Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 26
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 9677760980250929714296375932722228873871700280671937713461681871189/17474911227006623643937863932476603781518266745687914025362038292*t^35 + 4758253990583310088300420805205125221782817719718150704171100527529559/34949822454013247287875727864953207563036533491375828050724076584*t^33 - 229234777374127007505224926849209154675634318525622975162685852375694989/11649940818004415762625242621651069187678844497125276016908025528*t^31 + 65253625553933673889995397200910576573130424381690190172965729366452050219/34949822454013247287875727864953207563036533491375828050724076584*t^29 - 4300458815499615342371391563519482204513922298263249873764201100892457663997/34949822454013247287875727864953207563036533491375828050724076584*t^27 + 7524989455853686842775325311007710540104296818468555925738891961706172306515/1294437868667157306958360291294563243075427166347252890767558392*t^25 - 259439269578128536074970937134006332882697872180627314726436491228408094815425/1294437868667157306958360291294563243075427166347252890767558392*t^23 + 598620211391254930114632391356492975019981880398222582863649847467550520968975/117676169878832482450760026481323931188675196940659353706141672*t^21 - 11206638068362490007645514260531605245985400453795530195227815676451109170223525/117676169878832482450760026481323931188675196940659353706141672*t^19 + 154112464093225887246182943756196193477098369620365432269436211663617593533807075/117676169878832482450760026481323931188675196940659353706141672*t^17 - 1540837870802419301094147570820648029903471172823255379651210957439283258635240125/117676169878832482450760026481323931188675196940659353706141672*t^15 + 11003084701740830138636680475523673759821042164652829730396288042659580505658985625/117676169878832482450760026481323931188675196940659353706141672*t^13 - 54582289403737741643258876392907662856437220924301990066139471451485209740426253375/117676169878832482450760026481323931188675196940659353706141672*t^11 + 180287208498045758760871504344841942462323148574314337395600107700943168942848183875/117676169878832482450760026481323931188675196940659353706141672*t^9 - 371336395763594672528826390866627300258911489568298582852048598150625703917687276625/117676169878832482450760026481323931188675196940659353706141672*t^7 + 428604813259731233285957779194655792624361589682719369257061341577092040887203168125/117676169878832482450760026481323931188675196940659353706141672*t^5 - 228241990123102841642641235412367136689065688287006547625134632025350034090034458125/117676169878832482450760026481323931188675196940659353706141672*t^3 + 17831462585522020446778732358198722830316435255985870577135054102541799038308230625/58838084939416241225380013240661965594337598470329676853070836*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:
| (8.4703186603320227678 - 2.9101653081720719667e-664j)  +/-  (3.24e-247, 3.24e-247j)
| (-10.312979400117505402 - 6.6898828768960207257e-677j)  +/-  (1.04e-248, 1.04e-248j)
| (-8.4703186603320227678 + 3.7773025985568599731e-696j)  +/-  (3.19e-247, 3.19e-247j)
| (6.3655056935315424187 + 2.8510415809104724856e-721j)  +/-  (1.37e-246, 1.37e-246j)
| (-9.3074971798619382195 - 1.4770886990628028441e-735j)  +/-  (8.3e-248, 8.3e-248j)
| (9.3074971798619382195 - 1.1038613158709629932e-741j)  +/-  (8.86e-248, 8.86e-248j)
| (-6.3655056935315424187 + 2.4147613891520899537e-748j)  +/-  (1.42e-246, 1.42e-246j)
| (-4.5448979391212497356 + 2.2021764150712293099e-748j)  +/-  (5.18e-247, 5.18e-247j)
| (-3.2728782272458314193 - 2.3457299482246410243e-746j)  +/-  (3.45e-246, 3.45e-246j)
| (10.312979400117505402 - 1.8956725522234223025e-756j)  +/-  (1.07e-248, 1.07e-248j)
| (1.961016437141193946 - 8.4903075593871442791e-768j)  +/-  (3.66e-250, 3.66e-250j)
| (7.0229829932683285366 - 1.0450438642712482471e-770j)  +/-  (1.28e-246, 1.28e-246j)
| (-3.9699080310480870586 - 2.0154371755082753397e-779j)  +/-  (2.79e-247, 2.79e-247j)
| (-1.4846757465533850631 - 1.5574262641559478574e-783j)  +/-  (3.45e-251, 3.45e-251j)
| (-7.7192408523160606147 + 1.2079253442818038181e-779j)  +/-  (7.2e-247, 7.2e-247j)
| (4.5448979391212497356 + 2.0300205787336372233e-784j)  +/-  (4.96e-247, 4.96e-247j)
| (-1.961016437141193946 - 2.4990529685096001775e-795j)  +/-  (3.41e-250, 3.41e-250j)
| (-5.131960506593584746 + 8.3328110963490822708e-791j)  +/-  (8.28e-247, 8.28e-247j)
| (-3.2966762984667854445 + 3.6640216385932681371e-789j)  +/-  (3.47e-246, 3.47e-246j)
| (-1 + 2.2017212216692568096e-799j)  +/-  (1.82e-252, 1.82e-252j)
| (-7.0229829932683285366 - 2.5489578180910371757e-794j)  +/-  (1.26e-246, 1.26e-246j)
| (5.7372566375188701199 + 3.7908598074609116705e-797j)  +/-  (1.17e-246, 1.17e-246j)
| (7.7042258158595233097e-819 - 3.1160007912893433516e-819j)  +/-  (3.07e-817, 3.07e-817j)
| (-2.4494897427831780982 + 5.4919711546448626391e-805j)  +/-  (4.13e-249, 4.13e-249j)
| (-3.0157118962323483382 + 9.8947217946044382359e-804j)  +/-  (1.36e-247, 1.36e-247j)
| (3.2966762984667854445 - 5.1826631622502774514e-799j)  +/-  (3.23e-246, 3.23e-246j)
| (2.4494897427831780982 + 5.0497920990784491872e-813j)  +/-  (4.13e-249, 4.13e-249j)
| (3.9699080310480870586 + 1.2645432541581011729e-813j)  +/-  (3.12e-247, 3.12e-247j)
| (5.131960506593584746 - 1.6289605937558268684e-835j)  +/-  (8.21e-247, 8.21e-247j)
| (-0.50331705658134812136 - 6.850098523803053547e-857j)  +/-  (1.64e-253, 1.64e-253j)
| (7.7192408523160606147 + 5.8896913736770460197e-855j)  +/-  (7.24e-247, 7.24e-247j)
| (1 - 1.80770384898442163e-874j)  +/-  (1.93e-252, 1.93e-252j)
| (3.2728782272458314193 - 7.1927959006586949435e-867j)  +/-  (3.24e-246, 3.24e-246j)
| (0.50331705658134812136 + 3.5502925903012188993e-884j)  +/-  (1.64e-253, 1.64e-253j)
| (-5.7372566375188701199 - 1.2411607996200097383e-878j)  +/-  (1.18e-246, 1.18e-246j)
| (3.0157118962323483382 + 8.8787381820722115593e-890j)  +/-  (1.37e-247, 1.37e-247j)
| (1.4846757465533850631 + 5.3501291296214131533e-903j)  +/-  (3.24e-251, 3.24e-251j)
-------------------------------------------------
The weights are:
| (8.2652908951098864073e-17 + 1.1395192504933243392e-679j)  +/-  (2.7e-93, 5.17e-217j)
| (3.7106846244253552141e-24 + 1.1996750079009702916e-685j)  +/-  (1.14e-96, 2.18e-220j)
| (8.2652908951098864073e-17 + 1.4198617424835115895e-681j)  +/-  (4.85e-94, 9.31e-218j)
| (4.0686415160893134574e-10 - 9.0439425105445236606e-677j)  +/-  (6.48e-91, 1.24e-214j)
| (5.5376932388127187489e-20 - 2.3569790459831249694e-683j)  +/-  (2.54e-95, 4.87e-219j)
| (5.5376932388127187489e-20 + 5.0051379056180886199e-682j)  +/-  (1.76e-96, 3.37e-220j)
| (4.0686415160893134574e-10 - 1.2830973873207703059e-677j)  +/-  (3.7e-91, 7.1e-215j)
| (7.560838962485525144e-06 + 1.1586150216089702493e-674j)  +/-  (2.04e-87, 3.92e-211j)
| (-0.010493926530986767901 - 3.614542650606156463e-671j)  +/-  (7.1e-84, 1.36e-207j)
| (3.7106846244253552141e-24 - 1.2228975612569709507e-684j)  +/-  (3.15e-99, 6.05e-223j)
| (0.027865529948010521468 + 8.6861617100868766184e-672j)  +/-  (2.66e-80, 5.11e-204j)
| (5.2473816997018550888e-12 + 9.5062491016196387272e-678j)  +/-  (9.91e-94, 1.9e-217j)
| (8.6578502252067508543e-05 - 1.0302895036426572568e-673j)  +/-  (8.59e-87, 1.65e-210j)
| (0.063411528615731932213 - 7.2844158019287802505e-672j)  +/-  (1.88e-78, 3.6e-202j)
| (3.3057474028530326191e-14 - 4.4340657244750133066e-680j)  +/-  (1.27e-94, 2.44e-218j)
| (7.560838962485525144e-06 + 3.8415310186088187657e-674j)  +/-  (2.34e-91, 4.49e-215j)
| (0.027865529948010521468 + 5.4202890811320450131e-672j)  +/-  (3.94e-82, 7.56e-206j)
| (4.5366674942868791935e-07 - 1.3647819629348696942e-675j)  +/-  (3.01e-90, 5.78e-214j)
| (0.0099480665184692518146 + 3.1746638193017585504e-671j)  +/-  (4.6e-85, 8.83e-209j)
| (0.11886138157858671132 + 8.8619055811031724396e-672j)  +/-  (2.3e-82, 4.4e-206j)
| (5.2473816997018550888e-12 + 8.8804398780740362621e-679j)  +/-  (7.72e-94, 1.48e-217j)
| (1.7489694719055540009e-08 + 7.5286636065962633738e-676j)  +/-  (7.38e-95, 1.42e-218j)
| (0.20123094402707388939 + 1.0872081046316154518e-671j)  +/-  (2.34e-83, 4.48e-207j)
| (0.010026817070800917849 - 3.8253959685166692722e-672j)  +/-  (1.91e-85, 3.65e-209j)
| (0.0035386429897468548637 + 6.0913096243649625766e-672j)  +/-  (8.18e-86, 1.57e-209j)
| (0.0099480665184692518146 + 7.220493908306571481e-671j)  +/-  (9.47e-92, 1.82e-215j)
| (0.010026817070800917849 - 6.938013289249462675e-672j)  +/-  (1.9e-90, 3.65e-214j)
| (8.6578502252067508543e-05 - 2.8479701162521433566e-673j)  +/-  (1.32e-93, 2.52e-217j)
| (4.5366674942868791935e-07 - 5.5608608803809399165e-675j)  +/-  (1.78e-95, 3.41e-219j)
| (0.1761318768863002594 - 1.0044875810807401103e-671j)  +/-  (5.66e-89, 1.09e-212j)
| (3.3057474028530326191e-14 - 9.557674339894183855e-679j)  +/-  (6.26e-100, 1.2e-223j)
| (0.11886138157858671132 + 1.1234469854207233414e-671j)  +/-  (4.33e-91, 8.29e-215j)
| (-0.010493926530986767901 - 8.1667671907134149887e-671j)  +/-  (7.16e-92, 1.37e-215j)
| (0.1761318768863002594 - 1.131405023257245623e-671j)  +/-  (2.11e-91, 4.03e-215j)
| (1.7489694719055540009e-08 + 1.4482629269496966428e-676j)  +/-  (6.77e-97, 1.3e-220j)
| (0.0035386429897468548637 + 1.2826766713126913455e-671j)  +/-  (1.06e-92, 2.04e-216j)
| (0.063411528615731932213 - 1.0380765158006558318e-671j)  +/-  (1.82e-92, 3.47e-216j)
