Starting with polynomial:
P : 2*t
Extension levels are: 1 6 52
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P2 : 2*t^7 - 21*t^5 + 105/2*t^3 - 105/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^59 - 20272901550173121694599172315995340688525092889295501/12967689434123817553800621450329162601323511747202*t^57 + 1386441581282803288210920173345825568700053819801933350031/2437925613615277700114516832661882569048820208473976*t^55 - 14358746797147277253976121174840684640809757855200353737035085/112144578226302774205267774302446598176245729589802896*t^53 + 4489444398019304394930556259635980025064482471760750279118470865/224289156452605548410535548604893196352491459179605792*t^51 - 1036587417113168210440398154408511156175115310787887202195297821775/448578312905211096821071097209786392704982918359211584*t^49 + 1952449500926438180539811105975005476761897837020823318397530560425/9544219423515129719597257387442263674574104645940672*t^47 - 11813818004274626362865625851920137542189744083105689360998912875275/829932123783924323443239772821066406484704751820928*t^45 + 1314352230208759963968195444517126495311678836699488973289278226257625/1659864247567848646886479545642132812969409503641856*t^43 - 14784953566066101938962534595578672734689548187549525000697068220390375/414966061891962161721619886410533203242352375910464*t^41 + 17358309318677714433323643684138482118262660889025483272805424940916250875/13278913980542789175091836365137062503755276029134848*t^39 - 1044064285007874497479070558744669852837501688913252573269628491370335936375/26557827961085578350183672730274125007510552058269696*t^37 + 51631467335266124834148335342072674849652867610142225350597440802861979459875/53115655922171156700367345460548250015021104116539392*t^35 - 2101669122359628449486915378345107762905043457242014673753255531888526767985625/106231311844342313400734690921096500030042208233078784*t^33 + 17594494748944385388769618761960227237089104035156152118516127102888743818873125/53115655922171156700367345460548250015021104116539392*t^31 - 483651741902964191914987117512546870364320956333017993696696885920309362375255625/106231311844342313400734690921096500030042208233078784*t^29 + 84941326355000753070985507877637956601600783708569260369013251196668545502805625/1659864247567848646886479545642132812969409503641856*t^27 - 397559309802084048045656510020645243362040444142801390513581307381855427623080100625/849850494754738507205877527368772000240337665864630272*t^25 + 11735048167526070710044831836570652508948371022984752496090322515092860268068882234375/3399401979018954028823510109475088000961350663458521088*t^23 - 138457854513909035849500329280770038659124567835498765277632083170939251530470717921875/6798803958037908057647020218950176001922701326917042176*t^21 + 1289666344318983137566252485776345322054048440447693621791577465219097361944389123859375/13597607916075816115294040437900352003845402653834084352*t^19 - 9331429397250466051575768815568053769219549829852975762419611176178807364975567331265625/27195215832151632230588080875800704007690805307668168704*t^17 + 25680937712182869372464922610627378368421584915993396098325013717912014383439342678234375/27195215832151632230588080875800704007690805307668168704*t^15 - 104612386703708333417852096718135840410086285171652560733755299335962258892108492787421875/54390431664303264461176161751601408015381610615336337408*t^13 + 303946270857136099779407660528349249292950955455271302805835781701690530990305508703203125/108780863328606528922352323503202816030763221230672674816*t^11 - 299216462919582266625826907007426147677330215822427570401741670047718681013846243450328125/108780863328606528922352323503202816030763221230672674816*t^9 + 1482357832525645851011123525324247162415517435559008157421258894549627970418401706114328125/870246906628852231378818588025622528246105769845381398528*t^7 - 1028105291115911582992110397850422517300481573434051739988141526067482164946389697672390625/1740493813257704462757637176051245056492211539690762797056*t^5 + 325086924193912032931006284789417207958603668942397228378506493334152661444907508373203125/3480987626515408925515274352102490112984423079381525594112*t^3 - 29378913991473419250019369200245955176799956107233952385493240330212054366035412887734375/6961975253030817851030548704204980225968846158763051188224*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:
| (6.5019865990210512704 - 1.1489054548329415295e-938j)  +/-  (2.14e-241, 2.14e-241j)
| (-8.1312069834445043049 + 4.1850973928280991629e-937j)  +/-  (1.23e-242, 1.23e-242j)
| (-8.6088246890994570862 - 3.7796608621681203903e-942j)  +/-  (2.61e-243, 2.61e-243j)
| (7.6903289661109035346 + 2.0436887260905680554e-945j)  +/-  (3.55e-242, 3.55e-242j)
| (-9.7891123911718082843 - 1.9699763107679979026e-948j)  +/-  (1.86e-245, 1.86e-245j)
| (8.6088246890994570862 - 8.8918096921837824025e-946j)  +/-  (2.78e-243, 2.78e-243j)
| (-9.1436086449901767681 + 1.8977883259007472317e-945j)  +/-  (3.42e-244, 3.42e-244j)
| (3.80227927820133463 - 6.7472438177167877378e-946j)  +/-  (7.66e-243, 7.66e-243j)
| (-2.6519613568352334924 + 2.4606938856514899176e-946j)  +/-  (2.37e-244, 2.37e-244j)
| (4.1177964063184850901 + 8.8607811802218508389e-945j)  +/-  (1.99e-242, 1.99e-242j)
| (1.0982883151879952536 + 1.9339607661626367467e-952j)  +/-  (3.67e-250, 3.67e-250j)
| (9.1436086449901767681 + 1.864660974220441027e-947j)  +/-  (3.39e-244, 3.39e-244j)
| (-3.185962030533641467 - 1.8964971236356194551e-945j)  +/-  (1.07e-243, 1.07e-243j)
| (8.1312069834445043049 - 2.3241203165888103949e-945j)  +/-  (1.21e-242, 1.21e-242j)
| (-4.7639512302139718534 + 1.1492285044982227456e-942j)  +/-  (8.33e-242, 8.33e-242j)
| (9.7891123911718082843 + 1.6670798450963032126e-959j)  +/-  (1.72e-245, 1.72e-245j)
| (-6.5019865990210512704 - 3.2829433876768084697e-953j)  +/-  (2.1e-241, 2.1e-241j)
| (6.8809453278553908656 + 7.6952710370719843834e-967j)  +/-  (1.5e-241, 1.5e-241j)
| (5.0956745027204231163 + 8.6532051636697125087e-967j)  +/-  (1.28e-241, 1.28e-241j)
| (-1.673551628767471445 + 2.3873176730949716859e-974j)  +/-  (5.62e-248, 5.62e-248j)
| (2.6519613568352334924 + 1.0722506483306230601e-970j)  +/-  (2.35e-244, 2.35e-244j)
| (0.81628788285896466304 - 2.3400894947685417334e-979j)  +/-  (2.59e-251, 2.59e-251j)
| (-3.4914816915871459613 - 4.6763217158458407242e-970j)  +/-  (2.89e-243, 2.89e-243j)
| (7.2756759298179091604 - 2.0937848689913712469e-967j)  +/-  (8.53e-242, 8.53e-242j)
| (-1.9645856085086837719 + 3.8046389934917973965e-974j)  +/-  (6.7e-247, 6.7e-247j)
| (6.1358848375697673414 + 2.7172459398908065995e-967j)  +/-  (2.44e-241, 2.44e-241j)
| (3.4914816915871459613 + 3.1044010407244475565e-969j)  +/-  (2.85e-243, 2.85e-243j)
| (-7.6903289661109035346 - 2.9386912586793992413e-968j)  +/-  (3.62e-242, 3.62e-242j)
| (5.4341841850722075984 + 1.1443775153619751531e-971j)  +/-  (1.93e-241, 1.93e-241j)
| (-0.26779223049751287711 - 6.05242130739917934e-985j)  +/-  (9.05e-254, 9.05e-254j)
| (-3.80227927820133463 + 3.2799907664855475e-974j)  +/-  (6.99e-243, 6.99e-243j)
| (-5.0956745027204231163 - 2.9354725274637560314e-972j)  +/-  (1.39e-241, 1.39e-241j)
| (-1.0982883151879952536 + 6.3723508890506511574e-989j)  +/-  (3.36e-250, 3.36e-250j)
| (-6.8809453278553908656 + 9.4599737805450055196e-979j)  +/-  (1.58e-241, 1.58e-241j)
| (-2.2542234394500439369 - 8.9094828902050358886e-991j)  +/-  (8.01e-246, 8.01e-246j)
| (-4.438203531905721389 - 5.1331905930910565118e-986j)  +/-  (4.06e-242, 4.06e-242j)
| (2.5147183654050249437 + 2.1464792946065653271e-990j)  +/-  (1.03e-244, 1.03e-244j)
| (-1.384382017003539275 - 2.4913494810081363946e-994j)  +/-  (4.59e-249, 4.59e-249j)
| (-4.1177964063184850901 - 5.3807176365605728511e-987j)  +/-  (1.72e-242, 1.72e-242j)
| (1.673551628767471445 + 1.3882485882870809819e-992j)  +/-  (5.56e-248, 5.56e-248j)
| (-5.7804953108661366694 - 1.4096134421561025665e-984j)  +/-  (2.27e-241, 2.27e-241j)
| (2.2542234394500439369 + 1.2783720819819726241e-1006j)  +/-  (8.37e-246, 8.37e-246j)
| (-2.8900177412162554691 - 1.2484184569718132114e-1004j)  +/-  (4.58e-244, 4.58e-244j)
| (-7.2756759298179091604 + 4.3270748796646834219e-1003j)  +/-  (8.39e-242, 8.39e-242j)
| (4.7639512302139718534 - 5.2945117253918818441e-1018j)  +/-  (8.31e-242, 8.31e-242j)
| (4.438203531905721389 - 2.8352065173721678431e-1019j)  +/-  (4.16e-242, 4.16e-242j)
| (-5.4341841850722075984 - 5.0943343006482903976e-1020j)  +/-  (1.89e-241, 1.89e-241j)
| (5.7804953108661366694 + 9.2544004149410801291e-1040j)  +/-  (2.31e-241, 2.31e-241j)
| (0.5393548506922102899 + 7.9772923586932750503e-1054j)  +/-  (1.47e-252, 1.47e-252j)
| (3.185962030533641467 - 1.1776542131313493554e-1046j)  +/-  (9.37e-244, 9.37e-244j)
| (1.384382017003539275 + 1.7866501892417275872e-1056j)  +/-  (4.74e-249, 4.74e-249j)
| (-6.1358848375697673414 + 1.6892751631276860243e-1053j)  +/-  (2.71e-241, 2.71e-241j)
| (-2.5147183654050249437 + 3.7494983635668435297e-1065j)  +/-  (1e-244, 1e-244j)
| (-0.5393548506922102899 + 1.0884058160247957524e-1072j)  +/-  (1.47e-252, 1.47e-252j)
| (3.2324713396822097014e-1093 - 1.6964085617910013175e-1093j)  +/-  (2.15e-1091, 2.15e-1091j)
| (1.9645856085086837719 - 3.9148585024876500183e-1066j)  +/-  (6.97e-247, 6.97e-247j)
| (0.26779223049751287711 - 2.0536499559678326689e-1073j)  +/-  (9.05e-254, 9.05e-254j)
| (-0.81628788285896466304 - 5.023388031313814411e-1073j)  +/-  (2.55e-251, 2.55e-251j)
| (2.8900177412162554691 + 1.8387033179688865627e-1070j)  +/-  (4.05e-244, 4.05e-244j)
-------------------------------------------------
The weights are:
| (9.1611104828832693234e-20 + 7.3072409013962028328e-957j)  +/-  (2.25e-65, 3.42e-183j)
| (4.9804407782429873411e-30 + 9.5247470396897633471e-964j)  +/-  (2.54e-71, 3.86e-189j)
| (1.8418256225801370048e-33 - 1.3469359248560839273e-965j)  +/-  (6.98e-73, 1.06e-190j)
| (4.9731077581883073269e-27 + 1.2768496584131940995e-961j)  +/-  (1.48e-71, 2.24e-189j)
| (1.0159081768577398148e-42 - 1.7288728499199817949e-970j)  +/-  (4.58e-77, 6.95e-195j)
| (1.8418256225801370048e-33 + 3.1789471009338506873e-965j)  +/-  (6.4e-75, 9.7e-193j)
| (1.592667796881861396e-37 + 9.4001775564790090615e-968j)  +/-  (5.46e-75, 8.29e-193j)
| (9.2994670374493121515e-08 + 3.8223081522993001921e-951j)  +/-  (2.66e-57, 4.04e-175j)
| (7.5619438492697366928e-05 - 1.1124733454415511394e-948j)  +/-  (1.2e-50, 1.81e-168j)
| (7.7574223411559349964e-09 - 8.913892651250236599e-952j)  +/-  (4.42e-59, 6.7e-177j)
| (0.047997433831083746181 + 2.016356589343381707e-948j)  +/-  (1.88e-33, 2.86e-151j)
| (1.592667796881861396e-37 - 1.9868739143774006595e-967j)  +/-  (3.78e-77, 5.74e-195j)
| (6.6599425470546226964e-06 - 1.1343607182550351131e-949j)  +/-  (1.6e-56, 2.43e-174j)
| (4.9804407782429873411e-30 - 2.5144344992157322949e-963j)  +/-  (6.12e-74, 9.29e-192j)
| (2.5804730122216014554e-11 + 1.5775498243543936998e-952j)  +/-  (7.56e-66, 1.15e-183j)
| (1.0159081768577398148e-42 + 3.3234625936514602101e-970j)  +/-  (1.05e-79, 1.6e-197j)
| (9.1611104828832693234e-20 + 4.43972515832282902e-958j)  +/-  (1.49e-72, 2.25e-190j)
| (5.9649235683476311026e-22 + 1.9054728871962500503e-958j)  +/-  (2.74e-71, 4.15e-189j)
| (9.9903099389301255265e-13 + 4.8780682436958623969e-954j)  +/-  (2.93e-67, 4.45e-185j)
| (0.009953942931361346557 - 9.5063822798791851378e-949j)  +/-  (2.84e-50, 4.31e-168j)
| (7.5619438492697366928e-05 + 9.5066910060003793321e-949j)  +/-  (1.36e-57, 2.07e-175j)
| (0.081020202532745808277 - 2.2757178637926768368e-948j)  +/-  (4.28e-44, 6.49e-162j)
| (8.8358468854365590095e-07 + 4.3304169969225200718e-951j)  +/-  (1.68e-62, 2.55e-180j)
| (2.3338905921797295203e-24 - 4.9769973378106321903e-960j)  +/-  (1.63e-72, 2.47e-190j)
| (0.0034639138586520765812 + 9.1009480673882889967e-949j)  +/-  (3.58e-54, 5.44e-172j)
| (9.0670453224220510587e-18 - 3.3762775906882896044e-956j)  +/-  (3.19e-70, 4.84e-188j)
| (8.8358468854365590095e-07 - 1.3406732067475632849e-950j)  +/-  (1.28e-62, 1.94e-180j)
| (4.9731077581883073269e-27 - 3.9554267166869931444e-962j)  +/-  (8.3e-79, 1.26e-196j)
| (2.8897573446224399365e-14 - 9.2079908517496709089e-955j)  +/-  (6.76e-69, 1.03e-186j)
| (0.14136832636669260795 - 6.2621468561200753189e-949j)  +/-  (8.18e-51, 1.24e-168j)
| (9.2994670374493121515e-08 - 3.017939812156394244e-951j)  +/-  (1.82e-66, 2.76e-184j)
| (9.9903099389301255265e-13 + 1.4703687037421502583e-953j)  +/-  (4.52e-72, 6.86e-190j)
| (0.047997433831083746181 - 8.9788519883561515548e-949j)  +/-  (1.49e-53, 2.26e-171j)
| (5.9649235683476311026e-22 - 2.5323587831869844449e-959j)  +/-  (1.73e-77, 2.63e-195j)
| (0.0010007437870376085728 - 9.7352709457098201147e-949j)  +/-  (5.14e-61, 7.8e-179j)
| (5.0819171424003024213e-10 - 4.8592319626526030857e-952j)  +/-  (5.9e-70, 8.95e-188j)
| (0.00020458368425173718325 - 1.2777025313508965873e-948j)  +/-  (3.18e-65, 4.82e-183j)
| (0.023888223686454269039 + 9.7558907835467321068e-949j)  +/-  (5.52e-59, 8.37e-177j)
| (7.7574223411559349964e-09 + 1.1457189577619573052e-951j)  +/-  (6.95e-69, 1.05e-186j)
| (0.009953942931361346557 + 1.3486543888587012458e-948j)  +/-  (2.87e-63, 4.36e-181j)
| (6.0908920647068683364e-16 + 8.4593047692035437993e-956j)  +/-  (1.72e-75, 2.61e-193j)
| (0.0010007437870376085728 + 1.0249551305536687532e-948j)  +/-  (8.55e-66, 1.3e-183j)
| (3.8005914253708319368e-05 + 4.2967704548381779159e-949j)  +/-  (4.29e-66, 6.53e-184j)
| (2.3338905921797295203e-24 + 1.1529302773496476625e-960j)  +/-  (2.07e-79, 3.16e-197j)
| (2.5804730122216014554e-11 - 2.3266005868453662335e-953j)  +/-  (9.94e-74, 1.52e-191j)
| (5.0819171424003024213e-10 + 8.5470904881091186343e-953j)  +/-  (5.32e-73, 8.11e-191j)
| (2.8897573446224399365e-14 - 1.0421803293072261561e-954j)  +/-  (2.34e-75, 3.49e-193j)
| (6.0908920647068683364e-16 + 1.6642156429175265587e-955j)  +/-  (1.98e-76, 3.04e-194j)
| (0.11564519764917562369 + 2.3266588222427482095e-948j)  +/-  (2.19e-66, 3.32e-184j)
| (6.6599425470546226964e-06 + 5.1387594489181516751e-950j)  +/-  (4.98e-71, 7.6e-189j)
| (0.023888223686454269039 - 1.6755393805498096132e-948j)  +/-  (8.79e-68, 1.3e-185j)
| (9.0670453224220510587e-18 - 6.5249137574703969081e-957j)  +/-  (1.63e-77, 2.4e-195j)
| (0.00020458368425173718325 + 1.3192210155169756779e-948j)  +/-  (1.43e-68, 2.11e-186j)
| (0.11564519764917562369 - 1.1578914919908407122e-949j)  +/-  (4.69e-68, 6.91e-186j)
| (0.15067232301089093035 + 1.4301846326413436448e-948j)  +/-  (3.34e-68, 5.02e-186j)
| (0.0034639138586520765812 - 1.1034938411728032984e-948j)  +/-  (8.05e-70, 1.28e-187j)
| (0.14136832636669260795 - 2.0499435630412255369e-948j)  +/-  (1.51e-68, 2.19e-186j)
| (0.081020202532745808277 + 6.3175279386065452412e-949j)  +/-  (7.18e-69, 9.26e-187j)
| (3.8005914253708319368e-05 - 2.3457430236683744311e-949j)  +/-  (4.86e-71, 8.2e-189j)
