Starting with polynomial:
P : -t+1
Extension levels are: 1 5 21
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 2178210190657888968032606354325612194224486704314262919444825619290036991465106609625663407543280877317743808349/3649874640193201785901397492262578430773141231849664098068171807573074184576812003754097107266001032496025080*t^26 - 2399318814465907203184766722124249106694462837418849889445565381317149911157153478557093630145858086600214509957371/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^25 + 1377970002347067519129460578657862056320764518832994213986228436644947003395701402144488575495623344911368598766037779/49638295106627544288259005894771066658514720753155431733727136582993808910244643251055720658817614041945941088*t^24 - 40027704506181496633387848371479919398721450707257584549979409750977498186345584282785669915881292518195420289746801079/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^23 + 3400877396383378683687840138766918059922471997164841509018417246003642013129948142699313484283721114110730503788773283383/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^22 - 257978638697711635991149297997887870163763652987769652793112970274155044662581810615249306295964381800492817716544281927637/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^21 + 31408153298737883128080027969345908234436930208248337956204408211055282134246603699680423248933834222336142286552032781639467/35455925076162531634470718496265047613224800537968165524090811844995577793031888036468371899155438601389957920*t^20 - 31108651920226059434206596143685904584229481990948526392195834623341576373810426674976053266843720225440849035660029941191915/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^19 + 984892004920230191288759431217908130074527377404649622794246649489966368328044119346025215836280914139187255464471943646137465/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^18 - 25100816179519702088416347275508680429259560202110764809194516622595424476143610870902964070933583262875809624870727665830730085/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^17 + 30426766050018701323590379069720660921352113383038022724663817846139245285683677226000459632497406125027530036981747824974291073/52141066288474311227162821318036834725330589026423772829545311536758202636811600053629958675228586178514644*t^16 - 127004518372453027409960426477464965205366137734841974113050439474560511740804337815264686670723991466046370644534913678590257952/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^15 + 1717980223524146166672631380480480833123805114890020466710119873432349875608709268573167253192234303765584657692380365490279452000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^14 - 18788082012686348916360546586531854995020497133397669735685776272565598982913244571328442204789394046053551651831413811023795662800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^13 + 165423062979395149280025282295207138173568040861715918572022190752674565192906739947626861705932142242814561038513465215967029128400/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^12 - 1165049325848380523072683413213874162336760509310407022880879443915515898187994726961624664072355206699474495708938241293267631473280/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^11 + 6503447173233608940969685132746028761205632055208055013874032679664531794577329107611586390814757601533568462214074502144327255287680/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^10 - 28416559411501982712907621526925490492441097529614917756353909019224836453799244762796553502104931470509872726931178773578585848528000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^9 + 95577512151735491221181768429735954141574330767227459114813120289580707823285064092536303332790663776785754568196889000082957047824000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^8 - 241963468300567426418555235033867842669565713064139031823889596302106776506204075575451765151853247653788672968046360896615106472960000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^7 + 447262994941184232064911781320080038014072146711467496885094071524014461226712638183607974106612235240422901292653926577438693260492800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^6 - 578884227369599812286816174306864481684736271540943236661021749681007611840781985763953777148696899241937193672637920665718593370444800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^5 + 494221834857096704327692771815708748704342425528190034262174021262361139543307425643644810876267319342144151150338613252239236196480000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^4 - 254594066881147203788504136414773353349324510057564266662008500006176046965883383488840661911264810594536171951999832980938789196800000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^3 + 68540601908648547607492270048404751367032373215496720092263568519665573079962358503130482126575700940294758300401441950390024903680000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^2 - 7399650104028392804493461920183108791804995906252665052938739325766838499893834363208452439021508171450506367689409206248957082624000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t + 168397152523344985552981175571817058735962772517332133926818458618569313685043912927272957029562498643606517043043414848143412224000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661
-------------------------------------------------
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:
| (81.758272620557439426 - 7.5971416902665053772e-618j)  +/-  (1.35e-245, 1.35e-245j)
| (41.702475816401903131 - 1.2447863498090322731e-631j)  +/-  (1.96e-242, 1.96e-242j)
| (53.863789941001503625 + 6.9930992421763989928e-646j)  +/-  (4.51e-243, 4.51e-243j)
| (61.315498845095898385 + 1.6332159497239482584e-654j)  +/-  (1.24e-243, 1.24e-243j)
| (70.220763808677381738 - 5.5543050023084481194e-661j)  +/-  (1.99e-244, 1.99e-244j)
| (27.875300703054140104 - 1.3942481592157084494e-668j)  +/-  (2.9e-242, 2.9e-242j)
| (9.6472039903820062647 + 1.2586220900422261863e-681j)  +/-  (9.29e-243, 9.29e-243j)
| (47.406285883137051671 - 3.8237645677317920622e-693j)  +/-  (1.05e-242, 1.05e-242j)
| (14.829781217182764814 + 7.031301130620396649e-703j)  +/-  (5.84e-243, 5.84e-243j)
| (3.7106727988049865883 - 9.9037856536364281256e-716j)  +/-  (5.65e-247, 5.65e-247j)
| (2.5922508199253002476 - 1.6551916674329381459e-716j)  +/-  (2.57e-248, 2.57e-248j)
| (6.3723887517103681048 + 9.6405174095664071276e-711j)  +/-  (3.35e-244, 3.35e-244j)
| (12.280442143495462283 - 4.9067952531723662203e-724j)  +/-  (3.64e-243, 3.64e-243j)
| (36.606207571068375664 + 4.2920012553933283012e-742j)  +/-  (2.46e-242, 2.46e-242j)
| (20.715543912488348487 - 5.0222420543538997295e-763j)  +/-  (1.7e-242, 1.7e-242j)
| (1.6939361362181727213 + 1.1110722126870337551e-780j)  +/-  (1.41e-249, 1.41e-249j)
| (5.8324682943749641353 - 2.0332219612126828962e-780j)  +/-  (1.98e-244, 1.98e-244j)
| (24.120346779241774903 + 1.6307938961501327086e-798j)  +/-  (2.27e-242, 2.27e-242j)
| (32.020153328655959273 + 7.8736966009766319819e-814j)  +/-  (2.81e-242, 2.81e-242j)
| (17.628498948620865358 + 6.1362043277402920277e-821j)  +/-  (1.19e-242, 1.19e-242j)
| (0.18296039898248679851 + 5.8159672290598535849e-843j)  +/-  (1.46e-253, 1.46e-253j)
| (1 + 2.6578506109039533851e-841j)  +/-  (6.95e-251, 6.95e-251j)
| (8.7933122894963895877 - 5.7767735862691692418e-831j)  +/-  (2.58e-242, 2.58e-242j)
| (0.030411585988768041294 + 3.8438574544329401008e-860j)  +/-  (4.44e-255, 4.44e-255j)
| (8.9529512477548957267 + 4.2563408654290422789e-846j)  +/-  (3.31e-242, 3.31e-242j)
| (5.1384848875831238418 - 1.3149336693188719369e-855j)  +/-  (3.52e-245, 3.52e-245j)
| (0.50000938657902876657 - 8.282786065169783396e-871j)  +/-  (3.73e-252, 3.73e-252j)
-------------------------------------------------
The weights are:
| (4.2993715540367822667e-35 + 1.7406068342254916471e-652j)  +/-  (6.77e-102, 1.22e-221j)
| (4.165645275164949785e-18 - 1.6570907529982890224e-644j)  +/-  (7.95e-95, 1.43e-214j)
| (2.7943261665283532671e-23 - 2.965356292036343968e-647j)  +/-  (1.07e-97, 1.93e-217j)
| (1.8966058504529597507e-26 + 7.3490548247811706506e-649j)  +/-  (2.6e-99, 4.67e-219j)
| (3.1574231729499774024e-30 - 1.1581030095146290478e-650j)  +/-  (5.1e-101, 9.16e-221j)
| (3.0880170634371103298e-12 + 3.6238184523335490994e-641j)  +/-  (1.05e-93, 1.89e-213j)
| (0.00033591381766328808655 + 1.0202886167565360199e-634j)  +/-  (1.04e-85, 1.87e-205j)
| (1.5613925226765264138e-20 + 8.170901789606855113e-646j)  +/-  (3.53e-97, 6.35e-217j)
| (9.6658858482006842516e-07 + 1.7461030212980280076e-637j)  +/-  (1.96e-89, 3.52e-209j)
| (0.030307376260019683444 + 2.0864276804438204376e-634j)  +/-  (3.92e-80, 7.04e-200j)
| (0.075202604823931289478 - 1.9338989590554476897e-634j)  +/-  (6.11e-78, 1.1e-197j)
| (0.0041077788332558781899 - 5.2428925285830096281e-634j)  +/-  (4.61e-84, 8.3e-204j)
| (1.1373752157389714187e-05 - 1.5785064799022694505e-636j)  +/-  (2.42e-88, 4.35e-208j)
| (6.1076180459918575007e-16 + 2.6163331719472446011e-643j)  +/-  (1.63e-96, 2.92e-216j)
| (3.2660731912295841056e-09 + 2.8554999239185320997e-639j)  +/-  (3.64e-93, 6.55e-213j)
| (0.14597854819688294408 + 2.0214357686631295457e-634j)  +/-  (1.72e-81, 3.09e-201j)
| (-0.0036058565098863356461 + 8.8115436856169302504e-634j)  +/-  (6.81e-86, 1.22e-205j)
| (1.1962445620358105649e-10 - 3.3971025397288112135e-640j)  +/-  (3.06e-94, 5.51e-214j)
| (5.4060540300568519695e-14 - 3.3566219811388915513e-642j)  +/-  (3.03e-96, 5.45e-216j)
| (6.4875214207564865086e-08 - 2.2393362217144879395e-638j)  +/-  (1.37e-92, 2.47e-212j)
| (0.19186790898989323021 - 1.4845640567670796158e-634j)  +/-  (4.52e-87, 8.13e-207j)
| (0.21899799665867761512 - 2.0937276786003088726e-634j)  +/-  (3.73e-87, 6.71e-207j)
| (0.0025597858978449769949 + 8.5000709099810859581e-634j)  +/-  (9.99e-90, 1.8e-209j)
| (0.07924257347660313877 + 5.6054674913062851057e-635j)  +/-  (4.77e-89, 8.56e-209j)
| (-0.0023771678158465292315 - 8.9625281446976100555e-634j)  +/-  (1.04e-89, 1.86e-209j)
| (0.010854814580937159548 - 5.2448423819474944708e-634j)  +/-  (9.21e-90, 1.66e-209j)
| (0.24651531418522690363 + 1.9763777452878851491e-634j)  +/-  (1.32e-89, 2.35e-209j)
