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) | 
|---|---|
| -10.123149712280346123 + 2.6514003279878874183e-1715j | 1.11e-495, 1.11e-495j | 
| -8.8582351699418602499 - 2.2730891556644967717e-1713j | 1.22e-493, 1.22e-493j | 
| -7.7832334480617396422 + 8.4518246004164766071e-1718j | 1.23e-492, 1.23e-492j | 
| 9.669133179983421627 - 3.169726685247657018e-1727j | 7.5e-495, 7.5e-495j | 
| -10.632533304701463914 - 5.367567530959684941e-1730j | 1.05e-496, 1.05e-496j | 
| 8.1278027185494178122 + 1.7859155087843136563e-1724j | 7.03e-493, 7.03e-493j | 
| 7.1249241242290427311 - 1.3472424334989654806e-1723j | 2.26e-492, 2.26e-492j | 
| -1.4069485066048049533 + 5.4649815103979838513e-1736j | 1.19e-502, 1.19e-502j | 
| 5.3191005645007322705 - 2.4999958544258642595e-1725j | 6.77e-493, 6.77e-493j | 
| 4.7579793139961429849 - 8.5980494723124431283e-1727j | 2.31e-493, 2.31e-493j | 
| 11.248719630336091572 + 1.2657866539016551406e-1731j | 3.25e-498, 3.25e-498j | 
| -2.6809657294565513398 + 8.5851958003327213037e-1731j | 1.25e-497, 1.25e-497j | 
| 10.123149712280346123 - 2.7803865785069354617e-1728j | 1.08e-495, 1.08e-495j | 
| -9.2508610223456376648 + 9.8681834114199693816e-1726j | 3.55e-494, 3.55e-494j | 
| 10.632533304701463914 + 3.6474553712044309518e-1732j | 9.9e-497, 9.9e-497j | 
| 8.4852079335832892012 + 9.7293524704255261271e-1728j | 3.4e-493, 3.4e-493j | 
| 6.499020390687851905 - 3.3546422409352182055e-1726j | 2.57e-492, 2.57e-492j | 
| -3.4388419241577733064 + 4.2783129246226551649e-1730j | 5.5e-495, 5.5e-495j | 
| -1.9816567566958429259 - 4.205518563185003609e-1735j | 1.32e-499, 1.32e-499j | 
| 5.8985578662084005323 + 4.9055845780458323845e-1729j | 1.61e-492, 1.61e-492j | 
| 1.1571937124467801947 - 5.0882983235873727118e-1740j | 6.29e-504, 6.29e-504j | 
| 2.1885630273880580333 - 6.2460191999521602681e-1735j | 3.88e-499, 3.88e-499j | 
| 3.9471077243304570508 - 2.3620529534076515351e-1730j | 4.2e-494, 4.2e-494j | 
| -9.669133179983421627 + 3.3852140435153023123e-1728j | 7.25e-495, 7.25e-495j | 
| -3.6473028998600486888 + 8.1265118092568004893e-1728j | 2.06e-493, 2.06e-493j | 
| 7.7832334480617396422 + 3.5568359842379989294e-1729j | 1.26e-492, 1.26e-492j | 
| -5.8985578662084005323 + 1.0779311121091937531e-1727j | 1.63e-492, 1.63e-492j | 
| -5.6064065008008023012 - 2.8874452567286946965e-1735j | 1.11e-492, 1.11e-492j | 
| 4.4838301627422905975 + 1.9515808941624170052e-1749j | 1.26e-493, 1.26e-493j | 
| -0.56474674797970907162 + 6.8381493762856552062e-1764j | 1.48e-506, 1.48e-506j | 
| 6.1959336024230213249 - 1.1163056137630406174e-1747j | 2.28e-492, 2.28e-492j | 
| -4.2137509052179400579 + 1.576360239325979876e-1747j | 6.53e-494, 6.53e-494j | 
| 3.1822488578580910594 + 8.7169666425965556441e-1753j | 5.55e-496, 5.55e-496j | 
| 2.6809657294565513398 + 6.0252447970623871424e-1754j | 1.16e-497, 1.16e-497j | 
| 9.2508610223456376648 + 2.2201782105614938395e-1750j | 3.64e-494, 3.64e-494j | 
| -4.7579793139961429849 - 1.5242603518456054743e-1747j | 2.27e-493, 2.27e-493j | 
| -8.1278027185494178122 + 2.372483428118102728e-1772j | 7.28e-493, 7.28e-493j | 
| -6.499020390687851905 - 3.0299406261169102995e-1809j | 2.53e-492, 2.53e-492j | 
| -2.4326628723533155753 + 1.181418474628567412e-1845j | 1.91e-498, 1.91e-498j | 
| -7.4494570867239946346 - 1.8898161383748911816e-1841j | 2.06e-492, 2.06e-492j | 
| -3.1822488578580910594 + 6.9873938784772896631e-1864j | 5.11e-496, 5.11e-496j | 
| 7.4494570867239946346 + 8.4363994223418854509e-1862j | 1.99e-492, 1.99e-492j | 
| 2.4326628723533155753 - 3.3066325772536019232e-1867j | 1.93e-498, 1.93e-498j | 
| -11.248719630336091572 + 1.6568670464376547685e-1863j | 3.27e-498, 3.27e-498j | 
| -3.9471077243304570508 + 2.8297818390783021996e-1860j | 3.64e-494, 3.64e-494j | 
| -1.1571937124467801947 + 1.8616908338593750655e-1877j | 6.83e-504, 6.83e-504j | 
| 4.2137509052179400579 + 1.6052844066797460402e-1864j | 6.67e-494, 6.67e-494j | 
| 3.4388419241577733064 - 1.3011789910455431312e-1866j | 5.45e-495, 5.45e-495j | 
| 1.9816567566958429259 + 2.7416244634882501238e-1881j | 1.28e-499, 1.28e-499j | 
| -8.4852079335832892012 + 1.7289521177907047973e-1873j | 3.27e-493, 3.27e-493j | 
| -2.9306374202572440192 - 1.75382444945779073e-1902j | 7.97e-497, 7.97e-497j | 
| -6.8084297154241562749 - 3.7078168289289754939e-1907j | 2.73e-492, 2.73e-492j | 
| -7.1249241242290427311 - 9.0454046398002101539e-1930j | 2.25e-492, 2.25e-492j | 
| -3.6625956524073638163 - 8.5051890772239920601e-1938j | 2.23e-493, 2.23e-493j | 
| 1.6529282788355080641 + 2.24981471140997938e-1948j | 2.23e-501, 2.23e-501j | 
| -5.036357363748140926 - 4.3805549825587955005e-1940j | 3.97e-493, 3.97e-493j | 
| 5.6064065008008023012 + 9.390027248621271345e-1946j | 1.08e-492, 1.08e-492j | 
| -6.1959336024230213249 + 4.9851461741500925599e-1946j | 2.13e-492, 2.13e-492j | 
| -4.4838301627422905975 - 1.3595224848990797234e-1952j | 1.29e-493, 1.29e-493j | 
| 0.38118699020732211685 - 1.0781217358675556631e-1967j | 8.55e-508, 8.55e-508j | 
| 8.8582351699418602499 - 1.3866253997521117939e-1953j | 1.27e-493, 1.27e-493j | 
| -1.8651745430168657961 + 2.9644057308573662499e-1960j | 4.11e-500, 4.11e-500j | 
| -0.90900793673184624503 + 4.1705572657472939331e-1966j | 4.72e-505, 4.72e-505j | 
| -1.6529282788355080641 - 8.0593249242370436531e-1961j | 2.4e-501, 2.4e-501j | 
| 0.68012995068316637067 + 1.3052478682890880259e-1965j | 6.12e-506, 6.12e-506j | 
| -5.3191005645007322705 + 1.2299544780758993649e-1951j | 7.36e-493, 7.36e-493j | 
| 6.8084297154241562749 - 7.6422052006851458609e-1953j | 2.6e-492, 2.6e-492j | 
| -0.68012995068316637067 + 9.0716184489397085366e-1968j | 6.04e-506, 6.04e-506j | 
| -2.1885630273880580333 - 7.4518616789320466067e-1961j | 3.58e-499, 3.58e-499j | 
| 2.9306374202572440192 + 8.536635023754109438e-1958j | 7.39e-497, 7.39e-497j | 
| 0.56474674797970907162 + 1.6337075436836884762e-1967j | 1.68e-506, 1.68e-506j | 
| 0.90900793673184624503 + 1.4793445043954109106e-1966j | 4.97e-505, 4.97e-505j | 
| -0.15083573063806386109 + 2.7395307319844948211e-1972j | 2.89e-509, 2.89e-509j | 
| 3.6625956524073638163 - 7.5449367141344322067e-1953j | 2.24e-493, 2.24e-493j | 
| 0.15083573063806386109 + 3.5208084771075735916e-1972j | 3.6e-509, 3.6e-509j | 
| 5.036357363748140926 + 2.530772769907249116e-1957j | 4.23e-493, 4.23e-493j | 
| 1.8651745430168657961 + 5.0519212226923229353e-1965j | 3.98e-500, 3.98e-500j | 
| 1.4069485066048049533 + 8.1112003987424815458e-1968j | 1.15e-502, 1.15e-502j | 
| -0.38118699020732211685 + 2.9332696315895754298e-1973j | 8.57e-508, 8.57e-508j | 
| -8.5646104469116033464e-2014 - 1.6036985110285401997e-2014j | 7.06e-2012, 7.06e-2012j | 
| 3.6473028998600486888 - 7.0824101572234462738e-1971j | 2.15e-493, 2.15e-493j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 8.4011046822485437131e-46 - 6.3858252736596843482e-1754j | 5.31e-170, 3.25e-414j | 
| 1.7995393867919624253e-35 - 4.0422479487947021517e-1747j | 1.2e-165, 7.35e-410j | 
| 9.3856738622536794895e-28 + 1.6952210748282001133e-1743j | 1.38e-161, 8.49e-406j | 
| 6.1059032517297547192e-42 - 5.9665622413576830465e-1753j | 1.67e-171, 1.02e-415j | 
| 2.4748644123934000851e-50 + 1.5598888396439858974e-1756j | 2.99e-172, 1.83e-416j | 
| 4.0385614234384012689e-30 - 2.8487184297496181897e-1746j | 7.9e-166, 4.84e-410j | 
| 1.6228184871063535857e-23 + 2.2584173858157967767e-1742j | 9.25e-162, 5.67e-406j | 
| 0.019409280359629522461 - 1.0861962864394688088e-1726j | 3.48e-111, 2.13e-355j | 
| 8.2951977208175914257e-14 + 4.2853554334290075152e-1736j | 4.08e-153, 2.5e-397j | 
| 2.2961463384464926581e-11 + 2.7435797647218392038e-1734j | 7.28e-150, 4.46e-394j | 
| 4.4801303770917509825e-56 + 1.1207953653926702756e-1760j | 2.03e-178, 1.24e-422j | 
| 0.00010621105780129797302 - 1.3964912841981391846e-1728j | 1.24e-135, 7.62e-380j | 
| 8.4011046822485437131e-46 + 4.4089501002394632332e-1755j | 1.87e-174, 1.14e-418j | 
| 1.555180378746938575e-38 - 2.0552508235314763431e-1749j | 6.14e-173, 3.76e-417j | 
| 2.4748644123934000851e-50 - 1.4625072585318159115e-1757j | 2.18e-176, 1.33e-420j | 
| 1.1083232934961793814e-32 + 9.5888413551462367445e-1748j | 3.18e-169, 1.95e-413j | 
| 7.8329604823620190795e-20 + 4.1897497982798279559e-1740j | 2.5e-162, 1.53e-406j | 
| 1.0856591084248517888e-06 + 1.2998590383230660563e-1729j | 2.33e-148, 1.43e-392j | 
| 0.001612998846537992812 + 6.7620758796013834415e-1727j | 7.1e-133, 4.35e-377j | 
| 1.2894124499550021557e-16 + 4.9231903881404652414e-1738j | 6.28e-160, 3.85e-404j | 
| 0.036936591230738334727 + 1.4817623673583276136e-1726j | 1.6e-120, 9.83e-365j | 
| 0.0011166603130092951865 - 9.9558639325311881948e-1728j | 8.01e-137, 4.91e-381j | 
| 2.5682901450949871528e-08 - 1.596894447984721915e-1731j | 3.9e-151, 2.39e-395j | 
| 6.1059032517297547192e-42 + 1.3052701533319505145e-1751j | 2.45e-177, 1.5e-421j | 
| -4.7333613155149840564e-07 - 5.3676084709359071532e-1729j | 1.7e-151, 1.04e-395j | 
| 9.3856738622536794895e-28 + 6.7990146096058273757e-1745j | 6.77e-168, 4.15e-412j | 
| 1.2894124499550021557e-16 + 2.5639570904103171407e-1737j | 9.21e-166, 5.64e-410j | 
| 3.6532527244173807768e-15 - 2.1546048869334589692e-1736j | 1.95e-164, 1.19e-408j | 
| 2.8493232600677797803e-10 - 2.1200960548913183623e-1733j | 4.89e-156, 2.99e-400j | 
| 0.042188633810935152039 - 2.7643516081621323917e-1725j | 1.34e-128, 8.21e-373j | 
| 3.6004857253289930477e-18 - 4.7781986295969594194e-1739j | 8.46e-163, 5.18e-407j | 
| 2.9417768725936091961e-09 + 4.8102184015536095047e-1732j | 4.39e-158, 2.69e-402j | 
| 5.7132493874217884649e-06 - 9.933665948999163878e-1730j | 1.55e-150, 9.51e-395j | 
| 0.00010621105780129797302 - 7.4313446395556417498e-1729j | 2.84e-147, 1.74e-391j | 
| 1.555180378746938575e-38 + 4.7096678653192207456e-1751j | 3.56e-175, 2.18e-419j | 
| 2.2961463384464926581e-11 + 9.1556773864243941306e-1734j | 4.25e-162, 2.6e-406j | 
| 4.0385614234384012689e-30 - 5.1614177015262942316e-1745j | 7.91e-176, 4.85e-420j | 
| 7.8329604823620190795e-20 + 2.8867998425557060129e-1739j | 8.38e-171, 5.14e-415j | 
| 0.00037539047939517500922 + 4.3265396064317375246e-1728j | 4.61e-150, 2.82e-394j | 
| 1.4709934580401700941e-25 - 1.905125586947203204e-1742j | 4.61e-174, 2.83e-418j | 
| 5.7132493874217884649e-06 - 2.122655362266783377e-1729j | 4.44e-155, 2.72e-399j | 
| 1.4709934580401700941e-25 - 1.344220586725620804e-1743j | 6.8e-172, 4.17e-416j | 
| 0.00037539047939517500922 + 2.4490899321692136031e-1728j | 8.43e-152, 5.17e-396j | 
| 4.4801303770917509825e-56 - 9.1976931838823044867e-1760j | 4.8e-189, 2.94e-433j | 
| 2.5682901450949871528e-08 - 4.2018767317794920614e-1731j | 8.61e-160, 5.28e-404j | 
| 0.036936591230738334727 + 1.9317217025412517031e-1726j | 1.07e-142, 6.53e-387j | 
| 2.9417768725936091961e-09 + 1.6931437477355934119e-1732j | 5.78e-161, 3.55e-405j | 
| 1.0856591084248517888e-06 + 5.6829729014301235253e-1730j | 3.3e-158, 2.02e-402j | 
| 0.001612998846537992812 + 4.2714988054740309399e-1727j | 4.97e-151, 3.04e-395j | 
| 1.1083232934961793814e-32 + 3.9692644379987075275e-1746j | 5.15e-178, 3.16e-422j | 
| 2.6307819513160030884e-05 + 5.0936598440599098972e-1729j | 7.61e-157, 4.66e-401j | 
| 1.3034948893514852443e-21 - 2.6966084538455164866e-1740j | 2.46e-173, 1.51e-417j | 
| 1.6228184871063535857e-23 + 2.3160434243031536057e-1741j | 2.79e-174, 1.71e-418j | 
| 6.2717373856461582986e-07 + 4.7891518448746309817e-1729j | 2.46e-160, 1.51e-404j | 
| 0.0088210307673239552706 + 5.7895297004715805875e-1727j | 8.66e-156, 5.31e-400j | 
| 1.5260770641214386194e-12 - 1.2698730588212525523e-1734j | 2.06e-168, 1.26e-412j | 
| 3.6532527244173807768e-15 - 4.6194288397921951433e-1737j | 3.07e-172, 1.88e-416j | 
| 3.6004857253289930477e-18 - 2.8339163811840780628e-1738j | 3.75e-172, 2.3e-416j | 
| 2.8493232600677797803e-10 - 6.5209814661716424912e-1733j | 2.41e-166, 1.48e-410j | 
| 0.11268847101895342555 + 2.2046274819929652473e-1725j | 2.05e-157, 1.25e-401j | 
| 1.7995393867919624253e-35 - 2.4894426228799935234e-1749j | 2.75e-184, 1.69e-428j | 
| 0.0026909421737128832131 - 9.574178106401465855e-1727j | 1.88e-159, 1.15e-403j | 
| 0.060499511143984789348 - 4.7483991402943161763e-1726j | 1.67e-157, 1.02e-401j | 
| 0.0088210307673239552706 + 8.4754114415867452002e-1727j | 3.4e-159, 2.08e-403j | 
| 0.067379129528441601911 + 1.5816603220623903865e-1725j | 2.17e-159, 1.33e-403j | 
| 8.2951977208175914257e-14 + 1.6979990513580348189e-1735j | 7.5e-170, 4.6e-414j | 
| 1.3034948893514852443e-21 - 3.278586951187456471e-1741j | 1.56e-177, 9.59e-422j | 
| 0.067379129528441601911 + 1.8473223363135290586e-1725j | 8.99e-159, 5.51e-403j | 
| 0.0011166603130092951865 - 1.6568049319410942886e-1727j | 6.94e-161, 4.25e-405j | 
| 2.6307819513160030884e-05 + 2.5442518214914891983e-1729j | 2.01e-166, 1.23e-410j | 
| 0.042188633810935152039 - 2.4301776369611032719e-1725j | 4.5e-160, 2.76e-404j | 
| 0.060499511143984789348 - 3.8573019537967676494e-1726j | 1.93e-161, 1.18e-405j | 
| 0.1186967426349006349 - 3.3614890622227107501e-1725j | 4.74e-161, 2.91e-405j | 
| 6.2717373856461582986e-07 + 1.9713667339025200487e-1729j | 7.57e-169, 4.64e-413j | 
| 0.1186967426349006349 - 3.2479250641049316765e-1725j | 4.69e-163, 3.07e-407j | 
| 1.5260770641214386194e-12 - 3.469432606097521654e-1735j | 4.31e-174, 2.8e-418j | 
| 0.0026909421737128832131 - 6.2187970933369389845e-1727j | 5.29e-166, 3.52e-410j | 
| 0.019409280359629522461 - 7.8612452937827741418e-1727j | 8.61e-166, 5.88e-410j | 
| 0.11268847101895342555 + 2.404777722953338247e-1725j | 1.59e-164, 1.13e-408j | 
| 0.054890234269669983929 + 4.3982905890108131956e-1725j | 1.63e-164, 1.23e-408j | 
| -4.7333613155149840564e-07 - 2.2186493410478261828e-1729j | 8.21e-169, 5.02e-413j | 
All rules of Hermite (physicists') type can be downloaded here packed into a single file.