Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 27 30
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 4*t^29 - 28*t^27 + 351/4*t^25 - 325/2*t^23 + 6325/32*t^21 - 5313/32*t^19 + 100947/1024*t^17 - 10659/256*t^15 + 101745/8192*t^13 - 20995/8192*t^11 + 46189/131072*t^9 - 1989/65536*t^7 + 1547/1048576*t^5 - 35/1048576*t^3 + 15/67108864*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^59 - 58*t^57 + 399*t^55 - 3465/2*t^53 + 341055/64*t^51 - 1581255/128*t^49 + 2869685/128*t^47 - 8361535/256*t^45 + 318381525/8192*t^43 - 626358425/16384*t^41 + 1027227817/32768*t^39 - 1412200023/65536*t^37 + 52251400851/4194304*t^35 - 50883115395/8388608*t^33 + 10429458435/4194304*t^31 - 7184738033/8388608*t^29 + 132591074609/536870912*t^27 - 63665481789/1073741824*t^25 + 25264080075/2147483648*t^23 - 8205150525/4294967296*t^21 + 34461632205/137438953472*t^19 - 7195285845/274877906944*t^17 + 585262485/274877906944*t^15 - 72212175/549755813888*t^13 + 104306475/17592186044416*t^11 - 6556407/35184372088832*t^9 + 267003/70368744177664*t^7 - 6293/140737488355328*t^5 + 4495/18014398509481984*t^3 - 15/36028797018963968*t
-------------------------------------------------
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
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:
| (0.98768834059513772619 + 1.6457121172158612171e-887j)  +/-  (4.7e-235, 4.7e-235j)
| (-0.98768834059513772619 - 6.8512276398162884274e-892j)  +/-  (4.57e-235, 4.57e-235j)
| (-0.93358042649720174899 - 4.0999420252632748336e-903j)  +/-  (2.45e-235, 2.45e-235j)
| (-0.99862953475457387378 + 4.7512450827660729542e-912j)  +/-  (7.9e-236, 7.9e-236j)
| (0.9135454576426008955 - 1.1014721358249202715e-931j)  +/-  (1.27e-235, 1.27e-235j)
| (0.89100652418836786236 + 7.1732696904384642887e-935j)  +/-  (5.25e-236, 5.25e-236j)
| (-0.97814760073380563793 + 1.3111205290810102059e-934j)  +/-  (5.94e-235, 5.94e-235j)
| (-0.9135454576426008955 + 2.4501232676066952779e-951j)  +/-  (1.19e-235, 1.19e-235j)
| (-0.99452189536827333692 + 1.4413229085450264914e-958j)  +/-  (2.78e-235, 2.78e-235j)
| (0.99862953475457387378 + 1.0544966506716477689e-967j)  +/-  (8.28e-236, 8.28e-236j)
| (0.83867056794542402964 + 3.7262033731620948265e-974j)  +/-  (7.75e-237, 7.75e-237j)
| (0.96592582628906828675 + 3.6012585764292667051e-971j)  +/-  (4.75e-235, 4.75e-235j)
| (-0.86602540378443864676 + 6.3727979593646481227e-975j)  +/-  (2.19e-236, 2.19e-236j)
| (-0.83867056794542402964 - 1.7237428540170811796e-976j)  +/-  (6.86e-237, 6.86e-237j)
| (0.97814760073380563793 + 5.3876488734011355143e-973j)  +/-  (5.11e-235, 5.11e-235j)
| (0.86602540378443864676 - 8.5865734848076969312e-980j)  +/-  (2.4e-236, 2.4e-236j)
| (0.93358042649720174899 + 3.165680863757480596e-978j)  +/-  (2.39e-235, 2.39e-235j)
| (-0.052335956242943832722 - 3.3482019410914488568e-996j)  +/-  (1.07e-254, 1.07e-254j)
| (-0.74314482547739423501 + 4.3301777105388412726e-981j)  +/-  (1.51e-238, 1.51e-238j)
| (-0.96592582628906828675 + 3.9231182897179072226e-975j)  +/-  (5.66e-235, 5.66e-235j)
| (0.99452189536827333692 + 1.2727083759963646536e-989j)  +/-  (2.68e-235, 2.68e-235j)
| (0.7071067811865475244 - 4.060619189344145909e-998j)  +/-  (2.59e-239, 2.59e-239j)
| (0.95105651629515357212 - 2.0519781990246930259e-992j)  +/-  (3.87e-235, 3.87e-235j)
| (-0.8090169943749474241 + 3.0306765052193331044e-993j)  +/-  (2.17e-237, 2.17e-237j)
| (-0.77714596145697087998 + 4.5700442255176863839e-996j)  +/-  (6.23e-238, 6.23e-238j)
| (0.8090169943749474241 + 4.6402116478342619733e-996j)  +/-  (2.28e-237, 2.28e-237j)
| (0.74314482547739423501 - 2.3508836524948938627e-997j)  +/-  (1.63e-238, 1.63e-238j)
| (0.77714596145697087998 - 2.8615218623383075116e-996j)  +/-  (6.37e-238, 6.37e-238j)
| (-0.95105651629515357212 - 1.7652972682755559811e-996j)  +/-  (3.35e-235, 3.35e-235j)
| (-0.62932039104983745271 + 1.898062531499022993e-1009j)  +/-  (6.29e-241, 6.29e-241j)
| (-0.89100652418836786236 - 8.4913908643359979912e-1011j)  +/-  (5.76e-236, 5.76e-236j)
| (0.66913060635885821383 + 3.4186648254145006713e-1016j)  +/-  (4.23e-240, 4.23e-240j)
| (0.62932039104983745271 - 2.2718836428295766396e-1018j)  +/-  (6.45e-241, 6.45e-241j)
| (-0.15643446504023086901 + 9.4098739391489670334e-1030j)  +/-  (5.51e-252, 5.51e-252j)
| (-0.66913060635885821383 - 1.2311104385414406328e-1016j)  +/-  (4.18e-240, 4.18e-240j)
| (-0.7071067811865475244 - 8.146994800931942127e-1022j)  +/-  (2.72e-239, 2.72e-239j)
| (0.15643446504023086901 - 1.0942007066793773565e-1033j)  +/-  (5.37e-252, 5.37e-252j)
| (0.58778525229247312917 - 8.8782455838154718458e-1022j)  +/-  (7.88e-242, 7.88e-242j)
| (0.40673664307580020775 - 2.8566012298452156469e-1026j)  +/-  (7.88e-246, 7.88e-246j)
| (-0.45399049973954679156 - 2.1132674812026054357e-1026j)  +/-  (9.56e-245, 9.56e-245j)
| (-0.58778525229247312917 - 9.2581672493468133462e-1024j)  +/-  (7.85e-242, 7.85e-242j)
| (-0.3090169943749474241 + 5.451202758389417636e-1033j)  +/-  (4.01e-248, 4.01e-248j)
| (0.45399049973954679156 + 1.7244696711292361644e-1025j)  +/-  (8.81e-245, 8.81e-245j)
| (0.54463903501502708222 - 9.6995351866546762056e-1026j)  +/-  (9.08e-243, 9.08e-243j)
| (0.1045284632676534714 + 2.5354589821517149382e-1037j)  +/-  (2.36e-253, 2.36e-253j)
| (-0.54463903501502708222 + 1.5087532743505125674e-1027j)  +/-  (8.9e-243, 8.9e-243j)
| (-0.5 - 2.6390303255275557863e-1031j)  +/-  (9.46e-244, 9.46e-244j)
| (-6.1814075403690951831e-1056 + 3.2987593870874813799e-1055j)  +/-  (1.98e-1053, 1.98e-1053j)
| (0.5 + 2.6630467867214771287e-1029j)  +/-  (1.11e-243, 1.11e-243j)
| (0.2079116908177593371 - 1.0465619935605066523e-1036j)  +/-  (1.07e-250, 1.07e-250j)
| (-0.25881904510252076235 + 8.5616422155526152992e-1036j)  +/-  (2.1e-249, 2.1e-249j)
| (-0.40673664307580020775 + 1.2600471636296980788e-1032j)  +/-  (8.41e-246, 8.41e-246j)
| (-0.1045284632676534714 + 1.3183959341756277295e-1039j)  +/-  (2.6e-253, 2.6e-253j)
| (0.35836794954530027348 + 1.8954616080468421782e-1032j)  +/-  (5.31e-247, 5.31e-247j)
| (0.3090169943749474241 + 3.290362922328590272e-1034j)  +/-  (3.78e-248, 3.78e-248j)
| (0.052335956242943832722 - 4.0302930587969786705e-1040j)  +/-  (1.07e-254, 1.07e-254j)
| (-0.35836794954530027348 - 1.128526674158913602e-1033j)  +/-  (5.55e-247, 5.55e-247j)
| (-0.2079116908177593371 + 3.195670049520020387e-1037j)  +/-  (1.08e-250, 1.08e-250j)
| (0.25881904510252076235 + 8.604851218234849203e-1035j)  +/-  (2.15e-249, 2.15e-249j)
-------------------------------------------------
The weights are:
| (0.0004078623642070535657 - 4.0636280899705747215e-889j)  +/-  (9.23e-44, 1.34e-155j)
| (0.0004078623642070535657 - 3.4148718289425597502e-891j)  +/-  (4.5e-44, 6.54e-156j)
| (0.0021404597876883813749 - 1.8361760998619413011e-890j)  +/-  (1.46e-44, 2.12e-156j)
| (4.5650871931055525644e-05 - 3.7536985410144400692e-892j)  +/-  (1.62e-44, 2.35e-156j)
| (0.0027572449470095148848 + 6.1201272536305274977e-889j)  +/-  (1.12e-45, 1.62e-157j)
| (0.0034351228975627239236 - 5.8472582521576774433e-889j)  +/-  (1.02e-45, 1.48e-157j)
| (0.00072045451964499253748 + 6.0830670459327587855e-891j)  +/-  (4.09e-45, 5.95e-157j)
| (0.0027572449470095148848 + 2.3892250847194953203e-890j)  +/-  (2.93e-46, 4.27e-158j)
| (0.0001821033272182863506 + 1.4936389729628868024e-891j)  +/-  (1e-44, 1.46e-156j)
| (4.5650871931055525644e-05 + 6.8665426072957418483e-890j)  +/-  (9.48e-49, 1.38e-160j)
| (0.0049438613077016649354 - 5.4598857250215704412e-889j)  +/-  (9.43e-49, 1.37e-160j)
| (0.001116454968463011277 - 8.4427943212978798035e-889j)  +/-  (1.31e-48, 1.91e-160j)
| (0.0041666666666666666667 + 3.7014794568587555437e-890j)  +/-  (2.37e-48, 3.45e-160j)
| (0.0049438613077016649354 - 4.4571325540831419094e-890j)  +/-  (7.73e-49, 1.12e-160j)
| (0.00072045451964499253748 + 1.2427348294502625879e-888j)  +/-  (8.19e-49, 1.19e-160j)
| (0.0041666666666666666667 + 5.6361885857033031507e-889j)  +/-  (8.7e-50, 1.27e-161j)
| (0.0021404597876883813749 - 6.5102948389730187487e-889j)  +/-  (1.89e-49, 2.75e-161j)
| (0.016621015794735611141 - 2.6301955976719548857e-889j)  +/-  (1.51e-55, 2.2e-167j)
| (0.0074622628061028877383 + 7.0973650962580370981e-890j)  +/-  (2.67e-53, 3.89e-165j)
| (0.001116454968463011277 - 9.4400934586430044295e-891j)  +/-  (5.67e-50, 8.24e-162j)
| (0.0001821033272182863506 - 4.3855594800417162407e-889j)  +/-  (1.01e-49, 1.46e-161j)
| (0.0083333333333333333333 - 4.8878344655075577893e-889j)  +/-  (1.65e-54, 2.4e-166j)
| (0.0015915250468754381325 + 7.1500509865293025696e-889j)  +/-  (1.16e-49, 1.68e-161j)
| (0.0057581917135421047991 + 5.2764873694165686126e-890j)  +/-  (1.66e-53, 2.41e-165j)
| (0.0066007359098520055242 - 6.1573496202660157931e-890j)  +/-  (4.76e-54, 6.93e-166j)
| (0.0057581917135421047991 + 5.3037967799481840891e-889j)  +/-  (2.4e-53, 3.49e-165j)
| (0.0074622628061028877383 + 5.0219318020528349524e-889j)  +/-  (4.27e-55, 6.22e-167j)
| (0.0066007359098520055242 - 5.1595147088485965578e-889j)  +/-  (2.22e-54, 3.23e-166j)
| (0.0015915250468754381325 + 1.3539496705745190347e-890j)  +/-  (4.53e-54, 6.59e-166j)
| (0.010065930756814661143 - 1.0246534634799520151e-889j)  +/-  (1.63e-59, 2.38e-171j)
| (0.0034351228975627239236 - 3.0115569606420339974e-890j)  +/-  (8.66e-55, 1.26e-166j)
| (0.0092044038605637789283 + 4.7551569419951595712e-889j)  +/-  (5.94e-58, 8.64e-170j)
| (0.010065930756814661143 - 4.6225609961228251612e-889j)  +/-  (4.4e-59, 6.4e-171j)
| (0.016258804302459613101 - 2.3388087633720601726e-889j)  +/-  (6.54e-63, 9.51e-175j)
| (0.0092044038605637789283 + 9.1446798216097903881e-890j)  +/-  (1.41e-59, 2.06e-171j)
| (0.0083333333333333333333 - 8.0940262845277413824e-890j)  +/-  (6.7e-59, 9.74e-171j)
| (0.016258804302459613101 - 3.219007015152824488e-889j)  +/-  (2.48e-64, 3.61e-176j)
| (0.010908474953124561868 + 4.4891874155598702057e-889j)  +/-  (4.01e-61, 5.83e-173j)
| (0.013909421719657151782 + 3.9403105274248475613e-889j)  +/-  (7.03e-64, 1.02e-175j)
| (0.013231543769103942743 - 1.5105833625034627779e-889j)  +/-  (2.62e-64, 3.8e-176j)
| (0.010908474953124561868 + 1.1396670713813652612e-889j)  +/-  (1.59e-62, 2.32e-174j)
| (0.015075141619791228534 + 1.9134120873279643732e-889j)  +/-  (2.45e-65, 3.56e-177j)
| (0.013231543769103942743 - 4.0801453239766281243e-889j)  +/-  (1.82e-64, 2.65e-176j)
| (0.011722805358965001731 - 4.3545029423294247712e-889j)  +/-  (1.7e-63, 2.47e-175j)
| (0.016484563339448380316 + 3.0718966693491591793e-889j)  +/-  (2.81e-66, 4.09e-178j)
| (0.011722805358965001731 - 1.259204849068066185e-889j)  +/-  (3.4e-64, 4.95e-176j)
| (0.0125 + 1.3829518827194783349e-889j)  +/-  (9.07e-65, 1.32e-176j)
| (0.016666666666666666667 + 2.7771591534305657989e-889j)  +/-  (2.84e-67, 4.13e-179j)
| (0.0125 + 4.2182025887724892057e-889j)  +/-  (2.14e-65, 3.11e-177j)
| (0.015946212147021674129 + 3.3655261545946551482e-889j)  +/-  (1.35e-67, 1.96e-179j)
| (0.01555021169820365539 - 2.0531762681138636616e-889j)  +/-  (6.37e-68, 9.26e-180j)
| (0.013909421719657151782 + 1.6417657088391815656e-889j)  +/-  (2.65e-67, 3.85e-179j)
| (0.016484563339448380316 + 2.4839612683253615132e-889j)  +/-  (6e-68, 8.72e-180j)
| (0.014526206878978285292 - 3.7987677364014139897e-889j)  +/-  (1.62e-68, 2.35e-180j)
| (0.015075141619791228534 + 3.6556551172708219348e-889j)  +/-  (5.2e-69, 7.58e-181j)
| (0.016621015794735611141 - 2.9245054257292369958e-889j)  +/-  (4.02e-69, 5.92e-181j)
| (0.014526206878978285292 - 1.7761577685258191639e-889j)  +/-  (1.94e-69, 2.86e-181j)
| (0.015946212147021674129 + 2.1950944268929071093e-889j)  +/-  (1.45e-69, 2.15e-181j)
| (0.01555021169820365539 - 3.5111637894917704832e-889j)  +/-  (1.26e-69, 1.79e-181j)
