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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_161.38', 'a10': [-0.9954719225730846, 0.09505604330418266], 'a2': [0.7237340381050702, -0.690079011482112], 'a3': [-0.9819286972627067, -0.18925124436041021], 'a4': [0.0475819158237423, -0.998867339183008], 'a5': [-0.7860530947427875, -0.6181589862206052], 'a6': [-0.8412535328311812, 0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [0.9283679330160726, 0.3716624556603275], 'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.38', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.89', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^35', 'a^50', 'a^40', 'a^27', 0, 'a^42', 'a^4', 'a^32', 'a^41', 'a^19', 'a^21', 0, 'a^9', 'a^34', 'a^38', 'a^62', 'a^28', 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'188.62168774492994279301720373871', '189.66562301624399750544734762258', '190.66458402401619959205018164169', '191.250024563501419972015254782941', '191.91747518405927292047696716944', '193.00039741039939330713870179054', '193.22595478314814595045427373915', '194.357810090795537645456237459809', '194.77572895726576019920955112759', '195.35674148763570068486582345933', '196.243489410753581321657782710480', '196.43457433520784409014674992438', '197.79285132071846624061799401063', '198.86777192568302293032696456788', '199.58556469426044060843003647647'], 'prelabel': '1-161-161.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.44980981900790884, 'root_number': '-0.950686579868714124556729997562+0.310153231254370522377366982070*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.449809819008', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.552492836462101698351979124623-0.546813839723671175189271031198*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.416358963728', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.14681258631', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.01238436745', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'bad_primes': [7, 23], 'central_character': '161.38', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/38'], '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': '1-161-161.38-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': '1-161-161.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': 0.44980981900790884, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.416358963728', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_161.38', 'Lhash_array': ['dirichlet_L_161.38'], 'factors': ['1-161-161.38-r0-0-0'], 'label': '1-161-161.38-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/38'}
Lfunction data - 1-161-161.38-r0-0-0