{"count": 10, "status":"OK", "data":[{"pols": "[X^4, -784-16768*X-153216*X^2-272896*X^3+355072*X^4, 17825792+1849688064*X+17012097024*X^2-46858764288*X^3+35282485248*X^4, -16578573762560-131941395333120*X-381393095884800*X^2-527765581332480*X^3+559376540631040*X^4, -900719925474099200*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator\nAESZ 222/4.42", "degz": 4, "h3": "4", "sol": "1 784 3226896 20413907200 157477179235600 1361831571773616384 12684795211912342692096 124477818005324688955674624 1269631592734724062413342973200 13341061142213717890728655538233600", "n_discr_factors": "2", "c3": "640", "operator": "4 4 0 0 0 0 1 -784 -16768 -153216 -272896 355072 17825792 1849688064 17012097024 -46858764288 35282485248 -16578573762560 -131941395333120 -381393095884800 -527765581332480 559376540631040 -900719925474099200 -7205759403792793600 -21617278211378380800 -28823037615171174400 -14411518807585587200", "new_number": "4.43", "id": 141, "operator_tex": "\\theta^4+2^{4} x\\left(22192\\theta^4-17056\\theta^3-9576\\theta^2-1048\\theta-49\\right)+2^{20} x^{2}\\left(33648\\theta^4-44688\\theta^3+16224\\theta^2+1764\\theta+17\\right)+2^{34} 5 x^{3}\\left(6512\\theta^4-6144\\theta^3-4440\\theta^2-1536\\theta-193\\right)-2^{55} 5^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "93984 25265152551072", "discriminant": "4 1 355072 35282485248 559376540631040 -14411518807585587200", "aesz": "225", "n_sing_complex": "1", "inst_int": "", "c2h": "-8", "hash": "5993002ccf811247be9232b089dd8e3a", "dim_h": "0", "inst": " 93984 -1084521600 25265152551072 -787700706860008320 28889437619654310485088 -1175123711760789859743048320 51358422489334818184115432720928 -2366123613298324781338140979519579008 113498527327558067922532188570410940202752 -5620696211385822025421692623281080034910450048", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(536870912z^2-27392z-1)(1+163840z)^2", "discr_factors": "-14411518807585587200, z^2-107/2097152*z-1/536870912, (1/163840+z)^2", "dm_basis": null, "q": "0 1 -13632 349655136 -12475753895936 522338315529567792 -24006084551026067761152 1172497234208292982798672384 -59770287497610147774288093118464 3145077533503728165711567034217978520", "yuk": "1 93984 -8676078816 682159118972928 -50412845247716611296 3611179702456788810729984 -253826721740329927554055636992 17615938913841842637151593423372288 -1211455290008742288095541026761741063392 82740426421789831515525965468511734526779136", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"107/4194304-51/4194304*17^(1/2)","im":"0","approx_re":"-2.5e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/163840","im":"0","approx_re":"-6.103515625e-06","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"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":"107/4194304+51/4194304*17^(1/2)","im":"0","approx_re":"7.6e-05","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, -144-1536*X-6288*X^2-9504*X^3+432*X^4, 92160+497664*X-1492992*X^2-22394880*X^3-8957952*X^4, -398131200-3439853568*X-10749542400*X^2-15479341056*X^3-14189395968*X^4, -55037657088*(3*X+1)^2*(3*X+2)^2]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 144 147600 239904000 479672701200 1078954420287744 2618634987667835136 6702283021504364236800 17840666902138413842480400 48944005664385888179529120000", "n_discr_factors": "3", "c3": "-18", "operator": "4 4 0 0 0 0 1 -144 -1536 -6288 -9504 432 92160 497664 -1492992 -22394880 -8957952 -398131200 -3439853568 -10749542400 -15479341056 -14189395968 -220150628352 -1981355655168 -6439405879296 -8916100448256 -4458050224128", "new_number": "4.47", "id": 145, "operator_tex": "\\theta^4+2^{4} 3 x\\left(9\\theta^4-198\\theta^3-131\\theta^2-32\\theta-3\\right)-2^{11} 3^{2} x^{2}\\left(486\\theta^4+1215\\theta^3+81\\theta^2-27\\theta-5\\right)-2^{16} 3^{5} x^{3}\\left(891\\theta^4+972\\theta^3+675\\theta^2+216\\theta+25\\right)-2^{23} 3^{8} x^{4}(3\\theta+1)^2(3\\theta+2)^2", "superseek": "1584 171534960", "discriminant": "4 1 432 -8957952 -14189395968 -4458050224128", "aesz": "239", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "8e610c3437d7f38e552038bc55399495", "dim_h": "3", "inst": " 1584 -17874 171534960 30012731550 105934107802896 63775249469817750 127749832497630077616 131860871041114114038054 224001851211067044692907648 298697681537718689647638089370", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(432z+1)(3456z-1)(1+1728z)^2", "discr_factors": "-4458050224128, z+1/432, z-1/3456, (1/1728+z)^2", "dm_basis": null, "q": "0 1 -960 456480 -333224960 150643621680 -220108476321792 37434112216317440 -259405759761365729280 -112198587502907767173480", "yuk": "1 1584 -141408 4631445504 1920814677792 13241763475363584 13775453890111936512 43818192546687116623872 67512765973052347202161440 163297349532867875585761120896", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1728","im":"0","approx_re":"-0.000578703703704","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":"1/3456","im":"0","approx_re":"0.000289351851852","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","1/3","2/3","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2432*X^4-2560*X^3-1760*X^2-480*X-48, 1314816*X^4+540672*X^3-918528*X^2-522240*X-76800, -160432128*X^4+254803968*X^3+212336640*X^2+60162048*X+5898240, -452984832*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 48 26640 21907200 22048765200 24896521698048 30291889001197824 38838210495451361280 51763875861113556426000 71081695744396302602208000", "n_discr_factors": "3", "c3": "-60", "operator": "4 4 0 0 0 0 1 -48 -480 -1760 -2560 -2432 -76800 -522240 -918528 540672 1314816 5898240 60162048 212336640 254803968 -160432128 -905969664 -7700742144 -24008196096 -32614907904 -16307453952", "new_number": "4.48", "id": 146, "operator_tex": "\\theta^4-2^{4} x\\left(152\\theta^4+160\\theta^3+110\\theta^2+30\\theta+3\\right)+2^{10} 3 x^{2}\\left(428\\theta^4+176\\theta^3-299\\theta^2-170\\theta-25\\right)-2^{17} 3^{2} x^{3}\\left(136\\theta^4-216\\theta^3-180\\theta^2-51\\theta-5\\right)-2^{24} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "320 19748928", "discriminant": "4 1 -2432 1314816 -160432128 -16307453952", "aesz": "241", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "b4d16d8dd1eb7839630ecf8e8d242023", "dim_h": "3", "inst": " 320 61084 19748928 9428973876 5618509433280 3845253330631020 2892405836819922752 2330756708127722933332 1979363847140433024517632 1751890593945326994096072180", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(1728z-1)(-1+384z)^2", "discr_factors": "-16307453952, z-1/1728, z+1/64, (-1/384+z)^2", "dm_basis": null, "q": "0 1 -288 -36384 -12797952 -9672066000 -7623005064192 -6428933441480192 -5742516718520303616 -5358500671498636447080", "yuk": "1 320 488992 533221376 603454817056 702313679160320 830574719950010368 992095202029233504256 1193347434561997596683040 1442956244565375675406575104", "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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384","im":"0","approx_re":"0.00260416666667","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, -112-1152*X-4480*X^2-6656*X^3-1792*X^4, 94208+655360*X+884736*X^2-3670016*X^3-2686976*X^4, -8388608-50331648*X-100663296*X^2-201326592*X^3-805306368*X^4, -1073741824*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator\nAESZ 256/4.50", "degz": 4, "h3": "4", "sol": "1 112 93456 124614400 204621667600 378083696723712 753817928330928384 1585000160053962043392 3466049211031541759024400 7811601850118304222490105600", "n_discr_factors": "2", "c3": "-32", "operator": "4 4 0 0 0 0 1 -112 -1152 -4480 -6656 -1792 94208 655360 884736 -3670016 -2686976 -8388608 -50331648 -100663296 -201326592 -805306368 -1073741824 -8589934592 -25769803776 -34359738368 -17179869184", "new_number": "4.51", "id": 150, "operator_tex": "\\theta^4-2^{4} x\\left(112\\theta^4+416\\theta^3+280\\theta^2+72\\theta+7\\right)-2^{12} x^{2}\\left(656\\theta^4+896\\theta^3-216\\theta^2-160\\theta-23\\right)-2^{23} x^{3}\\left(96\\theta^4+24\\theta^3+12\\theta^2+6\\theta+1\\right)-2^{30} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "992 63721056", "discriminant": "4 1 -1792 -2686976 -805306368 -17179869184", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": "28", "hash": "1d45a05c9bcf007b5042b0f7a5672551", "dim_h": "3", "inst": " 992 98792 63721056 40943244128 36122052633760 35496785398316488 38573077037369045216 44817555891320272923488 54895973186351629390948608 70071414152078519333405737080", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(65536z^2+2816z-1)(1+512z)^2", "discr_factors": "-17179869184, (1/512+z)^2, z^2+11/256*z-1/65536", "dm_basis": null, "q": "0 1 -704 164960 -83273728 -15505781200 -38649728440320 -41146063608995328 -55445056673294450688 -74461017216300912797032", "yuk": "1 992 791328 1720469504 2620368415520 4515256579220992 7667305647757621248 13230565423817582510080 22946588616358600105241376 40019164452850337827722004736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/512-5/512*5^(1/2)","im":"0","approx_re":"-0.043321","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"0","approx_re":"-0.001953125","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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"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":"-11/512+5/512*5^(1/2)","im":"0","approx_re":"0.000352","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, -208-2368*X-11584*X^2-18432*X^3+9216*X^4, -4194304*X^4-130023424*X^3+21757952*X^2+7471104*X+786432, -5033164800-38654705664*X-111937585152*X^2-154618822656*X^3-167503724544*X^4, -9895604649984*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at\ninfinity, corresponding to Operator 4.33, reducible to 3.35.", "degz": 4, "h3": "4", "sol": "1 208 254736 490988800 1163138813200 3099609712459008 8912821490498306304 27028629149428355125248 85250093313365034252541200 277129736008042959585497324800", "n_discr_factors": "3", "c3": "136", "operator": "4 4 0 0 0 0 1 -208 -2368 -11584 -18432 9216 786432 7471104 21757952 -130023424 -4194304 -5033164800 -38654705664 -111937585152 -154618822656 -167503724544 -9895604649984 -79164837199872 -237494511599616 -316659348799488 -158329674399744", "new_number": "4.56", "id": 155, "operator_tex": "\\theta^4+2^{4} x\\left(576\\theta^4-1152\\theta^3-724\\theta^2-148\\theta-13\\right)-2^{17} x^{2}\\left(32\\theta^4+992\\theta^3-166\\theta^2-57\\theta-6\\right)-2^{26} 3 x^{3}\\left(832\\theta^4+768\\theta^3+556\\theta^2+192\\theta+25\\right)-2^{40} 3^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "4192 2124587232", "discriminant": "4 1 9216 -4194304 -167503724544 -158329674399744", "aesz": "277", "n_sing_complex": "0", "inst_int": "", "c2h": "16", "hash": "9d905a8d31566f4976cbeb2d3bf0624c", "dim_h": "2", "inst": " 4192 -1708008 2124587232 -2777042329304 4857272052090400 -8662038695645169608 17457595917396214851936 -35803804676519586643377240 78149966571561860853262927104 -173301643054058182072314357680760", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(1024z+1)(4096z-1)(1+6144z)^2", "discr_factors": "-158329674399744, z+1/1024, z-1/4096, (1/6144+z)^2", "dm_basis": null, "q": "0 1 -1536 2019168 -3416864768 6362636991024 -13293690316296192 28972568094420308480 -66676440369195119542272 157105050052992014772439704", "yuk": "1 4192 -13659872 57363859456 -177730722735328 607159006511304192 -1871000358202006439936 5987955399666901694218240 -18331547994378206092131882208 56971325630668596562086037718272", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/1024","im":"0","approx_re":"-0.0009765625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6144","im":"0","approx_re":"-0.000162760416667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","approx_im":"0.0","exponents":["0","1","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, -432-4416*X-16960*X^2-25088*X^3-7936*X^4, 7962624+63995904*X+154337280*X^2+74711040*X^3-3145728*X^4, 5096079360+53452210176*X+192216563712*X^2+260919263232*X^3+61001957376*X^4, 463856467968*(4*X+1)*(3*X+1)*(3*X+2)*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 432 982800 3259872000 12958462717200 57507674287295232 275104725474922447104 1389843863969427389952000 7317666838199613923550666000 39788554502561698105541549280000", "n_discr_factors": "3", "c3": "24", "operator": "4 4 0 0 0 0 1 -432 -4416 -16960 -25088 -7936 7962624 63995904 154337280 74711040 -3145728 5096079360 53452210176 192216563712 260919263232 61001957376 2783138807808 27367531610112 94162862997504 133590662774784 66795331387392", "new_number": "4.60", "id": 160, "operator_tex": "\\theta^4-2^{4} x\\left(496\\theta^4+1568\\theta^3+1060\\theta^2+276\\theta+27\\right)-2^{15} 3 x^{2}\\left(32\\theta^4-760\\theta^3-1570\\theta^2-651\\theta-81\\right)+2^{22} 3^{2} x^{3}\\left(1616\\theta^4+6912\\theta^3+5092\\theta^2+1416\\theta+135\\right)+2^{34} 3^{3} x^{4}(4\\theta+1)(3\\theta+1)(3\\theta+2)(4\\theta+3)", "superseek": "3616 264403872", "discriminant": "4 1 -7936 -3145728 61001957376 66795331387392", "aesz": "288", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "3373ebdbe30d220b5562cfd77d4e8f96", "dim_h": "3", "inst": " 3616 114144 264403872 424149521656 710239010095456 1276165652786715744 2488282041160304300320 5231049591044378569431928 11643937059631017192549541632 27039505146615533040287139508896", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(6912z-1)(4096z-1)(1+1536z)^2", "discr_factors": "66795331387392, (1/1536+z)^2, z-1/6912, z-1/4096", "dm_basis": null, "q": "0 1 -2688 4828512 -7377668096 9370263876144 -11657738493517824 11810397522454737408 -14798269700120886116352 8694811319106031657675416", "yuk": "1 3616 916768 7138908160 27145570302752 88779876261935616 275651781009070422016 853480740117984375013376 2678297390614748973119449888 8488430116471011533375754757888", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/1536","im":"0","approx_re":"-0.000651041666667","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":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","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":["1/4","1/3","2/3","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -13056*X^4+23040*X^3+14464*X^2+2944*X+272, 6029312+42991616*X+113246208*X^2-155189248*X^3+20971520*X^4, -11811160064-103079215104*X-317827579904*X^2-412316860416*X^3+85899345920*X^4, 35184372088832*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at\ninfinity, corresponding to Operator AESZ 296/4.65", "degz": 4, "h3": "4", "sol": "1 -272 93456 194502400 -587215823600 640732932419328 776446344050598144 -4713772249712944484352 8322330312713357740285200 2292816132708062002706579200", "n_discr_factors": "2", "c3": "192", "operator": "4 4 0 0 0 0 1 272 2944 14464 23040 -13056 6029312 42991616 113246208 -155189248 20971520 -11811160064 -103079215104 -317827579904 -412316860416 85899345920 35184372088832 281474976710656 844424930131968 1125899906842624 562949953421312", "new_number": "4.64", "id": 164, "operator_tex": "\\theta^4-2^{4} x\\left(816\\theta^4-1440\\theta^3-904\\theta^2-184\\theta-17\\right)+2^{18} x^{2}\\left(80\\theta^4-592\\theta^3+432\\theta^2+164\\theta+23\\right)+2^{30} x^{3}\\left(80\\theta^4-384\\theta^3-296\\theta^2-96\\theta-11\\right)+2^{45} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-5408 -4296119968", "discriminant": "4 1 -13056 20971520 85899345920 562949953421312", "aesz": "295", "n_sing_complex": "1", "inst_int": "", "c2h": "4", "hash": "e40629f953a095a2a764c68394321139", "dim_h": "1", "inst": " -5408 -3839480 -4296119968 -6482749129792 -11816577914904160 -23775821454252033176 -50868108154251421892640 -114383780266640218792887360 -267794278217800769868007067392 -646609344110586651247479818403880", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(8388608z^2+3328z+1)(-1+8192z)^2", "discr_factors": "562949953421312, z^2+13/32768*z+1/8388608, (-1/8192+z)^2", "dm_basis": null, "q": "0 1 1856 4507744 10996029440 27530323566128 70984202464897024 187308349528583004672 502803073483807579570176 1368671554155217410108316312", "yuk": "1 -5408 -30721248 -115995244544 -414895975027936 -1477072239363025408 -5135577434234465126400 -17447761096908237709180928 -58564495496520206917933356256 -195222028820776761233893147373312", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/65536","im":"-7/65536*7^(1/2)","approx_re":"-0.000198364257812","approx_im":"-0.000283","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/65536","im":"7/65536*7^(1/2)","approx_re":"-0.000198364257812","approx_im":"0.000283","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":"1/8192","im":"0","approx_re":"0.0001220703125","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": "[X^4, 240+2560*X+9456*X^2+13792*X^3+5936*X^4, 1628160+13957120*X+33556480*X^2+21186560*X^3+2293760*X^4, -3422617600*X^4-12288000000*X^3-9065267200*X^2-2457600000*X-221184000, 1048576000*(5*X+1)*(5*X+2)*(5*X+3)*(5*X+4)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 -240 378000 -941740800 2908743037200 -10151874959466240 38309871295625529600 -152614322407866908160000 632640146605662882986442000 -2703686438960809804123990368000", "n_discr_factors": "2", "c3": "-130", "operator": "4 4 0 0 0 0 1 240 2560 9456 13792 5936 1628160 13957120 33556480 21186560 2293760 -221184000 -2457600000 -9065267200 -12288000000 -3422617600 25165824000 262144000000 917504000000 1310720000000 655360000000", "new_number": "4.66", "id": 166, "operator_tex": "\\theta^4+2^{4} x\\left(371\\theta^4+862\\theta^3+591\\theta^2+160\\theta+15\\right)+2^{11} 5 x^{2}\\left(224\\theta^4+2069\\theta^3+3277\\theta^2+1363\\theta+159\\right)-2^{16} 5^{2} x^{3}\\left(2089\\theta^4+7500\\theta^3+5533\\theta^2+1500\\theta+135\\right)+2^{23} 5^{3} x^{4}(5\\theta+1)(5\\theta+2)(5\\theta+3)(5\\theta+4)", "superseek": "-1616 -283183120", "discriminant": "4 1 5936 2293760 -3422617600 655360000000", "aesz": "300", "n_sing_complex": "1", "inst_int": "", "c2h": "28", "hash": "edc54887effd2ebcaa636dcc93baf0b7", "dim_h": "3", "inst": " -1616 265534 -283183120 351860487150 -525536710386800 905847882475840870 -1717463745183584163280 3484895489379071632856310 -7449697893532490934280447360 16596414766862442506943198303050", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(6400000z^2+6576z+1)(-1+320z)^2", "discr_factors": "655360000000, (-1/320+z)^2, z^2+411/400000*z+1/6400000", "dm_basis": null, "q": "0 1 1600 1355040 1290306560 604823942960 991922734264320 -645735308412019200 2416007564491479449600 -5155873649461458449879400", "yuk": "1 -1616 2122656 -7645945856 22519073300256 -65692088798351616 195663142607137806336 -589090064597969368006656 1784266490562107195095730976 -5430829764385185891098092071296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-411/800000-41/800000*41^(1/2)","im":"0","approx_re":"-0.000842","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-411/800000+41/800000*41^(1/2)","im":"0","approx_re":"-0.000186","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_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"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":"1/320","im":"0","approx_re":"0.003125","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":["1/5","2/5","3/5","4/5"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*(4*X+1)^2*(4*X+3)^2]", "text": "A-incarnation: X(4,4) in P^5(1,1,1,1,2,2)", "degz": 1, "h3": "4", "sol": "1 144 176400 341510400 811620810000 2167695039654144 6243202569208340736 18955829541661309440000 59844220278907077932490000 194686629373739404697796000000", "n_discr_factors": null, "c3": "-144", "operator": "4 1 0 0 0 0 1 -144 -1536 -5632 -8192 -4096", "new_number": "1.10", "id": 550, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)^2(4\\theta+3)^2", "superseek": "928 170869536", "discriminant": null, "aesz": "10", "n_sing_complex": null, "inst_int": null, "c2h": "40", "hash": "51f8135aba94201bd0bbe9b2287a92d5", "dim_h": "4", "inst": " 928 245616 170869536 174999877936 221984814405088 322488630778883760 514506002990767360672 879128852394829927420720 1582934400557814144743504640 2970390071697000630704094306000", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": null, "discr_factors": null, "dm_basis": null, "q": "0 1 -960 213600 -160471040 -136981068240 -248123397445632 -445533681536171520 -850742163409138483200 -1692715844493003550786920", "yuk": "1 928 1965856 4613478400 11199994153760 27748101800636928 69657544252854335488 176475559025833204711424 450113972426164122833562400 1153959178006646511522628360960", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[X^4, -48*(6*X+1)*(2*X+1)^2*(6*X+5)]", "text": "A-incarnation: X(2,6) in P^5(1,1,1,1,1,3)", "degz": 1, "h3": "4", "sol": "1 240 498960 1633632000 6558930378000 29581300719210240 143836335737833939200 737207888088943616716800 3928439729428651009119690000 21570543432627516984564267360000", "n_discr_factors": "1", "c3": "-256", "operator": "4 1 0 0 0 0 1 -240 -2688 -9600 -13824 -6912", "new_number": "1.14", "id": 554, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(2\\theta+1)^2(6\\theta+5)", "superseek": "1248 683015008", "discriminant": "1 1 -6912", "aesz": "14", "n_sing_complex": "0", "inst_int": null, "c2h": "52", "hash": "03af56f4ae0cea2c4b219620b08dc49b", "dim_h": "5", "inst": " 1248 597192 683015008 1149904141056 2394928461766560 5709817000593540904 14946206719803262912992 41895512154532910436145920 123742261295599828266715963648 380879646657552011921330025755160", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-6912z", "discr_factors": "-6912, -1/6912+z", "dm_basis": null, "q": "0 1 -1728 933984 -967108608 -744650899920 -2811284045862912 -8045990099842309632 -25343000802383158444032 -82768843338570290975745384", "yuk": "1 1248 4778784 18441406464 73593869806368 299366057720821248 1233320472146651019264 5126548904892519179157504 21450502223120923737176517408 90208108484492274806454378905856", "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":"1/6912","im":"0","approx_re":"0.000144675925926","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":["1/6","1/2","1/2","5/6"],"monodromy":[],"monodromy_dm":[]}]}]}