Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 32
-------------------------------------------------
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 32 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^41 - 40082150283660036350745047326023784937669980246003286647533752489372206/29244707524374122511034934906912935209344674454314263475326945859459*t^39 + 129415633377040605398195384614683189046207386183887171985235055291087635529/614138858011856572731733633045171639396238163540599532981865863048639*t^37 - 213044631207018688989069814934794267566016771400506562904122188009529271055555/11054499444213418309171205394813089509132286943730791593673585534875502*t^35 + 12955311683062905386078917105350557845550995289852008636934475076857344620139105/11054499444213418309171205394813089509132286943730791593673585534875502*t^33 - 184931200729075464125558423965983041412172568872655303698847873367307873591070185/3684833148071139436390401798271029836377428981243597197891195178291834*t^31 + 20919966003237075054085922898878807056243435265438722344753537758627889758589745/13375074947626640422469697997354010295380867445530298358951706636268*t^29 - 138204182828468620531679004294780564815094501089515455219244791728552659072728805/3821449985036182977848485142101145798680247841580085245414773324648*t^27 + 20233139337026658326806017936892878124577448279914043571838277887756817272763277725/32270022095861100701831652311076342299966537328898497627946974741472*t^25 - 528294656298116264476672959732723643732309753282121280674241327475176883412928202125/64540044191722201403663304622152684599933074657796995255893949482944*t^23 + 10379840619088235057247028547661487688294029007917402512511548472908977323990032135375/129080088383444402807326609244305369199866149315593990511787898965888*t^21 - 152669581434789467205447317208859488984092838641096482169322845398020494382544090480125/258160176766888805614653218488610738399732298631187981023575797931776*t^19 + 5476634741357387881974942225879144058459384705103937001081151249497063831822353903375/1698422215571636879043771174267175910524554596257815664628788144288*t^17 - 349179121758274463514397268370431886710111852733682687645524581554457185998242169658125/27174755449146190064700338788274814568392873540125050634060610308608*t^15 + 1993196741067191998762592690251568299854767427215125719094410264697755956793735698926875/54349510898292380129400677576549629136785747080250101268121220617216*t^13 - 7926956768793421288102576164204965649553366848736728345638339442235059552612605331530625/108699021796584760258801355153099258273571494160500202536242441234432*t^11 + 84537444403092745956036447486519269725609452142091858430360661599485986246510141031923125/869592174372678082070410841224794066188571953284001620289939529875456*t^9 - 142774270193978988620589571052160837132962420945333689703987839906329840007564777258925625/1739184348745356164140821682449588132377143906568003240579879059750912*t^7 + 139260873768401161875385398001801206071136765436129737916616693811246280820069296927246875/3478368697490712328281643364899176264754287813136006481159758119501824*t^5 - 65711645242755198784747544597407153585456180055463753625885990188387714297909981164690625/6956737394981424656563286729798352529508575626272012962319516239003648*t^3 + 4829566479592857518072119536020752299306240358233807055596919057895176860064269966890625/6956737394981424656563286729798352529508575626272012962319516239003648*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:
| (7.7643781321583762863 - 1.5425239954458533433e-444j)  +/-  (1.26e-120, 1.26e-120j)
| (5.4936221831469474632 + 8.7193918845770299586e-442j)  +/-  (2.65e-118, 2.65e-118j)
| (7.0692493669608224783 - 7.2843694422645516231e-448j)  +/-  (1.27e-119, 1.27e-119j)
| (6.4911852215715563246 + 5.0675917225710650997e-449j)  +/-  (5.31e-119, 5.31e-119j)
| (-3.0360372526651063148 + 2.4719625279495787464e-455j)  +/-  (3.23e-119, 3.23e-119j)
| (-6.4911852215715563246 + 3.985377768960370118e-456j)  +/-  (5.27e-119, 5.27e-119j)
| (-7.0692493669608224783 + 3.7454695288328984885e-456j)  +/-  (1.23e-119, 1.23e-119j)
| (5.9731974137423477102 - 1.229412605147342391e-453j)  +/-  (1.38e-118, 1.38e-118j)
| (-5.9731974137423477102 + 4.9475066325668044991e-458j)  +/-  (1.33e-118, 1.33e-118j)
| (-5.4936221831469474632 + 3.9836032907528028274e-458j)  +/-  (2.39e-118, 2.39e-118j)
| (3.7952383000740513535 - 3.0393216920463595015e-459j)  +/-  (1.46e-118, 1.46e-118j)
| (4.6100198379963206139 + 7.5700528617371053837e-465j)  +/-  (3.26e-118, 3.26e-118j)
| (-5.0413955744675795427 - 9.8594802456101506443e-471j)  +/-  (3.06e-118, 3.06e-118j)
| (-2.6822224032999497583 + 3.2360617438353825396e-478j)  +/-  (1.29e-119, 1.29e-119j)
| (-4.1954434537665210485 - 6.1163556508587152956e-480j)  +/-  (2.61e-118, 2.61e-118j)
| (1.7320508075688772935 - 1.0911713225950918784e-489j)  +/-  (2.46e-121, 2.46e-121j)
| (5.0413955744675795427 + 2.5780798236770718632e-488j)  +/-  (3e-118, 3e-118j)
| (2.6822224032999497583 + 1.6062850507304357548e-491j)  +/-  (1.27e-119, 1.27e-119j)
| (-1.114115083558985177 - 2.7811185828748946246e-493j)  +/-  (3.94e-122, 3.94e-122j)
| (-4.6100198379963206139 + 5.8273267358339874001e-490j)  +/-  (3.35e-118, 3.35e-118j)
| (4.1954434537665210485 - 1.6985586469053798698e-491j)  +/-  (2.38e-118, 2.38e-118j)
| (1.114115083558985177 + 8.7112700386543661788e-501j)  +/-  (4.13e-122, 4.13e-122j)
| (2.3538312723195210159 - 1.8904058545508144978e-498j)  +/-  (4.51e-120, 4.51e-120j)
| (-2.3538312723195210159 + 4.6231958326283223041e-498j)  +/-  (4.19e-120, 4.19e-120j)
| (-1.3982455975797469252 + 6.9630680865123495854e-501j)  +/-  (6.03e-122, 6.03e-122j)
| (1.3982455975797469252 - 9.9826457727295038018e-501j)  +/-  (4.92e-122, 4.92e-122j)
| (2.0460446854551963286 - 1.2445530326049319509e-498j)  +/-  (1.17e-120, 1.17e-120j)
| (-7.7643781321583762863 + 9.2446932372530516423e-501j)  +/-  (1.26e-120, 1.26e-120j)
| (-1.7320508075688772935 + 2.2210795090479958499e-499j)  +/-  (2.43e-121, 2.43e-121j)
| (-0.7071067811865475244 + 3.8201181394122144402e-503j)  +/-  (1.51e-124, 1.51e-124j)
| (-3.4084409441468629422 - 8.7761597983023591468e-498j)  +/-  (7.36e-119, 7.36e-119j)
| (3.4084409441468629422 + 3.9208324226653433458e-501j)  +/-  (7.98e-119, 7.98e-119j)
| (1.0672470719421885588 - 5.0187399562944635793e-507j)  +/-  (2.46e-122, 2.46e-122j)
| (0.35376016649925797698 - 2.0462663392765397179e-512j)  +/-  (4.87e-126, 4.87e-126j)
| (-1.0672470719421885588 + 7.0575329783998432338e-508j)  +/-  (2.32e-122, 2.32e-122j)
| (-2.0460446854551963286 - 1.1896312039306072899e-506j)  +/-  (1.2e-120, 1.2e-120j)
| (6.9762285883003486309e-524 - 2.9667860800285419165e-523j)  +/-  (1.25e-521, 1.25e-521j)
| (0.7071067811865475244 + 2.2689396765964880368e-509j)  +/-  (1.65e-124, 1.65e-124j)
| (3.0360372526651063148 - 4.2924993428278563129e-507j)  +/-  (3.2e-119, 3.2e-119j)
| (-3.7952383000740513535 - 8.9094338494459929381e-509j)  +/-  (1.5e-118, 1.5e-118j)
| (-0.35376016649925797698 - 1.4726455943180822199e-515j)  +/-  (4.87e-126, 4.87e-126j)
-------------------------------------------------
The weights are:
| (2.9749804025283683067e-27 + 6.8254288043436360113e-463j)  +/-  (1.14e-31, 1.37e-90j)
| (2.0487667859650703636e-14 - 1.1241613594565272317e-454j)  +/-  (2.94e-26, 3.53e-85j)
| (6.9351585664914093503e-23 - 2.2287915042275196828e-460j)  +/-  (2.14e-30, 2.57e-89j)
| (1.5380422546032542483e-19 + 2.3826255168632756927e-458j)  +/-  (4.55e-29, 5.45e-88j)
| (2.0398051747722080053e-05 - 1.1193051081285245313e-450j)  +/-  (2.25e-20, 2.7e-79j)
| (1.5380422546032542483e-19 - 1.983193443105999471e-459j)  +/-  (4.37e-33, 5.24e-92j)
| (6.9351585664914093503e-23 + 2.7953357954524435202e-461j)  +/-  (9.45e-35, 1.13e-93j)
| (8.9536652461906546108e-17 - 1.709885925136445237e-456j)  +/-  (4.3e-30, 5.16e-89j)
| (8.9536652461906546108e-17 + 7.1512325458038459858e-458j)  +/-  (3.55e-32, 4.26e-91j)
| (2.0487667859650703636e-14 - 1.6258854230767693792e-456j)  +/-  (2.27e-31, 2.72e-90j)
| (1.2326385581924346667e-07 - 1.411461855819635108e-451j)  +/-  (2.99e-27, 3.58e-86j)
| (1.4042745097000669473e-10 - 3.6679763309575754118e-453j)  +/-  (3.64e-29, 4.37e-88j)
| (2.2800409540232382563e-12 + 2.6169929642942306456e-455j)  +/-  (4.53e-31, 5.43e-90j)
| (0.00014492993445239073376 + 5.9911293583651221755e-450j)  +/-  (1.07e-24, 1.28e-83j)
| (5.2094199212700963895e-09 + 3.1516988058791935638e-453j)  +/-  (1.31e-29, 1.57e-88j)
| (0.009100529850042942282 - 4.9057041900186569698e-448j)  +/-  (1.2e-21, 1.44e-80j)
| (2.2800409540232382563e-12 + 6.0965159632614667154e-454j)  +/-  (3.51e-31, 4.21e-90j)
| (0.00014492993445239073376 + 1.7422830780006773452e-449j)  +/-  (1.7e-26, 2.05e-85j)
| (-0.015149649154860131238 - 8.8484479917764720285e-447j)  +/-  (1.65e-19, 1.98e-78j)
| (1.4042745097000669473e-10 - 3.2077863387125553754e-454j)  +/-  (2.46e-31, 2.95e-90j)
| (5.2094199212700963895e-09 + 2.3522967930541704261e-452j)  +/-  (7.75e-30, 9.3e-89j)
| (-0.015149649154860131238 - 1.3350410956935364236e-446j)  +/-  (3.48e-21, 4.18e-80j)
| (0.00069738838733104312238 - 6.4974848871237400167e-449j)  +/-  (7.91e-26, 9.5e-85j)
| (0.00069738838733104312238 - 2.5996642204237863729e-449j)  +/-  (6.41e-27, 7.69e-86j)
| (0.027396248756863818548 + 9.679142767957103412e-448j)  +/-  (8.77e-24, 1.05e-82j)
| (0.027396248756863818548 + 1.6288458661725789531e-447j)  +/-  (2.58e-23, 3.1e-82j)
| (0.0026257445527750792157 + 1.8959770589067268631e-448j)  +/-  (2.5e-25, 3e-84j)
| (2.9749804025283683067e-27 - 1.1690211028382409831e-463j)  +/-  (1.97e-41, 2.36e-100j)
| (0.009100529850042942282 - 2.5538322133656943959e-448j)  +/-  (4.38e-26, 5.25e-85j)
| (0.12084347328323869494 - 1.5389060299344206008e-447j)  +/-  (1.96e-24, 2.34e-83j)
| (1.9309969021092094238e-06 + 1.8157485005761060844e-451j)  +/-  (3.08e-30, 3.65e-89j)
| (1.9309969021092094238e-06 + 7.7517999230969546392e-451j)  +/-  (2.42e-30, 2.82e-89j)
| (0.078469477155782124975 + 1.3299096911271540955e-446j)  +/-  (1.51e-24, 1.72e-83j)
| (0.17603406149420642114 + 1.4031128765689304868e-447j)  +/-  (5.8e-26, 6.56e-85j)
| (0.078469477155782124975 + 8.9724073535205505746e-447j)  +/-  (2.33e-25, 2.72e-84j)
| (0.0026257445527750792157 + 8.6695181008718407946e-449j)  +/-  (4.55e-28, 5.56e-87j)
| (0.19963067615102795039 - 1.2319543169001111425e-447j)  +/-  (1.64e-26, 1.81e-85j)
| (0.12084347328323869494 - 1.9935879014075022143e-447j)  +/-  (1.14e-26, 1.27e-85j)
| (2.0398051747722080053e-05 - 3.8848266384280850991e-450j)  +/-  (2.82e-30, 3.55e-89j)
| (1.2326385581924346667e-07 - 2.5807299733602928505e-452j)  +/-  (2.88e-32, 4.17e-91j)
| (0.17603406149420642114 + 1.2333393213156598983e-447j)  +/-  (7.59e-27, 7.08e-86j)
