Starting with polynomial:
P : -t+1
Extension levels are: 1 7 12
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : -t^8 + 19265/204*t^7 - 624113/204*t^6 + 1552467/34*t^5 - 11604425/34*t^4 + 21609490/17*t^3 - 36977850/17*t^2 + 23737980/17*t - 3293220/17
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^20 + 1226775058853916143304149911520559664174311340375636600318183687283/3945885944626245244193056853752619996849064308586889189222119012*t^19 - 851566068806410647916174730688595191154291245079213807641749165657467/19729429723131226220965284268763099984245321542934445946110595060*t^18 + 1166049086647473882505056089659417695355289019047019400382691275185488/328823828718853770349421404479384999737422025715574099101843251*t^17 - 316769274727203555164878603611359051354250597733848931931800666638465192/1644119143594268851747107022396924998687110128577870495509216255*t^16 + 24100575028201223411225888747498508011972767301345858631102337946158521981/3288238287188537703494214044793849997374220257155740991018432510*t^15 - 132622093850308686445957212757219433736427954616665534923070862294291527725/657647657437707540698842808958769999474844051431148198203686502*t^14 + 79094412753961599222183142236405622609405941196835716083027169585548667935/19342578159932574726436553204669705866907177983269064653049603*t^13 - 20293134405698950516334455894883460827334024820715374510548804091238197655625/328823828718853770349421404479384999737422025715574099101843251*t^12 + 844004155241081081130195464342186577799786977261400025067453068344364337540/1213372061693187344462809610625036899400081275703225457940381*t^11 - 1921305856000439225197007159240405257895232159934549144631179303924040973007260/328823828718853770349421404479384999737422025715574099101843251*t^10 + 11942187128366957504109375076977363194170896667439102400257309440985825307665400/328823828718853770349421404479384999737422025715574099101843251*t^9 - 54239168944282392048230673048483274388019497374937727420131346196341440459390760/328823828718853770349421404479384999737422025715574099101843251*t^8 + 176629590218146828095432661699061301781020461297038617655842865099198932159864000/328823828718853770349421404479384999737422025715574099101843251*t^7 - 401395262047064583702686967318935526494370087265300389705369058078411376559030720/328823828718853770349421404479384999737422025715574099101843251*t^6 + 612555388741629106313204231038549534103272659780652442349689658879142851487946880/328823828718853770349421404479384999737422025715574099101843251*t^5 - 593932864804844858779466277796365053905676257824653378568781506866108916112560000/328823828718853770349421404479384999737422025715574099101843251*t^4 + 337192894992695719530277154109098033821912889630641140006478199656606168397452800/328823828718853770349421404479384999737422025715574099101843251*t^3 - 99273581795281112317434492743485131819741891546125583325867627074835161845184000/328823828718853770349421404479384999737422025715574099101843251*t^2 + 12745939512776749329924745210070967437243670100824562408127552289509372721945600/328823828718853770349421404479384999737422025715574099101843251*t - 30207634096006294776058310930141768294490127913769104133627268508373921715200/19342578159932574726436553204669705866907177983269064653049603
-------------------------------------------------
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:   20 out of 20
Indefinite weights: 0 out of 20
Negative weights:   0 out of 20
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (57.228433557164904529 - 8.8987083302752449076e-374j)  +/-  (3.08e-120, 3.08e-120j)
| (32.766121056992691238 - 1.7294204903170581334e-371j)  +/-  (2.13e-118, 2.13e-118j)
| (39.138230909954930392 - 4.2049429974607153684e-377j)  +/-  (1.07e-118, 1.07e-118j)
| (46.925435925679186168 + 6.7184604916860453768e-381j)  +/-  (2.81e-119, 2.81e-119j)
| (27.378594248652106062 - 1.2171343174730927833e-385j)  +/-  (3.36e-118, 3.36e-118j)
| (4.7673099177671066141 + 9.1560661599810642855e-396j)  +/-  (3.52e-120, 3.52e-120j)
| (6.3011481094122368154 - 8.464592760760016687e-399j)  +/-  (1.48e-119, 1.48e-119j)
| (15.300146822083297294 - 8.5055809474786383937e-418j)  +/-  (2.46e-118, 2.46e-118j)
| (18.75251539166561618 + 1.4749642484684169168e-441j)  +/-  (3.89e-118, 3.89e-118j)
| (3.4466388648224408228 + 6.7975088279029902194e-457j)  +/-  (7.64e-121, 7.64e-121j)
| (1 + 2.1263816604771273726e-461j)  +/-  (1.06e-123, 1.06e-123j)
| (1.749385606379291932 + 6.126426349368769209e-461j)  +/-  (2.09e-122, 2.09e-122j)
| (0.18807558052466950658 + 1.2929546085972929677e-462j)  +/-  (8.71e-126, 8.71e-126j)
| (12.35199612685986194 + 2.9051279211635544879e-462j)  +/-  (1.66e-118, 1.66e-118j)
| (0.071803052476951600666 - 2.6209874931119909456e-477j)  +/-  (1.01e-126, 1.01e-126j)
| (9.90483711761762781 - 2.8639031518473683905e-478j)  +/-  (9.27e-119, 9.27e-119j)
| (0.42656231797579029713 + 2.1227008083168961869e-491j)  +/-  (6.91e-125, 6.91e-125j)
| (2.5000206754193299535 - 6.3180447633082430189e-488j)  +/-  (1.32e-121, 1.32e-121j)
| (22.751600472416912723 + 2.1134791886032232479e-484j)  +/-  (4.33e-118, 4.33e-118j)
| (7.9509208918881512072 - 7.7191760020325617942e-494j)  +/-  (4.6e-119, 4.6e-119j)
-------------------------------------------------
The weights are:
| (1.74403249422541835e-24 + 5.0795543468475199717e-392j)  +/-  (8.61e-52, 2.52e-110j)
| (3.432571569215471109e-14 + 3.4148512487857960942e-385j)  +/-  (1.17e-47, 3.42e-106j)
| (7.0194866618975384113e-17 + 2.7575024774370530877e-387j)  +/-  (4.02e-49, 1.18e-107j)
| (3.6520128661653157045e-20 - 1.8940770357665854065e-389j)  +/-  (1.09e-50, 3.19e-109j)
| (6.4093880919859774406e-12 - 2.3783410402102441544e-384j)  +/-  (2.93e-47, 8.6e-106j)
| (0.012386158462076906403 - 2.0719326614634426268e-378j)  +/-  (3.24e-38, 9.51e-97j)
| (0.002913143839402658246 + 7.4847864830646394507e-379j)  +/-  (6.11e-40, 1.79e-98j)
| (7.2424387460655206412e-07 + 1.3384352693721911381e-381j)  +/-  (2.47e-45, 7.24e-104j)
| (2.6662930922900785047e-08 - 1.7021785565655954664e-382j)  +/-  (1.96e-46, 5.75e-105j)
| (0.036714407616416657716 + 5.8320870100866669604e-378j)  +/-  (2.62e-39, 7.66e-98j)
| (0.25203552454679392796 - 1.8521337730501971488e-377j)  +/-  (4.89e-37, 1.43e-95j)
| (0.13454542860289254933 + 1.6413531533713567865e-377j)  +/-  (1.31e-37, 3.85e-96j)
| (0.043029891759799804492 - 3.4658988654907494237e-377j)  +/-  (3.04e-37, 8.9e-96j)
| (1.1668464420246537908e-05 - 9.4168581777563042816e-381j)  +/-  (8.29e-45, 2.43e-103j)
| (0.16261878810067943595 + 1.5494787263631227167e-377j)  +/-  (3.77e-38, 1.1e-96j)
| (0.00010939977724579436942 + 5.5993175590796608143e-380j)  +/-  (3.64e-44, 1.07e-102j)
| (0.29169600565091529611 + 2.9253304691693773454e-377j)  +/-  (1.54e-38, 4.53e-97j)
| (0.063321888553240684392 - 1.2296267047822362283e-377j)  +/-  (2.07e-40, 6.06e-99j)
| (5.651535641626107436e-10 + 1.9836305364649613028e-383j)  +/-  (2.11e-48, 6.22e-107j)
| (0.00061694314771316083614 - 2.4142538975124651297e-379j)  +/-  (1.67e-43, 4.89e-102j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 7 12
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : -t^8 + 19265/204*t^7 - 624113/204*t^6 + 1552467/34*t^5 - 11604425/34*t^4 + 21609490/17*t^3 - 36977850/17*t^2 + 23737980/17*t - 3293220/17
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^20 + 1226775058853916143304149911520559664174311340375636600318183687283/3945885944626245244193056853752619996849064308586889189222119012*t^19 - 851566068806410647916174730688595191154291245079213807641749165657467/19729429723131226220965284268763099984245321542934445946110595060*t^18 + 1166049086647473882505056089659417695355289019047019400382691275185488/328823828718853770349421404479384999737422025715574099101843251*t^17 - 316769274727203555164878603611359051354250597733848931931800666638465192/1644119143594268851747107022396924998687110128577870495509216255*t^16 + 24100575028201223411225888747498508011972767301345858631102337946158521981/3288238287188537703494214044793849997374220257155740991018432510*t^15 - 132622093850308686445957212757219433736427954616665534923070862294291527725/657647657437707540698842808958769999474844051431148198203686502*t^14 + 79094412753961599222183142236405622609405941196835716083027169585548667935/19342578159932574726436553204669705866907177983269064653049603*t^13 - 20293134405698950516334455894883460827334024820715374510548804091238197655625/328823828718853770349421404479384999737422025715574099101843251*t^12 + 844004155241081081130195464342186577799786977261400025067453068344364337540/1213372061693187344462809610625036899400081275703225457940381*t^11 - 1921305856000439225197007159240405257895232159934549144631179303924040973007260/328823828718853770349421404479384999737422025715574099101843251*t^10 + 11942187128366957504109375076977363194170896667439102400257309440985825307665400/328823828718853770349421404479384999737422025715574099101843251*t^9 - 54239168944282392048230673048483274388019497374937727420131346196341440459390760/328823828718853770349421404479384999737422025715574099101843251*t^8 + 176629590218146828095432661699061301781020461297038617655842865099198932159864000/328823828718853770349421404479384999737422025715574099101843251*t^7 - 401395262047064583702686967318935526494370087265300389705369058078411376559030720/328823828718853770349421404479384999737422025715574099101843251*t^6 + 612555388741629106313204231038549534103272659780652442349689658879142851487946880/328823828718853770349421404479384999737422025715574099101843251*t^5 - 593932864804844858779466277796365053905676257824653378568781506866108916112560000/328823828718853770349421404479384999737422025715574099101843251*t^4 + 337192894992695719530277154109098033821912889630641140006478199656606168397452800/328823828718853770349421404479384999737422025715574099101843251*t^3 - 99273581795281112317434492743485131819741891546125583325867627074835161845184000/328823828718853770349421404479384999737422025715574099101843251*t^2 + 12745939512776749329924745210070967437243670100824562408127552289509372721945600/328823828718853770349421404479384999737422025715574099101843251*t - 30207634096006294776058310930141768294490127913769104133627268508373921715200/19342578159932574726436553204669705866907177983269064653049603
-------------------------------------------------
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:   20 out of 20
Indefinite weights: 0 out of 20
Negative weights:   0 out of 20
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (57.228433557164904529 - 8.8987083302752449076e-374j)  +/-  (3.08e-120, 3.08e-120j)
| (32.766121056992691238 - 1.7294204903170581334e-371j)  +/-  (2.13e-118, 2.13e-118j)
| (39.138230909954930392 - 4.2049429974607153684e-377j)  +/-  (1.07e-118, 1.07e-118j)
| (46.925435925679186168 + 6.7184604916860453768e-381j)  +/-  (2.81e-119, 2.81e-119j)
| (27.378594248652106062 - 1.2171343174730927833e-385j)  +/-  (3.36e-118, 3.36e-118j)
| (4.7673099177671066141 + 9.1560661599810642855e-396j)  +/-  (3.52e-120, 3.52e-120j)
| (6.3011481094122368154 - 8.464592760760016687e-399j)  +/-  (1.48e-119, 1.48e-119j)
| (15.300146822083297294 - 8.5055809474786383937e-418j)  +/-  (2.46e-118, 2.46e-118j)
| (18.75251539166561618 + 1.4749642484684169168e-441j)  +/-  (3.89e-118, 3.89e-118j)
| (3.4466388648224408228 + 6.7975088279029902194e-457j)  +/-  (7.64e-121, 7.64e-121j)
| (1 + 2.1263816604771273726e-461j)  +/-  (1.06e-123, 1.06e-123j)
| (1.749385606379291932 + 6.126426349368769209e-461j)  +/-  (2.09e-122, 2.09e-122j)
| (0.18807558052466950658 + 1.2929546085972929677e-462j)  +/-  (8.71e-126, 8.71e-126j)
| (12.35199612685986194 + 2.9051279211635544879e-462j)  +/-  (1.66e-118, 1.66e-118j)
| (0.071803052476951600666 - 2.6209874931119909456e-477j)  +/-  (1.01e-126, 1.01e-126j)
| (9.90483711761762781 - 2.8639031518473683905e-478j)  +/-  (9.27e-119, 9.27e-119j)
| (0.42656231797579029713 + 2.1227008083168961869e-491j)  +/-  (6.91e-125, 6.91e-125j)
| (2.5000206754193299535 - 6.3180447633082430189e-488j)  +/-  (1.32e-121, 1.32e-121j)
| (22.751600472416912723 + 2.1134791886032232479e-484j)  +/-  (4.33e-118, 4.33e-118j)
| (7.9509208918881512072 - 7.7191760020325617942e-494j)  +/-  (4.6e-119, 4.6e-119j)
-------------------------------------------------
The weights are:
| (1.74403249422541835e-24 + 5.0795543468475199717e-392j)  +/-  (8.61e-52, 2.52e-110j)
| (3.432571569215471109e-14 + 3.4148512487857960942e-385j)  +/-  (1.17e-47, 3.42e-106j)
| (7.0194866618975384113e-17 + 2.7575024774370530877e-387j)  +/-  (4.02e-49, 1.18e-107j)
| (3.6520128661653157045e-20 - 1.8940770357665854065e-389j)  +/-  (1.09e-50, 3.19e-109j)
| (6.4093880919859774406e-12 - 2.3783410402102441544e-384j)  +/-  (2.93e-47, 8.6e-106j)
| (0.012386158462076906403 - 2.0719326614634426268e-378j)  +/-  (3.24e-38, 9.51e-97j)
| (0.002913143839402658246 + 7.4847864830646394507e-379j)  +/-  (6.11e-40, 1.79e-98j)
| (7.2424387460655206412e-07 + 1.3384352693721911381e-381j)  +/-  (2.47e-45, 7.24e-104j)
| (2.6662930922900785047e-08 - 1.7021785565655954664e-382j)  +/-  (1.96e-46, 5.75e-105j)
| (0.036714407616416657716 + 5.8320870100866669604e-378j)  +/-  (2.62e-39, 7.66e-98j)
| (0.25203552454679392796 - 1.8521337730501971488e-377j)  +/-  (4.89e-37, 1.43e-95j)
| (0.13454542860289254933 + 1.6413531533713567865e-377j)  +/-  (1.31e-37, 3.85e-96j)
| (0.043029891759799804492 - 3.4658988654907494237e-377j)  +/-  (3.04e-37, 8.9e-96j)
| (1.1668464420246537908e-05 - 9.4168581777563042816e-381j)  +/-  (8.29e-45, 2.43e-103j)
| (0.16261878810067943595 + 1.5494787263631227167e-377j)  +/-  (3.77e-38, 1.1e-96j)
| (0.00010939977724579436942 + 5.5993175590796608143e-380j)  +/-  (3.64e-44, 1.07e-102j)
| (0.29169600565091529611 + 2.9253304691693773454e-377j)  +/-  (1.54e-38, 4.53e-97j)
| (0.063321888553240684392 - 1.2296267047822362283e-377j)  +/-  (2.07e-40, 6.06e-99j)
| (5.651535641626107436e-10 + 1.9836305364649613028e-383j)  +/-  (2.11e-48, 6.22e-107j)
| (0.00061694314771316083614 - 2.4142538975124651297e-379j)  +/-  (1.67e-43, 4.89e-102j)
