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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_261.205', 'a10': [0.4338837391175581, -0.9009688679024191], 'a2': [-0.2947551744109042, -0.9555728057861407], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8262387743159949, 0.5633200580636221], 'a5': [0.7330518718298263, 0.6801727377709194], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8262387743159949, 0.5633200580636221], 'a8': [0.7818314824680298, 0.6234898018587335], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 28.04834537139713, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '261.205', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 261, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_261.247', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 0, 'a^34', 'a^10', 0, 'a^8', 'a^9', 0, 'a^69', 'a^47', 0, 'a^82', 'a^67', 0, 'a^68', 'a^63', 0, 'a^27', 'a^44', 0, 'a^22', 'a^4', 0, 'a^20', 'a^57', 0, 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'199.85002806525971409939134977759'], 'prelabel': '1-261-261.205-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 28.04834537139713, 'root_angle': 0.04054601700059754, 'root_number': '0.967724275892923393937857580936+0.252011360552489946959806545901*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0405460170006', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08028800606220209091745154814-0.152518604528873464165485777847*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25607900738', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.40812369523', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.31603226236', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 28.04834537139713, 'bad_primes': [3, 29], 'central_character': '261.205', 'conductor': 261, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/261/205'], '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': '1-261-261.205-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-261-261.205-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 28.04834537139713, 'root_angle': 0.04054601700059754, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25607900738', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_261.205', 'Lhash_array': ['dirichlet_L_261.205'], 'factors': ['1-261-261.205-r1-0-0'], 'label': '1-261-261.205-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/261/205'}
Lfunction data - 1-261-261.205-r1-0-0