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) | 
|---|---|
| 9.1075488611794088727 + 1.0082408410287642091e-1164j | 1.16e-488, 1.16e-488j | 
| -10.829272813534168045 + 1.2425878549550138239e-1181j | 5.41e-491, 5.41e-491j | 
| 8.2013547208892816223 - 2.9442086003083652202e-1178j | 4.23e-488, 4.23e-488j | 
| -9.7551273750832167558 - 2.560650431570647592e-1190j | 2.46e-489, 2.46e-489j | 
| -10.453442084393811949 + 9.4650004135364397168e-1192j | 2.45e-490, 2.45e-490j | 
| 10.829272813534168045 + 2.1982285174328570455e-1188j | 5.36e-491, 5.36e-491j | 
| 11.665452867466220216 - 8.959706558338862814e-1196j | 9.26e-493, 9.26e-493j | 
| -10.096678365124808763 - 3.8819716062804604085e-1201j | 8.64e-490, 8.64e-490j | 
| -12.746861799264025423 - 1.0856131413285476778e-1205j | 1.21e-495, 1.21e-495j | 
| -6.5392302982875889753 - 6.666581927221840043e-1197j | 2.19e-488, 2.19e-488j | 
| 1.7320508075688772935 + 2.9925496879562103176e-1210j | 1.19e-499, 1.19e-499j | 
| -11.230022720039603436 - 1.4277034598970303173e-1202j | 9.07e-492, 9.07e-492j | 
| -1.593468243410359475 + 4.1578323406707789533e-1211j | 1.91e-500, 1.91e-500j | 
| 7.912498089705349314 - 2.6877400559954396134e-1198j | 5.01e-488, 5.01e-488j | 
| -9.1075488611794088727 + 1.0089260187391677113e-1209j | 1.22e-488, 1.22e-488j | 
| -12.154516367570292414 + 9.0392954418436203005e-1217j | 5.55e-494, 5.55e-494j | 
| 5.5029020033299973065 + 6.4988568490387050621e-1209j | 2.49e-489, 2.49e-489j | 
| -8.4962623493192049594 + 1.823459611325768505e-1214j | 3.25e-488, 3.25e-488j | 
| -0.7071067811865475244 + 7.3325407306481450376e-1232j | 1.04e-505, 1.04e-505j | 
| -5.7579306028387025229 - 2.2345748144496088815e-1215j | 4.8e-489, 4.8e-489j | 
| 3.1427583224059007146 + 3.3026989516058636423e-1219j | 1.17e-493, 1.17e-493j | 
| 0.93157368698506392525 + 5.3142770196326690161e-1230j | 1.7e-504, 1.7e-504j | 
| 12.746861799264025423 - 4.7125288615345657244e-1221j | 1.26e-495, 1.26e-495j | 
| -4.0108807365021198406 + 3.8796742777869246568e-1218j | 1.94e-491, 1.94e-491j | 
| 10.096678365124808763 - 6.6618175090541471749e-1213j | 8.77e-490, 8.77e-490j | 
| -2.7800675753189594109 - 6.6086236911583593019e-1228j | 3.07e-495, 3.07e-495j | 
| 1.3838640636386493628 - 5.064814859000945364e-1234j | 7.71e-502, 7.71e-502j | 
| -3.6749852443872490457 + 2.8232739902692804649e-1222j | 1.91e-490, 1.91e-490j | 
| 10.453442084393811949 - 3.1435382467166972525e-1219j | 2.51e-490, 2.51e-490j | 
| 9.7551273750832167558 + 2.0810481610524387591e-1235j | 2.54e-489, 2.54e-489j | 
| 4.9996676859815507075 - 1.5990262074210012054e-1272j | 5.01e-490, 5.01e-490j | 
| 6.2758587585066707489 - 8.9455699079074547027e-1320j | 1.5e-488, 1.5e-488j | 
| 12.154516367570292414 + 1.0495198560463314832e-1362j | 5.45e-494, 5.45e-494j | 
| 5.2502146713148472345 - 3.6830431706376237481e-1429j | 1.09e-489, 1.09e-489j | 
| 7.3504220508398602665 - 6.7975402275576715478e-1480j | 5.03e-488, 5.03e-488j | 
| 2.5607755625350494119 - 1.8018345669240557187e-1513j | 2.79e-496, 2.79e-496j | 
| -4.2580918938723234208 + 3.342653230739996052e-1512j | 3.73e-491, 3.73e-491j | 
| 1.1587454282597314315 - 4.162039960250336616e-1536j | 3.36e-503, 3.36e-503j | 
| 6.8058994400492685949 - 8.8463446745555620922e-1533j | 3.14e-488, 3.14e-488j | 
| -1.1587454282597314315 - 3.2034444356897401e-1570j | 3.25e-503, 3.25e-503j | 
| -2.9734984797723849738 - 6.8932116184771536542e-1562j | 2.56e-494, 2.56e-494j | 
| -8.7980071385385987822 + 5.7170010636505896402e-1554j | 2.01e-488, 2.01e-488j | 
| 6.5392302982875889753 - 3.3385413327184988742e-1563j | 2.31e-488, 2.31e-488j | 
| 3.3458138508944375668 + 1.1525527234997167787e-1582j | 5.99e-493, 5.99e-493j | 
| -6.8058994400492685949 - 4.4545290875413665265e-1578j | 3.11e-488, 3.11e-488j | 
| 2.7800675753189594109 - 4.044296636462361623e-1585j | 3.3e-495, 3.3e-495j | 
| -5.5029020033299973065 + 1.0476923293143501419e-1580j | 2.34e-489, 2.34e-489j | 
| -7.6290380015512510669 - 6.0900351020316430241e-1578j | 5.24e-488, 5.24e-488j | 
| -8.2013547208892816223 + 1.8112626874316395531e-1579j | 4.27e-488, 4.27e-488j | 
| 4.2580918938723234208 + 1.1785314183323958956e-1580j | 4e-491, 4e-491j | 
| -0.93157368698506392525 - 1.2996088461080043285e-1594j | 1.63e-504, 1.63e-504j | 
| -3.7045500301318508604 - 2.0853599246866653196e-1581j | 1.34e-490, 1.34e-490j | 
| -6.0155080728209515942 + 6.8085350836355183156e-1579j | 8.8e-489, 8.8e-489j | 
| -11.665452867466220216 + 1.0968155185919008786e-1584j | 9.83e-493, 9.83e-493j | 
| -9.4260819061892751299 + 2.0958778373333529339e-1579j | 6.05e-489, 6.05e-489j | 
| -1.8904601289672687258 - 1.4428382382859349324e-1590j | 5.52e-499, 5.52e-499j | 
| -4.7510451839247759756 + 7.2290763902834866657e-1581j | 2.15e-490, 2.15e-490j | 
| 5.7579306028387025229 - 3.8022108993452305876e-1577j | 4.92e-489, 4.92e-489j | 
| -7.0761783342754597201 - 5.9330347042890991153e-1583j | 4.25e-488, 4.25e-488j | 
| 0.51198835281687566252 - 1.5341441838790325269e-1600j | 1.71e-506, 1.71e-506j | 
| 8.7980071385385987822 - 8.8885503462088282933e-1581j | 2.09e-488, 2.09e-488j | 
| 9.4260819061892751299 - 2.4681135475969739895e-1585j | 6.1e-489, 6.1e-489j | 
| -0.51198835281687566252 - 1.4870797961303053088e-1610j | 1.77e-506, 1.77e-506j | 
| 3.7045500301318508604 - 5.0293281684754108762e-1595j | 1.38e-490, 1.38e-490j | 
| 8.4962623493192049594 - 2.0725810557423412352e-1590j | 3.2e-488, 3.2e-488j | 
| -7.3504220508398602665 - 1.0169986236643673709e-1603j | 4.77e-488, 4.77e-488j | 
| -4.5040545022880217428 + 6.5522797134327770621e-1614j | 9.06e-491, 9.06e-491j | 
| 6.0155080728209515942 - 7.0308723165221904936e-1610j | 8.54e-489, 8.54e-489j | 
| -2.5607755625350494119 + 1.0400572000111671895e-1638j | 2.77e-496, 2.77e-496j | 
| 3.6749852443872490457 + 3.5307291732040175263e-1630j | 1.92e-490, 1.92e-490j | 
| 2.1073815878368520694 - 5.2348893930628494614e-1642j | 3.43e-498, 3.43e-498j | 
| 7.6290380015512510669 + 2.5372081666998387207e-1631j | 5.13e-488, 5.13e-488j | 
| -4.9996676859815507075 - 1.0542772667414848863e-1647j | 4.76e-490, 4.76e-490j | 
| -3.1427583224059007146 - 1.9734135977465358813e-1650j | 1.15e-493, 1.15e-493j | 
| 11.230022720039603436 - 1.5663265131740195762e-1643j | 8.51e-492, 8.51e-492j | 
| 2.3340614410930684954 + 4.9235675669082929599e-1657j | 2.93e-497, 2.93e-497j | 
| 7.0761783342754597201 + 3.1221442609788511551e-1646j | 4.23e-488, 4.23e-488j | 
| -3.3458138508944375668 + 1.6017584467852401743e-1661j | 5.9e-493, 5.9e-493j | 
| -1.3838640636386493628 - 3.0634935126610779015e-1670j | 8.2e-502, 8.2e-502j | 
| -3.6336683685012485862 + 1.8990498470453463639e-1659j | 6.89e-491, 6.89e-491j | 
| 1.8904601289672687258 - 5.4219816336396327447e-1667j | 5.15e-499, 5.15e-499j | 
| 2.9734984797723849738 - 1.9243926014592590668e-1662j | 2.59e-494, 2.59e-494j | 
| -7.912498089705349314 + 4.3885706844133971571e-1658j | 5e-488, 5e-488j | 
| -0.22276080049681409405 + 1.2077482688620842852e-1676j | 1.02e-508, 1.02e-508j | 
| -2.1073815878368520694 - 8.2978377665387901341e-1667j | 3.5e-498, 3.5e-498j | 
| -5.2502146713148472345 - 3.5286456368144275594e-1658j | 1.11e-489, 1.11e-489j | 
| 0.7071067811865475244 - 1.0840011882254167624e-1673j | 1.2e-505, 1.2e-505j | 
| 1.593468243410359475 + 8.3699587161817705525e-1669j | 1.79e-500, 1.79e-500j | 
| -6.2758587585066707489 + 2.4631976324282674958e-1658j | 1.45e-488, 1.45e-488j | 
| -0.41183732575728475763 + 3.2713824189672959778e-1675j | 3.17e-507, 3.17e-507j | 
| 4.5040545022880217428 - 1.7930882362698667926e-1658j | 8.98e-491, 8.98e-491j | 
| 3.6336683685012485862 - 3.4515667909972843515e-1660j | 6.83e-491, 6.83e-491j | 
| 0.41183732575728475763 - 1.6111060754274501104e-1675j | 3.17e-507, 3.17e-507j | 
| -1.29899989308548045e-1729 - 2.0923007913801351608e-1729j | 2.44e-1727, 2.44e-1727j | 
| -2.3340614410930684954 + 1.057389660019447795e-1665j | 2.85e-497, 2.85e-497j | 
| -1.7320508075688772935 - 9.8105607784718031523e-1669j | 1.16e-499, 1.16e-499j | 
| 0.22276080049681409405 + 2.5468600056916541146e-1723j | 1.02e-508, 1.02e-508j | 
| 4.0108807365021198406 + 3.180734952774160371e-1659j | 1.87e-491, 1.87e-491j | 
| 4.7510451839247759756 - 2.1145112566419162062e-1659j | 2.29e-490, 2.29e-490j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 1.6767964394761047928e-37 - 1.7015457414972137293e-1200j | 6.68e-139, 9.79e-379j | 
| 2.5594450394246330659e-52 + 7.4825782646452448625e-1211j | 1.18e-146, 1.73e-386j | 
| 1.0112184014124114968e-30 + 1.153704379474322691e-1197j | 3.65e-135, 5.34e-375j | 
| 8.8676599600525200927e-43 - 1.1367453049795136102e-1205j | 8.6e-143, 1.26e-382j | 
| 7.1953776462791016264e-49 - 5.4605722798593989264e-1209j | 1.99e-145, 2.91e-385j | 
| 2.5594450394246330659e-52 - 8.6645032918096204643e-1210j | 1.06e-148, 1.56e-388j | 
| 2.0516429766997323341e-60 - 2.7855268716235879602e-1214j | 4.61e-152, 6.76e-392j | 
| 1.0484416721113395817e-45 + 2.8566495686790883705e-1207j | 1.57e-144, 2.31e-384j | 
| 1.0521637729265030645e-71 + 3.5137343516277547209e-1221j | 1.6e-156, 2.35e-396j | 
| 4.0135293218232484271e-20 + 1.0767624022507220068e-1192j | 1.7e-131, 2.49e-371j | 
| 0.003196786906909953437 + 1.6720673465243722491e-1179j | 1.89e-82, 2.77e-322j | 
| 3.9822883766972640697e-56 - 6.7264318470333244821e-1213j | 5.01e-150, 7.34e-390j | 
| 0.0082709911224594815656 - 1.2926685789910414879e-1179j | 7.65e-81, 1.12e-320j | 
| 1.0416782486547731039e-28 - 1.2242101000407735176e-1196j | 5.2e-140, 7.62e-380j | 
| 1.6767964394761047928e-37 - 9.2813921626502185989e-1203j | 7.24e-143, 1.06e-382j | 
| 2.0612648742488581491e-65 - 7.5243693591278876226e-1218j | 1.5e-154, 2.2e-394j | 
| 1.010841502193585849e-14 + 1.3408032636705126923e-1188j | 1.04e-129, 1.53e-369j | 
| 7.5113800283787913903e-33 - 3.7404153180771761584e-1200j | 3.13e-141, 4.58e-381j | 
| 0.075262154453923946963 - 4.5804655192728680289e-1179j | 3.26e-86, 4.78e-326j | 
| 5.7759192865390872026e-16 - 4.826077103297591238e-1190j | 1.41e-129, 2.06e-369j | 
| 5.2022534168331593179e-06 - 1.6012769484099145433e-1181j | 4.64e-111, 6.81e-351j | 
| 0.053724040181747627377 + 2.6506258154960616089e-1179j | 3.14e-87, 4.6e-327j | 
| 1.0521637729265030645e-71 - 2.1100299638443433925e-1220j | 3.21e-162, 4.71e-402j | 
| 1.456802580685757253e-08 + 3.4069001793081405072e-1184j | 1.32e-119, 1.94e-359j | 
| 1.0484416721113395817e-45 - 5.5462653983316122274e-1206j | 5.81e-152, 8.52e-392j | 
| 5.2309664489915798394e-05 - 2.0969717464162006868e-1181j | 5.41e-109, 7.94e-349j | 
| 0.018437380681619400988 + 1.5433607071455772499e-1179j | 2.02e-87, 2.97e-327j | 
| -2.2161585318034032876e-06 + 1.8225519238024169141e-1181j | 1.44e-117, 2.11e-357j | 
| 7.1953776462791016264e-49 + 7.9363060219220993957e-1208j | 2.11e-153, 3.1e-393j | 
| 8.8676599600525200927e-43 + 3.3111133538501365147e-1204j | 5.65e-151, 8.28e-391j | 
| 1.9618065064568072595e-12 + 4.796677843890699041e-1187j | 1.82e-131, 2.67e-371j | 
| 1.1591145678454884507e-18 - 4.7683268992780232735e-1191j | 8.46e-139, 1.24e-378j | 
| 2.0612648742488581491e-65 + 5.2505854355905258636e-1217j | 7.21e-162, 1.06e-401j | 
| 1.516654245622667485e-13 - 8.1108410276208244919e-1188j | 3.44e-133, 5.04e-373j | 
| 5.3521392863127632101e-25 - 1.1665469439735375516e-1194j | 6.18e-144, 9.06e-384j | 
| 0.00017999514162850277089 + 6.0715366500851558359e-1181j | 1.52e-115, 2.22e-355j | 
| 1.8526994105183936343e-09 - 3.968110321031683273e-1185j | 1.22e-130, 1.79e-370j | 
| 0.033437083827080095737 - 1.7774106929733648095e-1179j | 3.84e-95, 5.62e-335j | 
| 1.1577142575324093617e-21 - 8.4898884332251125678e-1193j | 6.72e-142, 9.85e-382j | 
| 0.033437083827080095737 - 1.3761818841035631546e-1179j | 1.76e-96, 2.59e-336j | 
| 1.4163101883845628971e-05 + 1.4201980612703766593e-1181j | 4.72e-121, 6.92e-361j | 
| 4.1672964960251239027e-35 + 2.0141390031607323834e-1201j | 3.65e-152, 5.35e-392j | 
| 4.0135293218232484271e-20 + 6.5598807557954595094e-1192j | 8.41e-141, 1.23e-380j | 
| 1.7452665279993149552e-06 + 6.7361069898808494783e-1182j | 6.16e-125, 9.03e-365j | 
| 1.1577142575324093617e-21 - 1.2279391887649863287e-1193j | 6.24e-146, 9.15e-386j | 
| 5.2309664489915798394e-05 - 3.9396395932983205863e-1181j | 7.41e-121, 1.09e-360j | 
| 1.010841502193585849e-14 + 3.3079898191829814052e-1189j | 2.77e-140, 4.05e-380j | 
| 8.3782982660139833767e-27 + 1.090426465348098259e-1196j | 7.67e-150, 1.12e-389j | 
| 1.0112184014124114968e-30 + 6.0401292498421369839e-1199j | 1.86e-151, 2.73e-391j | 
| 1.8526994105183936343e-09 - 1.0936551738701357254e-1184j | 2.08e-135, 3.06e-375j | 
| 0.053724040181747627377 + 2.1586997030453720641e-1179j | 5.77e-107, 8.46e-347j | 
| 1.1819458498132040614e-06 - 8.903439496464289925e-1182j | 1.07e-130, 1.57e-370j | 
| 2.8123690297000741468e-17 + 6.700031881050833346e-1191j | 1.88e-143, 2.75e-383j | 
| 2.0516429766997323341e-60 + 3.4299859200331493122e-1215j | 6.44e-166, 9.43e-406j | 
| 4.7184013763808136689e-40 + 3.589317078571498206e-1204j | 7.22e-156, 1.06e-395j | 
| 0.0032003916747687682481 - 5.190082557425104516e-1180j | 6.06e-122, 8.89e-362j | 
| 2.1996246369491829962e-11 - 8.8646981286157384141e-1187j | 1.95e-139, 2.86e-379j | 
| 5.7759192865390872026e-16 - 2.1417948117766138675e-1189j | 3.54e-145, 5.19e-385j | 
| 2.7554128191962999323e-23 + 1.2922508739417194061e-1194j | 2.15e-148, 3.15e-388j | 
| 0.060813884128018828909 + 1.4623194371871227125e-1178j | 1.56e-115, 2.28e-355j | 
| 4.1672964960251239027e-35 + 1.1650861926792612255e-1199j | 3.87e-158, 5.68e-398j | 
| 4.7184013763808136689e-40 - 2.0884199765740170923e-1202j | 1.38e-160, 2.02e-400j | 
| 0.060813884128018828909 + 1.3066590341376536248e-1178j | 1.79e-119, 2.62e-359j | 
| 1.1819458498132040614e-06 - 2.1112672956066073495e-1181j | 1.91e-139, 2.79e-379j | 
| 7.5113800283787913903e-33 - 1.0771637166023790537e-1198j | 3.97e-157, 5.82e-397j | 
| 5.3521392863127632101e-25 - 1.2454578524135436038e-1195j | 2.5e-152, 3.66e-392j | 
| 2.1508653235661400562e-10 + 5.726078919039658182e-1186j | 2.18e-142, 3.2e-382j | 
| 2.8123690297000741468e-17 + 3.2769607690574582096e-1190j | 1.74e-148, 2.55e-388j | 
| 0.00017999514162850277089 + 3.4065708647632898819e-1181j | 2.1e-135, 3.08e-375j | 
| -2.2161585318034032876e-06 + 4.2883680281703019686e-1181j | 6.45e-140, 9.46e-380j | 
| 0.001493058526709152699 + 2.6477765522448028313e-1180j | 6.06e-134, 8.89e-374j | 
| 8.3782982660139833767e-27 + 1.234351248532716001e-1195j | 9.94e-155, 1.46e-394j | 
| 1.9618065064568072595e-12 + 1.3967448895687625492e-1187j | 3.62e-146, 5.3e-386j | 
| 5.2022534168331593179e-06 - 7.7967690513122241303e-1182j | 2.77e-139, 4.07e-379j | 
| 3.9822883766972640697e-56 + 6.4452755732571316959e-1212j | 9.47e-171, 1.39e-410j | 
| 0.0005529014595031520792 - 1.1427004036104297045e-1180j | 1.29e-137, 1.89e-377j | 
| 2.7554128191962999323e-23 + 1.0295234343229257181e-1193j | 5.14e-153, 7.54e-393j | 
| 1.7452665279993149552e-06 + 3.1165609140150867967e-1182j | 8.55e-141, 1.25e-380j | 
| 0.018437380681619400988 + 1.1362084131385712389e-1179j | 5.6e-135, 8.21e-375j | 
| 1.449342730595595672e-06 - 1.0279717982272717182e-1181j | 1.57e-140, 2.3e-380j | 
| 0.0032003916747687682481 - 7.9090858854878177588e-1180j | 1.56e-137, 2.29e-377j | 
| 1.4163101883845628971e-05 + 2.7970882116955939575e-1181j | 3.36e-141, 4.93e-381j | 
| 1.0416782486547731039e-28 - 8.5957061610552885977e-1198j | 2.99e-158, 4.38e-398j | 
| 0.11708217460698662656 + 8.4631197023284904136e-1179j | 3.73e-136, 5.46e-376j | 
| 0.001493058526709152699 + 1.6526967199998631457e-1180j | 2.44e-140, 3.58e-380j | 
| 1.516654245622667485e-13 - 2.1790458056631167436e-1188j | 3.71e-149, 5.44e-389j | 
| 0.075262154453923946963 - 5.3515864195395943245e-1179j | 5.28e-138, 7.74e-378j | 
| 0.0082709911224594815656 - 1.8409262926531493202e-1179j | 3.49e-139, 5.12e-379j | 
| 1.1591145678454884507e-18 - 8.7772647131561914477e-1192j | 9.3e-153, 1.36e-392j | 
| 0.06091103778811356219 - 1.4919817729085410668e-1178j | 3.93e-138, 5.77e-378j | 
| 2.1508653235661400562e-10 + 1.6930859255584191866e-1185j | 3.49e-150, 5.12e-390j | 
| 1.449342730595595672e-06 - 2.3927471571152991181e-1181j | 2.02e-145, 2.96e-385j | 
| 0.06091103778811356219 - 1.6333051783440889841e-1178j | 2.97e-140, 4.36e-380j | 
| 0.12672853484846303562 - 6.8648030127295811408e-1179j | 8.36e-141, 1.23e-380j | 
| 0.0005529014595031520792 - 6.7648404414109880048e-1181j | 9.41e-144, 1.38e-383j | 
| 0.003196786906909953437 + 1.1377107860666192629e-1179j | 1.99e-142, 2.92e-382j | 
| 0.11708217460698662656 + 8.8874970328222845973e-1179j | 2.25e-141, 3.31e-381j | 
| 1.456802580685757253e-08 + 8.7690975860024416531e-1184j | 9.65e-149, 1.41e-388j | 
| 2.1996246369491829962e-11 - 2.8199735797072250622e-1186j | 2.22e-151, 3.26e-391j | 
All rules of Hermite (physicists') type can be downloaded here packed into a single file.