Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 39
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^41 - 10193338076219/662305587370*t^39 + 339338581007439/4636139111590*t^37 - 7377634049849037/34457790694250*t^35 + 15490866049760634/35934553152575*t^33 - 146920893538483818/231941206712075*t^31 + 3749178052481026698/5334647754377725*t^29 - 30681168847995834714/51060199934758225*t^27 + 715783624294642214103/1787106997716537875*t^25 - 104699945860056716013/500389959360630605*t^23 + 113693660636701599597/1327121196565150735*t^21 - 306047402256384031581/11185735799620556195*t^19 + 75505296148622743338/11185735799620556195*t^17 - 70851950179778525274/55928678998102780975*t^15 + 164751716624241183534/931611995882683465955*t^13 - 115977012643524719466/6521283971178784261685*t^11 + 71479078486729685109/58098711743229168876830*t^9 - 149235933327366537639/2730639451931770937211010*t^7 + 2724155672775810039/1950456751379836383722150*t^5 - 5332041609931257/316489208714464016981330*t^3 + 509347284035616/8386964030933296450005245*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:
| (0.98031110349651422739 - 2.9157385490932007251e-875j)  +/-  (5.65e-241, 5.65e-241j)
| (-0.99849909578350419302 + 3.0953399429326075156e-900j)  +/-  (1.46e-241, 1.46e-241j)
| (-0.94051155602543865725 - 1.1477764484001647938e-900j)  +/-  (3.09e-241, 3.09e-241j)
| (0.99849909578350419302 + 3.6938178597315065426e-908j)  +/-  (1.53e-241, 1.53e-241j)
| (0.94051155602543865725 - 1.5748457992856050454e-928j)  +/-  (3.05e-241, 3.05e-241j)
| (0.96315238473097102667 + 1.2582875490234432712e-945j)  +/-  (4.46e-241, 4.46e-241j)
| (-0.87894873135818191454 - 1.0884190633503975428e-953j)  +/-  (6.41e-242, 6.41e-242j)
| (-0.91241127597506820524 + 5.5870752778782790292e-954j)  +/-  (1.56e-241, 1.56e-241j)
| (-0.98031110349651422739 + 2.3949129801701510929e-952j)  +/-  (5.32e-241, 5.32e-241j)
| (0.79661330276598377369 + 6.5680407967475641577e-958j)  +/-  (5.63e-243, 5.63e-243j)
| (0.91241127597506820524 + 3.7451645007203962889e-955j)  +/-  (1.51e-241, 1.51e-241j)
| (-0.99204959373389580181 - 1.2970951915927586612e-963j)  +/-  (4.12e-241, 4.12e-241j)
| (-0.96315238473097102667 + 1.4316879843920280491e-968j)  +/-  (4.84e-241, 4.84e-241j)
| (-0.79661330276598377369 + 7.1626473823662570789e-972j)  +/-  (5.62e-243, 5.62e-243j)
| (0.99204959373389580181 - 4.4031211372401870107e-970j)  +/-  (3.83e-241, 3.83e-241j)
| (0.87894873135818191454 + 1.4175116297941140418e-983j)  +/-  (6.3e-242, 6.3e-242j)
| (0.84028097800601346271 - 4.8176207534439952938e-989j)  +/-  (1.97e-242, 1.97e-242j)
| (-0.84028097800601346271 - 1.5457063299347369368e-994j)  +/-  (2.23e-242, 2.23e-242j)
| (-0.74819120483422523979 + 3.9491428293508914213e-995j)  +/-  (1.21e-243, 1.21e-243j)
| (-0.22895044993606806114 - 7.6826879387285585439e-1004j)  +/-  (1.02e-251, 1.02e-251j)
| (0.6382351642445890243 - 8.1210534986306664811e-995j)  +/-  (3.43e-245, 3.43e-245j)
| (0.74819120483422523979 - 2.5440955736739417894e-995j)  +/-  (1.3e-243, 1.3e-243j)
| (0.15340181725848333729 - 1.6020214008706605322e-1007j)  +/-  (4.4e-253, 4.4e-253j)
| (-0.69529487958595537749 - 1.0004012607603936298e-999j)  +/-  (2.42e-244, 2.42e-244j)
| (-0.57735026918962576451 + 3.1678396524519242471e-1002j)  +/-  (3.91e-246, 3.91e-246j)
| (0.076931927221067270328 - 9.6745361243291804651e-1010j)  +/-  (2.14e-254, 2.14e-254j)
| (0.69529487958595537749 - 4.0531117171523809426e-1003j)  +/-  (2.22e-244, 2.22e-244j)
| (0.44557757342561763168 + 3.6087549559825458912e-1008j)  +/-  (3.65e-248, 3.65e-248j)
| (-0.15340181725848333729 + 2.5232119325564673421e-1013j)  +/-  (4.4e-253, 4.4e-253j)
| (-0.6382351642445890243 + 3.1364073400289255323e-1007j)  +/-  (3.11e-245, 3.11e-245j)
| (-0.076931927221067270328 + 3.4271824644422072649e-1016j)  +/-  (2.38e-254, 2.38e-254j)
| (0.37547795047202195382 + 2.9936899362589254394e-1009j)  +/-  (2.77e-249, 2.77e-249j)
| (0.57735026918962576451 - 6.1020900711661823397e-1009j)  +/-  (4.13e-246, 4.13e-246j)
| (4.9487085269584400832e-1019 + 7.0542122726988186937e-1019j)  +/-  (3.53e-1017, 3.53e-1017j)
| (-0.44557757342561763168 + 1.0157906257540356223e-1013j)  +/-  (3.79e-248, 3.79e-248j)
| (-0.37547795047202195382 - 6.8861629164139027736e-1016j)  +/-  (2.8e-249, 2.8e-249j)
| (0.22895044993606806114 + 5.5750962050022078408e-1017j)  +/-  (9.91e-252, 9.91e-252j)
| (0.51300290286703822149 + 2.7259041441113045309e-1011j)  +/-  (4.13e-247, 4.13e-247j)
| (0.30312422659099277783 + 2.6778446675974967287e-1015j)  +/-  (1.64e-250, 1.64e-250j)
| (-0.30312422659099277783 + 1.9673701425024612883e-1016j)  +/-  (1.58e-250, 1.58e-250j)
| (-0.51300290286703822149 - 1.4485843490437283819e-1013j)  +/-  (3.91e-247, 3.91e-247j)
-------------------------------------------------
The weights are:
| (0.014431327317238711733 + 7.6392057417099875224e-876j)  +/-  (5.67e-73, 3.43e-189j)
| (0.0038570400037194831064 + 3.5362844857303190798e-878j)  +/-  (1.48e-73, 8.98e-190j)
| (0.025381048989001735125 + 4.021732392254780232e-877j)  +/-  (1.32e-73, 7.99e-190j)
| (0.0038570400037194831064 - 3.8473932127870550871e-876j)  +/-  (9.67e-74, 5.85e-190j)
| (0.025381048989001735125 + 1.9409855640169283016e-875j)  +/-  (5.79e-74, 3.5e-190j)
| (0.019896612446898296905 - 3.5253565392714735001e-875j)  +/-  (1.14e-73, 6.9e-190j)
| (0.036095665124602489694 + 5.6472446408540897318e-877j)  +/-  (5.71e-75, 3.46e-191j)
| (0.030803054762773037309 - 4.863451731896069755e-877j)  +/-  (9.01e-75, 5.46e-191j)
| (0.014431327317238711733 + 2.1461542781354559207e-877j)  +/-  (1.44e-75, 8.72e-192j)
| (0.046088847885879705612 + 6.8706831848433922135e-876j)  +/-  (1.6e-77, 9.7e-194j)
| (0.030803054762773037309 - 1.3556976903265454475e-875j)  +/-  (3.41e-76, 2.07e-192j)
| (0.0090685173654584272601 - 1.1795484054629534177e-877j)  +/-  (9.2e-76, 5.57e-192j)
| (0.019896612446898296905 - 3.1125154535729232229e-877j)  +/-  (8.84e-76, 5.35e-192j)
| (0.046088847885879705612 + 7.102887360451497029e-877j)  +/-  (9.14e-79, 5.53e-195j)
| (0.0090685173654584272601 + 1.9819370876223386211e-875j)  +/-  (1.09e-76, 6.58e-193j)
| (0.036095665124602489694 + 1.0358572828198208827e-875j)  +/-  (4.44e-78, 2.69e-194j)
| (0.041205496647483243243 - 8.3060055082067434158e-876j)  +/-  (1.1e-78, 6.65e-195j)
| (0.041205496647483243243 - 6.3885315412285343219e-877j)  +/-  (4.4e-79, 2.66e-195j)
| (0.050708582737060124517 - 7.8043588290161497099e-877j)  +/-  (1.06e-80, 6.44e-197j)
| (0.074936196460992836239 - 1.429587436530010911e-876j)  +/-  (1.82e-84, 1.1e-200j)
| (0.059030806890118619877 - 4.3610603410796167149e-876j)  +/-  (9.43e-83, 5.71e-199j)
| (0.050708582737060124517 - 5.8115880321928687397e-876j)  +/-  (2.53e-81, 1.53e-197j)
| (0.076085422753595939047 + 2.1095960276159809672e-876j)  +/-  (6.17e-85, 3.74e-201j)
| (0.055032207965305198667 + 8.5053480996446742656e-877j)  +/-  (1.16e-82, 7.02e-199j)
| (0.062678487100497261104 + 9.9496850146814886111e-877j)  +/-  (3.97e-84, 2.4e-200j)
| (0.076777773855388295801 - 1.9414046179815025724e-876j)  +/-  (1.47e-85, 8.92e-202j)
| (0.055032207965305198667 + 5.0002810255587548337e-876j)  +/-  (1.75e-83, 1.06e-199j)
| (0.068831219686668422462 + 3.0714971705150465339e-876j)  +/-  (6.73e-86, 4.07e-202j)
| (0.076085422753595939047 + 1.5387004183429443984e-876j)  +/-  (2.02e-86, 1.22e-202j)
| (0.059030806890118619877 - 9.2169982535695807576e-877j)  +/-  (2.83e-85, 1.72e-201j)
| (0.076777773855388295801 - 1.6588659879073471229e-876j)  +/-  (1.19e-86, 7.18e-203j)
| (0.071297949688735608816 - 2.7741920369086968661e-876j)  +/-  (2.92e-87, 1.77e-203j)
| (0.062678487100497261104 + 3.8460909096590452299e-876j)  +/-  (1.57e-86, 9.51e-203j)
| (0.077009027409239707977 + 1.7922317268000529845e-876j)  +/-  (3.08e-87, 1.86e-203j)
| (0.068831219686668422462 + 1.1518658862889442101e-876j)  +/-  (3.26e-88, 1.98e-204j)
| (0.071297949688735608816 - 1.2375991028010360105e-876j)  +/-  (2.51e-88, 1.52e-204j)
| (0.074936196460992836239 - 2.3008193416491011687e-876j)  +/-  (2.25e-88, 1.36e-204j)
| (0.065952117016998732992 - 3.4235670443439640406e-876j)  +/-  (2.49e-88, 1.51e-204j)
| (0.073337111596963976502 + 2.5201650576427779969e-876j)  +/-  (1.37e-88, 8.28e-205j)
| (0.073337111596963976502 + 1.3297301894869728771e-876j)  +/-  (2.17e-89, 1.33e-205j)
| (0.065952117016998732992 - 1.0713493266715263463e-876j)  +/-  (1.75e-89, 1.04e-205j)
