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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.25', 'a10': [-0.9396926207859084, 0.3420201433256687], 'a2': [0.5971585917027862, -0.8021231927550437], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.28680323271109026, -0.9579895123154889], 'a5': [-0.8354878114129364, -0.549508978070806], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6862416378687336, -0.7273736415730487], 'a8': [-0.9396926207859084, -0.3420201433256687], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.25', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^19', 'a^16', 0, 'a^17', 'a^15', 0, 'a^12', 'a^2', 0, 'a^22', 'a^13', 0, 'a^11', 'a^3', 0, 'a^24', 'a^8', 0, 'a^25', 'a^10', 0, 'a^5', 'a^18', 0, 'a^9', 'a^14', 0, 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'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.857889237984120007555047393271-0.720741034272757609035801603427*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.08184129531', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.35749710996', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.22309363683', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.25', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/25'], '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': '1-3e4-81.25-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': '1-3e4-81.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.34567901234567905, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08184129531', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.25', 'Lhash_array': ['dirichlet_L_81.25'], 'label': '1-3e4-81.25-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/25'}
Lfunction data - 1-3e4-81.25-r0-0-0