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lfunc_lfunctions • Show schema
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{'Lhash': '1579287414491834390602006148610', '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': '390.253', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2204546862365624892813234969407', 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'4.49565379833326418959625650042667', '5.53766689974829199838188244677489', '6.63375201868049375962458790066879', '7.82275704247602431620902000324353', '8.583953336183897249917823269705514', '9.331515239776040691629157756478874', '10.11647966098812629208454388915864', '11.02136352523829554670154863465559'], 'prelabel': '2-390-65.58-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': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24583809940017975522128328297', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80522247996991309674877062007', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49565379833326418959625650043', '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': '65.58', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/253/3'], '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': '2-390-65.58-c1-0-4', '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': '2-390-65.58-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': '1.24583809940017975522128328297', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1579287414491834390602006148610', 'Lhash_array': ['1579287414491834390602006148610'], 'label': '2-390-65.58-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/253/3'}