-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '774450569245829907520543133049', 'a10': [0.9128045651136837, 0.0], 'a2': [-0.6129897852332348, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.6242435231997128, 0.0], 'a5': [-1.4891024077446464, 0.0], 'a6': [0.6129897852332348, 0.0], 'a7': [1.0, 0.0], 'a8': [2.221624258919134, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.875119614032244, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 41], 'central_character': '861.1', 'coefficient_field': 'CDF', 'conductor': 861, 'conductor_radical': 861, 'conjugate': '774450569245829907520543133049', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6129897852332348, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.4891024077446464, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.135141115455066, 0], [11.0, 0]], [[1.0, 0], [6.184480992107427, 0], [13.0, 0]], [[1.0, 0], [0.8634646884613231, 0], [17.0, 0]], [[1.0, 0], [-5.947959975096728, 0], [19.0, 0]], [[1.0, 0], [4.860764540210412, 0], [23.0, 0]], [[1.0, 0], [-8.259028492943655, 0], [29.0, 0]], [[1.0, 0], [-2.3223222558134045, 0], [31.0, 0]], [[1.0, 0], [-6.602448338689006, 0], [37.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5108975922553536, 0], [43.0, 0]], [[1.0, 0], [1.4377442875027364, 0], [47.0, 0]], [[1.0, 0], [-12.785535134712822, 0], [53.0, 0]], [[1.0, 0], [5.159042787471633, 0], [59.0, 0]], [[1.0, 0], [-13.559643808162662, 0], [61.0, 0]], [[1.0, 0], [-14.752329178856533, 0], [67.0, 0]], [[1.0, 0], [-0.561543421075015, 0], [71.0, 0]], [[1.0, 0], [-2.947247683674479, 0], [73.0, 0]], [[1.0, 0], [-14.821372449357229, 0], [79.0, 0]], [[1.0, 0], [1.1708901861831629, 0], [83.0, 0]], [[1.0, 0], [-0.3393255014108287, 0], [89.0, 0]], [[1.0, 0], [7.485008063410124, 0], [97.0, 0]], [[1.0, 0], [13.656698784931846, 0], [101.0, 0]], [[1.0, 0], [0.12294450561441286, 0], [103.0, 0]], [[1.0, 0], [10.025993462678938, 0], [107.0, 0]], [[1.0, 0], [13.370356180298465, 0], [109.0, 0]], [[1.0, 0], [7.030348774226273, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-861-1.1-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/861/2/a/k/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.49903746480866024, 0.48041940420893403, 0.42308924326864283, 0.3230798874735152, 0.17518765404418962, -0.025287945678356284, -0.28065747278579195, -0.5890784194075691, -0.9431122315966383, -1.328761295886041, -1.7251363356486327, -2.104894165363983, -2.435551469908098, -2.681712179903979, -2.808145077750265, -2.7835237625624285, -2.5845086069196266, -2.1997300267428, -1.6331468608612223, -0.9062250168838208, -0.0584277554917639, 0.854359994783742, 1.763636673066172, 2.59419996250228, 3.2717354791658297, 3.731325745497242, 3.9258681671872897, 3.833239550566536, 3.461045304496176, 2.847971271055151, 2.061117601115162, 1.1892095040254178, 0.33219024257052626, -0.4116778797039893, -0.9595500494739869, -1.2565838363838817, -1.2853279568768363, -1.0701442659824112, -0.6754949664380794, -0.19779980446276138, 0.24840433941905976, 0.548245970616383, 0.6056502370689072, 0.3607442552438086, -0.19753413997462363, -1.0261496350659862, -2.03148105376193, -3.081690893604034, -4.026448916667049, -4.721070561238586, -5.051104876268067, -4.953023660428259, -4.427058167595264, -3.539399612902951, -2.412770159784908, -1.206489622606015, -0.08922367341345383, 0.7908092492493672, 1.3326275202885565, 1.5010032181713002, 1.3327814402325828, 0.9292974981406135, 0.4358930624749342, 0.012198619290771935, -0.2010822437901888, -0.11215744026387515, 0.30146513767426025, 0.9868151380845921, 1.82533073661198, 2.657203113097058, 3.3154236212289274, 3.6624260460437332, 3.6213266828692303, 3.194610483193771, 2.4656075469271603, 1.5817844173849778, 0.7229695053285866, 0.06122474868570004, -0.2786949284148745, -0.24908630404134752, 0.10808720618178884, 0.6693461966914757, 1.2574961211996123, 1.6832306875860887, 1.7911128928894633, 1.499015888987864, 0.8211793260236392, -0.131437257282484, -1.1745664406543865, -2.0930804161917345, -2.6928159254193105, -2.849327073897699, -2.5412789305008836, -1.8594383715130267, -0.9879028430725377, -0.16103692824011462, 0.3941031278171111, 0.5159169628087755, 0.1522099335106357, -0.6219279315841549, -1.618101630224281, -2.578353371843246, -3.2388232961592243, -3.397882160113861, -2.9713962471287068, -2.020285574417955, -0.7420059877023303, 0.5734626186545899, 1.6133214689620132, 2.1204655485508113, 1.9609231809641035, 1.1624118154724619, -0.08698677469119902, -1.4810643907151801, -2.6690583487566193, -3.3425040032426647, -3.3133071971368513, -2.562663123011079, -1.2475742598663462, 0.33744509002781764, 1.8341406375986788, 2.910901420409596, 3.3462157172306006, 3.083227237584713, 2.2409419743975563, 1.0791833344305166, -0.07312880891254554, -0.9068174694229073, -1.2141707561589854, -0.9413183968328395, -0.19725007227946298, 0.7823567588612858, 1.7056031604365496, 2.308587744499813, 2.429079165816742, 2.048612456197125, 1.2913825384959943, 0.38113301621092355, -0.430282905861298, -0.9405865554124094, -1.057156315382487, -0.8211509521596759, -0.3884777175032564, 0.026102834571987046, 0.22376293568181685, 0.09111093929832631, -0.3584231257235548, -0.9855152804108028, -1.5689808564102659, -1.8796560484251206, -1.7606337222181354, -1.1873429577821815, -0.28640536944270684, 0.6953007750539701, 1.4640972198097455, 1.773963905424525, 1.5124647040652093, 0.7496820922192289, -0.2680465676910775, -1.181205794193001, -1.6206539344944209, -1.3216377074593464, -0.21338875579664682, 1.5447074642085954, 3.594158819512178, 5.4692514838172475, 6.724426113437982, 7.060025266681565, 6.4086534983363315, 4.9554427004777475, 3.0851332720879605, 1.271138966161851, -0.060270406926652226, -0.6496080194415382, -0.47137912650866964, 0.2711538277581934, 1.2209867979452853, 1.9875431177503768, 2.273171286825794, 1.9653784467702295, 1.1655670999827645, 0.14595894568239093, -0.749901463225866, -1.228959134165004, -1.1512204287069934, -0.5779563236701446, 0.25124727103521527, 1.0051151387442376, 1.3814321977870876, 1.2200084511890368, 0.5677205382794913, -0.3288986381265966, -1.1035944927056922, -1.3977490077655768, -0.9927543363647717, 0.0983222151053984, 1.6133058231756419, 3.107240766837637, 4.084034528920728, 4.152413792831538, 3.1557920641427564, 1.2328983867343724, -1.2121830677932537, -3.6226263387130495, -5.44914326852479, -6.30723764022589, -6.081758800889349, -4.94657028089578, -3.295258569183101, -1.6080275463789226, -0.3003375849785335, 0.39644604885188234, 0.48460555993094256, 0.16719488965341175, -0.25095369001941537, -0.48951238831188515, -0.3991897891736654, -0.010320606440798772, 0.49214505449608087, 0.8550136473774078, 0.8693520147976773, 0.4643064267742957, -0.2551754657509207, -1.0424284693278343, -1.6027256073135152, -1.7106064817239814, -1.3046844446381867, -0.5210545534583945, 0.3509684758926229, 0.9773291191992035, 1.1127526010963955, 0.7083852598582893, -0.05012185741031363, -0.7934861926148414, -1.0951913437832788, -0.6306077767980409, 0.6886806955653836, 2.6567849273087907, 4.81761307135987, 6.600917019073585, 7.506072866223493, 7.2702924510213816, 5.961282718967835, 3.959617204587715, 1.834669510646918, 0.1561253402476155, -0.6931420907634982, -0.6367116820387064, 0.08564421929773995, 1.0210186663695873, 1.6810668098103054, 1.7286678446428643, 1.104293597405095, 0.044843678637193955, -1.012476570620617, -1.605608501966573, -1.436518541713827], 'positive_zeros': ['0.61093377710419326683388374037069', '2.50817914450711435724629112316695', '4.05261640853231440772611105597838', '4.92742690781786805270998580865885', '5.46276992179400699437585997738817', '7.01104938430838861021660731367116', '7.87955435238558959263160648498058', '8.169824756479855447631822961436424', '9.640447392555076365730022467488575', '9.970596409865966533931885082379811'], 'prelabel': '2-861-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61093377710419326683388374037', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50817914450711435724629112317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05261640853231440772611105598', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.875119614032244, 'bad_primes': [3, 7, 41], 'central_character': '1.1', 'conductor': 861, 'conductor_radical': 861, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/861/2/a/k/1/2'], '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': '2-861-1.1-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-861-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61093377710419326683388374037', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '774450569245829907520543133049', 'Lhash_array': ['774450569245829907520543133049'], 'label': '2-861-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/861/2/a/k/1/2'}