Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 34
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 15336933931005901546930628393292801598850451598540242/20059506747419960058056579667371585555506498480433*t^41 + 5288322184205571730035776815607944887300673535223579669/20059506747419960058056579667371585555506498480433*t^39 - 1090539690082734719528360968027986247505558577706064927043/20059506747419960058056579667371585555506498480433*t^37 + 150401439024545424137986941881490107856187814350504649784348/20059506747419960058056579667371585555506498480433*t^35 - 14698447451988240151112010271496672452663613958671157767775465/20059506747419960058056579667371585555506498480433*t^33 + 33947714381480272084134774593974033721822386593295554770881980/647080862819998711550212247334567275984080596143*t^31 - 1816163335923050490492322512605538884933771746859528322193552980/647080862819998711550212247334567275984080596143*t^29 + 73405088528756954908774759925065914053688138795690822173741372610/647080862819998711550212247334567275984080596143*t^27 - 2252087408031867798434939929856842226574490065555517359092929852560/647080862819998711550212247334567275984080596143*t^25 + 52432548646092829980350916814410559814343557353617812076832573916250/647080862819998711550212247334567275984080596143*t^23 - 921884982952121230146186761024921001495285151650187884741997197279750/647080862819998711550212247334567275984080596143*t^21 + 12127319138315958201755300550208197877221274364513501543095841022025500/647080862819998711550212247334567275984080596143*t^19 - 117677543945744959072766855130084602500930303415291930352326846281502250/647080862819998711550212247334567275984080596143*t^17 + 825634267939774074667544545898927197310801821751309336820444106416163500/647080862819998711550212247334567275984080596143*t^15 - 4075798567908040710036875572803744280183121033863709028308406437132722500/647080862819998711550212247334567275984080596143*t^13 + 13642969518169130880219279309759024292472915833167002849463155758984434375/647080862819998711550212247334567275984080596143*t^11 - 29434729669306302138280399314876539095552745095738485734234416766432216250/647080862819998711550212247334567275984080596143*t^9 + 38123286340579468912421916378365224863238683289983072327241009523025541875/647080862819998711550212247334567275984080596143*t^7 - 26716644994983363570748602427077799763813671295959198742986804091838373125/647080862819998711550212247334567275984080596143*t^5 + 8565801792379856340719646398923711604014819892919715615860082503613725000/647080862819998711550212247334567275984080596143*t^3 - 863817637993491677133618565073031744825507495853918668437442550713534375/647080862819998711550212247334567275984080596143*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
Positive weights:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-8.8372107900117969072 - 8.3152798563974338528e-667j)  +/-  (1.2e-245, 1.2e-245j)
| (-1.4488667235302982744 + 1.3057025538051180146e-672j)  +/-  (7.57e-251, 7.57e-251j)
| (-6.9384222166127685053 - 1.1920139369407413455e-666j)  +/-  (2.7e-245, 2.7e-245j)
| (-7.5389001707960836041 - 8.2288325519470710099e-667j)  +/-  (2.75e-245, 2.75e-245j)
| (-11.338404245107104921 - 1.6117568838346438392e-669j)  +/-  (7.33e-248, 7.33e-248j)
| (-10.366928808023277024 + 1.2653611731391037468e-668j)  +/-  (8.01e-247, 8.01e-247j)
| (-4.2270904715776487353 + 5.2910872962027406161e-668j)  +/-  (1.27e-246, 1.27e-246j)
| (-3.7313022243357029508 + 3.5342329954098531285e-668j)  +/-  (3.77e-247, 3.77e-247j)
| (-8.168757288917091561 + 1.4096868919657157683e-666j)  +/-  (2.2e-245, 2.2e-245j)
| (-5.8038548730707561445 + 4.441196275775141061e-666j)  +/-  (1.44e-245, 1.44e-245j)
| (1.0379709584894152952 - 1.0540640838827675242e-674j)  +/-  (1.08e-251, 1.08e-251j)
| (-3.2511682423481392712 + 2.0327687976284763264e-670j)  +/-  (9.42e-248, 9.42e-248j)
| (-1.0379709584894152952 - 5.1715075283122265631e-675j)  +/-  (1.02e-251, 1.02e-251j)
| (-2.3344142183389772393 + 3.7859164787381828572e-672j)  +/-  (3.74e-249, 3.74e-249j)
| (-6.3613946927985534245 - 3.9192188158450604648e-668j)  +/-  (2.51e-245, 2.51e-245j)
| (-2.7865746390280676369 + 5.0065092646748945743e-671j)  +/-  (2.06e-248, 2.06e-248j)
| (-4.7377992861742280514 - 2.1283253648467107863e-668j)  +/-  (3.3e-246, 3.3e-246j)
| (-2.0213350529043396856e-678 - 8.4578552780520569341e-680j)  +/-  (8.7e-677, 8.7e-677j)
| (-1.8889621522997963331 - 4.7937989660491225724e-673j)  +/-  (5.24e-250, 5.24e-250j)
| (-0.74196378430272585765 + 8.1881458946306345176e-682j)  +/-  (2.05e-252, 2.05e-252j)
| (-9.5598110890082529185 + 8.7938373831087113075e-669j)  +/-  (4.07e-246, 4.07e-246j)
| (0.74196378430272585765 + 8.3788247317114032967e-676j)  +/-  (1.82e-252, 1.82e-252j)
| (0.42066569906215461659 + 2.475511433162669244e-676j)  +/-  (1.7e-253, 1.7e-253j)
| (-0.42066569906215461659 + 2.9702518837444084512e-676j)  +/-  (1.8e-253, 1.8e-253j)
| (-5.263179782380259654 - 1.8691746543719533854e-667j)  +/-  (7.79e-246, 7.79e-246j)
| (1.4488667235302982744 + 5.1394216916566178532e-672j)  +/-  (6.97e-251, 6.97e-251j)
| (8.8372107900117969072 - 1.3899101029850299703e-668j)  +/-  (1.14e-245, 1.14e-245j)
| (10.366928808023277024 + 1.4161301013780556011e-684j)  +/-  (8.39e-247, 8.39e-247j)
| (11.338404245107104921 + 2.8744307530366258781e-701j)  +/-  (7.16e-248, 7.16e-248j)
| (6.9384222166127685053 - 7.2365677015739853334e-728j)  +/-  (2.92e-245, 2.92e-245j)
| (9.5598110890082529185 - 3.2715175326670887665e-744j)  +/-  (3.96e-246, 3.96e-246j)
| (4.7377992861742280514 + 1.4437092085358501835e-756j)  +/-  (3.42e-246, 3.42e-246j)
| (2.3344142183389772393 - 7.7380748730241515107e-770j)  +/-  (3.65e-249, 3.65e-249j)
| (8.168757288917091561 - 2.5881808471194769238e-772j)  +/-  (2.08e-245, 2.08e-245j)
| (3.2511682423481392712 + 3.2413790211272666877e-787j)  +/-  (9.04e-248, 9.04e-248j)
| (5.8038548730707561445 + 6.6727440151903680669e-792j)  +/-  (1.46e-245, 1.46e-245j)
| (1.8889621522997963331 - 4.3896243300330060719e-809j)  +/-  (5.16e-250, 5.16e-250j)
| (3.7313022243357029508 + 4.8910448810183064216e-804j)  +/-  (3.71e-247, 3.71e-247j)
| (4.2270904715776487353 - 3.3609825353469224374e-813j)  +/-  (1.21e-246, 1.21e-246j)
| (6.3613946927985534245 - 6.8145878918892897374e-844j)  +/-  (2.26e-245, 2.26e-245j)
| (7.5389001707960836041 + 3.4315326123917845948e-878j)  +/-  (2.66e-245, 2.66e-245j)
| (5.263179782380259654 - 7.1618325303430923011e-898j)  +/-  (7.41e-246, 7.41e-246j)
| (2.7865746390280676369 + 1.0000918170461823149e-909j)  +/-  (2.02e-248, 2.02e-248j)
-------------------------------------------------
The weights are:
| (3.0388706017234895021e-18 + 4.9822968829518854274e-680j)  +/-  (5.05e-65, 3.49e-186j)
| (0.060600263992876204664 - 2.6794012421815164846e-669j)  +/-  (1.9e-33, 1.31e-154j)
| (8.2493134455166614401e-12 - 6.3029356310666865854e-676j)  +/-  (4.85e-61, 3.35e-182j)
| (1.1155474801868701746e-13 + 3.047781975658480722e-677j)  +/-  (1.84e-62, 1.27e-183j)
| (5.4188787241313338874e-29 - 4.2342846139870054984e-686j)  +/-  (4.37e-71, 3.02e-192j)
| (1.5912516672036339924e-24 + 1.2616390441753283233e-683j)  +/-  (3.78e-69, 2.61e-190j)
| (2.6468708687641042177e-05 + 1.4626044764982975596e-672j)  +/-  (5.89e-56, 4.07e-177j)
| (0.00018456221971718079784 + 2.6272657291335977077e-671j)  +/-  (2.53e-54, 1.75e-175j)
| (8.3568853425773988253e-16 - 1.4446052614025454742e-678j)  +/-  (5.06e-65, 3.49e-186j)
| (1.0610820764235525593e-08 + 1.6131745611344946969e-673j)  +/-  (5.59e-61, 3.86e-182j)
| (0.085821381406640468478 + 4.6497050003676899706e-669j)  +/-  (1.23e-41, 8.48e-163j)
| (0.00095441113540359080956 - 8.7388423789395357764e-671j)  +/-  (5.84e-54, 4.03e-175j)
| (0.085821381406640468478 + 6.8445315249093398042e-669j)  +/-  (3.19e-42, 2.2e-163j)
| (0.011714207340238712143 - 4.8462786714609635703e-670j)  +/-  (7.36e-51, 5.08e-172j)
| (3.6891708736702472478e-10 + 1.1403833649872685741e-674j)  +/-  (3.19e-62, 2.2e-183j)
| (0.0037599745777965557711 + 2.0197360396973984021e-670j)  +/-  (4.25e-53, 2.93e-174j)
| (2.7606189420115163309e-06 + 2.1054297501574832274e-672j)  +/-  (4.23e-59, 2.92e-180j)
| (0.17257519981350182192 - 7.6614964862227067737e-669j)  +/-  (1.33e-46, 9.15e-168j)
| (0.029715920524917291214 + 1.1244929655815513505e-669j)  +/-  (8.63e-51, 5.95e-172j)
| (0.077540388955545309964 - 1.0618109317219527092e-668j)  +/-  (6.05e-47, 4.17e-168j)
| (4.318591274079584513e-21 - 1.1061901675666946946e-681j)  +/-  (2.74e-70, 1.89e-191j)
| (0.077540388955545309964 - 8.0708432832912289319e-669j)  +/-  (9.75e-48, 6.72e-169j)
| (0.1433918443648865347 + 8.2601107316180568737e-669j)  +/-  (1.77e-47, 1.22e-168j)
| (0.1433918443648865347 + 9.6420403292966976265e-669j)  +/-  (1.05e-47, 7.21e-169j)
| (2.0525949802941106134e-07 - 7.3494415664237507486e-673j)  +/-  (1.73e-60, 1.19e-181j)
| (0.060600263992876204664 - 1.5477909851172040512e-669j)  +/-  (5.58e-54, 3.85e-175j)
| (3.0388706017234895021e-18 - 1.073803459104728794e-680j)  +/-  (7.44e-80, 5.13e-201j)
| (1.5912516672036339924e-24 - 3.6719573268856073845e-684j)  +/-  (1.13e-82, 7.78e-204j)
| (5.4188787241313338874e-29 + 1.4050767920791822952e-686j)  +/-  (1.82e-84, 1.25e-205j)
| (8.2493134455166614401e-12 + 5.4751130886139276176e-677j)  +/-  (3.36e-78, 2.32e-199j)
| (4.318591274079584513e-21 + 2.7999787091730661609e-682j)  +/-  (1.23e-81, 8.46e-203j)
| (2.7606189420115163309e-06 + 1.8376236387264945777e-673j)  +/-  (8.2e-75, 5.66e-196j)
| (0.011714207340238712143 - 1.8812338126642358435e-670j)  +/-  (6.13e-68, 4.23e-189j)
| (8.3568853425773988253e-16 + 2.5732202109467288097e-679j)  +/-  (3.71e-80, 2.56e-201j)
| (0.00095441113540359080956 - 1.7239882091785671887e-671j)  +/-  (8.86e-72, 6.11e-193j)
| (1.0610820764235525593e-08 + 4.4949475130085298186e-675j)  +/-  (2.35e-77, 1.62e-198j)
| (0.029715920524917291214 + 5.3883874080839005297e-670j)  +/-  (3.27e-68, 2.26e-189j)
| (0.00018456221971718079784 + 4.3111764074850303691e-672j)  +/-  (1.75e-73, 1.2e-194j)
| (2.6468708687641042177e-05 - 9.4919418205588421175e-673j)  +/-  (1.22e-74, 8.44e-196j)
| (3.6891708736702472478e-10 - 5.4812172045921024092e-676j)  +/-  (7.63e-79, 5.26e-200j)
| (1.1155474801868701746e-13 - 4.3247164796730335047e-678j)  +/-  (6.81e-81, 4.69e-202j)
| (2.0525949802941106134e-07 - 3.1013178658899598234e-674j)  +/-  (3.37e-77, 2.33e-198j)
| (0.0037599745777965557711 + 6.053137542521516128e-671j)  +/-  (8.4e-74, 5.73e-195j)
