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) | 
|---|---|
| -0.99988876134358866069 + 6.8256150719872795676e-1696j | 2e-477, 2e-477j | 
| -0.97052802277417746491 - 9.1642953639037588585e-1709j | 2.13e-478, 2.13e-478j | 
| -0.92491477735576524157 - 3.3352937444792666574e-1715j | 7.73e-480, 7.73e-480j | 
| 0.99933888183715517208 - 3.2168830209037769997e-1709j | 3.71e-477, 3.71e-477j | 
| 0.93825582835274084978 + 6.1080139894663449421e-1737j | 1.95e-479, 1.95e-479j | 
| 0.95031557461792315437 - 6.6364356299598581283e-1736j | 5.25e-479, 5.25e-479j | 
| -0.99933888183715517208 + 2.8144935585169833066e-1732j | 3.79e-477, 3.79e-477j | 
| -0.93825582835274084978 + 1.0726379105806861519e-1738j | 2.09e-479, 2.09e-479j | 
| -0.95031557461792315437 - 8.7419053317448966911e-1738j | 4.89e-479, 4.89e-479j | 
| 0.96107771692069450679 - 2.1120349516838279372e-1735j | 1.04e-478, 1.04e-478j | 
| 0.85912690287453322245 + 3.431077478238728521e-1747j | 8.49e-482, 8.49e-482j | 
| 0.98544547375341350032 - 1.5486005428404067901e-1742j | 7.59e-478, 7.59e-478j | 
| -0.91031061962910991036 + 3.6833033871976605461e-1783j | 2.98e-480, 2.98e-480j | 
| -0.87739425538707176377 - 8.4103442714380479382e-1786j | 3.02e-481, 3.02e-481j | 
| 0.99988876134358866069 - 3.7636212900522221927e-1778j | 2e-477, 2e-477j | 
| 0.87739425538707176377 + 1.6805820245711818582e-1812j | 3.02e-481, 3.02e-481j | 
| 0.92491477735576524157 + 1.9125031668556314935e-1808j | 8.04e-480, 8.04e-480j | 
| -0.99779971295100584467 - 4.3354166761353378152e-1812j | 3.05e-477, 3.05e-477j | 
| -0.77459666924148337704 + 2.1859750378875638593e-1825j | 2.6e-484, 2.6e-484j | 
| -0.97865413764512959743 + 5.739397900848163152e-1816j | 4.22e-478, 4.22e-478j | 
| 0.91031061962910991036 + 5.4744393049404993798e-1816j | 2.84e-480, 2.84e-480j | 
| 0.797392160283688017 - 8.8140194051536658659e-1824j | 1.31e-483, 1.31e-483j | 
| 0.99500543531732884972 + 1.4968342213951372476e-1815j | 2e-477, 2e-477j | 
| -0.85912690287453322245 + 1.3138801660769327537e-1856j | 8.65e-482, 8.65e-482j | 
| -0.83968614637524280884 - 1.1726748766296785926e-1856j | 2.23e-482, 2.23e-482j | 
| 0.99779971295100584467 + 1.1839082264094858836e-1848j | 3.16e-477, 3.16e-477j | 
| 0.72586431796511602165 + 2.1681128569462020553e-1877j | 8.35e-486, 8.35e-486j | 
| 0.89446325430860287476 - 1.451932019514502021e-1871j | 9.67e-481, 9.67e-481j | 
| -0.96107771692069450679 - 5.2195116639750519576e-1870j | 1.05e-478, 1.05e-478j | 
| -0.64542174799487529885 + 1.1590443490072876571e-1880j | 2.37e-488, 2.37e-488j | 
| 0.97865413764512959743 - 1.9600405219496750999e-1867j | 3.98e-478, 3.98e-478j | 
| 0.83968614637524280884 - 1.9586629063452052683e-1891j | 2.42e-482, 2.42e-482j | 
| 0.69999401161208205264 - 2.3955460535237570647e-1895j | 1.23e-486, 1.23e-486j | 
| -0.98544547375341350032 + 3.196677005349106074e-1884j | 7.33e-478, 7.33e-478j | 
| -0.75074319529946827624 + 1.0610618984346739277e-1893j | 4.85e-485, 4.85e-485j | 
| -0.797392160283688017 + 2.6637910129326297411e-1892j | 1.3e-483, 1.3e-483j | 
| -0.99089501825791414073 - 4.0465575261409299279e-1885j | 1.33e-477, 1.33e-477j | 
| 0.61679433055058544069 - 1.7102107861077100095e-1899j | 2.82e-489, 2.82e-489j | 
| 0.81909853184898019962 + 1.096264520816469707e-1891j | 5.48e-483, 5.48e-483j | 
| -0.81909853184898019962 + 6.0827566734773979218e-1893j | 5.6e-483, 5.6e-483j | 
| -0.58732445339233239614 - 1.2143207788629498608e-1901j | 3.26e-490, 3.26e-490j | 
| -0.52601941863378848131 + 2.340664840659477679e-1903j | 2.68e-492, 2.68e-492j | 
| 0.77459666924148337704 + 2.8305938750698177085e-1893j | 2.6e-484, 2.6e-484j | 
| 0.64542174799487529885 - 1.2958999019599585249e-1897j | 2.58e-488, 2.58e-488j | 
| -0.14718617801380025857 - 1.5366131297220021287e-1916j | 1.29e-505, 1.29e-505j | 
| -0.61679433055058544069 - 2.7108014542890495305e-1900j | 2.74e-489, 2.74e-489j | 
| -0.72586431796511602165 + 4.7189181385699005963e-1896j | 8.1e-486, 8.1e-486j | 
| 0.99089501825791414073 + 5.1377267727057511547e-1888j | 1.22e-477, 1.22e-477j | 
| 0.49426799723683859419 - 6.4753498925549059911e-1932j | 2.49e-493, 2.49e-493j | 
| 0.75074319529946827624 - 4.4707596651398019038e-1923j | 4.81e-485, 4.81e-485j | 
| -0.69999401161208205264 + 2.4436766399850238604e-1923j | 1.24e-486, 1.24e-486j | 
| -0.49426799723683859419 + 4.5846447019475814704e-1931j | 2.35e-493, 2.35e-493j | 
| -0.99500543531732884972 + 1.4530174986692247826e-1918j | 2.06e-477, 2.06e-477j | 
| 0.5570523665246407664 - 5.5031143424799497014e-1934j | 3.07e-491, 3.07e-491j | 
| 0.58732445339233239614 - 2.009943695170194027e-1932j | 3.13e-490, 3.13e-490j | 
| 0.97052802277417746491 + 4.0226022123116888338e-1931j | 2.18e-478, 2.18e-478j | 
| -0.46184146907720902976 - 9.5643761943764509741e-1953j | 1.87e-494, 1.87e-494j | 
| -0.67316760748285544209 - 4.4176927295306391982e-1945j | 1.75e-487, 1.75e-487j | 
| 0.67316760748285544209 + 2.2358571219523623957e-1946j | 1.75e-487, 1.75e-487j | 
| 0.42878412349565830447 + 1.0273375303107436051e-1954j | 1.39e-495, 1.39e-495j | 
| 0.18360541550797299565 + 6.8617192317209440289e-1963j | 3.14e-504, 3.14e-504j | 
| -0.5570523665246407664 - 1.1261292886369343854e-1949j | 2.89e-491, 2.89e-491j | 
| -0.42878412349565830447 + 7.2974170828225959452e-1954j | 1.35e-495, 1.35e-495j | 
| -0.89446325430860287476 + 5.1957376399448729545e-1962j | 1.01e-480, 1.01e-480j | 
| 0.46184146907720902976 + 2.0475972644964313432e-1977j | 1.98e-494, 1.98e-494j | 
| 0.52601941863378848131 + 8.2781784551115343549e-1976j | 2.74e-492, 2.74e-492j | 
| 5.3973427339538837231e-2042 + 2.5801734703753828133e-2042j | 5.2e-2040, 5.2e-2040j | 
| -0.39514111339613461763 + 6.8156382202829366341e-1979j | 1.01e-496, 1.01e-496j | 
| -0.29116123856529143669 + 2.7535921128552382286e-1984j | 2.06e-500, 2.06e-500j | 
| 0.21977387039115541258 + 9.9897998561103597715e-1986j | 6.09e-503, 6.09e-503j | 
| 0.39514111339613461763 - 1.121458317263523719e-1979j | 9.86e-497, 9.86e-497j | 
| 0.14718617801380025857 + 3.9323425281872001823e-1988j | 1.34e-505, 1.34e-505j | 
| -0.25564214169224484281 + 2.5606039009754450567e-1984j | 1.17e-501, 1.17e-501j | 
| -0.36095839141911379512 - 2.8492869941033478193e-1980j | 6.1e-498, 6.1e-498j | 
| -0.036922520355545183064 + 5.9475268103591827433e-1992j | 1.32e-509, 1.32e-509j | 
| 0.36095839141911379512 + 1.5310066571024497884e-1980j | 6.12e-498, 6.12e-498j | 
| 0.25564214169224484281 - 1.8578366493539901507e-1984j | 1.2e-501, 1.2e-501j | 
| -0.073794608601719502957 - 5.6143748496848357479e-1991j | 2.76e-508, 2.76e-508j | 
| -0.32628264583620278827 + 1.2056582447981597037e-1981j | 3.63e-499, 3.63e-499j | 
| -0.11056590262412224025 + 4.8395601642802047382e-1990j | 6.1e-507, 6.1e-507j | 
| 0.036922520355545183064 - 5.7085065860687167597e-1992j | 1.07e-509, 1.07e-509j | 
| 0.32628264583620278827 + 2.7164383850056351637e-1982j | 3.71e-499, 3.71e-499j | 
| 0.11056590262412224025 - 7.2804734254550718737e-1990j | 5.65e-507, 5.65e-507j | 
| -0.18360541550797299565 + 6.3285388289898683413e-1987j | 3.06e-504, 3.06e-504j | 
| -0.21977387039115541258 - 1.5057346014481218566e-1985j | 6.57e-503, 6.57e-503j | 
| 0.073794608601719502957 + 2.6528484134347516376e-1991j | 2.81e-508, 2.81e-508j | 
| 0.29116123856529143669 + 4.2698340680294948165e-1983j | 1.99e-500, 1.99e-500j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.00027163132040367754158 + 5.5074737353546520474e-1696j | 1.62e-135, 2.02e-363j | 
| 0.0087901324843338179587 - 4.118013811558810206e-1698j | 5.45e-136, 6.79e-364j | 
| 0.013975782819376060054 - 1.0405084682743289917e-1698j | 2.03e-136, 2.53e-364j | 
| 0.0009583465259321214943 - 1.8416617382779072636e-1699j | 9.75e-137, 1.21e-364j | 
| 0.012703282357584955802 + 4.4123633339302152578e-1700j | 4.99e-137, 6.22e-365j | 
| 0.011413489621696297354 - 4.856788196471393489e-1700j | 3.49e-137, 4.35e-365j | 
| 0.0009583465259321214943 - 6.6958324745133029517e-1696j | 4.92e-136, 6.13e-364j | 
| 0.012703282357584955802 + 1.3875371020838587761e-1698j | 1.03e-136, 1.28e-364j | 
| 0.011413489621696297354 - 1.9106557446353635843e-1698j | 6.77e-137, 8.43e-365j | 
| 0.01010842670578872552 + 5.4162120864800312082e-1700j | 1.24e-137, 1.54e-365j | 
| 0.018858347971148227756 - 3.1342019593835704219e-1700j | 3.34e-139, 4.16e-367j | 
| 0.0061210945353003479013 - 8.3866112837697982015e-1700j | 1.01e-138, 1.26e-366j | 
| 0.015229216127214864656 + 8.0136490577897508201e-1699j | 5.83e-138, 7.27e-366j | 
| 0.017672197342870485295 + 5.0691050510773747029e-1699j | 2.52e-139, 3.14e-367j | 
| 0.00027163132040367754158 + 9.2712855010836408592e-1700j | 3.02e-138, 3.76e-366j | 
| 0.017672197342870485295 + 3.3076393561198434018e-1700j | 8.87e-140, 1.11e-367j | 
| 0.013975782819376060054 - 4.0529365034217148865e-1700j | 6.38e-139, 7.94e-367j | 
| 0.0021514277963663663595 + 1.5595653637521382499e-1696j | 8.81e-139, 1.1e-366j | 
| 0.023329794054048979416 - 2.0974946769340638322e-1699j | 5.78e-143, 7.2e-371j | 
| 0.0074603092711380646678 + 6.6044780739340692062e-1698j | 1.8e-139, 2.24e-367j | 
| 0.015229216127214864656 + 3.7579731105331412176e-1700j | 8.35e-140, 1.04e-367j | 
| 0.022255997573641829458 + 2.7543868878661349619e-1700j | 4.77e-143, 5.94e-371j | 
| 0.0034462136115757381563 - 1.2802558927926654826e-1699j | 5.85e-140, 7.29e-368j | 
| 0.018858347971148227756 - 4.1392821895812846755e-1699j | 2.31e-142, 2.88e-370j | 
| 0.0200187400672483247 + 3.429850797886128672e-1699j | 4.82e-143, 6e-371j | 
| 0.0021514277963663663595 + 1.6308886785234662219e-1699j | 1.23e-139, 1.53e-367j | 
| 0.025380368591159015903 - 2.5194464105179432521e-1700j | 1.59e-146, 1.98e-374j | 
| 0.016461919739327930432 - 3.5130108100256966662e-1700j | 5.54e-142, 6.91e-370j | 
| 0.01010842670578872552 + 2.7365948273106315085e-1698j | 3.36e-142, 4.18e-370j | 
| 0.02819305644286810178 + 1.1053570685731589359e-1699j | 2.81e-149, 3.51e-377j | 
| 0.0074603092711380646678 + 7.0882267298152906283e-1700j | 2.4e-141, 3e-369j | 
| 0.0200187400672483247 + 2.9869458670357150206e-1700j | 4.83e-144, 6.02e-372j | 
| 0.026354354818097008742 + 2.4642127438297111024e-1700j | 6.15e-148, 7.66e-376j | 
| 0.0061210945353003479013 - 1.1528003160045280783e-1697j | 1.1e-143, 1.37e-371j | 
| 0.024371723111711210516 + 1.8165485144785534965e-1699j | 7.26e-149, 9.04e-377j | 
| 0.022255997573641829458 + 2.4446864680392527776e-1699j | 8.8e-148, 1.1e-375j | 
| 0.0047782497874285984756 + 2.259777550304646188e-1697j | 4.5e-144, 5.61e-372j | 
| 0.02905526128699017471 - 2.3522351785000747727e-1700j | 5.21e-153, 6.49e-381j | 
| 0.021151805321517314918 - 2.8614748073607155584e-1700j | 1.58e-147, 1.97e-375j | 
| 0.021151805321517314918 - 2.87901969533454723e-1699j | 1.71e-147, 2.12e-375j | 
| 0.029877783818751233406 + 8.9657470543982551834e-1700j | 4.65e-154, 5.79e-382j | 
| 0.031399332747848111607 + 7.4302911746171085902e-1700j | 1.65e-155, 2.06e-383j | 
| 0.023329794054048979416 - 2.6630196889414450475e-1700j | 3.03e-150, 3.77e-378j | 
| 0.02819305644286810178 + 2.3813901178946481655e-1700j | 2.18e-153, 2.72e-381j | 
| 0.036528072446633151231 - 3.5526866980483748491e-1700j | 2.56e-159, 3.19e-387j | 
| 0.02905526128699017471 - 9.9265834623876866946e-1700j | 1.13e-153, 1.41e-381j | 
| 0.025380368591159015903 - 1.5866987439162853635e-1699j | 4.55e-152, 5.67e-380j | 
| 0.0047782497874285984756 + 1.0208973433608740976e-1699j | 4.29e-148, 5.34e-376j | 
| 0.032096281331450609599 - 2.3056806168893813303e-1700j | 1.62e-158, 2.02e-386j | 
| 0.024371723111711210516 + 2.5852664585971091444e-1700j | 4.94e-152, 6.15e-380j | 
| 0.026354354818097008742 + 1.3967809692862859256e-1699j | 2.96e-153, 3.69e-381j | 
| 0.032096281331450609599 - 6.813502374533666748e-1700j | 1.26e-157, 1.57e-385j | 
| 0.0034462136115757381563 - 5.2299908650721894644e-1697j | 1.73e-148, 2.16e-376j | 
| 0.030659497445912583545 - 2.3156535011022669577e-1700j | 9.95e-158, 1.24e-385j | 
| 0.029877783818751233406 + 2.3304665021811334121e-1700j | 7.77e-157, 9.69e-385j | 
| 0.0087901324843338179587 - 6.1361600206444823143e-1700j | 3.08e-150, 3.84e-378j | 
| 0.032749392454875851171 + 6.2760107319341345928e-1700j | 7.11e-160, 8.86e-388j | 
| 0.027292345389274912951 - 1.2384443622541176035e-1699j | 3.36e-155, 4.19e-383j | 
| 0.027292345389274912951 - 2.4184837915020316111e-1700j | 1.73e-155, 2.16e-383j | 
| 0.033357772144022826989 - 2.3207478747319864268e-1700j | 3.12e-162, 3.89e-390j | 
| 0.03630211059311798267 + 2.575545477897399921e-1700j | 6.6e-166, 8.22e-394j | 
| 0.030659497445912583545 - 8.1414631135600939223e-1700j | 3.88e-158, 4.83e-386j | 
| 0.033357772144022826989 - 5.8055728170466506179e-1700j | 1.41e-161, 1.76e-389j | 
| 0.016461919739327930432 - 6.3123994336570982956e-1699j | 2.95e-154, 3.67e-382j | 
| 0.032749392454875851171 + 2.3101325472199475705e-1700j | 7.8e-162, 9.72e-390j | 
| 0.031399332747848111607 + 2.3074698997343941142e-1700j | 2.48e-160, 3.09e-388j | 
| 0.0369309280688936748 - 2.9968409811941711509e-1700j | 1.23e-167, 1.53e-395j | 
| 0.033920588205293049642 + 5.3921815150490146265e-1700j | 1.36e-163, 1.7e-391j | 
| 0.035328294952639725635 - 4.418773343552040478e-1700j | 4.09e-166, 5.1e-394j | 
| 0.036026564578775565295 - 2.5181824951661774181e-1700j | 1.7e-167, 2.12e-395j | 
| 0.033920588205293049642 + 2.3375191797515297966e-1700j | 2.15e-165, 2.67e-393j | 
| 0.036528072446633151231 - 2.6409653120693198855e-1700j | 4.45e-168, 5.54e-396j | 
| 0.03570181179996045511 + 4.1641038448054188987e-1700j | 1.22e-167, 1.52e-395j | 
| 0.034437073350424121464 - 5.027603655522252256e-1700j | 5.56e-166, 6.93e-394j | 
| 0.036905706115932714683 + 3.113863165960823071e-1700j | 1.86e-169, 2.32e-397j | 
| 0.034437073350424121464 - 2.3605065836630450747e-1700j | 8.92e-168, 1.11e-395j | 
| 0.03570181179996045511 + 2.4683742971832758812e-1700j | 8.3e-169, 1.03e-396j | 
| 0.036830075569497238946 - 3.2444555675519095795e-1700j | 5.27e-170, 6.56e-398j | 
| 0.034906523111703232295 + 4.7050248133734167394e-1700j | 2.09e-168, 2.61e-396j | 
| 0.036704140624671556791 + 3.3901387634034986082e-1700j | 3.74e-170, 4.66e-398j | 
| 0.036905706115932714683 + 2.8920837965442479514e-1700j | 4.31e-171, 5.37e-399j | 
| 0.034906523111703232295 + 2.3898369929731005521e-1700j | 1.02e-170, 1.27e-398j | 
| 0.036704140624671556791 + 2.7150391586027765505e-1700j | 1.92e-171, 2.39e-399j | 
| 0.03630211059311798267 + 3.7341728100406694764e-1700j | 1.52e-171, 1.89e-399j | 
| 0.036026564578775565295 - 3.9370266160328290265e-1700j | 1.66e-171, 2.06e-399j | 
| 0.036830075569497238946 - 2.7984705864388232643e-1700j | 4.62e-172, 5.79e-400j | 
| 0.035328294952639725635 - 2.4257048803026150158e-1700j | 4.23e-172, 5.13e-400j | 
All rules of Legendre type can be downloaded here packed into a single file.