Starting with polynomial:
P : 2*t
Extension levels are: 1 16 32
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 2*t^17 - 136*t^15 + 3570*t^13 - 46410*t^11 + 1276275/4*t^9 - 2297295/2*t^7 + 16081065/8*t^5 - 11486475/8*t^3 + 34459425/128*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^49 - 167775971289269966314312/182562970566544874259*t^47 + 388498004513141631779904214/2008192676231993616849*t^45 - 16591685576526493358776114170/669397558743997872283*t^43 + 756419398883945534043379012135/349250900214259759452*t^41 - 10460844168145784602118096940451595/76311321696815757440262*t^39 + 662862091720779255144674726532182815/101748428929087676587016*t^37 - 72597552442879704890717277569248668415/305245286787263029761048*t^35 + 33052981955269782541097841005583381586925/4883924588596208476176768*t^33 - 2801874571013656264552864583267678899525/18499714350743213924912*t^31 + 198183358790258285884009779473183156316625/73998857402972855699648*t^29 - 2772587861394340298018993072968959573508625/73998857402972855699648*t^27 + 245058404552103906056628432348116291196805125/591990859223782845597184*t^25 - 46262581834110721630308588258516027003553125/12869366504864844469504*t^23 + 1253345588977994548334996622553669183684734375/51477466019459377878016*t^21 - 344629430938103673107060168899831669656556875/2709340316813651467264*t^19 + 43779794487183597046856973991206990888701345625/86698890138036846952448*t^17 - 32363918273679787763265592521446446584074705625/21674722534509211738112*t^15 + 277677180674128558396761478602074383703614565625/86698890138036846952448*t^13 - 416892135260491256910450239986259743625348803125/86698890138036846952448*t^11 + 3335353325699124195227542960106544045686516634375/693591121104294775619584*t^9 - 1033694733998729520489300822394655059874965471875/346795560552147387809792*t^7 + 1419110592087224202011879841510720254395261228125/1387182242208589551239168*t^5 - 220873332794455029344786075548737878159525484375/1387182242208589551239168*t^3 + 158205616476766585577348697879052420862924484375/22194915875337432819826688*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:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.4170783837337645164 - 2.2121322019052159379e-925j)  +/-  (1.8e-243, 1.8e-243j)
| (4.0619466758754743069 - 2.0551530829776145752e-927j)  +/-  (5.75e-244, 5.75e-244j)
| (-7.0382679626689445715 + 9.412603328196155067e-926j)  +/-  (3.17e-245, 3.17e-245j)
| (-6.0739463106403646466 - 2.8615454911707180954e-932j)  +/-  (3.35e-244, 3.35e-244j)
| (-7.5999261754226559004 + 2.8184588402591548252e-940j)  +/-  (5.09e-246, 5.09e-246j)
| (5.2322296115242037902 - 2.3552894582772682858e-937j)  +/-  (1.64e-243, 1.64e-243j)
| (-6.5365761073589136929 - 6.2690981049106130844e-942j)  +/-  (1.22e-244, 1.22e-244j)
| (-8.2772388343674490008 - 8.9641694098147064218e-951j)  +/-  (3.38e-247, 3.38e-247j)
| (7.0382679626689445715 + 5.6864849695725589192e-949j)  +/-  (3.34e-245, 3.34e-245j)
| (2.7577629157038887309 + 9.2153815934398986063e-951j)  +/-  (7.98e-246, 7.98e-246j)
| (3.3789320911414940834 + 2.0419930573489370429e-948j)  +/-  (8.41e-245, 8.41e-245j)
| (-3.3789320911414940834 - 6.1135447938844539574e-947j)  +/-  (8.18e-245, 8.18e-245j)
| (4.8713451936744030883 + 6.8413997494768412307e-947j)  +/-  (3.88e-243, 3.88e-243j)
| (5.6403270663375374616 + 2.7287876656544556547e-953j)  +/-  (7.45e-244, 7.45e-244j)
| (1.8893103839480120032 - 8.3679133435821424561e-958j)  +/-  (7.43e-248, 7.43e-248j)
| (4.6981704171593661163 - 1.3767527413844876521e-952j)  +/-  (4.62e-243, 4.62e-243j)
| (-4.8713451936744030883 - 6.0077387954107918646e-961j)  +/-  (3.86e-243, 3.86e-243j)
| (-4.4170783837337645164 - 3.8383949426358811743e-979j)  +/-  (1.76e-243, 1.76e-243j)
| (1.0676487257434505536 - 5.0130588954701047646e-1003j)  +/-  (1.76e-250, 1.76e-250j)
| (-2.4635018423138219454 + 1.4335792505483901411e-996j)  +/-  (2e-246, 2e-246j)
| (3.7134225911091402629 + 3.8246326949317333609e-996j)  +/-  (2.18e-244, 2.18e-244j)
| (-4.6981704171593661163 + 8.3877831315435210838e-995j)  +/-  (4.09e-243, 4.09e-243j)
| (1.3404580347432067635 + 2.7355322276706728149e-1008j)  +/-  (1.64e-249, 1.64e-249j)
| (-3.7134225911091402629 + 2.2788666823973449876e-1001j)  +/-  (2.2e-244, 2.2e-244j)
| (-3.0608677893558248551 - 1.7781512114464264817e-1008j)  +/-  (2.6e-245, 2.6e-245j)
| (-4.0619466758754743069 + 1.066007977105874086e-1006j)  +/-  (6.05e-244, 6.05e-244j)
| (2.4635018423138219454 + 3.3358623350135218252e-1019j)  +/-  (1.97e-246, 1.97e-246j)
| (-2.7577629157038887309 + 1.8977748912882870811e-1019j)  +/-  (8.85e-246, 8.85e-246j)
| (6.0739463106403646466 - 6.2340123101445503102e-1016j)  +/-  (3.18e-244, 3.18e-244j)
| (-0.79700462798940572694 - 4.1281326295533248501e-1028j)  +/-  (1.5e-251, 1.5e-251j)
| (6.5365761073589136929 + 2.016712533849917737e-1019j)  +/-  (1.21e-244, 1.21e-244j)
| (7.5999261754226559004 - 1.0771352222166506981e-1023j)  +/-  (4.92e-246, 4.92e-246j)
| (-1.8893103839480120032 - 5.4379581766210500264e-1025j)  +/-  (7.33e-248, 7.33e-248j)
| (3.0608677893558248551 - 6.5797983058043674683e-1021j)  +/-  (2.64e-245, 2.64e-245j)
| (-1.6129243142212313331 + 3.1230599152344886355e-1028j)  +/-  (1.14e-248, 1.14e-248j)
| (-1.3404580347432067635 - 1.6093564211839519854e-1029j)  +/-  (1.72e-249, 1.72e-249j)
| (-1.0676487257434505536 - 3.7863448515468803549e-1031j)  +/-  (1.8e-250, 1.8e-250j)
| (0.53163300134265473135 - 2.1582796586157778559e-1033j)  +/-  (1.08e-252, 1.08e-252j)
| (2.8430076446565929437e-1043 + 5.0951549987265896791e-1044j)  +/-  (1.42e-1041, 1.42e-1041j)
| (-5.6403270663375374616 - 1.2916092347075057721e-1024j)  +/-  (7.04e-244, 7.04e-244j)
| (-0.53163300134265473135 - 1.0444254323638667315e-1054j)  +/-  (1.17e-252, 1.17e-252j)
| (8.2772388343674490008 - 3.8672615112618204595e-1047j)  +/-  (3.52e-247, 3.52e-247j)
| (0.79700462798940572694 - 4.859826583587320958e-1052j)  +/-  (1.57e-251, 1.57e-251j)
| (2.1735028266666208193 - 7.4779216949666357725e-1048j)  +/-  (3.92e-247, 3.92e-247j)
| (-5.2322296115242037902 - 2.321888523658059321e-1049j)  +/-  (1.49e-243, 1.49e-243j)
| (-0.26742935122872640164 + 1.7931666744567164058e-1064j)  +/-  (7.61e-254, 7.61e-254j)
| (-2.1735028266666208193 + 1.9162394098521825409e-1059j)  +/-  (3.89e-247, 3.89e-247j)
| (1.6129243142212313331 - 1.2535741211491504102e-1060j)  +/-  (1.28e-248, 1.28e-248j)
| (0.26742935122872640164 - 4.3232091728665818911e-1067j)  +/-  (7.61e-254, 7.61e-254j)
-------------------------------------------------
The weights are:
| (6.6396171206437538758e-10 + 4.9473213744100882468e-934j)  +/-  (7.02e-66, 3.49e-186j)
| (1.3641935456370459893e-08 - 1.5819743515635661933e-933j)  +/-  (3.72e-64, 1.85e-184j)
| (9.1048183630732627908e-23 - 2.3938598559060314819e-944j)  +/-  (3.5e-77, 1.74e-197j)
| (2.3954052146534551638e-17 - 6.4632209555266959147e-941j)  +/-  (1.27e-74, 6.3e-195j)
| (2.8077295154220977907e-26 + 1.8999890963633626973e-946j)  +/-  (2.93e-79, 1.46e-199j)
| (2.8667653055235309034e-13 + 7.0552439384035531309e-937j)  +/-  (2.03e-73, 1.01e-193j)
| (7.5253700797127471341e-20 + 1.5429158870577203963e-942j)  +/-  (3.06e-76, 1.52e-196j)
| (7.7587070795165284637e-31 - 4.2423441145037300641e-949j)  +/-  (1.19e-81, 5.91e-202j)
| (9.1048183630732627908e-23 + 1.0570751659462568708e-943j)  +/-  (7.28e-81, 3.62e-201j)
| (8.355467696304192135e-05 - 1.2576372822780234885e-931j)  +/-  (7.4e-64, 3.68e-184j)
| (2.0268576675807128609e-06 - 1.2665922473957394781e-932j)  +/-  (6.8e-67, 3.38e-187j)
| (2.0268576675807128609e-06 - 1.726177314283494478e-933j)  +/-  (1.63e-69, 8.13e-190j)
| (8.1396040900515314422e-12 - 3.3792192096369797616e-935j)  +/-  (6.78e-73, 3.37e-193j)
| (3.6247463527697860644e-15 - 1.7178777645581803203e-938j)  +/-  (6.89e-77, 3.43e-197j)
| (0.0044531871233470617954 + 1.7779748126795371511e-930j)  +/-  (3.35e-62, 1.66e-182j)
| (2.2921866272554891356e-11 + 1.8461443768243383489e-934j)  +/-  (3.31e-72, 1.65e-192j)
| (8.1396040900515314422e-12 + 1.6148788350132375505e-936j)  +/-  (1.28e-77, 6.37e-198j)
| (6.6396171206437538758e-10 + 1.5822803368505219459e-935j)  +/-  (9.41e-77, 4.68e-197j)
| (0.04919120507442972769 - 9.0156120675742644984e-930j)  +/-  (1.86e-60, 9.26e-181j)
| (0.00038107114127390260281 + 9.6191334220398480344e-932j)  +/-  (1.76e-70, 8.75e-191j)
| (1.9809947980322566561e-07 + 3.8180951983171223012e-933j)  +/-  (1.65e-72, 8.22e-193j)
| (2.2921866272554891356e-11 - 5.531361411325228881e-936j)  +/-  (2.1e-77, 1.05e-197j)
| (0.025491178791924755544 + 5.8817183031679027145e-930j)  +/-  (1.34e-64, 6.64e-185j)
| (1.9809947980322566561e-07 + 3.468280372399951629e-934j)  +/-  (1.74e-75, 8.67e-196j)
| (1.491931259549354005e-05 + 7.7014655249109442234e-933j)  +/-  (5.65e-74, 2.81e-194j)
| (1.3641935456370459893e-08 - 6.7998222913918130526e-935j)  +/-  (1.47e-76, 7.29e-197j)
| (0.00038107114127390260281 + 3.3603881791606891535e-931j)  +/-  (1.25e-72, 6.2e-193j)
| (8.355467696304192135e-05 - 2.9398766723088122059e-932j)  +/-  (1.66e-73, 8.26e-194j)
| (2.3954052146534551638e-17 + 4.1359028107241305221e-940j)  +/-  (6.46e-85, 3.21e-205j)
| (0.080108609939504707282 + 8.7703446269081474949e-930j)  +/-  (6.48e-69, 3.22e-189j)
| (7.5253700797127471341e-20 - 8.0479662210620943915e-942j)  +/-  (5.36e-87, 2.67e-207j)
| (2.8077295154220977907e-26 - 7.214348824587387486e-946j)  +/-  (1.97e-91, 9.81e-212j)
| (0.0044531871233470617954 + 7.1625577306776202159e-931j)  +/-  (3.45e-75, 1.72e-195j)
| (1.491931259549354005e-05 + 4.1837315681056331235e-932j)  +/-  (8.56e-77, 4.26e-197j)
| (0.01143716538133365475 - 1.6112313726554220718e-930j)  +/-  (1.15e-74, 5.74e-195j)
| (0.025491178791924755544 + 3.1528534049236974665e-930j)  +/-  (3.47e-74, 1.73e-194j)
| (0.04919120507442972769 - 5.5188590928817215953e-930j)  +/-  (1.06e-73, 5.29e-194j)
| (0.11210354314338046828 - 1.5749571013083562987e-929j)  +/-  (1.97e-74, 9.78e-195j)
| (0.15142756231480036105 - 1.7008969534956528317e-929j)  +/-  (2.53e-74, 1.26e-194j)
| (3.6247463527697860644e-15 + 2.0626950355996088762e-939j)  +/-  (4.68e-86, 2.33e-206j)
| (0.11210354314338046828 - 1.2379606416960378078e-929j)  +/-  (5.29e-75, 2.63e-195j)
| (7.7587070795165284637e-31 + 1.4023396262740175975e-948j)  +/-  (1.56e-95, 7.78e-216j)
| (0.080108609939504707282 + 1.2610345817354879725e-929j)  +/-  (9.92e-76, 4.94e-196j)
| (0.0014411834603884741271 - 8.1152891145184604265e-931j)  +/-  (6.48e-78, 3.23e-198j)
| (2.8667653055235309034e-13 - 5.8617484701296514221e-938j)  +/-  (1.15e-84, 5.71e-205j)
| (0.1395783615030621839 + 1.5317422036179201543e-929j)  +/-  (4.29e-76, 2.13e-196j)
| (0.0014411834603884741271 - 2.7802574452846708949e-931j)  +/-  (4.12e-78, 2.06e-198j)
| (0.01143716538133365475 - 3.4509483658327463196e-930j)  +/-  (1.08e-77, 5.41e-198j)
| (0.1395783615030621839 + 1.7282050363542245884e-929j)  +/-  (2.02e-76, 9.81e-197j)
