Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 30
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^11 - 41*t^9 + 528*t^7 - 2520*t^5 + 4095*t^3 - 1575*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 75404912390772194612765920646155907056927856773/115660074511003364598682758700582224989132258*t^39 + 22030652926970663230182300949873550235518226949539/115660074511003364598682758700582224989132258*t^37 - 7647591851050245487772550298960785271800510345290055/231320149022006729197365517401164449978264516*t^35 + 881464923656760669869764509446166657228558145369620315/231320149022006729197365517401164449978264516*t^33 - 35727243596735122112718429580841754905696535158630580585/115660074511003364598682758700582224989132258*t^31 + 2104823836693513233598697785245541707616262719986696418785/115660074511003364598682758700582224989132258*t^29 - 91855992354996593084129608758600633298412187385203353773605/115660074511003364598682758700582224989132258*t^27 + 230754895997319292233267389472872505500961880845022941006825/8896928808538720353744827592352478845317866*t^25 - 5659754491512560780947804267276082902768415864275852087678875/8896928808538720353744827592352478845317866*t^23 + 104058237383178305630928517588328108284510911168176570052636375/8896928808538720353744827592352478845317866*t^21 - 711982675289266896531334713273537707334402905052396032766384750/4448464404269360176872413796176239422658933*t^19 + 7161035271058249666194301709602443802547710862874024509717864250/4448464404269360176872413796176239422658933*t^17 - 103901980781688889994547379957039133772327885722338548928788939375/8896928808538720353744827592352478845317866*t^15 + 529494610732702750468692707285708007136491436693248552928420404375/8896928808538720353744827592352478845317866*t^13 - 44573745360403046508031797859857973624496269664322603978573699375/216998263622895618384020185179328752324826*t^11 + 4058812807181001805489168367567995808065253357541727152644427718125/8896928808538720353744827592352478845317866*t^9 - 2685719915075550534107869725097173963297541077900480831185495985000/4448464404269360176872413796176239422658933*t^7 + 1850274792794892752720147218629515661490573153795278481984996509375/4448464404269360176872413796176239422658933*t^5 - 1931897254351260203101924567934088034292611995922782025371552553125/17793857617077440707489655184704957690635732*t^3 + 25578653615964767992711550028943631712038314741116762820425140625/17793857617077440707489655184704957690635732*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:
| (8.9816015890723243292 + 1.9309386461541567963e-518j)  +/-  (1.32e-246, 1.32e-246j)
| (-4.2378003427255921339 - 1.9917597679934597508e-528j)  +/-  (2.18e-246, 2.18e-246j)
| (-5.7103476095440873534 - 6.2877837790723607909e-528j)  +/-  (6.85e-246, 6.85e-246j)
| (-10.794587678934111532 + 1.0630877798516092103e-532j)  +/-  (2.86e-248, 2.86e-248j)
| (9.805011219998007382 - 8.2863575363646937156e-530j)  +/-  (2.86e-247, 2.86e-247j)
| (10.794587678934111532 + 4.2882929515292909579e-533j)  +/-  (3.05e-248, 3.05e-248j)
| (-5.1478442825588802766 + 1.1195055591536885585e-531j)  +/-  (5.48e-246, 5.48e-246j)
| (-8.9816015890723243292 + 4.823453979204227109e-533j)  +/-  (1.33e-246, 1.33e-246j)
| (-4.6328811754148542753 + 2.7926538929828319952e-533j)  +/-  (3.65e-246, 3.65e-246j)
| (-8.2433647174261652139 - 2.5112909078270455109e-532j)  +/-  (3.57e-246, 3.57e-246j)
| (4.2378003427255921339 - 1.4994460546410977127e-530j)  +/-  (2.14e-246, 2.14e-246j)
| (3.860809886511654479 + 1.1841108863299048119e-532j)  +/-  (6.98e-247, 6.98e-247j)
| (4.6328811754148542753 + 1.8380240252714593336e-537j)  +/-  (3.75e-246, 3.75e-246j)
| (-6.9146047436463990651 + 4.7360682323847999032e-551j)  +/-  (7.97e-246, 7.97e-246j)
| (6.2996891330197546213 - 7.5169024712506949144e-578j)  +/-  (7.91e-246, 7.91e-246j)
| (8.2433647174261652139 + 4.5980071505420854432e-611j)  +/-  (3.45e-246, 3.45e-246j)
| (-9.805011219998007382 + 5.2675859086044413568e-627j)  +/-  (3.27e-247, 3.27e-247j)
| (5.7103476095440873534 + 6.015282581644435243e-642j)  +/-  (6.82e-246, 6.82e-246j)
| (-0.74196378430272585765 + 1.9943868948737298678e-659j)  +/-  (5.34e-253, 5.34e-253j)
| (-3.860809886511654479 + 7.6574829987016814292e-662j)  +/-  (6.88e-247, 6.88e-247j)
| (5.1478442825588802766 + 1.8678507987542155778e-681j)  +/-  (4.96e-246, 4.96e-246j)
| (0.74196378430272585765 + 3.713298927278999471e-694j)  +/-  (5.54e-253, 5.54e-253j)
| (-2.8565782002360406292 + 2.1005372383700365919e-695j)  +/-  (1.59e-248, 1.59e-248j)
| (-2.3344142183389772393 - 3.3751126970769161737e-699j)  +/-  (2.22e-249, 2.22e-249j)
| (-1.2540024029178692629 + 6.5858357347256398291e-710j)  +/-  (3.92e-251, 3.92e-251j)
| (7.5595584866274731095 - 1.9940487849710555063e-728j)  +/-  (6.42e-246, 6.42e-246j)
| (2.8565782002360406292 + 3.4976515160213688495e-744j)  +/-  (1.78e-248, 1.78e-248j)
| (2.3344142183389772393 - 2.3754247801783901322e-745j)  +/-  (2.3e-249, 2.3e-249j)
| (1.2540024029178692629 - 1.0273621451260287203e-748j)  +/-  (3.58e-251, 3.58e-251j)
| (-3.3747086797406716539 - 4.2674678973024597041e-746j)  +/-  (1.2e-247, 1.2e-247j)
| (-6.2996891330197546213 + 2.9874663695349207613e-743j)  +/-  (8.13e-246, 8.13e-246j)
| (0.11820812436335886395 + 2.6596380450145507157e-760j)  +/-  (1.33e-254, 1.33e-254j)
| (1.8178978335467857625 + 3.9471251583250724678e-751j)  +/-  (4.53e-250, 4.53e-250j)
| (-0.11820812436335886395 + 1.5378964777727457701e-761j)  +/-  (1.33e-254, 1.33e-254j)
| (6.9146047436463990651 - 1.4631352472262274315e-752j)  +/-  (8.01e-246, 8.01e-246j)
| (-1.4655215253859805014 - 3.1750999693770745956e-769j)  +/-  (1.22e-250, 1.22e-250j)
| (3.3747086797406716539 + 1.1180163141223203551e-762j)  +/-  (1.18e-247, 1.18e-247j)
| (1.4655215253859805014 + 3.4047841800856931298e-768j)  +/-  (1.29e-250, 1.29e-250j)
| (-7.5595584866274731095 - 1.874295808637401514e-762j)  +/-  (6.3e-246, 6.3e-246j)
| (9.6909258179276069192e-780 + 3.7848886092768881929e-780j)  +/-  (4.27e-778, 4.27e-778j)
| (-1.8178978335467857625 - 1.0871858545898382448e-772j)  +/-  (3.86e-250, 3.86e-250j)
-------------------------------------------------
The weights are:
| (9.3829349984674299655e-19 - 9.2677725659856626105e-536j)  +/-  (3.77e-92, 3.71e-215j)
| (1.6913907798949436385e-05 - 1.3061417027884902035e-528j)  +/-  (1.42e-79, 1.4e-202j)
| (1.9109331238736606182e-08 + 2.9519942840411937716e-531j)  +/-  (7.99e-85, 7.84e-208j)
| (2.2658902265777001132e-26 - 5.1872515233479518437e-542j)  +/-  (2.87e-96, 2.82e-219j)
| (4.6931324421205303252e-22 - 3.0249661367612852185e-538j)  +/-  (1.67e-94, 1.64e-217j)
| (2.2658902265777001132e-26 + 5.6582659561334585146e-541j)  +/-  (1.92e-96, 1.89e-219j)
| (3.8308938403127385709e-07 - 3.1181738269939402431e-530j)  +/-  (2.37e-84, 2.32e-207j)
| (9.3829349984674299655e-19 - 1.0086181760939866418e-537j)  +/-  (3.07e-94, 3.02e-217j)
| (4.0929502023251814493e-06 + 2.8723212094212780286e-529j)  +/-  (1.71e-83, 1.68e-206j)
| (4.9531734403279346169e-16 + 3.933588407030651891e-536j)  +/-  (7.05e-93, 6.92e-216j)
| (1.6913907798949436385e-05 - 3.6395750321191108218e-528j)  +/-  (1.66e-86, 1.63e-209j)
| (0.00010269506296304976796 + 8.2687191264558490308e-528j)  +/-  (1.51e-85, 1.48e-208j)
| (4.0929502023251814493e-06 + 8.9932583388488977603e-529j)  +/-  (4.74e-88, 4.65e-211j)
| (1.0405628178801487776e-11 + 1.7646329597885496113e-533j)  +/-  (1.08e-92, 1.06e-215j)
| (5.7888280647478814456e-10 - 1.4198129233490214225e-531j)  +/-  (2.67e-93, 2.62e-216j)
| (4.9531734403279346169e-16 + 9.1779782042098692783e-535j)  +/-  (6.2e-97, 6.09e-220j)
| (4.6931324421205303252e-22 + 1.3258384645587941815e-539j)  +/-  (2.09e-99, 2.05e-222j)
| (1.9109331238736606182e-08 + 1.3260571906203564971e-530j)  +/-  (3.29e-92, 3.23e-215j)
| (0.16144779461938906929 - 1.7130748340510477908e-525j)  +/-  (1.78e-82, 1.75e-205j)
| (0.00010269506296304976796 + 3.2972316869562656027e-528j)  +/-  (2.67e-88, 2.62e-211j)
| (3.8308938403127385709e-07 - 1.149328550459950904e-529j)  +/-  (5.22e-91, 5.13e-214j)
| (0.16144779461938906929 - 2.0215924775090732587e-525j)  +/-  (4.6e-83, 4.52e-206j)
| (0.0035206318336198982101 + 2.4212105721787390563e-527j)  +/-  (3.99e-87, 3.92e-210j)
| (0.013634047796733383347 - 8.7244205619486176409e-527j)  +/-  (5.77e-86, 5.66e-209j)
| (0.084847411000489141741 + 2.0229339811344679979e-525j)  +/-  (1.31e-82, 1.29e-205j)
| (1.0298881979425620158e-13 - 1.1403646700565002564e-533j)  +/-  (1.14e-96, 1.12e-219j)
| (0.0035206318336198982101 + 4.6795848256908649622e-527j)  +/-  (6.6e-89, 6.48e-212j)
| (0.013634047796733383347 - 1.485220942274165926e-526j)  +/-  (5.38e-88, 5.29e-211j)
| (0.084847411000489141741 + 2.6794786822570805009e-525j)  +/-  (5.15e-85, 5.07e-208j)
| (0.00068566719961643448273 - 8.119629548325384749e-528j)  +/-  (1.61e-89, 1.59e-212j)
| (5.7888280647478814456e-10 - 2.491957526053004297e-532j)  +/-  (3.25e-95, 3.19e-218j)
| (0.65243156875552588383 + 2.0207594013895784033e-524j)  +/-  (7.88e-86, 7.84e-209j)
| (0.038652487310247853782 + 6.9945037059573234752e-526j)  +/-  (6.04e-88, 5.9e-211j)
| (0.65243156875552588383 + 1.9682594527116521415e-524j)  +/-  (5.27e-86, 5.19e-209j)
| (1.0405628178801487776e-11 + 1.3570541832244058123e-532j)  +/-  (2.09e-96, 2.04e-219j)
| (0.013071513082927356596 - 1.7231234622777538237e-525j)  +/-  (5.63e-88, 5.43e-211j)
| (0.00068566719961643448273 - 1.7893563691609821656e-527j)  +/-  (1.15e-90, 1.13e-213j)
| (0.013071513082927356596 - 2.3950872004787733548e-525j)  +/-  (4.47e-88, 4.36e-211j)
| (1.0298881979425620158e-13 - 9.8038601585882023686e-535j)  +/-  (2.92e-98, 2.91e-221j)
| (-0.93683045261524107081 - 3.772004912300922829e-524j)  +/-  (1.97e-87, 3.03e-210j)
| (0.038652487310247853782 + 4.6397169860602843194e-526j)  +/-  (2.31e-89, 2.09e-212j)
