Starting with polynomial:
P : 2*t
Extension levels are: 1 8 14 22
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : 2*t^9 - 36*t^7 + 189*t^5 - 315*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : 2*t^23 - 3309583/18099*t^21 + 82235713/12066*t^19 - 1089441955/8044*t^17 + 38063466049/24132*t^15 - 179492837615/16088*t^13 + 1547216966295/32176*t^11 - 7941468990455/64352*t^9 + 46161180640575/257408*t^7 - 70208873169435/514816*t^5 + 50216778386775/1029632*t^3 - 12961617443775/2059264*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^45 - 270914842079056499755805142859393030851086370215360664952509279564665842136216426404635535193/408543910097699181065381733384475056816080457697545810056152382610123841504082544119444730*t^43 + 81228959900797786575749673038284858881067049538662307321372777339777456767995603351521494105021/817087820195398362130763466768950113632160915395091620112304765220247683008165088238889460*t^41 - 102332660158663425405042870616316027204908334567383461219394070563686287536009879724017796077484521/11439229482735577069830688534765301590850252815531282681572266713083467562114311235344452440*t^39 + 825122827880387980463219637013071025514925249196415179160263495361617964862829347992952925291003573/1525230597698076942644091804635373545446700375404171024209635561744462341615241498045926992*t^37 - 177889802361956575457715500566019609303681210569223794069848522636577996020682259611125500423508471191/7626152988490384713220459023176867727233501877020855121048177808722311708076207490229634960*t^35 + 2265149732913023052877345877747104059962333089512210244329100398005977728252901297550434440870149991203/3050461195396153885288183609270747090893400750808342048419271123488924683230482996091853984*t^33 - 126904555050870742050397616192338094945174349291499981263432578701187064253150642918845160548303962907165/7117742789257692399005761754965076545417935085219464779644965954807490927537793657547659296*t^31 + 2328110935180264199352732812747582354838569051737232495227358482825024793607927538001590511528546659431677/7117742789257692399005761754965076545417935085219464779644965954807490927537793657547659296*t^29 - 262866898558767601693584693460520904689763279321107377080694833696315852324140179326421382659086034769056795/56941942314061539192046094039720612363343480681755718237159727638459927420302349260381274368*t^27 + 5720933260018283665202858965151661655251442251093937389787056268970170131827984560572466872289318117593751863/113883884628123078384092188079441224726686961363511436474319455276919854840604698520762548736*t^25 - 670699372642836733449522642334154770525476271485127365043872652568402252134501613258781161522701279109883064575/1594374384793723097377290633112177146173617459089160110640472373876877967768465779290675682304*t^23 + 8594689820094003564264105793238253509091978856889775735017959063359610316503801198262443228388900171809062486825/3188748769587446194754581266224354292347234918178320221280944747753755935536931558581351364608*t^21 - 156883730624901369472100754681364487001567411001268211970362269542216667899031334277088044720811531233487992125/11987777329276113514114967166256971023861785406685414365717837397570511035853126160080268288*t^19 + 1138644523372056712766376556335379513091717624843142899334513685125075695918302130852163577313369774722785372375/23975554658552227028229934332513942047723570813370828731435674795141022071706252320160536576*t^17 - 12125523442336740512765885902242091093847261028083431181382537505858398705902535092593919077766361675162850980375/95902218634208908112919737330055768190894283253483314925742699180564088286825009280642146304*t^15 + 13208631100780159633338435488841025037868189758092396435748211784359082276626962791756128458443008959385521509875/54801267790976518921668421331460438966225304716276179957567256674608050449614291017509797888*t^13 - 9987701322658323633921953447971413208855299030478383196336387453027313408944575702882086939375289157117449570375/31315010166272296526667669332263107980700174123586388547181289528347457399779594867148455936*t^11 + 864217671869053100570647824334525126768516029334095905571409507469003683027896631597510634500678328506759189033875/3068870996294685059613431594561784582108617064111466077623766373778050825178400296980548681728*t^9 - 967265096650991242580710722007314951065518460364621702343911064891245771252826962730696804165763245479052964615625/6137741992589370119226863189123569164217234128222932155247532747556101650356800593961097363456*t^7 + 91039500355906638688105225238515190409931008329002830334304727556557452059994192437727833496906995702499097559125/1753640569311248605493389482606734046919209750920837758642152213587457614387657312560313532416*t^5 - 15583902748701588185896410705426655070902553580007975919334471969213352754124923049795938062141523990060697073125/1753640569311248605493389482606734046919209750920837758642152213587457614387657312560313532416*t^3 + 2077470924148033391100194284450587236520913656325347919425636556480521319990287543652411234335264671447150173125/3507281138622497210986778965213468093838419501841675517284304427174915228775314625120627064832*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:
| (-3.7832466850882959409 + 9.9415154830160988749e-951j)  +/-  (4.34e-245, 4.34e-245j)
| (-5.2317324539479656178 + 3.4732499421290341843e-960j)  +/-  (2.27e-245, 2.27e-245j)
| (-7.516913544628227339 + 1.3142828647772462023e-963j)  +/-  (4.69e-248, 4.69e-248j)
| (3.7832466850882959409 + 4.5900860580201137424e-957j)  +/-  (4.58e-245, 4.58e-245j)
| (-6.8142089549665084248 - 4.3340858345982100847e-962j)  +/-  (5.38e-247, 5.38e-247j)
| (-5.7092008285993252819 + 4.3773928562634689072e-962j)  +/-  (9.14e-246, 9.14e-246j)
| (-4.798527904922514432 - 3.7463715841206166176e-959j)  +/-  (4.69e-245, 4.69e-245j)
| (6.8142089549665084248 + 1.8038707030963777383e-966j)  +/-  (4.84e-247, 4.84e-247j)
| (5.2317324539479656178 - 1.1373220865462371172e-962j)  +/-  (2.2e-245, 2.2e-245j)
| (-3.1862889002103061941 - 2.3217756360664941273e-957j)  +/-  (3.12e-243, 3.12e-243j)
| (-4.1485968518902974472 + 1.3313301864480305293e-980j)  +/-  (6.68e-245, 6.68e-245j)
| (3.1862889002103061941 - 4.4073779713700059587e-976j)  +/-  (3.44e-243, 3.44e-243j)
| (4.798527904922514432 - 1.1907942318596029341e-984j)  +/-  (4.68e-245, 4.68e-245j)
| (-1.814727923367589818 - 1.66714830255383135e-987j)  +/-  (6.39e-248, 6.39e-248j)
| (-2.6602671868269422397 - 2.7615518310327129502e-986j)  +/-  (1.41e-246, 1.41e-246j)
| (-4.4436725456953199306 - 6.9011899442231424281e-985j)  +/-  (6.96e-245, 6.96e-245j)
| (1.4685532892166679317 + 4.7093808173481763935e-989j)  +/-  (2.89e-249, 2.89e-249j)
| (3.2860018399445749314 - 1.4552203278575887925e-981j)  +/-  (2.46e-244, 2.46e-244j)
| (-0.72355101875283757332 - 5.7204914151744746631e-992j)  +/-  (3.79e-251, 3.79e-251j)
| (7.516913544628227339 - 1.7206323320497533718e-990j)  +/-  (4.16e-248, 4.16e-248j)
| (1.9366468705568828024 - 4.7644314626880652372e-988j)  +/-  (1.29e-247, 1.29e-247j)
| (3.1909932017815276072 - 1.086001446243748951e-982j)  +/-  (3.45e-243, 3.45e-243j)
| (-3.2860018399445749314 - 1.234375027141735078e-1001j)  +/-  (2.48e-244, 2.48e-244j)
| (-6.2304595514191580056 + 1.256992428446882476e-1032j)  +/-  (2.8e-246, 2.8e-246j)
| (-3.1909932017815276072 - 4.9889158776113973987e-1045j)  +/-  (3.7e-243, 3.7e-243j)
| (5.7092008285993252819 - 9.8766109032136655886e-1076j)  +/-  (8.98e-246, 8.98e-246j)
| (0.93588957168758885766 + 5.7287922458916976017e-1080j)  +/-  (3.01e-250, 3.01e-250j)
| (2.2665805845318431118 + 6.6768609412380468057e-1077j)  +/-  (2.7e-247, 2.7e-247j)
| (-1.4685532892166679317 - 8.3560140772451794526e-1080j)  +/-  (2.86e-249, 2.86e-249j)
| (-0.93588957168758885766 - 3.8988392425396488756e-1080j)  +/-  (2.94e-250, 2.94e-250j)
| (4.4436725456953199306 - 4.6846022392189275804e-1074j)  +/-  (7.16e-245, 7.16e-245j)
| (1.814727923367589818 + 5.5044446088334801594e-1080j)  +/-  (6.23e-248, 6.23e-248j)
| (4.1485968518902974472 + 1.9307326056170201552e-1078j)  +/-  (6.79e-245, 6.79e-245j)
| (6.2304595514191580056 - 5.9601878109478659534e-1082j)  +/-  (2.63e-246, 2.63e-246j)
| (-1.0601643046198575673 + 9.6865458326801414297e-1085j)  +/-  (4.61e-250, 4.61e-250j)
| (-1.9366468705568828024 + 1.0230039506476159213e-1082j)  +/-  (1.29e-247, 1.29e-247j)
| (2.6602671868269422397 - 5.1470617780494876653e-1082j)  +/-  (1.34e-246, 1.34e-246j)
| (0.72355101875283757332 - 3.7520983682912349017e-1086j)  +/-  (4.33e-251, 4.33e-251j)
| (1.0601643046198575673 - 3.9117426054021125936e-1085j)  +/-  (4.81e-250, 4.81e-250j)
| (-0.41986656060780574088 + 2.139150734357101971e-1087j)  +/-  (1.09e-252, 1.09e-252j)
| (-0.54431479141505793416 - 1.6541796356690144588e-1086j)  +/-  (7.02e-252, 7.02e-252j)
| (-3.9219883477726368688e-1111 - 2.6971272764434616782e-1111j)  +/-  (2.14e-1109, 2.14e-1109j)
| (0.41986656060780574088 + 1.3185165776140994014e-1087j)  +/-  (1.1e-252, 1.1e-252j)
| (0.54431479141505793416 + 6.7889717298864516348e-1087j)  +/-  (6.05e-252, 6.05e-252j)
| (-2.2665805845318431118 + 1.9063287618389369651e-1085j)  +/-  (2.71e-247, 2.71e-247j)
-------------------------------------------------
The weights are:
| (1.3711279692581382967e-07 + 8.5423007420593331558e-957j)  +/-  (2.47e-71, 4.03e-193j)
| (3.3465464134871626323e-13 - 2.3093023933322568099e-962j)  +/-  (9.44e-78, 1.54e-199j)
| (1.3199629278952733552e-25 - 5.2623420594739066881e-971j)  +/-  (2.32e-85, 3.79e-207j)
| (1.3711279692581382967e-07 + 1.8014678227201476349e-958j)  +/-  (4.86e-75, 7.95e-197j)
| (2.4177013381902591922e-21 + 2.7809605389271991952e-968j)  +/-  (1.92e-83, 3.14e-205j)
| (1.9617835046426179915e-15 + 3.7692480123290497713e-964j)  +/-  (3.62e-80, 5.91e-202j)
| (2.2760967004578600699e-11 + 1.1237634742205428983e-960j)  +/-  (2.27e-77, 3.71e-199j)
| (2.4177013381902591922e-21 - 7.9537953295725737836e-969j)  +/-  (3.18e-88, 5.19e-210j)
| (3.3465464134871626323e-13 + 3.7104924942484114738e-963j)  +/-  (2.23e-83, 3.65e-205j)
| (0.00083888858687890535441 - 1.7127583006740390111e-953j)  +/-  (2.97e-73, 4.86e-195j)
| (6.0925954968329487812e-09 + 4.0351857343903661007e-958j)  +/-  (3.35e-76, 5.47e-198j)
| (0.00083888858687890535441 - 1.4670481045242490254e-954j)  +/-  (5.02e-76, 8.21e-198j)
| (2.2760967004578600699e-11 - 1.329492442664363627e-961j)  +/-  (7.06e-83, 1.15e-204j)
| (0.0049775432520461452198 - 1.7990178059731983322e-953j)  +/-  (7.4e-69, 1.21e-190j)
| (0.00019324571148414761483 + 3.2049581446793317306e-955j)  +/-  (4.83e-73, 7.9e-195j)
| (4.5304665390197365184e-10 - 2.9853767232810412559e-959j)  +/-  (7.11e-78, 1.16e-199j)
| (0.024911568527701026149 + 9.6533155017906905339e-954j)  +/-  (7.87e-69, 1.29e-190j)
| (2.4493466134340613611e-05 - 4.4673470303942142555e-956j)  +/-  (1.09e-77, 1.78e-199j)
| (0.18940176925075854748 - 6.1294270387236499171e-952j)  +/-  (2.14e-70, 3.5e-192j)
| (1.3199629278952733552e-25 + 1.7387237815560325977e-971j)  +/-  (2.7e-93, 4.41e-215j)
| (0.0024175152382107897639 + 3.9259106178322660347e-954j)  +/-  (5.38e-74, 8.79e-196j)
| (-0.00084419133327799605132 + 1.5002579616363631801e-954j)  +/-  (4.09e-76, 6.68e-198j)
| (2.4493466134340613611e-05 - 6.351188233119153096e-955j)  +/-  (5.02e-77, 8.2e-199j)
| (4.2776785822431496959e-18 - 4.3801508551132217948e-966j)  +/-  (1.02e-87, 1.66e-209j)
| (-0.00084419133327799605132 + 1.7666358368891165566e-953j)  +/-  (1.58e-75, 2.58e-197j)
| (1.9617835046426179915e-15 - 7.6475693639738915314e-965j)  +/-  (2.12e-89, 3.46e-211j)
| (-0.056389736615070417297 + 2.6647438821382618996e-952j)  +/-  (3.33e-75, 5.44e-197j)
| (0.0012675817281393388331 - 3.702159828518397076e-955j)  +/-  (1.08e-78, 1.76e-200j)
| (0.024911568527701026149 + 2.1902394113616181319e-953j)  +/-  (7.04e-76, 1.15e-197j)
| (-0.056389736615070417297 + 4.4164800465102743348e-952j)  +/-  (6.23e-75, 1.02e-196j)
| (4.5304665390197365184e-10 + 2.3965611123277282879e-960j)  +/-  (1.94e-85, 3.17e-207j)
| (0.0049775432520461452198 - 6.3262095026061926762e-954j)  +/-  (4.78e-78, 7.81e-200j)
| (6.0925954968329487812e-09 - 1.858673484042179499e-959j)  +/-  (1.33e-84, 2.17e-206j)
| (4.2776785822431496959e-18 + 1.0704509240173178152e-966j)  +/-  (7.5e-92, 1.23e-213j)
| (0.096560824408200711603 - 2.1686283300838487386e-952j)  +/-  (8.56e-78, 1.4e-199j)
| (0.0024175152382107897639 + 1.2160632193154290848e-953j)  +/-  (3.92e-80, 6.41e-202j)
| (0.00019324571148414761483 + 5.5856050106926947204e-956j)  +/-  (1.44e-81, 2.36e-203j)
| (0.18940176925075854748 - 4.1613081803795034197e-952j)  +/-  (3.88e-79, 6.34e-201j)
| (0.096560824408200711603 - 1.2192543920149603761e-952j)  +/-  (5.65e-79, 9.24e-201j)
| (0.2726005943762424055 - 4.6507943619998584652e-952j)  +/-  (1.32e-79, 2.15e-201j)
| (-0.14716924308090554976 + 7.8420692420436830935e-952j)  +/-  (2.23e-79, 3.65e-201j)
| (0.22241800560384188143 + 1.0408349206202608919e-952j)  +/-  (9.7e-81, 1.59e-202j)
| (0.2726005943762424055 - 3.7216189549163407613e-952j)  +/-  (6.91e-81, 1.13e-202j)
| (-0.14716924308090554976 + 5.8693379882747364451e-952j)  +/-  (8.49e-81, 1.41e-202j)
| (0.0012675817281393388331 - 1.4767567122164712255e-954j)  +/-  (6.25e-84, 8.88e-206j)
