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lfunc_lfunctions • Show schema
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{'Lhash': '472269634561275155312798773999', 'a10': [-0.2869889761197691, 0.49707948785161127], 'a2': [1.2080455471101075, 0.4396926207859084], 'a3': [0.0, 0.0], 'a4': [-0.266044443118978, -0.22323779409789932], 'a5': [-0.07752967226297128, 0.4396926207859084], 'a6': [0.0, 0.0], 'a7': [-2.7057370639048863, 2.2703829723852866], 'a8': [-1.508813013470978, -2.613340798452839], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.568', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2727623928314621777337880361808', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2080455471101075, -0.4396926207859084], [1.532088886237956, 1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.07752967226297128, -0.4396926207859084], [-4.698463103929542, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40230894992880525534479445315', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/q/568/2'], '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': '2-3e6-27.4-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e6-27.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.3981481481481482, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37255505142840396154959470318', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '472269634561275155312798773999', 'Lhash_array': ['472269634561275155312798773999'], 'label': '2-3e6-27.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/q/568/2'}