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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1339.1102', 'a10': [0.9924205096719357, -0.12288829066471413], 'a2': [-0.8810121942857845, 0.47309355683601007], 'a3': [-0.6961339459629267, -0.717911923064442], 'a4': [0.5523649729605058, -0.8336023852211195], 'a5': [-0.9324722294043558, -0.3612416661871529], 'a6': [0.9529420004271566, 0.3031526741130435], 'a7': [-0.8161969123562217, 0.5777738314082511], 'a8': [-0.092268359463302, 0.9957341762950345], 'a9': [-0.030795058556170353, 0.9995257197133659], 'algebraic': True, 'analytic_conductor': 6.218289857762162, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [103, [1]]], 'bad_primes': [13, 103], 'central_character': '1339.1102', 'coeff_info': ['x^102 - 1', '0.998103328737044 + 0.0615609061339428*I', '\\\\zeta_{102}'], 'conductor': 1339, 'conductor_radical': 1339, 'conjugate': 'dirichlet_L_1339.1226', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^64', 'a^86', 'a^57', 'a^5', 'a^41', 'a^27', 'a^26', 'a^100', 'a^43', 'a^48', 0, 'a^84', 'a^19', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-1339-1339.1102-r0-0-0', 'leading_term': '0.0112086395725345069694119327198+0.0277017225550075807667955457763*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1339/1102', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.02988342406053227, 0.3192633252370981, 0.3194871693437507, -0.3378746188727614, -1.5355450443385337, -2.4087936020303706, -1.9380456331931537, -0.01114060487683451, 2.0114139314061465, 2.0330726747177006, -1.0238304971788361, -5.897502321393523, -9.53890300236157, -9.43173312641906, -5.767114021638802, -1.3755931272026682, 0.7186381508566155, -0.10818481085980847, -1.8473158017826652, -2.159799133207597, -0.7523523139895703, 0.6712445781153608, 0.6495087007393279, -0.31856306440899906, -0.5988739545782166, 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'197.235692909697934373397866385893', '198.05146377989055882652244844382', '198.77890118607345638496385089277', '199.30582840687053926720812456650', '199.62291988558697027373041998874'], 'prelabel': '1-1339-1339.1102-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.218289857762162, 'root_angle': 0.7552312804106035, 'root_number': '-0.718631750628848400519981632575+0.695390830388290816513232788678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.377615640205', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(102)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.369636847697922976366022528280-0.0350331618627247440197844550520*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.818518405022', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.18900587894', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.04710795523', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.218289857762162, 'bad_primes': [13, 103], 'central_character': '1339.1102', 'conductor': 1339, 'conductor_radical': 1339, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1339/1102'], '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': '1-1339-1339.1102-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': '1-1339-1339.1102-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.218289857762162, 'root_angle': 0.37761564020530175, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.818518405022', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1339.1102', 'Lhash_array': ['dirichlet_L_1339.1102'], 'label': '1-1339-1339.1102-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1339/1102'}
Lfunction data - 1-1339-1339.1102-r0-0-0