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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_1045.182', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.4067366430758002, -0.9135454576426009], 'a3': [-0.7431448254773942, -0.6691306063588582], 'a4': [-0.6691306063588582, -0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9135454576426009, 0.4067366430758002], 'a7': [-0.9510565162951535, -0.30901699437494745], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.182', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.178', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^49', 'a^37', 'a^38', 0, 'a^26', 'a^33', 'a^27', 'a^14', 0, 0, 'a^15', 'a^59', 'a^22', 0, 'a^16', 'a^1', 'a^3', 0, 0, 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0, 'data': '-0.29118679422', 'prec': 37}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.719244629769260627086664438325-0.591547212509012983011739130079*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.809886177178', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.57210544056', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.93220199378', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.182', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/182'], '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': '1-1045-1045.182-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1045-1045.182-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.2911867942199151, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.809886177178', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_1045.182', 'Lhash_array': ['dirichlet_L_1045.182'], 'factors': ['1-1045-1045.182-r0-0-0'], 'label': '1-1045-1045.182-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/182'}