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) | 
|---|---|
| -0.99860706164005261354 - 2.7911524832041008882e-892j | 6.63e-236, 6.63e-236j | 
| 0.99440647375811783848 + 2.0834083719317708921e-908j | 4.35e-235, 4.35e-235j | 
| -0.88768710757874640842 + 2.6797517999747477181e-938j | 6.91e-237, 6.91e-237j | 
| 0.99234294851369901008 - 6.7440046033038539779e-936j | 4.49e-235, 4.49e-235j | 
| 0.93476295693657606602 + 2.5155531253249626383e-948j | 3.74e-236, 3.74e-236j | 
| 0.95275482203958774276 - 2.2743938957762965078e-952j | 7.33e-236, 7.33e-236j | 
| 0.99860706164005261354 - 5.3752862238595919955e-962j | 6.25e-236, 6.25e-236j | 
| -0.91272979048656640233 - 3.5971912520607485966e-975j | 1.62e-236, 1.62e-236j | 
| 0.96844128104357345241 - 3.3011414249054903042e-973j | 1.05e-235, 1.05e-235j | 
| -0.99440647375811783848 - 9.7696875065230489749e-975j | 4.44e-235, 4.44e-235j | 
| 0.88768710757874640842 - 1.704822447108505852e-987j | 6.68e-237, 6.68e-237j | 
| 0.98218336611185065435 + 3.1685328453974276455e-993j | 1.5e-235, 1.5e-235j | 
| -0.86113631159405257522 + 4.535150164340127122e-1000j | 2.43e-237, 2.43e-237j | 
| -0.83156612025382607329 - 3.0307128286767205834e-1001j | 7e-238, 7e-238j | 
| 0.83156612025382607329 + 8.7164375837301380058e-1002j | 7.23e-238, 7.23e-238j | 
| 0.79771828569921420176 - 3.0498569023593964373e-1002j | 1.56e-238, 1.56e-238j | 
| 0.91272979048656640233 - 1.5512729692032828957e-1000j | 1.64e-236, 1.64e-236j | 
| -0.98218336611185065435 - 2.3832107790225112447e-996j | 1.61e-235, 1.61e-235j | 
| -0.79771828569921420176 - 1.4113909018440774382e-1002j | 1.58e-238, 1.58e-238j | 
| -0.93476295693657606602 - 3.1263633025977110344e-998j | 3.74e-236, 3.74e-236j | 
| -0.99234294851369901008 - 4.3620047751544170649e-998j | 5.14e-235, 5.14e-235j | 
| 0.76116213584564959094 - 1.4755920085117527457e-1012j | 3.53e-239, 3.53e-239j | 
| -0.95275482203958774276 + 4.5198567107188266324e-1005j | 6.69e-236, 6.69e-236j | 
| -0.72322064929065662618 + 1.3106036631203905805e-1011j | 6.83e-240, 6.83e-240j | 
| -0.6828055361053166099 - 1.6489443068889751711e-1012j | 1.24e-240, 1.24e-240j | 
| 0.86113631159405257522 + 3.2057480820098550923e-1011j | 2.41e-237, 2.41e-237j | 
| 0.72322064929065662618 + 2.7489563154302874377e-1014j | 6.56e-240, 6.56e-240j | 
| 0.6828055361053166099 - 8.8713928124809970104e-1015j | 1.13e-240, 1.13e-240j | 
| -0.96844128104357345241 - 6.2398780564678452918e-1014j | 1.01e-235, 1.01e-235j | 
| -0.63899664402486099033 + 1.5872553522003668674e-1020j | 1.42e-241, 1.42e-241j | 
| -0.76116213584564959094 - 5.657334019440706692e-1024j | 3.47e-239, 3.47e-239j | 
| 0.63899664402486099033 + 3.3745563823455182267e-1027j | 1.46e-241, 1.46e-241j | 
| 0.59311548012039520917 - 2.1222715364909076489e-1030j | 1.83e-242, 1.83e-242j | 
| -0.11513928820520961921 + 2.8778430971140936478e-1041j | 3.99e-253, 3.99e-253j | 
| -0.59311548012039520917 - 3.0896577606888102085e-1031j | 1.87e-242, 1.87e-242j | 
| -0.4976749486935251113 - 4.2391839916466854369e-1033j | 1.9e-244, 1.9e-244j | 
| 0.058107376415110318685 + 5.7431240685960860115e-1046j | 2.38e-254, 2.38e-254j | 
| 0.54633537010580514983 + 5.2234913541607825834e-1035j | 2.1e-243, 2.1e-243j | 
| 0.22900173719888928644 + 7.6554973892432577319e-1043j | 2.07e-250, 2.07e-250j | 
| -0.3399810435848562648 - 1.6400910452618423946e-1038j | 6.74e-248, 6.74e-248j | 
| -0.54633537010580514983 - 5.796878188370772681e-1035j | 2.09e-243, 2.09e-243j | 
| -0.17186219248919339981 + 3.7368378335673496627e-1043j | 1.01e-251, 1.01e-251j | 
| 0.44627998672758270108 + 8.0081095518934185491e-1038j | 1.57e-245, 1.57e-245j | 
| 0.4976749486935251113 + 1.9363791744655368089e-1037j | 2.02e-244, 2.02e-244j | 
| -1.1496415555548587582e-1063 - 1.5339123234216408445e-1063j | 1.05e-1061, 1.05e-1061j | 
| -0.44627998672758270108 - 1.4734915924463021395e-1036j | 1.63e-245, 1.63e-245j | 
| -0.2854265066947627734 + 2.1243608005280522981e-1041j | 3.7e-249, 3.7e-249j | 
| 0.17186219248919339981 + 3.4963857967426467416e-1044j | 9.27e-252, 9.27e-252j | 
| 0.39334503593503075507 - 4.012465519901450943e-1039j | 1.11e-246, 1.11e-246j | 
| 0.11513928820520961921 - 2.50072273338404287e-1046j | 4.71e-253, 4.71e-253j | 
| -0.22900173719888928644 - 3.5024659345118027095e-1042j | 2.01e-250, 2.01e-250j | 
| -0.39334503593503075507 - 3.5010083116740318138e-1038j | 1e-246, 1e-246j | 
| -0.058107376415110318685 + 3.8886719419402503318e-1047j | 2.38e-254, 2.38e-254j | 
| 0.2854265066947627734 - 2.3740604249105639858e-1042j | 4e-249, 4e-249j | 
| 0.3399810435848562648 + 3.687067663008407422e-1040j | 6.9e-248, 6.9e-248j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.003548716056508541287 - 6.1178488047945216157e-892j | 2.22e-38, 3.98e-151j | 
| 0.0010207799937846594205 + 4.0391243160893762822e-894j | 1.05e-38, 1.88e-151j | 
| 0.025841249808217567389 - 7.6790466586006286427e-893j | 1.21e-39, 2.17e-152j | 
| 0.0074234962644335203738 - 4.6573494345623508618e-894j | 8.97e-39, 1.61e-151j | 
| 0.019922847679952296754 - 3.6882467643363613385e-894j | 2.82e-40, 5.05e-153j | 
| 0.016477410316752335984 + 3.2561185201695811549e-894j | 2.94e-40, 5.27e-153j | 
| 0.003548716056508541287 - 4.9594119718333949756e-895j | 5.95e-40, 1.07e-152j | 
| 0.023905344927931137468 + 8.8660348378587804126e-893j | 4.21e-44, 7.55e-157j | 
| 0.014937639623502972371 - 2.5652272165215406965e-894j | 1.15e-40, 2.07e-153j | 
| 0.0010207799937846594205 + 1.9164054316640586088e-891j | 1.16e-45, 2.08e-158j | 
| 0.025841249808217567389 - 4.5155178683469148445e-894j | 3.59e-43, 6.43e-156j | 
| 0.012242927108274096227 + 2.2195180352584460021e-894j | 2.13e-40, 3.82e-153j | 
| 0.027601867263871973956 + 6.6638461784736555295e-893j | 1.54e-45, 2.75e-158j | 
| 0.031799613917595709687 - 5.3685100571585152722e-893j | 4.89e-46, 8.77e-159j | 
| 0.031799613917595709687 - 4.8998694913735287973e-894j | 6.78e-45, 1.22e-157j | 
| 0.035564939397482675636 + 4.8623288103377131406e-894j | 1.33e-45, 2.39e-158j | 
| 0.023905344927931137468 + 3.9835514968484176799e-894j | 4.03e-43, 7.23e-156j | 
| 0.012242927108274096227 + 2.6768640900054204452e-892j | 1.01e-47, 1.81e-160j | 
| 0.035564939397482675636 + 4.3478409623441921562e-893j | 1.85e-48, 3.32e-161j | 
| 0.019922847679952296754 - 1.1168996336308380695e-892j | 6.44e-48, 1.16e-160j | 
| 0.0074234962644335203738 - 1.4802653970314134614e-891j | 2.14e-47, 3.84e-160j | 
| 0.037274878082924773342 - 5.1329109264597195419e-894j | 1.04e-50, 1.86e-163j | 
| 0.016477410316752335984 + 1.3857263296988135191e-892j | 2.64e-48, 4.74e-161j | 
| 0.038853662429851424062 + 3.3885924938558789095e-893j | 4.85e-52, 8.69e-165j | 
| 0.042175998640031620878 - 2.9196146799424983312e-893j | 1.01e-52, 1.81e-165j | 
| 0.027601867263871973956 + 4.9258620599511470344e-894j | 1.14e-49, 2.05e-162j | 
| 0.038853662429851424062 + 5.4196614671316344567e-894j | 9.95e-53, 1.78e-165j | 
| 0.042175998640031620878 - 5.4835961805912447083e-894j | 7.31e-54, 1.31e-166j | 
| 0.014937639623502972371 - 1.6727317659582032285e-892j | 1.16e-50, 2.08e-163j | 
| 0.045166145728098011288 + 2.5371221149423458097e-893j | 1.21e-55, 2.17e-168j | 
| 0.037274878082924773342 - 3.8041404808299887129e-893j | 2.76e-53, 4.95e-166j | 
| 0.045166145728098011288 + 5.5714061963770703114e-894j | 5.18e-56, 9.29e-169j | 
| 0.046351788180319060944 - 5.891606857416737407e-894j | 3.87e-57, 6.94e-170j | 
| 0.056634076455871973432 + 1.1068547625485968226e-893j | 1.86e-61, 3.33e-174j | 
| 0.046351788180319060944 - 2.3126999103151631983e-893j | 6.77e-58, 1.21e-170j | 
| 0.050078868648881807801 - 1.8876431574754780745e-893j | 9.32e-60, 1.67e-172j | 
| 0.057602920620718629949 - 9.1892897314245982849e-894j | 1.15e-62, 2.07e-175j | 
| 0.047428327638843751177 + 6.2096999415413955015e-894j | 5.4e-60, 9.68e-173j | 
| 0.057071130283565058161 + 7.6499533936105007637e-894j | 6.96e-63, 1.25e-175j | 
| 0.053720863344420983893 + 1.4516458843992453443e-893j | 1.49e-62, 2.68e-175j | 
| 0.047428327638843751177 + 2.1212092438402402368e-893j | 5.07e-60, 9.09e-173j | 
| 0.056975651948927741382 - 1.1592828292842987837e-893j | 4.97e-63, 8.9e-176j | 
| 0.052461078590451585976 + 6.4380871749759391031e-894j | 4.26e-63, 7.64e-176j | 
| 0.050078868648881807801 - 6.3195378199624298869e-894j | 2.74e-62, 4.92e-175j | 
| 0.058388252000410294411 + 9.6212227148185200179e-894j | 1.66e-64, 2.98e-177j | 
| 0.052461078590451585976 + 1.6842029293709160789e-893j | 3.09e-63, 5.54e-176j | 
| 0.055542245030443909028 - 1.3266766964706598888e-893j | 2.93e-64, 5.26e-177j | 
| 0.056975651948927741382 - 8.1884349172289595154e-894j | 1.32e-65, 2.36e-178j | 
| 0.053181406018137034929 - 6.7729579938845744837e-894j | 1.67e-65, 3e-178j | 
| 0.056634076455871973432 + 8.7800109308589034296e-894j | 1.29e-65, 2.31e-178j | 
| 0.057071130283565058161 + 1.2202553436754493019e-893j | 1.33e-65, 2.38e-178j | 
| 0.053181406018137034929 - 1.5576118583342574817e-893j | 2.38e-65, 4.27e-178j | 
| 0.057602920620718629949 - 1.0324782971454097949e-893j | 4.47e-66, 8.02e-179j | 
| 0.055542245030443909028 - 7.3686548853153904443e-894j | 3.13e-67, 5.63e-180j | 
| 0.053720863344420983893 + 7.1425388044027687874e-894j | 3.05e-67, 5.46e-180j | 
All rules of Legendre type can be downloaded here packed into a single file.