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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1005.104', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 108.00224941859814, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [67, [1]]], 'bad_primes': [3, 5, 67], 'central_character': '1005.104', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 1005, 'conductor_radical': 1005, 'conjugate': 'dirichlet_L_1005.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 0, 0, 'a^1', 'a^0', 0, 0, 'a^1', 0, 'a^5', 'a^3', 0, 'a^2', 'a^2', 0, 'a^2', 0, 0, 'a^3', 'a^2', 0, 0, 'a^1', 0, 'a^5', 'a^1', 0, 'a^4', 'a^4', 0, 'a^4', 0, 0, 'a^5', 'a^4', 0, 0, 'a^1', 0, 'a^3', 'a^5', 0, 'a^4', 'a^4', 0, 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'192.911556352047732581326562246326', '193.85840846150214856408960241589', '194.32547862837108140553589368980', '195.2350068529394723207929100738', '195.77028310992868493018211126013', '195.972301760877442557497284406956', '196.89616283744566236874370759266', '197.22561198436004505683405855153', '198.05327097885667991916535944155', '198.6680583738115748770328421498', '198.959240265894210816039094488987', '199.67087434831690730332534096121'], 'prelabel': '1-1005-1005.104-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 108.00224941859814, 'root_angle': -0.8004006459994949, 'root_number': '-0.809756178963694129067499926103-0.586766504352555698644245732713*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.400200323', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.641964628264160855083005915271+0.465181187412017697741678590246*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.35042684478', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.09925647872', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.73798520358', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 108.00224941859814, 'bad_primes': [3, 5, 67], 'central_character': '1005.104', 'conductor': 1005, 'conductor_radical': 1005, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1005/104'], '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': '1-1005-1005.104-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': '1-1005-1005.104-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 108.00224941859814, 'root_angle': -0.40020032299974745, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35042684478', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1005.104', 'Lhash_array': ['dirichlet_L_1005.104'], 'label': '1-1005-1005.104-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1005/104'}
Lfunction data - 1-1005-1005.104-r1-0-0