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) | 
|---|---|
| 0.99927796258795845889 - 1.0975817211305371498e-1728j | 2.75e-484, 2.75e-484j | 
| -0.93655622336835242944 + 4.6964355701309104933e-1746j | 2.54e-484, 2.54e-484j | 
| -0.92070259415611115017 - 5.6955556754558436654e-1747j | 1.24e-484, 1.24e-484j | 
| -0.99381937293232952854 - 2.2050832839872191949e-1744j | 2.4e-483, 2.4e-483j | 
| 0.96243116182708369602 + 9.3958059164975816787e-1745j | 9.35e-484, 9.35e-484j | 
| 0.93655622336835242944 + 1.2972608789734770654e-1761j | 2.45e-484, 2.45e-484j | 
| 0.9722589657139301682 - 3.1664912038487871176e-1781j | 1.16e-483, 1.16e-483j | 
| -0.90411725637047485668 - 6.8650207595256163322e-1808j | 5.64e-485, 5.64e-485j | 
| -0.98931188621042412623 + 1.421703060891656117e-1804j | 2.06e-483, 2.06e-483j | 
| -0.99927796258795845889 + 9.4261676313566461155e-1808j | 2.81e-484, 2.81e-484j | 
| 0.90411725637047485668 - 2.2361814480860865428e-1820j | 5.32e-485, 5.32e-485j | 
| 0.99381937293232952854 + 1.6103260661838484263e-1848j | 2.42e-483, 2.42e-483j | 
| -0.86534135474544746183 + 1.98013956727783242e-1878j | 6.89e-486, 6.89e-486j | 
| -0.84331236630075609787 - 3.5642026539102812083e-1880j | 2.07e-486, 2.07e-486j | 
| 0.98931188621042412623 + 2.1033269054061374856e-1874j | 1.99e-483, 1.99e-483j | 
| 0.82049893693481308376 + 7.5165544147649502717e-1897j | 6.46e-487, 6.46e-487j | 
| 0.84331236630075609787 + 2.1315083194398757737e-1895j | 2.3e-486, 2.3e-486j | 
| -0.98156063424671925069 + 1.1939337793732461932e-1892j | 1.42e-483, 1.42e-483j | 
| -0.76990267419430468704 + 3.1335051112670660726e-1899j | 3.3e-488, 3.3e-488j | 
| -0.9722589657139301682 + 1.8080135915549286553e-1893j | 1.24e-483, 1.24e-483j | 
| 0.86534135474544746183 + 2.4168262731785703364e-1895j | 6.81e-486, 6.81e-486j | 
| 0.79620896839558338738 - 3.4395951373873776809e-1897j | 1.5e-487, 1.5e-487j | 
| -0.99650401095684314209 - 3.976777073064056137e-1893j | 1.51e-483, 1.51e-483j | 
| -0.82049893693481308376 - 5.9615416882879701756e-1898j | 6.34e-487, 6.34e-487j | 
| -0.79620896839558338738 + 3.9435716382181108658e-1898j | 1.69e-487, 1.69e-487j | 
| 0.98156063424671925069 - 9.9592445091312936141e-1892j | 1.41e-483, 1.41e-483j | 
| 0.71390619053787702443 + 3.1293820064308545752e-1910j | 1.33e-489, 1.33e-489j | 
| 0.74228094065277710866 + 9.0428724213930163924e-1910j | 7.46e-489, 7.46e-489j | 
| -0.96243116182708369602 - 1.3306892885339448033e-1903j | 9.42e-484, 9.42e-484j | 
| -0.62044163352444184052 + 3.3111171673063567773e-1914j | 4.19e-492, 4.19e-492j | 
| -0.95083686501931267603 - 5.433624264846776364e-1906j | 5.07e-484, 5.07e-484j | 
| 0.76990267419430468704 + 9.3250739682613881568e-1909j | 3.59e-488, 3.59e-488j | 
| 0.68424722586570544504 + 2.8334430900039903183e-1911j | 2.28e-490, 2.28e-490j | 
| 0.92070259415611115017 + 6.3705835780686952976e-1904j | 1.14e-484, 1.14e-484j | 
| -0.65290189927931623274 - 1.1356897910012827325e-1929j | 3.2e-491, 3.2e-491j | 
| -0.74228094065277710866 + 9.0558949795932374038e-1926j | 7.29e-489, 7.29e-489j | 
| 0.95083686501931267603 + 4.0591006036594305692e-1919j | 5.5e-484, 5.5e-484j | 
| 0.5873179542866174473 - 9.8208017629299042239e-1956j | 5.22e-493, 5.22e-493j | 
| 0.51761471334093533372 - 4.1303396079339859974e-1958j | 5.8e-495, 5.8e-495j | 
| -0.71390619053787702443 + 2.1198232322108392983e-1953j | 1.41e-489, 1.41e-489j | 
| -0.5873179542866174473 - 1.1604280194270172368e-1956j | 5.32e-493, 5.32e-493j | 
| -0.88589777274344432196 + 9.8261823836110307867e-1949j | 2.18e-485, 2.18e-485j | 
| 0.65290189927931623274 + 1.7597225915682398586e-1952j | 3.28e-491, 3.28e-491j | 
| 0.62044163352444184052 - 1.1346273896123408295e-1954j | 4.14e-492, 4.14e-492j | 
| 0.99650401095684314209 + 1.1401787731568772377e-1954j | 1.61e-483, 1.61e-483j | 
| -0.55313541069257211285 + 1.2619113263733403753e-1980j | 6.14e-494, 6.14e-494j | 
| -0.68424722586570544504 + 2.6356570300715089975e-1976j | 2.37e-490, 2.37e-490j | 
| 0.2888017454095650778 - 3.3055987214752771372e-1988j | 8.12e-502, 8.12e-502j | 
| 0.48121396649570514545 + 1.1159037073338782585e-1983j | 5.25e-496, 5.25e-496j | 
| 0.88589777274344432196 + 2.0302461833048242514e-1988j | 2.06e-485, 2.06e-485j | 
| -0.40654210072064775794 - 5.4061842935362291879e-2002j | 3.19e-498, 3.19e-498j | 
| -0.51761471334093533372 - 1.0786850384296781896e-1998j | 5.8e-495, 5.8e-495j | 
| -0.12523340851146891547 - 2.3976305162413062043e-2010j | 5.01e-507, 5.01e-507j | 
| 0.55313541069257211285 - 3.3817233703755092316e-2001j | 6.49e-494, 6.49e-494j | 
| 0.44428116303155462665 + 3.81549995448415228e-2005j | 4.35e-497, 4.35e-497j | 
| -0.083636658581811367118 - 2.0524176303316852145e-2014j | 2.66e-508, 2.66e-508j | 
| -0.48121396649570514545 - 7.961430778876215572e-2003j | 5.03e-496, 5.03e-496j | 
| -0.44428116303155462665 + 6.7757332738201244929e-2003j | 4.22e-497, 4.22e-497j | 
| 0.12523340851146891547 - 4.2819578598320743931e-2013j | 5.15e-507, 5.15e-507j | 
| 0.40654210072064775794 - 5.07802589998472578e-2006j | 3.03e-498, 3.03e-498j | 
| 0.16658494040686034256 - 9.7279669337245668189e-2013j | 1.09e-505, 1.09e-505j | 
| -0.16658494040686034256 + 4.7822697641075010212e-2012j | 1.08e-505, 1.08e-505j | 
| -0.36783149899818019375 - 5.9777554038025161694e-2006j | 2.33e-499, 2.33e-499j | 
| 0.041842286875995166032 - 1.8752099856238700951e-2015j | 1.25e-509, 1.25e-509j | 
| 0.36783149899818019375 + 1.3499893181668736171e-2006j | 2.24e-499, 2.24e-499j | 
| 0.24856873215645676574 - 3.6931850030498075189e-2010j | 4.6e-503, 4.6e-503j | 
| -1.577773649808011715e-2054 - 5.6603548105934277697e-2055j | 1.26e-2052, 1.26e-2052j | 
| -0.32850211354705606916 + 1.1067601715562298858e-2006j | 1.35e-500, 1.35e-500j | 
| -0.20774617492467426914 + 1.6859086287093915954e-2011j | 2.08e-504, 2.08e-504j | 
| 0.20774617492467426914 + 2.0490289042609085098e-2012j | 2.25e-504, 2.25e-504j | 
| 0.32850211354705606916 - 2.49643238269061801e-2007j | 1.32e-500, 1.32e-500j | 
| 0.083636658581811367118 + 6.1877133345078897135e-2015j | 2.48e-508, 2.48e-508j | 
| -0.24856873215645676574 - 5.7849034527168491721e-2010j | 4.95e-503, 4.95e-503j | 
| -0.2888017454095650778 + 1.7310287056231146293e-2008j | 8.11e-502, 8.11e-502j | 
| -0.041842286875995166032 + 2.1779075198102698489e-2015j | 1.25e-509, 1.25e-509j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0018316685726330648348 + 1.8621157621800028218e-1728j | 3.18e-144, 3.04e-379j | 
| 0.015302285658534019736 + 2.7908115909625425877e-1730j | 1.53e-144, 1.47e-379j | 
| 0.016225776353434755399 - 3.2914922078293048945e-1730j | 1.36e-144, 1.3e-379j | 
| 0.0025670561964871679434 + 1.2084270780374200561e-1730j | 1.41e-145, 1.35e-380j | 
| 0.010333781897831595996 + 1.2838567679470702471e-1728j | 4.88e-146, 4.68e-381j | 
| 0.015302285658534019736 + 8.6135182977509745772e-1729j | 1.39e-146, 1.33e-381j | 
| 0.0096060178746935380458 - 1.3773971653616545983e-1728j | 3.66e-146, 3.51e-381j | 
| 0.017146452341726291143 + 3.7900849711522684195e-1730j | 3.23e-146, 3.1e-381j | 
| 0.0064898294260193943416 - 1.2610109264246793833e-1730j | 3.98e-147, 3.81e-382j | 
| 0.0018316685726330648348 + 1.0059292908275112601e-1731j | 1.46e-147, 1.4e-382j | 
| 0.017146452341726291143 + 7.5808912105488655107e-1729j | 7.22e-149, 6.92e-384j | 
| 0.0025670561964871679434 + 4.4123353125166239124e-1728j | 2.27e-148, 2.18e-383j | 
| 0.021492759754438789706 + 4.2656838743129778015e-1730j | 1.53e-148, 1.47e-383j | 
| 0.022420846243187832413 - 4.7554323083061001976e-1730j | 5.37e-149, 5.14e-384j | 
| 0.0064898294260193943416 - 2.5161692852010746606e-1728j | 2.08e-148, 2e-383j | 
| 0.023360324004614064412 + 5.3395495198608932896e-1729j | 1.74e-151, 1.67e-386j | 
| 0.022420846243187832413 - 5.6181066783692625202e-1729j | 3.59e-151, 3.44e-386j | 
| 0.0087630324014468766198 + 1.3566382191913311749e-1730j | 3.3e-150, 3.16e-385j | 
| 0.02713029957571477917 + 5.8002524561257552885e-1730j | 1.06e-153, 1.02e-388j | 
| 0.0096060178746935380458 - 1.887658768697598611e-1730j | 9.35e-151, 8.96e-386j | 
| 0.021492759754438789706 + 5.9385381501031664317e-1729j | 3.97e-153, 3.8e-388j | 
| 0.025333087621253767885 - 4.8794680107201217465e-1729j | 2.32e-154, 2.22e-389j | 
| 0.0033007266629137295351 - 6.3821089796415951077e-1731j | 7.23e-150, 6.93e-385j | 
| 0.023360324004614064412 + 5.2456950126017645328e-1730j | 4.38e-153, 4.19e-388j | 
| 0.025333087621253767885 - 5.5186626203289633401e-1730j | 1.08e-153, 1.03e-388j | 
| 0.0087630324014468766198 + 1.5167531440168058487e-1728j | 2.99e-153, 2.86e-388j | 
| 0.028872246976932067077 + 4.0729262740783236241e-1729j | 9.78e-158, 9.37e-393j | 
| 0.02799649129383065886 - 4.2629977443059070937e-1729j | 3.43e-157, 3.29e-392j | 
| 0.010333781897831595996 + 2.4114693633875167765e-1730j | 9.98e-153, 9.56e-388j | 
| 0.032790276375849448315 - 7.9264524247730586839e-1730j | 1.22e-160, 1.16e-395j | 
| 0.013029523385983061359 - 2.5953510507535859005e-1730j | 5.12e-153, 4.9e-388j | 
| 0.02713029957571477917 + 4.4737575724440445481e-1729j | 1.95e-157, 1.87e-392j | 
| 0.030531410460856575718 - 3.7937070353776040607e-1729j | 1.01e-159, 9.68e-395j | 
| 0.016225776353434755399 - 8.0427253067075494286e-1729j | 8.5e-157, 8.14e-392j | 
| 0.032037818399595908199 + 7.4239185357400666527e-1730j | 2.97e-161, 2.84e-396j | 
| 0.02799649129383065886 - 6.2907876544648345547e-1730j | 1.61e-159, 1.55e-394j | 
| 0.013029523385983061359 - 1.0448220252954472411e-1728j | 1.17e-156, 1.12e-391j | 
| 0.03354710010068761126 + 3.2484988408726735363e-1729j | 2.28e-163, 2.19e-398j | 
| 0.036066130712425405797 + 2.8895377146271114306e-1729j | 1.1e-164, 1.05e-399j | 
| 0.028872246976932067077 + 6.7844322873426350883e-1730j | 5.59e-161, 5.35e-396j | 
| 0.03354710010068761126 + 8.4347349896690490418e-1730j | 7.1e-164, 6.81e-399j | 
| 0.019436837473216748874 - 4.0236739775507492228e-1730j | 4.16e-158, 3.99e-393j | 
| 0.032037818399595908199 + 3.5411363544378303785e-1729j | 1.57e-162, 1.51e-397j | 
| 0.032790276375849448315 - 3.3889649263033112732e-1729j | 2.9e-163, 2.78e-398j | 
| 0.0033007266629137295351 - 4.5917520377403346613e-1728j | 1.52e-159, 1.45e-394j | 
| 0.03487834459088246927 - 8.7985694853934400862e-1730j | 7.8e-166, 7.47e-401j | 
| 0.030531410460856575718 - 7.0989987584393949844e-1730j | 1.54e-162, 1.48e-397j | 
| 0.039926724497469746972 + 2.2172812324195305875e-1729j | 1.18e-170, 1.13e-405j | 
| 0.036665471133268309584 - 2.7721244324717418761e-1729j | 1.07e-167, 1.03e-402j | 
| 0.019436837473216748874 - 6.6901745002944006976e-1729j | 3e-161, 2.87e-396j | 
| 0.038250440473151962848 - 1.0658583925085081821e-1729j | 2.17e-170, 2.08e-405j | 
| 0.036066130712425405797 + 9.1752313564097758011e-1730j | 6.86e-168, 6.57e-403j | 
| 0.041464385349911440088 + 1.4489118716315177292e-1729j | 2.18e-173, 2.09e-408j | 
| 0.03487834459088246927 - 3.0615812988099833378e-1729j | 3.4e-167, 3.26e-402j | 
| 0.037264188827586998647 + 2.661905958723035067e-1729j | 9.01e-170, 8.63e-405j | 
| 0.041720548187521631775 - 1.5095000785088041108e-1729j | 4.93e-174, 4.72e-409j | 
| 0.036665471133268309584 - 9.7004099309083313061e-1730j | 7.42e-170, 7.11e-405j | 
| 0.037264188827586998647 + 1.023407535993644067e-1729j | 1.21e-170, 1.16e-405j | 
| 0.041464385349911440088 + 1.8641130681171321297e-1729j | 2.19e-175, 2.1e-410j | 
| 0.038250440473151962848 - 2.5279474538858792143e-1729j | 1.37e-172, 1.31e-407j | 
| 0.041255795616742009962 - 1.9411822215194399672e-1729j | 2.47e-175, 2.36e-410j | 
| 0.041255795616742009962 - 1.3864485150776118166e-1729j | 7.81e-176, 7.48e-411j | 
| 0.039096641058401615059 + 1.1099463407474686587e-1729j | 1.99e-174, 1.9e-409j | 
| 0.041837802933147650369 + 1.7105058360907190031e-1729j | 1.45e-176, 1.39e-411j | 
| 0.039096641058401615059 + 2.4030828134854731319e-1729j | 9.58e-175, 9.17e-410j | 
| 0.040552937695193634863 - 2.1164145562514976851e-1729j | 6.28e-176, 6.02e-411j | 
| 0.041841798837206788868 - 1.6406107140556203226e-1729j | 4.01e-177, 3.84e-412j | 
| 0.039513992801686135966 - 1.1658765374056942738e-1729j | 4.69e-177, 4.5e-412j | 
| 0.041040047652125847522 + 1.3256453074393667802e-1729j | 1.13e-177, 1.08e-412j | 
| 0.041040047652125847522 + 2.0215055273817296643e-1729j | 4.81e-177, 4.6e-412j | 
| 0.039513992801686135966 - 2.3078165974728835111e-1729j | 1.09e-176, 1.04e-411j | 
| 0.041720548187521631775 - 1.7852620873720712544e-1729j | 1.12e-177, 1.07e-412j | 
| 0.040552937695193634863 - 1.2732428987384635752e-1729j | 7.45e-179, 7.18e-414j | 
| 0.039926724497469746972 + 1.2230031826827775972e-1729j | 7.36e-179, 7.15e-414j | 
| 0.041837802933147650369 + 1.5730164808819961518e-1729j | 7.38e-179, 6.78e-414j | 
All rules of Legendre type can be downloaded here packed into a single file.