Starting with polynomial:
P : t
Extension levels are: 1 2 40
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 2807153741979615133/258514102252430055*t^41 + 229747488198109461902/4187928456489366891*t^39 - 993669601400192092558/5804321895836140077*t^37 + 7863293549110856669501/21282513618065846949*t^35 - 186787319153460529602553/319237704270987704235*t^33 + 2485710024507768939613096/3530962486633651880175*t^31 - 32960826972593423722981448/50139667310197856698485*t^29 + 1669533953693869300348486994/3459637044403652112195465*t^27 - 2406886355652454500869294614/8585025258334988574707265*t^25 + 28923094319363050315875548/223957180652217093253233*t^23 - 474242830913750982734292148/10078073129349769196395485*t^21 + 552207297677627161992400342/40984164059355728065341639*t^19 - 2416498744575773547331016242/806021893167329318618385567*t^17 + 1233090974327058850085999416/2418065679501987955855156701*t^15 - 574316787859105448787251720/8866240824840622504802241237*t^13 + 13971533575161096208650277993/2349553818582764963772593927805*t^11 - 48249465211960197588620399/128157481013605361660323305153*t^9 + 1528715034585807436433494/99678040788359725735807015119*t^7 - 15376605972467019966946/42719160337868453886774435051*t^5 + 1370418295555383073306411/343333891635448763888006134504887*t^3 - 53011847975560514091649/4005562069080235578693404902557015*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.98544547375341350032 + 5.2614079265810510752e-843j)  +/-  (4.6e-240, 4.6e-240j)
| (-0.99500543531732884972 + 1.2006869978040328277e-843j)  +/-  (4.82e-240, 4.82e-240j)
| (-0.92491477735576524157 + 1.5855688962745012664e-852j)  +/-  (1.17e-240, 1.17e-240j)
| (0.99933888183715517208 + 1.0538419297975599936e-850j)  +/-  (2.09e-240, 2.09e-240j)
| (0.92491477735576524157 + 1.2351513220638214152e-865j)  +/-  (1.22e-240, 1.22e-240j)
| (0.95031557461792315437 + 1.3436779722315666444e-874j)  +/-  (2.27e-240, 2.27e-240j)
| (-0.95031557461792315437 + 1.1065287829801373064e-887j)  +/-  (2.32e-240, 2.32e-240j)
| (-0.89446325430860287476 + 9.9395122158750761563e-890j)  +/-  (5.01e-241, 5.01e-241j)
| (-0.99933888183715517208 + 8.327553533572883572e-888j)  +/-  (2.02e-240, 2.02e-240j)
| (0.99500543531732884972 - 2.7050349310319311353e-897j)  +/-  (4.76e-240, 4.76e-240j)
| (0.81909853184898019962 - 1.9077838795105369788e-919j)  +/-  (4.74e-242, 4.74e-242j)
| (0.98544547375341350032 - 1.7390081595138051907e-921j)  +/-  (5.01e-240, 5.01e-240j)
| (-0.61679433055058544069 + 6.510091039849046288e-947j)  +/-  (5.54e-245, 5.54e-245j)
| (-0.85912690287453322245 - 1.9206425019997079339e-942j)  +/-  (1.63e-241, 1.63e-241j)
| (0.97052802277417746491 - 1.5098959827997713246e-941j)  +/-  (3.95e-240, 3.95e-240j)
| (0.85912690287453322245 + 3.5261176359921178697e-951j)  +/-  (1.7e-241, 1.7e-241j)
| (0.89446325430860287476 - 6.1618710866737946784e-955j)  +/-  (4.98e-241, 4.98e-241j)
| (-0.36095839141911379512 - 1.8925364310155225213e-967j)  +/-  (3.24e-249, 3.24e-249j)
| (-0.72586431796511602165 - 3.3086317884060353386e-960j)  +/-  (2.3e-243, 2.3e-243j)
| (-0.97052802277417746491 + 5.5925867938794757692e-961j)  +/-  (4e-240, 4e-240j)
| (0.77459666924148337704 + 2.890309871629560576e-965j)  +/-  (1.07e-242, 1.07e-242j)
| (0.72586431796511602165 - 2.447717673502056004e-969j)  +/-  (2.23e-243, 2.23e-243j)
| (0.21977387039115541258 - 2.1538783519628608407e-977j)  +/-  (1.04e-251, 1.04e-251j)
| (-0.81909853184898019962 - 3.2146714210141285573e-965j)  +/-  (4.57e-242, 4.57e-242j)
| (-0.77459666924148337704 + 2.3140466374148904391e-970j)  +/-  (1.14e-242, 1.14e-242j)
| (0.14718617801380025857 + 7.0434310850690340873e-983j)  +/-  (4.45e-253, 4.45e-253j)
| (0.61679433055058544069 - 4.0719929942861738858e-974j)  +/-  (5.15e-245, 5.15e-245j)
| (0.67316760748285544209 + 1.7894000804898859624e-975j)  +/-  (3.65e-244, 3.65e-244j)
| (-0.073794608601719502957 + 2.045551071252754898e-984j)  +/-  (2.15e-254, 2.15e-254j)
| (-0.67316760748285544209 + 3.5885190357429682198e-975j)  +/-  (3.65e-244, 3.65e-244j)
| (-0.29116123856529143669 + 1.7634233365978269588e-982j)  +/-  (1.81e-250, 1.81e-250j)
| (0.29116123856529143669 - 7.1384046994141296656e-984j)  +/-  (1.72e-250, 1.72e-250j)
| (0.49426799723683859419 + 1.1203283646538122953e-979j)  +/-  (5.09e-247, 5.09e-247j)
| (0.073794608601719502957 - 9.3175174605840448107e-987j)  +/-  (2.15e-254, 2.15e-254j)
| (-0.49426799723683859419 - 1.6822202148428910594e-977j)  +/-  (5.07e-247, 5.07e-247j)
| (-0.42878412349565830447 + 2.0183048073691764804e-979j)  +/-  (4.21e-248, 4.21e-248j)
| (1.337128677036748733e-995 - 6.2040974338179515958e-995j)  +/-  (2.73e-993, 2.73e-993j)
| (0.5570523665246407664 - 1.0389703999561569075e-982j)  +/-  (5.84e-246, 5.84e-246j)
| (0.36095839141911379512 + 8.1192088590134599583e-983j)  +/-  (3.08e-249, 3.08e-249j)
| (-0.21977387039115541258 + 3.6304868081487803472e-984j)  +/-  (9.18e-252, 9.18e-252j)
| (-0.5570523665246407664 + 2.1221228818940372257e-980j)  +/-  (5.5e-246, 5.5e-246j)
| (-0.14718617801380025857 - 1.0769008684593938324e-988j)  +/-  (4.69e-253, 4.69e-253j)
| (0.42878412349565830447 - 2.0724560423279233853e-984j)  +/-  (4.11e-248, 4.11e-248j)
-------------------------------------------------
The weights are:
| (0.012243642893484482319 - 1.0874383022818969662e-843j)  +/-  (1.37e-72, 1.13e-187j)
| (0.0068838127757909781959 + 4.9202134511821534607e-843j)  +/-  (8.51e-73, 7e-188j)
| (0.027951506197656432298 - 1.3902786539323661558e-843j)  +/-  (1.38e-73, 1.14e-188j)
| (0.0019961462059587492035 + 7.2316960009597547871e-846j)  +/-  (1.19e-73, 9.8e-189j)
| (0.027951506197656432298 - 4.2815337759935680784e-845j)  +/-  (4.79e-74, 3.94e-189j)
| (0.022827116117497172085 + 3.8070109466317519274e-845j)  +/-  (3.65e-74, 3e-189j)
| (0.022827116117497172085 + 2.1941150807693885819e-843j)  +/-  (8.37e-74, 6.89e-189j)
| (0.032923869285219561311 + 9.9668764207017538199e-844j)  +/-  (1.04e-74, 8.52e-190j)
| (0.0019961462059587492035 - 5.312219992932795021e-844j)  +/-  (4.58e-74, 3.77e-189j)
| (0.0068838127757909781959 - 1.8993024820435567624e-845j)  +/-  (2.5e-74, 2.06e-189j)
| (0.042303620788642913241 + 5.5956236594991575538e-845j)  +/-  (1.93e-76, 1.59e-191j)
| (0.012243642893484482319 + 2.6820208195405653622e-845j)  +/-  (9.72e-75, 7.99e-190j)
| (0.058110525101020146348 + 3.2284397166431175336e-844j)  +/-  (4.87e-78, 4.01e-193j)
| (0.037716679280047802895 - 7.6505694367559432025e-844j)  +/-  (6.44e-76, 5.3e-191j)
| (0.017579880053560131534 - 3.2865940778812236309e-845j)  +/-  (5.38e-75, 4.42e-190j)
| (0.037716679280047802895 - 5.1652072191097830755e-845j)  +/-  (4.02e-77, 3.31e-192j)
| (0.032923869285219561311 + 4.7301191792726105683e-845j)  +/-  (1.39e-76, 1.14e-191j)
| (0.068874147892548020782 + 2.071069137990475728e-844j)  +/-  (3.93e-81, 3.23e-196j)
| (0.050760741762691498882 + 4.2929040332330909923e-844j)  +/-  (1.04e-79, 8.58e-195j)
| (0.017579880053560131534 - 4.6746010460393997076e-843j)  +/-  (5.27e-77, 4.34e-192j)
| (0.04665958148608067867 - 6.0282959174014280848e-845j)  +/-  (1.73e-79, 1.42e-194j)
| (0.050760741762691498882 + 6.4691314146709682083e-845j)  +/-  (1.79e-80, 1.48e-195j)
| (0.072053130132997912935 + 1.0959775302670490029e-844j)  +/-  (1.55e-83, 1.27e-198j)
| (0.042303620788642913241 + 6.1356283976672288042e-844j)  +/-  (7.33e-80, 6.03e-195j)
| (0.04665958148608067867 - 5.0740485940553704151e-844j)  +/-  (2.4e-80, 1.97e-195j)
| (0.073056143975906456656 - 1.1744640665092337737e-844j)  +/-  (1.87e-84, 1.54e-199j)
| (0.058110525101020146348 + 7.3967162483933861349e-845j)  +/-  (1.81e-83, 1.49e-198j)
| (0.054584687449223886934 - 6.9235291080115394049e-845j)  +/-  (1.14e-82, 9.38e-198j)
| (0.073660152023406413986 + 1.465836922433993305e-844j)  +/-  (5.17e-86, 4.25e-201j)
| (0.054584687449223886934 - 3.6966875338057119959e-844j)  +/-  (1.3e-83, 1.07e-198j)
| (0.070656588841289703218 - 1.8862908110686292333e-844j)  +/-  (6.26e-86, 5.15e-201j)
| (0.070656588841289703218 - 1.0244781609230950478e-844j)  +/-  (3.83e-86, 3.15e-201j)
| (0.064192564290739329691 + 8.4209778154613518185e-845j)  +/-  (3.48e-86, 2.86e-201j)
| (0.073660152023406413986 + 1.2611977567376677365e-844j)  +/-  (2.04e-86, 1.68e-201j)
| (0.064192564290739329691 + 2.5439522128955545398e-844j)  +/-  (6.82e-87, 5.61e-202j)
| (0.06671554291567633528 - 2.2874688655123894552e-844j)  +/-  (6.58e-87, 5.42e-202j)
| (0.073861855264055507251 - 1.3577010553103562139e-844j)  +/-  (1.9e-87, 1.56e-202j)
| (0.061318992898533639909 - 7.8939995736118467522e-845j)  +/-  (1.79e-87, 1.46e-202j)
| (0.068874147892548020782 + 9.5890967545468874077e-845j)  +/-  (4.31e-88, 3.56e-203j)
| (0.072053130132997912935 + 1.7268337326777855581e-844j)  +/-  (1.24e-88, 1.03e-203j)
| (0.061318992898533639909 - 2.8521443282324770415e-844j)  +/-  (1.68e-88, 1.39e-203j)
| (0.073056143975906456656 - 1.587914357181049968e-844j)  +/-  (1.04e-88, 8.71e-204j)
| (0.06671554291567633528 - 8.983743843454286508e-845j)  +/-  (6.69e-89, 5.05e-204j)
