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lfunc_lfunctions • Show schema
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{'Lhash': '1338821290854864655340449902504', 'a10': [0.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, -3.9689140359382235e-80], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.235', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '2282175801263388020087686324566', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 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'3.34667348171865755274524163341', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'bad_primes': [2, 3, 19], 'central_character': '152.83', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/1/bz/a/235/1', 'ArtinRepresentation/2.1368.12t18.b.a'], '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': '2-1368-152.83-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': '2-1368-152.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.82626928859903, 'root_angle': -0.29945668930219493, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05614377543293206627987499296', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24604568
{'Lhash': '1338821290854864655340449902504', 'Lhash_array': ['1338821290854864655340449902504'], 'label': '2-1368-152.83-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1368.12t18.b.a'}
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id: 19822086
{'Lhash': '1338821290854864655340449902504', 'Lhash_array': ['1338821290854864655340449902504'], 'label': '2-1368-152.83-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/1/bz/a/235/1'}