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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6003.1022', 'a10': [-0.10182298670383538, 0.994802532857004], 'a2': [-0.9764184991921175, -0.21588634610695698], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9067861711291744, 0.42159084412364994], 'a5': [-0.11534243605582674, -0.9933257886739413], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9124357585551869, 0.40921997325377546], 'a8': [-0.7943870854121126, -0.6074118524777475], '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': '6003.1022', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.605', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^247', 0, 'a^32', 'a^338', 0, 'a^31', 'a^279', 0, 'a^123', 'a^358', 0, 'a^134', 'a^278', 0, 'a^64', 'a^210', 0, 'a^417', 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'-0.635260320068548803580142753966-0.772298080890018093407205927454*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.687170460245908105819095895653-0.231543749005083676713791362176*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.347820289591', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.26628204151', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.89066941901', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1022', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1022'], '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': '1-6003-6003.1022-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': '1-6003-6003.1022-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.3595535960959439, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.347820289591', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6003.1022', 'Lhash_array': ['dirichlet_L_6003.1022'], 'label': '1-6003-6003.1022-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1022'}
Lfunction data - 1-6003-6003.1022-r0-0-0