Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 8 46
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : 5/2*t^11 - 10483/1482*t^9 + 1617/221*t^7 - 69993/20995*t^5 + 68299/109174*t^3 - 3633/109174*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^57 - 29599400781930309069033617671812265285251286101140319525683154561950220900831923906802121014366404220372124908204124383/781599377871615966126627485738200992233417072122173039697533524062357724316443639189118939748977376680903552400593232*t^55 + 2071765202987821233583152404832765247384373901105148971357534783244765590948363373423612230557950424794224053322902291929493563/7613200785732968054311026216559862031090280561105983502268452890003881970371016241710819786501443845632784969203626800618512*t^53 - 422747137334139118108832549952364664886517449874894617166957257407224489607200031752146954778105118113563744478684248593258856949/342594035357983562443996179745193791399062625249769257602080380050174688666695730876986890392564973053475323614163206027833040*t^51 + 80914422981030893688091252515377261835535645587101939737687045565023830523007101286676245095858350509217393749014449085328574867691/20421017039653120901671792694935306128597020656259501451840876479515327285690761878508201792452556912245612541844083446764927536*t^49 - 12969105676530159585009670248982447864718948619547538514054546206708921401852933244598675727295061424646667733263052063890049766585529019/1353147641590014923747027163448150722346160081235395214952606077723884374268084108974649721272387552397674901053943579391261010854200*t^47 + 120133925188590749335159097699278550172342529682541370315606940342519009966613084934331981677299041457180232634907314109182725380777242461/6623301614098494100445975063193579851483836187099566052136440275174802463522727480770653898859581177525461357790355414915119684707400*t^45 - 1000948626807254203116671656884536822215261049546567038943776805928160114539720637245432351129022616001499906007385452169036851564993917577/36354566637385067618003463124640316073700167515857618108393349954848360188669193061118922511518145574417532341649284166311879158282840*t^43 + 2691048923705932237238238977360494978837070107278990370373510750181986505497360054784418923227713083915855062704578604470119916515594754637/78916010505543195561031907758365564159983290461251902723097759658085464799794102010721563500612559905442936058702104653701396221638360*t^41 - 95758565191616241316225240532985540078278370453217539489086006482773662028921043008976647381127773239263051665292714589461684683763228636441/2746277165592903205523910389991121632767418508051566214763802036101374175032834749973110409821317084709414174842833241948808588513014928*t^39 + 46741207997718022087332408749275211555275264629536962861664400486044634070806758146124352099474661949182920729180951087779740875193785720469/1575125229928453255529908118415960450642581465481667532084501842568264540335971347825333231004129232120784108378143222440274831468328400*t^37 - 15605829592552316251376088768817658425138193412318609989767345977770825181899689464979627507837788811652744600856783410634602387312992854877/738618045672664520954702676997314787589459105282363870977478265159129699705568485138433097024535176644209497149072810522840740180063600*t^35 + 524154587086355471646946422366778984041858494759376148775621390272661373775201581174735221073541733327206182278206768710391503517255971782723/41527713414937220536970871686707851410470883107581375757663160343476245116387197535018491419767689519796202198534340723395951733182634640*t^33 - 55838598002291775800659414714088221891633232561010235874070790302615320797043823159926276810323507188456436761158467590735163687754766221869/8819057418763549522636287266800860917815053133061636249611262546060815495146743562544249521939912559311559069043583110613656416455451980*t^31 + 14098400320657171275502404981192343595938844178209864764472350677621566861192309175364691055087482964538393897360141480909179067444884914675/5291434451258129713581772360080516550689031879836981749766757527636489297088046137526549713163947535586935441426149866368193849873271188*t^29 - 64172287668487227774543730423774819872361400378520909686754230183662947809007699109501900109575120168278547068563784468656785162884361411439/68423721352475815261833263276903231258909894997892005384914968029782189186483355226636418704706218132589682432234696547864575644912989500*t^27 + 3911271999141785326844513227867939805088575025385509440897945153987837339970259958306917384003298888204567107688456822272466907560578671919/14230574526298388929099225695766199093733396965373550977489437795367805728242977012947175400124085252646857030065905549840780689682758500*t^25 - 139978799863233627430945216820876409351823079592475000959181726811718293801507870344737638949132920769202690700573243190427346979498656465143/2101571246043746077049373650750752282162548063846366008355640173619917549946922845272038863090324910110887846200132931600486492252349775280*t^23 + 83388775960805403173091249873201813297221470552715338521267482680965982512479928459850990476149367592591695283428523275105329344189324744781/6304713738131238231148120952252256846487644191539098025066920520859752649840768535816116589270974730332663538600398794801459476757049325840*t^21 - 15194846225869506699353498199886455349586278037099572808578156233768600335556462214759160723939787173200847282065106219524187887571080456897/7145342236548736661967870412552557759352663417077644428409176590307719669819537673924932134507104694377018677080451967441654073657989235952*t^19 + 3701603167346297956296210809577735755772568235782990183141052869075789164504325181061278015714421075939035526287885801985026749116273484927/13580328812154031667482794643740241355494828131872716018906329776900636799364618386114637097747421202763339590942379470283845461630681296400*t^17 - 98129088795492547559657898601952815984950051540096433921548479802638909020536864492589689822040152584187470847067714610661628542911635229/3594792920864302500216033876284181535278042740789836593239910823297227388067104866912698055286082083084413421131806330369253210431650931400*t^15 + 91236710172063179215892810821646666225673192103037618245613090970200556364797528163572628910096557353713144479000954492051550994668753597/43856473634544490502635613290667014730392121437636006437526912044226174134418679376334916274490201413629843737808037230504889167266141363080*t^13 - 39114841655364783270718165805578963614674847529407706650970809220240827689746343576340848388997571884152875822050903515760580368570132817/335898041939195728765231959694972039364583541060185003110574844444647533299614237593227494812345989759015942786860354084591323024493498693720*t^11 + 39500025630945020942892062130341962553887642731537986822672472194221170568343131350209219377499340102037170152411907488837173284144417126247/8665564865555759249831207142602827665935399108978864747247231951951905993570108024277601556667864313001045095203980786745103869650488178000327304*t^9 - 294350879716994347743366352361758443949611603312224219060382016072921703735324062854485532609825849355397909498962747262964879216365183437/2533790896361333113985733082632405750273508511397328873464102909927457892856756732244912735867796582748843595088883270978100546681429291812961200*t^7 + 82944152529876435564646666177984296062682542137482540935292640047064354855830256742467915762058313358176666160791803125129874621172509231/48142027030865329165728928570015709255196661716549248595817955288621699964278377912653341981488135072228028306688782148583910386947156544446262800*t^5 - 5977907946747981089742371859223699412756140388187377532779945581214552534254352409436364682299412691548389588113398591407485118325777211/491048675714826357490435071414160234403005949508802335677343143943941339635639454709064088211178977736725888728225577915555885946860996753351880560*t^3 + 58058768999637711255341359983973541229572650126131057432318581244572061492135597055092095254133339495644867846625472420147869555489/2242231395958111221417511741617170020105049997757088290764123944949503833952691574013991270370680263638017756749888483632675278296168934946812240*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: 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:
| (0.99836332464896938352 - 2.1100020350923165488e-881j)  +/-  (2.95e-232, 2.95e-232j)
| (0.9997147729255778128 - 1.1658119903778327061e-895j)  +/-  (1.33e-232, 1.33e-232j)
| (-0.9225217132136291628 - 3.3759875016221679286e-908j)  +/-  (9.2e-235, 9.2e-235j)
| (-0.99556621253798272378 + 2.4565540140860001013e-904j)  +/-  (2.8e-232, 2.8e-232j)
| (0.95951363374730336604 + 1.0385268420984246725e-906j)  +/-  (9.21e-234, 9.21e-234j)
| (0.94266274130900158154 + 1.2399889958861655071e-907j)  +/-  (2.84e-234, 2.84e-234j)
| (-0.99836332464896938352 + 2.0994148276017331617e-905j)  +/-  (2.88e-232, 2.88e-232j)
| (-0.94266274130900158154 - 1.6197915453938299246e-908j)  +/-  (2.8e-234, 2.8e-234j)
| (-0.98343625153405642542 - 2.3362405724213519626e-907j)  +/-  (7.25e-233, 7.25e-233j)
| (-0.9997147729255778128 - 5.0692543850076863256e-907j)  +/-  (1.21e-232, 1.21e-232j)
| (0.8725474065000954693 - 9.6029901792075554671e-910j)  +/-  (4.53e-236, 4.53e-236j)
| (0.98343625153405642542 + 2.4353717500195162067e-904j)  +/-  (6.85e-233, 6.85e-233j)
| (-0.89912833067026404231 - 1.3244990385640386543e-920j)  +/-  (2.18e-235, 2.18e-235j)
| (-0.8725474065000954693 - 7.4096652111782767196e-922j)  +/-  (4.86e-236, 4.86e-236j)
| (0.9225217132136291628 + 1.2773507265731280127e-918j)  +/-  (7.8e-235, 7.8e-235j)
| (0.84286316957253506752 + 7.3676859514308104601e-922j)  +/-  (9.79e-237, 9.79e-237j)
| (0.89912833067026404231 - 4.1671930359293430438e-919j)  +/-  (2.04e-235, 2.04e-235j)
| (-0.99079325588510780584 - 2.9102032067799366403e-918j)  +/-  (1.6e-232, 1.6e-232j)
| (-0.77459666924148337704 + 2.9710027485296717473e-923j)  +/-  (3.01e-238, 3.01e-238j)
| (-0.95951363374730336604 - 4.4916473564639887223e-919j)  +/-  (8.91e-234, 8.91e-234j)
| (0.97307894116257979188 - 2.4734920864820442878e-915j)  +/-  (2.79e-233, 2.79e-233j)
| (0.81017529650645141929 - 8.7905443684205361152e-938j)  +/-  (1.9e-237, 1.9e-237j)
| (-0.05924460241488947031 + 1.7171449000028848133e-960j)  +/-  (2.19e-254, 2.19e-254j)
| (-0.84286316957253506752 + 4.3040240327028963584e-943j)  +/-  (1.02e-236, 1.02e-236j)
| (-0.81017529650645141929 - 2.3149005093124083117e-943j)  +/-  (1.89e-237, 1.89e-237j)
| (0.77459666924148337704 - 4.7658516018181198406e-941j)  +/-  (2.85e-238, 2.85e-238j)
| (0.69527663239541975566 + 1.622412524170306667e-945j)  +/-  (5.6e-240, 5.6e-240j)
| (0.73625196187499019361 + 1.3644645223745340177e-944j)  +/-  (4.15e-239, 4.15e-239j)
| (-0.97307894116257979188 + 2.4163165074480996403e-938j)  +/-  (2.85e-233, 2.85e-233j)
| (-0.65181611277473117012 + 1.1402938653357049192e-956j)  +/-  (6.31e-241, 6.31e-241j)
| (-0.4029363989030375033 - 9.7565641069265482261e-962j)  +/-  (1.96e-246, 1.96e-246j)
| (0.60602509373521855488 + 2.949198594054181248e-949j)  +/-  (6.18e-242, 6.18e-242j)
| (0.65181611277473117012 + 9.1666086584463972747e-949j)  +/-  (6.69e-241, 6.69e-241j)
| (0.05924460241488947031 - 1.2501390485317478367e-964j)  +/-  (2.19e-254, 2.19e-254j)
| (-0.73625196187499019361 - 3.442809762811772671e-955j)  +/-  (4.77e-239, 4.77e-239j)
| (-0.69527663239541975566 - 6.2940781482503952615e-956j)  +/-  (5.47e-240, 5.47e-240j)
| (0.99079325588510780584 + 2.613804532883013252e-953j)  +/-  (1.56e-232, 1.56e-232j)
| (0.55806685067819680295 - 5.2121308071051493399e-993j)  +/-  (5.66e-243, 5.66e-243j)
| (0.2919991541426287378 + 1.6933050468198677685e-999j)  +/-  (5.95e-249, 5.95e-249j)
| (-0.60602509373521855488 + 7.1847770510332556116e-993j)  +/-  (6.44e-242, 6.44e-242j)
| (-0.55806685067819680295 - 6.705690537918490928e-996j)  +/-  (5.46e-243, 5.46e-243j)
| (-0.11827721255658732086 + 3.8291084872330132505e-1006j)  +/-  (4.55e-253, 4.55e-253j)
| (0.23486305796025252237 + 1.1378065236417976718e-1001j)  +/-  (2.64e-250, 2.64e-250j)
| (0.5081125826269585003 + 2.3818103313338756399e-997j)  +/-  (4.35e-244, 4.35e-244j)
| (0.99556621253798272378 - 1.7386988448966627712e-1004j)  +/-  (2.65e-232, 2.65e-232j)
| (-0.5081125826269585003 - 6.0738126159341875584e-1029j)  +/-  (4.33e-244, 4.33e-244j)
| (-0.23486305796025252237 - 5.7399626916025627394e-1034j)  +/-  (2.81e-250, 2.81e-250j)
| (0.11827721255658732086 + 1.296266921261368903e-1038j)  +/-  (4.51e-253, 4.51e-253j)
| (0.45634074933163137426 - 1.9858405589965089625e-1029j)  +/-  (3.48e-245, 3.48e-245j)
| (0.17688660040263332025 + 5.9605355369274283128e-1035j)  +/-  (1.14e-251, 1.14e-251j)
| (-0.2919991541426287378 - 3.8791978990697754578e-1033j)  +/-  (6.04e-249, 6.04e-249j)
| (-0.45634074933163137426 + 3.5763223608735063812e-1029j)  +/-  (3.16e-245, 3.16e-245j)
| (-3.0654653647498356899e-1062 + 4.3729143126310133393e-1062j)  +/-  (3.04e-1060, 3.04e-1060j)
| (0.34809048239910185032 - 1.4032145079411915749e-1030j)  +/-  (1.13e-247, 1.13e-247j)
| (0.4029363989030375033 + 1.5745386005573695288e-1029j)  +/-  (2.01e-246, 2.01e-246j)
| (-0.17688660040263332025 + 7.2210483093165365297e-1036j)  +/-  (1.21e-251, 1.21e-251j)
| (-0.34809048239910185032 + 2.3666563087809536203e-1031j)  +/-  (1.23e-247, 1.23e-247j)
-------------------------------------------------
The weights are:
| (0.0020065483768573918484 - 2.6244658342989125649e-883j)  +/-  (2.04e-46, 2.15e-154j)
| (0.00075187905743797148252 + 1.2971082029769384758e-881j)  +/-  (1.83e-46, 1.92e-154j)
| (0.021776097370118953496 - 1.3524377456919741822e-885j)  +/-  (7.45e-48, 7.84e-156j)
| (0.0036782398753135872479 - 2.244078997081720889e-884j)  +/-  (3.78e-48, 3.98e-156j)
| (0.015202636231876497363 - 1.6975954867305854189e-883j)  +/-  (4.55e-48, 4.78e-156j)
| (0.018499424854799048968 + 7.2532288095000611962e-884j)  +/-  (2.29e-48, 2.41e-156j)
| (0.0020065483768573918484 + 2.1203809545832913269e-884j)  +/-  (1.99e-48, 2.1e-156j)
| (0.018499424854799048968 + 2.0814201461432695894e-885j)  +/-  (7.93e-50, 8.34e-158j)
| (0.0088077634598753038564 - 9.8509250950322612418e-885j)  +/-  (9.88e-50, 1.04e-157j)
| (0.00075187905743797148252 - 8.7733039445041670525e-885j)  +/-  (1.06e-48, 1.11e-156j)
| (0.02814800066397623377 - 9.7720820185944978283e-885j)  +/-  (1.38e-52, 1.45e-160j)
| (0.0088077634598753038564 - 1.3078625011115928632e-882j)  +/-  (1.46e-51, 1.53e-159j)
| (0.024999747550328211968 + 9.222412656707244388e-886j)  +/-  (9.53e-52, 1e-159j)
| (0.02814800066397623377 - 6.5715774190917756366e-886j)  +/-  (1.16e-52, 1.22e-160j)
| (0.021776097370118953496 - 3.4253985129986202721e-884j)  +/-  (3.6e-52, 3.79e-160j)
| (0.031203824982861242979 + 5.7670402242063087201e-885j)  +/-  (4.96e-54, 5.21e-162j)
| (0.024999747550328211968 + 1.7634354935082331156e-884j)  +/-  (9.65e-53, 1.02e-160j)
| (0.0059750146207443615759 + 1.6256569130752808272e-884j)  +/-  (5.54e-51, 5.83e-159j)
| (0.036983374300105651876 + 2.9612801070381373878e-886j)  +/-  (1.23e-56, 1.3e-164j)
| (0.015202636231876497363 - 3.3684987022661546415e-885j)  +/-  (1.38e-52, 1.45e-160j)
| (0.011939978027182554678 + 4.4457634300368118965e-883j)  +/-  (9.95e-54, 1.05e-161j)
| (0.034153084860263928243 - 3.5929362125657523715e-885j)  +/-  (1.54e-56, 1.62e-164j)
| (0.059173900187669547665 + 1.0540389202460288516e-886j)  +/-  (2.14e-61, 2.25e-169j)
| (0.031203824982861242979 + 4.87053413586297764e-886j)  +/-  (7.05e-56, 7.41e-164j)
| (0.034153084860263928243 - 3.7386405420119001192e-886j)  +/-  (1.09e-56, 1.15e-164j)
| (0.036983374300105651876 + 2.3462973743435642932e-885j)  +/-  (4.32e-58, 4.55e-166j)
| (0.042242957663960479425 + 1.127142485142691389e-885j)  +/-  (3.51e-60, 3.7e-168j)
| (0.039683450831160022679 - 1.5967678269600726132e-885j)  +/-  (2.42e-59, 2.54e-167j)
| (0.011939978027182554678 + 5.7018351185924428434e-885j)  +/-  (7.91e-55, 8.32e-163j)
| (0.044652288618503858116 - 1.7264281432954636524e-886j)  +/-  (3.66e-62, 3.85e-170j)
| (0.05415741581048101012 + 1.0714403583280508015e-886j)  +/-  (3.93e-64, 4.14e-172j)
| (0.046902525909167802028 + 6.1755437746309824858e-886j)  +/-  (1.26e-62, 1.33e-170j)
| (0.044652288618503858116 - 8.2208603175535638686e-886j)  +/-  (1.2e-61, 1.26e-169j)
| (0.059173900187669547665 + 1.1870276793482680519e-886j)  +/-  (4.42e-66, 4.65e-174j)
| (0.039683450831160022679 - 2.4128173803705782339e-886j)  +/-  (8.88e-62, 9.35e-170j)
| (0.042242957663960479425 + 2.0170868436318449332e-886j)  +/-  (1.16e-62, 1.22e-170j)
| (0.0059750146207443615759 + 4.2716734117021041917e-882j)  +/-  (6.66e-60, 7.01e-168j)
| (0.048985416003086934214 - 4.7654889368580658904e-886j)  +/-  (7.52e-65, 7.92e-173j)
| (0.056647490846673666022 + 1.8279281778053649274e-886j)  +/-  (1.5e-67, 1.58e-175j)
| (0.046902525909167802028 + 1.5101716589984489936e-886j)  +/-  (7.87e-65, 8.29e-173j)
| (0.048985416003086934214 - 1.3481028631459669627e-886j)  +/-  (7.84e-66, 8.25e-174j)
| (0.058856102423194344444 - 1.0166087904908438816e-886j)  +/-  (1.05e-68, 1.11e-176j)
| (0.057590621451776523021 - 1.5997668181841300584e-886j)  +/-  (6.55e-69, 6.89e-177j)
| (0.050893365609485714701 + 3.7692983196753661385e-886j)  +/-  (1.62e-67, 1.7e-175j)
| (0.0036782398753135872479 - 1.5996982668255527236e-881j)  +/-  (6.21e-62, 6.54e-170j)
| (0.050893365609485714701 + 1.2266384674313302908e-886j)  +/-  (7.73e-68, 8.13e-176j)
| (0.057590621451776523021 - 9.9042836704409122563e-887j)  +/-  (6.14e-70, 6.46e-178j)
| (0.058856102423194344444 - 1.2898585380954487414e-886j)  +/-  (8.46e-70, 8.91e-178j)
| (0.052619448208361126567 - 3.0502638225749284828e-886j)  +/-  (2.26e-69, 2.38e-177j)
| (0.058327709349894825514 + 1.424529724597092662e-886j)  +/-  (7.11e-70, 7.48e-178j)
| (0.056647490846673666022 + 1.0006358618469932589e-886j)  +/-  (4.88e-71, 5.14e-179j)
| (0.052619448208361126567 - 1.136527959246932228e-886j)  +/-  (3.51e-70, 3.69e-178j)
| (0.059279959886497591378 - 1.1098637986375463289e-886j)  +/-  (8.57e-71, 9.02e-179j)
| (0.055501712911594410441 - 2.1266719571198105782e-886j)  +/-  (3.58e-71, 3.77e-179j)
| (0.05415741581048101012 + 2.5215673208708916631e-886j)  +/-  (4.11e-71, 4.32e-179j)
| (0.058327709349894825514 + 9.9571843129636717751e-887j)  +/-  (4.64e-72, 4.92e-180j)
| (0.055501712911594410441 - 1.027080922383261961e-886j)  +/-  (4.89e-72, 5.09e-180j)
