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lfunc_lfunctions • Show schema
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{'Lhash': '894444131100675818374406404810', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.4229793010644913, -2.4229793010644913], 'a4': [0, 0], 'a5': [-1.7505957995226982, 1.39119170019573], 'a6': [0, 0], 'a7': [-1.8708286933869707, 1.8708286933869707], 'a8': [0, 0], 'a9': [0, 8.74165738677394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.943245026383407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.7505957995226982, -1.39119170019573]]], [7, [[1.0, 0], [1.8708286933869707, -1.8708286933869707]]]], 'bad_primes': [2, 5, 7], 'central_character': '1120.433', 'coefficient_field': 'CDF', 'conductor': 1120, 'conductor_radical': 70, 'conjugate': '474394508731073922154760069706', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.4229793010644913, 2.4229793010644913], [0, 3.0]], [[1.0, 0], [1.7505957995226982, -1.39119170019573]], [[1.0, 0], [1.8708286933869707, 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'4.67729793124261213896263995332270', '5.56358761249853124635414488151671', '6.60990459229695602744837743932175', '7.26545739921210890608633412664477', '8.697251085198788281539385608137064', '9.515225184868388486138617660848120', '9.942390721013077923152190164595714'], 'prelabel': '2-1120-280.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': 0.46246358164331103, 'root_number': '0.1176510152809158712724144807297743472623799983342670904 + 0.9930550028086912065609267206436069200798139189823899321*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23123179082165551', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70559200692970048444893506350', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29576215087412504629099815089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19875579638640161630627491565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.943245026383407, 'bad_primes': [2, 5, 7], 'central_character': '280.13', 'conductor': 1120, 'conductor_radical': 70, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1120/2/w/b/433/1'], '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': '2-1120-280.13-c1-0-9', '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': '2-1120-280.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': 0.23123179082165551, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70559200692970048444893506350', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '894444131100675818374406404810', 'Lhash_array': ['894444131100675818374406404810'], 'label': '2-1120-280.13-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1120/2/w/b/433/1'}