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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3724.151', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.07473009358642425, 0.9972037971811801], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8262387743159949, -0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9888308262251285, 0.14904226617617444], 'algebraic': True, 'analytic_conductor': 17.29418329373136, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [19, [1]]], 'bad_primes': [2, 7, 19], 'central_character': '3724.151', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 3724, 'conductor_radical': 266, 'conjugate': 'dirichlet_L_3724.1899', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^52', 0, 'a^38', 0, 0, 0, 'a^20', 0, 'a^43', 0, 'a^15', 0, 'a^48', 0, 'a^40', 0, 0, 0, 0, 0, 'a^23', 0, 'a^34', 0, 'a^30', 0, 'a^33', 0, 'a^28', 0, 'a^11', 0, 0, 0, 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'199.813109936097287767239297665730'], 'prelabel': '1-3724-3724.151-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.29418329373136, 'root_angle': 0.013605442176870748, 'root_number': '0.996348338021206957147313173874+0.0853814342956284787664064274263*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28129561142513932978340938700+0.205802635148263209074032124095*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.67532926851', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.88055233672', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.52187046962', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.29418329373136, 'bad_primes': [2, 7, 19], 'central_character': '3724.151', 'conductor': 3724, 'conductor_radical': 266, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3724/151'], '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': '1-3724-3724.151-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': '1-3724-3724.151-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.29418329373136, 'root_angle': 0.013605442176870748, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67532926851', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3724.151', 'Lhash_array': ['dirichlet_L_3724.151'], 'factors': ['1-3724-3724.151-r0-0-0'], 'label': '1-3724-3724.151-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3724/151'}
Lfunction data - 1-3724-3724.151-r0-0-0