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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_161.65', 'a10': [-0.7237340381050702, 0.690079011482112], 'a2': [0.9819286972627067, 0.18925124436041021], 'a3': [0.0475819158237423, 0.998867339183008], 'a4': [0.9283679330160726, 0.3716624556603275], 'a5': [-0.5800569095711982, 0.8145759520503357], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [-0.9954719225730846, 0.09505604330418266], 'algebraic': True, 'analytic_conductor': 17.30185289193463, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.65', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.109', '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^36', 0, 'a^39', 'a^8', 'a^7', 'a^34', 'a^59', 'a^27', 0, 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'unitary', 'types': ['DIR'], 'values': [[1, '1.14985203536415271643325278211+1.05990839254017796623672002099*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.66027749186', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.43489931745', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.71400807703', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.30185289193463, 'bad_primes': [7, 23], 'central_character': '161.65', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/65'], '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': '1-161-161.65-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': '1-161-161.65-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': 0.4818974920947667, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66027749186', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_161.65', 'Lhash_array': ['dirichlet_L_161.65'], 'label': '1-161-161.65-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/65'}
Lfunction data - 1-161-161.65-r1-0-0