Formats: - HTML - YAML - JSON - 2026-03-10T03:54:31.240878
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1210324932334745224833332459235', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [8.116843969807043, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.16087387467103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [11.0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '1584.1297', 'coefficient_field': 'CDF', 'conductor': 1584, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-8.116843969807043, 0], [25.0, 0]], [[1.0, 0], [0, 0], [-49.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [-169.0, 0]], [[1.0, 0], [0, 0], [-289.0, 0]], [[1.0, 0], [0, 0], [-361.0, 0]], [[1.0, 0], [-8.350531909421129, 0], [529.0, 0]], [[1.0, 0], [0, 0], [-841.0, 0]], [[1.0, 0], [-24.584219849035215, 0], [961.0, 0]], [[1.0, 0], [-72.81790778864931, 0], [1369.0, 0]], [[1.0, 0], [0, 0], [-1681.0, 0]], [[1.0, 0], [0, 0], [-1849.0, 0]], [[1.0, 0], [-50.0, 0], [2209.0, 0]], [[1.0, 0], [-70.0, 0], [2809.0, 0]], [[1.0, 0], [96.58421984903522, 0], [3481.0, 0]], [[1.0, 0], [0, 0], [-3721.0, 0]], [[1.0, 0], [-129.51897160749155, 0], [4489.0, 0]], [[1.0, 0], [-23.415780150964785, 0], [5041.0, 0]], [[1.0, 0], [0, 0], [-5329.0, 0]], [[1.0, 0], [0, 0], [-6241.0, 0]], [[1.0, 0], [0, 0], [-6889.0, 0]], [[1.0, 0], [177.75265954710565, 0], [7921.0, 0]], [[1.0, 0], [193.98634748671972, 0], [9409.0, 0]], [[1.0, 0], [0, 0], [-10201.0, 0]], [[1.0, 0], [-190.0, 0], [10609.0, 0]], [[1.0, 0], [0, 0], [-11449.0, 0]], [[1.0, 0], [0, 0], [-11881.0, 0]], [[1.0, 0], [-47.1820922113507, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23869630, 'index': 35, 'label': '2-1584-11.10-c2-0-35', 'leading_term': '2.7365811206095856427510383672656377455079645970513418546', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1584/3/j/c/1297/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.7365811206095856, 2.7243190807556013, 2.687595946603638, 2.62660474248732, 2.5416804515237033, 2.433318951175113, 2.302201627000122, 2.1492239036738843, 1.9755256076790086, 1.7825208624888693, 1.5719251188413184, 1.3457769371837929, 1.1064522588349268, 0.8566691160302847, 0.5994810266246307, 0.3382576845330812, 0.0766519802989965, -0.18144714353714497, -0.43197599092574107, -0.6707710209600324, -0.8936562763433142, -1.0965416929249248, -1.2755301155031116, -1.427030337095643, -1.5478730161542844, -1.6354259270911335, -1.6877046828899045, -1.703474853194334, -1.6823413047289968, -1.624820628820537, -1.5323927057470976, -1.4075277962767538, -1.2536860508234742, -1.075286984273984, -0.877647271595548, -0.6668861610510988, -0.44979885665474645, -0.2336993611600223, -0.026235460913039788, 0.16482026563434507, 0.3317983674469505, 0.46737323503087613, 0.5648095208116737, 0.618206401081108, 0.62273126291977, 0.5748341132103846, 0.4724340205403395, 0.3150692399019466, 0.1040033492691113, -0.1577192514473689, -0.4652737763769514, -0.8121150649018868, -1.1900988871846832, -1.589664132516182, -2.000073197124052, -2.4097055544360786, -2.8063971839355304, -3.1778163492893508, -3.5118642494869383, -3.7970874139476525, -4.023087463883038, -4.180913097521536, -4.263418941674281, -4.265576293772891, -4.184721782350718, -4.020731600738586, -3.776111192709545, -3.455993036688091, -3.0680384065259902, -2.6222425757055103, -2.130646749333849, -1.6069639069072372, -1.066129557567815, -0.5237919802913192, 0.004240324138339503, 0.502573665167434, 0.9568045195330024, 1.3540720446390804, 1.6835645073227925, 1.936957308445516, 2.108762213457374, 2.1965703072332206, 2.2011750019644123, 2.126566018012962, 1.9797904648848776, 1.7706827705583794, 1.511471009375393, 1.216272907093534, 0.9005001911994619, 0.5801947410084674, 0.27132392496839397, -0.01093463199243851, -0.25288701544075065, -0.4429636921741413, -0.5722761330193733, -0.6350613982569258, -0.628990880975221, -0.5553248784881095, -0.4189012255524117, -0.2279536113667349, 0.006236902123068452, 0.26984559797391905, 0.5471436832762002, 0.8212471651794697, 1.0749422704443472, 1.2915498124418352, 1.455787709293433, 1.554589526925837, 1.5778376063283486, 1.5189720861004616, 1.3754418988016528, 1.148970448109513, 0.8456169077665049, 0.47562357437368113, 0.05305002660266298, -0.40479449530454453, -0.8780986010030037, -1.3454445154882662, -1.7848119656032635, -2.1746432941977143, -2.4949182967525907, -2.728185130921578, -2.8604941756265725, -2.882184984853348, -2.7884824230500302, -2.5798664717109854, -2.262190709959596, -1.8465366201825353, -1.3488040725285884, -0.7890519407565176, -0.1906160920210914, 0.4209557394467991, 1.0191021257660884, 1.5775208648511232, 2.0714529550190646, 2.4789117663520885, 2.781792823495909, 2.9668043670507034, 3.0261669427095756, 2.958041341553312, 2.7666577684608256, 2.462134481832886, 2.059990538036454, 1.5803738170064692, 1.0470412935841615, 0.4861426578961759, -0.07512995306771486, -0.609954888727451, -1.0932806536926778, -1.5031357979905848, -1.8217761924580103, -2.0366046970387868, -2.140809903281007, -2.1336855696354005, -2.020609799517458, -1.8126820018049696, -1.5260351687380758, -1.180859894797031, -0.8001937333235518, -0.40854390528737416, -0.030422128391228834, 0.3111232941527112, 0.5958914783150765, 0.807745973889167, 0.9355902525527531, 0.974040277963011, 0.9237498398600846, 0.7913644128928966, 0.5891012569365756, 0.33397603748410437, 0.046718069605777686, -0.2495639577052898, -0.530887483802528, -0.7739824713329495, -0.9578615542586232, -1.0652757726319433, -1.0839626854154272, -1.0076044392021644, -0.8364294691573712, -0.5774120615182836, -0.2440478600401435, 0.14429083694392397, 0.563390010379133, 0.9855642146210722, 1.3812852810718073, 1.720974651129912, 1.9768521909249346, 2.124728337010081, 2.1456273104314856, 2.02713702603731, 1.7643958880987651, 1.3606471485643132, 0.8273167656964104, 0.18359926447691022, -0.5444337523312065, -1.3251579222215357, -2.1230810416679997, -2.9007926066655085, -3.6210637885729624, -4.2489722629212725, -4.753922588574428, -5.111437182879257, -5.304605240641316, -5.325096573906499, -5.173673194363188, -4.860161985650085, -4.402885149676634, -3.827579169417074, -3.1658656311666227, -2.453366263209611, -1.7275780374559606, -1.025640530256492, -0.382135768118956, 0.17294016416414884, 0.6159044816614053, 0.9307033018292786, 1.1097307738305446, 1.154098874484693, 1.0733407019563816, 0.884567312624647, 0.6111344302801618, 0.28090827480286273, -0.07575294262776255, -0.4281655432444509, -0.7474878137916223, -1.00874027585255, -1.1925397936483342, -1.2864271662663846, -1.2856949316728379, -1.1936559024158246, -1.0213312404562838, -0.7865770974573174, -0.512708255335161, -0.22671306524181467, 0.04281623729498145, 0.26789223085953207, 0.4233227550301144, 0.4887250365665065, 0.45021570920692655, 0.30164977921387404, 0.04531170109790621, -0.3080008380710094, -0.739517574073299, -1.2236337240367476, -1.7295753726585046, -2.2234832737570183, -2.670774336847325, -3.0386176454926743, -3.298350583781762, -3.427661531941569, -3.412378793129147, -3.247730222610198, -2.938972902890543, -2.501334855367055, -1.9592583165684596, -1.3449832489640634, -0.6965570409603173], 'positive_zeros': ['0.954778021733146979436581372229713', '2.23426977340438872556270924408350', '2.83711206751063116636007782583722', '4.33545581512937863458919565479851', '5.32961407865246960548285954206246', '5.85791914706453227652528984263335', '6.68666641823714000335451223329111', '7.63546658731444965585532985165948', '8.546743388893875586090151511043655', '9.379925407138494022336187500732978'], 'prelabel': '2-1584-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.5696935906228555, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.954778021733146979436581372230', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.23426977340438872556270924408', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83711206751063116636007782584', 'prec': 103}}