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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_837.184', 'a10': [0.6691306063588582, -0.7431448254773942], 'a2': [0.9902680687415704, -0.13917310096006544], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9612616959383189, -0.27563735581699916], 'a5': [0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5591929034707468, -0.8290375725550417], 'a8': [0.9135454576426009, -0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 89.94814205310114, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.184', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.232', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^88', 0, 'a^86', 'a^80', 0, 'a^76', 'a^84', 0, 'a^78', 'a^1', 0, 'a^47', 'a^74', 0, 'a^82', 'a^69', 0, 'a^48', 'a^76', 0, 'a^89', 'a^59', 0, 'a^70', 'a^45', 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'192.782547826355183076958630010871', '193.65555157208215400218261215797', '194.13989829421527509844268327675', '194.70428022169467527767913742199', '195.51743593272587284418875055814', '195.97076710735264860327189332930', '196.32867569468392627278729814221', '197.29351094927365936569354674604', '197.713981622122426276924615913076', '198.183208806591665620273281696461', '198.927428758465938447885032051177'], 'prelabel': '1-837-837.184-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.6221093556615321, 'root_number': '-0.374277808319758633431686957273-0.927316624567551908114970137601*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.311054677831', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.15884376224788435342359137645-1.05545083236764612334623244197*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.707491297258', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.7308004544', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.6023369174', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.94814205310114, 'bad_primes': [3, 31], 'central_character': '837.184', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/184'], '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': '1-837-837.184-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': '1-837-837.184-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.31105467783076607, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.707491297258', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_837.184', 'Lhash_array': ['dirichlet_L_837.184'], 'label': '1-837-837.184-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/184'}