Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^40 - 99442554902096924593335/2322703455426597460151*t^38 + 21538780564496573187125218383/111229623073468899171711088*t^36 - 2120534429171687103569224608105/3948651619108145920595743624*t^34 + 16868444888432463587420835479895/16512543134452246577036746064*t^32 - 97681423926441879382690525306977/69146274375518782541341374143*t^30 + 406193457982009545788326617295155/276585097502075130165365496572*t^28 - 161896809230037335577795135483537/138292548751037565082682748286*t^26 + 3051286182836152403591966331894300/4217922736906645735021823822723*t^24 - 342343134167101406311761190155975/983626250899178254412203974469*t^22 + 1024765794654711681153632508143595/7869010007193426035297631795752*t^20 - 26720679482982857257074416743425/709500902287931855641589752076*t^18 + 419868071499793997769225049975410585/50463961176131441164363712706157576*t^16 - 129834093040067287612309947003675/94149181298752688739484538630891*t^14 + 4214550074198823318064594104828225/25231980588065720582181856353078788*t^12 - 5371631691689313417618203119360245/377332800612437366888083215461950966*t^10 + 1218953262828200686536142298596275/1509331202449749467552332861847803864*t^8 - 32447898402564857579923014498780/1158950744738200484013398447490277967*t^6 + 390483831960526183509126024677175/760271688548259517512789381553622346352*t^4 - 1423305454099564209301911420975/380135844274129758756394690776811173176*t^2 + 314194402584060284061625815/69115608049841774319344489232147486032
-------------------------------------------------
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:
| (0.99031124941720165779 - 3.2506355164393988439e-903j)  +/-  (5.85e-242, 5.85e-242j)
| (0.97626241096230051027 - 2.0995458890107591906e-931j)  +/-  (7.17e-242, 7.17e-242j)
| (-0.93006861040614755216 - 2.548343669227631145e-948j)  +/-  (4.7e-242, 4.7e-242j)
| (0.99815799487495133163 + 1.9945465664977149011e-949j)  +/-  (2.15e-242, 2.15e-242j)
| (0.95612522480196763798 - 1.3327388528583662223e-960j)  +/-  (6.51e-242, 6.51e-242j)
| (0.93006861040614755216 - 9.2470435738409706588e-971j)  +/-  (4.67e-242, 4.67e-242j)
| (-0.99815799487495133163 + 9.8179843975431861023e-975j)  +/-  (2.07e-242, 2.07e-242j)
| (-0.89831436300683475349 - 1.3693833302368774869e-977j)  +/-  (2.53e-242, 2.53e-242j)
| (-0.97626241096230051027 - 1.733673362305091669e-976j)  +/-  (7.01e-242, 7.01e-242j)
| (-0.41070570615375869495 - 1.6688305839924985571e-986j)  +/-  (9.59e-249, 9.59e-249j)
| (0.86113631159405257522 + 1.6098337336748673176e-978j)  +/-  (1.08e-242, 1.08e-242j)
| (-0.72048559114179543323 - 1.0909468448369111166e-984j)  +/-  (2.77e-244, 2.77e-244j)
| (-0.95612522480196763798 - 2.1373610463647866695e-981j)  +/-  (6.56e-242, 6.56e-242j)
| (-0.81885757232070341251 + 3.3703172954840361109e-984j)  +/-  (3.97e-243, 3.97e-243j)
| (-0.99031124941720165779 - 1.502875326853914197e-983j)  +/-  (5.89e-242, 5.89e-242j)
| (0.89831436300683475349 - 7.9016799960205872985e-985j)  +/-  (2.54e-242, 2.54e-242j)
| (0.81885757232070341251 + 1.2757129764363841688e-993j)  +/-  (3.64e-243, 3.64e-243j)
| (-0.86113631159405257522 - 1.2878358242853503791e-995j)  +/-  (1.14e-242, 1.14e-242j)
| (-0.77184332627235683064 - 9.7183019291468113544e-1000j)  +/-  (1.06e-243, 1.06e-243j)
| (0.26697016614198892427 + 3.6918862100203427114e-1007j)  +/-  (3.45e-251, 3.45e-251j)
| (0.77184332627235683064 - 5.8607256733204837858e-999j)  +/-  (1.11e-243, 1.11e-243j)
| (0.72048559114179543323 + 5.4088715589796626277e-1006j)  +/-  (2.62e-244, 2.62e-244j)
| (0.11581832907896636967 - 7.2454716371064794014e-1022j)  +/-  (1.01e-253, 1.01e-253j)
| (-0.66517705861346393267 + 1.5753654518527281965e-1012j)  +/-  (5.26e-245, 5.26e-245j)
| (-0.54407997016198122439 - 2.6724287874579760846e-1013j)  +/-  (1.05e-246, 1.05e-246j)
| (0.038701306682959597228 - 8.5382389881729219394e-1022j)  +/-  (6.29e-255, 6.29e-255j)
| (0.66517705861346393267 + 2.1881649750507112933e-1012j)  +/-  (5.53e-245, 5.53e-245j)
| (0.47882012508176154018 - 1.325797588457587072e-1018j)  +/-  (1.08e-247, 1.08e-247j)
| (-0.19208678265377540863 + 2.1510335416975050905e-1024j)  +/-  (1.84e-252, 1.84e-252j)
| (-0.6062765227666561157 + 1.4952856828641649896e-1018j)  +/-  (8.14e-246, 8.14e-246j)
| (-0.11581832907896636967 - 3.4356405316710760607e-1026j)  +/-  (1.13e-253, 1.13e-253j)
| (0.41070570615375869495 - 1.8918654167904776489e-1020j)  +/-  (9.66e-249, 9.66e-249j)
| (0.6062765227666561157 + 1.5073234336549826752e-1021j)  +/-  (8.04e-246, 8.04e-246j)
| (-0.038701306682959597228 - 3.7155942306500220647e-1033j)  +/-  (7.13e-255, 7.13e-255j)
| (-0.47882012508176154018 - 2.4568728360951664321e-1026j)  +/-  (1.14e-247, 1.14e-247j)
| (-0.26697016614198892427 - 1.4095145051508334369e-1029j)  +/-  (3.65e-251, 3.65e-251j)
| (0.19208678265377540863 - 1.1229934087939488063e-1030j)  +/-  (1.8e-252, 1.8e-252j)
| (0.54407997016198122439 + 1.2153010330096544128e-1027j)  +/-  (1.12e-246, 1.12e-246j)
| (0.3399810435848562648 + 1.1508922665690742503e-1033j)  +/-  (5.88e-250, 5.88e-250j)
| (-0.3399810435848562648 + 1.7694208381860932902e-1043j)  +/-  (6.97e-250, 6.97e-250j)
-------------------------------------------------
The weights are:
| (0.010961752712356627273 + 1.8940916882289280117e-903j)  +/-  (2.16e-72, 4.33e-190j)
| (0.017116731728354458488 - 5.0701566849080346558e-903j)  +/-  (1.15e-72, 2.3e-190j)
| (0.028946777879403670603 + 8.8923633421890873532e-905j)  +/-  (4.34e-75, 8.68e-193j)
| (0.0047252792575559705627 + 1.2842931011559447112e-903j)  +/-  (7.17e-73, 1.44e-190j)
| (0.023129475464604955913 + 3.3972554590653369575e-903j)  +/-  (2.42e-73, 4.84e-191j)
| (0.028946777879403670603 - 2.8346559428510278297e-903j)  +/-  (5.04e-74, 1.01e-191j)
| (0.0047252792575559705627 + 5.0679793448361860759e-906j)  +/-  (1.53e-76, 3.07e-194j)
| (0.034516038830448467449 - 1.2498898836338291589e-904j)  +/-  (2.82e-76, 5.65e-194j)
| (0.017116731728354458488 + 3.6220261484415717278e-905j)  +/-  (1.41e-76, 2.82e-194j)
| (0.069465982586288492895 + 8.0937101836658653496e-904j)  +/-  (3.51e-78, 7.03e-196j)
| (0.039786099825751978358 - 2.4242642472606702931e-903j)  +/-  (9.97e-77, 2e-194j)
| (0.053396965366017110795 - 3.6218310150416708638e-904j)  +/-  (7.76e-78, 1.55e-195j)
| (0.023129475464604955913 - 5.9667325538808472549e-905j)  +/-  (1.16e-76, 2.33e-194j)
| (0.044710270326342636025 - 2.2275341122899943805e-904j)  +/-  (4.46e-78, 8.93e-196j)
| (0.010961752712356627273 - 1.799063815047147769e-905j)  +/-  (4.7e-77, 9.42e-195j)
| (0.034516038830448467449 + 2.5659281950161096751e-903j)  +/-  (1.21e-78, 2.42e-196j)
| (0.044710270326342636025 + 2.3504805108638801666e-903j)  +/-  (4.7e-80, 9.42e-198j)
| (0.039786099825751978358 + 1.6914018522660002881e-904j)  +/-  (4.95e-78, 9.91e-196j)
| (0.049252446652239471998 + 2.8697613934259224691e-904j)  +/-  (7.17e-79, 1.43e-196j)
| (0.07402301535023506701 - 1.6715274639405728656e-903j)  +/-  (2.45e-83, 4.91e-201j)
| (0.049252446652239471998 - 2.3147394353220230858e-903j)  +/-  (3e-81, 6.01e-199j)
| (0.053396965366017110795 + 2.2963780009562723014e-903j)  +/-  (4.36e-82, 8.73e-200j)
| (0.076785034768797969667 - 1.4078919664410759267e-903j)  +/-  (1.52e-84, 3.05e-202j)
| (0.057159755180676878155 + 4.4728325796565241924e-904j)  +/-  (1.76e-82, 3.53e-200j)
| (0.063763085205863729259 + 6.3327247550754372652e-904j)  +/-  (9.96e-84, 1.99e-201j)
| (0.077354882993450116841 + 1.2965343576358600062e-903j)  +/-  (2.78e-85, 5.56e-203j)
| (0.057159755180676878155 - 2.2774356708211482948e-903j)  +/-  (1.66e-84, 3.32e-202j)
| (0.066722916025055194122 + 2.0807509144001417297e-903j)  +/-  (6e-86, 1.2e-203j)
| (0.075662075677686228882 - 1.0353205346011955825e-903j)  +/-  (1.27e-86, 2.55e-204j)
| (0.060591939723305627854 - 5.3922269462212439421e-904j)  +/-  (7.73e-85, 1.55e-202j)
| (0.076785034768797969667 + 1.1130626837839889349e-903j)  +/-  (1.01e-86, 2.02e-204j)
| (0.069465982586288492895 - 1.956403856482652849e-903j)  +/-  (2.61e-87, 5.24e-205j)
| (0.060591939723305627854 + 2.2417669574478604623e-903j)  +/-  (7.88e-87, 1.58e-204j)
| (0.077354882993450116841 - 1.1990086792514744027e-903j)  +/-  (3.7e-87, 7.4e-205j)
| (0.066722916025055194122 - 7.2443189434402396461e-904j)  +/-  (3.45e-87, 6.9e-205j)
| (0.07402301535023506701 + 9.6166575877786965565e-904j)  +/-  (6.67e-88, 1.34e-205j)
| (0.075662075677686228882 + 1.5336049114589922012e-903j)  +/-  (3.23e-88, 6.53e-206j)
| (0.063763085205863729259 - 2.1775428375207978486e-903j)  +/-  (1.39e-88, 2.8e-206j)
| (0.071929474445565347849 + 1.8157895726576332256e-903j)  +/-  (1.25e-88, 2.52e-206j)
| (0.071929474445565347849 - 8.8767168895628438873e-904j)  +/-  (1.13e-88, 2.18e-206j)
