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lfunc_lfunctions • Show schema
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{'Lhash': '2250286284677331334000426223754', 'a10': [2.02785171187275, 0.0], 'a2': [0.5660923032940295, 0.0], 'a3': [2.3226687062301785, 0.0], 'a4': [-1.6795395041512606, 0.0], 'a5': [3.5821926920272573, 0.0], 'a6': [1.3148448776988053, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.082958992966358, 0.0], 'a9': [2.394789918900972, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 11], 'central_character': '539.1', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '2250286284677331334000426223754', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5660923032940295, 0], [2.0, 0]], [[1.0, 0], [-2.3226687062301785, 0], [3.0, 0]], [[1.0, 0], [-3.5821926920272573, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.1154202905722452, 0], [13.0, 0]], [[1.0, 0], 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'5.26873167160457150233481727072619', '5.95522124784685164641838436882787', '7.32184528555123041271931926005371', '8.505455282089661292763524243899329', '9.004081035090090135682489450646477', '9.902486215713594192926504408952046', '10.21669301023926917223250888930056'], 'prelabel': '2-539-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77516287553698706359422148543', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92059387744415445777463427238', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93302146905185047183585991821', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/a/l/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': '2-539-1.1-c1-0-17', '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': '2-539-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77516287553698706359422148543', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2250286284677331334000426223754', 'Lhash_array': ['2250286284677331334000426223754'], 'label': '2-539-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/a/l/1/6'}