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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_165.158', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9510565162951535, 0.30901699437494745], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5877852522924731, 0.8090169943749475], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.766256778589064, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '165.158', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 165, 'conductor_radical': 165, 'conjugate': 'dirichlet_L_165.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 0, 0, 'a^3', 'a^7', 0, 0, 0, 0, 'a^9', 'a^12', 0, 'a^16', 'a^1', 0, 'a^2', 0, 0, 0, 'a^15', 0, 0, 'a^18', 0, 'a^1', 'a^8', 0, 'a^4', 'a^5', 0, 'a^10', 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'195.75578599288657721087364308856', '196.31625601756086308498791771560', '197.10859496260873589392437861115', '197.91232121811433047506829918378', '198.62367747084279658948838874367', '199.10239278805722045855544105172', '199.83707410185608588114310688543'], 'prelabel': '1-165-165.158-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.766256778589064, 'root_angle': 0.16567964151478007, 'root_number': '0.505361147229774421814022041915+0.862907938815379227374756419888*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.165679641515', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.722589505512508738408693714407+0.205825233498766993204599266098*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.51699886668', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.83560788909', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.96210474786', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.766256778589064, 'bad_primes': [3, 5, 11], 'central_character': '165.158', 'conductor': 165, 'conductor_radical': 165, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/165/158'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-165-165.158-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-165-165.158-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.766256778589064, 'root_angle': 0.16567964151478007, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51699886668', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_165.158', 'Lhash_array': ['dirichlet_L_165.158'], 'factors': ['1-165-165.158-r0-0-0'], 'label': '1-165-165.158-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/165/158'}
Lfunction data - 1-165-165.158-r0-0-0