Starting with polynomial:
P : 2*t
Extension levels are: 1 16 26
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 2*t^17 - 136*t^15 + 3570*t^13 - 46410*t^11 + 1276275/4*t^9 - 2297295/2*t^7 + 16081065/8*t^5 - 11486475/8*t^3 + 34459425/128*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^43 - 1352578353572165/2052842729187*t^41 + 200578225677249925/2052842729187*t^39 - 59208580344489276909/6842809097290*t^37 + 126115954542826250196077/246341127502440*t^35 - 2114285554195652798282959/98536451000976*t^33 + 5412083496878520046956371/8211370916748*t^31 - 248758084223542070542490125/16422741833496*t^29 + 34633439322633374785663280179/131381934667968*t^27 - 306112727493524432843186607783/87587956445312*t^25 + 3095335162308968663297568079725/87587956445312*t^23 - 47593784883534988032977647079475/175175912890624*t^21 + 1104616095081852389397260209435125/700703651562496*t^19 - 9559670264986737661534792460311875/1401407303124992*t^17 + 15159040785154537788776900143127625/700703651562496*t^15 - 68780458262194109303588815208484375/1401407303124992*t^13 + 1726503075433078945316498283682708125/22422516849999872*t^11 - 3571035033979765233583255924481986875/44845033699999744*t^9 + 2268195334172479488547550170054038375/44845033699999744*t^7 - 1581234628208739836569509974826749625/89690067399999488*t^5 + 986781076304202437440732742510443125/358760269599997952*t^3 - 85800767760702964201608540801511875/717520539199995904*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
-------------------------------------------------
The nodes are:
| (-5.7905264429405314916 + 9.142023444517001426e-973j)  +/-  (4.23e-246, 4.23e-246j)
| (-6.8828927543522817979 + 1.551077159281912597e-977j)  +/-  (3.17e-247, 3.17e-247j)
| (-6.3059132338424485783 - 2.311351423160259302e-976j)  +/-  (1.5e-246, 1.5e-246j)
| (6.8828927543522817979 - 3.5999696780407540109e-979j)  +/-  (2.94e-247, 2.94e-247j)
| (5.7905264429405314916 - 1.393505981919064115e-977j)  +/-  (4.2e-246, 4.2e-246j)
| (-7.578242366860570706 + 1.9850407025881192238e-978j)  +/-  (2.82e-248, 2.82e-248j)
| (-4.4533113173909120033 + 2.1238183519666165245e-975j)  +/-  (1.26e-245, 1.26e-245j)
| (7.578242366860570706 + 4.4246880417507389255e-984j)  +/-  (3.09e-248, 3.09e-248j)
| (4.8713451936744030883 + 1.2976685453685534193e-980j)  +/-  (1.04e-245, 1.04e-245j)
| (6.3059132338424485783 + 2.0172053996507647534e-984j)  +/-  (1.39e-246, 1.39e-246j)
| (1.3303410702282595543 + 1.0575232164142891442e-986j)  +/-  (1.06e-249, 1.06e-249j)
| (2.4528467649768351962 - 2.1807224836888236824e-983j)  +/-  (5.49e-247, 5.49e-247j)
| (-1.3303410702282595543 - 2.9766007064527651373e-986j)  +/-  (9.86e-250, 9.86e-250j)
| (-0.80551731321255824132 + 2.7975460288854443174e-989j)  +/-  (1.42e-251, 1.42e-251j)
| (-2.7577629157038887309 + 3.5808815991899418985e-982j)  +/-  (1.68e-246, 1.68e-246j)
| (-3.3789320911414940834 + 1.7186945379851705407e-988j)  +/-  (6.95e-246, 6.95e-246j)
| (-4.8713451936744030883 + 9.3941615556311017014e-996j)  +/-  (1.12e-245, 1.12e-245j)
| (-5.3156505874246127022 - 5.3436288804650080235e-1011j)  +/-  (8.01e-246, 8.01e-246j)
| (-1.0676487257434505536 + 5.5517540294473277958e-1024j)  +/-  (1.54e-250, 1.54e-250j)
| (3.0707018084496295245 - 1.1135675377867157529e-1019j)  +/-  (3.97e-246, 3.97e-246j)
| (2.1735028266666208193 - 3.2745963142319756791e-1024j)  +/-  (1.93e-247, 1.93e-247j)
| (0.53163300134265473135 - 3.4621800287562064778e-1041j)  +/-  (9.91e-253, 9.91e-253j)
| (-4.0619466758754743069 + 1.8935841646484823774e-1033j)  +/-  (1.22e-245, 1.22e-245j)
| (-1.6129243142212313331 + 5.125875081998350518e-1051j)  +/-  (6.71e-249, 6.71e-249j)
| (-1.9002813667973098145 - 5.4648455079148373781e-1051j)  +/-  (3.92e-248, 3.92e-248j)
| (2.7577629157038887309 + 1.1363974647216625602e-1048j)  +/-  (1.63e-246, 1.63e-246j)
| (1.0676487257434505536 - 1.937860358731000137e-1059j)  +/-  (1.5e-250, 1.5e-250j)
| (1.9002813667973098145 + 4.3491177914468842529e-1055j)  +/-  (3.99e-248, 3.99e-248j)
| (-3.0707018084496295245 - 3.9186788198830354482e-1069j)  +/-  (3.96e-246, 3.96e-246j)
| (-3.7027483464678803754 - 7.676884743824101563e-1089j)  +/-  (1.2e-245, 1.2e-245j)
| (4.4533113173909120033 + 1.3435228631094345445e-1093j)  +/-  (1.36e-245, 1.36e-245j)
| (3.7027483464678803754 + 6.048410704643775586e-1095j)  +/-  (1.11e-245, 1.11e-245j)
| (0.26028331377121338169 + 1.4107868793660031555e-1104j)  +/-  (7.4e-254, 7.4e-254j)
| (5.3156505874246127022 + 4.313162470215216341e-1097j)  +/-  (8.51e-246, 8.51e-246j)
| (-0.26028331377121338169 - 1.4158087808336682648e-1104j)  +/-  (7.4e-254, 7.4e-254j)
| (4.0619466758754743069 + 2.8928340778280454756e-1096j)  +/-  (1.32e-245, 1.32e-245j)
| (1.6129243142212313331 + 2.2835974869128366762e-1100j)  +/-  (6.67e-249, 6.67e-249j)
| (0.80551731321255824132 - 1.5887460154484263341e-1102j)  +/-  (1.49e-251, 1.49e-251j)
| (3.3789320911414940834 - 3.7098493198238054978e-1098j)  +/-  (7.36e-246, 7.36e-246j)
| (-2.4528467649768351962 + 2.3873603258057058128e-1098j)  +/-  (5.29e-247, 5.29e-247j)
| (-0.53163300134265473135 + 1.3039076553216033137e-1106j)  +/-  (1e-252, 1e-252j)
| (-2.1735028266666208193 - 1.0901556555087302546e-1104j)  +/-  (1.91e-247, 1.91e-247j)
| (-4.4386370953928297729e-1241 - 1.1449615953033806106e-1241j)  +/-  (1.97e-1239, 1.97e-1239j)
-------------------------------------------------
The weights are:
| (7.6236465758545442192e-16 + 5.2203475479202300902e-987j)  +/-  (1.26e-83, 3.49e-206j)
| (9.3315444657603756783e-22 - 1.3976953124360328786e-991j)  +/-  (3.16e-87, 8.74e-210j)
| (1.6414661929880855053e-18 + 2.7741187575495806648e-989j)  +/-  (2.22e-85, 6.13e-208j)
| (9.3315444657603756783e-22 + 1.0673846170923015387e-992j)  +/-  (5.5e-90, 1.52e-212j)
| (7.6236465758545442192e-16 + 4.9500406383420548585e-989j)  +/-  (2.62e-87, 7.24e-210j)
| (5.1790595816620656146e-26 + 2.7010086671497128116e-994j)  +/-  (1.74e-90, 4.82e-213j)
| (5.5739509606304204114e-10 + 2.391043011224877465e-984j)  +/-  (2e-82, 5.53e-205j)
| (5.1790595816620656146e-26 - 3.2728443734705238188e-995j)  +/-  (2.21e-92, 6.12e-215j)
| (1.2020536987404970811e-11 + 3.4437084716265197183e-986j)  +/-  (6.86e-86, 1.9e-208j)
| (1.6414661929880855053e-18 - 1.01621411228513435e-990j)  +/-  (6.53e-89, 1.81e-211j)
| (0.026182003344280285131 - 3.3496309255556958071e-978j)  +/-  (5.76e-69, 1.59e-191j)
| (0.00040302876484556432679 - 7.0349148948140447754e-980j)  +/-  (2.14e-77, 5.93e-200j)
| (0.026182003344280285131 - 5.1408456540873392927e-978j)  +/-  (2.81e-70, 7.76e-193j)
| (0.07939094119593866362 - 1.2647879016162800268e-977j)  +/-  (2.48e-70, 6.87e-193j)
| (8.7902891789005708711e-05 + 4.058985045264586447e-980j)  +/-  (2.06e-79, 5.71e-202j)
| (1.9285493202980648984e-06 + 1.9189125288532529575e-981j)  +/-  (5.02e-82, 1.39e-204j)
| (1.2020536987404970811e-11 + 6.5706878607359021577e-985j)  +/-  (1.69e-86, 4.67e-209j)
| (1.3844003785086516972e-13 - 4.7607134169852986169e-986j)  +/-  (1.2e-87, 3.32e-210j)
| (0.046444271864447317057 + 8.9386506967723741691e-978j)  +/-  (1.7e-72, 4.71e-195j)
| (1.4056919812622758854e-05 - 3.4330547724577856214e-981j)  +/-  (3.25e-84, 8.99e-207j)
| (0.0013512778227004170726 + 2.3581509248476241669e-979j)  +/-  (5.71e-80, 1.58e-202j)
| (0.11713183867373952307 + 1.3549928797456116178e-977j)  +/-  (5.31e-74, 1.47e-196j)
| (1.4509898039143639361e-08 + 1.7383567748223417383e-983j)  +/-  (4.13e-85, 1.14e-207j)
| (0.012111828990528992431 + 2.4804105606354091166e-978j)  +/-  (2.79e-77, 7.7e-200j)
| (0.0042849477882970892281 - 1.1418978422422842322e-978j)  +/-  (5.09e-79, 1.41e-201j)
| (8.7902891789005708711e-05 + 1.6316926920334606769e-980j)  +/-  (1.33e-83, 3.67e-206j)
| (0.046444271864447317057 + 6.346492729137341711e-978j)  +/-  (4.81e-77, 1.33e-199j)
| (0.0042849477882970892281 - 6.1533115233724726116e-979j)  +/-  (2.77e-80, 7.67e-203j)
| (1.4056919812622758854e-05 - 9.4682927204319319326e-981j)  +/-  (1.68e-83, 4.65e-206j)
| (2.1355918191064277861e-07 - 2.7223081046934066197e-982j)  +/-  (4.78e-85, 1.32e-207j)
| (5.5739509606304204114e-10 - 5.9787637336477411572e-985j)  +/-  (5.61e-91, 1.55e-213j)
| (2.1355918191064277861e-07 - 8.7224000584091038746e-983j)  +/-  (2.93e-89, 8.12e-212j)
| (0.14002456463122658314 - 1.7668933946064759882e-977j)  +/-  (2.62e-82, 7.26e-205j)
| (1.3844003785086516972e-13 - 1.5365247600102083738e-987j)  +/-  (1.09e-93, 3.02e-216j)
| (0.14002456463122658314 - 1.9196946864050411383e-977j)  +/-  (1.76e-82, 4.87e-205j)
| (1.4509898039143639361e-08 + 8.266181695078947855e-984j)  +/-  (2.14e-90, 5.91e-213j)
| (0.012111828990528992431 + 1.4718871730863518976e-978j)  +/-  (8.27e-85, 2.29e-207j)
| (0.07939094119593866362 - 9.7754104684728740176e-978j)  +/-  (4.62e-84, 1.29e-206j)
| (1.9285493202980648984e-06 + 6.3761309857141002783e-982j)  +/-  (1.27e-88, 3.53e-211j)
| (0.00040302876484556432679 - 1.5765835562186486593e-979j)  +/-  (4.56e-88, 1.26e-210j)
| (0.11713183867373952307 + 1.6055024152795597173e-977j)  +/-  (1.33e-85, 4.4e-208j)
| (0.0013512778227004170726 + 4.8019784357388113276e-979j)  +/-  (1.4e-87, 3.79e-210j)
| (0.14514235984887770302 + 2.0160245736330384586e-977j)  +/-  (1.53e-85, 5.53e-208j)
