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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_896.51', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.06540312923014306, -0.9978589232386035], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6593458151000688, -0.7518398074789774], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9914448613738104, 0.1305261922200516], 'algebraic': True, 'analytic_conductor': 96.28857261598402, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.51', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.123', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^71', 0, 'a^157', 0, 0, 0, 'a^142', 0, 'a^113', 0, 'a^51', 0, 'a^36', 0, 'a^44', 0, 'a^139', 0, 0, 0, 'a^70', 0, 'a^122', 0, 'a^21', 0, 'a^15', 0, 'a^56', 0, 'a^88', 0, 0, 0, 'a^85', 0, 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'192.87885046238399771953823773736', '193.72647308765347828318426739290', '194.24917489091505284871299380052', '195.22771705364256439194940425039', '195.39887944337781891331789196485', '195.94890545834584780270086910729', '196.536145053018332908652712108532', '197.09500829395131781345102716576', '197.84818724500182696426338423636', '198.6377714661413717827945159434', '199.10784704008756335593509410250', '199.84030796200376529011190079668'], 'prelabel': '1-896-896.51-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': -0.20378538027938722, 'root_number': '0.801969938722272248572741498563-0.597364392465599588707603821950*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10189269014', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(96)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.702539171720962975571459504423-0.275170218367221895816814216172*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.525238373552', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.74707994846', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54819080432', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 96.28857261598402, 'bad_primes': [2, 7], 'central_character': '896.51', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/51'], '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': '1-896-896.51-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': '1-896-896.51-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': -0.10189269013969361, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.525238373552', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_896.51', 'Lhash_array': ['dirichlet_L_896.51'], 'label': '1-896-896.51-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/51'}