Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^48 - 116669712831346372992836758764227400444366848/947397510533097832003392609306155659087*t^46 + 435084524161696110401045486350891651804301510400/16105757679062663144057674358204646204479*t^44 - 635604650535370206575347977485385973885137610874880/177163334469689294584634417940251108249269*t^42 + 57223416813884672582944894703208408083882509995032880/177163334469689294584634417940251108249269*t^40 - 218004290133502978001944110393633521000554664132653920/10421372615864076152037318702367712249957*t^38 + 178839975824488728947067326088846904935748915382202037560/177163334469689294584634417940251108249269*t^36 - 6572365651279585092838100193152317521648106474057356681000/177163334469689294584634417940251108249269*t^34 + 997124310869871746738357969768965794161172876188818066200/947397510533097832003392609306155659087*t^32 - 22011800758171852220363272695477679331412324614451140200200/947397510533097832003392609306155659087*t^30 + 379442744045677504525146642788638709590042706113140696864600/947397510533097832003392609306155659087*t^28 - 5107619805592824747321175506832743270431090095452933245049150/947397510533097832003392609306155659087*t^26 + 428121114340594304078176908388898111185752775551421390379953125/7579180084264782656027140874449245272696*t^24 - 1734702523795553891073147864750198733055409774731418042427794375/3789590042132391328013570437224622636348*t^22 + 43073715628268288814177755528185725050905235323864494634524886875/15158360168529565312054281748898490545392*t^20 - 202094987224605760092958468587148401904202725273661459257048310625/15158360168529565312054281748898490545392*t^18 + 11262269130152386726031375567264209134435722638830546359945960664375/242533762696473044992868507982375848726272*t^16 - 3553944090767884750047897484920530918737670973472860699390352171875/30316720337059130624108563497796981090784*t^14 + 50382079932029806564463540258305773491286150083714937233550987253125/242533762696473044992868507982375848726272*t^12 - 29988306519536273470785147104034426865062187916989405158446399071875/121266881348236522496434253991187924363136*t^10 + 721238334279968779743512967357714511872101366322596950294966294978125/3880540203143568719885896127718013579620352*t^8 - 156152620935443136879945476894298152967869315040231264212792772815625/1940270101571784359942948063859006789810176*t^6 + 135010264765804844995359649047893928802054988567049286263306028828125/7761080406287137439771792255436027159240704*t^4 - 11272255353202649977953552434558552399483668959323303074553600484375/7761080406287137439771792255436027159240704*t^2 + 683631594066895310631927249899783673562538134223086406987696390625/31044321625148549759087169021744108636962816
-------------------------------------------------
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:   48 out of 48
Indefinite weights: 0 out of 48
Negative weights:   0 out of 48
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.5616726339087718254 - 2.9441310097756617263e-965j)  +/-  (3e-247, 3e-247j)
| (-7.8877520628600443656 - 3.4376179937731365356e-963j)  +/-  (3.92e-246, 3.92e-246j)
| (-5.9282881937814924513 - 4.8461796337738133338e-960j)  +/-  (2.33e-244, 2.33e-244j)
| (-7.3282295757075525961 + 1.0707572605140295166e-962j)  +/-  (2.4e-245, 2.4e-245j)
| (-4.3493047905937373177 - 2.6993989252579076965e-960j)  +/-  (1.31e-244, 1.31e-244j)
| (6.3645293957698831025 + 8.887912085634329629e-964j)  +/-  (1.47e-244, 1.47e-244j)
| (-6.3645293957698831025 - 1.0084592840835404711e-962j)  +/-  (1.52e-244, 1.52e-244j)
| (-6.8275470461726218605 - 9.9566634841151101403e-964j)  +/-  (6.99e-245, 6.99e-245j)
| (-5.5123105376090447559 + 2.2654112349140520155e-963j)  +/-  (2.72e-244, 2.72e-244j)
| (5.9282881937814924513 + 1.1527270179856900647e-963j)  +/-  (2.4e-244, 2.4e-244j)
| (0.86143482085380595392 + 1.7792344364822800479e-973j)  +/-  (2.31e-251, 2.31e-251j)
| (4.3493047905937373177 - 2.7850020848069047408e-964j)  +/-  (1.35e-244, 1.35e-244j)
| (3.2734686347640776668 + 1.728664976680967136e-966j)  +/-  (1.07e-245, 1.07e-245j)
| (-8.5616726339087718254 + 3.6239532058447655539e-968j)  +/-  (3.08e-247, 3.08e-247j)
| (-5.1123270339511243237 + 2.7779716376356897186e-965j)  +/-  (2.86e-244, 2.86e-244j)
| (1.7148376971465997163 + 4.0901311747446755e-972j)  +/-  (1.64e-248, 1.64e-248j)
| (-2.2774115353831733183 - 6.7574589640880124139e-969j)  +/-  (2.95e-247, 2.95e-247j)
| (6.8275470461726218605 + 4.257406115514595161e-968j)  +/-  (6.48e-245, 6.48e-245j)
| (5.5123105376090447559 - 5.5694636672180910353e-967j)  +/-  (2.84e-244, 2.84e-244j)
| (-4.7253698810260582365 - 9.9709330759662803686e-970j)  +/-  (1.9e-244, 1.9e-244j)
| (7.8877520628600443656 - 1.6845935624169329636e-976j)  +/-  (3.79e-246, 3.79e-246j)
| (2.9306374202572440192 + 1.6901718274511128605e-976j)  +/-  (3.31e-246, 3.31e-246j)
| (7.3282295757075525961 - 3.2932310770945658153e-976j)  +/-  (2.28e-245, 2.28e-245j)
| (5.1123270339511243237 - 9.0219728494512720233e-975j)  +/-  (2.87e-244, 2.87e-244j)
| (0.13857528499660969405 + 1.3941491974260939611e-991j)  +/-  (2.37e-254, 2.37e-254j)
| (-3.9825889647190106702 - 9.5638583952133928974e-982j)  +/-  (6.37e-245, 6.37e-245j)
| (1.4468774716878057628 - 1.2817255196311088971e-999j)  +/-  (2.47e-249, 2.47e-249j)
| (3.6241639629017906353 - 1.3612364954830928305e-993j)  +/-  (2.89e-245, 2.89e-245j)
| (-1.7148376971465997163 + 4.7060000640353235627e-1003j)  +/-  (1.68e-248, 1.68e-248j)
| (-0.59238927181853581263 + 1.0339813304506826321e-1012j)  +/-  (2.74e-252, 2.74e-252j)
| (-3.2734686347640776668 + 1.6598290597411554761e-1018j)  +/-  (1.03e-245, 1.03e-245j)
| (2.2774115353831733183 - 2.9883681633290628838e-1037j)  +/-  (2.86e-247, 2.86e-247j)
| (1.1571937124467801947 - 9.8598842155580749005e-1048j)  +/-  (2.38e-250, 2.38e-250j)
| (-2.9306374202572440192 - 3.2585085718765060071e-1055j)  +/-  (3.72e-246, 3.72e-246j)
| (-2.597125579113889378 + 1.8141435710378815216e-1073j)  +/-  (1.01e-246, 1.01e-246j)
| (-1.4468774716878057628 + 7.8489845204762281066e-1085j)  +/-  (2.51e-249, 2.51e-249j)
| (3.9825889647190106702 + 1.0028029718107518022e-1079j)  +/-  (6.49e-245, 6.49e-245j)
| (0.59238927181853581263 - 1.5567330841506390413e-1089j)  +/-  (2.79e-252, 2.79e-252j)
| (-3.6241639629017906353 + 2.2148541699562271531e-1082j)  +/-  (3.06e-245, 3.06e-245j)
| (-0.38118699020732211685 + 5.8874897495451437275e-1092j)  +/-  (3.75e-253, 3.75e-253j)
| (-0.86143482085380595392 + 2.9914130024157846031e-1090j)  +/-  (2.39e-251, 2.39e-251j)
| (4.7253698810260582365 - 3.4059710612526947141e-1086j)  +/-  (1.99e-244, 1.99e-244j)
| (2.597125579113889378 - 9.4506470342286310168e-1091j)  +/-  (9.99e-247, 9.99e-247j)
| (1.9816567566958429259 - 2.0062256257408525259e-1094j)  +/-  (7.99e-248, 7.99e-248j)
| (-0.13857528499660969405 - 7.639205496561973129e-1101j)  +/-  (3.17e-254, 3.17e-254j)
| (-1.1571937124467801947 - 1.1408723879084791366e-1097j)  +/-  (2.44e-250, 2.44e-250j)
| (-1.9816567566958429259 - 5.4626399046750741832e-1095j)  +/-  (7.52e-248, 7.52e-248j)
| (0.38118699020732211685 - 7.9796474740649220029e-1100j)  +/-  (3.57e-253, 3.57e-253j)
-------------------------------------------------
The weights are:
| (6.4170609362046219564e-33 - 3.5220057243131815414e-983j)  +/-  (3.09e-87, 1.71e-209j)
| (3.2391796336337123716e-28 + 4.0470197103115358658e-980j)  +/-  (7.6e-86, 4.22e-208j)
| (1.3090837219998670622e-16 + 1.828678261610986344e-973j)  +/-  (1.23e-80, 6.83e-203j)
| (1.4086554727824250923e-24 - 4.2914768236608791842e-978j)  +/-  (1.02e-84, 5.67e-207j)
| (1.2755380957011637016e-09 - 1.8422548389031603283e-968j)  +/-  (2.86e-76, 1.59e-198j)
| (6.4700626827117350311e-19 - 1.4437692361623803403e-975j)  +/-  (1.43e-85, 7.94e-208j)
| (6.4700626827117350311e-19 - 7.741759768204116412e-975j)  +/-  (2.06e-82, 1.14e-204j)
| (1.5395438856907315814e-21 + 2.2864030408712160043e-976j)  +/-  (8.46e-84, 4.69e-206j)
| (1.4627161168302265007e-14 - 3.6204766725272071649e-972j)  +/-  (1.41e-80, 7.84e-203j)
| (1.3090837219998670622e-16 + 2.8773045367894383256e-974j)  +/-  (4e-86, 2.22e-208j)
| (0.077941676887309103446 - 9.745760177443716599e-964j)  +/-  (2.26e-69, 1.25e-191j)
| (1.2755380957011637016e-09 + 3.9841943594456173783e-970j)  +/-  (1.1e-81, 6.1e-204j)
| (4.3436941195235048756e-06 - 9.4533502262930419292e-968j)  +/-  (2.03e-77, 1.12e-199j)
| (6.4170609362046219564e-33 - 1.0814697342514182041e-982j)  +/-  (5.97e-91, 3.31e-213j)
| (9.8902593146266296958e-13 + 6.2644256147967576749e-971j)  +/-  (4.43e-81, 2.45e-203j)
| (0.0077540237884846337095 + 1.012763175227277971e-964j)  +/-  (2.26e-69, 1.25e-191j)
| (0.00097763600695314210618 - 3.1436600819344365152e-965j)  +/-  (6.92e-73, 3.84e-195j)
| (1.5395438856907315814e-21 + 5.0469111255891999508e-977j)  +/-  (1.26e-89, 6.97e-212j)
| (1.4627161168302265007e-14 - 4.2997974781254720002e-973j)  +/-  (2.9e-86, 1.61e-208j)
| (4.3169372369670838629e-11 - 1.1765319841156712074e-969j)  +/-  (5e-82, 2.78e-204j)
| (3.2391796336337123716e-28 + 1.1675153064701831979e-980j)  +/-  (2.31e-93, 1.28e-215j)
| (3.5570619351867947324e-05 + 4.7832070840083945867e-967j)  +/-  (5.11e-80, 2.83e-202j)
| (1.4086554727824250923e-24 - 1.0913893451573821981e-978j)  +/-  (1.1e-91, 6.13e-214j)
| (9.8902593146266296958e-13 + 5.0647186695991798328e-972j)  +/-  (2.94e-86, 1.63e-208j)
| (0.15022389155687210798 + 3.3860615095661590349e-963j)  +/-  (6.42e-75, 3.56e-197j)
| (2.6442425515977441681e-08 + 6.2925068695508686007e-968j)  +/-  (8.19e-84, 4.54e-206j)
| (0.019443088729668503373 - 2.1564723336889900443e-964j)  +/-  (3.02e-75, 1.67e-197j)
| (3.9517466939711400265e-07 + 1.7092685549863257127e-968j)  +/-  (4.35e-83, 2.41e-205j)
| (0.0077540237884846337095 - 2.3298561417122323746e-964j)  +/-  (5.69e-78, 3.15e-200j)
| (0.094347146990260458916 - 2.9294420549299675857e-963j)  +/-  (3.84e-76, 2.13e-198j)
| (4.3436941195235048756e-06 + 6.6847634557654529507e-967j)  +/-  (3.36e-83, 1.86e-205j)
| (0.00097763600695314210618 + 9.8375193485497739567e-966j)  +/-  (1.6e-80, 8.88e-203j)
| (0.043850189931083866459 + 4.35771257532016932e-964j)  +/-  (2.22e-76, 1.23e-198j)
| (3.5570619351867947324e-05 - 2.4508992982473201147e-966j)  +/-  (1.2e-82, 6.67e-205j)
| (0.00021758743765439903896 + 8.9176333905082316219e-966j)  +/-  (6.35e-82, 3.52e-204j)
| (0.019443088729668503373 + 4.3044457690451470352e-964j)  +/-  (1.95e-79, 1.08e-201j)
| (2.6442425515977441681e-08 - 2.7795728353550807918e-969j)  +/-  (7.82e-86, 4.34e-208j)
| (0.094347146990260458916 + 2.2275085065985206126e-963j)  +/-  (1.44e-78, 7.97e-201j)
| (3.9517466939711400265e-07 - 1.8757109792257158062e-967j)  +/-  (1.01e-84, 5.59e-207j)
| (0.10209444561705146506 + 3.9183921993546963358e-963j)  +/-  (3.5e-79, 1.94e-201j)
| (0.077941676887309103446 + 1.455587324023250044e-963j)  +/-  (7.18e-80, 3.99e-202j)
| (4.3169372369670838629e-11 - 4.8754722963872200448e-971j)  +/-  (1.28e-87, 7.1e-210j)
| (0.00021758743765439903896 - 2.2518904508568820674e-966j)  +/-  (2.31e-83, 1.28e-205j)
| (0.0031099758043847626491 - 3.6824868553360935701e-965j)  +/-  (4.01e-82, 2.22e-204j)
| (0.15022389155687210798 - 3.608781025086730902e-963j)  +/-  (2.02e-80, 1.13e-202j)
| (0.043850189931083866459 - 7.5144227278362734e-964j)  +/-  (7.51e-82, 4.15e-204j)
| (0.0031099758043847626491 + 9.8397501734570212407e-965j)  +/-  (4.13e-83, 2.18e-205j)
| (0.10209444561705146506 - 3.2872786138496736967e-963j)  +/-  (5.13e-81, 3.26e-203j)
