Starting with polynomial:
P : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Extension levels are: 4 19
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P1 : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/24*t^23 - 490820724245111888642243025619357511858977/26179518719845772174359062447427227906936*t^22 + 100452953628062933532648367198216047553054417/26179518719845772174359062447427227906936*t^21 - 1379226132797374945298515034105261590326944265/2908835413316196908262118049714136434104*t^20 + 216009037524078659333978014424147579271279584546/5454066399967869202991471343214005813945*t^19 - 12940354307940011399367169508520689879075778011456/5454066399967869202991471343214005813945*t^18 + 191923239557325931620018479502082584059763982038699/1818022133322623067663823781071335271315*t^17 - 6481712693922755077337832765050686923099698059459887/1818022133322623067663823781071335271315*t^16 + 168406196416858205381491022472986885182340295890530368/1818022133322623067663823781071335271315*t^15 - 678481377841294204009768486431123641170713976592085312/363604426664524613532764756214267054263*t^14 + 10633628214749839657054973339173763327940783817980633792/363604426664524613532764756214267054263*t^13 - 129658246281011413408803906724371517569297664997094300864/363604426664524613532764756214267054263*t^12 + 1226046455170208039942643993104609703853796898260856317952/363604426664524613532764756214267054263*t^11 - 8934765468991167918471400263649408705283719618021570495488/363604426664524613532764756214267054263*t^10 + 49705173715648999636121498140139900526299906492534934074880/363604426664524613532764756214267054263*t^9 - 208315060656930071227648126153519515095365789617878608596480/363604426664524613532764756214267054263*t^8 + 646106696340581244975015037884956851031296071161547051970560/363604426664524613532764756214267054263*t^7 - 1448012887144750225245541823280963140453818242824200211066880/363604426664524613532764756214267054263*t^6 + 2269809497689484953363862530790639499637910420669322017157120/363604426664524613532764756214267054263*t^5 - 2377119266398113572098335319743382010274692519143675404595200/363604426664524613532764756214267054263*t^4 + 1553306142535761557440294007745636135705689315428799943475200/363604426664524613532764756214267054263*t^3 - 566020570325740947435598721025720867574705633481160140390400/363604426664524613532764756214267054263*t^2 + 92692085644973304444091224096510872499359108869690950451200/363604426664524613532764756214267054263*t - 3911190411675692675520594165041435482774233340115246284800/363604426664524613532764756214267054263
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (59.519785885414577365 - 7.1284725896979407668e-269j)  +/-  (6.08e-118, 6.08e-118j)
| (32.954448619172400177 - 1.7128347576623228035e-270j)  +/-  (1.98e-116, 1.98e-116j)
| (44.18286059330865395 - 4.4146253365202265646e-276j)  +/-  (7.23e-117, 7.23e-117j)
| (70.447827329357162508 + 1.6571100716825488339e-282j)  +/-  (5e-119, 5e-119j)
| (38.197215592752915922 - 2.0581762240074350543e-283j)  +/-  (1.54e-116, 1.54e-116j)
| (9.3950709123011331292 + 5.9909687839579605866e-288j)  +/-  (4.56e-118, 4.56e-118j)
| (51.142925087333869976 + 3.0925832422398384007e-295j)  +/-  (2.92e-117, 2.92e-117j)
| (20.495715276872524996 + 7.6236537009159194837e-317j)  +/-  (1.32e-116, 1.32e-116j)
| (17.204309405805683824 + 1.3689362212602079868e-341j)  +/-  (7.64e-117, 7.64e-117j)
| (4.5366202969211279833 + 3.3905812036351789463e-353j)  +/-  (1.51e-119, 1.51e-119j)
| (3.5458379644884790501 + 1.2488191906022428759e-357j)  +/-  (3.86e-120, 3.86e-120j)
| (2.5736360374764835742 - 8.1040694502164207181e-359j)  +/-  (5.57e-121, 5.57e-121j)
| (28.314104650328785989 + 9.2535913176066701711e-354j)  +/-  (2.29e-116, 2.29e-116j)
| (1.7457611011583465757 + 1.0611507350789897437e-365j)  +/-  (6.76e-122, 6.76e-122j)
| (0.062078186969820986272 + 3.3953504588769164951e-371j)  +/-  (4.83e-127, 4.83e-127j)
| (1.2173612832303334688 - 8.6617349337006930526e-367j)  +/-  (1.27e-122, 1.27e-122j)
| (11.675934514019887631 + 1.4115737980436601303e-360j)  +/-  (1.55e-117, 1.55e-117j)
| (14.273152722914868786 - 1.6497827702122216422e-371j)  +/-  (3.42e-117, 3.42e-117j)
| (24.183028389801147887 + 1.5753803421809534174e-381j)  +/-  (1.77e-116, 1.77e-116j)
| (0.3225476896193923118 - 1.3657449251307401897e-397j)  +/-  (2.39e-125, 2.39e-125j)
| (7.4250453297393575336 + 1.3208753280055073772e-393j)  +/-  (1.64e-118, 1.64e-118j)
| (0.75644607443693642199 - 9.7297030159361223552e-396j)  +/-  (1.05e-123, 1.05e-123j)
| (5.7868026404745694491 - 4.1815080243507256411e-392j)  +/-  (5.69e-119, 5.69e-119j)
-------------------------------------------------
The weights are:
| (1.3230457586448716055e-25 - 1.3807409772402191609e-291j)  +/-  (1.36e-45, 2.46e-102j)
| (2.400453647423909037e-14 + 2.2650516261603422808e-284j)  +/-  (1.64e-40, 2.96e-97j)
| (4.1625676962536629317e-19 - 9.3940647999096930858e-288j)  +/-  (3.06e-43, 5.53e-100j)
| (3.3367664182393721186e-30 + 3.7774035261408217049e-294j)  +/-  (3.28e-48, 5.92e-105j)
| (1.4394871721072445679e-16 + 4.7503773062847829182e-286j)  +/-  (2.41e-42, 4.36e-99j)
| (0.00017673598030713194399 - 1.6356465242656183518e-279j)  +/-  (2.45e-34, 4.43e-91j)
| (4.6531780804580735278e-22 + 1.5294892591876158114e-289j)  +/-  (7.97e-45, 1.44e-101j)
| (4.3723902838585288835e-09 - 3.2088680198261888959e-282j)  +/-  (9.56e-40, 1.73e-96j)
| (1.0483097348278605834e-07 + 1.7141692372436566637e-281j)  +/-  (6.82e-39, 1.23e-95j)
| (0.011389468141329829193 + 7.3442054318238477735e-278j)  +/-  (1.24e-32, 2.25e-89j)
| (0.028174789134800707215 - 1.3725851745985681043e-277j)  +/-  (1.41e-31, 2.55e-88j)
| (0.071288692756108602777 + 2.1173086879616593422e-277j)  +/-  (1.36e-30, 2.46e-87j)
| (2.2085793382797074031e-12 - 1.0988777389859755229e-283j)  +/-  (4.12e-42, 7.45e-99j)
| (0.1198429184256939039 - 3.4048947673122642558e-277j)  +/-  (1.25e-30, 2.27e-87j)
| (0.14932319685691048985 - 2.3803378947478954388e-278j)  +/-  (2.83e-30, 5.12e-87j)
| (0.12714618818057137188 + 3.8242679443626927854e-277j)  +/-  (2.49e-30, 4.51e-87j)
| (2.0703504329708157829e-05 + 3.8395894964987863218e-280j)  +/-  (3.55e-38, 6.41e-95j)
| (1.7467772167620029313e-06 - 8.4422538253250598438e-281j)  +/-  (4.42e-39, 7.99e-96j)
| (1.2260469955517990933e-10 + 5.6894299782918549342e-283j)  +/-  (1.18e-41, 2.14e-98j)
| (0.25931750125436576307 + 9.4912801397123418577e-278j)  +/-  (4.83e-34, 8.77e-91j)
| (0.0010797321043193713954 + 6.6509985435882378115e-279j)  +/-  (1.86e-37, 3.36e-94j)
| (0.22778083177599711377 - 2.4088943223962373457e-277j)  +/-  (3.87e-35, 7.36e-92j)
| (0.0044573857798480504115 - 2.5401016996218471955e-278j)  +/-  (7.94e-37, 1.43e-93j)
Starting with polynomial:
P : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Extension levels are: 4 19
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P1 : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/24*t^23 - 490820724245111888642243025619357511858977/26179518719845772174359062447427227906936*t^22 + 100452953628062933532648367198216047553054417/26179518719845772174359062447427227906936*t^21 - 1379226132797374945298515034105261590326944265/2908835413316196908262118049714136434104*t^20 + 216009037524078659333978014424147579271279584546/5454066399967869202991471343214005813945*t^19 - 12940354307940011399367169508520689879075778011456/5454066399967869202991471343214005813945*t^18 + 191923239557325931620018479502082584059763982038699/1818022133322623067663823781071335271315*t^17 - 6481712693922755077337832765050686923099698059459887/1818022133322623067663823781071335271315*t^16 + 168406196416858205381491022472986885182340295890530368/1818022133322623067663823781071335271315*t^15 - 678481377841294204009768486431123641170713976592085312/363604426664524613532764756214267054263*t^14 + 10633628214749839657054973339173763327940783817980633792/363604426664524613532764756214267054263*t^13 - 129658246281011413408803906724371517569297664997094300864/363604426664524613532764756214267054263*t^12 + 1226046455170208039942643993104609703853796898260856317952/363604426664524613532764756214267054263*t^11 - 8934765468991167918471400263649408705283719618021570495488/363604426664524613532764756214267054263*t^10 + 49705173715648999636121498140139900526299906492534934074880/363604426664524613532764756214267054263*t^9 - 208315060656930071227648126153519515095365789617878608596480/363604426664524613532764756214267054263*t^8 + 646106696340581244975015037884956851031296071161547051970560/363604426664524613532764756214267054263*t^7 - 1448012887144750225245541823280963140453818242824200211066880/363604426664524613532764756214267054263*t^6 + 2269809497689484953363862530790639499637910420669322017157120/363604426664524613532764756214267054263*t^5 - 2377119266398113572098335319743382010274692519143675404595200/363604426664524613532764756214267054263*t^4 + 1553306142535761557440294007745636135705689315428799943475200/363604426664524613532764756214267054263*t^3 - 566020570325740947435598721025720867574705633481160140390400/363604426664524613532764756214267054263*t^2 + 92692085644973304444091224096510872499359108869690950451200/363604426664524613532764756214267054263*t - 3911190411675692675520594165041435482774233340115246284800/363604426664524613532764756214267054263
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (59.519785885414577365 - 7.1284725896979407668e-269j)  +/-  (6.08e-118, 6.08e-118j)
| (32.954448619172400177 - 1.7128347576623228035e-270j)  +/-  (1.98e-116, 1.98e-116j)
| (44.18286059330865395 - 4.4146253365202265646e-276j)  +/-  (7.23e-117, 7.23e-117j)
| (70.447827329357162508 + 1.6571100716825488339e-282j)  +/-  (5e-119, 5e-119j)
| (38.197215592752915922 - 2.0581762240074350543e-283j)  +/-  (1.54e-116, 1.54e-116j)
| (9.3950709123011331292 + 5.9909687839579605866e-288j)  +/-  (4.56e-118, 4.56e-118j)
| (51.142925087333869976 + 3.0925832422398384007e-295j)  +/-  (2.92e-117, 2.92e-117j)
| (20.495715276872524996 + 7.6236537009159194837e-317j)  +/-  (1.32e-116, 1.32e-116j)
| (17.204309405805683824 + 1.3689362212602079868e-341j)  +/-  (7.64e-117, 7.64e-117j)
| (4.5366202969211279833 + 3.3905812036351789463e-353j)  +/-  (1.51e-119, 1.51e-119j)
| (3.5458379644884790501 + 1.2488191906022428759e-357j)  +/-  (3.86e-120, 3.86e-120j)
| (2.5736360374764835742 - 8.1040694502164207181e-359j)  +/-  (5.57e-121, 5.57e-121j)
| (28.314104650328785989 + 9.2535913176066701711e-354j)  +/-  (2.29e-116, 2.29e-116j)
| (1.7457611011583465757 + 1.0611507350789897437e-365j)  +/-  (6.76e-122, 6.76e-122j)
| (0.062078186969820986272 + 3.3953504588769164951e-371j)  +/-  (4.83e-127, 4.83e-127j)
| (1.2173612832303334688 - 8.6617349337006930526e-367j)  +/-  (1.27e-122, 1.27e-122j)
| (11.675934514019887631 + 1.4115737980436601303e-360j)  +/-  (1.55e-117, 1.55e-117j)
| (14.273152722914868786 - 1.6497827702122216422e-371j)  +/-  (3.42e-117, 3.42e-117j)
| (24.183028389801147887 + 1.5753803421809534174e-381j)  +/-  (1.77e-116, 1.77e-116j)
| (0.3225476896193923118 - 1.3657449251307401897e-397j)  +/-  (2.39e-125, 2.39e-125j)
| (7.4250453297393575336 + 1.3208753280055073772e-393j)  +/-  (1.64e-118, 1.64e-118j)
| (0.75644607443693642199 - 9.7297030159361223552e-396j)  +/-  (1.05e-123, 1.05e-123j)
| (5.7868026404745694491 - 4.1815080243507256411e-392j)  +/-  (5.69e-119, 5.69e-119j)
-------------------------------------------------
The weights are:
| (1.3230457586448716055e-25 - 1.3807409772402191609e-291j)  +/-  (1.36e-45, 2.46e-102j)
| (2.400453647423909037e-14 + 2.2650516261603422808e-284j)  +/-  (1.64e-40, 2.96e-97j)
| (4.1625676962536629317e-19 - 9.3940647999096930858e-288j)  +/-  (3.06e-43, 5.53e-100j)
| (3.3367664182393721186e-30 + 3.7774035261408217049e-294j)  +/-  (3.28e-48, 5.92e-105j)
| (1.4394871721072445679e-16 + 4.7503773062847829182e-286j)  +/-  (2.41e-42, 4.36e-99j)
| (0.00017673598030713194399 - 1.6356465242656183518e-279j)  +/-  (2.45e-34, 4.43e-91j)
| (4.6531780804580735278e-22 + 1.5294892591876158114e-289j)  +/-  (7.97e-45, 1.44e-101j)
| (4.3723902838585288835e-09 - 3.2088680198261888959e-282j)  +/-  (9.56e-40, 1.73e-96j)
| (1.0483097348278605834e-07 + 1.7141692372436566637e-281j)  +/-  (6.82e-39, 1.23e-95j)
| (0.011389468141329829193 + 7.3442054318238477735e-278j)  +/-  (1.24e-32, 2.25e-89j)
| (0.028174789134800707215 - 1.3725851745985681043e-277j)  +/-  (1.41e-31, 2.55e-88j)
| (0.071288692756108602777 + 2.1173086879616593422e-277j)  +/-  (1.36e-30, 2.46e-87j)
| (2.2085793382797074031e-12 - 1.0988777389859755229e-283j)  +/-  (4.12e-42, 7.45e-99j)
| (0.1198429184256939039 - 3.4048947673122642558e-277j)  +/-  (1.25e-30, 2.27e-87j)
| (0.14932319685691048985 - 2.3803378947478954388e-278j)  +/-  (2.83e-30, 5.12e-87j)
| (0.12714618818057137188 + 3.8242679443626927854e-277j)  +/-  (2.49e-30, 4.51e-87j)
| (2.0703504329708157829e-05 + 3.8395894964987863218e-280j)  +/-  (3.55e-38, 6.41e-95j)
| (1.7467772167620029313e-06 - 8.4422538253250598438e-281j)  +/-  (4.42e-39, 7.99e-96j)
| (1.2260469955517990933e-10 + 5.6894299782918549342e-283j)  +/-  (1.18e-41, 2.14e-98j)
| (0.25931750125436576307 + 9.4912801397123418577e-278j)  +/-  (4.83e-34, 8.77e-91j)
| (0.0010797321043193713954 + 6.6509985435882378115e-279j)  +/-  (1.86e-37, 3.36e-94j)
| (0.22778083177599711377 - 2.4088943223962373457e-277j)  +/-  (3.87e-35, 7.36e-92j)
| (0.0044573857798480504115 - 2.5401016996218471955e-278j)  +/-  (7.94e-37, 1.43e-93j)
