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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.725', 'a10': [-0.9781476007338057, -0.20791169081775934], 'a2': [0.374606593415912, -0.9271838545667874], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7193398003386512, -0.6946583704589973], 'a5': [-0.17364817766693036, -0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9975640502598242, -0.0697564737441253], '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': '837.725', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.695', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^73', 0, 'a^56', 'a^65', 0, 'a^46', 'a^39', 0, 'a^48', 'a^46', 0, 'a^77', 'a^29', 0, 'a^22', 'a^54', 0, 'a^78', 'a^31', 0, 'a^29', 'a^74', 0, 'a^40', 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'192.320888669729769867354669010880', '192.70463067603268761425502399751', '193.54519815524824556021741980699', '193.75184757520776029572028316352', '194.63415290859273903940632185687', '195.13870058312003915850160853162', '195.76604106139547661108837452871', '196.485371349954689779768332763546', '196.99411632734444516061650301663', '197.308226783505852581453223733793', '198.767851994925101821034987798088', '199.1850626918486273852103118139', '199.76303136477847403918078214523'], 'prelabel': '1-837-837.725-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.4414835119270294, '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, '0.516896192258228680917803463370-0.577229887763548983499407609792*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.140688005477', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.18805888862', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.65444555037', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.725', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/725'], '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': '1-837-837.725-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': '1-837-837.725-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': '0.140688005477', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.725', 'Lhash_array': ['dirichlet_L_837.725'], 'label': '1-837-837.725-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/725'}
Lfunction data - 1-837-837.725-r0-0-0