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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2009.1649', 'a10': [0.07473009358642425, 0.9972037971811801], 'a2': [0.9888308262251285, -0.14904226617617444], 'a3': [-0.5633200580636221, 0.8262387743159949], 'a4': [0.9555728057861407, -0.2947551744109042], 'a5': [-0.07473009358642425, 0.9972037971811801], 'a6': [-0.4338837391175581, 0.9009688679024191], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, -0.4338837391175581], 'a9': [-0.36534102436639504, -0.9308737486442042], 'algebraic': True, 'analytic_conductor': 9.329756776881393, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '2009.1649', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2009, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_2009.1836', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^82', 'a^29', 'a^80', 'a^22', 'a^27', 0, 'a^78', 'a^58', 'a^20', 'a^5', 'a^25', 'a^33', 0, 'a^51', 'a^76', 'a^11', 'a^56', 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'192.04111963601690453222514379351', '192.6407970400693465229995928039', '192.94845434563827561637657615083', '193.53252890770503705309770417931', '194.0793149201627219434988128407', '194.505791922820251247463210021723', '195.01353678272608388768783255270', '195.570069853637477147079097003862', '195.99638758496671130356436976561', '197.04869677710993368545061031814', '197.38730244516584672195822236776', '198.133654302380920954743219201767', '198.4014867924473100261254570664', '198.87909648944367288581026632081', '199.90330816417111698522535460831'], 'prelabel': '1-2009-2009.1649-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': 0.5325584242885723, 'root_number': '-0.102107043514949262086364000263+0.994773417248689983228431642108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.266279212144', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.59017330963922199728761448972+0.689479669342350907663274309840*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29367200206', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.47781294433', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.27219849054', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.329756776881393, 'bad_primes': [7, 41], 'central_character': '2009.1649', 'conductor': 2009, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2009/1649'], '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': '1-2009-2009.1649-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': '1-2009-2009.1649-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': 0.2662792121442861, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29367200206', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2009.1649', 'Lhash_array': ['dirichlet_L_2009.1649'], 'label': '1-2009-2009.1649-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2009/1649'}
Lfunction data - 1-2009-2009.1649-r0-0-0