Formats: - HTML - YAML - JSON - 2026-09-16T04:19:11.978819
  • lfunc_lfunctions • Show schema
    {'Lhash': '2945662507272104311338603317871', 'a10': [4.718970803171957, 0.0], 'a2': [3.7651059791906416, 0.0], 'a3': [9.311582590319283, 0.0], 'a4': [6.1760230345371205, 0.0], 'a5': [1.253343419615073, 0.0], 'a6': [35.059095286538614, 0.0], 'a7': [7.0, 0.0], 'a8': [-6.867466578570291, 0.0], 'a9': [59.70557033633717, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.499307510924243, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[7, [[1.0, 0], [-7.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [7, 23], 'central_character': '161.1', 'coefficient_field': 'CDF', 'conductor': 161, 'conductor_radical': 161, 'conjugate': '2945662507272104311338603317871', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.7651059791906416, 0], [8.0, 0]], [[1.0, 0], [-9.311582590319283, 0], [27.0, 0]], [[1.0, 0], [-1.253343419615073, 0], [125.0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [42.41328673670494, 0], [1331.0, 0]], [[1.0, 0], [78.80592447099389, 0], [2197.0, 0]], [[1.0, 0], [-118.6519427645201, 0], [4913.0, 0]], [[1.0, 0], [-2.873392472406863, 0], [6859.0, 0]], [[1.0, 0], [-23.0, 0]], [[1.0, 0], [112.1621462611462, 0], [24389.0, 0]], [[1.0, 0], [-138.98085610614888, 0], [29791.0, 0]], [[1.0, 0], [-389.0815271540664, 0], [50653.0, 0]], [[1.0, 0], [286.7332119968738, 0], [68921.0, 0]], [[1.0, 0], [103.73781156876873, 0], [79507.0, 0]], [[1.0, 0], [-515.5553523823288, 0], [103823.0, 0]], [[1.0, 0], [-424.566296566071, 0], [148877.0, 0]], [[1.0, 0], [631.4184963642504, 0], [205379.0, 0]], [[1.0, 0], [365.72813365277847, 0], [226981.0, 0]], [[1.0, 0], [285.49257272108315, 0], [300763.0, 0]], [[1.0, 0], [-531.9901837173535, 0], [357911.0, 0]], [[1.0, 0], [-151.74999686317832, 0], [389017.0, 0]], [[1.0, 0], [-115.82325998441908, 0], [493039.0, 0]], [[1.0, 0], [979.0502369839533, 0], [571787.0, 0]], [[1.0, 0], [-940.9512886929728, 0], [704969.0, 0]], [[1.0, 0], [688.5235671297853, 0], [912673.0, 0]], [[1.0, 0], [1130.935451375605, 0], [1030301.0, 0]], [[1.0, 0], [353.65816475468773, 0], [1092727.0, 0]], [[1.0, 0], [117.17470682564435, 0], [1225043.0, 0]], [[1.0, 0], [-1606.8924535276242, 0], [1295029.0, 0]], [[1.0, 0], [-1522.5761078335781, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-161-1.1-c3-0-24', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/161/4/a/d/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [5.226820253082684, 5.2087013622640495, 5.154037983595529, 5.061970162435661, 4.931259762642521, 4.760564786471067, 4.548788760810263, 4.295474752138451, 4.001209688883015, 3.668002890239737, 3.299602688546093, 2.901716606847139, 2.4821037856496004, 2.050513524839763, 1.6184512755271458, 1.1987634466991974, 0.8050450014457735, 0.450888667522695, 0.14901092031821245, -0.08969346481151078, -0.25710109581362006, -0.3487343393467591, -0.3644734595065521, -0.3090189854222606, -0.19202443442203457, -0.02783635829133229, 0.1651951913514666, 0.36583815004372006, 0.5514933006195248, 0.7000196500933149, 0.7917439338310795, 0.8114898476437304, 0.7504351970137548, 0.6075931791594753, 0.3907214699308974, 0.11649218703449457, -0.19019239616474007, -0.4977813345325186, -0.7705088184263634, -0.9715393123872269, -1.0665881709141942, -1.0276992494753086, -0.8368019574808949, -0.48864502368879204, 0.007279110243165398, 0.6261427431379649, 1.3287398800040284, 2.064060717199558, 2.7733791654061055, 3.3955656536964374, 3.8731650748078597, 4.158640469521223, 4.220098079716057, 4.045795977297557, 3.646807154395487, 3.0573602971906695, 2.3326085870997035, 1.5438592245151588, 0.7716048682866158, 0.0969968100110797, -0.40735061175482057, -0.6861714023049957, -0.7088752494711844, -0.4743789967399305, -0.012655996616267607, 0.6174353056904155, 1.3340460443771056, 2.0414815776170827, 2.641666847420559, 3.046629786714687, 3.190467019720069, 3.0392074952031605, 2.5971485022722423, 1.9086010768424528, 1.0545157165620536, 0.14410527640628534, -0.6977403732716622, -1.3458355589162423, -1.6909965117558936, -1.655136725052092, -1.2030793995150315, -0.34933651796231474, 0.8413011753863763, 2.259727392526293, 3.764513719428607, 5.198550145935554, 6.408243213760404, 7.262741553768263, 7.67056270269173, 7.59127603357748, 7.040531057999105, 6.08762960685132, 4.845899280331408, 3.45717916459223, 2.0726152525452757, 0.8325388177316381, -0.1516347720309235, -0.8108363925785651, -1.1251593953366552, -1.123144865747504, -0.8738073605173873, -0.47283245980531013, -0.025315914186195825, 0.37203181886699077, 0.6462258622802262, 0.7583477113407887, 0.7072344831520586, 0.5260580415915556, 0.2726254248464051, 0.015388602342548059, -0.18204024130617263, -0.2747721783763554, -0.2461104190322045, -0.11062366879676651, 0.08991117053343736, 0.29699458006514945, 0.4502564282733433, 0.5036005848715653, 0.43912175170041057, 0.27551428099617786, 0.06861504858459788, -0.0968109911713082, -0.12317647712907477, 0.07851831553997227, 0.5658985421094408, 1.345645229273749, 2.361546873731302, 3.4934985576457933, 4.568951358393416, 5.386041172117073, 5.745307339962893, 5.484990824427508, 4.513777370702147, 2.8347963580357844, 0.5557879412771972, -2.1175187295475633, -4.904947918418856, -7.489437697256939, -9.563028301422795, -10.873870416224081, -11.266283335962736, -10.706755828643459, -9.29097753967642, -7.230165857727566, -4.8185600903848, -2.3873343281087043, -0.25269282320999725, 1.3329403324761726, 2.2181948378162715, 2.372085415045973, 1.8822452111613324, 0.932771934626156, -0.23385258825567753, -1.3633988505323107, -2.236214578677861, -2.7045895222961085, -2.714412090564274, -2.30758035401873, -1.6055099774885198, -0.7778478291633178, -0.0033847998155240463, 0.568427522614855, 0.8473047659521105, 0.8172908299407682, 0.534533389999215, 0.10879582018603125, -0.3266121160700875, -0.6492972696899255, -0.7785545992799157, -0.6952770181394142, -0.4463680877962035, -0.13262010645199984, 0.11712065790820457, 0.1794333339574062, -0.03050530975680568, -0.5340733968988981, -1.2788987157697485, -2.1460251718948142, -2.973433849840584, -3.5909187259383804, -3.85850538641716, -3.6995434255767283, -3.1205927655309265, -2.213084952975148, -1.1358542119149744, -0.08206994964666886, 0.7621704152615475, 1.2582087909846682, 1.3448053486154214, 1.0506162441804778, 0.48603048620764233, -0.1839575665123113, -0.7796276985660283, -1.149789174316826, -1.2080426224437604, -0.9531601030314593, -0.46836785271803477, 0.10064000061692387, 0.5838952510795746, 0.8323425355290807, 0.758785730232623, 0.36404744963144964, -0.2588774118962543, -0.9446411293508321, -1.495342428369615, -1.7310857129643766, -1.5389109845700508, -0.9074703568277173, 0.06227709075469843, 1.1746170653534878, 2.1823315276146937, 2.846549033675106, 2.9994162631411942, 2.5942510091485347, 1.7299273953917713, 0.6416629708870331, -0.34202038208792424, -0.8683277849252694, -0.6407690105458039, 0.5066830935092775, 2.559277336780153, 5.307796276940092, 8.37647927984221, 11.288298420189772, 13.554761540028904, 14.77154011105994, 14.699467218592103, 13.313316443902684, 10.807670496215652, 7.558574202689057, 4.049388522491277, 0.777069233947338, -1.8408269053739343, -3.5386893456482977, -4.240308406057126, -4.054911928691622, -3.235014795793885, -2.107816440509311, -0.9973300940685307, -0.15559277446961817, 0.28196756230888337, 0.30869569695400767, 0.026552075313298843, -0.39824002147174753, -0.7901278504356876, -1.0144363511361605, -1.0099411656047268, -0.796598644039322, -0.45857489022079245, -0.10966394600926498, 0.14717242181726878, 0.25330827288661256, 0.21083317796833392, 0.07724606251290139, -0.059219882961646826, -0.11520032414632396, -0.04674139865918896], 'positive_zeros': ['2.32371799196226747716281917269538', '3.14390286796507210575197678729799', '4.42339533367375514170303391183537', '5.49838093473923829956289490152747', '7.39569403323221647441732035502512', '8.002825970027637702388691734173272', '9.395207519982842115764360626598804', '10.16506196423058432868857622510921', '11.97790980739291257161871964173835', '12.75726716869030014651025109461572'], 'prelabel': '2-161-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.082094662875273, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32371799196226747716281917270', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.14390286796507210575197678730', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.42339533367375514170303391184', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 9.499307510924243, 'bad_primes': [7, 23], 'central_character': '1.1', 'conductor': 161, 'conductor_radical': 161, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/161/4/a/d/1/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-161-1.1-c3-0-24', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-161-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.082094662875273, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32371799196226747716281917270', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2945662507272104311338603317871', 'Lhash_array': ['2945662507272104311338603317871'], 'factors': ['2-161-1.1-c3-0-24'], 'label': '2-161-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/161/4/a/d/1/9'}