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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1617.530', 'a10': [-0.7330518718298263, -0.6801727377709194], 'a2': [0.5256837698105047, -0.8506800656873396], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.4473131483156326, -0.8943774076663368], 'a5': [0.19325591779555326, -0.9811483833941727], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9959742939952391, -0.0896393089034335], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 173.77078339290867, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.530', 'coeff_info': ['x^210 - 1', '0.999552432283503 + 0.0299154661693985*I', '\\\\zeta_{210}'], 'conductor': 1617, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_1617.479', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^176', 0, 'a^142', 'a^164', 0, 0, 'a^108', 0, 'a^130', 0, 0, 'a^36', 0, 0, 'a^74', 'a^19', 0, 'a^98', 'a^96', 0, 0, 'a^65', 0, 'a^118', 'a^2', 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'196.878062265753513586138826627869', '197.08808740081982443263787605477', '198.09553807339002186627151474049', '198.73733771085687535618306907725', '199.475978134661120036222192739875', '199.88330220555203334927276655530'], 'prelabel': '1-1617-1617.530-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 173.77078339290867, 'root_angle': -0.5444132316428375, 'root_number': '-0.139075996675717777109009383316-0.990281711003821244362407457747*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.272206615821', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(210)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12281746099204834531351706189-0.783982621693427662625431054899*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.646347916178', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.57569484068', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.21108319531', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 173.77078339290867, 'bad_primes': [3, 7, 11], 'central_character': '1617.530', 'conductor': 1617, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1617/530'], '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': '1-1617-1617.530-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1617-1617.530-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 173.77078339290867, 'root_angle': -0.27220661582141875, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.646347916178', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1617.530', 'Lhash_array': ['dirichlet_L_1617.530'], 'label': '1-1617-1617.530-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1617/530'}
Lfunction data - 1-1617-1617.530-r1-0-0