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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.448', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.20791169081775934, -0.9781476007338057], 'a3': [-0.4067366430758002, 0.9135454576426009], 'a4': [-0.9135454576426009, 0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9781476007338057, 0.20791169081775934], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [-0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.448', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^19', 'a^26', 0, 'a^2', 'a^51', 'a^9', 'a^38', 0, 0, 'a^45', 'a^53', 'a^34', 0, 'a^52', 'a^7', 'a^21', 0, 0, 'a^10', 0, 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.772494795808006716158004838889-0.299736526813453449716405600604*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.578802713913', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66911252522', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.10507417717', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.448', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/448'], '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': '1-1045-1045.448-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': '1-1045-1045.448-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.259827511190355, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.578802713913', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.448', 'Lhash_array': ['dirichlet_L_1045.448'], 'factors': ['1-1045-1045.448-r0-0-0'], 'label': '1-1045-1045.448-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/448'}
Lfunction data - 1-1045-1045.448-r0-0-0