Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 11 14
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Trying to find an order 11 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : 35/8*t^15 - 638415/40664*t^13 + 11181153/503608*t^11 - 55088825/3525256*t^9 + 19993545/3525256*t^7 - 160318323/162665384*t^5 + 10517265/162665384*t^3 - 64053/91941304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^29 - 815296850751107497064801511534118007540305544419181831145/24304980630162332961987673699171723651527850226032093732*t^27 + 69600134000286068961262398203206829526618809661343840412253/602015674070174708750771610087176539676305213290948783208*t^25 - 84954903653358870455738972365120354522866049523116437347131515/359252853501376757447022958319522600051835136031373686379374*t^23 + 219377896933111222504900003892259943424719890669779263062774825/687266328437416405550826528959086713142641129799149660899672*t^21 - 5439394602560324496528139128526807769737440625453754593133621216835/18187079758987319096062554519663671755128487743508483251412241588*t^19 + 381318378750956186265887616773056423656123815636538290350464653295/1914429448314454641690795212596175974224051341421945605411814904*t^17 - 2671809786983198898943086055916206585667409354230166551721582461048175/28143281255253439848555133272242062428489588514941850557533452475837*t^15 + 1034768109084447270068070017858287585340281273496270100249629466440715/32163750006003931255491580882562357061130958302790686351466802829528*t^13 - 65790477358821079530883970898961772040354241259654931585989103066175/8659471155462596876478502545305249977996796466135954017702600761796*t^11 + 13283818288728624786482567359130095605219792615391905220390366375623/11021145106952396024609003239479409062905013684173032386166946424104*t^9 - 7658574237637809538898774581509026732509423278759991305685558346919/63371584364976277141501768627006602111703828683994936220459941938598*t^7 + 6101245439230396800352802743656620927517893253712431251455883421/883227656654721632634170991317165186225837333574842316661462605416*t^5 - 63915322204835955244227344163786437517335129565789870497829306351/344017172267014075911009601118035840034963641427401082339639684809532*t^3 + 267352007821064698928515869306630259676663270655363001054776195/178678719320822822036035539006077369324857731505183640886158332180744*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:
| (-0.99440647375811783848 + 1.5616368277636857002e-429j)  +/-  (2.57e-116, 2.57e-116j)
| (-0.98218336611185065435 - 9.076370816906716989e-434j)  +/-  (1.03e-116, 1.03e-116j)
| (-0.91272979048656640233 - 5.2163028289876461608e-436j)  +/-  (7.6e-118, 7.6e-118j)
| (-1.226921500287683168e-453 - 5.366090408670388633e-453j)  +/-  (1.6e-451, 1.6e-451j)
| (0.91272979048656640233 - 1.7027119689308849233e-434j)  +/-  (8.24e-118, 8.24e-118j)
| (0.95275482203958774276 - 8.0600783142555885823e-435j)  +/-  (2.55e-117, 2.55e-117j)
| (0.99440647375811783848 + 2.0496035846472788338e-435j)  +/-  (2.52e-116, 2.52e-116j)
| (-0.95275482203958774276 + 1.7543048820648403059e-456j)  +/-  (2.35e-117, 2.35e-117j)
| (-0.99234294851369901008 + 1.1126277280686608879e-457j)  +/-  (3.37e-116, 3.37e-116j)
| (0.98218336611185065435 - 1.7082984930547924205e-457j)  +/-  (9.8e-117, 9.8e-117j)
| (0.86113631159405257522 - 8.2401080493453959549e-474j)  +/-  (2.09e-118, 2.09e-118j)
| (0.99234294851369901008 - 8.5864638962262385769e-483j)  +/-  (3.24e-116, 3.24e-116j)
| (-0.86113631159405257522 + 8.742464047885564945e-498j)  +/-  (1.97e-118, 1.97e-118j)
| (-0.79771828569921420176 - 2.3159189239810748279e-500j)  +/-  (4.4e-119, 4.4e-119j)
| (-0.22900173719888928644 - 3.4932131328445173944e-505j)  +/-  (1.91e-125, 1.91e-125j)
| (0.72322064929065662618 - 4.205775411786555066e-497j)  +/-  (6.88e-120, 6.88e-120j)
| (0.54633537010580514983 + 6.124403145900662227e-501j)  +/-  (8.95e-122, 8.95e-122j)
| (-0.54633537010580514983 - 3.7691938470597699786e-502j)  +/-  (8.6e-122, 8.6e-122j)
| (-0.72322064929065662618 + 2.8623957650277667965e-501j)  +/-  (6.85e-120, 6.85e-120j)
| (-0.44627998672758270108 + 3.0775860905140900325e-503j)  +/-  (6.22e-123, 6.22e-123j)
| (0.44627998672758270108 + 4.9521958709146944403e-502j)  +/-  (6.48e-123, 6.48e-123j)
| (0.79771828569921420176 + 7.5408473060980771105e-502j)  +/-  (4.49e-119, 4.49e-119j)
| (0.11513928820520961921 + 1.9757591205583462844e-510j)  +/-  (8.35e-127, 8.35e-127j)
| (-0.3399810435848562648 + 5.6043049083258832043e-508j)  +/-  (3.7e-124, 3.7e-124j)
| (-0.63899664402486099033 + 4.5073174933747745399e-505j)  +/-  (8.68e-121, 8.68e-121j)
| (0.22900173719888928644 + 1.3937038045382239752e-510j)  +/-  (1.99e-125, 1.99e-125j)
| (0.63899664402486099033 - 2.6824148317974905038e-505j)  +/-  (9.3e-121, 9.3e-121j)
| (0.3399810435848562648 + 4.0875680338721544035e-508j)  +/-  (4.17e-124, 4.17e-124j)
| (-0.11513928820520961921 + 7.0621399018265806123e-511j)  +/-  (9.34e-127, 9.34e-127j)
-------------------------------------------------
The weights are:
| (0.028869746453752666288 + 2.8829234092184456598e-428j)  +/-  (2.55e-25, 3.61e-79j)
| (0.026192259217404401147 + 1.9738440643952674908e-429j)  +/-  (1.66e-25, 2.34e-79j)
| (0.045701376116963577013 + 9.811328206471758874e-431j)  +/-  (3.39e-26, 4.79e-80j)
| (0.11533602384041546447 + 3.3628305690585184292e-432j)  +/-  (1.06e-26, 1.5e-80j)
| (0.045701376116963577013 + 4.1905520185281099715e-432j)  +/-  (2.41e-27, 3.41e-81j)
| (0.034462755955841750044 - 5.3526033103494887534e-432j)  +/-  (1.71e-27, 2.42e-81j)
| (0.028869746453752666288 + 2.2603807431073892545e-431j)  +/-  (2.69e-28, 3.79e-82j)
| (0.034462755955841750044 - 2.5122958801579982321e-430j)  +/-  (2.2e-27, 3.1e-81j)
| (-0.024138565598628500824 - 3.061827501465159964e-428j)  +/-  (3.8e-26, 5.37e-80j)
| (0.026192259217404401147 + 1.2188936222742089233e-431j)  +/-  (7.43e-29, 1.05e-82j)
| (0.057543468249781590092 - 3.5310243467503246233e-432j)  +/-  (1.13e-30, 1.59e-84j)
| (-0.024138565598628500824 - 3.172271288724294036e-431j)  +/-  (2.28e-28, 3.22e-82j)
| (0.057543468249781590092 - 4.9018677752210011405e-431j)  +/-  (4.47e-31, 6.31e-85j)
| (0.069158444924908000837 + 2.7896334767303982713e-431j)  +/-  (6.4e-32, 9.04e-86j)
| (0.11271748561595662947 + 4.450758607154329906e-432j)  +/-  (6.16e-34, 8.69e-88j)
| (0.079598308450253512129 - 2.7839280855270217158e-432j)  +/-  (1.05e-33, 1.48e-87j)
| (0.09652481831194011157 - 2.5703639983239203681e-432j)  +/-  (2.04e-34, 2.88e-88j)
| (0.09652481831194011157 - 8.8359689092090870068e-432j)  +/-  (1.29e-34, 1.82e-88j)
| (0.079598308450253512129 - 1.7620997622331134337e-431j)  +/-  (6.38e-34, 9.01e-88j)
| (0.10340058234034555626 + 6.7514827778242604103e-432j)  +/-  (5.33e-35, 7.53e-89j)
| (0.10340058234034555626 + 2.5691822569014500818e-432j)  +/-  (3.79e-36, 5.36e-90j)
| (0.069158444924908000837 + 3.0653174861008793657e-432j)  +/-  (6.33e-35, 8.93e-89j)
| (0.11473672291894563937 - 3.0254547696596484812e-432j)  +/-  (1.04e-36, 1.47e-90j)
| (0.10893298238032092523 - 5.3736560728720952058e-432j)  +/-  (3.1e-36, 4.36e-90j)
| (0.088631602742006409134 + 1.210334335239017202e-431j)  +/-  (5.36e-36, 7.53e-90j)
| (0.11271748561595662947 + 2.7847661381974784146e-432j)  +/-  (3.46e-37, 4.91e-91j)
| (0.088631602742006409134 + 2.6346621850729152284e-432j)  +/-  (4.81e-37, 6.79e-91j)
| (0.10893298238032092523 - 2.6357526241076177136e-432j)  +/-  (2.11e-37, 3.03e-91j)
| (0.11473672291894563937 - 3.8176694108070021765e-432j)  +/-  (1.93e-37, 2.54e-91j)
