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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_384.5', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9807852804032304, -0.19509032201612828], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3826834323650898, 0.9238795325112867], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 41.26653112113601, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '384.5', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 384, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_384.77', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^17', 0, 'a^10', 0, 0, 0, 'a^37', 0, 'a^15', 0, 0, 0, 'a^44', 0, 'a^23', 0, 0, 0, 'a^30', 0, 'a^2', 0, 0, 0, 'a^43', 0, 'a^8', 0, 0, 0, 'a^27', 0, 'a^25', 0, 0, 0, 'a^46', 0, 'a^29', 0, 0, 0, 'a^28', 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44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.26653112113601, 'bad_primes': [2, 3], 'central_character': '384.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/384/5'], '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': '1-384-384.5-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': '1-384-384.5-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': -0.2734375, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.153310200788', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_384.5', 'Lhash_array': ['dirichlet_L_384.5'], 'label': '1-384-384.5-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/384/5'}