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lfunc_lfunctions • Show schema
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{'Lhash': '2196092319042007373884562623359', 'a10': [-0.5990335307586109, 0.34585217023709597], 'a2': [0.9659258262890683, 0.25881904510252074], 'a3': [1.6101394273373326, -0.6383189050418345], 'a4': [0.8660254037844386, 0.5], 'a5': [-0.4891088297254696, 0.4891088297254696], 'a6': [1.7204843462652344, -0.19983396672309928], 'a7': [0.25881904510252074, 0.9659258262890683], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [2.185097950932387, -2.0555648724453053], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [-1.6101394273373326, 0.6383189050418345]]], [7, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [13, [[1.0, 0], [-2.6771009826768375, 2.415187431349938]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.323', 'coefficient_field': 'CDF', 'conductor': 546, 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-1.2229756757551462], 'positive_zeros': ['1.73241137474838899826155329686540', '3.04341649001600749061865186038208', '4.15281630115718182372204747343815', '4.70172459333197693142075911864741', '6.17561170932159867855287949080045', '7.22708199404724083753282696211614', '8.128458510163010164263381341340796', '9.075764192607969254278788579526119', '9.905670714863189875434162219855910', '10.83760549930628311966494166170667'], 'prelabel': '2-546-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.03274051644099899, 'root_number': '0.9947148431903082 - 0.10267609622926138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0163702582205', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73241137474838899826155329687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04341649001600749061865186038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15281630115718182372204747344', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '39.11', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bu/b/323/14'], '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': '2-546-39.11-c1-0-21', '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': '2-546-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.016370258220499496, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73241137474838899826155329687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2196092319042007373884562623359', 'Lhash_array': ['2196092319042007373884562623359'], 'label': '2-546-39.11-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bu/b/323/14'}