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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.49', 'a10': [0.17364817766693036, 0.984807753012208], 'a2': [-0.8354878114129364, -0.549508978070806], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.39607976603915684, 0.918216106880274], 'a5': [-0.6862416378687336, -0.7273736415730487], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.993238357741943, 0.11609291412523023], 'a8': [0.17364817766693036, -0.984807753012208], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.49', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.43', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 0, 'a^5', 'a^17', 0, 'a^13', 'a^21', 0, 'a^6', 'a^19', 0, 'a^20', 'a^2', 0, 'a^10', 'a^15', 0, 'a^12', 'a^22', 0, 'a^8', 'a^14', 0, 'a^7', 'a^9', 0, 'a^18', 'a^25', 0, 'a^23', 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'188.9260787663820975974989462983', '189.55732940933775336308001939052', '190.61025859983834989884329141857', '191.16226123594121470827861172894', '191.91598820581954124087350094782', '192.541179558796390266732169932015', '193.47749413014003205780667536887', '194.28036344069606841831885892221', '194.89838413831626670849156596156', '196.407250148444995523743909335989', '196.66678476748073759785832555042', '197.708301162002223370870012804546', '198.660502189610359749358978349713', '199.393005995872974908543761439639'], 'prelabel': '1-3e4-81.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.8641975308641975, 'root_number': '-0.910362940966146659506126969701-0.413810724505139151460272061105*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.432098765432', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.413635150293203520561509959815-0.249330500338112267044705060383*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.440708990551', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.73204692186', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.08978519748', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.49', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/49'], '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': '1-3e4-81.49-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': '1-3e4-81.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.43209876543209874, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.440708990551', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.49', 'Lhash_array': ['dirichlet_L_81.49'], 'label': '1-3e4-81.49-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/49'}
Lfunction data - 1-3e4-81.49-r0-0-0