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lfunc_lfunctions • Show schema
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{'Lhash': '1749419075860625041785476920796', 'a10': [-2.414213562373095, 2.7929318987959157e-61], 'a2': [-1.953139800010316, -1.41903912784738], 'a3': [-0.8740320488976422, 2.6899940478558295], 'a4': [1.1830490432725895, 3.6410505641509827], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [5.524313588770527, -4.013648760279707], 'a7': [-0.6180339887498949, -1.902113032590307], 'a8': [1.3640670075736634, -4.198166572813375], 'a9': [-4.045084971874737, -2.9389262614623655], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.81', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '208125087948919127630623569935', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.953139800010316, 1.41903912784738], 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103}, 'z3': {'__RealLiteral__': 0, 'data': '5.22188734028503457312873362961', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '11.4', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/g/f/81/1'], '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': '2-605-11.4-c1-0-18', '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': '2-605-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': 0.38543426013921356, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38004831579431859270622861469', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1749419075860625041785476920796', 'Lhash_array': ['1749419075860625041785476920796'], 'label': '2-605-11.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/g/f/81/1'}