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lfunc_lfunctions • Show schema
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{'Lhash': '2140536678558507832970319034614', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7653668647301796, -0.7653668647301796], 'a4': [0.0, 0.0], 'a5': [0.41421356237309503, 0.41421356237309503], 'a6': [0.0, 0.0], 'a7': [0.0, -3.695518130045147], 'a8': [0.0, 0.0], 'a9': [0.0, 1.82842712474619], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.088340583489558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '512.385', 'coefficient_field': 'CDF', 'conductor': 512, 'conductor_radical': 2, 'conjugate': '1531996625270696853041389430377', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7653668647301796, 0.7653668647301796], [0, -3.0]], [[1.0, 0], [-0.41421356237309503, -0.41421356237309503], [0, 5.0]], [[1.0, 0], [0, 3.695518130045147], [-7.0, 0]], [[1.0, 0], [-2.9301512653149673, -2.9301512653149673], [0, 11.0]], [[1.0, 0], [-2.414213562373095, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03168973381028160062146801999', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.088340583489558, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 512, 'conductor_radical': 2, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/512/2/e/i/385/3'], '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': '2-2e9-16.5-c1-0-10', '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': '2-2e9-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68858570190644246044479542165', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2140536678558507832970319034614', 'Lhash_array': ['2140536678558507832970319034614'], 'label': '2-2e9-16.5-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/512/2/e/i/385/3'}