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lfunc_lfunctions • Show schema
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{'Lhash': '2273245034891058192502718849494', 'a10': [11.613952043641586, 0.0], 'a2': [-1.7054678860282548, 0.0], 'a3': [4.443794049538246, 0.0], 'a4': [-5.091379289726316, 0.0], 'a5': [-6.809833324207886, 0.0], 'a6': [-7.578748043610931, 0.0], 'a7': [13.876030162663575, 0.0], 'a8': [22.326926962443615, 0.0], 'a9': [-7.252694445288476, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7054678860282548, 0], [8.0, 0]], [[1.0, 0], [-4.443794049538246, 0], [27.0, 0]], [[1.0, 0], [6.809833324207886, 0], [125.0, 0]], [[1.0, 0], [-13.876030162663575, 0], [343.0, 0]], [[1.0, 0], [30.8360763724999, 0], [1331.0, 0]], [[1.0, 0], [-66.01296310690245, 0], [2197.0, 0]], [[1.0, 0], [0, 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'4.47425306285472296170645029836018', '5.82283062917530429177169208901435', '7.61540268124914233834787279671756', '8.215956500431459307518663541968151', '8.681910058503695006201109283211090', '9.751337378713901950011558783271300', '10.87439982539075284509575850818668'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79327413601333073144987967281', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47986080197519134405289144752', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47425306285472296170645029836', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/g/1/6'], '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': '2-17e2-1.1-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79327413601333073144987967281', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2273245034891058192502718849494', 'Lhash_array': ['2273245034891058192502718849494'], 'label': '2-17e2-1.1-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/6'}