Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 3/2*t^5 - 25/14*t^3 + 3/7*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^37 - 10492662711679377493332883892241/742986232235014574457042747838*t^35 + 4568513647463626618743809293298375/74670116339618964732932796157719*t^33 - 52317364023928890612265940449883900/323570504138348847176042116683449*t^31 + 1979349753527534122219135178556257570/6794980586905325790696884450352429*t^29 - 67279068445098721200167898713552181458/177640206771953517099647122059213501*t^27 + 32871528226644855115733302098025846608/89579249568762884691275044457210227*t^25 - 459095253195222532479443004723259276500/1702005741806494809134225844686994313*t^23 + 11226768826289831097702526448065356775/74000249643760643875401123682043231*t^21 - 256386526637355870964595777249086628775/3922013231119314125396259555148291243*t^19 + 4431023407688104352957980584786814530/206421749006279690810329450270962697*t^17 - 53688510256364986048464360317386961860/10114665701307704849706143063277172153*t^15 + 65817153642380915216761099690745150250/67912755423066018276598389139146727313*t^13 - 8613200017339300214022037892316803050/67912755423066018276598389139146727313*t^11 + 99716850016846451283389006131127074600/8760745449575516357681192198949927823377*t^9 - 1912963166908679418439266472483502340/2920248483191838785893730732983309274459*t^7 + 67536175946218301480090953837283707845/3112984883082500145762716961360207686573294*t^5 - 1057673481906213003642593190820399625/3112984883082500145762716961360207686573294*t^3 + 17382621041307992443983348780154725/10895447090788750510169509364760726903006529*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:
| (-0.98860137005389301787 - 5.5484968200204004332e-429j)  +/-  (7.97e-115, 7.97e-115j)
| (-0.99782147631138364499 - 1.3849724391705409997e-429j)  +/-  (2.37e-115, 2.37e-115j)
| (-0.92582009977255146157 + 3.8295128942943664281e-431j)  +/-  (1.08e-114, 1.08e-114j)
| (0.97242199147365972114 - 1.5127698254268998653e-435j)  +/-  (1.23e-114, 1.23e-114j)
| (0.92582009977255146157 - 2.5709224397665445121e-435j)  +/-  (1.11e-114, 1.11e-114j)
| (0.95048051682613869792 + 1.0190255863813053682e-437j)  +/-  (1.38e-114, 1.38e-114j)
| (-0.087928676564939440969 - 8.9857313470697132759e-450j)  +/-  (9.72e-127, 9.72e-127j)
| (-0.76858638835488541258 - 2.9078525490117652147e-438j)  +/-  (8.85e-117, 8.85e-117j)
| (-0.95048051682613869792 + 3.7194105966195901205e-436j)  +/-  (1.3e-114, 1.3e-114j)
| (0.99782147631138364499 - 1.2254654671545814912e-443j)  +/-  (2.41e-115, 2.41e-115j)
| (0.89920966153721461186 - 2.4492084528827704424e-445j)  +/-  (6.35e-115, 6.35e-115j)
| (0.98860137005389301787 + 6.9334495232813998021e-446j)  +/-  (7.3e-115, 7.3e-115j)
| (-0.97242199147365972114 + 6.5529863728861868358e-444j)  +/-  (1.08e-114, 1.08e-114j)
| (-0.82024959147336871801 - 2.1073629877640398003e-457j)  +/-  (4.71e-116, 4.71e-116j)
| (0.50362254419196807284 + 4.2438172195263745745e-479j)  +/-  (1.75e-120, 1.75e-120j)
| (0.86436896293311332568 - 5.2048509231034698753e-474j)  +/-  (2.11e-115, 2.11e-115j)
| (0.82024959147336871801 + 2.5541114045881691133e-475j)  +/-  (5e-116, 5e-116j)
| (-0.42590552813041067443 + 4.551192173265018217e-474j)  +/-  (1.35e-121, 1.35e-121j)
| (-0.86436896293311332568 + 2.6974428722887996688e-475j)  +/-  (1.97e-115, 1.97e-115j)
| (-0.57735026918962576451 + 8.7533607222267213706e-490j)  +/-  (2.11e-119, 2.11e-119j)
| (0.17516531259971187647 + 6.5045908809203282198e-497j)  +/-  (1.88e-125, 1.88e-125j)
| (0.76858638835488541258 - 1.3208187601321334326e-487j)  +/-  (9.23e-117, 9.23e-117j)
| (0.26102283089102283143 - 2.2097553382610597883e-496j)  +/-  (4.83e-124, 4.83e-124j)
| (-0.89920966153721461186 - 1.5231847252946412126e-490j)  +/-  (6.34e-115, 6.34e-115j)
| (-0.71043105813406843711 - 5.9297309302781671135e-495j)  +/-  (1.46e-117, 1.46e-117j)
| (4.5346655623474535666e-516 - 2.659283420659840364e-516j)  +/-  (1.95e-514, 1.95e-514j)
| (0.64648387241403861225 - 2.8137898259312236381e-493j)  +/-  (1.82e-118, 1.82e-118j)
| (0.42590552813041067443 - 1.6487468046611256107e-497j)  +/-  (1.28e-121, 1.28e-121j)
| (-0.26102283089102283143 - 8.6101040833770580766e-502j)  +/-  (4.93e-124, 4.93e-124j)
| (-0.64648387241403861225 + 5.5638939886140627244e-497j)  +/-  (1.89e-118, 1.89e-118j)
| (-0.17516531259971187647 - 5.6561330283655715037e-504j)  +/-  (1.9e-125, 1.9e-125j)
| (0.34482392787547794043 + 6.4758655803446294821e-499j)  +/-  (8.94e-123, 8.94e-123j)
| (0.57735026918962576451 + 1.1336489876991409622e-495j)  +/-  (2.12e-119, 2.12e-119j)
| (0.087928676564939440969 - 1.2270406916762567387e-503j)  +/-  (9.72e-127, 9.72e-127j)
| (-0.50362254419196807284 - 7.487721469972617859e-499j)  +/-  (1.77e-120, 1.77e-120j)
| (-0.34482392787547794043 - 5.5467091209333497618e-501j)  +/-  (8.32e-123, 8.32e-123j)
| (0.71043105813406843711 + 7.7869608288398215961e-499j)  +/-  (1.53e-117, 1.53e-117j)
-------------------------------------------------
The weights are:
| (0.012803925955723875402 - 7.2425547358793318694e-430j)  +/-  (1.7e-18, 8.93e-73j)
| (0.0055822859573999903541 - 3.8630901110099547578e-429j)  +/-  (1.16e-18, 6.1e-73j)
| (0.024925850423569530851 + 5.6360245833019876811e-429j)  +/-  (4.37e-19, 2.3e-73j)
| (0.019378431709898851453 + 4.970210758518252213e-431j)  +/-  (3.99e-20, 2.1e-74j)
| (0.024925850423569530851 + 1.6999545425838724769e-430j)  +/-  (1.48e-20, 7.8e-75j)
| (0.023978005872364203098 - 1.0204179575040726888e-430j)  +/-  (2.02e-20, 1.06e-74j)
| (0.087697746851534306577 - 1.4179076391625216133e-430j)  +/-  (4.89e-22, 2.57e-76j)
| (0.05504184034232807395 + 9.6809254488884869442e-430j)  +/-  (1.2e-21, 6.33e-76j)
| (0.023978005872364203098 - 5.8561989328321769427e-429j)  +/-  (2e-20, 1.05e-74j)
| (0.0055822859573999903541 + 5.4446302860617313016e-432j)  +/-  (1.07e-21, 5.64e-76j)
| (0.029839387545028959785 - 1.9532423405204413815e-430j)  +/-  (6.16e-22, 3.24e-76j)
| (0.012803925955723875402 - 2.103012562578610709e-431j)  +/-  (2.49e-21, 1.31e-75j)
| (0.019378431709898851453 + 7.5426373747413469091e-429j)  +/-  (7.15e-22, 3.76e-76j)
| (0.048119729620937002911 - 1.5230494427577337952e-429j)  +/-  (3.54e-23, 1.86e-77j)
| (0.075824743330860481118 + 9.7175441720367539106e-431j)  +/-  (2.26e-25, 1.19e-79j)
| (0.03980365288769554723 + 1.6768392936485202691e-430j)  +/-  (3.95e-23, 2.08e-77j)
| (0.048119729620937002911 - 1.3694366653017841661e-430j)  +/-  (4.34e-24, 2.28e-78j)
| (0.079505171543096444123 - 2.4835565678746880099e-430j)  +/-  (2.33e-26, 1.23e-80j)
| (0.03980365288769554723 + 2.6229119787237847417e-429j)  +/-  (2.95e-24, 1.55e-78j)
| (0.071530001952427118258 - 3.7777111395845381256e-430j)  +/-  (3.41e-26, 1.79e-80j)
| (0.086660931723671196024 + 1.1065410179795233349e-430j)  +/-  (1.24e-27, 6.53e-82j)
| (0.05504184034232807395 + 1.181341819128025666e-430j)  +/-  (4.53e-26, 2.38e-80j)
| (0.084941145949883633456 - 1.0478665637867280937e-430j)  +/-  (1.05e-27, 5.51e-82j)
| (0.029839387545028959785 - 4.4142837527041216324e-429j)  +/-  (4.66e-25, 2.45e-79j)
| (0.061155738386887982796 - 6.6814510018154748648e-430j)  +/-  (8.73e-27, 4.59e-81j)
| (0.088044183121389330689 + 1.2867020867185960603e-430j)  +/-  (1.29e-28, 6.81e-83j)
| (0.066638847032161403795 + 1.0112694878136546275e-430j)  +/-  (8.46e-29, 4.45e-83j)
| (0.079505171543096444123 - 9.8098681621011626202e-431j)  +/-  (6.47e-29, 3.4e-83j)
| (0.084941145949883633456 - 1.8066031369282842763e-430j)  +/-  (7.88e-30, 4.14e-84j)
| (0.066638847032161403795 + 4.9070168400762535371e-430j)  +/-  (7.65e-29, 4.02e-83j)
| (0.086660931723671196024 + 1.5870077648905131049e-430j)  +/-  (1.01e-29, 5.31e-84j)
| (0.082550471353836733473 + 1.0064019975850208974e-430j)  +/-  (4.45e-30, 2.34e-84j)
| (0.071530001952427118258 - 9.8045313426175827221e-431j)  +/-  (2.51e-30, 1.32e-84j)
| (0.087697746851534306577 - 1.1848533461255220571e-430j)  +/-  (2.4e-30, 1.26e-84j)
| (0.075824743330860481118 + 3.0176101183190490038e-430j)  +/-  (7.1e-31, 3.74e-85j)
| (0.082550471353836733473 + 2.095657280471866682e-430j)  +/-  (5.73e-31, 3e-85j)
| (0.061155738386887982796 - 1.0726641674376998162e-430j)  +/-  (4.63e-31, 2.43e-85j)
