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lfunc_lfunctions • Show schema
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{'Lhash': '627559988196297228986588394429', 'a10': [-0.17364817766693036, -0.984807753012208], 'a2': [-0.17364817766693036, 0.984807753012208], 'a3': [0.766044443118978, 0.6427876096865394], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [-0.9396926207859084, 0.3420201433256687], 'a6': [-0.766044443118978, 0.6427876096865394], 'a7': [-0.32635182233306964, -0.565257937423568], 'a8': [0.5, -0.8660254037844386], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [3, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [5, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [19, [[1.0, 0], [3.7908593693815895, -2.1516006231575173]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '570.511', 'coefficient_field': 'CDF', 'conductor': 570, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.468535018219', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49505754036901851570277907216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35082057719640196427356398328', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20653929455301551457809703071', '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': '19.17', 'conductor': 570, 'conductor_radical': 570, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/570/2/u/c/511/1'], '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': '2-570-19.17-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': '2-570-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': -0.4685350182194298, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49505754036901851570277907216', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '627559988196297228986588394429', 'Lhash_array': ['627559988196297228986588394429'], 'label': '2-570-19.17-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/570/2/u/c/511/1'}