{"count": 21, "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, 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{"pols": "[X^4, -4*(2*X+1)^2*(17*X^2+17*X+6), 1152*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast g$.", "degz": 2, "h3": "48", "sol": "1 24 1512 124800 11730600 1191081024 127328737536 14125302816768 1611627491845800 187994423786769600", "n_discr_factors": "2", "c3": "-16", "operator": "4 2 0 0 0 0 1 -24 -164 -436 -544 -272 10368 55296 101376 73728 18432", "new_number": "2.24", "id": 16, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 1684/3", "discriminant": "2 1 -272 18432", "aesz": "137", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "198d6c822d6c46225ac2553d60df6539", "dim_h": "16", "inst": " 20 2 1684/3 7602 173472 16800962/3 170592988 5706758282 581797416016/3 6746210337168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(144z-1)(128z-1)", "discr_factors": "18432, z-1/128, z-1/144", "dm_basis": ["-16*lambda", "12", "1", "1", "-4", "-24", "-1", "0", "0", "48", "0", "0", "-48", "0", "0", "0"], "q": "0 1 -68 3294 -132944 4754733 -156431544 4806781970 -140479337024 3915889529094", "yuk": "1 20 36 15176 486564 21684020 1209684456 58513394904 2921860726948 141376772107064", "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","48","1","0","0","0","1","1"]},{"re":"1/144","im":"0","approx_re":"0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+16*lambda","0","4/3*lambda",".125248e-3","4","1","1/3","-4/3*lambda","0","0","1","0","48","0","4","1-16*lambda"],"monodromy_dm":["1","-16","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[".924152876+.943952044*I",".188111204+1.275393351*I",".593885779-.164736576*I","-.98788356e-1-.111719004*I",".205812544+3.214663066*I","2.256285526+4.201440782*I","1.918711704-.844672672*I","-.387126151-.327818207*I","-.81202836e-1+5.639775328*I","1.617313859+7.506248400*I","4.465075410-1.211574339*I","-.630856884-.62528948587308939323761000463177396943029180176007410838351088466882816118573413617415470125057897174617878647522000926354793886058360352014821676702176933765632237146827234830940250115794349235757295*I","2.469750531+38.575956789*I","15.075426310+50.417289384*I","23.024540442-10.136072063*I","-3.645513812-3.933818487*I"],"monodromy_dm":["-1225771/500000+67903/250000*I","-3220853/200000+3212591/125000*I","131309/500000+123347/500000*I","-51453/1000000-401833/500000*I","505191/1000000-1/10000*I","1818059/500000-710951/200000*I","-17693/500000-7777/200000*I","-423/250000+23499/200000*I","-12124581/1000000+2401/1000000*I","-63266827/1000000+85314113/1000000*I","924629/500000+933237/1000000*I","40601/1000000-176243/62500*I","5051909/500000-2001/1000000*I","10544471/200000-35547547/500000*I","-141543/200000-777697/1000000*I","193233/200000+1174953/500000*I"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(7*X^2+7*X+2), -128*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "C*a", "degz": 2, "h3": "12", "sol": "1 24 4200 1034880 311711400 104849769024 37939351946496 14450910769152000 5718086730211026600 2330121882579042552000", "n_discr_factors": "2", "c3": "-228", "operator": "4 2 0 0 0 0 1 -24 -212 -660 -896 -448 -13440 -90112 -176128 -131072 -32768", "new_number": "2.3", "id": 33, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(7\\theta^2+7\\theta+2)-2^{7} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "52 220220", "discriminant": "2 1 -448 -32768", "aesz": "68", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "13a48045ff0a42a9fcfbdb710baf1997", "dim_h": "8", "inst": " 52 2814 220220 29135058 4512922272 813434977450 159977765979708 33749653506239610 7496689709059170544 1735643559203414845168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(64z+1)(512z-1)", "discr_factors": "-32768, z-1/512, z+1/64", "dm_basis": ["-1104893119/1000000000*I", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -116 478 113008 -56372435 -6168706136 -1532666623214 -363738855142208 -89086162864734458", "yuk": "1 52 22564 5945992 1864666276 564115284052 175701961097704 54872373731039896 17279822597059346596 5465086797904141272568", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+2.209786237*I","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","1+152*lambda","-.171535199-114*lambda","8","-3","8/3","-1-152*lambda","12","-6","5","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","24","-12","8","-2.-2.209786237*I"],"monodromy_dm":["-5","-24","-3","-2","3","13","3/2","1","-24","-96","-11","-8","18","72","9","7"]},{"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","12","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+1.104893119*I","0","57*lambda","276/2713","3","1","3/4","-57*lambda","0","0","1","0","12","0","3","1.-1.104893119*I"],"monodromy_dm":["1","-8","-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":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -128*X^4-256*X^3-252*X^2-124*X-24, 256*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"2.63\" from ...", "degz": 2, "h3": null, "sol": "1 24 936 43008 2145960 112521024 6098593536 338463166464 19121128195752 1095276775623360", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -24 -124 -252 -256 -128 3840 15872 24320 16384 4096", "new_number": "2.63", "id": 59, "operator_tex": "\\theta^4-2^{2} x\\left(32\\theta^4+64\\theta^3+63\\theta^2+31\\theta+6\\right)+2^{8} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-4 -44", "discriminant": "2 1 -128 4096", "aesz": "84", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "908b978c0c447d3643c3018c40e7f5d1", "dim_h": null, "inst": " -4 -11 -44 -156 -288 3207 55764 578820 4717904 29814248", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(64z-1)^2", "discr_factors": "4096, (z-1/64)^2", "dm_basis": ["-96*lambda", "-6", "1", "1", "-2", "24", "-1", "0", "0", "-48", "0", "0", "48", "0", "0", "0"], "q": "0 1 -28 478 -6064 64813 -610696 5253394 -42301888 320357638", "yuk": "1 -4 -92 -1192 -10076 -36004 691432 19127048 296345764 3439350824", "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","-48","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":["1+96*lambda","1/4","-4*lambda",".5907751e-2","2","1","-1/12","4*lambda","0","6","1","1/4","-48","0","2","1-96*lambda"],"monodromy_dm":["1","4","-1","-1","0","-2","1/8","0","0","-72","4","0","0","60","-5/2","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -600-5250*X-16895*X^2-23290*X^3-13085*X^4, -165120-1038720*X-1974144*X^2-935232*X^3+129216*X^4, 921600+9400320*X+32044032*X^2+39813120*X^3+8801280*X^4, -3538944*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "10", "sol": "1 24 3960 974400 292030200 98002929024 35404004091456 13469740411944960 5325269471817867000 2168604409044940152000", "n_discr_factors": "3", "c3": "-120", "operator": "4 4 0 0 0 0 25 -600 -5250 -16895 -23290 -13085 -165120 -1038720 -1974144 -935232 129216 921600 9400320 32044032 39813120 8801280 -7077888 -60162048 -187564032 -254803968 -127401984", "new_number": "4.44", "id": 142, "operator_tex": "5^{2} \\theta^4-5 x\\left(2617\\theta^4+4658\\theta^3+3379\\theta^2+1050\\theta+120\\right)+2^{6} 3 x^{2}\\left(673\\theta^4-4871\\theta^3-10282\\theta^2-5410\\theta-860\\right)+2^{10} 3^{2} x^{3}\\left(955\\theta^4+4320\\theta^3+3477\\theta^2+1020\\theta+100\\right)-2^{17} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "379/5 1364199/5", "discriminant": "4 25 -13085 129216 8801280 -127401984", "aesz": "232", "n_sing_complex": "0", "inst_int": "", "c2h": "52", "hash": "8d5ff690c87757ed51a092dee764eede", "dim_h": "6", "inst": " 379/5 3346 1364199/5 177727432/5 5658116533 5162925665472/5 1034132839801394/5 44368440569992104 50146684202347697994/5 2362720295938250247382", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(27z+1)(512z-1)(-5+96z)^2", "discr_factors": "-127401984, (-5/96+z)^2, z-1/512, z+1/27", "dm_basis": null, "q": "0 1 -114 1029 -116984 -43625010 -7822436202 -1800503860710 -431538538385184 -107734627015030629", "yuk": "1 379/5 134219/5 36833752/5 11374689867/5 3536322833504/5 1115191980709544/5 354707564051878521/5 113583207870554476107/5 36556932783511508671378/5", "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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/96","im":"0","approx_re":"0.0520833333333","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-184*X-545*X^2-722*X^3-289*X^4, 5136*X^4+65616*X^3+116664*X^2+63360*X+11232, 72576+746496*X+2449152*X^2+2985984*X^3+801216*X^4, 746496*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70", "degz": 4, "h3": "18", "sol": "1 24 1944 232800 34133400 5649061824 1011627229536 191367704601216 37683808295304600 7651704687834292800", "n_discr_factors": "3", "c3": "-64", "operator": "4 4 0 0 0 0 1 -24 -184 -545 -722 -289 11232 63360 116664 65616 5136 72576 746496 2449152 2985984 801216 746496 5971968 17915904 23887872 11943936", "new_number": "4.69", "id": 169, "operator_tex": "\\theta^4-x\\left(24+184\\theta+545\\theta^2+722\\theta^3+289\\theta^4\\right)+2^{3} 3 x^{2}\\left(214\\theta^4+2734\\theta^3+4861\\theta^2+2640\\theta+468\\right)+2^{6} 3^{2} x^{3}\\left(1391\\theta^4+5184\\theta^3+4252\\theta^2+1296\\theta+126\\right)+2^{10} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "49 173876/9", "discriminant": "4 1 -289 5136 801216 11943936", "aesz": "350", "n_sing_complex": "0", "inst_int": "", "c2h": "60", "hash": "e6de16eb3758d2ed5687f4b2a2abf36b", "dim_h": "8", "inst": " 49 136 173876/9 781152 57087750 12201523592/3 338790123846 29537353606592 24592780153285625/9 262707875156521480", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(256z-1)(81z-1)(1+24z)^2", "discr_factors": "11943936, z-1/256, (1/24+z)^2, z-1/81", "dm_basis": null, "q": "0 1 -88 4980 -282064 12865650 -690703872 23666776560 -1799987151264 3529620262935", "yuk": "1 49 1137 521677 49994865 7135968799 878510221389 116205012479227 15123125096569969 1992015192416657302", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -639*X^4-558*X^3-447*X^2-168*X-24, 151632*X^4+232848*X^3+204984*X^2+84672*X+12960, -16030656*X^4-31850496*X^3-27661824*X^2-10368000*X-1451520, 3317760*(2*X+1)^2*(51*X^2+69*X+32), -298598400*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.100\" from ...", "degz": 5, "h3": "36", "sol": "1 24 1944 218400 28488600 4048761024 608371749216 95064025769856 15292201195042200 2515650430048641600", "n_discr_factors": "3", "c3": "-16", "operator": "4 5 0 0 0 0 1 -24 -168 -447 -558 -639 12960 84672 204984 232848 151632 -1451520 -10368000 -27661824 -31850496 -16030656 106168320 653598720 1509580800 1592524800 676823040 -2687385600 -14332723200 -26276659200 -19110297600 -4777574400", "new_number": "5.100", "id": 182, "operator_tex": "\\theta^4-3 x\\left(213\\theta^4+186\\theta^3+149\\theta^2+56\\theta+8\\right)+2^{3} 3^{3} x^{2}\\left(702\\theta^4+1078\\theta^3+949\\theta^2+392\\theta+60\\right)-2^{6} 3^{3} x^{3}\\left(9277\\theta^4+18432\\theta^3+16008\\theta^2+6000\\theta+840\\right)+2^{13} 3^{4} 5 x^{4}(2\\theta+1)^2(51\\theta^2+69\\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "15 27140/3", "discriminant": "5 1 -639 151632 -16030656 676823040 -4777574400", "aesz": "347\n", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "f00de20026c099e75b447c475ab287e4", "dim_h": "13", "inst": " 15 1329/4 27140/3 220680 5952570 550577279/3 6782826234 302695932456 138944230607815/9 1711409037498435/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(192z-1)(1728z^2-207z+1)(-1+120z)^2", "discr_factors": "-4777574400, z-1/192, z^2-23/192*z+1/1728, (-1/120+z)^2", "dm_basis": null, "q": "0 1 -72 2484 -54576 1205874 -26096256 504161136 -10716165216 43953392151", "yuk": "1 15 2673 244275 14126193 744071265 39641811021 2326509398277 154980331543665 11254482679477290", "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":"23/384-11/1152*33^(1/2)","im":"0","approx_re":"0.005043","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192","im":"0","approx_re":"0.00520833333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/120","im":"0","approx_re":"0.00833333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"23/384+11/1152*33^(1/2)","im":"0","approx_re":"0.114748","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","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -594*X^4-216*X^3-234*X^2-126*X-24, 137052*X^4+128304*X^3+136728*X^2+60588*X+10224, -15274008*X^4-26453952*X^3-28308528*X^2-14224248*X-2807136, 816293376*X^4+2244806784*X^3+2692634400*X^2+1527715728*X+331304256, -51018336*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.12\" from ...", "degz": 5, "h3": "72", "sol": "1 24 1152 71520 5101200 396676224 32692889376 2808042450048 248675352512400 22544379039811200", "n_discr_factors": "3", "c3": "450", "operator": "4 5 0 0 0 0 1 -24 -126 -234 -216 -594 10224 60588 136728 128304 137052 -2807136 -14224248 -28308528 -26453952 -15274008 331304256 1527715728 2692634400 2244806784 816293376 -14285134080 -61528113216 -96883820064 -66119763456 -16529940864", "new_number": "5.12", "id": 214, "operator_tex": "\\theta^4-2 3 x\\left(99\\theta^4+36\\theta^3+39\\theta^2+21\\theta+4\\right)+2^{2} 3^{2} x^{2}\\left(3807\\theta^4+3564\\theta^3+3798\\theta^2+1683\\theta+284\\right)-2^{3} 3^{5} x^{3}\\left(7857\\theta^4+13608\\theta^3+14562\\theta^2+7317\\theta+1444\\right)+2^{4} 3^{9} x^{4}\\left(2592\\theta^4+7128\\theta^3+8550\\theta^2+4851\\theta+1052\\right)-2^{5} 3^{13} x^{5}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "-30 -14632", "discriminant": "5 1 -594 137052 -15274008 816293376 -16529940864", "aesz": "74", "n_sing_complex": "0", "inst_int": "", "c2h": "-36", "hash": "e668180adb7c88d4e5fbab5eb7ee61c7", "dim_h": "9", "inst": " -30 -516 -14632 -4227807/8 -22139868 -1021798708 -50464650036 -2619966661332 -141334834087546 -7859316901635348", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+54z)(162z-1)^2(108z-1)^2", "discr_factors": "-16529940864, (z-1/108)^2, -1/54+z, (z-1/162)^2", "dm_basis": null, "q": "0 1 -30 495 -8236 58839 -2049570 -24155251 -973292856 1233846432", "yuk": "1 -30 -4158 -395094 -33826614 -2767483530 -220708920150 -17309374962378 -1341422964428598 -103033094050216128", "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":"1/162","im":"0","approx_re":"0.00617283950617","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/6","7/6","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -3072*X^4-3840*X^3-3252*X^2-1332*X-216, 397312*X^4+901120*X^3+1025536*X^2+569856*X+118656, -24641536*X^4-75497472*X^3-99680256*X^2-60751872*X-13271040, 2097152*(2*X+1)*(176*X^3+552*X^2+622*X+231), -2147483648*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.17\" from ...", "degz": 5, "h3": null, "sol": "1 24 1128 67200 4634280 356457024 29883254016 2681828278272 253852820793000 25044278060218560", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 9 -216 -1332 -3252 -3840 -3072 118656 569856 1025536 901120 397312 -13271040 -60751872 -99680256 -75497472 -24641536 484442112 2273312768 3766484992 2684354560 738197504 -6442450944 -30064771072 -49392123904 -34359738368 -8589934592", "new_number": "5.17", "id": 224, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(256\\theta^4+320\\theta^3+271\\theta^2+111\\theta+18\\right)+2^{7} x^{2}\\left(3104\\theta^4+7040\\theta^3+8012\\theta^2+4452\\theta+927\\right)-2^{15} x^{3}\\left(752\\theta^4+2304\\theta^3+3042\\theta^2+1854\\theta+405\\right)+2^{21} x^{4}(2\\theta+1)(176\\theta^3+552\\theta^2+622\\theta+231)-2^{31} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "28/3 3892/3", "discriminant": "5 9 -3072 397312 -24641536 738197504 -8589934592", "aesz": "119", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "dc8ec37012f2c92c83e6519935956eeb", "dim_h": null, "inst": " 28/3 394/3 3892/3 108262/3 1044128 103730222/3 1261935036 148614445022/3 6125740231888/3 87828293979248", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+128z)(64z-1)^2(128z-3)^2", "discr_factors": "-8589934592, (z-1/64)^2, (z-3/128)^2, -1/128+z", "dm_basis": null, "q": "0 1 -52 2014 -71568 2248493 -69311704 1952525586 -57312184128 1467953048326", "yuk": "1 28/3 1060 105112/3 6931948/3 391548028/3 7468612072 1298531152072/3 76090602783212/3 4465664629151464/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","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","1/4","3/4","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128","im":"0","approx_re":"0.0234375","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -216-1764*X-5556*X^2-7584*X^3-3216*X^4, 56448+309504*X+547840*X^2+206848*X^3-57344*X^4, -552960-1179648*X+3096576*X^2+8257536*X^3+1703936*X^4, 524288*(8*X^2-28*X-33)*(2*X+1)^2, -16777216*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.32\" from ...", "degz": 5, "h3": "12", "sol": "1 24 2664 470400 102047400 24865372224 6530512133376 1807527662493696 520080121087698600 154177852438395614400", "n_discr_factors": "3", "c3": "-60", "operator": "4 5 0 0 0 0 9 -216 -1764 -5556 -7584 -3216 56448 309504 547840 206848 -57344 -552960 -1179648 3096576 8257536 1703936 -17301504 -83886080 -123731968 -41943040 16777216 -150994944 -805306368 -1476395008 -1073741824 -268435456", "new_number": "5.32", "id": 241, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(268\\theta^4+632\\theta^3+463\\theta^2+147\\theta+18\\right)-2^{7} x^{2}\\left(448\\theta^4-1616\\theta^3-4280\\theta^2-2418\\theta-441\\right)+2^{12} x^{3}\\left(416\\theta^4+2016\\theta^3+756\\theta^2-288\\theta-135\\right)+2^{19} x^{4}(8\\theta^2-28\\theta-33)(2\\theta+1)^2-2^{24} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "220/3 89212", "discriminant": "5 9 -3216 -57344 1703936 16777216 -268435456", "aesz": "215", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "ced61f5675491a3c4446c0e55e7bc36b", "dim_h": "6", "inst": " 220/3 3538/3 89212 7484350 2459418080/3 101765882498 41645703700340/3 2027421395102806 311986325809618928 50032192549267851440", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(4096z^2-384z+1)(3+64z)^2", "discr_factors": "-268435456, z-1/16, z^2-3/32*z+1/4096, (3/64+z)^2", "dm_basis": null, "q": "0 1 -100 4062 -254928 1863469 -1363683960 -138587625198 -25730687151168 -4253310930124026", "yuk": "1 220/3 9508 7226392/3 479007908 307427260220/3 21981433037800 4761492123072280 1038039754771644580 682314094545643821928/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64","im":"0","approx_re":"-0.046875","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":"3/64-1/32*2^(1/2)","im":"0","approx_re":"0.002681","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64+1/32*2^(1/2)","im":"0","approx_re":"0.091069","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","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -2904-24684*X-79068*X^2-108768*X^3-48048*X^4, 50688+204864*X-399968*X^2-2703872*X^3-1989248*X^4, -1297296-7767936*X-17613696*X^2-22758912*X^3-23232768*X^4, -18432*(964*X^2+1360*X+669)*(2*X+1)^2, -5308416*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.83\" from ...", "degz": 5, "h3": "11", "sol": "1 24 3240 675600 171901800 49034994624 15064673467536 4875632664439680 1640033450646762600 568302437330193508800", "n_discr_factors": "2", "c3": "-88", "operator": "4 5 0 0 0 0 121 -2904 -24684 -79068 -108768 -48048 50688 204864 -399968 -2703872 -1989248 -1297296 -7767936 -17613696 -22758912 -23232768 -12331008 -74391552 -167362560 -171343872 -71073792 -47775744 -254803968 -467140608 -339738624 -84934656", "new_number": "5.83", "id": 297, "operator_tex": "11^{2} \\theta^4-2^{2} 3 11 x\\left(364\\theta^4+824\\theta^3+599\\theta^2+187\\theta+22\\right)-2^{5} x^{2}\\left(62164\\theta^4+84496\\theta^3+12499\\theta^2-6402\\theta-1584\\right)-2^{4} 3 x^{3}\\left(484016\\theta^4+474144\\theta^3+366952\\theta^2+161832\\theta+27027\\right)-2^{11} 3^{2} x^{4}(964\\theta^2+1360\\theta+669)(2\\theta+1)^2-2^{16} 3^{4} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "852/11 1678156/11", "discriminant": "5 121 -48048 -1989248 -23232768 -71073792 -84934656", "aesz": "316", "n_sing_complex": "2", "inst_int": "", "c2h": "50", "hash": "b8201d587a016cc013e2477aadb5c1ff", "dim_h": "6", "inst": " 852/11 21572/11 1678156/11 15912512 22956446184/11 3433194654748/11 563991930666972/11 9018115493682352 18385133020280565556/11 322819093214895368408", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(2304z^3+1664z^2+432z-1)(11+192z)^2", "discr_factors": "-84934656, z^3+13/18*z^2+3/16*z-1/2304, (11/192+z)^2", "dm_basis": null, "q": "0 1 -108 3282 -216528 -12519609 -2779275096 -499664503174 -98806684879296 -20228146546192713", "yuk": "1 852/11 173428/11 45311064/11 11202581876/11 2869555773852/11 67415462809928 193449232218772248/11 50790026471621588340/11 13402761971784577601388/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"-1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"-0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/192","im":"0","approx_re":"-0.0572916666667","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":"1/216*(89027+11799*57^(1/2))^(1/3)-53/54/(89027+11799*57^(1/2))^(1/3)-13/54","im":"0","approx_re":"0.002294","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","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -152*X^4-200*X^3-212*X^2-112*X-24, 9872*X^4+25568*X^3+37776*X^2+28992*X+9376, -364032*X^4-1399808*X^3-2642176*X^2-2539008*X-1014016, 8529920*X^4+43130880*X^3+98770944*X^2+112343040*X+52101120, -135135232*X^4-830013440*X^3-2213789696*X^2-2879913984*X-1501495296, 1517879296*X^4+10569777152*X^3+31405178880*X^2+45223772160*X+25817448448, -12704546816*X^4-93967089664*X^3-293598134272*X^2-446554963968*X-269278511104, 83248545792*X^4+626159255552*X^3+1939722993664*X^2+2903272062976*X+1730242674688, -436207616000*X^4-3331284008960*X^3-10178669838336*X^2-14365726081024*X-7823954018304, 1791001362432*X^4+13958643712000*X^3+44105019162624*X^2+63200443760640*X+33853200662528, -5634997092352*X^4-43843026157568*X^3-140393890971648*X^2-210762635149312*X-122007135977472, 13194139533312*X^4+107752139522048*X^3+340298848796672*X^2+490931941801984*X+272060408397824, -1099511627776*(2*X+5)^4]", "text": "This is operator \"13.3\" from ...", "degz": 13, "h3": null, "sol": "1 24 464 8832 178960 4010368 100357376 2772019200 82738408720 2613822935424", "n_discr_factors": "4", "c3": null, "operator": "4 13 0 0 0 0 1 -24 -112 -212 -200 -152 9376 28992 37776 25568 9872 -1014016 -2539008 -2642176 -1399808 -364032 52101120 112343040 98770944 43130880 8529920 -1501495296 -2879913984 -2213789696 -830013440 -135135232 25817448448 45223772160 31405178880 10569777152 1517879296 -269278511104 -446554963968 -293598134272 -93967089664 -12704546816 1730242674688 2903272062976 1939722993664 626159255552 83248545792 -7823954018304 -14365726081024 -10178669838336 -3331284008960 -436207616000 33853200662528 63200443760640 44105019162624 13958643712000 1791001362432 -122007135977472 -210762635149312 -140393890971648 -43843026157568 -5634997092352 272060408397824 490931941801984 340298848796672 107752139522048 13194139533312 -687194767360000 -1099511627776000 -659706976665600 -175921860444160 -17592186044416", "new_number": "13.3", "id": 371, "operator_tex": "\\theta^4-2^{2} x\\left(38\\theta^4+50\\theta^3+53\\theta^2+28\\theta+6\\right)+2^{4} x^{2}\\left(617\\theta^4+1598\\theta^3+2361\\theta^2+1812\\theta+586\\right)-2^{8} x^{3}\\left(1422\\theta^4+5468\\theta^3+10321\\theta^2+9918\\theta+3961\\right)+2^{11} x^{4}\\left(4165\\theta^4+21060\\theta^3+48228\\theta^2+54855\\theta+25440\\right)-2^{14} x^{5}\\left(8248\\theta^4+50660\\theta^3+135119\\theta^2+175776\\theta+91644\\right)+2^{16} x^{6}\\left(23161\\theta^4+161282\\theta^3+479205\\theta^2+690060\\theta+393943\\right)-2^{20} x^{7}\\left(12116\\theta^4+89614\\theta^3+279997\\theta^2+425868\\theta+256804\\right)+2^{23} x^{8}\\left(9924\\theta^4+74644\\theta^3+231233\\theta^2+346097\\theta+206261\\right)-2^{27} x^{9}\\left(3250\\theta^4+24820\\theta^3+75837\\theta^2+107033\\theta+58293\\right)+2^{28} x^{10}\\left(6672\\theta^4+52000\\theta^3+164304\\theta^2+235440\\theta+126113\\right)-2^{32} x^{11}\\left(1312\\theta^4+10208\\theta^3+32688\\theta^2+49072\\theta+28407\\right)+2^{36} x^{12}\\left(192\\theta^4+1568\\theta^3+4952\\theta^2+7144\\theta+3959\\right)-2^{40} x^{13}\\left((2\\theta+5)^4\\right)", "superseek": "4 52", "discriminant": "13 1 -152 9872 -364032 8529920 -135135232 1517879296 -12704546816 83248545792 -436207616000 1791001362432 -5634997092352 13194139533312 -17592186044416", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9127ce057848ca38f220a7bb67e245a2", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3", "discr_factors": "-17592186044416, (z^3-1/16*z^2+5/128*z-1/512)^2, 1/256-3/16*z+z^2, (z-1/8)^2, (z-1/16)^3", "dm_basis": null, "q": "0 1 -16 192 -2304 24240 -254976 2316288 -22216704 157621400", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"-1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"-0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/32*5^(1/2)","im":"0","approx_re":"0.023873","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(64+3*3165^(1/2))^(1/3)-29/48/(64+3*3165^(1/2))^(1/3)+1/48","im":"0","approx_re":"0.050774","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":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/32*5^(1/2)","im":"0","approx_re":"0.163627","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":["5/2","5/2","5/2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(5*X^2+5*X+2)*(13*X^2+13*X+3), 17056*X^4+68224*X^3+100384*X^2+64320*X+13824, -500736*X^4-3004416*X^3-6319872*X^2-5439744*X-1416960, 7520256*X^4+60162048*X^3+164007936*X^2+174735360*X+51609600, -884736*(16*X^2+80*X+35)*(2*X+5)^2, 10616832*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.14\" from ...", "degz": 6, "h3": null, "sol": "1 24 1224 96000 9633960 1108344384 138551567616 18316669003776 2521698279071400 358052604022576320", "n_discr_factors": "4", "c3": null, "operator": "4 6 0 0 0 0 1 -24 -164 -424 -520 -260 13824 64320 100384 68224 17056 -1416960 -5439744 -6319872 -3004416 -500736 51609600 174735360 164007936 60162048 7520256 -774144000 -2388787200 -1893335040 -566231040 -56623104 4087480320 11720982528 8068792320 2038431744 169869312", "new_number": "6.14", "id": 397, "operator_tex": "\\theta^4-2^{2} x(5\\theta^2+5\\theta+2)(13\\theta^2+13\\theta+3)+2^{5} x^{2}\\left(533\\theta^4+2132\\theta^3+3137\\theta^2+2010\\theta+432\\right)-2^{8} 3 x^{3}\\left(652\\theta^4+3912\\theta^3+8229\\theta^2+7083\\theta+1845\\right)+2^{12} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)-2^{15} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2+2^{17} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "8 9928/3", "discriminant": "6 1 -260 17056 -500736 7520256 -56623104 169869312", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "44968de144621e2fa74ce3964a5435f7", "dim_h": null, "inst": " 8 471/2 9928/3 185385 6071232 2300082631/6 18155591704 2414821451639/2 208365112207712/3 4798279940094860", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2", "discr_factors": "169869312, (-1/16+z)^2, z-1/24, z^2-1/12*z+1/2304, z-1/12", "dm_basis": null, "q": "0 1 -68 3702 -227248 13651901 -867353208 53803343898 -3491324552128 219804608348118", "yuk": "1 8 1892 89360 11866532 758904008 82803065960 6227367954480 618194303486116 50632722266563376", "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":"1/24-1/48*3^(1/2)","im":"0","approx_re":"0.005582","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24+1/48*3^(1/2)","im":"0","approx_re":"0.077751","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","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","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, X*(39*X^3-30*X^2-19*X-4), 32*X^4-2140*X^3-2114*X^2-1352*X-384, -36*(3*X+2)*(171*X^3+566*X^2+600*X+316), -331776*X^4-1332288*X^3-2276640*X^2-1877472*X-606528, -1728*(X+1)*(1393*X^3+5571*X^2+8378*X+4584), -248832*(X+1)*(X+2)*(31*X^2+105*X+98), -8957952*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"7.3\" from ...", "degz": 7, "h3": null, "sol": "1 0 24 192 3384 51840 911040 16369920 307009080 5902176000", "n_discr_factors": "6", "c3": null, "operator": "4 7 0 0 0 0 1 0 -4 -19 -30 39 -384 -1352 -2114 -2140 32 -22752 -77328 -105552 -73440 -18468 -606528 -1877472 -2276640 -1332288 -331776 -7921152 -22398336 -24103872 -12033792 -2407104 -48771072 -125411328 -118195200 -49268736 -7713792 -107495424 -250822656 -206032896 -71663616 -8957952", "new_number": "7.3", "id": 446, "operator_tex": "\\theta^4+x\\theta(39\\theta^3-30\\theta^2-19\\theta-4)+2 x^{2}\\left(16\\theta^4-1070\\theta^3-1057\\theta^2-676\\theta-192\\right)-2^{2} 3^{2} x^{3}(3\\theta+2)(171\\theta^3+566\\theta^2+600\\theta+316)-2^{5} 3^{3} x^{4}\\left(384\\theta^4+1542\\theta^3+2635\\theta^2+2173\\theta+702\\right)-2^{6} 3^{3} x^{5}(\\theta+1)(1393\\theta^3+5571\\theta^2+8378\\theta+4584)-2^{10} 3^{5} x^{6}(\\theta+1)(\\theta+2)(31\\theta^2+105\\theta+98)-2^{12} 3^{7} x^{7}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "3 64", "discriminant": "7 1 39 32 -18468 -331776 -2407104 -7713792 -8957952", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "8413250555ca536f1bdccfeed506ea4e", "dim_h": null, "inst": " 3 -4 64 -253 4292 -25608 442008 -3202512 56565002 -457852636", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2", "discr_factors": "-8957952, z+1/4, z+1/3, z+1/8, (1/18+z)^2, z+1/12, z-1/24", "dm_basis": null, "q": "0 1 -4 -16 -40 604 -9872 56092 -1429424 10490134", "yuk": "1 3 -29 1731 -16221 536503 -5529629 151608747 -1639702365 41235888189", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3","im":"0","approx_re":"-0.333333333333","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":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/18","im":"0","approx_re":"-0.0555555555556","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":"1/24","im":"0","approx_re":"0.0416666666667","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": "[X^4, -4*(3*X^2+3*X+1)*(17*X^2+17*X+6), 10400*X^4+69248*X^3+97696*X^2+56896*X+13440, 470016*X^4-2820096*X^3-8607744*X^2-6607872*X-1880064, -58540032*X^4-117080064*X^3+214401024*X^2+272941056*X+98205696, 1082916864*X^4+10829168640*X^3+6157762560*X^2-615776256*X-1358954496, 55207526400*X^4-146767085568*X^3-252935405568*X^2-146767085568*X-24461180928, -48922361856*(3*X^2+3*X+1)*(17*X^2+17*X+6), 28179280429056*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "96", "sol": "1 24 840 34944 1618344 80725824 4249779456 232938823680 13169473126056 762911587628736", "n_discr_factors": "6", "c3": "472", "operator": "4 8 0 0 0 0 1 -24 -140 -344 -408 -204 13440 56896 97696 69248 10400 -1880064 -6607872 -8607744 -2820096 470016 98205696 272941056 214401024 -117080064 -58540032 -1358954496 -615776256 6157762560 10829168640 1082916864 -24461180928 -146767085568 -252935405568 -146767085568 55207526400 -293534171136 -1712282664960 -4207323119616 -4990080909312 -2495040454656 28179280429056 112717121716224 169075682574336 112717121716224 28179280429056", "new_number": "8.14", "id": 457, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{5} x^{2}\\left(325\\theta^4+2164\\theta^3+3053\\theta^2+1778\\theta+420\\right)+2^{10} 3^{2} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{14} 3^{2} x^{4}\\left(397\\theta^4+794\\theta^3-1454\\theta^2-1851\\theta-666\\right)+2^{18} 3^{4} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{21} 3^{4} x^{6}\\left(325\\theta^4-864\\theta^3-1489\\theta^2-864\\theta-144\\right)-2^{26} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{32} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "24 15448/3", "discriminant": "8 1 -204 10400 470016 -58540032 1082916864 55207526400 -2495040454656 28179280429056", "aesz": "176", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "e2a40a57f7e88dba6655d936b4abe327", "dim_h": "20", "inst": " 24 -509/2 15448/3 -128530 3746624 -718242157/6 4087498824 -292948763739/2 16349300937760/3 -208868645210788", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2", "discr_factors": "28179280429056, (z+1/48)^2, z-1/32, (z-1/48)^2, z-1/64, z-1/36, z-1/72", "dm_basis": null, "q": "0 1 -44 1814 -75664 3198717 -136975528 5934383866 -259779116352 11475414116374", "yuk": "1 24 -2012 139056 -8227932 468328024 -25856580632 1402012096656 -74994891745116 3972880128014736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, X*(3*X^3-6*X^2-4*X-1), -211*X^4-856*X^3-1433*X^2-1184*X-384, -1522*X^4-6576*X^3-12954*X^2-13308*X-5400, 4*(X+1)*(2013*X^3+17379*X^2+40726*X+28548), 8*(X+1)*(15719*X^3+126105*X^2+325408*X+269508), 288*(X+1)*(X+2)*(1817*X^2+11967*X+19631), 10368*(X+3)*(X+2)*(X+1)*(89*X+350), 594432*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.54\" from ...", "degz": 8, "h3": null, "sol": "1 0 24 72 1296 8640 103560 932400 10135440 102291840", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 0 -1 -4 -6 3 -384 -1184 -1433 -856 -211 -5400 -13308 -12954 -6576 -1522 114192 277096 232420 77568 8052 2156064 4759328 3612104 1134592 125752 11307456 23854176 17039808 5016384 523296 21772800 45453312 31923072 9165312 922752 14266368 29721600 20805120 5944320 594432", "new_number": "8.54", "id": 501, "operator_tex": "\\theta^4+x\\theta(3\\theta^3-6\\theta^2-4\\theta-1)-x^{2}\\left(211\\theta^4+856\\theta^3+1433\\theta^2+1184\\theta+384\\right)-2 x^{3}\\left(761\\theta^4+3288\\theta^3+6477\\theta^2+6654\\theta+2700\\right)+2^{2} x^{4}(\\theta+1)(2013\\theta^3+17379\\theta^2+40726\\theta+28548)+2^{3} x^{5}(\\theta+1)(15719\\theta^3+126105\\theta^2+325408\\theta+269508)+2^{5} 3^{2} x^{6}(\\theta+1)(\\theta+2)(1817\\theta^2+11967\\theta+19631)+2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(89\\theta+350)+2^{9} 3^{3} 43 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "0 1/3", "discriminant": "8 1 3 -211 -1522 8052 125752 523296 922752 594432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bb80872017d0578a4ae56172666b807c", "dim_h": null, "inst": " 0 1/2 1/3 -1 2 493/36 69/7 -62 737/3 1463", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2", "discr_factors": "594432, z+1/6, z^2+13/43*z+1/43, (z-1/12)^2, z+1/4, (z+1/2)^2", "dm_basis": null, "q": "0 1 -1 -25 5 730 631 -20569 -40309 559198", "yuk": "1 0 4 9 -60 250 2971 3381 -31804 179100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","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":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"-1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"-0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, 17*X*(165*X^3-114*X^2-74*X-17), -20619*X^4-122880*X^3-175353*X^2-126480*X-36992, -403714*X^4-1707888*X^3-2875346*X^2-2348244*X-751944, -2285100*X^4-10846464*X^3-21206284*X^2-19426696*X-6777488, -24*(X+1)*(295815*X^3+1523993*X^2+2924668*X+1983212), -32*(X+1)*(X+2)*(558823*X^2+2951265*X+4136951), -14208*(X+3)*(X+2)*(X+1)*(2797*X+9878), -44158464*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.68\" from ...", "degz": 8, "h3": null, "sol": "1 0 8 24 288 1920 18440 159600 1533280 14622720", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 289 0 -289 -1258 -1938 2805 -36992 -126480 -175353 -122880 -20619 -751944 -2348244 -2875346 -1707888 -403714 -6777488 -19426696 -21206284 -10846464 -2285100 -47597088 -117789120 -106767864 -43675392 -7099560 -264764864 -586028256 -451468544 -148087488 -17882336 -842079744 -1782251520 -1279217280 -378785280 -39739776 -1059803136 -2207923200 -1545546240 -441584640 -44158464", "new_number": "8.68", "id": 516, "operator_tex": "17^{2} \\theta^4+17 x\\theta(165\\theta^3-114\\theta^2-74\\theta-17)-x^{2}\\left(20619\\theta^4+122880\\theta^3+175353\\theta^2+126480\\theta+36992\\right)-2 x^{3}\\left(201857\\theta^4+853944\\theta^3+1437673\\theta^2+1174122\\theta+375972\\right)-2^{2} x^{4}\\left(571275\\theta^4+2711616\\theta^3+5301571\\theta^2+4856674\\theta+1694372\\right)-2^{3} 3 x^{5}(\\theta+1)(295815\\theta^3+1523993\\theta^2+2924668\\theta+1983212)-2^{5} x^{6}(\\theta+1)(\\theta+2)(558823\\theta^2+2951265\\theta+4136951)-2^{7} 3 37 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(2797\\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "6/17 33/17", "discriminant": "8 289 2805 -20619 -403714 -2285100 -7099560 -17882336 -39739776 -44158464", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0c0662f5b46ac6cb0bd298a63cf364c7", "dim_h": null, "inst": " 6/17 25/34 33/17 157/17 577/17 6115/34 15779/17 93410/17 553816/17 7017071/34", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2", "discr_factors": "-44158464, z-1/12, z+1/6, (z+17/74)^2, z^2-1/7*z+1/7, (z+1/4)^2", "dm_basis": null, "q": "0 1 -1 -10 -5 -10 -120 -620 -5381 -41914", "yuk": "1 6/17 106/17 897/17 10154/17 4243 661417/17 5412203/17 47836074/17 403732761/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/74","im":"0","approx_re":"-0.22972972973","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","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":"1/14","im":"-3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"-0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/14","im":"3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","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":[]}]}, {"pols": "[X^4, -X*(3*X^3-6*X^2-4*X-1), -211*X^4-856*X^3-1433*X^2-1184*X-384, 1522*X^4+6576*X^3+12954*X^2+13308*X+5400, 4*(X+1)*(2013*X^3+17379*X^2+40726*X+28548), -8*(X+1)*(15719*X^3+126105*X^2+325408*X+269508), 288*(X+1)*(X+2)*(1817*X^2+11967*X+19631), -10368*(X+3)*(X+2)*(X+1)*(89*X+350), 594432*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.82\" from ...", "degz": 8, "h3": null, "sol": "1 0 24 -72 1296 -8640 103560 -932400 10135440 -102291840", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 0 1 4 6 -3 -384 -1184 -1433 -856 -211 5400 13308 12954 6576 1522 114192 277096 232420 77568 8052 -2156064 -4759328 -3612104 -1134592 -125752 11307456 23854176 17039808 5016384 523296 -21772800 -45453312 -31923072 -9165312 -922752 14266368 29721600 20805120 5944320 594432", "new_number": "8.82", "id": 532, "operator_tex": "\\theta^4-x\\theta(3\\theta^3-6\\theta^2-4\\theta-1)-x^{2}\\left(211\\theta^4+856\\theta^3+1433\\theta^2+1184\\theta+384\\right)+2 x^{3}\\left(761\\theta^4+3288\\theta^3+6477\\theta^2+6654\\theta+2700\\right)+2^{2} x^{4}(\\theta+1)(2013\\theta^3+17379\\theta^2+40726\\theta+28548)-2^{3} x^{5}(\\theta+1)(15719\\theta^3+126105\\theta^2+325408\\theta+269508)+2^{5} 3^{2} x^{6}(\\theta+1)(\\theta+2)(1817\\theta^2+11967\\theta+19631)-2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(89\\theta+350)+2^{9} 3^{3} 43 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "0 -1/3", "discriminant": "8 1 -3 -211 1522 8052 -125752 523296 -922752 594432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "8bab1ddc8b31cb2c21f01402f27895ce", "dim_h": null, "inst": " 0 1/2 -1/3 -1 -2 124/9 -69/7 -62 -737/3 2927/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2", "discr_factors": "594432, (z+1/12)^2, (-1/2+z)^2, z-1/6, z-1/4, z^2-13/43*z+1/43", "dm_basis": null, "q": "0 1 1 -25 -5 730 -631 -20569 40309 559198", "yuk": "1 0 4 -9 -60 -250 2971 -3381 -31804 -179100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"13/86","im":"-1/86*3^(1/2)","approx_re":"0.151162790698","approx_im":"-0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/86","im":"1/86*3^(1/2)","approx_re":"0.151162790698","approx_im":"0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","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":"1/2","im":"0","approx_re":"0.5","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-212*X-804*X^2-1184*X^3+272*X^4, -306176*X^3+7296+56192*X+141824*X^2-152576*X^4, -5640192-33730560*X-74170368*X^2+16588800*X^3-32477184*X^4, -2047279104*X+4164157440*X^4-6641418240*X^3-461832192-3727687680*X^2, -84085309440-283766685696*X-208854319104*X^2+465441914880*X^3+26159874048*X^4, -11817468297216*X^4-14970242727936*X^3-15263776899072*X-20585442705408*X^2-4354090205184, 3913788948480*(107*X^2+216*X+108)*(X+1)^2, -11271712171622400*(X+1)^4]", "text": "This is operator \"8.85\" from ...", "degz": 8, "h3": null, "sol": "1 24 2472 412800 83283624 18774633024 4554940413696 1163856179847168 309041211448837800 84530694901570627776", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -24 -212 -804 -1184 272 7296 56192 141824 -306176 -152576 -5640192 -33730560 -74170368 16588800 -32477184 -461832192 -2047279104 -3727687680 -6641418240 4164157440 -84085309440 -283766685696 -208854319104 465441914880 26159874048 -4354090205184 -15263776899072 -20585442705408 -14970242727936 -11817468297216 422689206435840 1690756825743360 2532221449666560 1682929247846400 418775417487360 -11271712171622400 -45086848686489600 -67630273029734400 -45086848686489600 -11271712171622400", "new_number": "8.85", "id": 535, "operator_tex": "\\theta^4+2^{2} x\\left(68\\theta^4-296\\theta^3-201\\theta^2-53\\theta-6\\right)-2^{7} x^{2}\\left(1192\\theta^4+2392\\theta^3-1108\\theta^2-439\\theta-57\\right)-2^{12} 3^{2} x^{3}\\left(881\\theta^4-450\\theta^3+2012\\theta^2+915\\theta+153\\right)+2^{16} 3^{2} x^{4}\\left(7060\\theta^4-11260\\theta^3-6320\\theta^2-3471\\theta-783\\right)+2^{20} 3^{4} x^{5}\\left(308\\theta^4+5480\\theta^3-2459\\theta^2-3341\\theta-990\\right)-2^{26} 3^{4} x^{6}\\left(2174\\theta^4+2754\\theta^3+3787\\theta^2+2808\\theta+801\\right)+2^{30} 3^{6} 5 x^{7}(107\\theta^2+216\\theta+108)(\\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "196 1986884/3", "discriminant": "8 1 272 -152576 -32477184 4164157440 26159874048 -11817468297216 418775417487360 -11271712171622400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "d959f61fe3ba327116d3bae5ae5a0ade", "dim_h": null, "inst": " 196 -5988 1986884/3 -62128884 8854857504 -1146735352140 183415180420716 -27611245050623892 14126021120260010768/3 -772678094092466100512", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2", "discr_factors": "-11271712171622400, (-1/23040-1/80*z+z^2)^2, z+1/64, z^3-1/36*z^2+23/20736*z-1/331776", "dm_basis": null, "q": "0 1 -116 10846 -1487120 215580205 -35627325272 5931431854738 -1059924964623680 189652857748496902", "yuk": "1 196 -47708 17882152 -3976296284 1106857188196 -247694818227992 62911406884305784 -14136957469895728988 3432623132223200498776", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160-1/480*19^(1/2)","im":"0","approx_re":"-0.002831","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/864*(1828+372*93^(1/2))^(1/3)+53/216/(1828+372*93^(1/2))^(1/3)+1/108","im":"0","approx_re":"0.002907","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"-0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"-1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160+1/480*19^(1/2)","im":"0","approx_re":"0.015331","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 7*X*(165*X^3-102*X^2-65*X-14), -7360*X^4-93808*X^3-122216*X^2-75824*X-18816, -581040*X^4-2815776*X^3-4198608*X^2-2981664*X-829584, -9575424*X^4-41359104*X^3-64968192*X^2-48487680*X-14045184, -85045248*X^4-362741760*X^3-594708480*X^2-455307264*X-133816320, -461168640*X^4-2024497152*X^3-3506872320*X^2-2780946432*X-835411968, -1532805120*X^4-7174324224*X^3-13213974528*X^2-10964533248*X-3404021760, -191102976*(X+1)^2*(15*X^2+48*X+43), -2293235712*(X+1)^2*(X+2)^2]", "text": "This is operator \"9.2\" from ...", "degz": 9, "h3": null, "sol": "1 0 24 144 3240 43200 819600 14112000 269980200 5129712000", "n_discr_factors": "6", "c3": null, "operator": "4 9 0 0 0 0 49 0 -98 -455 -714 1155 -18816 -75824 -122216 -93808 -7360 -829584 -2981664 -4198608 -2815776 -581040 -14045184 -48487680 -64968192 -41359104 -9575424 -133816320 -455307264 -594708480 -362741760 -85045248 -835411968 -2780946432 -3506872320 -2024497152 -461168640 -3404021760 -10964533248 -13213974528 -7174324224 -1532805120 -8217427968 -25607798784 -29429858304 -14906032128 -2866544640 -9172942848 -27518828544 -29812064256 -13759414272 -2293235712", "new_number": "9.2", "id": 541, "operator_tex": "7^{2} \\theta^4+7 x\\theta(165\\theta^3-102\\theta^2-65\\theta-14)-2^{3} x^{2}\\left(920\\theta^4+11726\\theta^3+15277\\theta^2+9478\\theta+2352\\right)-2^{4} 3^{2} x^{3}\\left(4035\\theta^4+19554\\theta^3+29157\\theta^2+20706\\theta+5761\\right)-2^{8} 3^{2} x^{4}\\left(4156\\theta^4+17951\\theta^3+28198\\theta^2+21045\\theta+6096\\right)-2^{11} 3^{3} x^{5}\\left(1538\\theta^4+6560\\theta^3+10755\\theta^2+8234\\theta+2420\\right)-2^{13} 3^{4} x^{6}\\left(695\\theta^4+3051\\theta^3+5285\\theta^2+4191\\theta+1259\\right)-2^{14} 3^{5} x^{7}\\left(385\\theta^4+1802\\theta^3+3319\\theta^2+2754\\theta+855\\right)-2^{18} 3^{6} x^{8}(\\theta+1)^2(15\\theta^2+48\\theta+43)-2^{20} 3^{7} x^{9}(\\theta+1)^2(\\theta+2)^2", "superseek": "9/7 49/3", "discriminant": "9 49 1155 -7360 -581040 -9575424 -85045248 -461168640 -1532805120 -2866544640 -2293235712", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "356d4564e48d7a04e815fa223b6ccc46", "dim_h": null, "inst": " 9/7 47/7 49/3 1370/7 10063/7 304210/21 1079550/7 12454396/7 148504324/7 1876369987/7", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "8", "laurent": null, "discriminant_tex": "-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2", "discr_factors": "-2293235712, z-1/24, z+1/4, (7/288+1/4*z+z^2)^2, z+1/12, z+1/3, z+1/8", "dm_basis": null, "q": "0 1 -2 -43 -8 346 -5194 -66778 -677888 -9329903", "yuk": "1 9/7 55 3096/7 88065/7 1257884/7 21906592/7 370285659/7 6376738817/7 108259655292/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3","im":"0","approx_re":"-0.333333333333","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":"-1/8","im":"-1/24*5^(1/2)","approx_re":"-0.125","approx_im":"-0.093169","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"1/24*5^(1/2)","approx_re":"-0.125","approx_im":"0.093169","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","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":"1/24","im":"0","approx_re":"0.0416666666667","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","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "A-incarnation: X(2,2,3) in $P^6$.", "degz": 1, "h3": "12", "sol": "1 24 3240 672000 169785000 48057033024 14644935841536 4700530344407040 1567838026496313000 538671007365948600000", "n_discr_factors": "1", "c3": "-144", "operator": "4 1 0 0 0 0 1 -24 -204 -636 -864 -432", "new_number": "1.5", "id": 561, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "60 134292", "discriminant": "1 1 -432", "aesz": "5", "n_sing_complex": "0", "inst_int": null, "c2h": "60", "hash": "a6c4fb927cb2a4bb1103c1c739a252b0", "dim_h": "7", "inst": " 60 1869 134292 14016600 1806410976 266296492047 43088739232404 7465080466633896 1362691980781325904 259223846123852751912", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-432z", "discr_factors": "-432, -1/432+z", "dm_basis": null, "q": "0 1 -108 3294 -198000 -12287187 -2488535784 -449797446126 -87255883668672 -17612292986209530", "yuk": "1 60 15012 3625944 897077412 225801372060 57520045923048 14779437556714632 3822121199813632164 993402453989590209960", "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":"1/432","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}]}