Starting with polynomial:
P : t
Extension levels are: 1 16 32
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : t^17 - 136*t^15 + 7140*t^13 - 185640*t^11 + 2552550*t^9 - 18378360*t^7 + 64324260*t^5 - 91891800*t^3 + 34459425*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 167775971289269966314312/182562970566544874259*t^47 + 776996009026283263559808428/2008192676231993616849*t^45 - 66366742306105973435104456680/669397558743997872283*t^43 + 1512838797767891068086758024270/87312725053564939863*t^41 - 83686753345166276816944775523612760/38155660848407878720131*t^39 + 2651448366883117020578698906128731260/12718553616135959573377*t^37 - 580780419543037639125738220553989347320/38155660848407878720131*t^35 + 33052981955269782541097841005583381586925/38155660848407878720131*t^33 - 44829993136218500232845833332282862392400/1156232146921450870307*t^31 + 1585466870322066287072078235785465250533000/1156232146921450870307*t^29 - 44361405782309444768303889167503353176138000/1156232146921450870307*t^27 + 980233618208415624226513729392465164787220500/1156232146921450870307*t^25 - 740201309345771546084937412136256432056850000/50270962909628298709*t^23 + 10026764711823956386679972980429353469477875000/50270962909628298709*t^21 - 5514070895009658769712962702397306714504910000/2645840153138331511*t^19 + 43779794487183597046856973991206990888701345625/2645840153138331511*t^17 - 258911346189438302106124740171571572672597645000/2645840153138331511*t^15 + 1110708722696514233587045914408297534814458262500/2645840153138331511*t^13 - 3335137082083930055283601919890077949002790425000/2645840153138331511*t^11 + 6670706651398248390455085920213088091373033268750/2645840153138331511*t^9 - 8269557871989836163914406579157240478999723775000/2645840153138331511*t^7 + 5676442368348896808047519366042881017581044912500/2645840153138331511*t^5 - 1766986662355640234758288604389903025276203875000/2645840153138331511*t^3 + 158205616476766585577348697879052420862924484375/2645840153138331511*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:
| (11.705783418563714895 + 4.8929079991671189789e-640j)  +/-  (4.72e-247, 4.72e-247j)
| (9.2441145825109079279 + 2.6721341609477594145e-636j)  +/-  (1.63e-244, 1.63e-244j)
| (9.9536140084224740583 - 4.8318759444520042776e-640j)  +/-  (4.12e-245, 4.12e-245j)
| (-7.9766270334345972499 - 2.5958229426503934051e-644j)  +/-  (1.06e-243, 1.06e-243j)
| (-10.747918670317005884 + 5.2367879819546077759e-653j)  +/-  (7.35e-246, 7.35e-246j)
| (10.747918670317005884 + 2.4352568065009313658e-651j)  +/-  (7.48e-246, 7.48e-246j)
| (6.8891224398953322326 + 1.3181125650058908607e-662j)  +/-  (5.77e-243, 5.77e-243j)
| (-1.8956939325258284482 - 8.6166442913272511614e-683j)  +/-  (2.45e-249, 2.45e-249j)
| (-2.6718883685115980278 - 7.9006137600654833392e-676j)  +/-  (1.08e-247, 1.08e-247j)
| (-6.2466921563413200516 + 2.330299533523647337e-680j)  +/-  (2.62e-243, 2.62e-243j)
| (1.5098833077967407591 - 8.3957513844510566393e-696j)  +/-  (2.29e-250, 2.29e-250j)
| (-11.705783418563714895 + 4.1224588138645659565e-693j)  +/-  (4.98e-247, 4.98e-247j)
| (5.2515725911691863648 - 6.0738757892599742241e-688j)  +/-  (2.98e-244, 2.98e-244j)
| (-9.2441145825109079279 + 1.4059685487800628318e-695j)  +/-  (1.62e-244, 1.62e-244j)
| (-6.8891224398953322326 - 7.5584230438101288924e-702j)  +/-  (5.6e-243, 5.6e-243j)
| (-7.3994900780676394535 - 5.6487348722346406101e-714j)  +/-  (2.18e-243, 2.18e-243j)
| (3.0737971753281935585 - 3.92705580411595018e-723j)  +/-  (5.96e-247, 5.96e-247j)
| (7.3994900780676394535 + 3.505441837967080484e-718j)  +/-  (2.13e-243, 2.13e-243j)
| (3.900065717198009909 + 1.8456105556067628526e-728j)  +/-  (1.13e-245, 1.13e-245j)
| (8.589857249633627883 + 8.1900017710227197717e-733j)  +/-  (4.6e-244, 4.6e-244j)
| (-9.9536140084224740583 - 3.4026034927483090739e-742j)  +/-  (4.49e-245, 4.49e-245j)
| (-2.2810194402529888954 - 4.09694323953705734e-750j)  +/-  (1.85e-248, 1.85e-248j)
| (6.2466921563413200516 + 2.9379798463233627193e-744j)  +/-  (2.51e-243, 2.51e-243j)
| (-5.7444600786594061813 + 1.9093611586620725174e-751j)  +/-  (7.71e-244, 7.71e-244j)
| (-1.5098833077967407591 - 2.8312444632131959463e-763j)  +/-  (2.85e-250, 2.85e-250j)
| (6.644216322286837198 + 4.5325596933145773493e-756j)  +/-  (5.85e-243, 5.85e-243j)
| (1.8956939325258284482 - 5.3953389983740760844e-763j)  +/-  (2.39e-249, 2.39e-249j)
| (-4.7785315896299838271 - 2.272656773676878192e-756j)  +/-  (1.03e-244, 1.03e-244j)
| (-8.589857249633627883 - 3.29768056261357294e-761j)  +/-  (4.51e-244, 4.51e-244j)
| (-1.1271347541767408519 + 2.3704333221684311792e-774j)  +/-  (2.39e-251, 2.39e-251j)
| (-5.2515725911691863648 + 4.3475829029253668533e-767j)  +/-  (3.27e-244, 3.27e-244j)
| (3.4839177163313127953 + 2.0395698744710126111e-774j)  +/-  (2.78e-246, 2.78e-246j)
| (7.9766270334345972499 - 8.3654491030108677116e-772j)  +/-  (1.03e-243, 1.03e-243j)
| (-3.900065717198009909 - 1.9593925125925440857e-775j)  +/-  (1.12e-245, 1.12e-245j)
| (-0.75184260070389617074 + 2.0725275805316904377e-786j)  +/-  (1.74e-252, 1.74e-252j)
| (5.7444600786594061813 - 6.6614285981199026334e-779j)  +/-  (8.57e-244, 8.57e-244j)
| (4.1035535526771279823e-809 - 6.2103105307101496268e-808j)  +/-  (3.05e-806, 3.05e-806j)
| (2.6718883685115980278 - 1.4182191091923860159e-793j)  +/-  (1.11e-247, 1.11e-247j)
| (0.37820221548430280804 - 7.9107126535152752065e-800j)  +/-  (1.33e-253, 1.33e-253j)
| (-6.644216322286837198 - 5.7296594002518467692e-792j)  +/-  (5.93e-243, 5.93e-243j)
| (-3.4839177163313127953 + 1.8268468779995638483e-801j)  +/-  (2.76e-246, 2.76e-246j)
| (0.75184260070389617074 - 1.2615816285323291386e-809j)  +/-  (1.74e-252, 1.74e-252j)
| (2.2810194402529888954 + 5.8350570985376532153e-805j)  +/-  (1.85e-248, 1.85e-248j)
| (1.1271347541767408519 + 4.9620051915921707571e-808j)  +/-  (2.49e-251, 2.49e-251j)
| (4.328720740337961371 - 4.6307242303398031157e-800j)  +/-  (3.91e-245, 3.91e-245j)
| (-3.0737971753281935585 - 1.889698256952180431e-802j)  +/-  (5.95e-247, 5.95e-247j)
| (-4.328720740337961371 - 4.9109361971568216511e-802j)  +/-  (4.06e-245, 4.06e-245j)
| (-0.37820221548430280804 + 4.6335176740999576847e-811j)  +/-  (1.33e-253, 1.33e-253j)
| (4.7785315896299838271 - 1.053305637823067509e-808j)  +/-  (1.21e-244, 1.21e-244j)
-------------------------------------------------
The weights are:
| (7.7587070795165284637e-31 - 2.5998288211779294159e-662j)  +/-  (1.61e-84, 2.42e-206j)
| (7.5253700797127471341e-20 - 1.1601194438810300998e-654j)  +/-  (4.93e-80, 7.41e-202j)
| (9.1048183630732627908e-23 - 4.6089348243353790918e-657j)  +/-  (1.73e-81, 2.6e-203j)
| (3.6247463527697860644e-15 - 1.4329888739286118944e-653j)  +/-  (4.52e-80, 6.8e-202j)
| (2.8077295154220977907e-26 - 1.3568448893047393109e-660j)  +/-  (3.25e-86, 4.88e-208j)
| (2.8077295154220977907e-26 + 1.8038586947179615072e-659j)  +/-  (1.79e-83, 2.69e-205j)
| (8.1396040900515314422e-12 - 7.5766311097314297605e-650j)  +/-  (1.62e-76, 2.43e-198j)
| (0.025491178791924755544 - 1.9406724476863489481e-644j)  +/-  (6.15e-55, 9.24e-177j)
| (0.0044531871233470617954 - 4.5131796428819242001e-645j)  +/-  (3.09e-61, 4.63e-183j)
| (6.6396171206437538758e-10 - 1.0734783021658984753e-649j)  +/-  (8.31e-77, 1.25e-198j)
| (0.04919120507442972769 + 4.6617505116011030581e-644j)  +/-  (1.28e-53, 1.92e-175j)
| (7.7587070795165284637e-31 + 3.0548434397916567218e-663j)  +/-  (5.56e-89, 8.35e-211j)
| (1.9809947980322566561e-07 - 8.4036170152032778657e-648j)  +/-  (7.75e-75, 1.16e-196j)
| (7.5253700797127471341e-20 - 1.0876621472986380572e-656j)  +/-  (3.18e-84, 4.78e-206j)
| (8.1396040900515314422e-12 - 1.1059809003290102127e-650j)  +/-  (2.97e-79, 4.47e-201j)
| (2.8667653055235309034e-13 + 4.0424734409341862396e-652j)  +/-  (2.76e-80, 4.14e-202j)
| (0.0014411834603884741271 + 3.5351618634667947191e-645j)  +/-  (5.74e-70, 8.62e-192j)
| (2.8667653055235309034e-13 + 3.6473753138720141429e-651j)  +/-  (4.24e-82, 6.36e-204j)
| (8.355467696304192135e-05 + 4.6976453997300876246e-646j)  +/-  (5.17e-74, 7.76e-196j)
| (2.3954052146534551638e-17 + 1.2327922219501034682e-653j)  +/-  (1.48e-84, 2.22e-206j)
| (9.1048183630732627908e-23 + 1.7034586318917589447e-658j)  +/-  (5.33e-88, 8.01e-210j)
| (0.01143716538133365475 + 1.0038148609037787832e-644j)  +/-  (1.16e-68, 1.74e-190j)
| (6.6396171206437538758e-10 - 5.5477520757722430261e-649j)  +/-  (1.88e-80, 2.83e-202j)
| (1.3641935456370459893e-08 + 4.5764966118659003481e-649j)  +/-  (2.28e-80, 3.42e-202j)
| (0.04919120507442972769 + 3.352713971837448291e-644j)  +/-  (2.02e-66, 3.03e-188j)
| (2.2921866272554891356e-11 + 2.3069557340337331404e-649j)  +/-  (5.64e-81, 8.47e-203j)
| (0.025491178791924755544 - 2.941952201372578716e-644j)  +/-  (6.32e-70, 9.5e-192j)
| (2.0268576675807128609e-06 + 1.1419641215474801178e-647j)  +/-  (1.89e-79, 2.84e-201j)
| (2.3954052146534551638e-17 + 4.5226023064651389467e-655j)  +/-  (3.34e-86, 5.01e-208j)
| (0.080108609939504707282 - 5.2529833241709022462e-644j)  +/-  (4.82e-68, 7.23e-190j)
| (1.9809947980322566561e-07 - 2.3146129328721005631e-648j)  +/-  (4.08e-80, 6.12e-202j)
| (0.00038107114127390260281 - 1.3676666560221866415e-645j)  +/-  (1.97e-77, 2.96e-199j)
| (3.6247463527697860644e-15 - 1.9468523121470501936e-652j)  +/-  (1.37e-85, 2.05e-207j)
| (8.355467696304192135e-05 + 1.9099323667128953475e-646j)  +/-  (3.03e-79, 4.55e-201j)
| (0.11210354314338046828 + 7.3030676403492157122e-644j)  +/-  (4.95e-71, 7.43e-193j)
| (1.3641935456370459893e-08 + 1.960047152981978298e-648j)  +/-  (7.79e-82, 1.17e-203j)
| (0.15142756231480036105 + 9.6892629133598501262e-644j)  +/-  (9.57e-73, 1.44e-194j)
| (0.0044531871233470617954 - 8.1827674492569092239e-645j)  +/-  (6.75e-77, 1.02e-198j)
| (0.1395783615030621839 - 9.6461880411118019015e-644j)  +/-  (1.93e-73, 2.91e-195j)
| (2.2921866272554891356e-11 + 3.7750289422595593812e-650j)  +/-  (7.31e-83, 1.1e-204j)
| (0.00038107114127390260281 - 6.1895209107286310966e-646j)  +/-  (4.6e-79, 6.91e-201j)
| (0.11210354314338046828 + 8.5961836292341067343e-644j)  +/-  (2.18e-74, 3.25e-196j)
| (0.01143716538133365475 + 1.6614866344822089812e-644j)  +/-  (5.03e-77, 7.51e-199j)
| (0.080108609939504707282 - 6.711852938410215342e-644j)  +/-  (8.78e-76, 1.31e-197j)
| (1.491931259549354005e-05 - 1.394320197663226645e-646j)  +/-  (6.39e-81, 9.6e-203j)
| (0.0014411834603884741271 + 1.7708440951619205021e-645j)  +/-  (2.61e-79, 4.03e-201j)
| (1.491931259549354005e-05 - 5.049533477917202314e-647j)  +/-  (4.61e-81, 7.14e-203j)
| (0.1395783615030621839 - 8.8879084495948067491e-644j)  +/-  (1.94e-77, 3.2e-199j)
| (2.0268576675807128609e-06 + 3.5859405296984503182e-647j)  +/-  (6.97e-82, 1.02e-203j)
