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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.167', 'a10': [-0.9781476007338057, -0.20791169081775934], 'a2': [-0.9902680687415704, 0.13917310096006544], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9612616959383189, -0.27563735581699916], 'a5': [0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.4383711467890774, 0.898794046299167], 'a8': [-0.9135454576426009, 0.4067366430758002], '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': '837.167', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.416', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 0, 'a^86', 'a^5', 0, 'a^16', 'a^39', 0, 'a^48', 'a^16', 0, 'a^17', 'a^59', 0, 'a^82', 'a^54', 0, 'a^78', 'a^1', 0, 'a^59', 'a^14', 0, 'a^10', 'a^60', 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'193.48046496560457180353110249098', '194.83679632933914258605736475308', '195.28748918783000825077776751839', '196.13845838393956671921590134892', '196.51100107976370036330944141488', '197.356461847327660634544843072907', '197.79475642388416355222659103998', '198.2351460039293351948178890682', '198.98214649295348402739182597368', '199.5901641943515751330603784985'], 'prelabel': '1-837-837.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.2207417559635147, 'root_number': '0.182801257792218059928566072575+0.983149886919376620454111896595*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.220741755964', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.875312921222052492867466064066+0.306998774194324475746341684737*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43066071927', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.10944143507', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00154278129', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.167', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/167'], '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': '1-837-837.167-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': '1-837-837.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.2207417559635147, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43066071927', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.167', 'Lhash_array': ['dirichlet_L_837.167'], 'factors': ['1-837-837.167-r0-0-0'], 'label': '1-837-837.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/167'}
Lfunction data - 1-837-837.167-r0-0-0