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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4235.2887', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.983685841930732, -0.17989487036885388], 'a3': [0.7431448254773942, 0.6691306063588582], 'a4': [0.9352756712299465, 0.3539200740356119], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.6106478796354381, -0.7919022459222751], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8563490302515889, -0.5163974616389619], 'a9': [0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2887', 'coeff_info': ['x^660 - 1', '0.999954685354173 + 0.00951983393957664*I', '\\\\zeta_{660}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.1153', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^349', 'a^77', 'a^38', 0, 'a^426', 0, 'a^387', 'a^154', 0, 0, 'a^115', 'a^489', 0, 0, 'a^76', 'a^491', 'a^503', 'a^532', 0, 0, 0, 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'193.49910340440432889600978555476', '194.18101420101563922725282760196', '194.41326782161335059891582904507', '195.60314418952746260367474495147', '196.04099747933015776496962547566', '196.6688495561180963631937652969', '196.995416581668950434512141830125', '197.74282315281277417044459031681', '198.054121731603085699646403045142', '198.38849553782965258307155241917', '199.26540152336335922782009147432', '199.49937939079993924164687857937', '199.790184412722029266618191328310'], 'prelabel': '1-4235-4235.2887-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.46967179803412884, 'root_number': '0.0951347640416057232682967948993-0.995464402513092379975757146599*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(660)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.796592815208527144077499404572+0.0131955762060906934253434774914*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.287384781088', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.52409270382', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.3432103392', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.2887', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2887'], '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': '1-4235-4235.2887-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': '1-4235-4235.2887-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.23483589901706442, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.287384781088', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4235.2887', 'Lhash_array': ['dirichlet_L_4235.2887'], 'label': '1-4235-4235.2887-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2887'}
Lfunction data - 1-4235-4235.2887-r0-0-0