Starting with polynomial:
P : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Extension levels are: 7 12
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/5040*t^19 + 2527553045506323330569/47692466235470083411440*t^18 - 10407790373332594419102/1655988410953822340675*t^17 + 207377734977421796012343/473139545986806383050*t^16 - 265922851964044152647243697/13247907287630578725400*t^15 + 338415925128361719078993645/529916291505223149016*t^14 - 3859469563705537725777816655/264958145752611574508*t^13 + 64226324033944324589722988377/264958145752611574508*t^12 - 196575219858214367848417932207/66239536438152893627*t^11 + 1772865954965195487624743065671/66239536438152893627*t^10 - 11722956958789804973477128792830/66239536438152893627*t^9 + 8032176351772568654591013947910/9462790919736127661*t^8 - 192190181937354330159367216479024/66239536438152893627*t^7 + 65168144102636454063177435256848/9462790919736127661*t^6 - 103442994778359773468178545674464/9462790919736127661*t^5 + 103947145960380592834582465716000/9462790919736127661*t^4 - 60913979792079425097574186512000/9462790919736127661*t^3 + 18343437855919060890332066002560/9462790919736127661*t^2 - 2327060033404462374818105053440/9462790919736127661*t + 84114286100757541224523825920/9462790919736127661
-------------------------------------------------
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:   19 out of 19
Indefinite weights: 0 out of 19
Negative weights:   0 out of 19
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (51.37299662654459337 - 1.4183716243203296242e-289j)  +/-  (1.67e-120, 1.67e-120j)
| (28.577762474595956759 - 5.0599088272519535053e-287j)  +/-  (1.12e-118, 1.12e-118j)
| (41.731637185988835351 - 8.9156378734896228591e-293j)  +/-  (1.26e-119, 1.26e-119j)
| (23.618965674258227983 - 2.1503834729341131942e-294j)  +/-  (1.4e-118, 1.4e-118j)
| (34.480381123818781752 - 1.1818310693847753599e-301j)  +/-  (5.5e-119, 5.5e-119j)
| (3.5635223836984253032 + 3.1421725987776146133e-306j)  +/-  (5.03e-121, 5.03e-121j)
| (10.209632370751522807 - 2.5573110200642093336e-328j)  +/-  (4.99e-119, 4.99e-119j)
| (19.395727862262540312 + 6.2491297371844652588e-354j)  +/-  (1.45e-118, 1.45e-118j)
| (15.788945775021283236 - 9.5026572419804366812e-369j)  +/-  (1.22e-118, 1.22e-118j)
| (1.7697405885579477246 - 1.3484126565692455038e-381j)  +/-  (1.39e-122, 1.39e-122j)
| (1.0266648953391919503 + 3.7466142271687682891e-384j)  +/-  (1.08e-123, 1.08e-123j)
| (6.4663013474536723875 - 9.1931460385619113125e-384j)  +/-  (8.85e-120, 8.85e-120j)
| (12.734180291797813758 - 2.4779138352560512167e-390j)  +/-  (7.97e-119, 7.97e-119j)
| (0.0581056704164814673 + 1.1701993645468032281e-405j)  +/-  (4.46e-127, 4.46e-127j)
| (4.9003530845264845681 + 4.0825561261498508309e-399j)  +/-  (2.47e-120, 2.47e-120j)
| (0.46640397743098348848 - 6.4974791069250676316e-409j)  +/-  (6.48e-125, 6.48e-125j)
| (2.5678767449507462069 - 1.3911475566252059752e-405j)  +/-  (1.03e-121, 1.03e-121j)
| (0.19304367656036241384 - 2.3957789008189236917e-410j)  +/-  (6.57e-126, 6.57e-126j)
| (8.1821534445628607911 + 2.3543964360983262003e-405j)  +/-  (2.67e-119, 2.67e-119j)
-------------------------------------------------
The weights are:
| (5.712615127148456138e-22 + 1.2404198613744469644e-305j)  +/-  (8.39e-52, 1.35e-110j)
| (2.0895139350280219067e-12 + 6.4641095059996489463e-299j)  +/-  (1.03e-47, 1.65e-106j)
| (6.1404831176367370872e-18 - 4.2156377281413919172e-303j)  +/-  (1.46e-50, 2.34e-109j)
| (2.5229392292473258344e-10 - 4.3289871784362336361e-298j)  +/-  (3.54e-47, 5.67e-106j)
| (6.8723043459014467459e-15 + 5.6829051142778897674e-301j)  +/-  (2.54e-49, 4.07e-108j)
| (0.033281475442144406957 - 1.4920012331734820784e-292j)  +/-  (2.04e-38, 3.27e-97j)
| (8.3275565732588372592e-05 - 1.2781961971433000288e-294j)  +/-  (4.6e-44, 7.38e-103j)
| (1.4710849046242524529e-08 + 3.4318588606405915748e-297j)  +/-  (6.48e-47, 1.04e-105j)
| (4.6195395278038009269e-07 - 2.8073361363707385526e-296j)  +/-  (2.54e-46, 4.07e-105j)
| (0.13347817262758713269 - 4.5080137343670622104e-292j)  +/-  (2.17e-39, 3.48e-98j)
| (0.24119053119924664865 + 5.4516239137090949183e-292j)  +/-  (6.23e-39, 1e-97j)
| (0.0025464534333041557278 - 1.8781945164956716467e-293j)  +/-  (9.03e-44, 1.45e-102j)
| (8.2230504183096047992e-06 + 2.0753462477715536749e-295j)  +/-  (6.59e-46, 1.06e-104j)
| (0.1265141935115881962 - 3.3101701809582943252e-292j)  +/-  (5.55e-41, 9.44e-100j)
| (0.010983903924268787755 + 5.4051706573618097005e-293j)  +/-  (1.93e-43, 3.13e-102j)
| (0.2701689960126730069 - 7.5033526367286854418e-292j)  +/-  (2.05e-41, 3.51e-100j)
| (0.064753445815760582131 + 3.1490081972951940551e-292j)  +/-  (1.93e-42, 3.2e-101j)
| (0.11648001045398586641 + 7.8138756645676382728e-292j)  +/-  (1.28e-41, 2.38e-100j)
| (0.00051084204409817667449 + 5.7289103253030176106e-294j)  +/-  (1.08e-44, 1.73e-103j)
Starting with polynomial:
P : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Extension levels are: 7 12
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/5040*t^19 + 2527553045506323330569/47692466235470083411440*t^18 - 10407790373332594419102/1655988410953822340675*t^17 + 207377734977421796012343/473139545986806383050*t^16 - 265922851964044152647243697/13247907287630578725400*t^15 + 338415925128361719078993645/529916291505223149016*t^14 - 3859469563705537725777816655/264958145752611574508*t^13 + 64226324033944324589722988377/264958145752611574508*t^12 - 196575219858214367848417932207/66239536438152893627*t^11 + 1772865954965195487624743065671/66239536438152893627*t^10 - 11722956958789804973477128792830/66239536438152893627*t^9 + 8032176351772568654591013947910/9462790919736127661*t^8 - 192190181937354330159367216479024/66239536438152893627*t^7 + 65168144102636454063177435256848/9462790919736127661*t^6 - 103442994778359773468178545674464/9462790919736127661*t^5 + 103947145960380592834582465716000/9462790919736127661*t^4 - 60913979792079425097574186512000/9462790919736127661*t^3 + 18343437855919060890332066002560/9462790919736127661*t^2 - 2327060033404462374818105053440/9462790919736127661*t + 84114286100757541224523825920/9462790919736127661
-------------------------------------------------
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:   19 out of 19
Indefinite weights: 0 out of 19
Negative weights:   0 out of 19
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (51.37299662654459337 - 1.4183716243203296242e-289j)  +/-  (1.67e-120, 1.67e-120j)
| (28.577762474595956759 - 5.0599088272519535053e-287j)  +/-  (1.12e-118, 1.12e-118j)
| (41.731637185988835351 - 8.9156378734896228591e-293j)  +/-  (1.26e-119, 1.26e-119j)
| (23.618965674258227983 - 2.1503834729341131942e-294j)  +/-  (1.4e-118, 1.4e-118j)
| (34.480381123818781752 - 1.1818310693847753599e-301j)  +/-  (5.5e-119, 5.5e-119j)
| (3.5635223836984253032 + 3.1421725987776146133e-306j)  +/-  (5.03e-121, 5.03e-121j)
| (10.209632370751522807 - 2.5573110200642093336e-328j)  +/-  (4.99e-119, 4.99e-119j)
| (19.395727862262540312 + 6.2491297371844652588e-354j)  +/-  (1.45e-118, 1.45e-118j)
| (15.788945775021283236 - 9.5026572419804366812e-369j)  +/-  (1.22e-118, 1.22e-118j)
| (1.7697405885579477246 - 1.3484126565692455038e-381j)  +/-  (1.39e-122, 1.39e-122j)
| (1.0266648953391919503 + 3.7466142271687682891e-384j)  +/-  (1.08e-123, 1.08e-123j)
| (6.4663013474536723875 - 9.1931460385619113125e-384j)  +/-  (8.85e-120, 8.85e-120j)
| (12.734180291797813758 - 2.4779138352560512167e-390j)  +/-  (7.97e-119, 7.97e-119j)
| (0.0581056704164814673 + 1.1701993645468032281e-405j)  +/-  (4.46e-127, 4.46e-127j)
| (4.9003530845264845681 + 4.0825561261498508309e-399j)  +/-  (2.47e-120, 2.47e-120j)
| (0.46640397743098348848 - 6.4974791069250676316e-409j)  +/-  (6.48e-125, 6.48e-125j)
| (2.5678767449507462069 - 1.3911475566252059752e-405j)  +/-  (1.03e-121, 1.03e-121j)
| (0.19304367656036241384 - 2.3957789008189236917e-410j)  +/-  (6.57e-126, 6.57e-126j)
| (8.1821534445628607911 + 2.3543964360983262003e-405j)  +/-  (2.67e-119, 2.67e-119j)
-------------------------------------------------
The weights are:
| (5.712615127148456138e-22 + 1.2404198613744469644e-305j)  +/-  (8.39e-52, 1.35e-110j)
| (2.0895139350280219067e-12 + 6.4641095059996489463e-299j)  +/-  (1.03e-47, 1.65e-106j)
| (6.1404831176367370872e-18 - 4.2156377281413919172e-303j)  +/-  (1.46e-50, 2.34e-109j)
| (2.5229392292473258344e-10 - 4.3289871784362336361e-298j)  +/-  (3.54e-47, 5.67e-106j)
| (6.8723043459014467459e-15 + 5.6829051142778897674e-301j)  +/-  (2.54e-49, 4.07e-108j)
| (0.033281475442144406957 - 1.4920012331734820784e-292j)  +/-  (2.04e-38, 3.27e-97j)
| (8.3275565732588372592e-05 - 1.2781961971433000288e-294j)  +/-  (4.6e-44, 7.38e-103j)
| (1.4710849046242524529e-08 + 3.4318588606405915748e-297j)  +/-  (6.48e-47, 1.04e-105j)
| (4.6195395278038009269e-07 - 2.8073361363707385526e-296j)  +/-  (2.54e-46, 4.07e-105j)
| (0.13347817262758713269 - 4.5080137343670622104e-292j)  +/-  (2.17e-39, 3.48e-98j)
| (0.24119053119924664865 + 5.4516239137090949183e-292j)  +/-  (6.23e-39, 1e-97j)
| (0.0025464534333041557278 - 1.8781945164956716467e-293j)  +/-  (9.03e-44, 1.45e-102j)
| (8.2230504183096047992e-06 + 2.0753462477715536749e-295j)  +/-  (6.59e-46, 1.06e-104j)
| (0.1265141935115881962 - 3.3101701809582943252e-292j)  +/-  (5.55e-41, 9.44e-100j)
| (0.010983903924268787755 + 5.4051706573618097005e-293j)  +/-  (1.93e-43, 3.13e-102j)
| (0.2701689960126730069 - 7.5033526367286854418e-292j)  +/-  (2.05e-41, 3.51e-100j)
| (0.064753445815760582131 + 3.1490081972951940551e-292j)  +/-  (1.93e-42, 3.2e-101j)
| (0.11648001045398586641 + 7.8138756645676382728e-292j)  +/-  (1.28e-41, 2.38e-100j)
| (0.00051084204409817667449 + 5.7289103253030176106e-294j)  +/-  (1.08e-44, 1.73e-103j)
