Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 16
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Trying to find an order 16 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
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Ending with final polynomial:
P : -1/6*t^19 + 8165670912386045101475485777/149166955307993520144634422*t^18 - 199672327930814047843076894427/24861159217998920024105737*t^17 + 225353475959261194672383152406197/323195069833985960313374581*t^16 - 12930034434595590654694957904689472/323195069833985960313374581*t^15 + 518762056015408536566011806272239680/323195069833985960313374581*t^14 - 306565860784591992990453473249627520/6595817751713999190068869*t^13 + 501689829431928819481773932868723840/507370596285692245389913*t^12 - 55371886714878847281450148346317244160/3551594173999845717729391*t^11 + 648409432506571179468208803075909154560/3551594173999845717729391*t^10 - 5619662878951476413630567879758568179200/3551594173999845717729391*t^9 + 35737421231067109365186944346540547699200/3551594173999845717729391*t^8 - 164430104238931030121587378501658586931200/3551594173999845717729391*t^7 + 10944063073965780253531465112067016089600/72481513755098892198559*t^6 - 24568909397604794277794721499157086617600/72481513755098892198559*t^5 + 254588914346254014212236692718283925504000/507370596285692245389913*t^4 - 232365481723348633700351975145584830464000/507370596285692245389913*t^3 + 116552993198005116116010420461270820864000/507370596285692245389913*t^2 - 25664483060394284817539570117013884928000/507370596285692245389913*t + 1402671911392083932326512858295922688000/507370596285692245389913
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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:
| (59.524195890714593065 - 2.8938286849562985228e-375j)  +/-  (4.22e-120, 4.22e-120j)
| (29.358338568067093748 - 1.1190535617639422374e-371j)  +/-  (4.63e-118, 4.63e-118j)
| (34.858627558242178737 - 1.6094428019462442511e-390j)  +/-  (3.16e-118, 3.16e-118j)
| (20.438084292575541333 + 9.698663862768195294e-410j)  +/-  (3.74e-118, 3.74e-118j)
| (41.322183243833940493 + 9.9613104125518355504e-425j)  +/-  (1.35e-118, 1.35e-118j)
| (16.791901581622374034 - 2.649093157924029134e-438j)  +/-  (2.23e-118, 2.23e-118j)
| (13.59496667464126105 - 8.3643200834978347416e-454j)  +/-  (1.27e-118, 1.27e-118j)
| (10.800932552534910034 + 5.3088793431620018528e-467j)  +/-  (4.54e-119, 4.54e-119j)
| (3.0588564173797503478 - 1.6929966017204598994e-475j)  +/-  (2.81e-121, 2.81e-121j)
| (24.596848289190639994 - 1.9298143966148464391e-479j)  +/-  (5.17e-118, 5.17e-118j)
| (1.0255332847953890584 - 2.5566221681102702782e-494j)  +/-  (6.8e-124, 6.8e-124j)
| (8.3748864328354590246 + 1.0698480168920390206e-488j)  +/-  (1.56e-119, 1.56e-119j)
| (49.177839081907156744 + 3.3399017163471243869e-493j)  +/-  (3.63e-119, 3.63e-119j)
| (0.078768971996084027454 + 6.8218622536872214432e-501j)  +/-  (4.1e-127, 4.1e-127j)
| (0.41577455678347908331 - 3.5990763768331771613e-496j)  +/-  (2.07e-125, 2.07e-125j)
| (1.9241560394482797016 - 4.6843531748054002365e-491j)  +/-  (5.31e-122, 5.31e-122j)
| (2.2942803602790417198 + 1.7746921855774459727e-492j)  +/-  (1.6e-121, 1.6e-121j)
| (4.5248129848197571988 + 1.9976650898770060911e-491j)  +/-  (9.38e-121, 9.38e-121j)
| (6.2899450829374791969 - 1.5714625982533578648e-490j)  +/-  (4.38e-120, 4.38e-120j)
-------------------------------------------------
The weights are:
| (1.7604752844013862527e-25 - 1.1114567150665272364e-391j)  +/-  (1.56e-50, 3.56e-109j)
| (9.0709282247688870606e-13 + 5.2451797248361079965e-384j)  +/-  (2.07e-45, 4.74e-104j)
| (4.3092657051158722421e-15 + 1.1727655053534743193e-385j)  +/-  (9.36e-47, 2.14e-105j)
| (5.1738643221557718434e-09 + 1.0404486733730851235e-382j)  +/-  (6.02e-44, 1.38e-102j)
| (7.9946482793644066542e-18 - 2.1565207911961213232e-387j)  +/-  (1.95e-48, 4.46e-107j)
| (1.7396507195881901502e-07 - 4.8060083608115661966e-382j)  +/-  (2.6e-43, 5.94e-102j)
| (3.7263653929387435412e-06 + 2.0281698795321261515e-381j)  +/-  (8.29e-43, 1.9e-101j)
| (5.3090774171918888748e-05 - 7.6407056966480418063e-381j)  +/-  (2.28e-42, 5.21e-101j)
| (0.062426575245952916815 - 1.0929835891687943376e-378j)  +/-  (9.79e-39, 2.24e-97j)
| (9.2324599218594780412e-11 - 2.3534410752809275249e-383j)  +/-  (1.02e-45, 2.34e-104j)
| (0.26841235885889423902 + 7.0971581638953681709e-379j)  +/-  (2.35e-37, 5.37e-96j)
| (0.00051917710970372243254 + 2.5866807213036570834e-380j)  +/-  (2.27e-42, 5.19e-101j)
| (3.8645489232074050359e-21 + 2.6730810040737511091e-389j)  +/-  (2.94e-51, 6.71e-110j)
| (0.18691120055107816167 + 9.0924752369511294997e-380j)  +/-  (1.17e-37, 2.67e-96j)
| (0.31175614757498072716 - 3.219900213411470707e-379j)  +/-  (8.64e-38, 1.98e-96j)
| (0.15825072104629213926 - 2.657612431277360254e-378j)  +/-  (1.77e-39, 4.05e-98j)
| (-0.0093612231200491130316 + 3.0807543302310194705e-378j)  +/-  (9.08e-40, 2.08e-98j)
| (0.017463311089709488643 + 2.5225681248360744058e-379j)  +/-  (5.08e-42, 1.16e-100j)
| (0.0035647352717005701264 - 8.0925211029171603306e-380j)  +/-  (1.14e-42, 2.6e-101j)
