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) | 
|---|---|
| 0.99938447333658370872 + 3.0637547852351767433e-841j | 1.38e-235, 1.38e-235j | 
| -0.99630068584206501385 + 6.1038168746021134883e-852j | 3.69e-235, 3.69e-235j | 
| -0.95249531032932109025 + 9.9474891175561711333e-870j | 2.7e-235, 2.7e-235j | 
| -0.99938447333658370872 + 6.7933440007203933591e-882j | 1.53e-235, 1.53e-235j | 
| 0.91248695683407599658 + 8.4506449323583645105e-889j | 7.1e-236, 7.1e-236j | 
| 0.93397085039886354568 + 1.0036718663003186891e-888j | 1.4e-235, 1.4e-235j | 
| 0.96802512738080369216 - 3.1501278616617236827e-888j | 3.55e-235, 3.55e-235j | 
| -0.91248695683407599658 + 6.4380429618251898816e-894j | 7.29e-236, 7.29e-236j | 
| -0.9900406608617272176 - 6.9470183394592166168e-897j | 4.54e-235, 4.54e-235j | 
| 0.99630068584206501385 + 1.9806370289342309686e-902j | 3.83e-235, 3.83e-235j | 
| 0.86113225770363542512 - 8.1915089187764499278e-914j | 1.13e-236, 1.13e-236j | 
| -0.20986442850604162326 - 1.4019178718279084229e-926j | 2.18e-250, 2.18e-250j | 
| -0.93397085039886354568 - 3.2280959747163272969e-910j | 1.46e-235, 1.46e-235j | 
| -0.83145359763208178066 - 2.1115378430829454293e-920j | 4.18e-237, 4.18e-237j | 
| 0.95249531032932109025 - 5.2606127926829879011e-915j | 2.46e-235, 2.46e-235j | 
| 0.83145359763208178066 + 1.0196353550859351783e-920j | 4.16e-237, 4.16e-237j | 
| 0.88816662217708559894 + 7.2465300374172996864e-919j | 2.95e-236, 2.95e-236j | 
| -0.68908942003680862746 - 3.3084692683026566611e-924j | 1.86e-239, 1.86e-239j | 
| -0.79922869523492189954 - 1.9423105524215064324e-921j | 1.2e-237, 1.2e-237j | 
| -0.88816662217708559894 + 2.4169280652132724687e-919j | 3.06e-236, 3.06e-236j | 
| 0.98056638155134655011 - 1.9469531939227523529e-918j | 4.53e-235, 4.53e-235j | 
| 0.79922869523492189954 - 5.087970518923778939e-932j | 1.17e-237, 1.17e-237j | 
| -0.96802512738080369216 - 1.7669294038714628733e-928j | 3.67e-235, 3.67e-235j | 
| -0.86113225770363542512 + 2.1958038571748631551e-940j | 1.17e-236, 1.17e-236j | 
| -0.76464176160759511045 - 2.0601411458853515302e-942j | 3.21e-238, 3.21e-238j | 
| 0.9900406608617272176 - 6.0763026912393952322e-940j | 5.16e-235, 5.16e-235j | 
| 0.68908942003680862746 + 4.6681457042739248187e-955j | 1.9e-239, 1.9e-239j | 
| 0.72786962000958103135 - 2.435883392913941343e-954j | 8.4e-239, 8.4e-239j | 
| -0.72786962000958103135 - 1.8290997065391651797e-955j | 8.79e-239, 8.79e-239j | 
| -0.64906245851136032247 + 6.7131509699364679511e-957j | 4.66e-240, 4.66e-240j | 
| -0.017707343666350335061 - 1.6890159711275912811e-971j | 3.79e-255, 3.79e-255j | 
| 0.542047847949869028 - 1.4730205750474318672e-958j | 5.34e-242, 5.34e-242j | 
| 0.64906245851136032247 + 2.818459634729746989e-956j | 4.57e-240, 4.57e-240j | 
| -0.052239198747083744729 + 7.645325282531750802e-971j | 2.67e-254, 2.67e-254j | 
| -0.57735026918962576451 + 3.1900529932079797445e-958j | 3.22e-241, 3.22e-241j | 
| -0.61065426328216857249 + 1.5067641860269893585e-957j | 1.28e-240, 1.28e-240j | 
| 0.76464176160759511045 + 1.7659576847783397999e-956j | 3.28e-238, 3.28e-238j | 
| 0.61065426328216857249 - 6.684871224082768464e-961j | 1.21e-240, 1.21e-240j | 
| 0.31025923898595627797 + 4.9672522264452876597e-968j | 7.24e-248, 7.24e-248j | 
| -0.15655801081562154215 + 1.2359699200539371466e-971j | 9.64e-252, 9.64e-252j | 
| -0.542047847949869028 - 5.6522371821871895462e-963j | 5.23e-242, 5.23e-242j | 
| -0.98056638155134655011 - 3.8701273737765799184e-967j | 4.46e-235, 4.46e-235j | 
| 0.26011734650479527322 + 2.0725922198078930753e-981j | 4.31e-249, 4.31e-249j | 
| 0.57735026918962576451 - 8.7781570542713246711e-976j | 3.14e-241, 3.14e-241j | 
| 0.017707343666350335061 + 8.0974810972022255329e-991j | 3.79e-255, 3.79e-255j | 
| -0.45914059471659977185 - 2.5794509356768864681e-979j | 4.13e-244, 4.13e-244j | 
| -0.50189202417843397362 + 4.4530300087500834219e-980j | 4.91e-243, 4.91e-243j | 
| 0.15655801081562154215 + 4.6666202410857899856e-988j | 8.2e-252, 8.2e-252j | 
| 0.50189202417843397362 - 2.4347086047890396552e-980j | 5.57e-243, 5.57e-243j | 
| 0.20986442850604162326 + 1.3359204027542691023e-989j | 2.16e-250, 2.16e-250j | 
| -0.26011734650479527322 - 5.1726808256401902361e-989j | 4.63e-249, 4.63e-249j | 
| -0.41223030687927218271 - 4.2400656022873129576e-985j | 2.58e-245, 2.58e-245j | 
| -0.10154582981657319367 - 1.5912431810356164965e-992j | 4.1e-253, 4.1e-253j | 
| 0.41223030687927218271 - 2.6965104901795184878e-983j | 2.53e-245, 2.53e-245j | 
| 0.45914059471659977185 - 2.0767413463472642741e-983j | 4.39e-244, 4.39e-244j | 
| 0.10154582981657319367 - 5.4065656577812623523e-992j | 3.91e-253, 3.91e-253j | 
| -0.36169737844803468332 - 1.1487579974446104199e-986j | 1.43e-246, 1.43e-246j | 
| -0.31025923898595627797 - 2.8347110016803747224e-987j | 7.58e-248, 7.58e-248j | 
| 0.052239198747083744729 - 3.1092646011517705135e-993j | 2.67e-254, 2.67e-254j | 
| 0.36169737844803468332 - 8.7770148296038815934e-986j | 1.47e-246, 1.47e-246j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0016562948560485099236 - 3.2868783564167400811e-841j | 5.68e-46, 1.08e-158j | 
| 0.0046274641788811807181 - 7.5908850320358213628e-844j | 2.51e-46, 4.78e-159j | 
| 0.017025149495602990901 - 3.523452567593720919e-843j | 1.12e-46, 2.13e-159j | 
| 0.0016562948560485099236 + 2.5388033773233902742e-844j | 1.21e-46, 2.3e-159j | 
| 0.022926435690505676254 + 1.3572622909761810697e-841j | 3.06e-47, 5.82e-160j | 
| 0.020018818165548078675 - 1.3783377778451340658e-841j | 2.4e-47, 4.56e-160j | 
| 0.014038353527687946054 - 1.6419972456742707244e-841j | 7.05e-48, 1.34e-160j | 
| 0.022926435690505676254 - 6.1689672441909074872e-843j | 1.38e-48, 2.63e-161j | 
| 0.0078891489782907653741 + 1.280798149415441786e-843j | 1.6e-47, 3.05e-160j | 
| 0.0046274641788811807181 + 4.9124710018158959912e-841j | 2.19e-48, 4.16e-161j | 
| 0.028366365050814908799 + 1.4976548256493710387e-841j | 2.38e-49, 4.53e-162j | 
| 0.051562820903023499149 - 7.6760667655912427358e-841j | 2.3e-51, 4.37e-164j | 
| 0.020018818165548078675 + 4.663502177886657913e-843j | 9.2e-49, 1.75e-161j | 
| 0.030976082007227056867 + 1.530979970460986386e-842j | 1.61e-50, 3.06e-163j | 
| 0.017025149495602990901 + 1.4667260833888552633e-841j | 1.03e-48, 1.96e-161j | 
| 0.030976082007227056867 - 1.6691251115240507979e-841j | 1.39e-50, 2.63e-163j | 
| 0.025692617519397975003 - 1.3974691758175697557e-841j | 2.36e-49, 4.48e-162j | 
| 0.039637228505817554852 + 8.0863975410414668966e-842j | 1.55e-53, 2.95e-166j | 
| 0.033440777868756625469 - 2.1636388343017024717e-842j | 1.41e-52, 2.68e-165j | 
| 0.025692617519397975003 + 8.2341357071107937719e-843j | 7.69e-52, 1.46e-164j | 
| 0.011030900360617416157 + 1.9790611471250533165e-841j | 2.43e-51, 4.61e-164j | 
| 0.033440777868756625469 + 1.9442602841499259905e-841j | 2.42e-53, 4.6e-166j | 
| 0.014038353527687946054 + 2.6172465357481162899e-843j | 4.01e-52, 7.64e-165j | 
| 0.028366365050814908799 - 1.1128849012327220414e-842j | 1.38e-52, 2.62e-165j | 
| 0.035702375813656871452 + 3.1705384124810167612e-842j | 2.08e-54, 3.95e-167j | 
| 0.0078891489782907653741 - 2.7269939890555146845e-841j | 6.72e-52, 1.28e-164j | 
| 0.039637228505817554852 - 4.4002219808669756493e-841j | 4.35e-57, 8.27e-170j | 
| 0.037821363900701480372 + 3.1016577766837063718e-841j | 2.03e-56, 3.86e-169j | 
| 0.037821363900701480372 - 4.8756356082897079249e-842j | 9.4e-56, 1.79e-168j | 
| 0.039975614517337619196 - 1.5029818453225327444e-841j | 1.67e-57, 3.17e-170j | 
| 0.033387457272742508118 - 7.3880349473455797834e-840j | 3.39e-61, 6.45e-174j | 
| 0.038423338432006437361 - 1.6243377284565384966e-840j | 1.96e-60, 3.72e-173j | 
| 0.039975614517337619196 + 7.0723097804476489885e-841j | 7.92e-59, 1.51e-171j | 
| 0.04143101691474469428 + 4.5511186471252126589e-840j | 2.24e-61, 4.26e-174j | 
| 0.03246745309677520147 - 4.4039669731923203715e-841j | 4.05e-60, 7.7e-173j | 
| 0.035875663763911910697 + 2.9377270446345704612e-841j | 2.23e-59, 4.25e-172j | 
| 0.035702375813656871452 - 2.3825714962993112322e-841j | 1.15e-58, 2.18e-171j | 
| 0.035875663763911910697 - 1.2167447287307394772e-840j | 1.1e-60, 2.09e-173j | 
| 0.05095751688153687743 + 9.1315561156821117767e-841j | 1.23e-64, 2.35e-177j | 
| 0.054792636880166071324 + 1.0458375708430156933e-840j | 6.72e-64, 1.28e-176j | 
| 0.038423338432006437361 + 4.8193431843816979167e-841j | 2.82e-62, 5.36e-175j | 
| 0.011030900360617416157 - 1.8809635671453400254e-843j | 3.29e-60, 6.26e-173j | 
| 0.049584176599231081109 - 1.0419918061061835812e-840j | 4.27e-65, 8.12e-178j | 
| 0.03246745309677520147 + 1.6453376678457334095e-840j | 2.21e-62, 4.21e-175j | 
| 0.033387457272742508118 + 7.6545634624401307156e-840j | 1.05e-64, 2e-177j | 
| 0.044599450396888004913 + 4.1892041195250230628e-841j | 1.18e-64, 2.24e-177j | 
| 0.041351373806842746862 - 4.5743788594413538551e-841j | 7.79e-64, 1.48e-176j | 
| 0.054792636880166071324 - 1.4343736622347272431e-840j | 1.34e-66, 2.55e-179j | 
| 0.041351373806842746862 + 1.3804043627950691794e-840j | 4.91e-66, 9.34e-179j | 
| 0.051562820903023499149 + 1.1756858318786579594e-840j | 1.58e-66, 3.01e-179j | 
| 0.049584176599231081109 + 6.1159918670325988093e-841j | 3.11e-67, 5.92e-180j | 
| 0.049092081577986536388 - 3.8608278843784235463e-841j | 6.81e-67, 1.29e-179j | 
| 0.054166204870787632765 - 1.8968790192736670198e-840j | 1.03e-66, 1.96e-179j | 
| 0.049092081577986536388 + 9.2820625604085924344e-841j | 2.19e-68, 4.16e-181j | 
| 0.044599450396888004913 - 1.1309816669082264482e-840j | 5.58e-68, 1.06e-180j | 
| 0.054166204870787632765 + 2.3259542333380789524e-840j | 1.69e-68, 3.22e-181j | 
| 0.051483818166464142066 + 3.9980215195836700657e-841j | 3.86e-69, 7.33e-182j | 
| 0.05095751688153687743 - 4.8049600733649408467e-841j | 3.42e-69, 6.48e-182j | 
| 0.04143101691474469428 - 5.0531467898326179241e-840j | 8.9e-69, 1.71e-181j | 
| 0.051483818166464142066 - 8.5333929087442391592e-841j | 8.46e-70, 1.55e-182j | 
All rules of Legendre type can be downloaded here packed into a single file.