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lfunc_lfunctions • Show schema
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{'Lhash': '2204546862365624892813234969407', 'a10': [-0.4554754072701411, 2.189187555549341], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [0.5, -0.8660254037844386], 'a5': [1.489047051269676, -1.6681543331194157], 'a6': [-0.9659258262890683, 0.25881904510252074], 'a7': [0.32841057144042834, -0.5688237954775504], 'a8': [0.0, 1.0], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [-1.489047051269676, 1.6681543331194157]]], [13, [[1.0, 0], [-3.5453611560528198, 0.6560596567018983]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.37', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1579287414491834390602006148610', 'degree': 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'4.03579692871281489286445255973168', '5.84369468864848863099576441282646', '6.71478015362547810901355806455604', '7.82263243765371305492316188890072', '8.675729766092141646970410012596411', '9.499921425304570357504516703975425', '10.48269636140168625913756882636395', '11.01219679721627826732470923544273'], 'prelabel': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.06855213318452624, 'root_number': '0.9768989107960441 + 0.21370193748654395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0342760665923', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73908083344788817600136477820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80262817169839905041252031724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03579692871281489286445255973', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.37', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/3'], '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': '2-390-65.37-c1-0-7', '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': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.03427606659226312, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73908083344788817600136477820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2204546862365624892813234969407', 'Lhash_array': ['2204546862365624892813234969407'], 'label': '2-390-65.37-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/3'}