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lfunc_lfunctions • Show schema
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{'Lhash': '2022707219809289686018616237963', 'a10': [-4.613170820308937, 0.0], 'a2': [-2.2300872188881935, 0.0], 'a3': [1.6266712759867599, 0.0], 'a4': [2.9732890038484774, 0.0], 'a5': [2.068605560014297, 0.0], 'a6': [-3.6276188219106222, 0.0], 'a7': [3.3281012150719262, 0.0], 'a8': [-2.1705193677669117, 0.0], 'a9': [-0.3539405598796067, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.18769705477814, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [1.0, 0]]], [139, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [29, 139], 'central_character': '4031.1', 'coefficient_field': 'CDF', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2300872188881935, 0], [2.0, 0]], [[1.0, 0], [-1.6266712759867599, 0], [3.0, 0]], [[1.0, 0], [-2.068605560014297, 0], [5.0, 0]], [[1.0, 0], [-3.3281012150719262, 0], [7.0, 0]], [[1.0, 0], [2.004137117591924, 0], [11.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.18769705477814, 'bad_primes': [29, 139], 'central_character': '1.1', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 2, 'index': 268, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4031/2/a/c/1/8'], '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': '2-4031-1.1-c1-0-268', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4031-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.673420225470536, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59563464841583236358920066320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2022707219809289686018616237963', 'Lhash_array': ['2022707219809289686018616237963'], 'label': '2-4031-1.1-c1-0-268', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4031/2/a/c/1/8'}