Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 14 31
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : t^16 - 935281/8628*t^14 + 38001691/8628*t^12 - 245286041/2876*t^10 + 2383796415/2876*t^8 - 11245499265/2876*t^6 + 22854346515/2876*t^4 - 15081381315/2876*t^2 + 1321665345/2876
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 1732125991151833729636853908176152627054278575186609793780268990181976454747178650212465373000768373163/2147360433182848610947956482128645357000091383182922794620012912643067428749372383239240434864331444*t^45 + 13981127972967022109745464846606073441213823118237353482756684884332319269570437866494648752830883273993151/47241929530022669440855042606830197854002010430024301481640284078147483432486192431263289567015291768*t^43 - 2065389527889724425033412350927540655964996273183407523691369691126129759380477764513543623822412293510478457/31494619686681779627236695071220131902668006953349534321093522718764988954990794954175526378010194512*t^41 + 309563480198497495670036301900653258605493021127910292130039635850844425937041031808836967299470755303897101195/31494619686681779627236695071220131902668006953349534321093522718764988954990794954175526378010194512*t^39 - 632855880918823320916021307863158433972723086287285243765251263330622106517784406459934804887283044440987732577025/598397774046953812917497206353182506150692132113641152100776931656534790144825104129335001182193695728*t^37 + 78258166055709033366837692757520155643255032439341198710841672098056159198280110527558055522705526838249363751433115/924796559890746801781586591636736600414706022357445416883018894378281039314729706381699547281572075216*t^35 - 2379924573500361689875291515828268328421102521877587261406467590429560080725024996647009816581074206657136803643784595/462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608*t^33 + 111537356546861793676692305170899470578138847903836339801671985067991397811316205131136131677560365762478624699016939835/462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608*t^31 - 4059136033556172424365999895226519884339485753632223610592364202469296347708985486281668648201659739490757807698135100575/462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608*t^29 + 3110358782714704171129427596981887147800252885149470172870462502902409750119077682465374346263162609939107089892371652175/12497250809334416240291710697793737843441973275100613741662417491598392423172023059212156044345568584*t^27 - 1270241635076104772320121356824965251551305289934462078623924544537539040224924777962541833234093509082054520766564164948375/231199139972686700445396647909184150103676505589361354220754723594570259828682426595424886820393018804*t^25 + 21744838766906101287160553662834009038783519950863989246108157818106636955310900929068411523839338517314627082998320529390375/231199139972686700445396647909184150103676505589361354220754723594570259828682426595424886820393018804*t^23 - 12456117266728613466786008306496118136390208626138053399971052170993282310064940300170597740224645250633514640983867898521625/10052136520551595671538984691703658700159848069102667574815422764981315644725322895453255948712739948*t^21 + 62440578638815486160810954369181222767308026391311496394252307408342855362126522381228109439616324322237481898828045337024375/5026068260275797835769492345851829350079924034551333787407711382490657822362661447726627974356369974*t^19 - 98723289823771858925219327042456464612605020716347718037473205181376826183360754757264299067013876104371018412755703339801875/1058119633742273228583051020179332494753668217800280797348991869998033225760560304784553257759235784*t^17 + 31986749098583582937513896323822477477511444146707005046294608540100006361331117930806544094537565760528771449504570015700625/62242331396604307563708883539960734985509895164722399844058345294001954456503547340267838691719752*t^15 - 125618380358749398311133798480569597885981731667585242312295080247019615446902556814763445356058031070342828352359949751894375/62242331396604307563708883539960734985509895164722399844058345294001954456503547340267838691719752*t^13 + 42318509808927382528911910308941801862929288988367005928479806324261474800261163464024560667569008392575737180284050077235000/7780291424575538445463610442495091873188736895590299980507293161750244307062943417533479836464969*t^11 - 1187360231992559729377559653342786101109280446030105280154449132884703766869209560971844013150083534775006871628525897720384375/124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504*t^9 + 1253331878592363327058401995792140857623932843882077829393440665185005797372719269503470039791673433937630400764481276585528125/124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504*t^7 - 704466284715521764115660713634314446981219727024655387590185056679462707361507885103437102164119507545717907475908258301578125/124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504*t^5 + 170162263710157537339166355161491188915640234291350639283447249397195981995596705844562445364810537797659323134085761390515625/124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504*t^3 - 76279256453084276840471975895347039104748116150525158051544198923118499467928905948703945410074344146192737981695260921875/841112586440598750860930858648118040344728313036789187081869531000026411574372261354970793131348*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:
| (6.9627494436481757219 + 1.2380244310909071649e-787j)  +/-  (2.43e-244, 2.43e-244j)
| (-5.6628371750780867178 + 3.5101854655183845905e-795j)  +/-  (4.07e-244, 4.07e-244j)
| (-9.5679543176335030506 - 3.7086761219804039903e-800j)  +/-  (1.14e-245, 1.14e-245j)
| (-8.181441046264234913 + 1.7326683746003475667e-799j)  +/-  (9.13e-245, 9.13e-245j)
| (8.8472282099488412585 - 9.6963719551348117116e-799j)  +/-  (3.92e-245, 3.92e-245j)
| (-8.8472282099488412585 - 1.0500526994817203314e-806j)  +/-  (3.86e-245, 3.86e-245j)
| (10.373655329323480692 + 2.6841814364074188099e-806j)  +/-  (1.96e-246, 1.96e-246j)
| (-10.373655329323480692 - 8.2659253660844924222e-810j)  +/-  (2.16e-246, 2.16e-246j)
| (7.5557396480797264319 - 1.2004273821820502368e-807j)  +/-  (1.53e-244, 1.53e-244j)
| (2.947793470416438335 - 6.2785613097230925719e-823j)  +/-  (1.96e-247, 1.96e-247j)
| (2.5291115060537482634 - 2.7074342775951652613e-823j)  +/-  (3.46e-248, 3.46e-248j)
| (-5.9309347684744783437 - 1.2266550491919665821e-817j)  +/-  (5.32e-244, 5.32e-244j)
| (11.343963711290214099 + 1.5028289160052542664e-825j)  +/-  (1.68e-247, 1.68e-247j)
| (-2.947793470416438335 - 1.0648183607317450822e-822j)  +/-  (1.99e-247, 1.99e-247j)
| (-2.5291115060537482634 - 6.8612468852478796142e-827j)  +/-  (3.35e-248, 3.35e-248j)
| (-11.343963711290214099 - 3.0116895603675588818e-828j)  +/-  (1.6e-247, 1.6e-247j)
| (3.3633245069953754209 + 8.4557379118301001472e-825j)  +/-  (9.67e-247, 9.67e-247j)
| (-3.3633245069953754209 + 9.2679231734201875188e-828j)  +/-  (9.37e-247, 9.37e-247j)
| (-1.3825241009457848841 - 1.4801649895849677043e-839j)  +/-  (1.18e-250, 1.18e-250j)
| (5.2385718534747252466 - 4.2610627920113137783e-833j)  +/-  (1.36e-244, 1.36e-244j)
| (5.9309347684744783437 - 7.9633085139512400223e-851j)  +/-  (5.2e-244, 5.2e-244j)
| (4.2555162521877678015 + 6.3820490148606524653e-864j)  +/-  (1.16e-245, 1.16e-245j)
| (6.4037654380415055938 - 6.1422759201675455765e-869j)  +/-  (3.61e-244, 3.61e-244j)
| (9.5679543176335030506 - 1.0152252040861974582e-877j)  +/-  (1.09e-245, 1.09e-245j)
| (8.181441046264234913 + 1.2119980217169512987e-876j)  +/-  (9.39e-245, 9.39e-245j)
| (-6.4037654380415055938 + 1.0019101168805298758e-877j)  +/-  (3.78e-244, 3.78e-244j)
| (2.1174315361465777052 - 2.3390448021485800015e-887j)  +/-  (5.02e-249, 5.02e-249j)
| (5.6628371750780867178 - 2.828151577030224134e-882j)  +/-  (4.43e-244, 4.43e-244j)
| (-6.9627494436481757219 + 1.0660691430637362129e-883j)  +/-  (2.43e-244, 2.43e-244j)
| (-0.62829065843635177805 + 2.1713401534977278896e-897j)  +/-  (9.11e-253, 9.11e-253j)
| (-4.7421216319039014942 - 1.2286242664081216441e-888j)  +/-  (4.01e-245, 4.01e-245j)
| (3.7942825810806053574 - 4.2720962717074511981e-894j)  +/-  (3.41e-246, 3.41e-246j)
| (1 + 3.9491313675310876486e-900j)  +/-  (1.09e-251, 1.09e-251j)
| (4.7421216319039014942 + 1.6601064771692116204e-893j)  +/-  (3.86e-245, 3.86e-245j)
| (-4.2555162521877678015 + 6.3484996375969080573e-894j)  +/-  (1.15e-245, 1.15e-245j)
| (-1.7404508708598477666 - 2.944789620892820039e-902j)  +/-  (8.37e-250, 8.37e-250j)
| (-7.5557396480797264319 - 7.5616371154958051682e-898j)  +/-  (1.61e-244, 1.61e-244j)
| (0.32075040850526950902 - 3.0910877381894513775e-915j)  +/-  (1.19e-253, 1.19e-253j)
| (1.7404508708598477666 + 7.894834554342138705e-911j)  +/-  (8.75e-250, 8.75e-250j)
| (-5.2385718534747252466 + 3.5542481410957503742e-910j)  +/-  (1.51e-244, 1.51e-244j)
| (-1 - 6.0468623648312152257e-922j)  +/-  (1.29e-251, 1.29e-251j)
| (-3.7942825810806053574 + 1.0407519871732653379e-919j)  +/-  (3.48e-246, 3.48e-246j)
| (1.3825241009457848841 - 8.5818200063326812206e-924j)  +/-  (1.26e-250, 1.26e-250j)
| (0.62829065843635177805 + 1.4730985419408773668e-927j)  +/-  (9.1e-253, 9.1e-253j)
| (1.2384012620008450515e-936 - 3.7741399603934714341e-937j)  +/-  (6.08e-935, 6.08e-935j)
| (-2.1174315361465777052 + 1.4565638692088200159e-922j)  +/-  (5.39e-249, 5.39e-249j)
| (-0.32075040850526950902 - 1.2977628325579881838e-927j)  +/-  (7.92e-254, 7.92e-254j)
-------------------------------------------------
The weights are:
| (6.8410701081600976238e-12 - 4.5019583600581021162e-798j)  +/-  (8.41e-77, 7.37e-198j)
| (1.3112249925287926693e-08 + 7.0206459153740212394e-797j)  +/-  (4.97e-73, 4.36e-194j)
| (3.9865563529578817766e-21 - 4.2754314354249601624e-806j)  +/-  (9.8e-84, 8.6e-205j)
| (7.4960116990045926579e-16 - 9.4183925857328519441e-803j)  +/-  (6.56e-81, 5.75e-202j)
| (2.7724520575276205887e-18 - 2.0966790198086788482e-803j)  +/-  (3.97e-84, 3.49e-205j)
| (2.7724520575276205887e-18 + 2.499147176041221791e-804j)  +/-  (1.92e-82, 1.68e-203j)
| (1.4818790179708539068e-24 - 1.8891297119250863341e-807j)  +/-  (1.04e-87, 9.17e-209j)
| (1.4818790179708539068e-24 + 3.7168274376576251615e-808j)  +/-  (2.18e-86, 1.91e-207j)
| (9.7387506393500140466e-14 - 6.4422411324445886775e-800j)  +/-  (2.05e-81, 1.79e-202j)
| (0.0021530438883757313916 + 5.9222074327787908537e-793j)  +/-  (2.35e-67, 2.06e-188j)
| (0.0068334127763717993444 - 1.5703005766821632209e-792j)  +/-  (5.25e-65, 4.61e-186j)
| (3.2882452731046489394e-09 - 2.1628040663497150199e-797j)  +/-  (7.55e-78, 6.63e-199j)
| (5.082713221149957591e-29 + 3.8510934887386774782e-810j)  +/-  (4e-90, 3.51e-211j)
| (0.0021530438883757313916 + 2.3992031762732763063e-793j)  +/-  (3.64e-69, 3.19e-190j)
| (0.0068334127763717993444 - 7.3348578813321229525e-793j)  +/-  (3.15e-67, 2.76e-188j)
| (5.082713221149957591e-29 - 9.216544225412756202e-811j)  +/-  (4.55e-90, 3.99e-211j)
| (0.0005844996165535390526 - 2.0855119884065224442e-793j)  +/-  (7.19e-72, 6.31e-193j)
| (0.0005844996165535390526 - 7.2696026462223267411e-794j)  +/-  (1.43e-71, 1.25e-192j)
| (0.056551900928008830745 + 1.1217681061747466677e-791j)  +/-  (7.41e-62, 6.5e-183j)
| (2.1455908165639936094e-07 - 1.4599044066597415686e-795j)  +/-  (5.66e-79, 4.97e-200j)
| (3.2882452731046489394e-09 - 2.7026735598981183575e-796j)  +/-  (1.01e-80, 8.87e-202j)
| (2.2173248199897728623e-05 - 1.6796098081705237142e-794j)  +/-  (4.05e-77, 3.55e-198j)
| (2.6614411506659930801e-10 + 3.1258642735875945264e-797j)  +/-  (8.12e-82, 7.13e-203j)
| (3.9865563529578817766e-21 + 2.7128732225060470809e-805j)  +/-  (1.82e-89, 1.6e-210j)
| (7.4960116990045926579e-16 + 1.1703861338148097508e-801j)  +/-  (3.08e-86, 2.7e-207j)
| (2.6614411506659930801e-10 + 1.307226683329848242e-798j)  +/-  (9.73e-86, 8.54e-207j)
| (0.016882103979961639809 + 4.102233271291217481e-792j)  +/-  (3.67e-74, 3.22e-195j)
| (1.3112249925287926693e-08 + 6.8188954036119096077e-796j)  +/-  (3.42e-81, 3e-202j)
| (6.8410701081600976238e-12 - 6.081941685587590659e-800j)  +/-  (2.68e-87, 2.35e-208j)
| (0.11145824216848332302 + 4.2509577148951671809e-791j)  +/-  (1.95e-74, 1.71e-195j)
| (2.5859773856641228265e-06 + 8.5258491661984543373e-796j)  +/-  (9.3e-84, 8.16e-205j)
| (0.00013295384920783184835 + 6.2999637668419014581e-794j)  +/-  (2.35e-79, 2.06e-200j)
| (0.094164345497957052851 - 2.8418110410347664487e-791j)  +/-  (2.54e-76, 2.23e-197j)
| (2.5859773856641228265e-06 + 4.4939498642024345923e-795j)  +/-  (6.07e-81, 5.32e-202j)
| (2.2173248199897728623e-05 - 4.0532978646919361415e-795j)  +/-  (2.11e-83, 1.85e-204j)
| (0.031392368271138387686 - 5.5878568431702142915e-792j)  +/-  (1.45e-78, 1.27e-199j)
| (9.7387506393500140466e-14 + 2.631254774125222305e-801j)  +/-  (2.12e-89, 1.86e-210j)
| (0.11228221402213119011 - 7.1017495258827087253e-791j)  +/-  (3.51e-78, 3.08e-199j)
| (0.031392368271138387686 - 9.3124192221565880853e-792j)  +/-  (3.92e-79, 3.44e-200j)
| (2.1455908165639936094e-07 - 2.0630046030575485555e-796j)  +/-  (6.54e-85, 5.74e-206j)
| (0.094164345497957052851 - 2.1280347999073144513e-791j)  +/-  (2.78e-79, 2.44e-200j)
| (0.00013295384920783184835 + 1.8556449403907573286e-794j)  +/-  (4.42e-83, 3.88e-204j)
| (0.056551900928008830745 + 1.6776134585935212225e-791j)  +/-  (1.26e-79, 1.12e-200j)
| (0.11145824216848332302 + 5.0942299477997297988e-791j)  +/-  (1.89e-79, 1.69e-200j)
| (0.13507984908712986487 + 7.4329875599799046991e-791j)  +/-  (1.27e-79, 1.12e-200j)
| (0.016882103979961639809 + 2.1890121325694995046e-792j)  +/-  (1.69e-81, 1.43e-202j)
| (0.11228221402213119011 - 6.4762566179504764879e-791j)  +/-  (6.27e-80, 5.46e-201j)
