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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4000.139', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.7901550123756904, 0.6129070536529765], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.2486898871648548, -0.9685831611286311], 'algebraic': True, 'analytic_conductor': 429.8596991785001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '4000.139', 'coeff_info': ['x^200 - 1', '0.999506560365732 + 0.0314107590781283*I', '\\\\zeta_{200}'], 'conductor': 4000, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_4000.259', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^79', 0, 0, 0, 'a^170', 0, 'a^158', 0, 'a^197', 0, 'a^183', 0, 0, 0, 'a^256', 0, 'a^271', 0, 'a^49', 0, 'a^182', 0, 0, 0, 'a^37', 0, 'a^239', 0, 'a^156', 0, 'a^76', 0, 0, 0, 'a^313', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 429.8596991785001, 'bad_primes': [2, 5], 'central_character': '4000.139', 'conductor': 4000, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4000/139'], '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': '1-4000-4000.139-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': '1-4000-4000.139-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 429.8596991785001, 'root_angle': -0.32475000000000004, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.189472856028', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4000.139', 'Lhash_array': ['dirichlet_L_4000.139'], 'label': '1-4000-4000.139-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4000/139'}