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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_539.284', 'a10': [-0.9888308262251285, -0.14904226617617444], 'a2': [-0.5998218946879137, -0.8001335480112063], 'a3': [-0.7724169592245995, -0.6351157698421788], 'a4': [-0.28042738930600275, 0.9598752415428891], 'a5': [0.7123760969513449, -0.7017979028839914], 'a6': [-0.044864830350514924, 0.9989930665413147], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9362348706397372, -0.3513748240813427], 'a9': [0.19325591779555326, 0.9811483833941727], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.284', 'coeff_info': ['x^105 - 1', '0.998210129767735 + 0.0598041539450342*I', '\\\\zeta_{105}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.93', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^68', 'a^64', 'a^31', 'a^92', 'a^27', 0, 'a^99', 'a^23', 'a^55', 0, 'a^95', 'a^33', 0, 'a^51', 'a^62', 'a^67', 'a^91', 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'1-539-539.284-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.382172912382532, 'root_number': '-0.738246390892597994310263466780-0.674531145562644427519440173616*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.382172912383', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(105)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.537260304043149999486252647807-0.423216992863306061005457619492*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.62984166476', 'prec': 37}, 'z2': {'__RealLiteral__': 0, 'data': '1.74964852532', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.53001768328', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.284', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/284'], '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': '1-539-539.284-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-539-539.284-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.382172912382532, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62984166476', 'prec': 37}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_539.284', 'Lhash_array': ['dirichlet_L_539.284'], 'factors': ['1-539-539.284-r0-0-0'], 'label': '1-539-539.284-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/284'}