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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4024.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9992951222712527, -0.03754009329879296], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.18049178811206065, 0.9835764913945997], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9949911342282848, 0.09996320726703126], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9971814827902359, 0.07502726424618308], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.123', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.3795', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^254', 0, 'a^642', 0, 'a^745', 0, 'a^6', 0, 'a^358', 0, 'a^543', 0, 'a^394', 0, 'a^183', 0, 'a^299', 0, 'a^497', 0, 'a^481', 0, 'a^280', 0, 'a^260', 0, 'a^376', 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44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.123', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/123'], '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': '1-4024-4024.123-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': '1-4024-4024.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': 0.3242102372566153, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.752636965967', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4024.123', 'Lhash_array': ['dirichlet_L_4024.123'], 'label': '1-4024-4024.123-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/123'}