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lfunc_lfunctions • Show schema
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{'Lhash': '5275560717189348673079058238063', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 3.9689140359382235e-80], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.025951380656916125, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 13], 'central_character': '52.3', 'coefficient_field': 'CDF', 'conductor': 52, 'conductor_radical': 26, 'conjugate': '3869026637341873618601153327982', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 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['4.16168360291039984927090654038824', '6.04668941269644592254494882942762', '7.39766540537995423654738286953440', '8.532649398844231199448686039577298', '9.709118972498971638443287007627279', '11.24632239324280198745131969122074', '12.40865268975567652680377933238831', '14.12767115902838684115562210189567', '14.96124058887919042375486728325430', '15.86901024324633578237109774275620'], 'prelabel': '2-52-52.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16109432223674466, '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': '4.16168360291039984927090654039', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.04668941269644592254494882943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.39766540537995423654738286953', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.025951380656916125, 'bad_primes': [2, 13], 'central_character': '52.3', 'conductor': 52, 'conductor_radical': 26, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/52/1/j/a/3/1', 'ArtinRepresentation/2.52.6t5.b.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': '2-52-52.3-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': '2-52-52.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16109432223674466, 'root_angle': 0.12397952430371666, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.16168360291039984927090654039', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596349
{'Lhash': '5275560717189348673079058238063', 'Lhash_array': ['5275560717189348673079058238063'], 'label': '2-52-52.3-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.52.6t5.b.b'}
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id: 19806067
{'Lhash': '5275560717189348673079058238063', 'Lhash_array': ['5275560717189348673079058238063'], 'label': '2-52-52.3-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/52/1/j/a/3/1'}