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) | 
|---|---|
| -8.5518673286405291253 + 3.8919006353079945885e-1076j | 7.05e-489, 7.05e-489j | 
| -12.524069483433113627 + 1.5781203831980994326e-1100j | 5.35e-496, 5.35e-496j | 
| -11.436687132354313297 + 6.0431667914877527291e-1093j | 3.56e-493, 3.56e-493j | 
| -11.928492407974988071 - 1.4699053108737842436e-1096j | 2.18e-494, 2.18e-494j | 
| 7.3753751811590165898 - 7.1179876791832521513e-1099j | 1.56e-488, 1.56e-488j | 
| 4.9852846108943670023 + 2.2740948454806490306e-1101j | 2.63e-490, 2.63e-490j | 
| 11.928492407974988071 + 1.0032394102204653463e-1104j | 2.27e-494, 2.27e-494j | 
| 11.436687132354313297 + 1.3187027030852032681e-1103j | 3.48e-493, 3.48e-493j | 
| 10.595663892795050448 - 4.1137118423613672176e-1102j | 1.93e-491, 1.93e-491j | 
| 6.5470747839533992115 + 4.8157993569785668843e-1099j | 8.6e-489, 8.6e-489j | 
| -7.660659759668972115 - 1.4603839540946861396e-1097j | 1.53e-488, 1.53e-488j | 
| 9.1839200888488797118 - 4.0097443485668901739e-1111j | 2.1e-489, 2.1e-489j | 
| -10.998759398662108894 + 2.7870302212190238595e-1111j | 3.46e-492, 3.46e-492j | 
| -10.595663892795050448 + 7.2047604035714298956e-1110j | 1.93e-491, 1.93e-491j | 
| 10.217593037007864245 - 3.3221161069761336869e-1113j | 8.35e-491, 8.35e-491j | 
| 1.7394980379666080613 - 1.0162363984511059441e-1119j | 9.06e-499, 9.06e-499j | 
| -9.1839200888488797118 + 5.6553907790051575727e-1109j | 2e-489, 2e-489j | 
| -8.8633791087716304567 + 9.2835038176494614383e-1124j | 4.2e-489, 4.2e-489j | 
| 2.6519613568352334924 - 1.1866980932445598868e-1151j | 3.69e-495, 3.69e-495j | 
| 8.5518673286405291253 + 2.6214439433063803433e-1144j | 6.9e-489, 6.9e-489j | 
| 1.0442335424696797192 + 2.9455337528490171715e-1160j | 9.69e-504, 9.69e-504j | 
| 1.673551628767471445 + 1.6664288859739962314e-1155j | 4.05e-499, 4.05e-499j | 
| 6.8190111581038442899 + 5.6357438986354216014e-1144j | 1.17e-488, 1.17e-488j | 
| 5.2380310863000114008 - 2.2358585908634175473e-1149j | 5.57e-490, 5.57e-490j | 
| -1.4898159131061740308 - 1.1704318651229976675e-1166j | 9.89e-501, 9.89e-501j | 
| -2.1173675140549681161 - 2.0638281481530240715e-1163j | 1.67e-497, 1.67e-497j | 
| -10.217593037007864245 - 1.7853628237947173507e-1153j | 8.65e-491, 8.65e-491j | 
| 3.2536029059107203817 + 4.0580587853369963697e-1185j | 8.82e-494, 8.82e-494j | 
| 4.0720747256528713841 - 3.8327687655753839195e-1181j | 2.95e-491, 2.95e-491j | 
| -7.0949799493343667984 - 8.8136272453504262706e-1199j | 1.42e-488, 1.42e-488j | 
| 9.8586675581177959419 - 5.6963239395183137816e-1226j | 3.2e-490, 3.2e-490j | 
| -6.2788355628197208501 - 7.8441906490366053731e-1236j | 5.68e-489, 5.68e-489j | 
| 2.8065249276780741692 + 3.5719427975680538818e-1265j | 7.65e-495, 7.65e-495j | 
| 9.5150160619380533377 - 2.0921609117049761582e-1260j | 8.88e-490, 8.88e-490j | 
| -9.8586675581177959419 + 5.4151534219446142517e-1258j | 3.02e-490, 3.02e-490j | 
| -3.0233613236983110972 + 5.7433630124710270006e-1282j | 2.31e-494, 2.31e-494j | 
| 10.998759398662108894 + 1.6268609618675159827e-1280j | 3.22e-492, 3.22e-492j | 
| 3.0233613236983110972 - 8.7095669773548423379e-1283j | 2.17e-494, 2.17e-494j | 
| 8.8633791087716304567 + 3.5541136837692645566e-1275j | 4e-489, 4e-489j | 
| 5.7523706816452165333 + 7.3141676267330303352e-1277j | 1.94e-489, 1.94e-489j | 
| -6.8190111581038442899 + 7.6263227070283687212e-1284j | 1.14e-488, 1.14e-488j | 
| 12.524069483433113627 + 5.2525657306042898082e-1318j | 5.04e-496, 5.04e-496j | 
| 7.951380277917401354 - 4.6727025200472692787e-1311j | 1.28e-488, 1.28e-488j | 
| 0.81628788285896466304 + 6.0792150757288398893e-1327j | 3.3e-505, 3.3e-505j | 
| -6.5470747839533992115 - 1.6748445188744158869e-1308j | 8.51e-489, 8.51e-489j | 
| -1.2699316830802473781 + 4.116483327177748712e-1338j | 2.83e-502, 2.83e-502j | 
| -3.7192004394924598711 - 1.1751784898540762442e-1327j | 2.23e-492, 2.23e-492j | 
| -1.673551628767471445 + 1.7705262298865824683e-1335j | 3.56e-499, 3.56e-499j | 
| -4.2577189094428827413 - 1.93300208235941025e-1324j | 4.55e-491, 4.55e-491j | 
| 4.4911890799880322366 - 1.4010511971967306534e-1332j | 6.83e-491, 6.83e-491j | 
| -5.2380310863000114008 - 1.9642675500593447348e-1329j | 5.54e-490, 5.54e-490j | 
| 3.7192004394924598711 + 1.2844055095723867493e-1353j | 2.53e-492, 2.53e-492j | 
| 6.0140110816778574158 - 9.7152555436895410922e-1350j | 3.74e-489, 3.74e-489j | 
| -9.5150160619380533377 + 7.6901403883927614409e-1352j | 8.99e-490, 8.99e-490j | 
| 4.2577189094428827413 + 2.9836827009743443327e-1372j | 4.17e-491, 4.17e-491j | 
| 3.4873713796303588746 - 2.4634353291747983373e-1374j | 4.25e-493, 4.25e-493j | 
| -0.81628788285896466304 + 1.62970958444278345e-1385j | 3.27e-505, 3.27e-505j | 
| -3.4873713796303588746 + 4.106338661480002483e-1369j | 4.23e-493, 4.23e-493j | 
| 2.5162773474088356726 - 1.3138042773798685629e-1377j | 1.01e-495, 1.01e-495j | 
| 5.49374175842300534 - 1.5804842593237919239e-1371j | 1.13e-489, 1.13e-489j | 
| 2.3187675483450310393 + 2.0548226374022936409e-1378j | 1.13e-496, 1.13e-496j | 
| -3.928763082007146568 + 8.1534598876231111304e-1370j | 1.27e-491, 1.27e-491j | 
| -7.3753751811590165898 - 3.9818715702467171218e-1390j | 1.47e-488, 1.47e-488j | 
| 0.58797718851878777266 - 9.3996597475250145073e-1431j | 1.18e-506, 1.18e-506j | 
| 8.2481878423113978166 - 1.0784199802587692549e-1411j | 1.01e-488, 1.01e-488j | 
| 7.660659759668972115 - 1.5672388626215640192e-1411j | 1.58e-488, 1.58e-488j | 
| -4.7358707020660293007 - 1.6603864341650407068e-1415j | 1.29e-490, 1.29e-490j | 
| -2.8065249276780741692 - 3.6820249605016619651e-1436j | 8.1e-495, 8.1e-495j | 
| -1.7394980379666080613 + 1.7589992056041246902e-1440j | 8.94e-499, 8.94e-499j | 
| 7.0949799493343667984 - 2.2341116544123625859e-1431j | 1.4e-488, 1.4e-488j | 
| 1.2699316830802473781 + 1.5735349796736549655e-1444j | 2.83e-502, 2.83e-502j | 
| -3.2536029059107203817 - 6.9206433354732011656e-1431j | 8.32e-494, 8.32e-494j | 
| -1.0442335424696797192 - 1.0799490411380854771e-1459j | 1.01e-503, 1.01e-503j | 
| -0.58797718851878777266 - 1.0273726662355605398e-1462j | 1.21e-506, 1.21e-506j | 
| -5.49374175842300534 - 7.7902896004388544227e-1445j | 1.04e-489, 1.04e-489j | 
| 4.7358707020660293007 - 1.5484489115685993889e-1470j | 1.39e-490, 1.39e-490j | 
| 1.920961046345861026 + 7.3300894255009687051e-1478j | 2.66e-498, 2.66e-498j | 
| 3.928763082007146568 + 2.3978622756517957303e-1471j | 1.34e-491, 1.34e-491j | 
| -2.3187675483450310393 - 7.0319938135300404876e-1476j | 1.12e-496, 1.12e-496j | 
| -4.4911890799880322366 - 9.0713294614260205584e-1469j | 6.78e-491, 6.78e-491j | 
| 2.1173675140549681161 - 4.2394530454737149367e-1497j | 1.58e-497, 1.58e-497j | 
| -8.2481878423113978166 + 2.3224049152851238001e-1486j | 9.95e-489, 9.95e-489j | 
| 6.2788355628197208501 - 4.2197899899508743254e-1514j | 5.55e-489, 5.55e-489j | 
| -1.920961046345861026 + 1.3462165253606617159e-1523j | 2.55e-498, 2.55e-498j | 
| -2.5162773474088356726 - 1.4777630662404105081e-1521j | 9.9e-496, 9.9e-496j | 
| -6.0140110816778574158 - 4.0002983899310044496e-1513j | 3.39e-489, 3.39e-489j | 
| 1.4898159131061740308 + 3.3237390339160034818e-1543j | 1.08e-500, 1.08e-500j | 
| 0.14831483504099866421 + 6.6574203984214062126e-1551j | 3.03e-509, 3.03e-509j | 
| -7.951380277917401354 + 4.3145747596521676541e-1529j | 1.25e-488, 1.25e-488j | 
| -4.0720747256528713841 + 4.7324966854482036954e-1545j | 2.76e-491, 2.76e-491j | 
| -5.7523706816452165333 + 1.4237907525296231079e-1542j | 2e-489, 2e-489j | 
| 3.7490297567622166421e-1603 - 1.1115879168904803223e-1602j | 1.14e-1600, 1.14e-1600j | 
| 0.36182369793669724678 + 2.1406372847278486555e-1571j | 5.87e-508, 5.87e-508j | 
| -0.14831483504099866421 + 1.8761192944088922277e-1572j | 3.03e-509, 3.03e-509j | 
| -0.36182369793669724678 - 5.7863095616557604213e-1572j | 6.03e-508, 6.03e-508j | 
| -4.9852846108943670023 - 4.5361125157712934557e-1552j | 2.81e-490, 2.81e-490j | 
| -2.6519613568352334924 + 1.0808499158902350643e-1574j | 3.63e-495, 3.63e-495j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 3.001050575339669083e-33 + 1.1350429389020829681e-1107j | 2.56e-138, 1.83e-380j | 
| 2.9482376670899609285e-69 - 7.3468403363621972252e-1129j | 1.47e-154, 1.05e-396j | 
| 4.0718908682549253542e-58 - 8.8731131931220339592e-1123j | 3.94e-151, 2.81e-393j | 
| 4.7922936278680514267e-63 + 1.7448591735614945499e-1125j | 1.15e-152, 8.22e-395j | 
| 3.7921519419377724184e-25 + 3.7151029064191316021e-1105j | 2.43e-137, 1.73e-379j | 
| 2.2796794035808725979e-12 - 1.0415308807779329291e-1096j | 8.07e-122, 5.75e-364j | 
| 4.7922936278680514267e-63 - 2.876773318986719552e-1126j | 1.61e-157, 1.15e-399j | 
| 4.0718908682549253542e-58 + 1.2805994905765936743e-1123j | 7.2e-156, 5.13e-398j | 
| 3.8403672989995792476e-50 + 2.6917340034845133083e-1119j | 3.29e-153, 2.35e-395j | 
| 3.6911954006221127703e-20 - 4.3502697410885746902e-1102j | 4.57e-135, 3.26e-377j | 
| 5.2941099596424257697e-27 - 5.2989030939467526875e-1105j | 2.7e-142, 1.92e-384j | 
| 4.3024378677206385989e-38 + 1.2313697129486789988e-1112j | 2.64e-148, 1.88e-390j | 
| 6.8426064004231168227e-54 + 1.96688046478288258e-1120j | 4.94e-155, 3.52e-397j | 
| 3.8403672989995792476e-50 - 2.5217803853604491415e-1118j | 4.44e-154, 3.16e-396j | 
| 9.4830529563616453189e-47 - 1.935332363092296517e-1117j | 1.52e-153, 1.09e-395j | 
| 0.0034420784441346515422 - 5.6918817566453597188e-1088j | 1.61e-93, 1.15e-335j | 
| 4.3024378677206385989e-38 - 3.4552988035355769333e-1111j | 7.75e-150, 5.52e-392j | 
| 1.3579662772949004542e-35 + 1.7678091240034466335e-1109j | 1.98e-148, 1.41e-390j | 
| 5.5157274152903263036e-05 + 1.1603226610355092991e-1089j | 1.96e-110, 1.4e-352j | 
| 3.001050575339669083e-33 + 6.8287955085784697394e-1110j | 8.38e-149, 5.97e-391j | 
| 0.043076319905983359913 - 1.2926769184250695616e-1088j | 1.19e-81, 8.45e-324j | 
| 0.0034936719076039939606 + 6.1280586811919324746e-1088j | 2.45e-95, 1.74e-337j | 
| 9.8805956081350559859e-22 + 4.4988068338501139987e-1103j | 8.04e-141, 5.73e-383j | 
| 1.7416752753847846357e-13 + 1.4452300476378761885e-1097j | 6.54e-133, 4.66e-375j | 
| 0.013128070614597435143 - 3.2516979406668113923e-1088j | 4.18e-96, 2.98e-338j | 
| 0.0012630749872770524089 - 9.6601492533808360699e-1089j | 1.14e-107, 8.16e-350j | 
| 9.4830529563616453189e-47 + 2.180739836153557322e-1116j | 2.15e-155, 1.53e-397j | 
| 3.3189557892088967168e-06 - 1.4092158262428592497e-1091j | 1.39e-119, 9.92e-362j | 
| 5.0068677647842951028e-09 - 2.6436956126915893953e-1093j | 1.98e-126, 1.41e-368j | 
| 2.1567808983795420237e-23 - 4.5975910700052136737e-1103j | 3.51e-146, 2.5e-388j | 
| 1.2187314712167533036e-43 + 9.9956536636399453039e-1116j | 9.63e-155, 6.86e-397j | 
| 1.1365172403660697743e-18 + 2.5472033871337791756e-1100j | 4.15e-144, 2.96e-386j | 
| 4.2795467650055482692e-05 - 3.5459659257466816302e-1090j | 3.39e-117, 2.41e-359j | 
| 9.1193057657073426616e-41 - 3.9346625785457527097e-1114j | 1.46e-153, 1.04e-395j | 
| 1.2187314712167533036e-43 - 1.408213178566771897e-1114j | 3.47e-156, 2.48e-398j | 
| 1.369942325433765542e-05 + 1.3239374140870976955e-1090j | 1.34e-125, 9.54e-368j | 
| 6.8426064004231168227e-54 - 2.461682829449426729e-1121j | 5.09e-160, 3.63e-402j | 
| 1.369942325433765542e-05 + 6.3233273085013888321e-1091j | 8.16e-122, 5.81e-364j | 
| 1.3579662772949004542e-35 - 3.1621336461096181248e-1111j | 1.11e-151, 7.91e-394j | 
| 6.2500088993251097073e-16 + 2.6030867166065692247e-1099j | 1.93e-140, 1.37e-382j | 
| 9.8805956081350559859e-22 + 3.9905569979895437289e-1102j | 7.44e-149, 5.3e-391j | 
| 2.9482376670899609285e-69 + 1.3846660898270027024e-1129j | 1.64e-168, 1.17e-410j | 
| 5.7705793689224668979e-29 + 2.0419049582217438977e-1107j | 1.51e-149, 1.07e-391j | 
| 0.066187468187488072369 + 1.3871264585033859409e-1088j | 2.42e-104, 1.72e-346j | 
| 3.6911954006221127703e-20 - 3.2763724690085644374e-1101j | 3.06e-148, 2.18e-390j | 
| 0.025159670016353841084 + 1.9626225929180847598e-1088j | 1.54e-110, 1.09e-352j | 
| 1.2608537732623687696e-07 - 3.330118837763983432e-1092j | 5.27e-137, 3.76e-379j | 
| 0.0034936719076039939606 + 9.1100743474052972589e-1088j | 1.58e-117, 1.13e-359j | 
| 1.6698609581812671811e-09 + 1.4371808213856518791e-1093j | 1.69e-140, 1.2e-382j | 
| 2.3637792597722458433e-10 - 5.7804943632853517437e-1095j | 1e-137, 7.14e-380j | 
| 1.7416752753847846357e-13 + 6.0140496046569894762e-1097j | 4.85e-146, 3.46e-388j | 
| 1.2608537732623687696e-07 - 1.3114877489295144289e-1092j | 7.33e-134, 5.22e-376j | 
| 2.9107343684241364442e-17 - 3.279679055472656657e-1100j | 5.45e-145, 3.88e-387j | 
| 9.1193057657073426616e-41 + 7.3806970336221164122e-1113j | 9.01e-161, 6.42e-403j | 
| 1.6698609581812671811e-09 + 4.8178509731300704958e-1094j | 1.02e-136, 7.29e-379j | 
| 6.9000416589348631216e-07 + 3.8332593170972500279e-1092j | 5.97e-133, 4.26e-375j | 
| 0.066187468187488072369 + 1.6798762203035456892e-1088j | 5.55e-118, 3.96e-360j | 
| 6.9000416589348631216e-07 + 9.1123626939136813155e-1092j | 1.06e-139, 7.54e-382j | 
| 0.0001801905302594343597 - 1.8990004320896905535e-1089j | 2.17e-128, 1.55e-370j | 
| 1.1326748644578494764e-14 - 1.9724732303472833336e-1098j | 6.65e-143, 4.74e-385j | 
| 0.00053166431562532378121 + 2.8837950386328974141e-1089j | 3.3e-128, 2.35e-370j | 
| 1.9858977113191403874e-08 + 1.6505226564783582231e-1092j | 1.89e-142, 1.35e-384j | 
| 3.7921519419377724184e-25 + 5.0294721529646641802e-1104j | 2.23e-155, 1.59e-397j | 
| 0.090975535157811571018 - 1.7403224327448104442e-1088j | 6.32e-122, 4.5e-364j | 
| 4.8140073216401111735e-31 - 1.2647955713377296845e-1108j | 1.01e-154, 7.17e-397j | 
| 5.2941099596424257697e-27 - 2.9128232254287999009e-1106j | 9.6e-153, 6.84e-395j | 
| 2.5371542862823302319e-11 + 2.6364503456845901059e-1095j | 1.75e-148, 1.25e-390j | 
| 4.2795467650055482692e-05 - 7.0102822601876006968e-1090j | 1.53e-139, 1.09e-381j | 
| 0.0034420784441346515422 - 8.5986581586753983651e-1088j | 2.56e-132, 1.83e-374j | 
| 2.1567808983795420237e-23 - 4.2808447517283017611e-1104j | 2.4e-151, 1.71e-393j | 
| 0.025159670016353841084 + 1.4550991525175027253e-1088j | 2.61e-129, 1.86e-371j | 
| 3.3189557892088967168e-06 - 3.1399821079894440843e-1091j | 1.94e-141, 1.38e-383j | 
| 0.043076319905983359913 - 1.6522726675630340227e-1088j | 3.75e-130, 2.67e-372j | 
| 0.090975535157811571018 - 1.9972998327634973793e-1088j | 5.84e-130, 4.16e-372j | 
| 1.1326748644578494764e-14 - 9.059336280355795764e-1098j | 6.03e-152, 4.29e-394j | 
| 2.5371542862823302319e-11 + 7.5714057592152935155e-1096j | 4.46e-143, 3.18e-385j | 
| 0.0027561255034160460408 + 1.442879079036505405e-1088j | 9.49e-134, 6.76e-376j | 
| 1.9858977113191403874e-08 + 6.1139045474977150933e-1093j | 7e-140, 4.99e-382j | 
| 0.00053166431562532378121 + 5.0293889124224031234e-1089j | 5.8e-139, 4.14e-381j | 
| 2.3637792597722458433e-10 - 1.856717263307172807e-1094j | 5.96e-148, 4.24e-390j | 
| 0.0012630749872770524089 - 5.8259312402616544757e-1089j | 3.55e-135, 2.53e-377j | 
| 4.8140073216401111735e-31 - 6.9970598394058164185e-1107j | 6.07e-162, 4.33e-404j | 
| 1.1365172403660697743e-18 + 3.9039782910729999711e-1101j | 6.86e-150, 4.88e-392j | 
| 0.0027561255034160460408 + 2.2788777758714568604e-1088j | 2.34e-138, 1.66e-380j | 
| 0.0001801905302594343597 - 3.4824120902195028251e-1089j | 3.48e-141, 2.48e-383j | 
| 2.9107343684241364442e-17 - 1.8823527299489795221e-1099j | 8.39e-155, 5.98e-397j | 
| 0.013128070614597435143 - 2.2868335409454504615e-1088j | 3.49e-138, 2.49e-380j | 
| 0.10746198946079547541 - 5.1213593262911325321e-1088j | 1.73e-139, 1.23e-381j | 
| 5.7705793689224668979e-29 + 5.6117884763728654715e-1106j | 2.56e-161, 1.83e-403j | 
| 5.0068677647842951028e-09 - 7.4498672553614775602e-1093j | 6.85e-148, 4.89e-390j | 
| 6.2500088993251097073e-16 + 1.3300666745115752548e-1098j | 3.64e-154, 2.59e-396j | 
| 0.063434508115495452349 + 7.0527474697728085394e-1088j | 1.42e-141, 1.01e-383j | 
| 0.11051107290059515782 + 2.6271399353427927278e-1088j | 1.32e-141, 9.38e-384j | 
| 0.10746198946079547541 - 5.3021337224154073225e-1088j | 3.9e-142, 2.77e-384j | 
| 0.11051107290059515782 + 2.8592660458409894433e-1088j | 1.63e-142, 1.15e-384j | 
| 2.2796794035808725979e-12 - 3.9531851350747070356e-1096j | 2.82e-152, 2.03e-394j | 
| 5.5157274152903263036e-05 + 2.2034344913702680755e-1089j | 3.77e-145, 2.64e-387j | 
All rules of Hermite (physicists') type can be downloaded here packed into a single file.