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) | 
|---|---|
| 290.85148362538608695 + 3.1924969983936270898e-5966j | 2.72e-2008, 2.72e-2008j | 
| 338.34970536023274016 - 4.5316451910649717855e-5979j | 1.22e-2013, 1.22e-2013j | 
| 223.03090167046230628 - 1.9156324771328555081e-5963j | 6.92e-2002, 6.92e-2002j | 
| 268.08773416443093821 + 1.4411459037830978905e-5976j | 5.82e-2006, 5.82e-2006j | 
| 304.07415880848304284 - 8.8264708912019056632e-5985j | 9.67e-2010, 9.67e-2010j | 
| 51.212808080274191082 - 8.3511379934650464895e-5995j | 3.69e-2002, 3.69e-2002j | 
| 187.44585578479838774 + 3.3370120519907874163e-5989j | 2.36e-1999, 2.36e-1999j | 
| 239.57312836698998222 - 7.3434535182903790632e-6001j | 2.85e-2003, 2.85e-2003j | 
| 61.938509230299075752 - 1.9017408545667120469e-6009j | 1.76e-2000, 1.76e-2000j | 
| 22.476372473296887354 + 3.7726475635802660533e-6019j | 1.65e-2010, 1.65e-2010j | 
| 8.1821534445628607911 - 1.753626630333619529e-6027j | 7.73e-2018, 7.73e-2018j | 
| 257.97989981636932768 + 1.8278968597422454475e-6005j | 5.76e-2005, 5.76e-2005j | 
| 106.07735925992620969 - 4.2927948461436988398e-6008j | 2.43e-1997, 2.43e-1997j | 
| 200.84468561434279737 + 1.0468183976273240574e-6031j | 3.21e-2000, 3.21e-2000j | 
| 27.557713866828835822 + 9.0999220744490025887e-6059j | 2.02e-2008, 2.02e-2008j | 
| 70.802239113569912869 - 4.0329919384110099181e-6047j | 1.92e-1999, 1.92e-1999j | 
| 319.32078944492433445 - 2.6196960315108106032e-6059j | 1.86e-2011, 1.86e-2011j | 
| 59.142897055547190129 + 2.9582503504296253349e-6057j | 7.13e-2001, 7.13e-2001j | 
| 10.470859716890807354 + 2.9393035996569732439e-6077j | 2.42e-2017, 2.42e-2017j | 
| 80.416101393054990222 - 1.4698058632265694002e-6056j | 1.4e-1998, 1.4e-1998j | 
| 13.949974640750763633 - 4.0138293114637774474e-6126j | 4.74e-2015, 4.74e-2015j | 
| 278.97373216184503889 - 1.2782701121435363424e-6132j | 5.32e-2007, 5.32e-2007j | 
| 127.59030800162991058 + 2.9516919067315880703e-6314j | 3.7e-1997, 3.7e-1997j | 
| 137.06119893259304951 - 2.7195157419953172954e-6517j | 2.69e-1997, 2.69e-1997j | 
| 12.734180291797813758 - 8.9024956304299960533e-6609j | 7.94e-2016, 7.94e-2016j | 
| 169.03522449917760497 - 1.050253267598720501e-6650j | 2.24e-1998, 2.24e-1998j | 
| 53.781370809026925371 - 2.2539208039408553202e-6691j | 1.09e-2001, 1.09e-2001j | 
| 5.2271027010792648297 + 3.4449107622438941283e-6729j | 2.46e-2022, 2.46e-2022j | 
| 67.766618301652461303 + 6.8713867530692603161e-6704j | 9.12e-2000, 9.12e-2000j | 
| 56.424304230504903649 - 1.0720940702834152923e-6768j | 2.89e-2001, 2.89e-2001j | 
| 83.796106755507495037 - 4.3882885883927941731e-6909j | 2.51e-1998, 2.51e-1998j | 
| 174.96734961646374484 - 1.5446644501802340207e-7069j | 1.2e-1998, 1.2e-1998j | 
| 5.8898002262486093032 + 9.4553917982612359448e-7184j | 1.17e-2021, 1.17e-2021j | 
| 157.725043124768599 + 2.0155399048146319041e-7177j | 7.22e-1998, 7.22e-1998j | 
| 181.09968257475040816 - 3.2032663273809636605e-7230j | 5.61e-1999, 5.61e-1999j | 
| 20.905762421516562262 - 1.2093696199024024824e-7278j | 2.96e-2011, 2.96e-2011j | 
| 231.09961721658075971 + 4.6605846066506304442e-7264j | 1.56e-2002, 1.56e-2002j | 
| 94.49261612544208137 - 5.3404413526160959345e-7299j | 1.03e-1997, 1.03e-1997j | 
| 41.65873610615111801 - 1.0494190724081875168e-7343j | 3.67e-2004, 3.67e-2004j | 
| 147.08854619632440849 + 1.2117000711958090656e-7336j | 1.64e-1997, 1.64e-1997j | 
| 110.14994201416526319 + 2.0121070760490095988e-7371j | 2.94e-1997, 2.94e-1997j | 
| 4.9003530845264845681 - 2.7634124923080232167e-7419j | 7.22e-2023, 7.22e-2023j | 
| 248.50845763749412062 + 1.9811006726275957977e-7393j | 4.51e-2004, 4.51e-2004j | 
| 9.4153630285030565682 - 2.0329879198250855541e-7431j | 5.5e-2018, 5.5e-2018j | 
| 114.33362131681388289 - 6.2193285986239990646e-7409j | 3.38e-1997, 3.38e-1997j | 
| 1.6611113716427954205 - 8.142185777190945018e-7469j | 1.3e-2030, 1.3e-2030j | 
| 31.25973157617794574 + 2.9157892536743822756e-7445j | 4.21e-2007, 4.21e-2007j | 
| 33.207199715571364772 + 3.1439385177702510695e-7444j | 1.72e-2006, 1.72e-2006j | 
| 87.267300607081784479 + 1.3080880685799042134e-7434j | 4.26e-1998, 4.26e-1998j | 
| 90.831985163542931893 + 1.8426136159520658806e-7469j | 6.79e-1998, 6.79e-1998j | 
| 73.921139888208414012 - 1.1694083418225853207e-7509j | 4.03e-1999, 4.03e-1999j | 
| 15.223391576750514188 - 7.9144551036786835585e-7559j | 3.05e-2014, 3.05e-2014j | 
| 48.717393968892314288 + 9.6180046438469753557e-7542j | 1.2e-2002, 1.2e-2002j | 
| 3.6977320166121211493 + 1.1288563135792631335e-7608j | 1.26e-2025, 1.26e-2025j | 
| 0.19304367656036241384 - 7.1478462143450705988e-7622j | 2.28e-2038, 2.28e-2038j | 
| 1.3054529610522176527 - 4.635453070306462207e-7614j | 9.11e-2032, 9.11e-2032j | 
| 132.25911244458892025 + 1.7854433119877385205e-7578j | 3.21e-1997, 3.21e-1997j | 
| 64.812576973022888017 + 5.3893547352397118234e-7637j | 4.15e-2000, 4.15e-2000j | 
| 215.3219805197811811 + 1.8603391664379903609e-7704j | 2.77e-2001, 2.77e-2001j | 
| 0.078886361115268761626 - 4.8526776235700866792e-7800j | 6.83e-2040, 6.83e-2040j | 
| 163.29132425328905662 + 2.1370732347570840374e-7756j | 4.02e-1998, 4.02e-1998j | 
| 43.941431562034979319 - 1.4895933494429755998e-7796j | 1.27e-2003, 1.27e-2003j | 
| 29.376816533264870681 + 8.0044462802037006889e-7801j | 9.85e-2008, 9.85e-2008j | 
| 39.444888122615191593 + 8.6195615650128903583e-7798j | 1e-2004, 1e-2004j | 
| 11.575078304261264613 - 3.6034604264371666665e-7809j | 1.39e-2016, 1.39e-2016j | 
| 16.555103126590490798 + 4.0585562001913233263e-7807j | 1.66e-2013, 1.66e-2013j | 
| 98.251816941771815913 - 1.6225955244179125962e-7788j | 1.4e-1997, 1.4e-1997j | 
| 194.02149834674185602 + 4.0860731722705697087e-7821j | 9.26e-2000, 9.26e-2000j | 
| 77.125123093882160325 - 1.4968767989902933113e-7858j | 8.21e-1999, 8.21e-1999j | 
| 6.7022653918740552639 - 1.4466230829985582715e-7920j | 1.28e-2020, 1.28e-2020j | 
| 3.1066020759025409129 + 2.6032061307047674673e-7927j | 5.86e-2027, 5.86e-2027j | 
| 2.0847657903609615428 + 3.6084834230217045182e-7929j | 1.83e-2029, 1.83e-2029j | 
| 0.79032642239537165332 + 2.6038693685262450567e-7933j | 5.64e-2034, 5.64e-2034j | 
| 2.5678767449507462069 + 2.3815328786840443548e-7928j | 3.26e-2028, 3.26e-2028j | 
| 7.6335319189149864621 - 1.5148942826879089809e-7919j | 3.66e-2019, 3.66e-2019j | 
| 142.0022609780327201 - 1.1699565175653256282e-7895j | 2.22e-1997, 2.22e-1997j | 
| 152.32693632469026559 + 2.4712727018017717435e-7924j | 1.09e-1997, 1.09e-1997j | 
| 207.93653106113674619 + 6.2180103717020369949e-7935j | 1.04e-2000, 1.04e-2000j | 
| 46.293968824963435797 - 2.1885577270145215351e-7944j | 3.97e-2003, 3.97e-2003j | 
| 102.11239488904093453 - 6.8400189931441086784e-7938j | 1.92e-1997, 1.92e-1997j | 
| 118.6321484793153432 - 4.277269273123790305e-7937j | 3.6e-1997, 3.6e-1997j | 
| 8.2719876807685001318 - 7.5050491186463582881e-7970j | 8.81e-2018, 8.81e-2018j | 
| 4.3311004942518321453 + 4.4477547583643721233e-7976j | 3.52e-2024, 3.52e-2024j | 
| 19.395727862262540312 + 5.7689366501339560909e-7965j | 5.67e-2012, 5.67e-2012j | 
| 25.801717029351128485 + 3.8697529611889281396e-7961j | 4.19e-2009, 4.19e-2009j | 
| 35.219997994850915874 - 8.1974812857976070505e-7958j | 6.89e-2006, 6.89e-2006j | 
| 0.35541712585667932487 + 1.2632765151606856779e-7988j | 9.45e-2037, 9.45e-2037j | 
| 0.015001777164624114873 + 6.9840913852423480499e-8066j | 1.51e-2041, 1.51e-2041j | 
| 24.108151489943400005 + 5.0644792384028403809e-7962j | 8.62e-2010, 8.62e-2010j | 
| 123.04957893220442546 - 2.3826777648579637314e-7948j | 3.7e-1997, 3.7e-1997j | 
| 0.56007978805057608683 - 1.9891809835816682802e-8005j | 2.36e-2035, 2.36e-2035j | 
| 17.945695059399310275 + 6.2362484648742600383e-7981j | 9.68e-2013, 9.68e-2013j | 
| 1.0266648953391919503 + 7.6323367165349961911e-8001j | 8.39e-2033, 8.39e-2033j | 
| 37.29894199021953987 + 1.0916227992437742491e-7973j | 2.82e-2005, 2.82e-2005j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 6.0368285636438535927e-126 + 4.9709816949124992547e-6073j | 1.68e-365, 2.81e-1869j | 
| 2.548766853195417188e-146 - 1.7070893079946344888e-6083j | 5.23e-372, 8.76e-1876j | 
| 1.0853097717807895092e-96 - 6.4504773804582142827e-6058j | 5.22e-356, 8.74e-1860j | 
| 3.8982404507438240375e-116 + 5.6476947012900861806e-6068j | 6.54e-363, 1.09e-1866j | 
| 1.2324120369481487232e-131 - 5.8849588436387890512e-6076j | 6.9e-368, 1.15e-1871j | 
| 1.4520706301110275609e-22 + 6.817699862202404694e-6017j | 1.73e-303, 2.9e-1807j | 
| 2.5316579706724932086e-81 + 6.7599388598156562506e-6050j | 2.86e-351, 4.79e-1855j | 
| 7.8327943645785151005e-104 - 1.2966997024789176135e-6061j | 1.82e-359, 3.05e-1863j | 
| 3.5722190501797339319e-27 - 3.0728829259090418969e-6020j | 8.95e-313, 1.5e-1816j | 
| 2.7736535878692667916e-10 + 9.3664470677954233217e-6011j | 8.15e-277, 1.36e-1780j | 
| -0.00080974194113813094091 + 1.8269199368735876315e-6004j | 6.49e-241, 1.09e-1744j | 
| 8.9259444167723361374e-112 - 1.0070249189452688464e-6065j | 5.17e-362, 8.65e-1866j | 
| 3.4294258188418181878e-46 + 3.5088108015185117049e-6031j | 1.55e-333, 2.6e-1837j | 
| 4.135021855159858843e-87 + 6.3761631048121774543e-6053j | 3.84e-354, 6.43e-1858j | 
| 1.923388995735183396e-12 - 4.5784590045698892357e-6012j | 4.3e-287, 7.2e-1791j | 
| 5.4840497660458834215e-31 + 1.3715459667689764402e-6022j | 2.39e-319, 4.01e-1823j | 
| 3.4873938304235464208e-138 + 2.5469049105009299149e-6079j | 7.3e-372, 1.22e-1875j | 
| 5.6882987721571575111e-26 + 1.9179771559594506738e-6019j | 4.83e-313, 8.08e-1817j | 
| 3.0561817821118831438e-05 - 7.8002455733030887072e-6007j | 7.37e-259, 1.23e-1762j | 
| 3.9705012263094494156e-35 - 5.2693358592305268421e-6025j | 1.83e-324, 3.06e-1828j | 
| 1.0879058122367404377e-06 + 3.1878013320924625005e-6008j | 5.84e-269, 9.77e-1773j | 
| 7.9027947359853218986e-121 - 2.1466231784631051183e-6070j | 1.6e-365, 2.67e-1869j | 
| 1.7838676104873481576e-55 - 3.2657090439959476887e-6036j | 1.53e-341, 2.56e-1845j | 
| 1.4543148710189874443e-59 - 2.1082184248290540194e-6038j | 4.3e-344, 7.2e-1848j | 
| 3.5007393563888023723e-06 - 8.6908701818666712932e-6008j | 1.44e-270, 2.41e-1774j | 
| 2.2649589163114405733e-73 - 1.0122725687872407252e-6045j | 5.08e-351, 8.51e-1855j | 
| 1.1453678930552210346e-23 + 1.134845641600467374e-6017j | 1.36e-313, 2.28e-1817j | 
| 0.0025388748229654379442 + 1.6998304719670822994e-6004j | 6.98e-250, 1.17e-1753j | 
| 1.1108720005625619129e-29 - 8.3759830831819902026e-6022j | 8.05e-321, 1.35e-1824j | 
| 8.3841441166972359343e-25 - 1.2999235649483254146e-6018j | 5.99e-315, 1e-1818j | 
| 1.3883620092083415321e-36 + 7.7739011321587023209e-6026j | 9.37e-329, 1.57e-1832j | 
| 6.208267094212292201e-76 + 4.5433572166753317052e-6047j | 3.6e-353, 6.03e-1857j | 
| 0.0021188096247262959603 - 6.2049643897597748246e-6005j | 2.4e-260, 4.02e-1764j | 
| 1.7366836705690652676e-68 - 3.8278233237799332748e-6043j | 8.01e-351, 1.34e-1854j | 
| 1.3943471965203300454e-78 - 1.8475722971163706657e-6048j | 2.1e-354, 3.51e-1858j | 
| 1.2832963780581109691e-09 - 2.5006169149695764573e-6010j | 1.62e-296, 2.72e-1800j | 
| 3.5631650185125483879e-100 + 1.0232675908657874543e-6059j | 1.2e-363, 2.01e-1867j | 
| 3.401648106798363234e-41 - 1.9991728226991341963e-6028j | 1.54e-336, 2.57e-1840j | 
| 1.8182699995652211795e-18 + 2.7597824403306454499e-6015j | 4.31e-316, 7.21e-1820j | 
| 6.8077111176334186404e-64 - 1.0414020612479072924e-6040j | 1.69e-349, 2.83e-1853j | 
| 6.0003722043143043082e-48 - 3.8489469459659792296e-6032j | 1.91e-341, 3.19e-1845j | 
| 0.0029121264224203490165 - 1.9423489489744861704e-6004j | 1.23e-270, 2.05e-1774j | 
| 1.0899993217916124848e-107 + 1.3063625589867530896e-6063j | 8.42e-368, 1.41e-1871j | 
| 8.4530403038753465925e-05 + 3.061502788053717125e-6006j | 1.79e-285, 2.99e-1789j | 
| 9.3961837172546343505e-50 + 4.0116584261818177935e-6033j | 8.53e-343, 1.43e-1846j | 
| 0.074393959263766538015 - 1.0991702660134772312e-6004j | 7.64e-255, 1.28e-1758j | 
| 5.0845746906086660127e-14 - 5.725827945347741122e-6013j | 1.4e-313, 2.34e-1817j | 
| 7.4982811176820189649e-15 + 1.9873675064569224696e-6013j | 5e-315, 8.36e-1819j | 
| 4.4313120159122012216e-38 - 1.1070860263325572836e-6026j | 6.66e-336, 1.11e-1839j | 
| 1.2880895577940612819e-39 + 1.5179594489465693039e-6027j | 3.74e-337, 6.26e-1841j | 
| 2.4905747202530447719e-32 - 2.2045673508315457405e-6023j | 3.81e-332, 6.38e-1836j | 
| 3.1866197643210006026e-07 - 1.1984081987900668049e-6008j | 1.84e-303, 3.08e-1807j | 
| 1.7104249155907938629e-21 - 1.9562462496242221353e-6016j | 1.51e-324, 2.53e-1828j | 
| 0.015250923219252687903 - 7.6872901740307256713e-6005j | 7.91e-282, 1.32e-1785j | 
| 0.11442991748272886373 - 2.5198925905714635255e-6005j | 6.5e-267, 1.09e-1770j | 
| 0.085964858897878144936 + 1.4336202380791844657e-6004j | 6.5e-267, 1.09e-1770j | 
| 1.7213730445802107458e-57 + 2.7089128767299957984e-6037j | 2.32e-349, 3.88e-1853j | 
| 2.0735493228669437547e-28 + 5.0642007558801044921e-6021j | 2.67e-329, 4.46e-1833j | 
| 2.3137849802955466963e-93 + 3.5123713792609220051e-6056j | 1.22e-366, 2.05e-1870j | 
| 0.082440683320962873967 + 1.1707937489394209394e-6005j | 6.4e-273, 1.07e-1776j | 
| 6.8515789051400872015e-71 + 2.0560430511322861908e-6044j | 5.75e-356, 9.63e-1860j | 
| 1.9120024722990773474e-19 - 9.8912088518390202299e-6016j | 2.26e-325, 3.79e-1829j | 
| 3.2299135514708247814e-13 + 1.6298661379364295596e-6012j | 7.15e-320, 1.2e-1823j | 
| 1.6132739250235209591e-17 - 7.9754280723366637762e-6015j | 2.6e-324, 4.35e-1828j | 
| 1.0630490076868658568e-05 + 2.4844071668018247648e-6007j | 7.4e-307, 1.24e-1810j | 
| 8.7919763723143432139e-08 + 4.5571673090353141847e-6009j | 1.62e-312, 2.71e-1816j | 
| 8.14020324121186152e-43 + 2.5233969426496574971e-6029j | 2.21e-342, 3.7e-1846j | 
| 3.6589837643045778884e-84 - 2.2076674181322026603e-6051j | 7.88e-364, 1.32e-1867j | 
| 1.0386932036875654037e-33 + 3.4578796975502061827e-6024j | 1.09e-335, 1.82e-1839j | 
| 0.0010514549967465506448 + 3.3652406175815277902e-6005j | 5.76e-305, 9.64e-1809j | 
| 0.025312423670717419621 + 7.0917884089988992683e-6005j | 4.49e-299, 7.52e-1803j | 
| 0.056481061327129201131 + 8.7318260958851673949e-6005j | 2.37e-296, 3.97e-1800j | 
| 0.10610154980449664884 + 1.3128786910991575908e-6004j | 7.83e-293, 1.31e-1796j | 
| 0.039222260332415488042 - 7.5057878680267605744e-6005j | 5.02e-298, 8.4e-1802j | 
| 0.00054393993925879478896 - 4.7064852593422240241e-6005j | 1.67e-306, 2.8e-1810j | 
| 1.0697028837414425364e-61 + 1.534636194724764653e-6039j | 7.18e-354, 1.2e-1857j | 
| 3.7231600932329125266e-66 + 6.564133003356846062e-6042j | 5.27e-356, 8.82e-1860j | 
| 3.5784735020385721452e-90 - 1.6109690665114823492e-6054j | 9.33e-368, 1.56e-1871j | 
| 1.8740586396056382584e-20 + 3.8692471510579846233e-6016j | 1.26e-331, 2.11e-1835j | 
| 1.7602613912012273912e-44 - 3.0460044837636788337e-6030j | 1.82e-345, 3.05e-1849j | 
| 1.3119811492577879529e-51 - 3.9638788565783909918e-6034j | 6.5e-350, 1.09e-1853j | 
| 0.00090290579142862678124 - 1.5227463630304616822e-6004j | 2.14e-315, 3.58e-1819j | 
| 0.0084526308385076683553 + 1.0830979321809335204e-6004j | 2.09e-313, 3.49e-1817j | 
| 5.5819553127629952189e-09 + 6.6144641863753349308e-6010j | 8.32e-326, 1.39e-1829j | 
| 1.0743926116533518879e-11 + 1.2687410451664271528e-6011j | 9.84e-329, 1.65e-1832j | 
| 1.03513723765586714e-15 - 6.8301953463044803366e-6014j | 7.37e-332, 1.23e-1835j | 
| 0.12971787181147187151 + 4.6432239349578506365e-6005j | 4.82e-317, 8.06e-1821j | 
| 0.037909545810830339069 - 3.1905584446640937021e-6006j | 3.82e-317, 6.39e-1821j | 
| 5.6330296966062879867e-11 - 3.4690595162484081836e-6011j | 1.33e-328, 2.23e-1832j | 
| 1.6269031227461659844e-53 + 3.7042528343449571371e-6035j | 1.16e-352, 1.94e-1856j | 
| 0.12658020160597078822 - 8.1379967839926818829e-6005j | 1.04e-319, 1.73e-1823j | 
| 2.2837003856627055042e-08 - 1.7383594786871388019e-6009j | 6.22e-327, 1.04e-1830j | 
| 0.088352994970616980063 - 1.6088837083729883001e-6004j | 9.34e-321, 1.53e-1824j | 
| 1.3366898978515626469e-16 + 2.3333061649985658458e-6014j | 1.7e-332, 2.85e-1836j | 
All rules of Laguerre type can be downloaded here packed into a single file.