Starting with polynomial:
P : 2*t
Extension levels are: 1 8 14 26
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : 2*t^9 - 36*t^7 + 189*t^5 - 315*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : 2*t^23 - 3309583/18099*t^21 + 82235713/12066*t^19 - 1089441955/8044*t^17 + 38063466049/24132*t^15 - 179492837615/16088*t^13 + 1547216966295/32176*t^11 - 7941468990455/64352*t^9 + 46161180640575/257408*t^7 - 70208873169435/514816*t^5 + 50216778386775/1029632*t^3 - 12961617443775/2059264*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^49 - 20994346343936950498403800707026058824760494859858929445816829640473165770414656736973722326951579745280661181037/26847492324347190683258104751645364380113611833876334765419722350483053209001375079790079692342365588929292102*t^47 + 1143744195076654214236760103265847502862219312278473104459821071242581853039967553106305680901001812191169905348429233/8215332651250240349076980054003481500314765221166158438218435039247814281954420774415764385856763870212363383212*t^45 - 82113846553166609412748497710403269367792526017400271721118129192776140401418167982351071824693049853939148519687981755/5476888434166826899384653369335654333543176814110772292145623359498542854636280516277176257237842580141575588808*t^43 + 35962224124982232356820421877076221502571942856999355928466570560061025864896871299947198134441256825541652478360114139021/32861330605000961396307920216013926001259060884664633752873740156991257127817683097663057543427055480849453532848*t^41 - 11337975033432968540114258024301464596206041329053985340177678027022272752971255626641093018537974372580035436526352480814531/197167983630005768377847521296083556007554365307987802517242440941947542766906098585978345260562332885096721197088*t^39 + 296435981083164356445708278227573574031032307327279546035946438703652003475341703088415244799550407378623002263335753788492989/131445322420003845585231680864055704005036243538658535011494960627965028511270732390652230173708221923397814131392*t^37 - 5919322575283403966107212474192726688747886947329883411509170126316375234996858203448390287652783545671700011636430570872706111/87630214946669230390154453909370469336690829025772356674329973751976685674180488260434820115805481282265209420928*t^35 + 824671142364804732598950646306120857270160786728859611354282631577448061078058194711786768386473550609942041117205795233928394535/525781289680015382340926723456222816020144974154634140045979842511860114045082929562608920694832887693591256525568*t^33 - 4994827992012840526803887097043961922506022656350249844866186654191719881384747425303408765145170302661677093350315583602652141375/175260429893338460780308907818740938673381658051544713348659947503953371348360976520869640231610962564530418841856*t^31 + 47597132478042263984967309152762330603466478553737523490598308355477380256667320158842038797565219861112045196871910999128930224865/116840286595558973853539271879160625782254438701029808899106631669302247565573984347246426821073975043020279227904*t^29 - 3217411420615447543809440231647493970980685197566784460084475598206476776224100936710738474379451699233984575251204295465629276415715/701041719573353843121235631274963754693526632206178853394639790015813485393443906083478560926443850258121675367424*t^27 + 2114066654187450609791323855241157728710091928507330429117110526085094910332663705538455659359978803148939656106786620493587507564765/51929016264692877268239676390738055903224194978235470621825169630800998918032881932109523031588433352453457434624*t^25 - 29416036275805506407892898257229914783003941200104355217998430553853388756537854798759870974179417576463648658064123554726760464450125/103858032529385754536479352781476111806448389956470941243650339261601997836065763864219046063176866704906914869248*t^23 + 318850757983765116497309075631008207686466428147908841610249739714412332342631767990210282770048588110884923120105289389963826548873625/207716065058771509072958705562952223612896779912941882487300678523203995672131527728438092126353733409813829738496*t^21 - 2665467255432820263873594786503331672003234676437351683111491457526838762985789059666800220418798244337782669857483833363416068381105625/415432130117543018145917411125904447225793559825883764974601357046407991344263055456876184252707466819627659476992*t^19 + 498495083336450384532419303485513648914925999141413785775007420955116543843842329065891962735468345626534484260329374152748683178894375/24437184124561354008583377125053202777987856460346103822035373943906352432015473850404481426629850989389862322176*t^17 - 9467186302601486795926326189148784613386567781173741233608786625706146152423498584751800737223724466832950155722687838937841945820170625/195497472996490832068667017000425622223902851682768830576282991551250819456123790803235851413038807915118898577408*t^15 + 32742809911466960393632018258254467244403135803077010097500349930394096699241971232210467935599207032396734837288493503028733585793828125/390994945992981664137334034000851244447805703365537661152565983102501638912247581606471702826077615830237797154816*t^13 - 79779796483547503935763109170043481546749990924885439814441715387405927352293864870681625042366184114855537395102320154534375252003268125/781989891985963328274668068001702488895611406731075322305131966205003277824495163212943405652155231660475594309632*t^11 + 130734733531873512122844046379557769357154540501967210516601076351710357886824124153044123531705985234257369786830959512387992480201445625/1563979783971926656549336136003404977791222813462150644610263932410006555648990326425886811304310463320951188619264*t^9 - 134719215476321992952514769168067402388773071924540825301576284455540702294133764869296528325820365745016839768716081357992715882509513125/3127959567943853313098672272006809955582445626924301289220527864820013111297980652851773622608620926641902377238528*t^7 + 78674745079800699706859298489814672507510339102104231501021947234636566742817779373846973739139495639187669511233562443941971792509460625/6255919135887706626197344544013619911164891253848602578441055729640026222595961305703547245217241853283804754477056*t^5 - 21553872588401710738228946401522692571865352665061919994616822027148734401698840062096271251004928953316099559373326267790535504914340625/12511838271775413252394689088027239822329782507697205156882111459280052445191922611407094490434483706567609508954112*t^3 + 1685186845127382673824269330494937470004866243534082482931040765862865430004991700089068725149736818561694734479541907437747976425034375/25023676543550826504789378176054479644659565015394410313764222918560104890383845222814188980868967413135219017908224*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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: 1
  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:
| (-7.2171094125068892232 - 1.5083080966516202048e-859j)  +/-  (1.54e-246, 1.54e-246j)
| (5.668985002654550257 + 3.177761598859747097e-858j)  +/-  (6.54e-245, 6.54e-245j)
| (-7.9049372795856585164 + 3.2266503300343449218e-860j)  +/-  (1.18e-247, 1.18e-247j)
| (-4.4436725456953199306 + 4.540029906602026301e-856j)  +/-  (2.21e-244, 2.21e-244j)
| (1.4685532892166679317 - 5.1200522647146620143e-871j)  +/-  (5.28e-248, 5.28e-248j)
| (6.1375212115440669092 + 1.2238682582307188428e-868j)  +/-  (2.73e-245, 2.73e-245j)
| (7.2171094125068892232 - 2.9813564419072155019e-869j)  +/-  (1.44e-246, 1.44e-246j)
| (-2.9382321011972359479 + 1.8876980133605849642e-866j)  +/-  (6.85e-245, 6.85e-245j)
| (-5.668985002654550257 + 2.2416101736080852777e-871j)  +/-  (6.38e-245, 6.38e-245j)
| (-6.1375212115440669092 + 1.3809425873074289687e-874j)  +/-  (2.56e-245, 2.56e-245j)
| (5.2317324539479656178 + 3.2941726775052799672e-874j)  +/-  (1.34e-244, 1.34e-244j)
| (-6.6466797522227010501 + 1.0166839043389032279e-877j)  +/-  (8.87e-246, 8.87e-246j)
| (6.6466797522227010501 + 7.8633313910760589229e-878j)  +/-  (9.04e-246, 9.04e-246j)
| (-4.8225787874384532493 - 7.9748220762499574586e-875j)  +/-  (1.95e-244, 1.95e-244j)
| (4.0997623639174693016 - 9.4258004606431986083e-881j)  +/-  (2.74e-244, 2.74e-244j)
| (2.6602671868269422397 - 8.4556594628940607332e-891j)  +/-  (3.07e-245, 3.07e-245j)
| (-3.7832466850882959409 + 1.1874977934824393731e-902j)  +/-  (2.27e-244, 2.27e-244j)
| (3.7832466850882959409 - 8.4472768853191156567e-918j)  +/-  (2.27e-244, 2.27e-244j)
| (-1.4685532892166679317 - 6.3193649505284679053e-926j)  +/-  (5.38e-248, 5.38e-248j)
| (7.9049372795856585164 - 5.5102242211526840977e-933j)  +/-  (1.09e-247, 1.09e-247j)
| (-3.4755279338209517704 + 3.3639106794352663442e-928j)  +/-  (1.81e-244, 1.81e-244j)
| (-2.4627498551741779549 + 1.6388854037613052273e-943j)  +/-  (1.47e-245, 1.47e-245j)
| (4.8225787874384532493 + 7.2084992735814244044e-948j)  +/-  (1.7e-244, 1.7e-244j)
| (-3.1909932017815276072 - 4.1003344470659167977e-953j)  +/-  (1.27e-244, 1.27e-244j)
| (2.4627498551741779549 - 2.1815164572790782705e-963j)  +/-  (1.4e-245, 1.4e-245j)
| (-1.9366468705568828024 - 7.4614400247661664607e-965j)  +/-  (3.03e-247, 3.03e-247j)
| (0.72355101875283757332 + 6.6543193410981624317e-968j)  +/-  (2.8e-251, 2.8e-251j)
| (-5.2317324539479656178 - 6.2807600804721826121e-962j)  +/-  (1.21e-244, 1.21e-244j)
| (3.1909932017815276072 + 7.3243240433334437697e-962j)  +/-  (1.32e-244, 1.32e-244j)
| (-0.54431479141505793416 - 9.9122447434430845397e-976j)  +/-  (2.81e-252, 2.81e-252j)
| (-4.0997623639174693016 - 1.2067811372857115587e-967j)  +/-  (2.55e-244, 2.55e-244j)
| (-0.72355101875283757332 + 2.1110576860282675497e-982j)  +/-  (2.37e-251, 2.37e-251j)
| (1.2824912083026645136 + 7.1644276032981657198e-980j)  +/-  (5.11e-249, 5.11e-249j)
| (2.9382321011972359479 + 1.6651219233250053846e-974j)  +/-  (6.65e-245, 6.65e-245j)
| (1.5664430647489162541 - 3.0581243939451773874e-979j)  +/-  (8.36e-248, 8.36e-248j)
| (2.2665805845318431118 + 5.1935781303845794094e-976j)  +/-  (3.54e-246, 3.54e-246j)
| (3.4755279338209517704 - 3.0115599784413698521e-975j)  +/-  (1.87e-244, 1.87e-244j)
| (0.93588957168758885766 - 5.3462333420145155022e-982j)  +/-  (1.62e-250, 1.62e-250j)
| (0.24818520446629368019 + 1.9799829388643941411e-985j)  +/-  (6.29e-254, 6.29e-254j)
| (4.4436725456953199306 + 2.2548562221835119247e-977j)  +/-  (2.32e-244, 2.32e-244j)
| (-0.24818520446629368019 + 4.5809545625321900777e-987j)  +/-  (7.1e-254, 7.1e-254j)
| (-1.5664430647489162541 - 2.2388754668071038618e-981j)  +/-  (8.78e-248, 8.78e-248j)
| (-1.7740078453741537124e-1001 - 2.4727700484602848866e-1000j)  +/-  (1.21e-998, 1.21e-998j)
| (1.9366468705568828024 - 2.8798028294469045767e-980j)  +/-  (3.24e-247, 3.24e-247j)
| (-2.2665805845318431118 - 1.0256064008013305663e-980j)  +/-  (3.61e-246, 3.61e-246j)
| (-1.2824912083026645136 + 8.3281424446153898518e-986j)  +/-  (5.14e-249, 5.14e-249j)
| (-0.93588957168758885766 - 2.3208035395476526399e-986j)  +/-  (1.52e-250, 1.52e-250j)
| (-2.6602671868269422397 + 6.5990780250328307645e-987j)  +/-  (3.07e-245, 3.07e-245j)
| (0.54431479141505793416 + 7.3122646731234838816e-994j)  +/-  (2.86e-252, 2.86e-252j)
-------------------------------------------------
The weights are:
| (8.2893852573991399198e-24 - 1.2305510641394576794e-875j)  +/-  (1.97e-89, 5.58e-211j)
| (2.814436316009826028e-15 - 1.5477263689290307493e-870j)  +/-  (2.43e-85, 6.9e-207j)
| (3.2572484000295312589e-28 + 2.002660949983828692e-878j)  +/-  (1.8e-91, 5.12e-213j)
| (5.424475979706164566e-10 + 1.96940479041586419e-864j)  +/-  (1.37e-80, 3.88e-202j)
| (-0.014421413993247601686 - 2.3527597985990734123e-858j)  +/-  (4.66e-60, 1.32e-181j)
| (1.1998475194529683442e-17 + 3.0920296903876274017e-872j)  +/-  (2.46e-87, 6.98e-209j)
| (8.2893852573991399198e-24 + 2.9139379910936672106e-876j)  +/-  (4.12e-91, 1.17e-212j)
| (2.613049504478179365e-05 - 8.236126440683046154e-861j)  +/-  (8.74e-75, 2.48e-196j)
| (2.814436316009826028e-15 + 1.2174079556252942437e-869j)  +/-  (1.94e-86, 5.52e-208j)
| (1.1998475194529683442e-17 - 1.9578822452296372723e-871j)  +/-  (5.43e-88, 1.54e-209j)
| (3.0959786885338353333e-13 + 5.1105100769086539974e-869j)  +/-  (6.22e-87, 1.77e-208j)
| (1.9644453783001010004e-20 + 2.1463816222737278323e-873j)  +/-  (1.18e-89, 3.34e-211j)
| (1.9644453783001010004e-20 - 4.2350690114915068967e-874j)  +/-  (3.55e-91, 1.01e-212j)
| (1.7673794863316482299e-11 + 3.2748712264368530329e-866j)  +/-  (8.68e-85, 2.46e-206j)
| (9.252080099274661958e-09 - 4.1796757634117347749e-865j)  +/-  (1.9e-84, 5.39e-206j)
| (0.0001336193772032507225 + 1.0001447370479827149e-860j)  +/-  (6.53e-79, 1.86e-200j)
| (1.0649863477679264681e-07 + 5.6703689978407298705e-863j)  +/-  (8.44e-83, 2.4e-204j)
| (1.0649863477679264681e-07 + 4.5636715427084660097e-864j)  +/-  (1.22e-83, 3.47e-205j)
| (-0.014421413993247601686 - 4.6726841344098308573e-858j)  +/-  (1.59e-72, 4.53e-194j)
| (3.2572484000295312589e-28 - 5.5956470362970927022e-879j)  +/-  (1.09e-96, 3.08e-218j)
| (9.6800230990062679088e-07 - 3.5209118197472507522e-862j)  +/-  (3.99e-82, 1.13e-203j)
| (0.00015241417269951793021 - 1.0533046343176497984e-859j)  +/-  (2.07e-79, 5.87e-201j)
| (1.7673794863316482299e-11 - 1.347945774409274258e-867j)  +/-  (5.22e-88, 1.48e-209j)
| (5.5875793051289960803e-06 + 2.0080040945631429417e-861j)  +/-  (2.2e-81, 6.24e-203j)
| (0.00015241417269951793021 - 3.0245825548936290947e-860j)  +/-  (2.96e-81, 8.41e-203j)
| (0.0045887593110137392239 - 2.5921417722721409501e-859j)  +/-  (2.45e-78, 6.95e-200j)
| (0.034932128326139349604 + 5.2695923435009925241e-858j)  +/-  (2.81e-76, 7.97e-198j)
| (3.0959786885338353333e-13 - 6.192013772233588664e-868j)  +/-  (1.71e-88, 4.86e-210j)
| (5.5875793051289960803e-06 + 3.3004952538268578427e-862j)  +/-  (1.69e-84, 4.81e-206j)
| (0.11986500954046976368 - 6.8090678451262189106e-858j)  +/-  (2.81e-77, 7.98e-199j)
| (9.252080099274661958e-09 - 1.0349610927359504841e-863j)  +/-  (4.3e-85, 1.22e-206j)
| (0.034932128326139349604 + 7.317398049240834116e-858j)  +/-  (1.96e-77, 5.55e-199j)
| (0.042769095772447628598 + 1.7993904116062465375e-858j)  +/-  (5.47e-78, 1.55e-199j)
| (2.613049504478179365e-05 - 1.6821932187101965243e-861j)  +/-  (9.97e-84, 2.83e-205j)
| (0.023767859477484452363 + 1.3341166310118594492e-858j)  +/-  (8.84e-80, 2.51e-201j)
| (0.00099176649908915380632 + 4.760545948489408364e-860j)  +/-  (2.59e-82, 7.35e-204j)
| (9.6800230990062679088e-07 - 4.3134570468485222328e-863j)  +/-  (7.6e-86, 2.16e-207j)
| (0.074152343992411337489 - 2.6933889433997577177e-858j)  +/-  (4.79e-80, 1.36e-201j)
| (0.14958155115265065143 + 4.5978794352568075704e-858j)  +/-  (2.4e-80, 6.82e-202j)
| (5.424475979706164566e-10 + 2.7831001104399020208e-866j)  +/-  (3.83e-89, 1.09e-210j)
| (0.14958155115265065143 + 5.1413749197682416096e-858j)  +/-  (7.37e-81, 2.09e-202j)
| (0.023767859477484452363 + 2.7849947889794192431e-858j)  +/-  (3.4e-83, 9.66e-205j)
| (0.1269081279676605044 - 5.2607326730240506355e-858j)  +/-  (5.2e-81, 1.48e-202j)
| (0.0045887593110137392239 - 1.0193754114322676297e-859j)  +/-  (3.33e-83, 9.46e-205j)
| (0.00099176649908915380632 + 1.465808124898135673e-859j)  +/-  (4.75e-85, 1.35e-206j)
| (0.042769095772447628598 + 3.2577547889592978867e-858j)  +/-  (2.19e-83, 6.2e-205j)
| (0.074152343992411337489 - 4.1291029717268297816e-858j)  +/-  (3.82e-83, 1.08e-204j)
| (0.0001336193772032507225 + 3.9788125762399509661e-860j)  +/-  (5.77e-86, 1.65e-207j)
| (0.11986500954046976368 - 5.3240898758644342038e-858j)  +/-  (5.73e-83, 1.49e-204j)
