Starting with polynomial:
P : t
Extension levels are: 1 2 42
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 762527411580585593007/800788896593667320*t^43 + 330621627713348403455121/800788896593667320*t^41 - 8663631528680372585580561/80078889659366732*t^39 + 1535772869449538402062592667/80078889659366732*t^37 - 390704370723420465296997339291/160157779318733464*t^35 + 36917652528360486778214899215909/160157779318733464*t^33 - 330852861051256758479359872977199/20019722414841683*t^31 + 18229453024076752829950312788309255/20019722414841683*t^29 - 3108711955918656830557715636305084515/80078889659366732*t^27 + 102773515632197187781378336592581435485/80078889659366732*t^25 - 1314971476522493465593375286602560061275/40039444829683366*t^23 + 25900578182441782978707719481374119881825/40039444829683366*t^21 - 777877942203416774175780477037583950626375/80078889659366732*t^19 + 8781680252601220464036986745916532717429625/80078889659366732*t^17 - 18274177354789032174786779469600124085958375/20019722414841683*t^15 + 109221084024162892891526302692993204456438000/20019722414841683*t^13 - 3616185682017306092521939048990765354684416375/160157779318733464*t^11 + 9849018371448012774440664422186942602336295625/160157779318733464*t^9 - 8193392045325085515324066921275675746129670625/80078889659366732*t^7 + 7408941862531761611815879609450855109811466875/80078889659366732*t^5 - 5918878169021127078610941858630714939225504375/160157779318733464*t^3 + 652039258754883799125597180996577436696375625/160157779318733464*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:
| (-8.3717095823733048883 - 2.8549877515084801225e-548j)  +/-  (2.28e-244, 2.28e-244j)
| (-11.146478702298714542 - 1.1090779315364550835e-559j)  +/-  (4.18e-246, 4.18e-246j)
| (8.989731376741709065 - 3.2926109138173673689e-568j)  +/-  (1.52e-244, 1.52e-244j)
| (12.100327220539704426 + 1.6218301373167420691e-574j)  +/-  (3.31e-247, 3.31e-247j)
| (-10.35440637518547431 + 1.717796868616843957e-584j)  +/-  (2.44e-245, 2.44e-245j)
| (-9.6454847885967472738 - 1.415608897316930251e-614j)  +/-  (6.76e-245, 6.76e-245j)
| (5.0990041183285010953 + 3.0233546658889941208e-632j)  +/-  (2.04e-245, 2.04e-245j)
| (-12.100327220539704426 + 1.0270415022401972237e-632j)  +/-  (3.42e-247, 3.42e-247j)
| (10.35440637518547431 - 4.7062722295105350858e-646j)  +/-  (2.38e-245, 2.38e-245j)
| (-8.989731376741709065 - 5.2542928848581499236e-682j)  +/-  (1.5e-244, 1.5e-244j)
| (1.2794976424064099646 - 2.1939508664366806397e-708j)  +/-  (1.71e-251, 1.71e-251j)
| (-6.665886415343268239 - 2.8049101082598901405e-723j)  +/-  (1.82e-244, 1.82e-244j)
| (-7.7821612920617807029 - 1.3100185685321796442e-749j)  +/-  (2.48e-244, 2.48e-244j)
| (-3.6163077719094605864 - 1.7147467590162723351e-764j)  +/-  (4.4e-247, 4.4e-247j)
| (8.3717095823733048883 - 3.1962097127676821521e-764j)  +/-  (2.26e-244, 2.26e-244j)
| (11.146478702298714542 - 8.0772153709127003247e-767j)  +/-  (4.37e-246, 4.37e-246j)
| (6.665886415343268239 - 3.9410744382722387734e-764j)  +/-  (1.85e-244, 1.85e-244j)
| (-2.1933073817544791212 + 8.039447888503154981e-771j)  +/-  (1.78e-249, 1.78e-249j)
| (-1.2794976424064099646 - 1.2971549472794160978e-772j)  +/-  (1.87e-251, 1.87e-251j)
| (7.2149838415622979691 - 3.4461874395123205373e-765j)  +/-  (2.51e-244, 2.51e-244j)
| (-7.2149838415622979691 + 8.0303627060631519071e-767j)  +/-  (2.55e-244, 2.55e-244j)
| (2.1933073817544791212 - 2.7660120948726174944e-781j)  +/-  (1.69e-249, 1.69e-249j)
| (4.1031792286340766395 + 5.2748292974942461347e-779j)  +/-  (2.11e-246, 2.11e-246j)
| (7.7821612920617807029 + 2.192463697552787069e-776j)  +/-  (2.5e-244, 2.5e-244j)
| (-2.6614904582002893304 + 1.0825120433054741186e-781j)  +/-  (1.33e-248, 1.33e-248j)
| (5.6100411861661274343 + 1.4322857783682162963e-777j)  +/-  (5.31e-245, 5.31e-245j)
| (0.83876080401506300671 + 1.3190783390542704073e-785j)  +/-  (1.5e-252, 1.5e-252j)
| (2.6614904582002893304 + 1.3654865551403376759e-780j)  +/-  (1.24e-248, 1.24e-248j)
| (-6.1317084629494184553 - 2.4617088248854795351e-775j)  +/-  (1.21e-244, 1.21e-244j)
| (-5.0990041183285010953 - 6.5719902025299281696e-779j)  +/-  (2.22e-245, 2.22e-245j)
| (4.5971091188528217344 + 2.9307719616305986732e-784j)  +/-  (7.71e-246, 7.71e-246j)
| (1.7320508075688772935 + 2.2452481550773434273e-788j)  +/-  (2.17e-250, 2.17e-250j)
| (-4.1031792286340766395 + 3.417998893023708765e-783j)  +/-  (2.11e-246, 2.11e-246j)
| (-4.5971091188528217344 + 7.8054654633762515091e-782j)  +/-  (6.95e-246, 6.95e-246j)
| (-1.7320508075688772935 - 4.8373105068369604419e-792j)  +/-  (1.95e-250, 1.95e-250j)
| (-0.83876080401506300671 + 6.5713152248648122269e-795j)  +/-  (1.38e-252, 1.38e-252j)
| (9.6454847885967472738 - 4.326793499592116298e-785j)  +/-  (7.55e-245, 7.55e-245j)
| (0.4130495933989143287 + 1.4719983856766542302e-795j)  +/-  (9.18e-254, 9.18e-254j)
| (-3.1358549144160045807 - 5.4000222438936585301e-791j)  +/-  (7.62e-248, 7.62e-248j)
| (-5.6100411861661274343 - 1.941054429349957772e-785j)  +/-  (5.69e-245, 5.69e-245j)
| (-0.4130495933989143287 + 1.1298798421714195196e-802j)  +/-  (9.18e-254, 9.18e-254j)
| (6.1317084629494184553 + 4.0303652377154026539e-793j)  +/-  (1.07e-244, 1.07e-244j)
| (3.6163077719094605864 - 4.6574126083576586422e-798j)  +/-  (4.44e-247, 4.44e-247j)
| (-1.4606703154176708489e-808 - 2.2793008487312226158e-808j)  +/-  (1.22e-806, 1.22e-806j)
| (3.1358549144160045807 - 2.9964977975084724076e-800j)  +/-  (8.03e-248, 8.03e-248j)
-------------------------------------------------
The weights are:
| (1.4522368609504203839e-16 - 1.7842042954614978094e-563j)  +/-  (1.99e-77, 9.61e-198j)
| (3.5639359957775766053e-28 + 1.7645016077049606019e-570j)  +/-  (3.58e-83, 1.72e-203j)
| (7.1590329599101369508e-19 + 1.5631952420170597536e-566j)  +/-  (1.26e-80, 6.06e-201j)
| (7.0496588321346598955e-33 + 9.8052670973494402999e-574j)  +/-  (3.07e-86, 1.48e-206j)
| (1.5524151650503832455e-24 - 1.7531433425895223143e-568j)  +/-  (4.51e-82, 2.17e-202j)
| (1.69980244122030279e-21 + 9.6853376787309398904e-567j)  +/-  (4.69e-81, 2.26e-201j)
| (4.5653852144989224857e-07 - 2.7941128993464566285e-560j)  +/-  (9.79e-74, 4.72e-194j)
| (7.0496588321346598955e-33 - 5.3835981148778624423e-573j)  +/-  (4.22e-86, 2.03e-206j)
| (1.5524151650503832455e-24 + 1.8562053607754082758e-569j)  +/-  (1.46e-85, 7.04e-206j)
| (7.1590329599101369508e-19 - 4.3913211717046466133e-565j)  +/-  (2.94e-80, 1.42e-200j)
| (0.07870134468680223335 - 5.0225093276888880206e-557j)  +/-  (2.31e-55, 1.11e-175j)
| (4.8475757898551032512e-11 + 1.7552002887241973923e-561j)  +/-  (4.7e-78, 2.27e-198j)
| (1.6278091606361898758e-14 + 7.9992722061295869992e-563j)  +/-  (3.54e-79, 1.71e-199j)
| (0.00027899403592489461415 + 2.7011053927825345754e-558j)  +/-  (1.61e-71, 7.78e-192j)
| (1.4522368609504203839e-16 - 2.4762674872479191244e-565j)  +/-  (3.97e-84, 1.91e-204j)
| (3.5639359957775766053e-28 - 2.5084728673118943912e-571j)  +/-  (8.15e-89, 3.93e-209j)
| (4.8475757898551032512e-11 + 1.9910505081651262312e-562j)  +/-  (4.72e-82, 2.28e-202j)
| (0.016736925057110421657 - 2.4831213647014403197e-557j)  +/-  (1.88e-69, 9.08e-190j)
| (0.07870134468680223335 - 6.8347193682625294323e-557j)  +/-  (1.01e-63, 4.86e-184j)
| (1.1050079023313890567e-12 - 2.6846005353040735983e-563j)  +/-  (4.98e-83, 2.4e-203j)
| (1.1050079023313890567e-12 - 3.6174560687289783997e-562j)  +/-  (1.73e-81, 8.33e-202j)
| (0.016736925057110421657 - 1.452124739237611544e-557j)  +/-  (7.7e-72, 3.71e-192j)
| (4.3195471605151203201e-05 - 3.6044243670050757325e-559j)  +/-  (2.17e-78, 1.05e-198j)
| (1.6278091606361898758e-14 + 2.919397641294513131e-564j)  +/-  (3.8e-84, 1.83e-204j)
| (0.0054458926723527906258 + 1.3051418819295010965e-557j)  +/-  (8.44e-75, 4.07e-195j)
| (3.0160795556688670445e-08 + 6.3129489722304092075e-561j)  +/-  (3.35e-81, 1.61e-201j)
| (0.12167637440839641486 + 7.9967869798352870695e-557j)  +/-  (1.74e-69, 8.4e-190j)
| (0.0054458926723527906258 + 6.7547457732539658794e-558j)  +/-  (2.05e-75, 9.9e-196j)
| (1.4418555397992200922e-09 - 7.9060777065229261993e-561j)  +/-  (1.14e-82, 5.51e-203j)
| (4.5653852144989224857e-07 - 1.1500788973541030042e-559j)  +/-  (5.48e-82, 2.64e-202j)
| (5.115052176989434617e-06 + 1.0721255281203896111e-559j)  +/-  (7.01e-81, 3.38e-201j)
| (0.040707909449555950833 + 2.8340135250997543076e-557j)  +/-  (8.74e-75, 4.21e-195j)
| (4.3195471605151203201e-05 - 1.0534022129345963253e-558j)  +/-  (8.91e-81, 4.3e-201j)
| (5.115052176989434617e-06 + 3.6836220769658669509e-559j)  +/-  (1.32e-81, 6.37e-202j)
| (0.040707909449555950833 + 4.3126001757984524535e-557j)  +/-  (2.78e-77, 1.34e-197j)
| (0.12167637440839641486 + 9.7776012861833692577e-557j)  +/-  (1.84e-76, 8.89e-197j)
| (1.69980244122030279e-21 - 6.8473163718247407123e-568j)  +/-  (6.53e-91, 3.15e-211j)
| (0.15315768044041834177 - 1.1098302223266384406e-556j)  +/-  (3.4e-77, 1.64e-197j)
| (0.0013945736559458281146 - 6.2400080235266324137e-558j)  +/-  (6.28e-80, 3.03e-200j)
| (3.0160795556688670445e-08 + 3.1961143222501183599e-560j)  +/-  (3.41e-83, 1.65e-203j)
| (0.15315768044041834177 - 1.2250292439480959243e-556j)  +/-  (2.64e-78, 1.27e-198j)
| (1.4418555397992200922e-09 - 1.2210654659144192854e-561j)  +/-  (2.94e-85, 1.42e-205j)
| (0.00027899403592489461415 + 1.0714733800833921066e-558j)  +/-  (6.82e-83, 3.3e-203j)
| (0.16370301375788249464 + 1.2875153783078534255e-556j)  +/-  (3.84e-81, 5.61e-201j)
| (0.0013945736559458281146 - 2.8391563781535683126e-558j)  +/-  (1.97e-82, 9.41e-203j)
