Starting with polynomial:
P : 64*t^6 - 80*t^4 + 24*t^2 - 1
Extension levels are: 6 70
-------------------------------------------------
Trying to find an order 70 Kronrod extension for:
P1 : 64*t^6 - 80*t^4 + 24*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^76 - 1200*t^74 + 10804*t^72 - 62196*t^70 + 514395/2*t^68 - 13019909/16*t^66 + 131115985/64*t^64 - 33715539/8*t^62 + 924001221/128*t^60 - 5344712945/512*t^58 + 26372568651/2048*t^56 - 27970906145/2048*t^54 + 205263418941/16384*t^52 - 10468434365991/1048576*t^50 + 29078984349975/4194304*t^48 - 8817498480315/2097152*t^46 + 149608375854525/67108864*t^44 - 277508869722315/268435456*t^42 + 449972009097765/1073741824*t^40 - 159245992330425/1073741824*t^38 + 392806781081715/8589934592*t^36 - 841728816603675/68719476736*t^34 + 780512175396135/274877906944*t^32 - 38962765599485/68719476736*t^30 + 106596245508025/1099511627776*t^28 - 61989816618513/4398046511104*t^26 + 30387165009075/17592186044416*t^24 - 3106243534261/17592186044416*t^22 + 2091959931237/140737488355328*t^20 - 2284324062845/2251799813685248*t^18 + 495746924277/9007199254740992*t^16 - 10429458435/4503599627370496*t^14 + 21090682613/288230376151711744*t^12 - 1917334783/1152921504606846976*t^10 + 118030185/4611686018427387904*t^8 - 1124097/4611686018427387904*t^6 + 45695/36893488147419103232*t^4 - 741/295147905179352825856*t^2 + 1/1180591620717411303424
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   76 out of 76
Indefinite weights: 0 out of 76
Negative weights:   0 out of 76
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99916779934458287527 - 2.2936909301357293901e-1760j)  +/-  (2.46e-484, 2.46e-484j)
| (-0.91791658525375936974 - 5.804774403125845262e-1760j)  +/-  (3.33e-484, 3.33e-484j)
| (-0.93333652103736675804 - 1.2248860870854642686e-1762j)  +/-  (6.61e-484, 6.61e-484j)
| (-0.99251850249102774178 - 7.1943860812203382575e-1779j)  +/-  (1.58e-483, 1.58e-483j)
| (0.93333652103736675804 + 3.8035437634301028375e-1800j)  +/-  (6.82e-484, 6.82e-484j)
| (0.94720301029191007507 - 1.6130340204129886714e-1799j)  +/-  (1.11e-483, 1.11e-483j)
| (0.97926415875742112492 - 4.2752603078158138131e-1798j)  +/-  (2.27e-483, 2.27e-483j)
| (-0.8825215767863212466 + 1.7384270269305729984e-1799j)  +/-  (6.57e-485, 6.57e-485j)
| (0.95949297361449738989 - 2.7343807731792965414e-1801j)  +/-  (1.57e-483, 1.57e-483j)
| (-0.99916779934458287527 - 4.9590109875751842362e-1802j)  +/-  (2.32e-484, 2.32e-484j)
| (0.8825215767863212466 + 5.8613679385885659841e-1823j)  +/-  (7.18e-485, 7.18e-485j)
| (0.99251850249102774178 + 8.6349011069847711208e-1819j)  +/-  (1.55e-483, 1.55e-483j)
| (-0.94720301029191007507 - 4.3675570418118674739e-1818j)  +/-  (1.09e-483, 1.09e-483j)
| (-0.86260541560098070514 - 1.2747867204554091217e-1832j)  +/-  (2.7e-485, 2.7e-485j)
| (0.99667258249419325447 - 2.0163876337510255979e-1834j)  +/-  (8.16e-484, 8.16e-484j)
| (0.86260541560098070514 + 9.394673238408945726e-1844j)  +/-  (2.62e-485, 2.62e-485j)
| (0.84125353283118116886 - 1.0895381777446014818e-1846j)  +/-  (9.06e-486, 9.06e-486j)
| (-0.97018595557406448332 - 6.6707590350504163156e-1845j)  +/-  (1.97e-483, 1.97e-483j)
| (-0.74223412300426992182 - 1.2362033172073890298e-1873j)  +/-  (4.03e-488, 4.03e-488j)
| (-0.95949297361449738989 - 1.7840876214813473945e-1872j)  +/-  (1.65e-483, 1.65e-483j)
| (0.90096886790241912624 - 3.1156081648277429965e-1892j)  +/-  (1.55e-484, 1.55e-484j)
| (0.74223412300426992182 + 1.0164143787760801585e-1906j)  +/-  (3.92e-488, 3.92e-488j)
| (-0.99667258249419325447 + 7.4163207204462013005e-1909j)  +/-  (8.55e-484, 8.55e-484j)
| (-0.7943870854121126072 - 2.9763887212775049145e-1936j)  +/-  (7.38e-487, 7.38e-487j)
| (-0.81850146657859347133 + 7.7455234183526704615e-1937j)  +/-  (2.62e-486, 2.62e-486j)
| (-0.97926415875742112492 - 6.2318877585575721466e-1947j)  +/-  (2.18e-483, 2.18e-483j)
| (0.76895052533936202396 - 1.0300938508964649682e-1982j)  +/-  (1.73e-487, 1.73e-487j)
| (0.7943870854121126072 + 2.1395413570259839759e-1982j)  +/-  (7.72e-487, 7.72e-487j)
| (-0.98671247339128891623 - 2.8760773420375249329e-1979j)  +/-  (2.05e-483, 2.05e-483j)
| (-0.65486073394528506406 - 8.339588009267298832e-1999j)  +/-  (1.72e-490, 1.72e-490j)
| (-0.90096886790241912624 - 4.8626108011292409986e-1992j)  +/-  (1.51e-484, 1.51e-484j)
| (0.71428234522190360326 + 1.0734181649712333629e-1996j)  +/-  (8.2e-489, 8.2e-489j)
| (0.68514171496784418645 + 2.6994971881301000107e-1997j)  +/-  (1.08e-489, 1.08e-489j)
| (0.97018595557406448332 - 1.4407902961483822053e-1989j)  +/-  (2.03e-483, 2.03e-483j)
| (-0.71428234522190360326 - 5.1693083542772126765e-1999j)  +/-  (8.18e-489, 8.18e-489j)
| (-0.76895052533936202396 - 3.9983598857939609093e-1997j)  +/-  (1.74e-487, 1.74e-487j)
| (0.81850146657859347133 - 7.371748286771030413e-1995j)  +/-  (2.64e-486, 2.64e-486j)
| (0.59108113252867653444 - 8.6741594315836685894e-2002j)  +/-  (2.9e-492, 2.9e-492j)
| (0.91791658525375936974 + 9.4339248868078091295e-1992j)  +/-  (3.26e-484, 3.26e-484j)
| (-0.59108113252867653444 - 2.1618685464138652924e-2003j)  +/-  (3.04e-492, 3.04e-492j)
| (-0.5576886669868294164 - 5.4785133272770037344e-2004j)  +/-  (3.9e-493, 3.9e-493j)
| (0.26210168293910218124 + 3.8482181818271956603e-2013j)  +/-  (4.45e-502, 4.45e-502j)
| (0.65486073394528506406 + 2.2127961619996769367e-2001j)  +/-  (1.74e-490, 1.74e-490j)
| (0.5576886669868294164 + 3.2449404217047472217e-2003j)  +/-  (3.63e-493, 3.63e-493j)
| (-0.84125353283118116886 - 9.7584658929904581099e-1997j)  +/-  (8.67e-486, 8.67e-486j)
| (-0.52336798369661201426 - 6.21819008521570164e-2006j)  +/-  (4.54e-494, 4.54e-494j)
| (-0.68514171496784418645 + 1.4488916904381018595e-2000j)  +/-  (1.02e-489, 1.02e-489j)
| (0.0203985373914053545 + 9.6140316378264995986e-2021j)  +/-  (8.61e-511, 8.61e-511j)
| (0.45217190728268572167 + 2.3881718591047813764e-2006j)  +/-  (3.23e-496, 3.23e-496j)
| (0.62348980185873353053 + 6.1074254720944833492e-2002j)  +/-  (2.43e-491, 2.43e-491j)
| (-0.62348980185873353053 - 1.1451034925532772549e-2002j)  +/-  (2.39e-491, 2.39e-491j)
| (-0.48817620604828129299 - 2.1048344617626425989e-2006j)  +/-  (3.05e-495, 3.05e-495j)
| (0.98671247339128891623 + 6.4436055595047501084e-2014j)  +/-  (2.17e-483, 2.17e-483j)
| (0.52336798369661201426 + 7.3043001156765844105e-2027j)  +/-  (4.37e-494, 4.37e-494j)
| (0.48817620604828129299 - 7.6035339258151292627e-2030j)  +/-  (3.02e-495, 3.02e-495j)
| (-0.0203985373914053545 - 3.8507140436112703391e-2045j)  +/-  (8.61e-511, 8.61e-511j)
| (-0.45217190728268572167 + 3.4957461492932397407e-2031j)  +/-  (3.09e-496, 3.09e-496j)
| (-0.41541501300188642553 - 5.0861348695285185357e-2032j)  +/-  (2.64e-497, 2.64e-497j)
| (0.18256982083936167619 - 1.3437806409064769965e-2039j)  +/-  (1.33e-504, 1.33e-504j)
| (0.41541501300188642553 - 2.1466935093240876842e-2032j)  +/-  (2.59e-497, 2.59e-497j)
| (0.061161660821842706978 - 2.0572458319753426629e-2043j)  +/-  (7.53e-509, 7.53e-509j)
| (-0.33988930158261673067 - 2.3381215762220025542e-2035j)  +/-  (1.05e-499, 1.05e-499j)
| (-0.37796670142890656284 + 3.4017096300460703337e-2033j)  +/-  (2.16e-498, 2.16e-498j)
| (-0.10182298670383538469 + 1.337959599863067701e-2043j)  +/-  (3.25e-507, 3.25e-507j)
| (0.37796670142890656284 + 2.4033551959562184615e-2034j)  +/-  (2.03e-498, 2.03e-498j)
| (0.22252093395631440429 + 2.543898650956627783e-2038j)  +/-  (2.08e-503, 2.08e-503j)
| (-0.14231483827328514044 - 1.1040560986040503584e-2042j)  +/-  (6.03e-506, 6.03e-506j)
| (-0.30124618953723425369 + 4.8712364015996802354e-2036j)  +/-  (7.44e-501, 7.44e-501j)
| (-0.18256982083936167619 + 5.6140652610252102393e-2041j)  +/-  (1.3e-504, 1.3e-504j)
| (0.10182298670383538469 - 4.5951464695415271364e-2042j)  +/-  (3.54e-507, 3.54e-507j)
| (0.33988930158261673067 - 2.2351160790278134058e-2034j)  +/-  (1.14e-499, 1.14e-499j)
| (0.14231483827328514044 + 6.1451711717637537937e-2041j)  +/-  (5.92e-506, 5.92e-506j)
| (-0.22252093395631440429 - 3.7435573199382671166e-2039j)  +/-  (2.33e-503, 2.33e-503j)
| (-0.26210168293910218124 - 2.6468442515127400277e-2037j)  +/-  (4.38e-502, 4.38e-502j)
| (-0.061161660821842706978 + 1.1884787065279768803e-2043j)  +/-  (7.69e-509, 7.69e-509j)
| (0.30124618953723425369 - 1.6558554238450626355e-2036j)  +/-  (7.42e-501, 7.42e-501j)
-------------------------------------------------
The weights are:
| (2.1606607180563282689e-05 + 4.4579820129211569549e-1762j)  +/-  (5.01e-140, 2.79e-375j)
| (0.0020445343183906221659 - 9.9727768037096102764e-1762j)  +/-  (2.45e-140, 1.37e-375j)
| (0.0016738043960761693389 - 6.3230645324843031763e-1761j)  +/-  (2.23e-140, 1.24e-375j)
| (0.00019359769107750335504 - 1.5246718940406071208e-1762j)  +/-  (1.96e-141, 1.09e-376j)
| (0.0016738043960761693389 + 5.3081245634003491074e-1762j)  +/-  (6.23e-142, 3.48e-377j)
| (0.0013351487960252428104 - 5.4785911803034047182e-1762j)  +/-  (4.48e-142, 2.5e-377j)
| (0.00053300918666390019652 + 5.9796428821066281543e-1762j)  +/-  (5.81e-143, 3.24e-378j)
| (0.0028721515130725362571 - 4.668389360451560435e-1761j)  +/-  (7.01e-144, 3.91e-379j)
| (0.0010308212153819404619 + 5.6413561506113786691e-1762j)  +/-  (1.28e-142, 7.16e-378j)
| (2.1606607180563282689e-05 - 1.5644057789662025248e-1763j)  +/-  (5.42e-145, 3.03e-380j)
| (0.0028721515130725362571 - 4.7236292376199081384e-1762j)  +/-  (1.81e-144, 1.01e-379j)
| (0.00019359769107750335504 + 6.6194981928737448748e-1762j)  +/-  (1.49e-143, 8.31e-379j)
| (0.0013351487960252428104 + 2.6502984097115403254e-1761j)  +/-  (1.54e-145, 8.62e-381j)
| (0.0033235311295566149806 + 3.4412649072532236748e-1761j)  +/-  (4.26e-146, 2.38e-381j)
| (8.6282640316305738762e-05 - 7.9052982506448676418e-1762j)  +/-  (1.67e-143, 9.31e-379j)
| (0.0033235311295566149806 + 4.5009211382461669073e-1762j)  +/-  (6.54e-146, 3.65e-381j)
| (0.0037960064090786595745 - 4.2637092673670002183e-1762j)  +/-  (1.42e-146, 7.92e-382j)
| (0.00076284690398492697013 + 8.535286462949726944e-1762j)  +/-  (1.97e-147, 1.1e-382j)
| (0.0058323182681569130864 - 1.8465141692369955878e-1761j)  +/-  (1.3e-150, 7.28e-386j)
| (0.0010308212153819404619 - 1.4464467795014118548e-1761j)  +/-  (4.01e-147, 2.24e-382j)
| (0.0024448714165017303213 + 4.9320103597929172086e-1762j)  +/-  (2.24e-147, 1.25e-382j)
| (0.0058323182681569130864 - 3.1715837116163566152e-1762j)  +/-  (2.33e-151, 1.3e-386j)
| (8.6282640316305738762e-05 + 6.4420041900682473345e-1763j)  +/-  (5.87e-148, 3.28e-383j)
| (0.0047915475133824533686 - 2.1860952631829732224e-1761j)  +/-  (4.6e-151, 2.57e-386j)
| (0.0042864331066063848657 + 2.4441542179380635821e-1761j)  +/-  (1.12e-150, 6.28e-386j)
| (0.00053300918666390019652 - 5.0909701341107484779e-1762j)  +/-  (1.3e-148, 7.27e-384j)
| (0.0053079881763677813234 + 3.4656895158760836834e-1762j)  +/-  (7.71e-153, 4.3e-388j)
| (0.0047915475133824533686 - 3.7459212462068197219e-1762j)  +/-  (1.66e-152, 9.25e-388j)
| (0.0003428375955070774346 + 2.9244828784161008229e-1762j)  +/-  (1.17e-148, 6.52e-384j)
| (0.0074176288199563970159 + 1.5307007031370333276e-1761j)  +/-  (2.72e-156, 1.52e-391j)
| (0.0024448714165017303213 + 8.3351814051033250164e-1761j)  +/-  (5.71e-150, 3.19e-385j)
| (0.0063610484584973678279 + 2.8639316709269648949e-1762j)  +/-  (2e-155, 1.12e-390j)
| (0.0068906601352067708245 - 2.5430994077825809076e-1762j)  +/-  (2e-156, 1.12e-391j)
| (0.00076284690398492697013 - 5.8033104481478623365e-1762j)  +/-  (6.9e-153, 3.85e-388j)
| (0.0063610484584973678279 + 1.7245648371106465062e-1761j)  +/-  (2.34e-156, 1.31e-391j)
| (0.0053079881763677813234 + 1.9955557318692276491e-1761j)  +/-  (7.34e-155, 4.1e-390j)
| (0.0042864331066063848657 + 4.0119996691781575065e-1762j)  +/-  (1.32e-154, 7.38e-390j)
| (0.0084496505814106120369 + 1.5056076453235352242e-1762j)  +/-  (1.81e-160, 1.01e-395j)
| (0.0020445343183906221659 - 5.1265282751570188887e-1762j)  +/-  (8.15e-154, 4.55e-389j)
| (0.0084496505814106120369 + 1.3758063352251310473e-1761j)  +/-  (8.18e-161, 4.57e-396j)
| (0.0089478357235643283301 - 1.3071249475400928066e-1761j)  +/-  (1.4e-161, 7.84e-397j)
| (0.012094840361045329254 + 2.1735125487866151607e-1762j)  +/-  (1.67e-165, 9.34e-401j)
| (0.0074176288199563970159 + 2.2094835702055638374e-1762j)  +/-  (7.13e-160, 3.98e-395j)
| (0.0089478357235643283301 - 1.1362476345751937284e-1762j)  +/-  (2.59e-162, 1.45e-397j)
| (0.0037960064090786595745 - 2.821902297752315823e-1761j)  +/-  (3.56e-157, 1.99e-392j)
| (0.0094296877096278293615 + 1.2424625360608906786e-1761j)  +/-  (1.51e-163, 8.41e-399j)
| (0.0068906601352067708245 - 1.6211062860407117941e-1761j)  +/-  (3.51e-160, 1.96e-395j)
| (0.012981609086653135554 + 4.9720776691188148534e-1762j)  +/-  (2.29e-168, 1.28e-403j)
| (0.010331695665770626847 - 3.5847369553665879737e-1764j)  +/-  (1.26e-165, 7.01e-401j)
| (0.0079384476230929506772 - 1.8635057029509280459e-1762j)  +/-  (6.09e-162, 3.4e-397j)
| (0.0079384476230929506772 - 1.4497541563207650493e-1761j)  +/-  (4.3e-162, 2.4e-397j)
| (0.0098919998941338442485 - 1.1809046139364715992e-1761j)  +/-  (1.38e-165, 7.73e-401j)
| (0.0003428375955070774346 - 6.209203175115636798e-1762j)  +/-  (2.68e-160, 1.49e-395j)
| (0.0094296877096278293615 + 7.5589682942215046659e-1763j)  +/-  (1.21e-164, 6.77e-400j)
| (0.0098919998941338442485 - 3.6503605581550936279e-1763j)  +/-  (1.65e-165, 9.19e-401j)
| (0.012981609086653135554 - 5.4581112014221714691e-1762j)  +/-  (1.66e-170, 9.24e-406j)
| (0.010331695665770626847 + 1.1217714852574470337e-1761j)  +/-  (1.97e-167, 1.1e-402j)
| (0.010745848921722630286 - 1.064552850385759538e-1761j)  +/-  (1.47e-168, 8.21e-404j)
| (0.012554133253489394533 + 3.0819408254525013205e-1762j)  +/-  (2.09e-171, 1.16e-406j)
| (0.010745848921722630286 + 4.4626285071180940094e-1763j)  +/-  (7.45e-169, 4.16e-404j)
| (0.012938431834357322999 - 4.49120851743848647e-1762j)  +/-  (1.31e-171, 7.29e-407j)
| (0.011486691722982870285 - 9.5441004562320461833e-1762j)  +/-  (1.72e-171, 9.63e-407j)
| (0.01113170354040197145 + 1.008863100273567615e-1761j)  +/-  (1.41e-170, 7.88e-406j)
| (0.012852364667255981331 - 6.4452685152211406773e-1762j)  +/-  (1.05e-173, 5.84e-409j)
| (0.01113170354040197145 - 8.6571985386648458781e-1763j)  +/-  (8.4e-172, 4.69e-407j)
| (0.012343953687678046274 - 2.6243631616148558501e-1762j)  +/-  (6.87e-173, 3.83e-408j)
| (0.012723980348146086947 + 6.9464525612863799888e-1762j)  +/-  (2.79e-174, 1.56e-409j)
| (0.011808451081679178385 + 9.0097259264696501473e-1762j)  +/-  (6.29e-174, 3.51e-409j)
| (0.012554133253489394533 - 7.4529685224040390082e-1762j)  +/-  (1.03e-174, 5.75e-410j)
| (0.012852364667255981331 + 4.0157077199047149351e-1762j)  +/-  (6.23e-175, 3.48e-410j)
| (0.011486691722982870285 + 1.2937314661828487802e-1762j)  +/-  (5.6e-175, 3.12e-410j)
| (0.012723980348146086947 - 3.5458443413405172645e-1762j)  +/-  (4.74e-175, 2.65e-410j)
| (0.012343953687678046274 + 7.9652243425754881643e-1762j)  +/-  (5.38e-176, 3.01e-411j)
| (0.012094840361045329254 - 8.4838451107731337129e-1762j)  +/-  (5.75e-176, 3.21e-411j)
| (0.012938431834357322999 + 5.9491843191080680777e-1762j)  +/-  (3.23e-176, 1.83e-411j)
| (0.011808451081679178385 - 1.7298182589944821622e-1762j)  +/-  (2.39e-176, 1.25e-411j)
