Starting with polynomial:
P : t
Extension levels are: 1 18 20
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : t^19 - 19/4*t^17 + 19/2*t^15 - 665/64*t^13 + 1729/256*t^11 - 2717/1024*t^9 + 627/1024*t^7 - 627/8192*t^5 + 285/65536*t^3 - 19/262144*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 10*t^37 + 739/16*t^35 - 2091/16*t^33 + 8107/32*t^31 - 713/2*t^29 + 1541785/4096*t^27 - 1245231/4096*t^25 + 12435345/65536*t^23 - 3009435/32768*t^21 + 36063885/1048576*t^19 - 10367825/1048576*t^17 + 9026235/4194304*t^15 - 364021/1048576*t^13 + 5400883/134217728*t^11 - 429913/134217728*t^9 + 702525/4294967296*t^7 - 10317/2147483648*t^5 + 4579/68719476736*t^3 - 19/68719476736*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.99658449300666984982 + 6.0993128043958845534e-402j)  +/-  (9.93e-114, 9.93e-114j)
| (0.96940026593933041674 + 4.6978739991736171029e-405j)  +/-  (4.52e-114, 4.52e-114j)
| (-0.94581724170063467902 + 6.8108987216260520701e-405j)  +/-  (2.02e-114, 2.02e-114j)
| (0.94581724170063467902 - 1.4949914001627010673e-413j)  +/-  (2.28e-114, 2.28e-114j)
| (0.87947375120648907139 + 3.2682534107226610375e-414j)  +/-  (3.18e-115, 3.18e-115j)
| (0.24548548714079914892 + 1.6199069541131625742e-424j)  +/-  (2e-124, 2e-124j)
| (-1 + 4.7165572080829084799e-410j)  +/-  (4.78e-114, 4.78e-114j)
| (-0.91577332665505743992 - 1.5703590894717762367e-420j)  +/-  (1.06e-114, 1.06e-114j)
| (-0.9863613034027223736 + 5.9681893016444827621e-421j)  +/-  (7.05e-114, 7.05e-114j)
| (1 + 1.4205835129314310337e-430j)  +/-  (5.12e-114, 5.12e-114j)
| (0.83716647826252857481 - 1.3573596929427085306e-438j)  +/-  (9.97e-116, 9.97e-116j)
| (-0.96940026593933041674 - 1.8133297335481989233e-435j)  +/-  (3.87e-114, 3.87e-114j)
| (-0.83716647826252857481 - 2.543433387811663123e-441j)  +/-  (9.55e-116, 9.55e-116j)
| (-0.87947375120648907139 + 1.9100068461589688735e-443j)  +/-  (3.04e-115, 3.04e-115j)
| (-0.99658449300666984982 - 2.4553129852930894384e-447j)  +/-  (8.85e-114, 8.85e-114j)
| (0.78914050939639359922 - 5.0038946589921139567e-459j)  +/-  (2.38e-116, 2.38e-116j)
| (0.54694815812242687471 - 6.3233833785872551178e-463j)  +/-  (9.43e-120, 9.43e-120j)
| (-0.32469946920468348741 - 8.3597342555784771583e-467j)  +/-  (3.87e-123, 3.87e-123j)
| (-0.78914050939639359922 - 5.6358591474434859144e-461j)  +/-  (2.29e-116, 2.29e-116j)
| (-0.73572391067313162477 + 3.6652105903221411837e-461j)  +/-  (4.87e-117, 4.87e-117j)
| (0.32469946920468348741 + 8.4439266582850576119e-467j)  +/-  (3.89e-123, 3.89e-123j)
| (0.73572391067313162477 + 3.4018239128911599894e-460j)  +/-  (4.11e-117, 4.11e-117j)
| (0.91577332665505743992 + 2.4269505471249935533e-456j)  +/-  (9.17e-115, 9.17e-115j)
| (-0.67728157162574107476 + 1.7261060480022444546e-463j)  +/-  (7.04e-118, 7.04e-118j)
| (-0.54694815812242687471 - 1.5168482630273066384e-465j)  +/-  (9.41e-120, 9.41e-120j)
| (-0.16459459028073389414 - 2.0470240728568822181e-471j)  +/-  (1.01e-125, 1.01e-125j)
| (0.67728157162574107476 + 1.8524141990597446219e-461j)  +/-  (6.97e-118, 6.97e-118j)
| (0.16459459028073389414 - 8.6948759692787826992e-471j)  +/-  (1.09e-125, 1.09e-125j)
| (-0.0825793454723323246 - 1.4012202870113073897e-471j)  +/-  (6.07e-127, 6.07e-127j)
| (-0.61421271268966781744 - 1.1338906956307241123e-465j)  +/-  (9.05e-119, 9.05e-119j)
| (-0.24548548714079914892 - 6.1802249398649746514e-470j)  +/-  (2.19e-124, 2.19e-124j)
| (0.40169542465296945752 - 1.8346410427302233081e-466j)  +/-  (7.06e-122, 7.06e-122j)
| (0.61421271268966781744 + 4.9526136429261448585e-463j)  +/-  (1.05e-118, 1.05e-118j)
| (-4.1489834313895853733e-479 + 1.1380019053217610893e-479j)  +/-  (1.68e-477, 1.68e-477j)
| (-0.47594739303707354443 - 3.1251616983076215486e-468j)  +/-  (9.59e-121, 9.59e-121j)
| (-0.40169542465296945752 - 5.3700138425944999518e-467j)  +/-  (6.39e-122, 6.39e-122j)
| (0.0825793454723323246 + 2.4316864990727641276e-471j)  +/-  (7.3e-127, 7.3e-127j)
| (0.47594739303707354443 + 6.1836999583301292526e-465j)  +/-  (9.19e-121, 9.19e-121j)
| (0.9863613034027223736 + 2.6094813448116861406e-466j)  +/-  (6.67e-114, 6.67e-114j)
-------------------------------------------------
The weights are:
| (0.026315789473684210526 + 1.1732850058999282482e-401j)  +/-  (6.06e-17, 4.22e-69j)
| (0.026315789473684210526 - 5.9035610868700068754e-402j)  +/-  (3.12e-17, 2.17e-69j)
| (0.026315789473684210526 + 8.1894513077366532248e-404j)  +/-  (4.46e-18, 3.1e-70j)
| (0.026315789473684210526 + 3.166986054824428923e-402j)  +/-  (1.36e-17, 9.49e-70j)
| (0.026315789473684210526 + 1.3720409357338843575e-402j)  +/-  (1.59e-18, 1.11e-70j)
| (0.026315789473684210526 + 2.1401906597933009888e-403j)  +/-  (1.02e-20, 7.07e-73j)
| (0.013157894736842105263 + 3.857341041322910975e-404j)  +/-  (1.08e-18, 7.51e-71j)
| (0.026315789473684210526 - 8.9963446205949333432e-404j)  +/-  (1.16e-18, 8.06e-71j)
| (0.026315789473684210526 + 7.6586914055741991362e-404j)  +/-  (1.05e-18, 7.29e-71j)
| (0.013157894736842105263 - 2.3498958813286454246e-401j)  +/-  (5.1e-18, 3.55e-70j)
| (0.026315789473684210526 - 1.0078741786188888574e-402j)  +/-  (4.27e-19, 2.97e-71j)
| (0.026315789473684210526 - 7.4106333799611881012e-404j)  +/-  (5.34e-19, 3.71e-71j)
| (0.026315789473684210526 - 8.9248081029184769155e-404j)  +/-  (4.53e-21, 3.15e-73j)
| (0.026315789473684210526 + 8.8324588809679884056e-404j)  +/-  (1.69e-20, 1.18e-72j)
| (0.026315789473684210526 - 7.706190299995986077e-404j)  +/-  (3.23e-19, 2.24e-71j)
| (0.026315789473684210526 + 7.7453166727086576054e-403j)  +/-  (1.35e-22, 9.36e-75j)
| (0.026315789473684210526 + 3.5738615931920306247e-403j)  +/-  (3.75e-24, 2.61e-76j)
| (0.026315789473684210526 - 1.2186308400861639449e-403j)  +/-  (4.08e-25, 2.84e-77j)
| (0.026315789473684210526 + 9.1098352267548162016e-404j)  +/-  (2.01e-22, 1.4e-74j)
| (0.026315789473684210526 - 9.3581316314895169757e-404j)  +/-  (2.22e-23, 1.54e-75j)
| (0.026315789473684210526 - 2.392252421779568836e-403j)  +/-  (2.57e-25, 1.78e-77j)
| (0.026315789473684210526 - 6.1593838999831603924e-403j)  +/-  (1.5e-24, 1.05e-76j)
| (0.026315789473684210526 - 1.9886151460130217347e-402j)  +/-  (2.13e-23, 1.48e-75j)
| (0.026315789473684210526 + 9.6633256929986549906e-404j)  +/-  (6.84e-25, 4.75e-77j)
| (0.026315789473684210526 + 1.045184732000906469e-403j)  +/-  (3.46e-26, 2.41e-78j)
| (0.026315789473684210526 - 1.3856711196723013984e-403j)  +/-  (1.2e-27, 8.38e-80j)
| (0.026315789473684210526 + 5.0321689483477820597e-403j)  +/-  (1.24e-26, 8.63e-79j)
| (0.026315789473684210526 - 1.9323591500023821411e-403j)  +/-  (5.83e-28, 4.06e-80j)
| (0.026315789473684210526 + 1.4905903743842939944e-403j)  +/-  (2.79e-28, 1.94e-80j)
| (0.026315789473684210526 - 1.0026378989618557724e-403j)  +/-  (3.1e-27, 2.16e-79j)
| (0.026315789473684210526 + 1.2958409008961713578e-403j)  +/-  (3.55e-28, 2.47e-80j)
| (0.026315789473684210526 + 2.7016281819438971402e-403j)  +/-  (4.97e-29, 3.46e-81j)
| (0.026315789473684210526 - 4.2023303408025232878e-403j)  +/-  (1.11e-28, 7.74e-81j)
| (0.026315789473684210526 - 1.6137536136108686253e-403j)  +/-  (2.29e-29, 1.59e-81j)
| (0.026315789473684210526 - 1.0946852475875063032e-403j)  +/-  (2.36e-29, 1.64e-81j)
| (0.026315789473684210526 + 1.152093415060315124e-403j)  +/-  (1.82e-29, 1.26e-81j)
| (0.026315789473684210526 + 1.759234601069441841e-403j)  +/-  (6.67e-30, 4.61e-82j)
| (0.026315789473684210526 - 3.0866856197206569806e-403j)  +/-  (1.92e-30, 1.4e-82j)
| (0.026315789473684210526 + 1.5693210227307843784e-401j)  +/-  (2.08e-30, 1.32e-82j)
