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lfunc_lfunctions • Show schema
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{'Lhash': '533805122088395857730717930526', 'a10': [1.0057716130439973, 0.580682511534236], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.2083647843943806, 1.2409087588680814], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0057716130439973, 0.580682511534236], 'a6': [1.6788409011555672, 0.4260202208899988], 'a7': [2.199566998012359, 1.4703418042261123], 'a8': [1.0, 0.0], 'a9': [-0.07970909567104464, -2.9989408897254552], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [1.2083647843943806, -1.2409087588680814]]], [7, [[1.0, 0], [-2.199566998012359, -1.4703418042261123]]], [11, [[1.0, 0], [-0.8647674936792807, 3.2019021193465074]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.263', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '2291334389255868328191451726361', 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4.878549011269526], [54.5, 94.39676901250381]], [[1.0, 0], [0, 10.715908617884486], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-462-231.32-c1-0-5', '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/462/2/n/e/263/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5568478934998277, 0.40349150249111887, 0.24163570444539914, 0.06770910450564643, -0.12056677287978458, -0.323009992467162, -0.5361305631524239, -0.7526309149021913, -0.9612478640932967, -1.1469386156071546, -1.2914321001478426, -1.3741721725928266, -1.37366345954395, -1.269195768539412, -1.0428745331686209, -0.6818296890655272, -0.1804213022536774, 0.4577846111213545, 1.2185239943502375, 2.0760824244254534, 2.9935093967375757, 3.923962363935877, 4.813246219268144, 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'7.07154378905408852443526918794836', '8.022507108068166485041214754126702', '8.480131209359819833124090532666565', '10.12435474632610956292212896462244', '10.61160856745617255081116954546767'], 'prelabel': '2-462-231.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.6291934647574525, 'root_number': '-0.39482120680915944 - 0.9187579739266261*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.314596732379', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42109799182226468009848994810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03809010488631240399017613786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40609928262840295467012366219', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '231.32', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/n/e/263/3'], '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': '2-462-231.32-c1-0-5', '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': '2-462-231.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.31459673237872626, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42109799182226468009848994810', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '533805122088395857730717930526', 'Lhash_array': ['533805122088395857730717930526'], 'label': '2-462-231.32-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/n/e/263/3'}