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lfunc_lfunctions • Show schema
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{'Lhash': '1691794840690880585194343896356', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, 0.0], 'a6': [0.5, -0.8660254037844386], 'a7': [0.5, -0.8660254037844386], 'a8': [1.0, 3.9689140359382235e-80], 'a9': [-4.582907174201562e-80, 2.6459426906140066e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6747358970798193, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '1352.699', 'coefficient_field': 'CDF', 'conductor': 1352, 'conductor_radical': 26, 'conjugate': '1279739904976795721794346711201', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, 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'positive_zeros': ['1.33459080947564551581067895464435', '2.54358603099472396009383018559983', '4.05037507740436950626742637492784', '4.99992003657759727172325455196612', '6.01705003682056279250632511020374', '6.82256053180735567459924108778142', '7.81243000993520649585949784564706', '8.061293133847610931600101169268731', '8.637990824210638062983306887918974', '9.639883151340193740955985166157690'], 'prelabel': '2-1352-104.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8214230926141651, 'root_angle': 0.2479590486074333, 'root_number': '0.71162606906186618877952312899197 + 0.70255842307352351146774235171961*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12397952430371666', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33459080947564551581067895464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54358603099472396009383018560', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05037507740436950626742637493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6747358970798193, 'bad_primes': [2, 13], 'central_character': '104.75', 'conductor': 1352, 'conductor_radical': 26, 'degree': 2, 'index': 2, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1352/1/p/a/699/1', 'ArtinRepresentation/2.1352.6t5.a.b'], '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': '2-1352-104.75-c0-0-2', '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': '2-1352-104.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8214230926141651, 'root_angle': 0.12397952430371666, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33459080947564551581067895464', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24598177
{'Lhash': '1691794840690880585194343896356', 'Lhash_array': ['1691794840690880585194343896356'], 'label': '2-1352-104.75-c0-0-2', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1352.6t5.a.b'}
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id: 19815586
{'Lhash': '1691794840690880585194343896356', 'Lhash_array': ['1691794840690880585194343896356'], 'label': '2-1352-104.75-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1352/1/p/a/699/1'}