Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 780781682279720882343/1443135744069879083*t^33 + 186471484875607177921414/1443135744069879083*t^31 - 25997084365665776202465030/1443135744069879083*t^29 + 336858186496529456001490530/206162249152839869*t^27 - 20975482839242007337408576650/206162249152839869*t^25 + 922327330868405608740048918450/206162249152839869*t^23 - 29023863676342675913149325798850/206162249152839869*t^21 + 655479566214328987352464527355500/206162249152839869*t^19 - 10561482296555620048591106148943500/206162249152839869*t^17 + 119649585286753837705778506164510750/206162249152839869*t^15 - 929881890673668788545727114177850750/206162249152839869*t^13 + 4773528941045703430136329263073344750/206162249152839869*t^11 - 15279858255082981648320857749057683750/206162249152839869*t^9 + 27833730842281017405583496793902523750/206162249152839869*t^7 - 24583718100149400468277207005223173750/206162249152839869*t^5 + 7410609050729163897085013986179114375/206162249152839869*t^3 - 86800623777045184080147973836811875/206162249152839869*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:
| (7.0272089275710118333 - 6.3911530627827350577e-430j)  +/-  (3.16e-119, 3.16e-119j)
| (-7.7215445690898675411 + 3.9405888960663123155e-429j)  +/-  (2.19e-119, 2.19e-119j)
| (-9.3050096461322622276 + 3.5574488429483527635e-437j)  +/-  (2.95e-120, 2.95e-120j)
| (9.3050096461322622276 + 1.2935332023199512005e-444j)  +/-  (2.85e-120, 2.85e-120j)
| (-2.3344142183389772393 - 2.2806349423449974346e-448j)  +/-  (1.65e-122, 1.65e-122j)
| (6.3713398889438505984 - 6.6723603284657255129e-444j)  +/-  (3.33e-119, 3.33e-119j)
| (2.8743282649350853305 - 4.437764774751634468e-446j)  +/-  (1.06e-121, 1.06e-121j)
| (8.4704035882011370415 - 2.6767142532806056531e-444j)  +/-  (1.03e-119, 1.03e-119j)
| (10.307318632538731772 - 6.0242918188267394808e-447j)  +/-  (3.28e-121, 3.28e-121j)
| (-10.307318632538731772 - 7.555484901482936247e-443j)  +/-  (3.44e-121, 3.44e-121j)
| (3.9820192614263475371 + 9.407562808533323337e-450j)  +/-  (1.99e-120, 1.99e-120j)
| (-6.3713398889438505984 - 3.1210083266186412723e-447j)  +/-  (3.02e-119, 3.02e-119j)
| (4.5534945364172006729 - 7.2371298447325714302e-456j)  +/-  (6.32e-120, 6.32e-120j)
| (-3.4229555036037223027 - 1.9699769818079123163e-457j)  +/-  (5.36e-121, 5.36e-121j)
| (-1.8014169229168432241 - 1.3882358128669372655e-459j)  +/-  (2.02e-123, 2.02e-123j)
| (-8.4704035882011370415 + 4.5740208102744842145e-455j)  +/-  (9.62e-120, 9.62e-120j)
| (5.7443256209029419293 - 5.2252728149804399893e-457j)  +/-  (2.37e-119, 2.37e-119j)
| (-3.9820192614263475371 - 5.4385833361632794037e-457j)  +/-  (1.77e-120, 1.77e-120j)
| (-2.8743282649350853305 - 1.0976954825228896232e-459j)  +/-  (9.8e-122, 9.8e-122j)
| (-4.5534945364172006729 + 1.0044341027991213029e-456j)  +/-  (5.66e-120, 5.66e-120j)
| (3.4229555036037223027 + 1.1271982177417466389e-462j)  +/-  (4.73e-121, 4.73e-121j)
| (1.8014169229168432241 - 2.2052335473453976852e-465j)  +/-  (2.07e-123, 2.07e-123j)
| (7.7215445690898675411 - 3.3013764290205856997e-461j)  +/-  (2.09e-119, 2.09e-119j)
| (-5.7443256209029419293 + 1.5811819810402785796e-460j)  +/-  (2.37e-119, 2.37e-119j)
| (-1.2727473892000891084 - 4.2539521462456013395e-474j)  +/-  (2.16e-124, 2.16e-124j)
| (2.3344142183389772393 + 1.5685335005561103134e-472j)  +/-  (1.58e-122, 1.58e-122j)
| (1.2727473892000891084 + 8.3820185569985415224e-475j)  +/-  (1.82e-124, 1.82e-124j)
| (5.139850393792571075 + 1.2945837358717036284e-470j)  +/-  (1.52e-119, 1.52e-119j)
| (-5.139850393792571075 + 5.6817349846503634826e-473j)  +/-  (1.35e-119, 1.35e-119j)
| (-0.74196378430272585765 - 3.4914741304904612922e-491j)  +/-  (1.04e-125, 1.04e-125j)
| (-7.0272089275710118333 + 2.3100840624238608017e-488j)  +/-  (3.15e-119, 3.15e-119j)
| (-7.1585325079670549261e-509 - 3.0926033637124386052e-509j)  +/-  (2.73e-507, 2.73e-507j)
| (0.74196378430272585765 - 1.077487908565159176e-502j)  +/-  (1.04e-125, 1.04e-125j)
| (0.11045362964324491621 + 9.5294475586100661625e-504j)  +/-  (2.94e-127, 2.94e-127j)
| (-0.11045362964324491621 - 1.1195490287400422808e-503j)  +/-  (2.94e-127, 2.94e-127j)
-------------------------------------------------
The weights are:
| (5.0805104561088472811e-12 + 1.2121840085772121172e-440j)  +/-  (2.4e-30, 6.92e-89j)
| (3.2381446574259100802e-14 + 5.0839461159087590301e-442j)  +/-  (3.55e-32, 1.02e-90j)
| (5.6497244547842025448e-20 - 8.7539904493092249615e-446j)  +/-  (6.23e-35, 1.79e-93j)
| (5.6497244547842025448e-20 + 9.619962847254183377e-446j)  +/-  (2.14e-35, 6.16e-94j)
| (0.014022834890966238204 - 1.7865654949013974222e-438j)  +/-  (6.54e-18, 1.89e-76j)
| (3.911488674060320661e-10 - 5.0441685652474804919e-440j)  +/-  (2.59e-30, 7.46e-89j)
| (0.0034872478239210125755 - 6.87145125120395721e-437j)  +/-  (1.13e-21, 3.25e-80j)
| (8.2343920064479520882e-17 - 6.749293341547950764e-444j)  +/-  (3.34e-34, 9.63e-93j)
| (3.9211359044055294333e-24 - 4.7022109430522785355e-448j)  +/-  (1.53e-37, 4.4e-96j)
| (3.9211359044055294333e-24 + 3.9587240456008973891e-448j)  +/-  (2.04e-39, 5.88e-98j)
| (8.1226329136812468616e-05 - 9.5947755043671219709e-438j)  +/-  (5.1e-27, 1.47e-85j)
| (3.911488674060320661e-10 + 1.2200937107357902446e-440j)  +/-  (6.54e-34, 1.89e-92j)
| (7.2573410899853835002e-06 + 2.9526359143904195951e-438j)  +/-  (1.47e-28, 4.24e-87j)
| (0.00063071172040376944317 - 4.9175296676935893432e-438j)  +/-  (5.7e-28, 1.64e-86j)
| (0.041758049185687454669 - 3.440195821825217481e-437j)  +/-  (2.88e-22, 8.29e-81j)
| (8.2343920064479520882e-17 + 7.8313781379646447099e-444j)  +/-  (6.84e-37, 1.97e-95j)
| (1.6766168145029544925e-08 + 1.9694605690607211838e-439j)  +/-  (8.16e-32, 2.35e-90j)
| (8.1226329136812468616e-05 + 2.2625699963487704088e-438j)  +/-  (5.7e-30, 1.64e-88j)
| (0.0034872478239210125755 + 7.3045946509189064909e-438j)  +/-  (2.36e-27, 6.8e-86j)
| (7.2573410899853835002e-06 - 8.1443816992745864307e-439j)  +/-  (1.41e-31, 4.05e-90j)
| (0.00063071172040376944317 + 2.7355508806335214846e-437j)  +/-  (1.12e-29, 3.22e-88j)
| (0.041758049185687454669 - 3.0982131349902878652e-436j)  +/-  (2.94e-27, 8.47e-86j)
| (3.2381446574259100802e-14 + 3.2232200552783297045e-442j)  +/-  (2.34e-36, 6.75e-95j)
| (1.6766168145029544925e-08 - 5.8238642678451486112e-440j)  +/-  (1.34e-34, 3.87e-93j)
| (0.093699670708658459048 + 1.6009056677331794946e-436j)  +/-  (3.21e-27, 9.25e-86j)
| (0.014022834890966238204 + 1.534758068359718723e-436j)  +/-  (3.34e-29, 9.62e-88j)
| (0.093699670708658459048 + 5.8517908765370813054e-436j)  +/-  (5.04e-28, 1.45e-86j)
| (4.3517878194968955723e-07 - 8.0065738136503449574e-439j)  +/-  (7.91e-33, 2.28e-91j)
| (4.3517878194968955723e-07 + 2.3881864546226363454e-439j)  +/-  (6.48e-34, 1.87e-92j)
| (0.16289227472785392845 - 5.7288814154265068852e-436j)  +/-  (2e-29, 5.75e-88j)
| (5.0805104561088472811e-12 - 2.5054541787823290198e-441j)  +/-  (8.45e-37, 2.43e-95j)
| (-1.1029555928072224516 - 2.8174622594462959188e-434j)  +/-  (5.69e-30, 1.65e-88j)
| (0.16289227472785392845 - 1.1485083947827686852e-435j)  +/-  (7.25e-31, 2.11e-89j)
| (0.73489807133468162911 + 1.5427438481598421919e-434j)  +/-  (2.55e-30, 7.57e-89j)
| (0.73489807133468162911 + 1.3960461895502201468e-434j)  +/-  (2.37e-30, 6.53e-89j)
