Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 8 25
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P2 : 231/16*t^14 - 3731/80*t^12 + 1182181/20400*t^10 - 200960617/5814000*t^8 + 14859361517/1482570000*t^6 - 123220867/98838000*t^4 + 4422019/98838000*t^2 - 22771/889542000
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^39 - 352510894625716943282019567406875941364066438499931839512337949556060568254471874387318080777520906308757/2517922225887593349272077271280245468432084428018317944314011091577171950624307487189600411454260020080*t^37 + 1443542318383381678145159304717454311245423008088162955181885724328772477745483419589180801236311812005789789/2303898836687147914583950703221424603615357251636760919047320148793112334821241350778484376480647918373200*t^35 - 46348495065123056186364433133007552590509429522113205122705401938549042250591287110998281067121705117559986021999479/27001821080409391352059204359043773532725185833831677993085139746463460185283363799398129708993900038969414526000*t^33 + 325946143565646604687935799292666093978611234706950074539204088037224772513039708038311984453201013931457149977316403/101256829051535217570222016346414150747719446876868792474069274049237975694812614247742986408727125146135304472500*t^31 - 4186864364165923223730039324795605563752343268860541492004896261347518585861714570685461385830035352887059986421621091/956314496597832610385430154382800312617350331614871928921765366020580881562119134562017093860200626380166764462500*t^29 + 193438701613666448578183935676051974292279228022340501503806632735445319550767763302783223004672509556810171895567340534679/43335391413330784739615767445856596166255230277127921459089797561222622647987428582677804608274991384417256931618187500*t^27 - 307448270709593631486029246847539434648028260644116854029952266107630537371631450847216374922916782395407567154340207620801/88404198483194800868816165589547456179160669765340959776543187024894150201894354308662721400880982424211204140501102500*t^25 + 6040453822618156541238405694010724944824987874525686083034267800275347086748716689582151328902455350503738081485770776693499/2887870483784363495047994742591883568519248545667804686033744109479875573261882240749648899095445425857566001923036015000*t^23 - 57428109353618607382661772975473297441750832299263857520713858542902268230374117037374800421120347202742077122235565581031/58936132322129867245877443726364970786107113176893973184362124683262766801262902872441814267253988282807469427000735000*t^21 + 1302316077174676118425211138659505329459266498896119180577351909200070321982640604170699078678603869073206116698409505931907/3712976336294181636490278954760993159524748130144320310614813855045554308479562880963834298837001261816870573901046305000*t^19 - 23775188475791925614955987908179832107417799142226918425754569175580403220791283086520132265016995988496486721683138076953/245703266329100970097079093651466152446236025848269888206274231712771368520500467653808671668191834807826153705363175000*t^17 + 1067071429520139652175365018592761074496235316657939155260789701932789643392562246301576450076538915739170028451039872227809/52917257000631610695084452093300766114788468319898267158213637915880577150829903660052334681102986163640817444790952507500*t^15 - 12016263449891131543950447179641622710829354595272368663930420826628950221887250677466126759033985802152572680951312375079/3871994414680361758176911128778104837667448901455970767674168627991261742743651487320902537641681914412742739862752622500*t^13 + 18040630210422595868432727035894085296162134438069013801673913424862255260937464914080216113079121473976076289670556202163/52917257000631610695084452093300766114788468319898267158213637915880577150829903660052334681102986163640817444790952507500*t^11 - 9400207084416357752408757743403100508315914711492648375724237420182848827859429362697574717525212054699464157294901701481/370420799004421274865591164653105362803519278239287870107495465411164040055809325620366342767720903145485722113536667552500*t^9 + 86883462710198813190452116828695583379065015624972393790447110516785433381967282528353483721348254322429873306076613153/73838033024137131202443421525535952718309490678927814639367866859368247187204516734956746066655329530661605736917608150000*t^7 - 150876001846969802988678639063402916520912820550142242492680598191358851926641927323405430201104077521833276606978529/5162659219573815677569214838370806450223265201941294356898891503988348990324868649761203383522242552550323653150336830000*t^5 + 1366679230711048147713158607063430077371598622575916757240109597046923011818750940841369836791605155882138344021361/4922535534942475413496228101702396847887299378595187642624524457291216479146967782330449737777021968710773715794507210000*t^3 - 867562412155253821605607925802061825604038911614479212358073198012065757110452885916390181318982060969218333579981/5715063756068213955069120826076482740397154578549012853087072894915102332289629595285652145559122505673208284037422870810000*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:
| (0.96252666409549420803 + 2.5508760715403996653e-396j)  +/-  (2.44e-114, 2.44e-114j)
| (0.33439574413522875751 + 2.0569215939545420023e-407j)  +/-  (8.05e-123, 8.05e-123j)
| (-0.89273016073953821165 - 2.9466735875032406899e-398j)  +/-  (5.3e-115, 5.3e-115j)
| (0.98851944675836295466 - 3.0544284898069508144e-397j)  +/-  (5.04e-114, 5.04e-114j)
| (0.89273016073953821165 - 1.087951931157777067e-401j)  +/-  (5.02e-115, 5.02e-115j)
| (0.98124721612774456171 - 3.0473239465171087733e-402j)  +/-  (5.43e-114, 5.43e-114j)
| (-0.98851944675836295466 - 4.9978777401321570286e-401j)  +/-  (5.04e-114, 5.04e-114j)
| (-0.93246951420315202781 + 2.0315726855359488247e-411j)  +/-  (1.03e-114, 1.03e-114j)
| (-0.99744993945668490114 + 3.2174090360769622755e-415j)  +/-  (1.03e-114, 1.03e-114j)
| (0.93246951420315202781 + 3.1532420974857532233e-425j)  +/-  (1.05e-114, 1.05e-114j)
| (0.82190330787833020415 - 1.3613865435160028361e-426j)  +/-  (9.7e-115, 9.7e-115j)
| (-0.48595395887274710376 - 4.3225771475786134225e-431j)  +/-  (1.61e-119, 1.61e-119j)
| (-0.83705334935346344088 - 1.9105519621655347679e-425j)  +/-  (8.8e-115, 8.8e-115j)
| (-0.82190330787833020415 + 1.5205359170250775544e-426j)  +/-  (9.19e-115, 9.19e-115j)
| (0.99744993945668490114 + 1.1373830244656887681e-427j)  +/-  (1.13e-114, 1.13e-114j)
| (0.83705334935346344088 + 4.4932655608932480232e-430j)  +/-  (8.72e-115, 8.72e-115j)
| (0.66120938646626451366 + 9.9821930288548497997e-433j)  +/-  (5.32e-118, 5.32e-118j)
| (-0.02411517758027983534 + 4.7498197711341771262e-437j)  +/-  (1.13e-127, 1.13e-127j)
| (-0.80339065373224061481 + 8.7559203223787534932e-428j)  +/-  (2.83e-115, 2.83e-115j)
| (-0.96252666409549420803 - 2.2345599007225646274e-430j)  +/-  (2.47e-114, 2.47e-114j)
| (0.48595395887274710376 - 6.0981060283441635542e-450j)  +/-  (1.58e-119, 1.58e-119j)
| (0.80339065373224061481 + 2.4513499354559027708e-445j)  +/-  (2.71e-115, 2.71e-115j)
| (-0.66120938646626451366 - 7.7360940329202838733e-447j)  +/-  (5.03e-118, 5.03e-118j)
| (-0.33439574413522875751 - 3.1972169875173099082e-450j)  +/-  (8.72e-123, 8.72e-123j)
| (-0.73244792215948651672 + 3.2111037609284153402e-447j)  +/-  (5.61e-117, 5.61e-117j)
| (-0.14041851390971524844 + 9.0962597870049101684e-451j)  +/-  (4.87e-126, 4.87e-126j)
| (0.73244792215948651672 + 3.239732782762204674e-449j)  +/-  (5.84e-117, 5.84e-117j)
| (0.46194088448213480754 + 4.9977848996791743033e-452j)  +/-  (1.4e-119, 1.4e-119j)
| (-5.2532199169277374258e-451 - 9.9435321700497605225e-451j)  +/-  (4.39e-449, 4.39e-449j)
| (-0.58322136656433728579 - 2.112042415253573483e-451j)  +/-  (4.84e-119, 4.84e-119j)
| (-0.23861918608319690863 - 2.919712875733531273e-453j)  +/-  (1.62e-124, 1.62e-124j)
| (0.23861918608319690863 + 1.8595202432341189057e-455j)  +/-  (1.78e-124, 1.78e-124j)
| (0.44173229246410537146 - 2.4901777648469429046e-455j)  +/-  (4.02e-120, 4.02e-120j)
| (-0.98124721612774456171 + 1.455161209514506437e-456j)  +/-  (5.46e-114, 5.46e-114j)
| (-0.46194088448213480754 + 5.9770414217988769034e-468j)  +/-  (1.41e-119, 1.41e-119j)
| (-0.44173229246410537146 - 4.7551838545554992315e-470j)  +/-  (4.04e-120, 4.04e-120j)
| (0.02411517758027983534 + 5.4202271430142280829e-477j)  +/-  (1.13e-127, 1.13e-127j)
| (0.58322136656433728579 + 5.5754612684182666283e-469j)  +/-  (5.16e-119, 5.16e-119j)
| (0.14041851390971524844 - 3.9644487074169593368e-476j)  +/-  (4.62e-126, 4.62e-126j)
-------------------------------------------------
The weights are:
| (0.02508329855258132388 + 1.169329857288612447e-396j)  +/-  (9.03e-17, 9.85e-70j)
| (0.095469264468116565809 - 3.1866843155107243229e-397j)  +/-  (9.22e-18, 1.01e-70j)
| (0.044835193358186114942 - 6.9688609005702756364e-398j)  +/-  (1.22e-18, 1.33e-71j)
| (0.0085966081153332322232 + 2.775940068842750992e-396j)  +/-  (2.93e-17, 3.2e-70j)
| (0.044835193358186114942 - 1.4086143179266629918e-396j)  +/-  (5.26e-18, 5.74e-71j)
| (0.010763329791849968722 - 5.1256053826390722934e-396j)  +/-  (4.14e-17, 4.52e-70j)
| (0.0085966081153332322232 - 2.2213353254890388304e-398j)  +/-  (4.95e-20, 5.4e-73j)
| (0.03488103700219076649 + 1.1618564780296292035e-398j)  +/-  (4.42e-20, 4.82e-73j)
| (0.0064386194537041236679 + 3.80588080383905208e-399j)  +/-  (3.23e-20, 3.53e-73j)
| (0.03488103700219076649 + 2.1234841497083620319e-396j)  +/-  (3.41e-18, 3.72e-71j)
| (-0.11556025626664573465 - 1.033810712931485393e-395j)  +/-  (1.83e-19, 1.99e-72j)
| (0.20983215513485086792 + 1.1100384258902692671e-396j)  +/-  (6.07e-22, 6.63e-75j)
| (0.11006564274184708149 + 6.5750691261237825199e-397j)  +/-  (3.46e-21, 3.77e-74j)
| (-0.11556025626664573465 - 1.0858829874159508411e-396j)  +/-  (1.82e-21, 1.98e-74j)
| (0.0064386194537041236679 - 2.5017073897623080961e-397j)  +/-  (6.9e-20, 7.53e-73j)
| (0.11006564274184708149 + 6.6024729782126248532e-396j)  +/-  (2.26e-20, 2.46e-73j)
| (0.074367034798692332026 + 4.1327542727066321682e-397j)  +/-  (4.48e-23, 4.89e-76j)
| (0.27272491052889590378 + 2.107654145515904352e-396j)  +/-  (1.39e-24, 1.52e-77j)
| (0.10864839274115349981 + 5.5113067110034229692e-397j)  +/-  (3.39e-22, 3.7e-75j)
| (0.02508329855258132388 - 1.9926715513949840923e-398j)  +/-  (6.3e-23, 6.87e-76j)
| (0.20983215513485086792 + 3.2379183885263165766e-396j)  +/-  (3.98e-24, 4.34e-77j)
| (0.10864839274115349981 + 4.8528893299689958594e-396j)  +/-  (1.45e-21, 1.58e-74j)
| (0.074367034798692332026 + 8.3553182426935325504e-398j)  +/-  (1.5e-24, 1.64e-77j)
| (0.095469264468116565809 - 1.5797527629865791944e-397j)  +/-  (7.35e-26, 8.02e-79j)
| (0.068409847407270643152 - 9.6215934613061909166e-398j)  +/-  (4.86e-24, 5.31e-77j)
| (0.10038376133414832544 - 1.9272619530264402589e-397j)  +/-  (3.28e-26, 3.58e-79j)
| (0.068409847407270643152 - 6.2323312954230894492e-397j)  +/-  (4.12e-24, 4.49e-77j)
| (-0.29784207473347832609 - 6.4144953215090169387e-396j)  +/-  (2e-25, 2.18e-78j)
| (-0.36600814925819215952 - 4.0495039821082114051e-396j)  +/-  (2.49e-26, 2.72e-79j)
| (0.082112549291591177455 - 1.176997376636946257e-397j)  +/-  (8.81e-27, 9.61e-80j)
| (0.096630287035075382443 + 1.3710972391208687423e-397j)  +/-  (5.1e-27, 5.56e-80j)
| (0.096630287035075382443 + 2.2401987893163917727e-397j)  +/-  (1.28e-27, 1.4e-80j)
| (0.24716447387373283126 + 3.6377089159738265951e-396j)  +/-  (4e-26, 4.36e-79j)
| (0.010763329791849968722 + 3.0026802582690802499e-398j)  +/-  (4.54e-27, 4.95e-80j)
| (-0.29784207473347832609 - 2.3405585388007409722e-396j)  +/-  (2.57e-27, 2.81e-80j)
| (0.24716447387373283126 + 1.3970228038048094596e-396j)  +/-  (1.38e-27, 1.5e-80j)
| (0.27272491052889590378 + 2.2127678834976035649e-396j)  +/-  (9.28e-29, 1.02e-81j)
| (0.082112549291591177455 - 4.5165150415470486598e-397j)  +/-  (4.43e-30, 5.4e-83j)
| (0.10038376133414832544 - 2.5633670605951939711e-397j)  +/-  (5.96e-30, 6.34e-83j)
