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lfunc_lfunctions • Show schema
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{'Lhash': '2722574079108676041957317552311', 'a10': [0.9396926207859084, 0.3420201433256687], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [0.17364817766693036, -0.984807753012208], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [-0.17364817766693036, -0.984807753012208], 'a7': [-1.4396926207859084, -2.493620766483186], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.9396926207859084, -0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [3, [[1.0, 0], [-0.17364817766693036, 0.984807753012208]]], [5, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [19, [[1.0, 0], [-4.2168814171420514, 1.1035901022399774]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '570.271', 'coefficient_field': 'CDF', 'conductor': 570, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.258614409463', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14773225257693278840125029835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31344501039702360923875571529', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47736126460670508978353838089', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.551472915212984, 'bad_primes': [2, 3, 5, 19], 'central_character': '19.5', 'conductor': 570, 'conductor_radical': 570, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/570/2/u/c/271/1'], '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': '2-570-19.5-c1-0-10', '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': '2-570-19.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.25861440946293224, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14773225257693278840125029835', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2722574079108676041957317552311', 'Lhash_array': ['2722574079108676041957317552311'], 'label': '2-570-19.5-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/570/2/u/c/271/1'}