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lfunc_lfunctions • Show schema
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{'Lhash': '608307850042115546336608277017', 'a10': [1.5028682704787244, 0.0], 'a2': [-0.529982007605693, 0.0], 'a3': [-1.950818836198146, 0.0], 'a4': [-1.719119071614239, 0.0], 'a5': [-2.8356967763269036, 0.0], 'a6': [1.033898883283295, 0.0], 'a7': [-3.4462769756871907, 0.0], 'a8': [1.9710661920987358, 0.0], 'a9': [0.8056941316654885, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.06397754167328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[71, [[1.0, 0], [1.0, 0]]], [113, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [71, 113], 'central_character': '8023.1', 'coefficient_field': 'CDF', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.529982007605693, 0], [2.0, 0]], [[1.0, 0], [1.950818836198146, 0], [3.0, 0]], [[1.0, 0], [2.8356967763269036, 0], [5.0, 0]], [[1.0, 0], [3.4462769756871907, 0], [7.0, 0]], [[1.0, 0], [-0.2531102180803379, 0], [11.0, 0]], [[1.0, 0], 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'3.06944821251555215065847354034451', '3.47931363045849854809365619628080', '4.51812035961745377201888318505303', '4.80619529015159253405536571206541', '5.91824509493328153486813139245352', '6.43223534644385971191596257873969', '7.01499116923778262237991093947361', '8.003596158882037463292732048699690'], 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47987028123727077418160124130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.06396731996504602963956709566', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06944821251555215065847354034', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.06397754167328, 'bad_primes': [71, 113], 'central_character': '1.1', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'index': 123, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8023/2/a/e/1/65'], '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': '2-8023-1.1-c1-0-123', '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': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47987028123727077418160124130', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '608307850042115546336608277017', 'Lhash_array': ['608307850042115546336608277017'], 'label': '2-8023-1.1-c1-0-123', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8023/2/a/e/1/65'}