Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 46
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^52 - 96910730173583252789741653714404432172253538591/80964040822769236086438610409798986828626122*t^50 + 2190578021213532952928633995168620236945969557596873/3319525673733538679543983026801758459973671002*t^48 - 1478417127770253586971305973249196889401289277598818675/6639051347467077359087966053603516919947342004*t^46 + 48897949746638785790060949731265618724079495721648866655/948435906781011051298280864800502417135334572*t^44 - 57767876057473864822825345394666529287792625114667481049165/6639051347467077359087966053603516919947342004*t^42 + 25685160867328618607139313640891121007554269120530543119645/23132583092219781738982460117085424808178892*t^40 - 2537181742068409913914295178287396507034011059555062219113835/23132583092219781738982460117085424808178892*t^38 + 197038963526263401126993860772220011116370195120970535504086725/23132583092219781738982460117085424808178892*t^36 - 12153106968571775154867756749241050077094801066491402061269154175/23132583092219781738982460117085424808178892*t^34 + 599045256741150959441916597224990383402317321272313000316599324825/23132583092219781738982460117085424808178892*t^32 - 11836128753410428936201456347714056424975943814724228811016213340225/11566291546109890869491230058542712404089446*t^30 + 375187009722816583454422993868165433035814693341031771801408804588675/11566291546109890869491230058542712404089446*t^28 - 9523146971005637426495883232907412218835858733169852062450390480920375/11566291546109890869491230058542712404089446*t^26 + 192777169351650029296300419769224594852829503854298708658114858044875625/11566291546109890869491230058542712404089446*t^24 - 3092304002186597449945552375041688525321973191579320892411467566149486875/11566291546109890869491230058542712404089446*t^22 + 38949064139277880115669069119506272091526733952725959686233118861696436875/11566291546109890869491230058542712404089446*t^20 - 190236860392608381338390215991981928191120823133916680477436965858930447500/5783145773054945434745615029271356202044723*t^18 + 1417611775334972323999771194148840451360754030479806780788784859131954425000/5783145773054945434745615029271356202044723*t^16 - 31529565569182270414682110838246329416757242071233328929038189968746991690625/23132583092219781738982460117085424808178892*t^14 + 126957445333610129324635097262221306877274629221127529257258151749259467871875/23132583092219781738982460117085424808178892*t^12 - 355156020357775734655648097863687596177942506598132333460438285783285172559375/23132583092219781738982460117085424808178892*t^10 + 650310631216898479262356899961877099524288716565542164778964632430095535490625/23132583092219781738982460117085424808178892*t^8 - 712039729392315413194121441119861825350790883317773509577103617860684129859375/23132583092219781738982460117085424808178892*t^6 + 401253925882513843243752621840528266021556760064046056253546344502323810015625/23132583092219781738982460117085424808178892*t^4 - 86720426327224405950458476341784101866456955338684444866782958230861014859375/23132583092219781738982460117085424808178892*t^2 + 2982596674546431351816170394147241760734082906434382750366146651493793515625/23132583092219781738982460117085424808178892
-------------------------------------------------
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
Positive weights:   52 out of 52
Indefinite weights: 0 out of 52
Negative weights:   0 out of 52
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-12.857828364194572608 + 3.6121488906306517077e-534j)  +/-  (2.17e-246, 2.17e-246j)
| (-10.454070172906462789 + 1.7673733987061866219e-531j)  +/-  (8.28e-244, 8.28e-244j)
| (-3.6739274246308077709 - 9.086569880097166974e-532j)  +/-  (2.03e-245, 2.03e-245j)
| (4.5938043248288415668 - 9.0375446394894252419e-532j)  +/-  (1.21e-244, 1.21e-244j)
| (9.8134009805449896244 + 5.5766359863173192704e-536j)  +/-  (2.05e-243, 2.05e-243j)
| (-9.8134009805449896244 + 1.7791508433791846384e-549j)  +/-  (2.13e-243, 2.13e-243j)
| (10.454070172906462789 + 3.8806058340668063244e-564j)  +/-  (7.71e-244, 7.71e-244j)
| (-11.147406802456399926 - 6.6281573872934430963e-574j)  +/-  (2.06e-244, 2.06e-244j)
| (-3.3242574335521189524 - 3.6788937584515349742e-581j)  +/-  (1.74e-245, 1.74e-245j)
| (8.08306806291426153 - 3.2302908740838760636e-591j)  +/-  (6.67e-243, 6.67e-243j)
| (3.3242574335521189524 + 2.2548808934006917565e-603j)  +/-  (1.72e-245, 1.72e-245j)
| (5.0642108883881029295 - 2.8499040285112325386e-602j)  +/-  (3.06e-244, 3.06e-244j)
| (-4.5938043248288415668 + 4.4885558021675573666e-602j)  +/-  (1.28e-244, 1.28e-244j)
| (-1.4583975739989558964 - 1.768962377407442924e-608j)  +/-  (1.28e-250, 1.28e-250j)
| (-5.0642108883881029295 + 8.8386428160295380586e-603j)  +/-  (3.05e-244, 3.05e-244j)
| (1.4583975739989558964 + 9.1786886292888458816e-610j)  +/-  (1.25e-250, 1.25e-250j)
| (11.922891117938454214 + 3.1938443879798566591e-600j)  +/-  (3.37e-245, 3.37e-245j)
| (-7.54888676424920614 - 3.5655726782128486999e-601j)  +/-  (6.01e-243, 6.01e-243j)
| (-9.2102245741991811309 + 1.6286047393877562649e-604j)  +/-  (3.88e-243, 3.88e-243j)
| (11.147406802456399926 - 7.343228496685212085e-605j)  +/-  (2.2e-244, 2.2e-244j)
| (-11.922891117938454214 - 7.6106625608876296828e-609j)  +/-  (3.54e-245, 3.54e-245j)
| (2.3257505194368226166 + 2.5621489610420005356e-612j)  +/-  (2.53e-248, 2.53e-248j)
| (3.6739274246308077709 - 3.6787672596618678211e-610j)  +/-  (1.98e-245, 1.98e-245j)
| (-6.5234553242428059304 - 6.0709561993172881841e-606j)  +/-  (3.05e-243, 3.05e-243j)
| (-8.08306806291426153 - 6.1339337116712371535e-613j)  +/-  (6.1e-243, 6.1e-243j)
| (4.1301809875329036469 + 9.8178558456886235759e-619j)  +/-  (4.56e-245, 4.56e-245j)
| (5.5419752498857797978 - 4.8058828098642058658e-635j)  +/-  (7.22e-244, 7.22e-244j)
| (9.2102245741991811309 - 7.7853034395308612166e-670j)  +/-  (3.62e-243, 3.62e-243j)
| (7.54888676424920614 + 5.3664669874449074616e-699j)  +/-  (6.13e-243, 6.13e-243j)
| (-0.61670659019259415219 + 1.6984875505325824412e-722j)  +/-  (5.59e-253, 5.59e-253j)
| (-7.0298025381325684066 - 1.3883409583630662038e-711j)  +/-  (4.46e-243, 4.46e-243j)
| (12.857828364194572608 + 9.1770461535445195644e-716j)  +/-  (2.31e-246, 2.31e-246j)
| (3.2049120544668510562 - 1.0313196757574611062e-720j)  +/-  (8.9e-246, 8.9e-246j)
| (6.0280010633511181558 - 4.0940172665061876419e-727j)  +/-  (1.74e-243, 1.74e-243j)
| (-3.2049120544668510562 - 7.876910041471344333e-736j)  +/-  (8.86e-246, 8.86e-246j)
| (-4.1301809875329036469 + 3.302638011374808677e-737j)  +/-  (4.5e-245, 4.5e-245j)
| (8.635444252542347519 - 6.9316314041541433804e-739j)  +/-  (5.58e-243, 5.58e-243j)
| (1.0341603101372091818 + 1.8817813420638035608e-757j)  +/-  (8.54e-252, 8.54e-252j)
| (2.7671139682248079248 + 1.9478497346407563705e-753j)  +/-  (3.11e-247, 3.11e-247j)
| (-1.8891758777537106755 - 1.3153999166980577679e-755j)  +/-  (1.84e-249, 1.84e-249j)
| (-1.0341603101372091818 - 2.3289362956190421534e-757j)  +/-  (8.9e-252, 8.9e-252j)
| (-6.0280010633511181558 + 8.7156993491307183869e-749j)  +/-  (1.65e-243, 1.65e-243j)
| (0.20482585175296246807 + 1.6420318205443784116e-760j)  +/-  (3.77e-254, 3.77e-254j)
| (1.8891758777537106755 - 1.8796813137681730417e-758j)  +/-  (1.77e-249, 1.77e-249j)
| (-8.635444252542347519 - 1.0922577846817670756e-747j)  +/-  (5.75e-243, 5.75e-243j)
| (0.61670659019259415219 - 1.4545788048801022597e-759j)  +/-  (6.2e-253, 6.2e-253j)
| (-2.7671139682248079248 - 2.9734557610784314741e-755j)  +/-  (3.35e-247, 3.35e-247j)
| (6.5234553242428059304 + 1.321579966720007637e-751j)  +/-  (3.08e-243, 3.08e-243j)
| (7.0298025381325684066 + 6.0231040321822857114e-767j)  +/-  (4.59e-243, 4.59e-243j)
| (-5.5419752498857797978 + 3.6016773835299914439e-773j)  +/-  (7.87e-244, 7.87e-244j)
| (-0.20482585175296246807 - 1.2634456572501575152e-788j)  +/-  (3.77e-254, 3.77e-254j)
| (-2.3257505194368226166 + 1.5914489084160927404e-781j)  +/-  (2.71e-248, 2.71e-248j)
-------------------------------------------------
The weights are:
| (5.4247160289153980251e-37 + 3.3079957949492789517e-555j)  +/-  (3.09e-80, 8.28e-202j)
| (4.9135209105933668314e-25 - 8.9420445174453858645e-549j)  +/-  (7.55e-76, 2.02e-197j)
| (0.00021084521120967550678 - 9.6622692369234055605e-535j)  +/-  (3.04e-54, 8.15e-176j)
| (4.8721549395105418452e-06 + 1.5682849466957799838e-536j)  +/-  (5.32e-60, 1.42e-181j)
| (3.0299593911631669346e-22 - 1.8297477111507018142e-547j)  +/-  (1.52e-76, 4.07e-198j)
| (3.0299593911631669346e-22 + 3.085426355007222601e-547j)  +/-  (3.78e-75, 1.01e-196j)
| (4.9135209105933668314e-25 + 4.9261001358117233559e-549j)  +/-  (4.14e-78, 1.11e-199j)
| (3.0130888054725888175e-28 + 1.5938875656419289361e-550j)  +/-  (9.23e-78, 2.47e-199j)
| (8.9361692703206828722e-05 + 3.8732259685940971659e-534j)  +/-  (2.39e-55, 6.41e-177j)
| (1.4058166637393823208e-15 + 1.4068903100176924184e-543j)  +/-  (2.46e-73, 6.59e-195j)
| (8.9361692703206828722e-05 - 9.4547066859926811563e-535j)  +/-  (2.82e-57, 7.55e-179j)
| (5.1008272580674561101e-07 + 1.7754881264490953408e-537j)  +/-  (2.29e-64, 6.15e-186j)
| (4.8721549395105418452e-06 + 6.0460473937594085748e-537j)  +/-  (4.4e-63, 1.18e-184j)
| (0.058898780609336724627 - 9.5641385090342454298e-535j)  +/-  (3.65e-45, 9.79e-167j)
| (5.1008272580674561101e-07 - 7.9046128131618837322e-538j)  +/-  (4.01e-65, 1.08e-186j)
| (0.058898780609336724627 + 7.1627763570990296344e-535j)  +/-  (8.15e-47, 2.18e-168j)
| (4.503711489471266981e-32 + 6.4996726712034804802e-553j)  +/-  (3.65e-83, 9.77e-205j)
| (8.8667547346407069904e-14 + 2.2253829987817042218e-542j)  +/-  (2.67e-73, 7.16e-195j)
| (8.9106301115018971368e-20 - 7.4028188991606002008e-546j)  +/-  (2.28e-76, 6.12e-198j)
| (3.0130888054725888175e-28 - 8.1268196185429955408e-551j)  +/-  (4.21e-82, 1.13e-203j)
| (4.503711489471266981e-32 - 1.3878260914446734443e-552j)  +/-  (8.63e-82, 2.31e-203j)
| (0.011721598972538206904 + 4.4810754369390809387e-535j)  +/-  (1.84e-58, 4.94e-180j)
| (0.00021084521120967550678 + 1.788567216829099937e-535j)  +/-  (3.5e-64, 9.38e-186j)
| (1.147157111454086624e-10 + 1.9307095143400756544e-540j)  +/-  (2.76e-72, 7.41e-194j)
| (1.4058166637393823208e-15 - 1.8986433997485806746e-543j)  +/-  (5.96e-75, 1.6e-196j)
| (3.6285939964031370211e-05 - 5.1184459681697689111e-536j)  +/-  (1.28e-66, 3.44e-188j)
| (4.1148849312305790324e-08 - 1.5892559561923030236e-538j)  +/-  (8.82e-72, 2.36e-193j)
| (8.9106301115018971368e-20 + 4.7203554940256324377e-546j)  +/-  (2.59e-80, 6.94e-202j)
| (8.8667547346407069904e-14 - 1.7916973965922912876e-542j)  +/-  (1.33e-77, 3.56e-199j)
| (0.13665578794565096201 - 1.2423828631361010491e-534j)  +/-  (1.34e-60, 3.6e-182j)
| (3.7973918723431607453e-12 - 2.2164900095007147868e-541j)  +/-  (4.88e-76, 1.31e-197j)
| (5.4247160289153980251e-37 - 1.3992140262729800932e-555j)  +/-  (8.31e-89, 2.23e-210j)
| (0.00094973873697282099988 + 1.0271129332277310818e-534j)  +/-  (6.02e-67, 1.61e-188j)
| (2.5184540244906665599e-09 + 1.7383075079241267933e-539j)  +/-  (1.25e-74, 3.35e-196j)
| (0.00094973873697282099988 - 3.3948116957432538586e-534j)  +/-  (2.12e-69, 5.69e-191j)
| (3.6285939964031370211e-05 - 6.3073525525286107582e-536j)  +/-  (1.08e-71, 2.9e-193j)
| (1.440014477523615037e-17 - 9.1477499308656142937e-545j)  +/-  (7.12e-80, 1.91e-201j)
| (0.098344964240170423668 - 9.1227295475538033738e-535j)  +/-  (7.63e-66, 2.04e-187j)
| (0.0038434922065061626078 - 4.3177957531034328105e-535j)  +/-  (2.61e-68, 6.99e-190j)
| (0.029054757718052008254 + 8.2870497039563241778e-535j)  +/-  (2.18e-68, 5.84e-190j)
| (0.098344964240170423668 + 1.1099636196733557212e-534j)  +/-  (6.02e-66, 1.61e-187j)
| (2.5184540244906665599e-09 - 1.5140920215788897785e-539j)  +/-  (2.82e-76, 7.56e-198j)
| (0.16018896070332393227 - 1.2540084308669485126e-534j)  +/-  (8.23e-67, 2.2e-188j)
| (0.029054757718052008254 - 5.5494702086255070798e-535j)  +/-  (1.49e-68, 4e-190j)
| (1.440014477523615037e-17 + 1.3329749202046897729e-544j)  +/-  (1.12e-80, 2.99e-202j)
| (0.13665578794565096201 + 1.1086420529985346006e-534j)  +/-  (1.43e-68, 3.83e-190j)
| (0.0038434922065061626078 + 9.3237219638971019306e-535j)  +/-  (3e-71, 8.03e-193j)
| (1.147157111454086624e-10 - 1.911340445484518601e-540j)  +/-  (1.87e-77, 4.99e-199j)
| (3.7973918723431607453e-12 + 1.9601551482613860871e-541j)  +/-  (2.22e-78, 5.93e-200j)
| (4.1148849312305790324e-08 + 1.1061054302736950488e-538j)  +/-  (2.09e-76, 5.69e-198j)
| (0.16018896070332393227 + 1.3017423108336735885e-534j)  +/-  (8.58e-72, 2.94e-193j)
| (0.011721598972538206904 - 7.7510183255092759121e-535j)  +/-  (1.34e-72, 3.42e-194j)
