Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 24747738563437975468285027669966887760383013/67113240439461787943559573994801479684474*t^29 + 17725417157318966622701995809882101681630819078/302009581977578045746018082976606658580133*t^27 - 38563209336510252181855187499909817888828268266835/7248229967461873097904433991438559805923192*t^25 + 6640251448466817785130490905029652852531582609451525/21744689902385619293713301974315679417769576*t^23 - 253961358105313632491565957461907925890836179010183575/21744689902385619293713301974315679417769576*t^21 + 116458771764497610811399109415608112648408076504397825/381485787761151215679180736391503147680168*t^19 - 175144226296048893742324036140191647073942952514072925/31790482313429267973265061365958595640014*t^17 + 4361975814607064495233822396398462498771985286596135375/63580964626858535946530122731917191280028*t^15 - 12366749513046126558299303385104007030854306247171723625/21193654875619511982176707577305730426676*t^13 + 70363915337526784742963560241662641666019914636387081625/21193654875619511982176707577305730426676*t^11 - 516905761537828875556797479328819236449994876601158794625/42387309751239023964353415154611460853352*t^9 + 42762151387960858368773252338570284822158787898373742875/1569900361157000887568645005726350401976*t^7 - 471257905744955351842683326880370425812594563493359800625/14129103250413007988117805051537153617784*t^5 + 260227047861899491324338498760047735475599167584956454375/14129103250413007988117805051537153617784*t^3 - 6847833317295372070523864713987475840910366583407053125/2354850541735501331352967508589525602964*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: 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
-------------------------------------------------
The nodes are:
| (3.1841016959322287617 - 1.265834560834226731e-421j)  +/-  (2.25e-121, 2.25e-121j)
| (-9.174585993256518292 - 1.0182993153929665319e-423j)  +/-  (4.64e-122, 4.64e-122j)
| (9.174585993256518292 + 9.1853741658192529411e-421j)  +/-  (4.83e-122, 4.83e-122j)
| (2.0464186644188259188 - 5.2548987362667205467e-422j)  +/-  (1.87e-122, 1.87e-122j)
| (4.4234839029164975398 + 2.018770534242188779e-420j)  +/-  (9.64e-121, 9.64e-121j)
| (8.1349845666543560856 - 3.6675871091367039917e-422j)  +/-  (3.3e-121, 3.3e-121j)
| (-3.7932353000477464006 - 2.7221371707557673308e-429j)  +/-  (4.83e-121, 4.83e-121j)
| (6.4873602229183838257 + 5.7782101689786465884e-441j)  +/-  (1.47e-120, 1.47e-120j)
| (-5.0782145566345654809 + 4.4244360647407423681e-446j)  +/-  (1.57e-120, 1.57e-120j)
| (-6.4873602229183838257 - 3.4191014512816921186e-450j)  +/-  (1.45e-120, 1.45e-120j)
| (1 + 1.1849086318026808926e-458j)  +/-  (6.19e-125, 6.19e-125j)
| (5.7630530603155301904 + 5.144486939329980402e-454j)  +/-  (1.7e-120, 1.7e-120j)
| (-2.5850299512436075094 - 3.0662580989307302214e-457j)  +/-  (2.4e-121, 2.4e-121j)
| (-8.1349845666543560856 + 1.6973214568810058588e-458j)  +/-  (3.24e-121, 3.24e-121j)
| (-3.1841016959322287617 + 3.3947987586066175438e-466j)  +/-  (2.28e-121, 2.28e-121j)
| (1.5093152835436173382 - 8.07164367874806602e-470j)  +/-  (8.48e-124, 8.48e-124j)
| (-2.4494897427831780982 - 1.1401620065851279147e-467j)  +/-  (1.82e-121, 1.82e-121j)
| (-7.2673492935566155314 + 3.7283313070966142959e-466j)  +/-  (9.16e-121, 9.16e-121j)
| (-1 + 5.1109995525563107371e-472j)  +/-  (6.54e-125, 6.54e-125j)
| (-0.50114934569073247703 - 8.1598645495777201691e-474j)  +/-  (4.53e-126, 4.53e-126j)
| (5.0782145566345654809 - 2.0004611483981234759e-467j)  +/-  (1.39e-120, 1.39e-120j)
| (0.50114934569073247703 - 9.554136586769786261e-479j)  +/-  (4.53e-126, 4.53e-126j)
| (7.2673492935566155314 + 2.9831851624243748925e-472j)  +/-  (9.27e-121, 9.27e-121j)
| (-4.4234839029164975398 + 1.8310547750354967543e-475j)  +/-  (8.68e-121, 8.68e-121j)
| (3.7932353000477464006 + 1.9631186722603596841e-478j)  +/-  (4.98e-121, 4.98e-121j)
| (6.7243216805058203505e-497 - 9.2330184258294307278e-497j)  +/-  (3.54e-495, 3.54e-495j)
| (2.4494897427831780982 + 2.7531538926379230922e-478j)  +/-  (2.18e-121, 2.18e-121j)
| (2.5850299512436075094 - 6.8621146880097777154e-481j)  +/-  (2.52e-121, 2.52e-121j)
| (-2.0464186644188259188 - 1.0715919786366557033e-484j)  +/-  (1.62e-122, 1.62e-122j)
| (-1.5093152835436173382 + 6.5440895252610819672e-485j)  +/-  (7.69e-124, 7.69e-124j)
| (-5.7630530603155301904 - 1.5386385646418302185e-483j)  +/-  (1.67e-120, 1.67e-120j)
-------------------------------------------------
The weights are:
| (0.0015038277755032682481 - 6.688659691591856411e-424j)  +/-  (3.15e-26, 3.2e-86j)
| (2.5159656893958528703e-19 - 1.1038018898537107487e-434j)  +/-  (1.55e-40, 1.57e-100j)
| (2.5159656893958528703e-19 + 3.1985359546839796747e-434j)  +/-  (1.75e-40, 1.78e-100j)
| (0.027367232687845008481 + 1.0938967410995780572e-422j)  +/-  (2.39e-22, 2.43e-82j)
| (1.4432178432527784587e-05 - 9.7894659850958063623e-425j)  +/-  (1.37e-31, 1.39e-91j)
| (1.5825983794900687586e-15 - 5.3634338058169909947e-432j)  +/-  (3.96e-39, 4.03e-99j)
| (0.00018549033180804305006 + 2.5403247997432543523e-425j)  +/-  (1.69e-32, 1.71e-92j)
| (2.1693830043083160367e-10 - 9.364650586577699464e-429j)  +/-  (7.75e-37, 7.87e-97j)
| (6.702307382730135383e-07 + 3.2361101145895370019e-427j)  +/-  (5.06e-36, 5.14e-96j)
| (2.1693830043083160367e-10 + 1.7301663703039724958e-429j)  +/-  (4.99e-39, 5.07e-99j)
| (0.12119239473004141413 + 1.3724139362626299564e-422j)  +/-  (1.69e-27, 1.71e-87j)
| (1.720090924247798943e-08 + 2.1616008077982496427e-427j)  +/-  (1.92e-36, 1.95e-96j)
| (0.009125455617609904643 + 4.9081832601620259377e-423j)  +/-  (6.14e-31, 6.24e-91j)
| (1.5825983794900687586e-15 + 1.5613659729149132531e-432j)  +/-  (4.55e-42, 4.63e-102j)
| (0.0015038277755032682481 - 2.1611446944852086554e-424j)  +/-  (5.18e-33, 5.26e-93j)
| (0.066518934083366788933 - 1.3432189678468611922e-422j)  +/-  (1.38e-28, 1.4e-88j)
| (-0.001774816167263117299 - 7.5018757162626388885e-423j)  +/-  (4.2e-31, 4.26e-91j)
| (1.107298272793138206e-12 - 7.1197089153662988677e-431j)  +/-  (9.07e-41, 9.21e-101j)
| (0.12119239473004141413 + 8.3975348294752390166e-423j)  +/-  (6.13e-29, 6.23e-89j)
| (0.17566890006964331197 - 1.0958873409052695405e-422j)  +/-  (7.68e-29, 7.8e-89j)
| (6.702307382730135383e-07 - 4.9116137160948941115e-426j)  +/-  (1.68e-37, 1.71e-97j)
| (0.17566890006964331197 - 1.3910849372071971465e-422j)  +/-  (6.79e-30, 6.9e-90j)
| (1.107298272793138206e-12 + 2.98183116232146071e-430j)  +/-  (4.07e-41, 4.14e-101j)
| (1.4432178432527784587e-05 - 3.0583970991933639793e-426j)  +/-  (5.65e-37, 5.74e-97j)
| (0.00018549033180804305006 + 3.9125097309715191597e-424j)  +/-  (6.32e-36, 6.41e-96j)
| (0.20039492208663630603 + 1.2918528248465035986e-422j)  +/-  (1.67e-31, 1.69e-91j)
| (-0.001774816167263117299 - 1.4583516584712494532e-422j)  +/-  (3.45e-34, 3.49e-94j)
| (0.009125455617609904643 + 1.0795357139372150792e-422j)  +/-  (1.88e-34, 1.91e-94j)
| (0.027367232687845008481 + 5.2559260507340543129e-423j)  +/-  (3.19e-35, 3.11e-95j)
| (0.066518934083366788933 - 5.9776454612808509247e-423j)  +/-  (4.76e-35, 4.26e-95j)
| (1.720090924247798943e-08 - 2.7551614883767112093e-428j)  +/-  (7.3e-41, 8.45e-101j)
