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lfunc_lfunctions • Show schema
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{'Lhash': '1322537240085663722310568734507', 'a10': [3.9492540853303133, -3.7629481484990115], 'a2': [-0.6313952707620697, 2.356399230142752], 'a3': [0.10285099002360565, 1.728994411168285], 'a4': [-3.4219065363077696, -1.9756386598790308], 'a5': [-1.9089260779343669, -1.1644746579389849], 'a6': [-4.139140728092169, -0.8493209006746603], 'a7': [1.8214762003660743, 1.918912309486801], 'a8': [3.365961102432382, -3.365961102432382], 'a9': [-2.978843347702328, 0.3556575738678784], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.10285099002360565, -1.728994411168285]]], [5, [[1.0, 0], [1.9089260779343669, 1.1644746579389849]]], [7, [[1.0, 0], [-1.8214762003660743, -1.918912309486801]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.53', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': 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-1.6302278954803224, -0.03002212595561719], 'positive_zeros': ['1.04329792440247530466316119725230', '2.89990731448436892295095019110171', '4.21765563703980365538959664094349', '6.70908269094004262879872380371866', '8.024826083373493206378317253070492', '8.836801804910031763258746822863688', '10.47751874907441208167313684005528', '11.38214123556977187418393221307473', '11.73307404335252538349903607468460', '12.96908453551851637475127838031747'], 'prelabel': '2-105-105.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.4717232330040891, 'root_number': '-0.9842584846938098 + 0.17673492950813438*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.471723233004', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04329792440247530466316119725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89990731448436892295095019110', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21765563703980365538959664094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'bad_primes': [3, 5, 7], 'central_character': '105.53', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/2/x/a/53/1'], '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': '2-105-105.53-c1-0-1', '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': '2-105-105.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.4717232330040891, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04329792440247530466316119725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1322537240085663722310568734507', 'Lhash_array': ['1322537240085663722310568734507'], 'factors': ['2-105-105.53-c1-0-1'], 'label': '2-105-105.53-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/x/a/53/1'}