Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 32
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^40 - 32753391346002444711417368697663296609362685370786172381/2114350332602141585512026716786491322371454032005135076*t^38 + 470015681484128861739235836489762190758001310596778149583/6343050997806424756536080150359473967114362096015405228*t^36 - 5964197815312781979905770036030854259260375827831491531426415/27381138857245248124035819129058889266327811350756785682068*t^34 + 92416158490809897518930872562208687544238575358562492473004845/209922064572213568950941279989451484375179887022468690229188*t^32 - 1211839545719891642216270324715682992066467784157883230917177113/1868762727006988184465444655558269192426873124689150622801141*t^30 + 9299187918329782352944776376114658552310586123286569008335863577/12915635990102484841404033752454441758497059083442750363497541*t^28 - 52046735513167368225281220944656917353142072416127147698266914177/84669169268449622849204221266090229305702942880346919049594991*t^26 + 18603509486637788584655181557793512650439614454994935473204626350/45591091144549796918802272989433200395378507704802187180551149*t^24 - 9225989212073178741700484195591484871926162681539660820057355075/43608869790438936183202174163805669943405529108941222520527186*t^22 + 2569216589891272150926082197135296111024925532678915190454935235/30016494790821605424801496502359746844162247308751750566077154*t^20 - 806225269402030912496269305853212169823879012908733265962524565/30016494790821605424801496502359746844162247308751750566077154*t^18 + 179349349533590738989043110670980852770027570880039085682907795/27751098957552050298401383558785426327621700342053505240335482*t^16 - 247584688501248643810879537063088038470579449228953128860775/211383766132546517076066876777181315803959488089801060324487*t^14 + 49091910020260100864848409871107143738969816652319949912600325/315173195303626856960415713274777341863703596741893380943810117*t^12 - 1388693389518931591834867578914044115599359252372471085787391995/94867131786391683945085129695707979900974782619309907664086845217*t^10 + 2115075181255436346739256154400251170225609825134783087729105005/2299483810721720439775837043064519210933061712042895497719438374002*t^8 - 1235448431146257475962024881279002321624327833978387791023144015/34820754848071766659462675223548433765557791639506703251180066806316*t^6 + 329356703684638554031405072731550161847982145526033597729903675/452669813024932966573014777906129638952251291313587142265340868482108*t^4 - 18874565734151527689487616699107620380174468109113224722828675/3168688691174530766011103445342907472665759039195109995857386079374756*t^2 + 40621451744539340969902545135889519476673752824180248376625/4979367943274262632303162556967426028474764204449458564918749553303188
-------------------------------------------------
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:
| (0.98219129046748981137 - 4.7996679027367274711e-871j)  +/-  (1.25e-240, 1.25e-240j)
| (-0.99254806707324229715 - 8.0157239588945720981e-878j)  +/-  (9.01e-241, 9.01e-241j)
| (-0.92164320501362577831 + 3.7975425178417665791e-897j)  +/-  (2.34e-241, 2.34e-241j)
| (0.96749992431397659206 - 2.9961762796366418848e-905j)  +/-  (9.63e-241, 9.63e-241j)
| (0.92164320501362577831 - 2.8269294072298385999e-908j)  +/-  (2.52e-241, 2.52e-241j)
| (0.94759182575520632727 + 1.1801656899949650006e-909j)  +/-  (5.83e-241, 5.83e-241j)
| (-0.99855771856394390988 + 1.1531840349311919462e-914j)  +/-  (3.16e-241, 3.16e-241j)
| (-0.88944081338324464004 + 5.583166247002301101e-928j)  +/-  (8.85e-242, 8.85e-242j)
| (-0.96749992431397659206 + 1.9043030676635981472e-939j)  +/-  (1.01e-240, 1.01e-240j)
| (0.99855771856394390988 + 3.3680883490721919558e-953j)  +/-  (3.26e-241, 3.26e-241j)
| (0.88944081338324464004 - 5.2887779380363714958e-962j)  +/-  (7.87e-242, 7.87e-242j)
| (-0.98219129046748981137 - 2.5779443592672988108e-964j)  +/-  (1.22e-240, 1.22e-240j)
| (-0.94759182575520632727 - 1.4892235008948990668e-980j)  +/-  (5.37e-241, 5.37e-241j)
| (-0.85110112875893547946 - 1.0554804363621574776e-988j)  +/-  (2.28e-242, 2.28e-242j)
| (0.99254806707324229715 + 5.3362787272059028508e-990j)  +/-  (8.62e-241, 8.62e-241j)
| (0.80685833450468893114 + 2.8845152589775871999e-993j)  +/-  (4.81e-243, 4.81e-243j)
| (0.85110112875893547946 + 2.3030646796338306951e-995j)  +/-  (2.2e-242, 2.2e-242j)
| (-0.43671106473956595259 - 1.6043074262402694043e-1002j)  +/-  (1.27e-248, 1.27e-248j)
| (-0.80685833450468893114 - 1.22971458945768109e-996j)  +/-  (5.21e-243, 5.21e-243j)
| (-0.75700494099401599158 + 8.0864718511652794643e-999j)  +/-  (9.02e-244, 9.02e-244j)
| (0.28387047696054923783 - 5.6743386536873578362e-1007j)  +/-  (4.34e-251, 4.34e-251j)
| (0.75700494099401599158 + 2.6819446816925801898e-1000j)  +/-  (9.34e-244, 9.34e-244j)
| (0.2041968861768067152 + 4.0160096542984880826e-1010j)  +/-  (2.04e-252, 2.04e-252j)
| (-0.70187819513669373146 - 5.0732228316280544664e-1002j)  +/-  (1.44e-244, 1.44e-244j)
| (-0.57735026918962576451 - 7.7901741337311109091e-1007j)  +/-  (1.86e-246, 1.86e-246j)
| (-0.041127073714634074403 - 1.1947380710680723846e-1014j)  +/-  (5.31e-255, 5.31e-255j)
| (0.70187819513669373146 - 1.4478279020471714387e-1002j)  +/-  (1.48e-244, 1.48e-244j)
| (0.50880994877518660445 + 7.2782254793200174339e-1007j)  +/-  (1.57e-247, 1.57e-247j)
| (-0.12309310924509818556 + 1.3261216731167716937e-1012j)  +/-  (9.68e-254, 9.68e-254j)
| (-0.64185535758148376428 + 2.8818231043702842167e-1004j)  +/-  (2.05e-245, 2.05e-245j)
| (-0.2041968861768067152 - 1.0043850590210922886e-1010j)  +/-  (2.52e-252, 2.52e-252j)
| (0.43671106473956595259 + 7.7640888408338692058e-1008j)  +/-  (1.34e-248, 1.34e-248j)
| (0.64185535758148376428 - 6.1596891448399594173e-1005j)  +/-  (1.82e-245, 1.82e-245j)
| (0.041127073714634074403 + 3.2307821445010620537e-1016j)  +/-  (5.31e-255, 5.31e-255j)
| (-0.50880994877518660445 + 3.9140509356670302898e-1011j)  +/-  (1.74e-247, 1.74e-247j)
| (-0.3615562793746976671 + 6.9399929172052993547e-1012j)  +/-  (8.2e-250, 8.2e-250j)
| (0.12309310924509818556 - 7.9108490493767038748e-1015j)  +/-  (9.7e-254, 9.7e-254j)
| (0.57735026918962576451 + 2.2849189651152151661e-1009j)  +/-  (1.97e-246, 1.97e-246j)
| (0.3615562793746976671 - 5.8045523239159419482e-1013j)  +/-  (7.76e-250, 7.76e-250j)
| (-0.28387047696054923783 + 3.115819761694648226e-1013j)  +/-  (4.12e-251, 4.12e-251j)
-------------------------------------------------
The weights are:
| (0.012440677988038557814 + 9.9333958989022705731e-872j)  +/-  (1.67e-72, 1.92e-188j)
| (0.008254896376858942619 + 1.7152214653966837841e-873j)  +/-  (3.8e-73, 4.37e-189j)
| (0.029078461716552356307 + 3.6513839274311215245e-873j)  +/-  (3.73e-73, 4.29e-189j)
| (0.017114922674639161385 - 5.1296416294985225591e-871j)  +/-  (5.87e-73, 6.74e-189j)
| (0.029078461716552356307 - 1.148123354438609015e-871j)  +/-  (8.98e-74, 1.03e-189j)
| (0.022846791050314586414 + 2.2128758644184391052e-871j)  +/-  (2.29e-73, 2.63e-189j)
| (0.003683826198091459011 - 5.0263027859932077896e-874j)  +/-  (4.96e-75, 5.7e-191j)
| (0.035303723329160442962 - 3.2454950117004265194e-873j)  +/-  (8.48e-76, 9.74e-192j)
| (0.017114922674639161385 + 3.8652427131771231673e-873j)  +/-  (1.47e-75, 1.68e-191j)
| (0.003683826198091459011 - 6.0826976055239277032e-872j)  +/-  (1.88e-76, 2.16e-192j)
| (0.035303723329160442962 + 6.5491783216301660741e-872j)  +/-  (1.3e-76, 1.49e-192j)
| (0.012440677988038557814 - 3.0395764538524257995e-873j)  +/-  (1.4e-75, 1.61e-191j)
| (0.022846791050314586414 - 3.9674758252354799328e-873j)  +/-  (4.46e-76, 5.12e-192j)
| (0.041335892077163462472 + 2.8829005970525879703e-873j)  +/-  (3.35e-78, 3.85e-194j)
| (0.008254896376858942619 + 3.2705153411422430704e-871j)  +/-  (5.09e-77, 5.84e-193j)
| (0.047100780812612468738 + 2.6441032055241464707e-872j)  +/-  (3.33e-80, 3.83e-196j)
| (0.041335892077163462472 - 4.0317389569556134376e-872j)  +/-  (2.9e-79, 3.33e-195j)
| (0.073712591150455341064 - 1.9274287192272936664e-873j)  +/-  (3.89e-83, 4.47e-199j)
| (0.047100780812612468738 - 2.5913063600878812552e-873j)  +/-  (8.27e-81, 9.49e-197j)
| (0.052549730988702992937 + 2.3664548870519210796e-873j)  +/-  (9.93e-82, 1.14e-197j)
| (0.078771566285587627392 + 3.5936589981833936676e-873j)  +/-  (1.38e-85, 1.58e-201j)
| (0.052549730988702992937 - 1.8277019296427011804e-872j)  +/-  (1.37e-83, 1.57e-199j)
| (0.080482614061529013534 - 3.1360245299870049915e-873j)  +/-  (9.4e-86, 1.08e-201j)
| (0.05764082842691444501 - 2.1978872552171484098e-873j)  +/-  (1.27e-83, 1.46e-199j)
| (0.066599798156442486754 - 1.9933014538944903364e-873j)  +/-  (4.72e-85, 5.42e-201j)
| (0.082206094132044959046 + 2.3185299037414941234e-873j)  +/-  (5.04e-87, 5.79e-203j)
| (0.05764082842691444501 + 1.3204516630246512987e-872j)  +/-  (1.62e-85, 1.86e-201j)
| (0.070401336983553508406 - 6.1255798314983178908e-873j)  +/-  (4.89e-87, 5.62e-203j)
| (0.081630216721059421245 - 2.166616883584109859e-873j)  +/-  (1.71e-87, 1.96e-203j)
| (0.062335816659777993741 + 2.0759591326176622961e-873j)  +/-  (9.73e-86, 1.12e-201j)
| (0.080482614061529013534 + 2.056501553761362635e-873j)  +/-  (7.52e-88, 8.63e-204j)
| (0.073712591150455341064 + 5.0136268559594243577e-873j)  +/-  (6.13e-88, 7.06e-204j)
| (0.062335816659777993741 - 9.9062633648534287625e-873j)  +/-  (2.13e-87, 2.45e-203j)
| (0.082206094132044959046 - 2.5211821496530879095e-873j)  +/-  (2.96e-88, 3.4e-204j)
| (0.070401336983553508406 + 1.9448230863821919546e-873j)  +/-  (8.44e-88, 9.65e-204j)
| (0.076509434210500773152 + 1.9397754201084287494e-873j)  +/-  (1.35e-88, 1.55e-204j)
| (0.081630216721059421245 + 2.7874905667168662021e-873j)  +/-  (6.62e-89, 7.77e-205j)
| (0.066599798156442486754 + 7.6786650049980462727e-873j)  +/-  (3.98e-89, 4.66e-205j)
| (0.076509434210500773152 - 4.1998425986433039114e-873j)  +/-  (2.37e-89, 2.79e-205j)
| (0.078771566285587627392 - 1.982151528489568869e-873j)  +/-  (1.79e-89, 1.87e-205j)
