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) | 
|---|---|
| 0.98930732004477920636 + 1.3295743578533039423e-1857j | 2.02e-481, 2.02e-481j | 
| -0.98240771299532367948 + 1.5926246667426375014e-1855j | 1.8e-481, 1.8e-481j | 
| -0.9390545945854208559 - 8.460912765326942746e-1864j | 8.23e-482, 8.23e-482j | 
| -0.99965905896802560367 - 2.0788787771050704398e-1863j | 4.05e-482, 4.05e-482j | 
| 0.92494080796092924165 + 7.2966605865161832554e-1875j | 5.78e-482, 5.78e-482j | 
| 0.96381476440658411766 - 1.957267090033848243e-1873j | 1.5e-481, 1.5e-481j | 
| -0.84961864014768022281 + 1.8122136458499687459e-1875j | 3.19e-483, 3.19e-483j | 
| -0.89479284776640817415 + 2.403783090302780893e-1874j | 2.87e-482, 2.87e-482j | 
| -0.98930732004477920636 - 1.2137312698420573306e-1872j | 1.99e-481, 1.99e-481j | 
| 0.99452381513974088284 - 4.7191322266170451234e-1883j | 1.65e-481, 1.65e-481j | 
| 0.87918641166918605722 - 4.7780204482554335994e-1885j | 1.72e-482, 1.72e-482j | 
| -0.99796335851602133935 + 3.4267545097392996317e-1882j | 1.23e-481, 1.23e-481j | 
| -0.92494080796092924165 + 3.2793079868750831179e-1897j | 6.17e-482, 6.17e-482j | 
| -0.87918641166918605722 - 5.5631208181401290023e-1912j | 1.78e-482, 1.78e-482j | 
| -0.99452381513974088284 + 2.4419097743226697853e-1930j | 1.65e-481, 1.65e-481j | 
| 0.86506336668898451073 + 2.6156080493804307601e-1961j | 9.44e-483, 9.44e-483j | 
| 0.9390545945854208559 - 5.9939884020553828784e-1959j | 8.81e-482, 8.81e-482j | 
| 0.78665243882535449765 + 1.0706753040287847225e-1964j | 3.01e-485, 3.01e-485j | 
| -0.78665243882535449765 + 1.5576014813984909623e-1960j | 2.89e-485, 2.89e-485j | 
| -0.95214288160745204474 + 3.5335155681339005358e-1965j | 1.18e-481, 1.18e-481j | 
| -0.91019337304803359399 - 6.3685583895276312485e-2000j | 4.08e-482, 4.08e-482j | 
| 0.76196431590397501264 + 8.0007093297079324879e-2023j | 5.16e-486, 5.16e-486j | 
| 0.97390652851717172008 - 1.1931167360200563501e-2015j | 1.72e-481, 1.72e-481j | 
| -0.83056913118909175115 + 1.0720519832247269247e-2019j | 7.58e-484, 7.58e-484j | 
| -0.80946053280165822421 - 2.3378882870012143691e-2026j | 1.48e-484, 1.48e-484j | 
| 0.99965905896802560367 - 7.6157770625594195217e-2021j | 4.21e-482, 4.21e-482j | 
| 0.73559437130606183486 - 7.6070617798139857736e-2037j | 8.05e-487, 8.05e-487j | 
| 0.91019337304803359399 + 6.2103165555109419439e-2031j | 4.14e-482, 4.14e-482j | 
| -0.97390652851717172008 + 9.5470742275188348431e-2046j | 1.85e-481, 1.85e-481j | 
| -0.64994491157929067668 - 3.7450614184299328063e-2077j | 2.79e-489, 2.79e-489j | 
| -9.0124421836364628887e-2141 + 3.9653170119375215548e-2140j | 3.38e-2138, 3.38e-2138j | 
| 0.46466974896293070634 - 3.234682860769680099e-2082j | 1.14e-494, 1.14e-494j | 
| 0.70797644440199598032 - 4.8152464022390297274e-2075j | 1.26e-487, 1.26e-487j | 
| 0.99796335851602133935 - 1.2969270632358808416e-2066j | 1.16e-481, 1.16e-481j | 
| -0.67940956829902440623 - 4.2893286324085621768e-2079j | 2.04e-488, 2.04e-488j | 
| -0.76196431590397501264 + 4.4758285601553484728e-2076j | 5.4e-486, 5.4e-486j | 
| 0.89479284776640817415 + 3.4332833810390981692e-2071j | 2.86e-482, 2.86e-482j | 
| 0.61962833094212869037 + 1.3772574793000273656e-2081j | 3.98e-490, 3.98e-490j | 
| 0.80946053280165822421 + 2.0798418678421145827e-2075j | 1.51e-484, 1.51e-484j | 
| -0.86506336668898451073 - 1.3218290235160900051e-2071j | 1.02e-482, 1.02e-482j | 
| -0.55795190843102211023 + 5.9590804207477928413e-2089j | 6.47e-492, 6.47e-492j | 
| 0.84961864014768022281 + 8.6531740764028374907e-2077j | 3.28e-483, 3.28e-483j | 
| 0.67940956829902440623 + 3.7554808189803824873e-2083j | 1.98e-488, 1.98e-488j | 
| 0.58880030790290703897 - 1.3514739506031392816e-2086j | 5.49e-491, 5.49e-491j | 
| -0.58880030790290703897 + 4.4496855237424631355e-2088j | 5.85e-491, 5.85e-491j | 
| -0.61962833094212869037 + 9.363622906833568848e-2087j | 4.03e-490, 4.03e-490j | 
| -0.70797644440199598032 - 1.0665307108319696725e-2083j | 1.27e-487, 1.27e-487j | 
| 0.83056913118909175115 + 4.6617407499229433633e-2078j | 7.9e-484, 7.9e-484j | 
| 0.49599179888091973177 + 8.5334919978718516466e-2090j | 9.68e-494, 9.68e-494j | 
| 0.98240771299532367948 - 2.0805067591437644662e-2077j | 2.1e-481, 2.1e-481j | 
| -0.73559437130606183486 + 2.7443947057636695389e-2084j | 8.49e-487, 8.49e-487j | 
| -0.49599179888091973177 + 1.5712769689398259794e-2092j | 9.83e-494, 9.83e-494j | 
| -0.96381476440658411766 - 9.5528823652511257401e-2087j | 1.31e-481, 1.31e-481j | 
| 0.55795190843102211023 - 8.2729275784141282505e-2102j | 6.7e-492, 6.7e-492j | 
| 0.52713663151855623783 + 1.0829205379600968676e-2102j | 8.48e-493, 8.48e-493j | 
| -0.18621132389317012633 + 1.0735016590222446435e-2114j | 2e-504, 2e-504j | 
| -0.4333953941292471908 + 4.6787548619263687871e-2107j | 1.07e-495, 1.07e-495j | 
| -0.46466974896293070634 - 1.462119889180444459e-2105j | 1.09e-494, 1.09e-494j | 
| 0.95214288160745204474 + 2.0862363077968192014e-2103j | 1.15e-481, 1.15e-481j | 
| 0.40123868202724423168 + 3.4179087200137887812e-2120j | 8.73e-497, 8.73e-497j | 
| 0.64994491157929067668 + 2.8952766895028403589e-2120j | 3.05e-489, 3.05e-489j | 
| -0.52713663151855623783 - 2.8805428392962865372e-2127j | 8.76e-493, 8.76e-493j | 
| -0.40123868202724423168 - 5.4144100335035449903e-2131j | 8.46e-497, 8.46e-497j | 
| -0.074159887138375149369 - 3.2720762243011263808e-2142j | 1.95e-508, 1.95e-508j | 
| 0.36749222036032573104 - 5.9598654695743513729e-2132j | 5.6e-498, 5.6e-498j | 
| 0.4333953941292471908 - 3.1247643632551137021e-2130j | 1.04e-495, 1.04e-495j | 
| -0.036882744206528549318 - 7.6351735401825435905e-2144j | 1.14e-509, 1.14e-509j | 
| -0.36749222036032573104 + 7.7426256546120195948e-2132j | 5.89e-498, 5.89e-498j | 
| -0.22367436679155302337 - 5.0279714337423382893e-2137j | 4.43e-503, 4.43e-503j | 
| 0.14887433898163121088 + 2.0918512305566731083e-2140j | 1.06e-505, 1.06e-505j | 
| 0.33265736549637234666 + 1.3849782974446052746e-2133j | 3.24e-499, 3.24e-499j | 
| 0.11158228866731494088 - 3.1017689830687070089e-2141j | 4.86e-507, 4.86e-507j | 
| -0.26082413050363595004 - 5.0279055657996727565e-2136j | 8.88e-502, 8.88e-502j | 
| -0.29715510770640448885 + 1.9162539887623954675e-2134j | 1.9e-500, 1.9e-500j | 
| 0.074159887138375149369 + 2.1606079423799221004e-2142j | 2.02e-508, 2.02e-508j | 
| 0.29715510770640448885 - 1.2890998728343949272e-2134j | 1.93e-500, 1.93e-500j | 
| 0.18621132389317012633 - 1.3331881618028228407e-2138j | 2.01e-504, 2.01e-504j | 
| -0.11158228866731494088 + 4.7819250070724965715e-2141j | 5.01e-507, 5.01e-507j | 
| -0.33265736549637234666 - 3.797410081366309315e-2133j | 3.59e-499, 3.59e-499j | 
| -0.14887433898163121088 - 1.3865454649216328982e-2139j | 9.71e-506, 9.71e-506j | 
| 0.22367436679155302337 + 8.7746816913116671602e-2138j | 4.22e-503, 4.22e-503j | 
| 0.26082413050363595004 + 1.3886999430362366133e-2136j | 8.68e-502, 8.68e-502j | 
| 0.036882744206528549318 + 7.1181806818247585283e-2144j | 1.12e-509, 1.12e-509j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0060760675989774684486 - 7.9188998561959964285e-1858j | 1.09e-139, 5.07e-372j | 
| 0.0077083109500883225751 + 4.9128931130219977584e-1856j | 5.31e-140, 2.48e-372j | 
| 0.013681591617409355473 + 1.6862365789781524955e-1855j | 2.57e-140, 1.2e-372j | 
| 0.00091480952971966764206 - 5.6390217672378104523e-1857j | 8.08e-141, 3.78e-373j | 
| 0.014468828361814412073 - 8.6473632907436771281e-1857j | 5.65e-142, 2.64e-374j | 
| 0.010891304894707227046 + 2.538240275273235076e-1857j | 8.19e-142, 3.83e-374j | 
| 0.017479212058077015834 + 5.3954649631306021673e-1855j | 3.06e-141, 1.43e-373j | 
| 0.015728008370318157365 - 4.3145536720432367165e-1855j | 5.36e-141, 2.51e-373j | 
| 0.0060760675989774684486 + 1.1717915243422601896e-1855j | 5.81e-141, 2.71e-373j | 
| 0.0043392333510879128867 - 7.3090338770261036675e-1858j | 1.19e-143, 5.58e-376j | 
| 0.015048857559665513831 + 3.9551289808757432096e-1856j | 4.27e-144, 1.99e-376j | 
| 0.0025407110944661109471 + 1.9045886529112892589e-1856j | 3.43e-141, 1.6e-373j | 
| 0.014468828361814412073 - 2.2150979342810844929e-1855j | 1.75e-142, 8.19e-375j | 
| 0.015048857559665513831 + 6.105681469597317753e-1855j | 4.53e-143, 2.12e-375j | 
| 0.0043392333510879128867 - 4.2793284316548862197e-1856j | 2.25e-141, 1.05e-373j | 
| 0.013813267643325478805 - 4.9857810034248017299e-1856j | 2.62e-146, 1.22e-378j | 
| 0.013681591617409355473 + 5.2569334472292308139e-1857j | 4.46e-146, 2.09e-378j | 
| 0.023741254977415962023 - 2.2519252155573338958e-1856j | 7.91e-148, 3.7e-380j | 
| 0.023741254977415962023 - 1.8738831919660843977e-1855j | 3.08e-146, 1.44e-378j | 
| 0.012426839671227646942 - 1.4529645312335782756e-1855j | 1.98e-143, 9.27e-376j | 
| 0.015042490314902112296 + 3.0632607913989205292e-1855j | 2.68e-143, 1.25e-375j | 
| 0.025596230878509284142 + 1.979712054924220172e-1856j | 9.7e-150, 4.53e-382j | 
| 0.00929350562282844222 - 2.1441782404744404357e-1857j | 1.33e-148, 6.2e-381j | 
| 0.020263390496662939745 - 3.5997525417106647065e-1855j | 7.98e-146, 3.73e-378j | 
| 0.02192202944951631117 + 2.5361797030468812197e-1855j | 1.75e-146, 8.19e-379j | 
| 0.00091480952971966764206 - 4.4821963884572505772e-1859j | 8.11e-150, 3.79e-382j | 
| 0.027064480552624816062 - 1.8752223940298100337e-1856j | 2.48e-151, 1.16e-383j | 
| 0.015042490314902112296 + 1.4476548307369613419e-1856j | 2.92e-149, 1.36e-381j | 
| 0.00929350562282844222 - 2.1745028393780439225e-1855j | 9.3e-146, 4.35e-378j | 
| 0.029917397566474928392 + 1.1166472096054246455e-1855j | 2.31e-152, 1.08e-384j | 
| 0.03677582368734931022 - 1.0134201821413701154e-1855j | 6.38e-156, 2.98e-388j | 
| 0.031248992800205925918 + 7.7228372100722661787e-1856j | 1.65e-155, 7.71e-388j | 
| 0.028119233688078027439 + 1.9207723535241132183e-1856j | 1.45e-152, 6.78e-385j | 
| 0.0025407110944661109471 + 1.9240280996366357574e-1858j | 7.85e-150, 3.67e-382j | 
| 0.029010817428417559126 - 1.0896601686627668894e-1855j | 7.73e-153, 3.61e-385j | 
| 0.025596230878509284142 + 1.4568301609888104336e-1855j | 7.02e-151, 3.28e-383j | 
| 0.015728008370318157365 - 2.4122497753774691815e-1856j | 1.82e-150, 8.49e-383j | 
| 0.030656901781172168794 - 2.8359210458231838408e-1856j | 1.35e-155, 6.33e-388j | 
| 0.02192202944951631117 + 2.6889707368215386417e-1856j | 2.77e-152, 1.29e-384j | 
| 0.013813267643325478805 - 6.8385427104151123429e-1855j | 3.2e-149, 1.5e-381j | 
| 0.030780304733585995407 - 1.5745637422991375258e-1855j | 3.66e-157, 1.71e-389j | 
| 0.017479212058077015834 + 4.4200340948717899749e-1856j | 7.15e-152, 3.34e-384j | 
| 0.029010817428417559126 - 2.0894330515183693665e-1856j | 5.34e-155, 2.5e-387j | 
| 0.030904666949104528836 + 3.5347556878968067802e-1856j | 5.19e-157, 2.43e-389j | 
| 0.030904666949104528836 + 1.3611698209815315008e-1855j | 3.4e-157, 1.59e-389j | 
| 0.030656901781172168794 - 1.2030723472084893429e-1855j | 1.18e-156, 5.53e-389j | 
| 0.028119233688078027439 + 1.1179131708555855722e-1855j | 1.26e-155, 5.91e-388j | 
| 0.020263390496662939745 - 3.3560778937450726847e-1856j | 4.96e-154, 2.32e-386j | 
| 0.031320719017247520719 - 6.6777393397428526627e-1856j | 1.51e-160, 7.08e-393j | 
| 0.0077083109500883225751 + 2.4026583993029436667e-1857j | 9.39e-155, 4.39e-387j | 
| 0.027064480552624816062 - 1.2243220986191208345e-1855j | 2.25e-155, 1.05e-387j | 
| 0.031320719017247520719 - 1.9770542500753142836e-1855j | 2.53e-161, 1.18e-393j | 
| 0.010891304894707227046 + 1.5073330969990888235e-1855j | 4.1e-154, 1.92e-386j | 
| 0.030780304733585995407 - 4.4813375230442613457e-1856j | 2.76e-160, 1.29e-392j | 
| 0.030935821439280866168 + 5.5616734812642642376e-1856j | 6.96e-161, 3.25e-393j | 
| 0.037432212927359609137 + 1.0772002439384482815e-1855j | 1.72e-166, 8.02e-399j | 
| 0.03149220154048406643 - 2.0995659640228040355e-1855j | 1.11e-163, 5.19e-396j | 
| 0.031248992800205925918 + 2.1081132854928820409e-1855j | 6.95e-163, 3.25e-395j | 
| 0.012426839671227646942 - 3.454788599152133494e-1857j | 5.01e-158, 2.34e-390j | 
| 0.032961022187123722433 + 8.2308167915723542951e-1856j | 1.12e-165, 5.24e-398j | 
| 0.029917397566474928392 + 2.3787705585311052362e-1856j | 1.65e-160, 7.69e-393j | 
| 0.030935821439280866168 + 1.7911630790696495431e-1855j | 4.66e-162, 2.18e-394j | 
| 0.032961022187123722433 + 1.9225762605563752951e-1855j | 3.69e-165, 1.73e-397j | 
| 0.037425870542381293259 - 1.0402702311970812272e-1855j | 1.99e-169, 9.3e-402j | 
| 0.034414747146822244205 - 7.8370631199739286381e-1856j | 1.59e-167, 7.44e-400j | 
| 0.03149220154048406643 - 8.3166951711314441791e-1856j | 1.11e-165, 5.2e-398j | 
| 0.037070953550491551244 + 1.0349930733740845362e-1855j | 7.23e-170, 3.38e-402j | 
| 0.034414747146822244205 - 1.6915389743061160352e-1855j | 9.12e-168, 4.26e-400j | 
| 0.037410470790233137996 - 1.1178425775777798708e-1855j | 9.14e-170, 4.27e-402j | 
| 0.037264619868154545723 - 7.8706791232590284595e-1856j | 5.33e-172, 2.49e-404j | 
| 0.035176168324561491032 + 7.5102514011950668779e-1856j | 3.04e-170, 1.42e-402j | 
| 0.037362162822051578714 + 8.3920738413931787335e-1856j | 4.5e-172, 2.1e-404j | 
| 0.036792434409006880825 + 1.2060107922764109809e-1855j | 5.85e-171, 2.74e-403j | 
| 0.035873943650743545566 - 1.3380226293580915052e-1855j | 6.93e-171, 3.24e-403j | 
| 0.037425870542381293259 - 8.9690043683037413524e-1856j | 7.68e-173, 3.59e-405j | 
| 0.035873943650743545566 - 7.2593237640752210885e-1856j | 9.26e-173, 4.32e-405j | 
| 0.037432212927359609137 + 7.3957705836808355902e-1856j | 1.76e-173, 8.25e-406j | 
| 0.037362162822051578714 + 1.0495313407848171093e-1855j | 1.85e-173, 8.67e-406j | 
| 0.035176168324561491032 + 1.4975390385402110009e-1855j | 1.23e-172, 5.75e-405j | 
| 0.037264619868154545723 - 1.0617548176420350647e-1855j | 1.49e-173, 7.01e-406j | 
| 0.037410470790233137996 - 7.098548708902480543e-1856j | 2.02e-174, 9.28e-407j | 
| 0.036792434409006880825 + 7.0783393828359644318e-1856j | 2.17e-174, 9.82e-407j | 
| 0.037070953550491551244 + 9.6150574055435410437e-1856j | 1.66e-174, 8.52e-407j | 
All rules of Legendre type can be downloaded here packed into a single file.