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lfunc_lfunctions • Show schema
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{'Lhash': '1704420496271167601166806767637', 'a10': [-0.2153703234534297, 1.4979335021248712], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [-0.9594929736144974, 0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [1.2731001747286013, 0.8181718023242559], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [0.36921466354468385, 2.5679443905322183], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]]], [3, [[1.0, 0], [0.9594929736144974, -0.28173255684142967]]], [23, [[1.0, 0], [-4.6653284862419175, 1.1111751056695338]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.73', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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1.0497311788708907, 'root_angle': -0.5209962758421128, 'root_number': '-0.06591392361220859 - 0.9978253127046056*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.260498137921', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34455069556571945032477136924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54561354565591521200043278808', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03237322461664153753809636446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.4', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/a/73/1'], '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': '2-138-23.4-c1-0-0', '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': '2-138-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.2604981379210564, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34455069556571945032477136924', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1704420496271167601166806767637', 'Lhash_array': ['1704420496271167601166806767637'], 'label': '2-138-23.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/a/73/1'}