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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.400', 'a10': [0.6691306063588582, 0.7431448254773942], 'a2': [-0.882947592858927, -0.46947156278589075], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5591929034707468, 0.8290375725550417], 'a5': [-0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7193398003386512, 0.6946583704589973], 'a8': [-0.10452846326765347, -0.9945218953682733], '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': '837.400', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.475', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 0, 'a^7', 'a^25', 0, 'a^17', 'a^33', 0, 'a^6', 'a^17', 0, 'a^4', 'a^43', 0, 'a^14', 'a^18', 0, 'a^21', 'a^32', 0, 'a^43', 'a^43', 0, 'a^5', 'a^30', 0, 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'191.76517632316391436282583192393', '192.430332166375288195067854182515', '192.76492486347426549306010860308', '193.57312178880927087497414158016', '194.056992362938726523035898174811', '194.804273339176928890755013003214', '195.48653402611499360640650062042', '196.27946735852601024377001515198', '196.72235344622511318776660327154', '197.44083101955988249553884930379', '198.11106003634721462775910289265', '198.8552388996110846566797763758', '199.3310470389300836220818007568', '199.68538475699398775754539943696'], 'prelabel': '1-837-837.400-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.781254206794222, 'root_number': '-0.773018837458328893130052124953-0.634383067975945977586822716844*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.390627103397', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.453119972328655795797523033784-0.0347531644033731893263938365011*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0979287807599', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.69406718311', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67388671121', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.400', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/400'], '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': '1-837-837.400-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': '1-837-837.400-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.390627103397111, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0979287807599', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.400', 'Lhash_array': ['dirichlet_L_837.400'], 'label': '1-837-837.400-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/400'}
Lfunction data - 1-837-837.400-r0-0-0