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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_539.60', 'a10': [-0.7330518718298263, 0.6801727377709194], 'a2': [0.5256837698105047, 0.8506800656873396], 'a3': [0.5756170656856735, 0.8177193856644314], 'a4': [-0.4473131483156326, 0.8943774076663368], 'a5': [0.19325591779555326, 0.9811483833941727], 'a6': [-0.3930250316539236, 0.9195277725514507], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9959742939952391, 0.0896393089034335], 'a9': [-0.33732998738283, 0.9413864666609032], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.60', 'coeff_info': ['x^105 - 1', '0.998210129767735 + 0.0598041539450342*I', '\\\\zeta_{105}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^16', 'a^34', 'a^23', 'a^33', 0, 'a^51', 'a^32', 'a^40', 0, 'a^50', 'a^87', 0, 'a^39', 'a^68', 'a^43', 'a^49', 'a^56', 'a^57', 0, 0, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.4409563393181483, 'root_number': '-0.931971695054669849441136927488-0.362531046417993655533973415092*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.440956339318', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(105)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.734118901220216662837332297499+1.27039712955587208770070004089*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.37860000244', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.26699340441', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.07899363834', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.60', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/60'], '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': '1-539-539.60-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': '1-539-539.60-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.4409563393181483, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37860000244', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_539.60', 'Lhash_array': ['dirichlet_L_539.60'], 'factors': ['1-539-539.60-r0-0-0'], 'label': '1-539-539.60-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/60'}
Lfunction data - 1-539-539.60-r0-0-0