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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.123', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9945218953682733, -0.10452846326765347], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [0.9781476007338057, 0.20791169081775934], 'a5': [0.5877852522924731, 0.8090169943749475], 'a6': [0.9945218953682733, -0.10452846326765347], 'a7': [-0.20791169081775934, 0.9781476007338057], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.123', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.50', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^28', 'a^2', 'a^9', 'a^59', 'a^17', 'a^33', 'a^56', 'a^40', 0, 'a^30', 0, 'a^48', 'a^37', 'a^4', 'a^44', 'a^27', 'a^23', 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'193.22272842554440743877337787822', '193.60311902809445136725818636757', '194.0442253360254063208136585563', '195.320448377188746012612715489190', '196.03829333774622535413991552693', '196.86619235283455587777056884822', '197.87398395592827593645036877655', '198.235373694616146385453231646652', '199.17724726155914591861896857590', '199.72252109489891932534064003016'], 'prelabel': '1-143-143.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.6140439287121576, 'root_number': '-0.350663566468255729568174022516+0.936501501948482299346844727515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.307021964356', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.493642950543257697616962129726+0.205722550285874747770900652765*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.77392717606', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.18743346837', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.41010098595', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.123', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/123'], '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': '1-143-143.123-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': '1-143-143.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.3070219643560788, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77392717606', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.123', 'Lhash_array': ['dirichlet_L_143.123'], 'label': '1-143-143.123-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/123'}
Lfunction data - 1-143-143.123-r0-0-0