Formats: - HTML - YAML - JSON - 2025-11-30T08:15:51.848765
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '/ModularForm/GL3/Q/Maass/1/1/29.41987_3.039198/1.28208217/', 'a10': [-0.09170978, -1.09391513], 'a2': [1.282082173, -0.042361941], 'a3': [-0.288209136, -0.280928879], 'a4': [0.359857991, -0.150984921], 'a5': [-0.04329252, -0.8546637], 'a6': [-0.381408488, -0.347964809], 'a7': [-0.28710221, 0.40390937], 'a8': [-0.19055773, -0.20881935], 'a9': [0.2923526, -0.11899633], 'algebraic': False, 'analytic_conductor': 11.642928352395352, 'analytic_normalization': 0, 'bad_lfactors': [], 'bad_primes': [], 'central_character': '1.1', 'conductor': 1, 'conductor_radical': 1, 'conjugate': '/ModularForm/GL3/Q/Maass/1/1/-29.4198_-3.03919/1.28208217/', 'credit': 'Stefan Lemurell', 'degree': 3, 'dirichlet_coefficients': ['(1.0)', '(1.282082173 - 0.042361941*I)', '(-0.288209136 - 0.280928879*I)', '(0.359857991 - 0.150984921*I)', '(-0.04329252 - 0.8546637*I)', '(-0.381408488 - 0.347964809*I)', '(-0.28710221 + 0.40390937*I)', '(-0.19055773 - 0.20881935*I)', '(0.2923526 - 0.11899633*I)', '(-0.09170978 - 1.09391513*I)', '(-0.24629967 - 0.39158966*I)', '(-0.1461303 - 0.0575792*I)', '(-1.1368273 - 1.8300771*I)', '(-0.3509782 + 0.5300072*I)', '(-0.2276224 + 0.258484*I)', '(0.5611619 - 0.1236823*I)', '(0.840175 + 0.041681*I)', '(0.369779 - 0.164947*I)', '(0.06281 + 0.472417*I)', '(-0.14462 - 0.301021*I)', '(0.196215 - 0.035755*I)', '(-0.33236 - 0.49161*I)', '(0.27584 + 0.75746*I)', '(-0.00374 + 0.11371*I)', '(-0.68528 - 0.78066*I)', '(-1.53503 - 2.29815*I)', '(0.7203 - 0.0478*I)', '(-0.0423 + 0.1886*I)', '(0.6604 + 0.0588*I)', '(-0.2808 + 0.341*I)', '(0.2136 + 0.5209*I)', '(1.297 - 0.017*I)', '(-0.039 + 0.182*I)', '(1.078 + 0.017*I)', '(0.357 + 0.227*I)', '(0.087 - 0.086*I)', '(-0.98 - 1.05*I)', '(0.1 + 0.6*I)', '(-0.18 + 0.84*I)', '(-0.17 + 0.17*I)', '(-2.57 + 1.04*I)', '(0.2)'], 'euler_factors': [[1, '-1.282082173 + 0.042361941*I', '1.282082173 + 0.042361941*I', -1], [1, '0.288209136 + 0.280928879*I', '-0.288209136 + 0.280928879*I', -1], [1, '0.04329252 + 0.8546637*I', '-0.04329252 + 0.8546637*I', -1], [1, '0.28710221 - 0.40390937*I', '-0.28710221 - 0.40390937*I', -1], [1, '0.24629967 + 0.39158966*I', '-0.24629967 + 0.39158966*I', -1], [1, '1.1368273 + 1.8300771*I', '-1.1368273 + 1.8300771*I', -1], [1, '-0.840175 - 0.041681*I', '0.840175 - 0.041681*I', -1], [1, '-0.06281 - 0.472417*I', '0.06281 - 0.472417*I', -1], [1, '-0.27584 - 0.75746*I', '0.27584 - 0.75746*I', -1], [1, '-0.6604 - 0.0588*I', '0.6604 - 0.0588*I', -1], [1, '-0.2136 - 0.5209*I', '0.2136 - 0.5209*I', -1], [1, '0.98 + 1.05*I', '-0.98 + 1.05*I', -1], [1, '2.57 - 1.04*I', '-2.57 - 1.04*I', -1]], 'gamma_factors': [['29.41987002*I', '3.039198812*I', '-32.45906884*I'], []], 'group': 'GL3', 'id': 9397572, 'index': 0, 'label': '3-1-1.1-r0e3-p3.04p29.42m32.46-0', 'load_key': 'Maass', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '3.039198812', 'prec': 37}, {'__RealLiteral__': 0, 'data': '29.41987002', 'prec': 37}, {'__RealLiteral__': 0, 'data': '-32.45906884', 'prec': 40}], 'mu_real': [0, 0, 0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL3/Q/Maass/1/1/29.41987_3.039198/1.28208217/', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.360977130747291, 1.7012438884147139, 0.9097537218311915, 0.05007426723819248, -0.7992815036850485, -1.5534453467651412, -2.1320696221573474, -2.471062276239807, -2.5333397986502604, -2.316612744744644, -1.856427801926151, -1.2232805799761355, -0.5135369785941633, 0.1649689724101968, 0.7106517218559542, 1.0462777136184733, 1.1340607808293373, 0.9845088574359994, 0.6566231401144308, 0.2485060944413581, -0.12071627792202029, -0.33485040054302534, -0.3061106070698973, 0.0030595046950662643, 0.5667962803140909, 1.294935731972187, 2.0458769444464617, 2.6518087235610763, 2.9520994989613727, 2.82845605144223, 2.2344500915667056, 1.2125473450955886, -0.10611074803038921, -1.5205515995654975, -2.7948441715787795, -3.7026740507126146, -4.072695397578022, -3.8249561351943044, -2.9900609573348285, -1.7060949666861993, -0.19303703395441218, 1.2905663953136879, 2.4996858968941043, 3.252338568953023, 3.4654557181372265, 3.168812737538439, 2.4936484463663575, 1.6384854181518724, 0.8201358919224392, 0.22157872058301278, -0.05066335715611849, 0.010831216565015662, 0.3173720970944475, 0.7120699801270378, 1.0156108744806407, 1.0781142441839395, 0.8234818698241507, 0.2742901779050529, -0.4499275515307478, -1.1613641978447697, -1.6528439880626895, -1.7546506209046002, -1.3844645311853037, -0.5768746474265599, 0.5162149596273787, 1.65569282303842, 2.569411778092366, 3.017554174435905, 2.8530438799004108, 2.0616489566054175, 0.7711593341358003, -0.7734326856995504, -2.2633681910868493, -3.395585569363261, -3.94151989518703, -3.798613722756873, -3.012156563499075, -1.7624091504630546, -0.3205333552664038, 1.0155404182339316, 1.989439774575032, 2.442304227057226, 2.3432552224634167, 1.7879282039913373, 0.9667171392356362, 0.11184513949186811, -0.5626791813480695, -0.9129145249375462, -0.8960024191552207, -0.573460383479542, -0.08716344364797018, 0.38465230230904546, 0.6792236191230616, 0.6952395611840695, 0.4212446318814595, -0.06040143556261171, -0.5944747827384457, -0.992941345450754, -1.0837141873594411, -0.7558714429290734, 0.009676809148489007, 1.1312295793003073, 2.4407926284104335, 3.718207125095439, 4.736684986176645, 5.309275273416666, 5.3260739089749345, 4.774577145677777, 3.7397054389628086, 2.3846285531293456, 0.9175243948275993, -0.4480414192061266, -1.530754862186504, -2.2100231902790566, -2.440656558513236, -2.2524011699619435, -1.736129712876035, -1.0209045494466815, -0.24736850764244891, 0.4571167227889919, 0.9972875913255611], 'positive_zeros': ['0.764420', '3.185940', '4.910034', '5.748282', '7.981056', '10.031348', '12.418132', '12.736384', '14.348671', '15.886867', '17.626933', '19.556330', '21.285755', '22.542985', '23.721749', '24.997488'], 'precision': 8, 'prelabel': '3-1-1.1-r0e3-p3.04p29.42m32.46', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.266491397238425, 'root_angle': 0.0, 'root_number': '1.0', 'self_dual': False, 'spectral_label': 'r0e3-p3.04p29.42m32.46', 'st_group': 'Unknown', 'z1': {'__RealLiteral__': 0, 'data': '0.76442', 'prec': 24}, 'z2': {'__RealLiteral__': 0, 'data': '3.18594', 'prec': 24}, 'z3': {'__RealLiteral__': 0, 'data': '4.910034', 'prec': 27}}