{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -12*(3*X+1)*(3*X+2)*(3*X^2+3*X+1), 288*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "B*d", "degz": 2, "h3": "24", "sol": "1 24 1800 188160 23423400 3257077824 488795763456 77515931750400 12811645904789160 2186013527216376000", "n_discr_factors": "2", "c3": "-162", "operator": "4 2 0 0 0 0 1 -24 -180 -504 -648 -324 11520 67392 127008 93312 23328", "new_number": "2.14", "id": 5, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(3\\theta^2+3\\theta+1)+2^{5} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "24 5832", "discriminant": "2 1 -324 23328", "aesz": "48", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "8081a3989d09a7d612953dac3341d90c", "dim_h": "11", "inst": " 24 291/2 5832 247116 12634944 1428093585/2 44538150984 5965179917793/2 210544112347488 15478336155532764", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(216z-1)(108z-1)", "discr_factors": "23328, z-1/216, z-1/108", "dm_basis": ["-162*lambda", "15/2", "1", "1", "-7/2", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -84 4950 -267760 12647805 -598963032 25047931322 -1164686536896 41143256426646", "yuk": "1 24 1188 157488 15816612 1579368024 154234265832 15276585787536 1527086074771620 153486657901476240", "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":["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","24","1","0","0","0","1","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+162*lambda","0","189/8*lambda",".25679681e-1","7/2","1","49/96","-189/8*lambda","0","0","1","0","24","0","7/2","1-162*lambda"],"monodromy_dm":["1","-11","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["13/4+324*lambda","-9/16-81*lambda","21/64+189/4*lambda","-.54109387e-1-243/8*lambda","7+1/500000000*I","-3/4+1/1000000000*I","49/48-1/1000000000*I","-21/64-189/4*lambda","12+1/250000000*I","-3+1/500000000*I","11/4-1/500000000*I","-9/16-81*lambda","48.+.19e-7*I","-11.999999983+.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","7-1/125000000*I","-5/4-324*lambda"],"monodromy_dm":["-3","-28","-5/2","-2","1","8","5/8","1/2","-12","-84","-13/2","-6","9","63","45/8","11/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -59*X^4-118*X^3-105*X^2-46*X-8, 96*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"2.69\" from ...", "degz": 2, "h3": "160", "sol": "1 8 120 2240 46840 1051008 24757824 604538880 15179095800 389772468800", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -46 -105 -118 -59 768 3264 5088 3456 864", "new_number": "2.69", "id": 65, "operator_tex": "\\theta^4-x\\left(59\\theta^4+118\\theta^3+105\\theta^2+46\\theta+8\\right)+2^{5} 3 x^{2}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "1 5", "discriminant": "2 1 -59 864", "aesz": "205", "n_sing_complex": "0", "inst_int": "", "c2h": "160", "hash": "4fb2e7002e630237d0458c3985cd6a18", "dim_h": "40", "inst": " 1 7/4 5 24 759/5 4475/4 8822 72536 615358 107517313/20", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(32z-1)(27z-1)", "discr_factors": "864, z-1/27, z-1/32", "dm_basis": ["-310145437/500000000*I", "100/3", "1", "1", "-20/3", "-80", "-1", "0", "0", "160", "0", "0", "-160", "0", "0", "0"], "q": "0 1 -14 133 -1032 6990 -43798 253594 -1428704 7475227", "yuk": "1 1 15 136 1551 18976 241800 3025947 37139983 448596118", "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":["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","160","1","0","0","0","1","1"]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","16/3*lambda",".2404755e-2","20/3","1","5/18","-16/3*lambda","0","0","1","0","160","0","20/3","1.-.620290874*I"],"monodromy_dm":["1","-40","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.333327178+1.235680918*I","-.293785798-.155290034*I",".97173439e-1+.52174089e-1*I","-.12126753e-1-.18089273e-1*I","13.327492354-.18865422e-1*I","-.677351606+.3680160e-2*I",".556724039+.2392839e-2*I","-.96900942e-1-.51907518e-1*I","39.969803488-.74697659e-1*I","-5.030457990+.13317419e-1*I","2.669647034+1/243*I*Pi^(1/6)*Zeta(5)^7","-.290681436-.15554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498740554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498741*I","319.859816505-.452770130*I","-40.256438534+.88323845e-1*I","13.361376945+.57428145e-1*I","-1.325622606-1.245780435*I"],"monodromy_dm":["-3001219/1000000-1031/500000*I","-50063529/500000+81061/1000000*I","-2250727/1000000+1691/500000*I","-499781/250000+283/100000*I","249997/500000+31/1000000*I","6755959/500000-15801/1000000*I","70313/250000-11/20000*I","249811/1000000-467/1000000*I","-39999541/1000000-2481/1000000*I","-500476737/500000+1264109/1000000*I","-21500131/1000000+5501/125000*I","-9992451/500000+37349/1000000*I","27999679/1000000+1737/1000000*I","87583429/125000-221219/250000*I","3937523/250000-6161/200000*I","14989431/1000000-817/31250*I"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -172*X^4-344*X^3-286*X^2-114*X-18, 36*(X+1)^2*(236*X^2+472*X+187), -32400*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 103 =$c \\ast c$.", "degz": 3, "h3": "36", "sol": "1 18 630 28980 1593270 99340668 6771183804 491734025640 37390439327670 2942412630737580", "n_discr_factors": "2", "c3": "-48", "operator": "4 3 0 0 0 0 1 -18 -114 -286 -344 -172 6732 30456 49212 33984 8496 -324000 -1263600 -1587600 -777600 -129600", "new_number": "3.10", "id": 71, "operator_tex": "\\theta^4-2 x\\left(86\\theta^4+172\\theta^3+143\\theta^2+57\\theta+9\\right)+2^{2} 3^{2} x^{2}(\\theta+1)^2(236\\theta^2+472\\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "10 664", "discriminant": "3 1 -172 8496 -129600", "aesz": "~103", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "9239615e8ac132ca232c13367a39ae3b", "dim_h": "12", "inst": " 10 24 664 9088 234388 5667648 162977404 4849452496 154029465758 5070777681360", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(100z-1)(-1+36z)^2", "discr_factors": "-129600, z-1/100, (-1/36+z)^2", "dm_basis": ["-48*lambda", "9", "1", "1", "-3", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -42 1407 -46436 1436487 -44122518 1303343085 -38697997416 1108968963840", "yuk": "1 10 202 17938 581834 29298510 1224230098 55901249582 2482920259786 112287480555520", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/100","im":"0","approx_re":"0.01","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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": "[X^4, -4*(3*X^2+3*X+1)*(17*X^2+17*X+6), 10400*X^4+69248*X^3+97696*X^2+56896*X+13440, 470016*X^4-2820096*X^3-8607744*X^2-6607872*X-1880064, -58540032*X^4-117080064*X^3+214401024*X^2+272941056*X+98205696, 1082916864*X^4+10829168640*X^3+6157762560*X^2-615776256*X-1358954496, 55207526400*X^4-146767085568*X^3-252935405568*X^2-146767085568*X-24461180928, -48922361856*(3*X^2+3*X+1)*(17*X^2+17*X+6), 28179280429056*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "96", "sol": "1 24 840 34944 1618344 80725824 4249779456 232938823680 13169473126056 762911587628736", "n_discr_factors": "6", "c3": "472", "operator": "4 8 0 0 0 0 1 -24 -140 -344 -408 -204 13440 56896 97696 69248 10400 -1880064 -6607872 -8607744 -2820096 470016 98205696 272941056 214401024 -117080064 -58540032 -1358954496 -615776256 6157762560 10829168640 1082916864 -24461180928 -146767085568 -252935405568 -146767085568 55207526400 -293534171136 -1712282664960 -4207323119616 -4990080909312 -2495040454656 28179280429056 112717121716224 169075682574336 112717121716224 28179280429056", "new_number": "8.14", "id": 457, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{5} x^{2}\\left(325\\theta^4+2164\\theta^3+3053\\theta^2+1778\\theta+420\\right)+2^{10} 3^{2} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{14} 3^{2} x^{4}\\left(397\\theta^4+794\\theta^3-1454\\theta^2-1851\\theta-666\\right)+2^{18} 3^{4} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{21} 3^{4} x^{6}\\left(325\\theta^4-864\\theta^3-1489\\theta^2-864\\theta-144\\right)-2^{26} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{32} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "24 15448/3", "discriminant": "8 1 -204 10400 470016 -58540032 1082916864 55207526400 -2495040454656 28179280429056", "aesz": "176", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "e2a40a57f7e88dba6655d936b4abe327", "dim_h": "20", "inst": " 24 -509/2 15448/3 -128530 3746624 -718242157/6 4087498824 -292948763739/2 16349300937760/3 -208868645210788", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2", "discr_factors": "28179280429056, (z+1/48)^2, z-1/32, (z-1/48)^2, z-1/64, z-1/36, z-1/72", "dm_basis": null, "q": "0 1 -44 1814 -75664 3198717 -136975528 5934383866 -259779116352 11475414116374", "yuk": "1 24 -2012 139056 -8227932 468328024 -25856580632 1402012096656 -74994891745116 3972880128014736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}