Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 56
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^58 - 29*t^56 + 1595/8*t^54 - 13833/16*t^52 + 339677/128*t^50 - 1570205/256*t^48 + 5676895/512*t^46 - 16458225/1024*t^44 + 311389617/16384*t^42 - 607951157/32768*t^40 + 7903365041/524288*t^38 - 10746742019/1048576*t^36 + 49061213565/8388608*t^34 - 47048445829/16777216*t^32 + 18941582087/16777216*t^30 - 12774555361/33554432*t^28 + 114970998249/1073741824*t^26 - 53609145525/2147483648*t^24 + 82200689805/17179869184*t^22 - 25625316255/34359738368*t^20 + 25625316255/274877906944*t^18 - 5045911695/549755813888*t^16 + 764532075/1099511627776*t^14 - 86425365/2199023255552*t^12 + 55922295/35184372088832*t^10 - 3050307/70368744177664*t^8 + 1642473/2251799813685248*t^6 - 29435/4503599627370496*t^4 + 841/36028797018963968*t^2 - 1/72057594037927936
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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
-------------------------------------------------
The nodes are:
| (0.99084559657880676279 + 2.6706799026010959057e-884j)  +/-  (7.13e-235, 7.13e-235j)
| (0.99670118956022274624 - 4.2748935074261216786e-891j)  +/-  (4.95e-235, 4.95e-235j)
| (-0.93865916474715050407 + 1.270500623447118143e-894j)  +/-  (2.39e-235, 2.39e-235j)
| (-0.99670118956022274624 - 1.5921577260225333877e-904j)  +/-  (6.68e-235, 6.68e-235j)
| (0.91861293776362177172 - 2.3630723544544590972e-912j)  +/-  (8.08e-236, 8.08e-236j)
| (0.93865916474715050407 - 1.5647169888826542762e-916j)  +/-  (1.85e-235, 1.85e-235j)
| (-0.99963328622328394947 + 1.1921064375084990068e-913j)  +/-  (2.15e-235, 2.15e-235j)
| (-0.91861293776362177172 + 1.7696964293710265767e-922j)  +/-  (9.56e-236, 9.56e-236j)
| (-0.97044114825321141749 + 7.1326936497836693499e-920j)  +/-  (5.27e-235, 5.27e-235j)
| (0.99963328622328394947 - 2.0664691424483668123e-923j)  +/-  (2.3e-235, 2.3e-235j)
| (0.84258207361664910304 - 6.5128352859097679835e-939j)  +/-  (4.56e-237, 4.56e-237j)
| (0.97044114825321141749 - 2.652338609283793954e-936j)  +/-  (5.61e-235, 5.61e-235j)
| (-0.95595214267161160962 + 3.1095926401142953647e-936j)  +/-  (3.72e-235, 3.72e-235j)
| (-0.77941338204159160664 - 1.123514044633115412e-947j)  +/-  (3.12e-238, 3.12e-238j)
| (0.98208368274215600109 + 1.9596505583836952452e-942j)  +/-  (6.71e-235, 6.71e-235j)
| (0.87050383605617205221 - 7.1838071494192180709e-951j)  +/-  (1.59e-236, 1.59e-236j)
| (0.89587226075868795312 - 4.454221982168111054e-950j)  +/-  (3.93e-236, 3.93e-236j)
| (-0.98208368274215600109 + 8.4958662148785189396e-956j)  +/-  (6.56e-235, 6.56e-235j)
| (-0.81218887278021113418 - 9.0804831864559580664e-980j)  +/-  (1.27e-237, 1.27e-237j)
| (-0.99084559657880676279 - 1.6878782056449834407e-977j)  +/-  (7.52e-235, 7.52e-235j)
| (0.95595214267161160962 + 5.4951574453682109059e-994j)  +/-  (3.69e-235, 3.69e-235j)
| (0.7071067811865475244 - 9.0650918273191659697e-1006j)  +/-  (1.22e-239, 1.22e-239j)
| (-0.84258207361664910304 + 1.4649238473546977042e-1003j)  +/-  (4.26e-237, 4.26e-237j)
| (-0.74435173756227027532 - 1.0997826312095264444e-1005j)  +/-  (6.31e-239, 6.31e-239j)
| (-0.7071067811865475244 + 3.1308469189982411478e-1006j)  +/-  (1.23e-239, 1.23e-239j)
| (0.81218887278021113418 - 1.5173320729983920914e-1003j)  +/-  (1.22e-237, 1.22e-237j)
| (0.74435173756227027532 - 5.4206091814806016194e-1005j)  +/-  (6.32e-239, 6.32e-239j)
| (0.77941338204159160664 + 4.8281602469280544044e-1004j)  +/-  (3.14e-238, 3.14e-238j)
| (-0.87050383605617205221 - 1.3550937337611177872e-1002j)  +/-  (1.34e-236, 1.34e-236j)
| (-0.66778775878869561567 + 6.7224105393390017434e-1010j)  +/-  (1.88e-240, 1.88e-240j)
| (-0.89587226075868795312 - 2.0394057318729780305e-1012j)  +/-  (3.34e-236, 3.34e-236j)
| (0.62650999983598662941 + 1.2680786284140718763e-1014j)  +/-  (2.68e-241, 2.68e-241j)
| (0.66778775878869561567 + 4.0751085285295358317e-1018j)  +/-  (1.92e-240, 1.92e-240j)
| (0.13500001385329010394 + 3.5490116982272719097e-1030j)  +/-  (9.93e-253, 9.93e-253j)
| (-0.62650999983598662941 - 3.6699459321941061702e-1019j)  +/-  (2.43e-241, 2.43e-241j)
| (-0.58339457910749394741 - 1.288492142973009048e-1022j)  +/-  (3.03e-242, 3.03e-242j)
| (0.081158725527431270252 + 3.5379622556623394665e-1033j)  +/-  (5.76e-254, 5.76e-254j)
| (0.53856796156090431844 - 9.4460972845326656046e-1021j)  +/-  (2.89e-243, 2.89e-243j)
| (0.44431170635390355089 + 2.2558983445655294157e-1023j)  +/-  (2.58e-245, 2.58e-245j)
| (-0.29352257310393475414 - 7.7856577222027786604e-1029j)  +/-  (8.48e-249, 8.48e-249j)
| (-0.53856796156090431844 - 8.4763929674194515387e-1025j)  +/-  (3.5e-243, 3.5e-243j)
| (-0.13500001385329010394 + 5.0413526219813451831e-1032j)  +/-  (1.23e-252, 1.23e-252j)
| (0.29352257310393475414 - 9.1109638480403700973e-1028j)  +/-  (7.48e-249, 7.48e-249j)
| (0.58339457910749394741 - 7.6421847482105590346e-1025j)  +/-  (3e-242, 3e-242j)
| (-0.081158725527431270252 + 5.2939363520708924646e-1037j)  +/-  (5.76e-254, 5.76e-254j)
| (-0.49216163138900733507 - 4.2307545724487061912e-1029j)  +/-  (2.77e-244, 2.77e-244j)
| (-0.34484630262797043417 - 4.3085293706611300729e-1031j)  +/-  (1.29e-247, 1.29e-247j)
| (0.1884453238783182943 + 4.5176812529196461929e-1034j)  +/-  (2.19e-251, 2.19e-251j)
| (0.49216163138900733507 + 1.1755888540838170238e-1027j)  +/-  (2.86e-244, 2.86e-244j)
| (0.24133789129970564692 - 8.2778618057107521179e-1033j)  +/-  (4.93e-250, 4.93e-250j)
| (-0.1884453238783182943 + 6.9022802768673699993e-1035j)  +/-  (2.19e-251, 2.19e-251j)
| (-0.44431170635390355089 + 4.4369106900507186565e-1029j)  +/-  (2.47e-245, 2.47e-245j)
| (0.027079384676134495101 - 4.8129371802489592463e-1038j)  +/-  (3.36e-255, 3.36e-255j)
| (0.3951585385301554552 + 5.7100920749227678144e-1029j)  +/-  (2.12e-246, 2.12e-246j)
| (0.34484630262797043417 - 5.6207147350328855218e-1030j)  +/-  (1.32e-247, 1.32e-247j)
| (-0.027079384676134495101 + 4.3243694426810539219e-1038j)  +/-  (2.56e-255, 2.56e-255j)
| (-0.3951585385301554552 - 5.4630172593292306676e-1030j)  +/-  (2.07e-246, 2.07e-246j)
| (-0.24133789129970564692 + 6.6386489519683507946e-1033j)  +/-  (5.08e-250, 5.08e-250j)
-------------------------------------------------
The weights are:
| (0.017241379310344827586 - 1.2517077265348069533e-884j)  +/-  (8.62e-40, 2.3e-152j)
| (0.017241379310344827586 - 4.7274214057460186387e-884j)  +/-  (6.37e-40, 1.7e-152j)
| (0.017241379310344827586 + 6.0959285263923481269e-886j)  +/-  (3.27e-41, 8.74e-154j)
| (0.017241379310344827586 - 1.3927655134112423957e-886j)  +/-  (1.34e-41, 3.58e-154j)
| (0.017241379310344827586 + 1.8659410024367961942e-884j)  +/-  (6.89e-41, 1.84e-153j)
| (0.017241379310344827586 - 2.253866071201091457e-884j)  +/-  (8.56e-41, 2.29e-153j)
| (0.017241379310344827586 + 4.6402498340880381702e-887j)  +/-  (9.76e-42, 2.61e-154j)
| (0.017241379310344827586 - 7.0586441231629206752e-886j)  +/-  (2.13e-42, 5.7e-155j)
| (0.017241379310344827586 + 4.1970540969551789834e-886j)  +/-  (3.12e-42, 8.34e-155j)
| (0.017241379310344827586 + 1.0510526205914698039e-884j)  +/-  (7.32e-42, 1.96e-154j)
| (0.017241379310344827586 - 1.2389858370549726591e-884j)  +/-  (2.87e-44, 7.68e-157j)
| (0.017241379310344827586 - 4.03423114588113123e-884j)  +/-  (7.39e-43, 1.97e-155j)
| (0.017241379310344827586 - 5.1425771845240825374e-886j)  +/-  (2.15e-44, 5.75e-157j)
| (0.017241379310344827586 + 1.2071225096917662345e-885j)  +/-  (4.87e-47, 1.3e-159j)
| (0.017241379310344827586 + 7.3357832054104831069e-884j)  +/-  (1.74e-42, 4.64e-155j)
| (0.017241379310344827586 + 1.3949271738953319603e-884j)  +/-  (4.77e-45, 1.28e-157j)
| (0.017241379310344827586 - 1.5956814783937851228e-884j)  +/-  (1.4e-44, 3.74e-157j)
| (0.017241379310344827586 - 3.2578718251288560392e-886j)  +/-  (2.66e-45, 7.1e-158j)
| (0.017241379310344827586 - 1.1036173184135349538e-885j)  +/-  (2.29e-48, 6.12e-161j)
| (0.017241379310344827586 + 2.3235818763144443502e-886j)  +/-  (2.25e-45, 6.01e-158j)
| (0.017241379310344827586 + 2.8691792189204023344e-884j)  +/-  (8.08e-45, 2.16e-157j)
| (0.017241379310344827586 - 8.5001462074023611143e-885j)  +/-  (3.77e-50, 1.01e-162j)
| (0.017241379310344827586 + 1.0019288453849711516e-885j)  +/-  (2.07e-48, 5.54e-161j)
| (0.017241379310344827586 - 1.3126523757880380657e-885j)  +/-  (8.25e-50, 2.2e-162j)
| (0.017241379310344827586 + 1.4204293702410751612e-885j)  +/-  (1.07e-50, 2.86e-163j)
| (0.017241379310344827586 + 1.1137896229984413175e-884j)  +/-  (1.11e-49, 2.97e-162j)
| (0.017241379310344827586 + 9.2404366575444553453e-885j)  +/-  (1.66e-51, 4.43e-164j)
| (0.017241379310344827586 - 1.0106877288587789674e-884j)  +/-  (9.55e-51, 2.55e-163j)
| (0.017241379310344827586 - 9.0186179436875542111e-886j)  +/-  (4.93e-51, 1.32e-163j)
| (0.017241379310344827586 - 1.53069251511450917e-885j)  +/-  (1.81e-54, 4.85e-167j)
| (0.017241379310344827586 + 8.0323189110056819493e-886j)  +/-  (8.02e-51, 2.14e-163j)
| (0.017241379310344827586 - 7.2966984451261094607e-885j)  +/-  (6.8e-56, 1.82e-168j)
| (0.017241379310344827586 + 7.8588331730658180385e-885j)  +/-  (7.79e-55, 2.08e-167j)
| (0.017241379310344827586 - 3.9488507241440994379e-885j)  +/-  (1.34e-60, 3.59e-173j)
| (0.017241379310344827586 + 1.6436997510246348878e-885j)  +/-  (7.42e-57, 1.98e-169j)
| (0.017241379310344827586 - 1.7597306177418720054e-885j)  +/-  (6.13e-58, 1.64e-170j)
| (0.017241379310344827586 + 3.7370868957087797027e-885j)  +/-  (1.66e-61, 4.43e-174j)
| (0.017241379310344827586 - 6.3542931724308975799e-885j)  +/-  (1.22e-59, 3.27e-172j)
| (0.017241379310344827586 - 5.5909954417523717975e-885j)  +/-  (6.88e-61, 1.84e-173j)
| (0.017241379310344827586 - 2.5386729980426268151e-885j)  +/-  (4.61e-63, 1.23e-175j)
| (0.017241379310344827586 + 1.8790893280579592304e-885j)  +/-  (1.41e-60, 3.76e-173j)
| (0.017241379310344827586 + 3.0018382798516786963e-885j)  +/-  (1.09e-63, 2.92e-176j)
| (0.017241379310344827586 + 4.6758685412322782077e-885j)  +/-  (1.64e-63, 4.38e-176j)
| (0.017241379310344827586 + 6.7989488554858209202e-885j)  +/-  (1.74e-60, 4.65e-173j)
| (0.017241379310344827586 - 3.1712361748873597978e-885j)  +/-  (4.95e-64, 1.32e-176j)
| (0.017241379310344827586 - 2.0021083108003477998e-885j)  +/-  (9.12e-63, 2.44e-175j)
| (0.017241379310344827586 + 2.3969654800095515433e-885j)  +/-  (5.86e-64, 1.57e-176j)
| (0.017241379310344827586 + 4.1746260053878961093e-885j)  +/-  (1.88e-64, 5.03e-177j)
| (0.017241379310344827586 + 5.9539533995865568107e-885j)  +/-  (1.57e-63, 4.19e-176j)
| (0.017241379310344827586 - 4.4162459022898188041e-885j)  +/-  (1.23e-64, 3.3e-177j)
| (0.017241379310344827586 - 2.8404535209648165413e-885j)  +/-  (8.39e-66, 2.24e-178j)
| (0.017241379310344827586 + 2.1291523153786623142e-885j)  +/-  (2.77e-65, 7.41e-178j)
| (0.017241379310344827586 - 3.5377664501559079477e-885j)  +/-  (7.35e-66, 1.96e-178j)
| (0.017241379310344827586 + 5.2598642921488766047e-885j)  +/-  (1.18e-65, 3.16e-178j)
| (0.017241379310344827586 - 4.9560539775602715618e-885j)  +/-  (8.86e-66, 2.37e-178j)
| (0.017241379310344827586 + 3.3495393406665481772e-885j)  +/-  (1.12e-66, 3e-179j)
| (0.017241379310344827586 - 2.2606231910071780869e-885j)  +/-  (2.41e-67, 6.52e-180j)
| (0.017241379310344827586 + 2.686296616915214777e-885j)  +/-  (2.72e-67, 7.2e-180j)
