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.
    
Warning: This rule has negative weights!
| Node (ball center) | Error (ball radius) | 
|---|---|
| 11.222360654498656083 - 7.3640180125144887069e-5286j | 1.44e-2020, 1.44e-2020j | 
| 10.034002312376933965 + 6.4829958445459816514e-5286j | 2.31e-2021, 2.31e-2021j | 
| 6.0408291028972552765 + 1.9616199817158321294e-5289j | 1.08e-2024, 1.08e-2024j | 
| 1.0406748406401594478 + 2.7267766366791971598e-5298j | 9.9e-2034, 9.9e-2034j | 
| 13.826676500019434022 - 1.1825958334277674905e-5283j | 5.32e-2019, 5.32e-2019j | 
| 8.9213535273612976327 + 1.1727029270195678014e-5286j | 3.43e-2022, 3.43e-2022j | 
| 6.9239565457104964806 + 2.4389969891244262077e-5290j | 7.28e-2024, 7.28e-2024j | 
| 12.486507079040894342 + 2.591495658504650126e-5285j | 1e-2019, 1e-2019j | 
| 2.8945937603333959614 - 2.836571583025001148e-5294j | 6.21e-2029, 6.21e-2029j | 
| 7.8845290390640303665 + 6.1580319818338087605e-5291j | 5.06e-2023, 5.06e-2023j | 
| 1.4333723087750014368 - 2.2677338963941701048e-5297j | 1.5e-2032, 1.5e-2032j | 
| 5.2387374443037801502 - 2.777364359501693581e-5290j | 1.63e-2025, 1.63e-2025j | 
| 1.8790786004628987087 + 4.2220148518817194393e-5297j | 2.47e-2031, 2.47e-2031j | 
| 0.019010054023773081519 + 6.0262759452189454112e-5306j | 1.25e-2041, 1.25e-2041j | 
| 3.4142135623730950488 - 1.5488240370234038159e-5292j | 7.42e-2028, 7.42e-2028j | 
| 2.3716244759903799252 + 6.2732469545252097706e-5295j | 4.16e-2030, 4.16e-2030j | 
| 0.47193845768537280597 + 4.7503228861714058843e-5301j | 8.77e-2036, 8.77e-2036j | 
| 0.5857864376269049512 + 2.5766187443655967782e-5299j | 7.21e-2035, 7.21e-2035j | 
| 3.9297526718306817494 + 1.253627359202679479e-5291j | 4.56e-2027, 4.56e-2027j | 
| 0.10024344156550959678 - 7.3521894209174049847e-5305j | 7.64e-2040, 7.64e-2040j | 
| 0.68913176265686354771 - 9.0560895238379955197e-5300j | 1.54e-2034, 1.54e-2034j | 
| 0.24717079878134425053 - 3.1537593181143083795e-5302j | 5.63e-2038, 5.63e-2038j | 
| 4.5284880022025632207 + 7.9395190633812446872e-5291j | 2.87e-2026, 2.87e-2026j | 
| 266.11724773402626291 + 1.6099900611890143588e-5279j | 8.27e-2019, 8.27e-2019j | 
| 222.54050278657823335 - 3.1291719753834536285e-5270j | 5.15e-2014, 5.15e-2014j | 
| 248.60125635311858578 + 2.2991737058536781133e-5274j | 8.23e-2017, 8.23e-2017j | 
| 234.62148703855322689 - 5.1824791245716943159e-5273j | 2.74e-2015, 2.74e-2015j | 
| 211.7251601655228958 + 3.4771337444371604262e-5271j | 5.89e-2013, 5.89e-2013j | 
| 74.963182505245492782 - 2.8443470509096580837e-5285j | 1.26e-2006, 1.26e-2006j | 
| 67.804954852414414468 - 1.8545976420182486491e-5313j | 5.23e-2007, 5.23e-2007j | 
| 49.006807590033791892 - 7.9727989710603724799e-5338j | 7.56e-2009, 7.56e-2009j | 
| 61.109958636133906247 + 7.7017660314619369858e-5375j | 1.62e-2007, 1.62e-2007j | 
| 43.556051049424497069 - 6.8175175275291292655e-5444j | 1.11e-2009, 1.11e-2009j | 
| 124.37478500892590134 - 2.4186242747116771156e-5579j | 1.23e-2006, 1.23e-2006j | 
| 64.401317198134587969 - 3.6417648462961773561e-5768j | 2.92e-2007, 2.92e-2007j | 
| 176.13499744386963187 + 3.4053015643492260169e-5916j | 9.04e-2010, 9.04e-2010j | 
| 27.35314587138340584 - 1.7239886729821624815e-5976j | 2.25e-2013, 2.25e-2013j | 
| 16.736699027341182492 - 1.08448184789034562e-6009j | 1.97e-2017, 1.97e-2017j | 
| 29.407303549465267688 - 9.8154130522480849232e-6070j | 9.28e-2013, 9.28e-2013j | 
| 168.54661243275562927 + 8.0437968008155931598e-6197j | 3.82e-2009, 3.82e-2009j | 
| 135.67832821196725938 - 3.0029840059080737196e-6301j | 4.03e-2007, 4.03e-2007j | 
| 141.68123986883995257 + 4.2544852393231348021e-6355j | 2.02e-2007, 2.02e-2007j | 
| 15.243241664252259153 + 9.0528635107987818372e-6396j | 3.28e-2018, 3.28e-2018j | 
| 33.770219539289062009 + 1.1218219832750286856e-6387j | 1.2e-2011, 1.2e-2011j | 
| 51.878757082265902533 + 2.2398832539590119664e-6383j | 1.84e-2008, 1.84e-2008j | 
| 161.34535434450143071 - 1.1464541783367058219e-6381j | 1.19e-2008, 1.19e-2008j | 
| 95.105774810336596679 - 3.3804131505780344542e-6394j | 3.98e-2006, 3.98e-2006j | 
| 184.1639146619322836 - 4.298739608299759425e-6414j | 2.03e-2010, 2.03e-2010j | 
| 36.081790095165298106 + 8.3030338222933763398e-6443j | 4.14e-2011, 4.14e-2011j | 
| 119.04255869482828023 + 2.563098276576013261e-6438j | 1.86e-2006, 1.86e-2006j | 
| 201.84581108208423942 + 1.6935648023217867452e-6453j | 5.24e-2012, 5.24e-2012j | 
| 23.493125697281854548 - 2.8680915979827505293e-6478j | 1.24e-2014, 1.24e-2014j | 
| 86.639180969021736347 + 7.7260704736681352927e-6469j | 3.15e-2006, 3.15e-2006j | 
| 71.324327956424898643 + 5.8904551070795484378e-6512j | 8.57e-2007, 8.57e-2007j | 
| 154.48906024647061213 + 6.1751422258257619389e-6570j | 3.44e-2008, 3.44e-2008j | 
| 31.545876085006168242 - 1.2118551106254978785e-6616j | 3.27e-2012, 3.27e-2012j | 
| 25.382142639669076584 + 4.0395208266295678253e-6619j | 5.31e-2014, 5.31e-2014j | 
| 38.482149566698645211 - 2.5970458508465791104e-6611j | 1.33e-2010, 1.33e-2010j | 
| 147.94368814613552343 - 7.4334010644419593851e-6614j | 8.8e-2008, 8.8e-2008j | 
| 78.7255875879940033 + 8.1935778091014646497e-6635j | 1.84e-2006, 1.84e-2006j | 
| 54.851531787745577048 - 1.1060617297483405664e-6666j | 3.94e-2008, 3.94e-2008j | 
| 113.9057049550427683 - 4.0923594850677615304e-6761j | 2.48e-2006, 2.48e-2006j | 
| 104.17451213852532231 + 8.3834158040039728906e-6925j | 3.58e-2006, 3.58e-2006j | 
| 108.95299927313349003 - 4.4610570456632224504e-7061j | 3.2e-2006, 3.2e-2006j | 
| 129.91515835167888677 + 1.7954877487496078068e-7129j | 7.32e-2007, 7.32e-2007j | 
| 40.972971949512450384 + 2.3710445542070345026e-7164j | 3.97e-2010, 3.97e-2010j | 
| 19.956827184554027054 + 7.6298672026706875445e-7175j | 5.45e-2016, 5.45e-2016j | 
| 18.307657082097240087 + 1.7355688234770153973e-7175j | 1.02e-2016, 1.02e-2016j | 
| 21.685016902765754057 + 1.0155661573565511554e-7174j | 2.65e-2015, 2.65e-2015j | 
| 82.615974263808170404 + 4.1496340125300805455e-7164j | 2.4e-2006, 2.4e-2006j | 
| 90.800506852596939228 + 2.2875414234995432874e-7201j | 3.4e-2006, 3.4e-2006j | 
| 192.70291269386628068 + 2.4168368686565143198e-7234j | 3.67e-2011, 3.67e-2011j | 
| 46.233309259759625381 - 4.4442319216139279053e-7251j | 2.95e-2009, 2.95e-2009j | 
| 99.561406482296109995 + 3.843758965378416902e-7265j | 3.75e-2006, 3.75e-2006j | 
| 57.927683518510524137 + 2.672037981159983962e-7278j | 8.58e-2008, 8.58e-2008j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 1.6396873416385180515e-05 + 4.3345147855249488235e-5289j | 3.38e-275, 1.28e-1791j | 
| 5.0486653249541035953e-05 - 7.927000935485614466e-5289j | 9.27e-272, 3.51e-1788j | 
| 0.0020073490664788682527 - 1.2880259469982730628e-5287j | 6.29e-257, 2.38e-1773j | 
| 0.12928178930758798809 + 3.2827980360915764012e-5286j | 1.03e-204, 3.91e-1721j | 
| 1.3629900771182031213e-06 + 1.1105598224312807864e-5289j | 5.63e-283, 2.13e-1799j | 
| 0.00014349046410658330965 + 1.4840862656978529341e-5288j | 8.88e-269, 3.36e-1785j | 
| 0.00090734011728198669167 + 6.0363444334133072182e-5288j | 7.76e-262, 2.94e-1778j | 
| 4.9184184412337069953e-06 - 3.1581071736607174905e-5289j | 8.32e-280, 3.15e-1796j | 
| 0.029212049162629678962 + 1.68885396627768703e-5286j | 2.53e-239, 9.6e-1756j | 
| 0.00037607521806903259905 - 2.906933326182894051e-5288j | 1.17e-265, 4.43e-1782j | 
| 0.10009212542910460034 - 2.2615674595982375409e-5286j | 2.4e-221, 9.08e-1738j | 
| 0.004027802999230324195 + 2.8093820107541629624e-5287j | 3.22e-255, 1.22e-1771j | 
| 0.071898176465275401433 + 1.8800881924676025479e-5286j | 7.61e-229, 2.88e-1745j | 
| 0.047873925396008152529 + 1.3163711914537910885e-5287j | 1.24e-214, 4.72e-1731j | 
| 0.01671973152943396745 - 1.563022989698313589e-5286j | 1.28e-244, 4.84e-1761j | 
| 0.047768056866759101822 - 1.7287204805435841494e-5286j | 1.27e-235, 4.82e-1752j | 
| 0.19121145685950054235 - 8.9032375838583134742e-5286j | 4.11e-216, 1.56e-1732j | 
| -0.10151204448688335976 + 1.8646480896215628946e-5285j | 2.23e-216, 8.46e-1733j | 
| 0.010665971110755250164 + 1.135050740197850275e-5286j | 1.27e-248, 4.8e-1765j | 
| 0.10294858893669182252 - 5.3834015809569069229e-5287j | 1.49e-216, 5.66e-1733j | 
| 0.19802042027205659302 - 1.288680538839589399e-5285j | 3.45e-217, 1.31e-1733j | 
| 0.14118528535500422072 + 1.5314825696326408569e-5286j | 8.94e-217, 3.39e-1733j | 
| 0.0070987910236411162338 - 6.0770258329071380882e-5287j | 1.88e-252, 7.13e-1769j | 
| 5.5130270029582549904e-115 - 1.5894345197245132446e-5349j | 1.01e-386, 3.83e-1903j | 
| 2.5580846271269547553e-96 + 6.50574302661049625e-5340j | 2.2e-381, 8.32e-1898j | 
| 1.6546680655538258577e-107 + 1.1114714240152153746e-5345j | 5.28e-385, 2e-1901j | 
| 1.6413051544634301683e-101 - 1.3626425714536814892e-5342j | 3.16e-383, 1.2e-1899j | 
| 1.1535427030839778985e-91 - 1.6529839477879755971e-5337j | 1.14e-380, 4.32e-1897j | 
| 1.0282439485965545619e-32 + 2.2778932781196718603e-5306j | 3.7e-352, 1.4e-1868j | 
| 1.2355834796442996289e-29 + 1.1610538749213603296e-5304j | 2.44e-349, 9.24e-1866j | 
| 1.4696826586139129587e-21 + 4.5558695367192367545e-5300j | 6.51e-341, 2.47e-1857j | 
| 9.3396708589034024999e-27 + 4.7807561994654950726e-5303j | 5.7e-347, 2.16e-1863j | 
| 3.1898937461295062785e-19 + 1.0862344208640471894e-5298j | 3.22e-338, 1.22e-1854j | 
| 5.2461288353443853291e-54 - 7.7261326392975884214e-5318j | 5.52e-370, 2.09e-1886j | 
| 3.5934519868665631915e-28 - 7.6436594742804440549e-5304j | 1.92e-348, 7.29e-1865j | 
| 2.4978113468227299689e-76 - 1.4959322872671184194e-5329j | 5.15e-380, 1.95e-1896j | 
| 2.6569861014045944434e-12 - 2.4290386207045859063e-5294j | 1.89e-328, 7.18e-1845j | 
| 8.2533518370792681988e-08 - 7.9542716770000554392e-5291j | 2.77e-315, 1.05e-1831j | 
| 3.5480694972283158546e-13 + 6.3147213731366662328e-5295j | 2.2e-330, 8.33e-1847j | 
| 4.6730825480596944104e-73 + 7.5916449824614954683e-5328j | 3.29e-379, 1.25e-1895j | 
| 6.9988725504709588453e-59 - 2.0499829095561799623e-5320j | 7.57e-374, 2.87e-1890j | 
| 1.8030873059638202364e-61 + 8.8794309017361932883e-5322j | 3.66e-375, 1.39e-1891j | 
| 3.4896592768058617492e-07 + 4.392410469750171287e-5290j | 1.65e-317, 6.25e-1834j | 
| 4.8906512466413096355e-15 + 3.9723330626862700556e-5296j | 3.83e-338, 1.45e-1854j | 
| 8.6102382424723149313e-23 - 8.7707663662294243767e-5301j | 4.83e-348, 1.83e-1864j | 
| 5.9579274334871215734e-70 - 3.1769622125965726711e-5326j | 4.37e-379, 1.66e-1895j | 
| 2.1751740930745636661e-41 - 4.2595877387818051346e-5311j | 1.31e-366, 4.97e-1883j | 
| 8.6331598425807957394e-80 + 2.3663705407873897674e-5331j | 1.83e-383, 6.95e-1900j | 
| 5.034969394720901995e-16 - 9.549177902167852951e-5297j | 5.49e-343, 2.08e-1859j | 
| 1.0451701636236184766e-51 + 1.2817417380441811924e-5316j | 3.12e-372, 1.18e-1888j | 
| 2.0725425836566975554e-87 + 2.6323463105128946904e-5335j | 8.61e-387, 3.26e-1903j | 
| 1.1584009376395042766e-10 - 3.4245498789094968091e-5293j | 8.26e-337, 3.13e-1853j | 
| 9.6593420458469178307e-38 - 4.0299017760754473299e-5309j | 3.79e-365, 1.44e-1881j | 
| 3.7838557127701394358e-31 - 1.6720410052200768928e-5305j | 3.02e-359, 1.14e-1875j | 
| 5.3957382349067915821e-67 + 1.1198498825401875103e-5324j | 8.15e-379, 3.09e-1895j | 
| 4.3501107992818451473e-14 - 1.6047657166194446239e-5295j | 2e-343, 7.56e-1860j | 
| 1.8289127161356339422e-11 + 9.1755463779820067897e-5294j | 3.15e-340, 1.19e-1856j | 
| 4.7396615747842097675e-17 + 2.2236330160334839151e-5297j | 9.64e-348, 3.65e-1864j | 
| 3.5894675345505416349e-64 - 3.3824860366754088558e-5323j | 4.61e-378, 1.75e-1894j | 
| 2.469528992189185438e-34 - 2.9288828626033165406e-5307j | 1.9e-363, 7.2e-1880j | 
| 4.5589770934913777495e-24 + 1.6163865769369317598e-5301j | 8.14e-356, 3.08e-1872j | 
| 1.7142412828508880922e-49 - 1.9321930336777389933e-5315j | 3.31e-373, 1.26e-1889j | 
| 2.6863640034546991553e-45 - 3.3692367157314283091e-5313j | 5.79e-372, 2.2e-1888j | 
| 2.3405107293894290039e-47 + 2.6620633219658911847e-5314j | 9.17e-373, 3.47e-1889j | 
| 2.1406569465042952781e-56 + 4.2043065104384704814e-5319j | 1.02e-376, 3.86e-1893j | 
| 4.073084746712863442e-18 - 5.0043787419675419642e-5298j | 9.78e-355, 3.7e-1871j | 
| 3.6338818307148453484e-09 - 4.7905039789804607581e-5292j | 1.46e-347, 5.55e-1864j | 
| 1.8025798861644217141e-08 + 1.8664966935960138719e-5291j | 9.67e-347, 3.66e-1863j | 
| 6.7576714618311623182e-10 + 1.2740156222745177528e-5292j | 2.13e-348, 8.06e-1865j | 
| 5.2190261517125185141e-36 + 3.5454785271023993065e-5308j | 1.64e-368, 6.23e-1885j | 
| 1.5574540299026209328e-39 + 4.2885550930259740197e-5310j | 7.96e-371, 3.01e-1887j | 
| 1.802149281628069479e-83 - 2.9019780822119794224e-5333j | 2.64e-393, 9.99e-1910j | 
| 2.272474550038875237e-20 - 2.2695255644323664684e-5299j | 4.45e-360, 1.69e-1876j | 
| 2.6147362083909040134e-43 + 3.9353468001950635877e-5312j | 4.35e-373, 1.65e-1889j | 
| 2.1761858121275950459e-25 - 2.8464324214310227539e-5302j | 2.76e-363, 1.05e-1879j | 
All rules of Laguerre type can be downloaded here packed into a single file.