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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.147', 'a10': [0.9906859460363308, 0.1361666490962466], 'a2': [-0.648582089462756, -0.7611447124089648], 'a3': [0.9906859460363308, 0.1361666490962466], 'a4': [-0.1586825464562513, 0.9873296559154696], 'a5': [-0.7461836858476855, 0.6657401196974406], 'a6': [-0.5388986359155754, -0.8423706192694116], 'a7': [-0.11358018605047483, -0.9935288326650312], 'a8': [0.8544194045464886, -0.5195839500354336], 'a9': [0.9629172873477992, 0.2697967711570243], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.147', 'coeff_info': ['x^138 - 1', '0.998963673646728 + 0.0455145991329636*I', '\\\\zeta_{138}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.546', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^88', 'a^3', 'a^38', 'a^53', 'a^91', 'a^101', 'a^126', 'a^6', 'a^3', 'a^6', 'a^41', 'a^17', 'a^51', 'a^56', 'a^76', 'a^36', 'a^94', 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'0.109414483665328724854289280226+0.993996212650857897446272693320*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.232551210475', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(138)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.989437320315929376522591697057+0.00598656126843874510020029091563*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.23681213671', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.96250740274', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.36398160511', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.147', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/147'], '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': '1-967-967.147-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': '1-967-967.147-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': 0.23255121047487, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23681213671', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.147', 'Lhash_array': ['dirichlet_L_967.147'], 'label': '1-967-967.147-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/147'}