Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 26
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : 4*t^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^35 - 37416868408907001350164610342873279623358444517881629/35698938314212875519871034234589270444069604139811*t^33 + 285252499918350706726367558808162738929490224006579802877/2356129928738049784311488259482891849308593873227526*t^31 - 115291645452434364061420262756323262526795872317246292164891/14136779572428298705868929556897351095851563239365156*t^29 + 10101069438667294302645992209165257753034683392387485586725453/28273559144856597411737859113794702191703126478730312*t^27 - 22510821670623937393673385952975452739465997854670551611954275/2094337714433822030499100675095903866052083442868912*t^25 + 41654169958018244605753644410488153266830296616982979939614775/182116322994245393956443536964861205743659429814688*t^23 - 115722757691397332829409919810727571839059406824677936608614825/33112058726226435264807915811792946498847169057216*t^21 + 2553098965416784588549677699611940158616139779251690230917939075/66224117452452870529615831623585892997694338114432*t^19 - 40572002583441250555776569734023110197151641437307831521283882725/132448234904905741059231663247171785995388676228864*t^17 + 460079983914481425880632611416882647323499485613759282945905206875/264896469809811482118463326494343571990777352457728*t^15 - 3659960693568904822830512102115998793048934013148169593435363789375/529792939619622964236926652988687143981554704915456*t^13 + 19882985996759883716699056073130960983491945723343226788441814971625/1059585879239245928473853305977374287963109409830912*t^11 - 70788850608395094578385754739091455110911801838714017309714866569125/2119171758478491856947706611954748575926218819661824*t^9 + 154844383884378914024499689394540151792991296055544669295022843982375/4238343516956983713895413223909497151852437639323648*t^7 - 186938820123665265741407368919046665974526001454811946403784182591875/8476687033913967427790826447818994303704875278647296*t^5 + 102151000078898067830186167829334890717473523162678199600590778511875/16953374067827934855581652895637988607409750557294592*t^3 - 7956343795587733477005769760097282790008451887153514103373255459375/16953374067827934855581652895637988607409750557294592*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-5.3648198803231331175 + 3.7972843268514425303e-460j)  +/-  (1.04e-119, 1.04e-119j)
| (-1.7320508075688772935 - 1.4312619387456015151e-469j)  +/-  (8.43e-122, 8.43e-122j)
| (5.3648198803231331175 + 5.6246910430594100089e-468j)  +/-  (1.14e-119, 1.14e-119j)
| (-4.8632820898073187521 + 1.4486998994559788548e-467j)  +/-  (1.41e-119, 1.41e-119j)
| (5.9069634010743338039 + 9.6874986590506481362e-476j)  +/-  (5.07e-120, 5.07e-120j)
| (-5.9069634010743338039 - 1.8404397800141391658e-476j)  +/-  (4.75e-120, 4.75e-120j)
| (7.2464742925166877855 + 6.2481448198079770687e-482j)  +/-  (1.66e-121, 1.66e-121j)
| (-4.3903827407648849748 - 2.0617500776689983839e-478j)  +/-  (1.58e-119, 1.58e-119j)
| (6.5132957865499978292 + 5.8198855307316975964e-483j)  +/-  (1.4e-120, 1.4e-120j)
| (-7.2464742925166877855 - 1.0812333245308454226e-483j)  +/-  (1.66e-121, 1.66e-121j)
| (0.7071067811865475244 - 7.5440019453217118656e-487j)  +/-  (5.73e-125, 5.73e-125j)
| (3.5052284637800393951 + 8.975318092759887123e-481j)  +/-  (7.43e-120, 7.43e-120j)
| (-3.5052284637800393951 - 1.9271668008432576252e-482j)  +/-  (8.24e-120, 8.24e-120j)
| (-2.2994934268891748752 - 5.6139324330419399237e-488j)  +/-  (6.18e-121, 6.18e-121j)
| (1.7320508075688772935 - 5.6528129571197414282e-490j)  +/-  (7.89e-122, 7.89e-122j)
| (3.9391327146807163417 + 4.7004288179026050775e-488j)  +/-  (1.16e-119, 1.16e-119j)
| (1.9742777784447147529 - 7.0020484526724375942e-490j)  +/-  (2.46e-121, 2.46e-121j)
| (-2.6822224032999497583 + 1.0610859637610505821e-489j)  +/-  (1.6e-120, 1.6e-120j)
| (-1.9742777784447147529 + 1.6136461834261386509e-492j)  +/-  (2.56e-121, 2.56e-121j)
| (-3.9391327146807163417 + 2.0628670468569020079e-490j)  +/-  (1.17e-119, 1.17e-119j)
| (4.8632820898073187521 + 1.5842634531976753185e-493j)  +/-  (1.45e-119, 1.45e-119j)
| (-0.35140417434854589099 - 4.0507740901303918701e-502j)  +/-  (3.6e-126, 3.6e-126j)
| (4.3903827407648849748 + 3.8221365334494776289e-495j)  +/-  (1.52e-119, 1.52e-119j)
| (-3.0862771695528392808 - 1.9520918472991476006e-496j)  +/-  (3.87e-120, 3.87e-120j)
| (-1.0303636268308812029e-512 + 1.0516831753307122292e-512j)  +/-  (5.15e-511, 5.15e-511j)
| (2.2994934268891748752 + 9.6294515453971988218e-503j)  +/-  (5.85e-121, 5.85e-121j)
| (1.0672470719421885588 - 1.1424554811401316087e-506j)  +/-  (9.08e-124, 9.08e-124j)
| (2.6822224032999497583 + 9.9822306700679762226e-503j)  +/-  (1.67e-120, 1.67e-120j)
| (-1.0672470719421885588 - 9.1874413249905943426e-508j)  +/-  (8.29e-124, 8.29e-124j)
| (-0.7071067811865475244 + 2.4919468645097224398e-509j)  +/-  (5.9e-125, 5.9e-125j)
| (0.35140417434854589099 + 7.6478567276295436433e-510j)  +/-  (3.6e-126, 3.6e-126j)
| (3.0862771695528392808 + 2.0901637485155928452e-508j)  +/-  (3.55e-120, 3.55e-120j)
| (-6.5132957865499978292 - 1.3362809585061252259e-513j)  +/-  (1.53e-120, 1.53e-120j)
| (1.4230339927990597369 + 1.1144539348759302939e-522j)  +/-  (1.09e-122, 1.09e-122j)
| (-1.4230339927990597369 - 1.7566209862311107963e-529j)  +/-  (1.09e-122, 1.09e-122j)
-------------------------------------------------
The weights are:
| (9.2731334339239192055e-14 + 2.0656373509403164173e-472j)  +/-  (2.87e-34, 3.15e-93j)
| (0.0072540681827728183772 - 1.6028464372346857702e-466j)  +/-  (3.2e-18, 3.51e-77j)
| (9.2731334339239192055e-14 + 3.2818224702908839303e-474j)  +/-  (3.14e-35, 3.44e-94j)
| (1.4659497418834761023e-11 - 1.1601456195237093127e-471j)  +/-  (3.22e-33, 3.54e-92j)
| (2.2532032896129156341e-16 - 1.2011649618177586401e-475j)  +/-  (7.83e-37, 8.59e-96j)
| (2.2532032896129156341e-16 + 2.4973529285271452828e-474j)  +/-  (1.52e-36, 1.66e-95j)
| (7.5004471512865031977e-24 - 1.2875946943361360205e-479j)  +/-  (1.17e-40, 1.28e-99j)
| (1.1067935830855144455e-09 + 7.021732176060584496e-471j)  +/-  (4.36e-33, 4.79e-92j)
| (1.3869160299165877601e-19 + 2.2582561049167326278e-477j)  +/-  (8.17e-39, 8.96e-98j)
| (7.5004471512865031977e-24 + 8.6297486337932469205e-479j)  +/-  (6.92e-41, 7.59e-100j)
| (0.12264044203903341023 + 1.7986640848783367085e-466j)  +/-  (7.16e-25, 7.86e-84j)
| (1.1091931938325165243e-06 + 5.0547305310679245942e-470j)  +/-  (4.08e-33, 4.47e-92j)
| (1.1091931938325165243e-06 + 2.4110394629090794901e-469j)  +/-  (6.82e-32, 7.48e-91j)
| (0.0010408920599994559325 - 2.570055728479363961e-467j)  +/-  (2.77e-28, 3.04e-87j)
| (0.0072540681827728183772 - 8.2046944093321938745e-467j)  +/-  (3.25e-27, 3.57e-86j)
| (4.5501821819395825638e-08 - 6.6208189387292707873e-471j)  +/-  (1.09e-34, 1.19e-93j)
| (0.0030936122629575585231 + 4.2813326409944994226e-467j)  +/-  (1.17e-28, 1.29e-87j)
| (0.00016755701922070329744 + 5.6841871374800923957e-468j)  +/-  (1.55e-30, 1.7e-89j)
| (0.0030936122629575585231 + 9.2670204044600567478e-467j)  +/-  (3.2e-28, 3.52e-87j)
| (4.5501821819395825638e-08 - 4.3206904556621722142e-470j)  +/-  (1.33e-33, 1.46e-92j)
| (1.4659497418834761023e-11 - 5.6888250605475258995e-473j)  +/-  (1.37e-37, 1.5e-96j)
| (0.1760630701581780782 - 2.5704090360342534364e-466j)  +/-  (1.39e-29, 1.53e-88j)
| (1.1067935830855144455e-09 + 7.0139619877431478015e-472j)  +/-  (1.1e-36, 1.21e-95j)
| (1.6958280937046386942e-05 - 1.214750886976121239e-468j)  +/-  (4.79e-33, 5.25e-92j)
| (0.19776026874515188389 + 2.5524637367495753162e-466j)  +/-  (1.27e-29, 1.39e-88j)
| (0.0010408920599994559325 - 1.0279019399557096378e-467j)  +/-  (4.06e-33, 4.45e-92j)
| (0.065151226470520262162 - 1.361602258254658362e-466j)  +/-  (5.84e-31, 6.41e-90j)
| (0.00016755701922070329744 + 1.8949214099238880046e-468j)  +/-  (2.35e-34, 2.57e-93j)
| (0.065151226470520262162 - 2.0378902931138171314e-466j)  +/-  (3.25e-32, 3.47e-91j)
| (0.12264044203903341023 + 2.3447980076833001208e-466j)  +/-  (9.94e-32, 1.08e-90j)
| (0.1760630701581780782 - 2.2543743097655372296e-466j)  +/-  (1.46e-31, 1.63e-90j)
| (1.6958280937046386942e-05 - 3.2751710260585709569e-469j)  +/-  (2.47e-35, 2.73e-94j)
| (1.3869160299165877601e-19 - 2.3355970288659007684e-476j)  +/-  (8.8e-44, 9.66e-103j)
| (0.025690883337243035729 + 1.0630828057204876255e-466j)  +/-  (7.6e-33, 8.78e-92j)
| (0.025690883337243035729 + 1.8306897787804968088e-466j)  +/-  (5.86e-33, 5.82e-92j)
