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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_475.131', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9612616959383189, -0.27563735581699916], 'a3': [0.9902680687415704, 0.13917310096006544], 'a4': [0.848048096156426, -0.5299192642332049], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9902680687415704, -0.13917310096006544], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.6691306063588582, -0.7431448254773942], 'a9': [0.9612616959383189, 0.27563735581699916], 'algebraic': True, 'analytic_conductor': 2.205890726241245, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.131', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.446', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^1', 'a^41', 0, 'a^44', 'a^15', 'a^39', 'a^2', 0, 'a^3', 'a^42', 'a^17', 'a^13', 0, 'a^37', 'a^34', 'a^0', 0, 0, 'a^16', 'a^1', 'a^23', 'a^40', 0, 'a^15', 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0, 'data': '-0.00918220987624', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.42398207007423117133001577067-0.123617947725805727837625910528*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.77681216166', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51703062585', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.56205746301', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.205890726241245, 'bad_primes': [5, 19], 'central_character': '475.131', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/131'], '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': '1-475-475.131-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': '1-475-475.131-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.205890726241245, 'root_angle': -0.00918220987623829, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77681216166', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_475.131', 'Lhash_array': ['dirichlet_L_475.131'], 'factors': ['1-475-475.131-r0-0-0'], 'label': '1-475-475.131-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/131'}
Lfunction data - 1-475-475.131-r0-0-0