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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_128.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9807852804032304, 0.19509032201612828], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.5555702330196022, -0.8314696123025452], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9238795325112867, 0.3826834323650898], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9238795325112867, -0.3826834323650898], 'algebraic': True, 'analytic_conductor': 13.755510373712003, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '128.11', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 128, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_128.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^15', 0, 'a^21', 0, 'a^2', 0, 'a^30', 0, 'a^9', 0, 'a^27', 0, 'a^4', 0, 'a^12', 0, 'a^19', 0, 'a^17', 0, 'a^22', 0, 'a^10', 0, 'a^13', 0, 'a^23', 0, 'a^24', 0, 'a^24', 0, 'a^23', 0, 'a^13', 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'199.23249234157622408814984718639'], 'prelabel': '1-2e7-128.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.755510373712003, 'root_angle': -0.4296875, 'root_number': '-0.903989293123443331586200297231-0.427555093430282094320966856889*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4296875', 'prec': 24}, 'spectral_label': 'r1-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.633298510348411683551625191039-0.0840456496718058614532840625554*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.154983092605', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.78509843557', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.21764573552', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 13.755510373712003, 'bad_primes': [2], 'central_character': '128.11', 'conductor': 128, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/128/11'], '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': '1-2e7-128.11-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e7-128.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.755510373712003, 'root_angle': -0.4296875, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.154983092605', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_128.11', 'Lhash_array': ['dirichlet_L_128.11'], 'factors': ['1-2e7-128.11-r1-0-0'], 'label': '1-2e7-128.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/128/11'}