Formats: - HTML - YAML - JSON - 2026-10-08T04:40:13.445937
  • lfunc_lfunctions • Show schema
    {'Lhash': '673954995931993147638310061603,691426922337849756605936147534,1028240685304560608413576063256,2027988589754906635961640709826', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -96, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4552103.856286754, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '288.1', 'coefficient_field': '1.1.1.1', 'conductor': 6879707136, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1], [1], [1, 0, -7028, 0, 24404246, 0, -68632812500, 0, 95367431640625], [1, 96, 33308, 3101664, 882709158, 52129666848, 9408685593692, 455765904954528, 79792266297612001], [1, 0, -296436, 0, 49128544726, 0, -7688786399022036, 0, 672749994932560009201], [1, 0, -894228, 0, 396323515894, 0, -123276923449147572, 0, 19004963774880799438801], [1, 200, 5544924, 837463800, 11719230862342, 1189078838676600, 11178532962453270876, 572484610301963158600, 4064231406647572522401601], [1, 0, -6794580, 0, 21506967947254, 0, -41658020173929518580, 0, 37589973457545958193355601], [1, -2336, 21475164, -38524875168, 201526726533862, -247959310613430624, 889641122260951313436, -622859910044817949737952, 1716155831334586342923895201], [1, 0, -31255380, 0, 976386653995702, 0, -13149364445546436331380, 0, 176994576151109753197786640401], [1, -12928, 171809404, -1210606426240, 8258394345291910, -34658634178395322240, 140819847487712379252604, -303358907030568099702406528, 671790528819082282036142601601], [1, 0, -241262580, 0, 24149916431784598, 0, -1160131471837211087790420, 0, 23122483666661158726686253786801], [1, -4568, 298423164, -1198914790440, 49546596595861030, -138901712943089518440, 4005632460629736828616764, -7103689102881345176939129368, 180167782956420929503029846064801], [1, 0, -466346868, 0, 96250708269010006, 0, -10078447089637504314882132, 0, 467056167777397914441056671494001], [1, 54720, 1931246012, 44907785415360, 798240538650932934, 10299376360440237107520, 101581864365107425641014588, 660106421756890550022503568960, 2766668711962335809450748011342401], [1, 0, -1039152180, 0, 595616955270391126, 0, -181734696085008281686796820, 0, 30585627290848204916791848989276401], [1, 0, -1537424180, 0, 1399694789142612374, 0, -785803255327500899406476180, 0, 261240335504588722483367157995242801], [1, 0, 741098540, 0, 1478044222094100534, 0, 528657390352711267792502540, 0, 508858109619679129936596364708525201], [1, 0, -1366835860, 0, 3274116308996825526, 0, -2491520078225018774658761140, 0, 3322737661703085672358476688602579601], [1, -206688, 23115456284, -1658044175781600, 83709015377411926950, -2991491967199766085741600, 75246439997141832953748917084, -1213921193333468850324130816925088, 10596610576391421032662867140133202401], [1, -39976, 5482725884, -184476226332888, 16711464530914690982, -382432424394548674450584, 23562704376262671569058486716, -356157618131462402903834279923432, 18469587772135192290560825407466407201], [1, -247872, 35071990844, -3205725049525056, 210603881501493890886, -9864196777075665475633344, 332071292078352972502059027644, -7221606832174341205547651588334528, 89648251976843595444986830377401534401], [1, 0, -10047855188, 0, 55381071937674414326, 0, -155902934940088013801502343412, 0, 240747534123068430155382383568465195601], [1, -84632, 10375446204, -835864615445736, 100786271186270136166, -4667517703964513457559464, 323524257681558785491362500604, -14736172741300491554778947241492568, 972299657790850297934682879408841327201], [1, 99576, 35261587868, 2487280198131144, 458735253741197890758, 21359121375850509036664008, 2600274564648869486082452773532, 63056620409484939904645246454552568, 5437943429267472574499737549036572950401], [1, 0, -35324188916, 0, 532130858920566996374, 0, -3901988063881883229470445304916, 0, 12201900399479668244827490915525641902001], [1, 180448, 32522036636, 4291698356279904, 606138092715331178534, 49752546391512173012928672, 4370689772475000674942645907164, 281132104390774767026102958995938336, 18061112346694138117573133075817258818401], [1, 0, -2634732660, 0, 325347597745377394006, 0, -518291792821414683236783552340, 0, 38696844624861790832365403138487376998001], [1, 0, -45852872340, 0, 969819894553659446902, 0, -10855042435342565310137443628340, 0, 56044107677782919374398655242916531006801], [1, 303816, 90205935452, 15795180952179192, 2655841353255899413638, 291015970497042143382491256, 30621012686278817663302915126748, 1900147409070478102474991964778064712, 115230877647233745723406127208308085892801]], 'euler_factors_factorization': [[1], [1], [[[1, 0, -7028, 0, 24404246, 0, -68632812500, 0, 95367431640625], 1]], [[[1, 48, 15502, 806736, 282475249], 2]], [[[1, 0, -296436, 0, 49128544726, 0, -7688786399022036, 0, 672749994932560009201], 1]], [[[1, 0, -894228, 0, 396323515894, 0, -123276923449147572, 0, 19004963774880799438801], 1]], [[[1, 100, 2767462, 141985700, 2015993900449], 2]], [[[1, 0, -6794580, 0, 21506967947254, 0, -41658020173929518580, 0, 37589973457545958193355601], 1]], [[[1, -1168, 10055470, -7517648624, 41426511213649], 2]], [[[1, 0, -31255380, 0, 976386653995702, 0, -13149364445546436331380, 0, 176994576151109753197786640401], 1]], [[[1, -6464, 65013054, -185058832064, 819628286980801], 2]], [[[1, 0, -241262580, 0, 24149916431784598, 0, -1160131471837211087790420, 0, 23122483666661158726686253786801], 1]], [[[1, -2284, 146603254, -264615563084, 13422659310152401], 2]], [[[1, 0, -466346868, 0, 96250708269010006, 0, -10078447089637504314882132, 0, 467056167777397914441056671494001], 1]], [[[1, 27360, 591338206, 6274879391520, 52599132235830049], 2]], [[[1, 0, -1039152180, 0, 595616955270391126, 0, -181734696085008281686796820, 0, 30585627290848204916791848989276401], 1]], [[[1, 0, -1537424180, 0, 1399694789142612374, 0, -785803255327500899406476180, 0, 261240335504588722483367157995242801], 1]], [[[1, 0, 741098540, 0, 1478044222094100534, 0, 528657390352711267792502540, 0, 508858109619679129936596364708525201], 1]], [[[1, 0, -1366835860, 0, 3274116308996825526, 0, -2491520078225018774658761140, 0, 3322737661703085672358476688602579601], 1]], [[[1, -103344, 6217736974, -186456278049744, 3255243551009881201], 2]], [[[1, -19988, 2541602870, -41436555000884, 4297625829703557649], 2]], [[[1, -123936, 9855929374, -381358061866464, 9468276082626847201], 2]], [[[1, 0, -10047855188, 0, 55381071937674414326, 0, -155902934940088013801502343412, 0, 240747534123068430155382383568465195601], 1]], [[[1, -42316, 4292401174, -236295059643884, 31181719929966183601], 2]], [[[1, 49788, 16391371462, 427546496715516, 73742412689492826049], 2]], [[[1, 0, -35324188916, 0, 532130858920566996374, 0, -3901988063881883229470445304916, 0, 12201900399479668244827490915525641902001], 1]], [[[1, 90224, 12190833230, 1045943440796432, 134391637934412192049], 2]], [[[1, 0, -2634732660, 0, 325347597745377394006, 0, -518291792821414683236783552340, 0, 38696844624861790832365403138487376998001], 1]], [[[1, 0, -45852872340, 0, 969819894553659446902, 0, -10855042435342565310137443628340, 0, 56044107677782919374398655242916531006801], 1]], [[[1, 151908, 33564947494, 2798806432171044, 339456738992222314849], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-288e4-1.1-c5e4-0-0', 'leading_term': '7.3716515954587078734107820380660586653953171421417974592048653461538366739847602516063559', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [5, 5, 5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/288/6/d/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.017578125', 'prec': 27}, 'plot_values': [7.371651595458707, 7.330282755600749, 7.261986715848754, 7.156991681130372, 7.006443818273748, 6.8079720375703925, 6.566870029830985, 6.289357739019808, 5.981521261582279, 5.647722344452547, 5.291824301779258, 4.917974924961019, 4.530852876251384, 4.135678037904784, 3.7377103441900643, 3.342078183042098, 2.9536397358307114, 2.576957717623855, 2.2162638322505788, 1.8754102145678098, 1.5578174233951096, 1.2663853323357157, 1.0034488218918862, 0.7707453272678998, 0.5693882061717717, 0.39985382981718115, 0.26198376793642814, 0.15499497464113013, 0.07749882020426903, 0.027535268948679623, 0.0026168898002736233, -0.00021764138526023032, 0.015659716535280557, 0.046536844398850766, 0.08843917670796461, 0.13721265980420877, 0.1886091707193243, 0.23837595980246962, 0.28234636791144074, 0.3165251570592144, 0.33717282836833584, 0.34089077657998806, 0.32469337049903474, 0.28607152122263696, 0.22305377329093345, 0.13425660821529606, 0.018915529503720115, -0.12309076120039447, -0.2912239467383728, -0.4842908099393579, -0.7004603201778178, -0.9372898334959393, -1.1917665980133412, -1.4603609052490518, -1.7390910273364757, -2.0236030191116376, -2.309252914325082, -2.591190557837168, -2.864465795575759, -3.124142288467025, -3.3653812485696304, -3.5835389364571455, -3.774299954626786, -3.9337680521327076, -4.058528543015795, -4.145740877856755, -4.193257922111504, -4.199644454021242, -4.164208795684294, -4.087074587308232, -3.9692149108740793, -3.812404867968557, -3.619212712556653, -3.3930185488314617, -3.137935823172703, -2.8587232632621435, -2.5607368624024205, -2.249853345079642, -1.9323290272430023, -1.6146867512878773, -1.303628084441469, -1.0058798843959946, -0.7280498437242844, -0.4765093622142739, -0.257271492403127, -0.07583979317884415, 0.06290681929446619, 0.1548115066535774, 0.1965474536118884, 0.18570584854936195, 0.1208566564635904, 0.0015979754102171237, -0.17140965478675507, -0.3964369785563285, -0.670702674894304, -0.9904031166719152, -1.35076542347648, -1.7461238571386448, -2.170028090216874, -2.615345886097069, -3.074381767874915, -3.539027840028972, -4.000942482958728, -4.451680357040543, -4.882845440192243, -5.286287957732528, -5.6542833946381705, -5.979644748069236, -6.255878631916448, -6.477351260903973, -6.639407674097785, -6.738432014767942, -6.771963862355978, -6.7387442473749255, -6.6387574802832905, -6.473222470700982, -6.244596419907116, -5.956491552730388, -5.6136369452614785, -5.221793243433656, -4.787606679185988, -4.318455003070691, -3.8223412584776524, -3.3077226250559266, -2.783285831441599, -2.2577745730142484, -1.7398446340536555, -1.237848275632001, -0.7596400145661032, -0.3124273885476647, 0.09737318691065669, 0.46429099621889, 0.7839061504074295, 1.0529353174516605, 1.269306535737634, 1.4321826639440915, 1.5419584645391402, 1.6002505176279291, 1.6098460288458782, 1.5746016242931828, 1.49933958857815, 1.3897244903313375, 1.2521086205383283, 1.0933506910471944, 0.9206417220478, 0.7413105879684786, 0.5626361114656069, 0.3916492102885229, 0.2349476861906645, 0.09852356005181667, -0.012389954646983725, -0.09346198345622408, -0.1413738938600982, -0.15389907740310352, -0.1299648851846236, -0.06967685029358105, 0.025698975034104853, 0.15377512826205011, 0.3111070295440701, 0.4933055621472198, 0.6951656337647043, 0.910815119890146, 1.1338967032478635, 1.3577507933458828, 1.5756024301693747, 1.7807805532494545, 1.966925567405371, 2.128151902022372, 2.2592270760933273, 2.3557787560453414, 2.414400702676339, 2.4327346302159634, 2.409580721204078, 2.3449652843464, 2.2401012221699292, 2.0973553408401377, 1.9202343083671973, 1.7132548574427084, 1.4817934576470773, 1.2319443607060125, 0.9703521520431017, 0.7039727345824245, 0.4398653585670622, 0.1849833888282052, -0.054063096247453195, -0.2712257052360876, -0.4612136335304151, -0.6196842829484909, -0.7433936611753436, -0.8303100727191013, -0.8797200167124802, -0.8922719200961816, -0.8699572594543719, -0.8160758742821104, -0.7351806741128892, -0.6329196851512371, -0.5158619826339811, -0.39131762432227934, -0.2671075004965014, -0.15128667398190632, -0.05188182291688866, 0.023377799923290508, 0.0673498501753458, 0.07374503199443228, 0.03737362121287014, -0.045624167446259634, -0.17759414867334286, -0.35922619745465756, -0.5894429561044864, -0.8653534969754009, -1.182272738173915, -1.533780786074007, -1.9118349910451709, -2.306944107421216, -2.708410005609481, -3.104600313119053, -3.483240121571494, -3.8317338904749723, -4.137574015856903, -4.388719207541699, -4.57389903816595, -4.682964667158394, -4.707334022423528, -4.640240491879853, -4.476912113104187, -4.214811285587579, -3.8539035532503494, -3.396614292963332, -2.847806265364741, -2.2147844332519506, -1.5072085468885388, -0.7368041758615128, 0.0828923586937804, 0.9368386674473674, 1.808845670645657, 2.6819921767038037, 3.5390760019856145, 4.363105383337193, 5.137683377065188, 5.847424239468667, 6.47847435435833, 7.018847376864878, 7.458676025822593, 7.790514177808613, 8.00963460822381, 8.114002965256507, 8.104325621952848, 7.984132818550926, 7.75958751806973, 7.439184226782438, 7.033589634453685, 6.555387756433254, 6.018522963280287, 5.437882148000843, 4.8290035693681945, 4.207539663836195, 3.588703495178748, 2.9868898353056554, 2.41535924264255, 1.8857616059521978, 1.4078270824357098, 0.989182812647485, 0.6351914389679142, 0.34882300765189445, 0.13066850950188444, -0.02096089386142287, -0.10989120118478038, -0.14186271938702757, -0.1242292850657248, -0.06560874470297628, 0.02448484270953665, 0.13604462224963204, 0.2590078867459349, 0.38365084567181007, 0.5009567702824099, 0.602978438193752, 0.6831571415029236, 0.736513842218862, 0.7598150906154663, 0.7516959440084673, 0.7126358572152435, 0.644850698033287, 0.5521629345524436, 0.43978269526422487, 0.3139664108288286, 0.18167482316762562, 0.05020323859688075, -0.07325289073456401, -0.1820192600104047, -0.27033933188316955, -0.33377517170590776, -0.36953290051954335, -0.3767187302072533, -0.3565581535211578, -0.3125219823037762, -0.25031238052001054, -0.17779011459165261, -0.10482751421010753, -0.04301495129780327, -0.005296120893144813, -0.005548369954209626, -0.05807780359938929, -0.1770702700482768, -0.37603255825009657, -0.6671994061200895, -1.0609735745548992, -1.565419842288211, -2.1857886100661514, -2.924107882056659, -3.7789134571323064, -4.745075225425808, -5.813718946465092, -6.97228374241125, -8.204692266621086, -9.491716993925383, -10.811449278160943, -12.139729569594664, -13.450734995555775, -14.717927057320704, -15.914721879534103, -17.015029264328106, -17.994094432991265, -18.829688795069753, -19.50238264742025, -19.995965637356736, -20.298306338655888, -20.40199654228424, -20.304055872163783, -20.006042511164182, -19.514520602985957, -18.840718362634608, -17.999836601166606, -17.010824415350612, -15.896015879692287, -14.680234973413462, -13.389922729743658, -12.052624012678038, -10.69603895015128, -9.347194876276722, -8.031685453844837, -6.773039180386049, -5.5919718944028975, -4.50594827772215, -3.5287959144767687, -2.6704083334420345, -1.936630849715855, -1.3293237687057258, -0.846499368197495, -0.48262293174210275, -0.22903277865429675, -0.0744329418653529, -0.005479812558075782, -0.007417590328143511, -0.0647158035660678, -0.16173109344188305, -0.28332448316486053, -0.41540053542159217, -0.5454181544569704, -0.6628060790614557, -0.7591983329745173, -0.8286030769999905, -0.8675246292224581, -0.8748461379011048, -0.8516193609342192, -0.8008420872087688, -0.7271218610457713, -0.6361926334454032, -0.5344737560653705, -0.42865029417758677, -0.32516720522948855, -0.2297874949868889, -0.14724851165207303, -0.08096495693682856, -0.032796404055014, -0.002946796141903696, 0.010031128041461779, 0.009139526731953649, -0.001269457316135396, -0.01578828332382553, -0.028324915545383113, -0.03252886973420337, -0.022245618064476815, 0.008010808943208094, 0.06260666947005245, 0.14439143707338786, 0.25435636913025417, 0.39137756988420036, 0.5520852757581842, 0.7308342651289631, 0.9197976148982444, 1.1092299726656738, 1.2878044986740567, 1.4430511986192904, 1.5619500092698733, 1.6315947410484974, 1.639802488170321, 1.5758114821004576, 1.4310071055926779, 1.1995210832497725, 0.8787104373936083, 0.46965609010141623, -0.022564251687420954, -0.5887880763855505, -1.2158083299842903, -1.8865395838671923, -2.5804464760244117, -3.2741768856554074, -3.942258821844399, -4.557896791225641, -5.09388937056641, -5.523819045189716, -5.823055254868684, -5.969589340327634, -5.94498210106772, -5.7355640437095, -5.332948659846058, -4.734360235360816, -3.9430698873293353, -2.9688412303377127, -1.8274946246180297, -0.5404950583280661, 0.8655097792085593, 2.3593670941102336, 3.906494404792755, 5.469948999093047, 7.011752280360106, 8.494068202099502, 9.88033209175914, 11.136596261601053, 12.23287603606535, 13.143941847078306, 13.849957865953867, 14.337476588063552, 14.59968661187634, 14.636475643009652, 14.454293627309587, 14.066024758414839, 13.490048358055958, 12.749646756183639, 11.872148427592457, 10.88762502449158, 9.827597628724067, 8.724180042020196, 7.608840969762503, 6.510991921271371, 5.457096557965514, 4.470103680765526, 3.5685725713892973, 2.766153311629875, 2.071493301569726, 1.488344880448189, 1.0156766070334533, 0.6481434164544612, 0.3767543605523611, 0.18965120306845426, 0.07295844039891652, 0.011718712441530877, -0.009166097094330404, -0.004037622225298745, 0.014320523402358457, 0.035365624195776164, 0.05131915705312558, 0.05749236913698172, 0.05241641805506482, 0.0377721424995158, 0.01810568065443694, 0.00036915033656948284, -0.006700350432584268, 0.006675113227289738, 0.05049565595240533, 0.1341137599165791, 0.2653897852608309, 0.44992641833876507, 0.6903786056967606, 0.9858942769227778, 1.3318456111646506, 1.7196594657900046, 2.136835260570012, 2.567340022117913, 2.992190947278593, 3.390015407237262, 3.7379342471202834, 4.0128594630313605, 4.192356005139328, 4.255603591369296, 4.184755521406089, 3.9660518587117233, 3.590310889215305, 3.0536468057099255, 2.3583411869080577, 1.5127719541543754, 0.5311975409839595, -0.566350966859929, -1.754567538424895, -3.003938582891585, -4.281716786850039, -5.5530657874962515, -6.782422090701385, -7.934843215799839, -8.977387024178729, -9.88056550758626, -10.619249315230398, -11.173672298458646, -11.530539910055378, -11.683323506690714, -11.63215988198164, -11.384098413732932, -10.95303055770366, -10.35844924346112, -9.624555894619194, -8.77972277091558, -7.855021416985451, -6.882543819411681, -5.894265659879179, -4.921044894318789, -3.991007171177535, -3.1284785714137717, -2.353299767472916, -1.6801850374222431, -1.1182433784578414, -0.6709479608030295, -0.3363378532088302, -0.10745544458769417, 0.026970679300938834, 0.08167631136703633, 0.07385703421631028, 0.022055995521590144, -0.054928943341280144, -0.13912663762327449, -0.21438884767583125, -0.2672039218758526, -0.28735880443564094, -0.26841200226937073, -0.20783352373639327, -0.1069495809385705, 0.02928744604417015, 0.19283450901869528, 0.3732715563675935, 0.5585975986407212, 0.7361484033674982, 0.8935650371148869, 1.0196879188075814, 1.105424264685485, 1.1444744155600124, 1.1338135463539853, 1.0740199590129962, 0.9694258978410276, 0.8278993751913418, 0.6604459177374369, 0.48066330293335363, 0.30391231212796127, 0.14637150936456442, 0.024068435983156493, -0.04816645852941745, -0.057759407134709784, 0.004759522734090526, 0.1449881392956055, 0.3640415539023423, 0.6583002762252281, 1.01936738789982, 1.434218276735821, 1.8857113097969052, 2.3534557574581285, 2.81469820673267, 3.24542784946991, 3.621620876380501, 3.9206926322204882, 4.122717611561158, 4.211517734084817, 4.1756454704513, 4.009432951230669, 3.71346263437584, 3.2945808791349194, 2.765857093751315, 2.146415539950212, 1.4604957197621637, 0.736341387670376, 0.005059495159576983, -0.7007937373678383, -1.3488478754491924, -1.9083963553090675, -2.3519247355372745, -2.6566244974486803, -2.8054101473486646, -2.787770127652303, -2.6005101687828502, -2.247991957585052, -1.7418596506577861, -1.1006030690417463, -0.34872155430128027, 0.4843891548917315, 1.3657954535439258, 2.260639521539099, 3.1338216112893984, 3.951511125578584, 4.682726234956029, 5.300948107282005, 5.785079704055677, 6.120330458828176, 6.298995996908675, 6.32051581457989, 6.1910712693794885, 5.923346265614908, 5.53581495275919, 5.051182073385511, 4.49509270941716, 3.8950972828917134, 3.278893788540734, 2.6726280219436154, 2.099722236862383, 1.5799241960052954, 1.1281113405730896, 0.7537098206618102, 0.4605553031372688, 0.24696065851112864, 0.10605639642146202, 0.026556993041313072, -0.006233192137707326, -0.009261644309557648, -0.00042281636035106335, 0.002792126771039442, -0.015409708115115316, -0.06795303195200976, -0.16391757051248584, -0.3078396844536142, -0.49931097186225976, -0.7329059311243534, -0.9984765666052547, -1.2818082273162477, -1.5654506985619734, -1.8298955326290387, -2.055012659646636, -2.2213969124895847, -2.3116735045882297, -2.312018910746902, -2.21342386840509, -2.0123600771730756, -1.711393738783775, -1.3197143613337563, -0.8528407100605745, -0.3319549886901247, 0.2168876617788047, 0.7639411284567964, 1.2773897241672814, 1.7249592300559486, 2.0757574485699273, 2.3021768850971136, 2.3813822797248108, 2.296744903575586, 2.0393219968040146, 1.6085253587705037, 1.0123011511292224, 0.2672302985827992, -0.6018883942522624, -1.5632623749919137, -2.5794724612608113, -3.6090704776229745, -4.60861156027307, -5.534861649328147, -6.34687118570374, -7.008105652649914, -7.48815871253602, -7.764491622387988, -7.8237269714932305, -7.662172483199144, -7.285889764778176, -6.7108333718148385, -5.962074638468054, -5.0721259687199955, -4.0794193260963505, -3.026768776728205, -1.958906814412888, -0.9201267540148728, 0.04773152175982433, 0.907332810866677, 1.6277614024307177, 2.1858291117360955, 2.567114736809228, 2.766656693102713, 2.788763370103099, 2.6464684340343894, 2.36074667686992, 1.959191584087495, 1.4741405825249816, 0.9407784588010255, 0.39513456603790864, -0.12786224680402208, -0.596400801147123, -0.9835293853092735, -1.2685008379943084, -1.4376529451402624, -1.4850472159805992, -1.4125614156537998, -1.2294600365997592, -0.9516043743056765, -0.6002348478135119, -0.200475884125082, 0.2202401745765609, 0.6339678457549499, 1.014205045032122, 1.3373027214286919, 1.583787292111109, 1.7397458594061237, 1.7975148097067772, 1.7557465599429105, 1.619428912942988, 1.399644046584321, 1.1123956628943832, 0.7774191017719096, 0.41693988387843617, 0.05408748431697253, -0.2887606517069923, -0.5913909312181435, -0.8371423920192802, -1.0139873342180068, -1.1151900544966518, -1.139751270512996, -1.0924779835649796, -0.9834432310715692, -0.8272059375364539, -0.641873720054434, -0.44769888116039264, -0.2655807034583728, -0.11560108664433584, -0.015571738586738732, 0.020320631019974732, -0.017436225614269434, -0.13291365003476402, -0.324340640583011, -0.5841029113315787, -0.899142694522958, -1.2517603272368885, -1.6206707613534872, -1.9823037052564418, -2.3124801714013077, -2.5879926520159664, -2.7879862429786417, -2.895424868990758, -2.8985908092407904, -2.7916649072581254, -2.5751296444760645, -2.2560986956901785, -1.8480337273556142, -1.36974460706597, -0.8443815223917239, -0.2981647604768234, 0.24134851703041432, 0.7469230636070339, 1.1932939389577009, 1.5588540960005086, 1.8269317689435538, 1.9867218212082651, 2.034132528424299, 1.9719439574485964, 1.809470241681544, 1.5619477780492512, 1.2495866596193086, 0.8960026681195097, 0.5266204311616716, 0.1669580808075467, -0.15922098400582463, -0.4315842408828493, -0.6346841293133734, -0.7591837546100038, -0.8025289827939459, -0.7692020086447193, -0.6706491983445505, -0.5245595453323962, -0.3536439675376018, -0.1841884340369779, -0.04430996067519919, 0.03810394630662291, 0.0373859724335507, -0.06798820648078947, -0.29365067286048574, -0.6479785311240562, -1.1311262091360736, -1.7345712400251116, -2.441249014412054, -3.2261256869835493, -4.057405011925204, -4.898310173187789, -5.708932831937633, -6.448348739209251, -7.077466809405537, -7.5611288743798, -7.869987063246008, -7.982622522210222, -7.88744725095833, -7.582758160909272, -7.077063572095414, -6.389554698911408, -5.548747132199881, -4.590439738036227, -3.5562052469602827, -2.491531491263575, -1.4425130693645358, -0.45330358263797155, 0.4359545588797518, 1.1915759371275239, 1.7884005445091118, 2.210985147937352, 2.4543249846618425, 2.524070932154138, 2.435955662668132, 2.2147085789297845, 1.8922844957297575, 1.5057107717821177, 1.0947470510376418, 0.699356988239495, 0.35686723286162675, 0.09975224033125404, -0.046355979371806966, -0.06440916826246111, 0.05296819240530363, 0.303222480955859, 0.6739923617483548, 1.1439128358934096, 1.6842768215288, 2.260887372701855, 2.836207328086068, 3.3718439770286315, 3.8314718075735845, 4.1830624253795685, 4.400807434776669, 4.4668464468671, 4.373013597650684, 4.121144669799854, 3.7226748720346565, 3.198112627849953, 2.57623277492462, 1.8918308453293196, 1.1834179000142682, 0.49100296222386675, -0.14639220353756544, -0.6933810680811368, -1.1203069232947171, -1.405082198628753, -1.5346903685044246, -1.5057859760329706, -1.324773082164002, -1.0074162009542431, -0.5777148239349637, -0.06621247014983014, 0.49199411723172054, 1.059644906379523, 1.5997846847787538, 2.0779776535347474, 2.464585148782892, 2.736644559934403, 2.8793036384725688, 2.8864310515540277, 2.760920381102375, 2.514206121710038, 2.1654962293352282, 1.7401128430113737, 1.267518740544666, 0.7792513261328046, 0.30680734799207704, -0.1207690441244617, -0.47884155934596345, -0.7487065498179192, -0.9189721987293377, -0.9861780230037313, -0.9546581397936416, -0.8360596600727502, -0.648583735091153, -0.41511771680801635, -0.16122619579917544, 0.08684700092890134, 0.3041866848124237, 0.46956986258256295, 0.5673287027922527, 0.5887323648832109, 0.5328310283529839, 0.40697372321181335, 0.22654839256273782, 0.014047654250174532, -0.20233648206186652, -0.3905651323360928, -0.517092121369538, -0.5492735148029068, -0.4577892994497388, -0.2190479769444716, 0.18282244175118348, 0.7544315722840861, 1.4920024758898929, 2.3812289343912387, 3.3976788655153682, 4.507485230284345, 5.669038874581669, 6.835854848127976, 7.95846144104556, 8.98685597773724, 9.87449498401304, 10.580988656248742, 11.073305153365542, 11.327897247003499, 11.333187740496163, 11.08925177821977, 10.607571974255999, 9.912439177739445, 9.03938843127001, 8.030373565218175, 6.930807260725147, 5.78591286604124, 4.641907522573246, 3.54460827766197, 2.5391009677651124, 1.662133389028841, 0.9326479440904492], 'positive_zeros': ['0.53165674816913544331693987421417', '0.54543966784961438716635172697423', '0.811138877794429212437438204469684', '1.50303773501428859636856697213569', '1.59980091469193879661132269132819', '2.28081684856554294278192896635399', '2.63450772598622689659552819522092', '2.73801624779992579458299459931237', '3.23027113170659459449867045506112', '3.52699034977226172506393414421082', '3.59512446852714993596139320886703', '4.07638563962504100767418256541797', '4.65525050074578693126863890415724', '4.74178007411790854998854416100219', '5.03430027716428851880899563510739', '5.26305641055301408736743077913045', '5.26649295916102066225488697585007', '6.17421100959674518707073979630485', '6.18184632296640829864592583884657', '6.57683677947969463346714252114782', '6.62526604134952859068826132781602', '6.71126608463499125381783007705000', '7.04807935144683120879317297866935', '7.38972688672310205566512998695075', '8.022183387557427283346709360863988', '8.055421777994481797335486752037369', '8.191875417616264626066574729469997', '8.221369700145145211813844998833662', '8.639575829049295757144312262544832', '9.188736839143973598558126814002942', '9.251547355972995621733537971655981', '9.400835539203121263593938980059477', '9.707677973087422992148568227120147', '9.755013691841420947030381622494402', '10.14270081095083580207701261713407', '10.36104433762695947101427960217821', '10.84020334647214684597804972587717', '10.88171391089330536346112034657568', '10.90404054043884902667984011189881', '11.26067956501859052248184691165605'], 'prelabel': '8-288e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.796362270077901, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e4-0', 'trace_hash': 214969634383713503, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53165674816913544331693987421', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.54543966784961438716635172697', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.811138877794429212437438204470', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4552103.856286754, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6879707136, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 2336, 0, 7028, 0, 0, 0, 0, 0, 12928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4568, 0, 0, 0, 0, 0, -54720, 0, -24092, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 206688, 0, 39976, 0, 0, 0, 0, 0, 247872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84632, 0, 0, 0, 0, 0, 0, 0, -99576, 0, 0, 0], 'euler11': [1, 0, -296436, 0, 49128544726, 0, -7688786399022036, 0, 672749994932560009201], 'euler13': [1, 0, -894228, 0, 396323515894, 0, -123276923449147572, 0, 19004963774880799438801], 'euler17': [1, 200, 5544924, 837463800, 11719230862342, 1189078838676600, 11178532962453270876, 572484610301963158600, 4064231406647572522401601], 'euler19': [1, 0, -6794580, 0, 21506967947254, 0, -41658020173929518580, 0, 37589973457545958193355601], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2336, 21475164, -38524875168, 201526726533862, -247959310613430624, 889641122260951313436, -622859910044817949737952, 1716155831334586342923895201], 'euler29': [1, 0, -31255380, 0, 976386653995702, 0, -13149364445546436331380, 0, 176994576151109753197786640401], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -12928, 171809404, -1210606426240, 8258394345291910, -34658634178395322240, 140819847487712379252604, -303358907030568099702406528, 671790528819082282036142601601], 'euler37': [1, 0, -241262580, 0, 24149916431784598, 0, -1160131471837211087790420, 0, 23122483666661158726686253786801], 'euler41': [1, -4568, 298423164, -1198914790440, 49546596595861030, -138901712943089518440, 4005632460629736828616764, -7103689102881345176939129368, 180167782956420929503029846064801], 'euler43': [1, 0, -466346868, 0, 96250708269010006, 0, -10078447089637504314882132, 0, 467056167777397914441056671494001], 'euler47': [1, 54720, 1931246012, 44907785415360, 798240538650932934, 10299376360440237107520, 101581864365107425641014588, 660106421756890550022503568960, 2766668711962335809450748011342401], 'euler5': [1, 0, -7028, 0, 24404246, 0, -68632812500, 0, 95367431640625], 'euler53': [1, 0, -1039152180, 0, 595616955270391126, 0, -181734696085008281686796820, 0, 30585627290848204916791848989276401], 'euler59': [1, 0, -1537424180, 0, 1399694789142612374, 0, -785803255327500899406476180, 0, 261240335504588722483367157995242801], 'euler61': [1, 0, 741098540, 0, 1478044222094100534, 0, 528657390352711267792502540, 0, 508858109619679129936596364708525201], 'euler67': [1, 0, -1366835860, 0, 3274116308996825526, 0, -2491520078225018774658761140, 0, 3322737661703085672358476688602579601], 'euler7': [1, 96, 33308, 3101664, 882709158, 52129666848, 9408685593692, 455765904954528, 79792266297612001], 'euler71': [1, -206688, 23115456284, -1658044175781600, 83709015377411926950, -2991491967199766085741600, 75246439997141832953748917084, -1213921193333468850324130816925088, 10596610576391421032662867140133202401], 'euler73': [1, -39976, 5482725884, -184476226332888, 16711464530914690982, -382432424394548674450584, 23562704376262671569058486716, -356157618131462402903834279923432, 18469587772135192290560825407466407201], 'euler79': [1, -247872, 35071990844, -3205725049525056, 210603881501493890886, -9864196777075665475633344, 332071292078352972502059027644, -7221606832174341205547651588334528, 89648251976843595444986830377401534401], 'euler83': [1, 0, -10047855188, 0, 55381071937674414326, 0, -155902934940088013801502343412, 0, 240747534123068430155382383568465195601], 'euler89': [1, -84632, 10375446204, -835864615445736, 100786271186270136166, -4667517703964513457559464, 323524257681558785491362500604, -14736172741300491554778947241492568, 972299657790850297934682879408841327201], 'euler97': [1, 99576, 35261587868, 2487280198131144, 458735253741197890758, 21359121375850509036664008, 2600274564648869486082452773532, 63056620409484939904645246454552568, 5437943429267472574499737549036572950401], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -7028, 0, 24404246, 0, -68632812500, 0, 95367431640625], [1, 96, 33308, 3101664, 882709158, 52129666848, 9408685593692, 455765904954528, 79792266297612001], [1, 0, -296436, 0, 49128544726, 0, -7688786399022036, 0, 672749994932560009201], [1, 0, -894228, 0, 396323515894, 0, -123276923449147572, 0, 19004963774880799438801], [1, 200, 5544924, 837463800, 11719230862342, 1189078838676600, 11178532962453270876, 572484610301963158600, 4064231406647572522401601], [1, 0, -6794580, 0, 21506967947254, 0, -41658020173929518580, 0, 37589973457545958193355601], [1, -2336, 21475164, -38524875168, 201526726533862, -247959310613430624, 889641122260951313436, -622859910044817949737952, 1716155831334586342923895201], [1, 0, -31255380, 0, 976386653995702, 0, -13149364445546436331380, 0, 176994576151109753197786640401], [1, -12928, 171809404, -1210606426240, 8258394345291910, -34658634178395322240, 140819847487712379252604, -303358907030568099702406528, 671790528819082282036142601601], [1, 0, -241262580, 0, 24149916431784598, 0, -1160131471837211087790420, 0, 23122483666661158726686253786801], [1, -4568, 298423164, -1198914790440, 49546596595861030, -138901712943089518440, 4005632460629736828616764, -7103689102881345176939129368, 180167782956420929503029846064801], [1, 0, -466346868, 0, 96250708269010006, 0, -10078447089637504314882132, 0, 467056167777397914441056671494001], [1, 54720, 1931246012, 44907785415360, 798240538650932934, 10299376360440237107520, 101581864365107425641014588, 660106421756890550022503568960, 2766668711962335809450748011342401], [1, 0, -1039152180, 0, 595616955270391126, 0, -181734696085008281686796820, 0, 30585627290848204916791848989276401], [1, 0, -1537424180, 0, 1399694789142612374, 0, -785803255327500899406476180, 0, 261240335504588722483367157995242801], [1, 0, 741098540, 0, 1478044222094100534, 0, 528657390352711267792502540, 0, 508858109619679129936596364708525201], [1, 0, -1366835860, 0, 3274116308996825526, 0, -2491520078225018774658761140, 0, 3322737661703085672358476688602579601], [1, -206688, 23115456284, -1658044175781600, 83709015377411926950, -2991491967199766085741600, 75246439997141832953748917084, -1213921193333468850324130816925088, 10596610576391421032662867140133202401], [1, -39976, 5482725884, -184476226332888, 16711464530914690982, -382432424394548674450584, 23562704376262671569058486716, -356157618131462402903834279923432, 18469587772135192290560825407466407201], [1, -247872, 35071990844, -3205725049525056, 210603881501493890886, -9864196777075665475633344, 332071292078352972502059027644, -7221606832174341205547651588334528, 89648251976843595444986830377401534401], [1, 0, -10047855188, 0, 55381071937674414326, 0, -155902934940088013801502343412, 0, 240747534123068430155382383568465195601], [1, -84632, 10375446204, -835864615445736, 100786271186270136166, -4667517703964513457559464, 323524257681558785491362500604, -14736172741300491554778947241492568, 972299657790850297934682879408841327201], [1, 99576, 35261587868, 2487280198131144, 458735253741197890758, 21359121375850509036664008, 2600274564648869486082452773532, 63056620409484939904645246454552568, 5437943429267472574499737549036572950401]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/6/d/b'], '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': '8-288e4-1.1-c5e4-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '8-288e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.796362270077901, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e4-0', 'trace_hash': 214969634383713503, 'z1': {'__RealLiteral__': 0, 'data': '0.53165674816913544331693987421', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '673954995931993147638310061603,691426922337849756605936147534,1028240685304560608413576063256,2027988589754906635961640709826', 'Lhash_array': ['673954995931993147638310061603', '691426922337849756605936147534', '1028240685304560608413576063256', '2027988589754906635961640709826'], 'factors': ['2-288-8.5-c5-0-6', '2-288-8.5-c5-0-7', '2-288-8.5-c5-0-12', '2-288-8.5-c5-0-20'], 'label': '8-288e4-1.1-c5e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/6/d/b'}