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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_1045.348', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.13917310096006544, 0.9902680687415704], 'a3': [0.9702957262759965, -0.24192189559966773], 'a4': [-0.9612616959383189, 0.27563735581699916], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.374606593415912, 0.9271838545667874], 'a7': [-0.4067366430758002, 0.9135454576426009], 'a8': [-0.4067366430758002, -0.9135454576426009], 'a9': [0.882947592858927, -0.46947156278589075], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.348', 'coeff_info': ['x^180 - 1', '0.999390827019096 + 0.0348994967025010*I', '\\\\zeta_{180}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.1042', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^173', 'a^82', 0, 'a^34', 'a^57', 'a^123', 'a^166', 0, 0, 'a^75', 'a^151', 'a^98', 0, 'a^164', 'a^149', 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40}, 'spectral_label': 'r0-0', 'st_group': 'mu(180)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.34737032338923126169295068306+0.518621908273963748857898864055*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.885476250898', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.54875472188', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.20969254796', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.348', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/348'], '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': '1-1045-1045.348-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1045-1045.348-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.11508430179614193, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.885476250898', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_1045.348', 'Lhash_array': ['dirichlet_L_1045.348'], 'factors': ['1-1045-1045.348-r0-0-0'], 'label': '1-1045-1045.348-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/348'}