Starting with polynomial:
P : t
Extension levels are: 1 16 28
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^17 - 136*t^15 + 7140*t^13 - 185640*t^11 + 2552550*t^9 - 18378360*t^7 + 64324260*t^5 - 91891800*t^3 + 34459425*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 437043667621911734/543076105530597*t^43 + 74934495009974702599/257246576303967*t^41 - 307850324217720039064876/4887684949775373*t^39 + 44533267916315144809389911/4887684949775373*t^37 - 13721957282944178055707950394/14663054849326119*t^35 + 1036416474319522765749983733485/14663054849326119*t^33 - 19609556410234545164031632650640/4887684949775373*t^31 + 847686302560343426152480458160210/4887684949775373*t^29 - 1479716590749413828361854076512740/257246576303967*t^27 + 26572238906909343775188019818049190/181025368510199*t^25 - 521178389189577930175561250541487000/181025368510199*t^23 + 7819473567718568023740984636726852250/181025368510199*t^21 - 4683009993014726982858144617949727500/9527650974221*t^19 + 39897657767627268365100444569487768750/9527650974221*t^17 - 249940485048907143197631580161916410000/9527650974221*t^15 + 1123036671520224205242425136711878000625/9527650974221*t^13 - 3497210572105777995402590169027092328750/9527650974221*t^11 + 7189897628627433272298320071317771575625/9527650974221*t^9 - 9072674548466232550802360729855978947500/9527650974221*t^7 + 6219205748323418114443922714143824526875/9527650974221*t^5 - 1809189523529778260460431823800962893750/9527650974221*t^3 + 109505253801035390420274266693525821875/9527650974221*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:
| (-9.6685393513589566158 - 1.4768834088278934005e-925j)  +/-  (2.47e-246, 2.47e-246j)
| (-6.8891224398953322326 + 5.0601057343649065671e-925j)  +/-  (3.69e-245, 3.69e-245j)
| (12.278074224522850696 - 1.6383836564197724544e-928j)  +/-  (1.55e-248, 1.55e-248j)
| (10.596340887522578636 + 5.273939844342021604e-925j)  +/-  (3.76e-247, 3.76e-247j)
| (-12.278074224522850696 + 4.0240933165564272055e-937j)  +/-  (1.38e-248, 1.38e-248j)
| (-5.7444600786594061813 + 2.2719405404664332425e-933j)  +/-  (3.27e-245, 3.27e-245j)
| (9.6685393513589566158 - 2.7314663862518384628e-938j)  +/-  (2.42e-246, 2.42e-246j)
| (-10.596340887522578636 - 2.7641901223027942924e-952j)  +/-  (3.9e-247, 3.9e-247j)
| (-5.2324806306757987712 - 3.5014748267785163839e-950j)  +/-  (2.84e-245, 2.84e-245j)
| (8.8816092347236892342 - 1.5382680123366732366e-957j)  +/-  (8.05e-246, 8.05e-246j)
| (2.2810194402529888954 - 3.4908509827380154722e-972j)  +/-  (8.58e-249, 8.58e-249j)
| (-7.5108122921748166579 + 6.5884617822530403489e-969j)  +/-  (3.31e-245, 3.31e-245j)
| (8.1708224024717826758 - 1.7535590546331601319e-967j)  +/-  (1.87e-245, 1.87e-245j)
| (-2.7193065633459941153 + 2.6252630926204045968e-978j)  +/-  (7.87e-248, 7.87e-248j)
| (-4.3511166341788700268 + 6.3289044967470039499e-975j)  +/-  (8.16e-246, 8.16e-246j)
| (-8.1708224024717826758 + 1.9896213648663730259e-975j)  +/-  (1.87e-245, 1.87e-245j)
| (4.7785315896299838271 - 1.3114237033090491262e-974j)  +/-  (1.76e-245, 1.76e-245j)
| (3.4503851060805041109 + 1.0906958157757776037e-983j)  +/-  (1.09e-246, 1.09e-246j)
| (-4.7785315896299838271 + 1.1150533460340236843e-985j)  +/-  (1.73e-245, 1.73e-245j)
| (-3.900065717198009909 - 2.546547978327578313e-988j)  +/-  (3.22e-246, 3.22e-246j)
| (6.3001087997407780881 + 1.3242804277126303129e-988j)  +/-  (3.76e-245, 3.76e-245j)
| (-1.4061350779868092647e-1012 - 6.4751637966765719347e-1013j)  +/-  (6.97e-1011, 6.97e-1011j)
| (-6.3001087997407780881 + 6.2854624078304538069e-1002j)  +/-  (3.7e-245, 3.7e-245j)
| (5.7444600786594061813 - 1.032085643180351766e-1007j)  +/-  (3.6e-245, 3.6e-245j)
| (-3.0737971753281935585 - 9.0441771546558176002e-1021j)  +/-  (3.18e-247, 3.18e-247j)
| (-8.8816092347236892342 + 5.2392400256833679091e-1022j)  +/-  (7.74e-246, 7.74e-246j)
| (1.209353781062846993 - 8.8144769836588768858e-1031j)  +/-  (3.39e-251, 3.39e-251j)
| (2.7193065633459941153 + 1.3634937270396866939e-1025j)  +/-  (7.5e-248, 7.5e-248j)
| (7.5108122921748166579 + 1.137447957566239212e-1028j)  +/-  (2.9e-245, 2.9e-245j)
| (-1.209353781062846993 + 2.6557198004497602539e-1043j)  +/-  (3.7e-251, 3.7e-251j)
| (0.75184260070389617074 - 3.2396610664866415991e-1044j)  +/-  (1.11e-252, 1.11e-252j)
| (4.3511166341788700268 + 2.7915179389154451107e-1037j)  +/-  (8.35e-246, 8.35e-246j)
| (-0.28322589551676584235 + 1.3466659508949822007e-1049j)  +/-  (5.49e-254, 5.49e-254j)
| (6.8891224398953322326 + 2.7570167162084726622e-1041j)  +/-  (3.59e-245, 3.59e-245j)
| (-1.8273035112819915085 - 4.4358576334937086856e-1051j)  +/-  (1.35e-249, 1.35e-249j)
| (3.0737971753281935585 - 2.465959016498037656e-1047j)  +/-  (3.18e-247, 3.18e-247j)
| (-1.5098833077967407591 - 1.0050141704052074149e-1051j)  +/-  (2.81e-250, 2.81e-250j)
| (1.8273035112819915085 - 4.0682339057110714412e-1050j)  +/-  (1.26e-249, 1.26e-249j)
| (3.900065717198009909 + 8.0169566777902459658e-1047j)  +/-  (3.11e-246, 3.11e-246j)
| (0.28322589551676584235 - 6.370843405805862418e-1056j)  +/-  (5.49e-254, 5.49e-254j)
| (-0.75184260070389617074 - 1.4778120692664864161e-1055j)  +/-  (1.11e-252, 1.11e-252j)
| (-2.2810194402529888954 - 1.790588864693200864e-1051j)  +/-  (9.64e-249, 9.64e-249j)
| (5.2324806306757987712 - 8.4235554320231669055e-1050j)  +/-  (2.71e-245, 2.71e-245j)
| (1.5098833077967407591 - 1.204876608084567019e-1054j)  +/-  (2.98e-250, 2.98e-250j)
| (-3.4503851060805041109 - 1.229878108267323078e-1055j)  +/-  (1.11e-246, 1.11e-246j)
-------------------------------------------------
The weights are:
| (1.6833859633701595671e-21 - 2.0258034588984540537e-942j)  +/-  (5.73e-91, 8.07e-213j)
| (1.1933700280147471866e-11 + 2.8288122231077769016e-935j)  +/-  (1.23e-84, 1.73e-206j)
| (6.2047359152679623972e-33 + 2.7337325046326332268e-949j)  +/-  (1.22e-96, 1.71e-218j)
| (1.7389812452242487181e-25 - 1.9119718488428037056e-945j)  +/-  (5.67e-94, 7.98e-216j)
| (6.2047359152679623972e-33 - 9.7230103129889094661e-949j)  +/-  (8.71e-97, 1.22e-218j)
| (1.4619217301598086271e-08 + 9.8424041197310736731e-934j)  +/-  (2.61e-83, 3.67e-205j)
| (1.6833859633701595671e-21 + 3.3983185486541115734e-943j)  +/-  (4.8e-93, 6.75e-215j)
| (1.7389812452242487181e-25 + 9.0142479852832514735e-945j)  +/-  (6.98e-94, 9.81e-216j)
| (2.1901232440723818179e-07 - 6.7622867198871588965e-933j)  +/-  (1.81e-82, 2.55e-204j)
| (2.2010294665533819696e-18 - 2.2816329419390418158e-941j)  +/-  (2.73e-92, 3.85e-214j)
| (0.013627803511544386209 + 1.1403002420520677315e-929j)  +/-  (2.7e-73, 3.8e-195j)
| (1.4352392310205102766e-13 + 5.2141578320735880109e-937j)  +/-  (2.04e-88, 2.87e-210j)
| (8.6658531327375345818e-16 + 8.6980773828236308245e-940j)  +/-  (1.4e-91, 1.98e-213j)
| (0.0039612436014605218592 - 1.1960959057424133171e-929j)  +/-  (1.76e-76, 2.48e-198j)
| (1.3492979393047949754e-05 - 1.4232994772343911236e-931j)  +/-  (6.17e-82, 8.67e-204j)
| (8.6658531327375345818e-16 - 1.0220812230674958088e-938j)  +/-  (3.12e-90, 4.39e-212j)
| (1.8841794697557522261e-06 + 6.5084625092837051745e-933j)  +/-  (9.87e-87, 1.39e-208j)
| (0.0004413603573824296171 - 7.1115251185071323185e-931j)  +/-  (1.42e-82, 1.99e-204j)
| (1.8841794697557522261e-06 + 3.5980144406245842147e-932j)  +/-  (3.14e-83, 4.42e-205j)
| (9.1346978574835092593e-05 + 5.3410106111097092399e-931j)  +/-  (7.41e-82, 1.04e-203j)
| (5.498674954570017337e-10 - 6.8583352969189197512e-936j)  +/-  (4.21e-91, 5.92e-213j)
| (0.058062215129688910368 + 2.8856560826370178576e-928j)  +/-  (2.28e-77, 3.2e-199j)
| (5.498674954570017337e-10 - 1.5357541351887025404e-934j)  +/-  (4.06e-87, 5.72e-209j)
| (1.4619217301598086271e-08 + 8.9175367703769634494e-935j)  +/-  (3.94e-90, 5.54e-212j)
| (0.0011819598710887596791 + 6.2732361947748297452e-930j)  +/-  (1.13e-81, 1.58e-203j)
| (2.2010294665533819696e-18 + 1.8061589997029236534e-940j)  +/-  (4.69e-93, 6.59e-215j)
| (0.079693181416967438217 - 8.7844869866896893172e-929j)  +/-  (2.25e-77, 3.16e-199j)
| (0.0039612436014605218592 - 5.1907271955197243565e-930j)  +/-  (1.09e-83, 1.54e-205j)
| (1.4352392310205102766e-13 - 2.251030742607118651e-938j)  +/-  (6.72e-94, 9.46e-216j)
| (0.079693181416967438217 - 1.2525354214979915205e-928j)  +/-  (6.04e-80, 8.49e-202j)
| (0.14317681378214453 + 9.2841802831258474479e-929j)  +/-  (1.73e-79, 2.43e-201j)
| (1.3492979393047949754e-05 - 3.213727580086936211e-932j)  +/-  (1.6e-88, 2.24e-210j)
| (0.16875163496333496795 - 2.112337661922843504e-928j)  +/-  (2.49e-80, 3.49e-202j)
| (1.1933700280147471866e-11 + 4.3825743601061062948e-937j)  +/-  (5.34e-93, 7.51e-215j)
| (0.031920414620337582403 - 6.2590032977386515469e-929j)  +/-  (7.15e-84, 1e-205j)
| (0.0011819598710887596791 + 2.4023369525207061454e-930j)  +/-  (2.71e-86, 3.79e-208j)
| (0.028107521979969992802 + 1.2039992063101324113e-928j)  +/-  (8.04e-84, 1.12e-205j)
| (0.031920414620337582403 - 3.6347276576347006536e-929j)  +/-  (1.11e-84, 1.55e-206j)
| (9.1346978574835092593e-05 + 1.4796710712820090512e-931j)  +/-  (5.12e-88, 7.12e-210j)
| (0.16875163496333496795 - 1.9455102272917459721e-928j)  +/-  (3.46e-83, 4.68e-205j)
| (0.14317681378214453 + 1.1558898098796433491e-928j)  +/-  (3.94e-84, 5.34e-206j)
| (0.013627803511544386209 + 2.2692114421966517297e-929j)  +/-  (3.6e-86, 4.92e-208j)
| (2.1901232440723818179e-07 - 9.241793001738813129e-934j)  +/-  (8.19e-91, 1.2e-212j)
| (0.028107521979969992802 + 7.7111291654934479721e-929j)  +/-  (1.65e-85, 2.57e-207j)
| (0.0004413603573824296171 - 2.1382903857034129455e-930j)  +/-  (6.24e-88, 7.79e-210j)
