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) | 
|---|---|
| 0.99964153853917963513 - 4.8107365181351942871e-1714j | 2.69e-484, 2.69e-484j | 
| -0.94910791234275852453 - 1.0690740695436935452e-1727j | 3.49e-484, 3.49e-484j | 
| -0.93498103642239154162 + 4.1367592400586954256e-1728j | 1.91e-484, 1.91e-484j | 
| -0.99784612344852210871 - 1.6990007703168686269e-1726j | 8.14e-484, 8.14e-484j | 
| 0.90203388458741291848 + 1.0564090985843743543e-1729j | 4.32e-485, 4.32e-485j | 
| 0.91927944102079721186 - 2.1313978211969547486e-1741j | 9.38e-485, 9.38e-485j | 
| 0.98868775153792583362 - 1.1597855626402727164e-1759j | 1.11e-483, 1.11e-483j | 
| -0.91927944102079721186 + 4.5168126992951756425e-1789j | 9.48e-485, 9.48e-485j | 
| -0.98139085440145282256 - 2.4936925867553709596e-1787j | 1.02e-483, 1.02e-483j | 
| -0.99964153853917963513 - 2.0050741521340274102e-1788j | 2.85e-484, 2.85e-484j | 
| 0.8832767929424487679 + 3.6775553105302006384e-1789j | 1.78e-485, 1.78e-485j | 
| 0.99784612344852210871 - 7.5045366003056193184e-1816j | 7.38e-484, 7.38e-484j | 
| -0.8832767929424487679 + 1.3686895752978583156e-1850j | 1.72e-485, 1.72e-485j | 
| -0.86307451812359299498 + 5.9825510715722241621e-1853j | 6.72e-486, 6.72e-486j | 
| 0.98139085440145282256 - 1.2686008007273337752e-1847j | 1.06e-483, 1.06e-483j | 
| 0.86307451812359299498 + 9.5365141706816264056e-1866j | 6.4e-486, 6.4e-486j | 
| 0.79418608920443608857 - 5.2035953264665519857e-1869j | 1.69e-487, 1.69e-487j | 
| -0.98868775153792583362 - 1.1482906261508885076e-1863j | 1.08e-483, 1.08e-483j | 
| -0.79418608920443608857 - 8.126025316291095375e-1872j | 1.56e-487, 1.56e-487j | 
| -0.96159125459099586695 - 1.4858261328063293423e-1866j | 5.72e-484, 5.72e-484j | 
| 0.93498103642239154162 - 3.9994321926811588629e-1864j | 1.89e-484, 1.89e-484j | 
| 0.6836267794908846579 - 2.5942814961470185916e-1884j | 2.43e-490, 2.43e-490j | 
| -0.994202017165507384 + 4.68175193067653378e-1878j | 1.09e-483, 1.09e-483j | 
| -0.84148519136966672985 - 5.9074171905559339079e-1881j | 2.08e-486, 2.08e-486j | 
| -0.76851400329291491016 + 1.4405252009235475577e-1883j | 3.53e-488, 3.53e-488j | 
| 0.994202017165507384 - 1.6867468534878992666e-1876j | 1.06e-483, 1.06e-483j | 
| 0.76851400329291491016 + 1.7345884502566975051e-1897j | 3.54e-488, 3.54e-488j | 
| 0.84148519136966672985 + 1.2846374571924262794e-1894j | 2.18e-486, 2.18e-486j | 
| -0.97235933101661391008 + 2.2120437563804571205e-1894j | 8.43e-484, 8.43e-484j | 
| -0.65275488458376128405 - 1.2704081662255790931e-1901j | 3.52e-491, 3.52e-491j | 
| -0.81852084172440107155 - 7.7986085610247658739e-1898j | 6.25e-487, 6.25e-487j | 
| 0.81852084172440107155 - 2.2260458073801583802e-1895j | 5.94e-487, 5.94e-487j | 
| 0.74153118559939443986 - 9.005280724562580105e-1898j | 7.03e-489, 7.03e-489j | 
| 0.97235933101661391008 + 1.0376241780925515911e-1891j | 8.03e-484, 8.03e-484j | 
| -0.6836267794908846579 + 8.3042046215408175316e-1912j | 2.41e-490, 2.41e-490j | 
| -0.71323338896140600261 + 2.8788924079173714638e-1911j | 1.39e-489, 1.39e-489j | 
| 0.96159125459099586695 + 4.4062777810041640557e-1904j | 5.51e-484, 5.51e-484j | 
| 0.65275488458376128405 + 3.9286462072183870829e-1934j | 3.74e-491, 3.74e-491j | 
| 0.94910791234275852453 + 4.732111727951892786e-1933j | 3.36e-484, 3.36e-484j | 
| -0.74153118559939443986 - 9.7248765258828830254e-1959j | 7.59e-489, 7.59e-489j | 
| -0.55301677795294993595 - 4.9982952273541094629e-1965j | 6.73e-494, 6.73e-494j | 
| -0.90203388458741291848 - 1.4275576208875795857e-1965j | 4.21e-485, 4.21e-485j | 
| 0.58740451714137191543 + 2.2682333240080411187e-1971j | 5.78e-493, 5.78e-493j | 
| 0.55301677795294993595 - 1.2686201666712067108e-1972j | 6.32e-494, 6.32e-494j | 
| 0.62066801549804592241 - 3.3564124041034130044e-1971j | 5.26e-492, 5.26e-492j | 
| -0.58740451714137191543 + 1.5910231788839600797e-1973j | 5.43e-493, 5.43e-493j | 
| -0.62066801549804592241 - 7.0729923559856775882e-1973j | 4.75e-492, 4.75e-492j | 
| 0.71323338896140600261 - 4.3198763366611129697e-1979j | 1.39e-489, 1.39e-489j | 
| 0.51758562187726784074 + 6.8331418492513725949e-1985j | 5.92e-495, 5.92e-495j | 
| 0.20662717414130210908 + 1.9760043782722851235e-1995j | 2.28e-504, 2.28e-504j | 
| -0.51758562187726784074 + 1.2238230083614376527e-1986j | 5.96e-495, 5.96e-495j | 
| -0.48119644370188802369 - 1.2052935006761879818e-1988j | 5.88e-496, 5.88e-496j | 
| -0.12438944276720320083 + 4.903347518476150293e-2001j | 5.73e-507, 5.73e-507j | 
| 0.44392316342065541073 + 1.5134591043417046608e-1988j | 4.45e-497, 4.45e-497j | 
| 0.48119644370188802369 - 8.9202232274358643584e-1989j | 5.28e-496, 5.28e-496j | 
| 1.0473661182678906422e-2016 + 2.7104370487845587179e-2017j | 8.11e-2015, 8.11e-2015j | 
| -0.40584515137739716691 - 7.394614357423196818e-1991j | 3.26e-498, 3.26e-498j | 
| -0.44392316342065541073 + 6.4708491172780024292e-1990j | 4.13e-497, 4.13e-497j | 
| 0.24736277927426844744 + 6.6026114579998603441e-1996j | 4.58e-503, 4.58e-503j | 
| 0.40584515137739716691 - 9.694159501593790899e-1991j | 3.3e-498, 3.3e-498j | 
| 0.041521319845574659748 - 1.6347959805634991085e-2002j | 9.99e-510, 9.99e-510j | 
| -0.16561533960274229959 + 1.147959999236137181e-1999j | 1.11e-505, 1.11e-505j | 
| -0.36705948753898270572 + 3.1874217381729735786e-1993j | 2.07e-499, 2.07e-499j | 
| -0.041521319845574659748 + 2.1482360302675783749e-2002j | 9.99e-510, 9.99e-510j | 
| 0.32766326206750472751 + 1.6229670849568326255e-1993j | 1.39e-500, 1.39e-500j | 
| 0.28773799695667453611 + 2.6005237292872181366e-1995j | 8.33e-502, 8.33e-502j | 
| -0.083003770784361174585 - 3.6963285298587783496e-2002j | 2.21e-508, 2.21e-508j | 
| -0.32766326206750472751 + 1.6114502929140885042e-1994j | 1.39e-500, 1.39e-500j | 
| -0.20662717414130210908 - 4.3669688919044102376e-2000j | 2.23e-504, 2.23e-504j | 
| 0.16561533960274229959 + 1.8023590813749990649e-1998j | 1.14e-505, 1.14e-505j | 
| 0.36705948753898270572 - 3.4423663665973601426e-1992j | 2.19e-499, 2.19e-499j | 
| 0.12438944276720320083 - 7.340832948184277314e-2000j | 5.73e-507, 5.73e-507j | 
| -0.24736277927426844744 + 1.4037060566140846142e-1997j | 4.57e-503, 4.57e-503j | 
| -0.28773799695667453611 - 5.3003165577310855292e-1996j | 8.05e-502, 8.05e-502j | 
| 0.083003770784361174585 + 4.7317473969810196325e-2001j | 2.56e-508, 2.56e-508j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0009644786972996856751 + 5.1450174572087701958e-1714j | 6.38e-144, 8.9e-379j | 
| 0.013319182623224480414 - 4.3726213768963609349e-1716j | 3.1e-144, 4.33e-379j | 
| 0.014922316674705628567 + 5.3147783165544299011e-1716j | 2.8e-144, 3.91e-379j | 
| 0.0026939324381584941423 - 6.889033429599506188e-1717j | 2.2e-145, 3.07e-380j | 
| 0.01800978855065073355 + 1.4735505259490129027e-1714j | 7.91e-146, 1.1e-380j | 
| 0.016476698634070814464 - 1.5240361927481306092e-1714j | 6.78e-146, 9.47e-381j | 
| 0.0064194403104300537328 - 2.9809808724772646729e-1714j | 1.35e-146, 1.89e-381j | 
| 0.016476698634070814464 - 6.3824798649326607661e-1716j | 6.93e-146, 9.67e-381j | 
| 0.0081662145214355963802 + 2.2107438422032346955e-1716j | 9.28e-147, 1.3e-381j | 
| 0.0009644786972996856751 + 2.3207583465974426861e-1717j | 1.15e-146, 1.61e-381j | 
| 0.019492355390678281515 - 1.4330202304886505929e-1714j | 1.28e-147, 1.78e-382j | 
| 0.0026939324381584941423 - 7.6643887807370561184e-1714j | 2.04e-147, 2.85e-382j | 
| 0.019492355390678281515 - 8.8560949122838576384e-1716j | 6.99e-148, 9.76e-383j | 
| 0.020901604687196324164 + 1.02459275279872197e-1715j | 1.85e-148, 2.59e-383j | 
| 0.0081662145214355963802 + 2.3996662978105706472e-1714j | 5.16e-148, 7.21e-383j | 
| 0.020901604687196324164 + 1.3975009239865902039e-1714j | 1.07e-148, 1.49e-383j | 
| 0.025010303786222474717 - 1.2572923411576469869e-1714j | 2.91e-150, 4.06e-385j | 
| 0.0064194403104300537328 - 1.6422344979379456825e-1716j | 5.64e-148, 7.87e-383j | 
| 0.025010303786222474717 - 1.4400355915100906661e-1715j | 1.06e-151, 1.48e-386j | 
| 0.01163432987879694488 + 3.5587256588434457432e-1716j | 1.73e-148, 2.42e-383j | 
| 0.014922316674705628567 + 1.5901655222877069779e-1714j | 5.18e-151, 7.23e-386j | 
| 0.030248544095378816885 - 9.7697595255695048601e-1715j | 2.48e-154, 3.46e-389j | 
| 0.004592186312957240445 + 1.1450123476225844504e-1716j | 5.44e-148, 7.59e-383j | 
| 0.022275983783383036963 - 1.1675511605301638826e-1715j | 4.37e-151, 6.1e-386j | 
| 0.026328827256117806232 + 1.5619469859808260285e-1715j | 5.33e-153, 7.44e-388j | 
| 0.004592186312957240445 + 4.1970153865854133777e-1714j | 3.12e-151, 4.35e-386j | 
| 0.026328827256117806232 + 1.1949096486317441683e-1714j | 2.08e-154, 2.91e-389j | 
| 0.022275983783383036963 - 1.3591674875210621359e-1714j | 2.64e-153, 3.68e-388j | 
| 0.0098988185584637342564 - 2.8478604551866998044e-1716j | 3.5e-150, 4.89e-385j | 
| 0.031486442671908101723 + 1.9007263414099962115e-1715j | 9.7e-158, 1.35e-392j | 
| 0.023652796111646742441 + 1.3074592920823525132e-1715j | 1.08e-153, 1.5e-388j | 
| 0.023652796111646742441 + 1.3124802081633290672e-1714j | 8.33e-154, 1.16e-388j | 
| 0.02763851250625891748 - 1.1256856176323069642e-1714j | 8.1e-156, 1.13e-390j | 
| 0.0098988185584637342564 - 2.0584783284937122527e-1714j | 7.93e-154, 1.11e-388j | 
| 0.030248544095378816885 - 1.8341628422327585335e-1715j | 2.96e-158, 4.13e-393j | 
| 0.02895664662280256532 + 1.758381268848925875e-1715j | 6.72e-158, 9.39e-393j | 
| 0.01163432987879694488 + 1.834280520292039381e-1714j | 2.65e-154, 3.7e-389j | 
| 0.031486442671908101723 + 9.0541200477545870676e-1715j | 1.79e-160, 2.5e-395j | 
| 0.013319182623224480414 - 1.6862323463412881094e-1714j | 2.02e-154, 2.82e-389j | 
| 0.02763851250625891748 - 1.6687093017193878219e-1715j | 7.6e-158, 1.06e-392j | 
| 0.034924401536824426727 - 2.0810738172238897127e-1715j | 4.27e-163, 5.97e-398j | 
| 0.01800978855065073355 + 7.5633206418524715529e-1716j | 8.59e-156, 1.2e-390j | 
| 0.033837039973617684395 + 7.7748791839853360141e-1715j | 6.95e-163, 9.7e-398j | 
| 0.034924401536824426727 - 7.2347009272432349643e-1715j | 5.56e-164, 7.76e-399j | 
| 0.032681549859728225887 - 8.3854525320887765193e-1715j | 3.85e-162, 5.37e-397j | 
| 0.033837039973617684395 + 2.01953372749707898e-1715j | 7.7e-164, 1.07e-398j | 
| 0.032681549859728225887 - 1.9612699810764096876e-1715j | 5.74e-163, 8.02e-398j | 
| 0.02895664662280256532 + 1.051606664416427196e-1714j | 1.61e-161, 2.25e-396j | 
| 0.035923327979178295404 + 6.7692969389356223192e-1715j | 5.1e-166, 7.12e-401j | 
| 0.040885984686796626865 + 4.9220238171714736314e-1715j | 3.87e-171, 5.4e-406j | 
| 0.035923327979178295404 + 2.1507521920204301278e-1715j | 5.29e-167, 7.38e-402j | 
| 0.036843126793975669448 - 2.2311067262129810779e-1715j | 3.25e-168, 4.53e-403j | 
| 0.04131548575089313764 + 3.6430136139023476232e-1715j | 4.57e-173, 6.38e-408j | 
| 0.037690495873735108557 + 6.0374058233288344999e-1715j | 8.25e-170, 1.15e-404j | 
| 0.036843126793975669448 - 6.3727241621287283014e-1715j | 9.75e-169, 1.36e-403j | 
| 0.041526726218663177939 - 4.2275881879682309214e-1715j | 3e-174, 4.18e-409j | 
| 0.038448938380160261685 - 2.4329248808076877491e-1715j | 6.34e-172, 8.86e-407j | 
| 0.037690495873735108557 + 2.3241752513892053713e-1715j | 6.59e-171, 9.2e-406j | 
| 0.0405708077402920748 - 5.0449830665310584316e-1715j | 3.21e-174, 4.48e-409j | 
| 0.038448938380160261685 - 5.7586129041368674293e-1715j | 2.47e-172, 3.44e-407j | 
| 0.041509874077500830777 + 4.3940171947513800555e-1715j | 1.96e-175, 2.73e-410j | 
| 0.041127659157477998931 - 3.437733372531765801e-1715j | 7.38e-176, 1.03e-410j | 
| 0.03910585431065133485 + 2.5596169940262619187e-1715j | 1.71e-174, 2.39e-409j | 
| 0.041509874077500830777 + 4.043552535201106555e-1715j | 7.5e-176, 1.05e-410j | 
| 0.039673331321470100669 - 5.3414242172059118283e-1715j | 1.87e-175, 2.6e-410j | 
| 0.040164336203738224447 + 5.1822219652286778983e-1715j | 1.34e-175, 1.87e-410j | 
| 0.041445019132841936 - 3.8465869864390803592e-1715j | 1.44e-176, 2.01e-411j | 
| 0.039673331321470100669 - 2.7042176278902772029e-1715j | 4.77e-177, 6.67e-412j | 
| 0.040885984686796626865 + 3.2357927780893661166e-1715j | 1.55e-177, 2.16e-412j | 
| 0.041127659157477998931 - 4.8030175343028769809e-1715j | 5.46e-178, 7.62e-413j | 
| 0.03910585431065133485 + 5.5300828826386876706e-1715j | 3.72e-177, 5.19e-412j | 
| 0.04131548575089313764 + 4.678492273400088638e-1715j | 1.92e-178, 2.69e-413j | 
| 0.0405708077402920748 - 3.0434807222308858508e-1715j | 4.74e-179, 6.69e-414j | 
| 0.040164336203738224447 + 2.8656989400516122449e-1715j | 4.56e-179, 6.47e-414j | 
| 0.041445019132841936 - 4.5432225294110510162e-1715j | 4.79e-179, 6.51e-414j | 
All rules of Legendre type can be downloaded here packed into a single file.