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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_459.275', 'a10': [0.6087614290087207, -0.7933533402912352], 'a2': [0.573576436351046, 0.8191520442889918], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.3420201433256687, 0.9396926207859084], 'a5': [-0.3007057995042731, -0.9537169507482269], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6755902076156602, 0.7372773368101241], 'a8': [-0.9659258262890683, 0.25881904510252074], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.1315870386204874, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '459.275', 'coeff_info': ['x^144 - 1', '0.999048221581858 + 0.0436193873653360*I', '\\\\zeta_{144}'], 'conductor': 459, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_459.227', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 0, 'a^44', 'a^101', 0, 'a^19', 'a^66', 0, 'a^123', 'a^7', 0, 'a^68', 'a^41', 0, 'a^88', 0, 0, 'a^30', 'a^1', 0, 'a^29', 'a^143', 0, 'a^58', 'a^90', 0, 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'spectral_label': 'r0-0', 'st_group': 'mu(144)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15632954632381299217813799596+0.715143736819989726437586234781*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.51066520794', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.03614654285', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.40905758467', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.1315870386204874, 'bad_primes': [3, 17], 'central_character': '459.275', 'conductor': 459, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/459/275'], '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': '1-459-459.275-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': '1-459-459.275-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1315870386204874, 'root_angle': 0.2958442860221298, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51066520794', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_459.275', 'Lhash_array': ['dirichlet_L_459.275'], 'factors': ['1-459-459.275-r0-0-0'], 'label': '1-459-459.275-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/459/275'}
Lfunction data - 1-459-459.275-r0-0-0