Starting with polynomial:
P : t
Extension levels are: 1 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 1378*t^51 + 878475*t^49 - 344362200*t^47 + 93063884550*t^45 - 18426649140900*t^43 + 2773210695705450*t^41 - 324861824354067000*t^39 + 30090326480795455875*t^37 - 2226684159578863734750*t^35 + 132487707494942392217625*t^33 - 6359409959757234826446000*t^31 + 246427135940592849524782500*t^29 - 7696109014760053608235515000*t^27 + 192952447441484201177904697500*t^25 - 3859048948829684023558093950000*t^23 + 61021211503369378622512360584375*t^21 - 753791436218092324160446807218750*t^19 + 7161018644071877079524244668578125*t^17 - 51257817662830278042910382890875000*t^15 + 269103542729858959725279510177093750*t^13 - 999527444425190421836752466372062500*t^11 + 2498818611062976054591881165930156250*t^9 - 3911194347750745128926422694499375000*t^7 + 3422295054281901987810619857686953125*t^5 - 1368918021712760795124247943074781250*t^3 + 157952079428395476360490147277859375*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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (13.414102674077400257 - 8.7943956321288355936e-1196j)  +/-  (7.74e-501, 7.74e-501j)
| (12.491064901151382985 + 2.8133144721578806309e-1194j)  +/-  (1.43e-499, 1.43e-499j)
| (7.6687809542175221748 - 7.5382255767517585008e-1193j)  +/-  (3.35e-497, 3.35e-497j)
| (11.725853304460930687 - 9.3256619150712729154e-1194j)  +/-  (1.11e-498, 1.11e-498j)
| (9.8159586541761790411 + 9.3804051512966885651e-1192j)  +/-  (2.32e-497, 2.32e-497j)
| (3.9126566886050585192 - 1.0430121196867643898e-1197j)  +/-  (1.13e-500, 1.13e-500j)
| (8.1797574487693003196 - 3.1051763534205971214e-1192j)  +/-  (5.03e-497, 5.03e-497j)
| (2.1553234688986636177 + 7.3826446797603297931e-1200j)  +/-  (6.2e-504, 6.2e-504j)
| (1.7219855340823049653 + 4.5613232896586721109e-1202j)  +/-  (4.84e-505, 4.84e-505j)
| (6.2043348677979508315 + 1.2059399504695357741e-1193j)  +/-  (6.89e-498, 6.89e-498j)
| (7.1704061234905543273 + 1.1853674498089834686e-1192j)  +/-  (2.57e-497, 2.57e-497j)
| (3.4687818206790903646 + 9.2718489211412894841e-1197j)  +/-  (2.39e-501, 2.39e-501j)
| (2.5906042482581873375 - 4.1336688932931847834e-1199j)  +/-  (5.05e-503, 5.05e-503j)
| (11.042016505058145231 + 2.5891774711734352306e-1193j)  +/-  (3.88e-498, 3.88e-498j)
| (4.8127715654902021472 + 2.8517960141174803774e-1195j)  +/-  (2.65e-499, 2.65e-499j)
| (8.7057040377995828304 + 7.8362092219410516614e-1192j)  +/-  (4.47e-497, 4.47e-497j)
| (4.3604479421980043226 + 2.9705294807370722982e-1200j)  +/-  (6.84e-500, 6.84e-500j)
| (3.0282670954407400602 + 6.727254074881151213e-1203j)  +/-  (3.95e-502, 3.95e-502j)
| (1.2901751689598202931 + 6.2123623375278216497e-1207j)  +/-  (4.23e-506, 4.23e-506j)
| (6.6827622727174249944 - 1.3960180886669198326e-1197j)  +/-  (1.38e-497, 1.38e-497j)
| (5.270318097134819632 + 1.146964370962223557e-1200j)  +/-  (8.22e-499, 8.22e-499j)
| (5.733871654716649696 + 1.4933399076703216989e-1200j)  +/-  (3.21e-498, 3.21e-498j)
| (9.2497102062867253123 - 5.7617972472033305372e-1201j)  +/-  (3.73e-497, 3.73e-497j)
| (0.85949531535741307494 + 1.3115676617684232761e-1231j)  +/-  (3.22e-507, 3.22e-507j)
| (10.410390996415877003 + 4.7981728860165329735e-1236j)  +/-  (1.09e-497, 1.09e-497j)
| (0.42956205686532875135 + 7.5660181918766182522e-1260j)  +/-  (8.62e-509, 8.62e-509j)
| (-8.7057040377995828304 - 1.8231122213594703489e-1299j)  +/-  (4.43e-497, 4.43e-497j)
| (-12.491064901151382985 + 6.5149337609716962454e-1360j)  +/-  (1.34e-499, 1.34e-499j)
| (-2.1553234688986636177 - 1.7559502117402199987e-1394j)  +/-  (6.27e-504, 6.27e-504j)
| (-9.8159586541761790411 + 8.5508370962415570592e-1398j)  +/-  (2.51e-497, 2.51e-497j)
| (-13.414102674077400257 - 5.268741948106455789e-1409j)  +/-  (7.97e-501, 7.97e-501j)
| (-3.0282670954407400602 + 5.7467038708072523766e-1425j)  +/-  (3.8e-502, 3.8e-502j)
| (-5.270318097134819632 - 1.0770774129758069287e-1419j)  +/-  (7.66e-499, 7.66e-499j)
| (-8.1797574487693003196 + 2.2222473194795897242e-1456j)  +/-  (5.48e-497, 5.48e-497j)
| (-0.85949531535741307494 - 1.5779190670288841106e-1497j)  +/-  (3.27e-507, 3.27e-507j)
| (-11.725853304460930687 + 2.5468514949812312431e-1493j)  +/-  (1.17e-498, 1.17e-498j)
| (-7.6687809542175221748 - 1.8711580695339318325e-1531j)  +/-  (3.34e-497, 3.34e-497j)
| (-9.2497102062867253123 - 5.5018059238349075259e-1572j)  +/-  (3.51e-497, 3.51e-497j)
| (-10.410390996415877003 - 7.9500621112004787852e-1593j)  +/-  (1.07e-497, 1.07e-497j)
| (-4.8127715654902021472 - 9.2253303962043298206e-1605j)  +/-  (2.82e-499, 2.82e-499j)
| (-3.4687818206790903646 + 1.6474822194280079972e-1607j)  +/-  (2.44e-501, 2.44e-501j)
| (-2.5906042482581873375 + 1.3885959511326244397e-1609j)  +/-  (4.63e-503, 4.63e-503j)
| (-5.733871654716649696 - 5.7336969214498947584e-1603j)  +/-  (3.05e-498, 3.05e-498j)
| (-6.6827622727174249944 + 2.4107667946625329625e-1602j)  +/-  (1.37e-497, 1.37e-497j)
| (-1.7219855340823049653 + 1.5944626969712447784e-1625j)  +/-  (6e-505, 6e-505j)
| (-7.1704061234905543273 + 5.5999335271162593737e-1617j)  +/-  (2.33e-497, 2.33e-497j)
| (-3.9126566886050585192 + 1.0398951185400373273e-1631j)  +/-  (1.12e-500, 1.12e-500j)
| (-6.2043348677979508315 - 7.0372567168893081147e-1647j)  +/-  (7.02e-498, 7.02e-498j)
| (-1.2901751689598202931 + 2.1898206637453187049e-1677j)  +/-  (4.76e-506, 4.76e-506j)
| (-11.042016505058145231 - 3.9690257228679495166e-1681j)  +/-  (3.67e-498, 3.67e-498j)
| (-0.42956205686532875135 + 3.8248158153918718308e-1703j)  +/-  (8.62e-509, 8.62e-509j)
| (-4.3604479421980043226 - 3.2030770677312474908e-1694j)  +/-  (6.7e-500, 6.7e-500j)
| (-1.3460997810232181977e-1713 + 7.9797037459810146552e-1714j)  +/-  (8.29e-1712, 8.29e-1712j)
-------------------------------------------------
The weights are:
| (3.5930201153507351423e-40 + 8.9967659707074849018e-1219j)  +/-  (4.27e-174, 4.11e-422j)
| (4.3226896508794229272e-35 - 3.6326874829292600815e-1216j)  +/-  (1.29e-172, 1.24e-420j)
| (3.4131103516925490931e-14 - 7.2817140431171460197e-1205j)  +/-  (2.62e-163, 2.52e-411j)
| (3.981523339099432814e-31 + 4.0356951329677330877e-1214j)  +/-  (9.92e-172, 9.54e-420j)
| (2.7599847130640565545e-22 - 1.7472141786110055529e-1209j)  +/-  (1.11e-168, 1.07e-416j)
| (8.4276409796202008582e-05 - 5.7724495337542293392e-1200j)  +/-  (4.32e-152, 4.16e-400j)
| (6.1132455633269240964e-16 + 7.5838175468020680149e-1206j)  +/-  (3.78e-165, 3.64e-413j)
| (0.016978459001015047059 + 1.534527861727773339e-1199j)  +/-  (7.77e-142, 7.47e-390j)
| (0.039175127473033394679 - 1.8198628405133016407e-1199j)  +/-  (6.37e-138, 6.13e-386j)
| (8.2814361174072158743e-10 - 4.0780609538904209242e-1202j)  +/-  (3.34e-161, 3.21e-409j)
| (1.3457193312052334084e-12 - 2.971398193128241244e-1204j)  +/-  (2.9e-163, 2.79e-411j)
| (0.00043015419958156174976 - 5.155780948850844566e-1200j)  +/-  (9.33e-152, 8.97e-400j)
| (0.0060738766336914101327 - 1.4361734994198473768e-1199j)  +/-  (3.76e-147, 3.61e-395j)
| (8.7273196309986530628e-28 - 2.1988395309790980381e-1212j)  +/-  (1.15e-172, 1.11e-420j)
| (1.6943815671498184467e-06 - 9.5733009106529887584e-1201j)  +/-  (4.41e-158, 4.24e-406j)
| (7.4358676868981614665e-18 - 4.8851842207966309532e-1207j)  +/-  (1.08e-167, 1.03e-415j)
| (1.3345751808167237821e-05 + 2.9831725569400168025e-1200j)  +/-  (1.33e-156, 1.28e-404j)
| (0.0017867124559233027839 + 1.6544406371596298585e-1199j)  +/-  (7.28e-152, 7.01e-400j)
| (0.074836935768288671733 + 2.1271894529037891086e-1199j)  +/-  (2.53e-143, 2.43e-391j)
| (3.8640067341278044573e-11 - 1.8599253567015903402e-1203j)  +/-  (2.45e-163, 2.36e-411j)
| (1.7081206861240522041e-07 - 4.7342441751848710165e-1201j)  +/-  (2.45e-160, 2.36e-408j)
| (1.3516762957947920342e-08 + 1.3380089583073828857e-1201j)  +/-  (1.41e-161, 1.35e-409j)
| (5.8367133295093192977e-20 + 3.1069549332827113145e-1208j)  +/-  (1.42e-170, 1.37e-418j)
| (0.11863440402280581893 - 2.334804296412632979e-1199j)  +/-  (1.16e-149, 1.11e-397j)
| (7.1362429170911497344e-25 + 7.4039280270087978207e-1211j)  +/-  (1.47e-173, 1.41e-421j)
| (0.15631190842787289344 + 2.3904848297001844898e-1199j)  +/-  (2.61e-151, 2.51e-399j)
| (7.4358676868981614665e-18 + 5.7079118960040260774e-1208j)  +/-  (1.19e-185, 1.14e-433j)
| (4.3226896508794229272e-35 + 1.0964616977055053122e-1216j)  +/-  (6.37e-193, 6.13e-441j)
| (0.016978459001015047059 + 4.9951027129504219351e-1200j)  +/-  (8.22e-165, 7.9e-413j)
| (2.7599847130640565545e-22 + 3.2346703791990989345e-1210j)  +/-  (1.88e-188, 1.8e-436j)
| (3.5930201153507351423e-40 - 3.012464360336077312e-1219j)  +/-  (1.1e-194, 1.06e-442j)
| (0.0017867124559233027839 + 1.4534561303938733027e-1200j)  +/-  (1.08e-171, 1.04e-419j)
| (1.7081206861240522041e-07 - 1.1301185431410492617e-1202j)  +/-  (6.06e-180, 5.83e-428j)
| (6.1132455633269240964e-16 - 5.3667735088366991183e-1207j)  +/-  (5.92e-186, 5.69e-434j)
| (0.11863440402280581893 - 1.6036045905305341632e-1199j)  +/-  (1.79e-163, 1.72e-411j)
| (3.981523339099432814e-31 - 1.0972575779893577312e-1214j)  +/-  (1.55e-192, 1.49e-440j)
| (3.4131103516925490931e-14 + 4.1597735279453247821e-1206j)  +/-  (8.93e-186, 8.59e-434j)
| (5.8367133295093192977e-20 - 4.877487585862535209e-1209j)  +/-  (4.13e-188, 3.98e-436j)
| (7.1362429170911497344e-25 - 1.5856496704507564264e-1211j)  +/-  (1.34e-190, 1.29e-438j)
| (1.6943815671498184467e-06 + 3.7128107257639948508e-1202j)  +/-  (2.9e-182, 2.79e-430j)
| (0.00043015419958156174976 - 6.7838806333072649416e-1201j)  +/-  (1.9e-179, 1.83e-427j)
| (0.0060738766336914101327 - 2.8249779248668482956e-1200j)  +/-  (4.51e-177, 4.34e-425j)
| (1.3516762957947920342e-08 + 3.051796643501254804e-1203j)  +/-  (2.25e-184, 2.16e-432j)
| (3.8640067341278044573e-11 + 1.5086769009345812496e-1204j)  +/-  (1.87e-186, 1.8e-434j)
| (0.039175127473033394679 - 8.0552729267761306333e-1200j)  +/-  (3.99e-178, 3.84e-426j)
| (1.3457193312052334084e-12 - 2.7109100953286145527e-1205j)  +/-  (4.21e-187, 4.05e-435j)
| (8.4276409796202008582e-05 + 2.8631371273829729174e-1201j)  +/-  (5.79e-183, 5.58e-431j)
| (8.2814361174072158743e-10 - 7.2599569448612475953e-1204j)  +/-  (4.92e-186, 4.73e-434j)
| (0.074836935768288671733 + 1.1874527004015632157e-1199j)  +/-  (8.09e-181, 7.39e-429j)
| (8.7273196309986530628e-28 + 5.3413369613644711682e-1213j)  +/-  (2.93e-195, 2.81e-443j)
| (0.15631190842787289344 + 1.9883007495234818761e-1199j)  +/-  (6.86e-181, 5.5e-429j)
| (1.3345751808167237821e-05 - 1.0886208556318657431e-1201j)  +/-  (7.62e-184, 7.38e-432j)
| (0.1713458405552413235 - 2.2690146852336970543e-1199j)  +/-  (7.6e-181, 5.77e-429j)
