Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^46 - 58150556269699455354703425525/1192044575353714673205208984*t^44 + 270169689851449993205748104734557/1064495805790867203172251622712*t^42 - 2493117999986844532286857514591103/3046660409677309581492996023624*t^40 + 211613978989864646504531559591607045/115538737074685663359695926126664*t^38 - 1451198726455484551776436228119880245/480397906784219337127156745474024*t^36 + 5482218677898395559472679633660204075/1441193720352658011381470236422072*t^34 - 528274698121729202464652823415314737/141293501995358628566810807492360*t^32 + 14997285172133599566237258034698976951/5157212822830589942688594473471140*t^30 - 40999399177907173916502434724507397781/22727303405439634299158702541710748*t^28 + 2261436916251126872852981400625997385/2525255933937737144350966949078972*t^26 - 60157459403362020298878030543278643975/169192147573828388671514785588291124*t^24 + 19023098554081143237942552549596315257/169192147573828388671514785588291124*t^22 - 4753165940958363792155576333812597989/169192147573828388671514785588291124*t^20 + 735162045491439615611274600794849669265/134169373026045912216511224971514861332*t^18 - 6490555033165591645570503352551516666055/7915993008536708820774162273319376818588*t^16 + 1455096876333216826422155864299336379625/15831986017073417641548324546638753637176*t^14 - 9092497912468918307388819044260472697/1217845078236416741657563426664519510552*t^12 + 81220092104565445848182376747820284971/193637367439590261923552584839658602177768*t^10 - 982033322986958773268249809076470845/64545789146530087307850861613219534059256*t^8 + 282789520446973845347353227402255/884188892418220374080148789222185398072*t^6 - 47102970247785497832996711050979925/14624919776619003812246028808213220097814408*t^4 + 70116914736113801282319404187389997/6859087375234312787943387511052000225874957352*t^2 - 10867813639967629873750291807569/6859087375234312787943387511052000225874957352
-------------------------------------------------
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: 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:
| (0.96689092921835009486 - 4.1792577162278471786e-840j)  +/-  (8.29e-240, 8.29e-240j)
| (-0.98212561584392262702 - 2.5889005319547604218e-846j)  +/-  (8.5e-240, 8.5e-240j)
| (-0.94707726193498441869 + 3.5184444384407903432e-855j)  +/-  (6.87e-240, 6.87e-240j)
| (0.99271519633075330712 - 3.4181930502738036022e-864j)  +/-  (6.25e-240, 6.25e-240j)
| (0.94707726193498441869 + 4.4712500753992657491e-880j)  +/-  (6.6e-240, 6.6e-240j)
| (0.92277162270717414344 + 3.4927503336469708825e-894j)  +/-  (3.48e-240, 3.48e-240j)
| (-0.99271519633075330712 + 3.9901799203876761586e-895j)  +/-  (5.9e-240, 5.9e-240j)
| (-0.92277162270717414344 - 3.2073076073193807221e-899j)  +/-  (3.56e-240, 3.56e-240j)
| (0.78309499725657700476 - 2.6195523769763150235e-903j)  +/-  (5.86e-242, 5.86e-242j)
| (0.99861616469502664426 - 3.3144409056420386778e-905j)  +/-  (2.02e-240, 2.02e-240j)
| (0.89408180003437574258 + 2.7315493746879994294e-920j)  +/-  (1.86e-240, 1.86e-240j)
| (-0.99861616469502664426 + 2.884848935024934643e-921j)  +/-  (2e-240, 2e-240j)
| (-0.86113631159405257522 + 6.2512964002529756812e-926j)  +/-  (6.65e-241, 6.65e-241j)
| (-0.78309499725657700476 + 5.2196599250734973178e-927j)  +/-  (6.08e-242, 6.08e-242j)
| (0.98212561584392262702 + 1.3130875979201381317e-932j)  +/-  (8.45e-240, 8.45e-240j)
| (0.86113631159405257522 + 1.617798022527625724e-940j)  +/-  (6.61e-241, 6.61e-241j)
| (0.82408425217062029856 - 1.9542616413540625585e-944j)  +/-  (2.31e-241, 2.31e-241j)
| (-0.96689092921835009486 + 7.7670575784766174896e-946j)  +/-  (8.4e-240, 8.4e-240j)
| (-0.82408425217062029856 + 2.4884834456277859228e-950j)  +/-  (2.32e-241, 2.32e-241j)
| (-0.89408180003437574258 - 3.4658221518802236673e-956j)  +/-  (1.74e-240, 1.74e-240j)
| (0.46637401584580201328 - 1.0032148319758835462e-965j)  +/-  (5.04e-247, 5.04e-247j)
| (0.73835774726211562588 - 6.9241038182857752822e-963j)  +/-  (1.31e-242, 1.31e-242j)
| (0.52636877438374223633 - 1.0308676171604173168e-966j)  +/-  (5.38e-246, 5.38e-246j)
| (-0.73835774726211562588 + 3.1381724425276311501e-963j)  +/-  (1.24e-242, 1.24e-242j)
| (-0.69008091451335593885 + 3.0902166190295183366e-966j)  +/-  (2.51e-243, 2.51e-243j)
| (-0.012777243886479415201 - 4.3565285097307016011e-970j)  +/-  (1.77e-255, 1.77e-255j)
| (0.69008091451335593885 + 5.6119070799625658623e-966j)  +/-  (2.48e-243, 2.48e-243j)
| (0.27421975056972706784 - 6.418382612557504321e-972j)  +/-  (1.68e-250, 1.68e-250j)
| (-0.20721956620699809339 - 1.9587239649565206769e-973j)  +/-  (9.32e-252, 9.32e-252j)
| (-0.63849137106028361228 + 2.9455040244933684544e-970j)  +/-  (3.91e-244, 3.91e-244j)
| (-0.27421975056972706784 + 1.2345518964552100954e-975j)  +/-  (1.66e-250, 1.66e-250j)
| (0.3399810435848562648 - 7.314314832067141878e-973j)  +/-  (2.81e-249, 2.81e-249j)
| (0.63849137106028361228 - 1.6918105791904630493e-970j)  +/-  (3.7e-244, 3.7e-244j)
| (0.012777243886479415201 + 1.7432370347289736804e-974j)  +/-  (1.77e-255, 1.77e-255j)
| (-0.58383359399162970254 - 1.9322704560165905906e-974j)  +/-  (4.89e-245, 4.89e-245j)
| (-0.4041418932976043975 + 3.941358585844266251e-977j)  +/-  (4.06e-248, 4.06e-248j)
| (0.071781092459819505462 + 3.0522612404834081222e-978j)  +/-  (2.43e-254, 2.43e-254j)
| (0.58383359399162970254 + 1.2695944929009295575e-976j)  +/-  (5.04e-245, 5.04e-245j)
| (0.13943297812458426778 + 7.6199933150897834375e-982j)  +/-  (4.39e-253, 4.39e-253j)
| (-0.3399810435848562648 - 4.4749475760243005835e-981j)  +/-  (3.05e-249, 3.05e-249j)
| (-0.52636877438374223633 - 5.48736107434000696e-979j)  +/-  (5.37e-246, 5.37e-246j)
| (-0.13943297812458426778 + 3.1184657360367328537e-983j)  +/-  (4.78e-253, 4.78e-253j)
| (0.20721956620699809339 + 4.2436748083391447759e-983j)  +/-  (8.63e-252, 8.63e-252j)
| (0.4041418932976043975 - 6.9093777561296393536e-980j)  +/-  (4.08e-248, 4.08e-248j)
| (-0.071781092459819505462 - 4.2078866658763345866e-983j)  +/-  (2.94e-254, 2.94e-254j)
| (-0.46637401584580201328 - 6.4558520559581176786e-981j)  +/-  (5.06e-247, 5.06e-247j)
-------------------------------------------------
The weights are:
| (0.017536945596132990409 + 1.134817332380515406e-840j)  +/-  (2.12e-69, 5.15e-185j)
| (0.012921396757076424766 + 2.3582843610801178793e-842j)  +/-  (6.44e-70, 1.57e-185j)
| (0.022075887035609680066 + 5.4747053873211204419e-842j)  +/-  (6.32e-70, 1.54e-185j)
| (0.0082503343049614699135 - 9.046394517633685694e-841j)  +/-  (2.47e-70, 6.01e-186j)
| (0.022075887035609680066 - 5.2886869458305751467e-840j)  +/-  (3.93e-70, 9.55e-186j)
| (0.026517426059785966092 + 3.178025076895516065e-840j)  +/-  (1.41e-70, 3.43e-186j)
| (0.0082503343049614699135 - 1.1923210759993504545e-842j)  +/-  (6.7e-72, 1.63e-187j)
| (0.026517426059785966092 - 7.4197912183059534477e-842j)  +/-  (4.27e-72, 1.04e-187j)
| (0.042896409789099248097 + 1.763435681521623141e-840j)  +/-  (1.45e-72, 3.53e-188j)
| (0.0035506220652060331582 + 2.1013180434577173016e-841j)  +/-  (2.59e-71, 6.29e-187j)
| (0.03084079722595927903 - 2.4659647483665039954e-840j)  +/-  (8.78e-72, 2.14e-187j)
| (0.0035506220652060331582 + 3.392030071267572268e-843j)  +/-  (9.77e-73, 2.38e-188j)
| (0.035025325617413830496 - 1.2197592973979983086e-841j)  +/-  (2.3e-74, 5.59e-190j)
| (0.042896409789099248097 - 1.8520734950504704051e-841j)  +/-  (2.81e-75, 6.83e-191j)
| (0.012921396757076424766 + 3.017141135282113596e-840j)  +/-  (1.4e-71, 3.41e-187j)
| (0.035025325617413830496 + 2.1084447169396789457e-840j)  +/-  (3.97e-73, 9.66e-189j)
| (0.039050556378559998417 - 1.89720559643343985e-840j)  +/-  (8.85e-74, 2.15e-189j)
| (0.017536945596132990409 - 3.7897058735351139484e-842j)  +/-  (9.88e-74, 2.4e-189j)
| (0.039050556378559998417 + 1.5127591427470312766e-841j)  +/-  (1.21e-75, 2.95e-191j)
| (0.03084079722595927903 + 9.6477496024176102841e-842j)  +/-  (9.44e-75, 2.3e-190j)
| (0.061163493825138926421 + 1.7261555524537328553e-840j)  +/-  (6.17e-79, 1.5e-194j)
| (0.046543342191803564982 - 1.6784112678684439463e-840j)  +/-  (7.94e-77, 1.93e-192j)
| (0.058777266912238757814 - 1.6532724202247534418e-840j)  +/-  (9.4e-79, 2.29e-194j)
| (0.046543342191803564982 + 2.2493537585564167745e-841j)  +/-  (3.51e-78, 8.55e-194j)
| (0.049972496905307261356 - 2.7210044176538617305e-841j)  +/-  (3.39e-79, 8.24e-195j)
| (0.038688545821892509107 + 1.7512016600651542673e-839j)  +/-  (2.85e-82, 6.94e-198j)
| (0.049972496905307261356 + 1.628787088961184673e-840j)  +/-  (7.81e-79, 1.9e-194j)
| (0.066445199359572414064 - 2.3485387063143897809e-840j)  +/-  (1.06e-81, 2.57e-197j)
| (0.067483109322299820271 - 1.868215386110600309e-840j)  +/-  (6.42e-83, 1.56e-198j)
| (0.05316582869611947687 + 3.2904531022346699318e-841j)  +/-  (2.22e-81, 5.41e-197j)
| (0.066445199359572414064 + 1.310732134834886622e-840j)  +/-  (3.27e-83, 7.94e-199j)
| (0.065017803338095236323 + 2.0383958798298135209e-840j)  +/-  (2.25e-82, 5.47e-198j)
| (0.05316582869611947687 - 1.6085442931515357685e-840j)  +/-  (3.49e-81, 8.5e-197j)
| (0.038688545821892509107 - 1.7981050077262687297e-839j)  +/-  (4.64e-83, 1.13e-198j)
| (0.05610617967248176325 - 3.9919549687701582847e-841j)  +/-  (3.05e-83, 7.4e-199j)
| (0.063249359457715398706 + 7.580188085743415355e-841j)  +/-  (2.32e-84, 5.65e-200j)
| (0.066755349005340080314 + 6.9839530037869835408e-840j)  +/-  (6.46e-84, 1.57e-199j)
| (0.05610617967248176325 + 1.616060661191629921e-840j)  +/-  (4.98e-83, 1.21e-198j)
| (0.067966324662189870078 - 3.9737659455302828252e-840j)  +/-  (2.19e-84, 5.33e-200j)
| (0.065017803338095236323 - 9.778226962918732221e-841j)  +/-  (6.52e-85, 1.58e-200j)
| (0.058777266912238757814 + 4.8772597658273335256e-841j)  +/-  (3.71e-85, 9.03e-201j)
| (0.067966324662189870078 + 2.9721158780410385157e-840j)  +/-  (3.52e-85, 8.6e-201j)
| (0.067483109322299820271 + 2.8874231654079873361e-840j)  +/-  (2.35e-85, 5.72e-201j)
| (0.063249359457715398706 - 1.8467737613131347477e-840j)  +/-  (1.45e-85, 3.52e-201j)
| (0.066755349005340080314 - 6.0186503302559082783e-840j)  +/-  (2.82e-85, 6.95e-201j)
| (0.061163493825138926421 - 6.0279749533121105605e-841j)  +/-  (3.26e-86, 7.51e-202j)
