Starting with polynomial:
P : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Extension levels are: 5 12
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Trying to find an order 12 Kronrod extension for:
P1 : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Solvable: 1
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Ending with final polynomial:
P : -1/120*t^17 + 52446507051977349311/27721953074260051080*t^16 - 1309222495970093703217/6930488268565012770*t^15 + 15216524107080774855025/1386097653713002554*t^14 - 1148051444007899591391725/2772195307426005108*t^13 + 207872689497266409606928255/19405367151982035756*t^12 - 316425934159802502334196710/1617113929331836313*t^11 + 4142299804041087947398432930/1617113929331836313*t^10 - 39031596457743393037641144950/1617113929331836313*t^9 + 11459490388222753154204897850/70309301275297231*t^8 - 1258894282051271458164984318720/1617113929331836313*t^7 + 593730176502478721270475335040/231016275618833759*t^6 - 1307043618557196527100628175520/231016275618833759*t^5 + 1817225701238915643391074612000/231016275618833759*t^4 - 1467342198446801939952056928000/231016275618833759*t^3 + 598990923152942837031227116800/231016275618833759*t^2 - 94974975213378886331777491200/231016275618833759*t + 2997042974599927483784505600/231016275618833759
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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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
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The nodes are:
| (46.735852545163440078 + 2.0451133608318001925e-335j)  +/-  (5.24e-121, 5.24e-121j)
| (24.72693506657745053 + 9.3117010062429060508e-352j)  +/-  (2.68e-119, 2.68e-119j)
| (37.382889734649106581 - 1.5489575847131514397e-364j)  +/-  (4.2e-120, 4.2e-120j)
| (30.387318609737179774 + 1.1992063951621905015e-372j)  +/-  (1.29e-119, 1.29e-119j)
| (5.1811993834357654337 + 7.8249505193501177088e-375j)  +/-  (1.03e-120, 1.03e-120j)
| (7.0858100058588375569 + 2.0527318642518211273e-373j)  +/-  (7.97e-120, 7.97e-120j)
| (9.9024690599812282384 + 2.8301152860219790554e-377j)  +/-  (3.72e-119, 3.72e-119j)
| (16.012689987088371753 + 1.1389140332852514823e-392j)  +/-  (3.77e-119, 3.77e-119j)
| (0.72189614000581592994 - 1.1113163559376126576e-406j)  +/-  (1.09e-124, 1.09e-124j)
| (0.041262597584574485475 + 5.705195653516118237e-407j)  +/-  (1.37e-127, 1.37e-127j)
| (1.4134030591065167922 + 7.7970158693057174119e-406j)  +/-  (1.69e-123, 1.69e-123j)
| (2.3543598957341142456 - 2.39005134769516024e-405j)  +/-  (1.41e-122, 1.41e-122j)
| (20.003738477049717777 - 1.218514947368725018e-411j)  +/-  (3.44e-119, 3.44e-119j)
| (8.5745490094835932551 + 2.4537234171159606648e-422j)  +/-  (2.59e-119, 2.59e-119j)
| (0.2635603197181409102 - 4.0592883094387737093e-438j)  +/-  (6.16e-126, 6.16e-126j)
| (3.5964257710407220812 - 1.0815548449701220015e-431j)  +/-  (1.11e-121, 1.11e-121j)
| (12.640800844275782659 - 2.3482079785600074808e-437j)  +/-  (3.45e-119, 3.45e-119j)
-------------------------------------------------
The weights are:
| (5.7361918508416064915e-20 - 6.4273953809317444831e-355j)  +/-  (1.03e-54, 3.01e-113j)
| (9.3926853466951231423e-11 + 9.741889751677810144e-351j)  +/-  (8.14e-51, 2.39e-109j)
| (4.5963875069966754705e-16 + 1.8656011531417573847e-353j)  +/-  (1.43e-53, 4.19e-112j)
| (3.9610015922811147326e-13 - 5.109564837676204153e-352j)  +/-  (3.1e-52, 9.09e-111j)
| (0.009892160067039706963 - 1.1646436029601996736e-345j)  +/-  (2.47e-44, 7.26e-103j)
| (0.0016637298280539860868 + 7.7317454079391558321e-346j)  +/-  (5.06e-46, 1.48e-104j)
| (0.00011384382308916609444 + 1.8618351479732770406e-346j)  +/-  (5.13e-48, 1.51e-106j)
| (4.0765511467324984773e-07 + 1.5589761853452749086e-348j)  +/-  (1.03e-50, 3.02e-109j)
| (0.27975753041878895799 - 5.5143409056213436006e-345j)  +/-  (5.71e-43, 1.68e-101j)
| (0.10968183575778560768 - 1.7405334849809537349e-345j)  +/-  (2.93e-43, 8.61e-102j)
| (0.19697211979905479605 + 5.0094885230263383324e-345j)  +/-  (2.7e-43, 7.92e-102j)
| (0.10274977632665827555 - 3.5679782763819426905e-345j)  +/-  (7.67e-45, 2.25e-103j)
| (8.8957858844535600395e-09 - 1.3706764367684695842e-349j)  +/-  (8.6e-52, 2.52e-110j)
| (0.00015053924544858342734 - 5.2406339323788217251e-346j)  +/-  (3.22e-48, 9.46e-107j)
| (0.26036033059498755805 + 4.4476315304226369476e-345j)  +/-  (8.22e-46, 2.45e-104j)
| (0.038647747506323189571 + 2.1098187348045923031e-345j)  +/-  (3.08e-47, 9.09e-106j)
| (9.9699875462014967613e-06 - 1.6168338150697329728e-347j)  +/-  (5.97e-50, 1.75e-108j)
