Starting with polynomial:
P : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Extension levels are: 4 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/24*t^35 - 94097489629049189130811296665262401482097934589538489690407690979524481809806409490238836267/2050660479259540254493591239887802794823465773172244530044394330552602914447509877994847912*t^34 + 170719805583369935315862928960948625197634062349050928190293758125751997863344767629808249938855/7177311677408390890727569339607309781882130206102855855155380156934110200566284572981967692*t^33 - 18479652182331650091576738450868323355499854401203858465095418251006671522632486452324662561463487/2392437225802796963575856446535769927294043402034285285051793385644703400188761524327322564*t^32 + 18995404879242748124109011018828899174596241439441072752673706014333456254540206855284196978915481199/10765967516112586336091354009410964672823195309154283782733070235401165300849426859472951538*t^31 - 3248962038929901765429233668603317103278047520721592904925176647254106102548148307220490456881715290799/10765967516112586336091354009410964672823195309154283782733070235401165300849426859472951538*t^30 + 24027507665028597446821276679601150855462574852716153289359414269282802268159169374575150466115212284695/598109306450699240893964111633942481823510850508571321262948346411175850047190381081830641*t^29 - 7663689117228983051199798862855016294861906716443166923129789941083080148742815166313903012747215762168975/1794327919352097722681892334901827445470532551525713963788845039233527550141571143245491923*t^28 + 94667827119979469646556697621697400656543730932481466938679604383800170731550143225850609233835521308786340/256332559907442531811698904985975349352933221646530566255549291319075364305938734749355989*t^27 - 749497315214336263348024420937070521603060875254149669162593525695964476072689355897624280538325720365626260/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^26 + 44431718419510916630259640079084020068412941681420630910429431748131677670278779173313210578724255125672099960/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^25 - 2206840729750226252613843683983560790786772897468989988043058008468441170425326896483685342637348748393608605000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^24 + 92295527546547538152982594315154224103687719053375497330168053366437698807277945032138086420364603791642703400000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^23 - 3261395580061351730223822176017735686851707233757276909930289599375352045285572645467438006242870039449683041640000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^22 + 97574817765917213357325364366406130419188655118615484690274287682037983076689460171362256512764387911357670759440000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^21 - 2473843611640155142340766265876057050265123112557930665464801861166628806624307079004922857156919455936376427352240000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^20 + 53141207946360384842735565591824376792792469608761998047562311100800443671047261089022690378365085909110969556571200000/28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221*t^19 - 50844596237249665051465186302959556622012797578513948561748152841164213303785276203900203274738387022745765178840000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^18 + 780486191196496850681935070496878400072502494586686522899723048300277928660737413008705953870690879178719143934518400000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^17 - 10084006751054566683494525866557769007339527561960065333620585242263454388111283525017035699160170466404751615923094400000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^16 + 109183797224579823157432643407303325544008213523241565425561240282871867708261075189101599713344432470018836784044390400000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^15 - 985171775660478265916087256465352370682950873605639115134437763297870301649211403326343414632504962131515654031106816000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^14 + 7356119364474427000632722288136942947961843406220107002514487723424925658043776340808861549228928978093709184197342720000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^13 - 45060358693887987363365310544695574866553994166857275393034713496582907719208248956727149554658137942432310414128480768000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^12 + 224023630046892544498984869426891013273040614876983782996523562221124382033189676507140020029055107609138148315625269248000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^11 - 892066357215897500111500557566698659044171602647950373086427540962508462792720276978752802963188675763324785395963840512000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^10 + 2798773829914640173358837798314404012500836478165302446602909452722680333304480464236080701868780772974623541186256121856000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^9 - 6777428829971632751831707332961547993533370691394585291986853222030681671209751984168586106084320979524097795400150896640000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^8 + 12340705319674522698878116635254609091546732134590735607618596121731043881030245296105673558867724678683783650204767715328000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^7 - 16335434932852523263943205869961891640090360219300307560491090398797563565785848186650651187610116575765258478702426554368000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^6 + 15032976389534025176865328545868642291312477954690556869076725495321548947603705568588844087679919390018310461709049069568000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^5 - 9049454457703576485009612081872425848282942314573550681315016233345186481931578487758334475648458389198674804704342507520000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^4 + 3267230060161173733899246267389754883318208439520661097361718536509512946710190708840382549129010675110233552839815987200000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^3 - 620170343648784604457881869476968050434291169785585508564446346046681835741623553414158046572119850500144338645054914560000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t^2 + 49430499135478029953097926049457028855986670819715013157729296924049382915936922700044942865098474558777332208891330560000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959*t - 984282964290848288897297207545795178775441699427126481329396647805514093070838164843362863069284919067500397930741760000000/1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959
-------------------------------------------------
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:
| (115.64591369982012377 - 1.7505322813306618925e-570j)  +/-  (5.59e-243, 5.59e-243j)
| (76.058679691378246414 - 5.6162166668408705703e-564j)  +/-  (2.31e-239, 2.31e-239j)
| (102.56919944052403825 + 6.8626832030999757409e-570j)  +/-  (1.23e-241, 1.23e-241j)
| (38.733112226630209983 + 1.7669440591596868779e-565j)  +/-  (3.46e-238, 3.46e-238j)
| (19.302388811017662806 + 3.4988754773985386179e-574j)  +/-  (9.19e-240, 9.19e-240j)
| (34.876280963343722294 + 1.9176278701811112092e-575j)  +/-  (2.66e-238, 2.66e-238j)
| (21.970412800404259855 - 3.0125604282248896507e-579j)  +/-  (2.13e-239, 2.13e-239j)
| (69.235760843340195382 - 6.2215185710070852032e-586j)  +/-  (7.17e-239, 7.17e-239j)
| (92.342692487849018989 + 2.3099198966360575876e-596j)  +/-  (1.18e-240, 1.18e-240j)
| (10.637021905631593693 - 9.8633676433375455009e-603j)  +/-  (1.84e-241, 1.84e-241j)
| (14.567090899191457463 + 1.3120110087037587387e-607j)  +/-  (1.15e-240, 1.15e-240j)
| (57.380495461917207762 - 2.1922566533016418004e-632j)  +/-  (2.6e-238, 2.6e-238j)
| (8.5906216725542729683 + 1.5751412513036398855e-659j)  +/-  (3.85e-242, 3.85e-242j)
| (63.045100197634194513 + 5.5885386178315431116e-683j)  +/-  (1.4e-238, 1.4e-238j)
| (12.491770732192292861 + 4.1278600564462684856e-712j)  +/-  (3.9e-241, 3.9e-241j)
| (52.166689226644265939 - 3.4336396710402443275e-727j)  +/-  (3.52e-238, 3.52e-238j)
| (83.673400476698255426 + 4.9949976631897968843e-754j)  +/-  (6.14e-240, 6.14e-240j)
| (42.881266614725417578 + 7.2542966893584204269e-776j)  +/-  (4.31e-238, 4.31e-238j)
| (47.34788281233258515 + 3.0966524904850777529e-791j)  +/-  (4.69e-238, 4.69e-238j)
| (9.3950709123011331292 - 2.1275827203207948409e-803j)  +/-  (9.7e-242, 9.7e-242j)
| (4.5366202969211279833 - 1.2689111609888066967e-805j)  +/-  (1.67e-245, 1.67e-245j)
| (3.4535054971565860205 - 2.6060107226547209389e-806j)  +/-  (1.58e-246, 1.58e-246j)
| (2.5235193918400731128 - 2.1395980141003899449e-808j)  +/-  (1.25e-247, 1.25e-247j)
| (7.1534850158295998046 - 1.8865537404290131609e-803j)  +/-  (2.65e-243, 2.65e-243j)
| (31.288566596090160387 + 2.7397531292321607544e-798j)  +/-  (1.81e-238, 1.81e-238j)
| (24.849832777002298853 + 1.7684750158667449862e-800j)  +/-  (4.88e-239, 4.88e-239j)
| (0.13549238389123714217 + 6.6391306342456045006e-818j)  +/-  (2.28e-253, 2.28e-253j)
| (1.7457611011583465757 + 7.6035291273345891564e-814j)  +/-  (8.8e-249, 8.8e-249j)
| (27.951556528827397295 + 2.1157945897760478612e-802j)  +/-  (9.89e-239, 9.89e-239j)
| (16.836807166897032583 + 4.6597047486274582244e-808j)  +/-  (3.04e-240, 3.04e-240j)
| (5.772552766923680775 - 4.6476552535094707841e-813j)  +/-  (2.17e-244, 2.17e-244j)
| (0.64481849434397614317 + 2.2634329311580231506e-819j)  +/-  (4.54e-251, 4.54e-251j)
| (1.1194736575668098921 + 7.5448639926565398366e-818j)  +/-  (6.55e-250, 6.55e-250j)
| (0.028941560437096631795 - 1.405702221970932004e-822j)  +/-  (8.19e-255, 8.19e-255j)
| (0.3225476896193923118 + 2.2988578602159248513e-820j)  +/-  (2.73e-252, 2.73e-252j)
-------------------------------------------------
The weights are:
| (9.2853273303268398626e-50 - 8.7036479079111525713e-601j)  +/-  (6.6e-88, 2.94e-206j)
| (6.6776587291111094786e-33 - 9.4485356034283031906e-592j)  +/-  (2.49e-82, 1.11e-200j)
| (3.2208673043282579495e-44 + 7.47786271764471632e-598j)  +/-  (2.73e-86, 1.22e-204j)
| (6.0299279784455502525e-17 - 5.8268520707173127883e-582j)  +/-  (5.99e-74, 2.67e-192j)
| (1.0623009079976838419e-08 - 3.030697279066356945e-578j)  +/-  (1.14e-65, 5.09e-184j)
| (2.6536300680713233241e-15 + 2.2225299595115445407e-581j)  +/-  (7.56e-73, 3.37e-191j)
| (7.9647925876538797188e-10 + 7.1212922274814241608e-579j)  +/-  (1.69e-67, 7.54e-186j)
| (5.5366323058928304567e-30 + 3.8868526063024349229e-590j)  +/-  (4.01e-82, 1.79e-200j)
| (7.3451339354907388308e-40 - 1.5917499576116529205e-595j)  +/-  (3.56e-86, 1.59e-204j)
| (4.083973287472414912e-05 - 1.2210102948624500058e-575j)  +/-  (9.63e-63, 4.29e-181j)
| (1.0248524767493375852e-06 - 5.2094407538130390164e-577j)  +/-  (1.39e-65, 6.21e-184j)
| (6.526074046532449297e-25 + 2.989206071087276371e-587j)  +/-  (1.04e-80, 4.64e-199j)
| (0.00024177660056429364776 - 5.4343468434375374158e-575j)  +/-  (9.24e-63, 4.12e-181j)
| (2.4641650172318988008e-27 - 1.2023519796486892015e-588j)  +/-  (1.05e-81, 4.69e-200j)
| (7.4216818297269973176e-06 + 2.2790295988454304502e-576j)  +/-  (2.5e-66, 1.11e-184j)
| (1.1065748619226336673e-22 - 6.3562024629923264374e-586j)  +/-  (3.55e-80, 1.58e-198j)
| (3.7051250419740886516e-36 + 1.5819439045805664279e-593j)  +/-  (2.98e-86, 1.33e-204j)
| (1.0247341828020918339e-18 - 2.7891086143627487004e-583j)  +/-  (6.63e-79, 2.95e-197j)
| (1.2684106343700421734e-20 + 1.254980353570433312e-584j)  +/-  (1.05e-79, 4.67e-198j)
| (5.2843923841493100791e-05 + 4.2698142658153343545e-575j)  +/-  (1.36e-68, 6.06e-187j)
| (0.012421030370953252506 + 8.212266581190129267e-575j)  +/-  (4.27e-67, 1.9e-185j)
| (0.031838009317691488552 - 1.1960315854061797271e-574j)  +/-  (3.59e-66, 1.6e-184j)
| (0.068447678418139064791 + 1.7364400892929703613e-574j)  +/-  (2.62e-65, 1.17e-183j)
| (0.0011289368260456838593 + 4.6625404271609905838e-575j)  +/-  (6.35e-69, 2.83e-187j)
| (8.9242081856899984458e-14 - 8.1999360547716963415e-581j)  +/-  (2.5e-78, 1.11e-196j)
| (4.82304208340752916e-11 - 1.6215988345396455067e-579j)  +/-  (3.03e-77, 1.35e-195j)
| (0.12136916247789645571 - 4.5753446639336357979e-574j)  +/-  (8.29e-70, 3.7e-188j)
| (0.12249816960676590607 - 2.4782028636163121559e-574j)  +/-  (8.42e-70, 3.75e-188j)
| (2.3347822586810319405e-12 + 3.6120198505340590494e-580j)  +/-  (4.98e-78, 2.22e-196j)
| (1.1535354365038455092e-07 + 1.2577177851676754377e-577j)  +/-  (3.8e-75, 1.69e-193j)
| (0.0040801569024158105108 - 5.8176388781567818836e-575j)  +/-  (4.68e-72, 2.09e-190j)
| (0.20907394233401068291 - 4.6696693184311343825e-574j)  +/-  (4.03e-72, 1.8e-190j)
| (0.17974942365265437034 + 3.4578163434436838199e-574j)  +/-  (3.25e-72, 1.45e-190j)
| (0.069633052316979732901 + 1.608757430237434012e-574j)  +/-  (9.74e-73, 4.43e-191j)
| (0.17941640416117141535 + 5.6304785890753328612e-574j)  +/-  (2.55e-72, 1.12e-190j)
