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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.40', 'a10': [-0.9396926207859084, -0.3420201433256687], 'a2': [-0.993238357741943, 0.11609291412523023], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9730448705798238, -0.23061587074244017], 'a5': [0.8936326403234123, 0.44879918020046217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.28680323271109026, -0.9579895123154889], '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': '81.40', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.79', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^26', 'a^2', 0, 'a^19', 'a^12', 0, 'a^15', 'a^7', 0, 'a^23', 'a^5', 0, 'a^25', 'a^24', 0, 'a^3', 'a^1', 0, 'a^20', 'a^8', 0, 'a^4', 'a^9', 0, 'a^18', 'a^22', 0, 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'0.790377974837778792792091901939+0.0293298741012499583128584161019*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.50120548673', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.21123333482', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.58684710458', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.40', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/40'], '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': '1-3e4-81.40-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': '1-3e4-81.40-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': 0.01234567901234568, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50120548673', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.40', 'Lhash_array': ['dirichlet_L_81.40'], 'factors': ['1-3e4-81.40-r0-0-0'], 'label': '1-3e4-81.40-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/40'}
Lfunction data - 1-3e4-81.40-r0-0-0