{"count": 7, "status":"OK", "data":[{"pols": "[169*X^4, -59397*X^4-117546*X^3-86827*X^2-28054*X-3380, 102176*X^4-28384*X^3-286368*X^2-185536*X-33904, 17152*X^4+319488*X^3+279296*X^2+79872*X+6656, -4096*(2*X+1)^4]", "text": "Sporadic Operator.\nThere is a second MUM point hidden at infinity. That is operator AESZ 207/4.38\nA-Incarnation: $5 \\times 5$-Pfaffian in P^5\n\nA-Incarnation: 5 \\times 5 Pfaffian in P^5", "degz": 4, "h3": "13", "sol": "1 20 2196 369200 75562900 17321033520 4274237444400 1110816764291520 299987146348074900 83448532078002462800", "n_discr_factors": "2", "c3": "-120", "operator": "4 4 0 0 0 0 169 -3380 -28054 -86827 -117546 -59397 -33904 -185536 -286368 -28384 102176 6656 79872 279296 319488 17152 -4096 -32768 -98304 -131072 -65536", "new_number": "4.34", "id": 131, "operator_tex": "13^{2} \\theta^4-13 x\\left(4569\\theta^4+9042\\theta^3+6679\\theta^2+2158\\theta+260\\right)+2^{4} x^{2}\\left(6386\\theta^4-1774\\theta^3-17898\\theta^2-11596\\theta-2119\\right)+2^{8} x^{3}\\left(67\\theta^4+1248\\theta^3+1091\\theta^2+312\\theta+26\\right)-2^{12} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "647/13 942613/13", "discriminant": "4 169 -59397 102176 17152 -65536", "aesz": "99", "n_sing_complex": "1", "inst_int": "", "c2h": "58", "hash": "f6c6b846edc829f336d8e4ae1dcb5618", "dim_h": "7", "inst": " 647/13 16166/13 942613/13 80218296/13 8418215008/13 1010635571652/13 133175036459554/13 18790105726249800/13 2793397258503481492/13 432766737883812461716/13", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(256z^2+349z-1)(-13+16z)^2", "discr_factors": "-65536, (-13/16+z)^2, z^2+349/256*z-1/256", "dm_basis": null, "q": "0 1 -86 1891 -93168 -5986827 -897060226 -133756443955 -21091605379872 -3466693323446225", "yuk": "1 647/13 129975/13 25451198/13 5134100919/13 1052276876647/13 218297309057358/13 3513772115817513 9620534136973998519/13 2036386601449063458866/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-349/512-85/512*17^(1/2)","im":"0","approx_re":"-1.366141","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-349/512+85/512*17^(1/2)","im":"0","approx_re":"0.002859","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/16","im":"0","approx_re":"0.8125","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","1/2","1/2","1/2"],"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": "[25*X^4, -8080*X^4-21920*X^3-15460*X^2-4500*X-500, -1070336*X^4-2198528*X^3-1617536*X^2-844800*X-186000, -3840*(2*X+1)*(5672*X^3+9500*X^2+8422*X+2689), -294912*(2*X+1)*(1208*X^3+2892*X^2+2842*X+969), -28311552*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.37\" from ...", "degz": 5, "h3": "10", "sol": "1 20 2988 618320 156299500 44234633520 13477733161200 4325154502743360 1442412961677873900 495512411116338902000", "n_discr_factors": "3", "c3": "-32", "operator": "4 5 0 0 0 0 25 -500 -4500 -15460 -21920 -8080 -186000 -844800 -1617536 -2198528 -1070336 -10325760 -52992000 -101160960 -94740480 -43560960 -285769728 -1409679360 -2529165312 -2062024704 -712507392 -2972712960 -14042529792 -23328718848 -16307453952 -4076863488", "new_number": "5.37", "id": 246, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(404\\theta^4+1096\\theta^3+773\\theta^2+225\\theta+25\\right)-2^{4} x^{2}\\left(66896\\theta^4+137408\\theta^3+101096\\theta^2+52800\\theta+11625\\right)-2^{8} 3 5 x^{3}(2\\theta+1)(5672\\theta^3+9500\\theta^2+8422\\theta+2689)-2^{15} 3^{2} x^{4}(2\\theta+1)(1208\\theta^3+2892\\theta^2+2842\\theta+969)-2^{20} 3^{3} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "492/5 872164/5", "discriminant": "5 25 -8080 -1070336 -43560960 -712507392 -4076863488", "aesz": "221", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "b7ce7a734c057660ce3d6341a7572078", "dim_h": "5", "inst": " 492/5 10376/5 872164/5 91316176/5 12181916784/5 1850294589528/5 61762450157748 55187365344835504/5 10392704764770167864/5 2039663615626409751968/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+432z)(16z+1)^2(192z+5)^2", "discr_factors": "-4076863488, (z+5/192)^2, -1/432+z, (z+1/16)^2", "dm_basis": null, "q": "0 1 -100 1574 -102288 -20602367 -2977974168 -588048101710 -116875168258112 -24320631644865004", "yuk": "1 492/5 16700 4709784 5844318764/5 1522739598492/5 399663654969976/5 105922602020538312/5 28255931062400096812/5 7576281773517475921776/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/192","im":"0","approx_re":"-0.0260416666667","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":"1/432","im":"0","approx_re":"0.00231481481481","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","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[8281*X^4, 91*X*(782*X^3-1874*X^2-1210*X-273), -2515785*X^4-11622522*X^3-15227939*X^2-9962953*X-2649920, -59827597*X^4-258678126*X^3-432607868*X^2-348819198*X-110445426, -612043042*X^4-2998881218*X^3-5901995820*X^2-5439732380*X-1915723890, -3762840342*X^4-21226829058*X^3-47503242813*X^2-48522700563*X-18479595006, -15265487382*X^4-98210309094*X^3-244753624741*X^2-271941545379*X-110147546634, -42103272002*X^4-304487632282*X^3-831965057114*X^2-991829482602*X-422269162452, -2*(X+1)*(39253400626*X^3+275108963001*X^2+654332416678*X+521254338620), -(X+1)*(X+2)*(94987355417*X^2+545340710193*X+799002779040), -1540*(X+3)*(X+2)*(X+1)*(43765159*X+149264765), -21292817700*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"11.3\" from ...", "degz": 11, "h3": null, "sol": "1 0 20 186 2940 46680 803990 14453460 269264380 5154560880", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 8281 0 -24843 -110110 -170534 71162 -2649920 -9962953 -15227939 -11622522 -2515785 -110445426 -348819198 -432607868 -258678126 -59827597 -1915723890 -5439732380 -5901995820 -2998881218 -612043042 -18479595006 -48522700563 -47503242813 -21226829058 -3762840342 -110147546634 -271941545379 -244753624741 -98210309094 -15265487382 -422269162452 -991829482602 -831965057114 -304487632282 -42103272002 -1042508677240 -2351173510596 -1858882759358 -628724727254 -78506801252 -1598005558080 -3487689757506 -2624999620453 -830302776444 -94987355417 -1379206428600 -2932935188260 -2120588222060 -634257807260 -67398344860 -511027624800 -1064640885000 -745248619500 -212928177000 -21292817700", "new_number": "11.3", "id": 340, "operator_tex": "7^{2} 13^{2} \\theta^4+7 13 x\\theta(782\\theta^3-1874\\theta^2-1210\\theta-273)-x^{2}\\left(2515785\\theta^4+11622522\\theta^3+15227939\\theta^2+9962953\\theta+2649920\\right)-x^{3}\\left(59827597\\theta^4+258678126\\theta^3+432607868\\theta^2+348819198\\theta+110445426\\right)-2 x^{4}\\left(306021521\\theta^4+1499440609\\theta^3+2950997910\\theta^2+2719866190\\theta+957861945\\right)-3 x^{5}\\left(1254280114\\theta^4+7075609686\\theta^3+15834414271\\theta^2+16174233521\\theta+6159865002\\right)-x^{6}\\left(15265487382\\theta^4+98210309094\\theta^3+244753624741\\theta^2+271941545379\\theta+110147546634\\right)-2 x^{7}\\left(21051636001\\theta^4+152243816141\\theta^3+415982528557\\theta^2+495914741301\\theta+211134581226\\right)-2 x^{8}(\\theta+1)(39253400626\\theta^3+275108963001\\theta^2+654332416678\\theta+521254338620)-x^{9}(\\theta+1)(\\theta+2)(94987355417\\theta^2+545340710193\\theta+799002779040)-2^{2} 5 7 11 x^{10}(\\theta+3)(\\theta+2)(\\theta+1)(43765159\\theta+149264765)-2^{2} 3 5^{2} 7^{2} 11^{2} 11971 x^{11}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "118/91 268/13", "discriminant": "11 8281 71162 -2515785 -59827597 -612043042 -3762840342 -15265487382 -42103272002 -78506801252 -94987355417 -67398344860 -21292817700", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "082df0c6e37c18b98ea10260e3e1c195", "dim_h": null, "inst": " 118/91 373/91 268/13 12732/91 105020/91 141027/13 10132651/91 15899010/13 183821689/13 15497571885/91", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "10", "laurent": null, "discriminant_tex": "-(3z+1)(11971z^6+16085z^5+8704z^4+2334z^3+289z^2+7z-1)(91+573z+770z^2)^2", "discr_factors": "-21292817700, z^6+16085/11971*z^5+8704/11971*z^4+2334/11971*z^3+289/11971*z^2+7/11971*z-1/11971, (13/110+573/770*z+z^2)^2, z+1/3", "dm_basis": null, "q": "0 1 -3 -27 -36 94 -2425 -45899 -523849 -6234311", "yuk": "1 118/91 3102/91 50770/91 116850/13 1875374/13 213286578/91 3475499411/91 8140409970/13 938042129737/91", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-573/1540-1/1540*48049^(1/2)","im":"0","approx_re":"-0.514416","approx_im":"0.0","exponents":["0","1","3","4"],"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":"-573/1540+1/1540*48049^(1/2)","im":"0","approx_re":"-0.22974","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","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[27*X^4, 432*X^4-540-2628*X-5760*X^3-5508*X^2, 295872*X+306240*X^2+112464-33792*X^3-129024*X^4, -1102080+17825792*X^3+6772736*X^2+1005568*X+335872*X^4, -65896448*X+209977344*X^4-7311360-67010560*X^2-67633152*X^3, -8728018944-20230963200*X-14659092480*X^3-3407872000*X^4-20752105472*X^2, -66441969664*X^2+32568770560*X-88264933376*X^4-76369887232*X^3+50988056576, 11803408990208+10383083438080*X^3+25540291461120*X+22371679338496*X^2+1950720458752*X^4, 14018773254144*X^3+16522739187712*X^4-88707717660672-43752831844352*X^2-124506806943744*X, -11378553778077696*X-8578509978992640*X^2-428603376402432*X^4-5853482078699520-3110518394978304*X^3, 20472631631282176*X^2+44573995231608832-2308974418329600*X^3+58566861243023360*X-2196824232296448*X^4, 1383827742532829184*X^2+1060244769013235712+1993713648320643072*X+419679190275588096*X^3+43980465111040000*X^4, -3489322140979691520+790803947068588032*X^2+250512729272483840*X^4+1173187702930014208*X^3-2883851873889026048*X, -86645879130887815168*X^2-137928368087755653120*X-76746685674950754304-21527206218830970880*X^3-1639310264362860544*X^4, -454233058416588226560*X^2-640682082989726760960*X-14771806777775226880*X^4-138350580552821637120*X^3-332635868477584834560, -28823037615171174400*(X+2)^4]", "text": "This is operator \"15.3\" from ...", "degz": 15, "h3": null, "sol": "1 20 388 7344 141636 2777360 55728816 1143301440 23982011716 513499103440", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 27 -540 -2628 -5508 -5760 432 112464 295872 306240 -33792 -129024 -1102080 1005568 6772736 17825792 335872 -7311360 -65896448 -67010560 -67633152 209977344 -8728018944 -20230963200 -20752105472 -14659092480 -3407872000 50988056576 32568770560 -66441969664 -76369887232 -88264933376 11803408990208 25540291461120 22371679338496 10383083438080 1950720458752 -88707717660672 -124506806943744 -43752831844352 14018773254144 16522739187712 -5853482078699520 -11378553778077696 -8578509978992640 -3110518394978304 -428603376402432 44573995231608832 58566861243023360 20472631631282176 -2308974418329600 -2196824232296448 1060244769013235712 1993713648320643072 1383827742532829184 419679190275588096 43980465111040000 -3489322140979691520 -2883851873889026048 790803947068588032 1173187702930014208 250512729272483840 -76746685674950754304 -137928368087755653120 -86645879130887815168 -21527206218830970880 -1639310264362860544 -332635868477584834560 -640682082989726760960 -454233058416588226560 -138350580552821637120 -14771806777775226880 -461168601842738790400 -922337203685477580800 -691752902764108185600 -230584300921369395200 -28823037615171174400", "new_number": "15.3", "id": 391, "operator_tex": "3^{3} \\theta^4+2^{2} 3^{2} x\\left(12\\theta^4-160\\theta^3-153\\theta^2-73\\theta-15\\right)-2^{4} 3 x^{2}\\left(2688\\theta^4+704\\theta^3-6380\\theta^2-6164\\theta-2343\\right)+2^{8} x^{3}\\left(1312\\theta^4+69632\\theta^3+26456\\theta^2+3928\\theta-4305\\right)+2^{12} x^{4}\\left(51264\\theta^4-16512\\theta^3-16360\\theta^2-16088\\theta-1785\\right)-2^{16} x^{5}\\left(52000\\theta^4+223680\\theta^3+316652\\theta^2+308700\\theta+133179\\right)-2^{21} x^{6}\\left(42088\\theta^4+36416\\theta^3+31682\\theta^2-15530\\theta-24313\\right)+2^{25} x^{7}\\left(58136\\theta^4+309440\\theta^3+666728\\theta^2+761160\\theta+351769\\right)+2^{29} x^{8}\\left(30776\\theta^4+26112\\theta^3-81496\\theta^2-231912\\theta-165231\\right)-2^{33} 3 x^{9}\\left(16632\\theta^4+120704\\theta^3+332890\\theta^2+441546\\theta+227145\\right)-2^{36} x^{10}\\left(31968\\theta^4+33600\\theta^3-297916\\theta^2-852260\\theta-648637\\right)+2^{40} x^{11}\\left(40000\\theta^4+381696\\theta^3+1258584\\theta^2+1813272\\theta+964287\\right)+2^{44} x^{12}\\left(14240\\theta^4+66688\\theta^3+44952\\theta^2-163928\\theta-198345\\right)-2^{48} x^{13}\\left(5824\\theta^4+76480\\theta^3+307828\\theta^2+490020\\theta+272659\\right)-2^{54} 5 x^{14}\\left(164\\theta^4+1536\\theta^3+5043\\theta^2+7113\\theta+3693\\right)-2^{60} 5^{2} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "44/3 220588/81", "discriminant": "15 27 432 -129024 335872 209977344 -3407872000 -88264933376 1950720458752 16522739187712 -428603376402432 -2196824232296448 43980465111040000 250512729272483840 -1639310264362860544 -14771806777775226880 -28823037615171174400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ae51313cd958206bb1b7a3c8ae23e509", "dim_h": null, "inst": " 44/3 -1421/9 220588/81 -14752264/243 1138508000/729 -10709297389/243 26132550216580/19683 -2479083315913288/59049 37209718959808/27 -222890635279564684376/4782969", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1+16z)(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z+3)^3(16z-1)^3", "discr_factors": "-28823037615171174400, (z^2-1/40*z-1/1280)^2, (z+3/16)^3, (z^2+1/16*z-1/256)^2, 1/16+z, (z-1/16)^3", "dm_basis": null, "q": "0 1 -52/3 1034/3 -685232/81 58632847/243 -7584520 1665120615890/6561 -174404409876800/19683 956870278022/3", "yuk": "1 44/3 -11236/9 73544 -944448268/243 142313510692/729 -9519303176 8963464724575624/19683 -1269290887248532580/59049 1004662411988360", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/16","im":"0","approx_re":"-0.1875","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32-1/32*5^(1/2)","im":"0","approx_re":"-0.101127","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"1/80-1/80*6^(1/2)","im":"0","approx_re":"-0.018119","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":"-1/32+1/32*5^(1/2)","im":"0","approx_re":"0.038627","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/80+1/80*6^(1/2)","im":"0","approx_re":"0.043119","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","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2","2","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -65533*X^4-99242*X^3-74971*X^2-25350*X-3380, 5957080*X^4+12486736*X^3+12080808*X^2+6145360*X+1248624, -236733120*X^4-654585984*X^3-804420096*X^2-464488128*X-99535488, 4723212800*X^4+17241773056*X^3+25236014080*X^2+16307101184*X+3735926784, -208896*(X+1)*(222704*X^3+833160*X^2+989659*X+317310), 45086441472*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "This is operator \"6.8\" from ...", "degz": 6, "h3": null, "sol": "1 20 1524 196400 31587220 5722985520 1118464762800 230426664262080 49357356300638100 10893607292632235600", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 169 -3380 -25350 -74971 -99242 -65533 1248624 6145360 12080808 12486736 5957080 -99535488 -464488128 -804420096 -654585984 -236733120 3735926784 16307101184 25236014080 17241773056 4723212800 -66284789760 -273020596224 -380779597824 -220565766144 -46521974784 450864414720 1758371217408 2209235632128 1082074595328 180345765888", "new_number": "6.8", "id": 430, "operator_tex": "13^{2} \\theta^4-13 x\\left(5041\\theta^4+7634\\theta^3+5767\\theta^2+1950\\theta+260\\right)+2^{3} x^{2}\\left(744635\\theta^4+1560842\\theta^3+1510101\\theta^2+768170\\theta+156078\\right)-2^{6} 3 x^{3}\\left(1232985\\theta^4+3409302\\theta^3+4189688\\theta^2+2419209\\theta+518414\\right)+2^{9} x^{4}\\left(9225025\\theta^4+33675338\\theta^3+49289090\\theta^2+31849807\\theta+7296732\\right)-2^{12} 3 17 x^{5}(\\theta+1)(222704\\theta^3+833160\\theta^2+989659\\theta+317310)+2^{15} 3^{2} 17^{2} 23^{2} x^{6}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "567/13 512341/13", "discriminant": "6 169 -65533 5957080 -236733120 4723212800 -46521974784 180345765888", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "00104510dfaa4ae75940f08df0a52bf5", "dim_h": null, "inst": " 567/13 11392/13 512341/13 34191454/13 2850663840/13 271552091292/13 28401421258434/13 3181262602886126/13 375500615867335284/13 46192689096277540140/13", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(1-293z+4232z^2)(408z-13)^2(16z-1)^2", "discr_factors": "180345765888, (z-13/408)^2, 1/4232-293/4232*z+z^2, (z-1/16)^2", "dm_basis": null, "q": "0 1 -70 1683 -88400 -661915 -345043794 -32308316307 -4302717734816 -553378095040209", "yuk": "1 567/13 91703/13 13833774/13 2188344759/13 356332980567/13 58655265643982/13 9741687491643429/13 1628806454866041271/13 273739948967301255810/13", "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":"293/8464-41/8464*41^(1/2)","im":"0","approx_re":"0.0036","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/408","im":"0","approx_re":"0.031862745098","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"293/8464+41/8464*41^(1/2)","im":"0","approx_re":"0.065634","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","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -4*X*(2*X^3+82*X^2+53*X+12), -4895*X^4-18410*X^3-26199*X^2-18308*X-5120, -60679*X^4-272424*X^3-497452*X^2-430092*X-143808, -344527*X^4-1870838*X^3-4034628*X^2-3987101*X-1478544, -(X+1)*(1076509*X^3+5847783*X^2+11226106*X+7492832), -2*(X+1)*(X+2)*(944887*X^2+4249317*X+5045304), -3328*(X+3)*(X+2)*(X+1)*(518*X+1381), -621920*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.40\" from ...", "degz": 8, "h3": null, "sol": "1 0 20 168 2652 40080 666920 11536560 207013660 3816224160", "n_discr_factors": "6", "c3": null, "operator": "4 8 0 0 0 0 16 0 -48 -212 -328 -8 -5120 -18308 -26199 -18410 -4895 -143808 -430092 -497452 -272424 -60679 -1478544 -3987101 -4034628 -1870838 -344527 -7492832 -18718938 -17073889 -6924292 -1076509 -20181216 -47269092 -39366058 -14167956 -1889774 -27575808 -60899072 -46538752 -14939392 -1723904 -14926080 -31096000 -21767200 -6219200 -621920", "new_number": "8.40", "id": 486, "operator_tex": "2^{4} \\theta^4-2^{2} x\\theta(2\\theta^3+82\\theta^2+53\\theta+12)-x^{2}\\left(4895\\theta^4+18410\\theta^3+26199\\theta^2+18308\\theta+5120\\right)-x^{3}\\left(60679\\theta^4+272424\\theta^3+497452\\theta^2+430092\\theta+143808\\right)-x^{4}\\left(344527\\theta^4+1870838\\theta^3+4034628\\theta^2+3987101\\theta+1478544\\right)-x^{5}(\\theta+1)(1076509\\theta^3+5847783\\theta^2+11226106\\theta+7492832)-2 x^{6}(\\theta+1)(\\theta+2)(944887\\theta^2+4249317\\theta+5045304)-2^{8} 13 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(518\\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "5/4 35/2", "discriminant": "8 16 -8 -4895 -60679 -344527 -1076509 -1889774 -1723904 -621920", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d3cb0fbbc65d6c5dace733d3d1ca181b", "dim_h": null, "inst": " 5/4 57/16 35/2 459/4 3615/4 97217/12 317945/4 833711 110476691/12 1694285265/16", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2", "discr_factors": "-621920, z+1/5, z+1/2, (z+4/13)^2, (z+1/4)^2, z-1/23, z+1", "dm_basis": null, "q": "0 1 -3 -25 -15 88 -2373 -34656 -361587 -4196900", "yuk": "1 5/4 119/4 1895/4 29495/4 112970 7001633/4 27263785 1707469623/4 6711459452", "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":"-4/13","im":"0","approx_re":"-0.307692307692","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","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/5","im":"0","approx_re":"-0.2","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":"1/23","im":"0","approx_re":"0.0434782608696","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}]}