Starting with polynomial:
P : t
Extension levels are: 1 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 1485*t^53 + 1023165*t^51 - 434845125*t^49 + 127844466750*t^47 - 27639973711350*t^45 + 4560595662372750*t^43 - 588316840446084750*t^41 + 60302476145723686875*t^39 - 4964903869331250219375*t^37 + 330662597697461264610375*t^35 - 17885840511817222949379375*t^33 + 786976982519957809772692500*t^31 - 28149561297829260118792462500*t^29 + 816337277637048543444981412500*t^27 - 19102292296706935916612565052500*t^25 + 358167980563255048436485594734375*t^23 - 5330382298970795720848873851046875*t^21 + 62187793487992616743236861595546875*t^19 - 559690141391933550689131754359921875*t^17 + 3805892961465148144686095929647468750*t^15 - 19029464807325740723430479648237343750*t^13 + 67468102498700353473980791480114218750*t^11 - 161336766844718236568214936148099218750*t^9 + 242005150267077354852322404222148828125*t^7 - 203284326224344978075950819546605015625*t^5 + 78186279317055760798442622902540390625*t^3 - 8687364368561751199826958100282265625*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
-------------------------------------------------
The nodes are:
| (-12.775823992273535003 - 1.5160842215479422756e-554j)  +/-  (1.37e-244, 1.37e-244j)
| (11.337169050201639602 - 7.084142462718979145e-551j)  +/-  (4.63e-243, 4.63e-243j)
| (-13.692684344388135257 + 8.5799868683853515802e-563j)  +/-  (6.43e-246, 6.43e-246j)
| (-9.0197011280396206553 - 3.662709965884423082e-558j)  +/-  (5.6e-242, 5.6e-242j)
| (-12.015989368182868068 + 4.7679608440602275307e-560j)  +/-  (1.02e-243, 1.02e-243j)
| (-10.120649984906492265 - 6.9090285805408925696e-559j)  +/-  (2.99e-242, 2.99e-242j)
| (8.4984074303033877887 - 4.4535051029397946661e-557j)  +/-  (5.89e-242, 5.89e-242j)
| (12.015989368182868068 - 1.239355007389683175e-563j)  +/-  (1.09e-243, 1.09e-243j)
| (-4.2763590547739861449 + 1.0603180476868507097e-565j)  +/-  (3.99e-245, 3.99e-245j)
| (-11.337169050201639602 + 2.0868054887329469748e-564j)  +/-  (4.2e-243, 4.2e-243j)
| (13.692684344388135257 - 3.8093247368414406433e-566j)  +/-  (7.98e-246, 7.98e-246j)
| (10.120649984906492265 + 1.9920614982292759354e-561j)  +/-  (2.97e-242, 2.97e-242j)
| (10.71036645106534255 - 5.3270178194571943106e-565j)  +/-  (1.26e-242, 1.26e-242j)
| (12.775823992273535003 + 2.5897532616414716853e-571j)  +/-  (1.5e-244, 1.5e-244j)
| (-9.559063352980156742 + 7.6418355303114745414e-570j)  +/-  (3.69e-242, 3.69e-242j)
| (5.6180759344615990646 + 7.8735925538387471523e-569j)  +/-  (1.97e-243, 1.97e-243j)
| (9.0197011280396206553 + 2.6192631109878920989e-578j)  +/-  (5.44e-242, 5.44e-242j)
| (7.9921139870456924433 - 1.8760925322960282562e-599j)  +/-  (5.54e-242, 5.54e-242j)
| (-1.2666005818235954089 + 1.0054511157487796412e-625j)  +/-  (2.14e-251, 2.14e-251j)
| (-2.1155851387622140699 + 7.6043283664561444518e-623j)  +/-  (2.2e-249, 2.2e-249j)
| (4.2763590547739861449 - 1.3346776643699443521e-615j)  +/-  (3.98e-245, 3.98e-245j)
| (3.4033551178542079317 + 1.0665250392852935306e-623j)  +/-  (1.41e-246, 1.41e-246j)
| (9.559063352980156742 + 1.8810553465417605376e-619j)  +/-  (5.25e-242, 5.25e-242j)
| (-6.5420647489152079141 - 3.0201325330496263035e-637j)  +/-  (1.06e-242, 1.06e-242j)
| (7.0156204864888853148 - 2.1334981449886781595e-653j)  +/-  (2.36e-242, 2.36e-242j)
| (-5.1657110971046495566 - 8.2304067906433405366e-665j)  +/-  (6.39e-244, 6.39e-244j)
| (2.5425390626106777093 - 1.9998232795058709412e-670j)  +/-  (2.85e-248, 2.85e-248j)
| (-4.718697950167026697 + 2.2899659800996293438e-665j)  +/-  (1.77e-244, 1.77e-244j)
| (2.1155851387622140699 + 9.4129591651085036218e-671j)  +/-  (2.57e-249, 2.57e-249j)
| (-3.8380920672292542077 - 1.3020685262048075634e-668j)  +/-  (7.7e-246, 7.7e-246j)
| (-7.0156204864888853148 - 2.3933538497698852065e-662j)  +/-  (2.16e-242, 2.16e-242j)
| (-5.6180759344615990646 - 3.6420542222352498295e-669j)  +/-  (2.05e-243, 2.05e-243j)
| (0.84383369153166388192 + 5.7557684035210903159e-681j)  +/-  (1.45e-252, 1.45e-252j)
| (-8.4984074303033877887 + 4.2377222131092782334e-669j)  +/-  (6.28e-242, 6.28e-242j)
| (-7.4984700754085535705 + 6.767817592927804138e-685j)  +/-  (3.9e-242, 3.9e-242j)
| (-2.5425390626106777093 + 1.026604475939863517e-704j)  +/-  (2.52e-248, 2.52e-248j)
| (2.9716552425124964266 + 9.3119268068648895255e-702j)  +/-  (1.86e-247, 1.86e-247j)
| (4.718697950167026697 + 2.6535517525402310857e-714j)  +/-  (1.8e-244, 1.8e-244j)
| (6.0765638208469264256 - 7.6821316569979276813e-738j)  +/-  (5.11e-243, 5.11e-243j)
| (1.6903975781557298485 - 1.4053038096213957408e-764j)  +/-  (2.61e-250, 2.61e-250j)
| (-0.84383369153166388192 + 1.080801982385888397e-767j)  +/-  (1.22e-252, 1.22e-252j)
| (-10.71036645106534255 + 8.6701976278000753572e-756j)  +/-  (1.25e-242, 1.25e-242j)
| (6.5420647489152079141 - 3.7868172051972895371e-771j)  +/-  (1.12e-242, 1.12e-242j)
| (1.2666005818235954089 - 4.0269898024719227716e-792j)  +/-  (2.58e-251, 2.58e-251j)
| (-7.9921139870456924433 - 1.4574447171068643841e-781j)  +/-  (4.76e-242, 4.76e-242j)
| (-3.4033551178542079317 + 1.8656497060224219181e-791j)  +/-  (1.52e-246, 1.52e-246j)
| (-2.9716552425124964266 + 9.849159447935065881e-793j)  +/-  (1.84e-247, 1.84e-247j)
| (7.4984700754085535705 + 5.8140691806430753022e-788j)  +/-  (3.53e-242, 3.53e-242j)
| (3.8380920672292542077 - 3.2329887676684352789e-799j)  +/-  (9.17e-246, 9.17e-246j)
| (-0.42174754708524104575 - 1.5952705187788411496e-807j)  +/-  (6.86e-254, 6.86e-254j)
| (8.8040899521831842942e-830 - 7.6121496827521945972e-832j)  +/-  (4.84e-828, 4.84e-828j)
| (-1.6903975781557298485 + 3.166709479263926565e-804j)  +/-  (3.05e-250, 3.05e-250j)
| (-6.0765638208469264256 + 3.770161492320804727e-797j)  +/-  (5.35e-243, 5.35e-243j)
| (0.42174754708524104575 + 1.699362344628999776e-807j)  +/-  (6.86e-254, 6.86e-254j)
| (5.1657110971046495566 + 1.791159485339825698e-797j)  +/-  (5.92e-244, 5.92e-244j)
-------------------------------------------------
The weights are:
| (1.1759544331197208047e-36 + 3.8422218752516338041e-585j)  +/-  (1.92e-63, 8.52e-186j)
| (3.186394189538746436e-29 + 1.3372373653592461417e-578j)  +/-  (4.62e-62, 2.05e-184j)
| (8.1816673003541132554e-42 - 9.6548820490982903385e-588j)  +/-  (2.92e-65, 1.29e-187j)
| (4.5599345458077143773e-19 - 5.5247776136778915292e-576j)  +/-  (7.1e-57, 3.15e-179j)
| (1.2621982459866922792e-32 - 4.2011478652739996461e-583j)  +/-  (1.28e-62, 5.65e-185j)
| (1.3131616407495595689e-23 + 1.8840668941393652368e-578j)  +/-  (2.05e-59, 9.09e-182j)
| (4.2492757974395330313e-17 + 7.1236930198790610736e-573j)  +/-  (3.99e-59, 1.77e-181j)
| (1.2621982459866922792e-32 + 5.6920865591851263324e-581j)  +/-  (2.39e-66, 1.06e-188j)
| (1.8773395812165767626e-05 + 1.450145351348845143e-569j)  +/-  (1.15e-45, 5.1e-168j)
| (3.186394189538746436e-29 + 2.2605193301242127386e-581j)  +/-  (2.14e-62, 9.51e-185j)
| (8.1816673003541132554e-42 + 3.2596553415207306337e-586j)  +/-  (3e-70, 1.33e-192j)
| (1.3131616407495595689e-23 + 1.8393154371202640564e-576j)  +/-  (1.17e-63, 5.18e-186j)
| (2.9805284545398795103e-26 - 1.3278399844245339513e-577j)  +/-  (1.51e-64, 6.71e-187j)
| (1.1759544331197208047e-36 - 2.2791723878118063001e-583j)  +/-  (8.36e-69, 3.71e-191j)
| (3.1552135089755289118e-21 - 4.2432387790922368756e-577j)  +/-  (2.99e-63, 1.33e-185j)
| (2.5434728215500947928e-08 + 4.9425576568599132651e-570j)  +/-  (1.04e-56, 4.62e-179j)
| (4.5599345458077143773e-19 + 4.9251044746386414532e-574j)  +/-  (1.11e-62, 4.92e-185j)
| (2.688531753864499695e-15 - 2.3538391390075775776e-572j)  +/-  (1.53e-61, 6.77e-184j)
| (0.075703318917566572724 - 5.0391103679183964787e-568j)  +/-  (2.66e-36, 1.18e-158j)
| (0.018131777713818180713 - 2.9999198305152906164e-568j)  +/-  (1.91e-44, 8.48e-167j)
| (1.8773395812165767626e-05 - 5.3111093268361524741e-569j)  +/-  (1.37e-54, 6.08e-177j)
| (0.00052766643123977635857 - 1.5425197058585449415e-568j)  +/-  (8.92e-52, 3.96e-174j)
| (3.1552135089755289118e-21 - 2.8001449781810643954e-575j)  +/-  (9.32e-64, 4.13e-186j)
| (9.5235164169590773964e-11 - 1.817538375947270137e-572j)  +/-  (2.99e-63, 1.33e-185j)
| (3.9134694306753897513e-12 - 2.0448382233068598553e-571j)  +/-  (3.43e-61, 1.52e-183j)
| (2.8788921476249844369e-07 + 9.7999370131577943229e-571j)  +/-  (4.82e-60, 2.14e-182j)
| (0.0067386218635711245757 - 2.8078930001242465022e-568j)  +/-  (3.78e-51, 1.68e-173j)
| (2.5931384967000675019e-06 - 2.1372814229728869359e-570j)  +/-  (8.34e-59, 3.7e-181j)
| (0.018131777713818180713 + 3.0552676392506748059e-568j)  +/-  (6.73e-50, 2.99e-172j)
| (0.00011016039915215328869 - 3.5573106685825530756e-569j)  +/-  (5.82e-57, 2.58e-179j)
| (3.9134694306753897513e-12 + 3.3107598869827255199e-573j)  +/-  (4.08e-65, 1.81e-187j)
| (2.5434728215500947928e-08 - 3.1092329745875480218e-571j)  +/-  (4.29e-62, 1.9e-184j)
| (0.11802697453147851199 + 7.3066784878878050082e-570j)  +/-  (1.63e-49, 7.23e-172j)
| (4.2492757974395330313e-17 + 1.1570841317576000195e-575j)  +/-  (2.06e-68, 9.16e-191j)
| (1.201584756290999617e-13 - 4.5517302379142861517e-574j)  +/-  (1.54e-66, 6.83e-189j)
| (0.0067386218635711245757 + 1.9700534809850345069e-568j)  +/-  (4.26e-57, 1.89e-179j)
| (0.0020756177757301351151 + 2.2182969525795913551e-568j)  +/-  (9.37e-59, 4.16e-181j)
| (2.5931384967000675019e-06 + 2.6596627448191315087e-569j)  +/-  (1.43e-63, 6.33e-186j)
| (1.7673215155940583538e-09 - 1.8486909064087338646e-570j)  +/-  (2.74e-66, 1.21e-188j)
| (0.040572443299451616654 - 2.7059589619750694692e-568j)  +/-  (2.79e-57, 1.24e-179j)
| (0.11802697453147851199 + 5.4452081103404564613e-568j)  +/-  (4.11e-56, 1.82e-178j)
| (2.9805284545398795103e-26 - 7.6306604309147559958e-580j)  +/-  (2.52e-74, 1.12e-196j)
| (9.5235164169590773964e-11 + 6.3544951242328325208e-571j)  +/-  (3.43e-67, 1.52e-189j)
| (0.075703318917566572724 + 1.6304391136369904631e-568j)  +/-  (6.98e-58, 3.09e-180j)
| (2.688531753864499695e-15 + 2.8613000931412733295e-575j)  +/-  (4.05e-69, 1.79e-191j)
| (0.00052766643123977635857 + 6.4820695175424548614e-569j)  +/-  (4.03e-63, 1.79e-185j)
| (0.0020756177757301351151 - 1.1752406621670960336e-568j)  +/-  (1.17e-62, 5.18e-185j)
| (1.201584756290999617e-13 + 6.4566631189743869646e-572j)  +/-  (2.66e-69, 1.18e-191j)
| (0.00011016039915215328869 + 9.55617126203306838e-569j)  +/-  (1.69e-64, 7.32e-187j)
| (0.15397650652511948678 - 5.0743722780555659021e-568j)  +/-  (9.58e-62, 4.06e-184j)
| (0.16823046163605511761 + 3.875367226260635917e-568j)  +/-  (6.2e-62, 2.62e-184j)
| (0.040572443299451616654 + 4.1140590268839607659e-568j)  +/-  (4.04e-63, 1.71e-185j)
| (1.7673215155940583538e-09 + 8.1952040907136078693e-572j)  +/-  (1.37e-67, 5.88e-190j)
| (0.15397650652511948678 - 2.0660293549170299129e-568j)  +/-  (8.24e-63, 2.85e-185j)
| (2.8788921476249844369e-07 - 1.203961221180324336e-569j)  +/-  (1.09e-66, 5.15e-189j)
