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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1112', 'a10': [-0.24236173709321235, -0.9701859555740645], 'a2': [0.3077232751585818, 0.9514758987623784], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8106127718513515, 0.5855825596032286], 'a5': [-0.9976889015579163, -0.06794744813573399], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6949843990150795, 0.7190248153754145], 'a8': [-0.80661210923753, -0.5910811325286766], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1112', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.5339', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^185', 0, 'a^370', 'a^472', 0, 'a^344', 'a^555', 0, 'a^657', 'a^761', 0, 'a^250', 'a^529', 0, 'a^740', 'a^609', 0, 'a^447', 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27.87781479921304, 'root_angle': -0.5900734087413505, 'root_number': '-0.279212561896022345184435273091-0.960229319110523666357965110326*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(924)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.592697893429915126287815298354+0.456816609289447083477337086657*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.01268379599', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.53760271714', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15972508812', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1112', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1112'], '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': '1-6003-6003.1112-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': '1-6003-6003.1112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.29503670437067525, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01268379599', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1112', 'Lhash_array': ['dirichlet_L_6003.1112'], 'label': '1-6003-6003.1112-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1112'}