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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_179.168', 'a10': [0.22743433812110636, 0.9737934184638004], 'a2': [-0.8630688675320841, -0.5050862598575473], 'a3': [0.8048472460553258, 0.5934820220673563], 'a4': [0.4897757402062284, 0.8718484526025386], 'a5': [-0.6881411722458688, -0.7255768236789827], 'a6': [-0.39487898637059127, -0.9187331419530561], 'a7': [0.844705995854882, -0.5352305863520993], 'a8': [0.0176484806431286, -0.9998442534369986], 'a9': [0.29555817896568404, 0.9553247420885155], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.168', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.65', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^9', 'a^15', 'a^56', 'a^61', 'a^81', 'a^67', 'a^18', 'a^19', 'a^68', 'a^24', 'a^54', 'a^44', 'a^65', 'a^30', 'a^88', 'a^70', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-179-179.168-r0-0-0', 'leading_term': '0.844266828055842492810585854931-0.430170931517723612565850375603*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/179/168', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9475407681352284, 0.8741409286048709, 0.6984348192132808, 0.20510533913467804, -0.5483149987499137, -1.3000978858396377, -1.710524816196871, -1.5302708260954758, -0.7586584094097688, 0.2951661958514107, 1.113368315333075, 1.2211709833672784, 0.48050604405931485, -0.7413839204570016, -1.6639332738303216, -1.4545603877253854, 0.2972022578016506, 3.2544245301814123, 6.379780260944477, 8.389840541305901, 8.406023359101688, 6.4397164676552645, 3.4074371325437505, 0.6341783439115484, -0.8778197674396274, -0.9701179109182995, 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'0.587792104387417526131777784443-0.809012015992229412218583158878*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.149998652008', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.870895274693655118755354901413-0.230551859079560618225669969191*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.03017923872', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.72505311648', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87808451071', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.168', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/168'], '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': '1-179-179.168-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': '1-179-179.168-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.14999865200837073, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03017923872', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_179.168', 'Lhash_array': ['dirichlet_L_179.168'], 'label': '1-179-179.168-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/168'}
Lfunction data - 1-179-179.168-r0-0-0