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) | 
|---|---|
| -0.99086717916839647793 + 4.1385668953719232039e-884j | 2.24e-235, 2.24e-235j | 
| 0.99857629549154871341 - 2.6710769633028011471e-892j | 4.43e-236, 4.43e-236j | 
| -0.88623325615748496016 - 3.58932469618932453e-897j | 6.54e-237, 6.54e-237j | 
| 0.99444997880691468328 + 6.1029743180316993788e-896j | 2.04e-235, 2.04e-235j | 
| 0.88623325615748496016 - 5.8335383024305263846e-902j | 6.3e-237, 6.3e-237j | 
| 0.93736205400631741089 - 5.3415640016608995907e-901j | 5.01e-236, 5.01e-236j | 
| 0.99086717916839647793 - 1.4252212705078187939e-900j | 2.26e-235, 2.26e-235j | 
| -0.91309867913380980692 - 2.6609673170376699493e-899j | 1.6e-236, 1.6e-236j | 
| 0.97995439855893244894 - 5.4451017184291517221e-909j | 1.33e-235, 1.33e-235j | 
| -0.99857629549154871341 + 3.6490657833337092239e-906j | 4.57e-236, 4.57e-236j | 
| 0.86113631159405257522 + 5.1131290265499574365e-929j | 2.82e-237, 2.82e-237j | 
| 0.96498796916933250698 + 2.3549188190770015224e-926j | 1.33e-235, 1.33e-235j | 
| -0.86113631159405257522 + 1.5370467954308860245e-925j | 2.73e-237, 2.73e-237j | 
| -0.75979837061900765716 + 9.7725709542030882081e-932j | 3.54e-239, 3.54e-239j | 
| 0.54627694908708365616 - 1.9831350286167975633e-940j | 2.11e-243, 2.11e-243j | 
| 0.83285345162631603364 + 1.1211406490688881343e-934j | 8.1e-238, 8.1e-238j | 
| 0.91309867913380980692 + 1.3076690979342380841e-931j | 1.58e-236, 1.58e-236j | 
| -0.99444997880691468328 - 1.2229625807552628415e-934j | 2.02e-235, 2.02e-235j | 
| -0.7975424410785595081 + 6.8819675223275152515e-947j | 1.53e-238, 1.53e-238j | 
| -0.95280406968027788258 - 1.838278661475967986e-953j | 1.08e-235, 1.08e-235j | 
| -0.83285345162631603364 - 5.9471459184366724209e-965j | 7.91e-238, 7.91e-238j | 
| 0.72317255923281838433 - 4.4747337836986468689e-972j | 7.42e-240, 7.42e-240j | 
| -0.97995439855893244894 - 5.4687493374311957107e-967j | 1.26e-235, 1.26e-235j | 
| -0.72317255923281838433 - 8.8612409803189641927e-986j | 7.76e-240, 7.76e-240j | 
| -0.68393993120655567189 + 3.1235851168490304833e-986j | 1.22e-240, 1.22e-240j | 
| 0.95280406968027788258 - 3.3966473325409602583e-982j | 1.16e-235, 1.16e-235j | 
| 0.68393993120655567189 + 1.9773337593278845397e-989j | 1.2e-240, 1.2e-240j | 
| 0.7975424410785595081 - 2.5396827130227276331e-986j | 1.53e-238, 1.53e-238j | 
| -0.96498796916933250698 - 3.6944398359582429555e-984j | 1.38e-235, 1.38e-235j | 
| -0.63903832758025874306 - 2.8598052442905498659e-1007j | 1.38e-241, 1.38e-241j | 
| -0.93736205400631741089 - 1.1957905187011376966e-1008j | 5.01e-236, 5.01e-236j | 
| 0.75979837061900765716 + 6.5296861783202765146e-1016j | 3.28e-239, 3.28e-239j | 
| 0.63903832758025874306 - 9.2375597889555029627e-1020j | 1.39e-241, 1.39e-241j | 
| -0.17130896646320733372 - 7.1771119315875444146e-1031j | 1.08e-251, 1.08e-251j | 
| -0.59211724255805436047 - 4.6063803983983255441e-1021j | 1.88e-242, 1.88e-242j | 
| -0.49849886439259081231 - 3.1263644661373079839e-1023j | 2.06e-244, 2.06e-244j | 
| 0.059078319309769109397 + 8.1820810827374685288e-1035j | 2.3e-254, 2.3e-254j | 
| 0.59211724255805436047 + 5.591572974600821546e-1024j | 1.86e-242, 1.86e-242j | 
| 0.22923457827971255848 - 2.2322538583152448227e-1033j | 2.09e-250, 2.09e-250j | 
| -0.3399810435848562648 - 5.3535840461733560594e-1029j | 7.39e-248, 7.39e-248j | 
| -0.44614011312884109303 + 5.6938465187952468964e-1025j | 1.4e-245, 1.4e-245j | 
| -0.11539569344883949077 + 1.0348453587529844348e-1034j | 4.74e-253, 4.74e-253j | 
| 0.39234832539267916927 - 4.9110326349893722235e-1029j | 1.04e-246, 1.04e-246j | 
| 0.44614011312884109303 - 9.0035935044991019593e-1028j | 1.51e-245, 1.51e-245j | 
| -1.2529144389987316309e-1047 - 2.4188160875425024724e-1047j | 1.5e-1045, 1.5e-1045j | 
| -0.54627694908708365616 - 1.9362477882190349121e-1026j | 2.1e-243, 2.1e-243j | 
| -0.28641874689355641689 + 3.2384793506400221158e-1033j | 4.13e-249, 4.13e-249j | 
| 0.17130896646320733372 - 6.8365101684004858358e-1035j | 1.06e-251, 1.06e-251j | 
| 0.49849886439259081231 - 1.6776340569418546525e-1027j | 2e-244, 2e-244j | 
| 0.11539569344883949077 - 4.0192742800939051459e-1036j | 5.17e-253, 5.17e-253j | 
| -0.22923457827971255848 - 5.6948659831874371719e-1034j | 1.89e-250, 1.89e-250j | 
| -0.39234832539267916927 + 1.2287407171873809413e-1029j | 1.06e-246, 1.06e-246j | 
| -0.059078319309769109397 - 9.4570808502843095928e-1039j | 2.25e-254, 2.25e-254j | 
| 0.28641874689355641689 + 7.4510422927141958208e-1033j | 4.1e-249, 4.1e-249j | 
| 0.3399810435848562648 - 1.4176605724003503663e-1031j | 7.04e-248, 7.04e-248j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0074909092702870182359 - 4.3934004469523371997e-884j | 9.43e-48, 3.23e-159j | 
| 0.0035690317194691326785 + 2.2169758324662594005e-887j | 4.31e-48, 1.48e-159j | 
| 0.026362312829274447353 + 5.5174344628544239846e-885j | 8.4e-49, 2.88e-160j | 
| 0.0025766272678347112239 - 1.1926802845514261876e-886j | 3.1e-48, 1.06e-159j | 
| 0.026362312829274447353 + 3.0755467835037826931e-886j | 9.56e-50, 3.28e-161j | 
| 0.021146017942585764988 + 3.0040333042312208669e-886j | 9.57e-50, 3.28e-161j | 
| 0.0074909092702870182359 + 1.5643772467098838488e-886j | 8.48e-49, 2.91e-160j | 
| 0.026408032504926308361 - 6.1000675058508592033e-885j | 2.6e-52, 8.9e-164j | 
| 0.013536425557373275252 - 1.3771105666092782521e-886j | 1.22e-49, 4.17e-161j | 
| 0.0035690317194691326785 - 5.7210677775831170998e-885j | 1.07e-53, 3.67e-165j | 
| 0.024952444535882619933 - 3.5969393976480642468e-886j | 7.61e-52, 2.61e-163j | 
| 0.015205891297031048572 + 2.5444883289656217047e-886j | 1.98e-50, 6.79e-162j | 
| 0.024952444535882619933 - 5.1348938882355244631e-885j | 4.44e-54, 1.52e-165j | 
| 0.037331421869209794051 + 2.6207741668870602045e-885j | 2.98e-55, 1.02e-166j | 
| 0.045868234685544827399 - 4.248282585706883336e-886j | 1.73e-55, 5.94e-167j | 
| 0.032309848005158587746 + 3.3225938347958492343e-886j | 6.07e-53, 2.08e-164j | 
| 0.026408032504926308361 - 2.4916062752031459932e-886j | 1.8e-51, 6.17e-163j | 
| 0.0025766272678347112239 + 6.6088652621012237715e-884j | 3.52e-55, 1.21e-166j | 
| 0.037399682714207604246 - 2.8501642911849455983e-885j | 1.7e-56, 5.82e-168j | 
| 0.01039830596301164345 - 1.819536155710021032e-884j | 1.41e-56, 4.83e-168j | 
| 0.032309848005158587746 + 3.8347816917160257603e-885j | 2.17e-56, 7.45e-168j | 
| 0.036748494719912779322 - 3.8229562797036388863e-886j | 1.53e-58, 5.24e-170j | 
| 0.013536425557373275252 - 2.4870224264527432317e-884j | 2.32e-56, 7.96e-168j | 
| 0.036748494719912779322 - 2.4478258560613801672e-885j | 1.56e-58, 5.33e-170j | 
| 0.042334916478937664481 + 2.0139631202743110562e-885j | 1.93e-59, 6.62e-171j | 
| 0.01039830596301164345 - 3.5632192169673582726e-886j | 4.37e-56, 1.5e-167j | 
| 0.042334916478937664481 + 3.6908144398186697891e-886j | 8.77e-61, 3e-172j | 
| 0.037399682714207604246 - 3.0809908621715282426e-886j | 2.44e-59, 8.35e-171j | 
| 0.015205891297031048572 + 1.9230279191833788179e-884j | 8.85e-58, 3.03e-169j | 
| 0.046710432833169687167 - 1.6577841312589701463e-885j | 3.61e-62, 1.24e-173j | 
| 0.021146017942585764988 + 1.0825992606406053173e-884j | 5.54e-58, 1.9e-169j | 
| 0.037331421869209794051 + 3.4591373466277815712e-886j | 1.85e-60, 6.34e-172j | 
| 0.046710432833169687167 - 3.5784672124377351823e-886j | 1.46e-62, 5.02e-174j | 
| 0.057013155976489941462 + 7.6938861753227385383e-886j | 1.38e-67, 4.74e-179j | 
| 0.046477639734976837497 + 1.5529053785087942791e-885j | 4.26e-64, 1.46e-175j | 
| 0.050242554624320978055 + 1.2706619982601679654e-885j | 8.02e-66, 2.75e-177j | 
| 0.057804616145680882526 + 6.0153280946111859649e-886j | 4.65e-69, 1.59e-180j | 
| 0.046477639734976837497 + 3.9117312938557687075e-886j | 2.25e-65, 7.7e-177j | 
| 0.058259624849507128225 - 4.9763183079044122751e-886j | 3.39e-69, 1.16e-180j | 
| 0.052140699990842887814 - 1.0033259476915076111e-885j | 1.12e-68, 3.85e-180j | 
| 0.053814581061377254351 - 1.1000770663762537983e-885j | 1.06e-67, 3.62e-179j | 
| 0.05534053409380737271 - 7.4642813754223459172e-886j | 1.2e-69, 4.11e-181j | 
| 0.053168215046940310804 + 4.5304947496801027235e-886j | 1.2e-69, 4.1e-181j | 
| 0.053814581061377254351 - 4.1700677846686030876e-886j | 3.1e-69, 1.06e-180j | 
| 0.059771969614651365561 - 6.1522163134914221799e-886j | 1.97e-70, 6.74e-182j | 
| 0.045868234685544827399 - 1.4688181950153113633e-885j | 3.47e-68, 1.19e-179j | 
| 0.055503363474913809317 + 8.9421488829632851839e-886j | 4.35e-70, 1.49e-181j | 
| 0.057013155976489941462 + 5.4256729690251970337e-886j | 2.33e-71, 7.98e-183j | 
| 0.050242554624320978055 + 4.2006714552595520446e-886j | 2.16e-70, 7.38e-182j | 
| 0.05534053409380737271 - 5.9070639838350551952e-886j | 2.41e-71, 8.27e-183j | 
| 0.058259624849507128225 - 7.9718417768428626848e-886j | 2.37e-71, 8.12e-183j | 
| 0.053168215046940310804 + 1.0470263870176037575e-885j | 4.14e-71, 1.42e-182j | 
| 0.057804616145680882526 + 6.7781091775112918104e-886j | 8.66e-72, 2.97e-183j | 
| 0.055503363474913809317 + 4.9317719727499299865e-886j | 5.51e-73, 1.89e-184j | 
| 0.052140699990842887814 - 4.9070281593305475931e-886j | 5.49e-73, 1.87e-184j | 
All rules of Legendre type can be downloaded here packed into a single file.