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lfunc_lfunctions • Show schema
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{'Lhash': '2877770205206320279533103977572', 'a10': [1.1133407984528387, 0.4052229112310005], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [-0.17364817766693036, 0.984807753012208], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.9076037345479523, 0.7615699589143088], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [-0.266044443118978, -0.46080249255343814], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.9396926207859084, -0.3420201433256687], '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], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [3.9396926207859084, 1.8651600611542862]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.43', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3330815339508562394756401898466', 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{'__RealLiteral__': 0, 'data': '-0.0191633683148', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27016040909711471604506682140', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.27285914981551215958887180856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.74595489274388053617687269860', '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': '19.5', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/i/d/43/1'], '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': '2-114-19.5-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': '2-114-19.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.019163368314845542, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27016040909711471604506682140', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2877770205206320279533103977572', 'Lhash_array': ['2877770205206320279533103977572'], 'label': '2-114-19.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/i/d/43/1'}