Starting with polynomial:
P : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Extension levels are: 12 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^40 - 5776621802918408724/9396449026283357*t^38 + 1592778324328691578137/9396449026283357*t^36 - 4962111172521335525225610/178532531499383783*t^34 + 540898323249049979803689330/178532531499383783*t^32 - 705702686256213932259967759920/3035053035489524311*t^30 + 39394568065592650140040769433090/3035053035489524311*t^28 - 1629591202473303895138295940670020/3035053035489524311*t^26 + 50420290775041956074122953482346000/3035053035489524311*t^24 - 61556989867006367872997547751062000/159739633446817069*t^22 + 20265009683216202949376932908520212000/3035053035489524311*t^20 - 290898180410025609445563592491438000/3398715605251427*t^18 + 7506479316035115741256426248979475250/9396449026283357*t^16 - 49823883721780593669345180722462820000/9396449026283357*t^14 + 227399977079370933591767255089814216250/9396449026283357*t^12 - 680168795109965922163083311680692142500/9396449026283357*t^10 + 1241840605512032198616835133456170831875/9396449026283357*t^8 - 1237214637359902919348331574881474967500/9396449026283357*t^6 + 551325444213682517849984922389390784375/9396449026283357*t^4 - 70540916221776515833750434269448431250/9396449026283357*t^2 + 260093236198698624611063967667875000/9396449026283357
-------------------------------------------------
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:
| (3.7374186883633427909 - 4.6596270514069302429e-574j)  +/-  (1.98e-247, 1.98e-247j)
| (-5.5009017044677476008 - 7.6294697920228280761e-579j)  +/-  (9.54e-245, 9.54e-245j)
| (8.6756813075957122428 + 4.9390073302111785231e-594j)  +/-  (1.04e-246, 1.04e-246j)
| (10.498233312059440093 + 2.6352315682360958899e-617j)  +/-  (2.31e-248, 2.31e-248j)
| (9.5033380207491050311 - 1.6228964454468255131e-651j)  +/-  (2.29e-247, 2.29e-247j)
| (7.9338073270546162509 + 1.5722558020399675549e-682j)  +/-  (3.3e-246, 3.3e-246j)
| (-6.5980566999708007786 - 9.0998671068045656427e-695j)  +/-  (1.15e-245, 1.15e-245j)
| (-3.2237098287700974717 + 5.7079341750050931753e-703j)  +/-  (4.38e-248, 4.38e-248j)
| (-2.7317991703159681935 - 5.7270924990774705791e-704j)  +/-  (8.75e-249, 8.75e-249j)
| (-8.6756813075957122428 + 5.1417097344511168264e-701j)  +/-  (1.08e-246, 1.08e-246j)
| (3.2237098287700974717 + 2.2114148313615023922e-701j)  +/-  (4.35e-248, 4.35e-248j)
| (-4.8268625635223405184 - 2.7397322478102747114e-707j)  +/-  (4.02e-246, 4.02e-246j)
| (5.5009017044677476008 + 2.6798833582378221674e-714j)  +/-  (9.12e-245, 9.12e-245j)
| (4.8268625635223405184 - 1.3469225003436919336e-724j)  +/-  (3.82e-246, 3.82e-246j)
| (-7.2466754381394526966 - 1.6762261884741606031e-729j)  +/-  (7.16e-246, 7.16e-246j)
| (7.2466754381394526966 + 8.7968450323928368238e-729j)  +/-  (6.16e-246, 6.16e-246j)
| (6.5980566999708007786 + 2.333010129760547911e-738j)  +/-  (1.03e-245, 1.03e-245j)
| (-5.9754534217327671447 + 9.8863333442905179399e-745j)  +/-  (2.08e-245, 2.08e-245j)
| (-9.5033380207491050311 + 7.8899946972053661576e-755j)  +/-  (2.4e-247, 2.4e-247j)
| (-3.7374186883633427909 + 3.8840283325002935028e-755j)  +/-  (1.98e-247, 1.98e-247j)
| (-4.271825847932281723 + 1.6408461652409395704e-753j)  +/-  (9.33e-247, 9.33e-247j)
| (0.061635743622292182377 + 1.3640060009779321898e-760j)  +/-  (5.46e-255, 5.46e-255j)
| (-1.7983775792473323132 - 4.4328332627900997968e-757j)  +/-  (1.67e-250, 1.67e-250j)
| (2.7317991703159681935 - 1.4861571266925819376e-751j)  +/-  (8.38e-249, 8.38e-249j)
| (-1.3403751971516167215 + 2.3596953610506132786e-759j)  +/-  (1.74e-251, 1.74e-251j)
| (5.4332149195171735224 - 1.3326223173529365913e-750j)  +/-  (9.46e-245, 9.46e-245j)
| (1.3403751971516167215 + 1.4979400401471676397e-766j)  +/-  (1.93e-251, 1.93e-251j)
| (-10.498233312059440093 + 6.9963040130456633535e-764j)  +/-  (2.6e-248, 2.6e-248j)
| (-5.4332149195171735224 + 1.2047125307527366856e-759j)  +/-  (9.28e-245, 9.28e-245j)
| (-0.8861580480937797068 + 9.0710280391619315159e-774j)  +/-  (1.45e-252, 1.45e-252j)
| (5.9754534217327671447 + 5.5260349768648928295e-768j)  +/-  (2.17e-245, 2.17e-245j)
| (-0.061635743622292182377 + 2.6790234840548836836e-782j)  +/-  (5.46e-255, 5.46e-255j)
| (0.8861580480937797068 - 6.6331058493317157837e-780j)  +/-  (1.45e-252, 1.45e-252j)
| (-7.9338073270546162509 - 1.7856323601833836526e-774j)  +/-  (3.03e-246, 3.03e-246j)
| (2.2594644510007991239 - 3.9920252449114215777e-778j)  +/-  (1.36e-249, 1.36e-249j)
| (-2.2594644510007991239 + 3.0768901831116152704e-778j)  +/-  (1.45e-249, 1.45e-249j)
| (0.4444030019441389453 + 2.0662810159424792478e-781j)  +/-  (8.47e-254, 8.47e-254j)
| (1.7983775792473323132 - 1.2556345679958890016e-777j)  +/-  (1.9e-250, 1.9e-250j)
| (4.271825847932281723 - 1.2468569240573102325e-778j)  +/-  (8.35e-247, 8.35e-247j)
| (-0.4444030019441389453 + 1.1442001101240260642e-787j)  +/-  (1.03e-253, 1.03e-253j)
-------------------------------------------------
The weights are:
| (0.000193773105087765379 + 2.206954039590403005e-577j)  +/-  (7.13e-77, 8.02e-199j)
| (-4.2139685946706962823e-08 - 9.3153078697277837073e-580j)  +/-  (5.25e-84, 5.91e-206j)
| (1.4043921015986882865e-17 + 6.252104904424378772e-587j)  +/-  (1.46e-91, 1.64e-213j)
| (5.3437893896440232435e-25 + 2.3144458228322069656e-591j)  +/-  (2.75e-95, 3.1e-217j)
| (8.6813698261182678061e-21 - 6.8913819822726617879e-589j)  +/-  (2.1e-93, 2.36e-215j)
| (6.086976875001029806e-15 - 3.0373302996679773257e-585j)  +/-  (7.16e-91, 8.06e-213j)
| (8.8942931776373427956e-11 - 7.8886171122602068942e-583j)  +/-  (7.51e-91, 8.46e-213j)
| (0.0011110127085065349419 + 4.4219230831199246292e-578j)  +/-  (1.06e-80, 1.19e-202j)
| (0.0045999106841118747572 - 1.4662728626233601652e-577j)  +/-  (1.46e-78, 1.64e-200j)
| (1.4043921015986882865e-17 + 2.4872545987005439431e-587j)  +/-  (3.4e-96, 3.82e-218j)
| (0.0011110127085065349419 - 5.9920279253992681509e-577j)  +/-  (1.14e-81, 1.28e-203j)
| (1.9722961049912482531e-06 - 8.8297084788831939855e-580j)  +/-  (8.76e-87, 9.86e-209j)
| (-4.2139685946706962823e-08 - 4.8800193043206375029e-579j)  +/-  (5.28e-89, 5.94e-211j)
| (1.9722961049912482531e-06 - 6.9411692242950431473e-579j)  +/-  (1.89e-87, 2.13e-209j)
| (1.0493475684159776857e-12 + 3.2474870452229746077e-584j)  +/-  (3.93e-94, 4.42e-216j)
| (1.0493475684159776857e-12 + 1.0164743677956349721e-583j)  +/-  (1.02e-92, 1.14e-214j)
| (8.8942931776373427956e-11 - 2.8501536967420333151e-582j)  +/-  (9.74e-92, 1.1e-213j)
| (4.3457076213454410047e-09 + 2.2497237828152612531e-581j)  +/-  (7.8e-92, 8.77e-214j)
| (8.6813698261182678061e-21 - 3.0009732685052589075e-589j)  +/-  (2.97e-100, 3.34e-222j)
| (0.000193773105087765379 - 1.2079329807705847799e-578j)  +/-  (4.62e-88, 5.2e-210j)
| (2.3673485793313387582e-05 + 3.1487538200249119606e-579j)  +/-  (3.53e-89, 3.97e-211j)
| (0.092030046798841107606 + 7.959212699966557028e-575j)  +/-  (7.91e-84, 8.89e-206j)
| (0.036326058962071986485 - 1.1026376498795329831e-576j)  +/-  (2.23e-84, 2.51e-206j)
| (0.0045999106841118747572 + 9.432632524477130561e-577j)  +/-  (8.85e-88, 9.96e-210j)
| (0.074261679671215358053 + 2.6512205237276223392e-576j)  +/-  (4.98e-84, 5.6e-206j)
| (1.4694760573593198589e-07 + 6.1390488314825018348e-579j)  +/-  (1.36e-91, 1.53e-213j)
| (0.074261679671215358053 - 5.6162317669634586626e-576j)  +/-  (5.66e-85, 6.37e-207j)
| (5.3437893896440232435e-25 + 1.0991797623678261234e-591j)  +/-  (2.24e-103, 2.52e-225j)
| (1.4694760573593198589e-07 + 1.1352021639818330846e-579j)  +/-  (2.62e-91, 2.95e-213j)
| (0.12118334032327451074 - 6.4166397509533708003e-576j)  +/-  (2.33e-86, 2.62e-208j)
| (4.3457076213454410047e-09 + 9.7635941527490748773e-581j)  +/-  (7.35e-94, 8.28e-216j)
| (0.092030046798841107606 - 7.7009526393316287712e-575j)  +/-  (1.01e-85, 1.13e-207j)
| (0.12118334032327451074 + 1.0405161308445721521e-575j)  +/-  (2.09e-87, 2.35e-209j)
| (6.086976875001029806e-15 - 1.0920721165198510165e-585j)  +/-  (1.32e-97, 1.48e-219j)
| (0.014445908147351315722 - 1.7338271112371803875e-576j)  +/-  (8.01e-90, 9e-212j)
| (0.014445908147351315722 + 4.2730813782359173435e-577j)  +/-  (4.12e-89, 4.64e-211j)
| (0.15582251457401545073 - 2.2768630689887038626e-575j)  +/-  (1.48e-87, 1.66e-209j)
| (0.036326058962071986485 + 3.1479361826851771634e-576j)  +/-  (2.29e-89, 2.57e-211j)
| (2.3673485793313387582e-05 + 4.719088258581790902e-578j)  +/-  (2.74e-92, 3.11e-214j)
| (0.15582251457401545073 + 1.7929376909780111569e-575j)  +/-  (4.89e-88, 5.31e-210j)
