-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3257443305295904938424536915902', 'a10': [-188.15016433068752, 0.0], 'a2': [7.526006573227501, 0.0], 'a3': [9.0, 0.0], 'a4': [24.640774940263547, 0.0], 'a5': [-25.0, 0.0], 'a6': [67.7340591590475, 0.0], 'a7': [-234.12622311090976, 0.0], 'a8': [-55.385576173437094, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.526006573227501, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [234.12622311090976, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-236.18415854364503, 0], [371293.0, 0]], [[1.0, 0], [608.0152663884905, 0], [1419857.0, 0]], [[1.0, 0], [1799.808434245112, 0], [2476099.0, 0]], [[1.0, 0], [4773.402672689825, 0], [6436343.0, 0]], [[1.0, 0], [-2804.9937550280565, 0], [20511149.0, 0]], [[1.0, 0], [-10258.314060959638, 0], [28629151.0, 0]], [[1.0, 0], [7629.836875429719, 0], [69343957.0, 0]], [[1.0, 0], [-8355.476547560753, 0], [115856201.0, 0]], [[1.0, 0], [11967.875155050982, 0], [147008443.0, 0]], [[1.0, 0], [-8385.47871687175, 0], [229345007.0, 0]], [[1.0, 0], [-3452.9986355134915, 0], [418195493.0, 0]], [[1.0, 0], [51032.410126669325, 0], [714924299.0, 0]], [[1.0, 0], [-9988.235323875018, 0], [844596301.0, 0]], [[1.0, 0], [36567.60603100562, 0], [1350125107.0, 0]], [[1.0, 0], [30522.252136197414, 0], [1804229351.0, 0]], [[1.0, 0], [-83879.48446016338, 0], [2073071593.0, 0]], [[1.0, 0], [-103504.94543056731, 0], [3077056399.0, 0]], [[1.0, 0], [4341.541907618857, 0], [3939040643.0, 0]], [[1.0, 0], [45464.118864859745, 0], [5584059449.0, 0]], [[1.0, 0], [183169.95838045163, 0], [8587340257.0, 0]], [[1.0, 0], [28833.324311266308, 0], [10510100501.0, 0]], [[1.0, 0], [59444.55612689817, 0], [11592740743.0, 0]], [[1.0, 0], [-13840.644475855124, 0], [14025517307.0, 0]], [[1.0, 0], [13278.138381355593, 0], [15386239549.0, 0]], [[1.0, 0], [-130085.59402234016, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-165-1.1-c5-0-31', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/165/6/a/b/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [-3.1248773983166007e-60, 0.4205831605785474, 0.8371886385772127, 1.2458684492742196, 1.642734422980799, 2.023989129363607, 2.385957934835643, 2.7251224286988407, 3.038155338227748, 3.321956916100975, 3.57369263027533, 3.790831821990408, 3.9711868280650284, 4.112951895378878, 4.214741055054039, 4.275623978092143, 4.295158709753644, 4.273420083229301, 4.211022550193918, 4.109136142111571, 3.9694942963754047, 3.794392349249119, 3.5866756157134363, 3.349716145948062, 3.0873774690146014, 2.8039669043840383, 2.5041753374981695, 2.19300471089148, 1.8756838699130465, 1.557573812245647, 1.244063811868021, 0.9404603078435784, 0.651870851949796, 0.3830857812423541, 0.13846060610997854, -0.07819763496190463, -0.263736621558303, -0.4157540790754368, -0.5326786886881668, -0.6138332176262927, -0.6594767699798829, -0.6708234486347824, -0.6500352367815327, -0.6001875471891033, -0.525206638439951, -0.4297789436869199, -0.3192332781057593, -0.19939786001038937, -0.07643506702353398, 0.043342181556647666, 0.15366760910354976, 0.24852670224187204, 0.3223634453821072, 0.3702818245072812, 0.38823493734128034, 0.37319446340654405, 0.32329342241418396, 0.23793559904889824, 0.11786574331813855, -0.03480433548789316, -0.216617391648517, -0.4228421859172748, -0.6475951477970388, -0.8840108061924395, -1.1244576015214784, -1.36079374046887, -1.5846558631000178, -1.7877715416160247, -1.9622851023638295, -2.1010850373645136, -2.1981204223415673, -2.2486933493166483, -2.2497144645368516, -2.199909311640713, -2.0999643310511495, -1.9526030534012808, -1.7625852178662378, -1.5366241921191144, -1.283221092110269, -1.012417297578862, -0.73547051400183, -0.4644630083345891, -0.21185399775954009, 0.010008754708765688, 0.18940043840881413, 0.31573401578551763, 0.3800572262859592, 0.3755100779877252, 0.2977214682822752, 0.14512485100638672, -0.08082490913870966, -0.37554821705367347, -0.7313617115381886, -1.1376295733395343, -1.5810459932658485, -2.0460440159932425, -2.515320244697363, -2.9704592799047926, -3.3926365327950494, -3.7633734582563148, -4.065315543634365, -4.283000787806839, -4.403585097420992, -4.417491149988624, -4.318948906107459, -4.106399108769021, -3.782735729298605, -3.355369277284125, -2.836099985359602, -2.240797842704109, -1.588894960457083, -0.9027044400074716, -0.20658838372327512, 0.4739944724488137, 1.1135242162764412, 1.6874956152805047, 2.1734880106758605, 2.5521812127611825, 2.8082698575106075, 2.9312314331961473, 2.9159081627879666, 2.7628699969482993, 2.4785348881075016, 2.07503292946409, 1.569812413641407, 0.9849978803400736, 0.34652221547205786, -0.3169337543671974, -0.9751505451520405, -1.5976761170979972, -2.1551705419956737, -2.620727424624006, -2.9711096207456884, -3.1878392021273894, -3.258087070750492, -3.175315952511668, -2.939641382390852, -2.5578882601666413, -2.04333501345876, -1.415152657908704, -0.6975613299073625, 0.08125860669955674, 0.8904507921105981, 1.6979016310294763, 2.4717249454530443, 3.181739444592343, 3.8008652153316174, 4.306368569933847, 4.680891507820178, 4.913212478123977, 4.998698591016066, 4.939425258521704, 4.74395663875976, 4.426798289881016, 4.007551128161022, 3.509812137342917, 2.959881350409904, 2.3853455815818325, 1.8136165424436133, 1.2705038491555023, 0.7789017700052492, 0.3576623832268051, 0.02071738728284937, -0.22350334093051408, -0.3723254483738608, -0.4287441821349196, -0.40100696089364324, -0.3018922939738783, -0.14773116408515624, 0.042767344438237334, 0.2498123217021791, 0.4538676941910224, 0.6369450371614299, 0.7837707940896659, 0.8827538005311195, 0.9266914153643206, 0.913169039873334, 0.8446273869508, 0.7280933599629607, 0.5745924722523679, 0.39828197143214433, 0.21536283246799937, 0.042844262798924594, -0.10275477135434102, -0.2066770570168004, -0.2570822351411883, -0.24600256454867417, -0.17002869730546294, -0.030672162703201784, 0.16562735031957143, 0.40785771914236724, 0.6811356703073509, 0.9677114364382277, 1.248212100321431, 1.5030402671474328, 1.7138312640421043, 1.8648649443845078, 1.9443280701680126, 1.9453304017527782, 1.8665917964774734, 1.7127380729112418, 1.4941689464493646, 1.2264904021925598, 0.9295345608308674, 0.6260203486029488, 0.3399359914144336, 0.09474749884240001, -0.08844589421643385, -0.19267931425865023, -0.20668249271655725, -0.12611099690039118, 0.045655697741658306, 0.29722795059559115, 0.6094781518566355, 0.9563814038473772, 1.3063958621581633, 1.624315381160843, 1.8734915648382224, 2.018292322974435, 2.0266418490481235, 1.872474394895319, 1.537932551686843, 1.0151504912835372, 0.3074835490580196, -0.569923362936537, -1.5902964701797153, -2.716145311518515, -3.9008998922391065, -5.091197510106682, -6.229698432647581, -7.25827057839426, -8.121353672598374, -8.769295314497452, -9.16144659116146, -9.268814029512209, -9.076087588184041, -8.582899902496692, -7.804218061303966, -6.769822986008081, -5.522889565084546, -4.117739252179095, -2.616891911806644, -1.0875914842739365, 0.40198285911848247, 1.7865847305829476, 3.007604008523668, 4.01636989212035, 4.776841361270329, 5.267511177395251, 5.482400043688475, 5.431076923260089, 5.137705826680795, 4.639184250498452, 3.9824993892863247, 3.2214809766290062, 2.413170372100517, 1.6140513328229578], 'positive_zeros': ['2.56966967452185228844934593381348', '3.60938486706975797715607150314173', '4.36323270705408538979636450099007', '6.15650676064698743725429505115097', '6.65570257910159012740639350911241', '8.334723813427079207734442182447044', '9.390463505813236589480313996393675', '10.45728332715078813167465920634297', '12.02877356937638650620117121052510'], 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.56966967452185228844934593381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60938486706975797715607150314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36323270705408538979636450099', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/a/b/1/3'], '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': '2-165-1.1-c5-0-31', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.56966967452185228844934593381', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3257443305295904938424536915902', 'Lhash_array': ['3257443305295904938424536915902'], 'label': '2-165-1.1-c5-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/a/b/1/3'}