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lfunc_lfunctions • Show schema
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{'Lhash': '2307651577183482529718888896551', 'a10': [-0.137054624375387, -3.1593062576991997], 'a2': [0.541196100146197, 1.3065629648763766], 'a3': [1.3065629648763766, 1.137054624375387], 'a4': [-1.4142135623730951, 1.4142135623730951], 'a5': [-2.1010029896154587, -0.7653668647301796], 'a6': [-0.7785266800637528, 2.322476309551706], 'a7': [2.274109248750774, 0.0], 'a8': [-2.613125929752753, -1.082392200292394], 'a9': [0.41421356237309503, 2.9712669225006008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.541196100146197, -1.3065629648763766]]], [3, [[1.0, 0], [-1.3065629648763766, -1.137054624375387]]], [5, [[1.0, 0], [2.1010029896154587, 0.7653668647301796]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '4417794277864106778164665965569', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.541196100146197, -1.3065629648763766]], [[1.0, 0], [-1.3065629648763766, -1.137054624375387]], [[1.0, 0], [2.1010029896154587, 0.7653668647301796]], [[1.0, 0], [-2.274109248750774, 0], [7.0, 0]], [[1.0, 0], [0, 4.2020059792309175], [-11.0, 0]], [[1.0, 0], [-3.216076141901435, 0], [13.0, 0]], [[1.0, 0], [-1.5307337294603591, 0], [17.0, 0]], [[1.0, 0], [4.82842712474619, 0], [19.0, 0]], [[1.0, 0], [0, -1.082392200292394], [-23.0, 0]], [[1.0, 0], [1.7405278657702838, 0], [29.0, 0]], [[1.0, 0], [0, 6.82842712474619], [-31.0, 0]], [[1.0, 0], [7.7642946394029835, 0], [37.0, 0]], [[1.0, 0], [0, -2.4614781134606334], [-41.0, 0]], [[1.0, 0], [0, 8.706261532553643], [-43.0, 0]], [[1.0, 0], [0, 1.082392200292394], [-47.0, 0]], [[1.0, 0], [0, -11.086554390135442], [-53.0, 0]], [[1.0, 0], [0, -4.2020059792309175], [-59.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-61.0, 0]], [[1.0, 0], [0, 2.274109248750774], [-67.0, 0]], [[1.0, 0], [11.885067690002403, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/m/b/59/12'], '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': '2-120-120.59-c1-0-6', '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': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.2679225813414896, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82041611211165762078027645365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2307651577183482529718888896551', 'Lhash_array': ['2307651577183482529718888896551'], 'label': '2-120-120.59-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/m/b/59/12'}