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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_669.245', 'a10': [0.07069756565199466, -0.9974977965944997], 'a2': [0.2928227712765504, 0.956166734739251], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8285096492438421, 0.5599747861375954], 'a5': [-0.9330723539826373, -0.35968872964453574], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9963974885425265, 0.08480592447550919], 'a8': [-0.7780357543184395, -0.6282199972956423], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.1068229386429325, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [223, [1]]], 'bad_primes': [3, 223], 'central_character': '669.245', 'coeff_info': ['x^222 - 1', '0.999599507118322 + 0.0282988580831181*I', '\\\\zeta_{222}'], 'conductor': 669, 'conductor_radical': 669, 'conjugate': 'dirichlet_L_669.71', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^45', 0, 'a^90', 'a^124', 0, 'a^108', 'a^135', 0, 'a^169', 'a^184', 0, 'a^9', 'a^153', 0, 'a^180', 'a^147', 0, 'a^80', 'a^214', 0, 'a^7', 'a^50', 0, 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'194.854707758040711525616821353784', '195.26646328078789185564731083062', '195.81893150606933157087043374871', '196.67437735880146772574583545775', '196.99351478700193590733337051406', '197.73769183763649824390974492435', '198.25063891426651934468583842818', '199.01467328185504428288227757424', '199.74974035784882804329466533198'], 'prelabel': '1-669-669.245-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1068229386429325, 'root_angle': 0.2477440937949942, 'root_number': '0.0141738021004947618376055770991+0.999899546621567385875634767240*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.252255906205', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(222)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.777113507646111182568381055641+0.406033786245847023267379083885*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.867559525301', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.10460913351', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.75313750715', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1068229386429325, 'bad_primes': [3, 223], 'central_character': '669.245', 'conductor': 669, 'conductor_radical': 669, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/669/245'], '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': '1-669-669.245-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': '1-669-669.245-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1068229386429325, 'root_angle': 0.2477440937949942, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867559525301', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_669.245', 'Lhash_array': ['dirichlet_L_669.245'], 'factors': ['1-669-669.245-r0-0-0'], 'label': '1-669-669.245-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/669/245'}
Lfunction data - 1-669-669.245-r0-0-0