Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 31
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : t^14 - 477/7*t^12 + 11241/7*t^10 - 112815/7*t^8 + 68715*t^6 - 108945*t^4 + 46845*t^2 - 2835
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 313184886534140510874390202541895666360815441042003990866981471/424635023160733130132146032946621864188665857294391564658621*t^43 + 313294481007066316354388741858236259098502737055661770548948484534/1273905069482199390396438098839865592565997571883174693975863*t^41 - 480615285560216941834212573885041732786157275816175046692639305274800/9766605532696861993039358757772302876339314717771005987148283*t^39 + 236877677394598710426074641479182910651299567649414112816575642063504705/35810886953221827307810982111831777213244153965160355286210371*t^37 - 3241841520623864261306128105406329193646018733030809745752829830091677265/5115840993317403901115854587404539601892021995022907898030053*t^35 + 229211701765728049699069233614961817044968519186328382618294236693210885810/5115840993317403901115854587404539601892021995022907898030053*t^33 - 12222693836187529209603633855620902149993121173182731047478922792141243509080/5115840993317403901115854587404539601892021995022907898030053*t^31 + 498174742001843719564510872442831359479417270651007402746593031813563485529050/5115840993317403901115854587404539601892021995022907898030053*t^29 - 15637262467543102532849682367961025463227246750802717170631939884450607738203150/5115840993317403901115854587404539601892021995022907898030053*t^27 + 379166936660307277332277149360898448066050519498804958928556737227798013015125100/5115840993317403901115854587404539601892021995022907898030053*t^25 - 7096391051940188494179291210708089170336998168301554578948331806940683734519791000/5115840993317403901115854587404539601892021995022907898030053*t^23 + 403371969706603424093334518902796076150681215902076049980064812209841971574544750/20220715388606339530102192045077231628031707490209122126601*t^21 - 4420123689718302653308478612633016066873606004167592004483467720803772894417751250/20220715388606339530102192045077231628031707490209122126601*t^19 + 36435588832619072125405170044460464141685514962169807704448006269173890822066987500/20220715388606339530102192045077231628031707490209122126601*t^17 - 221823980142965935563730726244808391727434995622084024841508114408988857028814985000/20220715388606339530102192045077231628031707490209122126601*t^15 + 972212950534848376270502734013187587599321534235013118485072060479794177363876093125/20220715388606339530102192045077231628031707490209122126601*t^13 - 2959942725129121966875276497069053095650609325055580570317341308848043335539961854375/20220715388606339530102192045077231628031707490209122126601*t^11 + 5950768119985266928356311882302984137082560546034165085964239905775369207705689256250/20220715388606339530102192045077231628031707490209122126601*t^9 - 7326599103419609029190709697659804405771415138175503508131866132770325457993661775000/20220715388606339530102192045077231628031707490209122126601*t^7 + 4878625787542456685702186341444310132053474219547688215438546771329583504494029009375/20220715388606339530102192045077231628031707490209122126601*t^5 - 59454488797338681920246858457230338256375180838530176898692189401749096866357359375/879161538635058240439225741090314418610074238704744440287*t^3 + 75787130948750217569484330301875869205673258063564133350929727994216436151547156250/20220715388606339530102192045077231628031707490209122126601*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:
| (-8.6056625039739728007 - 1.2468590996895245631e-796j)  +/-  (1.24e-245, 1.24e-245j)
| (10.151485820951753177 - 1.7750467031547944896e-806j)  +/-  (8.45e-247, 8.45e-247j)
| (-9.3363002551083138156 + 3.8588353876132751593e-803j)  +/-  (4.22e-246, 4.22e-246j)
| (6.6812845187341496262 - 3.8945673788014749474e-811j)  +/-  (4.41e-245, 4.41e-245j)
| (7.9289711802558403298 + 9.1462552310408476747e-811j)  +/-  (2.26e-245, 2.26e-245j)
| (4.9990438103739162897 + 7.8312561647768105774e-812j)  +/-  (4.29e-245, 4.29e-245j)
| (8.6056625039739728007 + 8.7713440756593089092e-813j)  +/-  (1.28e-245, 1.28e-245j)
| (-10.151485820951753177 - 8.0416656616554738338e-815j)  +/-  (8.74e-247, 8.74e-247j)
| (9.3363002551083138156 + 6.6333743172828274242e-824j)  +/-  (4.26e-246, 4.26e-246j)
| (-6.6812845187341496262 + 2.5511006866862355706e-833j)  +/-  (4.27e-245, 4.27e-245j)
| (0.74196378430272585765 + 3.4534818833231581428e-856j)  +/-  (1.04e-252, 1.04e-252j)
| (-6.0956322026601262552 + 3.8265914759252502313e-847j)  +/-  (4.5e-245, 4.5e-245j)
| (-7.9289711802558403298 - 1.507316420384849998e-856j)  +/-  (2.47e-245, 2.47e-245j)
| (-5.5317060638607199116 - 7.4961249846766750835e-864j)  +/-  (3.98e-245, 3.98e-245j)
| (-4.5999761864586902744 - 2.4972784885993534063e-877j)  +/-  (4.12e-245, 4.12e-245j)
| (6.0956322026601262552 - 2.0630031958709309581e-879j)  +/-  (4.62e-245, 4.62e-245j)
| (1.845537122954151311 - 6.7380503809118761402e-885j)  +/-  (1.2e-249, 1.2e-249j)
| (2.8795316813990172403 - 5.5710588549296201315e-882j)  +/-  (4.91e-247, 4.91e-247j)
| (3.8300942322375058914 + 5.6044624005291110576e-881j)  +/-  (5.28e-246, 5.28e-246j)
| (-3.2762772292662860982 - 1.6432934793124702949e-883j)  +/-  (2.64e-246, 2.64e-246j)
| (-11.131618575216660677 + 1.3202391071794285648e-887j)  +/-  (7.18e-248, 7.18e-248j)
| (-3.0786740710195173233 - 9.1463382005091214223e-885j)  +/-  (1.87e-246, 1.87e-246j)
| (11.131618575216660677 - 1.0057975940186249947e-889j)  +/-  (7.71e-248, 7.71e-248j)
| (1.4656205133845524345 - 6.2751238570681226066e-892j)  +/-  (2.08e-250, 2.08e-250j)
| (-2.8795316813990172403 + 1.3020546479735847977e-888j)  +/-  (5.11e-247, 5.11e-247j)
| (4.5999761864586902744 - 8.1113017820032125257e-887j)  +/-  (4.16e-245, 4.16e-245j)
| (-4.9990438103739162897 + 8.5045980045855139e-886j)  +/-  (4.38e-245, 4.38e-245j)
| (-2.3344142183389772393 + 1.3951362991154114907e-899j)  +/-  (1.26e-248, 1.26e-248j)
| (7.2905700121185031094 + 2.6032685726233079463e-896j)  +/-  (3.82e-245, 3.82e-245j)
| (2.8054032086852592941e-912 + 2.6963453527588948477e-912j)  +/-  (1.75e-910, 1.75e-910j)
| (-4.3114957943342286437 - 1.4644212750025328788e-895j)  +/-  (2.42e-245, 2.42e-245j)
| (4.3114957943342286437 + 2.1354407499741629243e-902j)  +/-  (2.51e-245, 2.51e-245j)
| (5.5317060638607199116 + 3.8967055183494148165e-906j)  +/-  (4.58e-245, 4.58e-245j)
| (3.2762772292662860982 - 7.6526772028295523622e-909j)  +/-  (2.66e-246, 2.66e-246j)
| (-1.845537122954151311 - 3.6159402854441342776e-912j)  +/-  (1.24e-249, 1.24e-249j)
| (-0.74196378430272585765 + 1.0216083315684556609e-915j)  +/-  (1.11e-252, 1.11e-252j)
| (-7.2905700121185031094 - 1.9776769972192275062e-910j)  +/-  (3.67e-245, 3.67e-245j)
| (2.3344142183389772393 + 3.4878080778883624241e-916j)  +/-  (1.24e-248, 1.24e-248j)
| (1.1804796449283756069 + 3.8965557678164778499e-919j)  +/-  (2.97e-251, 2.97e-251j)
| (-1.4656205133845524345 + 6.8531368619025646613e-920j)  +/-  (1.88e-250, 1.88e-250j)
| (-1.1804796449283756069 - 1.5938438329345507747e-920j)  +/-  (2.96e-251, 2.96e-251j)
| (0.26842728825432580984 - 1.1671785450766569819e-922j)  +/-  (3.6e-254, 3.6e-254j)
| (3.0786740710195173233 - 2.7010707522065301602e-920j)  +/-  (1.94e-246, 1.94e-246j)
| (-0.26842728825432580984 - 4.263538238759181701e-928j)  +/-  (3.6e-254, 3.6e-254j)
| (-3.8300942322375058914 - 3.8304317280250224547e-927j)  +/-  (4.97e-246, 4.97e-246j)
-------------------------------------------------
The weights are:
| (2.316332909736108927e-17 - 1.5149416530547053454e-812j)  +/-  (4e-85, 8.61e-208j)
| (1.4646746843005020762e-23 - 3.3151100626586320121e-818j)  +/-  (5.91e-89, 1.27e-211j)
| (3.6059652472952912775e-20 - 8.1244037564789921023e-815j)  +/-  (6.91e-87, 1.49e-209j)
| (4.8237865879403675836e-11 + 2.4135000611639657182e-810j)  +/-  (1.11e-81, 2.4e-204j)
| (5.8320845163584317361e-15 + 5.4431378446559400629e-813j)  +/-  (8.15e-85, 1.76e-207j)
| (7.4999640566779584958e-07 - 9.5550492380961426901e-807j)  +/-  (5.79e-78, 1.25e-200j)
| (2.316332909736108927e-17 - 1.6780467686234472971e-814j)  +/-  (1.67e-86, 3.6e-209j)
| (1.4646746843005020762e-23 + 4.0225821308287581066e-817j)  +/-  (9.24e-92, 1.99e-214j)
| (3.6059652472952912775e-20 + 3.3084433759745600976e-816j)  +/-  (2.86e-88, 6.15e-211j)
| (4.8237865879403675836e-11 + 1.9172453466855434736e-809j)  +/-  (1.5e-85, 3.24e-208j)
| (0.14327681579414141852 + 2.6428214076797097105e-802j)  +/-  (8.82e-73, 1.9e-195j)
| (1.9588571593495915047e-09 - 2.2866120877135248876e-808j)  +/-  (1.72e-84, 3.71e-207j)
| (5.8320845163584317361e-15 + 1.3300050731429475749e-811j)  +/-  (2.89e-88, 6.24e-211j)
| (4.9916310441666403064e-08 + 2.7357016218829774794e-807j)  +/-  (1e-83, 2.16e-206j)
| (2.6576600747324878625e-06 + 2.6349986220226089294e-805j)  +/-  (3.99e-82, 8.59e-205j)
| (1.9588571593495915047e-09 - 3.9040545516793773531e-809j)  +/-  (3.94e-86, 8.48e-209j)
| (0.033495920143954602312 - 7.1294209332641554342e-803j)  +/-  (8.79e-73, 1.89e-195j)
| (0.0043694309796016788292 - 2.9825656038174626572e-803j)  +/-  (2.61e-78, 5.62e-201j)
| (0.00013480687435709422935 + 7.7061172487773014124e-805j)  +/-  (1.33e-81, 2.87e-204j)
| (0.0013038992850615751029 - 2.6182594257725081182e-803j)  +/-  (5.75e-81, 1.24e-203j)
| (5.578400074357974314e-28 - 7.4972952386616633398e-820j)  +/-  (4.92e-98, 1.06e-220j)
| (-0.0014474215066759942073 + 6.7545663183909237013e-803j)  +/-  (1.49e-80, 3.2e-203j)
| (5.578400074357974314e-28 + 9.5949579648780310558e-821j)  +/-  (5.39e-99, 1.16e-221j)
| (0.037453831902234247855 + 1.8512394526003062782e-802j)  +/-  (3.24e-75, 6.98e-198j)
| (0.0043694309796016788292 - 5.9822847484509241359e-803j)  +/-  (1.9e-80, 4.1e-203j)
| (2.6576600747324878625e-06 + 7.9927811139703002084e-806j)  +/-  (1.18e-85, 2.54e-208j)
| (7.4999640566779584958e-07 - 3.6043077847736031468e-806j)  +/-  (5.88e-86, 1.27e-208j)
| (0.0132907357193743071 + 4.6046432360265299527e-803j)  +/-  (7.31e-81, 1.57e-203j)
| (7.1329233056915107664e-13 - 1.2846341221513352986e-811j)  +/-  (2.84e-91, 6.12e-214j)
| (0.037939785676063836442 + 8.7840015711629544361e-802j)  +/-  (6.48e-79, 1.4e-201j)
| (1.4947113024929710894e-05 - 6.5870014832529817064e-805j)  +/-  (6.28e-85, 1.35e-207j)
| (1.4947113024929710894e-05 - 2.1897759471316513497e-805j)  +/-  (8.52e-86, 1.84e-208j)
| (4.9916310441666403064e-08 + 5.9483684014965096895e-808j)  +/-  (3.06e-88, 6.58e-211j)
| (0.0013038992850615751029 - 1.1743632405893983331e-803j)  +/-  (6.4e-85, 1.38e-207j)
| (0.033495920143954602312 - 1.1022133043686606407e-802j)  +/-  (2.44e-83, 5.22e-206j)
| (0.14327681579414141852 + 3.1415378105201489832e-802j)  +/-  (2.2e-82, 4.81e-205j)
| (7.1329233056915107664e-13 - 1.5528065653766156777e-810j)  +/-  (1.13e-92, 2.43e-215j)
| (0.0132907357193743071 + 2.6395483104162757942e-803j)  +/-  (3.46e-84, 7.49e-207j)
| (0.073680445640246857891 - 2.4464498689651995294e-802j)  +/-  (1.85e-82, 4.04e-205j)
| (0.037453831902234247855 + 2.6112390478349609969e-802j)  +/-  (1.05e-83, 2.25e-206j)
| (0.073680445640246857891 - 3.2243389315839439142e-802j)  +/-  (1.6e-83, 3.53e-206j)
| (0.17545323563604234965 - 5.8179526486315404669e-802j)  +/-  (4.13e-83, 9.84e-206j)
| (-0.0014474215066759942073 + 3.1950816995518336049e-803j)  +/-  (8.77e-85, 1.89e-207j)
| (0.17545323563604234965 - 6.1925845762494191228e-802j)  +/-  (2.78e-83, 6.97e-206j)
| (0.00013480687435709422935 + 2.0067014826216328675e-804j)  +/-  (1.09e-86, 2.15e-209j)
