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) | 
|---|---|
| 0.9985734331923466931 + 6.5181295272188109876e-854j | 9.96e-234, 9.96e-234j | 
| -0.9985734331923466931 - 2.9189064761097855123e-856j | 1.05e-233, 1.05e-233j | 
| -0.92689157269311465836 + 2.0337760471097980386e-880j | 1.52e-235, 1.52e-235j | 
| -0.99961888506430402214 + 6.1676721924389316771e-877j | 6.38e-234, 6.38e-234j | 
| 0.87741019897171705299 - 2.9278184837128148565e-903j | 1.78e-236, 1.78e-236j | 
| 0.94701511288615728208 - 6.7342280122721276438e-902j | 3.74e-235, 3.74e-235j | 
| -0.9948599046638616492 + 1.8279051733814097783e-898j | 6.04e-234, 6.04e-234j | 
| -0.90365367469341298698 + 1.7496478525422834874e-914j | 5.78e-236, 5.78e-236j | 
| -0.97755705854629352665 + 2.9390401141838977173e-918j | 1.96e-234, 1.96e-234j | 
| 0.99961888506430402214 + 6.7028444243274356824e-924j | 5.9e-234, 5.9e-234j | 
| 0.90365367469341298698 - 3.9921574244242853186e-929j | 5.89e-236, 5.89e-236j | 
| 0.98786180179615492351 - 9.7320959681509898203e-926j | 3.46e-234, 3.46e-234j | 
| -0.94701511288615728208 - 9.6483392230954995288e-931j | 3.89e-235, 3.89e-235j | 
| -0.87741019897171705299 - 2.9658322600877018282e-937j | 1.89e-236, 1.89e-236j | 
| 0.92689157269311465836 - 2.6280108731941887152e-937j | 1.51e-235, 1.51e-235j | 
| 0.81641357233552832956 + 5.6465428950963420644e-940j | 1.42e-237, 1.42e-237j | 
| 0.84828378070105010962 + 1.7069081905211381427e-938j | 5.32e-237, 5.32e-237j | 
| -0.98786180179615492351 - 4.6133130196254433335e-935j | 3.75e-234, 3.75e-234j | 
| -0.81641357233552832956 - 6.9056584776883214687e-955j | 1.45e-237, 1.45e-237j | 
| -0.96392874096524810675 + 3.6837390085775335351e-952j | 8.88e-235, 8.88e-235j | 
| 0.96392874096524810675 + 9.6346653269609827688e-957j | 8.45e-235, 8.45e-235j | 
| 0.78195575060159014815 + 9.0528288903390287589e-964j | 3.02e-238, 3.02e-238j | 
| 0.97755705854629352665 + 1.2879102106556389311e-961j | 1.73e-234, 1.73e-234j | 
| -0.74508170807163485788 + 1.6516629894232838819e-971j | 7.06e-239, 7.06e-239j | 
| -0.70597668298275892218 + 3.3069958465273082565e-972j | 1.17e-239, 1.17e-239j | 
| 0.9948599046638616492 - 2.5651625840786164124e-969j | 6.19e-234, 6.19e-234j | 
| 0.66484053768732027695 + 1.7938679750037572193e-976j | 1.9e-240, 1.9e-240j | 
| 0.70597668298275892218 - 3.2498282562558829385e-975j | 1.21e-239, 1.21e-239j | 
| -0.84828378070105010962 + 1.5247135087759745783e-976j | 5.14e-237, 5.14e-237j | 
| -0.66484053768732027695 + 5.5692605935400230803e-982j | 1.82e-240, 1.82e-240j | 
| -0.78195575060159014815 + 1.3493798467406329976e-983j | 2.92e-238, 2.92e-238j | 
| 0.53146280233533502459 + 8.4623075231650018429e-986j | 4.23e-243, 4.23e-243j | 
| 0.62188874585941807607 + 5.9906412910011871394e-984j | 2.66e-241, 2.66e-241j | 
| 0.095856026731708034484 - 1.1636343525023401828e-996j | 3.61e-253, 3.61e-253j | 
| -0.62188874585941807607 - 3.6215124003391865079e-986j | 2.86e-241, 2.86e-241j | 
| -0.57735026918962576451 + 4.5483243800237509033e-987j | 3.53e-242, 3.53e-242j | 
| -0.047839249042893614639 - 9.402256089819083942e-999j | 2.02e-254, 2.02e-254j | 
| 0.57735026918962576451 - 9.869669258556331661e-985j | 3.41e-242, 3.41e-242j | 
| 0.29036229308829455553 - 3.2593028831410132848e-992j | 2.2e-248, 2.2e-248j | 
| -0.33934902919334446926 - 8.4324813679814862219e-992j | 2.89e-247, 2.89e-247j | 
| -0.53146280233533502459 - 1.2253292910424280442e-987j | 3.99e-243, 3.99e-243j | 
| -0.095856026731708034484 + 5.6156721221743055243e-997j | 3.83e-253, 3.83e-253j | 
| 0.33934902919334446926 + 4.7506487523917901899e-993j | 2.97e-247, 2.97e-247j | 
| 0.4844701706795229243 + 1.0187497331434321175e-987j | 4.07e-244, 4.07e-244j | 
| -0.14410996994804539671 - 3.3075366445177494523e-996j | 5.97e-252, 5.97e-252j | 
| -0.4844701706795229243 + 8.3986774381227970259e-989j | 4.06e-244, 4.06e-244j | 
| -0.29036229308829455553 + 4.1142403138152839511e-993j | 2.2e-248, 2.2e-248j | 
| 0.74508170807163485788 - 4.3443436113519542895e-990j | 6.35e-239, 6.35e-239j | 
| 0.43662266912372229814 - 2.98945555314922547e-997j | 3.76e-245, 3.76e-245j | 
| 0.19262176287680599048 + 4.207146048092269448e-1002j | 1.05e-250, 1.05e-250j | 
| -0.19262176287680599048 - 3.2736949650954360547e-1002j | 1.06e-250, 1.06e-250j | 
| -0.43662266912372229814 + 2.0872422346123124627e-997j | 4.01e-245, 4.01e-245j | 
| 0.047839249042893614639 - 5.7823936012732337892e-1006j | 2.02e-254, 2.02e-254j | 
| 0.38817106928816062228 - 2.8189280169782082882e-998j | 3.34e-246, 3.34e-246j | 
| 0.24139919846369651189 - 4.088318286609248643e-1001j | 1.57e-249, 1.57e-249j | 
| -1.0780724493451602644e-1016 + 1.7518749693491459674e-1017j | 6.44e-1015, 6.44e-1015j | 
| -0.38817106928816062228 - 1.0206052372477650642e-998j | 3.6e-246, 3.6e-246j | 
| -0.24139919846369651189 + 4.5999451989936629088e-1001j | 1.71e-249, 1.71e-249j | 
| 0.14410996994804539671 - 2.6312357346577086455e-1003j | 6.19e-252, 6.19e-252j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0020430228262040584382 + 5.2918546613563869534e-854j | 1.39e-41, 8.04e-153j | 
| 0.0020430228262040584382 + 1.7029918085079908929e-856j | 6.92e-42, 4e-153j | 
| 0.021697816124379954715 - 2.5320283963431852813e-857j | 6.48e-43, 3.75e-154j | 
| 0.00068769504682523709247 - 2.9226631657719437044e-856j | 4.85e-42, 2.8e-153j | 
| 0.02770669258053288349 - 3.6674346774214492162e-856j | 1.88e-44, 1.09e-155j | 
| 0.018533230915148534144 + 8.8436846473239084227e-856j | 1.81e-44, 1.05e-155j | 
| 0.0053615192916048087249 + 1.6353694258779302998e-856j | 1.35e-42, 7.81e-154j | 
| 0.024759875323745450342 + 2.4753041544336933072e-857j | 1.27e-44, 7.34e-156j | 
| 0.011968699202947502312 + 4.1557568655615165785e-857j | 8.15e-44, 4.72e-155j | 
| 0.00068769504682523709247 - 7.3898948016691125102e-854j | 2.29e-45, 1.32e-156j | 
| 0.024759875323745450342 + 4.5530987072511875522e-856j | 2.82e-46, 1.63e-157j | 
| 0.0086438179550827597097 - 6.6497049725506174186e-855j | 3.08e-46, 1.78e-157j | 
| 0.018533230915148534144 + 2.7392936792063513236e-857j | 3.34e-45, 1.93e-156j | 
| 0.02770669258053288349 - 2.5321683459410130598e-857j | 1.85e-46, 1.07e-157j | 
| 0.021697816124379954715 - 6.0720803726119078844e-856j | 1.73e-46, 1e-157j | 
| 0.033191388453183641452 - 2.8305973294326983948e-856j | 1.34e-48, 7.77e-160j | 
| 0.030522960195973245731 + 3.1381727898872817844e-856j | 7.31e-48, 4.23e-159j | 
| 0.0086438179550827597097 - 6.5634488017438926552e-857j | 8.82e-46, 5.1e-157j | 
| 0.033191388453183641452 - 2.9663333501202078332e-857j | 2.24e-50, 1.29e-161j | 
| 0.015281164442399402131 - 3.1929876887185374317e-857j | 1.57e-46, 9.05e-158j | 
| 0.015281164442399402131 - 1.4428509595947177194e-855j | 1.8e-48, 1.04e-159j | 
| 0.035695661302012592715 + 2.6758560510495010013e-856j | 2.81e-51, 1.63e-162j | 
| 0.011968699202947502312 + 2.7498749813554494991e-855j | 1.43e-48, 8.25e-160j | 
| 0.038021569334901741417 - 3.9523338571103343081e-857j | 2.29e-53, 1.32e-164j | 
| 0.040155197545644286054 + 4.7615964116423933329e-857j | 5.02e-54, 2.9e-165j | 
| 0.0053615192916048087249 + 2.5790553278064398693e-854j | 1.68e-48, 9.71e-160j | 
| 0.042081144972786465543 - 2.8735599842144591477e-856j | 2.36e-55, 1.37e-166j | 
| 0.040155197545644286054 + 2.7054657995491224052e-856j | 1.21e-54, 7e-166j | 
| 0.030522960195973245731 + 2.6932662473068390597e-857j | 5.07e-53, 2.93e-164j | 
| 0.042081144972786465543 - 5.8886517627757668468e-857j | 1.47e-56, 8.49e-168j | 
| 0.035695661302012592715 + 3.3734145530927165522e-857j | 3.31e-54, 1.91e-165j | 
| 0.046481225704383970573 + 4.1268444742559351071e-856j | 3.69e-59, 2.13e-170j | 
| 0.043784183639725886088 + 3.1525845472856097848e-856j | 1.12e-57, 6.49e-169j | 
| 0.04813263819251037152 - 1.8796765638982202611e-855j | 4.05e-62, 2.34e-173j | 
| 0.043784183639725886088 + 7.4617529266611508899e-857j | 1.41e-58, 8.16e-170j | 
| 0.045253104259305587381 - 9.6662051401958998167e-857j | 9.6e-60, 5.55e-171j | 
| 0.047908401493773456875 + 1.7765121954945241566e-855j | 3.36e-63, 1.94e-174j | 
| 0.045253104259305587381 - 3.5610867102892286975e-856j | 7.22e-60, 4.17e-171j | 
| 0.049005394463711712812 - 1.0672590270473232241e-855j | 3.79e-63, 2.19e-174j | 
| 0.048936696017156241112 + 4.3466299478655226449e-856j | 1.4e-63, 8.12e-175j | 
| 0.046481225704383970573 + 1.2766353970829568118e-856j | 1.89e-61, 1.09e-172j | 
| 0.04813263819251037152 - 1.5530929602130558915e-855j | 6.6e-64, 3.81e-175j | 
| 0.048936696017156241112 + 8.7614958903378059559e-856j | 7.04e-64, 4.07e-175j | 
| 0.047462247959955872074 - 4.886883473423317851e-856j | 6.05e-63, 3.5e-174j | 
| 0.048378206269740311857 + 1.2906203977181637107e-855j | 1.22e-64, 7.07e-176j | 
| 0.047462247959955872074 - 1.7132830621375696e-856j | 9.44e-64, 5.46e-175j | 
| 0.049005394463711712812 - 5.8973820958754115075e-856j | 5.51e-65, 3.19e-176j | 
| 0.038021569334901741417 - 2.6391092778199911505e-856j | 9.01e-63, 5.21e-174j | 
| 0.04819061297227863425 + 5.8853522217896532324e-856j | 1.46e-64, 8.45e-176j | 
| 0.048648671384821761366 - 1.5116365640145744642e-855j | 3.35e-66, 1.93e-177j | 
| 0.048648671384821761366 - 1.0264187436446781926e-855j | 5.03e-66, 2.91e-177j | 
| 0.04819061297227863425 + 2.3266843201259102102e-856j | 7.96e-66, 4.61e-177j | 
| 0.047908401493773456875 + 1.9536205075084057011e-855j | 1.15e-66, 6.65e-178j | 
| 0.048673391813157381932 - 7.1663783995625074919e-856j | 3.2e-66, 1.85e-177j | 
| 0.048892537236759025679 + 1.2843490366074730762e-855j | 9.09e-67, 5.26e-178j | 
| 0.047802466158694444943 - 1.9194684903306687578e-855j | 5.46e-67, 3.17e-178j | 
| 0.048673391813157381932 - 3.1802431136305767489e-856j | 7.63e-68, 4.44e-179j | 
| 0.048892537236759025679 + 7.8786919306957726638e-856j | 1.05e-67, 6.13e-179j | 
| 0.048378206269740311857 + 1.7214313830536356857e-855j | 1.41e-67, 7.99e-179j | 
All rules of Legendre type can be downloaded here packed into a single file.