Starting with polynomial:
P : t^7 - 21*t^5 + 105*t^3 - 105*t
Extension levels are: 7 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 20272901550173121694599172315995340688525092889295501/12967689434123817553800621450329162601323511747202*t^57 + 1386441581282803288210920173345825568700053819801933350031/1218962806807638850057258416330941284524410104236988*t^55 - 14358746797147277253976121174840684640809757855200353737035085/28036144556575693551316943575611649544061432397450724*t^53 + 4489444398019304394930556259635980025064482471760750279118470865/28036144556575693551316943575611649544061432397450724*t^51 - 1036587417113168210440398154408511156175115310787887202195297821775/28036144556575693551316943575611649544061432397450724*t^49 + 1952449500926438180539811105975005476761897837020823318397530560425/298256856984847803737414293357570739830440770185646*t^47 - 11813818004274626362865625851920137542189744083105689360998912875275/12967689434123817553800621450329162601323511747202*t^45 + 1314352230208759963968195444517126495311678836699488973289278226257625/12967689434123817553800621450329162601323511747202*t^43 - 59139814264264407755850138382314690938758192750198100002788272881561500/6483844717061908776900310725164581300661755873601*t^41 + 17358309318677714433323643684138482118262660889025483272805424940916250875/25935378868247635107601242900658325202647023494404*t^39 - 1044064285007874497479070558744669852837501688913252573269628491370335936375/25935378868247635107601242900658325202647023494404*t^37 + 51631467335266124834148335342072674849652867610142225350597440802861979459875/25935378868247635107601242900658325202647023494404*t^35 - 2101669122359628449486915378345107762905043457242014673753255531888526767985625/25935378868247635107601242900658325202647023494404*t^33 + 17594494748944385388769618761960227237089104035156152118516127102888743818873125/6483844717061908776900310725164581300661755873601*t^31 - 483651741902964191914987117512546870364320956333017993696696885920309362375255625/6483844717061908776900310725164581300661755873601*t^29 + 10872489773440096393086145008337658445004900314696865327233696153173573824359120000/6483844717061908776900310725164581300661755873601*t^27 - 397559309802084048045656510020645243362040444142801390513581307381855427623080100625/12967689434123817553800621450329162601323511747202*t^25 + 11735048167526070710044831836570652508948371022984752496090322515092860268068882234375/25935378868247635107601242900658325202647023494404*t^23 - 138457854513909035849500329280770038659124567835498765277632083170939251530470717921875/25935378868247635107601242900658325202647023494404*t^21 + 1289666344318983137566252485776345322054048440447693621791577465219097361944389123859375/25935378868247635107601242900658325202647023494404*t^19 - 9331429397250466051575768815568053769219549829852975762419611176178807364975567331265625/25935378868247635107601242900658325202647023494404*t^17 + 25680937712182869372464922610627378368421584915993396098325013717912014383439342678234375/12967689434123817553800621450329162601323511747202*t^15 - 104612386703708333417852096718135840410086285171652560733755299335962258892108492787421875/12967689434123817553800621450329162601323511747202*t^13 + 303946270857136099779407660528349249292950955455271302805835781701690530990305508703203125/12967689434123817553800621450329162601323511747202*t^11 - 299216462919582266625826907007426147677330215822427570401741670047718681013846243450328125/6483844717061908776900310725164581300661755873601*t^9 + 1482357832525645851011123525324247162415517435559008157421258894549627970418401706114328125/25935378868247635107601242900658325202647023494404*t^7 - 1028105291115911582992110397850422517300481573434051739988141526067482164946389697672390625/25935378868247635107601242900658325202647023494404*t^5 + 325086924193912032931006284789417207958603668942397228378506493334152661444907508373203125/25935378868247635107601242900658325202647023494404*t^3 - 29378913991473419250019369200245955176799956107233952385493240330212054366035412887734375/25935378868247635107601242900658325202647023494404*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
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:
| (-10.875767522984701836 - 1.6104151344368184249e-1214j)  +/-  (2.79e-497, 2.79e-497j)
| (-11.499263194450040529 + 3.8706701383985234229e-1215j)  +/-  (8.76e-498, 8.76e-498j)
| (-12.931015354776986456 - 2.8937018486941030805e-1217j)  +/-  (2.48e-499, 2.48e-499j)
| (-7.6850969749625011487 - 3.8574827653310368458e-1215j)  +/-  (1.49e-496, 1.49e-496j)
| (-4.9377007610198976555 - 2.4479176095647152944e-1217j)  +/-  (1.99e-498, 1.99e-498j)
| (-10.289359575379965991 - 1.732809634621010221e-1215j)  +/-  (6.56e-497, 6.56e-497j)
| (-6.7372444402525897737 - 1.2895396908688344577e-1214j)  +/-  (6.1e-497, 6.1e-497j)
| (-2.3667594107345412886 + 4.3646493437315284941e-1224j)  +/-  (4.22e-503, 4.22e-503j)
| (-6.276567627393242657 + 8.2342414168058029698e-1216j)  +/-  (3.28e-497, 3.28e-497j)
| (-1.5532142307347593997 - 1.2715178332392099634e-1225j)  +/-  (2.55e-505, 2.55e-505j)
| (-1.1544053947399681272 + 2.89773900191604412e-1227j)  +/-  (1.89e-506, 1.89e-506j)
| (-3.7504397177257422563 + 4.8761223313784036838e-1220j)  +/-  (1.85e-499, 1.85e-499j)
| (-13.843895507189689713 - 4.4603357742533885316e-1221j)  +/-  (1.34e-500, 1.34e-500j)
| (-3.1879533606895775612 + 5.5565096156005440378e-1221j)  +/-  (6.48e-501, 6.48e-501j)
| (-9.7311262046008767699 - 8.3670706231732949658e-1217j)  +/-  (1.16e-496, 1.16e-496j)
| (-12.174716631416795646 - 9.4907010004186487422e-1219j)  +/-  (2.09e-498, 2.09e-498j)
| (-2.7783436119959803485 - 2.795320942713272583e-1223j)  +/-  (5.18e-502, 5.18e-502j)
| (-9.1951976307036856376 + 1.0269916432664168781e-1216j)  +/-  (1.6e-496, 1.6e-496j)
| (0.37871540426772467338 + 3.2512039122748962388e-1229j)  +/-  (8.24e-509, 8.24e-509j)
| (-8.1748548658609706246 - 5.6332784908174933266e-1216j)  +/-  (1.93e-496, 1.93e-496j)
| (-8.6774515544506003482 - 2.0218670291523152368e-1216j)  +/-  (2.1e-496, 2.1e-496j)
| (-4.0871022851268861695 + 5.0523618236505283829e-1220j)  +/-  (3.13e-499, 3.13e-499j)
| (-0.76276294478063950407 + 1.3099440226196763648e-1228j)  +/-  (1.13e-507, 1.13e-507j)
| (-7.2063719911859991928 - 1.0958939252998830401e-1215j)  +/-  (1.04e-496, 1.04e-496j)
| (-3.5563488179044868696 + 1.236080976094723983e-1221j)  +/-  (7.43e-500, 7.43e-500j)
| (-1.9578118239518259208 + 2.4969574314351044591e-1227j)  +/-  (3.4e-504, 3.4e-504j)
| (-5.3772349231625099731 + 2.3197069562823957872e-1219j)  +/-  (5.21e-498, 5.21e-498j)
| (-1.6104197006262507957e-1249 - 3.595474079705258641e-1249j)  +/-  (2.32e-1247, 2.32e-1247j)
| (-5.8234435249067935569 - 1.5474067630386365795e-1217j)  +/-  (1.44e-497, 1.44e-497j)
| (-0.37871540426772467338 - 1.9317261414127439153e-1234j)  +/-  (8.24e-509, 8.24e-509j)
| (-4.5056307127864005192 - 6.2545058050899866374e-1222j)  +/-  (8.07e-499, 8.07e-499j)
| (7.6850969749625011487 + 7.3825804388758518474e-1231j)  +/-  (1.51e-496, 1.51e-496j)
| (11.499263194450040529 + 3.0210974203783944419e-1269j)  +/-  (9.44e-498, 9.44e-498j)
| (10.289359575379965991 + 1.6012621798434712431e-1300j)  +/-  (6.53e-497, 6.53e-497j)
| (12.174716631416795646 - 1.0370201309685913312e-1340j)  +/-  (1.91e-498, 1.91e-498j)
| (12.931015354776986456 + 6.7794861852030077605e-1392j)  +/-  (2.67e-499, 2.67e-499j)
| (2.7783436119959803485 - 9.2426366560511641622e-1454j)  +/-  (5.13e-502, 5.13e-502j)
| (7.2063719911859991928 + 2.2988895815017330164e-1495j)  +/-  (1.03e-496, 1.03e-496j)
| (8.6774515544506003482 + 1.1803980623658433557e-1574j)  +/-  (1.94e-496, 1.94e-496j)
| (9.1951976307036856376 + 3.7757756701005920395e-1630j)  +/-  (1.61e-496, 1.61e-496j)
| (1.9578118239518259208 + 3.9148186057347143875e-1666j)  +/-  (3.74e-504, 3.74e-504j)
| (9.7311262046008767699 + 1.3649497814349527829e-1658j)  +/-  (1.16e-496, 1.16e-496j)
| (6.7372444402525897737 + 7.0934345865648354657e-1666j)  +/-  (5.95e-497, 5.95e-497j)
| (3.1879533606895775612 - 2.0334032001748543555e-1678j)  +/-  (6e-501, 6e-501j)
| (13.843895507189689713 + 1.9030548939890508468e-1675j)  +/-  (1.44e-500, 1.44e-500j)
| (1.5532142307347593997 - 3.0527207907514376715e-1685j)  +/-  (2.52e-505, 2.52e-505j)
| (8.1748548658609706246 - 8.2275068468016027076e-1677j)  +/-  (1.88e-496, 1.88e-496j)
| (5.3772349231625099731 + 2.9288450408991453311e-1684j)  +/-  (5.29e-498, 5.29e-498j)
| (3.5563488179044868696 + 9.7718586314266451361e-1688j)  +/-  (7.46e-500, 7.46e-500j)
| (4.5056307127864005192 + 3.2620451498469387912e-1686j)  +/-  (7.88e-499, 7.88e-499j)
| (1.1544053947399681272 + 5.1692884843404991833e-1694j)  +/-  (1.93e-506, 1.93e-506j)
| (6.276567627393242657 - 2.2919483272971240732e-1683j)  +/-  (3.14e-497, 3.14e-497j)
| (4.9377007610198976555 + 2.0392030996446257322e-1689j)  +/-  (2.11e-498, 2.11e-498j)
| (2.3667594107345412886 - 3.3659070510721156107e-1696j)  +/-  (4.1e-503, 4.1e-503j)
| (4.0871022851268861695 + 1.1632411444925496401e-1691j)  +/-  (3.04e-499, 3.04e-499j)
| (0.76276294478063950407 - 1.4606833228119535737e-1700j)  +/-  (1.18e-507, 1.18e-507j)
| (5.8234435249067935569 - 8.9783518105354706104e-1689j)  +/-  (1.36e-497, 1.36e-497j)
| (3.7504397177257422563 - 3.2053558197182318524e-1699j)  +/-  (1.68e-499, 1.68e-499j)
| (10.875767522984701836 + 1.5140374348356520709e-1700j)  +/-  (2.9e-497, 2.9e-497j)
-------------------------------------------------
The weights are:
| (4.9731077581883073269e-27 + 2.6853341244651056232e-1234j)  +/-  (4.67e-155, 2.96e-402j)
| (4.9804407782429873411e-30 - 6.1934515300219666443e-1236j)  +/-  (1.29e-156, 8.21e-404j)
| (1.592667796881861396e-37 - 5.8958540152772624762e-1240j)  +/-  (3.48e-160, 2.21e-407j)
| (2.8897573446224399365e-14 + 7.7713953887844689805e-1227j)  +/-  (1.83e-148, 1.16e-395j)
| (8.8358468854365590095e-07 - 2.5298424629249504551e-1222j)  +/-  (3.58e-139, 2.27e-386j)
| (2.3338905921797295203e-24 - 8.0819702637806619434e-1233j)  +/-  (1.28e-154, 8.11e-402j)
| (2.5804730122216014554e-11 - 1.1233768157857020121e-1224j)  +/-  (4.45e-146, 2.83e-393j)
| (0.009953942931361346557 + 2.1094635522427925249e-1220j)  +/-  (9.6e-126, 6.09e-373j)
| (5.0819171424003024213e-10 + 5.6020140410762582688e-1224j)  +/-  (8.93e-145, 5.66e-392j)
| (0.047997433831083746181 + 3.6558878391268840334e-1220j)  +/-  (6.83e-118, 4.34e-365j)
| (0.081020202532745808277 - 4.6447022542628140574e-1220j)  +/-  (1.4e-112, 8.9e-360j)
| (7.5619438492697366928e-05 + 1.4183831791932840364e-1220j)  +/-  (1.67e-135, 1.06e-382j)
| (1.0159081768577398148e-42 + 1.0497316590600741859e-1242j)  +/-  (2.16e-164, 1.37e-411j)
| (0.0010007437870376085728 + 1.5117702338131279898e-1220j)  +/-  (3.83e-133, 2.43e-380j)
| (5.9649235683476311026e-22 + 1.8319700756115980456e-1231j)  +/-  (9.13e-155, 5.79e-402j)
| (1.8418256225801370048e-33 + 8.7188794087333798259e-1238j)  +/-  (2.42e-160, 1.54e-407j)
| (0.0034639138586520765812 - 1.6598242843117161404e-1220j)  +/-  (4.78e-133, 3.03e-380j)
| (9.1611104828832693234e-20 - 3.3179724687144304214e-1230j)  +/-  (3.78e-154, 2.4e-401j)
| (0.14136832636669260795 - 5.5096597817943992288e-1220j)  +/-  (8.38e-123, 5.31e-370j)
| (6.0908920647068683364e-16 - 6.8472039624957699529e-1228j)  +/-  (1.73e-152, 1.1e-399j)
| (9.0670453224220510587e-18 + 5.0454054012429922487e-1229j)  +/-  (1.53e-153, 9.7e-401j)
| (3.8005914253708319368e-05 - 3.6243465811781608558e-1221j)  +/-  (1.14e-142, 7.25e-390j)
| (0.11564519764917562369 + 5.5857493004291518006e-1220j)  +/-  (7.86e-127, 4.99e-374j)
| (9.9903099389301255265e-13 - 1.2553128239554109281e-1225j)  +/-  (8.18e-151, 5.19e-398j)
| (0.00020458368425173718325 - 1.8880341912411273511e-1220j)  +/-  (1.08e-140, 6.86e-388j)
| (0.023888223686454269039 - 2.7861554888148917573e-1220j)  +/-  (4.75e-135, 3.01e-382j)
| (9.2994670374493121515e-08 + 4.0660562359152915839e-1223j)  +/-  (1.32e-147, 8.39e-395j)
| (0.15067232301089093035 + 6.1938047029244632371e-1220j)  +/-  (8.14e-132, 5.17e-379j)
| (7.7574223411559349964e-09 - 1.5567416507229284901e-1223j)  +/-  (9.44e-149, 5.99e-396j)
| (0.14136832636669260795 - 6.1985368558766161687e-1220j)  +/-  (9.87e-133, 6.26e-380j)
| (6.6599425470546226964e-06 + 9.0289202318053762625e-1222j)  +/-  (3.2e-145, 2.03e-392j)
| (2.8897573446224399365e-14 - 6.3328155320374741812e-1228j)  +/-  (2.05e-171, 1.3e-418j)
| (4.9804407782429873411e-30 + 1.6934581386786264475e-1236j)  +/-  (3.5e-180, 2.22e-427j)
| (2.3338905921797295203e-24 + 1.7824901722565555058e-1233j)  +/-  (4.04e-178, 2.56e-425j)
| (1.8418256225801370048e-33 - 2.6146098263155770784e-1238j)  +/-  (8.52e-182, 5.41e-429j)
| (1.592667796881861396e-37 + 1.9295446484427440812e-1240j)  +/-  (1.32e-183, 8.37e-431j)
| (0.0034639138586520765812 - 6.5448285745548640912e-1221j)  +/-  (5.02e-159, 3.19e-406j)
| (9.9903099389301255265e-13 + 4.8625517926814116015e-1227j)  +/-  (3.67e-173, 2.33e-420j)
| (9.0670453224220510587e-18 - 6.866229747502954666e-1230j)  +/-  (1.94e-176, 1.23e-423j)
| (9.1611104828832693234e-20 + 5.4846605544217201422e-1231j)  +/-  (1.28e-177, 8.11e-425j)
| (0.023888223686454269039 - 1.4840909024983209052e-1220j)  +/-  (6.73e-159, 4.27e-406j)
| (5.9649235683476311026e-22 - 3.542421782886820371e-1232j)  +/-  (9.75e-179, 6.19e-426j)
| (2.5804730122216014554e-11 - 3.2909239449553604258e-1226j)  +/-  (1.82e-174, 1.15e-421j)
| (0.0010007437870376085728 + 5.0454725062161113472e-1221j)  +/-  (1.35e-166, 8.54e-414j)
| (1.0159081768577398148e-42 - 3.7536483415648854807e-1243j)  +/-  (8.18e-189, 5.19e-436j)
| (0.047997433831083746181 + 2.2328743341546871792e-1220j)  +/-  (1.99e-160, 1.26e-407j)
| (6.0908920647068683364e-16 + 7.1494844714123810867e-1229j)  +/-  (3.14e-176, 1.99e-423j)
| (9.2994670374493121515e-08 + 5.646640334852197207e-1224j)  +/-  (1.07e-173, 6.81e-421j)
| (0.00020458368425173718325 - 5.3325413836555126233e-1221j)  +/-  (1.08e-169, 6.84e-417j)
| (6.6599425470546226964e-06 + 1.3718275624190825546e-1222j)  +/-  (1.46e-172, 9.24e-420j)
| (0.081020202532745808277 - 3.2311778962881280602e-1220j)  +/-  (2.24e-164, 1.42e-411j)
| (5.0819171424003024213e-10 + 1.9946042055331309889e-1225j)  +/-  (1.75e-175, 1.11e-422j)
| (8.8358468854365590095e-07 - 2.7712902611835671268e-1223j)  +/-  (1.42e-173, 9e-421j)
| (0.009953942931361346557 + 9.7190902710830014116e-1221j)  +/-  (2.7e-169, 1.71e-416j)
| (3.8005914253708319368e-05 - 7.6876351050398206933e-1222j)  +/-  (1.86e-172, 1.18e-419j)
| (0.11564519764917562369 + 4.4018879544068205703e-1220j)  +/-  (1.73e-169, 1.11e-416j)
| (7.7574223411559349964e-09 - 1.1009080218927002462e-1224j)  +/-  (1.76e-175, 1.13e-422j)
| (7.5619438492697366928e-05 + 3.6359752663543671675e-1221j)  +/-  (8.05e-172, 5.02e-419j)
| (4.9731077581883073269e-27 - 6.6363624949507299743e-1235j)  +/-  (7.4e-186, 4.92e-433j)
