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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.137', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.10452846326765347, 0.9945218953682733], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [-0.9135454576426009, 0.4067366430758002], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.137', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.86', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^13', 0, 0, 'a^21', 0, 'a^20', 0, 0, 'a^12', 0, 0, 'a^28', 'a^23', 0, 'a^16', 'a^27', 0, 0, 'a^25', 0, 'a^26', 'a^19', 0, 0, 'a^9', 0, 'a^2', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0492973202093', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.713041320549199581181090108338+0.348978417286307146546950890677*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.419394720375', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.81281861204', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.18150374611', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.82439762755838, 'bad_primes': [3, 7, 11], 'central_character': '231.137', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/137'], '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': '1-231-231.137-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-231-231.137-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.04929732020930039, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.419394720375', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.137', 'Lhash_array': ['dirichlet_L_231.137'], 'factors': ['1-231-231.137-r1-0-0'], 'label': '1-231-231.137-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/137'}