Starting with polynomial:
P : t
Extension levels are: 1 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 903*t^41 + 370230*t^39 - 91446810*t^37 + 15225893865*t^35 - 1811881369935*t^33 + 159445560554280*t^31 - 10591740808248600*t^29 + 537530846018616450*t^27 - 20963702994726041550*t^25 + 628911089841781246500*t^23 - 14464955066360968669500*t^21 + 253136713661316951716250*t^19 - 3329721387391169134113750*t^17 + 32345864906085643017105000*t^15 - 226421054342599501119735000*t^13 + 1103802639920172567958708125*t^11 - 3571126187977028896336996875*t^9 + 7142252375954057792673993750*t^7 - 7894068415528169139271256250*t^5 + 3947034207764084569635628125*t^3 - 563862029680583509947946875*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
Positive weights:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.1804905114486618262 - 1.6128772932259508819e-565j)  +/-  (7.03e-245, 7.03e-245j)
| (10.176437001879133613 + 1.4772228609560335833e-582j)  +/-  (1e-245, 1e-245j)
| (-11.932057301056317452 + 4.9600481283223902847e-597j)  +/-  (1.09e-247, 1.09e-247j)
| (-9.4630967355223121218 + 7.5803942145463174741e-594j)  +/-  (2.42e-245, 2.42e-245j)
| (8.8029547057222341609 - 4.642068743843465014e-601j)  +/-  (5.18e-245, 5.18e-245j)
| (11.932057301056317452 + 1.6404535599389251656e-611j)  +/-  (1.11e-247, 1.11e-247j)
| (-10.176437001879133613 + 1.9006995368700329997e-618j)  +/-  (7.72e-246, 7.72e-246j)
| (-10.973099524957786382 - 2.364933483028415831e-620j)  +/-  (1.41e-246, 1.41e-246j)
| (7.5863830525708615775 - 4.6760380803429922987e-617j)  +/-  (8.25e-245, 8.25e-245j)
| (-8.1804905114486618262 + 2.1688474003521655479e-626j)  +/-  (7.25e-245, 7.25e-245j)
| (10.973099524957786382 - 4.1959426225632686673e-626j)  +/-  (1.37e-246, 1.37e-246j)
| (-5.3936834231253809986 - 1.5495489475604940798e-635j)  +/-  (1.01e-245, 1.01e-245j)
| (-8.8029547057222341609 + 1.9513352115735119133e-632j)  +/-  (5.08e-245, 5.08e-245j)
| (-5.9209784614715200246 - 5.3770753715444585551e-633j)  +/-  (2.27e-245, 2.27e-245j)
| (-7.5863830525708615775 - 5.3972508370793992491e-633j)  +/-  (7.97e-245, 7.97e-245j)
| (9.4630967355223121218 - 8.2811705978570149912e-632j)  +/-  (2.49e-245, 2.49e-245j)
| (5.9209784614715200246 - 1.2944742948773453948e-655j)  +/-  (2.18e-245, 2.18e-245j)
| (-3.3712358171480526595 - 6.8356137262925232333e-674j)  +/-  (4.89e-248, 4.89e-248j)
| (-7.0144733541827294045 - 5.2434320734360528165e-670j)  +/-  (6.84e-245, 6.84e-245j)
| (-6.4604133308954666008 + 5.0031231555571812239e-675j)  +/-  (5.16e-245, 5.16e-245j)
| (2.3947734288425255683 + 3.8848877753888327428e-683j)  +/-  (1.31e-249, 1.31e-249j)
| (0.95345327562973769009 - 1.0805403749724763341e-695j)  +/-  (1.11e-252, 1.11e-252j)
| (4.8765512847065944515 - 6.8374466695729849578e-705j)  +/-  (3.42e-246, 3.42e-246j)
| (-1.9119592749517121403 - 9.8909601427108011709e-730j)  +/-  (1.47e-250, 1.47e-250j)
| (-1.4317493644516902135 + 5.6414207464112073358e-735j)  +/-  (1.4e-251, 1.4e-251j)
| (1.9119592749517121403 + 1.1305222039082311332e-733j)  +/-  (1.69e-250, 1.69e-250j)
| (6.4604133308954666008 - 1.6536526560313805593e-738j)  +/-  (5.04e-245, 5.04e-245j)
| (2.8809307774503764409 - 3.4656122909499867875e-761j)  +/-  (1.05e-248, 1.05e-248j)
| (7.0144733541827294045 + 1.1880494032610171223e-764j)  +/-  (6.65e-245, 6.65e-245j)
| (-2.3947734288425255683 - 2.5652992516728169635e-778j)  +/-  (1.32e-249, 1.32e-249j)
| (-4.8765512847065944515 + 1.9042750346815668898e-773j)  +/-  (3.97e-246, 3.97e-246j)
| (3.8665796556922060917 - 2.454030848563472436e-772j)  +/-  (2.92e-247, 2.92e-247j)
| (1.3726585854899860454e-799 + 1.5968621561675124576e-798j)  +/-  (6.89e-797, 6.89e-797j)
| (4.3679669348066756788 - 4.415365088251908798e-775j)  +/-  (1.25e-246, 1.25e-246j)
| (-4.3679669348066756788 - 3.9921867239679269985e-783j)  +/-  (1.02e-246, 1.02e-246j)
| (3.3712358171480526595 - 3.1377656200317623145e-781j)  +/-  (4.9e-248, 4.9e-248j)
| (5.3936834231253809986 - 3.5303502794361456175e-792j)  +/-  (1.16e-245, 1.16e-245j)
| (0.47641488610849427988 + 1.5486817292664995534e-816j)  +/-  (6.1e-254, 6.1e-254j)
| (-3.8665796556922060917 - 9.0949293898810518941e-809j)  +/-  (2.64e-247, 2.64e-247j)
| (-0.47641488610849427988 - 1.4527919974460463716e-817j)  +/-  (6.1e-254, 6.1e-254j)
| (-0.95345327562973769009 - 2.0769745441068044466e-816j)  +/-  (9.32e-253, 9.32e-253j)
| (-2.8809307774503764409 - 3.9624819336851374079e-811j)  +/-  (1.07e-248, 1.07e-248j)
| (1.4317493644516902135 - 9.1048482438429187002e-811j)  +/-  (1.4e-251, 1.4e-251j)
-------------------------------------------------
The weights are:
| (7.121219095949836797e-16 + 4.6979135974016017922e-580j)  +/-  (5.08e-79, 2.75e-201j)
| (9.7059611743871922575e-24 + 6.7181374097248718448e-585j)  +/-  (4.03e-83, 2.18e-205j)
| (5.3520752240799096366e-32 - 4.9507673319260165452e-590j)  +/-  (2.67e-87, 1.44e-209j)
| (9.772188868028616492e-21 + 2.4115015105670532348e-584j)  +/-  (1.73e-83, 9.33e-206j)
| (3.79745385179088823e-18 + 1.3474429278280357307e-581j)  +/-  (2.98e-81, 1.61e-203j)
| (5.3520752240799096366e-32 + 2.654158922287590672e-589j)  +/-  (2.34e-87, 1.27e-209j)
| (9.7059611743871922575e-24 - 7.3046226147782992772e-586j)  +/-  (4.89e-85, 2.64e-207j)
| (2.4385097855866963231e-27 + 1.1096616204427818652e-587j)  +/-  (1.88e-86, 1.01e-208j)
| (7.3864287975093105214e-14 - 1.9689321689041214279e-579j)  +/-  (5.03e-81, 2.72e-203j)
| (7.121219095949836797e-16 + 7.0201490753337243195e-582j)  +/-  (5.13e-83, 2.77e-205j)
| (2.4385097855866963231e-27 - 7.610805398922721554e-587j)  +/-  (3.74e-87, 2.02e-209j)
| (1.0030066755417815115e-07 - 1.0041925697604939356e-577j)  +/-  (6.18e-79, 3.34e-201j)
| (3.79745385179088823e-18 - 4.9385443629076462267e-583j)  +/-  (6.93e-84, 3.74e-206j)
| (5.1867054608185025639e-09 + 2.1981632286014714021e-578j)  +/-  (2.07e-80, 1.12e-202j)
| (7.3864287975093105214e-14 - 7.419082057205078743e-581j)  +/-  (5.85e-83, 3.16e-205j)
| (9.772188868028616492e-21 - 3.3172720121970123219e-583j)  +/-  (3.1e-87, 1.68e-209j)
| (5.1867054608185025639e-09 + 1.3718594935508878654e-577j)  +/-  (1.74e-83, 9.41e-206j)
| (0.00066916839169690166212 - 9.638275134954545723e-576j)  +/-  (2.45e-77, 1.32e-199j)
| (4.6416475761066535806e-12 + 6.1026000951803530492e-580j)  +/-  (7.89e-83, 4.26e-205j)
| (1.884798249393542386e-10 - 4.0359246385520199326e-579j)  +/-  (3.83e-82, 2.07e-204j)
| (0.01098373316809109537 - 7.7964391824421862855e-575j)  +/-  (1.36e-77, 7.36e-200j)
| (0.12093036830966250338 + 2.0710276498315844523e-574j)  +/-  (1.45e-73, 7.85e-196j)
| (1.4020888279499707889e-06 + 1.5425321191009431049e-576j)  +/-  (6.61e-84, 3.57e-206j)
| (0.030875167245633445184 + 7.4935319565913530325e-575j)  +/-  (1.28e-75, 6.91e-198j)
| (0.068587049431093171781 - 1.1726676958417873774e-574j)  +/-  (1.44e-73, 7.78e-196j)
| (0.030875167245633445184 + 1.2064723320569765579e-574j)  +/-  (1.57e-76, 8.49e-199j)
| (1.884798249393542386e-10 - 3.4352868124780170457e-578j)  +/-  (4.85e-86, 2.62e-208j)
| (0.0030700123957878347397 + 4.4999612551286184129e-575j)  +/-  (6.63e-81, 3.58e-203j)
| (4.6416475761066535806e-12 + 7.9526092180404843856e-579j)  +/-  (1.05e-86, 5.66e-209j)
| (0.01098373316809109537 - 4.2654246377243174749e-575j)  +/-  (3.08e-80, 1.66e-202j)
| (1.4020888279499707889e-06 + 3.9032059913508549932e-577j)  +/-  (2.53e-84, 1.37e-206j)
| (0.00011268240163838016711 + 1.0590961335320306196e-575j)  +/-  (4.86e-84, 2.63e-206j)
| (0.19002072478258652824 + 2.293504737416842711e-574j)  +/-  (2.61e-79, 1.41e-201j)
| (1.4488711829612319205e-05 - 4.2971533359812523602e-576j)  +/-  (1.07e-84, 5.77e-207j)
| (1.4488711829612319205e-05 - 1.3055786718042573527e-576j)  +/-  (3.1e-85, 1.68e-207j)
| (0.00066916839169690166212 - 2.3150929554772732871e-575j)  +/-  (8.04e-84, 4.34e-206j)
| (1.0030066755417815115e-07 - 4.8912910631130712556e-577j)  +/-  (4.98e-86, 2.69e-208j)
| (0.16974545978387677358 - 2.3017441488701564245e-574j)  +/-  (3.55e-82, 1.92e-204j)
| (0.00011268240163838016711 + 3.7924958054908053768e-576j)  +/-  (3.95e-85, 2.14e-207j)
| (0.16974545978387677358 - 2.0484006903995791819e-574j)  +/-  (6.02e-83, 3.23e-205j)
| (0.12093036830966250338 + 1.6386562355373237627e-574j)  +/-  (4.02e-83, 2.15e-205j)
| (0.0030700123957878347397 + 2.1559447786483886947e-575j)  +/-  (1.63e-84, 8.87e-207j)
| (0.068587049431093171781 - 1.670231964988962138e-574j)  +/-  (1.13e-83, 5.53e-206j)
