Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 7 26
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : 3/2*t^13 - 11979409/2770390*t^11 + 54031549/11635638*t^9 - 751494029/329676410*t^7 + 11821062/23548315*t^5 - 193274/4709663*t^3 + 52009/70644945*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^39 - 261320498117384211209882265410982701049964830239178247807785568281463485027970378683875059143885643374353550607407991635449183708321/18044390914018788019132510443726087062913465438125839408959758961352123300937300267114588906221936468191974689488539745293616960410*t^37 + 4366114293470662809845254487561267987586265379134595262879814520033722456004353375694093621707419998464070554335598264863817102430713/67808921645312708661371644509581190331159022751693943884196146833712715983522275740630613047591908622574052254183249358629697419646*t^35 - 77559792471343817364948666271183667429499238230864715106164329121343458463417870914930728503089596967122512216830425373353148539564617/443720860897245118686788286024234843061822909215035462204015079097633444988982761976235382606037057731705140470204883950635461136930*t^33 + 14660419536458296824622483246860650605025599162213156187892667997148990081873866367769921667512066476779175308954533084425451227769093544439/45264408740988871802357959845618220575579616791934982534893782233828685356771120531957747615024446296268973084506070416688274026039366230*t^31 - 1268493501650854426547578830284564568118772227546651405115623920117988093734965671071223274216579941154395919667901965429937535802801973990729/2924080804667881118432324206026937049182443244758999871754138332305333074047414386364470495930579230738975661259092148918062502082143058458*t^29 + 19031993006565027424225255037425504321356643660228789168820787746598433450941780653853135606614326038309410084576719878303347490927452370827459/43861212070018216776484863090404055737736648671384998076312074984579996110711215795467057438958688461084634918886382233770937531232145876870*t^27 - 3936664034574513034298665038780015880969085808296166005316775504796004040262502095409774139339671488662345031241174184898303420714771109798453/11921252511338284559762552532263666431282268613248230246382256277860204071116381729024379714178515325320439234363991068665947123873352469098*t^25 + 39122053481392456500359101647652170874967049906172032303085921460952258127153232165495308702086644800090636390338899654175095009612459370331371/202661292692750837515963393048482329331798566425219914188498356723623469208978489393414455141034760530447466984187848167321101105846991974666*t^23 - 14629578194631454949640766200826694613081031371427861386193302681031659280106537723593511181868171322265500995584321061819742960455339723437717/168311921049911712513257733209756510800985250081962301614176601346738135444744847123344208506961072304947896308901772206758202613330552656926*t^21 + 42631912566222312462753530173332466808975375152914544385989692864528709181303228056223553618195436316082575153615482277000077789220224959730905/1418629048849255862611743751339376305322589964976539399319488497065364284462849425753901185987243323713132268889314937171247707740928943822662*t^19 - 590549818376772126334646925224474673059853468899461515088112526449317147173763513896608166047440757230781835691387950627132167938513364283463/74664686781539782242723355333651384490662629735607336806288868266598120234886811881784272946697017037533277309963944061644616196890997043298*t^17 + 294934638626935025886741210221882122805501161640565113696982476904926514034116328636828941715071061976402917034407373075663349862973328466845/188857737153306508025712016432177031358734886978300910745318902086101127652948994759807278629880690153760642607555858508865793909783110168342*t^15 - 82376002020860768742199616610829721901656923323003707212501486522486251699917030263429175929557597679266892233233933529377270534492765582822643/363928859494421640965547055664805139428282127207185855006229524319916872987232712902148625919780089926296758304760139346584384864152053294395034*t^13 + 110469530535142604423913419589190748552272318692366733261873271051955330521836552159726596320522961997957872047540322619297098041235586461518403/4731075173427481332552111723642466812567667653693416115080983816158919348834025267727932136957141169041857857961881811505597003233976692827135442*t^11 - 7760185870119468383948540917487745516190870261014046081871649037539347088014493001038998525788830208355800522463613458964711376831650307682995/4731075173427481332552111723642466812567667653693416115080983816158919348834025267727932136957141169041857857961881811505597003233976692827135442*t^9 + 93629316510795026445161275371348229917899271176303406190887941733689445388154570881929831782278808535419681295609119470891697035796527221411/1273751008230475743379414694826817987998987445225150492521803335119709055455314495157520190719230314742038654066660487713045347024532186530382619*t^7 - 4479503087689132067436024481931334094279467337129653992655174041430094032159797615601441236028175297090119421692755187928591664318317579290/2365537586713740666276055861821233406283833826846708057540491908079459674417012633863966068478570584520928928980940905752798501616988346413567721*t^5 + 27289317923426200604215683602663089267434617034760444650701363672217391241714521003216152442657035710318530726290304538092960710089853/1177470177557859963303163694286328226124357305548386290463161726271508050979100365288186196355684711060691353400169689274663266110994697069969*t^3 - 4711928198537453398317226681160654819769376583978417385499121783181259411387168784560089191430746918572362750474754664881396243039278/55012502016598620145954787484214730378693809926667629245127718792545573823651456601487582987873734523742533232114904784948802363185775497989947*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:
| (0.98475192553972407787 + 7.6387849643918022495e-851j)  +/-  (1.03e-241, 1.03e-241j)
| (-0.9679248644390362874 + 6.6866318238149820306e-854j)  +/-  (6.44e-242, 6.44e-242j)
| (-0.91248695683407599658 - 2.9149518668099063748e-873j)  +/-  (1.16e-242, 1.16e-242j)
| (-0.99977988521658691113 + 4.2832553271008853931e-901j)  +/-  (5.26e-242, 5.26e-242j)
| (0.91248695683407599658 - 1.2192476115948142016e-921j)  +/-  (1.05e-242, 1.05e-242j)
| (0.94400339045914642512 + 2.7458505094124246649e-921j)  +/-  (3.05e-242, 3.05e-242j)
| (-0.98475192553972407787 + 9.146400869299748171e-929j)  +/-  (1.06e-241, 1.06e-241j)
| (-0.87334489891384996108 - 9.9300303576925814302e-940j)  +/-  (3.8e-243, 3.8e-243j)
| (0.99525911341032138914 - 1.4798788941146893054e-939j)  +/-  (1.07e-241, 1.07e-241j)
| (-0.99525911341032138914 + 3.5099643183606588225e-944j)  +/-  (1.1e-241, 1.1e-241j)
| (0.87334489891384996108 - 7.4256244750373668684e-959j)  +/-  (3.55e-243, 3.55e-243j)
| (0.99977988521658691113 + 8.8037061084575649913e-958j)  +/-  (5.31e-242, 5.31e-242j)
| (-0.94400339045914642512 - 6.4209738070259041761e-960j)  +/-  (3.1e-242, 3.1e-242j)
| (-0.77338516233180687365 - 1.6685428552506175448e-970j)  +/-  (1.74e-244, 1.74e-244j)
| (0.9679248644390362874 + 6.7933581593398421561e-972j)  +/-  (6.29e-242, 6.29e-242j)
| (0.82683737873288324971 + 4.4125026075354971347e-977j)  +/-  (9.03e-244, 9.03e-244j)
| (0.77338516233180687365 + 6.6304323792814908639e-977j)  +/-  (1.91e-244, 1.91e-244j)
| (-0.35268668944600305388 - 1.5561395664189149403e-981j)  +/-  (6.97e-250, 6.97e-250j)
| (-0.82683737873288324971 + 9.1646915648459288623e-977j)  +/-  (8.63e-244, 8.63e-244j)
| (-0.29071164807792222361 + 2.2723583230725902461e-989j)  +/-  (1.05e-250, 1.05e-250j)
| (0.42655044341779478524 - 7.2227175097354596817e-986j)  +/-  (6.19e-249, 6.19e-249j)
| (0.71352491030123838397 - 3.5097553640804578936e-983j)  +/-  (3.07e-245, 3.07e-245j)
| (0.078231966853946646155 + 2.4972170478537071469e-991j)  +/-  (2.02e-254, 2.02e-254j)
| (-0.71352491030123838397 - 2.6402648227591287445e-985j)  +/-  (3.12e-245, 3.12e-245j)
| (-0.57735026918962576451 - 5.64910324943171102e-986j)  +/-  (5.1e-247, 5.1e-247j)
| (-3.75532284390813572e-996 - 8.5870774399208088828e-995j)  +/-  (3.35e-993, 3.35e-993j)
| (0.6479098243965518494 - 1.7289213216777516912e-985j)  +/-  (4.45e-246, 4.45e-246j)
| (0.35268668944600305388 - 1.2601064112871699651e-990j)  +/-  (6.77e-250, 6.77e-250j)
| (-0.23032784208368240043 + 1.8920076291363172608e-992j)  +/-  (1.08e-251, 1.08e-251j)
| (-0.6479098243965518494 + 1.3648202847024233466e-987j)  +/-  (4.72e-246, 4.72e-246j)
| (-0.15655801081562154215 - 1.1397737095039096861e-996j)  +/-  (4.86e-253, 4.86e-253j)
| (0.29071164807792222361 - 3.1670507367664392959e-992j)  +/-  (1.19e-250, 1.19e-250j)
| (0.50294564930174198008 - 6.526755312010318528e-987j)  +/-  (6.09e-248, 6.09e-248j)
| (-0.078231966853946646155 - 5.0934074073860155535e-996j)  +/-  (2.02e-254, 2.02e-254j)
| (-0.50294564930174198008 + 4.1708948736680607031e-989j)  +/-  (6.12e-248, 6.12e-248j)
| (-0.42655044341779478524 + 6.2853691424518666043e-991j)  +/-  (6.13e-249, 6.13e-249j)
| (0.15655801081562154215 - 2.8177942628455067641e-994j)  +/-  (5.41e-253, 5.41e-253j)
| (0.57735026918962576451 + 6.7755301889131163588e-989j)  +/-  (5.45e-247, 5.45e-247j)
| (0.23032784208368240043 + 4.0327893984966904093e-994j)  +/-  (1.02e-251, 1.02e-251j)
-------------------------------------------------
The weights are:
| (0.013551540869912373033 + 1.147940355866108282e-851j)  +/-  (3.54e-77, 4.45e-194j)
| (0.020248570313975096334 + 5.2007143839875989713e-853j)  +/-  (1.73e-77, 2.18e-194j)
| (0.035354608317443996377 + 4.8849636815356660573e-853j)  +/-  (8.95e-78, 1.12e-194j)
| (0.0014747059402083718307 - 1.6439990568543498875e-853j)  +/-  (3.73e-78, 4.68e-195j)
| (0.035354608317443996377 + 1.2280891117320669489e-851j)  +/-  (2.52e-79, 3.16e-196j)
| (0.027679350233292072554 - 2.3769439250032774262e-851j)  +/-  (2.97e-79, 3.73e-196j)
| (0.013551540869912373033 - 4.4587277659818979062e-853j)  +/-  (2.27e-78, 2.85e-195j)
| (0.042884074470142297766 - 4.6320908875940400559e-853j)  +/-  (5.96e-80, 7.48e-197j)
| (0.0075193132856541143811 - 8.1177570671763543089e-851j)  +/-  (5.01e-80, 6.28e-197j)
| (0.0075193132856541143811 + 3.9034106488278678969e-853j)  +/-  (2.41e-78, 3.02e-195j)
| (0.042884074470142297766 - 7.5343834083431840056e-852j)  +/-  (2.82e-81, 3.54e-198j)
| (0.0014747059402083718307 + 2.3616569427343553434e-851j)  +/-  (2.22e-80, 2.79e-197j)
| (0.027679350233292072554 - 5.5463290084414813418e-853j)  +/-  (2.97e-80, 3.73e-197j)
| (0.056754808229849694576 - 5.0901224877350023935e-853j)  +/-  (2.79e-83, 3.5e-200j)
| (0.020248570313975096334 + 6.2085667315565517589e-851j)  +/-  (1.75e-80, 2.19e-197j)
| (0.050060205100692493774 + 5.2935771444546832452e-852j)  +/-  (9.73e-83, 1.22e-199j)
| (0.056754808229849694576 - 4.1855780902559001638e-852j)  +/-  (1.13e-83, 1.42e-200j)
| (0.069466858038018593047 - 5.8932291933016616056e-852j)  +/-  (2.31e-86, 2.9e-203j)
| (0.050060205100692493774 + 4.6906142510207423722e-853j)  +/-  (1.22e-83, 1.54e-200j)
| (0.056165199753945519992 + 9.4976452310042560825e-852j)  +/-  (1.42e-86, 1.79e-203j)
| (0.076312818123355475955 + 7.3835315945556507183e-852j)  +/-  (1.23e-87, 1.54e-204j)
| (0.062857415743575704153 + 3.6927750564246801179e-852j)  +/-  (9.65e-86, 1.21e-202j)
| (0.078514323639099877515 - 1.0818702264497426904e-851j)  +/-  (2.46e-88, 3.09e-205j)
| (0.062857415743575704153 + 5.9474079753562838799e-853j)  +/-  (1.09e-86, 1.36e-203j)
| (0.072702286387918522358 + 1.0488318641193594663e-852j)  +/-  (9.42e-88, 1.18e-204j)
| (0.078044021388912259597 + 9.8306226090122682732e-852j)  +/-  (1.02e-88, 1.28e-205j)
| (0.068239500912566153793 - 3.6303732208623679211e-852j)  +/-  (2.53e-88, 3.17e-205j)
| (0.069466858038018593047 - 1.2442646398457737175e-851j)  +/-  (3e-89, 3.76e-206j)
| (0.067924872701730190661 - 1.0313666760178454231e-851j)  +/-  (4.95e-89, 6.22e-206j)
| (0.068239500912566153793 - 7.5374806593554049852e-853j)  +/-  (9.24e-89, 1.16e-205j)
| (0.077445846804564496164 + 9.3024038323608184747e-852j)  +/-  (1.47e-89, 1.84e-206j)
| (0.056165199753945519992 + 1.7424118166043674511e-851j)  +/-  (1.37e-90, 1.72e-207j)
| (0.075821690439598825937 - 5.0275558207379109447e-852j)  +/-  (9.63e-91, 1.21e-207j)
| (0.078514323639099877515 - 9.2301841453178947575e-852j)  +/-  (3.24e-90, 4.06e-207j)
| (0.075821690439598825937 - 1.6342837948168323729e-852j)  +/-  (5.48e-91, 6.88e-208j)
| (0.076312818123355475955 + 2.9286981622725072983e-852j)  +/-  (6.22e-91, 7.81e-208j)
| (0.077445846804564496164 + 1.2808258618735292705e-851j)  +/-  (1.38e-91, 1.73e-208j)
| (0.072702286387918522358 + 4.0021705765988476937e-852j)  +/-  (1.75e-92, 2.1e-209j)
| (0.067924872701730190661 - 1.6589387363383772747e-851j)  +/-  (1.04e-91, 1.31e-208j)
