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lfunc_lfunctions • Show schema
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{'Lhash': '1148966725028851319956077511008', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.8740320488976422], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [2.23606797749979, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.126696990427405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '4900.2549', 'coefficient_field': 'CDF', 'conductor': 4900, 'conductor_radical': 70, 'conjugate': '1103363054713917437632359252839', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.8740320488976422], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [0, -2.288245611270737], [-13.0, 0]], [[1.0, 0], [0, -1.7480640977952844], [-17.0, 0]], [[1.0, 0], [0.33385053542218923, 0], [19.0, 0]], [[1.0, 0], [0, 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'4.63234520784146947024844422401204', '5.23718265130157534917579314670002', '6.21273972549388719754154495407165', '6.85406966430489700419297818664046', '7.59162055040451576173163212831019', '8.320278904821672093323068645591475'], 'prelabel': '2-70e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': 0.07379180882521663, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.906374930775081013627623394138', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.89801809607118125196645979346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17736928476432911444484070313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.126696990427405, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 4900, 'conductor_radical': 70, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4900/2/e/u/2549/3'], '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': '2-70e2-5.4-c1-0-31', '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': '2-70e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.906374930775081013627623394138', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1148966725028851319956077511008', 'Lhash_array': ['1148966725028851319956077511008'], 'factors': ['2-70e2-5.4-c1-0-31'], 'label': '2-70e2-5.4-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4900/2/e/u/2549/3'}