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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_155.57', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [0.8660254037844386, -0.5], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5, 0.8660254037844386], 'a7': [0.8660254037844386, -0.5], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.7198169738260906, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [31, [1]]], 'bad_primes': [5, 31], 'central_character': '155.57', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 155, 'conductor_radical': 155, 'conjugate': 'dirichlet_L_155.68', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^11', 'a^6', 0, 'a^2', 'a^11', 'a^9', 'a^10', 0, 'a^10', 'a^5', 'a^7', 'a^2', 0, 'a^0', 'a^5', 'a^1', 'a^2', 0, 'a^10', 'a^1', 'a^3', 'a^8', 0, 'a^10', 'a^9', 'a^5', 'a^0', 0, 0, 'a^3', 'a^9', 'a^8', 0, 'a^4', 'a^5', 'a^5', 'a^6', 0, 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'195.585996982166154248935637589107', '196.17216296271738117169993592094', '197.018089978950973937117631745118', '197.64176515787085953586556498385', '198.11943284488295650849617764177', '198.83714281081226966553822511476', '199.70234934591960356305151683738'], 'prelabel': '1-155-155.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7198169738260906, 'root_angle': 0.09823884141414292, 'root_number': '0.952751693047112602313271709096+0.303750245095967828367282311495*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0491194207071', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.27562382984928525253708959967+0.248212396480645127842194393443*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.35366039424', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.34631579517', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.5819416386', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7198169738260906, 'bad_primes': [5, 31], 'central_character': '155.57', 'conductor': 155, 'conductor_radical': 155, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/155/57'], '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': '1-155-155.57-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': '1-155-155.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7198169738260906, 'root_angle': 0.04911942070707146, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35366039424', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_155.57', 'Lhash_array': ['dirichlet_L_155.57'], 'label': '1-155-155.57-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/155/57'}
Lfunction data - 1-155-155.57-r0-0-0