One starts from the polynomial
      
      and extends one by one with
      
      until the final polynomial defining this rule is reached.
      Note: Polynomials might be truncated due to size!
      The complete polynomials are included in the download.
    
| Node (ball center) | Error (ball radius) | 
|---|---|
| 0.99915807917252916619 - 2.2774471598247138451e-814j | 1.23e-233, 1.23e-233j | 
| -0.14887433898163121088 + 3.1766643635965125518e-833j | 1.1e-251, 1.1e-251j | 
| -0.91044872380491633118 - 2.0936648826884584242e-813j | 7.11e-234, 7.11e-234j | 
| -0.96251898264773627813 - 2.3758083268922776557e-815j | 6.27e-233, 6.27e-233j | 
| 0.94774634367342754567 - 7.0910456708050917058e-834j | 3.29e-233, 3.29e-233j | 
| 0.9302253655382177185 - 1.8032888248095936964e-833j | 1.74e-233, 1.74e-233j | 
| -0.99915807917252916619 + 1.3825218098734939185e-830j | 1.19e-233, 1.19e-233j | 
| -0.9302253655382177185 + 2.1073038001513023379e-855j | 1.69e-233, 1.69e-233j | 
| -0.98966554633182805236 + 3.3625122365568300953e-868j | 7.65e-233, 7.65e-233j | 
| 0.99563121933714870557 + 3.1803877976032984055e-883j | 4.06e-233, 4.06e-233j | 
| 0.88872469201295299281 - 9.0571162683106865921e-888j | 3.19e-234, 3.19e-234j | 
| -0.88872469201295299281 - 2.6761511837277380386e-885j | 3.05e-234, 3.05e-234j | 
| -0.99563121933714870557 + 1.2837834016233073853e-891j | 4.11e-233, 4.11e-233j | 
| -0.83922494413037315594 + 5.4400315484444530348e-906j | 3.74e-235, 3.74e-235j | 
| 0.98966554633182805236 + 1.9456750027975828918e-903j | 8.6e-233, 8.6e-233j | 
| 0.86506336668898451073 + 5.5415046267053040452e-907j | 1.03e-234, 1.03e-234j | 
| 0.83922494413037315594 + 1.9346018805414918034e-908j | 3.41e-235, 3.41e-235j | 
| -0.98229145352179634579 - 4.9658992882387741047e-902j | 1.12e-232, 1.12e-232j | 
| -0.74850619214623857477 + 8.9137730511561625252e-919j | 5.21e-237, 5.21e-237j | 
| -0.97390652851717172008 + 2.902324271905606155e-912j | 1.04e-232, 1.04e-232j | 
| 0.67940956829902440623 + 1.915721150950838561e-921j | 1.68e-238, 1.68e-238j | 
| 0.78071202180714091681 - 5.2488973958043563936e-920j | 2.09e-236, 2.09e-236j | 
| 0.1002166500568261273 + 3.5720304629853197297e-936j | 5.17e-253, 5.17e-253j | 
| -0.71472414760103676849 + 5.0186519575514446916e-921j | 1.11e-237, 1.11e-237j | 
| -0.78071202180714091681 + 9.5266927602311596914e-920j | 2.17e-236, 2.17e-236j | 
| 0.91044872380491633118 + 4.4705742040420864826e-916j | 7.64e-234, 7.64e-234j | 
| 0.81106009108196866754 - 2.8512997898938387452e-918j | 1.05e-235, 1.05e-235j | 
| 0.96251898264773627813 - 2.6999500622321003752e-914j | 6.65e-233, 6.65e-233j | 
| -0.94774634367342754567 + 3.6719151815667560295e-917j | 3.04e-233, 3.04e-233j | 
| -0.64238526921078909395 - 4.8043457480513472344e-929j | 2.37e-239, 2.37e-239j | 
| 0.010245530496497745818 - 2.6566700896788909101e-944j | 1.72e-255, 1.72e-255j | 
| 0.64238526921078909395 - 5.6028304491387116435e-929j | 2.32e-239, 2.32e-239j | 
| 0.71472414760103676849 - 6.08498899859038178e-927j | 9.75e-238, 9.75e-238j | 
| -0.010245530496497745818 + 2.606979610619478617e-944j | 1.72e-255, 1.72e-255j | 
| -0.47767576735112117681 - 9.40428701830695538e-933j | 3.01e-243, 3.01e-243j | 
| -0.67940956829902440623 + 2.2790284351980492165e-928j | 1.61e-238, 1.61e-238j | 
| 0.52088863674875188368 - 1.6892553840705479029e-931j | 3.67e-242, 3.67e-242j | 
| 0.5629262430263026964 - 5.2348909861272571702e-930j | 3.55e-241, 3.55e-241j | 
| 0.74850619214623857477 - 3.6144841996544002477e-926j | 4.87e-237, 4.87e-237j | 
| -0.81106009108196866754 + 4.781521203438425877e-925j | 1.03e-235, 1.03e-235j | 
| -0.5629262430263026964 - 2.3560918032181071045e-931j | 3.37e-241, 3.37e-241j | 
| -0.86506336668898451073 + 4.8916135187430079446e-924j | 1.08e-234, 1.08e-234j | 
| 0.24592639358583283007 + 7.0268204433315927797e-939j | 3.79e-249, 3.79e-249j | 
| 0.60352029855101648642 - 4.0822130927680644248e-929j | 3.13e-240, 3.13e-240j | 
| 0.98229145352179634579 + 3.0769664051351702808e-920j | 1.17e-232, 1.17e-232j | 
| -0.60352029855101648642 + 7.8562495516345345806e-934j | 2.9e-240, 2.9e-240j | 
| -0.24592639358583283007 - 5.1486626802412442394e-943j | 3.62e-249, 3.62e-249j | 
| 0.97390652851717172008 - 1.5746754603341443925e-941j | 1.07e-232, 1.07e-232j | 
| 0.47767576735112117681 + 1.3154727822349703657e-953j | 3.22e-243, 3.22e-243j | 
| 0.29404468164678598008 - 2.5347654365793560694e-958j | 7.06e-248, 7.06e-248j | 
| -0.19747232048538983732 - 4.3967299735218671363e-960j | 1.91e-250, 1.91e-250j | 
| -0.52088863674875188368 - 4.763149104318002507e-954j | 3.77e-242, 3.77e-242j | 
| 0.38801042998904342938 - 1.532770188106719105e-957j | 1.74e-245, 1.74e-245j | 
| 0.14887433898163121088 - 1.5596414686432424179e-963j | 1.05e-251, 1.05e-251j | 
| 0.34150820085761671704 + 2.0075028500406942193e-958j | 1.19e-246, 1.19e-246j | 
| -0.1002166500568261273 - 6.5200400457278231465e-965j | 4.72e-253, 4.72e-253j | 
| -0.38801042998904342938 + 7.4113173681350448204e-959j | 1.77e-245, 1.77e-245j | 
| -0.4333953941292471908 + 1.0760467553941979296e-956j | 2.4e-244, 2.4e-244j | 
| 0.19747232048538983732 + 7.2062752793940271481e-962j | 2e-250, 2e-250j | 
| 0.4333953941292471908 + 1.7459543744618530044e-956j | 2.36e-244, 2.36e-244j | 
| 0.051960499878277184659 - 2.325076760571764561e-966j | 2.93e-254, 2.93e-254j | 
| -0.29404468164678598008 + 2.2556455496992039085e-961j | 6.11e-248, 6.11e-248j | 
| -0.34150820085761671704 + 5.9217676553695408591e-960j | 1.15e-246, 1.15e-246j | 
| -0.051960499878277184659 + 4.6675084782865952598e-966j | 2.98e-254, 2.98e-254j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0021537561916891629013 + 3.189550210660608227e-814j | 4.44e-44, 8.51e-155j | 
| 0.048644097094191461157 - 1.1709657578732588342e-813j | 2.58e-44, 4.95e-155j | 
| 0.020781167808532876347 - 2.3431651634886822032e-814j | 8.03e-45, 1.54e-155j | 
| 0.01318619294240741462 - 6.3566515636417206897e-814j | 6.6e-45, 1.27e-155j | 
| 0.016243133284730954826 + 3.0693334399268870149e-814j | 1.81e-45, 3.46e-156j | 
| 0.018717797862504872608 - 2.5683017510986435618e-814j | 1.56e-45, 3e-156j | 
| 0.0021537561916891629013 + 1.2215542083174257392e-815j | 8.84e-47, 1.7e-157j | 
| 0.018717797862504872608 - 1.9036354916528720283e-813j | 3.19e-46, 6.12e-157j | 
| 0.0069064916457238763697 + 1.4981330945709368164e-814j | 8.41e-47, 1.61e-157j | 
| 0.0048486798460160639317 - 5.8360093416630259188e-814j | 5e-48, 9.59e-159j | 
| 0.022665318486965814463 - 2.2733289086551918485e-814j | 1.29e-48, 2.48e-159j | 
| 0.022665318486965814463 + 2.3419608027770192684e-813j | 1.12e-47, 2.16e-158j | 
| 0.0048486798460160639317 - 5.3119335697284115509e-815j | 4.94e-47, 9.49e-158j | 
| 0.027000753919183341613 + 9.1061271829701098218e-814j | 3.2e-49, 6.13e-160j | 
| 0.0069064916457238763697 + 5.7395567808712965617e-814j | 6.33e-49, 1.21e-159j | 
| 0.024704687778413776259 + 2.1936440075952793104e-814j | 6.43e-50, 1.23e-160j | 
| 0.027000753919183341613 - 2.102224176311577103e-814j | 1.28e-50, 2.45e-161j | 
| 0.0076761866649064433929 - 3.2457038073981184055e-814j | 1.95e-47, 3.73e-158j | 
| 0.033025558048873360109 - 5.6487241169803962992e-814j | 7.18e-52, 1.38e-162j | 
| 0.0095880356252198975289 + 4.8201139433969771982e-814j | 1.04e-47, 2e-158j | 
| 0.036133064657544188428 + 2.2039985744453523133e-814j | 6.17e-54, 1.18e-164j | 
| 0.0313354383045405359 - 2.0178094129275093227e-814j | 8.04e-53, 1.54e-163j | 
| 0.048623921429291430834 - 1.5273211693411068247e-813j | 1.14e-55, 2.19e-166j | 
| 0.034531205344341520476 + 5.3250499981598634387e-814j | 7.33e-53, 1.41e-163j | 
| 0.0313354383045405359 + 6.1992669185190145261e-814j | 5.8e-52, 1.11e-162j | 
| 0.020781167808532876347 + 2.3640984596352489208e-814j | 4.07e-52, 7.8e-163j | 
| 0.029302494633408495102 + 2.0323416411695079782e-814j | 4.38e-53, 8.4e-164j | 
| 0.01318619294240741462 - 4.1631221657301981028e-814j | 6.31e-53, 1.21e-163j | 
| 0.016243133284730954826 + 9.3137977591362144351e-814j | 1.7e-50, 3.27e-161j | 
| 0.037941178483015237172 + 4.8285869734913020993e-814j | 3.08e-55, 5.91e-166j | 
| 0.028501046460530589671 - 7.2244005669449392005e-813j | 1.32e-57, 2.54e-168j | 
| 0.037941178483015237172 - 2.2573393647008318851e-814j | 1.47e-56, 2.81e-167j | 
| 0.034531205344341520476 - 2.1348040324739306677e-814j | 1.23e-55, 2.35e-166j | 
| 0.028501046460530589671 + 7.2988486095211373235e-813j | 8.14e-58, 1.56e-168j | 
| 0.043748651607282521692 + 4.7097053126626138193e-814j | 1.01e-58, 1.94e-169j | 
| 0.036133064657544188428 - 5.0694595001201062106e-814j | 7.11e-56, 1.36e-166j | 
| 0.042659327398607609826 + 2.5860259338671603213e-814j | 4.95e-59, 9.49e-170j | 
| 0.041368497302330237431 - 2.4203458074178254682e-814j | 1.52e-58, 2.91e-169j | 
| 0.033025558048873360109 + 2.0610581967624889628e-814j | 3.36e-56, 6.44e-167j | 
| 0.029302494633408495102 - 7.22201040530383768e-814j | 2.81e-56, 5.39e-167j | 
| 0.041368497302330237431 + 4.5475386736333701022e-814j | 5.78e-60, 1.11e-170j | 
| 0.024704687778413776259 - 1.2823322198670400564e-813j | 6.57e-56, 1.26e-166j | 
| 0.048332134676758742818 + 5.7005239211543022847e-814j | 1.31e-62, 2.5e-173j | 
| 0.039768454616338275256 + 2.3178239808152316527e-814j | 4.02e-59, 7.71e-170j | 
| 0.0076761866649064433929 - 6.4373621696843809892e-814j | 1.67e-58, 3.21e-169j | 
| 0.039768454616338275256 - 4.6370549750428080882e-814j | 1.34e-60, 2.57e-171j | 
| 0.048332134676758742818 - 7.3209220633440008392e-814j | 1.67e-64, 3.19e-175j | 
| 0.0095880356252198975289 + 5.7961677983834880417e-814j | 1.99e-58, 3.82e-169j | 
| 0.043748651607282521692 - 2.8159181185233548041e-814j | 1.31e-62, 2.51e-173j | 
| 0.047848582822901605889 - 4.6394829470580009188e-814j | 2.05e-64, 3.93e-175j | 
| 0.048543824902148152432 + 8.9805814880619495088e-814j | 4.87e-65, 9.35e-176j | 
| 0.042659327398607609826 - 4.5782051459122601412e-814j | 7.72e-64, 1.48e-174j | 
| 0.045953182840294082891 - 3.462103198726434715e-814j | 1.32e-64, 2.54e-175j | 
| 0.048644097094191461157 + 1.0080167952771754967e-813j | 1.73e-65, 3.32e-176j | 
| 0.047024787617359416179 + 3.9417466613855533068e-814j | 6.82e-65, 1.31e-175j | 
| 0.048623921429291430834 + 1.6888700001148181278e-813j | 7.09e-66, 1.36e-176j | 
| 0.045953182840294082891 + 5.1958365147273876718e-814j | 3.9e-67, 7.47e-178j | 
| 0.044821661096125757799 - 4.9143514498068749482e-814j | 1.1e-66, 2.11e-177j | 
| 0.048543824902148152432 - 7.3550802547250403098e-814j | 1.59e-66, 3.08e-177j | 
| 0.044821661096125757799 + 3.1039522290420339623e-814j | 2.45e-66, 4.72e-177j | 
| 0.047420688607822284077 + 2.8939425847965510842e-813j | 8.86e-67, 1.71e-177j | 
| 0.047848582822901605889 + 6.2715573455792596467e-814j | 3.1e-68, 5.75e-179j | 
| 0.047024787617359416179 - 5.6124265289432093577e-814j | 2.71e-68, 4.92e-179j | 
| 0.047420688607822284077 - 3.0485008602879222448e-813j | 1.33e-67, 2.93e-178j | 
All rules of Legendre type can be downloaded here packed into a single file.