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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.140', 'a10': [0.12649469532214946, -0.991967283762603], 'a2': [0.8923315129986835, -0.4513806275301149], 'a3': [0.3164306917211476, 0.9486156320327407], 'a4': [0.5925110581810394, -0.8055623166044853], 'a5': [0.5606300178972284, -0.8280664122113355], 'a6': [0.7105477971745666, 0.703648937987098], 'a7': [-0.8225573016153944, -0.568682236015159], 'a8': [0.16510106503159225, -0.9862766540506949], 'a9': [-0.7997432346737522, 0.6003422012432275], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.140', 'coeff_info': ['x^161 - 1', '0.999238582475670 + 0.0390160901682098*I', '\\\\zeta_{161}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.670', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^149', 'a^32', 'a^137', 'a^136', 'a^20', 'a^96', 'a^125', 'a^64', 'a^124', 'a^18', 'a^8', 'a^143', 'a^84', 'a^7', 'a^113', 'a^108', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.170038974022', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(161)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.94528400288256587753662691647-0.562453720082283622199059267016*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.958261547086', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.15297158278', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.35346091544', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.140', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/140'], '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': '1-967-967.140-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': '1-967-967.140-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.1700389740217608, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.958261547086', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.140', 'Lhash_array': ['dirichlet_L_967.140'], 'label': '1-967-967.140-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/140'}