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  • lfunc_lfunctions • Show schema
    {'Lhash': '5269266009882996914623845562584', 'a10': [-3.1926873182701505, 1.5375171782675785], 'a2': [-0.2225209339563144, -0.9749279121818236], 'a3': [-2.0691975164114167, -0.9964730052033131], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [-0.7885286486601444, -3.4547697399324817], 'a6': [-0.5110495826164587, 2.2390545183468937], 'a7': [3.728565087655383, 1.7955823107867006], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [1.4181505062480528, 1.7783044876713427], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.2225209339563144, 0.9749279121818236]]], [29, [[1.0, 0], [-0.12737196509834153, -5.383658271334371]]]], 'bad_primes': [2, 29], 'central_character': '58.7', 'coefficient_field': 'CDF', 'conductor': 58, 'conductor_radical': 58, 'conjugate': '1641586654671430181559642415427', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'data': '0.318281423221', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.15671795440660988422127086633', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.64285772551687805729814546390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.92607481815687046129847119977', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '29.7', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/58/2/d/b/7/1'], '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': '2-58-29.7-c1-0-2', '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': '2-58-29.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.31828142322073205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.15671795440660988422127086633', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '5269266009882996914623845562584', 'Lhash_array': ['5269266009882996914623845562584'], 'factors': ['2-58-29.7-c1-0-2'], 'label': '2-58-29.7-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/d/b/7/1'}