Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 10 23
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : t^12 - 8477/152*t^10 + 155745/152*t^8 - 563535/76*t^6 + 1500975/76*t^4 - 2132865/152*t^2 + 110565/152
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 87831838483004721172497261052311145174474953329557/170468394619153668336242982827250419222961621976*t^33 + 330160321281965263939728981404654588857847177567137077/2897962708525612361716130708063257126790347573592*t^31 - 41562525783158140029842358092122133390747595146556558675/2897962708525612361716130708063257126790347573592*t^29 + 23282701522672331249466521994835054036722622004392985589855/20285738959679286532012914956442799887532433015144*t^27 - 178748345971783060462267701080839460580635393327183443576095/2897962708525612361716130708063257126790347573592*t^25 + 46478103318336452119582769678051486794453310216189159586510195/20285738959679286532012914956442799887532433015144*t^23 - 172819000466514476203622334958166112195892320769769450873590155/2897962708525612361716130708063257126790347573592*t^21 + 3161611611675967210588641194216256574998006115984074079021847025/2897962708525612361716130708063257126790347573592*t^19 - 2127867094249190507622389874239412190275913891497153384522438075/152524353080295387458743721477013532988965661768*t^17 + 1103546319452758578773421162727814801667276412139807598582096525/8972020769429140438749630675118443116997980104*t^15 - 6557634813306287837798832824369238217848292987034154793472767275/8972020769429140438749630675118443116997980104*t^13 + 25402123650516251192238570101935041647141509762484167378255455825/8972020769429140438749630675118443116997980104*t^11 - 61205267201423971693659221335495600186660601260168226337481377375/8972020769429140438749630675118443116997980104*t^9 + 85981214363605155272889912466336366834316787276086682915916489125/8972020769429140438749630675118443116997980104*t^7 - 63961412666440002918388375946288503688243234452574380427984980875/8972020769429140438749630675118443116997980104*t^5 + 20307084658707043834465430148286508319890465031133838662266839625/8972020769429140438749630675118443116997980104*t^3 - 476879449806310210796004990029132812063040705802943023196579125/4486010384714570219374815337559221558498990052*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:
| (-3.3881256086954252244 - 9.5722912043498465053e-681j)  +/-  (8.77e-249, 8.77e-249j)
| (-3.9544879426500450264 - 1.6031366723108815337e-693j)  +/-  (1.93e-248, 1.93e-248j)
| (-6.5807625661680946401 - 6.6948425767359376947e-705j)  +/-  (1.14e-247, 1.14e-247j)
| (-11.642864569453401113 + 4.0233448151308515886e-723j)  +/-  (2.8e-250, 2.8e-250j)
| (9.1845652223207890338 - 1.1324334392940355826e-741j)  +/-  (6.88e-249, 6.88e-249j)
| (7.3418747083508014902 + 2.1622929732841065481e-765j)  +/-  (7.29e-248, 7.29e-248j)
| (2.8901633840314029187 + 1.4245918446487889657e-775j)  +/-  (3.45e-249, 3.45e-249j)
| (1 + 2.4765217403268810421e-783j)  +/-  (4.06e-250, 4.06e-250j)
| (5.8722276658213863302 - 2.1580166786950956753e-802j)  +/-  (1.23e-247, 1.23e-247j)
| (-5.2019365924015129919 + 5.8986121158549797779e-813j)  +/-  (8.48e-248, 8.48e-248j)
| (-7.3418747083508014902 + 2.4894240563125846615e-815j)  +/-  (8.14e-248, 8.14e-248j)
| (-8.1845253144504689109 - 2.1759736143753766075e-816j)  +/-  (3.6e-248, 3.6e-248j)
| (4.5628512951616784443 - 3.4106859883003909018e-821j)  +/-  (4.47e-248, 4.47e-248j)
| (11.642864569453401113 + 1.8797182740247502915e-832j)  +/-  (2.82e-250, 2.82e-250j)
| (-5.8722276658213863302 + 2.9540887577694357524e-831j)  +/-  (1.2e-247, 1.2e-247j)
| (8.1845253144504689109 - 1.2686539402626087634e-840j)  +/-  (3.83e-248, 3.83e-248j)
| (5.2019365924015129919 - 7.1659974657117800446e-863j)  +/-  (8.22e-248, 8.22e-248j)
| (1.9137355618993510628 + 2.7827075757227702442e-876j)  +/-  (1.51e-250, 1.51e-250j)
| (-1.9137355618993510628 + 9.9413704851561372296e-879j)  +/-  (1.38e-250, 1.38e-250j)
| (6.5807625661680946401 + 1.5021363659638082337e-883j)  +/-  (1.17e-247, 1.17e-247j)
| (-1.2900539882844451977 - 1.2639724038930867009e-896j)  +/-  (3.12e-251, 3.12e-251j)
| (2.4299035623031287317 - 7.7695061848250423609e-893j)  +/-  (8.59e-250, 8.59e-250j)
| (-1.0046073797622031812 - 3.5777641603284301208e-895j)  +/-  (3.9e-250, 3.9e-250j)
| (-4.5628512951616784443 + 1.0124628424630285647e-892j)  +/-  (4.94e-248, 4.94e-248j)
| (-2.8901633840314029187 + 3.2434537326836036133e-895j)  +/-  (3.02e-249, 3.02e-249j)
| (-0.23704314987094039888 + 2.1004657361358721842e-898j)  +/-  (2.07e-254, 2.07e-254j)
| (1.2900539882844451977 + 1.355576594915892067e-896j)  +/-  (3.12e-251, 3.12e-251j)
| (-9.1845652223207890338 + 2.0011470647544949938e-901j)  +/-  (6.81e-249, 6.81e-249j)
| (-1 - 1.8574318864900465638e-897j)  +/-  (3.61e-250, 3.61e-250j)
| (0.23704314987094039888 - 1.5816204773665219311e-897j)  +/-  (2.07e-254, 2.07e-254j)
| (3.3881256086954252244 - 5.5981314384216123979e-899j)  +/-  (8.82e-249, 8.82e-249j)
| (-3.5410082150293800535e-908 + 2.4744663820536147754e-908j)  +/-  (1.51e-906, 1.51e-906j)
| (1.0046073797622031812 - 1.3386391449853727396e-909j)  +/-  (4.67e-250, 4.67e-250j)
| (3.9544879426500450264 + 4.7932897725238394245e-921j)  +/-  (2e-248, 2e-248j)
| (-2.4299035623031287317 - 8.2449792152896026867e-928j)  +/-  (8.17e-250, 8.17e-250j)
-------------------------------------------------
The weights are:
| (0.00068836209924980539842 - 2.3346758097758158019e-683j)  +/-  (2.93e-84, 1.82e-207j)
| (9.4748477982440614722e-05 - 1.6415341923506796144e-684j)  +/-  (1.21e-86, 7.53e-210j)
| (1.1516608812730394277e-10 - 1.9201544827141121764e-689j)  +/-  (7e-95, 4.34e-218j)
| (3.5780940805939205415e-28 - 3.0220323598784711516e-699j)  +/-  (8.7e-104, 5.4e-227j)
| (2.1909730226027946265e-19 - 4.7878713688083730402e-695j)  +/-  (9.06e-102, 5.62e-225j)
| (6.2574837399567902388e-13 - 2.4782190215516255688e-691j)  +/-  (9.31e-99, 5.78e-222j)
| (0.0028322953000650992362 + 5.2901449376067387231e-684j)  +/-  (1.81e-87, 1.12e-210j)
| (8.5023057635739871786 - 1.1157603440226664774e-679j)  +/-  (6.34e-75, 3.93e-198j)
| (8.9213626876284414905e-09 - 1.041150685328553008e-688j)  +/-  (3.93e-96, 2.44e-219j)
| (3.4710119536953028874e-07 - 6.3347633384460310282e-687j)  +/-  (4.57e-94, 2.83e-217j)
| (6.2574837399567902388e-13 + 6.7255888567324075902e-691j)  +/-  (7.32e-99, 4.54e-222j)
| (1.0224469592284425024e-15 - 1.3686246541595140154e-692j)  +/-  (9.87e-101, 6.13e-224j)
| (7.5057998972159853767e-06 - 1.4036955772770510767e-686j)  +/-  (1.41e-95, 8.76e-219j)
| (3.5780940805939205415e-28 + 1.6596437071741152114e-699j)  +/-  (3.68e-108, 2.28e-231j)
| (8.9213626876284414905e-09 + 3.8812508248159490489e-688j)  +/-  (5.11e-97, 3.17e-220j)
| (1.0224469592284425024e-15 + 5.6724003273707213797e-693j)  +/-  (2.36e-102, 1.46e-225j)
| (3.4710119536953028874e-07 + 1.337599548579026644e-687j)  +/-  (1.29e-97, 7.98e-221j)
| (0.035280554345004396332 + 7.4014986458981996531e-683j)  +/-  (6.14e-91, 3.81e-214j)
| (0.035280554345004396332 + 2.6615561031609596539e-682j)  +/-  (1.88e-91, 1.16e-214j)
| (1.1516608812730394277e-10 + 6.1494883461806799067e-690j)  +/-  (6.52e-100, 4.05e-223j)
| (0.16237234131706341341 - 2.5078980597078487049e-681j)  +/-  (1.81e-89, 1.13e-212j)
| (0.0099852962824786327578 - 1.9518647012204178438e-683j)  +/-  (4.96e-93, 3.08e-216j)
| (-8.4328291857873979202 + 2.0644618373329161962e-679j)  +/-  (3.08e-89, 1.91e-212j)
| (7.5057998972159853767e-06 + 9.5007296116487852091e-686j)  +/-  (5.14e-97, 3.19e-220j)
| (0.0028322953000650992362 + 6.669794833155748351e-683j)  +/-  (1.62e-94, 1e-217j)
| (0.29909799493403518597 + 4.3631342402047683456e-681j)  +/-  (5.11e-91, 3.18e-214j)
| (0.16237234131706341341 - 1.1247429981853579476e-681j)  +/-  (1.07e-91, 6.67e-215j)
| (2.1909730226027946265e-19 + 1.038506919268170206e-694j)  +/-  (7.79e-106, 4.83e-229j)
| (8.5023057635739871786 - 2.0501838433227808386e-679j)  +/-  (2.35e-89, 1.46e-212j)
| (0.29909799493403518597 + 3.7925395162135343329e-681j)  +/-  (2.19e-91, 1.37e-214j)
| (0.00068836209924980539842 - 9.723964263817306471e-685j)  +/-  (1.86e-96, 1.16e-219j)
| (-0.15967206496143272882 - 6.6418694757175132171e-681j)  +/-  (3.96e-92, 2.52e-215j)
| (-8.4328291857873979202 + 1.1201870077579334126e-679j)  +/-  (6.48e-91, 4.07e-214j)
| (9.4748477982440614722e-05 + 1.26617468009771279e-685j)  +/-  (2.01e-97, 1.24e-220j)
| (0.0099852962824786327578 - 1.185112136826597197e-682j)  +/-  (2.79e-95, 1.69e-218j)
