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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_837.319', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [-0.7193398003386512, 0.6946583704589973], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.03489949670250097, -0.9993908270190958], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.374606593415912, 0.9271838545667874], 'a8': [0.6691306063588582, 0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.319', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.286', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 0, 'a^34', 'a^10', 0, 'a^14', 'a^6', 0, 'a^27', 'a^29', 0, 'a^43', 'a^31', 0, 'a^23', 'a^6', 0, 'a^27', 'a^44', 0, 'a^1', 'a^16', 0, 'a^20', 'a^15', 0, 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'2.66282099359', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.6216536986', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.319', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/319'], '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': '1-837-837.319-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': '1-837-837.319-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.45776094164835335, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53726332885', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_837.319', 'Lhash_array': ['dirichlet_L_837.319'], 'label': '1-837-837.319-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/319'}