Starting with polynomial:
P : -t+1
Extension levels are: 1 3 5 8
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Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P3 : -t^9 + 8913807221/174577516*t^8 - 346896933499/349155032*t^7 + 3329250396937/349155032*t^6 - 8538378231899/174577516*t^5 + 23551735187795/174577516*t^4 - 8100489458905/43644379*t^3 + 4370729197935/43644379*t^2 - 409117906830/43644379*t + 10559938470/43644379
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^17 + 4055728404665695424150487561567307142216787970984648823381029355868705734035089732022630232176040887498454045/22709335132155034484118668651120753194103624874639864020081080858438417419937945649224645053704691414629068*t^16 - 5688866074094752280267338940098663660790819613465234215237715766660440197885571792207812059490080626537016056427/408768032378790620714136035720173557493865247743517552361459455451891513558883021686043610966684445463323224*t^15 + 255919100446266938142570773553880797674174456892674998597358321356709535724438239787320949447559368552783095555161/408768032378790620714136035720173557493865247743517552361459455451891513558883021686043610966684445463323224*t^14 - 18529484131849208343760341877469877401181405099240277421653034058987004372305726895886452476474984364242385599576551/1021920080946976551785340089300433893734663119358793880903648638629728783897207554215109027416711113658308060*t^13 + 364843177542174149936486226609141022324672886155479999078451733696636771350674596168338303986241381653214606321824863/1021920080946976551785340089300433893734663119358793880903648638629728783897207554215109027416711113658308060*t^12 - 1257174777551570460991936002612553468472242662190117346012167935491753108861228654358525430961976720186670431681536897/255480020236744137946335022325108473433665779839698470225912159657432195974301888553777256854177778414577015*t^11 + 12306961944008063562008663678168343157400707493571617287246550940593594387619247244531763770152461949034627831360005511/255480020236744137946335022325108473433665779839698470225912159657432195974301888553777256854177778414577015*t^10 - 429658067732297683320900137369458174198152228401050665151644983908998463544044271101420909089141890875313658970382844182/1277400101183720689731675111625542367168328899198492351129560798287160979871509442768886284270888892072885075*t^9 + 710117866607899456498586515820313798632003793141004287075021981871419654778211005307561830000734013120439690532921528634/425800033727906896577225037208514122389442966399497450376520266095720326623836480922962094756962964024295025*t^8 - 34745997503847953580804614205740930887511845013922026104271656256503750412436177284635721300040813644327730184478076368/5997183573632491501087676580401607357597788259147851413753806564728455304561077196098057672633281183440775*t^7 + 5858008830425210844774090709437497058460095171009406513419406311675347317679079229625471299416468139491856283349871395344/425800033727906896577225037208514122389442966399497450376520266095720326623836480922962094756962964024295025*t^6 - 26910723250350475194329209692752613819083672124731624241051314953370990674591416918123741401709321662906102464686541984/1256047297132468721466740522738979712063253588199107523234573056329558485616036816881894084828799303906475*t^5 + 580142538900482676931400185802351301109289048536284724503859134427977324034871942058660419681450220623238061525841553952/28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335*t^4 - 301986809178225440647035215715629848371277238424653124780569317893711054336461775258856310560074285157009792191944277632/28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335*t^3 + 70113216786054456482631848857422110478206650757427966612277105625214178595056617474836868121826747174262689405013688704/28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335*t^2 - 5311909685178429765874471191030228972891439995192303057700448015734783784176958450212800420411155763237402306280173312/28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335*t + 125149408280716053669664082388714207750132682858323070354983233838598204160979121959126156368713885473805575792292608/28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335
-------------------------------------------------
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:
| (39.346590167737391166 + 1.0095290225426202575e-258j)  +/-  (2.58e-121, 2.58e-121j)
| (30.611856661971518448 + 3.9386057589486348088e-258j)  +/-  (1.58e-120, 1.58e-120j)
| (19.12622188851013496 + 3.4559123503856843818e-256j)  +/-  (1.23e-119, 1.23e-119j)
| (15.159617414162606815 + 2.4311217283265445574e-259j)  +/-  (1.87e-119, 1.87e-119j)
| (24.18865083900516942 - 1.6542117105043076071e-264j)  +/-  (5.3e-120, 5.3e-120j)
| (7.8232631436879996743 - 8.6959696388476509454e-268j)  +/-  (5.12e-120, 5.12e-120j)
| (3.7068293223182415456 + 4.0256694093291783554e-283j)  +/-  (9.88e-120, 9.88e-120j)
| (0.052485028214125533477 - 6.8793567784365922905e-296j)  +/-  (4.83e-126, 4.83e-126j)
| (12.438835636362665227 - 1.5118328938176281e-311j)  +/-  (2.07e-119, 2.07e-119j)
| (3.369839231310923141 - 2.9589547462930913939e-332j)  +/-  (1.19e-119, 1.19e-119j)
| (1 + 4.6791224763103780546e-344j)  +/-  (4.29e-124, 4.29e-124j)
| (0.36331649980077032239 + 5.9551263677564680728e-346j)  +/-  (1.3e-125, 1.3e-125j)
| (0.056897625001077184683 - 8.5590542646760468701e-346j)  +/-  (6.2e-126, 6.2e-126j)
| (10.266215947476093795 + 2.6668864031138271332e-346j)  +/-  (1.36e-119, 1.36e-119j)
| (5.6343288036648703018 + 2.222962375798213508e-354j)  +/-  (2.29e-120, 2.29e-120j)
| (1.9631203948605024828 - 2.467641122702736987e-362j)  +/-  (1.35e-122, 1.35e-122j)
| (3.4849364779110753601 - 2.5157064114853866399e-371j)  +/-  (2.15e-119, 2.15e-119j)
-------------------------------------------------
The weights are:
| (8.7291801619510040529e-17 - 6.0566667172317098984e-271j)  +/-  (3.14e-55, 4.64e-114j)
| (3.7138738300680006931e-13 + 2.2689153663370139287e-268j)  +/-  (1.31e-53, 1.94e-112j)
| (2.2254444131775272314e-08 - 6.208127178673374397e-264j)  +/-  (2.96e-51, 4.37e-110j)
| (8.8390190893520724741e-07 + 5.303295158236530199e-263j)  +/-  (2.53e-50, 3.74e-109j)
| (1.769994928218651495e-10 - 3.6967816370659797967e-266j)  +/-  (1.02e-52, 1.51e-111j)
| (0.00095252682348712439975 - 6.7064933600035281114e-261j)  +/-  (3.01e-48, 4.45e-107j)
| (0.16020407634293170772 - 6.8281319897530699753e-258j)  +/-  (1.18e-45, 1.74e-104j)
| (-0.03473770537790141171 + 2.8924536487174864625e-257j)  +/-  (5.31e-42, 7.86e-101j)
| (8.5191881024867276728e-06 - 3.4752924690200280793e-262j)  +/-  (3.46e-50, 5.12e-109j)
| (0.37012265990971641643 - 1.6229925071949781928e-257j)  +/-  (8.67e-46, 1.28e-104j)
| (0.29682656896403943815 - 7.2839498619937275541e-259j)  +/-  (1.83e-44, 2.7e-103j)
| (0.32387551151613136791 + 1.2469935334487681283e-258j)  +/-  (1.12e-43, 1.66e-102j)
| (0.18452632697970582311 - 2.9759112042022606298e-257j)  +/-  (5.18e-42, 7.66e-101j)
| (8.2850435012431331261e-05 + 1.3769783140925421585e-261j)  +/-  (6.39e-50, 9.45e-109j)
| (0.0070460233210504642657 + 5.3352515706082707303e-260j)  +/-  (2.25e-48, 3.33e-107j)
| (0.15499308785516822756 + 7.2015414692866333582e-259j)  +/-  (4.02e-47, 6.01e-106j)
| (-0.46390135229116811037 + 2.2606157662876391958e-257j)  +/-  (7e-46, 1.03e-104j)
