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) | 
|---|---|
| -0.99375217062038950026 + 1.6268733787679091306e-1646j | 3.78e-478, 3.78e-478j | 
| -0.98318486356168595383 - 3.1451962389698427799e-1671j | 1.7e-478, 1.7e-478j | 
| -0.93374144331550561532 + 8.84497919718328234e-1697j | 8.26e-480, 8.26e-480j | 
| 0.96722683856630629432 - 2.8372898850327831305e-1705j | 6.71e-479, 6.71e-479j | 
| 0.93374144331550561532 - 2.5229145693355478128e-1710j | 7.9e-480, 7.9e-480j | 
| 0.92009933415040082879 + 9.0997390340526537912e-1712j | 3.24e-480, 3.24e-480j | 
| -0.99699450903751817407 + 3.2308555035466138079e-1711j | 4.15e-478, 4.15e-478j | 
| -0.92009933415040082879 + 5.7839536001304557104e-1729j | 3.61e-480, 3.61e-480j | 
| -0.94614721677851262707 - 2.1743129046003790409e-1729j | 1.87e-479, 1.87e-479j | 
| 0.97586317702800962567 + 8.3663022494335191321e-1740j | 1.06e-478, 1.06e-478j | 
| 0.87183115713276194754 + 1.0945536815513526163e-1743j | 1.62e-481, 1.62e-481j | 
| 0.98318486356168595383 - 4.4565199557737703988e-1739j | 1.77e-478, 1.77e-478j | 
| -0.95731297403773694858 + 1.1986216625043456542e-1745j | 3.39e-479, 3.39e-479j | 
| -0.87183115713276194754 + 9.8377412817388411317e-1756j | 1.47e-481, 1.47e-481j | 
| 0.99375217062038950026 - 1.502377058705868661e-1749j | 3.78e-478, 3.78e-478j | 
| 0.85336336458331728365 + 1.0093687115611648534e-1754j | 4.56e-482, 4.56e-482j | 
| 0.88912831533118433426 + 1.2512849264321414558e-1753j | 4.66e-481, 4.66e-481j | 
| 0.99984110595082128654 - 1.3460508313973123192e-1749j | 1.62e-478, 1.62e-478j | 
| -0.76843996347567790862 + 5.3736722998679643507e-1767j | 1.6e-484, 1.6e-484j | 
| -0.90522470434606184383 - 9.3620815806130549162e-1761j | 1.35e-480, 1.35e-480j | 
| 0.95731297403773694858 + 2.7715126996839931528e-1764j | 3.69e-479, 3.69e-479j | 
| 0.7445819129779974081 + 3.4070287854963235631e-1780j | 3.06e-485, 3.06e-485j | 
| -0.99984110595082128654 - 2.6770241840947861168e-1769j | 1.61e-478, 1.61e-478j | 
| -0.88912831533118433426 - 4.8769036912243404946e-1798j | 5.04e-481, 5.04e-481j | 
| -0.79127130831913763447 + 3.5454214155779654422e-1801j | 6.92e-484, 6.92e-484j | 
| -0.96722683856630629432 - 1.3040641255540755342e-1794j | 6.62e-479, 6.62e-479j | 
| 0.76843996347567790862 + 7.5931418284688486968e-1813j | 1.67e-484, 1.67e-484j | 
| 0.83375944419717048192 - 2.2494267279404300098e-1810j | 1.26e-482, 1.26e-482j | 
| 0.98915461735609335844 + 1.3434292868503503671e-1803j | 2.58e-478, 2.58e-478j | 
| -0.63949181144957367785 + 8.0074922557831155618e-1818j | 1.69e-488, 1.69e-488j | 
| 0.99699450903751817407 - 4.1473989388031696584e-1804j | 4.31e-478, 4.31e-478j | 
| 0.90522470434606184383 - 6.0020144711450986829e-1819j | 1.32e-480, 1.32e-480j | 
| 0.69389648899581847009 + 4.1854680156463953015e-1826j | 9.02e-487, 9.02e-487j | 
| -0.99896193068731718686 + 3.7130194609638258344e-1815j | 4.02e-478, 4.02e-478j | 
| -0.81305258084753191325 - 1.2754289158434579114e-1836j | 3.1e-483, 3.1e-483j | 
| -0.7445819129779974081 + 1.0723585058771748894e-1839j | 3.01e-485, 3.01e-485j | 
| 0.99896193068731718686 + 1.8982794249209568053e-1831j | 3.75e-478, 3.75e-478j | 
| 0.61099712378976603905 - 1.8597603421607016132e-1844j | 2.08e-489, 2.08e-489j | 
| 0.79127130831913763447 - 4.8320479356389554522e-1839j | 7.39e-484, 7.39e-484j | 
| -0.98915461735609335844 + 4.5270516233738984255e-1833j | 2.61e-478, 2.61e-478j | 
| -0.55161883588721980706 - 1.2881638682969804024e-1870j | 2.28e-491, 2.28e-491j | 
| -0.69389648899581847009 - 4.1270515023619986404e-1865j | 8.87e-487, 8.87e-487j | 
| 0.71972345257202475786 + 1.2368057980283022688e-1867j | 5.65e-486, 5.65e-486j | 
| 0.55161883588721980706 - 2.0514348734708462146e-1871j | 2.36e-491, 2.36e-491j | 
| -0.21738009387172883298 + 4.6575216985211151573e-1885j | 5.83e-503, 5.83e-503j | 
| -0.58169397387151027312 - 2.4698825326269827746e-1869j | 2.34e-490, 2.34e-490j | 
| -0.61099712378976603905 - 3.1662211677060255472e-1868j | 2.08e-489, 2.08e-489j | 
| -0.97586317702800962567 - 7.8384212784177824996e-1862j | 1.16e-478, 1.16e-478j | 
| 0.4892959088956686414 - 3.5344542502404819313e-1895j | 1.93e-493, 1.93e-493j | 
| 0.94614721677851262707 + 4.4180702626579501737e-1885j | 1.72e-479, 1.72e-479j | 
| -0.85336336458331728365 + 2.497469553284140996e-1887j | 4.7e-482, 4.7e-482j | 
| -0.4892959088956686414 + 1.1727387648677965779e-1900j | 1.85e-493, 1.85e-493j | 
| 5.4914631907927328697e-1949 + 1.6806918729533216717e-1948j | 1.54e-1946, 1.54e-1946j | 
| 0.66713880419741231931 + 4.9725897914380558419e-1897j | 1.25e-487, 1.25e-487j | 
| 0.52080713992583826064 + 1.2113782839555412985e-1900j | 2.42e-492, 2.42e-492j | 
| -0.71972345257202475786 - 4.1073041768530805764e-1894j | 5.53e-486, 5.53e-486j | 
| -0.52080713992583826064 - 2.0922877116742161307e-1899j | 2.25e-492, 2.25e-492j | 
| -0.83375944419717048192 - 2.2770507780312752755e-1896j | 1.26e-482, 1.26e-482j | 
| 0.81305258084753191325 - 6.2436845628551487583e-1903j | 3.2e-483, 3.2e-483j | 
| 0.390992485291680285 - 3.6312002777469075767e-1915j | 8.16e-497, 8.16e-497j | 
| 0.63949181144957367785 - 2.8942595259162988504e-1907j | 1.64e-488, 1.64e-488j | 
| -0.66713880419741231931 + 1.2308711440803856024e-1913j | 1.32e-487, 1.32e-487j | 
| -0.45712589592863912333 - 1.5265889022570361674e-1919j | 1.6e-494, 1.6e-494j | 
| 0.10933572935123227691 - 6.2231583969200557184e-1931j | 5.37e-507, 5.37e-507j | 
| 0.42434212020743878357 - 2.6242961844926937062e-1921j | 1.22e-495, 1.22e-495j | 
| 0.45712589592863912333 + 8.146710406034737074e-1917j | 1.67e-494, 1.67e-494j | 
| -0.14556185416089509094 - 3.0679332060084673877e-1930j | 1.34e-505, 1.34e-505j | 
| -0.390992485291680285 - 1.4636858889696098251e-1922j | 7.78e-497, 7.78e-497j | 
| -0.2880213168024010966 + 4.6587954934471899664e-1925j | 2.01e-500, 2.01e-500j | 
| 0.58169397387151027312 + 1.6342429047584637403e-1919j | 2.6e-490, 2.6e-490j | 
| 0.3571252536599210773 + 3.564113267547838424e-1927j | 5.36e-498, 5.36e-498j | 
| 0.14556185416089509094 + 1.7835819684285376487e-1936j | 1.15e-505, 1.15e-505j | 
| -0.42434212020743878357 - 1.1953099857885876937e-1924j | 1.19e-495, 1.19e-495j | 
| -0.3571252536599210773 - 1.4402599525680915297e-1927j | 5.15e-498, 5.15e-498j | 
| -0.036506278248779427515 - 2.3229309150089854082e-1938j | 1.27e-509, 1.27e-509j | 
| 0.32278686645374824515 + 9.5473082581631704278e-1929j | 3.12e-499, 3.12e-499j | 
| 0.18159384998658417049 - 6.8909333389331345995e-1934j | 2.73e-504, 2.73e-504j | 
| -0.072967247595790589088 + 2.4289786272800852424e-1937j | 2.79e-508, 2.79e-508j | 
| -0.32278686645374824515 - 1.898361121679547792e-1929j | 3.26e-499, 3.26e-499j | 
| -0.10933572935123227691 - 5.3968731803344943575e-1937j | 6.27e-507, 6.27e-507j | 
| 0.21738009387172883298 - 1.7723213282747984484e-1932j | 5.5e-503, 5.5e-503j | 
| 0.2880213168024010966 + 1.2900527792666417474e-1929j | 1.99e-500, 1.99e-500j | 
| 0.072967247595790589088 + 6.2858142926381560015e-1938j | 2.65e-508, 2.65e-508j | 
| -0.25287125980962215979 + 5.3935790922911108953e-1931j | 1.04e-501, 1.04e-501j | 
| -0.18159384998658417049 + 7.6718490549956150286e-1934j | 2.56e-504, 2.56e-504j | 
| 0.036506278248779427515 + 2.4034889578325603141e-1938j | 1.27e-509, 1.27e-509j | 
| 0.25287125980962215979 - 1.9087055896086042152e-1931j | 1.11e-501, 1.11e-501j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0039128723404168525414 - 3.0705196404839025897e-1647j | 1.74e-128, 5.8e-359j | 
| 0.0066511448747032880161 + 5.7146867077453580555e-1647j | 1.07e-128, 3.56e-359j | 
| 0.013024292791206665733 - 1.0118296367884019951e-1647j | 4.59e-129, 1.53e-359j | 
| 0.0092805702098014474428 + 3.0355219994976547533e-1649j | 7.87e-130, 2.62e-360j | 
| 0.013024292791206665733 - 3.1502377996634937623e-1649j | 4.35e-130, 1.45e-360j | 
| 0.01425940707607564386 + 3.1772750101324032357e-1649j | 3.46e-130, 1.15e-360j | 
| 0.0025845411546588937598 + 1.9231981092122654671e-1646j | 3.23e-130, 1.07e-360j | 
| 0.01425940707607564386 + 8.2560738332057115872e-1648j | 9.51e-131, 3.17e-361j | 
| 0.011786790200522704539 + 1.2687187889167089832e-1647j | 1.67e-130, 5.56e-361j | 
| 0.0079857197764905477413 - 3.0246038190810844209e-1649j | 3.63e-132, 1.21e-362j | 
| 0.017888062495293152666 - 3.2386918121703924877e-1649j | 4.99e-133, 1.66e-363j | 
| 0.0066511448747032880161 + 3.0546673030495241102e-1649j | 6.95e-133, 2.31e-363j | 
| 0.010542852270956712723 - 1.6443487540316529251e-1647j | 5.77e-132, 1.92e-362j | 
| 0.017888062495293152666 - 4.9557080241371744322e-1648j | 5.61e-134, 1.87e-364j | 
| 0.0039128723404168525414 + 3.2028850015831355458e-1649j | 4.11e-134, 1.37e-364j | 
| 0.019041667608371639017 + 3.2695462745462551452e-1649j | 1.91e-134, 6.35e-365j | 
| 0.016701144495218484254 + 3.2156092675908141991e-1649j | 1.04e-133, 3.47e-364j | 
| 0.0004403599164839186698 - 1.0289530116101978219e-1649j | 5.54e-135, 1.84e-365j | 
| 0.023348715071460850202 + 2.6927099361082039889e-1648j | 1.5e-137, 4.99e-368j | 
| 0.015488116014640135946 - 6.8579600381844120867e-1648j | 1.46e-134, 4.85e-365j | 
| 0.010542852270956712723 - 3.0710787726720623973e-1649j | 9.85e-134, 3.28e-364j | 
| 0.024363051031743469868 - 3.488477658468970585e-1649j | 1.53e-138, 5.1e-369j | 
| 0.0004403599164839186698 + 3.3689203358780360272e-1647j | 2.61e-135, 8.69e-366j | 
| 0.016701144495218484254 + 5.7870243107132722244e-1648j | 2.66e-135, 8.86e-366j | 
| 0.022310149737048753246 - 2.9949369429055108417e-1648j | 3.94e-138, 1.31e-368j | 
| 0.0092805702098014474428 + 2.2441170239838748826e-1647j | 9.84e-135, 3.27e-365j | 
| 0.023348715071460850202 + 3.4428732665762766414e-1649j | 2.45e-139, 8.14e-370j | 
| 0.020160583258905720043 - 3.3080464490770861607e-1649j | 7.21e-138, 2.4e-368j | 
| 0.0052846535944675279418 - 3.1275510330535250853e-1649j | 4.22e-136, 1.4e-366j | 
| 0.028077631258135944115 - 1.7089719958495582715e-1648j | 1.69e-144, 5.62e-375j | 
| 0.0025845411546588937598 - 3.1323217448840343615e-1649j | 1.24e-136, 4.13e-367j | 
| 0.015488116014640135946 - 3.1970785636964805944e-1649j | 1.89e-137, 6.3e-368j | 
| 0.026299032482554312534 - 3.5868471978329939433e-1649j | 2.04e-143, 6.79e-374j | 
| 0.0013799374327883251103 - 9.7350634893539721577e-1647j | 1.47e-138, 4.89e-369j | 
| 0.021248398530176360823 + 3.3512968486325818784e-1648j | 1.6e-142, 5.32e-373j | 
| 0.024363051031743469868 - 2.4337333319658590142e-1648j | 4.66e-144, 1.55e-374j | 
| 0.0013799374327883251103 + 2.5451390634792554799e-1649j | 2.72e-137, 9.05e-368j | 
| 0.028905199491307677675 + 3.7755096850016433865e-1649j | 3.14e-147, 1.04e-377j | 
| 0.022310149737048753246 - 3.3972517554651566381e-1649j | 1.05e-142, 3.49e-373j | 
| 0.0052846535944675279418 - 1.3489005600752144607e-1646j | 1.63e-139, 5.44e-370j | 
| 0.030449365430118803176 + 1.3715958094972282774e-1648j | 5.1e-149, 1.7e-379j | 
| 0.026299032482554312534 - 2.0187504311657424965e-1648j | 1.67e-146, 5.55e-377j | 
| 0.025348556837644927803 + 3.5356999392045836333e-1649j | 1.46e-144, 4.85e-375j | 
| 0.030449365430118803176 + 3.9241594840679759275e-1649j | 4.28e-149, 1.43e-379j | 
| 0.035646656922654052342 + 7.8054875332416026344e-1649j | 5.19e-153, 1.73e-383j | 
| 0.029695053051166887913 - 1.4713417107530495771e-1648j | 5.52e-149, 1.84e-379j | 
| 0.028905199491307677675 + 1.5829305330430322903e-1648j | 1.76e-148, 5.87e-379j | 
| 0.0079857197764905477413 - 3.3301516219200185099e-1647j | 1.45e-142, 4.81e-373j | 
| 0.031847785298200257618 + 4.0858656944530490776e-1649j | 8.24e-153, 2.74e-383j | 
| 0.011786790200522704539 + 3.1134243238091369723e-1649j | 3.42e-143, 1.14e-373j | 
| 0.019041667608371639017 + 4.3017886448774436521e-1648j | 1.32e-145, 4.4e-376j | 
| 0.031847785298200257618 + 1.2012013193377300811e-1648j | 2.07e-152, 6.9e-383j | 
| 0.036513759178065283819 + 6.1013973624706234352e-1649j | 5.97e-157, 1.99e-387j | 
| 0.027209372159188705592 + 3.64372367899032918e-1649j | 6.61e-150, 2.2e-380j | 
| 0.031167894438134238853 - 4.0030125552717115681e-1649j | 1.23e-152, 4.1e-383j | 
| 0.025348556837644927803 + 2.2108396885908462433e-1648j | 1.04e-148, 3.47e-379j | 
| 0.031167894438134238853 - 1.2819248627935876384e-1648j | 2.34e-152, 7.78e-383j | 
| 0.020160583258905720043 - 3.7786050923668777023e-1648j | 6.3e-147, 2.1e-377j | 
| 0.021248398530176360823 + 3.3516513904614312562e-1649j | 1.43e-148, 4.75e-379j | 
| 0.033616377545230787646 - 4.3739605326137751746e-1649j | 1.23e-157, 4.1e-388j | 
| 0.028077631258135944115 - 3.706862169455072233e-1649j | 4.69e-152, 1.56e-382j | 
| 0.027209372159188705592 + 1.8529026657554484655e-1648j | 5.26e-151, 1.75e-381j | 
| 0.03248471242149427539 - 1.1286291170486235587e-1648j | 1.08e-155, 3.58e-386j | 
| 0.036305826870955521501 - 5.4915440000232421471e-1649j | 7.5e-161, 2.5e-391j | 
| 0.033074808976199288943 + 4.2701365978648012531e-1649j | 2.07e-157, 6.9e-388j | 
| 0.03248471242149427539 - 4.1743827586491116767e-1649j | 1.1e-156, 3.66e-387j | 
| 0.036137756746928945507 + 7.1406613017261947144e-1649j | 9.25e-162, 3.08e-392j | 
| 0.033616377545230787646 - 1.0048479717757181643e-1648j | 1.29e-159, 4.29e-390j | 
| 0.034964899681647671168 + 8.5917639484815727327e-1649j | 4.13e-161, 1.37e-391j | 
| 0.029695053051166887913 - 3.8482966507867820101e-1649j | 2.17e-156, 7.22e-387j | 
| 0.034110334720829223614 + 4.4857487801179056235e-1649j | 8.37e-161, 2.79e-391j | 
| 0.036137756746928945507 + 5.3160407381133629164e-1649j | 2.06e-163, 6.85e-394j | 
| 0.033074808976199288943 + 1.0634614415561279707e-1648j | 7.34e-160, 2.44e-390j | 
| 0.034110334720829223614 + 9.5184425864143922818e-1649j | 2.77e-161, 9.21e-392j | 
| 0.036491279686043783822 - 6.3330891529084826828e-1649j | 1.7e-164, 5.66e-395j | 
| 0.034559128092761081075 - 4.6048060735288972381e-1649j | 2.22e-163, 7.37e-394j | 
| 0.035917591925700656831 - 5.1538683503694689044e-1649j | 8.9e-165, 2.96e-395j | 
| 0.036422811117010986908 + 6.5813488575127736921e-1649j | 4.9e-165, 1.63e-395j | 
| 0.034559128092761081075 - 9.0353508837339423593e-1649j | 8.37e-164, 2.79e-394j | 
| 0.036305826870955521501 - 6.8493251096672597287e-1649j | 3.86e-165, 1.28e-395j | 
| 0.035646656922654052342 + 5.003551423642219282e-1649j | 4.66e-166, 1.55e-396j | 
| 0.034964899681647671168 + 4.7305338787714263388e-1649j | 7.71e-166, 2.57e-396j | 
| 0.036422811117010986908 + 5.6809754258498156788e-1649j | 1.32e-166, 4.42e-397j | 
| 0.035328015375628233922 - 8.1827148786271310924e-1649j | 2.28e-166, 7.58e-397j | 
| 0.035917591925700656831 - 7.458617984251729843e-1649j | 1.26e-166, 4.19e-397j | 
| 0.036491279686043783822 - 5.8842745568347098995e-1649j | 4.39e-167, 1.48e-397j | 
| 0.035328015375628233922 - 4.8630701976224765211e-1649j | 3.92e-167, 1.27e-397j | 
All rules of Legendre type can be downloaded here packed into a single file.