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) | 
|---|---|
| 0.99978494779442052958 - 6.6496105886555845297e-1759j | 4.13e-483, 4.13e-483j | 
| -0.96745178896399913487 - 9.7286932959516497778e-1762j | 2.35e-483, 2.35e-483j | 
| -0.9274951474090583421 - 2.7930073091704916566e-1788j | 2.65e-484, 2.65e-484j | 
| -0.99978494779442052958 - 3.3266210436531475492e-1813j | 4.02e-483, 4.02e-483j | 
| 0.94249070272268796989 + 1.8457083129530920166e-1849j | 6.11e-484, 6.11e-484j | 
| 0.9274951474090583421 + 2.9652466829856562277e-1850j | 2.71e-484, 2.71e-484j | 
| 0.91086167316030996451 - 1.1400773866065983418e-1850j | 1.12e-484, 1.12e-484j | 
| -0.91086167316030996451 - 3.7638606491754659289e-1849j | 1.07e-484, 1.07e-484j | 
| 0.95582394957139775518 - 1.1639862502933441033e-1856j | 1.24e-483, 1.24e-483j | 
| -0.99156516842093094673 - 8.1706851044239513371e-1854j | 7.91e-483, 7.91e-483j | 
| 0.89260246649755573921 + 3.9684649368911302812e-1878j | 3.71e-485, 3.71e-485j | 
| 0.99156516842093094673 - 4.3042362161098629795e-1875j | 7.86e-483, 7.86e-483j | 
| -0.94249070272268796989 + 3.1395075522078945397e-1875j | 5.89e-484, 5.89e-484j | 
| -0.8512614839549979707 - 2.6962893933233053419e-1885j | 3.8e-486, 3.8e-486j | 
| 0.99593997734518047069 + 3.0933620031594572658e-1882j | 1.01e-482, 1.01e-482j | 
| 0.82823638185176396428 - 1.9872226922253518702e-1887j | 1.05e-486, 1.05e-486j | 
| 0.8512614839549979707 - 3.144828950408324597e-1886j | 3.7e-486, 3.7e-486j | 
| -0.99859651643055150742 - 3.7965998014596847773e-1880j | 9.3e-483, 9.3e-483j | 
| -0.77772775029255652518 - 9.4882934502575308632e-1906j | 5.97e-488, 5.97e-488j | 
| -0.95582394957139775518 + 4.3606244050535076031e-1900j | 1.19e-483, 1.19e-483j | 
| 0.96745178896399913487 - 5.1799774569081633854e-1918j | 2.19e-483, 2.19e-483j | 
| 0.75036505635902229785 - 2.023975347056066376e-1924j | 1.17e-488, 1.17e-488j | 
| 0.99859651643055150742 - 1.2760378566636311626e-1916j | 9.27e-483, 9.27e-483j | 
| -0.82823638185176396428 + 3.6603041586889703552e-1922j | 1.1e-486, 1.1e-486j | 
| -0.80370495897252311568 + 1.2900523026342952426e-1926j | 2.65e-487, 2.65e-487j | 
| 0.87272885201684050249 + 7.5030171694552187581e-1930j | 1.28e-485, 1.28e-485j | 
| 0.72166992327418943232 + 4.4358715040457547577e-1933j | 2.03e-489, 2.03e-489j | 
| 0.97731704962157666034 - 3.1848203340998771778e-1926j | 3.9e-483, 3.9e-483j | 
| -0.98536477117224722794 + 2.4261098080027052866e-1924j | 5.88e-483, 5.88e-483j | 
| -0.62802376237896618507 - 1.1496785197034838552e-1954j | 5.84e-492, 5.84e-492j | 
| -0.89260246649755573921 + 1.4396759925088932824e-1945j | 4.01e-485, 4.01e-485j | 
| 0.77772775029255652518 + 2.754050119583331794e-1959j | 5.31e-488, 5.31e-488j | 
| 0.69168704306035320787 - 3.0029781020324767902e-1961j | 3.18e-490, 3.18e-490j | 
| -0.99593997734518047069 + 2.2704506099898209256e-1951j | 1.04e-482, 1.04e-482j | 
| -0.69168704306035320787 - 3.3965517894533334667e-1983j | 3.18e-490, 3.18e-490j | 
| -0.75036505635902229785 - 1.8364484932170236756e-1981j | 1.14e-488, 1.14e-488j | 
| 0.98536477117224722794 - 2.4666721448257433656e-1977j | 5.72e-483, 5.72e-483j | 
| 0.59443989838629185438 + 2.1746797347098853701e-1989j | 6.36e-493, 6.36e-493j | 
| 0.80370495897252311568 - 2.8860778297643626031e-1983j | 2.54e-487, 2.54e-487j | 
| -0.72166992327418943232 - 7.8051995036251850315e-1983j | 1.97e-489, 1.97e-489j | 
| -0.55977083107394753461 - 2.210652516386015112e-1988j | 7.07e-494, 7.07e-494j | 
| -0.97731704962157666034 - 9.2158816788940720237e-1986j | 3.61e-483, 3.61e-483j | 
| 0.66045711694402080612 + 8.1092233950286530093e-2008j | 4.57e-491, 4.57e-491j | 
| 0.62802376237896618507 - 1.8939929627190642542e-2008j | 6.03e-492, 6.03e-492j | 
| -0.87272885201684050249 + 1.9993326029740141806e-2010j | 1.25e-485, 1.25e-485j | 
| -0.59443989838629185438 - 1.1738706983516428015e-2016j | 6.62e-493, 6.62e-493j | 
| -0.66045711694402080612 + 4.0280334437538761961e-2023j | 4.59e-491, 4.59e-491j | 
| 0.21055260102903231553 + 1.0961427225676660862e-2037j | 2.62e-504, 2.62e-504j | 
| 0.48748173749781995875 + 7.4954874258906143602e-2028j | 5.8e-496, 5.8e-496j | 
| 0.55977083107394753461 + 6.2979817378188859291e-2027j | 7.38e-494, 7.38e-494j | 
| -0.16885305857357954056 + 1.5495325597566356417e-2039j | 1.25e-505, 1.25e-505j | 
| -0.45001348478961689136 + 3.2662984573934853731e-2030j | 5.28e-497, 5.28e-497j | 
| -0.12689236510498180303 - 9.586855894188943703e-2041j | 5.51e-507, 5.51e-507j | 
| 0.52409197316681862632 + 5.8478227481398002403e-2031j | 6.73e-495, 6.73e-495j | 
| 0.45001348478961689136 - 3.6084385200350473627e-2033j | 5.09e-497, 5.09e-497j | 
| -0.0037762088409933203275 - 4.292786466020456787e-2046j | 4.39e-511, 4.39e-511j | 
| -0.48748173749781995875 + 2.351246145857577657e-2029j | 5.64e-496, 5.64e-496j | 
| -0.52409197316681862632 + 4.7872054612978661262e-2031j | 6.3e-495, 6.3e-495j | 
| 0.042651889527379573632 - 5.3207778726392424485e-2045j | 1.6e-509, 1.6e-509j | 
| 0.41175116146284264604 - 1.1778322808586951997e-2034j | 3.94e-498, 3.94e-498j | 
| 0.084775013041735301242 + 7.0552320661443729463e-2044j | 2.82e-508, 2.82e-508j | 
| -0.41175116146284264604 + 4.6600775164517478144e-2034j | 3.56e-498, 3.56e-498j | 
| -0.37275055614765271772 - 1.2143111489037032139e-2035j | 2.62e-499, 2.62e-499j | 
| -0.042651889527379573632 + 5.4643226820286428e-2045j | 1.6e-509, 1.6e-509j | 
| 0.37275055614765271772 - 3.9794273892921744076e-2037j | 2.58e-499, 2.58e-499j | 
| 0.25188622569150550959 + 8.1259049171077754957e-2039j | 5.44e-503, 5.44e-503j | 
| -0.084775013041735301242 - 1.0072666397016282745e-2043j | 2.82e-508, 2.82e-508j | 
| -0.33306496018034047177 + 1.0178775688146317665e-2036j | 1.83e-500, 1.83e-500j | 
| -0.21055260102903231553 + 2.0636234926369267431e-2040j | 2.6e-504, 2.6e-504j | 
| 0.12689236510498180303 - 1.4862746371425818931e-2042j | 6.12e-507, 6.12e-507j | 
| 0.33306496018034047177 - 1.5226242783404048039e-2036j | 1.71e-500, 1.71e-500j | 
| 0.0037762088409933203275 - 5.2862582722852941645e-2047j | 4.39e-511, 4.39e-511j | 
| -0.25188622569150550959 - 4.9494438017148649025e-2039j | 5.47e-503, 5.47e-503j | 
| -0.29275301062654972345 + 5.3152423678491313291e-2038j | 9.65e-502, 9.65e-502j | 
| 7.5832567018799857494e-2082 + 5.167019214524905226e-2082j | 7.07e-2080, 7.07e-2080j | 
| 0.29275301062654972345 + 4.3860432217256400288e-2038j | 9.57e-502, 9.57e-502j | 
| 0.16885305857357954056 + 1.5566445763881048561e-2041j | 1.28e-505, 1.28e-505j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.00059577862883845374987 + 6.0983337998079270445e-1759j | 2.09e-143, 2.25e-376j | 
| 0.010756590956444491917 + 6.8959859852915500546e-1762j | 9.62e-144, 1.03e-376j | 
| 0.015817210986372928137 - 4.1469196337429311348e-1762j | 7.44e-144, 8e-377j | 
| 0.00059577862883845374987 + 3.0247323359138364576e-1762j | 2.22e-144, 2.39e-377j | 
| 0.014169961837318022996 + 2.2724737823488464353e-1760j | 8.1e-145, 8.71e-378j | 
| 0.015817210986372928137 - 1.8757153773187898679e-1760j | 5.21e-145, 5.61e-378j | 
| 0.017447910738201467284 + 1.5903526596656447374e-1760j | 1.95e-145, 2.1e-378j | 
| 0.017447910738201467284 + 5.2755864095031316697e-1762j | 1.65e-146, 1.77e-379j | 
| 0.012489272383547695662 - 2.8600952586618861763e-1760j | 6.68e-146, 7.18e-379j | 
| 0.0052782076645404567212 - 1.0713543809775063459e-1761j | 9.17e-148, 9.86e-381j | 
| 0.019068790588430750655 - 1.3761476541838217711e-1760j | 3.19e-146, 3.43e-379j | 
| 0.0052782076645404567212 - 1.5237637928690620424e-1759j | 2.23e-147, 2.39e-380j | 
| 0.014169961837318022996 + 2.2619359403652434509e-1762j | 2.12e-148, 2.28e-381j | 
| 0.02225363399288419867 - 7.5372845715422959972e-1762j | 2.59e-150, 2.79e-383j | 
| 0.0034884414422285052115 + 3.1621417799540814254e-1759j | 2.52e-147, 2.71e-380j | 
| 0.023787888533297678234 + 9.9053852567790394865e-1761j | 1.3e-149, 1.4e-382j | 
| 0.02225363399288419867 - 1.0860662651537618108e-1760j | 4.81e-149, 5.17e-382j | 
| 0.0018643303349882083045 - 7.6044951551596875121e-1762j | 1.21e-149, 1.3e-382j | 
| 0.026679543490899008336 + 9.9904241099656172885e-1762j | 7.87e-153, 8.46e-386j | 
| 0.012489272383547695662 + 2.7797537126237539362e-1762j | 9.72e-150, 1.05e-382j | 
| 0.010756590956444491917 + 3.7999432818155457225e-1760j | 9.33e-149, 1e-381j | 
| 0.028036987079838109886 - 8.320552273523465665e-1761j | 5.18e-153, 5.57e-386j | 
| 0.0018643303349882083045 - 8.268784396746733386e-1759j | 2.36e-148, 2.54e-381j | 
| 0.023787888533297678234 + 8.2628445531107325612e-1762j | 1.78e-153, 1.91e-386j | 
| 0.025264697172602544564 - 9.0683233031816094253e-1762j | 6.51e-154, 7e-387j | 
| 0.020675101355583384733 + 1.2120242616215953658e-1760j | 2.07e-150, 2.23e-383j | 
| 0.029345911297597195412 + 8.0821856895271729805e-1761j | 1.72e-154, 1.85e-387j | 
| 0.0089643771344325544969 - 5.4362192373652694009e-1760j | 2.49e-149, 2.68e-382j | 
| 0.0071256728248354104291 + 1.2093397619606575178e-1761j | 1.29e-152, 1.39e-385j | 
| 0.033018438939476624374 - 1.7485122733425771537e-1761j | 1.11e-158, 1.2e-391j | 
| 0.019068790588430750655 - 6.1191353193850758049e-1762j | 9.45e-154, 1.02e-386j | 
| 0.026679543490899008336 + 8.6810566825379166744e-1761j | 8.08e-155, 8.69e-388j | 
| 0.030613187924530234661 - 7.9463717187483785974e-1761j | 4.9e-157, 5.27e-390j | 
| 0.0034884414422285052115 + 9.7269134976964886386e-1762j | 3.36e-152, 3.61e-385j | 
| 0.030613187924530234661 - 1.3739801618745864502e-1761j | 2.88e-158, 3.09e-391j | 
| 0.028036987079838109886 - 1.1057450760624531954e-1761j | 3.81e-157, 4.1e-390j | 
| 0.0071256728248354104291 + 8.5644247037749608081e-1760j | 4.01e-152, 4.31e-385j | 
| 0.034138365927625484136 + 8.1404113382536322435e-1761j | 1.23e-160, 1.33e-393j | 
| 0.025264697172602544564 - 9.1954221880057771734e-1761j | 1.91e-155, 2.06e-388j | 
| 0.029345911297597195412 + 1.2295833702762750544e-1761j | 6.78e-158, 7.29e-391j | 
| 0.03518707096620657044 - 2.3119363168340129242e-1761j | 4.07e-162, 4.38e-395j | 
| 0.0089643771344325544969 - 1.6723093297498294986e-1761j | 9.25e-155, 9.94e-388j | 
| 0.031839507748624676671 + 7.9062032088947476925e-1761j | 2.71e-159, 2.92e-392j | 
| 0.033018438939476624374 - 7.9662662738651766579e-1761j | 2.95e-160, 3.18e-393j | 
| 0.020675101355583384733 + 6.8434965940391965615e-1762j | 3.15e-156, 3.39e-389j | 
| 0.034138365927625484136 + 1.9988516839371535452e-1761j | 9.62e-162, 1.03e-394j | 
| 0.031839507748624676671 + 1.5442254592291149227e-1761j | 3.7e-160, 3.98e-393j | 
| 0.041534058548745681668 + 3.3180573742286033651e-1760j | 1.79e-168, 1.92e-401j | 
| 0.03705073808753202216 - 9.5860846369598484969e-1761j | 1.09e-165, 1.18e-398j | 
| 0.03518707096620657044 - 8.4494267993270255885e-1761j | 8.48e-164, 9.11e-397j | 
| 0.041847439271721812397 - 3.471322143265852996e-1760j | 3.29e-170, 3.54e-403j | 
| 0.037875134722857757431 + 3.898198027879471845e-1761j | 2.57e-168, 2.76e-401j | 
| 0.04205687707027648853 + 6.411643298732910638e-1760j | 2.09e-170, 2.25e-403j | 
| 0.036157429030320321806 + 8.919911868826785452e-1761j | 6.84e-166, 7.36e-399j | 
| 0.037875134722857757431 + 1.0496411954977225282e-1760j | 7.32e-168, 7.87e-401j | 
| 0.020185126623438251892 - 4.0727252284130546194e-1757j | 7.07e-172, 7.6e-405j | 
| 0.03705073808753202216 - 3.2245519541920455317e-1761j | 1.11e-168, 1.2e-401j | 
| 0.036157429030320321806 + 2.7102953950215532243e-1761j | 5.58e-168, 6e-401j | 
| 0.042002580859928921563 + 6.7211419259931704866e-1759j | 1.55e-172, 1.67e-405j | 
| 0.038640313785407878888 - 1.1727115555245801313e-1760j | 7.81e-171, 8.4e-404j | 
| 0.042157030134640915482 - 1.7834153226373927942e-1759j | 7.45e-173, 8.02e-406j | 
| 0.038640313785407878888 - 4.7971529383566551184e-1761j | 1.13e-171, 1.21e-404j | 
| 0.039352150776063699473 + 6.0281798180625542675e-1761j | 1.36e-172, 1.46e-405j | 
| 0.042002580859928921563 + 6.161625497177261947e-1759j | 8.4e-174, 9.03e-407j | 
| 0.039352150776063699473 + 1.3406194066283761419e-1760j | 1.19e-173, 1.28e-406j | 
| 0.041116196161189976316 - 2.445745348430628599e-1760j | 9.36e-175, 1.01e-407j | 
| 0.042157030134640915482 - 1.49997679661828886e-1759j | 2.47e-174, 2.66e-407j | 
| 0.040009403126751390546 - 7.7748694278156914871e-1761j | 5.84e-175, 6.27e-408j | 
| 0.041534058548745681668 + 2.1464087840981913039e-1760j | 2e-175, 2.16e-408j | 
| 0.04205687707027648853 + 8.3144573501329333116e-1760j | 6.03e-176, 6.49e-409j | 
| 0.040009403126751390546 - 1.575692962346434182e-1760j | 3.9e-176, 4.19e-409j | 
| 0.020185126623438251892 - 4.1041671246886950765e-1757j | 1.89e-174, 2.03e-407j | 
| 0.041116196161189976316 - 1.4471719544674662593e-1760j | 4.68e-177, 5.03e-410j | 
| 0.040602646075946892608 + 1.0371907330260971272e-1760j | 4.09e-177, 4.4e-410j | 
| 0.0030119915516666671195 + 8.0713268024360521429e-1757j | 2.8e-174, 3.01e-407j | 
| 0.040602646075946892608 + 1.9183447518787190419e-1760j | 1.21e-178, 1.31e-411j | 
| 0.041847439271721812397 - 4.9129544343538245317e-1760j | 3.64e-178, 3.89e-411j | 
All rules of Legendre type can be downloaded here packed into a single file.