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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.50', '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': '143.50', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.123', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^32', 'a^58', 'a^51', 'a^1', 'a^43', 'a^27', 'a^4', 'a^20', 0, 'a^30', 0, 'a^12', 'a^23', 'a^56', 'a^16', 'a^33', 'a^37', 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'190.75104874909218717518865483110', '191.83241455951745690816393418913', '192.49244716922080609336941517237', '193.11530185076470156511762752470', '194.06819313195615934528269065725', '194.63150056885545176326278426317', '195.743440914014203233642449662399', '196.371553700717521234516447053361', '197.11069966696462910705017603825', '197.75206180901635542102636715504', '198.81842232739637008762334539571', '199.31206945746590351881187816642'], 'prelabel': '1-143-143.50-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': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.493642950543257697616962129726-0.205722550285874747770900652765*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.62819300418', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.94735210102', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.34863514008', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.50', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/50'], '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': '1-143-143.50-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': '1-143-143.50-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': '0.62819300418', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.50', 'Lhash_array': ['dirichlet_L_143.50'], 'label': '1-143-143.50-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/50'}
Lfunction data - 1-143-143.50-r0-0-0