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lfunc_lfunctions • Show schema
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{'Lhash': '2355477437312377754929223056325', 'a10': [-0.9909695034853946, 2.72266633419428], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [0.7799360522823928, 1.5465121255102259], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [1.8624134596982016, -2.2195379314911436], 'a6': [-1.261838451836549, -1.1864921919114095], 'a7': [0.5620825889262131, 0.9735556020700527], 'a8': [-0.5, 0.8660254037844386], 'a9': [-1.7833995087003132, 2.412361123954596], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [3, [[1.0, 0], [-0.7799360522823928, -1.5465121255102259]]], [19, [[1.0, 0], [-4.13616708012598, 1.375544214222911]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.71', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2830526063624602780768702894173', 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85814406342591140448233541344', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28313176425333694518102268593', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.96600367815899857367305574140', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.14', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/l/b/71/2'], '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': '2-114-57.14-c1-0-1', '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': '2-114-57.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.11682451404748416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85814406342591140448233541344', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2355477437312377754929223056325', 'Lhash_array': ['2355477437312377754929223056325'], 'factors': ['2-114-57.14-c1-0-1'], 'label': '2-114-57.14-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/l/b/71/2'}