Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 48
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^59 - 11982954477701461220176213422837746738093234409465894191150450321204569790265447059327700088/1026756831816408822689166684730024563406024079681980894780703722893334797076566661632991*t^57 + 1221203090880091132026579422221750830649635824930803543727218577681611158327240708450295364614512/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^55 - 255191027310035732317855182788557977142763096967171030857412082863819836452725626736420519852817320/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^53 + 36917076290505607373739684042107947946250667378371545923329032754173494617088342295870028730502719995/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^51 - 7862240547358036562946625709622152084563458139733807445833126944148582239498028696241928474319566031355/618107612753478111258878344207474787170426495968552498657983641181787547840093130303060582*t^49 + 45694976368361303936292257420363122505428944931004078796888939341050628884383836353296326592354714929160/44150543768105579375634167443391056226459035426325178475570260084413396274292366450218613*t^47 - 2911374723954061732492528097757941442294509345705905592935812812759433150508303533686822859770635601520990/44150543768105579375634167443391056226459035426325178475570260084413396274292366450218613*t^45 + 4995385613469543289141693100190256344826058712514202574253776038075473989264862986836857741196038484598825/1493464482642049196638787905061853910408762297719244937862841778753941523020460598738896*t^43 - 408064177782434781861260066299583789875741837944199297132153943727579952212391941428033052511237229059388025/2986928965284098393277575810123707820817524595438489875725683557507883046040921197477792*t^41 + 6761823770843008375444945383828641687363284099700999697899890671467824293602496649147527663617156220118925025/1493464482642049196638787905061853910408762297719244937862841778753941523020460598738896*t^39 - 365416812763474643535562424700789721283009765857196751973830225002167953804108766563384070573832707962457277775/2986928965284098393277575810123707820817524595438489875725683557507883046040921197477792*t^37 + 64567400375521718627836888891693012391408794387813782627586615468734597184165114596669974894305485592681214887425/23895431722272787146220606480989662566540196763507919005805468460063064368327369579822336*t^35 - 2332905590501484340392328042539287589625838969966275000475634714924632938085150590022601350582193045076650889802625/47790863444545574292441212961979325133080393527015838011610936920126128736654739159644672*t^33 + 2152221412755213317243360832241793011171264561673498832822408319590278413988034113852438135671769046054550322256375/2986928965284098393277575810123707820817524595438489875725683557507883046040921197477792*t^31 - 25887644006989508862412752310131769269624542271467917116544353097498008557536826861833465186052356168614591801509625/2986928965284098393277575810123707820817524595438489875725683557507883046040921197477792*t^29 + 32341192664547681489123434342432178404273553748722705819444919515256157222390424652475857079670966168167410371116670375/382326907556364594339529703695834601064643148216126704092887495361009029893237913277157376*t^27 - 509245707617924748025707804465523869580529227821405682108184286779623346720150013997790276798406455913859579003120812375/764653815112729188679059407391669202129286296432253408185774990722018059786475826554314752*t^25 + 1604697467842206997294531662029545749748775706594144988178548260176652696454501399360890822037507264514868341341720996875/382326907556364594339529703695834601064643148216126704092887495361009029893237913277157376*t^23 - 1457698357962801080655994406634972873157841860280114447344685237858580952894048593052336099174236595657637320238034946875/69513983192066289879914491581060836557207845130204855289615908247456187253315984232210432*t^21 + 45632449135299488126631753144844228681440302433143050180210705429175745939162856083494468730873614043713289929619799978125/556111865536530319039315932648486692457662761041638842316927265979649498026527873857683456*t^19 - 275499921040293716568548589494727335983667404604069670797282219229477411875556451862384549219935046394096653734205101978125/1112223731073060638078631865296973384915325522083277684633854531959298996053055747715366912*t^17 + 4917219869222531685854779373150684186257923285987298610563678336815832700167992150669420719908813461701962291002813028125/8689247899008286234989311447632604569650980641275606911201988530932023406664498029026304*t^15 - 265427160560513150985927367492375351373556310320396629893876124210603523196115115951368795325893424338037972369298416609375/278055932768265159519657966324243346228831380520819421158463632989824749013263936928841728*t^13 + 10236811672963344259755070240769652204010474716062017936378738558220867203869944652108487900110904383321842357656244648765625/8897789848584485104629054922375787079322604176666221477070836255674391968424445981722935296*t^11 - 16842638187470089935037296409458826610923299239828367753395670569450733895414770503786124237694022305616001953619455906015625/17795579697168970209258109844751574158645208353332442954141672511348783936848891963445870592*t^9 + 4420279367455212611363791194752065860709501854472781132580171133000071012168347960624780246587032662578599463042157184140625/8897789848584485104629054922375787079322604176666221477070836255674391968424445981722935296*t^7 - 2657060697704508821738405432504046708244564394218508929776082204090621852280202937253310598487597780475401013779406090234375/17795579697168970209258109844751574158645208353332442954141672511348783936848891963445870592*t^5 + 3002728248808490344476916285769778450674123805531008141384226117492127954607162677958744328112190808400942538628698544140625/142364637577351761674064878758012593269161666826659543633133380090790271494791135707566964736*t^3 - 251527118863511410654670827811834054237585294396890096243967481690228028147935284668283297961721439489772513621675744140625/284729275154703523348129757516025186538323333653319087266266760181580542989582271415133929472*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
Positive weights:   59 out of 59
Indefinite weights: 0 out of 59
Negative weights:   0 out of 59
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.6033942541484024834 - 9.4084198157062144254e-895j)  +/-  (9.88e-246, 9.88e-246j)
| (-8.9543588667544129635 - 2.2057440111691531541e-891j)  +/-  (1.74e-244, 1.74e-244j)
| (-5.9292397572533795239 + 6.8056576045675001267e-894j)  +/-  (8.73e-242, 8.73e-242j)
| (8.4165691054702628398 + 2.5671610311913523104e-919j)  +/-  (1.24e-243, 1.24e-243j)
| (3.9021795049782405751 - 2.2321113157348934679e-918j)  +/-  (4.71e-243, 4.71e-243j)
| (-5.5718556499475067078 + 7.220297969740057656e-916j)  +/-  (7.49e-242, 7.49e-242j)
| (5.9292397572533795239 + 3.6379729988004829862e-928j)  +/-  (7.85e-242, 7.85e-242j)
| (-8.4165691054702628398 + 8.9846361425164778755e-929j)  +/-  (1.3e-243, 1.3e-243j)
| (7.9362128566258358437 + 5.3982729390657148672e-937j)  +/-  (5.01e-243, 5.01e-243j)
| (1.6506801238857845559 + 1.631472140124515656e-941j)  +/-  (2.44e-247, 2.44e-247j)
| (-6.2974538112588878632 - 3.2863361453923465371e-934j)  +/-  (7.99e-242, 7.99e-242j)
| (4.5503053216179873058 + 4.0815753754158744371e-945j)  +/-  (2.36e-242, 2.36e-242j)
| (9.6033942541484024834 + 4.1274061354443492011e-949j)  +/-  (8.96e-246, 8.96e-246j)
| (-7.492770403233464797 - 5.0400601718886062261e-944j)  +/-  (1.44e-242, 1.44e-242j)
| (6.2974538112588878632 - 1.1103628917105897625e-949j)  +/-  (7.79e-242, 7.79e-242j)
| (-2.6736355255386522539 + 3.241047405315486056e-957j)  +/-  (4.05e-245, 4.05e-245j)
| (3.5863812468521002751 + 3.862576846290637259e-954j)  +/-  (1.59e-243, 1.59e-243j)
| (1.2424124415919969644 + 4.4083408183349141132e-960j)  +/-  (8.59e-249, 8.59e-249j)
| (-1.8744827444998148494 - 8.5112042387186684343e-959j)  +/-  (9.34e-247, 9.34e-247j)
| (-4.883494182585859043 - 4.0900793371932262504e-955j)  +/-  (3.66e-242, 3.66e-242j)
| (-7.9362128566258358437 + 3.3117273993590546007e-957j)  +/-  (4.89e-243, 4.89e-243j)
| (8.9543588667544129635 - 2.0267862027523522949e-973j)  +/-  (1.55e-244, 1.55e-244j)
| (1.8744827444998148494 - 1.0601662950110917849e-975j)  +/-  (9.47e-247, 9.47e-247j)
| (-1.6506801238857845559 - 3.2865773538224109042e-976j)  +/-  (2.35e-247, 2.35e-247j)
| (7.0756841238798668278 + 3.3348447485457773228e-971j)  +/-  (3.36e-242, 3.36e-242j)
| (-7.0756841238798668278 + 1.2034843350484250765e-969j)  +/-  (3.42e-242, 3.42e-242j)
| (4.883494182585859043 - 6.0436702223604432499e-985j)  +/-  (3.85e-242, 3.85e-242j)
| (2.1166040169656903522 + 1.4220596172193843083e-990j)  +/-  (3.63e-246, 3.63e-246j)
| (-2.1166040169656903522 - 5.2007646112335922235e-990j)  +/-  (3.67e-246, 3.67e-246j)
| (2.3862793919737297977 - 5.7032029483872016312e-990j)  +/-  (1.27e-245, 1.27e-245j)
| (4.2233799139046038616 + 7.5107814202650633003e-986j)  +/-  (1.05e-242, 1.05e-242j)
| (6.6786311554875159194 + 1.3279217202625737554e-984j)  +/-  (5.86e-242, 5.86e-242j)
| (3.2759416955673464603 + 2.0584127887885923119e-989j)  +/-  (5.25e-244, 5.25e-244j)
| (1.4319959244320462706 - 2.9663230976176037978e-993j)  +/-  (4.48e-248, 4.48e-248j)
| (-1.0362802085752798674 + 2.8022833447026885383e-995j)  +/-  (7.97e-250, 7.97e-250j)
| (-6.6786311554875159194 - 8.7448367163450216367e-987j)  +/-  (5.57e-242, 5.57e-242j)
| (7.492770403233464797 - 2.0559225316566093154e-991j)  +/-  (1.5e-242, 1.5e-242j)
| (1.0362802085752798674 - 7.2811706611682549264e-999j)  +/-  (8.5e-250, 8.5e-250j)
| (5.5718556499475067078 + 2.7715925739603089866e-990j)  +/-  (7.44e-242, 7.44e-242j)
| (-2.9712664864559443421 - 2.2525906074384873303e-995j)  +/-  (1.54e-244, 1.54e-244j)
| (-0.78724553365258876257 - 1.4114069175019083623e-1000j)  +/-  (4.57e-251, 4.57e-251j)
| (-0.26135224821164453214 + 1.3336901277348005303e-1002j)  +/-  (1.2e-253, 1.2e-253j)
| (2.6736355255386522539 - 2.4412466979128196453e-995j)  +/-  (4.69e-245, 4.69e-245j)
| (5.2236885836493921545 - 1.8677991039571954832e-993j)  +/-  (6.24e-242, 6.24e-242j)
| (2.9712664864559443421 + 5.7770044570465000883e-997j)  +/-  (1.56e-244, 1.56e-244j)
| (-5.2236885836493921545 - 1.712505083914181933e-990j)  +/-  (5.54e-242, 5.54e-242j)
| (-1.4319959244320462706 - 1.7962894898680687157e-1003j)  +/-  (4.47e-248, 4.47e-248j)
| (0.78724553365258876257 + 3.1380740031577220224e-1006j)  +/-  (4.04e-251, 4.04e-251j)
| (0.52464762327529031788 - 1.4662799860843501503e-1007j)  +/-  (2.14e-252, 2.14e-252j)
| (-4.5503053216179873058 - 1.6140687600375869815e-996j)  +/-  (2.26e-242, 2.26e-242j)
| (-2.3862793919737297977 + 2.0598759236215025665e-1003j)  +/-  (1.26e-245, 1.26e-245j)
| (-0.52464762327529031788 - 1.2802936342916128381e-1010j)  +/-  (2.1e-252, 2.1e-252j)
| (-3.5863812468521002751 + 6.5650478436373348365e-1000j)  +/-  (1.52e-243, 1.52e-243j)
| (0.26135224821164453214 - 1.1474288813850105511e-1012j)  +/-  (1.37e-253, 1.37e-253j)
| (1.1329128102428568845e-1043 + 1.8474598738255165397e-1043j)  +/-  (1.28e-1041, 1.28e-1041j)
| (-3.9021795049782405751 + 4.5847997948905917238e-1001j)  +/-  (4.3e-243, 4.3e-243j)
| (-1.2424124415919969644 + 1.3450483823070511758e-1012j)  +/-  (8.68e-249, 8.68e-249j)
| (-3.2759416955673464603 - 1.0170008615848026115e-1012j)  +/-  (5.46e-244, 5.46e-244j)
| (-4.2233799139046038616 + 5.2478510826828153172e-1020j)  +/-  (1.05e-242, 1.05e-242j)
-------------------------------------------------
The weights are:
| (3.7438284093590303193e-41 - 9.8786754784738966599e-924j)  +/-  (3.34e-78, 3.81e-197j)
| (4.9204576700641238245e-36 + 6.2155519319315576227e-921j)  +/-  (1.68e-76, 1.92e-195j)
| (1.103363350898604166e-16 + 5.1181831985006461332e-909j)  +/-  (2.96e-67, 3.38e-186j)
| (4.8893847691292298196e-32 + 1.7936868745118518933e-919j)  +/-  (1.19e-77, 1.36e-196j)
| (4.3800922288562050687e-08 + 1.4699281139813976757e-905j)  +/-  (1.45e-59, 1.65e-178j)
| (6.5420372332629697543e-15 - 2.2458715733143807218e-908j)  +/-  (1.89e-66, 2.16e-185j)
| (1.103363350898604166e-16 + 6.3322760930733622598e-911j)  +/-  (9.13e-70, 1.04e-188j)
| (4.8893847691292298196e-32 - 1.0345155183836389573e-918j)  +/-  (3.35e-76, 3.83e-195j)
| (1.1493135033550243098e-28 - 1.216445518270435432e-917j)  +/-  (1.39e-76, 1.59e-195j)
| (0.0082453551821544288896 + 1.6163823347323536876e-900j)  +/-  (1.81e-43, 2.07e-162j)
| (1.2630228397720145419e-18 + 1.5910321970041154121e-910j)  +/-  (4.8e-70, 5.48e-189j)
| (1.8953343380872787774e-10 + 3.8679810542911394879e-907j)  +/-  (9.67e-65, 1.1e-183j)
| (3.7438284093590303193e-41 + 2.3367368884292437089e-924j)  +/-  (3.44e-82, 3.93e-201j)
| (1.0042662832898501041e-25 - 4.2872778124165000964e-915j)  +/-  (9.08e-75, 1.04e-193j)
| (1.2630228397720145419e-18 - 4.7914894568416866963e-912j)  +/-  (5.94e-72, 6.79e-191j)
| (0.00013008841316599682381 + 2.3778459562768473476e-902j)  +/-  (2.55e-57, 2.91e-176j)
| (4.5836602718914876338e-07 - 7.9584695049886341062e-905j)  +/-  (2.22e-61, 2.54e-180j)
| (0.022060594753373289886 + 5.5383393495102830531e-900j)  +/-  (6.3e-44, 7.19e-163j)
| (0.0038429057479634831271 - 1.1567637371684481569e-900j)  +/-  (2.16e-51, 2.47e-170j)
| (8.3405852173163255294e-12 - 5.5422841071748172006e-907j)  +/-  (1.22e-67, 1.39e-186j)
| (1.1493135033550243098e-28 + 8.4039693973828423789e-917j)  +/-  (4.37e-76, 5e-195j)
| (4.9204576700641238245e-36 - 1.2633441109005594706e-921j)  +/-  (1.03e-80, 1.17e-199j)
| (0.0038429057479634831271 - 6.0104601038976650303e-901j)  +/-  (4.19e-53, 4.78e-172j)
| (0.0082453551821544288896 + 2.8635916599513931151e-900j)  +/-  (1.07e-51, 1.23e-170j)
| (4.1411402780472249638e-23 - 1.4071568559042529751e-914j)  +/-  (1.41e-75, 1.61e-194j)
| (4.1411402780472249638e-23 + 1.5962355712343474512e-913j)  +/-  (1.22e-74, 1.39e-193j)
| (8.3405852173163255294e-12 - 5.3601807512656385789e-908j)  +/-  (9.41e-69, 1.07e-187j)
| (0.0016435084975368638786 + 1.7290570520077628987e-901j)  +/-  (5.29e-57, 6.04e-176j)
| (0.0016435084975368638786 + 3.6488462330070118996e-901j)  +/-  (2.36e-58, 2.7e-177j)
| (0.0005320137947750061283 - 4.0708546030398518741e-902j)  +/-  (3.62e-59, 4.13e-178j)
| (3.2769745922364991482e-09 - 2.5014287194762140266e-906j)  +/-  (1.3e-66, 1.49e-185j)
| (9.3228232772914782066e-21 + 2.9386964255561745917e-913j)  +/-  (6e-75, 6.85e-194j)
| (3.7910641328888510729e-06 + 4.0286129752254432547e-904j)  +/-  (2.1e-64, 2.4e-183j)
| (0.015032652171882715454 - 3.6415402894585192382e-900j)  +/-  (9.21e-56, 1.05e-174j)
| (0.04488334430313924584 - 8.1478083123365498015e-900j)  +/-  (1.86e-55, 2.13e-174j)
| (9.3228232772914782066e-21 - 4.9441027722796548175e-912j)  +/-  (7.11e-77, 8.12e-196j)
| (1.0042662832898501041e-25 + 4.9942575396380707938e-916j)  +/-  (9.42e-78, 1.08e-196j)
| (0.04488334430313924584 - 5.7234633598113471573e-900j)  +/-  (1.7e-57, 1.95e-176j)
| (6.5420372332629697543e-15 - 6.9788059031962084512e-910j)  +/-  (2.73e-72, 3.12e-191j)
| (2.4919646549940185756e-05 - 5.8296785895983959749e-903j)  +/-  (2.29e-69, 2.61e-188j)
| (0.078734121052183804206 + 6.857801620410241258e-900j)  +/-  (3.25e-59, 3.71e-178j)
| (0.13819203816872816941 + 6.1503741361457077815e-900j)  +/-  (2.45e-60, 2.8e-179j)
| (0.00013008841316599682381 + 8.9985337376800882722e-903j)  +/-  (3.07e-64, 3.5e-183j)
| (2.7379283324406360137e-13 + 6.560658641392732174e-909j)  +/-  (1.77e-71, 2.02e-190j)
| (2.4919646549940185756e-05 - 1.937421926451039492e-903j)  +/-  (2.88e-65, 3.29e-184j)
| (2.7379283324406360137e-13 + 1.0370690773179547862e-907j)  +/-  (1.37e-76, 1.57e-195j)
| (0.015032652171882715454 - 5.9605917748193542533e-900j)  +/-  (6.12e-65, 6.99e-184j)
| (0.078734121052183804206 + 5.2501830957641731348e-900j)  +/-  (1.21e-62, 1.38e-181j)
| (0.11308855909500270031 - 5.2941827003268202477e-900j)  +/-  (4.51e-63, 5.15e-182j)
| (1.8953343380872787774e-10 + 2.9395647787892431189e-906j)  +/-  (4.7e-76, 5.37e-195j)
| (0.0005320137947750061283 - 9.5545143405472515051e-902j)  +/-  (1.23e-69, 1.4e-188j)
| (0.11308855909500270031 - 6.322041939406384457e-900j)  +/-  (2.53e-65, 2.89e-184j)
| (4.5836602718914876338e-07 - 3.2323661525700679859e-904j)  +/-  (1.1e-74, 1.25e-193j)
| (0.13819203816872816941 + 5.6310655117585135192e-900j)  +/-  (1.66e-66, 1.9e-185j)
| (0.14717120493466586311 - 5.9629268837428938798e-900j)  +/-  (1.31e-66, 1.49e-185j)
| (4.3800922288562050687e-08 + 7.1292782371615202312e-905j)  +/-  (9.28e-76, 1.06e-194j)
| (0.022060594753373289886 + 8.4746116524599560976e-900j)  +/-  (8e-69, 9.14e-188j)
| (3.7910641328888510729e-06 + 1.3976608156748941064e-903j)  +/-  (2.82e-74, 3.22e-193j)
| (3.2769745922364991482e-09 - 1.4887535171352405713e-905j)  +/-  (1.43e-76, 1.64e-195j)
