Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 11 28
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 35/8*t^15 - 638415/40664*t^13 + 11181153/503608*t^11 - 55088825/3525256*t^9 + 19993545/3525256*t^7 - 160318323/162665384*t^5 + 10517265/162665384*t^3 - 64053/91941304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^43 - 3244488800839734480167646753999010401523322222816914359520882508048147950553594335713877784672218371148143133876084821/68880093946072843602749195490209685131270297056459569494665239257993922904114607039607797601087258885396330016925408*t^41 + 66642593907309792308989240485843773998150588702123215943831021929854808300958821014021821804689913273514187787277564153903/282787225695602059411086822085055862306430204565294762560348139773694050482842519201109813051263741353994632884487262544*t^39 - 14203312743852663129622245067413422086749631052046672456548513905879899103061736506881223467292031860022718351038007935590901724/19529569046948630388453905819834668043051848002404021221050014676340795996187334787205728134245205131493962690985948050870515*t^37 + 96848935343255872174914885972871699665490383565795836780806752083488080960488370894192034884796821810433318424883326839468797169/62494620950235617243052498623470937737765913607692867907360046964290547187799471319058330029584656420780680611155033762785648*t^35 - 22153408126791411582187573610744075886354251986829655790005689525029114547073542689347957929502595305589983604022273524754639294201/9159925870705963327338837655383026016992546765927554638993058312194585916383179653336263801479122498245854043863580662945439264*t^33 + 3364342520285327350759379075280401377232506874270838836555559748860123767805350885611547920545801690519009467679655540239217919579/1175832235086413642608731264685110662955693082326558991958284000513193899199019273681633190004685337527350792667673443686178020*t^31 - 36156786915320992618396829347123567490888349978761184925049903206368984113949940692660575002707892289885910822807254029403705023954231/13798508861962572737377722264206242140851353890410402426529658574422381726490411078581333648023982904417214287034414629001667682502*t^29 + 1208814586171346517579269344641924274402443350927358609911219973678892219299636108276507108153844863696964530630326665905342997086868/642787679905088792113869049574824944449597230919739243471878505019676167383093683784844735156396719149870230762472731164673960365*t^27 - 43651999152626747659563734748653291410206636844850176924523308089294827753268041635293147106673362945875337371414415616221592023679/41021208062319056818662868121014469389376005619949171093362047043990729770317089791397498767815631079649838088545268313643010576*t^25 + 1296469880629449491202531816045872459656353677891662429799266139150979934395490716871719589546540652800916067486042770364236514943985/2727910336144217278441080730047462214393504373726619877708576128425383529726086471127933668059739466796714232888260342857260203304*t^23 - 1935646873780954753167782390588553587290537799174889914932141774618229301148776443652860030800375030161612442162215966071272595482241/11593618928612923433374593102701714411172393588338134480261448545807880001335867502293718089253892733886035489775106457143355864042*t^21 + 3335264067294838835288743464574462273054354526965767112066049928351626841834070922336484746720278961564346805245984952925842210338965/72874176122709804438354585216982204870226473983839702447357676573649531436968310014417656561024468612997937364300669159186808288264*t^19 - 184652043739096863549024386980209631233405708596447727226187106660946305947069179650688908102531817923191049899190864947885242044347937/19108376075965276090099081239526597087550962809867863031196628667890629769419795815359408683527573822629248628891891250056246257480592*t^17 + 50689861861914548797622653076755267614757162184979416681513127092971363625304532504921635810483850733511687458970010801999566897332875/32877647071881430919729301544479586165345038952272646686029493443282407103266413388191923764304796135994442493828695239067364884194548*t^15 - 330404745889569363028591332639193925486736555896205940580343556832702528172266133372373000870102877726535247083842796184354701559715/1826535948437857273318294530248865898074724386237369260334971857960133727959245188232884653572488674221913471879371957725964715788586*t^13 + 177214708753930115589628682688443697604327889542103457527269087708162829745108779884392124638888432394814297986302324424988058427253/11802232282213846996825903118531133495252065264918385989856741236050094857582815062427870069237619125741594741374403419152387394326248*t^11 - 75119304408335798615580809634802474516165432404539050139970959937918276681067318448955762204281366357119858436738042756413823339165/90126137427814831612125078359692292145561225659376765740724205802564360730632405931267371437814546051117632570495444291709140102127712*t^9 + 142078387432598995138032604961440641226428180340986155717110545838665509435730649760277835971762517796457097336773572073664854841/5007007634878601756229171019982905119197845869965375874484678100142464485035133662848187302100808113950979587249746905094952227895984*t^7 - 45805094110772394458405317777476386023381672101232576236889958578962778730963589044231583595478823262115118014283571902756715/89410850622832174218378053928266162842818676249381712044369251788258294375627386836574773251800144891981778343745480448124146926714*t^5 + 34121744535394439172887229279556039156122165779516461128949904846826798892814851578561509735896528473395694058930406735172175/9298728464774546118711317608539680935653142329935698052614402185978862615065248231003776418187215068766104947749529966604911280378256*t^3 - 1555027295356344404263579460322079100920432813252958737605352405556098592961522211940867052567375409428811540335396731/366041233088926569910103631725537069130361656068482612735032660301882127071673125002608948301896001289826399816935853980944014816*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.99440647375811783848 + 1.5451065789748951813e-843j)  +/-  (5.34e-240, 5.34e-240j)
| (0.98582474861890022967 + 1.2991005445034611835e-856j)  +/-  (5.68e-240, 5.68e-240j)
| (-0.95275482203958774276 - 1.1653804904038372306e-857j)  +/-  (2.23e-240, 2.23e-240j)
| (0.99440647375811783848 + 3.6353248349518528297e-868j)  +/-  (5.38e-240, 5.38e-240j)
| (0.92771362013525931284 + 1.5120714440817854208e-869j)  +/-  (1.01e-240, 1.01e-240j)
| (0.95275482203958774276 + 2.9874449147885685647e-870j)  +/-  (2.24e-240, 2.24e-240j)
| (-0.3399810435848562648 + 2.1568043546768974314e-879j)  +/-  (7.23e-250, 7.23e-250j)
| (-0.89711395246867255836 - 4.4042977389837002791e-869j)  +/-  (3.61e-241, 3.61e-241j)
| (-0.97211348155404357097 + 6.1438479240031942995e-882j)  +/-  (3.98e-240, 3.98e-240j)
| (0.41138123298667837882 - 8.3460021859216580485e-910j)  +/-  (1.21e-248, 1.21e-248j)
| (0.89711395246867255836 + 8.9288779411251918793e-902j)  +/-  (3.7e-241, 3.7e-241j)
| (-0.26652617568911483634 - 2.9610883543761768458e-911j)  +/-  (4.33e-251, 4.33e-251j)
| (-0.92771362013525931284 - 4.9765217468019955165e-901j)  +/-  (1.03e-240, 1.03e-240j)
| (-0.86113631159405257522 - 9.6651883559046822484e-915j)  +/-  (1.06e-241, 1.06e-241j)
| (0.99892528954925553049 + 2.3287009613538900391e-919j)  +/-  (2e-240, 2e-240j)
| (0.86113631159405257522 + 1.3371005370074161861e-925j)  +/-  (1.18e-241, 1.18e-241j)
| (0.66816037253120853036 - 8.4555528511563640024e-930j)  +/-  (1.61e-244, 1.61e-244j)
| (-0.98582474861890022967 + 4.9711070987708874825e-924j)  +/-  (5.71e-240, 5.71e-240j)
| (-0.72322064929065662618 - 4.8214768568598470869e-949j)  +/-  (1.12e-243, 1.12e-243j)
| (-0.99892528954925553049 + 3.646372250417332043e-947j)  +/-  (2.2e-240, 2.2e-240j)
| (0.97211348155404357097 - 9.7995423901450498639e-967j)  +/-  (4.03e-240, 4.03e-240j)
| (0.72322064929065662618 - 4.0617763677377985321e-969j)  +/-  (1.16e-243, 1.16e-243j)
| (0.19144416672496167952 - 1.824112474068966058e-980j)  +/-  (2.11e-252, 2.11e-252j)
| (-0.81999475826211169486 + 4.5923737362643090313e-967j)  +/-  (2.85e-242, 2.85e-242j)
| (-0.77393231018977488346 + 1.3286331272244951295e-969j)  +/-  (5.85e-243, 5.85e-243j)
| (-9.6474044572706973302e-983 - 7.2356074457053378968e-983j)  +/-  (5.19e-981, 5.19e-981j)
| (0.77393231018977488346 + 6.4741370015733731919e-968j)  +/-  (6.13e-243, 6.13e-243j)
| (0.81999475826211169486 - 1.2194476835524696985e-973j)  +/-  (2.74e-242, 2.74e-242j)
| (0.11513928820520961921 + 3.1839875903735122615e-985j)  +/-  (9.32e-254, 9.32e-254j)
| (-0.66816037253120853036 - 1.2647245954829325242e-976j)  +/-  (1.73e-244, 1.73e-244j)
| (-0.41138123298667837882 + 5.9361789635194844289e-982j)  +/-  (1.23e-248, 1.23e-248j)
| (0.54633537010580514983 - 4.6113980121882480724e-978j)  +/-  (2.28e-246, 2.28e-246j)
| (0.48030338925494173885 - 1.4941214437863194167e-981j)  +/-  (1.83e-247, 1.83e-247j)
| (0.037641498697210702271 - 1.262051264722200457e-987j)  +/-  (3.89e-255, 3.89e-255j)
| (-0.60908029926987201505 + 1.1820037391805050292e-979j)  +/-  (1.9e-245, 1.9e-245j)
| (-0.54633537010580514983 - 8.7908011344107418921e-982j)  +/-  (2.14e-246, 2.14e-246j)
| (-0.037641498697210702271 + 1.6406889640327171715e-988j)  +/-  (3.89e-255, 3.89e-255j)
| (0.60908029926987201505 + 1.1026813011483196135e-980j)  +/-  (2.03e-245, 2.03e-245j)
| (0.3399810435848562648 - 5.6420279060067256699e-986j)  +/-  (7.67e-250, 7.67e-250j)
| (-0.19144416672496167952 - 1.5783432526915287024e-988j)  +/-  (2.08e-252, 2.08e-252j)
| (-0.48030338925494173885 + 1.0011655123596604442e-983j)  +/-  (1.79e-247, 1.79e-247j)
| (-0.11513928820520961921 - 5.2320554282624705007e-991j)  +/-  (9.32e-254, 9.32e-254j)
| (0.26652617568911483634 - 7.9718775926290635849e-987j)  +/-  (4.42e-251, 4.42e-251j)
-------------------------------------------------
The weights are:
| (0.0063754727871913720888 + 4.2411577519636382987e-844j)  +/-  (1.8e-74, 2.55e-190j)
| (0.010996651807989057083 - 7.0563037117176208954e-846j)  +/-  (7.12e-75, 1.01e-190j)
| (0.022213300175377497327 - 3.5798505883162970014e-844j)  +/-  (3.64e-75, 5.15e-191j)
| (0.0063754727871913720888 + 4.9530977559422586018e-846j)  +/-  (4.62e-75, 6.54e-191j)
| (0.027847154030707244757 + 7.5391295568286421505e-846j)  +/-  (9.96e-76, 1.41e-191j)
| (0.022213300175377497327 - 7.6576445018511248656e-846j)  +/-  (1.34e-75, 1.89e-191j)
| (0.072498777177282029644 - 4.1453777037251794289e-845j)  +/-  (5.67e-77, 8.02e-193j)
| (0.033321822523611179662 - 1.4553030106602884866e-844j)  +/-  (4.4e-77, 6.22e-193j)
| (0.016504468121340429808 + 6.7688425256047608747e-844j)  +/-  (6.27e-77, 8.87e-193j)
| (0.070230947271350425892 + 1.6180589173466291722e-845j)  +/-  (1.74e-78, 2.46e-194j)
| (0.033321822523611179662 - 7.4855178503152795765e-846j)  +/-  (6.66e-77, 9.42e-193j)
| (0.074339410792714510576 + 4.7005993612391981967e-845j)  +/-  (6.48e-78, 9.17e-194j)
| (0.027847154030707244757 + 2.17281337121111487e-844j)  +/-  (3.49e-77, 4.94e-193j)
| (0.038597728059504660252 + 1.050082362639995343e-844j)  +/-  (4.79e-78, 6.77e-194j)
| (0.0027365183638340126671 - 1.7079649453541969431e-846j)  +/-  (2.19e-77, 3.1e-193j)
| (0.038597728059504660252 + 7.5419789756185645696e-846j)  +/-  (1.55e-78, 2.19e-194j)
| (0.057127248110226779023 + 9.2410454956888872964e-846j)  +/-  (2.45e-80, 3.47e-196j)
| (0.010996651807989057083 - 1.6282405574467830856e-843j)  +/-  (2.47e-78, 3.5e-194j)
| (0.052938466423850669726 - 5.4101282778673936012e-845j)  +/-  (1.07e-81, 1.51e-197j)
| (0.0027365183638340126671 + 7.5341437527060943497e-844j)  +/-  (7.35e-79, 1.04e-194j)
| (0.016504468121340429808 + 7.673339558467804969e-846j)  +/-  (7.87e-79, 1.11e-194j)
| (0.052938466423850669726 - 8.5417264190901270103e-846j)  +/-  (8.53e-82, 1.21e-197j)
| (0.075755434621871090593 - 3.9841452821910832855e-845j)  +/-  (7.48e-84, 1.06e-199j)
| (0.043644877931373649485 - 8.0361383181602638256e-845j)  +/-  (3.98e-81, 5.63e-197j)
| (0.048434745362695980782 + 6.4564320637168132914e-845j)  +/-  (1.11e-81, 1.56e-197j)
| (-0.0046798912628058500777 + 3.8910078706266963386e-844j)  +/-  (6.71e-85, 9.49e-201j)
| (0.048434745362695980782 + 8.0497949363922970441e-846j)  +/-  (5.14e-83, 7.28e-199j)
| (0.043644877931373649485 - 7.724844126535740688e-846j)  +/-  (1.06e-82, 1.49e-198j)
| (0.076810232901186924229 + 7.0509692301150750657e-845j)  +/-  (2.16e-85, 3.06e-201j)
| (0.057127248110226779023 + 4.7092841288821947142e-845j)  +/-  (6.52e-85, 9.22e-201j)
| (0.070230947271350425892 + 3.9014560189272049883e-845j)  +/-  (6.89e-86, 9.74e-202j)
| (0.064453140622554151572 + 1.1557188931190679652e-845j)  +/-  (8.78e-86, 1.24e-201j)
| (0.067544611719411396522 - 1.3447012002422329029e-845j)  +/-  (5.9e-86, 8.34e-202j)
| (0.078995251148247099939 - 2.3620425660291293225e-844j)  +/-  (3.02e-86, 4.27e-202j)
| (0.06097368567908276341 - 4.2495762664326797257e-845j)  +/-  (6.21e-87, 8.78e-203j)
| (0.064453140622554151572 + 3.9740667136477401809e-845j)  +/-  (2.12e-87, 3e-203j)
| (0.078995251148247099939 - 2.5478997503732000514e-844j)  +/-  (1.42e-87, 2.01e-203j)
| (0.06097368567908276341 - 1.0211951813291529178e-845j)  +/-  (1.2e-87, 1.7e-203j)
| (0.072498777177282029644 - 2.0330230549467572789e-845j)  +/-  (1.57e-88, 2.22e-204j)
| (0.075755434621871090593 - 5.8839639087423015777e-845j)  +/-  (5.2e-89, 7.4e-205j)
| (0.067544611719411396522 - 3.8572889029028002936e-845j)  +/-  (3.85e-89, 5.43e-205j)
| (0.076810232901186924229 + 8.8976060468901370394e-845j)  +/-  (6.34e-89, 9.07e-205j)
| (0.074339410792714510576 + 2.7134468011928041919e-845j)  +/-  (2.43e-89, 3.28e-205j)
