Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 13 18
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Trying to find an order 13 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 35/8*t^17 - 20554887/1192364*t^15 + 16554685/596182*t^13 - 43561973/1850220*t^11 + 927511585/82273116*t^9 - 83298215/27424372*t^7 + 1686197513/3907973010*t^5 - 14357343/521063068*t^3 + 2723149/5210630680*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^35 - 518314344812687970808252457270465158224519460506987694234652110304776671069/14135785039874689002573043478302730158205509620767976562081970768437233368*t^33 + 2544154249594504128777776704250992819909273876975781179008553080865281191273135/18150990526882731346985722964480628374506701876230662268284254192617427518756*t^31 - 9781183538488501840780826319639470180612098228043612126636193532082271640779715831/30221399227259747692731228735860246243553658623924052676693283230708016818728740*t^29 + 73274742286838692013765341459082403680209975852653641240404996538109281178511159367/145410088695757820507784969526794242270707603447984005177744923682464090118618972*t^27 - 135546194070265104779467017257236699856398260379549561202908170728845849225738624761/242350147826263034179641615877990403784512672413306675296241539470773483531031620*t^25 + 789951122514721503818614112766433952553791039345530215786250222100047896422541216204533/1731600618951297606960236786961546089236844299399345769779838390120111840683167507868*t^23 - 66041597257807635857159662508166851279774910194624923759133936211911176615776952001461959/237681006696923762833629023323373956683509454487118895443258686852573612218989557493012*t^21 + 4616127826052313157210931717922904111578342294130891902578670884075911912116294632836877463/36305773772955104772836833312645371883406069172907411278957764416730619266450654907057583*t^19 - 58202627033225695323502387639430337788914984064695730577739316569863284576894736528021880/1333975799006294812904630419630465501177780098706627822563492833583945295788157131639653*t^17 + 22022015669660745041603365627195979580778063592594935790500627558410004241872955468475822267/1979620085725341502350471542731610803747825666480635688684223365038574818949625183353245052*t^15 - 109199878980124890528395003701600292864852103045583996273690404323248655811648305794184277/52725958699706432265993188789461788961806494748878916647763818439284075080982753067519844*t^13 + 196644314917637578382433255382421946409525217265509269465510770446644935892488100619218051/717884206911387577775445724287287434326134582350120634358015066442560099179534407150077876*t^11 - 263962884722656316484150082422434897906876980075709822453136552357222532145366187415709/10692676939101304445551066258002740418827890543478941138357697445728938303136362510196332*t^9 + 30928514857651563451634800180051795114696677243745198659450745243947328378057219555245/21754066876102653871983203766281437403822260071215776798727729286138184823622254762123572*t^7 - 394257050188582586064909575819818827368287082175931800970612064092725877376432551853/8366948798501020719993539910108245155316253873544529537972203571591609547547021062355220*t^5 + 8272944725558005523871118714033390306822960778023780058538033463615145987863368282579/11161509697200361640471382240084399037191882667308402403654919564503207136427726097181863480*t^3 - 3566737357166539268789964728497308202808639983786175327065370450384146326825291786453/1015697382445232909282895783847680312384461322725064618732597680369791849414923074843549576680*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: 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:
| (-0.97026176866008936825 + 9.8819658524046764788e-433j)  +/-  (2.67e-116, 2.67e-116j)
| (-0.99813543109442915864 - 7.0885542926167704933e-442j)  +/-  (9.61e-117, 9.61e-117j)
| (-0.94220752437321014121 - 4.034786536956529017e-454j)  +/-  (1.84e-116, 1.84e-116j)
| (0.99813543109442915864 - 1.7951533594399442785e-458j)  +/-  (9.29e-117, 9.29e-117j)
| (0.68778526159288828469 + 8.1894168919376111803e-464j)  +/-  (1.21e-118, 1.21e-118j)
| (0.90554302517723779865 + 7.8439909689986542892e-462j)  +/-  (1.16e-116, 1.16e-116j)
| (0.98889990878051281863 + 8.9101025128530799567e-461j)  +/-  (2.12e-116, 2.12e-116j)
| (-0.86113631159405257522 + 7.2983215731187577927e-463j)  +/-  (5.28e-117, 5.28e-117j)
| (-0.98889990878051281863 - 5.3195889206684541416e-468j)  +/-  (2.37e-116, 2.37e-116j)
| (0.94220752437321014121 - 4.3535419982040888154e-477j)  +/-  (1.84e-116, 1.84e-116j)
| (0.8095180048154960996 - 2.6190446061076954322e-482j)  +/-  (1.77e-117, 1.77e-117j)
| (0.97026176866008936825 + 2.4264167861461767162e-481j)  +/-  (2.55e-116, 2.55e-116j)
| (-0.90554302517723779865 + 3.2504251402416872331e-482j)  +/-  (1.07e-116, 1.07e-116j)
| (-0.8095180048154960996 - 2.0317670379186530345e-490j)  +/-  (1.77e-117, 1.77e-117j)
| (-0.41256868661901400799 - 5.9987493547075793263e-497j)  +/-  (8.19e-122, 8.19e-122j)
| (0.86113631159405257522 + 7.7797277837195649486e-493j)  +/-  (4.52e-117, 4.52e-117j)
| (0.62190453863441120775 - 7.292489845408498395e-495j)  +/-  (2.86e-119, 2.86e-119j)
| (-0.3399810435848562648 - 1.0314773526036253497e-497j)  +/-  (7.97e-123, 7.97e-123j)
| (-0.75122694779756385225 - 8.4689325207799587019e-493j)  +/-  (5.01e-118, 5.01e-118j)
| (-0.088477152547857679914 + 9.7294467461353506189e-500j)  +/-  (9.16e-127, 9.16e-127j)
| (0.26209606839263577306 + 3.5707866612692432974e-501j)  +/-  (4.73e-124, 4.73e-124j)
| (0.75122694779756385225 + 1.2962454242655086775e-497j)  +/-  (5.68e-118, 5.68e-118j)
| (0.17687947303552314887 - 4.148413410668292525e-501j)  +/-  (1.99e-125, 1.99e-125j)
| (-0.62190453863441120775 + 1.2916346742087797437e-494j)  +/-  (2.98e-119, 2.98e-119j)
| (-0.55489150653867117637 - 2.7282438031228423062e-496j)  +/-  (5.46e-120, 5.46e-120j)
| (0.088477152547857679914 + 2.162151658214959234e-503j)  +/-  (9.16e-127, 9.16e-127j)
| (0.55489150653867117637 + 9.7899493790645510045e-499j)  +/-  (5.41e-120, 5.41e-120j)
| (0.3399810435848562648 + 1.1404093562897282792e-501j)  +/-  (7.95e-123, 7.95e-123j)
| (-0.17687947303552314887 + 2.1781783071182309883e-503j)  +/-  (2.09e-125, 2.09e-125j)
| (-0.68778526159288828469 - 6.5606955378652370744e-502j)  +/-  (1.35e-118, 1.35e-118j)
| (-0.26209606839263577306 - 1.9884863155118379861e-509j)  +/-  (4.54e-124, 4.54e-124j)
| (0.41256868661901400799 + 7.4911386467365163459e-504j)  +/-  (7.96e-122, 7.96e-122j)
| (0.48484586606682079734 + 9.4137592170625481058e-506j)  +/-  (7.41e-121, 7.41e-121j)
| (-1.7435002221465993501e-509 + 1.8447974003601222865e-509j)  +/-  (8.88e-508, 8.88e-508j)
| (-0.48484586606682079734 - 9.1919661782106509363e-505j)  +/-  (7.07e-121, 7.07e-121j)
-------------------------------------------------
The weights are:
| (0.02344463432931215934 + 2.6827117784115905648e-433j)  +/-  (1.32e-22, 3.88e-77j)
| (0.0049971305231933615926 - 1.5608414821029781272e-433j)  +/-  (3.87e-23, 1.14e-77j)
| (0.032518637873459207006 - 1.286609756390776928e-432j)  +/-  (8.2e-23, 2.42e-77j)
| (0.0049971305231933615926 + 2.2102433564054903479e-435j)  +/-  (1.71e-24, 5.04e-79j)
| (0.065143795166906021579 + 1.7699275773868971954e-433j)  +/-  (1.6e-24, 4.73e-79j)
| (0.040657197721137484006 + 2.9192803314013934623e-434j)  +/-  (1.44e-24, 4.23e-79j)
| (0.013809311293678285888 - 6.762714623148306112e-435j)  +/-  (1.06e-24, 3.12e-79j)
| (0.048073459751394089008 - 7.5209822594665653838e-433j)  +/-  (1.52e-25, 4.47e-80j)
| (0.013809311293678285888 + 7.1086767627779614386e-433j)  +/-  (4.22e-24, 1.24e-78j)
| (0.032518637873459207006 - 1.8873434739543362881e-434j)  +/-  (2.58e-25, 7.6e-80j)
| (0.055093305750978335883 + 6.8898765923764253569e-434j)  +/-  (1.72e-26, 5.06e-81j)
| (0.02344463432931215934 + 1.193899848276828579e-434j)  +/-  (3.37e-25, 9.93e-80j)
| (0.040657197721137484006 + 8.4612273767731779869e-433j)  +/-  (6.4e-26, 1.89e-80j)
| (0.055093305750978335883 + 7.6285777493870585339e-433j)  +/-  (4.79e-27, 1.41e-81j)
| (0.072207833918686464135 + 1.8477486705783408044e-432j)  +/-  (2.06e-29, 6.08e-84j)
| (0.048073459751394089008 - 4.4814430864206838813e-434j)  +/-  (7.71e-27, 2.27e-81j)
| (0.066322291624774330333 - 2.8698281937575982801e-433j)  +/-  (1.13e-28, 3.34e-83j)
| (0.074119248285201095093 - 1.7245516390302834431e-432j)  +/-  (6.32e-30, 1.86e-84j)
| (0.061244319489915471319 - 8.5245241317186282249e-433j)  +/-  (5.04e-29, 1.48e-83j)
| (0.088673726720475115153 + 9.6049207595075577836e-433j)  +/-  (5.54e-31, 1.63e-85j)
| (0.082003248977193311647 + 8.0926812431732414451e-433j)  +/-  (1.74e-31, 5.14e-86j)
| (0.061244319489915471319 - 1.0846237899392000245e-433j)  +/-  (2.28e-29, 6.71e-84j)
| (0.087582771689739644843 - 7.7741052616871985865e-433j)  +/-  (9.37e-32, 2.76e-86j)
| (0.066322291624774330333 - 1.3116546361617020516e-432j)  +/-  (2.79e-31, 8.23e-86j)
| (0.068189018770195837714 + 1.5754510605382887623e-432j)  +/-  (1.95e-31, 5.74e-86j)
| (0.088673726720475115153 + 7.9995844065251633005e-433j)  +/-  (3.3e-32, 9.73e-87j)
| (0.068189018770195837714 + 4.2906869138515306816e-433j)  +/-  (3.34e-32, 9.83e-87j)
| (0.074119248285201095093 - 8.2958032457837373831e-433j)  +/-  (7.87e-33, 2.32e-87j)
| (0.087582771689739644843 - 1.1240478659809290333e-432j)  +/-  (6.27e-33, 1.85e-87j)
| (0.065143795166906021579 + 1.0388910547262388328e-432j)  +/-  (7.15e-33, 2.1e-87j)
| (0.082003248977193311647 + 1.4082974011810368259e-432j)  +/-  (5.74e-33, 1.69e-87j)
| (0.072207833918686464135 + 7.4519377771499002239e-433j)  +/-  (1.51e-33, 4.46e-88j)
| (0.071753748625303822698 - 5.8692844980031476961e-433j)  +/-  (1.3e-33, 3.83e-88j)
| (0.088332638976911925527 - 8.6500160981157101067e-433j)  +/-  (5.57e-34, 1.69e-88j)
| (0.071753748625303822698 - 1.7594068587471987601e-432j)  +/-  (3.71e-34, 9.93e-89j)
