Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 15 18
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 231/16*t^21 - 5205313449/70709920*t^19 + 14289790791591/89448048800*t^17 - 53308908835107/277288951280*t^15 + 1126298183287221/8041379587120*t^13 - 254450630417893/4020689793560*t^11 + 11958624144649/685344851175*t^9 - 1164763374231093/420344842054000*t^7 + 9423837253467/42034484205400*t^5 - 1187724569941/168137936821600*t^3 + 6211503831/168137936821600*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^39 - 24496586214174993567851145436125155971772239835478244157426998582068770065852489562642896290205459487749608124248629756719828191785903587299/175007105223931352823140275107280929569576929939423063330345368250307904899118918234120869830508749429967763260496416956084013758525821920*t^37 + 138662962222555709255326220965514074108863769176811007051806071455395520919210934886626971224619781122097605605930772998936295075796171800262041/221383988108273161321272448010710375905514816373370175112886890836639499697385431566162900335593568028909220524527967449446277404535164728800*t^35 - 14530677660712633415314512303569715582645212089463481876196564615176247526993070105117184436471712298956974014863564659165372117077440270280048909713/8469509371457017159984052170790547922054870881477660126311225071426401003872844193969850694428836691438782940528918903510211179293042250546174480*t^33 + 1670500775076647548537524408928182090621963485170766005233801652528022398635856736701812674552236038788763557689328007114230097580671194764200588303/519272244761635301563504255714431056531905402881294172649102594231216974867468248678912621857159120616754133774500313323036203381603013247017040*t^31 - 904388497994778644453281014343136064018070275627924939821836313472973302482108461811349910388840052968171346435824404362371476620517871780705165774903/206720605567849717954684065153928828021298212159937141440728229529272538285142763127305182785135506694560089190680915055470638255882670531659267440*t^29 + 963803191702209405579932879608539890734881044434087843739839666628412937170593529204463171808046367520355292284043851162397834253260960601616987105984137/216094315785840144820560256384184566257436389711327394578471595799306793038417340144974366073495961567089279441913515169192841335416660591974161808400*t^27 - 8260679670089790151208247935406916071859820415148923539118128775505997914323292046022053467346578606791166056040375719465058922256610092289969488596109226113/2377397630837217993267530420653337203108896014140786886020818339785373568077654770494959650751911403840593889326785189386403242758475627612702403495414000*t^25 + 10532408496397920826294233135860618331593329284426831958799483910054036627922150033166865145148196205636981070488083238345231272813743688520967980014496623567/5040082977374902145727164491785074870590859549978468198364134880344991964324628113449314459594052176142059045372784601499174874647968330538929095410277680*t^23 - 1316375714317080782467838780340758720918465921989180624125791982926963315158108127211465226540697820249755637114264463280223488506890394415561680747353175796499/1352166609212688421313455152024339325607865167527919044261125838224729257211526859740825864040221693603677188672729016676115589739795155808280955792570366280*t^21 + 59239360887103990292351265626016277779924529962047323930138871221664913679719022655217507941318324736667800256580675185062818695894616288531368884310175988963/169020826151586052664181894003042415700983145940989880532640729778091157151440857467603233005027711700459648584091127084514448717474394476035119474071295785*t^19 - 261620239503014742525738245935401401638341359574494552933800366931683057053158642887117212066752596973731369678293609832489687734808149468929157449940903948621/2704333218425376842626910304048678651215730335055838088522251676449458514423053719481651728080443387207354377345458033352231179479590311616561911585140732560*t^17 + 1910846044588032796323131139599352366332528781796906840112015747105373466856474598975634003923328364284951096060546148921613455340824445032383357205138812970523/94651662644888189491941860641703752792550561726954333098278808675731048004806880181857810482815518552257403207091031167328091281785660906579666905479925639600*t^15 - 1973399649519199646347085381266785404883081871755944276952953962984293699047891566355694185654899616501115086794712295213491131507274766320213772168139284123/632929051120832878061617305202882237518575184800302531356271668956256248056459381155280191678401643814487194697873156742011552644159434633663426115671235280*t^13 + 318558486627638945594345464188688605304017234452244792360943282877885708067193984718263008940457147757117860715366848375932779550498310125967539079076944620107/922177627483053503335776413680599420064564044254040788186087821669265353418261318343243239275431195037707842674801189373110832202540296261247611850532989802960*t^11 - 63787951269913694758893284454965911260715124487255730179307310578852427629208871813517895074994893073528278249981986476830841988209609529509435323344228386423/2431195563364413781521592363339762107442941571215198441581504257128063204466325293814004903544318605099411585233566771983655830352151690143289158515041518571440*t^9 + 16150272520221603714906366094594029025934490147885137262926711900627255993518713030888026171087993862416813665842297046312365581233463319330013801586928/12657203057915523643906665781652239209927850745601824456380176265764593942452755590451920572388164333087315624914445918282256509538482351849693661573518943*t^7 - 34633295265622256321236134788526823306017686592907326829789906149677005299537819500900191340093760349636886921753843377838896417714173309690428646629821113/972478225345765512608636945335904842977176628486079376632601702851225281786530117525601961417727442039764634093426708793462332140860676057315663406016607428576*t^5 + 10473717932790966092255639767609075956170064122858763919721642832496969695986327400406985686748181452011612287961965159458189649363475404859855965186143217/22366999182952606789998649742725811388475062455179825662549839165578181481090192703088845112607731166914586584148814302249633639239795549318260258338381970857248*t^3 - 71987027336416214611237107336032888497626212851969982541908979488181457645622995717227163761201921511581819894909163165245810759206314654663482188156205/39142248570167061882497637049770169929831359296564694909462218539761817591907837230405478947063529542100526522260425028936858868669642211306955452092168449000184*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:
| (0.93246951420315202781 + 6.4276109639898910713e-845j)  +/-  (3.9e-242, 3.9e-242j)
| (0.9607244911958471624 - 2.4755269542736239785e-866j)  +/-  (8.24e-242, 8.24e-242j)
| (-0.89888808667390635433 - 7.2221221707433380047e-881j)  +/-  (2.01e-242, 2.01e-242j)
| (0.9973240486058117504 + 9.020042505793443568e-888j)  +/-  (1.9e-242, 1.9e-242j)
| (0.86361570851789323889 + 3.1882185771189278097e-913j)  +/-  (9.73e-243, 9.73e-243j)
| (0.97722740884937972953 + 6.2673151560445380778e-927j)  +/-  (1.19e-241, 1.19e-241j)
| (-0.98705236205671016601 - 3.4457623517761616735e-936j)  +/-  (8.88e-242, 8.88e-242j)
| (-0.93246951420315202781 + 2.3500193648828259226e-938j)  +/-  (4.15e-242, 4.15e-242j)
| (-0.9973240486058117504 + 6.5020889633114053479e-938j)  +/-  (1.75e-242, 1.75e-242j)
| (-0.97722740884937972953 - 1.0825196526163142124e-939j)  +/-  (1.29e-241, 1.29e-241j)
| (0.89888808667390635433 - 3.3577533995473175038e-942j)  +/-  (1.96e-242, 1.96e-242j)
| (-0.31622805000534114366 - 4.687555459728008635e-959j)  +/-  (1.53e-250, 1.53e-250j)
| (-0.86361570851789323889 + 1.271494728709303699e-950j)  +/-  (8.58e-243, 8.58e-243j)
| (-0.71780444508126923918 + 8.6352398070814679626e-954j)  +/-  (1.34e-244, 1.34e-244j)
| (0.98705236205671016601 - 1.1269763346868721383e-952j)  +/-  (8.66e-242, 8.66e-242j)
| (0.7724087312063641925 + 1.1319391697656040172e-961j)  +/-  (6.52e-244, 6.52e-244j)
| (0.82236194656462557885 - 3.4268765598844955147e-960j)  +/-  (2.79e-243, 2.79e-243j)
| (-0.080302367445227604052 + 2.5802241267774702021e-971j)  +/-  (2.02e-254, 2.02e-254j)
| (-0.7724087312063641925 + 1.2910639384314125871e-964j)  +/-  (6.69e-244, 6.69e-244j)
| (-0.9607244911958471624 + 1.6386718414447245295e-965j)  +/-  (8.48e-242, 8.48e-242j)
| (0.4625954259989831815 + 4.0337781968087182898e-975j)  +/-  (2.89e-248, 2.89e-248j)
| (0.71780444508126923918 + 2.822261643269581273e-970j)  +/-  (1.33e-244, 1.33e-244j)
| (-0.23861918608319690863 - 5.0761363558331691794e-978j)  +/-  (8.05e-252, 8.05e-252j)
| (-0.39081014757983207619 - 8.0712454526643313589e-977j)  +/-  (2.38e-249, 2.38e-249j)
| (-0.53290119180335118279 + 3.8678980425004188033e-974j)  +/-  (3.46e-247, 3.46e-247j)
| (0.080302367445227604052 - 4.4660691602481936893e-977j)  +/-  (2.02e-254, 2.02e-254j)
| (0.66120938646626451366 - 2.2400546378187506932e-972j)  +/-  (2.22e-245, 2.22e-245j)
| (0.39081014757983207619 - 2.7348196222519748178e-976j)  +/-  (2.36e-249, 2.36e-249j)
| (-0.82236194656462557885 + 3.1551829168656805785e-973j)  +/-  (2.66e-243, 2.66e-243j)
| (-0.66120938646626451366 + 2.9860738827963752126e-977j)  +/-  (2.2e-245, 2.2e-245j)
| (-0.15975108160349158022 - 1.997804970175201921e-986j)  +/-  (4.64e-253, 4.64e-253j)
| (0.31622805000534114366 + 4.7830592078245902891e-983j)  +/-  (1.67e-250, 1.67e-250j)
| (0.53290119180335118279 - 7.8267616529859566877e-980j)  +/-  (3.26e-247, 3.26e-247j)
| (8.6119417108116566514e-986 - 6.2350392776354374295e-986j)  +/-  (4.15e-984, 4.15e-984j)
| (-0.60003882698358178303 - 4.6977899649399262581e-980j)  +/-  (3.13e-246, 3.13e-246j)
| (-0.4625954259989831815 - 2.2050558709447745618e-981j)  +/-  (2.79e-248, 2.79e-248j)
| (0.23861918608319690863 + 1.9018497497518401392e-984j)  +/-  (7.79e-252, 7.79e-252j)
| (0.60003882698358178303 + 1.5989821412280592098e-981j)  +/-  (3.09e-246, 3.09e-246j)
| (0.15975108160349158022 - 6.0172768089989609071e-988j)  +/-  (4.28e-253, 4.28e-253j)
-------------------------------------------------
The weights are:
| (0.031793869075564528304 - 1.0374121128300905893e-845j)  +/-  (1.32e-78, 1.76e-195j)
| (0.023769478161012253773 - 6.8059038160980026136e-845j)  +/-  (8.93e-79, 1.19e-195j)
| (0.034539861726500507036 + 1.5279686680434949007e-846j)  +/-  (4.5e-81, 5.99e-198j)
| (0.0067870853270923222025 + 2.382145736702081123e-846j)  +/-  (7.43e-80, 9.89e-197j)
| (0.037012809395722765409 - 5.1061294104413030316e-845j)  +/-  (3.28e-80, 4.36e-197j)
| (0.0093208262258375805316 + 4.1570847034933833307e-845j)  +/-  (3.16e-79, 4.2e-196j)
| (0.012205266059233516521 + 5.1409736329095426249e-847j)  +/-  (3.2e-82, 4.26e-199j)
| (0.031793869075564528304 - 1.0957925076638763477e-846j)  +/-  (3.56e-82, 4.74e-199j)
| (0.0067870853270923222025 - 8.0056725035509947882e-848j)  +/-  (8.02e-83, 1.07e-199j)
| (0.0093208262258375805316 - 9.7430307892517554896e-847j)  +/-  (1.84e-82, 2.45e-199j)
| (0.034539861726500507036 + 8.3327518810404347391e-845j)  +/-  (3.21e-82, 4.27e-199j)
| (0.07632109449526581352 + 4.9946323420889657673e-846j)  +/-  (1.44e-85, 1.92e-202j)
| (0.037012809395722765409 - 1.9574596894554750386e-846j)  +/-  (1.08e-83, 1.43e-200j)
| (0.055582686294827126714 + 2.7383998089376536315e-846j)  +/-  (3.93e-85, 5.24e-202j)
| (0.012205266059233516521 - 1.8079326641440013938e-845j)  +/-  (2.52e-82, 3.35e-199j)
| (0.05307649994292009001 - 2.4645237322585777281e-845j)  +/-  (2.27e-85, 3.03e-202j)
| (0.045998096771354210232 + 3.3898835505266769855e-845j)  +/-  (1.51e-84, 2.02e-201j)
| (0.079895179607914952364 - 6.4657867888975507189e-846j)  +/-  (4.6e-88, 6.12e-205j)
| (0.05307649994292009001 - 2.31379337123701911e-846j)  +/-  (1.97e-86, 2.62e-203j)
| (0.023769478161012253773 + 1.0157472250067517521e-846j)  +/-  (8.12e-85, 1.08e-201j)
| (0.07100659006103427459 + 1.2331829654554608797e-845j)  +/-  (7.48e-89, 9.95e-206j)
| (0.055582686294827126714 + 2.1051910836193748816e-845j)  +/-  (4.25e-87, 5.66e-204j)
| (0.078525514858959484172 - 5.4048417611460918886e-846j)  +/-  (2.39e-88, 3.19e-205j)
| (0.072892868210055324485 - 4.6216025022881115159e-846j)  +/-  (1.6e-88, 2.12e-205j)
| (0.069277319716122149171 - 3.7006131205524247648e-846j)  +/-  (5.39e-89, 7.17e-206j)
| (0.079895179607914952364 - 7.6843692900416459492e-846j)  +/-  (3.21e-90, 4.28e-207j)
| (0.058213623827016105061 - 1.8618939197830713638e-845j)  +/-  (4.51e-89, 6e-206j)
| (0.072892868210055324485 - 1.1290624648933945722e-845j)  +/-  (1.89e-90, 2.52e-207j)
| (0.045998096771354210232 + 2.1269953307255976533e-846j)  +/-  (2.14e-88, 2.85e-205j)
| (0.058213623827016105061 - 3.1691301321787175541e-846j)  +/-  (2.06e-89, 2.74e-206j)
| (0.079104453564360014732 + 5.9238365420988394852e-846j)  +/-  (4.38e-90, 5.83e-207j)
| (0.07632109449526581352 + 1.0120684183110196356e-845j)  +/-  (1.51e-91, 2.01e-208j)
| (0.069277319716122149171 - 1.3571571511354470927e-845j)  +/-  (3.14e-91, 4.18e-208j)
| (0.080534369847689971616 + 7.0316332652273669904e-846j)  +/-  (2.61e-91, 3.47e-208j)
| (0.064409691755361995364 + 3.4236057105255334343e-846j)  +/-  (5.31e-91, 7.08e-208j)
| (0.07100659006103427459 + 4.1535035738074013774e-846j)  +/-  (3.93e-91, 5.23e-208j)
| (0.078525514858959484172 - 9.1223551489330487867e-846j)  +/-  (7.94e-93, 1.06e-209j)
| (0.064409691755361995364 + 1.5782851914779665826e-845j)  +/-  (5.8e-93, 8.35e-210j)
| (0.079104453564360014732 + 8.373213326495720296e-846j)  +/-  (8.13e-93, 1.06e-209j)
