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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.275', 'a10': [0.9135454576426009, 0.4067366430758002], 'a2': [-0.4383711467890774, -0.898794046299167], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6156614753256583, 0.7880107536067219], 'a5': [-0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.03489949670250097, 0.9993908270190958], 'a8': [0.9781476007338057, 0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.275', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.767', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^61', 0, 'a^32', 'a^35', 0, 'a^22', 'a^3', 0, 'a^6', 'a^82', 0, 'a^29', 'a^83', 0, 'a^64', 'a^78', 0, 'a^66', 'a^67', 0, 'a^53', 'a^68', 0, 'a^70', 'a^0', 0, 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'193.86005416991070226118105225354', '194.43811457038581153392159690676', '195.12035315088527291123622820452', '195.497604975599523619298225386436', '196.191144373967540473199878484', '197.25185162148933621629334197135', '197.78948519107046377111758634879', '198.478057310159554091521290686397', '198.902859840146072314747012462276', '199.54448021768286197917435031877', '199.989146425863735039693200889425'], 'prelabel': '1-837-837.275-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.05095686139378686, 'root_number': '0.949181486546705938120748060557+0.314729257611975906684847420712*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0509568613938', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.764963765482286537525042882464-0.0803740447335886241132517584467*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.997179481145', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.45968465993', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.99159507941', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.275', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/275'], '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': '1-837-837.275-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': '1-837-837.275-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.05095686139378686, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.997179481145', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.275', 'Lhash_array': ['dirichlet_L_837.275'], 'factors': ['1-837-837.275-r0-0-0'], 'label': '1-837-837.275-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/275'}
Lfunction data - 1-837-837.275-r0-0-0