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lfunc_lfunctions • Show schema
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{'Lhash': '1994454477791918054009556932519', 'a10': [0.0, 0.0], 'a2': [0.8660254037844386, 0.5], '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': [3.9689140359382235e-80, 1.0], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3912669699042739, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.667', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'conjugate': '2805892231889311022562817295406', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3660254037844386, 0.36602540378443865], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88932592050006074511414690820', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3912669699042739, 'bad_primes': [2, 7], 'central_character': '112.107', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/1/v/a/667/1'], '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': '2-28e2-112.107-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': '2-28e2-112.107-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6255133650884479, 'root_angle': -0.16732704694605388, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57334716477303286272011606463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1994454477791918054009556932519', 'Lhash_array': ['1994454477791918054009556932519'], 'label': '2-28e2-112.107-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/1/v/a/667/1'}