Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 7 26
-------------------------------------------------
Trying to find an order 7 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 26 Kronrod extension for:
P2 : 231/16*t^13 - 3731/80*t^11 + 1182181/20400*t^9 - 200960617/5814000*t^7 + 1942171/193800*t^5 - 241297/193800*t^3 + 38549/872100*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^39 - 13640066672580399234353401431815196623953318860322845627133527504693209611656148987985496271801687646180919893933/97510861869517726116167567708233972938412354667967597736609175303082803642232640674766864246202094036986656400*t^37 + 15554395563606382538639140314913614545746253232433700695961518998296948560719528767303651567474344694788645129561621/24865269776727020159622729765599663099295150440331737422835339702286114928769323372065550382781533979431597382000*t^35 - 1785360421986956493884958733954375000211996423071533178145964173528610242686864109641114268527159417699289893870219839109/1042564195164962886145687496233703286013593753330109262290334565276118142911931891750455489975937393972303008231110000*t^33 + 11345379813369922863325634861778867859483779571070023206300011041955296688493564185493618767494196032473264816835681352453/3535131466363954613942273694125775510046093761291749797421249388005228185735861012257291603941396910595740085381350000*t^31 - 54538670819341120199275877188998621598517346744448892120234203756302954202251999910271006498693038803262467724709976807253/12502294210311546805405602088981401194065453546031798064050760030750197242236581628714811770036647610643471033665750000*t^29 + 67177760038090582247592052182298592906657762441908969715623737589036837262343025575901813827298599852531232558459245925646771/15112687018705905974603220042387690305447050829522230383975841133722350494020805827399921606849471792796788865005271250000*t^27 - 4107460271971421980698616727501218641828128182072570470122393638284893167768047045532640832341563060398643846791818409942461/1186625795542834098746623203328218646205472139206930682001066044573754927678670679781030881722995562989970088659673150000*t^25 + 41977299957446577618981951068658426394331426842957673989644698006062155652888404777609322335222051670904042403342513653553943/20172638524228179678692594456579716985493026366517821594018122757753833770537401556277524989290924570829491507214443550000*t^23 - 2873522715858807377609712585292138484777371338201841306627319505704410246843155243118519046404808999358569662888306042249254601/2965377863061542412767811385117218396867474875878119774320664045389813564268998028772796173425765911911935251560523201850000*t^21 + 49242930688419351267202434014175167485560929526948139281056708364494744840679200579280142791819307047960615091410489642523469/141208469669597257750848161196058018898451184565624751158126859304276836393761810893942674925036471995806440550501104850000*t^19 - 3575470902428468353244459863627536259700636851854628049309175364795840536964193191789068804533874673521923403576833708789507/37160123597262436250223200314752110236434522254111776620559699816914956945726792340511230243430650525212221197500290750000*t^17 + 1131952394525142750692043031238796738640198252963596799399455376069461784361066343838992622637167704987757222096084788195511/56395952282904167956221092242388496711765333773887284518261191486847405247044190728540572957677104914733841582088676550000*t^15 - 112254577704869602200546109571670170193225253253887716542917933622544017779488136058856405848788810889226967488971715400506643/36225000016385443883879348250360877721190599394093599088896438665051649970351385177965894696481260390230704242894959903950000*t^13 + 4971632397027151344453419276626393244702772710678001831832137257950847932917671655840767378596793706256612771834772032643/14484206324024567726461154838209067461491643100397280723269267758917093150880201990390201797873354814166615051137528950000*t^11 - 8499618675983267851715428417850997128753858327536791159201689770949736864806562572573288666708820871628615595852658638196847/326025000147468994954914134253247899490715394546842391800067947985464849733162466601693052268331343512076338186054639135550000*t^9 + 1331492027721283370584887759815611577095485957569371829740344536501564847877052710669841648938855313262183645855392378773/1049565397825737198622332109902840000200058757279201960357098802381463368346273577176164167530500094087810139487850659468750*t^7 - 642579258409253270255489243184659780975372571060762787797407074389703553528372682800400025993886456617739492848191660713/18112500008192721941939674125180438860595299697046799544448219332525824985175692588982947348240630195115352121447479951975000*t^5 + 3183723526499121158935623803711742776793871997644633702914961476425099832824573435911328168367885066517508369572810456/6792187503072270728227377796942664572723237386392549829168082249697184369440884720868605255590236323168257045542804981990625*t^3 - 4150324301609033533006004971843387391018068966310776408370175216663569482573713714994555958833580686998827651457226417/2232365626009752979344064835928489089568370687661018043853243032733807929422904111592148260670657671547967148968401904080918750*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.9887032026126788575 + 7.7930135151595389057e-319j)  +/-  (1.89e-114, 1.89e-114j)
| (0.95429589941949188254 - 1.5724637240967147705e-316j)  +/-  (3.71e-114, 3.71e-114j)
| (-0.93246951420315202781 + 2.573666375702122917e-315j)  +/-  (2.61e-114, 2.61e-114j)
| (0.99782015418196270146 + 9.5297390682755513001e-330j)  +/-  (6.71e-115, 6.71e-115j)
| (0.90316898226877035448 - 1.2067560951105776219e-329j)  +/-  (1.12e-114, 1.12e-114j)
| (0.93246951420315202781 + 6.8221776566905244073e-329j)  +/-  (2.77e-114, 2.77e-114j)
| (-0.97332971675818423048 + 2.0105614332706855601e-327j)  +/-  (3.12e-114, 3.12e-114j)
| (-0.86557249299352529241 - 2.0716397363986893439e-333j)  +/-  (3.73e-115, 3.73e-115j)
| (-0.99782015418196270146 + 1.8071860569205871939e-340j)  +/-  (6.65e-115, 6.65e-115j)
| (-0.9887032026126788575 + 4.3052859859150493892e-352j)  +/-  (2.06e-114, 2.06e-114j)
| (0.86557249299352529241 - 3.2924339965177371681e-366j)  +/-  (3.96e-115, 3.96e-115j)
| (0.16060746268709987636 - 1.3096962554401131709e-375j)  +/-  (1.97e-125, 1.97e-125j)
| (-0.90316898226877035448 + 4.5439822523975961122e-363j)  +/-  (1.23e-114, 1.23e-114j)
| (-0.82137334086502794005 - 2.2900515442941491416e-374j)  +/-  (1.09e-115, 1.09e-115j)
| (0.97332971675818423048 + 1.9596182050246799768e-389j)  +/-  (3.36e-114, 3.36e-114j)
| (0.77201391063484626612 + 6.4603929163412553908e-393j)  +/-  (2.63e-116, 2.63e-116j)
| (0.82137334086502794005 + 2.4424623802606507409e-391j)  +/-  (1.24e-115, 1.24e-115j)
| (-0.080870831863248935509 - 1.8776937816817377223e-399j)  +/-  (9.39e-127, 9.39e-127j)
| (-0.77201391063484626612 + 1.1510083567626754797e-389j)  +/-  (3.09e-116, 3.09e-116j)
| (-0.95429589941949188254 - 3.3488361465658301547e-411j)  +/-  (3.7e-114, 3.7e-114j)
| (0.46311821247530461216 - 5.0802797146615020584e-432j)  +/-  (1.2e-120, 1.2e-120j)
| (0.71853465287533800138 - 8.9762399405238173395e-429j)  +/-  (6.22e-117, 6.22e-117j)
| (-0.23861918608319690863 - 1.5680671412284283329e-435j)  +/-  (3.46e-124, 3.46e-124j)
| (-0.71853465287533800138 - 1.3818112893359646919e-425j)  +/-  (6.51e-117, 6.51e-117j)
| (-0.66120938646626451366 + 3.5846388499142189517e-429j)  +/-  (1.01e-117, 1.01e-117j)
| (-0.38999225895144085063 + 3.155453976651376463e-435j)  +/-  (9.36e-122, 9.36e-122j)
| (0.66120938646626451366 + 7.3878257076564593489e-433j)  +/-  (1.01e-117, 1.01e-117j)
| (0.38999225895144085063 + 6.6688878234826891189e-437j)  +/-  (9.17e-122, 9.17e-122j)
| (-0.31501433542563828443 - 1.8743477831062949172e-436j)  +/-  (6.68e-123, 6.68e-123j)
| (-0.59956932893528627138 + 2.2786404994467806836e-432j)  +/-  (1.3e-118, 1.3e-118j)
| (-0.16060746268709987636 + 7.0601503437529656985e-441j)  +/-  (2e-125, 2e-125j)
| (0.31501433542563828443 - 4.6313069874881777818e-439j)  +/-  (6.65e-123, 6.65e-123j)
| (0.53334837650026075422 - 6.6713119103445764351e-436j)  +/-  (1.4e-119, 1.4e-119j)
| (0.080870831863248935509 + 1.9227423066696637477e-442j)  +/-  (7.94e-127, 7.94e-127j)
| (-0.53334837650026075422 - 1.1334791173827267111e-433j)  +/-  (1.5e-119, 1.5e-119j)
| (-0.46311821247530461216 - 1.4500100768465101956e-436j)  +/-  (1.31e-120, 1.31e-120j)
| (5.5069014777468847405e-444 + 2.9031580645559178463e-444j)  +/-  (2.43e-442, 2.43e-442j)
| (0.59956932893528627138 - 2.924953440177561018e-433j)  +/-  (1.47e-118, 1.47e-118j)
| (0.23861918608319690863 + 1.4016384319624065684e-439j)  +/-  (3.82e-124, 3.82e-124j)
-------------------------------------------------
The weights are:
| (0.012517717093902102839 - 2.4276636633520951075e-317j)  +/-  (6.41e-17, 6.73e-70j)
| (0.019927227449554214778 + 3.6857087525764783394e-317j)  +/-  (2.89e-17, 3.04e-70j)
| (0.024876440030956050048 - 1.3860537776763300059e-316j)  +/-  (2.25e-18, 2.36e-71j)
| (0.0055746646198004218337 + 4.5177582203171344821e-318j)  +/-  (1.95e-17, 2.05e-70j)
| (0.033717650288427442731 + 4.5791954975377269286e-317j)  +/-  (3.66e-18, 3.85e-71j)
| (0.024876440030956050048 - 1.5318725590350461214e-316j)  +/-  (7.15e-18, 7.51e-71j)
| (0.017776781393371690958 - 6.222199409473951121e-316j)  +/-  (1.08e-18, 1.13e-71j)
| (0.04116720887454608445 + 9.7451577460600466828e-316j)  +/-  (2.92e-19, 3.07e-72j)
| (0.0055746646198004218337 - 3.6704725128399642834e-317j)  +/-  (1.52e-19, 1.6e-72j)
| (0.012517717093902102839 + 1.7620404833158993555e-316j)  +/-  (3.37e-19, 3.54e-72j)
| (0.04116720887454608445 - 1.0498343553302836331e-317j)  +/-  (2.09e-19, 2.2e-72j)
| (0.07890728490216751954 - 1.0792401501225507845e-316j)  +/-  (3.37e-22, 3.54e-75j)
| (0.033717650288427442731 - 2.2254910926855105404e-315j)  +/-  (7.59e-20, 7.98e-73j)
| (0.046992917710366733225 - 6.2917945533243788292e-316j)  +/-  (7.96e-21, 8.36e-74j)
| (0.017776781393371690958 + 1.0073648131217078168e-316j)  +/-  (4.65e-19, 4.89e-72j)
| (0.051543999214901628969 + 1.8859626593071356104e-317j)  +/-  (5.65e-22, 5.94e-75j)
| (0.046992917710366733225 - 6.4744557310751046464e-318j)  +/-  (2.73e-21, 2.86e-74j)
| (0.080463197067952517225 + 1.4236857390278818603e-316j)  +/-  (1.43e-24, 1.5e-77j)
| (0.051543999214901628969 + 4.9005005023083102421e-316j)  +/-  (7.91e-23, 8.31e-76j)
| (0.019927227449554214778 + 2.2340053845961088929e-315j)  +/-  (5.02e-21, 5.28e-74j)
| (0.071878663026813857035 - 6.5757130466155578104e-317j)  +/-  (8.9e-25, 9.35e-78j)
| (0.055366512352683126562 - 3.0144714536043383115e-317j)  +/-  (3.09e-23, 3.24e-76j)
| (0.077146341275239839162 + 1.7855783452230199171e-316j)  +/-  (2.14e-25, 2.25e-78j)
| (0.055366512352683126562 - 4.1526359144683877711e-316j)  +/-  (4.16e-24, 4.37e-77j)
| (0.05938289071208127913 + 3.58366113472556962e-316j)  +/-  (6.09e-25, 6.39e-78j)
| (0.074189191324275892627 + 2.1218082251423001754e-316j)  +/-  (1.08e-26, 1.13e-79j)
| (0.05938289071208127913 + 4.0389756610249616422e-317j)  +/-  (6.54e-26, 6.87e-79j)
| (0.074189191324275892627 + 7.6053451973588454512e-317j)  +/-  (3.32e-27, 3.49e-80j)
| (0.075692331488751261139 - 1.9548514186069238643e-316j)  +/-  (5.42e-27, 5.69e-80j)
| (0.063953664680265188593 - 3.0716979858782108636e-316j)  +/-  (7.99e-27, 8.39e-80j)
| (0.07890728490216751954 - 1.6010556738718742611e-316j)  +/-  (2.04e-27, 2.15e-80j)
| (0.075692331488751261139 - 8.7487820856921868032e-317j)  +/-  (1.5e-28, 1.58e-81j)
| (0.068385493929017431528 + 5.7090269601451395876e-317j)  +/-  (2.37e-28, 2.49e-81j)
| (0.080463197067952517225 + 1.1694481855580983046e-316j)  +/-  (6e-29, 6.31e-82j)
| (0.068385493929017431528 + 2.6449872947295389129e-316j)  +/-  (1.19e-28, 1.25e-81j)
| (0.071878663026813857035 - 2.3347306656462580312e-316j)  +/-  (9.34e-29, 9.81e-82j)
| (0.081079645129851435258 - 1.2785762272263430454e-316j)  +/-  (1.35e-29, 1.43e-82j)
| (0.063953664680265188593 - 4.9133078893835091031e-317j)  +/-  (3.72e-30, 4.06e-83j)
| (0.077146341275239839162 + 9.84502950006242737e-317j)  +/-  (5.18e-30, 5.35e-83j)
