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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1792.219', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9994645874763657, -0.032719082821776144], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9359059267573256, 0.3522500479212335], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9978589232386035, 0.06540312923014306], 'algebraic': True, 'analytic_conductor': 192.57714523196805, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1792.219', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 1792, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_1792.851', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^97', 0, 'a^203', 0, 0, 0, 'a^194', 0, 'a^199', 0, 'a^69', 0, 'a^108', 0, 'a^244', 0, 'a^221', 0, 0, 0, 'a^314', 0, 'a^214', 0, 'a^99', 0, 'a^9', 0, 'a^184', 0, 'a^296', 0, 0, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 192.57714523196805, 'bad_primes': [2, 7], 'central_character': '1792.219', 'conductor': 1792, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1792/219'], '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': '1-1792-1792.219-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': '1-1792-1792.219-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': 0.4202427265269731, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28218274388', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1792.219', 'Lhash_array': ['dirichlet_L_1792.219'], 'label': '1-1792-1792.219-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1792/219'}