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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4024.1181', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.5704394624531183, -0.8213396493998067], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.45231688414446564, -0.8918572959380004], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8890091817823071, 0.4578893695061644], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.3491976393523949, -0.9370490961901168], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.1181', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.1029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^425', 0, 'a^339', 0, 'a^38', 0, 'a^348', 0, 'a^433', 0, 'a^621', 0, 'a^262', 0, 'a^72', 0, 'a^525', 0, 'a^463', 0, 'a^288', 0, 'a^176', 0, 'a^271', 0, 'a^473', 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'196.24941946935004743134195969186', '196.590628161753449175429323869130', '197.24163836224642061249473909184', '197.66489872729739305579253167544', '198.41002373152394380263672476176', '198.76636272577308631728597125536', '199.524257472184993554117529410', '199.986132220020219307614993725763'], 'prelabel': '1-4024-4024.1181-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.408999335697805, 'root_number': '0.282008578161583178901127226150-0.959411883313565295841929184367*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(502)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.32287851257049138022377860862-0.535594820974958744529172096090*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.823281267823', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.50451146421', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.11023301669', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.1181', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/1181'], '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': '1-4024-4024.1181-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': '1-4024-4024.1181-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.2044996678489025, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.823281267823', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4024.1181', 'Lhash_array': ['dirichlet_L_4024.1181'], 'label': '1-4024-4024.1181-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/1181'}
Lfunction data - 1-4024-4024.1181-r0-0-0