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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.129', 'a10': [-0.6691306063588582, 0.7431448254773942], 'a2': [0.9945218953682733, -0.10452846326765347], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [0.9781476007338057, -0.20791169081775934], 'a5': [-0.7431448254773942, 0.6691306063588582], 'a6': [-0.9876883405951378, -0.15643446504023087], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9510565162951535, -0.30901699437494745], 'a9': [0.8660254037844386, 0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.129', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.89', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^118', 'a^65', 'a^116', 'a^46', 'a^63', 0, 'a^114', 'a^10', 'a^44', 'a^89', 'a^61', 'a^33', 0, 'a^111', 'a^112', 'a^119', 'a^8', 'a^7', 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'3.98677852339', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.129', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/129'], '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': '1-287-287.129-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': '1-287-287.129-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.009198413151708941, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30995574011', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.129', 'Lhash_array': ['dirichlet_L_287.129'], 'label': '1-287-287.129-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/129'}
Lfunction data - 1-287-287.129-r0-0-0