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lfunc_lfunctions • Show schema
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{'Lhash': '1613745793215157268790280294431', 'a10': [-0.20784530347798755, -0.17440291749030917], 'a2': [-0.6862416378687336, -0.7273736415730487], 'a3': [-1.7016935756126703, 0.32286061190328713], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [0.26948818667794827, -0.03149865152700387], 'a6': [1.4026132854797373, 1.0162066578190367], 'a7': [1.701734813345894, 0.8546433452473509], 'a8': [0.766044443118978, -0.6427876096865394], 'a9': [2.79152205056287, -1.0988196581883987], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6862416378687336, 0.7273736415730487]]], [3, [[1.0, 0], [1.7016935756126703, -0.32286061190328713]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1909844361308517990730474170936', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.1373550513119213, 'root_angle': 0.032872051348416594, 'root_number': '0.9946723295128984 + 0.10308713256941417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0164360256742', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27302096723230869400929266977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.15359594269836394976969549568', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.65520859516271516585732285044', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/b/103/1'], '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': '2-162-81.22-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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.016436025674208297, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27302096723230869400929266977', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1613745793215157268790280294431', 'Lhash_array': ['1613745793215157268790280294431'], 'label': '2-162-81.22-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/103/1'}