Starting with polynomial:
P : 1048576*t^20 - 99614720*t^18 + 3810263040*t^16 - 76205260800*t^14 + 866834841600*t^12 - 5721109954560*t^10 + 21454162329600*t^8 - 42908324659200*t^6 + 40226554368000*t^4 - 13408851456000*t^2 + 670442572800
Extension levels are: 20 29
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P1 : 1048576*t^20 - 99614720*t^18 + 3810263040*t^16 - 76205260800*t^14 + 866834841600*t^12 - 5721109954560*t^10 + 21454162329600*t^8 - 42908324659200*t^6 + 40226554368000*t^4 - 13408851456000*t^2 + 670442572800
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1048576*t^49 - 3123904189828687122124488708471652352/7221058742728048922645934429*t^47 + 587755166720981397224418323623502675968/7221058742728048922645934429*t^45 - 7443444051020270885878707046874507509760/802339860303116546960659381*t^43 + 575855177548463640755062859415539425607680/802339860303116546960659381*t^41 - 32113687037077783688951055856064213974876160/802339860303116546960659381*t^39 + 1338260970426397677786559580610542031420948480/802339860303116546960659381*t^37 - 42637647969184886423511550952224093448897617920/802339860303116546960659381*t^35 + 1054005114430135688713371706127946256298652364800/802339860303116546960659381*t^33 - 20401734747460542906044286454551692953451092070400/802339860303116546960659381*t^31 + 310768252643210235182265743648751825169839353548800/802339860303116546960659381*t^29 - 3731218588576951363322371492201085517579720020198400/802339860303116546960659381*t^27 + 35262043370581562964796644728288967797263033799961600/802339860303116546960659381*t^25 - 261190075765628609159137649722954494382736333748960000/802339860303116546960659381*t^23 + 1505405876275264615240614022960607152414638372120480000/802339860303116546960659381*t^21 - 6680567713523293792357951596625940795079501225884760000/802339860303116546960659381*t^19 + 22497940286990404129407828001624780906570439166064830000/802339860303116546960659381*t^17 - 56389665498854130051283982725548599765694844937636145000/802339860303116546960659381*t^15 + 102488777827481494517221106589337585383598624734533325000/802339860303116546960659381*t^13 - 130375505904698264926857613231447937060673955839627131250/802339860303116546960659381*t^11 + 110445671954530667118754169307541411568974269524039231250/802339860303116546960659381*t^9 - 115751225666324556011788178195976064045077985823870184375/1604679720606233093921318762*t^7 + 33346060815891923295392075423630956708138902235074065625/1604679720606233093921318762*t^5 - 17162252197169927508468063833962649263473437775233296875/6418718882424932375685275048*t^3 + 1279859128938081913908961497320531987031420297621890625/12837437764849864751370550096*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:
| (-6.789832445256453311 + 1.3209847788465000323e-964j)  +/-  (1.2e-245, 1.2e-245j)
| (6.789832445256453311 - 2.1423467771300860302e-973j)  +/-  (1.24e-245, 1.24e-245j)
| (-5.8207622462770144326 + 7.2008627064433427506e-973j)  +/-  (1.06e-244, 1.06e-244j)
| (6.2850423318628514854 + 6.4826213141827713513e-986j)  +/-  (4.44e-245, 4.44e-245j)
| (8.0386338757717737438 + 3.5745587016129193878e-988j)  +/-  (1.68e-247, 1.68e-247j)
| (-7.3557482117301517967 - 1.4164035992525918059e-984j)  +/-  (2.09e-246, 2.09e-246j)
| (-5.387480890011232862 + 3.9991873728702719338e-988j)  +/-  (1.75e-244, 1.75e-244j)
| (-2.2549740020892755231 + 3.4522971560428013802e-999j)  +/-  (2.15e-246, 2.15e-246j)
| (-8.0386338757717737438 - 3.1210342073266618211e-1005j)  +/-  (1.7e-247, 1.7e-247j)
| (4.2587513624619382129 + 7.3707842259857638583e-1001j)  +/-  (3.86e-244, 3.86e-244j)
| (-3.9447640401156252104 + 1.2006572076452895818e-1001j)  +/-  (3.34e-244, 3.34e-244j)
| (2.7888060584281304805 - 8.1291469942118334996e-1019j)  +/-  (2.23e-245, 2.23e-245j)
| (-6.2850423318628514854 + 2.037045447131911991e-1019j)  +/-  (3.91e-245, 3.91e-245j)
| (-1.4459803393497923057 - 4.8871546693205545576e-1029j)  +/-  (1e-248, 1e-248j)
| (4.98145626850662985 + 1.2962283492952218683e-1023j)  +/-  (2.84e-244, 2.84e-244j)
| (1.7385377121165862068 + 2.6782505549161150726e-1037j)  +/-  (6.51e-248, 6.51e-248j)
| (-4.6036824495507442731 - 5.3666294244405000716e-1033j)  +/-  (3.7e-244, 3.7e-244j)
| (3.3478545673832163269 - 1.2280920751710318355e-1049j)  +/-  (1.31e-244, 1.31e-244j)
| (-1.0255115773001672342 - 1.0796143944629586693e-1055j)  +/-  (2.7e-250, 2.7e-250j)
| (-4.98145626850662985 + 1.4095501962756170105e-1049j)  +/-  (2.78e-244, 2.78e-244j)
| (-3.3478545673832163269 - 6.3777205722916691612e-1054j)  +/-  (1.28e-244, 1.28e-244j)
| (-3.6435111352311490305 + 1.086949647186427336e-1060j)  +/-  (2.41e-244, 2.41e-244j)
| (7.3557482117301517967 - 1.9188682083047743875e-1068j)  +/-  (2.07e-246, 2.07e-246j)
| (2.5066949774301229205 + 3.3624896951211746954e-1067j)  +/-  (8.2e-246, 8.2e-246j)
| (-2.7888060584281304805 - 1.8691954257625770408e-1065j)  +/-  (2.12e-245, 2.12e-245j)
| (3.6435111352311490305 + 3.9545819348833668923e-1069j)  +/-  (2.4e-244, 2.4e-244j)
| (1.4459803393497923057 + 3.9795911808712176529e-1075j)  +/-  (9.27e-249, 9.27e-249j)
| (5.387480890011232862 - 1.4797387224445669156e-1069j)  +/-  (1.79e-244, 1.79e-244j)
| (3.9447640401156252104 + 2.0640115955595818221e-1070j)  +/-  (3.62e-244, 3.62e-244j)
| (-1.2340762153953230079 + 4.6479473328713673988e-1076j)  +/-  (2.48e-249, 2.48e-249j)
| (2.2549740020892755231 - 9.6429708972215112891e-1073j)  +/-  (2.14e-246, 2.14e-246j)
| (3.0667198326018712936 + 5.9463573507666980934e-1072j)  +/-  (6.16e-245, 6.16e-245j)
| (1.2340762153953230079 - 7.8241382537205693569e-1077j)  +/-  (2.3e-249, 2.3e-249j)
| (5.8207622462770144326 - 1.0238777237123833493e-1072j)  +/-  (1.01e-244, 1.01e-244j)
| (-0.73747372854539435871 + 3.5696625999960710459e-1079j)  +/-  (1.33e-251, 1.33e-251j)
| (-2.0205048988011777089 - 1.8622284182538409864e-1073j)  +/-  (4.74e-247, 4.74e-247j)
| (-1.7385377121165862068 + 2.6164346500491710424e-1074j)  +/-  (6.22e-248, 6.22e-248j)
| (1.0255115773001672342 + 1.6948827054423625879e-1077j)  +/-  (2.95e-250, 2.95e-250j)
| (-3.0667198326018712936 - 3.5116806413714574729e-1072j)  +/-  (6.38e-245, 6.38e-245j)
| (0.2453407083009012499 - 2.1576930351301551821e-1089j)  +/-  (8.04e-254, 8.04e-254j)
| (-0.46634542899944835792 - 7.5514200807802322763e-1088j)  +/-  (9.16e-253, 9.16e-253j)
| (-4.2587513624619382129 + 4.0173903853950320716e-1082j)  +/-  (3.97e-244, 3.97e-244j)
| (0.73747372854539435871 + 6.7918302410336669767e-1094j)  +/-  (1.36e-251, 1.36e-251j)
| (2.0205048988011777089 - 6.6617397071828743577e-1089j)  +/-  (4.9e-247, 4.9e-247j)
| (4.6036824495507442731 - 1.3559781243383613823e-1090j)  +/-  (3.57e-244, 3.57e-244j)
| (-0.2453407083009012499 - 3.4547360390369378355e-1099j)  +/-  (8.04e-254, 8.04e-254j)
| (-1.0799807573157644054e-1115 + 1.065735107310949824e-1115j)  +/-  (7.43e-1114, 7.43e-1114j)
| (-2.5066949774301229205 + 4.9246726001491844422e-1096j)  +/-  (6.97e-246, 6.97e-246j)
| (0.46634542899944835792 - 2.635239503767345286e-1103j)  +/-  (9.73e-253, 9.73e-253j)
-------------------------------------------------
The weights are:
| (2.8463049499388545356e-21 + 3.1996435595563418347e-984j)  +/-  (2.63e-86, 6.76e-208j)
| (2.8463049499388545356e-21 + 2.7687926593238108261e-986j)  +/-  (7.93e-87, 2.04e-208j)
| (4.8754151532600637324e-16 + 1.0278974798490154003e-981j)  +/-  (1.1e-83, 2.82e-205j)
| (1.9026925351232063825e-18 - 1.8577047206975265832e-984j)  +/-  (1.84e-85, 4.74e-207j)
| (3.8382694761687099498e-29 + 4.3145726921385655589e-991j)  +/-  (7.98e-91, 2.05e-212j)
| (1.0909130897475524011e-24 + 5.1707093958737811075e-987j)  +/-  (5.51e-89, 1.42e-210j)
| (5.8708726412307248951e-14 - 2.0919973528440143934e-980j)  +/-  (2.66e-83, 6.84e-205j)
| (0.00079741440044646681239 - 3.3035043997560446023e-972j)  +/-  (1.05e-69, 2.69e-191j)
| (3.8382694761687099498e-29 - 5.1231912524950804295e-990j)  +/-  (1.39e-91, 3.58e-213j)
| (2.4547566236862586184e-09 + 1.3842863593936811106e-977j)  +/-  (2.09e-82, 5.39e-204j)
| (2.9946659952927145098e-08 - 4.8998768128934416594e-976j)  +/-  (1.16e-79, 2.99e-201j)
| (6.6777144512126947068e-05 - 1.2159955238922791325e-973j)  +/-  (3.5e-76, 9e-198j)
| (1.9026925351232063825e-18 - 4.8117497508802659254e-983j)  +/-  (3.96e-86, 1.02e-207j)
| (0.01895040019208788374 + 3.9369807883365426586e-971j)  +/-  (2.25e-66, 5.79e-188j)
| (3.7003806576798477737e-12 + 5.6402474919481545818e-980j)  +/-  (1.22e-85, 3.13e-207j)
| (0.008178801140579542203 - 8.2161643774177506582e-972j)  +/-  (2.68e-70, 6.9e-192j)
| (1.2763038499638780912e-10 - 5.362909852585578312e-978j)  +/-  (2.66e-82, 6.85e-204j)
| (2.2122687995231763886e-06 - 5.7893809922614793262e-975j)  +/-  (1.4e-80, 3.61e-202j)
| (0.052791321859645850155 + 9.3050655573420093631e-971j)  +/-  (1.15e-65, 2.95e-187j)
| (3.7003806576798477737e-12 + 3.6714156452955541643e-979j)  +/-  (3.61e-83, 9.28e-205j)
| (2.2122687995231763886e-06 - 1.7051515219050761969e-974j)  +/-  (1.66e-79, 4.28e-201j)
| (2.9027920907897091881e-07 + 3.1187703329866862107e-975j)  +/-  (3.95e-80, 1.02e-201j)
| (1.0909130897475524011e-24 - 2.0686224556265799845e-988j)  +/-  (9.98e-95, 2.57e-216j)
| (0.00028939794210866729925 + 5.053999854062710718e-973j)  +/-  (5.49e-79, 1.41e-200j)
| (6.6777144512126947068e-05 - 2.9111485983923275439e-973j)  +/-  (4.83e-79, 1.24e-200j)
| (2.9027920907897091881e-07 + 9.4050889313033041777e-976j)  +/-  (1.39e-83, 3.58e-205j)
| (0.01895040019208788374 + 2.5545314110056086039e-971j)  +/-  (4.37e-75, 1.13e-196j)
| (5.8708726412307248951e-14 - 2.4091632350684000048e-981j)  +/-  (6.3e-90, 1.62e-211j)
| (2.9946659952927145098e-08 - 1.2986499080154047314e-976j)  +/-  (6.02e-85, 1.55e-206j)
| (0.020201687104151906306 - 7.8615496993384805116e-971j)  +/-  (1.46e-76, 3.75e-198j)
| (0.00079741440044646681239 - 1.6563012311447644019e-972j)  +/-  (3.35e-80, 8.62e-202j)
| (1.2802737307959284297e-05 + 2.8748647972041060739e-974j)  +/-  (2.63e-82, 6.77e-204j)
| (0.020201687104151906306 - 5.4433387119741695624e-971j)  +/-  (6.7e-78, 1.72e-199j)
| (4.8754151532600637324e-16 + 7.8989336380775510363e-983j)  +/-  (1.47e-91, 3.8e-213j)
| (0.095458091779541977841 - 1.0662990630583683509e-970j)  +/-  (8.85e-78, 2.28e-199j)
| (0.0024478197023557979575 + 6.7933263622032745908e-972j)  +/-  (6.6e-82, 1.7e-203j)
| (0.008178801140579542203 - 1.3871788790463308576e-971j)  +/-  (4.52e-81, 1.16e-202j)
| (0.052791321859645850155 + 6.8630865543921325851e-971j)  +/-  (4.38e-80, 1.12e-201j)
| (1.2802737307959284297e-05 + 7.6109052919818374454e-974j)  +/-  (4.26e-85, 1.09e-206j)
| (0.11788096877974689582 - 1.900126583617078473e-970j)  +/-  (7.47e-81, 1.91e-202j)
| (0.1095479511068245169 + 1.6416567739486033715e-970j)  +/-  (1.98e-80, 5.07e-202j)
| (2.4547566236862586184e-09 + 6.0426379395719895702e-977j)  +/-  (1.65e-88, 4.24e-210j)
| (0.095458091779541977841 - 8.5736174230091110717e-971j)  +/-  (2.87e-81, 7.33e-203j)
| (0.0024478197023557979575 + 3.6774525031266269624e-972j)  +/-  (6.16e-83, 1.58e-204j)
| (1.2763038499638780912e-10 - 1.0290171776595662023e-978j)  +/-  (9.68e-90, 2.47e-211j)
| (0.11788096877974689582 - 2.0425909497356967443e-970j)  +/-  (3.45e-82, 8.91e-204j)
| (0.14674806205975053228 + 2.0116196651087713409e-970j)  +/-  (2.73e-82, 6.99e-204j)
| (0.00028939794210866729925 + 1.0969680841521348928e-972j)  +/-  (1.51e-85, 5.15e-207j)
| (0.1095479511068245169 + 1.43064232734128007e-970j)  +/-  (1.35e-82, 3.04e-204j)
