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) | 
|---|---|
| 1.8140052216398370587 - 1.7344614115594381542e-5193j | 2.02e-2032, 2.02e-2032j | 
| 1.3941001065258449138 + 1.3941938974570807132e-5194j | 1.47e-2033, 1.47e-2033j | 
| 1 + 6.8974648449644590125e-5196j | 7.05e-2035, 7.05e-2035j | 
| 2.2432515555021113989 + 2.407423796058613386e-5192j | 1.82e-2031, 1.82e-2031j | 
| 0.38766885667794714321 + 2.8533312780998537611e-5199j | 9.32e-2038, 9.32e-2038j | 
| 0.056897625001077184683 + 1.1350701134881464638e-5201j | 6.36e-2041, 6.36e-2041j | 
| 0.66053416156490857934 + 4.8876024531261388103e-5197j | 2.63e-2036, 2.63e-2036j | 
| 0.18585323911106078637 + 1.9805474182605538577e-5200j | 2.75e-2039, 2.75e-2039j | 
| 0.001850203994642906245 - 3.1758794149344980579e-5262j | 4.93e-2043, 4.93e-2043j | 
| 236.16937730022646204 + 2.0290556549691602784e-5181j | 5.67e-2021, 5.67e-2021j | 
| 166.09067957380803546 + 1.0681761791152456058e-5170j | 7.96e-2014, 7.96e-2014j | 
| 194.46933095031594685 - 2.4557122982004400087e-5179j | 1.81e-2016, 1.81e-2016j | 
| 206.00290398383513311 + 5.6512455755011161693e-5184j | 1.32e-2017, 1.32e-2017j | 
| 158.00131258860077342 - 6.2101120195583667931e-5197j | 3.72e-2013, 3.72e-2013j | 
| 14.33445721760110642 + 1.3540863331908680588e-5242j | 1.27e-2020, 1.27e-2020j | 
| 136.46824469374680008 + 4.2463718878854261049e-5240j | 1.32e-2011, 1.32e-2011j | 
| 184.16416030846556132 + 2.4735228401880088918e-5303j | 1.95e-2015, 1.95e-2015j | 
| 143.2495870347057445 - 1.3167403895346165506e-5376j | 4.43e-2012, 4.43e-2012j | 
| 36.377808914171052958 - 2.588222086773541885e-5435j | 1.11e-2013, 1.11e-2013j | 
| 7.8232631436879996743 - 6.0137303459575414436e-5467j | 7.02e-2025, 7.02e-2025j | 
| 21.069730372358274495 + 2.4876099041790982575e-5502j | 1.07e-2017, 1.07e-2017j | 
| 74.963043212739449692 - 1.7435999952320898651e-5656j | 4.85e-2010, 4.85e-2010j | 
| 38.958136508120321049 + 2.036541659858530816e-5904j | 3.32e-2013, 3.32e-2013j | 
| 96.967848560353129068 + 5.1134063628718942334e-6039j | 5.53e-2010, 5.53e-2010j | 
| 87.65437493765376378 + 3.5663256251162355761e-6140j | 6.72e-2010, 6.72e-2010j | 
| 10.179617115692389247 + 6.7078299555427307822e-6188j | 4.23e-2023, 4.23e-2023j | 
| 27.059618020371698029 + 1.1423372237658375351e-6176j | 7.86e-2016, 7.86e-2016j | 
| 219.37624403432206522 - 3.6751017885983939069e-6184j | 4.28e-2019, 4.28e-2019j | 
| 83.261985963750947059 - 8.7895963443465468782e-6209j | 6.18e-2010, 6.18e-2010j | 
| 41.643361616795944221 - 1.2747337620233122545e-6230j | 9.14e-2013, 9.14e-2013j | 
| 19.254535434558206019 + 5.3458000067118019697e-6259j | 2.19e-2018, 2.19e-2018j | 
| 53.488710942947522084 - 7.0735246764757301729e-6261j | 2.78e-2011, 2.78e-2011j | 
| 71.041988288547072486 + 1.0666593897009341306e-6297j | 3.54e-2010, 3.54e-2010j | 
| 33.899959413704609015 + 1.779967104510313167e-6330j | 3.32e-2014, 3.32e-2014j | 
| 101.90939157961978886 + 1.4113433201955687589e-6353j | 4.44e-2010, 4.44e-2010j | 
| 12.865785577489110287 - 2.6089040149674328703e-6388j | 1.98e-2021, 1.98e-2021j | 
| 6.7674114701871861735 + 2.1024807944251421352e-6392j | 8.6e-2026, 8.6e-2026j | 
| 56.742100299518290821 - 1.313140378812026787e-6377j | 5.92e-2011, 5.92e-2011j | 
| 79.034088006084771677 - 2.16924947473552438e-6406j | 5.64e-2010, 5.64e-2010j | 
| 63.625654805014783875 + 4.8576237508867549952e-6443j | 1.61e-2010, 1.61e-2010j | 
| 3.369839231310923141 + 1.6083756580577874253e-6496j | 1.18e-2029, 1.18e-2029j | 
| 31.522343049200972463 + 1.2319204694671276637e-6476j | 9.98e-2015, 9.98e-2015j | 
| 130.02520617878835942 + 8.0540276651292364291e-6534j | 3.48e-2011, 3.48e-2011j | 
| 118.02806302440738213 - 1.5127338520193927449e-6607j | 1.36e-2010, 1.36e-2010j | 
| 4.9001371421013381584 - 9.5520050391962584629e-6671j | 9.27e-2028, 9.27e-2028j | 
| 24.970771272424497404 - 1.3080793031866474748e-6663j | 2.05e-2016, 2.05e-2016j | 
| 92.219795487378648316 - 4.7341187223256752527e-6742j | 6.35e-2010, 6.35e-2010j | 
| 123.887514730993629 - 1.5620652063111918213e-6843j | 6.98e-2011, 6.98e-2011j | 
| 50.35559159185245999 - 2.2501927311583224647e-6928j | 1.31e-2011, 1.31e-2011j | 
| 112.42420786546886736 + 5.2179132855402166278e-7012j | 2.26e-2010, 2.26e-2010j | 
| 150.41004714226090753 - 8.3459426153413420189e-7072j | 1.43e-2012, 1.43e-2012j | 
| 4.0908896242867985101 - 3.6679986365767539054e-7116j | 1.07e-2028, 1.07e-2028j | 
| 2.7488673519096523852 + 7.2083718473053367137e-7124j | 1.54e-2030, 1.54e-2030j | 
| 29.242875007960464542 + 1.9574534097475168215e-7103j | 2.89e-2015, 2.89e-2015j | 
| 174.76890323797878957 - 1.9997113376713891544e-7138j | 1.47e-2014, 1.47e-2014j | 
| 8.9605300353960174383 - 6.2006604869348166077e-7177j | 5.74e-2024, 5.74e-2024j | 
| 15.888090919872913685 - 6.1225011153467651407e-7170j | 7.39e-2020, 7.39e-2020j | 
| 107.05678518978004703 + 7.642037547302864038e-7169j | 3.29e-2010, 3.29e-2010j | 
| 11.481122867472712326 - 1.8375145706255106095e-7194j | 2.9e-2022, 2.9e-2022j | 
| 67.264729336046040823 + 1.9368750089940924712e-7180j | 2.6e-2010, 2.6e-2010j | 
| 47.339154392272342161 - 9.293922430027003142e-7185j | 5.76e-2012, 5.76e-2012j | 
| 60.119662854876954374 + 1.2413822598358577643e-7182j | 9.88e-2011, 9.88e-2011j | 
| 22.974660674483330326 - 8.6485386255800665315e-7192j | 4.37e-2017, 4.37e-2017j | 
| 44.436094413664006752 + 3.8044106560763263647e-7187j | 2.32e-2012, 2.32e-2012j | 
| 5.7928782121422054367 - 1.8065452872544675821e-7201j | 9.6e-2027, 9.6e-2027j | 
| 17.527735708445867153 + 4.9339176239176405512e-7194j | 4.11e-2019, 4.11e-2019j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.068595575748667911957 + 3.1581729078509914592e-5193j | 3.64e-264, 1.22e-1775j | 
| 0.1025639664664359771 - 1.7560183287092008336e-5193j | 4e-257, 1.34e-1768j | 
| 0.13606241359599903767 + 1.0323166893338817682e-5193j | 1.44e-252, 4.83e-1764j | 
| 0.048041750933256375536 - 8.1662797882635555666e-5194j | 1.76e-270, 5.92e-1782j | 
| 0.16136478104549110789 + 5.0649097278693391703e-5194j | 7.2e-253, 2.42e-1764j | 
| 0.087104416583349045669 + 2.6700428674025156211e-5194j | 3.32e-253, 1.11e-1764j | 
| 0.15873342680822829698 - 6.8930128456703130496e-5194j | 3.27e-254, 1.1e-1765j | 
| 0.13749273595881097049 - 3.7978962576278777298e-5194j | 1.99e-253, 6.67e-1765j | 
| 0.016909134649344754756 - 1.0499097878711013248e-5194j | 1.55e-253, 5.21e-1765j | 
| 5.3675609923486893368e-102 - 1.1688857167497437052e-5248j | 7.48e-403, 2.51e-1914j | 
| 6.1696522530602470177e-72 - 2.7831595824022469432e-5233j | 2.16e-393, 7.26e-1905j | 
| 3.7887609928775357715e-84 + 1.527776744475511034e-5239j | 7.33e-398, 2.46e-1909j | 
| 4.2108006503439839938e-89 - 4.4694337312673414636e-5242j | 1.48e-399, 4.96e-1911j | 
| 1.8815844105785005533e-68 + 1.7194232667420959322e-5231j | 6.98e-393, 2.34e-1904j | 
| 8.9925879343486765437e-07 + 2.4848828814749290528e-5198j | 4.09e-334, 1.37e-1845j | 
| 3.56895467777115554e-59 - 1.0393100421751139256e-5226j | 2.01e-390, 6.75e-1902j | 
| 1.0237978783344114373e-79 - 2.8405524412806051712e-5237j | 2.36e-397, 7.93e-1909j | 
| 4.2688497923609445708e-62 + 3.2255515663506288652e-5228j | 2.28e-391, 7.65e-1903j | 
| 4.0199041201804229499e-16 - 6.3747524481155947079e-5204j | 1.07e-361, 3.6e-1873j | 
| 0.00043894834816039281292 - 2.5450823474877873686e-5196j | 3.64e-325, 1.22e-1836j | 
| 1.3152423358967716522e-09 + 3.8920561030798121566e-5200j | 9.85e-349, 3.31e-1860j | 
| 1.110393619345908453e-32 - 6.8839606219655801131e-5213j | 2.27e-379, 7.63e-1891j | 
| 3.1698682264511485646e-17 + 1.5399661060019857026e-5204j | 7.41e-364, 2.49e-1875j | 
| 3.7368139561261848456e-42 + 7.1733001855430613116e-5218j | 1.68e-385, 5.65e-1897j | 
| 3.8301380509602594363e-38 + 9.0702869708569314671e-5216j | 2.45e-383, 8.22e-1895j | 
| 4.7805994947293566691e-05 - 4.1944483893610627124e-5197j | 8.88e-338, 2.98e-1849j | 
| 3.7819012752162765159e-12 - 1.1895932543357556886e-5201j | 1.65e-358, 5.55e-1870j | 
| 7.8010739434723909456e-95 + 5.2726994919810779962e-5245j | 3.13e-406, 1.05e-1917j | 
| 2.9794443437176107294e-36 - 8.9565336731856567163e-5215j | 2.32e-382, 7.79e-1894j | 
| 2.2492353029775557029e-18 - 3.5443578366419266858e-5205j | 2.23e-368, 7.47e-1880j | 
| 7.6917775409810396121e-09 - 1.1556986579115416899e-5199j | 1.34e-353, 4.49e-1865j | 
| 1.880601400243331641e-23 - 5.9273694901885936416e-5208j | 9.11e-375, 3.06e-1886j | 
| 5.3964903625001358247e-31 + 5.39838015383912476e-5212j | 3.01e-380, 1.01e-1891j | 
| 4.5980228908490054247e-15 + 2.5180972007579942312e-5203j | 1.42e-365, 4.78e-1877j | 
| 2.7793264114687234641e-44 - 5.5438953941108495805e-5219j | 9.85e-389, 3.31e-1900j | 
| 3.6875431626857601058e-06 - 6.5208240975769221208e-5198j | 8.32e-351, 2.79e-1862j | 
| 0.0011681724741815525606 + 6.2509225849051922056e-5196j | 9.02e-342, 3.03e-1853j | 
| 7.545289932894141798e-25 + 1.0435478101159507945e-5208j | 1.27e-376, 4.27e-1888j | 
| 1.966972901999535316e-34 + 8.1591331891865831021e-5214j | 1.85e-382, 6.23e-1894j | 
| 8.329268885717104985e-28 + 2.6994751434525907847e-5210j | 3.8e-379, 1.28e-1890j | 
| 0.023177942049048690618 + 3.5561350075193698099e-5194j | 8.79e-338, 2.95e-1849j | 
| 4.7538122627985063837e-14 - 9.5060286001065328078e-5203j | 3.71e-367, 1.24e-1878j | 
| 2.1335574881643907874e-56 + 2.8303144254492051123e-5225j | 4.28e-396, 1.44e-1907j | 
| 3.1555965730836031667e-51 + 1.3497684861669398757e-5222j | 2.03e-394, 6.8e-1906j | 
| 0.0063394364498602120455 + 4.0292310330869959216e-5195j | 1.5e-348, 5.03e-1860j | 
| 2.9203316677307237333e-11 + 3.9551897830671123361e-5201j | 2.22e-367, 7.44e-1879j | 
| 4.1435734579298390103e-40 - 8.437021849816347016e-5217j | 7.69e-388, 2.58e-1899j | 
| 9.4207685267870739815e-54 - 6.6227500086968062688e-5224j | 1.16e-395, 3.9e-1907j | 
| 4.1550594894776548487e-22 + 3.1790395235064102258e-5207j | 1.77e-379, 5.95e-1891j | 
| 8.1993799170527453603e-49 - 2.4234640812228114646e-5221j | 1.13e-393, 3.79e-1905j | 
| 3.507411229045892131e-65 - 8.2899313352300612762e-5230j | 1.03e-401, 3.45e-1913j | 
| 0.01281658704677943036 - 1.1190458332560327357e-5194j | 3.8e-357, 1.28e-1868j | 
| 0.036125669699491396519 - 1.4901171537454090083e-5193j | 4.94e-354, 1.66e-1865j | 
| 4.4513353698709531423e-13 + 3.4347296067170982306e-5202j | 3.38e-374, 1.13e-1885j | 
| 1.1313939169536929392e-75 + 3.360602910081837302e-5235j | 6.4e-407, 2.15e-1918j | 
| 0.00015124117885925447081 + 1.0374743225703562802e-5196j | 1.64e-365, 5.51e-1877j | 
| 2.0093097009503170496e-07 - 9.2145555952995615861e-5199j | 2.01e-370, 6.74e-1882j | 
| 1.6841909765019440397e-46 + 3.8704190232671523225e-5220j | 6.02e-393, 2.02e-1904j | 
| 1.3863468528299975532e-05 + 1.6705217646986793407e-5197j | 1.77e-368, 5.95e-1880j | 
| 2.2717166557627306784e-29 - 3.9474641969736644053e-5211j | 1.68e-385, 5.63e-1897j | 
| 8.1666455164666440064e-21 - 1.6131803065544730866e-5206j | 7.12e-382, 2.39e-1893j | 
| 2.6733229908827598395e-26 - 1.7310824344741952497e-5209j | 1.57e-384, 5.27e-1896j | 
| 2.0527049111395269539e-10 - 1.2643399955526224788e-5200j | 2.95e-376, 9.89e-1888j | 
| 1.4325147490540167817e-19 + 7.7596031490456623688e-5206j | 2.53e-381, 8.48e-1893j | 
| 0.0028472934171754278473 - 1.5584535696326081651e-5195j | 1.83e-371, 6.12e-1883j | 
| 4.1104685063785201501e-08 + 3.3162815893408963254e-5199j | 5.95e-375, 2e-1886j | 
All rules of Laguerre type can be downloaded here packed into a single file.