Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 32
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^38 - 426508646085454018340044123/700595787372387283311781*t^36 + 346683113024500619340181725035/2101787362117161849935343*t^34 - 239869565992784539479089913889735/9107745235841034683053153*t^32 + 3599061977049624789516729067425660/1301106462263004954721879*t^30 - 1840261866257062232371781870766366460/9107745235841034683053153*t^28 + 13772391545298501179996552794258949340/1301106462263004954721879*t^26 - 40470872452775648393467715394678670500/100085112481769611901683*t^24 + 1135542409180436883959957333179596404250/100085112481769611901683*t^22 - 2127537122479900573648745363502920447250/9098646589251782900153*t^20 + 32007649316364586639460310146453905809750/9098646589251782900153*t^18 - 347180456952427323458645302429820408699250/9098646589251782900153*t^16 + 2663214120190447439675499171201971818192500/9098646589251782900153*t^14 - 14051945959824318267618994559937552262867500/9098646589251782900153*t^12 + 329035230890205330745434573414957374302500/61064742209743509397*t^10 - 106831146310537688550892586998844414338657500/9098646589251782900153*t^8 + 133231971690197589573051168691884520603850625/9098646589251782900153*t^6 - 82029198926422262900053390708781415481809375/9098646589251782900153*t^4 + 18501201902498849290951060686243859083403125/9098646589251782900153*t^2 - 615962444143380278091548235801288166884375/9098646589251782900153
-------------------------------------------------
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: 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:   38 out of 38
Indefinite weights: 0 out of 38
Negative weights:   0 out of 38
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.3987016189401844383 - 2.2783404949603358788e-962j)  +/-  (2.29e-246, 2.29e-246j)
| (-9.6519989222929654458 + 1.0450272892434635748e-976j)  +/-  (1.48e-247, 1.48e-247j)
| (8.8258807281900106991 - 8.6789603133884003838e-976j)  +/-  (5.84e-247, 5.84e-247j)
| (5.5363416542048151003 + 6.2725289929826210034e-978j)  +/-  (1.4e-246, 1.4e-246j)
| (-8.0850942319595855918 + 1.0085274484936409184e-977j)  +/-  (1.45e-246, 1.45e-246j)
| (-6.7508378798831262033 - 5.8592638974944318119e-992j)  +/-  (2.54e-246, 2.54e-246j)
| (9.6519989222929654458 + 1.61744392999026715e-1003j)  +/-  (1.52e-247, 1.52e-247j)
| (10.64472789025145422 - 1.0245523556771271822e-1006j)  +/-  (1.55e-248, 1.55e-248j)
| (-4.3992030777676133627 - 1.2665517359691811317e-1009j)  +/-  (2.59e-247, 2.59e-247j)
| (-10.64472789025145422 - 2.2082430653858433977e-1017j)  +/-  (1.71e-248, 1.71e-248j)
| (8.0850942319595855918 + 6.9876726475017921949e-1018j)  +/-  (1.36e-246, 1.36e-246j)
| (1.8891758777537106755 + 7.8783761852229063813e-1031j)  +/-  (2.81e-250, 2.81e-250j)
| (-1.0511259774590467418 + 4.3260463116317200342e-1030j)  +/-  (3.68e-252, 3.68e-252j)
| (-6.1320768369974286068 + 4.5389925251692117434e-1029j)  +/-  (2.11e-246, 2.11e-246j)
| (2.3310770501988055001 - 1.6436859596682855374e-1042j)  +/-  (1.66e-249, 1.66e-249j)
| (2.8136148995836558835 - 9.6864424479332221454e-1042j)  +/-  (6.45e-249, 6.45e-249j)
| (1.4755331497403582589 - 4.7478251511350824734e-1044j)  +/-  (4.28e-251, 4.28e-251j)
| (6.7508378798831262033 - 1.4021539922071030513e-1038j)  +/-  (2.54e-246, 2.54e-246j)
| (-1.8891758777537106755 - 1.3817350567788531032e-1045j)  +/-  (2.65e-250, 2.65e-250j)
| (-8.8258807281900106991 - 1.5598332074655616449e-1042j)  +/-  (5.87e-247, 5.87e-247j)
| (1.0511259774590467418 - 1.0134383468240765049e-1052j)  +/-  (3.59e-252, 3.59e-252j)
| (3.3242574335521189524 - 7.9017192483825746996e-1053j)  +/-  (2.84e-248, 2.84e-248j)
| (-5.5363416542048151003 + 2.0048075013619884288e-1052j)  +/-  (1.49e-246, 1.49e-246j)
| (7.3987016189401844383 + 2.905854260685149984e-1062j)  +/-  (2.1e-246, 2.1e-246j)
| (3.8539418560456038916 + 4.6733588827540144161e-1063j)  +/-  (8.7e-248, 8.7e-248j)
| (-4.959582609322924333 - 5.8731694866195845163e-1063j)  +/-  (6.56e-247, 6.56e-247j)
| (0.61670659019259415219 + 2.3934572952442861528e-1078j)  +/-  (3.03e-253, 3.03e-253j)
| (4.959582609322924333 + 1.5089311915133433854e-1069j)  +/-  (6.85e-247, 6.85e-247j)
| (-3.8539418560456038916 + 1.1103389438347857442e-1071j)  +/-  (8.91e-248, 8.91e-248j)
| (-0.61670659019259415219 - 1.6473136726737745122e-1081j)  +/-  (3.03e-253, 3.03e-253j)
| (-2.3310770501988055001 - 5.8637772243215422172e-1078j)  +/-  (1.58e-249, 1.58e-249j)
| (4.3992030777676133627 - 1.3892783719368655731e-1074j)  +/-  (2.65e-247, 2.65e-247j)
| (-0.19978143849109734366 - 1.4852958882177057784e-1083j)  +/-  (2.22e-254, 2.22e-254j)
| (6.1320768369974286068 + 1.2324267407041110165e-1077j)  +/-  (2.28e-246, 2.28e-246j)
| (-2.8136148995836558835 - 5.6814611125392395371e-1082j)  +/-  (6.48e-249, 6.48e-249j)
| (-1.4755331497403582589 + 2.576859071153698266e-1086j)  +/-  (4.41e-251, 4.41e-251j)
| (-3.3242574335521189524 - 9.522845596661066469e-1090j)  +/-  (2.66e-248, 2.66e-248j)
| (0.19978143849109734366 - 9.7795207147967073271e-1100j)  +/-  (2.22e-254, 2.22e-254j)
-------------------------------------------------
The weights are:
| (3.4437587839510597774e-13 - 3.2282165038709824562e-974j)  +/-  (1.93e-93, 9.96e-216j)
| (2.0861605047080517191e-21 - 1.2028263364368819246e-979j)  +/-  (5.26e-98, 2.71e-220j)
| (3.7665399865441514966e-18 + 9.3221501700081822485e-979j)  +/-  (6.74e-98, 3.47e-220j)
| (5.161680057184899238e-08 - 5.7619754394845355766e-973j)  +/-  (5.99e-91, 3.09e-213j)
| (1.8097216435326343858e-15 - 6.3133872782213317883e-976j)  +/-  (2.48e-95, 1.28e-217j)
| (3.2022577069000089962e-11 + 1.5483646777404237486e-973j)  +/-  (5.79e-93, 2.98e-215j)
| (2.0861605047080517191e-21 - 1.589568319342749424e-980j)  +/-  (7.15e-100, 3.68e-222j)
| (1.133108469602283446e-25 + 8.2220826809770211472e-983j)  +/-  (8.36e-102, 4.31e-224j)
| (1.3834874876971774484e-05 + 8.4006273047892103883e-971j)  +/-  (3.05e-90, 1.57e-212j)
| (1.133108469602283446e-25 + 4.5703440722014406137e-982j)  +/-  (1.2e-101, 6.18e-224j)
| (1.8097216435326343858e-15 - 2.7987080381512856056e-977j)  +/-  (6.55e-98, 3.37e-220j)
| (0.028232908732397179983 + 1.6274257817068157554e-968j)  +/-  (2.4e-82, 1.24e-204j)
| (0.099566360501894253295 - 7.2665392545844799294e-968j)  +/-  (2.24e-76, 1.16e-198j)
| (1.6536449674403437507e-09 - 7.6621811445909807574e-973j)  +/-  (6.23e-94, 3.21e-216j)
| (0.012225258707645929936 - 5.9611601273646233476e-969j)  +/-  (4.3e-85, 2.22e-207j)
| (0.0037995055989104453709 + 1.7460565797504018834e-969j)  +/-  (2.23e-87, 1.15e-209j)
| (0.05565138275192627269 - 3.3118951472928461192e-968j)  +/-  (1.6e-81, 8.25e-204j)
| (3.2022577069000089962e-11 - 7.0894839342842264453e-975j)  +/-  (4.42e-97, 2.28e-219j)
| (0.028232908732397179983 - 2.7434904573470489319e-968j)  +/-  (3.16e-86, 1.63e-208j)
| (3.7665399865441514966e-18 + 1.0597688272296937406e-977j)  +/-  (1.15e-99, 5.92e-222j)
| (0.099566360501894253295 + 5.4586803155515554863e-968j)  +/-  (7.86e-82, 4.05e-204j)
| (0.00082833762445007336581 - 4.4964308984857439986e-970j)  +/-  (2e-90, 1.03e-212j)
| (5.161680057184899238e-08 + 4.0019868908094010418e-972j)  +/-  (4.39e-95, 2.26e-217j)
| (3.4437587839510597774e-13 + 5.3023189043486982286e-976j)  +/-  (2.93e-98, 1.51e-220j)
| (0.00012770839154437274141 + 1.040191654460368745e-970j)  +/-  (1.05e-92, 5.41e-215j)
| (1.0331776457551530369e-06 - 1.9306630428730511145e-971j)  +/-  (4.66e-95, 2.4e-217j)
| (0.14175281271776707463 - 8.1221287804493673634e-968j)  +/-  (1.67e-87, 8.61e-210j)
| (1.0331776457551530369e-06 + 3.8104941123395269524e-972j)  +/-  (2.71e-95, 1.4e-217j)
| (0.00012770839154437274141 - 3.3020307767590241748e-970j)  +/-  (1.93e-94, 9.95e-217j)
| (0.14175281271776707463 + 9.5992665029228402562e-968j)  +/-  (1.56e-88, 8.07e-211j)
| (0.012225258707645929936 + 1.1445356273689687424e-968j)  +/-  (2.37e-92, 1.22e-214j)
| (1.3834874876971774484e-05 - 2.135774952707674158e-971j)  +/-  (1.68e-94, 8.66e-217j)
| (0.15780080361812736533 - 1.1280136793304562455e-967j)  +/-  (2.54e-90, 1.32e-212j)
| (1.6536449674403437507e-09 + 7.1726165298383207962e-974j)  +/-  (3.04e-97, 1.57e-219j)
| (0.0037995055989104453709 - 3.8889738718316383056e-969j)  +/-  (3.25e-94, 1.68e-216j)
| (0.05565138275192627269 + 4.9619616965409829641e-968j)  +/-  (1.13e-92, 6.2e-215j)
| (0.00082833762445007336581 + 1.183352678623634644e-969j)  +/-  (7.03e-95, 3.58e-217j)
| (0.15780080361812736533 + 1.068697578000508089e-967j)  +/-  (3e-92, 1.89e-214j)
