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lfunc_lfunctions • Show schema
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{'Lhash': '78131033559389543548074894485', 'a10': [-4.667066119817022, 0.0], 'a2': [1.7879145193439079, 0.0], 'a3': [-1.5511553913307867, 0.0], 'a4': [1.196638328480757, 0.0], 'a5': [-2.6103407457810937, 0.0], 'a6': [-2.7733332459188946, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.436341996793646, 0.0], 'a9': [-0.593916951945434, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.69090517784281, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 127], 'central_character': '6223.1', 'coefficient_field': 'CDF', 'conductor': 6223, 'conductor_radical': 889, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7879145193439079, 0], [2.0, 0]], [[1.0, 0], [1.5511553913307867, 0], [3.0, 0]], [[1.0, 0], [2.6103407457810937, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.6742711950571794, 0], [11.0, 0]], [[1.0, 0], [4.838267485547331, 0], [13.0, 0]], [[1.0, 0], 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['0.06163451785951328735651630834037', '2.22401667516944744367819212276396', '3.01054704867887093865472258455956', '3.81269596316101762725884517627181', '4.72392770022070562007361016821604', '4.96710979895652962296234911897908', '5.63632287325006880901598598528658', '6.57950058624467540392191435999752', '7.01352094723134159478391764654279', '7.958661304899351627307153047846044'], 'prelabel': '2-6223-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.049177624222758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06163451785951328735651630834', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22401667516944744367819212276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01054704867887093865472258456', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.69090517784281, 'bad_primes': [7, 127], 'central_character': '1.1', 'conductor': 6223, 'conductor_radical': 889, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6223/2/a/l/1/14'], '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': '2-6223-1.1-c1-0-4', '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': '2-6223-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.049177624222758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06163451785951328735651630834', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '78131033559389543548074894485', 'Lhash_array': ['78131033559389543548074894485'], 'label': '2-6223-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6223/2/a/l/1/14'}