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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.669', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.24192189559966773, 0.9702957262759965], 'a3': [-0.03489949670250097, -0.9993908270190958], 'a4': [-0.882947592858927, 0.46947156278589075], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9612616959383189, -0.27563735581699916], 'a7': [-0.6691306063588582, 0.7431448254773942], 'a8': [-0.6691306063588582, -0.7431448254773942], 'a9': [-0.9975640502598242, 0.0697564737441253], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.669', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.214', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^67', 'a^38', 0, 'a^86', 'a^33', 'a^57', 'a^44', 0, 0, 'a^15', 'a^59', 'a^52', 0, 'a^76', 'a^1', 'a^63', 0, 0, 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.824640021187604458460372457144+0.299622581901491764227247714708*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02553698507', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.67472103259', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24867839528', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.669', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/669'], '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': '1-1045-1045.669-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': '1-1045-1045.669-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.3010801227180291, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02553698507', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.669', 'Lhash_array': ['dirichlet_L_1045.669'], 'factors': ['1-1045-1045.669-r0-0-0'], 'label': '1-1045-1045.669-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/669'}
Lfunction data - 1-1045-1045.669-r0-0-0