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lfunc_lfunctions • Show schema
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{'Lhash': '1004975737761115217918069492863', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-10.776388834631177, 0.0], 'a4': [0.0, 0.0], 'a5': [-106.10555533852471, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-126.86944368483648, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 125.74091473337684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [10.776388834631177, 0], [243.0, 0]], [[1.0, 0], [106.10555533852471, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-93.43472184241824, 0], [161051.0, 0]], [[1.0, 0], [661.1305563151635, 0], [371293.0, 0]], [[1.0, 0], [455.9194456381141, 0], [1419857.0, 0]], [[1.0, 0], [-1106.2791645506159, 0], [2476099.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 125.74091473337684, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/6/a/bb/1/1'], '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': '2-28e2-1.1-c5-0-41', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.792786070215387526813688467770', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1004975737761115217918069492863', 'Lhash_array': ['1004975737761115217918069492863'], 'factors': ['2-28e2-1.1-c5-0-41'], 'label': '2-28e2-1.1-c5-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/bb/1/1'}