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) | 
|---|---|
| -0.99951167658614431612 - 1.1776985905023403246e-774j | 7.55e-230, 7.55e-230j | 
| -0.98527567974291773555 + 1.052705939981620861e-774j | 2.88e-229, 2.88e-229j | 
| -0.9225217132136291628 + 2.5365274401621837057e-778j | 2.46e-231, 2.46e-231j | 
| -0.99750760639318964363 + 1.4665101435234463164e-774j | 2.88e-229, 2.88e-229j | 
| 0.95442025435770299539 + 7.6769021746185253046e-773j | 1.97e-230, 1.97e-230j | 
| 0.93959500297914781346 - 5.9199516363911353151e-775j | 7.17e-231, 7.17e-231j | 
| 0.97728765431782963432 - 1.5107348986384318035e-772j | 1.31e-229, 1.31e-229j | 
| -0.93959500297914781346 - 5.5245291148420405426e-797j | 7.18e-231, 7.18e-231j | 
| 0.99079325588510780584 - 2.9520219327200117812e-792j | 4.84e-229, 4.84e-229j | 
| 0.99442035932225605554 - 2.5461242864922882714e-826j | 4.73e-229, 4.73e-229j | 
| 0.8817171031303486119 - 1.186692188622123559e-846j | 1.96e-232, 1.96e-232j | 
| 0.99951167658614431612 + 2.6191777959568300006e-841j | 7.72e-230, 7.72e-230j | 
| -0.90321953764349526637 + 8.704195575367148051e-861j | 7.28e-232, 7.28e-232j | 
| -0.8322722014060994695 + 1.7519152793857483892e-862j | 1.04e-233, 1.04e-233j | 
| 0.67385724014661555763 - 1.7970295673816296519e-865j | 1.1e-237, 1.1e-237j | 
| 0.85805232991808761223 + 1.0234766376253176116e-860j | 4.54e-233, 4.54e-233j | 
| 0.9225217132136291628 + 5.2523908165086788748e-858j | 2.43e-231, 2.43e-231j | 
| -0.99442035932225605554 - 3.3529838534305955689e-857j | 5.2e-229, 5.2e-229j | 
| -0.85805232991808761223 - 4.979202321025210934e-861j | 4.71e-233, 4.71e-233j | 
| -0.95442025435770299539 - 3.7449394389430000142e-858j | 2.11e-230, 2.11e-230j | 
| 0.90321953764349526637 + 1.7592573759528013377e-858j | 7.37e-232, 7.37e-232j | 
| 0.77459666924148337704 + 2.1164955566325504037e-863j | 3.49e-235, 3.49e-235j | 
| -0.96698721654849048993 - 5.989893063772337234e-858j | 5.31e-230, 5.31e-230j | 
| -0.80443238939560229407 + 2.212768311823900641e-863j | 2.01e-234, 2.01e-234j | 
| -0.77459666924148337704 + 2.0214588485877909115e-863j | 3.51e-235, 3.51e-235j | 
| -0.97728765431782963432 + 1.7232009411325409967e-857j | 1.25e-229, 1.25e-229j | 
| 0.74283617056808660312 + 2.2468845945689984193e-863j | 5.5e-236, 5.5e-236j | 
| 0.98527567974291773555 - 3.4221937693646648112e-855j | 2.7e-229, 2.7e-229j | 
| -0.99079325588510780584 + 3.9206338738699328407e-868j | 4.77e-229, 4.77e-229j | 
| -0.63681064033973478087 - 2.8272333828714617408e-880j | 1.2e-238, 1.2e-238j | 
| -0.19629557322443271077 - 1.2169964014621034235e-891j | 2.61e-250, 2.61e-250j | 
| 0.80443238939560229407 + 8.0596503137608403205e-873j | 2.12e-234, 2.12e-234j | 
| 0.70922855920206954096 + 5.057889902412470068e-876j | 8.14e-237, 8.14e-237j | 
| 0.99750760639318964363 - 2.270037748151546724e-871j | 2.84e-229, 2.84e-229j | 
| -0.67385724014661555763 - 1.7946793511343393362e-890j | 1.06e-237, 1.06e-237j | 
| -0.70922855920206954096 - 5.8669977355978575644e-890j | 7.91e-237, 7.91e-237j | 
| 0.96698721654849048993 - 2.3420928302976631935e-890j | 5.05e-230, 5.05e-230j | 
| 0.63681064033973478087 + 2.8462549817409586512e-900j | 1.2e-238, 1.2e-238j | 
| 0.8322722014060994695 + 9.9646439740851366468e-898j | 1.05e-233, 1.05e-233j | 
| -0.74283617056808660312 - 2.8484508776375087546e-897j | 5.73e-236, 5.73e-236j | 
| -0.51656663744804107342 - 3.1243643026631366059e-904j | 9.97e-242, 9.97e-242j | 
| -0.8817171031303486119 - 4.9799141487762887776e-908j | 1.93e-232, 1.93e-232j | 
| 0.55806685067819680295 + 7.2819710612904092291e-913j | 1.24e-240, 1.24e-240j | 
| 0.51656663744804107342 + 2.4047473869749571063e-915j | 1.05e-241, 1.05e-241j | 
| 0.098638994020953553308 - 2.7993923900248085707e-927j | 4.31e-253, 4.31e-253j | 
| -0.59818159670099740546 - 1.1999377602907954334e-914j | 1.32e-239, 1.32e-239j | 
| -0.55806685067819680295 - 4.7249973859361777826e-915j | 1.36e-240, 1.36e-240j | 
| 0.049381040330247523029 - 7.7952069858474934271e-929j | 2.2e-254, 2.2e-254j | 
| 0.47378435355414501928 + 5.8817866142594490843e-916j | 7.87e-243, 7.87e-243j | 
| 0.59818159670099740546 + 2.0339671768466970012e-916j | 1.39e-239, 1.39e-239j | 
| -0.33882110537955243584 + 2.7926842723330905693e-924j | 1.94e-246, 1.94e-246j | 
| -0.47378435355414501928 - 2.5269813906816465455e-920j | 7.67e-243, 7.67e-243j | 
| -0.14765115619613792876 - 6.2811165264377995092e-929j | 1.32e-251, 1.32e-251j | 
| 0.38480139332359670424 - 1.4514984166609720613e-923j | 3.32e-245, 3.32e-245j | 
| 0.33882110537955243584 - 1.9761618301993133874e-924j | 2.16e-246, 2.16e-246j | 
| 5.6102896689868307564e-976 - 1.5053400041753463238e-975j | 1.08e-973, 1.08e-973j | 
| -0.42982628683776222528 + 5.7607087629445776736e-921j | 5.59e-244, 5.59e-244j | 
| -0.2919991541426287378 - 1.2582799499918255539e-924j | 1.1e-247, 1.1e-247j | 
| 0.14765115619613792876 + 8.2355336509826851719e-929j | 1.1e-251, 1.1e-251j | 
| 0.42982628683776222528 + 1.2788354743154924368e-921j | 5.44e-244, 5.44e-244j | 
| 0.19629557322443271077 + 1.1520319266826375527e-927j | 2.5e-250, 2.5e-250j | 
| -0.24445138838062664382 + 9.8043962169897748374e-927j | 5.56e-249, 5.56e-249j | 
| -0.38480139332359670424 - 2.8045752549541496126e-922j | 3.51e-245, 3.51e-245j | 
| -0.049381040330247523029 - 8.9491585807140747296e-932j | 2.42e-254, 2.42e-254j | 
| 0.24445138838062664382 + 1.5232113337933013453e-926j | 5.6e-249, 5.6e-249j | 
| 0.2919991541426287378 + 4.505000736495519473e-925j | 1.09e-247, 1.09e-247j | 
| -0.098638994020953553308 - 2.1865571047339250032e-930j | 5.12e-253, 5.12e-253j | 
| Weight (ball center) | Error (ball radius) | 
|---|---|
| 0.0012457230084094943631 - 1.0987011699897578459e-774j | 5.25e-26, 6.17e-133j | 
| 0.00678476667636701237 - 1.2531656404679875183e-774j | 1.43e-26, 1.68e-133j | 
| 0.018191719129099433719 - 1.0005754657417737817e-775j | 3.5e-27, 4.12e-134j | 
| 0.0026899245389003417134 + 3.9834779309326392417e-774j | 3.35e-26, 3.95e-133j | 
| 0.013697193340081389205 + 6.1581340078134380994e-773j | 4.42e-28, 5.2e-135j | 
| 0.015951669478483779282 + 3.8680848178809153381e-773j | 3.2e-28, 3.77e-135j | 
| 0.0091595732697093362916 + 1.574588443918593674e-773j | 9.62e-29, 1.13e-135j | 
| 0.015951669478483779282 + 1.2708266314097909191e-775j | 2.78e-28, 3.27e-135j | 
| 0.0042980820943514007712 - 8.5669164920291418744e-773j | 1.56e-29, 1.83e-136j | 
| 0.0033054793424684830842 + 4.5091310300681410193e-773j | 6.6e-30, 7.76e-137j | 
| 0.022590688310970373254 - 2.5446520640634916637e-774j | 2.32e-32, 2.73e-139j | 
| 0.0012457230084094943631 + 2.8676817197949103294e-774j | 1.35e-30, 1.58e-137j | 
| 0.020407857271408034304 + 7.997347423245565077e-776j | 9.5e-33, 1.12e-139j | 
| 0.026819947043602362896 - 4.5093884473506057454e-776j | 5.57e-34, 6.55e-141j | 
| 0.036224083321185908914 + 1.5297331967100859672e-775j | 2.53e-35, 2.98e-142j | 
| 0.024731021458805583596 + 1.4446407472727066655e-774j | 1.37e-33, 1.61e-140j | 
| 0.018191719129099433719 - 1.1812815881821943355e-773j | 2.78e-32, 3.27e-139j | 
| 0.0033054793424684830842 - 5.1023235542888663794e-774j | 4.34e-33, 5.1e-140j | 
| 0.024731021458805583596 + 5.3810271427468101824e-776j | 1.37e-35, 1.61e-142j | 
| 0.013697193340081389205 - 1.6518528673012167284e-775j | 2.32e-34, 2.73e-141j | 
| 0.020407857271408034304 + 5.0057543153536230835e-774j | 6.24e-35, 7.35e-142j | 
| 0.03081053650061543095 - 3.9230084324405174189e-775j | 3.75e-38, 4.42e-145j | 
| 0.011435835179046009148 + 2.3370519420996809447e-775j | 1.47e-34, 1.73e-141j | 
| 0.028849035012740998837 + 3.8344897040829479604e-776j | 3.99e-38, 4.7e-145j | 
| 0.03081053650061543095 - 3.3079879580192876961e-776j | 4.12e-39, 4.85e-146j | 
| 0.0091595732697093362916 - 4.9943508414512647604e-775j | 9.65e-35, 1.14e-141j | 
| 0.032697503118193155966 + 2.777400748849457385e-775j | 5.52e-41, 6.5e-148j | 
| 0.00678476667636701237 + 1.5512503041321025462e-772j | 2.87e-37, 3.38e-144j | 
| 0.0042980820943514007712 + 3.8304139318910162986e-774j | 1.55e-34, 1.82e-141j | 
| 0.037853635080186778303 - 2.1001277060476207453e-776j | 1.32e-43, 1.56e-150j | 
| 0.048420151227740000182 - 1.4942115424362282515e-776j | 2.17e-46, 2.55e-153j | 
| 0.028849035012740998837 + 5.7594229197954875942e-775j | 9.22e-41, 1.09e-147j | 
| 0.034503806769407897378 - 2.0320484573049519576e-775j | 3.93e-42, 4.62e-149j | 
| 0.0026899245389003417134 - 1.4672211257351031492e-773j | 9.31e-38, 1.1e-144j | 
| 0.036224083321185908914 + 2.3073270776099629446e-776j | 6.33e-44, 7.45e-151j | 
| 0.034503806769407897378 - 2.5672395170141689417e-776j | 1.67e-43, 1.97e-150j | 
| 0.011435835179046009148 - 2.1030262640191436254e-772j | 1.38e-38, 1.62e-145j | 
| 0.037853635080186778303 - 1.1808768932911951293e-775j | 2.02e-45, 2.38e-152j | 
| 0.026819947043602362896 - 8.8590879863384116127e-775j | 2.05e-41, 2.42e-148j | 
| 0.032697503118193155966 + 2.8943165122351426922e-776j | 2e-43, 2.35e-150j | 
| 0.042158730372076880189 + 1.6997626389963788926e-776j | 1.84e-48, 2.16e-155j | 
| 0.022590688310970373254 - 6.5149895920481600729e-776j | 2.22e-41, 2.61e-148j | 
| 0.040824458865710040846 - 7.5087701958577165024e-776j | 2.98e-48, 3.5e-155j | 
| 0.042158730372076880189 + 6.1597970563677097584e-776j | 3.83e-49, 4.51e-156j | 
| 0.049155458138741107016 - 1.9543007191999887311e-776j | 5.42e-53, 6.38e-160j | 
| 0.039388321816323713068 + 1.9348502101880331744e-776j | 4.33e-48, 5.09e-155j | 
| 0.040824458865710040846 - 1.8034136672743918251e-776j | 5.97e-49, 7.03e-156j | 
| 0.049339992244033464415 + 1.8229048077279471529e-776j | 4.75e-54, 5.59e-161j | 
| 0.043388119093779641274 - 5.1384616420327423905e-776j | 2.29e-51, 2.69e-158j | 
| 0.039388321816323713068 + 9.3220843705796633014e-776j | 5.87e-49, 6.91e-156j | 
| 0.046420257514327303641 + 1.4887543141760347887e-776j | 9.49e-54, 1.12e-160j | 
| 0.043388119093779641274 - 1.6193737343990509101e-776j | 7.54e-52, 8.87e-159j | 
| 0.048848534821887318098 + 1.5249343547234875434e-776j | 9.83e-55, 1.16e-161j | 
| 0.045521360205917595764 - 3.7411888846559634709e-776j | 2.3e-54, 2.71e-161j | 
| 0.046420257514327303641 + 3.2587463476967914402e-776j | 5.21e-55, 6.13e-162j | 
| 0.049401567584315181499 - 1.7177312245495660419e-776j | 5.47e-56, 6.44e-163j | 
| 0.044509851844888629206 + 1.5589007211848013998e-776j | 2.65e-54, 3.12e-161j | 
| 0.047204333507921934837 - 1.4763431204808487871e-776j | 1.6e-55, 1.89e-162j | 
| 0.048848534821887318098 + 2.1171153469651983814e-776j | 7.18e-57, 8.46e-164j | 
| 0.044509851844888629206 + 4.3531652447260458254e-776j | 1.32e-55, 1.55e-162j | 
| 0.048420151227740000182 - 2.3182122083480461494e-776j | 2.47e-57, 2.9e-164j | 
| 0.047871566610461576368 + 1.478169161891280587e-776j | 5.53e-57, 6.48e-164j | 
| 0.045521360205917595764 - 1.5159206264620105331e-776j | 1.78e-56, 2.09e-163j | 
| 0.049339992244033464415 + 1.6348483043798285459e-776j | 4.75e-58, 5.62e-165j | 
| 0.047871566610461576368 + 2.5666950483806386852e-776j | 1.79e-58, 2.15e-165j | 
| 0.047204333507921934837 - 2.8747309620462523308e-776j | 1.85e-58, 2.24e-165j | 
| 0.049155458138741107016 - 1.5713054973505346605e-776j | 1.5e-58, 1.67e-165j | 
All rules of Legendre type can be downloaded here packed into a single file.