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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.238', 'a10': [0.2518156701278019, 0.9677752157800312], 'a2': [-0.999922905547776, -0.012417043162265879], 'a3': [-0.42667792655710846, 0.9044036416274134], 'a4': [0.9996916340782128, 0.024832171754250083], 'a5': [-0.2638131631623638, -0.9645737996349828], 'a6': [0.43787505111028246, -0.8990358388936269], 'a7': [-0.11769153717617022, 0.993050201186783], 'a8': [-0.9993062212508053, -0.03724347150087643], 'a9': [-0.6358918939778535, -0.7717781411605659], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.238', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.509', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^127', 'a^81', 'a^1', 'a^179', 'a^208', 'a^68', 'a^128', 'a^162', 'a^53', 'a^170', 'a^82', 'a^108', 'a^195', 'a^7', 'a^2', 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'a^141'], [1, 'a^41'], [1, 'a^224'], [1, 'a^245'], [1, 'a^30']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.238-r0-0-0', 'leading_term': '0.523815889798189678179604757382+0.0189559022328508888322260037901*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/529/238', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5241587666294731, 0.4085601814575731, -0.045162687752840255, -0.969498857534641, -2.0413052747571294, -2.6113981527792403, -2.11705857515163, -0.5515195666127811, 1.3426380418414232, 2.397054993393282, 1.7596671843577552, -0.4181224994214983, -2.9097033075693535, -4.149817148980998, -3.346126749660031, -1.1337068959020302, 0.8258018080031108, 1.1043550606742145, -0.3267629115219699, -2.0175647834457546, -2.2074994177434264, -0.3275070821831932, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.238', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/238'], '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': '1-23e2-529.238-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': '1-23e2-529.238-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.011514005842928337, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.604428613517', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.238', 'Lhash_array': ['dirichlet_L_529.238'], 'label': '1-23e2-529.238-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/238'}