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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.109', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.996917333733128, -0.07845909572784494], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9876883405951378, -0.15643446504023087], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9876883405951378, 0.15643446504023087], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.109', 'coeff_info': ['x^80 - 1', '0.996917333733128 + 0.0784590957278449*I', '\\\\zeta_{80}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.1893', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^41', 0, 'a^35', 0, 'a^78', 0, 'a^82', 0, 'a^63', 0, 'a^61', 0, 'a^76', 0, 'a^52', 0, 'a^69', 0, 'a^119', 0, 'a^42', 0, 'a^70', 0, 'a^123', 0, 'a^129', 0, 0, 0, 'a^104', 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'194.10790530715920413032683631872', '194.48220604067279870731851811115', '194.87378891880572718840295520004', '195.62576542615922664238269024875', '195.659318206771911561485862190235', '196.63145528799171202834152767650', '197.26096727764307355826715282651', '198.05887515356280309074336036194', '198.494446998861540105605591199450', '199.15871726558879172384734734998', '199.362575753613229081110002467590'], 'prelabel': '1-1984-1984.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.4382665008110822, 'root_number': '-0.925711839856461905808712395243-0.378229546108661673056353161610*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.438266500811', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(80)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.652222286980203296145861010336-0.181472373609823316386757874766*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.262914416138', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.07771287476', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.42422669773', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.109', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/109'], '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': '1-1984-1984.109-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': '1-1984-1984.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.4382665008110822, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.262914416138', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.109', 'Lhash_array': ['dirichlet_L_1984.109'], 'factors': ['1-1984-1984.109-r0-0-0'], 'label': '1-1984-1984.109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/109'}
Lfunction data - 1-1984-1984.109-r0-0-0