Starting with polynomial:
P : t
Extension levels are: 1 22 38
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^23 - 253*t^21 + 26565*t^19 - 1514205*t^17 + 51482970*t^15 - 1081142370*t^13 + 14054850810*t^11 - 110430970650*t^9 + 496939367925*t^7 - 1159525191825*t^5 + 1159525191825*t^3 - 316234143225*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^61 - 1022611450644699413430127163258571869/758974758347076231570764048418186*t^59 + 1233382930727918279473768309058053682909/1459566842975146599174546246958050*t^57 - 4151430932986201264461425778730492898771831/12649579305784603859512734140303100*t^55 + 1120457175045612193644679441528579759193248751/12649579305784603859512734140303100*t^53 - 44715754519396708454966686215256727529659387581/2529915861156920771902546828060620*t^51 + 2284070534334229849305757791927896249353170966439/843305287052306923967515609353540*t^49 - 45936993287754455949735495549778823086842474250149/140550881175384487327919268225590*t^47 + 4441226376706374487914927836501716004450663580634543/140550881175384487327919268225590*t^45 - 174101246280858729271376110895047809516487934036193714/70275440587692243663959634112795*t^43 + 2232568749587461509075424638850164240460586953144676652/14055088117538448732791926822559*t^41 - 470903675704104170376244474997665089701215022885952058365/56220352470153794931167707290236*t^39 + 1576300078011349090057482777016815288129740066363823756609/4324642497704138071628285176172*t^37 - 56695780476539678755951014460127410777582332648109386223659/4324642497704138071628285176172*t^35 + 1685325356303511942911460881306156389191454244620397709996819/4324642497704138071628285176172*t^33 - 10333903177844793205695472444858950344261030964177031958885655/1081160624426034517907071294043*t^31 + 208466468068136127363133195030354159760100908599361899765952940/1081160624426034517907071294043*t^29 - 6885054089803541704612066312149739886618282020534528304157207495/2162321248852069035814142588086*t^27 + 92472772443061835348903865915413747402818752566491546134906432075/2162321248852069035814142588086*t^25 - 2003426696365094459762825984658432488140574710519060526990812738725/4324642497704138071628285176172*t^23 + 17318033050371925841347938629126000887188647203876970460792366880125/4324642497704138071628285176172*t^21 - 117866348616128760547425755555351705736139355979782517365474788804875/4324642497704138071628285176172*t^19 + 621008289315102283717436307302900297326848383383837702910255036857875/4324642497704138071628285176172*t^17 - 1239493550570826701724094778006617872017147591014944615204082919860125/2162321248852069035814142588086*t^15 + 3645938568684221069169668353839830098247861383048528246388561634133875/2162321248852069035814142588086*t^13 - 3808154861741871138372420610015821121944977257649138276945048744450625/1081160624426034517907071294043*t^11 + 5369368540347360468150581007274043847621474673565124986216377516704375/1081160624426034517907071294043*t^9 - 18964341089642951574292569777307359762874747521995057012225263510764375/4324642497704138071628285176172*t^7 + 9271636300008381574681591985582291537096006606691456689128388425284375/4324642497704138071628285176172*t^5 - 1966286603320798098596118003397128383007297431202945638774951620303125/4324642497704138071628285176172*t^3 + 91112778854295652373889111602546018731285016284285541680280964478125/4324642497704138071628285176172*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
Sufficient bits for target precision reached
Positive weights:   61 out of 61
Indefinite weights: 0 out of 61
Negative weights:   0 out of 61
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.2933860274173525895 + 1.411671035988358548e-585j)  +/-  (4.85e-241, 4.85e-241j)
| (-12.091920038077550536 + 9.3314854892623926292e-587j)  +/-  (2.42e-244, 2.42e-244j)
| (10.634041816402556234 - 2.1041359928391525012e-590j)  +/-  (1.03e-242, 1.03e-242j)
| (5.8819481764947254266 - 1.5464840130505761859e-594j)  +/-  (1.91e-241, 1.91e-241j)
| (12.091920038077550536 + 1.4610066768498048388e-594j)  +/-  (2.45e-244, 2.45e-244j)
| (-11.321832769263944517 - 1.2086491026816864797e-598j)  +/-  (2.08e-243, 2.08e-243j)
| (-7.3316638250548663031 + 7.8651494278982359275e-615j)  +/-  (4.22e-240, 4.22e-240j)
| (13.021172177507966085 + 2.5961808843038306433e-633j)  +/-  (1.25e-245, 1.25e-245j)
| (7.7736666980548559201 - 2.1596970715670562969e-628j)  +/-  (1.04e-240, 1.04e-240j)
| (4.0047753217333040671 + 1.1330982857722948582e-630j)  +/-  (1.58e-243, 1.58e-243j)
| (2.3341194683185281844 - 1.6300580587647319567e-634j)  +/-  (4.23e-247, 4.23e-247j)
| (-5.4934739864717941286 + 4.3208198449238756134e-626j)  +/-  (1e-241, 1e-241j)
| (-10.634041816402556234 - 4.373935632183081695e-628j)  +/-  (1.04e-242, 1.04e-242j)
| (11.321832769263944517 + 2.7458877672964072162e-632j)  +/-  (2e-243, 2e-243j)
| (8.8359196499433079107 + 6.2369809384960591799e-629j)  +/-  (2.18e-241, 2.18e-241j)
| (1.9573275529334241074 - 7.2666658908207768565e-639j)  +/-  (2.97e-248, 2.97e-248j)
| (7.214659435051861386 - 1.7826120504259028193e-629j)  +/-  (3.7e-240, 3.7e-240j)
| (-7.7736666980548559201 + 7.2493574593454314027e-638j)  +/-  (9.6e-241, 9.6e-241j)
| (-1.0403658571990540134 + 1.14775933381761031e-666j)  +/-  (4.95e-251, 4.95e-251j)
| (-2.6243236340591817707 + 7.1786669552858881015e-662j)  +/-  (2.79e-246, 2.79e-246j)
| (-13.021172177507966085 - 6.4260427112597926842e-655j)  +/-  (1.32e-245, 1.32e-245j)
| (1.0403658571990540134 + 7.9326174872643369162e-672j)  +/-  (5.48e-251, 5.48e-251j)
| (4.7307241974514732943 + 4.9277370661615974977e-661j)  +/-  (1.28e-242, 1.28e-242j)
| (-6.3103498544483998284 - 2.9170267991139535245e-663j)  +/-  (3.68e-241, 3.68e-241j)
| (-6.7696729197170564546 + 4.5929873844514685304e-686j)  +/-  (8.68e-241, 8.68e-241j)
| (7.3316638250548663031 - 1.4363549297369835542e-699j)  +/-  (4.12e-240, 4.12e-240j)
| (5.4934739864717941286 - 2.5866894379562966774e-709j)  +/-  (8.97e-242, 8.97e-242j)
| (-9.4028534795153445429 - 6.0642452582717472741e-720j)  +/-  (9.23e-242, 9.23e-242j)
| (-8.8359196499433079107 - 2.760051078149331343e-742j)  +/-  (2.08e-241, 2.08e-241j)
| (-0.64847115353449581672 + 5.6723950527292120549e-772j)  +/-  (1.49e-252, 1.49e-252j)
| (-7.214659435051861386 + 1.4512048692452166575e-758j)  +/-  (4.2e-240, 4.2e-240j)
| (5.1193820942351298196 - 3.0422514796945502072e-772j)  +/-  (3.95e-242, 3.95e-242j)
| (4.3466221662349542806 - 7.8958151358328214268e-779j)  +/-  (4.8e-243, 4.8e-243j)
| (3.6760925108446639006 - 3.7355563498416516997e-779j)  +/-  (3.97e-244, 3.97e-244j)
| (-1.5690537818266475594 + 1.0321744329120350258e-786j)  +/-  (2.82e-249, 2.82e-249j)
| (-1.29987646830397887 - 1.3083803528638861912e-786j)  +/-  (5.49e-250, 5.49e-250j)
| (6.7696729197170564546 + 6.0996548989755793271e-776j)  +/-  (7.79e-241, 7.79e-241j)
| (3.3050400217529645672 - 2.8955898172986552348e-792j)  +/-  (6.6e-245, 6.6e-245j)
| (9.4028534795153445429 + 2.6618071231532568777e-786j)  +/-  (9.4e-242, 9.4e-242j)
| (-3.6760925108446639006 - 6.2861008112890581807e-792j)  +/-  (3.92e-244, 3.92e-244j)
| (9.9993412134292522417 + 5.3225671860179381377e-789j)  +/-  (3.59e-242, 3.59e-242j)
| (-4.7307241974514732943 + 3.1421708448590660369e-788j)  +/-  (1.24e-242, 1.24e-242j)
| (-4.3466221662349542806 + 3.6176604334667298496e-790j)  +/-  (4.86e-243, 4.86e-243j)
| (-3.3050400217529645672 + 8.0025308713328601154e-793j)  +/-  (6.41e-245, 6.41e-245j)
| (0.25023943122517731041 - 2.3258032976386658085e-801j)  +/-  (5.5e-254, 5.5e-254j)
| (-5.8819481764947254266 - 2.2280668648907569318e-787j)  +/-  (1.91e-241, 1.91e-241j)
| (2.6243236340591817707 + 3.2967897089640539975e-799j)  +/-  (2.83e-246, 2.83e-246j)
| (-2.9281339876060298491 - 1.9633200566516136485e-798j)  +/-  (1.24e-245, 1.24e-245j)
| (0.64847115353449581672 - 1.6473996102287090748e-804j)  +/-  (1.63e-252, 1.63e-252j)
| (6.3103498544483998284 - 1.8352385286525658359e-794j)  +/-  (3.46e-241, 3.46e-241j)
| (-2.3341194683185281844 - 3.9326446062654663044e-800j)  +/-  (4.49e-247, 4.49e-247j)
| (-5.1193820942351298196 - 4.0056396756099997898e-792j)  +/-  (3.86e-242, 3.86e-242j)
| (-9.9993412134292522417 - 4.0858089460858736993e-803j)  +/-  (3.62e-242, 3.62e-242j)
| (1.29987646830397887 + 5.0925166137060686354e-831j)  +/-  (5.74e-250, 5.74e-250j)
| (1.5690537818266475594 + 1.7709870010135937307e-830j)  +/-  (2.72e-249, 2.72e-249j)
| (-2.5712390094359901094e-842 - 1.4961727233331101277e-842j)  +/-  (1.81e-840, 1.81e-840j)
| (-1.9573275529334241074 + 1.7379785803039311102e-825j)  +/-  (2.81e-248, 2.81e-248j)
| (2.9281339876060298491 - 4.162714415945485611e-826j)  +/-  (1.18e-245, 1.18e-245j)
| (-8.2933860274173525895 - 2.2746699448551954683e-820j)  +/-  (4.68e-241, 4.68e-241j)
| (-0.25023943122517731041 + 4.7055097272541027859e-842j)  +/-  (5.5e-254, 5.5e-254j)
| (-4.0047753217333040671 - 2.2590244944035622888e-832j)  +/-  (1.54e-243, 1.54e-243j)
-------------------------------------------------
The weights are:
| (2.4593553336710859233e-16 - 2.2730912112680525925e-600j)  +/-  (4.91e-56, 5e-175j)
| (5.8787939669516670225e-33 - 2.8032712139580359989e-613j)  +/-  (9.93e-67, 1.01e-185j)
| (7.3031065323987572509e-26 + 4.814424172632682715e-608j)  +/-  (8.16e-63, 8.31e-182j)
| (4.9993255728990104885e-09 - 4.2497011866270547856e-596j)  +/-  (1.17e-48, 1.19e-167j)
| (5.8787939669516670225e-33 + 1.5044314319994376743e-612j)  +/-  (1.43e-66, 1.46e-185j)
| (4.214204443054835599e-29 + 5.8705876881040348008e-611j)  +/-  (1.42e-66, 1.44e-185j)
| (1.8116008164145129061e-13 - 3.4916168921672110232e-599j)  +/-  (9.53e-57, 9.71e-176j)
| (6.515977929573047914e-38 - 1.5609117424991895705e-615j)  +/-  (5.18e-69, 5.28e-188j)
| (1.5253234280458803336e-14 + 2.3343835444073194982e-599j)  +/-  (2.47e-56, 2.52e-175j)
| (4.2096915809985413635e-05 + 3.6421033233032065029e-593j)  +/-  (3.03e-43, 3.09e-162j)
| (0.008963335109137715628 - 1.9627905093447036302e-591j)  +/-  (2.68e-32, 2.73e-151j)
| (4.1715382922816290156e-08 + 4.0504931593547160603e-596j)  +/-  (2.6e-52, 2.64e-171j)
| (7.3031065323987572509e-26 - 5.9537369115031519481e-609j)  +/-  (2.37e-66, 2.42e-185j)
| (4.214204443054835599e-29 - 3.8023830146676112833e-610j)  +/-  (2.29e-65, 2.33e-184j)
| (2.4607534351717041772e-18 - 2.0051000256658008408e-602j)  +/-  (9.31e-60, 9.49e-179j)
| (0.023229471677688348681 + 2.8588246995600720734e-591j)  +/-  (3.19e-32, 3.25e-151j)
| (6.042955872747112024e-13 + 9.3301368884800236683e-598j)  +/-  (9.01e-56, 9.18e-175j)
| (1.5253234280458803336e-14 + 7.5510032632982853239e-601j)  +/-  (3.68e-61, 3.75e-180j)
| (0.082906371113330144321 - 8.4462840535639845193e-591j)  +/-  (3.43e-24, 3.49e-143j)
| (0.0033239030209415386227 + 6.9993247080781173194e-592j)  +/-  (1.1e-41, 1.12e-160j)
| (6.515977929573047914e-38 + 3.4622687517358608823e-616j)  +/-  (1.43e-73, 1.46e-192j)
| (0.082906371113330144321 - 1.0869337079023846721e-590j)  +/-  (4.41e-26, 4.5e-145j)
| (2.1641277638916446988e-06 + 2.9262486282146128006e-594j)  +/-  (1.57e-50, 1.6e-169j)
| (4.0164496453953160611e-10 + 1.0481636380778538814e-597j)  +/-  (8.84e-58, 9.01e-177j)
| (2.0921649003567026152e-11 - 1.6485850633978333768e-598j)  +/-  (6.84e-59, 6.97e-178j)
| (1.8116008164145129061e-13 - 5.6728141277189977676e-598j)  +/-  (9.9e-58, 1.01e-176j)
| (4.1715382922816290156e-08 + 1.99447577934191076e-595j)  +/-  (4.4e-54, 4.48e-173j)
| (1.4655851326253270906e-20 - 1.7271227095978755427e-605j)  +/-  (5.02e-67, 5.12e-186j)
| (2.4607534351717041772e-18 + 6.3507158485540008978e-604j)  +/-  (1.01e-65, 1.03e-184j)
| (0.13148817625104753412 + 7.9651813674254350356e-591j)  +/-  (4.58e-36, 4.67e-155j)
| (6.042955872747112024e-13 + 6.4899617354128432164e-599j)  +/-  (1.63e-60, 1.66e-179j)
| (3.0933536550221958549e-07 - 7.7155281779694972151e-595j)  +/-  (3.95e-55, 4.02e-174j)
| (1.158441053244908132e-05 - 1.1492073230589513451e-593j)  +/-  (1.9e-53, 1.93e-172j)
| (0.00016220046105253788898 - 8.6375280228840919265e-593j)  +/-  (2.93e-52, 2.98e-171j)
| (0.042180575635307481373 - 4.4866501757666362002e-591j)  +/-  (8.84e-46, 9e-165j)
| (0.032247454996140427904 + 8.2604952719241852949e-591j)  +/-  (1.81e-43, 1.84e-162j)
| (2.0921649003567026152e-11 - 1.6297520854669250805e-597j)  +/-  (2.63e-60, 2.68e-179j)
| (0.00065141062464957725861 + 2.0603050956931233068e-592j)  +/-  (2.3e-52, 2.34e-171j)
| (1.4655851326253270906e-20 + 2.7547990898798694631e-604j)  +/-  (3.78e-68, 3.85e-187j)
| (0.00016220046105253788898 - 3.3319747492693489765e-593j)  +/-  (1.23e-59, 1.26e-178j)
| (4.7539432943136583707e-23 - 4.0458745532274047277e-606j)  +/-  (6.02e-70, 6.13e-189j)
| (2.1641277638916446988e-06 + 8.0045653699799534969e-595j)  +/-  (1.16e-62, 1.19e-181j)
| (1.158441053244908132e-05 - 3.5883281874192144872e-594j)  +/-  (5.69e-62, 5.8e-181j)
| (0.00065141062464957725861 + 8.8611283713659096095e-593j)  +/-  (9.38e-60, 9.56e-179j)
| (0.1433769713274944778 - 1.5779523712266861252e-590j)  +/-  (1.59e-51, 1.62e-170j)
| (4.9993255728990104885e-09 - 7.2293856804468105885e-597j)  +/-  (4.49e-65, 4.58e-184j)
| (0.0033239030209415386227 + 1.3479583184577942857e-591j)  +/-  (2.73e-57, 2.78e-176j)
| (0.0019455490800001687205 - 2.8688172764349687265e-592j)  +/-  (3.03e-59, 3.09e-178j)
| (0.13148817625104753412 + 9.3164562532321953301e-591j)  +/-  (3.44e-54, 3.51e-173j)
| (4.0164496453953160611e-10 + 7.7190297919681534227e-597j)  +/-  (3.83e-64, 3.9e-183j)
| (0.008963335109137715628 - 1.1006149481707644161e-591j)  +/-  (2.27e-58, 2.32e-177j)
| (3.0933536550221958549e-07 - 1.8258064120687627917e-595j)  +/-  (6.5e-64, 6.63e-183j)
| (4.7539432943136583707e-23 + 3.7731247077354423626e-607j)  +/-  (3.92e-76, 3.99e-195j)
| (0.032247454996140427904 + 1.1331235129945345264e-590j)  +/-  (6.06e-58, 6.16e-177j)
| (0.042180575635307481373 - 6.5804777086788265971e-591j)  +/-  (1.86e-58, 1.89e-177j)
| (0.058936757551324305501 + 2.1208642640821981612e-590j)  +/-  (3.1e-58, 3.22e-177j)
| (0.023229471677688348681 + 1.7670652629936323859e-591j)  +/-  (1.07e-59, 1.08e-178j)
| (0.0019455490800001687205 - 6.0001825949762655935e-592j)  +/-  (1.24e-60, 1.26e-179j)
| (2.4593553336710859233e-16 - 2.0931130403211277753e-602j)  +/-  (6.25e-72, 6.42e-191j)
| (0.1433769713274944778 - 1.4855171556432831869e-590j)  +/-  (1.53e-59, 2.08e-178j)
| (4.2096915809985413635e-05 + 1.2700729942160635774e-593j)  +/-  (5.21e-63, 5.19e-182j)
