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lfunc_lfunctions • Show schema
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{'Lhash': '1239111786818471954370519490055', 'a10': [0.0, 0.0], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.8660254037844386, -0.5], 'a4': [-4.582907173931562e-80, -2.6459426907612794e-80], 'a5': [0.0, 0.0], 'a6': [0.8660254037844386, -0.5], 'a7': [0.5, 0.8660254037844386], 'a8': [-1.0, -1.3229713449218603e-80], 'a9': [4.582907174078835e-80, 2.6459426906630975e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2011232000911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, -1.0]]], [31, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [13, 31], 'central_character': '403.61', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '2504708500292231834596777694798', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.977486845819645189753550122434', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.82270671716034486608668257237', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26209016594983671575054917896', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2011232000911, 'bad_primes': [13, 31], 'central_character': '403.61', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/1/p/a/61/1', 'ArtinRepresentation/2.403.16t60.a.d'], 'is_instance_Artin': True, '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': '2-403-403.61-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-403-403.61-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.44846761320200146, 'root_angle': -0.29064619097038336, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.977486845819645189753550122434', 'prec': 107}}
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lfunc_instances • Show schema
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id: 24603167
{'Lhash': '1239111786818471954370519490055', 'Lhash_array': ['1239111786818471954370519490055'], 'label': '2-403-403.61-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.403.16t60.a.d'}
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id: 19805308
{'Lhash': '1239111786818471954370519490055', 'Lhash_array': ['1239111786818471954370519490055'], 'label': '2-403-403.61-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/1/p/a/61/1'}