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) | 
|---|---|
| 11.117379349101090879 - 8.8182207926808241207e-1724j | 7.32e-494, 7.32e-494j | 
| -9.1778579510011689174 + 2.2986100024671357011e-1718j | 1.13e-490, 1.13e-490j | 
| 9.8872357581921909682 - 6.061681478386962236e-1725j | 1.39e-491, 1.39e-491j | 
| -11.613394920050297114 - 1.9425997681479375708e-1728j | 4.96e-495, 4.96e-495j | 
| 10.675586251719491427 - 7.2299351948279588547e-1727j | 6e-493, 6e-493j | 
| -9.5248777996633493413 + 5.4858401951720602932e-1722j | 4.21e-491, 4.21e-491j | 
| -7.0152454274859507744 + 4.4670520899745857862e-1728j | 8.98e-490, 8.98e-490j | 
| -1.1082012875144997416 + 1.2700269230563041478e-1748j | 4.66e-503, 4.66e-503j | 
| -1.9072865624118656773 - 1.7748027552330010111e-1744j | 1.22e-499, 1.22e-499j | 
| 3.9268135162497144207 + 3.7601927495997999951e-1738j | 8.19e-493, 8.19e-493j | 
| 1.1082012875144997416 - 2.0772706960237342588e-1748j | 4.57e-503, 4.57e-503j | 
| -8.204814510767702279 + 1.0307270351762533143e-1733j | 6.1e-490, 6.1e-490j | 
| -1.7281759088743055938 - 3.4036094257631357939e-1752j | 2.65e-500, 2.65e-500j | 
| -1.5478881666047928113 + 1.2652285742324868111e-1752j | 3.66e-501, 3.66e-501j | 
| -8.5196024914362764207 + 2.5551300265339466412e-1740j | 4.01e-490, 4.01e-490j | 
| 10.26883129731562295 + 1.4580221192481660776e-1755j | 3.29e-492, 3.29e-492j | 
| -12.213895245183783151 - 4.0570775175456748706e-1758j | 1.34e-496, 1.34e-496j | 
| 9.5248777996633493413 + 1.7739731991850281007e-1753j | 4.16e-491, 4.16e-491j | 
| 8.8434379291434994962 + 7.4915307205918858391e-1753j | 2.27e-490, 2.27e-490j | 
| 5.9054847393912450345 - 2.803959362510723883e-1752j | 2.5e-490, 2.5e-490j | 
| -7.8978681142187515532 + 1.3998403429820539942e-1750j | 8.12e-490, 8.12e-490j | 
| 2.3506049736744922228 + 1.1249438528487288912e-1777j | 3.65e-498, 3.65e-498j | 
| 7.3038066988064421106 - 8.3742006903796429613e-1768j | 1.05e-489, 1.05e-489j | 
| -6.1770435023858571681 + 7.1347017451077855527e-1768j | 3.94e-490, 3.94e-490j | 
| 11.613394920050297114 + 6.4803937595461117666e-1791j | 5.3e-495, 5.3e-495j | 
| 5.3724246076122737297 + 4.1793575992596767119e-1786j | 6.99e-491, 6.99e-491j | 
| -7.5977957280120946766 + 7.3294459091605592043e-1784j | 9.54e-490, 9.54e-490j | 
| -5.1106076595385866946 - 3.7892029563351043032e-1805j | 3.46e-491, 3.46e-491j | 
| 6.452292554471648081 - 4.0432143852062228744e-1813j | 6.45e-490, 6.45e-490j | 
| -11.117379349101090879 - 3.911585979165021509e-1819j | 7.15e-494, 7.15e-494j | 
| -10.26883129731562295 + 2.0889604620768159746e-1815j | 3.02e-492, 3.02e-492j | 
| 8.204814510767702279 - 1.0647342818942154476e-1814j | 6.19e-490, 6.19e-490j | 
| -9.8872357581921909682 - 1.1506934690273557488e-1814j | 1.32e-491, 1.32e-491j | 
| -10.675586251719491427 - 1.5438526586807667475e-1819j | 6.85e-493, 6.85e-493j | 
| 3.0701613138889128067 - 2.7579529555160451122e-1828j | 9.47e-496, 9.47e-496j | 
| -6.452292554471648081 - 2.1306859145647206138e-1821j | 5.91e-490, 5.91e-490j | 
| 1.7281759088743055938 - 5.6026698396050873723e-1850j | 2.7e-500, 2.7e-500j | 
| 5.1106076595385866946 + 2.7170967581761105205e-1840j | 3.63e-491, 3.63e-491j | 
| 4.1108152807287541899 + 1.936907804626192256e-1841j | 1.55e-492, 1.55e-492j | 
| -3.5517547697054951901 - 3.1197139522620385929e-1841j | 4.63e-494, 4.63e-494j | 
| 8.5196024914362764207 + 1.6841724901415645282e-1838j | 4.12e-490, 4.12e-490j | 
| -3.7709163338688759015 + 9.3194158334458278719e-1841j | 3.06e-493, 3.06e-493j | 
| -8.8434379291434994962 + 6.1922564332093968078e-1843j | 2.42e-490, 2.42e-490j | 
| 2.1202214064344157181 - 1.2570097676771274267e-1863j | 6.64e-499, 6.64e-499j | 
| 2.587732052106509866 - 2.1294191517843772762e-1861j | 2.08e-497, 2.08e-497j | 
| 12.213895245183783151 - 3.774085371216380527e-1862j | 1.31e-496, 1.31e-496j | 
| 7.5977957280120946766 + 2.9194233693824177104e-1853j | 9.32e-490, 9.32e-490j | 
| 6.7315621736699192904 + 3.6377396540462665504e-1853j | 7.77e-490, 7.77e-490j | 
| 1.5478881666047928113 - 7.0835349696184028527e-1870j | 3.73e-501, 3.73e-501j | 
| 3.3125307911686668706 - 4.2819164987692844325e-1862j | 7.27e-495, 7.27e-495j | 
| -7.3038066988064421106 - 2.0883461088602990598e-1856j | 1.02e-489, 1.02e-489j | 
| -0.95452011014285350763 + 1.0254056330561999558e-1884j | 1.65e-503, 1.65e-503j | 
| 5.6373462354686513898 - 2.7634526879285442545e-1871j | 1.4e-490, 1.4e-490j | 
| 7.0152454274859507744 + 8.235198336569254469e-1872j | 9.74e-490, 9.74e-490j | 
| 0.66057200447970670507 + 3.6932829256959982504e-1887j | 6.05e-506, 6.05e-506j | 
| -4.5968791750767061343 + 1.188932614148219342e-1870j | 6.25e-492, 6.25e-492j | 
| -1.3358490740136969497 + 1.3841469448631779514e-1891j | 3.64e-502, 3.64e-502j | 
| -4.1108152807287541899 + 1.8013715297967775495e-1878j | 1.6e-492, 1.6e-492j | 
| 6.1770435023858571681 - 7.7352608430968772748e-1887j | 3.85e-490, 3.85e-490j | 
| 7.8978681142187515532 + 5.9060253550751110832e-1887j | 8.5e-490, 8.5e-490j | 
| 4.5968791750767061343 + 3.7020948949237349348e-1895j | 6.25e-492, 6.25e-492j | 
| -2.8280939962445144939 + 1.0523023883837586013e-1892j | 1.36e-496, 1.36e-496j | 
| 9.1778579510011689174 + 5.1595514143622331442e-1893j | 1.06e-490, 1.06e-490j | 
| -5.6373462354686513898 + 4.5510366781909477795e-1891j | 1.33e-490, 1.33e-490j | 
| -3.0701613138889128067 - 5.1086144814843275034e-1915j | 9.66e-496, 9.66e-496j | 
| -6.7315621736699192904 - 3.3550212767572527768e-1908j | 7.66e-490, 7.66e-490j | 
| 3.5517547697054951901 - 2.4046529930385014389e-1924j | 4.76e-494, 4.76e-494j | 
| -2.1202214064344157181 - 3.043927362696518637e-1929j | 6.56e-499, 6.56e-499j | 
| -0.8952681375077315078 - 6.9244215262631031928e-1934j | 7.09e-504, 7.09e-504j | 
| -4.8519460488273854963 - 8.0122784082075658305e-1920j | 1.46e-491, 1.46e-491j | 
| 0.43607741192761650868 + 2.7446199251218853732e-1943j | 1.54e-507, 1.54e-507j | 
| 1.3358490740136969497 + 4.7222782166327844434e-1939j | 3.47e-502, 3.47e-502j | 
| 4.3471301541829114048 - 1.8777448117452501485e-1928j | 3.03e-492, 3.03e-492j | 
| -0.66057200447970670507 + 3.1800768812485384339e-1941j | 6.63e-506, 6.63e-506j | 
| -2.587732052106509866 + 9.8572465936839345068e-1933j | 2.22e-497, 2.22e-497j | 
| 1.9072865624118656773 + 2.7326674054965066372e-1935j | 1.35e-499, 1.35e-499j | 
| 4.8519460488273854963 - 3.3804263030118100284e-1928j | 1.47e-491, 1.47e-491j | 
| -4.3471301541829114048 - 6.3757781708130485077e-1926j | 2.96e-492, 2.96e-492j | 
| -5.9054847393912450345 + 2.4655264956239874144e-1935j | 2.36e-490, 2.36e-490j | 
| -5.3724246076122737297 - 6.6779952395081027671e-1960j | 7.25e-491, 7.25e-491j | 
| 2.8280939962445144939 - 8.5243853374550841845e-1971j | 1.38e-496, 1.38e-496j | 
| 0.21635554412511755427 + 5.1274766435229754483e-1983j | 7.68e-509, 7.68e-509j | 
| 0.95452011014285350763 + 1.0182791146234286748e-1977j | 1.6e-503, 1.6e-503j | 
| -3.9268135162497144207 + 2.1333634115442635608e-1971j | 8.87e-493, 8.87e-493j | 
| -0.43607741192761650868 + 3.5384794988942074412e-1985j | 1.96e-507, 1.96e-507j | 
| -3.3125307911686668706 + 2.1327357573016990415e-1974j | 7.2e-495, 7.2e-495j | 
| 0.8952681375077315078 - 1.1862597528925785061e-1981j | 6.62e-504, 6.62e-504j | 
| 3.7709163338688759015 - 6.6588515121424573836e-1980j | 2.86e-493, 2.86e-493j | 
| -0.21635554412511755427 - 1.1725613093666391461e-1993j | 7.68e-509, 7.68e-509j | 
| -2.3506049736744922228 - 4.6619719628803131388e-1984j | 3.75e-498, 3.75e-498j | 
| -2.2676985561171093928e-2257 + 9.2135640011546222839e-2258j | 2.23e-2255, 2.23e-2255j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 5.5107612463002270157e-55 - 4.5357863683551147663e-1766j | 3.24e-160, 5.78e-403j | 
| 5.0277115770371718552e-38 + 1.1554915114136548673e-1754j | 1.46e-153, 2.61e-396j | 
| 7.3369832107140594762e-44 + 4.190313805378053703e-1760j | 3.05e-156, 5.45e-399j | 
| 8.0496857634547521438e-60 - 1.0498656786547892297e-1767j | 1.9e-163, 3.4e-406j | 
| 7.6056836012836606948e-51 + 7.3401818976597088791e-1764j | 6e-159, 1.07e-401j | 
| 7.9431202327205801377e-41 + 1.0018228151079082996e-1756j | 3.04e-155, 5.43e-398j | 
| 6.8332082082551728718e-23 - 1.555957338599764855e-1747j | 1.95e-145, 3.48e-388j | 
| 0.038758160319013020455 + 5.1640164744803206881e-1733j | 1.2e-80, 2.15e-323j | 
| 0.002927442002278737574 + 2.5528840573456502263e-1734j | 3.03e-100, 5.41e-343j | 
| 1.636600697359080156e-08 - 2.8029277205577467746e-1738j | 1.69e-126, 3.02e-369j | 
| 0.038758160319013020455 + 4.0516543463599429959e-1733j | 1.01e-81, 1.8e-324j | 
| 1.0173918129042983675e-30 - 1.2538968321239608641e-1751j | 8.99e-151, 1.61e-393j | 
| 0.0047887405644800797763 - 5.8583296732683039016e-1734j | 1.3e-97, 2.33e-340j | 
| 0.010180486966820036042 + 9.7621056341597038e-1734j | 3.54e-94, 6.32e-337j | 
| 5.4033803607296835869e-33 + 1.0119851896025506906e-1752j | 5.81e-152, 1.04e-394j | 
| 3.5472424892404193546e-47 - 6.8190788709783269352e-1762j | 1.03e-160, 1.84e-403j | 
| 6.3892055268482988795e-66 + 5.1950059887360887853e-1771j | 4.56e-168, 8.14e-411j | 
| 7.9431202327205801377e-41 - 1.857078369230466612e-1758j | 7.9e-159, 1.41e-401j | 
| 2.0128029335321979615e-35 - 1.6964896912182621874e-1755j | 2.5e-157, 4.47e-400j | 
| 1.0878515547341322243e-16 - 1.204855920842385444e-1744j | 6.51e-146, 1.16e-388j | 
| 1.3921882455570943928e-28 + 1.4979142865418842163e-1750j | 1.11e-152, 1.98e-395j | 
| 0.00052753150867431308205 + 1.5037721493714997166e-1735j | 6.31e-118, 1.13e-360j | 
| 1.1165638046236163131e-24 + 1.9195890962241756005e-1749j | 1.19e-152, 2.13e-395j | 
| 4.1425524721452930844e-18 + 7.9996744214501012716e-1745j | 2.1e-147, 3.75e-390j | 
| 8.0496857634547521438e-60 + 1.2291962952917191986e-1768j | 5.15e-168, 9.21e-411j | 
| 4.3346836662117232975e-14 - 5.8864436067537081615e-1743j | 9.26e-144, 1.65e-386j | 
| 1.4247919879896972185e-26 - 1.6625658164076525991e-1749j | 3.05e-152, 5.44e-395j | 
| 6.6651145203404667242e-13 + 1.3419938016016727807e-1741j | 2.17e-143, 3.88e-386j | 
| 1.2990768550954689013e-19 - 1.8882826287761691762e-1746j | 9.01e-150, 1.61e-392j | 
| 5.5107612463002270157e-55 + 4.7489951079493668201e-1765j | 1.75e-167, 3.13e-410j | 
| 3.5472424892404193546e-47 + 1.2163570514866985968e-1760j | 1.45e-164, 2.59e-407j | 
| 1.0173918129042983675e-30 - 7.0067404454816389779e-1753j | 1.32e-159, 2.36e-402j | 
| 7.3369832107140594762e-44 - 1.1270529934080419667e-1758j | 4.8e-163, 8.57e-406j | 
| 7.6056836012836606948e-51 - 9.7360904916914339463e-1763j | 2.52e-166, 4.51e-409j | 
| 1.1029189351314742533e-05 - 5.8911419879223045998e-1737j | 1.57e-136, 2.8e-379j | 
| 1.2990768550954689013e-19 - 1.0793018172193276416e-1745j | 1.67e-152, 2.99e-395j | 
| 0.0047887405644800797763 - 4.0022794052160655713e-1734j | 2.13e-123, 3.8e-366j | 
| 6.6651145203404667242e-13 + 3.8232894196757688453e-1742j | 9.83e-149, 1.76e-391j | 
| 5.7129499401271374237e-09 + 6.7266802980389971304e-1739j | 1.45e-143, 2.59e-386j | 
| 4.3980736060521185694e-07 - 2.3028431784142466602e-1737j | 3.36e-142, 6.01e-385j | 
| 5.4033803607296835869e-33 + 3.7587575287844509975e-1754j | 2.6e-162, 4.65e-405j | 
| 7.2301298005616728327e-08 + 1.3543640943322155745e-1737j | 1.16e-143, 2.07e-386j | 
| 2.0128029335321979615e-35 - 9.1529147179160947171e-1754j | 1.57e-160, 2.81e-403j | 
| 0.0014137480586794681255 - 5.0300292540028142694e-1735j | 2.69e-131, 4.81e-374j | 
| 0.00016663754356262415823 - 4.814457268274533685e-1736j | 2.07e-135, 3.7e-378j | 
| 6.3892055268482988795e-66 - 7.3695758561030817914e-1772j | 2.74e-178, 4.89e-421j | 
| 1.4247919879896972185e-26 - 1.5605472050910189342e-1750j | 2.07e-160, 3.7e-403j | 
| 3.3202285173649623982e-21 + 2.0910754171256068472e-1747j | 1.05e-157, 1.87e-400j | 
| 0.010180486966820036042 + 6.9453519600756327532e-1734j | 2.43e-130, 4.35e-373j | 
| 2.3407985775094274995e-06 + 2.2866981831812532816e-1737j | 1.18e-143, 2.1e-386j | 
| 1.1165638046236163131e-24 + 1.6997542774648953459e-1748j | 1.08e-160, 1.93e-403j | 
| -0.012329250865960376594 - 1.7877410142564296831e-1732j | 1.77e-127, 3.17e-370j | 
| 2.3735036306873136635e-15 + 8.6650336450610744424e-1744j | 4.97e-154, 8.88e-397j | 
| 6.8332082082551728718e-23 - 2.1090974081502719268e-1748j | 7.39e-159, 1.32e-401j | 
| 0.082820652211898959085 - 3.5008555706275922087e-1733j | 4.22e-130, 7.54e-373j | 
| 9.4880219116676970845e-11 + 4.5543955832997597677e-1740j | 3.11e-155, 5.55e-398j | 
| 0.021023446176933828063 - 1.6826911483930555176e-1733j | 5.52e-134, 9.85e-377j | 
| 5.7129499401271374237e-09 + 1.7632523945590887273e-1738j | 4.25e-153, 7.58e-396j | 
| 4.1425524721452930844e-18 + 1.5667612534906311953e-1745j | 1.37e-156, 2.45e-399j | 
| 1.3921882455570943928e-28 + 1.1202296984038471412e-1751j | 6.26e-163, 1.12e-405j | 
| 9.4880219116676970845e-11 + 1.5155851988541072219e-1740j | 2.43e-153, 4.33e-396j | 
| 4.5777542453768194457e-05 + 3.0941902671206747638e-1736j | 2.95e-150, 5.26e-393j | 
| 5.0277115770371718552e-38 + 6.289544892961363846e-1757j | 3.03e-168, 5.4e-411j | 
| 2.3735036306873136635e-15 + 3.6213376240911368674e-1743j | 4.52e-161, 8.08e-404j | 
| 1.1029189351314742533e-05 - 1.1810232671341429678e-1736j | 4.86e-152, 8.68e-395j | 
| 3.3202285173649623982e-21 + 1.3508526196011905091e-1746j | 2.57e-163, 4.59e-406j | 
| 4.3980736060521185694e-07 - 1.0181685580849052836e-1737j | 4.78e-152, 8.55e-395j | 
| 0.0014137480586794681255 - 8.0507496062231417285e-1735j | 3.7e-148, 6.61e-391j | 
| 0.068080405186430768737 + 1.6229647423486710099e-1732j | 1.46e-141, 2.61e-384j | 
| 8.6587287071912553257e-12 - 7.8198022057212709492e-1741j | 1.18e-158, 2.11e-401j | 
| 0.10357013340969829466 + 2.7769619212913911971e-1733j | 1.64e-143, 2.93e-386j | 
| 0.021023446176933828063 - 1.2552294099201242143e-1733j | 2.89e-144, 5.15e-387j | 
| 8.6010801868929104488e-10 - 9.8380119098806449295e-1740j | 7.27e-155, 1.3e-397j | 
| 0.082820652211898959085 - 4.0436732202720175604e-1733j | 2.36e-144, 4.21e-387j | 
| 0.00016663754356262415823 - 8.5934043518260850642e-1736j | 1.34e-151, 2.39e-394j | 
| 0.002927442002278737574 + 1.6746670064047077064e-1734j | 8.06e-148, 1.44e-390j | 
| 8.6587287071912553257e-12 - 2.4128980359368025901e-1741j | 1.96e-156, 3.49e-399j | 
| 8.6010801868929104488e-10 - 2.7529042818126443887e-1739j | 9.69e-158, 1.73e-400j | 
| 1.0878515547341322243e-16 - 5.5447031150407827702e-1744j | 1.03e-162, 1.85e-405j | 
| 4.3346836662117232975e-14 - 2.2484187290481585112e-1742j | 3.36e-161, 6e-404j | 
| 4.5777542453768194457e-05 + 1.6369035640026644901e-1736j | 5.38e-154, 9.68e-397j | 
| 0.11716713091098831958 - 2.6691423116283174884e-1733j | 1.66e-150, 3.01e-393j | 
| -0.012329250865960376594 - 1.4510236562180597208e-1732j | 3.92e-150, 7.05e-393j | 
| 1.636600697359080156e-08 - 6.9919343340399076563e-1738j | 3.27e-157, 5.83e-400j | 
| 0.10357013340969829466 + 3.0539104976552581307e-1733j | 1.56e-151, 2.89e-394j | 
| 2.3407985775094274995e-06 + 4.8679627310141668036e-1737j | 1.61e-156, 2.86e-399j | 
| 0.068080405186430768737 + 1.3345719213965434835e-1732j | 5.85e-151, 1.1e-393j | 
| 7.2301298005616728327e-08 + 5.6576917524995084122e-1738j | 3.5e-157, 6.27e-400j | 
| 0.11716713091098831958 - 2.7979757745260865773e-1733j | 2.18e-152, 4.19e-395j | 
| 0.00052753150867431308205 + 2.5387340279866851175e-1735j | 8.07e-155, 1.38e-397j | 
| 0.12169010664828899796 + 2.7081953654165588153e-1733j | 1.78e-152, 3.49e-395j | 
All rules of Hermite (physicists') type can be downloaded here packed into a single file.