Starting with polynomial:
P : t
Extension levels are: 1 2 68
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 682318202587104478637369101538978335987/281883215233401101190419706483682719*t^69 + 259685236589810023339269185894208000066269/93961071744467033730139902161227573*t^67 - 16923131749860167100598912556807256541028607/8541915613133366702739991105566143*t^65 + 8552623377065592571482730622525340080360939320/8541915613133366702739991105566143*t^63 - 3244018246186042656705462835078560180216563371800/8541915613133366702739991105566143*t^61 + 959951449393530780771880182144610370138463872788440/8541915613133366702739991105566143*t^59 - 227435245423035005883763525071276380538129813470193240/8541915613133366702739991105566143*t^57 + 43936070421289529119452067241430568050466812513888008820/8541915613133366702739991105566143*t^55 - 7012303547812789803240396353138347200290159994677956932900/8541915613133366702739991105566143*t^53 + 933616424608344846184071582056521662636504178404973274166900/8541915613133366702739991105566143*t^51 - 104426837356210113935369190634498938942555090424339836890884500/8541915613133366702739991105566143*t^49 + 9862626280470574283086930075456120964883416169379570702690257000/8541915613133366702739991105566143*t^47 - 789248286348861119226830885053737302490888045294224478359216421000/8541915613133366702739991105566143*t^45 + 53628389403971875367482556504564901487400412832774809355242552405000/8541915613133366702739991105566143*t^43 - 3097028129251112009696280725475854442379299296248573441996019005365000/8541915613133366702739991105566143*t^41 + 151988394839634752516343216905566218029876054173160297241329863242386250/8541915613133366702739991105566143*t^39 - 6331369803462715339470133326658630461933496905027274902061737680748461250/8541915613133366702739991105566143*t^37 + 223399846555166463959579161590391065963954548779927997489889714227356496250/8541915613133366702739991105566143*t^35 - 6655826904074548100708643005588190467244209404417834739162084467835624006250/8541915613133366702739991105566143*t^33 + 166734776867317465197570589102326832240925938014571727671379763528914850525000/8541915613133366702739991105566143*t^31 - 3493162448199337626163873634693491800389105128805636546496639578797175747025000/8541915613133366702739991105566143*t^29 + 60795557450030824559950263424599869094092235538144411090434875629925554562025000/8541915613133366702739991105566143*t^27 - 871798382243441199110203344157884655697451917323174393647482409906126358992825000/8541915613133366702739991105566143*t^25 + 10197546151216019423112397483276163103291529088574637942957363863901055903477812500/8541915613133366702739991105566143*t^23 - 96115838746816921436354202025537132264892881211369111169050519752232387073798562500/8541915613133366702739991105566143*t^21 + 719108738196108558664242219971811297082302018836007928254931869706733790958628812500/8541915613133366702739991105566143*t^19 - 4192015855614817172169462144234056458722971776623244609632834787933920013367551312500/8541915613133366702739991105566143*t^17 + 18601285222416027344069990634378924745919958964908608510114871852760459703224107375000/8541915613133366702739991105566143*t^15 - 60977303804958930498216287574489841472223302639757001248668184387358528650331426875000/8541915613133366702739991105566143*t^13 + 141973329243732112213789955967159366840521560022596747070269041027933124878958546875000/8541915613133366702739991105566143*t^11 - 222493928151658234911998904297918807159014171774206161263549811150979810957678906875000/8541915613133366702739991105566143*t^9 + 217237152955556046512376453203608096002708611446861484618054916586370313303630440859375/8541915613133366702739991105566143*t^7 - 117198223380316004658298088500400248878243996139471569518392188126838034087191343671875/8541915613133366702739991105566143*t^5 + 28280771221338496708447133010255315596321059757763212221343415045076057668256590234375/8541915613133366702739991105566143*t^3 - 1893555149364347217457371831159728500253929669243317821514530273437289698914793359375/8541915613133366702739991105566143*t
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (11.188845857940793994 - 3.7907359175408142302e-1503j)  +/-  (1.28e-493, 1.28e-493j)
| (14.03632488242263318 + 1.2882331824113506344e-1505j)  +/-  (3.3e-496, 3.3e-496j)
| (-13.38906608636114049 + 6.4338990003001878731e-1503j)  +/-  (2.11e-495, 2.11e-495j)
| (-14.03632488242263318 + 4.484423353752289181e-1506j)  +/-  (3.43e-496, 3.43e-496j)
| (-8.4202602308455819836 - 5.2600790481425219734e-1504j)  +/-  (1.58e-493, 1.58e-493j)
| (-14.762167704974838053 - 6.6731979615058630658e-1515j)  +/-  (3e-497, 3e-497j)
| (6.3395580110041025053 - 1.2070936982535441329e-1519j)  +/-  (3.5e-495, 3.5e-495j)
| (-2.1011542400546784113 + 6.6252196696774687789e-1529j)  +/-  (2.23e-503, 2.23e-503j)
| (-12.792468803948605534 - 9.6120998950049172605e-1518j)  +/-  (9.14e-495, 9.14e-495j)
| (8.4202602308455819836 + 3.3788171832560792821e-1526j)  +/-  (1.66e-493, 1.66e-493j)
| (2.1011542400546784113 + 2.577808665719320839e-1548j)  +/-  (2.38e-503, 2.38e-503j)
| (-10.218574517678719552 + 2.1664291054108450607e-1536j)  +/-  (2.43e-493, 2.43e-493j)
| (12.232155784047923171 - 2.5727416750514471965e-1549j)  +/-  (2.78e-494, 2.78e-494j)
| (-1.3669748595750212726 + 3.279430190768840945e-1563j)  +/-  (2.03e-505, 2.03e-505j)
| (-4.3707914475270885432 + 3.3962274716815967822e-1556j)  +/-  (3.99e-498, 3.99e-498j)
| (5.1481205611446734795 - 1.430034429226127819e-1554j)  +/-  (8.61e-497, 8.61e-497j)
| (11.699507452325737814 - 1.2770618088455822196e-1549j)  +/-  (6.57e-494, 6.57e-494j)
| (12.792468803948605534 + 1.3131518324435128815e-1553j)  +/-  (8.54e-495, 8.54e-495j)
| (-2.8480089523064150665 - 3.3473067041224411189e-1566j)  +/-  (1.94e-501, 1.94e-501j)
| (-15.639770020674098737 + 2.7742407566064778331e-1558j)  +/-  (1.22e-498, 1.22e-498j)
| (14.762167704974838053 - 2.8725602662995495174e-1559j)  +/-  (3.03e-497, 3.03e-497j)
| (15.639770020674098737 - 3.8505897614008078394e-1561j)  +/-  (1.13e-498, 1.13e-498j)
| (-11.699507452325737814 - 2.3699464619438941567e-1565j)  +/-  (6.53e-494, 6.53e-494j)
| (-9.3000343753374752502 - 9.2934403643016562859e-1591j)  +/-  (2.65e-493, 2.65e-493j)
| (9.3000343753374752502 + 1.1975830724004909111e-1606j)  +/-  (2.57e-493, 2.57e-493j)
| (4.7579591875243408039 + 2.3482403230590696103e-1610j)  +/-  (2.07e-497, 2.07e-497j)
| (13.38906608636114049 + 1.0753804532677416931e-1607j)  +/-  (2.11e-495, 2.11e-495j)
| (3.2250951854013963292 + 2.4465091718937254643e-1613j)  +/-  (1.75e-500, 1.75e-500j)
| (10.696181269824406128 + 1.6096670091449625088e-1605j)  +/-  (2.01e-493, 2.01e-493j)
| (-12.232155784047923171 - 1.6800715410571072799e-1613j)  +/-  (2.83e-494, 2.83e-494j)
| (3.9863790854717406106 - 1.4532086592609749054e-1633j)  +/-  (8.02e-499, 8.02e-499j)
| (-6.7449001868803277909 - 6.6089498843766431907e-1628j)  +/-  (1.03e-494, 1.03e-494j)
| (4.3707914475270885432 + 2.9376850141406029067e-1633j)  +/-  (4.28e-498, 4.28e-498j)
| (8.8559159872031427952 - 4.4431239896050823861e-1627j)  +/-  (2.07e-493, 2.07e-493j)
| (9.7537805072263401514 + 6.8141593197165548865e-1633j)  +/-  (2.79e-493, 2.79e-493j)
| (-3.2250951854013963292 - 2.4339729430363753471e-1648j)  +/-  (1.74e-500, 1.74e-500j)
| (-5.5415542498109896346 - 2.9364110538893337103e-1640j)  +/-  (3.43e-496, 3.43e-496j)
| (7.9920954723175291253 + 4.7742553522936988644e-1670j)  +/-  (8.86e-494, 8.86e-494j)
| (-8.8559159872031427952 - 3.9085508139213039997e-1751j)  +/-  (2.08e-493, 2.08e-493j)
| (-10.696181269824406128 - 3.9637733357789309834e-1837j)  +/-  (2e-493, 2e-493j)
| (5.9385793606861091472 - 4.7830082528902163331e-1901j)  +/-  (1.24e-495, 1.24e-495j)
| (-11.188845857940793994 - 4.9594858408014319493e-1953j)  +/-  (1.36e-493, 1.36e-493j)
| (1.0078652865767709999 - 1.9697172486245190521e-1995j)  +/-  (1.53e-506, 1.53e-506j)
| (2.8480089523064150665 + 8.7473651532033777148e-1990j)  +/-  (1.88e-501, 1.88e-501j)
| (-9.7537805072263401514 + 1.9441916221987771235e-1980j)  +/-  (2.74e-493, 2.74e-493j)
| (-6.3395580110041025053 + 2.5012446958561110609e-1995j)  +/-  (3.66e-495, 3.66e-495j)
| (10.218574517678719552 + 3.7071154711571882172e-1992j)  +/-  (2.51e-493, 2.51e-493j)
| (-3.6045276816864020937 + 3.6435303952189012642e-1998j)  +/-  (1.27e-499, 1.27e-499j)
| (-0.65821209240711835135 - 4.5916847380854751175e-2006j)  +/-  (1.15e-507, 1.15e-507j)
| (7.1550709146615768951 - 9.5801011862214487624e-1994j)  +/-  (2.44e-494, 2.44e-494j)
| (-7.9920954723175291253 - 5.5621702083816257476e-1991j)  +/-  (9.44e-494, 9.44e-494j)
| (-1.0078652865767709999 + 1.3103671980038534826e-2008j)  +/-  (1.43e-506, 1.43e-506j)
| (-7.1550709146615768951 + 2.7719752457508319777e-1995j)  +/-  (2.41e-494, 2.41e-494j)
| (-3.9863790854717406106 - 3.267637400903923979e-2000j)  +/-  (7.7e-499, 7.7e-499j)
| (-5.1481205611446734795 - 4.1066014846150017357e-1998j)  +/-  (8.82e-497, 8.82e-497j)
| (2.4732980105082074701 + 3.2524744545594102179e-2004j)  +/-  (2.39e-502, 2.39e-502j)
| (-1.7320508075688772935 - 9.4612277856480293793e-2007j)  +/-  (2.27e-504, 2.27e-504j)
| (7.5706000723432376042 - 2.7953668829186041492e-1997j)  +/-  (5.17e-494, 5.17e-494j)
| (6.7449001868803277909 - 1.600368620544481713e-1996j)  +/-  (1.06e-494, 1.06e-494j)
| (1.7320508075688772935 - 1.7607354409214016603e-2006j)  +/-  (2.32e-504, 2.32e-504j)
| (3.6045276816864020937 - 3.0926664965847278314e-2002j)  +/-  (1.24e-499, 1.24e-499j)
| (-4.7579591875243408039 + 1.3995654861037212336e-1998j)  +/-  (2e-497, 2e-497j)
| (0.65821209240711835135 + 3.4378812971633859087e-2009j)  +/-  (1.26e-507, 1.26e-507j)
| (-5.9385793606861091472 + 1.2726766895884192293e-1996j)  +/-  (1.3e-495, 1.3e-495j)
| (1.3669748595750212726 - 5.0981951390301273627e-2007j)  +/-  (2.08e-505, 2.08e-505j)
| (5.5415542498109896346 - 3.5373613016897880914e-1998j)  +/-  (3.73e-496, 3.73e-496j)
| (-0.32248795385325742986 + 3.2792929589999729377e-2043j)  +/-  (7.73e-509, 7.73e-509j)
| (-2.4732980105082074701 - 1.769011575906151867e-2004j)  +/-  (2.35e-502, 2.35e-502j)
| (-7.5706000723432376042 + 4.4017034293236937434e-1994j)  +/-  (5.24e-494, 5.24e-494j)
| (-5.4300613575783552019e-2043 - 4.8975905246240141459e-2043j)  +/-  (5.19e-2041, 5.19e-2041j)
| (0.32248795385325742986 + 1.0620067227263372092e-2014j)  +/-  (7.73e-509, 7.73e-509j)
-------------------------------------------------
The weights are:
| (1.3065111923524306545e-28 - 1.9202932700267284158e-1527j)  +/-  (1.29e-161, 4.66e-406j)
| (4.4814507820604122252e-44 + 2.4814486059902914962e-1535j)  +/-  (1.49e-168, 5.37e-413j)
| (2.9181909282432165187e-40 + 9.4851017873116702033e-1533j)  +/-  (2.22e-168, 8e-413j)
| (4.4814507820604122252e-44 - 9.9214052962050093569e-1535j)  +/-  (5.39e-170, 1.94e-414j)
| (6.9222176002411168584e-17 - 1.5758664671779133992e-1519j)  +/-  (7.97e-157, 2.87e-401j)
| (1.4893031296353834532e-48 + 4.8164928352016816171e-1537j)  +/-  (5.06e-172, 1.82e-416j)
| (3.0141370573010082925e-10 + 6.8163143987225900496e-1518j)  +/-  (1.03e-150, 3.71e-395j)
| (0.016266764088012793848 - 3.3452076798683920045e-1513j)  +/-  (1.69e-120, 6.07e-365j)
| (6.7033288151120476034e-37 - 5.4064464370538883198e-1531j)  +/-  (8.78e-168, 3.16e-412j)
| (6.9222176002411168584e-17 - 2.1619583000118312455e-1521j)  +/-  (7.1e-159, 2.55e-403j)
| (0.016266764088012793848 - 2.0090960706441072899e-1513j)  +/-  (6.24e-123, 2.24e-367j)
| (3.976100482353193346e-24 + 4.0037634906230235345e-1524j)  +/-  (3.78e-163, 1.36e-407j)
| (7.027304973657126042e-34 - 3.8760010054182306947e-1530j)  +/-  (3.31e-169, 1.19e-413j)
| (0.056817662174198717186 - 8.0097514287068326299e-1513j)  +/-  (2.24e-114, 8.07e-359j)
| (1.0936514891889982915e-05 - 6.8122426505426654925e-1515j)  +/-  (8.84e-144, 3.18e-388j)
| (2.7468295387226137177e-07 - 2.7465934297107060582e-1516j)  +/-  (5.42e-148, 1.95e-392j)
| (3.9342541734910161518e-31 + 9.8432681296224820086e-1529j)  +/-  (5.69e-168, 2.05e-412j)
| (6.7033288151120476034e-37 + 1.1145271032545159652e-1531j)  +/-  (5.64e-171, 2.03e-415j)
| (0.0025982681046509296954 - 1.1487924280294034312e-1513j)  +/-  (1e-136, 3.6e-381j)
| (3.1074412487326806142e-54 - 5.7694515330583682534e-1540j)  +/-  (3.35e-178, 1.21e-422j)
| (1.4893031296353834532e-48 - 1.3177332670485008202e-1537j)  +/-  (1.28e-176, 4.61e-421j)
| (3.1074412487326806142e-54 + 1.7313121080529528037e-1540j)  +/-  (4.33e-179, 1.56e-423j)
| (3.9342541734910161518e-31 - 6.0362090114860897993e-1528j)  +/-  (3.2e-171, 1.15e-415j)
| (2.9626548490967589364e-20 + 7.7577677415446957451e-1522j)  +/-  (3.1e-166, 1.12e-410j)
| (2.9626548490967589364e-20 - 3.8510864746012185337e-1523j)  +/-  (2.74e-166, 9.85e-411j)
| (1.8819991944892585673e-06 + 7.9948821836596477578e-1516j)  +/-  (2.52e-153, 9.06e-398j)
| (2.9181909282432165187e-40 - 2.1612606842892092605e-1533j)  +/-  (6.32e-174, 2.27e-418j)
| (0.00083194306321715147291 + 2.7667451729788566824e-1514j)  +/-  (1.46e-147, 5.24e-392j)
| (2.7729943194273629903e-26 + 3.004104894105304369e-1526j)  +/-  (6.36e-169, 2.29e-413j)
| (7.027304973657126042e-34 + 2.0994318933475618394e-1529j)  +/-  (3.22e-174, 1.16e-418j)
| (5.4136719870868537218e-05 + 5.4081612144102051925e-1515j)  +/-  (7.99e-152, 2.88e-396j)
| (2.149790900853768803e-11 - 1.5086638722007147058e-1517j)  +/-  (8.93e-165, 3.21e-409j)
| (1.0936514891889982915e-05 - 2.1566153629173486558e-1515j)  +/-  (3.21e-153, 1.15e-397j)
| (1.6361254254211259833e-18 + 3.0817049631301311576e-1522j)  +/-  (3.79e-166, 1.36e-410j)
| (4.0193866457940867375e-22 + 4.1712260803401104868e-1524j)  +/-  (5.65e-168, 2.03e-412j)
| (0.00083194306321715147291 + 6.2019583346484265854e-1514j)  +/-  (1.65e-153, 5.95e-398j)
| (3.383457805855403177e-08 + 4.2271098413073043898e-1516j)  +/-  (2.13e-163, 7.66e-408j)
| (2.2857170893383133693e-15 + 1.3424588025500770602e-1520j)  +/-  (1.37e-165, 4.93e-410j)
| (1.6361254254211259833e-18 - 1.2221868044991991653e-1520j)  +/-  (1.08e-170, 3.88e-415j)
| (2.7729943194273629903e-26 - 2.5245671176269882514e-1525j)  +/-  (1.35e-174, 4.86e-419j)
| (3.4973829922790500784e-09 - 2.5454082766835567961e-1517j)  +/-  (9.39e-164, 3.38e-408j)
| (1.3065111923524306545e-28 + 1.3620850544579630604e-1526j)  +/-  (1.36e-175, 4.91e-420j)
| (0.085251442565289790961 + 9.104017025831829458e-1513j)  +/-  (7.53e-146, 2.71e-390j)
| (0.0025982681046509296954 - 5.680801343274220177e-1514j)  +/-  (2.4e-156, 8.64e-401j)
| (4.0193866457940867375e-22 - 5.6857558343525093367e-1523j)  +/-  (4.95e-173, 1.78e-417j)
| (3.0141370573010082925e-10 + 4.8354553403172525604e-1517j)  +/-  (1.07e-168, 3.86e-413j)
| (3.976100482353193346e-24 - 3.8619370493302848821e-1525j)  +/-  (2.73e-173, 9.83e-418j)
| (0.00022913629909474075222 - 3.1580206838470708195e-1514j)  +/-  (1.86e-162, 6.68e-407j)
| (0.11029960032431284359 - 1.5819489501828070124e-1512j)  +/-  (3.03e-151, 1.09e-395j)
| (1.2581761082202506733e-12 + 3.7031773179350447371e-1519j)  +/-  (6.58e-169, 2.37e-413j)
| (2.2857170893383133693e-15 + 5.1462410699933147915e-1519j)  +/-  (1.06e-171, 3.81e-416j)
| (0.085251442565289790961 + 1.1579816606438913152e-1512j)  +/-  (3.9e-155, 1.4e-399j)
| (1.2581761082202506733e-12 + 4.5590873311887257769e-1518j)  +/-  (1.3e-170, 4.69e-415j)
| (5.4136719870868537218e-05 + 1.5133099837466705955e-1514j)  +/-  (5.47e-165, 1.97e-409j)
| (2.7468295387226137177e-07 - 1.1389436469250133052e-1515j)  +/-  (9.48e-168, 3.41e-412j)
| (0.0069958535403269614107 + 1.0986435422676632228e-1513j)  +/-  (1.12e-162, 4.02e-407j)
| (0.032696895546569166727 + 5.2953699900421453153e-1513j)  +/-  (1.41e-160, 5.06e-405j)
| (5.9831758909703450711e-14 - 7.4382396076408157212e-1520j)  +/-  (9.11e-172, 3.28e-416j)
| (2.149790900853768803e-11 - 1.6666127639124165444e-1518j)  +/-  (1.33e-170, 4.79e-415j)
| (0.032696895546569166727 + 3.4884948611516407404e-1513j)  +/-  (1.66e-163, 5.98e-408j)
| (0.00022913629909474075222 - 1.2647151411684722046e-1514j)  +/-  (4.81e-166, 1.73e-410j)
| (1.8819991944892585673e-06 + 2.8769024770411796806e-1515j)  +/-  (5.7e-169, 2.05e-413j)
| (0.11029960032431284359 - 1.3525547138510417934e-1512j)  +/-  (1.73e-164, 6.22e-409j)
| (3.4973829922790500784e-09 - 1.4728063082873086076e-1516j)  +/-  (5.76e-171, 2.07e-415j)
| (0.056817662174198717186 - 5.772288037113236845e-1513j)  +/-  (3.35e-165, 1.21e-409j)
| (3.383457805855403177e-08 + 8.715370618392272613e-1517j)  +/-  (5.36e-170, 1.93e-414j)
| (0.12421750407426661789 + 1.9641932386000250754e-1512j)  +/-  (8.85e-166, 3.19e-410j)
| (0.0069958535403269614107 + 2.0125006709156191051e-1513j)  +/-  (2.71e-167, 9.75e-412j)
| (5.9831758909703450711e-14 - 1.3999795420342921025e-1518j)  +/-  (9.26e-174, 3.33e-418j)
| (0.12745532529391227277 - 2.0812135298082318846e-1512j)  +/-  (1.89e-166, 6.87e-411j)
| (0.12421750407426661789 + 1.819287036165630242e-1512j)  +/-  (1.34e-166, 4.74e-411j)
