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lfunc_lfunctions • Show schema
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{'Lhash': '451322975244229115855850821553', 'a10': [-2125.777236210359, 0.0], 'a2': [1.2343696176833245, 0.0], 'a3': [81.0, 0.0], 'a4': [-510.4763316469403, 0.0], 'a5': [-1722.1561562735446, 0.0], 'a6': [99.98393903234928, 0.0], 'a7': [4577.429566702609, 0.0], 'a8': [-1262.113718585282, 0.0], 'a9': [6561.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 91.16134300100556, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-81.0, 0]]], [59, [[1.0, 0], [12117361.0, 0]]]], 'bad_primes': [3, 59], 'central_character': '177.1', 'coefficient_field': 'CDF', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2343696176833245, 0], [512.0, 0]], [[1.0, 0], [-81.0, 0]], [[1.0, 0], [1722.1561562735446, 0], [1953125.0, 0]], [[1.0, 0], [-4577.429566702609, 0], [40353607.0, 0]], [[1.0, 0], [75628.82301546329, 0], [2357947691.0, 0]], [[1.0, 0], [128893.11395552938, 0], [10604499373.0, 0]], 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'data': '2.20109354769548604789409875274', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54358410357225273106957077132', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 91.16134300100556, 'bad_primes': [3, 59], 'central_character': '1.1', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/177/10/a/d/1/12'], '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': '2-177-1.1-c9-0-5', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-177-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.547844940142543, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35603105079820288194391628244', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '451322975244229115855850821553', 'Lhash_array': ['451322975244229115855850821553'], 'label': '2-177-1.1-c9-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/177/10/a/d/1/12'}