Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 44
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^51 - 1005602208226355264863399521925600079452611046394881794120863277946/441205073237585111427986598071543479440417793326604661306488215*t^49 + 1578648344836693772765510286824389712465748760765073651756033524771339/2647230439425510668567919588429260876642506759959627967838929290*t^47 - 503867042966654807842557410376747824396673842085911962738813493936065801/5294460878851021337135839176858521753285013519919255935677858580*t^45 + 2442320492300985512437979835094949247982001421045204714070626175476797009/235309372393378726094926185638156522368222823107522486030127048*t^43 - 9429091354233355031527991495031583927646842827348282245342427198885465751/11478505970408718346093960275032025481376723078415731025859856*t^41 + 1122695456505320414296696019614199303262168053123764658509494574071168080233/22957011940817436692187920550064050962753446156831462051719712*t^39 - 102864654767907028028524881724921997713096609682385776580269122840769024019099/45914023881634873384375841100128101925506892313662924103439424*t^37 + 7358912885180672359380219917173250546849355472340251618576003897967460566361081/91828047763269746768751682200256203851013784627325848206878848*t^35 - 414777971664272962311676291438951672762847650279877540245713829824128710409224215/183656095526539493537503364400512407702027569254651696413757696*t^33 + 9254435879929143477638519776476018511091857215662559690204510782845868693610380955/183656095526539493537503364400512407702027569254651696413757696*t^31 - 327436308925677321056070661482031501009178932193023187407841986871272754205504433065/367312191053078987075006728801024815404055138509303392827515392*t^29 + 9172624170635292761088268343119128239022270991648846358983400634191291698626662741445/734624382106157974150013457602049630808110277018606785655030784*t^27 - 202595193177776064810482061291945960611090434717381661527632653783114151947108185282155/1469248764212315948300026915204099261616220554037213571310061568*t^25 + 3503515113744404513682514953241690798866056186857441444231891709555390205693523507133625/2938497528424631896600053830408198523232441108074427142620123136*t^23 - 46967162539282914228537165325081273169099960985083571215453007008186421343621787408278875/5876995056849263793200107660816397046464882216148854285240246272*t^21 + 240817352237233470261080518108019398307539286918342057640279813884708866574686404530296125/5876995056849263793200107660816397046464882216148854285240246272*t^19 - 1856740398550340787592204414966204247648939795113778036854762433541750853755739155889019625/11753990113698527586400215321632794092929764432297708570480492544*t^17 + 42116610256241757962203702323850437178982826588543882906261416564058781201408511564071870875/94031920909588220691201722573062352743438115458381668563843940352*t^15 - 170829067366143724909574776874798516776125015505559465161527695580501543283320396940118105625/188063841819176441382403445146124705486876230916763337127687880704*t^13 + 478443700645597413324555951381348023304569186064074054638290237438917310499473830846786488125/376127683638352882764806890292249410973752461833526674255375761408*t^11 - 884839217779094461151583205591670638725305015574576249854656083853450494439105826414928451875/752255367276705765529613780584498821947504923667053348510751522816*t^9 + 1019735435000173567567120060098283728257090768966904321912110976940879198724858053717858543125/1504510734553411531059227561168997643895009847334106697021503045632*t^7 - 673858582897466298140717704369352787723460028257109961088543289073291498794044050963328269375/3009021469106823062118455122337995287790019694668213394043006091264*t^5 + 218723989830113167227044348670347886187337668236811373747945748063243474216680227475279090625/6018042938213646124236910244675990575580039389336426788086012182528*t^3 - 22941860727408634407145518307317406655924897303854607634057799027572598365988321418988909375/12036085876427292248473820489351981151160078778672853576172024365056*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:
| (-8.3258977441499024561 + 8.4094049369938766243e-591j)  +/-  (1.47e-245, 1.47e-245j)
| (-3.4539732931295847091 - 2.0653334221330776113e-590j)  +/-  (4.6e-245, 4.6e-245j)
| (-7.2833055068866304613 + 4.6023607619554591557e-590j)  +/-  (3.15e-244, 3.15e-244j)
| (-8.9893634617718392219 + 1.5362507129975055534e-592j)  +/-  (1.05e-246, 1.05e-246j)
| (-2.7891834353705420644 + 5.1587913717859599337e-591j)  +/-  (2.99e-246, 2.99e-246j)
| (-1.8217012280327741202 + 1.6954992718041759928e-593j)  +/-  (1.98e-248, 1.98e-248j)
| (-5.5995595999326094305 - 1.0563635696552494939e-589j)  +/-  (2.03e-243, 2.03e-243j)
| (-3.7937209692808930218 + 1.4762453942803291021e-589j)  +/-  (1.38e-244, 1.38e-244j)
| (-2.1407450959608822851 + 2.4540284931700494982e-592j)  +/-  (1.23e-247, 1.23e-247j)
| (-0.85449450269241699599 - 1.9411510221934169438e-595j)  +/-  (1.01e-250, 1.01e-250j)
| (-6.8284392577506947691 + 2.1861148657322121402e-589j)  +/-  (7.75e-244, 7.75e-244j)
| (-4.4914069267682216972 - 1.1138273501156439758e-588j)  +/-  (6.84e-244, 6.84e-244j)
| (-4.8512419476656990626 - 1.6061704922162980057e-589j)  +/-  (1.15e-243, 1.15e-243j)
| (-4.1392493976380221226 - 1.1122913355294397849e-589j)  +/-  (3.5e-244, 3.5e-244j)
| (-1.4775917009963931368e-615 + 1.4236980939521274978e-615j)  +/-  (1.05e-613, 1.05e-613j)
| (-2.4631197782145911371 + 9.9458333030556005565e-592j)  +/-  (7.26e-247, 7.26e-247j)
| (-0.65350976120820342009 + 5.8132091979514301069e-596j)  +/-  (4.31e-251, 4.31e-251j)
| (-7.7754886728225648477 + 2.4648694385163105903e-590j)  +/-  (8.96e-245, 8.96e-245j)
| (-5.2200673136101050789 - 7.587161098214128667e-589j)  +/-  (1.74e-243, 1.74e-243j)
| (-1.5054482028623358456 - 2.7867822055305143723e-594j)  +/-  (2.75e-249, 2.75e-249j)
| (-1.1902088616956247245 - 7.3123243338743916496e-595j)  +/-  (4.28e-250, 4.28e-250j)
| (-0.7071067811865475244 - 6.8032779946426785641e-596j)  +/-  (9.08e-251, 9.08e-251j)
| (0.3044941579536236322 + 2.8838185586831296627e-598j)  +/-  (1.32e-253, 1.32e-253j)
| (-5.9919174821245687141 + 1.4361673549813689593e-588j)  +/-  (1.97e-243, 1.97e-243j)
| (-0.3044941579536236322 - 2.6664652597187107484e-598j)  +/-  (1.49e-253, 1.49e-253j)
| (-6.4001272690694489428 - 1.2364836540909005726e-588j)  +/-  (1.52e-243, 1.52e-243j)
| (-3.1193152237293773227 + 1.1268844049434759329e-590j)  +/-  (1.25e-245, 1.25e-245j)
| (7.7754886728225648477 + 7.9133490703791071587e-588j)  +/-  (8.43e-245, 8.43e-245j)
| (5.5995595999326094305 + 4.5288448229284703468e-602j)  +/-  (2.1e-243, 2.1e-243j)
| (8.3258977441499024561 - 3.1206150526927295239e-615j)  +/-  (1.53e-245, 1.53e-245j)
| (6.8284392577506947691 + 6.7678257328269061628e-627j)  +/-  (8.2e-244, 8.2e-244j)
| (6.4001272690694489428 - 1.8790263633743157621e-647j)  +/-  (1.38e-243, 1.38e-243j)
| (4.1392493976380221226 + 4.2821923631887948506e-661j)  +/-  (3.29e-244, 3.29e-244j)
| (1.1902088616956247245 - 5.8030975148014037214e-678j)  +/-  (3.93e-250, 3.93e-250j)
| (1.5054482028623358456 - 4.3281878679830295011e-677j)  +/-  (2.97e-249, 2.97e-249j)
| (8.9893634617718392219 + 2.7137175773844745902e-671j)  +/-  (1.03e-246, 1.03e-246j)
| (7.2833055068866304613 + 2.4615676544675873879e-675j)  +/-  (3.25e-244, 3.25e-244j)
| (2.7891834353705420644 + 1.6679918909294666723e-692j)  +/-  (3.32e-246, 3.32e-246j)
| (5.9919174821245687141 + 9.5217593714675104272e-719j)  +/-  (2.1e-243, 2.1e-243j)
| (0.65350976120820342009 + 5.7916287651924515121e-746j)  +/-  (4.02e-251, 4.02e-251j)
| (1.8217012280327741202 - 2.9996339220180047129e-743j)  +/-  (2.06e-248, 2.06e-248j)
| (4.4914069267682216972 - 1.3273518718442865315e-737j)  +/-  (7.04e-244, 7.04e-244j)
| (3.1193152237293773227 - 3.045767566986985149e-755j)  +/-  (1.25e-245, 1.25e-245j)
| (0.85449450269241699599 + 2.8210647446315701649e-773j)  +/-  (1.02e-250, 1.02e-250j)
| (2.1407450959608822851 - 5.8277071069076039783e-765j)  +/-  (1.25e-247, 1.25e-247j)
| (5.2200673136101050789 - 3.8481010555508263298e-771j)  +/-  (1.7e-243, 1.7e-243j)
| (2.4631197782145911371 + 8.0183132806332338259e-790j)  +/-  (7.51e-247, 7.51e-247j)
| (3.4539732931295847091 - 1.0689184152460001745e-786j)  +/-  (4.65e-245, 4.65e-245j)
| (4.8512419476656990626 + 6.9740687496811539284e-804j)  +/-  (1.17e-243, 1.17e-243j)
| (0.7071067811865475244 + 1.9407966826688825994e-833j)  +/-  (8.95e-251, 8.95e-251j)
| (3.7937209692808930218 - 2.9562502648761810165e-824j)  +/-  (1.37e-244, 1.37e-244j)
-------------------------------------------------
The weights are:
| (2.6197411328884315762e-31 + 4.8235520499544322912e-610j)  +/-  (4.21e-62, 1.44e-182j)
| (1.2533700065926849335e-06 - 2.4171115522736873589e-595j)  +/-  (4.63e-44, 1.58e-164j)
| (2.4367037046626328612e-24 + 2.6889263457412625617e-606j)  +/-  (1.38e-59, 4.7e-180j)
| (3.4732107730485473174e-36 - 1.2455369927992437508e-612j)  +/-  (3.9e-64, 1.33e-184j)
| (7.7397015020520008677e-05 - 9.2689870335087553292e-595j)  +/-  (3.37e-41, 1.15e-161j)
| (0.0064855983493854003701 + 2.0048360590784726661e-593j)  +/-  (7.73e-34, 2.64e-154j)
| (5.249542191488816307e-15 + 3.2588216639317157217e-601j)  +/-  (3.63e-55, 1.24e-175j)
| (1.0854125757326133001e-07 + 4.6437646380609292921e-596j)  +/-  (1.85e-47, 6.3e-168j)
| (0.0018499946344094857399 - 8.8401487283947801253e-594j)  +/-  (4.33e-38, 1.48e-158j)
| (0.1163725398627228025 - 1.2427611776326314809e-591j)  +/-  (1.15e-35, 3.93e-156j)
| (1.3964616309796177438e-21 - 8.5946633061034272293e-605j)  +/-  (3.89e-59, 1.33e-179j)
| (3.4811727517602764377e-10 - 3.4238393871164656048e-597j)  +/-  (1.79e-51, 6.11e-172j)
| (1.2351039099896948869e-11 - 3.0607406217254842301e-599j)  +/-  (3.83e-53, 1.31e-173j)
| (7.1273084294098130997e-09 + 1.3934752942572556075e-596j)  +/-  (3.01e-50, 1.03e-170j)
| (0.17085401579780080227 - 4.610186310222220164e-592j)  +/-  (5.46e-37, 1.86e-157j)
| (0.00042397336924751144921 + 3.4887774623008596004e-594j)  +/-  (1.53e-43, 5.24e-164j)
| (0.28295942920690418467 - 4.2874952845194854428e-591j)  +/-  (1.16e-36, 3.97e-157j)
| (1.6133728721842963634e-27 - 5.1515746431500042332e-608j)  +/-  (1.91e-63, 6.53e-184j)
| (3.0901442671504362662e-13 - 4.6671711141192636527e-600j)  +/-  (5.03e-55, 1.72e-175j)
| (0.01843947159596942475 - 5.485095486300733049e-593j)  +/-  (1.04e-40, 3.55e-161j)
| (0.043319507797358984234 + 1.6102438677563370638e-592j)  +/-  (4.96e-39, 1.69e-159j)
| (-0.21395377658162094653 + 5.0714733333770464449e-591j)  +/-  (1.23e-36, 4.21e-157j)
| (0.15858633864307392257 + 4.854346282957280266e-592j)  +/-  (3.99e-38, 1.36e-158j)
| (5.7630671792696565868e-17 - 2.9264644079722306502e-602j)  +/-  (2.56e-58, 8.73e-179j)
| (0.15858633864307392257 + 5.7754948578331951951e-592j)  +/-  (5.05e-39, 1.73e-159j)
| (3.8245511072502248842e-19 + 1.884463235963377338e-603j)  +/-  (9.82e-60, 3.35e-180j)
| (1.1148809273077487745e-05 + 1.4637092133367331628e-594j)  +/-  (3.27e-49, 1.12e-169j)
| (1.6133728721842963634e-27 + 2.1865579408423600105e-608j)  +/-  (1.16e-77, 3.97e-198j)
| (5.249542191488816307e-15 - 1.3035590995657347591e-601j)  +/-  (2.78e-72, 9.51e-193j)
| (2.6197411328884315762e-31 - 2.1645983108048070084e-610j)  +/-  (2.54e-79, 8.68e-200j)
| (1.3964616309796177438e-21 + 3.2754267167562034807e-605j)  +/-  (5.62e-76, 1.92e-196j)
| (3.8245511072502248842e-19 - 6.8630467492314263163e-604j)  +/-  (3.97e-75, 1.36e-195j)
| (7.1273084294098130997e-09 - 4.4445160251560500721e-598j)  +/-  (1.96e-70, 6.7e-191j)
| (0.043319507797358984234 + 7.9933992437703793472e-593j)  +/-  (7.04e-55, 2.41e-175j)
| (0.01843947159596942475 - 2.2226322447522253014e-593j)  +/-  (5.85e-58, 2e-178j)
| (3.4732107730485473174e-36 + 5.9311276303000032385e-613j)  +/-  (1.5e-82, 5.14e-203j)
| (2.4367037046626328612e-24 - 1.0806195398515949649e-606j)  +/-  (1.91e-77, 6.53e-198j)
| (7.7397015020520008677e-05 - 1.806333407903295421e-595j)  +/-  (1.76e-67, 6e-188j)
| (5.7630671792696565868e-17 + 1.069828330839784755e-602j)  +/-  (6.74e-75, 2.3e-195j)
| (0.28295942920690418467 - 2.9441512814407063085e-591j)  +/-  (3.14e-59, 1.07e-179j)
| (0.0064855983493854003701 + 6.9037988917219432471e-594j)  +/-  (6.54e-64, 2.23e-184j)
| (3.4811727517602764377e-10 + 7.3687657928064709221e-599j)  +/-  (1.12e-72, 3.83e-193j)
| (1.1148809273077487745e-05 + 4.6838122840751360492e-596j)  +/-  (1.88e-69, 6.43e-190j)
| (0.1163725398627228025 - 7.5777121155754791676e-592j)  +/-  (3.78e-61, 1.29e-181j)
| (0.0018499946344094857399 - 2.1495917518359041422e-594j)  +/-  (1.46e-66, 4.99e-187j)
| (3.0901442671504362662e-13 + 1.2864522659543278852e-600j)  +/-  (1.11e-74, 3.81e-195j)
| (0.00042397336924751144921 + 6.4318817971757176646e-595j)  +/-  (4.54e-68, 1.55e-188j)
| (1.2533700065926849335e-06 - 1.106427533844014457e-596j)  +/-  (3.34e-71, 1.14e-191j)
| (1.2351039099896948869e-11 - 1.0562228149693743251e-599j)  +/-  (1.62e-74, 5.6e-195j)
| (-0.21395377658162094653 + 3.3745555268738419288e-591j)  +/-  (9.74e-66, 4.21e-186j)
| (1.0854125757326133001e-07 + 2.3520103397380578147e-597j)  +/-  (3.62e-72, 1.23e-192j)
