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lfunc_lfunctions • Show schema
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{'Lhash': '1775106208834930525247041923263', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-9.149017001543054, 0.0], 'a4': [0.0, 0.0], 'a5': [17.138280545635, 0.0], 'a6': [0.0, 0.0], 'a7': [8.963609388934108, 0.0], 'a8': [0.0, 0.0], 'a9': [56.704512094523864, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.009359924087335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [89.0, 0]]]], 'bad_primes': [2, 89], 'central_character': '712.1', 'coefficient_field': 'CDF', 'conductor': 712, 'conductor_radical': 178, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [9.149017001543054, 0], [27.0, 0]], [[1.0, 0], [-17.138280545635, 0], [125.0, 0]], [[1.0, 0], [-8.963609388934108, 0], [343.0, 0]], [[1.0, 0], [38.42873120510856, 0], [1331.0, 0]], [[1.0, 0], [40.935184747725415, 0], [2197.0, 0]], [[1.0, 0], [-16.638372148446663, 0], [4913.0, 0]], [[1.0, 0], [128.06574517409655, 0], 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'5.87682027272927844623200167086496', '6.66072518691308448386330491392904', '7.56403205732864370933084149011963', '8.993890630461300143318318032553248', '9.913431219253213471742743871127773'], 'prelabel': '2-712-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.481462792000532, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40031189076496171777068371518', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51163314987384794134775000605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63753530118609828258508580708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.009359924087335, 'bad_primes': [2, 89], 'central_character': '1.1', 'conductor': 712, 'conductor_radical': 178, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/712/4/a/c/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': '2-712-1.1-c3-0-44', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-712-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.481462792000532, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40031189076496171777068371518', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1775106208834930525247041923263', 'Lhash_array': ['1775106208834930525247041923263'], 'label': '2-712-1.1-c3-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/712/4/a/c/1/1'}