Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 11 28
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 16*t^15 - 2564/3*t^13 + 116464/7*t^11 - 1045605/7*t^9 + 4515555/7*t^7 - 5082165/4*t^5 + 1931985/2*t^3 - 2916045/16*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^43 - 21689700740120204064175909610475898581468381110060875112070969083653/3879590084687788890950393626479453022082099588203765723188928341*t^41 + 31990365628308358527850625433428761581283013388075388558475729530731831/36209507457086029648870340513808228206099596156568480083096664516*t^39 - 758366722725562929995536617412243481781316464734584979984129482695419058/9052376864271507412217585128452057051524899039142120020774166129*t^37 + 14676554509044845804596983829975200280562082902230908813695062350451613102073/2751922566738538253314145879049425343663569307899204486315346503216*t^35 - 11873551593737651731357006245967751767126969210192042749198003978109348037445/49141474406045325952038319268739738279706594783914365827059758986*t^33 + 6335308036349144922858234857959136768997246168404240287549894141524401266197465/786263590496725215232613108299835812475305516542629853232956143776*t^31 - 79330580697103707718690203420408912735719696200064976233861321845413284304446205/393131795248362607616306554149917906237652758271314926616478071888*t^29 + 12072006704789286902575708876040078623164625704072721784508531532595027049938931405/3145054361986900860930452433199343249901222066170519412931824575104*t^27 - 21910685330046320261753122836157870329210796387715757182491086788993487063276864765/393131795248362607616306554149917906237652758271314926616478071888*t^25 + 971355843046508637194993840207901148969849733293482066032621367546103858858012672125/1572527180993450430465226216599671624950611033085259706465912287552*t^23 - 16360620845475494050401781288833812026588471087581647023668756814323392087727431083875/3145054361986900860930452433199343249901222066170519412931824575104*t^21 + 1365324528788799833993490269468315299821866227690135676234944292104151607354421401375/41382294236669748170137532015780832235542395607506834380681902304*t^19 - 411723671840606523477413623750747216412481437793141194372288780758017069675219574050375/2648466831146863882888802049009973263074713318880437400363641747456*t^17 + 5655548944046286494952532265566443606471830969345793758114349249131268288707329807219125/10593867324587455531555208196039893052298853275521749601454566989824*t^15 - 6894339260222245258734201550013621543310460880974331707960147882717761607634144638734375/5296933662293727765777604098019946526149426637760874800727283494912*t^13 + 92105253599976559057282763803302338662449801889340034846303367635234888097542251591600625/42375469298349822126220832784159572209195413102086998405818267959296*t^11 - 200358846604990143497892619380591232239656237640034645430305291261545320999829746724350625/84750938596699644252441665568319144418390826204173996811636535918592*t^9 + 527121529945982154111338651304890275751722155494685909974547290759073631637303028845439375/339003754386798577009766662273276577673563304816695987246546143674368*t^7 - 23245829889147206192147203432818313240232752547443430725193749867983176285564775464668125/42375469298349822126220832784159572209195413102086998405818267959296*t^5 + 112191711225739870573554388775019421953290737099974799427061635688580606464122896226596875/1356015017547194308039066649093106310694253219266783948986184574697472*t^3 - 2030705825440907966568944460560334442951858787285077552838731387587942504018136378415625/678007508773597154019533324546553155347126609633391974493092287348736*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:
| (-6.9549930326311249115 - 3.8919862830132159426e-867j)  +/-  (6.24e-247, 6.24e-247j)
| (3.6927320602322334284 - 4.6455024270186324189e-864j)  +/-  (8.86e-246, 8.86e-246j)
| (-7.6533029598461418537 + 2.1998338841310882815e-867j)  +/-  (4.89e-248, 4.89e-248j)
| (6.3736743435706765844 + 7.7373697665532602455e-865j)  +/-  (3.05e-246, 3.05e-246j)
| (7.6533029598461418537 - 6.5690536635628184097e-867j)  +/-  (5.22e-248, 5.22e-248j)
| (4.8704922097422193661 + 8.3531991429505424703e-862j)  +/-  (1.87e-244, 1.87e-244j)
| (-6.3736743435706765844 + 1.5491938252142980487e-872j)  +/-  (2.95e-246, 2.95e-246j)
| (-5.8515280608962671134 + 5.667016327825544245e-871j)  +/-  (1.08e-245, 1.08e-245j)
| (4.6758378429530981643 - 6.7024826422239738119e-871j)  +/-  (3.95e-244, 3.95e-244j)
| (-2.2679277353884325143 + 4.7220382579313797686e-879j)  +/-  (1e-247, 1e-247j)
| (1.3446794140865058093 - 4.4068247049294810145e-881j)  +/-  (6.06e-250, 6.06e-250j)
| (2.9368597740916132369 + 9.8469131973188699419e-878j)  +/-  (1.12e-246, 1.12e-246j)
| (5.3643483787074013654 - 1.9201504584267661217e-875j)  +/-  (2.77e-245, 2.77e-245j)
| (-1.071585516319553479 + 6.186055618956250903e-888j)  +/-  (1.02e-250, 1.02e-250j)
| (-4.0986697433175044098 - 3.8487664076024593934e-880j)  +/-  (2.51e-245, 2.51e-245j)
| (-5.3643483787074013654 - 2.2730780195281887511e-905j)  +/-  (2.82e-245, 2.82e-245j)
| (9.8720790961808719742e-932 - 3.5981377478324107968e-932j)  +/-  (4.52e-930, 4.52e-930j)
| (-4.5708160026008657742 + 7.5008371875064175804e-931j)  +/-  (2.74e-244, 2.74e-244j)
| (-1.3446794140865058093 - 1.2600479215799920516e-955j)  +/-  (6.75e-250, 6.75e-250j)
| (6.9549930326311249115 + 8.2809346902971966181e-952j)  +/-  (5.93e-247, 5.93e-247j)
| (3.3058066755302886227 + 3.16045358949683815e-953j)  +/-  (3.37e-246, 3.37e-246j)
| (1.071585516319553479 - 2.02454563419891839e-963j)  +/-  (1.04e-250, 1.04e-250j)
| (-3.3058066755302886227 - 1.3357193312245144454e-956j)  +/-  (3.22e-246, 3.22e-246j)
| (-1.6506801238857845559 + 2.7015067904366040586e-965j)  +/-  (3.92e-249, 3.92e-249j)
| (-4.6758378429530981643 + 1.6469813251846137179e-959j)  +/-  (4.16e-244, 4.16e-244j)
| (-2.9368597740916132369 - 1.4715527682912089754e-969j)  +/-  (1.07e-246, 1.07e-246j)
| (0.52464762327529031788 - 3.7101895382019590963e-975j)  +/-  (7.08e-253, 7.08e-253j)
| (2.5897923976951487129 - 1.8507076929046039719e-970j)  +/-  (3.65e-247, 3.65e-247j)
| (1.9606349438216749445 - 1.0988290170022010336e-970j)  +/-  (2.33e-248, 2.33e-248j)
| (-2.5897923976951487129 - 6.0025691616012108755e-970j)  +/-  (3.53e-247, 3.53e-247j)
| (5.8515280608962671134 - 3.223475527518684537e-966j)  +/-  (1.1e-245, 1.1e-245j)
| (4.5708160026008657742 - 3.8973025335513122808e-968j)  +/-  (2.79e-244, 2.79e-244j)
| (1.6506801238857845559 + 1.0039546065583708031e-982j)  +/-  (4.14e-249, 4.14e-249j)
| (-0.22650076089447544038 - 1.6231528179133313484e-986j)  +/-  (3.93e-254, 3.93e-254j)
| (-0.81603786813753696232 + 8.29755424359235481e-984j)  +/-  (1.24e-251, 1.24e-251j)
| (-1.9606349438216749445 + 1.5487611610765229685e-980j)  +/-  (2.36e-248, 2.36e-248j)
| (-3.6927320602322334284 + 2.5041292811588498222e-979j)  +/-  (8.87e-246, 8.87e-246j)
| (4.0986697433175044098 - 2.9214288246665970434e-984j)  +/-  (2.58e-245, 2.58e-245j)
| (0.22650076089447544038 - 1.1128151261269529075e-995j)  +/-  (5.06e-254, 5.06e-254j)
| (-4.8704922097422193661 + 3.8107725309006486579e-990j)  +/-  (1.68e-244, 1.68e-244j)
| (-0.52464762327529031788 - 8.7361799014399900748e-1001j)  +/-  (6.63e-253, 6.63e-253j)
| (2.2679277353884325143 + 3.2350703237336092695e-996j)  +/-  (1.12e-247, 1.12e-247j)
| (0.81603786813753696232 + 2.4841319481371084957e-1000j)  +/-  (1.35e-251, 1.35e-251j)
-------------------------------------------------
The weights are:
| (3.4603440140945690796e-22 - 5.6411292471883071066e-882j)  +/-  (3.74e-96, 1.16e-217j)
| (2.6704160315100282218e-07 + 4.1035454548133941472e-870j)  +/-  (1.45e-85, 4.48e-207j)
| (1.6560095162290956784e-26 + 1.6896795866669989968e-884j)  +/-  (5.1e-98, 1.58e-219j)
| (7.0197921828261541914e-19 - 2.121423022725748062e-878j)  +/-  (8.23e-96, 2.55e-217j)
| (1.6560095162290956784e-26 - 2.7425338984225292135e-883j)  +/-  (2.47e-99, 7.65e-221j)
| (1.7442503674643719629e-11 - 1.9698299410762177197e-871j)  +/-  (2.06e-91, 6.38e-213j)
| (7.0197921828261541914e-19 + 5.7239141984207462667e-880j)  +/-  (1.9e-96, 5.88e-218j)
| (3.8131121253031440713e-16 - 3.1990754335031213244e-878j)  +/-  (1.72e-95, 5.33e-217j)
| (-1.1379849405081710522e-10 + 6.9727055922620712455e-871j)  +/-  (2.24e-91, 6.93e-213j)
| (0.0010247977866262353219 - 5.1479573391084697292e-870j)  +/-  (1.52e-83, 4.7e-205j)
| (0.027250770790397770257 - 9.3563160907382672566e-868j)  +/-  (4.09e-76, 1.27e-197j)
| (3.6355744517693873016e-05 + 2.3600225615892021761e-869j)  +/-  (2.25e-86, 6.97e-208j)
| (8.5525118139405671918e-14 - 2.1560267839340757067e-874j)  +/-  (5.33e-94, 1.65e-215j)
| (0.045235192180923764486 - 5.2033030895919834285e-869j)  +/-  (4.74e-75, 1.47e-196j)
| (1.1948663844391848373e-08 + 2.7650211654435564883e-873j)  +/-  (1.18e-92, 3.64e-214j)
| (8.5525118139405671918e-14 + 1.3802433511962831389e-876j)  +/-  (6.26e-96, 1.94e-217j)
| (0.10674097932930982954 + 1.6870132483197159095e-867j)  +/-  (1.11e-78, 3.44e-200j)
| (3.9424649836563748439e-10 - 1.5092246016447232801e-873j)  +/-  (2.46e-94, 7.61e-216j)
| (0.027250770790397770257 + 5.2026012767958913505e-869j)  +/-  (3.44e-82, 1.06e-203j)
| (3.4603440140945690796e-22 + 1.3460584752896151422e-880j)  +/-  (1.85e-101, 5.72e-223j)
| (3.829176970651634519e-06 - 1.2084494267395289401e-869j)  +/-  (6.89e-91, 2.13e-212j)
| (0.045235192180923764486 + 1.4848284992620058869e-867j)  +/-  (1.91e-81, 5.92e-203j)
| (3.829176970651634519e-06 + 7.422094425536378162e-872j)  +/-  (4.21e-92, 1.3e-213j)
| (0.011527718024069551582 - 2.9152898335251398358e-869j)  +/-  (8.78e-86, 2.72e-207j)
| (-1.1379849405081710522e-10 + 1.1424311819964382046e-873j)  +/-  (8.18e-95, 2.53e-216j)
| (3.6355744517693873016e-05 - 3.5982132337569050615e-871j)  +/-  (3.45e-91, 1.07e-212j)
| (0.13050892691801458196 + 1.6646813779612696344e-867j)  +/-  (1.23e-83, 3.81e-205j)
| (0.00023057496470131185634 - 5.7438671207049215606e-869j)  +/-  (3.03e-91, 9.37e-213j)
| (0.003708481375847686947 - 2.7057979113678504853e-868j)  +/-  (1.02e-89, 3.15e-211j)
| (0.00023057496470131185634 + 1.522495184460167713e-870j)  +/-  (9.77e-91, 3.02e-212j)
| (3.8131121253031440713e-16 + 2.0912073961795652997e-876j)  +/-  (4.39e-100, 1.36e-221j)
| (3.9424649836563748439e-10 - 6.6008031214795720087e-871j)  +/-  (7.15e-96, 2.21e-217j)
| (0.011527718024069551582 + 5.051128418845763021e-868j)  +/-  (1.09e-89, 3.37e-211j)
| (0.14840945847903488294 - 8.7655849913333469899e-868j)  +/-  (7.48e-88, 2.32e-209j)
| (0.078693125605997543857 - 2.8226182223805135746e-869j)  +/-  (1.58e-88, 4.9e-210j)
| (0.003708481375847686947 + 1.3478449780662710418e-869j)  +/-  (6.86e-91, 2.13e-212j)
| (2.6704160315100282218e-07 - 1.4231465546333242341e-872j)  +/-  (2.74e-95, 8.49e-217j)
| (1.1948663844391848373e-08 + 9.5269464951394911352e-871j)  +/-  (1.63e-96, 5.02e-218j)
| (0.14840945847903488294 - 1.8448527046205015823e-867j)  +/-  (8.19e-90, 2.54e-211j)
| (1.7442503674643719629e-11 - 1.4291293010698789271e-874j)  +/-  (1.05e-97, 3.25e-219j)
| (0.13050892691801458196 + 2.5343665542054130782e-868j)  +/-  (4.16e-90, 1.29e-211j)
| (0.0010247977866262353219 + 1.3361806549707781752e-868j)  +/-  (3.95e-93, 1.2e-214j)
| (0.078693125605997543857 - 1.712210692104898741e-867j)  +/-  (8.03e-91, 2.48e-212j)
