Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 49
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 451261493390660924679193591805572348338819647869267555/338071256417604147929271014526164762694207273539701*t^53 + 3063133597273350873226082394833122049069738012996792143895/3718783820593645627221981159787812389636280008936711*t^51 - 561167442386030421079468183650662891420867949085426448364495/1796715778489064741242080785066021716341124049261557*t^49 + 13047140420016694370019930160851080762184491753330640569271185430/159907704285526761970545189870875932754360040384278573*t^47 - 2495554367940309582699404915516829440496889351529306451273467502090/159907704285526761970545189870875932754360040384278573*t^45 + 32963953366630701802956231783154683537333703592299744209889832523450/14537064025956978360958653624625084795850912762207143*t^43 - 86654435143940940742126025191672739739616586444420184338927812153050/338071256417604147929271014526164762694207273539701*t^41 + 7741900548580754677214243575121618458662201522649186822619102678077575/338071256417604147929271014526164762694207273539701*t^39 - 29076851698398510152833391154955370022790354418138404272706202684097675/17793224021979165680487948132956040141800382817879*t^37 + 1668301435827925743750985974349213840302843609548357078255098256128977525/17793224021979165680487948132956040141800382817879*t^35 - 4065295151665844901210824515166617824952311426482425323639299643775507125/936485474841008720025681480681896849568441200941*t^33 + 2888993173584244114477385069812423705941347622788818288120736193181526059500/17793224021979165680487948132956040141800382817879*t^31 - 4589320839063717477682809138185373476075200521983480940412821247056512569500/936485474841008720025681480681896849568441200941*t^29 + 2117045027404276008504006094400706351808322664159217076335044989779645807705500/17793224021979165680487948132956040141800382817879*t^27 - 41127947831478949850272526450707723835151989703077171972204254579153569392536500/17793224021979165680487948132956040141800382817879*t^25 + 634536288777780564814503894722473883214695391693166437980564062530948389632790625/17793224021979165680487948132956040141800382817879*t^23 - 7697018965317305490353286562133365191485313981658527762487679304473272882316784375/17793224021979165680487948132956040141800382817879*t^21 + 72452797542102041637142978290235383589697801659554133765696861074679083335175590625/17793224021979165680487948132956040141800382817879*t^19 - 27387898630214713066417356856280458413206309047161201551541975176619656685081440625/936485474841008720025681480681896849568441200941*t^17 + 2789502315028622222295656431283191557650691245669799762756343749776688937832314631250/17793224021979165680487948132956040141800382817879*t^15 - 10838417695210334963781225851152770123613709363372493658482122049393603257654631468750/17793224021979165680487948132956040141800382817879*t^13 + 29315148941854219395233132710122584192932303525821954863332418436407126591281468406250/17793224021979165680487948132956040141800382817879*t^11 - 52060413129361548752335677791175008971441909912014565426567272580406988850100965968750/17793224021979165680487948132956040141800382817879*t^9 + 55419124056555958030372154729067193657452057866516426039550719731162827761120222296875/17793224021979165680487948132956040141800382817879*t^7 - 30160231788089941534287376467415081947935734052196563660506576851267099079186735078125/17793224021979165680487948132956040141800382817879*t^5 + 5917386825307713939043380126258033542434490762153289339140924397290006621137486171875/17793224021979165680487948132956040141800382817879*t^3 - 50921732550984757027110272708475065757538784426139582027427669641357679954964765625/17793224021979165680487948132956040141800382817879*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:
| (-9.1000161688553042219 + 3.6382083945090203761e-842j)  +/-  (2.22e-242, 2.22e-242j)
| (11.58431330926214196 + 3.2085992475199171991e-846j)  +/-  (6.61e-244, 6.61e-244j)
| (-12.351917588152873084 - 4.9700080865486315796e-847j)  +/-  (9.1e-245, 9.1e-245j)
| (-8.5541733412070849177 - 5.096363168634775244e-844j)  +/-  (2.76e-242, 2.76e-242j)
| (12.351917588152873084 + 3.1279253843385326105e-846j)  +/-  (9.67e-245, 9.67e-245j)
| (13.277746098693704559 - 2.7077083882837600722e-847j)  +/-  (6.04e-246, 6.04e-246j)
| (6.0451177362175191523 - 3.4533923404625273184e-843j)  +/-  (3.92e-243, 3.92e-243j)
| (-1.8891758777537106755 + 7.5073095384273627956e-854j)  +/-  (3.42e-249, 3.42e-249j)
| (-11.58431330926214196 + 2.0730964133489240124e-850j)  +/-  (6.86e-244, 6.86e-244j)
| (-8.0264625816864125213 - 2.7120523163102748945e-847j)  +/-  (2.76e-242, 2.76e-242j)
| (2.9108779412926827998 - 4.8126144583019720757e-856j)  +/-  (6.9e-247, 6.9e-247j)
| (7.0138562127744048326 - 2.554724800028181688e-851j)  +/-  (1.46e-242, 1.46e-242j)
| (-5.5737150192778112958 + 2.6499535901358098177e-863j)  +/-  (1.72e-243, 1.72e-243j)
| (-10.264583850295106162 - 2.5923319272295514397e-861j)  +/-  (7.03e-243, 7.03e-243j)
| (8.0264625816864125213 + 3.5932877467524965377e-870j)  +/-  (2.9e-242, 2.9e-242j)
| (5.1096775260330162966 + 1.2974096844089886066e-879j)  +/-  (5.77e-244, 5.77e-244j)
| (9.6681707081351498692 + 1.1415512231297419772e-884j)  +/-  (1.43e-242, 1.43e-242j)
| (10.264583850295106162 - 2.6658295478951639596e-900j)  +/-  (6.91e-243, 6.91e-243j)
| (10.898280793595460185 - 5.7135528613220912671e-915j)  +/-  (2.46e-243, 2.46e-243j)
| (-13.277746098693704559 + 2.3932957159831255641e-923j)  +/-  (5.73e-246, 5.73e-246j)
| (3.3242574335521189524 + 5.0908446742235151178e-924j)  +/-  (2.79e-246, 2.79e-246j)
| (2.2512216943876266105 + 2.8421702074032337053e-925j)  +/-  (3.74e-248, 3.74e-248j)
| (-9.6681707081351498692 - 2.4738238797270871341e-919j)  +/-  (1.46e-242, 1.46e-242j)
| (4.6523933290893768019 - 5.2785154157352410586e-920j)  +/-  (1.67e-244, 1.67e-244j)
| (-4.6523933290893768019 - 2.227544813345142352e-921j)  +/-  (1.79e-244, 1.79e-244j)
| (-5.1096775260330162966 - 6.2494009515710294167e-921j)  +/-  (5.59e-244, 5.59e-244j)
| (1.0529527464134947028 + 2.0963270520014950615e-929j)  +/-  (1.21e-251, 1.21e-251j)
| (4.2016497930204818728 - 4.0017710168070990301e-922j)  +/-  (4.27e-245, 4.27e-245j)
| (-6.524779021154395759 - 7.6191250588867644031e-919j)  +/-  (8.59e-243, 8.59e-243j)
| (-2.2512216943876266105 - 2.3104657269266948565e-929j)  +/-  (3.37e-248, 3.37e-248j)
| (-2.2388724773903341939e-943 + 2.7082312460797299752e-943j)  +/-  (1.93e-941, 1.93e-941j)
| (5.5737150192778112958 - 6.9500392988321132349e-923j)  +/-  (1.77e-243, 1.77e-243j)
| (1.8891758777537106755 - 2.3007336819271635394e-945j)  +/-  (3.52e-249, 3.52e-249j)
| (-3.3242574335521189524 - 9.3293310012121221267e-941j)  +/-  (2.81e-246, 2.81e-246j)
| (8.5541733412070849177 + 1.3155105529325003215e-936j)  +/-  (2.95e-242, 2.95e-242j)
| (-0.094934995233002178922 + 2.2882253180327999737e-963j)  +/-  (1.08e-254, 1.08e-254j)
| (-0.61670659019259415219 - 9.042828262102179184e-962j)  +/-  (5.37e-253, 5.37e-253j)
| (1.4789617885053988463 + 2.280242803420901403e-959j)  +/-  (2.13e-250, 2.13e-250j)
| (-2.5535564438309519944 - 1.4671402341033963835e-956j)  +/-  (1.77e-247, 1.77e-247j)
| (-1.4789617885053988463 + 8.9934659847412092933e-960j)  +/-  (2.26e-250, 2.26e-250j)
| (7.5138058125815985211 - 4.436617299829971819e-950j)  +/-  (2.28e-242, 2.28e-242j)
| (-2.9108779412926827998 + 1.8210552480574762654e-962j)  +/-  (6.57e-247, 6.57e-247j)
| (9.1000161688553042219 + 4.5264763836231108942e-957j)  +/-  (2.28e-242, 2.28e-242j)
| (2.5535564438309519944 - 3.9108712491753518793e-965j)  +/-  (1.66e-247, 1.66e-247j)
| (-7.0138562127744048326 - 1.2420100592810857849e-958j)  +/-  (1.5e-242, 1.5e-242j)
| (-4.2016497930204818728 + 8.5935353356178898472e-963j)  +/-  (4.33e-245, 4.33e-245j)
| (6.524779021154395759 + 1.1862922552327380099e-960j)  +/-  (8.28e-243, 8.28e-243j)
| (-3.758025582059955605 + 1.6671977578243008107e-966j)  +/-  (1.08e-245, 1.08e-245j)
| (3.758025582059955605 + 8.551276944179198723e-967j)  +/-  (1.13e-245, 1.13e-245j)
| (-7.5138058125815985211 - 3.7418340767863347353e-962j)  +/-  (2.31e-242, 2.31e-242j)
| (-1.0529527464134947028 - 2.0371576576299618675e-973j)  +/-  (1.11e-251, 1.11e-251j)
| (-10.898280793595460185 - 1.0898344532638235436e-965j)  +/-  (2.5e-243, 2.5e-243j)
| (-6.0451177362175191523 - 6.1673309569374057569e-972j)  +/-  (3.96e-243, 3.96e-243j)
| (0.094934995233002178922 + 1.1580509717811231621e-984j)  +/-  (1.08e-254, 1.08e-254j)
| (0.61670659019259415219 - 5.3937466978490849476e-983j)  +/-  (5.37e-253, 5.37e-253j)
-------------------------------------------------
The weights are:
| (2.3126062530864308201e-19 + 1.4073099958327579673e-858j)  +/-  (6.08e-67, 5.95e-188j)
| (2.0790417534014428667e-30 - 5.2864913058329764207e-864j)  +/-  (2.11e-73, 2.06e-194j)
| (2.4419225731923036583e-34 - 1.4120211115512633539e-866j)  +/-  (8.24e-75, 8.08e-196j)
| (2.7588018089743498003e-17 - 1.9114442993779042419e-857j)  +/-  (8.69e-66, 8.51e-187j)
| (2.4419225731923036583e-34 + 4.1288370659667040171e-866j)  +/-  (3.12e-75, 3.06e-196j)
| (2.223703691941569146e-39 - 8.7010816252172173435e-869j)  +/-  (3.18e-77, 3.11e-198j)
| (2.2010257055141022877e-09 + 2.7204937882788455861e-851j)  +/-  (1.63e-61, 1.59e-182j)
| (0.026444500587955789637 + 1.2064950411236645235e-847j)  +/-  (5.2e-38, 5.09e-159j)
| (2.0790417534014428667e-30 + 1.655948489998599334e-864j)  +/-  (2.02e-74, 1.98e-195j)
| (2.1241296703985382191e-15 + 2.1146546191070307465e-856j)  +/-  (1.62e-66, 1.59e-187j)
| (0.0022744154107038305152 - 4.9122052383660482173e-848j)  +/-  (4.4e-49, 4.31e-170j)
| (4.0970375974028650047e-12 - 2.0700610395156398704e-853j)  +/-  (9.64e-66, 9.44e-187j)
| (3.3482424709081255211e-08 - 3.3682015395598970547e-852j)  +/-  (1.32e-61, 1.29e-182j)
| (3.2322691020330189938e-24 + 3.2377436098399890583e-861j)  +/-  (4.73e-72, 4.63e-193j)
| (2.1241296703985382191e-15 - 1.4918001059798986101e-855j)  +/-  (5.71e-69, 5.59e-190j)
| (3.933377499247510755e-07 + 1.9392521586903647503e-850j)  +/-  (2.95e-61, 2.89e-182j)
| (1.1685305283038509778e-21 + 3.3611472474619533936e-859j)  +/-  (4.61e-73, 4.52e-194j)
| (3.2322691020330189938e-24 - 1.2591480854890823339e-860j)  +/-  (2.26e-74, 2.21e-195j)
| (4.2372658978799152413e-27 + 3.2904147178401429978e-862j)  +/-  (1.43e-75, 1.4e-196j)
| (2.223703691941569146e-39 + 3.2505369153990278849e-869j)  +/-  (5.18e-83, 5.07e-204j)
| (0.00067813728352547209222 + 1.5588329703920601478e-848j)  +/-  (2.03e-58, 1.99e-179j)
| (0.010157872514983037367 - 1.9948167758188563894e-847j)  +/-  (1.42e-53, 1.4e-174j)
| (1.1685305283038509778e-21 - 7.6579505659726745764e-860j)  +/-  (4.26e-75, 4.17e-196j)
| (3.6131644604462388308e-06 - 5.5395607019939356435e-850j)  +/-  (2.37e-63, 2.32e-184j)
| (3.6131644604462388308e-06 - 7.2197484850122005281e-851j)  +/-  (1.93e-66, 1.89e-187j)
| (3.933377499247510755e-07 + 1.6283200746013943428e-851j)  +/-  (1.96e-67, 1.92e-188j)
| (0.098688114874972918433 + 3.6900297831506507921e-847j)  +/-  (2.65e-49, 2.59e-170j)
| (2.6188099156980285308e-05 + 1.6578609723325616235e-849j)  +/-  (2.19e-63, 2.14e-184j)
| (1.0998657023240564223e-10 - 1.05034304829491041e-853j)  +/-  (3.28e-71, 3.21e-192j)
| (0.010157872514983037367 - 9.1259453305413342544e-848j)  +/-  (3.69e-59, 3.62e-180j)
| (-0.84862864108158567755 - 1.5210343361961288268e-845j)  +/-  (1.48e-51, 1.45e-172j)
| (3.3482424709081255211e-08 - 8.2891156479381036765e-851j)  +/-  (3.67e-67, 3.6e-188j)
| (0.026444500587955789637 + 2.3026054149524644662e-847j)  +/-  (6.87e-57, 6.73e-178j)
| (0.00067813728352547209222 + 4.5297795533921467004e-849j)  +/-  (1.23e-64, 1.21e-185j)
| (2.7588018089743498003e-17 + 1.0964120639102061027e-856j)  +/-  (1.58e-74, 1.54e-195j)
| (0.57824650144840497236 + 7.8531024382772540387e-846j)  +/-  (2.3e-54, 2.25e-175j)
| (0.14662983408626957028 - 5.0564489950008884323e-847j)  +/-  (2.42e-55, 2.37e-176j)
| (0.056203886650641485841 - 2.719311684658300338e-847j)  +/-  (5.45e-58, 5.34e-179j)
| (0.0048104689557290372802 + 5.1705176502218899051e-848j)  +/-  (1.1e-62, 1.08e-183j)
| (0.056203886650641485841 - 1.6506985492486952207e-847j)  +/-  (5.05e-59, 4.95e-180j)
| (1.1104126487287825574e-13 + 1.798232773332622992e-854j)  +/-  (1.28e-72, 1.25e-193j)
| (0.0022744154107038305152 - 1.7200178677778066e-848j)  +/-  (2.03e-64, 1.99e-185j)
| (2.3126062530864308201e-19 - 6.7818156864708275345e-858j)  +/-  (1.03e-75, 1.01e-196j)
| (0.0048104689557290372802 + 1.2727479543501036873e-847j)  +/-  (8.34e-63, 8.17e-184j)
| (4.0970375974028650047e-12 + 1.540216460677507638e-854j)  +/-  (8.34e-75, 8.17e-196j)
| (2.6188099156980285308e-05 + 2.9853133039214459529e-850j)  +/-  (2.52e-69, 2.47e-190j)
| (1.0998657023240564223e-10 + 2.7461588452693504889e-852j)  +/-  (7.25e-72, 7.1e-193j)
| (0.00015035832859215804425 - 1.175758556821851536e-849j)  +/-  (1.53e-68, 1.5e-189j)
| (0.00015035832859215804425 - 5.0357790035833233928e-849j)  +/-  (8.38e-68, 8.21e-189j)
| (1.1104126487287825574e-13 - 1.9559543570146958715e-855j)  +/-  (4.56e-76, 4.47e-197j)
| (0.098688114874972918433 + 2.5957134703457389365e-847j)  +/-  (3.61e-66, 3.54e-187j)
| (4.2372658978799152413e-27 - 9.3863746621850142851e-863j)  +/-  (1.91e-83, 1.87e-204j)
| (2.2010257055141022877e-09 + 6.2985405646037872935e-853j)  +/-  (1.45e-73, 1.42e-194j)
| (0.57824650144840497236 + 8.103564611100478004e-846j)  +/-  (2.14e-66, 2.16e-187j)
| (0.14662983408626957028 - 6.2046980411855960611e-847j)  +/-  (1.11e-67, 1.04e-188j)
