Starting with polynomial:
P : t
Extension levels are: 1 6 8 16
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^7 - 21/13*t^5 + 105/143*t^3 - 35/429*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : t^15 - 825/221*t^13 + 336705/60401*t^11 - 8310395/1960287*t^9 + 8381629155/4854324041*t^7 - 250360401/693474863*t^5 + 300170185/9015173219*t^3 - 88221135/99166905409*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 22823157060610658871115730418540993373758924538995986648144983104868352501100563436229/2864927552749720237118062263788953487770180837869410330893932022105876130184814071921*t^29 + 149363049642843434127100931142364507244522960987884793099408772303173303061407185359725416279/5205215247402147955813879375521554868092447309803984894942912742663613694029534066921466875*t^27 - 7366631444158399017092821248931153496346880942380311314393658223822916872838498268144498602813/119245401152024705734186336349198925055075124837988155385287639212986090352397388695485798125*t^25 + 197644159487752325277513108235696577661280979374726802652497275262292576647044180352774277774428971/2232402694599146678026161137700261011870065818101963296020400716717449636374459705559285265561975*t^23 - 2356603366141964504071357718103715636097788476851834530765415593304963963960233115887392855498089/26471178196827826221654084636761988283044258712671501533838743676491497664519285046157532793225*t^21 + 411653767482084348982324965244242341052345674803378424434075677846579523141243915519039612093787/6382274041440693941160709127961161084784104481601499868559616896437298434402895291830462793755*t^19 - 465456722765954047326139736845959706965173141039726990103029508287465026791009700389391372265783/13676301517372915588201519559916773753108795317717499718342036206651353788006204196779563129475*t^17 + 2844262635109002704577804127222640738829109832954983883065074497757518904115664377664811445525213/217694540623594762245137128994910528093602353704373848457844411618815078531439932685208810755055*t^15 - 42599171104604213689655514039810080439709123677813128175594866074801059706027862540166435608071/11812882049342351439658603898948633307404778883183077048100084351408570152868833556561718413065*t^13 + 27303176491737894204457256838862731200612404609034582866553617301536582976980054194297131598817/39073379086286239377332305204214710170646576305913254851407971316197578197950757148627222443215*t^11 - 61344637727382997637100550506924811032600086767657132894122720607025040045807823554443832394859/671351695209827203846891425781507292932018447437964106083282416251031116310244827371867731069785*t^9 + 70579128441925847619498653371497012727159245992528510125290236478553708927574568075366497361491/9324329100136488942317936469187601290722478436638390362267811336819876615420067046831496264858125*t^7 - 10957399023242417444473062984048723359725942536272920902790451170573515423528958418280427426063/30637081329019892239044648398759261383802429148954711190308522963836737450665934582446344870248125*t^5 + 2983734193807702394834605181171038664518854609074078506085209491534411511616888728417665206881/375523082575700964872861547516220660961464060140044888589781610042456010466733883881985198552469875*t^3 - 579354826196938765947234421232693137268688874678414260426503268116363976609958509564329287/10974416607903368123069783744156745310453684904114693514049869069577378464529906955900688070199625*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:
| (-0.99868710967846672979 - 4.0407953504583863646e-410j)  +/-  (5.36e-117, 5.36e-117j)
| (-0.99145537112081263921 + 8.6368506626229299318e-410j)  +/-  (1.22e-116, 1.22e-116j)
| (-0.91220488278326287835 - 1.2639280617516060583e-410j)  +/-  (2.7e-117, 2.7e-117j)
| (0.99868710967846672979 - 2.6288963177737016236e-408j)  +/-  (5.35e-117, 5.35e-117j)
| (0.91220488278326287835 + 8.5736980286933844605e-420j)  +/-  (2.49e-117, 2.49e-117j)
| (0.94910791234275852453 - 6.9321491705978925858e-431j)  +/-  (6.38e-117, 6.38e-117j)
| (0.99145537112081263921 - 8.0517535008836960965e-440j)  +/-  (1.22e-116, 1.22e-116j)
| (-0.94910791234275852453 + 8.0268290923307171396e-450j)  +/-  (6.18e-117, 6.18e-117j)
| (-0.97538358820889336968 - 1.2908274135334461765e-452j)  +/-  (1.08e-116, 1.08e-116j)
| (0.97538358820889336968 - 1.0917028768180553177e-453j)  +/-  (1.09e-116, 1.09e-116j)
| (0.86486442335976907279 - 2.6252180637341224598e-463j)  +/-  (8.6e-118, 8.6e-118j)
| (0.49863678655283200429 + 3.8046547242242052082e-473j)  +/-  (7.39e-122, 7.39e-122j)
| (-0.86486442335976907279 + 1.1564558452123205222e-469j)  +/-  (8.34e-118, 8.34e-118j)
| (-0.80768893917243750909 + 1.4569205393632205498e-470j)  +/-  (2.1e-118, 2.1e-118j)
| (-3.7555356739730522374e-480 - 1.2268834461406884046e-479j)  +/-  (3.98e-478, 3.98e-478j)
| (0.74153118559939443986 + 6.637860406711059762e-470j)  +/-  (4.43e-119, 4.43e-119j)
| (0.80768893917243750909 - 1.3470177156442841493e-473j)  +/-  (2.37e-118, 2.37e-118j)
| (-0.3085792479105877789 - 1.3582344115088183454e-480j)  +/-  (3.44e-124, 3.44e-124j)
| (-0.74153118559939443986 + 3.5666005570501637764e-475j)  +/-  (4.45e-119, 4.45e-119j)
| (-0.40584515137739716691 + 2.0935862040959633164e-480j)  +/-  (5.92e-123, 5.92e-123j)
| (0.40584515137739716691 - 2.6194372278601769028e-479j)  +/-  (6.18e-123, 6.18e-123j)
| (0.66734809810430017543 - 1.6786775912927704403e-477j)  +/-  (7.21e-120, 7.21e-120j)
| (0.1045282738107807134 - 3.7649689397198397123e-485j)  +/-  (1.1e-126, 1.1e-126j)
| (-0.49863678655283200429 - 6.8049245201299495438e-480j)  +/-  (7.83e-122, 7.83e-122j)
| (-0.58608723546769113029 + 1.1609926673361707912e-476j)  +/-  (8.36e-121, 8.36e-121j)
| (0.2077849550078984676 - 9.691251819260692289e-484j)  +/-  (2.08e-125, 2.08e-125j)
| (0.58608723546769113029 - 2.7602216371612377403e-479j)  +/-  (7.48e-121, 7.48e-121j)
| (0.3085792479105877789 + 1.5183879029987240857e-483j)  +/-  (3.34e-124, 3.34e-124j)
| (-0.1045282738107807134 - 3.6331831645418123712e-485j)  +/-  (1.1e-126, 1.1e-126j)
| (-0.66734809810430017543 + 1.0198599146847136902e-480j)  +/-  (7.38e-120, 7.38e-120j)
| (-0.2077849550078984676 - 1.2303131967884508303e-486j)  +/-  (2.19e-125, 2.19e-125j)
-------------------------------------------------
The weights are:
| (0.0036349311950498838561 + 2.4178063439433974502e-410j)  +/-  (1.2e-23, 1.85e-78j)
| (0.011319468444683435107 + 3.4009377147717916617e-410j)  +/-  (9.78e-24, 1.5e-78j)
| (0.042193500584546594485 - 3.0961808153402773792e-411j)  +/-  (1.91e-24, 2.93e-79j)
| (0.0036349311950498838561 + 2.4154056554157493332e-408j)  +/-  (1.2e-25, 1.85e-80j)
| (0.042193500584546594485 + 3.350411250671094079e-409j)  +/-  (5.03e-26, 7.74e-81j)
| (0.031577706217045857274 - 6.0184322441613247406e-409j)  +/-  (5.26e-26, 8.09e-81j)
| (0.011319468444683435107 - 3.2768438295431282578e-408j)  +/-  (6.73e-26, 1.04e-80j)
| (0.031577706217045857274 + 8.1778666486134693326e-411j)  +/-  (1.4e-26, 2.15e-81j)
| (0.021039446258726795607 - 7.1053604656492543794e-410j)  +/-  (3.01e-26, 4.63e-81j)
| (0.021039446258726795607 + 1.2541699478032276078e-408j)  +/-  (1.24e-26, 1.91e-81j)
| (0.052384370820982692472 - 2.0973801196533310271e-409j)  +/-  (3.31e-28, 5.09e-83j)
| (0.09026180214655860231 + 5.5428263082171823703e-410j)  +/-  (7.42e-31, 1.14e-85j)
| (0.052384370820982692472 + 8.2267747809166158134e-411j)  +/-  (9.87e-29, 1.52e-83j)
| (0.061821985645449856431 + 2.0317684729341850547e-411j)  +/-  (1.71e-29, 2.63e-84j)
| (0.10474321356480584473 - 2.5944440256196280424e-410j)  +/-  (9.05e-32, 1.39e-86j)
| (0.070332046410400650935 - 1.0654393979398804873e-409j)  +/-  (2.25e-30, 3.46e-85j)
| (0.061821985645449856431 + 1.4418220670826296017e-409j)  +/-  (9.97e-30, 1.53e-84j)
| (0.09919685766743291249 + 1.853744601825507948e-410j)  +/-  (7.2e-33, 1.11e-87j)
| (0.070332046410400650935 - 6.7161609622858906552e-411j)  +/-  (8.68e-32, 1.34e-86j)
| (0.095178029931830680121 - 1.6520367317103319121e-410j)  +/-  (5.39e-33, 8.29e-88j)
| (0.095178029931830680121 - 4.6544749079422499633e-410j)  +/-  (2.62e-33, 4.03e-88j)
| (0.077875347115245996421 + 8.299865489003810643e-410j)  +/-  (1.15e-32, 1.76e-87j)
| (0.10409995547269735501 + 2.9502567191620796775e-410j)  +/-  (6.89e-34, 1.06e-88j)
| (0.09026180214655860231 + 1.4478949317306087484e-410j)  +/-  (5.21e-34, 8.02e-89j)
| (0.084498765301243021195 - 1.2296563371350869525e-410j)  +/-  (3.77e-34, 5.79e-89j)
| (0.10221418000570274392 - 3.3958112911670566017e-410j)  +/-  (1.09e-34, 1.67e-89j)
| (0.084498765301243021195 - 6.7034980011955889094e-410j)  +/-  (3.57e-34, 5.48e-89j)
| (0.09919685766743291249 + 3.9541576827500488291e-410j)  +/-  (8.2e-35, 1.26e-89j)
| (0.10409995547269735501 + 2.3068343441856469417e-410j)  +/-  (1.16e-35, 1.79e-90j)
| (0.077875347115245996421 + 9.8199753280700387369e-411j)  +/-  (7.23e-36, 1.17e-90j)
| (0.10221418000570274392 - 2.0664396480384341701e-410j)  +/-  (7.25e-36, 1.1e-90j)
