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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1169.667', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [1.0, 0.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 125.62649708491665, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [167, [1]]], 'bad_primes': [7, 167], 'central_character': '1169.667', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 1169, 'conductor_radical': 1169, 'conjugate': 'dirichlet_L_1169.333', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^4', 'a^3', 0, 'a^3', 'a^4', 'a^5', 'a^2', 'a^4', 'a^3', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^4', 'a^3', 0, 'a^0', 'a^1', 'a^2', 'a^5', 'a^1', 'a^3', 0, 'a^3', 'a^4', 'a^5', 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'190.52700121151660169356779079210', '191.23994014889809531519362058167', '191.61282158935504088866458071122', '192.44741643292176148911993894782', '193.10425957531036936528748720399', '193.49584837361798920213079478187', '193.811329181526848155955568387682', '194.397024539505651333430581846591', '194.99500813579142340870489445521', '195.75317136424385696243214025715', '196.48537478036761930079691947814', '197.56429292897585589258740320321', '197.88921454901014725545010907029', '198.42681469190329966569031460777', '198.99218386817454678065281435456', '199.27764057078581924712979633177'], 'prelabel': '1-1169-1169.667-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 125.62649708491665, 'root_angle': -0.14649371361272057, 'root_number': '0.895953219663104777747250207705-0.444148430342060668918079670489*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0732468568064', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635317031018616980310938044734+0.0403173361375996216491830022219*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.319877550966', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.83312066628', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83341351621', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 125.62649708491665, 'bad_primes': [7, 167], 'central_character': '1169.667', 'conductor': 1169, 'conductor_radical': 1169, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1169/667'], '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': '1-1169-1169.667-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': '1-1169-1169.667-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 125.62649708491665, 'root_angle': -0.07324685680636028, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.319877550966', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1169.667', 'Lhash_array': ['dirichlet_L_1169.667'], 'label': '1-1169-1169.667-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1169/667'}
Lfunction data - 1-1169-1169.667-r1-0-0