Formats: - HTML - YAML - JSON - 2026-10-17T02:51:23.856874
  • lfunc_lfunctions • Show schema
    {'Lhash': '3940772206999379218349904855911', 'a10': [-12.928932188134524, 0.0], 'a2': [2.585786437626905, 0.0], 'a3': [6.656854249492381, 0.0], 'a4': [-1.3137084989847605, 0.0], 'a5': [-5.0, 0.0], 'a6': [17.213203435596427, 0.0], 'a7': [-7.0, 0.0], 'a8': [-24.083261120685233, 0.0], 'a9': [17.31370849898476, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '3940772206999379218349904855911', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.585786437626905, 0], [8.0, 0]], [[1.0, 0], [-6.656854249492381, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [-38.254833995939045, 0], [1331.0, 0]], [[1.0, 0], [-19.34314575050762, 0], [2197.0, 0]], [[1.0, 0], [87.22539674441619, 0], [4913.0, 0]], [[1.0, 0], [44.22539674441618, 0], [6859.0, 0]], [[1.0, 0], [-218.16652224137047, 0], [12167.0, 0]], [[1.0, 0], [46.94112549695428, 0], [24389.0, 0]], [[1.0, 0], [-194.55844122715712, 0], [29791.0, 0]], [[1.0, 0], [-366.8528137423857, 0], [50653.0, 0]], [[1.0, 0], [339.3624817342638, 0], [68921.0, 0]], [[1.0, 0], [226.16652224137047, 0], [79507.0, 0]], [[1.0, 0], [-11.676190233248546, 0], [103823.0, 0]], [[1.0, 0], [209.01933598375618, 0], [148877.0, 0]], [[1.0, 0], [616.0, 0], [205379.0, 0]], [[1.0, 0], [-320.73506473629425, 0], [226981.0, 0]], [[1.0, 0], [-14.509667991878084, 0], [300763.0, 0]], [[1.0, 0], [952.0, 0], [357911.0, 0]], [[1.0, 0], [-824.4894654563446, 0], [389017.0, 0]], [[1.0, 0], [-156.27503653147244, 0], [493039.0, 0]], [[1.0, 0], [1036.528137423857, 0], [571787.0, 0]], [[1.0, 0], [170.22539674441617, 0], [704969.0, 0]], [[1.0, 0], [-1059.873016277919, 0], [912673.0, 0]], [[1.0, 0], [241.83347775862953, 0], [1030301.0, 0]], [[1.0, 0], [1679.576910659136, 0], [1092727.0, 0]], [[1.0, 0], [-1506.8813844421313, 0], [1225043.0, 0]], [[1.0, 0], [1252.4095218659884, 0], [1295029.0, 0]], [[1.0, 0], [-1370.2034611053284, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-35-1.1-c3-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/35/4/a/b/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [2.149354578834316, 2.1499756046398284, 2.151665419172679, 2.153909896337203, 2.155870777218811, 2.1564127743066916, 2.15414011984987, 2.1474416362850555, 2.134543608695591, 2.113570022895288, 2.0826099670681324, 2.0397920718669456, 1.9833657207337834, 1.9117883844152705, 1.8238178452563198, 1.7186073269718032, 1.5958006968352467, 1.455624028365944, 1.2989689750104796, 1.1274626816150772, 0.9435184238075462, 0.7503608881588835, 0.5520200574552685, 0.3532881080166993, 0.1596346104301028, -0.02292331552087937, -0.18799739709011512, -0.32905035328698806, -0.43966026840745115, -0.513820642811223, -0.546266357181407, -0.5328125682153892, -0.47069053893645996, -0.358861832793924, -0.19829042063363775, 0.007848682616153308, 0.25404538296007734, 0.5324345723314844, 0.8328966407486066, 1.1432900598911009, 1.449821416180381, 1.7375506685371387, 1.9910207401018352, 2.194991246336478, 2.3352467553791554, 2.3994411108375107, 2.3779317305281085, 2.2645521599872644, 2.057268212358527, 1.7586633850571838, 1.3762033773980453, 0.9222377002688914, 0.4137085617441957, -0.12844688308147512, -0.6801958587740963, -1.215584751489209, -1.7081413506416907, -2.1324353932148954, -2.46570948907305, -2.689477868687023, -2.7909815273262777, -2.7643866481224424, -2.6116196914703598, -2.3427477377359445, -1.9758364255019967, -1.5362492891478903, -1.0553898840495037, -0.5689295154151859, -0.11460578550196811, 0.27028275117953593, 0.551526271594334, 0.7006131045918764, 0.697101463427122, 0.5305577829035106, 0.2018835369850561, -0.27611402819247055, -0.8790035332332, -1.5718994328840938, -2.3114878762920616, -3.048804673137981, -3.7325931378785313, -4.313010236754732, -4.745405168599352, -4.993870436304994, -5.034265421076207, -4.85643841963511, -4.465424796420542, -3.8814736872023303, -3.138848537765957, -2.283450522558041, -1.3694197891484612, -0.45496781904005595, 0.40222476966110127, 1.1496557840291515, 1.744283493966585, 2.1560480345814743, 2.370291243303147, 2.3888237745440115, 2.2295071203422308, 1.9243559838583657, 1.5163106760097624, 1.0549656561108296, 0.591654644640771, 0.17437183164087572, -0.15695769592979475, -0.37436327055551377, -0.4644455605701782, -0.42942019341404813, -0.2864408409188444, -0.06523577750769165, 0.19572157041430704, 0.45411596156607736, 0.6692385861350588, 0.8073664329342333, 0.8464388346374829, 0.7794479165643025, 0.6160797162221981, 0.3823227087586332, 0.11798343117565271, -0.12770816380556965, -0.3019849262022594, -0.35530024855526027, -0.248196291164602, 0.04253865761442578, 0.5192124948948047, 1.160732638965005, 1.9227183628560114, 2.740390585506236, 3.5340908303712384, 4.216962288205073, 4.704042834141212, 4.921808284498315, 4.8170936462646035, 4.364329810960335, 3.570168965694258, 2.4748249562639084, 1.1498012488146414, -0.3079174121541559, -1.7847184924332153, -3.161391876547195, -4.325176381264778, -5.181495043806472, -5.664035725745329, -5.74197784618685, -5.423460168553289, -4.7547990342684825, -3.815455376966078, -2.70925492890737, -1.5528271714275752, -0.4625856478050718, 0.45822323062042897, 1.1308548818517432, 1.509408387031332, 1.5851477278407347, 1.3862613724892214, 0.9730855521527124, 0.4293918328563895, -0.14915082728833287, -0.6678539277207614, -1.04555337019089, -1.22517456977757, -1.1809215336535983, -0.9211316064757608, -0.48641316710681676, 0.05667899740821666, 0.6255622712175455, 1.1337655563222184, 1.5035927733736663, 1.677521369234735, 1.6267036970178845, 1.3553297510185205, 0.9001844292516027, 0.3254139913091538, -0.2867902643422888, -0.848277458282131, -1.2780502161518197, -1.5144808106468415, -1.524800962155276, -1.310403045928898, -0.9070830615171035, -0.3800924390294054, 0.18535882863079356, 0.6968058052861176, 1.068580757067401, 1.2351056934842906, 1.1613796268742658, 0.8489899860247834, 0.33661825703253645, -0.30517312617907716, -0.984211649983375, -1.600583641753938, -2.0620435334895872, -2.2986075232240633, -2.2740335555239004, -1.9923067230578961, -1.4979731855736704, -0.8700942650491917, -0.21058749460569368, 0.3713705423680016, 0.7765295099561609, 0.9316609605257905, 0.8019706399550562, 0.3977315077486782, -0.2261106922668768, -0.9775310864975131, -1.7412477393347598, -2.3967717228647154, -2.8379362890212434, -2.9908186814167834, -2.8271107458773956, -2.3706125456526945, -1.6955357328300624, -0.916563376588197, -0.1719280795653451, 0.3980676762872543, 0.6738472341886961, 0.5770993473820045, 0.08571622432140225, -0.7594486024158335, -1.8573789195763546, -3.0591675143121386, -4.188185286916423, -5.06528519531422, -5.535308185855071, -5.490855362485619, -4.889618332103382, -3.7624809833422375, -2.210986967153692, -0.3943961932280993, 1.4918259827696292, 3.2428922888546947, 4.672895706882447, 5.640053885040907, 6.065177969808353, 5.940619931613088, 5.328467919414143, 4.348472788282471, 3.1578195051767843, 1.926134461604616, 0.8098304952486238, -0.07008372038267509, -0.64326806612051, -0.8961677283818755, -0.8683633035780582, -0.6402221926506576, -0.3143970672138497, 0.005272594520888856, 0.23353470460205447, 0.31859687656410896, 0.24950886159660257, 0.05492310643774475, -0.20624215241039406, -0.46016123636296696, -0.6362475358665088, -0.6843124938751036, -0.587143335949961, -0.36578821487918683], 'positive_zeros': ['3.10872113048333480481099347311898', '4.37067012632211651815365282125868', '6.59579649322808839307610539272179', '8.534471157471106185264744217797643', '9.307324458736904324545130481122867', '11.43979415134699257168741039486564', '12.93596040644060945302808781536205', '13.65726969307803711827536505876374', '14.80723333190656598792553549477864', '15.36080296278189108756728642989508'], 'prelabel': '2-35-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.10872113048333480481099347312', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.37067012632211651815365282126', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.59579649322808839307610539272', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/4/a/b/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-35-1.1-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-35-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.10872113048333480481099347312', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3940772206999379218349904855911', 'Lhash_array': ['3940772206999379218349904855911'], 'factors': ['2-35-1.1-c3-0-3'], 'label': '2-35-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/4/a/b/1/1'}