Starting with polynomial:
P : t
Extension levels are: 1 20 22
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^21 - 210/41*t^19 + 5985/533*t^17 - 271320/19721*t^15 + 203490/19721*t^13 - 81396/16687*t^11 + 67830/47027*t^9 - 348840/1363783*t^7 + 33915/1363783*t^5 - 4522/4091349*t^3 + 2261/156835045*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 19823/1845*t^41 + 66431474/1237275*t^39 - 1286508148622/7764852375*t^37 + 2667193630954157/7545547760625*t^35 - 109504976674009178093/197957445499996875*t^33 + 38012393182426670482563752/57815901436014314578125*t^31 - 28035935678183574928939058776/46243396003418546127890625*t^29 + 1486043198956788735459651315386362/3382696444650755715023108203125*t^27 - 114575214288433215563187381367411093054/454989585287749897449183168861328125*t^25 + 134198371311099897378943373504210786530149716/1173047323945097469355022308210743251953125*t^23 - 13472461789633675568271466371948256994616268/327870370046766373422211204158282275390625*t^21 + 253377074314281655367196017988036963716782/21858024669784424894814080277218818359375*t^19 - 39934028056166810561327273205833699014282/15722438797564235450655741953788974609375*t^17 + 15335820185172600198007404932717412473864/36069124300294422504445525658692353515625*t^15 - 1817688606456804286640369167457994151496/34219425618228041863191908958246591796875*t^13 + 1191380666694345126935740808153099247251/248575072887128228628846885828772412109375*t^11 - 214170983736513862382978877568264626689/718607937982788879127030088123178427734375*t^9 + 85982544745612840840111490665998874/7216341456905233318088089644256083984375*t^7 - 8435522716368226455139205955244040482/30763263630787009635009526153463686025390625*t^5 + 2474222748712072630566579046552932907/830608118031249260145257206143519522685546875*t^3 - 9556867509833570735257493967697541/988819188132439595411020483504189907958984375*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:
| (-0.99896193068731718686 + 3.6704944623784685816e-923j)  +/-  (1e-240, 1e-240j)
| (0.99896193068731718686 - 2.5667656657259431074e-937j)  +/-  (9.49e-241, 9.49e-241j)
| (-0.92009933415040082879 - 1.5216815983235797621e-941j)  +/-  (8.7e-241, 8.7e-241j)
| (0.99375217062038950026 - 9.1113195826193670571e-954j)  +/-  (2.25e-240, 2.25e-240j)
| (0.88912831533118433426 + 3.8313807159344538806e-955j)  +/-  (3.59e-241, 3.59e-241j)
| (0.96722683856630629432 + 2.2288585467616026303e-953j)  +/-  (2.37e-240, 2.37e-240j)
| (-0.98318486356168595383 + 5.2346799589905860124e-952j)  +/-  (2.62e-240, 2.62e-240j)
| (-0.88912831533118433426 + 1.1060663227307639309e-965j)  +/-  (3.41e-241, 3.41e-241j)
| (-0.072967247595790589088 + 3.5945187932415688513e-984j)  +/-  (2.28e-254, 2.28e-254j)
| (0.71972345257202475786 + 9.8670362547105053861e-978j)  +/-  (1.76e-243, 1.76e-243j)
| (0.81305258084753191325 - 1.2008857964166149508e-976j)  +/-  (3.85e-242, 3.85e-242j)
| (0.98318486356168595383 - 2.7713354215427671771e-974j)  +/-  (2.66e-240, 2.66e-240j)
| (-0.94614721677851262707 - 3.1976850415233597978e-973j)  +/-  (1.58e-240, 1.58e-240j)
| (-0.85336336458331728365 - 2.1456185738177665524e-987j)  +/-  (1.2e-241, 1.2e-241j)
| (-0.99375217062038950026 + 9.0904906396208919201e-1000j)  +/-  (2.16e-240, 2.16e-240j)
| (0.85336336458331728365 + 1.401680696396459564e-1015j)  +/-  (1.25e-241, 1.25e-241j)
| (0.92009933415040082879 + 3.9451366237781165842e-1014j)  +/-  (8.09e-241, 8.09e-241j)
| (-0.42434212020743878357 - 1.2258753935635057216e-1024j)  +/-  (4.13e-248, 4.13e-248j)
| (-0.71972345257202475786 + 7.5155701584216522406e-1018j)  +/-  (1.79e-243, 1.79e-243j)
| (-0.3571252536599210773 - 1.6035038891891890412e-1025j)  +/-  (2.59e-249, 2.59e-249j)
| (0.94614721677851262707 + 4.357217265366847151e-1016j)  +/-  (1.54e-240, 1.54e-240j)
| (0.76843996347567790862 + 2.421070685095164626e-1019j)  +/-  (8.96e-243, 8.96e-243j)
| (0.14556185416089509094 + 5.7214069205251631915e-1029j)  +/-  (4.63e-253, 4.63e-253j)
| (-0.81305258084753191325 - 1.1811874629881546439e-1016j)  +/-  (3.45e-242, 3.45e-242j)
| (-0.76843996347567790862 + 1.9282295099973683778e-1023j)  +/-  (8.7e-243, 8.7e-243j)
| (0.21738009387172883298 - 7.7333262756588939373e-1037j)  +/-  (8.69e-252, 8.69e-252j)
| (0.66713880419741231931 - 2.003945451109434793e-1030j)  +/-  (2.88e-244, 2.88e-244j)
| (0.4892959088956686414 - 1.6416540308756657972e-1034j)  +/-  (4.66e-247, 4.66e-247j)
| (-0.14556185416089509094 + 2.5965350196064482641e-1033j)  +/-  (4.63e-253, 4.63e-253j)
| (-0.66713880419741231931 - 1.123122822903850468e-1029j)  +/-  (2.76e-244, 2.76e-244j)
| (-0.96722683856630629432 - 1.0142950772789306179e-1041j)  +/-  (2.49e-240, 2.49e-240j)
| (0.3571252536599210773 + 6.2863465729441128354e-1061j)  +/-  (2.78e-249, 2.78e-249j)
| (0.61099712378976603905 + 1.261367224730284647e-1057j)  +/-  (3.9e-245, 3.9e-245j)
| (1.0791069514847775438e-1065 + 8.3824184077176515542e-1067j)  +/-  (4.65e-1064, 4.65e-1064j)
| (-0.61099712378976603905 + 3.2329612790576829571e-1055j)  +/-  (4.07e-245, 4.07e-245j)
| (-0.4892959088956686414 - 3.437413647665318727e-1057j)  +/-  (5.12e-247, 5.12e-247j)
| (0.072967247595790589088 - 3.9250243524380317282e-1067j)  +/-  (2.28e-254, 2.28e-254j)
| (0.55161883588721980706 - 2.3900808624975202846e-1059j)  +/-  (4.96e-246, 4.96e-246j)
| (0.2880213168024010966 - 2.9748657728693770154e-1065j)  +/-  (1.75e-250, 1.75e-250j)
| (-0.2880213168024010966 + 5.7413507744410583165e-1062j)  +/-  (1.74e-250, 1.74e-250j)
| (-0.55161883588721980706 + 1.9944924258397331371e-1059j)  +/-  (5.23e-246, 5.23e-246j)
| (-0.21738009387172883298 + 1.6887333415270367902e-1065j)  +/-  (1.02e-251, 1.02e-251j)
| (0.42434212020743878357 + 1.4273375136011315008e-1063j)  +/-  (3.84e-248, 3.84e-248j)
-------------------------------------------------
The weights are:
| (0.0027954812324115695086 + 3.8986542068993834382e-923j)  +/-  (3.86e-78, 1.68e-193j)
| (0.0027954812324115695086 + 5.1357304358156675478e-926j)  +/-  (1.64e-78, 7.13e-194j)
| (0.028518426570204953083 - 1.3318717611536270737e-923j)  +/-  (5.49e-79, 2.39e-194j)
| (0.0078183373021241792478 - 1.5102007774567510301e-925j)  +/-  (1.27e-78, 5.53e-194j)
| (0.033402546320807622071 + 6.4935381959850451829e-925j)  +/-  (7.35e-80, 3.19e-195j)
| (0.018560055408876216262 - 3.4337547428750938717e-925j)  +/-  (1.26e-79, 5.48e-195j)
| (0.013304642607088317448 + 3.095291198571765792e-923j)  +/-  (1.75e-80, 7.6e-196j)
| (0.033402546320807622071 + 1.1162690120171738774e-923j)  +/-  (1.13e-80, 4.92e-196j)
| (0.072845652830508441029 + 2.8874848873867572401e-924j)  +/-  (2.32e-81, 1.01e-196j)
| (0.050697197796517511975 + 1.0827099920832469485e-924j)  +/-  (5e-81, 2.17e-196j)
| (0.042496932881118485504 + 8.6083613467366844903e-925j)  +/-  (1.04e-80, 4.5e-196j)
| (0.013304642607088317448 + 2.4637235322315111804e-925j)  +/-  (1.37e-79, 5.97e-195j)
| (0.023574199083029030565 + 1.6383496337531177576e-923j)  +/-  (3.58e-81, 1.55e-196j)
| (0.038083153453465002584 - 9.5839571454853976831e-924j)  +/-  (4.86e-82, 2.11e-197j)
| (0.0078183373021241792478 - 5.7764625364227002822e-923j)  +/-  (5.6e-81, 2.43e-196j)
| (0.038083153453465002584 - 7.5332903002930943873e-925j)  +/-  (1.8e-81, 7.81e-197j)
| (0.028518426570204953083 - 5.4732419054724993537e-925j)  +/-  (2.82e-81, 1.23e-196j)
| (0.066149577815951110014 - 4.2235012317717427933e-924j)  +/-  (1.68e-85, 7.29e-201j)
| (0.050697197796517511975 + 6.6639735693371408756e-924j)  +/-  (2.51e-85, 1.09e-200j)
| (0.06822070626102521507 + 3.9013620366845098042e-924j)  +/-  (1.25e-85, 5.43e-201j)
| (0.023574199083029030565 + 4.4485404483353286027e-925j)  +/-  (5.83e-82, 2.53e-197j)
| (0.046697324731514497925 - 9.7083163465701828667e-925j)  +/-  (9.88e-84, 4.29e-199j)
| (0.072275482222034062651 - 2.3170271406565516272e-924j)  +/-  (2.73e-87, 1.18e-202j)
| (0.042496932881118485504 + 8.3903664308783284726e-924j)  +/-  (1.33e-85, 5.79e-201j)
| (0.046697324731514497925 - 7.4433239086094594442e-924j)  +/-  (4.68e-86, 2.03e-201j)
| (0.071293346363784556102 + 2.1513836383937347555e-924j)  +/-  (8.04e-88, 3.49e-203j)
| (0.054418675178383649262 - 1.1979854161479505733e-924j)  +/-  (1.53e-86, 6.66e-202j)
| (0.063695615249100799842 + 1.5709267361570134298e-924j)  +/-  (3.01e-88, 1.31e-203j)
| (0.072275482222034062651 - 3.1074436780158307887e-924j)  +/-  (1.46e-88, 6.36e-204j)
| (0.054418675178383649262 - 6.0151454883176906488e-924j)  +/-  (5.45e-88, 2.37e-203j)
| (0.018560055408876216262 - 2.1274272612996558043e-923j)  +/-  (3.22e-86, 1.4e-201j)
| (0.06822070626102521507 + 1.8465164145856772335e-924j)  +/-  (2.39e-89, 1.04e-204j)
| (0.057810457497609522303 + 1.318002240631320139e-924j)  +/-  (2.43e-88, 1.06e-203j)
| (0.073027487962769082973 - 2.6842164222005392804e-924j)  +/-  (1.41e-89, 6.13e-205j)
| (0.057810457497609522303 + 5.4693869222157351665e-924j)  +/-  (1.9e-89, 8.25e-205j)
| (0.063695615249100799842 + 4.5872079568449185429e-924j)  +/-  (6.62e-90, 2.88e-205j)
| (0.072845652830508441029 + 2.4943771541976820418e-924j)  +/-  (6.75e-90, 2.93e-205j)
| (0.060898680204661962686 - 1.442383875337609962e-924j)  +/-  (5.41e-90, 2.35e-205j)
| (0.06992976500839875338 - 1.9952015165642945086e-924j)  +/-  (2.39e-90, 1.04e-205j)
| (0.06992976500839875338 - 3.6118219680159765071e-924j)  +/-  (2.59e-91, 1.13e-206j)
| (0.060898680204661962686 - 4.999591412303177237e-924j)  +/-  (3.11e-91, 1.35e-206j)
| (0.071293346363784556102 + 3.3481053513075110023e-924j)  +/-  (2.25e-91, 9.86e-207j)
| (0.066149577815951110014 - 1.7051223003521831202e-924j)  +/-  (1.61e-91, 6.6e-207j)
