 211352179540230144 167509943656644608 60106108802433024 7556977777442816 -95841748533641216 -101598860136153088 -10464945514741760 14362095759917056 4944435070631936 -84379545972506624 -472903799397154816 -509670368718356480 -186492565233598464 -21130414462599168 51558299249672192 43844125669195776 -6772991627100160 -22430037206630400 -11272193207959552 212667539044433920 503796227846963200 449031752690696192 174197826211807232 25297563531870208 66656792922292224 236614902297395200 296129267685654528 151644643702865920 26194765020135424 -280419445547991040 -658651445502935040 -591801138534154240 -240661105087610880 -37295434414161920 112589990684262400 225179981368524800 168884986026393600 56294995342131200 7036874417766400", "new_number": "24.14", "id": 589, "operator_tex": "3^{3} \\theta^4-2^{2} 3^{2} x\\left(30\\theta^4+68\\theta^3+54\\theta^2+20\\theta+3\\right)+2^{4} 3 x^{2}\\left(129\\theta^4+1036\\theta^3+1445\\theta^2+626\\theta+57\\right)+2^{6} x^{3}\\left(6560\\theta^4+16168\\theta^3+28438\\theta^2+29162\\theta+11793\\right)-2^{10} x^{4}\\left(4293\\theta^4-840\\theta^3-26162\\theta^2-17539\\theta-3471\\right)+2^{10} x^{5}\\left(4576\\theta^4-45960\\theta^3-527326\\theta^2-531090\\theta-17739\\right)+2^{12} x^{6}\\left(253469\\theta^4+268652\\theta^3-420979\\theta^2-1072742\\theta-642319\\right)-2^{14} x^{7}\\left(268866\\theta^4-966996\\theta^3-216550\\theta^2-153200\\theta-178363\\right)-2^{16} x^{8}\\left(275621\\theta^4+368724\\theta^3+3817808\\theta^2+1152648\\theta-238416\\right)+2^{19} x^{9}\\left(1243022\\theta^4-155108\\theta^3-180362\\theta^2+244748\\theta+432025\\right)+2^{21} x^{10}\\left(71199\\theta^4+1979580\\theta^3+6105329\\theta^2+7846418\\theta+3871903\\right)-2^{23} x^{11}\\left(2529316\\theta^4+8376456\\theta^3+16354702\\theta^2+16114830\\theta+6536563\\right)-2^{27} x^{12}\\left(6408\\theta^4-138306\\theta^3+103491\\theta^2+823698\\theta+691409\\right)+2^{27} x^{13}\\left(2135212\\theta^4+13297720\\theta^3+38159702\\theta^2+52119782\\theta+27312351\\right)-2^{29} x^{14}\\left(16747\\theta^4+2690700\\theta^3+12019727\\theta^2+19459890\\theta+113394717\\right)-2^{31} x^{15}\\left(904020\\theta^4+7252460\\theta^3+24658966\\theta^2+39551016\\theta+23394717\\right)-2^{32} x^{16}\\left(80943\\theta^4-2350848\\theta^3-16468568\\theta^2-35556904\\theta-24607808\\right)+2^{34} x^{17}\\left(439874\\theta^4+3498636\\theta^3+9750362\\theta^2+12302316\\theta+5737785\\right)+2^{36} x^{18}\\left(71951\\theta^4+208996\\theta^3-152285\\theta^2-1478458\\theta-1394681\\right)-2^{38} x^{19}\\left(76872\\theta^4+678456\\theta^3+1854170\\theta^2+1720414\\theta+306971\\right)-2^{42} x^{20}\\left(2563\\theta^4+5100\\theta^3+1540\\theta^2-9969\\theta-11723\\right)+2^{42} x^{21}\\left(5752\\theta^4+39608\\theta^3+102098\\theta^2+114550\\theta+48355\\right)+2^{44} x^{22}\\left(1489\\theta^4+8620\\theta^3+16833\\theta^2+13450\\theta+3789\\right)-2^{46} 5 x^{23}\\left(106\\theta^4+684\\theta^3+1682\\theta^2+1872\\theta+797\\right)+2^{48} 5^{2} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "16/3 -880/81", "discriminant": "24 27 -1080 6192 419840 -4396032 4685824 1038209024 -4405100544 -18063097856 651701518336 149315125248 -21217440432128 -860067201024 286583303438336 -8990977163264 -1941368167464960 -347647537840128 7556977777442816 4944435070631936 -21130414462599168 -11272193207959552 25297563531870208 26194765020135424 -37295434414161920 7036874417766400", "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "13173bd8cb75baee8a898c9c6303c117", "dim_h": null, "inst": " 16/3 -133/18 -880/81 -247636/243 44329772416/11390625 -10102523899147/369056250 6287467962653104496/7236516459375 -2356715252638153139/1181472075000 2418459802034766478019968/26161779208753125 -4580667016504767623896545268/3027983704716796875", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": "27-1080z+26194765020135424z^22-37295434414161920z^23+7036874417766400z^24+1038209024z^6-4405100544z^7-18063097856z^8+651701518336z^9+149315125248z^10-347647537840128z^16+7556977777442816z^17+6192z^2+419840z^3-4396032z^4+4685824z^5+4944435070631936z^18-21217440432128z^11-860067201024z^12+286583303438336z^13-8990977163264z^14-1941368167464960z^15-21130414462599168z^19-11272193207959552z^20+25297563531870208z^21", "discr_factors": "7036874417766400, -27/175921860444160*z+1489/400*z^22-53/10*z^23+z^24+253469/1717986918400*z^6-134433/214748364800*z^7-275621/107374182400*z^8+621511/6710886400*z^9+71199/3355443200*z^10-80943/1638400*z^16+219937/204800*z^17+387/439804651110400*z^2+41/687194767360*z^3-4293/6871947673600*z^4+143/214748364800*z^5+71951/102400*z^18-632329/209715200*z^11-801/6553600*z^12+533803/13107200*z^13-16747/13107200*z^14-45201/163840*z^15-9609/3200*z^19-2563/1600*z^20+719/200*z^21+27/7036874417766400", "dm_basis": null, "q": "0 1 -32/3 242/3 -11008/81 132799/243 -762180928/28125 12747768376706/20503125 -678516030381589504/49228003125 8667116936088297514/49228003125", "yuk": "1 16/3 -484/9 -288 -15861772/243 44330258416/91125 -40412467884088/6834375 6287468075174254496/21097715625 -150839416210342838396/147684009375 2418459791699248765919968/35887214278125", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[25*X^4, -2120*X^4-5720*X^3-800*X-100, 23824*X^4+52672*X^3+13584*X^2-30560*X-14640, 368128*X^4+410112*X^3+159872*X^2+167040*X+180160, -2624512*X^4-15773696*X^3-33230848*X^2-37831680*X-14932992, -78716928*X^4+65003520*X^3+380557312*X^2-15050752*X-87170048, 294711296*X^4+1501642752*X^3+1313026048*X^2+2718916608*X+1770876928, 7206895616*X^4+333512704*X^3-11214487552*X^2-19800588288*X-13377585152, -5304680448*X^4-196502618112*X^3+27580694528*X^2-31652839424*X-48077209600, -473972080640*X^4+10601103360*X^3-1489463410688*X^2-516050386944*X+328545599488, -35121004544*X^4+5361838850048*X^3+7806742691840*X^2+6571379654656*X+1609541091328, 17911456464896*X^4+31742291345408*X^3+80685574389760*X^2+77788988047360*X+29303311958016, -860067201024*X^4-25443654696960*X^3-145910642245632*X^2-195285988933632*X-89516916342784, -339479046914048*X^4-1591563482300416*X^3-3596974712422400*X^2-3989570693627904*X-1769408280133632, 38224672063488*X^4-756981543469056*X^3-2181448786247680*X^2-2631340704923648*X-1125621270839296, 2669369419104256*X^4+21688047246508032*X^3+65676092974825472*X^2+87342034024660992*X+43701930039443456, -1183783181090816*X^4+6366309763776512*X^3+50211294426431488*X^2+91518984209301504*X+53087788643385344, -4619082708025344*X^4-53565526445654016*X^3-206814873009520640*X^2-334915777306034176*X-194126697803546624, 17349537572061184*X^4+120334675712409600*X^3+276689695948144640*X^2+291646146462351360*X+117478488100831232, 1257841302175744*X^4+22696119020552192*X^3-38961744286056448*X^2-241964576122339328*X-215400100317364224, 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x^{4}\\left(2563\\theta^4+15404\\theta^3+32452\\theta^2+36945\\theta+14583\\right)-2^{10} x^{5}\\left(76872\\theta^4-63480\\theta^3-371638\\theta^2+14698\\theta+85127\\right)+2^{12} x^{6}\\left(71951\\theta^4+366612\\theta^3+320563\\theta^2+663798\\theta+432343\\right)+2^{14} x^{7}\\left(439874\\theta^4+20356\\theta^3-684478\\theta^2-1208532\\theta-816503\\right)-2^{16} x^{8}\\left(80943\\theta^4+2998392\\theta^3-420848\\theta^2+482984\\theta+733600\\right)-2^{19} x^{9}\\left(904030\\theta^4-20220\\theta^3+2840926\\theta^2+984288\\theta-626651\\right)-2^{21} x^{10}\\left(16747\\theta^4-2556724\\theta^3-3722545\\theta^2-3133478\\theta-767489\\right)+2^{23} x^{11}\\left(2135212\\theta^4+3783976\\theta^3+9618470\\theta^2+9273170\\theta+3493227\\right)-2^{27} x^{12}\\left(6408\\theta^4+189570\\theta^3+1087119\\theta^2+1454994\\theta+666953\\right)-2^{27} x^{13}\\left(2529316\\theta^4+11858072\\theta^3+26799550\\theta^2+29724618\\theta+13183119\\right)+2^{29} x^{14}\\left(71199\\theta^4-1409988\\theta^3-4063265\\theta^2-4901254\\theta-2096633\\right)+2^{31} x^{15}\\left(1243022\\theta^4+10099284\\theta^3+30582814\\theta^2+40671804\\theta+20350297\\right)-2^{32} x^{16}\\left(275621\\theta^4-1482272\\theta^3-11690728\\theta^2-21308424\\theta-12360464\\right)-2^{34} x^{17}\\left(268866\\theta^4+3117924\\theta^3+12038210\\theta^2+19494664\\theta+11299661\\right)+2^{36} x^{18}\\left(252469\\theta^4+1751100\\theta^3+4026365\\theta^2+4244010\\theta+1709537\\right)+2^{38} x^{19}\\left(4576\\theta^4+82568\\theta^3-141742\\theta^2-880262\\theta-783621\\right)-2^{42} x^{20}\\left(4293\\theta^4+35184\\theta^3+81910\\theta^2+60347\\theta+2367\\right)+2^{42} x^{21}\\left(6560\\theta^4+36312\\theta^3+88870\\theta^2+100494\\theta+42837\\right)+2^{44} 3 x^{22}\\left(3129\\theta^4-4\\theta^3-1675\\theta^2-315\\theta-1639\\right)-2^{46} 3^{2} x^{23}\\left(30\\theta^4+172\\theta^3+366\\theta^2+340\\theta+115\\right)+2^{48} 3^{3} 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operator \"24.17\" from ...", "degz": 24, "h3": null, "sol": "1 4 -36 8912/15 688859/150 -9770883334/78125 4112622736484/6328125 88400861714108432/2170546875 -8422692226097100307/19293750000 -2153040823073365919180863/158232867187500", "n_discr_factors": "1", "c3": null, "operator": "4 24 0 0 0 0 25 -100 -400 0 -460 940 14480 69600 116656 88768 -2864 -1973120 -4327680 -1064576 896256 -375680 7148544 10417152 -84850688 -94066688 -5579776 -876990464 -1812004864 -562589696 -420372480 67719168 3507961856 57022218240 12597936128 39060897792 6177505280 158619009024 405700083712 560988291072 -7620263936 -31300648960 -8397823934464 -17687289790464 -12966527238144 -9818471399424 -2439754285056 -7426292056064 12720518725632 2214542180352 25152939098112 232263778304 -59410336448512 101764149805056 17716337442816 201223512784896 386846496391168 -12435125933441024 -32834097264984064 -33225011229622272 -16571972397826048 -6082737769283584 -2158051539585859584 -457985153185087488 -377264034585509888 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x^{6}\\left(377045\\theta^4+2384088\\theta^3+768917\\theta^2+3480360\\theta+214109\\right)-2^{17} x^{7}\\left(238805\\theta^4+58138\\theta^3-4280001\\theta^2-3095246\\theta-1210167\\right)-2^{20} x^{8}\\left(2326731\\theta^4+9363624\\theta^3+12365844\\theta^2+16867914\\theta+8008789\\right)+2^{23} x^{9}\\left(27688\\theta^4+2998464\\theta^3+263994\\theta^2+1516404\\theta-885283\\right)+2^{26} x^{10}\\left(5764462\\theta^4+2998464\\theta^3+263994\\theta^2+1516404\\theta-885283\\right)-2^{29} x^{11}\\left(11329982\\theta^4+30867704\\theta^3+61886406\\theta^2+61158272\\theta+23162227\\right)-2^{32} x^{12}\\left(2120418\\theta^4+36058992\\theta^3+87838628\\theta^2+106632978\\theta+502460529\\right)+2^{35} x^{13}\\left(16849298\\theta^4+91712872\\theta^3+212023454\\theta^2+244238244\\theta+110360529\\right)-2^{38} x^{14}\\left(10049328\\theta^4+37236768\\theta^3+66644650\\theta^2+63907082\\theta+25441423\\right)-2^{41} x^{15}\\left(4736512\\theta^4+53071212\\theta^3+174736084\\theta^2+241175316\\theta+122040421\\right)+2^{44} x^{16}\\left(8122336\\theta^4+67434512\\theta^3+211414476\\theta^2+291782162\\theta+149636409\\right)-2^{47} x^{17}\\left(3596934\\theta^4+30695376\\theta^3+102692394\\theta^2+149709348\\theta+804776873\\right)+2^{50} x^{18}\\left(344350\\theta^4+4792416\\theta^3+22792344\\theta^2+40780218\\theta+25076261\\right)+2^{53} x^{19}\\left(255290\\theta^4+1201696\\theta^3+241498\\theta^2-4145416\\theta-4163853\\right)-2^{56} x^{20}\\left(91962\\theta^4+642936\\theta^3+1364188\\theta^2+959498\\theta+45723\\right)+2^{59} x^{21}\\left(6076\\theta^4+85188\\theta^3+269096\\theta^2+322380\\theta+129693\\right)+2^{62} 3 x^{22}\\left(777\\theta^4+2264\\theta^3+431\\theta^2-3906\\theta-3016\\right)-2^{65} 3^{2} x^{23}\\left(51\\theta^4+314\\theta^3+741\\theta^2+794\\theta+326\\right)+2^{68} 3^{3} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "-24 -9598768/30375", "discriminant": "24 25 940 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