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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.87', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5, -0.8660254037844386], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.87', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.1033', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^5', 'a^10', 0, 'a^10', 'a^9', 'a^3', 'a^10', 0, 0, 'a^3', 'a^7', 'a^2', 0, 'a^8', 'a^5', 'a^3', 0, 0, 'a^2', 0, 'a^1', 'a^8', 0, 'a^0', 'a^3', 'a^7', 'a^4', 0, 'a^0', 'a^1', 0, 'a^10', 0, 'a^8', 'a^3', 0, 'a^0', 0, 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'191.99216678935540251841454650312', '192.780474894678256706337843383799', '193.1838082033069054842696063297', '194.0802689273943544664770583289', '194.43122725674937106272255829266', '195.34472135095504439694192594937', '195.62486977279076902629713969581', '196.424480755667823382376168290771', '197.23892902344670215997046743418', '197.706924075019569824294742946740', '198.21471326911601873982404663634', '198.86853927362343062103292248944', '199.3561276627003776302048113126', '199.82845152071395413786403998388'], 'prelabel': '1-1045-1045.87-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.08937185409627321, 'root_number': '0.960842370587495933535790496733-0.277095541075278093993939251505*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0446859270481', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.520929754216103412992444683688+0.0768948418167745828562586196988*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.501241818465', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.55962597801', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08503598014', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.87', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/87'], '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': '1-1045-1045.87-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': '1-1045-1045.87-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.044685927048136606, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.501241818465', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.87', 'Lhash_array': ['dirichlet_L_1045.87'], 'label': '1-1045-1045.87-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/87'}
Lfunction data - 1-1045-1045.87-r0-0-0