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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4024.1213', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.7722655219809714, 0.6352999004875238], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9434395666870733, -0.33154454302447417], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7048907320120865, 0.7093159070001637], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.19278807288108468, 0.9812404185289136], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.1213', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.3261', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^557', 0, 'a^475', 0, 'a^188', 0, 'a^110', 0, 'a^623', 0, 'a^417', 0, 'a^28', 0, 'a^92', 0, 'a^629', 0, 'a^745', 0, 'a^368', 0, 'a^448', 0, 'a^667', 0, 'a^451', 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.1213', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/1213'], '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': '1-4024-4024.1213-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': '1-4024-4024.1213-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': 0.18477820394234382, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0618552678', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4024.1213', 'Lhash_array': ['dirichlet_L_4024.1213'], 'label': '1-4024-4024.1213-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/1213'}