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lfunc_lfunctions • Show schema
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{'Lhash': '2993267552265047806813234283093', 'a10': [-1.2153703234534297, 1.4026121234953608], 'a2': [0.8412535328311812, -0.5406408174555976], 'a3': [0.0, 0.0], 'a4': [0.41541501300188644, -0.9096319953545183], 'a5': [-1.7807439433230365, 0.5228735988991808], 'a6': [0.0, 0.0], 'a7': [-2.544869156606746, -2.936935568431139], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8412535328311812, 0.5406408174555976]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-4.406440051556995, -1.8929569651828824]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.127', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'conjugate': '853963476632757483919867301731', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [0, 0]], 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47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36127175084848787855739697153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74926837812827055996931266916', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58847026335952082043984023068', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'bad_primes': [2, 3, 23], 'central_character': '23.12', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/2/i/a/127/1'], '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': '2-414-23.12-c1-0-8', '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': '2-414-23.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8181877360935557, 'root_angle': 0.3437477994789986, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36127175084848787855739697153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2993267552265047806813234283093', 'Lhash_array': ['2993267552265047806813234283093'], 'label': '2-414-23.12-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/2/i/a/127/1'}