Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 11 28
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 256*t^19 - 19308928/1347*t^17 + 418651520/1347*t^15 - 1521292480/449*t^13 + 9071700160/449*t^11 - 30031939520/449*t^9 + 52723966680/449*t^7 - 43021232100/449*t^5 + 12604959675/449*t^3 - 2144332575/898*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^47 - 152893897695473708737943791081366129318519567964828880902121411678331000501411117834436758456176493733186033102976/1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619*t^45 + 27550874203881065842848651940208219942072783480863085866194813382138281149113581500372389242695782798412961769511360/1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619*t^43 - 80684983581242653048604835083738203030875759306038703413633532056347501387439443082410196385319754491062854636202857440/40574960503270819633672323725798625532824391996238759696370861221373048180312856121369521986078131660879950713*t^41 + 112070707174291222560774081453756667454499856297949090935697653211876684371352413527902806843842778368137414550575856783440/770924249562145573039774150790173885123663447928536434231046363206087915425944266306020917735484501556719063547*t^39 - 1953219320434281348427900539242238519448717153168219797771423256824349320659633545810255856909672781578381321010606833441000/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^37 + 75650630560426024862690754265696299195760518764695858818687479969912527532782337857969207723554529093585613835577979350210700/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^35 - 2218326900172152758934945104728005192756452068700897724505021702249900498759830268706085863859271816120144973723794109580660850/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^33 + 1512596881374461495206085914053469862049143567392985690107030191333164968240867954518824238134523727372690058170534666642397050/7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753*t^31 - 26317493622063405546887681105263701853279033202975169514588654301743243523773413636010484613125785534396096315176464876086640375/7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753*t^29 + 17324837925013316574645719675476310083263791150251376205401496824627639481865236293200415238216755785602886315791078890681641225/379859201558090945079957699329969886732526951430665895161885372360723289197311784334082738475232570365468866*t^27 - 4952999474381225608347088655969657438593064758704250934278111991712634478889534256501072654778547152366719131808667424073045491225/10382818175921152498852177115019176904022403339104867801091533511193103238059855438464928184989690256656149004*t^25 + 79951936698838913250292830655121348773115203356984410917505606350721248185291842973224435966324657425849471328032375552417667128125/20765636351842304997704354230038353808044806678209735602183067022386206476119710876929856369979380513312298008*t^23 - 987847397720016065104960716330854080776804338740051970492916268984734737793576103592787203887509748198116530357974085269645540299375/41531272703684609995408708460076707616089613356419471204366134044772412952239421753859712739958761026624596016*t^21 + 485684749249701031154661676420351871689695056896591928948259261868541250228724170065182658305843415900689012700489911145894667766875/4371712916177327367937758785271232380641011932254681179406961478397096100235728605669443446311448529118378528*t^19 - 3371096364211807839949022212131120824999962474916979015982652644453259506229849104373480040447961764647041577027070670340249646860625/8743425832354654735875517570542464761282023864509362358813922956794192200471457211338886892622897058236757056*t^17 + 33942952627386772681881020463923135608030554519899484620931610739981048372912732502311045589962470830964876248976846587455934074623125/34973703329418618943502070282169859045128095458037449435255691827176768801885828845355547570491588232947028224*t^15 - 119868461960642203569398623164698443108682277686155351706036330971069561504620258773007573513383977701108679016065113259880527979859375/69947406658837237887004140564339718090256190916074898870511383654353537603771657690711095140983176465894056448*t^13 + 283278436595349206763707735515524837563051285135611119182693365852765705866162873813281051302516051373499512261074026966614551586315625/139894813317674475774008281128679436180512381832149797741022767308707075207543315381422190281966352931788112896*t^11 - 418667837777642410288654889155512012648845994846673089485263494108112422629560319755006306019864812756886952793610568015479001963271875/279789626635348951548016562257358872361024763664299595482045534617414150415086630762844380563932705863576225792*t^9 + 350159195596690367225265420925996693975950985949315077468073968833597965055899277868416508231234375428044889217282310628638676311671875/559579253270697903096033124514717744722049527328599190964091069234828300830173261525688761127865411727152451584*t^7 - 141868284307233351915800133795887572636183750736354986968569779470325580908903492595364025518023810261607927101875169165721120782390625/1119158506541395806192066249029435489444099054657198381928182138469656601660346523051377522255730823454304903168*t^5 + 20654718585953766957297460447266768104540193117786730514966459393805898521156417308775379322019290060370472385866977616215356621109375/2238317013082791612384132498058870978888198109314396763856364276939313203320693046102755044511461646908609806336*t^3 - 149581533247864174744375346975316623874146815318221828045695623595289777465459838088324379548023157448550525277180632365005767078125/4476634026165583224768264996117741957776396218628793527712728553878626406641386092205510089022923293817219612672*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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (6.7893681156313923762 - 3.7746184676921116556e-958j)  +/-  (4.78e-246, 4.78e-246j)
| (7.3721262056716741051 - 1.5798065434370561046e-959j)  +/-  (9.91e-247, 9.91e-247j)
| (-6.2686145719459958623 - 7.497063303270626715e-958j)  +/-  (1.65e-245, 1.65e-245j)
| (-4.4838301627422905975 - 4.8551239254732110024e-956j)  +/-  (7.4e-245, 7.4e-245j)
| (-7.3721262056716741051 + 3.2871876096839113325e-959j)  +/-  (9.74e-247, 9.74e-247j)
| (-8.0765771070346398733 - 2.5386242183349634049e-959j)  +/-  (9.43e-248, 9.43e-248j)
| (-3.6473028998600486888 + 2.4278384482659848709e-953j)  +/-  (1.2e-243, 1.2e-243j)
| (5.7872204425131881418 + 2.1599856238097803933e-957j)  +/-  (3.11e-245, 3.11e-245j)
| (-1.9816567566958429259 - 9.1171888236834723805e-961j)  +/-  (2.91e-247, 2.91e-247j)
| (4.4838301627422905975 - 1.8610589267194411553e-955j)  +/-  (7.7e-245, 7.7e-245j)
| (1.5003220079015141594 - 2.9116161245453687144e-961j)  +/-  (2.44e-249, 2.44e-249j)
| (-5.7872204425131881418 - 3.1115730240919699891e-958j)  +/-  (3.27e-245, 3.27e-245j)
| (8.0765771070346398733 + 3.792303478493624418e-960j)  +/-  (8.83e-248, 8.83e-248j)
| (-2.5596386236645893381 - 2.3705081633200485401e-959j)  +/-  (1.05e-246, 1.05e-246j)
| (-1.1571937124467801947 + 7.93394525673211062e-963j)  +/-  (1.68e-250, 1.68e-250j)
| (2.9306374202572440192 - 1.9472673098988576713e-955j)  +/-  (4.26e-246, 4.26e-246j)
| (2.1885630273880580333 - 2.1959886664930103414e-962j)  +/-  (4.35e-247, 4.35e-247j)
| (4.9006550064984739309 - 2.2681498894675531403e-959j)  +/-  (6.49e-245, 6.49e-245j)
| (-3.3087860442865752885 + 1.8371645400650349256e-961j)  +/-  (2.61e-245, 2.61e-245j)
| (6.2686145719459958623 - 3.9970070938692518452e-961j)  +/-  (1.43e-245, 1.43e-245j)
| (-4.0793849663282630898 + 3.5580601380228666449e-960j)  +/-  (9e-245, 9e-245j)
| (1.8651745430168657961 + 2.6822650937778587471e-962j)  +/-  (1.15e-247, 1.15e-247j)
| (-1.8651745430168657961 - 5.346985750173213982e-963j)  +/-  (1.13e-247, 1.13e-247j)
| (5.3335603170609469186 - 3.2393567941703851131e-960j)  +/-  (4.6e-245, 4.6e-245j)
| (-2.1885630273880580333 - 1.1936316878346353835e-962j)  +/-  (3.94e-247, 3.94e-247j)
| (-6.7893681156313923762 - 2.8756623497743031301e-962j)  +/-  (5.65e-246, 5.65e-246j)
| (1.1571937124467801947 + 3.0758998692300298798e-965j)  +/-  (1.69e-250, 1.69e-250j)
| (2.5596386236645893381 - 1.2904546160763887567e-960j)  +/-  (1.14e-246, 1.14e-246j)
| (-0.061785547072976840363 + 2.4483990622552617971e-969j)  +/-  (5.59e-255, 5.59e-255j)
| (-0.56474674797970907162 + 2.1286446874145684611e-967j)  +/-  (2.15e-252, 2.15e-252j)
| (-0.38118699020732211685 + 7.8644277180390103391e-968j)  +/-  (2.99e-253, 2.99e-253j)
| (3.3087860442865752885 + 7.5160941687217330252e-958j)  +/-  (2.66e-245, 2.66e-245j)
| (-4.9006550064984739309 + 6.794535688156266231e-979j)  +/-  (6.68e-245, 6.68e-245j)
| (4.0793849663282630898 - 1.5795082998765718595e-982j)  +/-  (8.48e-245, 8.48e-245j)
| (0.83186754224030276654 - 4.5911174542373801887e-1011j)  +/-  (1.45e-251, 1.45e-251j)
| (-2.9306374202572440192 + 3.5033598676132902201e-1003j)  +/-  (4.31e-246, 4.31e-246j)
| (-5.3335603170609469186 - 3.9526496383367509748e-1006j)  +/-  (5.27e-245, 5.27e-245j)
| (0.56474674797970907162 - 2.7551458146411620796e-1021j)  +/-  (2.11e-252, 2.11e-252j)
| (3.6473028998600486888 - 3.7587943429676882471e-1025j)  +/-  (1.14e-243, 1.14e-243j)
| (-3.6629020745954378401 - 1.0071627345821026114e-1058j)  +/-  (1.26e-243, 1.26e-243j)
| (-0.83186754224030276654 + 6.1800051169539306978e-1075j)  +/-  (1.41e-251, 1.41e-251j)
| (0.38118699020732211685 - 9.913527887129021382e-1076j)  +/-  (2.99e-253, 2.99e-253j)
| (3.6629020745954378401 + 1.5137230317498541126e-1071j)  +/-  (1.12e-243, 1.12e-243j)
| (1.9816567566958429259 + 1.7632703719600610766e-1088j)  +/-  (3.02e-247, 3.02e-247j)
| (-1.5003220079015141594 - 1.180930577671603146e-1089j)  +/-  (2.54e-249, 2.54e-249j)
| (0.061785547072976840363 + 2.0887632530538122645e-1095j)  +/-  (5.59e-255, 5.59e-255j)
| (1.0035427564652364339e-1226 - 1.1296870073947742279e-1225j)  +/-  (5.33e-1224, 5.33e-1224j)
-------------------------------------------------
The weights are:
| (2.950791910379294885e-21 - 2.0014230603925524023e-971j)  +/-  (4.07e-90, 3.19e-212j)
| (8.8271669402251592391e-25 + 1.6411606066345673849e-973j)  +/-  (8.87e-92, 6.96e-214j)
| (2.4171511201100099611e-18 - 2.4876506967794511818e-969j)  +/-  (2.9e-90, 2.28e-212j)
| (4.2939727667245704861e-10 - 2.8719272755337588072e-963j)  +/-  (3.05e-84, 2.39e-206j)
| (8.8271669402251592391e-25 - 2.8836631568082220227e-973j)  +/-  (8.47e-94, 6.65e-216j)
| (2.1538337430281983207e-29 + 6.1873420295072702945e-976j)  +/-  (7.57e-96, 5.93e-218j)
| (-6.3809254761420043116e-07 + 8.9257153160796132642e-958j)  +/-  (7.82e-82, 6.13e-204j)
| (7.4909527353012788437e-16 - 4.7764513755797626241e-968j)  +/-  (4.21e-91, 3.3e-213j)
| (-0.0011680644275554887203 + 3.0305365433291847083e-957j)  +/-  (2.69e-73, 2.11e-195j)
| (4.2939727667245704861e-10 + 1.4325903665055318615e-963j)  +/-  (1.57e-87, 1.23e-209j)
| (0.020774555887641572227 - 5.8843110011112361496e-958j)  +/-  (7.95e-71, 6.24e-193j)
| (7.4909527353012788437e-16 + 1.0712077397162536588e-967j)  +/-  (1.88e-90, 1.47e-212j)
| (2.1538337430281983207e-29 - 3.7454461637617163694e-976j)  +/-  (8.76e-98, 6.87e-220j)
| (0.00029701714159395521347 + 8.7695520742478215736e-959j)  +/-  (8.35e-79, 6.55e-201j)
| (0.049713063102060696497 - 5.0698703068481797267e-957j)  +/-  (7.29e-69, 5.72e-191j)
| (3.9279603909867421369e-05 + 2.9231040500748170137e-959j)  +/-  (2.78e-82, 2.18e-204j)
| (0.0018027887629870198136 + 4.5856969262840427681e-958j)  +/-  (2.79e-78, 2.19e-200j)
| (8.8880777223109961287e-12 - 2.8219929337897980391e-965j)  +/-  (2.58e-89, 2.02e-211j)
| (3.8105842635308505672e-06 + 1.406912647578744739e-959j)  +/-  (7.51e-84, 5.89e-206j)
| (2.4171511201100099611e-18 + 1.2249510938760976027e-969j)  +/-  (3.24e-93, 2.54e-215j)
| (1.33626864605407302e-08 + 1.053613511734368497e-961j)  +/-  (6.15e-87, 4.82e-209j)
| (0.0073075514041899694337 + 1.4173539380814610604e-957j)  +/-  (1.13e-78, 8.83e-201j)
| (0.0073075514041899694337 - 3.3153295171530026831e-957j)  +/-  (4.17e-78, 3.27e-200j)
| (1.1037866870001781057e-13 + 1.3456992116888161967e-966j)  +/-  (7.53e-91, 5.91e-213j)
| (0.0018027887629870198136 - 7.2139568742246067542e-958j)  +/-  (6.69e-80, 5.25e-202j)
| (2.950791910379294885e-21 + 3.7582913032526007519e-971j)  +/-  (6.65e-96, 5.22e-218j)
| (0.049713063102060696497 + 3.5378243877304197451e-958j)  +/-  (4.53e-77, 3.55e-199j)
| (0.00029701714159395521347 - 1.0003583471109498366e-958j)  +/-  (1.95e-83, 1.53e-205j)
| (0.56586922339106684806 - 8.2049973358777226508e-955j)  +/-  (1.03e-76, 8.09e-199j)
| (0.083837004417334615383 - 5.4045737390316502041e-956j)  +/-  (4.29e-77, 3.37e-199j)
| (0.10643460162522516989 + 9.409071548007173041e-956j)  +/-  (5.53e-77, 4.34e-199j)
| (3.8105842635308505672e-06 + 6.2932311190661269697e-960j)  +/-  (1.2e-86, 9.38e-209j)
| (8.8880777223109961287e-12 + 9.5860113917037437494e-965j)  +/-  (1.4e-91, 1.1e-213j)
| (1.33626864605407302e-08 - 2.5852572973893638547e-962j)  +/-  (1.98e-89, 1.55e-211j)
| (0.087432104453201267014 + 1.9242258954104767947e-957j)  +/-  (2.03e-80, 1.59e-202j)
| (3.9279603909867421369e-05 - 2.3936830296224819147e-959j)  +/-  (3.68e-86, 2.88e-208j)
| (1.1037866870001781057e-13 - 3.4791243542660124e-966j)  +/-  (5.5e-93, 4.31e-215j)
| (0.083837004417334615383 - 1.7152287200802679917e-956j)  +/-  (4.69e-82, 3.68e-204j)
| (-6.3809254761420043116e-07 - 1.1943334337876516278e-959j)  +/-  (1.1e-88, 8.62e-211j)
| (8.8711958789488457461e-07 - 8.9993974645990709993e-958j)  +/-  (3.05e-88, 2.39e-210j)
| (0.087432104453201267014 + 1.5874421625288757867e-956j)  +/-  (4.62e-84, 3.62e-206j)
| (0.10643460162522516989 + 4.5740580221024908072e-956j)  +/-  (8.66e-84, 6.79e-206j)
| (8.8711958789488457461e-07 + 1.0641156911972302449e-959j)  +/-  (9.85e-89, 7.72e-211j)
| (-0.0011680644275554887203 - 1.4966759651408596239e-957j)  +/-  (6.06e-86, 4.75e-208j)
| (0.020774555887641572227 + 2.4192851947466321129e-957j)  +/-  (6.58e-86, 5.15e-208j)
| (0.56586922339106684806 - 7.3414500065203333758e-955j)  +/-  (3.29e-84, 2.53e-206j)
| (-0.84468639754808449775 + 1.4717202663816867425e-954j)  +/-  (5.18e-84, 4.17e-206j)
