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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_448.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3826834323650898, 0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 48.14428630799201, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '448.13', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 448, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_448.69', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^21', 0, 'a^23', 0, 0, 0, 'a^10', 0, 'a^11', 0, 'a^9', 0, 'a^12', 0, 'a^12', 0, 'a^17', 0, 0, 0, 'a^2', 0, 'a^14', 0, 'a^15', 0, 'a^5', 0, 'a^0', 0, 'a^0', 0, 0, 0, 'a^7', 0, 'a^14', 0, 'a^10', 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{'__RealLiteral__': 0, 'data': '0.676171190525', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.95334776689', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.46013234626', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 48.14428630799201, 'bad_primes': [2, 7], 'central_character': '448.13', 'conductor': 448, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/448/13'], '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': '1-448-448.13-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-448-448.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 48.14428630799201, 'root_angle': 0.23437500000000003, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.676171190525', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_448.13', 'Lhash_array': ['dirichlet_L_448.13'], 'label': '1-448-448.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/448/13'}
Lfunction data - 1-448-448.13-r1-0-0