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lfunc_lfunctions • Show schema
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{'Lhash': '4587579974262382209817249750266', 'a10': [-0.42633737220400286, -0.0641923800074477], 'a2': [0.18624303216961835, -0.04990367006577284], 'a3': [1.5329472784187943, -0.8062708239719526], 'a4': [-1.6998547168231772, 0.9814115783411165], 'a5': [-2.0496342016605915, -0.893867797486379], 'a6': [0.24526487610572528, -0.22666201821686902], 'a7': [0.6320074464439881, 2.35868390089083], 'a8': [-0.5402887813124031, 0.5402887813124031], 'a9': [1.6998547168231772, -2.4719413305525673], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5329472784187943, 0.8062708239719526]]], [5, [[1.0, 0], [2.0496342016605915, 0.893867797486379]]]], 'bad_primes': [3, 5], 'central_character': '45.38', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '4081064434961777324332975820560', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'7.39477596190944703343819281460156', '8.456429090018229660350434918856885', '9.976005614845232100625842974184363', '10.78940850557615796307973086991729', '12.75974420927033405520912497223154', '13.85471825835248330716911031787168', '14.78597163194048070104720306109309', '15.48759207724960288791790452513398'], 'prelabel': '2-45-45.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738915, 'root_angle': 0.05441530512623302, 'root_number': '0.9854234759903995 + 0.17011929040234872*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0272076525631', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.61896249127040887007475587932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.86688862183632899891884717176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.39477596190944703343819281460', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'bad_primes': [3, 5], 'central_character': '45.38', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/2/l/a/38/3'], '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': '2-45-45.38-c1-0-2', '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': '2-45-45.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738915, 'root_angle': 0.02720765256311651, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.61896249127040887007475587932', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4587579974262382209817249750266', 'Lhash_array': ['4587579974262382209817249750266'], 'label': '2-45-45.38-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/2/l/a/38/3'}