Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 36
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^42 - 199097463822235860028643931918410178917/12929578683859425743227577424470076064*t^40 + 285168766138679841058016877413435263629993/3891803183841687148711500804765492895264*t^38 - 304671812314423622561850018765914721305009407/1420508162102215809279697793739404906771360*t^36 + 1245323226447397677224846957535154221780032151/2881602271693066355967386953014221382307616*t^34 - 52030534748248406768204207774768181046329699/81863700900371203294528038437904016542830*t^32 + 356193372574226986280549317838652806833465748907/504607852349888097107470828931240357970004120*t^30 - 8711588189574063399080895728172281920058913303/14417367209996802774499166540892581656285832*t^28 + 203530799064527956543660477693314045551437480713/504607852349888097107470828931240357970004120*t^26 - 18191993962824867302090051236013671374593786732955/86187021181360886985956017581455853141276703696*t^24 + 1740723583981711871284567190644097718512975062221/20098949603558467716092510028877056661404448688*t^22 - 79633272368646510739664209419305731625545406841/2871278514794066816584644289839579523057778384*t^20 + 2385359982076467299385436521906554548040339111805/347424700290082084806741959070589122289991184464*t^18 - 11916307863985703593806674880243511512292700294367/9206754557687175247378661915370611740684766388296*t^16 + 3919116539774835467194251923117771177998013895/21561486083576522827584688326394875270924511448*t^14 - 1187840417845019403331212243302111408942689417293/64447281903810226731650633407594282184793364718072*t^12 + 52924237421978584821959969414937454269701866737/41011906666061053374686766713923634117595777547864*t^10 - 9579703795327944478307465874877493396026364355/164047626664244213498747066855694536470383110191456*t^8 + 72927842206065407039660456955411453421210820049/47362893355491079354423974587908379743806323670990368*t^6 - 935719971358212080914766762202420706098236835/47362893355491079354423974587908379743806323670990368*t^4 + 3994727003890353065099015874438473085328647/47362893355491079354423974587908379743806323670990368*t^2 - 4929916250893266608172739693442608503/153775627777568439462415501908793440726643908022696
-------------------------------------------------
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:
| (0.98040567633242411892 - 5.2892021929167196132e-859j)  +/-  (5.29e-241, 5.29e-241j)
| (-0.99851105949928519129 - 2.1029635722757505755e-870j)  +/-  (1.85e-241, 1.85e-241j)
| (-0.94061932901805627254 + 1.5558889614714198898e-874j)  +/-  (3.3e-241, 3.3e-241j)
| (0.99851105949928519129 - 1.1766199426583865043e-876j)  +/-  (1.64e-241, 1.64e-241j)
| (0.91248695683407599658 - 5.5519931578033180317e-897j)  +/-  (1.56e-241, 1.56e-241j)
| (0.94061932901805627254 - 2.5678306911689528728e-916j)  +/-  (3.2e-241, 3.2e-241j)
| (-0.3042598527464201821 - 8.0916832872408080202e-937j)  +/-  (1.83e-250, 1.83e-250j)
| (-0.91248695683407599658 - 1.2287663310689281127e-926j)  +/-  (1.68e-241, 1.68e-241j)
| (-0.98040567633242411892 + 1.3341664488579187755e-925j)  +/-  (5.92e-241, 5.92e-241j)
| (0.99210203675286631524 - 2.5666295923646388137e-930j)  +/-  (4.79e-241, 4.79e-241j)
| (0.87897669460789045246 - 2.4630520092961779544e-939j)  +/-  (6.33e-242, 6.33e-242j)
| (-0.99210203675286631524 + 2.1956956901920624906e-944j)  +/-  (4.33e-241, 4.33e-241j)
| (-0.96326778093049967835 + 5.4853459614084031372e-947j)  +/-  (4.83e-241, 4.83e-241j)
| (-0.79654065260956471698 + 4.2897121281469306409e-952j)  +/-  (5.54e-243, 5.54e-243j)
| (0.96326778093049967835 + 2.7807615675336584176e-951j)  +/-  (5.2e-241, 5.2e-241j)
| (0.84025595811263113901 + 2.2613329911211961231e-959j)  +/-  (2.1e-242, 2.1e-242j)
| (0.79654065260956471698 + 3.904944888341038819e-963j)  +/-  (5.7e-243, 5.7e-243j)
| (-0.4459311574120021154 + 1.3832148521360721651e-973j)  +/-  (3.72e-248, 3.72e-248j)
| (-0.74808679440977429644 + 4.137268394187455825e-969j)  +/-  (1.25e-243, 1.25e-243j)
| (-0.87897669460789045246 + 3.7225680944118344179e-968j)  +/-  (6.89e-242, 6.89e-242j)
| (0.51314160997085617842 + 4.3488544806825783957e-975j)  +/-  (4.25e-247, 4.25e-247j)
| (0.74808679440977429644 + 5.5191860747315986062e-972j)  +/-  (1.27e-243, 1.27e-243j)
| (0.15655801081562154215 + 1.2133245363460573611e-979j)  +/-  (5.61e-253, 5.61e-253j)
| (-0.84025595811263113901 + 2.5699914163565254706e-974j)  +/-  (2.11e-242, 2.11e-242j)
| (-0.69518496586957738843 + 8.1242363167400484707e-978j)  +/-  (2.28e-244, 2.28e-244j)
| (0.23081009518813896127 + 2.0313359575563058395e-985j)  +/-  (1.11e-251, 1.11e-251j)
| (0.69518496586957738843 + 5.4745516933693405223e-978j)  +/-  (2.3e-244, 2.3e-244j)
| (0.4459311574120021154 + 2.1437269617668623404e-983j)  +/-  (3.85e-248, 3.85e-248j)
| (-0.08327020363365321691 + 3.489393117152884655e-988j)  +/-  (3.17e-254, 3.17e-254j)
| (-0.63815642272838958413 - 1.3293109525706979099e-980j)  +/-  (3.28e-245, 3.28e-245j)
| (-0.23081009518813896127 + 5.3271827878750689553e-988j)  +/-  (1.22e-251, 1.22e-251j)
| (0.37614791095545046364 - 7.1033468539679927396e-985j)  +/-  (2.91e-249, 2.91e-249j)
| (0.57735026918962576451 - 6.9322018592618710909e-982j)  +/-  (3.96e-246, 3.96e-246j)
| (0.020496697440753133861 + 1.5799542596378968424e-989j)  +/-  (2.6e-255, 2.6e-255j)
| (-0.57735026918962576451 + 1.2280474309113906096e-986j)  +/-  (4.08e-246, 4.08e-246j)
| (-0.37614791095545046364 - 5.5670010476408068896e-990j)  +/-  (3e-249, 3e-249j)
| (0.08327020363365321691 - 9.5234840322870397543e-991j)  +/-  (3.17e-254, 3.17e-254j)
| (0.63815642272838958413 - 2.5176943657749343423e-990j)  +/-  (3.27e-245, 3.27e-245j)
| (0.3042598527464201821 + 5.6313333858625027133e-996j)  +/-  (2e-250, 2e-250j)
| (-0.15655801081562154215 + 4.016452273758137459e-997j)  +/-  (5.88e-253, 5.88e-253j)
| (-0.51314160997085617842 + 1.4708947877174468005e-994j)  +/-  (4.4e-247, 4.4e-247j)
| (-0.020496697440753133861 - 1.9405091182169459916e-1004j)  +/-  (2.6e-255, 2.6e-255j)
-------------------------------------------------
The weights are:
| (0.014397367401655287556 + 1.4221928662371459945e-859j)  +/-  (1.35e-75, 6.86e-192j)
| (0.0038277003290558215844 - 6.3570014379607411026e-862j)  +/-  (3.63e-76, 1.84e-192j)
| (0.025402136100528861046 - 7.5114146225283887965e-861j)  +/-  (3.44e-76, 1.74e-192j)
| (0.0038277003290558215844 - 6.9481967696961838073e-860j)  +/-  (2.73e-76, 1.38e-192j)
| (0.030844625965374638548 - 2.6053754683096226713e-859j)  +/-  (1.35e-76, 6.85e-193j)
| (0.025402136100528861046 + 3.6267755866996880159e-859j)  +/-  (2.09e-76, 1.06e-192j)
| (0.072769349822576244931 - 7.9732653412940010148e-860j)  +/-  (4.67e-78, 2.37e-194j)
| (0.030844625965374638548 + 9.3483255491810483394e-861j)  +/-  (6.61e-78, 3.35e-194j)
| (0.014397367401655287556 - 3.8836263969168486227e-861j)  +/-  (3.36e-78, 1.7e-194j)
| (0.0090221902803483992828 + 3.5808973180312333886e-859j)  +/-  (9.53e-78, 4.83e-194j)
| (0.036147784498103737572 + 2.0666736002780113976e-859j)  +/-  (2.03e-79, 1.03e-195j)
| (0.0090221902803483992828 + 2.1233613164057196142e-861j)  +/-  (3.17e-78, 1.61e-194j)
| (0.019889997899206872358 + 5.6988011276298593919e-861j)  +/-  (1.85e-78, 9.4e-195j)
| (0.046130282941859653459 - 1.5734294207213060284e-860j)  +/-  (5.83e-81, 2.96e-197j)
| (0.019889997899206872358 - 6.4632256332022688003e-859j)  +/-  (1.08e-78, 5.47e-195j)
| (0.041257569040180295192 - 1.7368273005479139293e-859j)  +/-  (8.65e-81, 4.39e-197j)
| (0.046130282941859653459 + 1.5206261507674028714e-859j)  +/-  (7.73e-82, 3.92e-198j)
| (0.068571022185606868536 - 4.693440859196346605e-860j)  +/-  (5.99e-84, 3.03e-200j)
| (0.050728939521516235695 + 1.8488698820719258763e-860j)  +/-  (7.29e-83, 3.7e-199j)
| (0.036147784498103737572 - 1.1273668188429504293e-860j)  +/-  (8.14e-82, 4.13e-198j)
| (0.065778530886860815176 - 1.2073459787722818948e-859j)  +/-  (3.25e-85, 1.65e-201j)
| (0.050728939521516235695 - 1.375591016949258736e-859j)  +/-  (3.18e-83, 1.61e-199j)
| (0.074254470034961491331 + 2.4269010988630879532e-859j)  +/-  (2.96e-86, 1.5e-202j)
| (0.041257569040180295192 + 1.3369637289041182293e-860j)  +/-  (9.71e-83, 4.92e-199j)
| (0.055021128084395476649 - 2.1791275256333172494e-860j)  +/-  (1.84e-84, 9.35e-201j)
| (0.07401141637585844378 - 1.8195051383861209766e-859j)  +/-  (8.99e-87, 4.56e-203j)
| (0.055021128084395476649 + 1.2801755118222716421e-859j)  +/-  (2.04e-85, 1.03e-201j)
| (0.068571022185606868536 + 1.2525251134329300421e-859j)  +/-  (1.02e-86, 5.17e-203j)
| (0.07126009927324623759 + 3.2993913116398859084e-859j)  +/-  (2.85e-88, 1.45e-204j)
| (0.058977742398665990424 + 2.586180778032868488e-860j)  +/-  (5.83e-87, 2.95e-203j)
| (0.07401141637585844378 + 1.1260528831289654865e-859j)  +/-  (3.51e-88, 1.78e-204j)
| (0.070917955470659167185 - 1.3462987022547677416e-859j)  +/-  (5.07e-88, 2.57e-204j)
| (0.06257203746057818326 + 1.1989773996343609308e-859j)  +/-  (1.01e-87, 5.1e-204j)
| (0.048217654028761278845 + 6.9644439941787599569e-859j)  +/-  (5.25e-89, 2.66e-205j)
| (0.06257203746057818326 - 3.1022466989418805147e-860j)  +/-  (4.6e-89, 2.33e-205j)
| (0.070917955470659167185 + 5.9968987070380112013e-860j)  +/-  (3.29e-89, 1.67e-205j)
| (0.07126009927324623759 - 3.9118762589960392219e-859j)  +/-  (2.4e-89, 1.22e-205j)
| (0.058977742398665990424 - 1.2230542928726980164e-859j)  +/-  (2.48e-89, 1.25e-205j)
| (0.072769349822576244931 + 1.5149068116323772332e-859j)  +/-  (1.35e-89, 6.82e-206j)
| (0.074254470034961491331 - 1.7585406001505169427e-859j)  +/-  (2.44e-90, 1.22e-206j)
| (0.065778530886860815176 + 3.7772449304417863675e-860j)  +/-  (7.4e-91, 3.54e-207j)
| (0.048217654028761278845 - 6.6792051834206574998e-859j)  +/-  (7.27e-90, 3.75e-206j)
