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) | 
|---|---|
| -9.3137120604790312021 + 1.3968548137229025247e-1719j | 3.58e-498, 3.58e-498j | 
| -8.317410037161215475 + 6.9428628681400944385e-1718j | 2.56e-496, 2.56e-496j | 
| -8.7868245462062068281 - 2.2297698255281984036e-1718j | 3.9e-497, 3.9e-497j | 
| -7.8854050302061512098 - 8.5314333280276951384e-1717j | 1.14e-495, 1.14e-495j | 
| 9.3137120604790312021 + 8.6359604767660999385e-1720j | 3.63e-498, 3.63e-498j | 
| 7.0976178292052166741 - 2.723932768990828497e-1716j | 1.62e-494, 1.62e-494j | 
| 9.9510430273160501685 + 8.8754793939213477604e-1722j | 1.33e-499, 1.33e-499j | 
| -1.2247448713915890491 - 1.5393307182066385311e-1725j | 3.96e-503, 3.96e-503j | 
| 8.317410037161215475 + 5.5703897796058583139e-1718j | 2.71e-496, 2.71e-496j | 
| 5.3961532286066677345 - 3.7154489566766687598e-1715j | 1.33e-493, 1.33e-493j | 
| 1.0751107194236474918 - 2.3287939243567755154e-1725j | 5.5e-504, 5.5e-504j | 
| -6.0045998804986600715 + 5.6466942307852467954e-1714j | 3.75e-493, 3.75e-493j | 
| -2.0232301911005156592 - 1.1942658071769445563e-1732j | 3.9e-500, 3.9e-500j | 
| -9.9510430273160501685 - 2.1092872708724247422e-1731j | 1.45e-499, 1.45e-499j | 
| -6.1722632102931131075 - 2.2869820342440145192e-1724j | 3.75e-493, 3.75e-493j | 
| -6.3931459674616635863 - 6.9271034034807527538e-1745j | 1.74e-493, 1.74e-493j | 
| 4.0882571835761899744 - 4.4415981318326485881e-1761j | 1.29e-494, 1.29e-494j | 
| 6.7335549105641932502 + 1.0164916734875789958e-1758j | 4.78e-494, 4.78e-494j | 
| -1.0751107194236474918 + 2.0056470192577151531e-1779j | 5.82e-504, 5.82e-504j | 
| -5.1111671092429644623 + 4.2397370475231336352e-1768j | 1.08e-493, 1.08e-493j | 
| -7.0976178292052166741 - 1.6948274730579997229e-1786j | 1.5e-494, 1.5e-494j | 
| 0.52403354748695764515 - 5.5204057238158360012e-1811j | 8.15e-507, 8.15e-507j | 
| 2.0232301911005156592 - 5.7884281861520196616e-1804j | 4.3e-500, 4.3e-500j | 
| -2.9592107790638377223 + 5.8595136327364697174e-1799j | 1.05e-496, 1.05e-496j | 
| 6.0045998804986600715 - 4.4541951974649654395e-1796j | 3.38e-493, 3.38e-493j | 
| 4.848988972613464028 + 7.2297676795010141481e-1800j | 7.2e-494, 7.2e-494j | 
| 2.2833403693622945843 - 4.8336798038394337405e-1815j | 2.57e-499, 2.57e-499j | 
| 3.3998220836348869732 + 6.9633703225230697195e-1808j | 7.12e-496, 7.12e-496j | 
| 5.6999526611305889188 - 1.1881571266459748782e-1807j | 1.94e-493, 1.94e-493j | 
| -4.3406126076143357547 + 1.2308219461745740039e-1828j | 2.52e-494, 2.52e-494j | 
| -4.0882571835761899744 - 2.2638276505744917891e-1846j | 1.29e-494, 1.29e-494j | 
| -5.6999526611305889188 + 2.566836463959386871e-1847j | 1.89e-493, 1.89e-493j | 
| 3.1485020473072701033 + 2.3706417579889257211e-1855j | 2.39e-496, 2.39e-496j | 
| -5.3961532286066677345 - 1.5594784067381229784e-1851j | 1.31e-493, 1.31e-493j | 
| -3.641718756806205729 + 2.8298458869423079518e-1863j | 2.59e-495, 2.59e-495j | 
| 7.480694682675180463 - 1.1761018015330569431e-1879j | 4.64e-495, 4.64e-495j | 
| -3.859641678951973708 - 4.305246811944422726e-1882j | 6.75e-495, 6.75e-495j | 
| 6.1722632102931131075 + 3.5379147567830262144e-1892j | 3.69e-493, 3.69e-493j | 
| -7.480694682675180463 - 3.8804911930510017595e-1899j | 5.06e-495, 5.06e-495j | 
| 2.8009079705169224571 - 8.7837350939840189832e-1909j | 2.85e-497, 2.85e-497j | 
| 3.641718756806205729 - 2.1290023053128697261e-1906j | 2.51e-495, 2.51e-495j | 
| 8.7868245462062068281 - 1.7166777186281409915e-1909j | 3.99e-497, 3.99e-497j | 
| 1.2247448713915890491 + 1.0683882516700066238e-1914j | 3.83e-503, 3.83e-503j | 
| 7.8854050302061512098 + 9.3203488626410141123e-1908j | 1.23e-495, 1.23e-495j | 
| 3.859641678951973708 + 8.4906008050452506425e-1906j | 6.44e-495, 6.44e-495j | 
| -0.52403354748695764515 + 1.1793544741145372415e-1918j | 7.56e-507, 7.56e-507j | 
| -2.2833403693622945843 - 1.2306035337837947501e-1911j | 2.75e-499, 2.75e-499j | 
| 4.3406126076143357547 + 2.3397052221234855972e-1905j | 2.53e-494, 2.53e-494j | 
| 1.807293775014019636 + 7.6686202686402128727e-1913j | 9.07e-501, 9.07e-501j | 
| -2.8009079705169224571 + 3.5038228166261964387e-1906j | 2.92e-497, 2.92e-497j | 
| 1.6321716520540069475 - 7.9917218709406835715e-1925j | 1.89e-501, 1.89e-501j | 
| -0.81784265210787922472 - 8.5218120716457962647e-1929j | 1.37e-505, 1.37e-505j | 
| -4.848988972613464028 + 1.0423409209274582636e-1916j | 7.34e-494, 7.34e-494j | 
| -3.3998220836348869732 - 3.2972954904464349166e-1932j | 7.07e-496, 7.07e-496j | 
| 2.9592107790638377223 + 6.3430992441559830794e-1941j | 1.05e-496, 1.05e-496j | 
| -6.7335549105641932502 - 2.1079167650284443613e-1939j | 4.65e-494, 4.65e-494j | 
| -1.6321716520540069475 - 3.14091933421646197e-1952j | 1.84e-501, 1.84e-501j | 
| -1.807293775014019636 + 2.9282486859838662959e-1952j | 8.49e-501, 8.49e-501j | 
| 6.3931459674616635863 + 1.0049959526943362091e-1942j | 1.61e-493, 1.61e-493j | 
| 2.5508337609312682057 + 6.7856505993671600931e-1950j | 2.54e-498, 2.54e-498j | 
| 1.4058983460303288311 - 2.5666518552066113682e-1953j | 2.26e-502, 2.26e-502j | 
| -3.1485020473072701033 - 4.6075265766050753561e-1945j | 2.47e-496, 2.47e-496j | 
| -1.4058983460303288311 - 4.6165684789254736862e-1959j | 2.07e-502, 2.07e-502j | 
| -4.5969667521814689322 + 6.329534719552971961e-1951j | 4.62e-494, 4.62e-494j | 
| 4.5969667521814689322 + 1.2958467446519732849e-1956j | 4.54e-494, 4.54e-494j | 
| 0.81784265210787922472 + 4.5006421354072647146e-1970j | 1.33e-505, 1.33e-505j | 
| 5.1111671092429644623 + 4.297021929656908564e-1970j | 1.07e-493, 1.07e-493j | 
| -0.40103385448943630946 + 4.219747587369097398e-1984j | 2.72e-507, 2.72e-507j | 
| -2.5508337609312682057 - 1.1091109499994786518e-1978j | 2.54e-498, 2.54e-498j | 
| 0.30590020450152775097 - 6.541222850755296803e-1986j | 4.91e-508, 4.91e-508j | 
| -6.512397030768366846e-2024 - 2.7643339837459434523e-2024j | 5.16e-2022, 5.16e-2022j | 
| 0.40103385448943630946 + 4.8856008437419363682e-1985j | 2.63e-507, 2.63e-507j | 
| -0.30590020450152775097 + 5.5275190101381433582e-1986j | 4.58e-508, 4.58e-508j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 6.8013475533442577719e-39 + 1.7498204749545002372e-1746j | 9.05e-174, 8.68e-422j | 
| 2.285511457426989994e-31 + 1.4512139007362218415e-1741j | 1.33e-170, 1.27e-418j | 
| 8.194416883480549168e-35 - 7.3385898553017805127e-1744j | 2.64e-172, 2.53e-420j | 
| 2.3304382796367473785e-28 - 1.794939728021437248e-1739j | 1.95e-169, 1.88e-417j | 
| 6.8013475533442577719e-39 + 1.672485353562648077e-1746j | 9.56e-179, 9.17e-427j | 
| 2.7893990750826492051e-23 - 8.7315461689721729877e-1736j | 3.97e-171, 3.8e-419j | 
| 4.1067827127670068181e-44 - 9.8453348633156629178e-1750j | 3.83e-181, 3.67e-429j | 
| 0.014355567458802604262 + 5.9134565802283243525e-1719j | 1.25e-122, 1.2e-370j | 
| 2.285511457426989994e-31 + 1.2741979334944221637e-1741j | 9.21e-176, 8.84e-424j | 
| 3.7714521848725514404e-14 + 1.1287301781288388744e-1727j | 1.67e-164, 1.6e-412j | 
| 0.039691736524117024274 - 6.4381980104078741054e-1719j | 2.58e-121, 2.47e-369j | 
| 3.4684271266578288498e-17 + 8.3795311639342129061e-1730j | 1.7e-167, 1.63e-415j | 
| 0.002331136248810555987 + 2.410879877875315311e-1720j | 5.11e-140, 4.91e-388j | 
| 4.1067827127670068181e-44 - 9.914352769467307269e-1750j | 8.67e-182, 8.32e-430j | 
| 1.6737648925273913821e-18 + 3.1486196317165438019e-1730j | 2.3e-168, 2.21e-416j | 
| 3.1901150787631119913e-19 - 1.0108970136942671914e-1731j | 1.49e-169, 1.43e-417j | 
| 7.5620055602150122259e-09 - 2.2640265482829873183e-1724j | 1.48e-162, 1.42e-410j | 
| 4.0707827139007701977e-21 + 5.7134480759860698922e-1734j | 2.69e-174, 2.58e-422j | 
| 0.039691736524117024274 - 6.0590831144693571799e-1719j | 7.57e-131, 7.26e-379j | 
| 6.955682491905073756e-13 - 1.5155998982570263375e-1727j | 2.26e-166, 2.16e-414j | 
| 2.7893990750826492051e-23 - 1.2706923447033942645e-1735j | 4.29e-173, 4.11e-421j | 
| 0.15266696419137781166 - 1.9711412246061234067e-1718j | 2.03e-132, 1.95e-380j | 
| 0.002331136248810555987 + 2.7248726295286551079e-1720j | 9.81e-148, 9.41e-396j | 
| 1.1599703615754545717e-05 + 1.2483682785805203296e-1721j | 1.85e-155, 1.78e-403j | 
| 3.4684271266578288498e-17 - 3.3929177634271398814e-1730j | 2.2e-172, 2.11e-420j | 
| 8.7913233720051665075e-12 + 2.067127645268469494e-1726j | 4.09e-168, 3.92e-416j | 
| 0.0008198612352513668335 - 8.1100340211322254478e-1721j | 1.12e-152, 1.08e-400j | 
| 1.3595406743884736036e-06 + 1.0463963838883160804e-1722j | 2.1e-161, 2.02e-409j | 
| 1.3566123539995472539e-15 + 4.5592721488394953973e-1729j | 3.19e-171, 3.06e-419j | 
| 9.5431183606850544195e-10 + 2.7943951847460340545e-1725j | 4.28e-167, 4.11e-415j | 
| 7.5620055602150122259e-09 - 1.5308506287997952354e-1724j | 3.81e-166, 3.66e-414j | 
| 1.3566123539995472539e-15 - 4.3418034048050712055e-1729j | 6e-172, 5.76e-420j | 
| 6.7224404603687381677e-06 - 4.8007657733697449533e-1722j | 2.82e-163, 2.71e-411j | 
| 3.7714521848725514404e-14 + 2.214049656435257018e-1728j | 3.88e-171, 3.72e-419j | 
| 2.2382788631870093517e-07 - 2.3054263822276143988e-1723j | 1.08e-165, 1.04e-413j | 
| 1.1030210003078322871e-25 + 1.2683341763369675683e-1737j | 3.74e-183, 3.59e-431j | 
| 4.1292138065081099038e-08 + 6.8271147617066690518e-1724j | 1.55e-166, 1.49e-414j | 
| 1.6737648925273913821e-18 + 7.1951636852545283342e-1731j | 2.24e-177, 2.14e-425j | 
| 1.1030210003078322871e-25 + 1.6411399597068850331e-1737j | 1.25e-180, 1.2e-428j | 
| 4.8389535281209375179e-05 - 2.3697157636483663082e-1721j | 1.49e-164, 1.43e-412j | 
| 2.2382788631870093517e-07 - 3.1004628122772052772e-1723j | 1.74e-168, 1.67e-416j | 
| 8.194416883480549168e-35 - 6.7417022123374711895e-1744j | 3.46e-189, 3.32e-437j | 
| 0.014355567458802604262 + 6.3401415522025583319e-1719j | 1.66e-156, 1.59e-404j | 
| 2.3304382796367473785e-28 - 1.4909347066179680626e-1739j | 2.31e-185, 2.21e-433j | 
| 4.1292138065081099038e-08 + 9.5672993878290065683e-1724j | 2.2e-170, 2.11e-418j | 
| 0.15266696419137781166 - 1.9147612982889473428e-1718j | 1.5e-157, 1.44e-405j | 
| 0.0008198612352513668335 - 7.0347495750535793696e-1721j | 1.11e-166, 1.07e-414j | 
| 9.5431183606850544195e-10 + 4.473039553133037436e-1725j | 9.32e-173, 8.94e-421j | 
| 0.0038213866273272293572 - 8.6622804185169012433e-1720j | 2.7e-163, 2.59e-411j | 
| 4.8389535281209375179e-05 - 1.9635297856113453895e-1721j | 5.82e-169, 5.58e-417j | 
| 0.0078641224284217669325 + 1.658995142047212082e-1719j | 7.47e-163, 7.17e-411j | 
| 0.079505493794590272438 + 5.3572097767556784529e-1719j | 2.09e-160, 2e-408j | 
| 8.7913233720051665075e-12 + 9.526186783576451329e-1727j | 1.11e-175, 1.07e-423j | 
| 1.3595406743884736036e-06 + 8.0793430232578146965e-1723j | 2.63e-171, 2.52e-419j | 
| 1.1599703615754545717e-05 + 1.5314324147649001053e-1721j | 5.3e-169, 5.09e-417j | 
| 4.0707827139007701977e-21 + 9.8036479601983817813e-1734j | 3.15e-182, 3.02e-430j | 
| 0.0078641224284217669325 + 1.5080798956120693671e-1719j | 9.46e-167, 9.07e-415j | 
| 0.0038213866273272293572 - 7.7821536689812741756e-1720j | 2.37e-167, 2.28e-415j | 
| 3.1901150787631119913e-19 - 4.186288330908274201e-1732j | 6.57e-182, 6.3e-430j | 
| 0.00022336177951260000642 + 3.4545112783303916263e-1721j | 2.76e-169, 2.65e-417j | 
| 0.018274296386945638591 - 3.3740286371820000155e-1719j | 1.63e-166, 1.56e-414j | 
| 6.7224404603687381677e-06 - 3.8301681706409088341e-1722j | 1.28e-171, 1.23e-419j | 
| 0.018274296386945638591 - 3.1119853441769944146e-1719j | 1.3e-167, 1.25e-415j | 
| 9.5038732392944724878e-11 - 5.1917460708385545021e-1726j | 9.91e-176, 9.51e-424j | 
| 9.5038732392944724878e-11 - 9.3409429993569190359e-1726j | 1.03e-176, 9.88e-425j | 
| 0.079505493794590272438 + 5.6075827933306424317e-1719j | 2.13e-169, 2.06e-417j | 
| 6.955682491905073756e-13 - 4.9109143875206631597e-1727j | 1.73e-178, 1.66e-426j | 
| -0.10584216958214380441 + 3.9244851241311792832e-1718j | 1.08e-169, 1.03e-417j | 
| 0.00022336177951260000642 + 2.93009069696383462e-1721j | 3.78e-172, 3.7e-420j | 
| 0.20431643234797103781 - 2.7863068624955861509e-1718j | 1.71e-170, 1.69e-418j | 
| 0.16380693119615532647 + 8.5890868832122380948e-1719j | 4.48e-171, 4.23e-419j | 
| -0.10584216958214380441 + 4.0124003099853258572e-1718j | 1.98e-170, 2.04e-418j | 
| 0.20431643234797103781 - 2.739682845031153004e-1718j | 1.1e-170, 9.32e-419j | 
All rules of Hermite (physicists') type can be downloaded here packed into a single file.