Starting with polynomial:
P : 131072*t^17 - 8912896*t^15 + 233963520*t^13 - 3041525760*t^11 + 20910489600*t^9 - 75277762560*t^7 + 131736084480*t^5 - 94097203200*t^3 + 17643225600*t
Extension levels are: 17 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 131072*t^17 - 8912896*t^15 + 233963520*t^13 - 3041525760*t^11 + 20910489600*t^9 - 75277762560*t^7 + 131736084480*t^5 - 94097203200*t^3 + 17643225600*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 131072*t^45 - 28642093801269607399424/543076105530597*t^43 + 2455453532486851054764032/257246576303967*t^41 - 5043819711983125120038928384/4887684949775373*t^39 + 364816530770453666278522150912/4887684949775373*t^37 - 56205137030939353316179764813824/14663054849326119*t^35 + 2122580939406382624255966686177280/14663054849326119*t^33 - 20080185764080174247968391834255360/4887684949775373*t^31 + 434015386910895834190069994578027520/4887684949775373*t^29 - 378807447231849940060634643587261440/257246576303967*t^27 + 3401246580084396003224066536710296320/181025368510199*t^25 - 33355416908132987531235920034655168000/181025368510199*t^23 + 250223154166994176759711508375259272000/181025368510199*t^21 - 74928159888235631725730313887195640000/9527650974221*t^19 + 319181262141018146920803556555902150000/9527650974221*t^17 - 999761940195628572790526320647665640000/9527650974221*t^15 + 2246073343040448410484850273423756001250/9527650974221*t^13 - 3497210572105777995402590169027092328750/9527650974221*t^11 + 7189897628627433272298320071317771575625/19055301948442*t^9 - 2268168637116558137700590182463994736875/9527650974221*t^7 + 6219205748323418114443922714143824526875/76221207793768*t^5 - 904594761764889130230215911900481446875/76221207793768*t^3 + 109505253801035390420274266693525821875/304884831175072*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: 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:   45 out of 45
Indefinite weights: 0 out of 45
Negative weights:   0 out of 45
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.0619466758754743069 - 2.0683842067353477272e-948j)  +/-  (2.58e-245, 2.58e-245j)
| (-8.6819095440718685674 - 1.9492384688760544723e-960j)  +/-  (1.07e-248, 1.07e-248j)
| (-7.4927444973314948042 + 6.910435013107410828e-958j)  +/-  (2.89e-247, 2.89e-247j)
| (7.4927444973314948042 - 2.769128382247708006e-955j)  +/-  (2.85e-247, 2.85e-247j)
| (8.6819095440718685674 - 3.2874095379283385254e-961j)  +/-  (1.1e-248, 1.1e-248j)
| (6.2802461177221835343 + 7.7553116165315686957e-959j)  +/-  (6.05e-246, 6.05e-246j)
| (-4.8713451936744030883 - 2.1666383949499365694e-964j)  +/-  (2.64e-245, 2.64e-245j)
| (-3.0767040777614653993 + 1.2436467727795418053e-970j)  +/-  (6.29e-246, 6.29e-246j)
| (6.8366897395149018687 - 7.0370808618540217211e-967j)  +/-  (1.83e-246, 1.83e-246j)
| (1.6129243142212313331 + 2.1131938540213978913e-976j)  +/-  (6.9e-249, 6.9e-249j)
| (1.2920987041134851452 - 2.0664373311835473027e-979j)  +/-  (9.15e-250, 9.15e-250j)
| (4.8713451936744030883 + 3.6442350088355639904e-975j)  +/-  (2.8e-245, 2.8e-245j)
| (-2.1735028266666208193 + 4.2166812606628834936e-985j)  +/-  (2.28e-247, 2.28e-247j)
| (-2.7577629157038887309 - 4.0824300581289728064e-984j)  +/-  (1.95e-246, 1.95e-246j)
| (-4.4548496545097449284 + 3.2395261958375040934e-982j)  +/-  (2.61e-245, 2.61e-245j)
| (-5.7776439286587553827 + 9.1980263508518837728e-983j)  +/-  (1.36e-245, 1.36e-245j)
| (0.85514225944313044986 - 2.6153799615218005421e-994j)  +/-  (2.6e-251, 2.6e-251j)
| (5.3109463040160895355 + 2.5776686814616879727e-987j)  +/-  (2.14e-245, 2.14e-245j)
| (-1.9228401110670383956 - 1.8426642648811331318e-996j)  +/-  (4.71e-248, 4.71e-248j)
| (-6.8366897395149018687 - 4.0058264445076665917e-995j)  +/-  (1.76e-246, 1.76e-246j)
| (-1.2920987041134851452 + 1.8973602167586811393e-998j)  +/-  (9.15e-250, 9.15e-250j)
| (1.9228401110670383956 + 2.1347434503368847672e-997j)  +/-  (5.3e-248, 5.3e-248j)
| (-4.0619466758754743069 - 9.5607476552425954957e-993j)  +/-  (2.48e-245, 2.48e-245j)
| (-3.6999225363781202318 + 1.9638257471042255751e-996j)  +/-  (2e-245, 2e-245j)
| (2.4397907062145895885 + 3.5676291833560610843e-998j)  +/-  (6.77e-247, 6.77e-247j)
| (4.4548496545097449284 - 1.1532161432678081961e-997j)  +/-  (2.8e-245, 2.8e-245j)
| (3.0767040777614653993 - 1.1869511244543592808e-1007j)  +/-  (6.25e-246, 6.25e-246j)
| (3.6999225363781202318 + 2.6281521373769675576e-1015j)  +/-  (1.88e-245, 1.88e-245j)
| (-1.6129243142212313331 + 2.124428139771443536e-1028j)  +/-  (6.31e-249, 6.31e-249j)
| (-2.4397907062145895885 + 1.1958080449803673251e-1026j)  +/-  (6.9e-247, 6.9e-247j)
| (-1.0676487257434505536 + 6.8170853217548363672e-1030j)  +/-  (2.19e-250, 2.19e-250j)
| (2.7577629157038887309 + 3.1375608372668430268e-1025j)  +/-  (2.11e-246, 2.11e-246j)
| (-6.2802461177221835343 - 5.8232264813415114397e-1025j)  +/-  (6.44e-246, 6.44e-246j)
| (5.7776439286587553827 - 4.384318324306638425e-1030j)  +/-  (1.51e-245, 1.51e-245j)
| (9.080907409295286327e-1056 - 2.1104563442069329488e-1055j)  +/-  (1.03e-1053, 1.03e-1053j)
| (-5.3109463040160895355 + 8.5773901419622623377e-1041j)  +/-  (2.13e-245, 2.13e-245j)
| (-0.20027095132753771597 + 1.4532747568050543534e-1058j)  +/-  (4.57e-254, 4.57e-254j)
| (0.53163300134265473135 + 9.068294868939457877e-1057j)  +/-  (1.02e-252, 1.02e-252j)
| (1.0676487257434505536 - 1.3845325312544790373e-1052j)  +/-  (2.09e-250, 2.09e-250j)
| (-0.53163300134265473135 - 2.7832128753797498299e-1057j)  +/-  (8.54e-253, 8.54e-253j)
| (-0.85514225944313044986 - 3.3214839353434100566e-1057j)  +/-  (2.31e-251, 2.31e-251j)
| (3.3789320911414940834 + 2.8826109399403419735e-1057j)  +/-  (1.31e-245, 1.31e-245j)
| (2.1735028266666208193 + 1.106845071189557692e-1072j)  +/-  (2e-247, 2e-247j)
| (0.20027095132753771597 - 2.1518282344065406101e-1080j)  +/-  (3.08e-254, 3.08e-254j)
| (-3.3789320911414940834 - 1.3851037985292889998e-1076j)  +/-  (1.38e-245, 1.38e-245j)
-------------------------------------------------
The weights are:
| (1.4619217301598086271e-08 + 1.9657668218692166808e-955j)  +/-  (1.82e-82, 1.58e-203j)
| (6.2047359152679623972e-33 + 1.103609355534891917e-971j)  +/-  (2.64e-97, 2.29e-218j)
| (1.7389812452242487181e-25 - 7.7636778954946412435e-968j)  +/-  (1.53e-94, 1.33e-215j)
| (1.7389812452242487181e-25 + 2.6147533349186374647e-967j)  +/-  (1.88e-95, 1.64e-216j)
| (6.2047359152679623972e-33 - 3.0442320319803594285e-971j)  +/-  (1.43e-98, 1.24e-219j)
| (2.2010294665533819696e-18 + 4.3536557307311869967e-963j)  +/-  (8.54e-93, 7.43e-214j)
| (1.1933700280147471866e-11 + 1.8142389513821530351e-959j)  +/-  (2.7e-90, 2.35e-211j)
| (1.3492979393047949754e-05 - 1.3581664295911148261e-954j)  +/-  (5.9e-83, 5.14e-204j)
| (1.6833859633701595671e-21 - 5.4426043175614984878e-965j)  +/-  (3.48e-94, 3.03e-215j)
| (0.013627803511544386209 + 1.1460068426088553151e-951j)  +/-  (1.14e-73, 9.96e-195j)
| (0.031920414620337582403 - 3.0700046349607564234e-951j)  +/-  (1.32e-70, 1.15e-191j)
| (1.1933700280147471866e-11 - 2.0023666608479745321e-958j)  +/-  (1.42e-89, 1.23e-210j)
| (0.0011819598710887596791 + 1.0302378108712974175e-952j)  +/-  (2.18e-79, 1.9e-200j)
| (9.1346978574835092593e-05 + 6.2830813917038741647e-954j)  +/-  (1.72e-82, 1.49e-203j)
| (5.498674954570017337e-10 - 2.8506598818207516002e-958j)  +/-  (3.51e-90, 3.06e-211j)
| (8.6658531327375345818e-16 + 3.5731372481836201971e-962j)  +/-  (5.95e-95, 5.18e-216j)
| (0.079693181416967438217 - 5.95431461069475678e-951j)  +/-  (1.24e-75, 1.08e-196j)
| (1.4352392310205102766e-13 + 6.9656466924942407516e-960j)  +/-  (2.92e-93, 2.54e-214j)
| (0.0039612436014605218592 - 2.2367457227522485389e-952j)  +/-  (2.25e-80, 1.96e-201j)
| (1.6833859633701595671e-21 + 1.3856622060496227238e-965j)  +/-  (5.77e-98, 5.03e-219j)
| (0.031920414620337582403 - 1.5882282476028321898e-951j)  +/-  (8.36e-78, 7.28e-199j)
| (0.0039612436014605218592 - 6.2579613692489250659e-952j)  +/-  (2.05e-82, 1.78e-203j)
| (1.4619217301598086271e-08 + 3.7221264327577171422e-957j)  +/-  (1.2e-89, 1.04e-210j)
| (2.1901232440723818179e-07 - 3.8737730232215193906e-956j)  +/-  (1.25e-88, 1.09e-209j)
| (0.0004413603573824296171 - 1.2166192153952303777e-952j)  +/-  (6.4e-87, 5.57e-208j)
| (5.498674954570017337e-10 + 6.1792582242720497698e-957j)  +/-  (4.23e-93, 3.68e-214j)
| (1.3492979393047949754e-05 - 9.840698955490387824e-954j)  +/-  (4.04e-90, 3.52e-211j)
| (2.1901232440723818179e-07 - 8.3054460417886121981e-955j)  +/-  (1e-91, 8.73e-213j)
| (0.013627803511544386209 + 4.9456567189909140968e-952j)  +/-  (5.29e-85, 4.61e-206j)
| (0.0004413603573824296171 - 3.0354134703962303871e-953j)  +/-  (1.14e-87, 9.93e-209j)
| (0.028107521979969992802 + 3.3888109306835320835e-951j)  +/-  (7.56e-85, 6.58e-206j)
| (9.1346978574835092593e-05 + 3.285487194384318724e-953j)  +/-  (1.76e-89, 1.53e-210j)
| (2.2010294665533819696e-18 - 9.3381667410550757548e-964j)  +/-  (7.33e-100, 6.38e-221j)
| (8.6658531327375345818e-16 - 2.0492081361618024219e-961j)  +/-  (2.07e-98, 1.8e-219j)
| (0.058062215129688910368 + 1.3135857576043034248e-950j)  +/-  (1.06e-85, 9.27e-207j)
| (1.4352392310205102766e-13 - 9.2821822967027802193e-961j)  +/-  (5.45e-97, 4.74e-218j)
| (0.16875163496333496795 - 8.7870591405903243734e-951j)  +/-  (7.88e-86, 6.88e-207j)
| (0.14317681378214453 + 5.3934034229533079898e-951j)  +/-  (2.35e-86, 2.05e-207j)
| (0.028107521979969992802 + 5.8054439659967126389e-951j)  +/-  (1.22e-86, 1.06e-207j)
| (0.14317681378214453 + 4.1450039390314872073e-951j)  +/-  (9.3e-87, 8.12e-208j)
| (0.079693181416967438217 - 3.8832574805088973505e-951j)  +/-  (7.98e-87, 6.95e-208j)
| (1.8841794697557522261e-06 + 2.984120519310137562e-954j)  +/-  (2.39e-92, 2.09e-213j)
| (0.0011819598710887596791 + 3.4017404584143887567e-952j)  +/-  (1.14e-89, 9.95e-211j)
| (0.16875163496333496795 - 9.6984731582255757743e-951j)  +/-  (1.52e-87, 1.39e-208j)
| (1.8841794697557522261e-06 + 2.7391896859379068712e-955j)  +/-  (1.41e-92, 1.17e-213j)
