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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_161.39', 'a10': [0.0475819158237423, -0.998867339183008], 'a2': [0.9283679330160726, 0.3716624556603275], 'a3': [-0.9954719225730846, 0.09505604330418266], 'a4': [0.7237340381050702, 0.690079011482112], 'a5': [-0.32706796331742166, -0.9450008187146685], 'a6': [-0.9594929736144974, -0.28173255684142967], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [0.9819286972627067, -0.18925124436041021], 'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.39', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.128', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^16', 'a^4', 'a^23', 'a^18', 0, 'a^6', 'a^32', 'a^25', 'a^31', 'a^20', 'a^3', 0, 'a^6', 'a^8', 'a^7', 'a^1', 'a^26', 'a^27', 0, 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'189.16220721211870416030031070327', '189.84234908603201625164775173695', '190.64689505557476575172755763296', '192.15825319216927890881864873411', '192.59020118472859515139098544095', '192.93767968600449766098517035617', '194.278194643054017252198365792337', '194.5267470085292166875093057759', '195.31551484048901868167898906631', '195.790114826240103722932532504439', '196.60522960474540122112782169667', '197.34421405200201978801217549096', '198.17182602666144147838448282408', '199.15726036411106271785749562514', '199.600361140024264229341131086894'], 'prelabel': '1-161-161.39-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.12759364217888422, 'root_number': '0.920730729191846208247265621837+0.390198570373920207437712206826*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0637968210894', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.35052908116069306109655616464+0.218315453819333417119498362644*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44486781501', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.77727091104', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.54426358597', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'bad_primes': [7, 23], 'central_character': '161.39', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/39'], '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': '1-161-161.39-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': '1-161-161.39-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.06379682108944211, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44486781501', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_161.39', 'Lhash_array': ['dirichlet_L_161.39'], 'label': '1-161-161.39-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/39'}
Lfunction data - 1-161-161.39-r0-0-0