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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2057.1675', 'a10': [-0.9771468659711595, 0.21256528955297668], 'a2': [0.9995921928281892, 0.028556050793696254], 'a3': [-0.9876883405951378, -0.15643446504023087], 'a4': [0.9983691039261356, 0.057088810862767986], 'a5': [-0.9706783532658525, 0.24038205944099247], 'a6': [-0.9828184036767557, -0.1845751483658454], 'a7': [0.5525983594269026, 0.8334476907153177], 'a8': [0.9963317308626913, 0.08557500847883974], 'a9': [0.9510565162951535, 0.30901699437494745], 'algebraic': True, 'analytic_conductor': 9.552667839743666, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [17, [1]]], 'bad_primes': [11, 17], 'central_character': '2057.1675', 'coeff_info': ['x^440 - 1', '0.999898043009433 + 0.0142794812897873*I', '\\\\zeta_{440}'], 'conductor': 2057, 'conductor_radical': 187, 'conjugate': 'dirichlet_L_2057.70', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^231', 'a^4', 'a^203', 'a^233', 'a^69', 'a^6', 'a^22', 'a^205', 0, 'a^235', 'a^92', 'a^71', 'a^434', 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'spectral_label': 'r0-0', 'st_group': 'mu(440)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.46590166670651236965495401346+0.231818803261267509361732379964*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.00524519112', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.12399075279', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00458548006', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.552667839743666, 'bad_primes': [11, 17], 'central_character': '2057.1675', 'conductor': 2057, 'conductor_radical': 187, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2057/1675'], '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': '1-2057-2057.1675-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': '1-2057-2057.1675-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.552667839743666, 'root_angle': 0.1133972610819766, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00524519112', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2057.1675', 'Lhash_array': ['dirichlet_L_2057.1675'], 'factors': ['1-2057-2057.1675-r0-0-0'], 'label': '1-2057-2057.1675-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2057/1675'}
Lfunction data - 1-2057-2057.1675-r0-0-0