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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1005.29', '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': '1005.29', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 1005, 'conductor_radical': 1005, 'conjugate': 'dirichlet_L_1005.104', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^2', 0, 0, 'a^5', 'a^0', 0, 0, 'a^5', 0, 'a^1', 'a^3', 0, 'a^4', 'a^4', 0, 'a^4', 0, 0, 'a^3', 'a^4', 0, 0, 'a^5', 0, 'a^1', 'a^5', 0, 'a^2', 'a^2', 0, 'a^2', 0, 0, 'a^1', 'a^2', 0, 0, 'a^5', 0, 'a^3', 'a^1', 0, 'a^2', 'a^2', 0, 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'192.71003339034086183052858941508', '193.50466907891934892805572212202', '194.24151093852938504731701550184', '194.69209569279913601890438832132', '195.20385010081852224978534023742', '195.67066221578715973727753127845', '196.9467907245530763067794670492', '197.333980944658189855753511167235', '197.91995533646389169952522050733', '198.564796752121534968563985879926', '199.00172712557489913361707607456', '199.869844170310227206330974194980'], 'prelabel': '1-1005-1005.29-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': 37}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.641964628264160855083005915271-0.465181187412017697741678590246*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.2351428866', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.1026243308', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.14042345267', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 108.00224941859814, 'bad_primes': [3, 5, 67], 'central_character': '1005.29', 'conductor': 1005, 'conductor_radical': 1005, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1005/29'], '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': '1-1005-1005.29-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': '1-1005-1005.29-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': '0.2351428866', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1005.29', 'Lhash_array': ['dirichlet_L_1005.29'], 'label': '1-1005-1005.29-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1005/29'}
Lfunction data - 1-1005-1005.29-r1-0-0