Starting with polynomial:
P : t
Extension levels are: 1 34 36
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^35 - 595/69*t^33 + 52360/1541*t^31 - 1623160/20033*t^29 + 23535820/180297*t^27 - 14121492/94001*t^25 + 706074600/5546059*t^23 - 369848600/4581527*t^21 + 176518650/4581527*t^19 - 176518650/12780049*t^17 + 47071640/12780049*t^15 - 9169800/12780049*t^13 + 59603700/600662303*t^11 - 16811300/1801986909*t^9 + 100867800/180799353203*t^7 - 20173560/1058967640189*t^5 + 4202825/13766579322457*t^3 - 741675/509363434930909*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 89389/5037*t^69 + 1346186909/8926075*t^67 - 7954810930399/9735150425*t^65 + 3080571657300729688/971699062516875*t^63 - 4509346482815508710136/480775102820849375*t^61 + 357980206852187549778164990648/16271106478187095411078125*t^59 - 819425452494274766141526582616232/19507953541483399459210734375*t^57 + 95149984548062639639787880203924139868/1430951172867679024454728442578125*t^55 - 2013796185185304154037543632073135464245060676/22764364291119041188741172875035689296875*t^53 + 1174618901297983883215874476868965535566952043572/11758008914516674576260181272718905556640625*t^51 - 140667105918364439191271835727239380482928494348/1458072999811016196288935844164769755859375*t^49 + 30769816671619461718653985763061647114181161526911794069522504/384108324948714874178020014233767362230479485920654296875*t^47 - 29902145304008293178436058373549255074777366465276345224926877112/520826371077801068435979521002207664416728237409305908203125*t^45 + 2748882878939679946018178660982502788736864273697738219074473596827448/77202382332846384485969931053446687767416302591313308831787109375*t^43 - 799648108440232224022142460782198617270240377314315762617270000452909801896/41790836318972585398072854519333629955028357666538658212440264892578125*t^41 + 8975754459795922814309788593347996608834876619624091064738115059543614048994326154/1007019948932213961428084716874105618398238888610492216052897503173675537109375*t^39 - 4264216536964141943996608749605187705594174605736437608324811587976615685613255834126/1185623974233858165817778613966879684102357308931486438064125503928863067626953125*t^37 + 462142567402153481534428427457921863410263516915743852419026508150789111402194984193449762974/368191684544596562621123819974356805162126861844970115406192941098762019742443084716796875*t^35 - 20343334908104078299367345904379642481810443659268118735814700135701598541207686835599524902/53836431185512438568130709811376541259000062152121680740065186345533270113600921630859375*t^33 + 3669050311605962750894630049715837015019185605911634794995456089045240379635972507831416504/37522361129296548092939585626110922695666709984812080515803008665068642806449127197265625*t^31 - 1755554449615040309914457006107136889993151523821037896616759318349317862381385918562541016/81096715989124797491192007643530058729344179644593851437380696147083840904261016845703125*t^29 + 4000502739669895794264893435468873898755235811074208309311564852521752348864160499705322712/981549907316648411014082575271691400482751967422497994983469805090566488186055755615234375*t^27 - 9057313132759368788279662456658992410458867443500846344788122201216752902753966275753032/13982192411918068532964139248884492884369686145619629558169085542600662224872589111328125*t^25 + 2938226327347468453349874038097870789426895149916096080369775217376179638800747040274156/34116549485080087220432499767278162637862034195311896121932568723945615828689117431640625*t^23 - 93087994611047443465584749096234742134684851470100337918885794781474571196572368594948/9828041109512724498050655013173132645503617848870364867489991315733229019238739013671875*t^21 + 23166321069339866604608653943464480289433828542895805390102493413880324957167615352956/27259195989148095348613565387825246127614640294329747364708773727400595398403778076171875*t^19 - 5351762876212524641973656983149458670624057157346685387812429591577043857960244589572/87516366070422832435022499403017895462341739892321820486696589335338753647506866455078125*t^17 + 240248288539765656240350969305647661092349692576623701662436929358222970257021521874904/69575511025986151785842887025399226892561683214395847286923788521594309149767958831787109375*t^15 - 98703143725287307283176863305093979704517851282903850825770520724537424282244348562136/663286538447734647025035522975472629709088046643907077468673450572532413894454540863037109375*t^13 + 240691653021829938538544537477552782627360997468703033211083212017027949448055472744/51022041419056511309618117151959433054545234357223621343744111582502493376496503143310546875*t^11 - 3488852342889405759428314031518521027270473440963365738959053168111012290753278417032/33354499985857761166133080039976389372294070932981369189351264217252311806398759463958740234375*t^9 + 9445179604203901624737008429123651357757962942355553919859318913981744974370618459/6261955936042261674867896252715873866829155079371981188805409757261928270166816910858154296875*t^7 - 4142918584565436516626704767084342657724491891541388321448831933907580641517513519/328094918161542029771439774249440954283023377478019350522703612071664897180589104531097412109375*t^5 + 6884903456863841944132147163095245134293067056058234069947440736660806843904853767/137209294775156876850416113591116207081160376461307692388594650568370260000922363514904937744140625*t^3 - 35511686012536238048779054127617403430643639568420470730395355083643701162647449/594573610692346466351803158894836897351694964665666667017243485796271126670663575231254730224609375*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.99770656909960029726 + 2.0002962268133262817e-862j)  +/-  (7.56e-230, 7.56e-230j)
| (-0.97043761603922983322 - 2.0351640212637257463e-866j)  +/-  (6.92e-230, 6.92e-230j)
| (-0.95883869699584307892 - 2.5444942414826607484e-874j)  +/-  (4.33e-230, 4.33e-230j)
| (-0.99961929856058782042 + 2.6814521059084183585e-888j)  +/-  (2.83e-230, 2.83e-230j)
| (0.91285426135931761446 + 9.8396961975255092602e-907j)  +/-  (5.73e-231, 5.73e-231j)
| (0.93000375305070609923 - 1.1452148712524088304e-906j)  +/-  (1.29e-230, 1.29e-230j)
| (0.97043761603922983322 - 6.4456563057672251193e-905j)  +/-  (6.94e-230, 6.94e-230j)
| (-0.89391630583904940482 + 4.8089032211424192879e-905j)  +/-  (2.35e-231, 2.35e-231j)
| (0.98013165785134098802 - 1.5541554709185067626e-904j)  +/-  (9.08e-230, 9.08e-230j)
| (-0.99382029303890921226 - 4.3594667674711725059e-906j)  +/-  (1.02e-229, 1.02e-229j)
| (0.89391630583904940482 + 1.3994261247013475428e-921j)  +/-  (2.39e-231, 2.39e-231j)
| (0.98793576444385149804 - 3.5550600081191295639e-917j)  +/-  (1e-229, 1e-229j)
| (-0.85081354468109158704 + 1.059509998645138132e-921j)  +/-  (2.75e-232, 2.75e-232j)
| (-0.87321912502522233152 - 4.8679989722366855482e-921j)  +/-  (8.79e-232, 8.79e-232j)
| (0.99382029303890921226 - 2.1347782435874057343e-918j)  +/-  (1.01e-229, 1.01e-229j)
| (0.82674989909222540683 + 2.8760097049051833332e-925j)  +/-  (8e-233, 8e-233j)
| (0.85081354468109158704 - 5.4924598683708618445e-922j)  +/-  (2.94e-232, 2.94e-232j)
| (-0.93000375305070609923 + 4.8691315996147830869e-918j)  +/-  (1.27e-230, 1.27e-230j)
| (-0.77381025228691255527 - 6.1821849805701923285e-926j)  +/-  (5.12e-234, 5.12e-234j)
| (-0.91285426135931761446 + 1.4115772900368552734e-920j)  +/-  (5.82e-231, 5.82e-231j)
| (0.99770656909960029726 + 5.551658430127510922e-922j)  +/-  (7.56e-230, 7.56e-230j)
| (0.8010672131257057147 - 1.4745280223248808358e-926j)  +/-  (2.08e-233, 2.08e-233j)
| (-0.94534514820782732954 - 1.3387714500540636547e-920j)  +/-  (2.55e-230, 2.55e-230j)
| (-0.8010672131257057147 - 9.7515325236472218172e-937j)  +/-  (2.11e-233, 2.11e-233j)
| (-0.82674989909222540683 - 2.986344935044663308e-935j)  +/-  (7.99e-233, 7.99e-233j)
| (0.94534514820782732954 + 8.268284889546683002e-933j)  +/-  (2.7e-230, 2.7e-230j)
| (0.71481450155662878326 - 1.3231252376405438624e-939j)  +/-  (1.97e-235, 1.97e-235j)
| (0.74503897566640677164 + 1.8885236154414007176e-938j)  +/-  (1e-234, 1e-234j)
| (0.99961929856058782042 + 4.5433442307254340692e-932j)  +/-  (2.94e-230, 2.94e-230j)
| (-0.61598571048722183054 - 5.1886661450183578094e-946j)  +/-  (6.25e-238, 6.25e-238j)
| (-0.13233927061341662561 - 3.3302351265672178538e-961j)  +/-  (9.16e-252, 9.16e-252j)
| (0.65022436466589038868 + 4.2897495065656515693e-947j)  +/-  (5.01e-237, 5.01e-237j)
| (0.68319041848815657678 - 4.0430785713440122796e-946j)  +/-  (3.13e-236, 3.13e-236j)
| (-0.98793576444385149804 - 3.2422932404371673694e-937j)  +/-  (1.06e-229, 1.06e-229j)
| (-0.65022436466589038868 + 1.0744456129855217025e-964j)  +/-  (4.42e-237, 4.42e-237j)
| (-0.74503897566640677164 - 6.1526303862298359939e-962j)  +/-  (1e-234, 1e-234j)
| (0.77381025228691255527 + 3.0715217745206910595e-961j)  +/-  (5.2e-234, 5.2e-234j)
| (0.58054534474976450993 + 1.7735488603011552018e-967j)  +/-  (7.5e-239, 7.5e-239j)
| (0.95883869699584307892 + 5.7919573502059869701e-959j)  +/-  (4.45e-230, 4.45e-230j)
| (-0.71481450155662878326 - 1.6800386734389395909e-963j)  +/-  (1.88e-235, 1.88e-235j)
| (-0.54396835169625813821 - 6.4131073492439224252e-969j)  +/-  (7.67e-240, 7.67e-240j)
| (-0.98013165785134098802 + 2.237621485837984436e-966j)  +/-  (9.6e-230, 9.6e-230j)
| (0.54396835169625813821 + 1.1748887459707517934e-987j)  +/-  (7.24e-240, 7.24e-240j)
| (0.61598571048722183054 + 1.9606287112927914334e-984j)  +/-  (6.18e-238, 6.18e-238j)
| (-0.088371343275659263601 + 2.6165332116569534767e-1000j)  +/-  (4.68e-253, 4.68e-253j)
| (-0.58054534474976450993 - 6.4236161303977490576e-986j)  +/-  (7.19e-239, 7.19e-239j)
| (-0.68319041848815657678 + 4.9098429121277256566e-983j)  +/-  (3.22e-236, 3.22e-236j)
| (0.87321912502522233152 + 2.8747617666261062608e-997j)  +/-  (8.83e-232, 8.83e-232j)
| (0.46768618346152964902 + 1.7299308482430582612e-1008j)  +/-  (6.45e-242, 6.45e-242j)
| (0.17605106116598956997 + 9.3633958773584224968e-1016j)  +/-  (1.98e-250, 1.98e-250j)
| (-0.38775069602784231261 + 9.5537236948750481537e-1008j)  +/-  (3.71e-244, 3.71e-244j)
| (-0.50632277324148861502 + 3.1424476608239479195e-1006j)  +/-  (7.66e-241, 7.66e-241j)
| (0.13233927061341662561 + 3.2855797169593195275e-1020j)  +/-  (9.24e-252, 9.24e-252j)
| (0.38775069602784231261 - 5.5203789169974483284e-1011j)  +/-  (3.63e-244, 3.63e-244j)
| (0.50632277324148861502 + 1.1775428913098489157e-1009j)  +/-  (7.36e-241, 7.36e-241j)
| (1.0675081805487886078e-1044 + 1.3705817617711963678e-1044j)  +/-  (1.23e-1042, 1.23e-1042j)
| (-0.46768618346152964902 - 1.2541742051905865049e-1008j)  +/-  (6.75e-242, 6.75e-242j)
| (-0.30477400147105037962 + 7.2695572851900238926e-1013j)  +/-  (1.33e-246, 1.33e-246j)
| (0.044230407960476319025 + 5.4162438841239789572e-1021j)  +/-  (2.29e-254, 2.29e-254j)
| (0.42813754151781425419 - 2.5208401210610437803e-1010j)  +/-  (4.98e-243, 4.98e-243j)
| (0.088371343275659263601 + 2.104080031950593641e-1020j)  +/-  (5.04e-253, 5.04e-253j)
| (-0.26235294120929605797 - 1.5741977873055637252e-1013j)  +/-  (8.19e-248, 8.19e-248j)
| (-0.42813754151781425419 + 1.2833436414775621117e-1008j)  +/-  (5.01e-243, 5.01e-243j)
| (-0.044230407960476319025 + 1.6788597363426516457e-1020j)  +/-  (2.56e-254, 2.56e-254j)
| (0.30477400147105037962 - 1.6635754453456588978e-1013j)  +/-  (1.39e-246, 1.39e-246j)
| (0.26235294120929605797 - 8.7742691521480945419e-1015j)  +/-  (8.86e-248, 8.86e-248j)
| (-0.17605106116598956997 + 2.3787782916550388979e-1016j)  +/-  (1.87e-250, 1.87e-250j)
| (-0.34660155443081394588 + 7.2453497058229990297e-1012j)  +/-  (2.39e-245, 2.39e-245j)
| (-0.21941825841501800319 + 1.5722939619226394873e-1015j)  +/-  (4.26e-249, 4.26e-249j)
| (0.21941825841501800319 - 4.1863581264111904212e-1016j)  +/-  (4.45e-249, 4.45e-249j)
| (0.34660155443081394588 - 2.5608145711441239439e-1012j)  +/-  (2.43e-245, 2.43e-245j)
-------------------------------------------------
The weights are:
| (0.0028722600144707018818 + 5.920873083273546342e-863j)  +/-  (7.79e-24, 2.43e-131j)
| (0.010644126760803645485 + 7.4718476641866150368e-863j)  +/-  (2.86e-24, 8.94e-132j)
| (0.012552138631619428563 - 6.1596283847748816735e-863j)  +/-  (2.06e-24, 6.44e-132j)
| (0.0010255091107466680101 + 1.0229755441247979913e-862j)  +/-  (2.66e-24, 8.31e-132j)
| (0.018046651129558703662 + 1.8037470910543720878e-864j)  +/-  (5.41e-26, 1.69e-133j)
| (0.016249771999849792514 - 1.608203351719947287e-864j)  +/-  (4.41e-26, 1.38e-133j)
| (0.010644126760803645485 + 1.0351497480209195715e-864j)  +/-  (5.8e-27, 1.81e-134j)
| (0.019824630731925684309 - 3.6439143765061313163e-863j)  +/-  (3.07e-27, 9.6e-135j)
| (0.0087480347678970122676 - 8.4383049247343153572e-865j)  +/-  (2.03e-27, 6.35e-135j)
| (0.0048980908903161470913 - 2.4048232845680956707e-862j)  +/-  (9.97e-26, 3.12e-133j)
| (0.019824630731925684309 - 1.9994290628660024528e-864j)  +/-  (1.31e-27, 4.08e-135j)
| (0.0068554872187842001349 + 6.5289857942280763435e-865j)  +/-  (4.66e-28, 1.46e-135j)
| (0.023241810895466635025 - 3.018522313046825399e-863j)  +/-  (7.54e-29, 2.36e-136j)
| (0.021560729002820740844 + 3.3021622591040234599e-863j)  +/-  (2.22e-28, 6.93e-136j)
| (0.0048980908903161470913 - 4.6921961260872716928e-865j)  +/-  (6.77e-29, 2.12e-136j)
| (0.024879389864978961423 + 2.6027141753860485783e-864j)  +/-  (1.34e-30, 4.19e-138j)
| (0.023241810895466635025 - 2.3987291782615365486e-864j)  +/-  (4.29e-30, 1.34e-137j)
| (0.016249771999849792514 - 4.5787351307552513057e-863j)  +/-  (7.41e-30, 2.32e-137j)
| (0.028024859270480325029 + 2.3871968591587015366e-863j)  +/-  (5.55e-33, 1.73e-140j)
| (0.018046651129558703662 + 4.0611745449061771241e-863j)  +/-  (4.46e-30, 1.39e-137j)
| (0.0028722600144707018818 + 2.8789785262537065705e-865j)  +/-  (6.77e-32, 2.11e-139j)
| (0.026478729839244521543 - 2.8083809301391943701e-864j)  +/-  (5.89e-34, 1.84e-141j)
| (0.014426148625293634297 + 5.2472389251654807557e-863j)  +/-  (5.18e-30, 1.62e-137j)
| (0.026478729839244521543 - 2.5689484952345682871e-863j)  +/-  (5.72e-33, 1.79e-140j)
| (0.024879389864978961423 + 2.7775754829949585598e-863j)  +/-  (2.96e-32, 9.24e-140j)
| (0.014426148625293634297 + 1.4141889235504267909e-864j)  +/-  (3.27e-33, 1.02e-140j)
| (0.030932985690892541246 + 3.4469056662302390455e-864j)  +/-  (1.52e-37, 4.75e-145j)
| (0.029507312940483805032 - 3.2302123557788642302e-864j)  +/-  (4.83e-37, 1.51e-144j)
| (0.0010255091107466680101 - 9.7954881548284069036e-866j)  +/-  (5.4e-34, 1.69e-141j)
| (0.034850776289816578629 - 1.7418034172781144652e-863j)  +/-  (9.57e-41, 2.99e-148j)
| (0.043854154924597308573 - 9.6681836434074546068e-864j)  +/-  (4.4e-43, 1.37e-150j)
| (0.033614549627794942441 + 3.8907703344590764569e-864j)  +/-  (1.35e-39, 4.23e-147j)
| (0.032305749674860325618 - 3.6666891190705098345e-864j)  +/-  (1.03e-38, 3.23e-146j)
| (0.0068554872187842001349 + 1.327055286439307039e-862j)  +/-  (5.15e-36, 1.61e-143j)
| (0.033614549627794942441 + 1.8451805941917835018e-863j)  +/-  (4.81e-41, 1.5e-148j)
| (0.029507312940483805032 - 2.2279767715502824232e-863j)  +/-  (2.32e-39, 7.25e-147j)
| (0.028024859270480325029 + 3.0171408532019236273e-864j)  +/-  (1.65e-38, 5.15e-146j)
| (0.036019321064432511603 + 4.3548047727187132315e-864j)  +/-  (7.19e-43, 2.24e-150j)
| (0.012552138631619428563 - 1.2239489412093556448e-864j)  +/-  (8.05e-37, 2.52e-144j)
| (0.030932985690892541246 + 2.0866056210536473437e-863j)  +/-  (1.05e-40, 3.28e-148j)
| (0.03712347803674947652 - 1.560904997831172982e-863j)  +/-  (2.17e-44, 6.77e-152j)
| (0.0087480347678970122676 - 9.4991197642731765701e-863j)  +/-  (2.26e-37, 7.06e-145j)
| (0.03712347803674947652 - 4.5940016335295853068e-864j)  +/-  (2.06e-44, 6.42e-152j)
| (0.034850776289816578629 - 4.1202832042900957732e-864j)  +/-  (1.57e-42, 4.91e-150j)
| (0.044067983466935987077 + 9.2465310656014014447e-864j)  +/-  (1.37e-48, 4.29e-156j)
| (0.036019321064432511603 + 1.6475502282913291998e-863j)  +/-  (2.72e-44, 8.5e-152j)
| (0.032305749674860325618 - 1.9596053420427336225e-863j)  +/-  (2.41e-42, 7.53e-150j)
| (0.021560729002820740844 + 2.1972510974298268655e-864j)  +/-  (6.13e-41, 1.92e-148j)
| (0.039105315164666643093 - 5.0911630036299776081e-864j)  +/-  (1.78e-47, 5.56e-155j)
| (0.043554545416973102985 + 7.0785414189036974855e-864j)  +/-  (1.2e-50, 3.76e-158j)
| (0.040781344758592937971 - 1.275548835591203216e-863j)  +/-  (1.38e-49, 4.31e-157j)
| (0.038154553938451798028 + 1.4811349807980901576e-863j)  +/-  (2.36e-47, 7.38e-155j)
| (0.043854154924597308573 - 7.4037146227041147471e-864j)  +/-  (3.68e-51, 1.15e-158j)
| (0.040781344758592937971 - 5.6156962311384704361e-864j)  +/-  (2.86e-50, 8.94e-158j)
| (0.038154553938451798028 + 4.8390601593915967607e-864j)  +/-  (6.3e-48, 1.97e-155j)
| (0.044245665721056228432 + 8.4597630769825957835e-864j)  +/-  (3.94e-52, 1.23e-159j)
| (0.039105315164666643093 - 1.407592157748370455e-863j)  +/-  (5.2e-50, 1.62e-157j)
| (0.042138022897423816145 - 1.1601587401239771371e-863j)  +/-  (2.3e-52, 7.18e-160j)
| (0.044200097525898969472 - 8.0931327162345933875e-864j)  +/-  (1.25e-52, 3.91e-160j)
| (0.039979834860934887793 + 5.3500944213304710747e-864j)  +/-  (1.91e-51, 5.97e-159j)
| (0.044067983466935987077 + 7.7418028048115585124e-864j)  +/-  (9.98e-53, 3.12e-160j)
| (0.042690934844493889368 + 1.1077007143149093158e-863j)  +/-  (1e-53, 3.14e-161j)
| (0.039979834860934887793 + 1.3393241699061241333e-863j)  +/-  (2.71e-52, 8.48e-160j)
| (0.044200097525898969472 - 8.8439882186545596533e-864j)  +/-  (2.19e-53, 6.84e-161j)
| (0.042138022897423816145 - 6.1721722887447691426e-864j)  +/-  (8.13e-55, 2.54e-162j)
| (0.042690934844493889368 + 6.4644022910568301574e-864j)  +/-  (6.25e-55, 1.95e-162j)
| (0.043554545416973102985 + 1.011188096225550361e-863j)  +/-  (5.19e-55, 1.62e-162j)
| (0.041502791141104966361 + 1.2159288646637805689e-863j)  +/-  (5.72e-55, 1.79e-162j)
| (0.04316504612011059575 - 1.0580986284804310787e-863j)  +/-  (3.32e-55, 1.04e-162j)
| (0.04316504612011059575 - 6.7660025336933339881e-864j)  +/-  (4.23e-56, 1.33e-163j)
| (0.041502791141104966361 + 5.8892697599480214169e-864j)  +/-  (3.75e-56, 1.16e-163j)
