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lfunc_lfunctions • Show schema
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{'Lhash': '831163371112756035773703205539', 'a10': [-2.53401936627528, 0.0], 'a2': [-2.53401936627528, 0.0], 'a3': [0.2742213920582248, 0.0], 'a4': [4.421254148658173, 0.0], 'a5': [1.0, 0.0], 'a6': [-0.6948823181225081, 0.0], 'a7': [1.0, 0.0], 'a8': [-6.135504903374177, 0.0], 'a9': [-2.924802628137649, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.23151279558737, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7, 13], 'central_character': '5915.1', 'coefficient_field': 'CDF', 'conductor': 5915, 'conductor_radical': 455, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.53401936627528, 0], [2.0, 0]], [[1.0, 0], [-0.2742213920582248, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6966126462858124, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7073021243615525, 0], [17.0, 0]], [[1.0, 0], 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'2.41294740107538353486314711797879', '3.23553937928328124697126469689592', '4.41284673901110485243707541529523', '5.71614851063240463995992282518855', '6.02062983640987615394016986073835', '6.98521727982747559118393710790011', '7.62754148350234748635277848610873', '8.274767620032139375855836681085001'], 'prelabel': '2-5915-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8725186646226994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65567228932255650066638465822', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65148349716207249439386668457', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.41294740107538353486314711798', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.23151279558737, 'bad_primes': [5, 7, 13], 'central_character': '1.1', 'conductor': 5915, 'conductor_radical': 455, 'degree': 2, 'index': 81, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5915/2/a/bp/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': '2-5915-1.1-c1-0-81', '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': '2-5915-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8725186646226994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65567228932255650066638465822', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '831163371112756035773703205539', 'Lhash_array': ['831163371112756035773703205539'], 'label': '2-5915-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5915/2/a/bp/1/2'}