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lfunc_lfunctions • Show schema
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{'Lhash': '256270492994002870988783077145', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0, 0], 'a5': [0.5860385573908876, 2.1579061168760814], 'a6': [0, 0], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0, 0], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-0.5860385573908876, -2.1579061168760814]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.463', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '2405909540648866530289484033995', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.5860385573908876, -2.1579061168760814]], 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'-0.97246637874682335984013570573451978194472396464730356580 + 0.2330432196118134219749263511507222201631600310067025007*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4625658186433472', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20216177308468406871116797418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55272080534882733681455626172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52823054175718555478528327344', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.414867539575111, 'bad_primes': [2, 3, 5, 7], 'central_character': '20.3', 'conductor': 1680, 'conductor_radical': 210, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/bl/d/463/6'], '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': '2-1680-20.3-c1-0-5', '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': '2-1680-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': 0.46256581864334717, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20216177308468406871116797418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '256270492994002870988783077145', 'Lhash_array': ['256270492994002870988783077145'], 'label': '2-1680-20.3-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/bl/d/463/6'}