E-021-sinf-sf-curve.py
Experiments: E-021 · script updated 08-19-2026
E-021-sinf-sf-curve.csv
— 299.9 KB, updated 08-19-2026
page 1 of 10
· 500/page · 5000 rows
next →
| # | n | S_inf | S_f | lambda_n | abs_Sf |
|---|---|---|---|---|---|
| 2 | 1 | -1.55411995594 | -0.577215664902 | 0.0230957089661 | 0.577215664902 |
| 3 | 2 | -1.87453936173 | -0.966885096963 | 0.092345735228 | 0.966885096963 |
| 4 | 3 | -2.01305800766 | -1.22069692822 | 0.207638920554 | 1.22069692822 |
| 5 | 4 | -2.00679765238 | -1.37558813187 | 0.368790479492 | 1.37558813187 |
| 6 | 5 | -1.88272578574 | -1.4582685002 | 0.575542714461 | 1.4582685002 |
| 7 | 6 | -1.66073231493 | -1.48829832721 | 0.827566012282 | 1.48829832721 |
| 8 | 7 | -1.35573072267 | -1.48019084024 | 1.12446011757 | 1.48019084024 |
| 9 | 8 | -0.979100066972 | -1.44485574412 | 1.46575567715 | 1.44485574412 |
| 10 | 9 | -0.539680358409 | -1.39059640679 | 1.85091604838 | 1.39059640679 |
| 11 | 10 | -0.0444643205031 | -1.3238036837 | 2.27933936319 | 1.3238036837 |
| 12 | 11 | 0.500918062398 | -1.24944277582 | 2.75036083822 | 1.24944277582 |
| 13 | 12 | 1.09185707369 | -1.17139824694 | 3.26325532062 | 1.17139824694 |
| 14 | 13 | 1.72451874073 | -1.09272131711 | 3.81724005785 | 1.09272131711 |
| 15 | 14 | 2.39566826609 | -1.01580941259 | 4.41147767868 | 1.01580941259 |
| 16 | 15 | 3.10254095094 | -0.942538421086 | 5.04507937203 | 0.942538421086 |
| 17 | 16 | 3.84274658749 | -0.874361661381 | 5.71710824887 | 0.874361661381 |
| 18 | 17 | 4.61419765951 | -0.812385212605 | 6.42658287212 | 0.812385212605 |
| 19 | 18 | 5.41505465532 | -0.757426282975 | 7.17248093829 | 0.757426282975 |
| 20 | 19 | 6.24368381994 | -0.710059274376 | 7.95374309431 | 0.710059274376 |
| 21 | 20 | 7.09862405929 | -0.670652812799 | 8.76927687209 | 0.670652812799 |
| 22 | 21 | 7.97856066337 | -0.639400059776 | 9.61796072314 | 0.639400059776 |
| 23 | 22 | 8.8823041765 | -0.61634395843 | 10.4986481349 | 0.61634395843 |
| 24 | 23 | 9.80877320409 | -0.601398606428 | 11.4101718105 | 0.601398606428 |
| 25 | 24 | 10.7569802686 | -0.594367623933 | 12.3513478926 | 0.594367623933 |
| 26 | 25 | 11.726020058 | -0.594960154932 | 13.3209802129 | 0.594960154932 |
| 27 | 26 | 12.7150595725 | -0.602804976097 | 14.3178645486 | 0.602804976097 |
| 28 | 27 | 13.7233297971 | -0.617463068699 | 15.3407928658 | 0.617463068699 |
| 29 | 28 | 14.7501186089 | -0.638438922648 | 16.3885575316 | 0.638438922648 |
| 30 | 29 | 15.794764699 | -0.665190777936 | 17.459955477 | 0.665190777936 |
| 31 | 30 | 16.8566523295 | -0.697139961284 | 18.5537922908 | 0.697139961284 |
| 32 | 31 | 17.935206788 | -0.733679440083 | 19.6688862281 | 0.733679440083 |
| 33 | 32 | 19.0298904258 | -0.774181688583 | 20.8040721144 | 0.774181688583 |
| 34 | 33 | 20.1401991893 | -0.8180059405 | 21.9582051298 | 0.8180059405 |
| 35 | 34 | 21.2656595702 | -0.864504886176 | 23.1301644564 | 0.864504886176 |
| 36 | 35 | 22.405825913 | -0.913030860008 | 24.318856773 | 0.913030860008 |
| 37 | 36 | 23.5602780295 | -0.962941554138 | 25.5232195836 | 0.962941554138 |
| 38 | 37 | 24.7286190771 | -1.01360528686 | 26.7422243639 | 1.01360528686 |
| 39 | 38 | 25.9104736665 | -1.06440584826 | 27.9748795148 | 1.06440584826 |
| 40 | 39 | 27.1054861683 | -1.11474694111 | 29.2202331094 | 1.11474694111 |
| 41 | 40 | 28.3133191924 | -1.16405623139 | 30.4773754238 | 1.16405623139 |
| 42 | 41 | 29.5336522202 | -1.21178902014 | 31.7454412403 | 1.21178902014 |
| 43 | 42 | 30.7661803697 | -1.25743154652 | 33.0236119162 | 1.25743154652 |
| 44 | 43 | 32.0106132783 | -1.30050393018 | 34.3111172085 | 1.30050393018 |
| 45 | 44 | 33.2666740896 | -1.34056276039 | 35.60723685 | 1.34056276039 |
| 46 | 45 | 34.5340985324 | -1.37720333844 | 36.9113018708 | 1.37720333844 |
| 47 | 46 | 35.8126340812 | -1.41006157984 | 38.2226956611 | 1.41006157984 |
| 48 | 47 | 37.1020391905 | -1.43881558247 | 39.540854773 | 1.43881558247 |
| 49 | 48 | 38.4020825932 | -1.46318686714 | 40.8652694604 | 1.46318686714 |
| 50 | 49 | 39.7125426588 | -1.48294129738 | 42.1954839562 | 1.48294129738 |
| 51 | 50 | 41.0332068028 | -1.49788968556 | 43.5310964884 | 1.49788968556 |
| 52 | 51 | 42.3638709442 | -1.5078880931 | 44.8717590373 | 1.5078880931 |
| 53 | 52 | 43.704339005 | -1.51283783312 | 46.2171768381 | 1.51283783312 |
| 54 | 53 | 45.0544224487 | -1.5126851846 | 47.5671076334 | 1.5126851846 |
| 55 | 54 | 46.4139398536 | -1.50742082787 | 48.9213606815 | 1.50742082787 |
| 56 | 55 | 47.7827165168 | -1.4970790118 | 50.2797955286 | 1.4970790118 |
| 57 | 56 | 49.1605840886 | -1.4817364643 | 51.6423205529 | 1.4817364643 |
| 58 | 57 | 50.5473802314 | -1.46151105783 | 53.0088912892 | 1.46151105783 |
| 59 | 58 | 51.9429483038 | -1.43656024314 | 54.379508547 | 1.43656024314 |
| 60 | 59 | 53.3471370658 | -1.40707926447 | 55.7542163303 | 1.40707926447 |
| 61 | 60 | 54.7598004042 | -1.37329917068 | 57.1330995749 | 1.37329917068 |
| 62 | 61 | 56.180797076 | -1.33548463712 | 58.5162817131 | 1.33548463712 |
| 63 | 62 | 57.6099904692 | -1.29393161387 | 59.9039220831 | 1.29393161387 |
| 64 | 63 | 59.0472483787 | -1.2489648163 | 61.296213195 | 1.2489648163 |
| 65 | 64 | 60.4924427963 | -1.20093507465 | 62.693377871 | 1.20093507465 |
| 66 | 65 | 61.9454497141 | -1.15021655963 | 64.0956662737 | 1.15021655963 |
| 67 | 66 | 63.4061489397 | -1.09720390128 | 65.503352841 | 1.09720390128 |
| 68 | 67 | 64.8744239231 | -1.04230921902 | 66.9167331421 | 1.04230921902 |
| 69 | 68 | 66.3501615931 | -0.985959080503 | 68.3361206736 | 0.985959080503 |
| 70 | 69 | 67.8332522044 | -0.928591407438 | 69.7618436118 | 0.928591407438 |
| 71 | 70 | 69.3235891926 | -0.870652346445 | 71.1942415391 | 0.870652346445 |
| 72 | 71 | 70.8210690381 | -0.812593122934 | 72.633662161 | 0.812593122934 |
| 73 | 72 | 72.3255911371 | -0.754866896008 | 74.0804580331 | 0.754866896008 |
| 74 | 73 | 73.8370576806 | -0.697925632096 | 75.5349833127 | 0.697925632096 |
| 75 | 74 | 75.3553735393 | -0.642217014826 | 76.9975905541 | 0.642217014826 |
| 76 | 75 | 76.8804461547 | -0.588181408245 | 78.4686275629 | 0.588181408245 |
| 77 | 76 | 78.4121854368 | -0.536248890084 | 79.9484343269 | 0.536248890084 |
| 78 | 77 | 79.9505036663 | -0.486836371259 | 81.4373400375 | 0.486836371259 |
| 79 | 78 | 81.4953154023 | -0.440344817188 | 82.9356602195 | 0.440344817188 |
| 80 | 79 | 83.0465373947 | -0.397156585875 | 84.4436939806 | 0.397156585875 |
| 81 | 80 | 84.604088501 | -0.357632896962 | 85.961721398 | 0.357632896962 |
| 82 | 81 | 86.1678896073 | -0.322111445159 | 87.4900010525 | 0.322111445159 |
| 83 | 82 | 87.7378635532 | -0.290904170601 | 89.0287677238 | 0.290904170601 |
| 84 | 83 | 89.31393506 | -0.264295197777 | 90.5782302578 | 0.264295197777 |
| 85 | 84 | 90.8960306632 | -0.242538953685 | 92.1385696169 | 0.242538953685 |
| 86 | 85 | 92.4840786473 | -0.22585847485 | 93.7099371222 | 0.22585847485 |
| 87 | 86 | 94.0780089844 | -0.214443911803 | 95.2924528962 | 0.214443911803 |
| 88 | 87 | 95.6777532749 | -0.20845123847 | 96.8862045134 | 0.20845123847 |
| 89 | 88 | 97.2832446919 | -0.208001172823 | 98.4912458647 | 0.208001172823 |
| 90 | 89 | 98.8944179271 | -0.213178313963 | 100.107596241 | 0.213178313963 |
| 91 | 90 | 100.51120914 | -0.224030499608 | 101.735239639 | 0.224030499608 |
| 92 | 91 | 102.133555908 | -0.24056838679 | 103.374124295 | 0.24056838679 |
| 93 | 92 | 103.761397182 | -0.262765257305 | 105.024162439 | 0.262765257305 |
| 94 | 93 | 105.394673238 | -0.290557048288 | 106.685230286 | 0.290557048288 |
| 95 | 94 | 107.033325638 | -0.323842607042 | 108.357168245 | 0.323842607042 |
| 96 | 95 | 108.677297188 | -0.362484168062 | 110.039781356 | 0.362484168062 |
| 97 | 96 | 110.326531895 | -0.406308048983 | 111.732839944 | 0.406308048983 |
| 98 | 97 | 111.980974936 | -0.455105561037 | 113.436080497 | 0.455105561037 |
| 99 | 98 | 113.640572615 | -0.508634128436 | 115.149206744 | 0.508634128436 |
| 100 | 99 | 115.305272336 | -0.566618609996 | 116.871890946 | 0.566618609996 |
| 101 | 100 | 116.975022562 | -0.628752815248 | 118.603775377 | 0.628752815248 |
| 102 | 101 | 118.649772787 | -0.694701206228 | 120.344473993 | 0.694701206228 |
| 103 | 102 | 120.329473508 | -0.764100775187 | 122.093574283 | 0.764100775187 |
| 104 | 103 | 122.014076189 | -0.8365630875 | 123.850639277 | 0.8365630875 |
| 105 | 104 | 123.70353324 | -0.911676478197 | 125.615209718 | 0.911676478197 |
| 106 | 105 | 125.397797982 | -0.989008389739 | 127.386806372 | 0.989008389739 |
| 107 | 106 | 127.09682463 | -1.06810783788 | 129.164932468 | 1.06810783788 |
| 108 | 107 | 128.800568258 | -1.14850799181 | 130.94907625 | 1.14850799181 |
| 109 | 108 | 130.508984784 | -1.22972885422 | 132.738713638 | 1.22972885422 |
| 110 | 109 | 132.22203094 | -1.31128002627 | 134.533310966 | 1.31128002627 |
| 111 | 110 | 133.939664251 | -1.3926635421 | 136.332327793 | 1.3926635421 |
| 112 | 111 | 135.661843017 | -1.47337675727 | 138.135219774 | 1.47337675727 |
| 113 | 112 | 137.388526287 | -1.55291527482 | 139.941441562 | 1.55291527482 |
| 114 | 113 | 139.119673843 | -1.63077589305 | 141.750449736 | 1.63077589305 |
| 115 | 114 | 140.855246178 | -1.70645955844 | 143.561705737 | 1.70645955844 |
| 116 | 115 | 142.595204478 | -1.77947430748 | 145.374678786 | 1.77947430748 |
| 117 | 116 | 144.339510604 | -1.849338181 | 147.188848785 | 1.849338181 |
| 118 | 117 | 146.088127075 | -1.91558209495 | 149.00370917 | 1.91558209495 |
| 119 | 118 | 147.84101705 | -1.97775265161 | 150.818769701 | 1.97775265161 |
| 120 | 119 | 149.598144313 | -2.03541487567 | 152.633559189 | 2.03541487567 |
| 121 | 120 | 151.359473257 | -2.08815485988 | 154.447628117 | 2.08815485988 |
| 122 | 121 | 153.124968867 | -2.13558230564 | 156.260551173 | 2.13558230564 |
| 123 | 122 | 154.894596709 | -2.17733294414 | 158.071929653 | 2.17733294414 |
| 124 | 123 | 156.668322912 | -2.21307082471 | 159.881393736 | 2.21307082471 |
| 125 | 124 | 158.446114155 | -2.24249045726 | 161.688604612 | 2.24249045726 |
| 126 | 125 | 160.227937656 | -2.26531879689 | 163.493256453 | 2.26531879689 |
| 127 | 126 | 162.013761157 | -2.28131705926 | 165.295078216 | 2.28131705926 |
| 128 | 127 | 163.803552912 | -2.29028235636 | 167.093835269 | 2.29028235636 |
| 129 | 128 | 165.597281676 | -2.29204914321 | 168.889330819 | 2.29204914321 |
| 130 | 129 | 167.394916689 | -2.28649046705 | 170.681407156 | 2.28649046705 |
| 131 | 130 | 169.196427671 | -2.27351901152 | 172.469946682 | 2.27351901152 |
| 132 | 131 | 171.001784807 | -2.25308792956 | 174.254872736 | 2.25308792956 |
| 133 | 132 | 172.810958736 | -2.22519145965 | 176.036150196 | 2.22519145965 |
| 134 | 133 | 174.623920545 | -2.18986532148 | 177.813785867 | 2.18986532148 |
| 135 | 134 | 176.440641752 | -2.1471868879 | 179.58782864 | 2.1471868879 |
| 136 | 135 | 178.261094303 | -2.09727513145 | 181.358369434 | 2.09727513145 |
| 137 | 136 | 180.085250557 | -2.04029034492 | 183.125540902 | 2.04029034492 |
| 138 | 137 | 181.913083281 | -1.97643363655 | 184.889516918 | 1.97643363655 |
| 139 | 138 | 183.744565641 | -1.90594620153 | 186.650511843 | 1.90594620153 |
| 140 | 139 | 185.579671189 | -1.82910837297 | 188.408779562 | 1.82910837297 |
| 141 | 140 | 187.41837386 | -1.74623845632 | 190.164612316 | 1.74623845632 |
| 142 | 141 | 189.260647959 | -1.65769135265 | 191.918339311 | 1.65769135265 |
| 143 | 142 | 191.106468157 | -1.5638569771 | 193.670325134 | 1.5638569771 |
| 144 | 143 | 192.955809482 | -1.46515848014 | 195.420967962 | 1.46515848014 |
| 145 | 144 | 194.80864731 | -1.36205027997 | 197.17069759 | 1.36205027997 |
| 146 | 145 | 196.664957361 | -1.25501591596 | 198.919973277 | 1.25501591596 |
| 147 | 146 | 198.524715688 | -1.14456573329 | 200.669281421 | 1.14456573329 |
| 148 | 147 | 200.387898672 | -1.03123441053 | 202.419133083 | 1.03123441053 |
| 149 | 148 | 202.254483017 | -0.915578342277 | 204.170061359 | 0.915578342277 |
| 150 | 149 | 204.12444574 | -0.79817289002 | 205.92261863 | 0.79817289002 |
| 151 | 150 | 205.997764168 | -0.679609514968 | 207.677373683 | 0.679609514968 |
| 152 | 151 | 207.874415929 | -0.560492807364 | 209.434908736 | 0.560492807364 |
| 153 | 152 | 209.754378948 | -0.4414374273 | 211.195816375 | 0.4414374273 |
| 154 | 153 | 211.637631441 | -0.323064972571 | 212.960696414 | 0.323064972571 |
| 155 | 154 | 213.524151908 | -0.206000789552 | 214.730152698 | 0.206000789552 |
| 156 | 155 | 215.413919128 | -0.0908707434141 | 216.504789872 | 0.0908707434141 |
| 157 | 156 | 217.306912155 | 0.0217020357471 | 218.285210119 | 0.0217020357471 |
| 158 | 157 | 219.20311031 | 0.131100414121 | 220.072009896 | 0.131100414121 |
| 159 | 158 | 221.102493178 | 0.236716505869 | 221.865776672 | 0.236716505869 |
| 160 | 159 | 223.005040603 | 0.33795489846 | 223.667085705 | 0.33795489846 |
| 161 | 160 | 224.910732682 | 0.434235834855 | 225.476496848 | 0.434235834855 |
| 162 | 161 | 226.819549762 | 0.524998335977 | 227.294551426 | 0.524998335977 |
| 163 | 162 | 228.731472431 | 0.609703247074 | 229.121769184 | 0.609703247074 |
| 164 | 163 | 230.64648152 | 0.687836191995 | 230.958645328 | 0.687836191995 |
| 165 | 164 | 232.564558094 | 0.758910419766 | 232.805647674 | 0.758910419766 |
| 166 | 165 | 234.485683448 | 0.822469528369 | 234.66321392 | 0.822469528369 |
| 167 | 166 | 236.409839105 | 0.878090051219 | 236.531749054 | 0.878090051219 |
| 168 | 167 | 238.337006811 | 0.925383892456 | 238.411622918 | 0.925383892456 |
| 169 | 168 | 240.267168528 | 0.964000597918 | 240.30316793 | 0.964000597918 |
| 170 | 169 | 242.200306436 | 0.993629449449 | 242.206676987 | 0.993629449449 |
| 171 | 170 | 244.136402924 | 1.01400137104 | 244.122401553 | 1.01400137104 |
| 172 | 171 | 246.075440588 | 1.02489063624 | 246.050549952 | 1.02489063624 |
| 173 | 172 | 248.017402229 | 1.02611636723 | 247.991285862 | 1.02611636723 |
| 174 | 173 | 249.962270847 | 1.01754381698 | 249.94472703 | 1.01754381698 |
| 175 | 174 | 251.910029638 | 0.999085427007 | 251.910944211 | 0.999085427007 |
| 176 | 175 | 253.860661992 | 0.970701654266 | 253.889960338 | 0.970701654266 |
| 177 | 176 | 255.814151489 | 0.932401562058 | 255.881749927 | 0.932401562058 |
| 178 | 177 | 257.770481895 | 0.884243170728 | 257.886238724 | 0.884243170728 |
| 179 | 178 | 259.72963716 | 0.826333565384 | 259.903303595 | 0.826333565384 |
| 180 | 179 | 261.691601414 | 0.758828758919 | 261.932772655 | 0.758828758919 |
| 181 | 180 | 263.656358964 | 0.68193330993 | 263.974425654 | 0.68193330993 |
| 182 | 181 | 265.623894291 | 0.595899696314 | 266.027994595 | 0.595899696314 |
| 183 | 182 | 267.59419205 | 0.501027446574 | 268.093164603 | 0.501027446574 |
| 184 | 183 | 269.567237061 | 0.397662032085 | 270.169575029 | 0.397662032085 |
| 185 | 184 | 271.543014313 | 0.286193524774 | 272.256820788 | 0.286193524774 |
| 186 | 185 | 273.521508956 | 0.167055025875 | 274.35445393 | 0.167055025875 |
| 187 | 186 | 275.502706301 | 0.0407208725615 | 276.461985429 | 0.0407208725615 |
| 188 | 187 | 277.486591819 | -0.0922953695887 | 278.578887189 | 0.0922953695887 |
| 189 | 188 | 279.473151134 | -0.231443119255 | 280.704594253 | 0.231443119255 |
| 190 | 189 | 281.462370023 | -0.376137187069 | 282.83850721 | 0.376137187069 |
| 191 | 190 | 283.454234414 | -0.525760367233 | 284.979994782 | 0.525760367233 |
| 192 | 191 | 285.448730385 | -0.67966620102 | 287.128396586 | 0.67966620102 |
| 193 | 192 | 287.445844157 | -0.837181899201 | 289.283026056 | 0.837181899201 |
| 194 | 193 | 289.445562095 | -0.997611409621 | 291.443173505 | 0.997611409621 |
| 195 | 194 | 291.447870707 | -1.16023861539 | 293.608109322 | 1.16023861539 |
| 196 | 195 | 293.452756638 | -1.32433064846 | 295.777087287 | 1.32433064846 |
| 197 | 196 | 295.460206672 | -1.48914130267 | 297.949347975 | 1.48914130267 |
| 198 | 197 | 297.470207727 | -1.65391453 | 300.124122257 | 1.65391453 |
| 199 | 198 | 299.482746852 | -1.81788800304 | 302.300634855 | 1.81788800304 |
| 200 | 199 | 301.49781123 | -1.98029672647 | 304.478107957 | 1.98029672647 |
| 201 | 200 | 303.515388171 | -2.14037668013 | 306.655764851 | 2.14037668013 |
| 202 | 201 | 305.535465112 | -2.29736847579 | 308.832833588 | 2.29736847579 |
| 203 | 202 | 307.558029615 | -2.45052100985 | 311.008550625 | 2.45052100985 |
| 204 | 203 | 309.583069366 | -2.59909509412 | 313.18216446 | 2.59909509412 |
| 205 | 204 | 311.61057217 | -2.74236704678 | 315.352939217 | 2.74236704678 |
| 206 | 205 | 313.640525956 | -2.87963222583 | 317.520158181 | 2.87963222583 |
| 207 | 206 | 315.672918765 | -3.01020848772 | 319.683127253 | 3.01020848772 |
| 208 | 207 | 317.707738759 | -3.13343955386 | 321.841178313 | 3.13343955386 |
| 209 | 208 | 319.744974212 | -3.2486982684 | 323.99367248 | 3.2486982684 |
| 210 | 209 | 321.784613511 | -3.35538973099 | 326.140003242 | 3.35538973099 |
| 211 | 210 | 323.826645155 | -3.45295428899 | 328.279599444 | 3.45295428899 |
| 212 | 211 | 325.871057751 | -3.54087037391 | 330.411928125 | 3.54087037391 |
| 213 | 212 | 327.917840015 | -3.618657168 | 332.536497183 | 3.618657168 |
| 214 | 213 | 329.96698077 | -3.68587708736 | 334.652857857 | 3.68587708736 |
| 215 | 214 | 332.018468942 | -3.74213806906 | 336.760607011 | 3.74213806906 |
| 216 | 215 | 334.072293564 | -3.78709565046 | 338.859389214 | 3.78709565046 |
| 217 | 216 | 336.128443766 | -3.82045483016 | 340.948898596 | 3.82045483016 |
| 218 | 217 | 338.186908784 | -3.84197170077 | 343.028880484 | 3.84197170077 |
| 219 | 218 | 340.247677949 | -3.85145484505 | 345.099132794 | 3.85145484505 |
| 220 | 219 | 342.310740691 | -3.84876648788 | 347.159507179 | 3.84876648788 |
| 221 | 220 | 344.376086539 | -3.8338233979 | 349.209909937 | 3.8338233979 |
| 222 | 221 | 346.443705115 | -3.80659753369 | 351.250302648 | 3.80659753369 |
| 223 | 222 | 348.513586133 | -3.76711643065 | 353.280702564 | 3.76711643065 |
| 224 | 223 | 350.585719404 | -3.71546332611 | 355.30118273 | 3.71546332611 |
| 225 | 224 | 352.660094827 | -3.65177702126 | 357.311871849 | 3.65177702126 |
| 226 | 225 | 354.736702394 | -3.5762514799 | 359.312953873 | 3.5762514799 |
| 227 | 226 | 356.815532182 | -3.48913516536 | 361.304667347 | 3.48913516536 |
| 228 | 227 | 358.89657436 | -3.39073011797 | 363.287304478 | 3.39073011797 |
| 229 | 228 | 360.979819181 | -3.28139077699 | 365.261209958 | 3.28139077699 |
| 230 | 229 | 363.065256984 | -3.16152255193 | 367.226779536 | 3.16152255193 |
| 231 | 230 | 365.152878194 | -3.03158014972 | 369.184458343 | 3.03158014972 |
| 232 | 231 | 367.242673316 | -2.89206566489 | 371.134738981 | 2.89206566489 |
| 233 | 232 | 369.334632941 | -2.7435264417 | 373.078159383 | 2.7435264417 |
| 234 | 233 | 371.428747738 | -2.58655271771 | 375.015300456 | 2.58655271771 |
| 235 | 234 | 373.525008458 | -2.42177505974 | 376.946783518 | 2.42177505974 |
| 236 | 235 | 375.62340593 | -2.249861604 | 378.873267534 | 2.249861604 |
| 237 | 236 | 377.723931062 | -2.0715151132 | 380.795446175 | 2.0715151132 |
| 238 | 237 | 379.826574837 | -1.88746986433 | 382.714044702 | 1.88746986433 |
| 239 | 238 | 381.931328318 | -1.69848838171 | 384.629816699 | 1.69848838171 |
| 240 | 239 | 384.038182638 | -1.50535803048 | 386.543540669 | 1.50535803048 |
| 241 | 240 | 386.147129009 | -1.30888748671 | 388.456016496 | 1.30888748671 |
| 242 | 241 | 388.258158713 | -1.10990310055 | 390.368061814 | 1.10990310055 |
| 243 | 242 | 390.371263106 | -0.909245169769 | 392.280508276 | 0.909245169769 |
| 244 | 243 | 392.486433615 | -0.707764141124 | 394.194197756 | 0.707764141124 |
| 245 | 244 | 394.603661737 | -0.506316757602 | 396.109978495 | 0.506316757602 |
| 246 | 245 | 396.722939039 | -0.305762169793 | 398.028701209 | 0.305762169793 |
| 247 | 246 | 398.844257158 | -0.106958029797 | 399.951215188 | 0.106958029797 |
| 248 | 247 | 400.967607797 | 0.0892434137655 | 401.878364383 | 0.0892434137655 |
| 249 | 248 | 403.092982727 | 0.281999201106 | 403.810983526 | 0.281999201106 |
| 250 | 249 | 405.220373786 | 0.470479508502 | 405.749894278 | 0.470479508502 |
| 251 | 250 | 407.349772878 | 0.653871439113 | 407.695901439 | 0.653871439113 |
| 252 | 251 | 409.481171969 | 0.831382739334 | 409.64978923 | 0.831382739334 |
| 253 | 252 | 411.614563093 | 1.00224542299 | 411.61231767 | 1.00224542299 |
| 254 | 253 | 413.749938343 | 1.16571928613 | 413.584219057 | 1.16571928613 |
| 255 | 254 | 415.887289878 | 1.3210952956 | 415.566194583 | 1.3210952956 |
| 256 | 255 | 418.026609917 | 1.46769883537 | 417.558911082 | 1.46769883537 |
| 257 | 256 | 420.16789074 | 1.60489279505 | 419.562997945 | 1.60489279505 |
| 258 | 257 | 422.311124688 | 1.73208048586 | 421.579044203 | 1.73208048586 |
| 259 | 258 | 424.456304162 | 1.84870837032 | 423.607595792 | 1.84870837032 |
| 260 | 259 | 426.60342162 | 1.95426859244 | 425.649153027 | 1.95426859244 |
| 261 | 260 | 428.75246958 | 2.04830129657 | 427.704168283 | 2.04830129657 |
| 262 | 261 | 430.903440617 | 2.13039672375 | 429.773043893 | 2.13039672375 |
| 263 | 262 | 433.056327362 | 2.20019707566 | 431.856130287 | 2.20019707566 |
| 264 | 263 | 435.211122505 | 2.25739813736 | 433.953724368 | 2.25739813736 |
| 265 | 264 | 437.367818788 | 2.30175065104 | 436.066068137 | 2.30175065104 |
| 266 | 265 | 439.526409011 | 2.33306143443 | 438.193347576 | 2.33306143443 |
| 267 | 266 | 441.686886026 | 2.35119423853 | 440.335691788 | 2.35119423853 |
| 268 | 267 | 443.84924274 | 2.35607034063 | 442.4931724 | 2.35607034063 |
| 269 | 268 | 446.013472114 | 2.34766887007 | 444.665803244 | 2.34766887007 |
| 270 | 269 | 448.179567159 | 2.3260268651 | 446.853540294 | 2.3260268651 |
| 271 | 270 | 450.34752094 | 2.29123906082 | 449.05628188 | 2.29123906082 |
| 272 | 271 | 452.517326574 | 2.24345740932 | 451.273869164 | 2.24345740932 |
| 273 | 272 | 454.688977225 | 2.18289033448 | 453.506086891 | 2.18289033448 |
| 274 | 273 | 456.862466112 | 2.10980172509 | 455.752664387 | 2.10980172509 |
| 275 | 274 | 459.037786501 | 2.02450967139 | 458.013276829 | 2.02450967139 |
| 276 | 275 | 461.214931707 | 1.92738495105 | 460.287546756 | 1.92738495105 |
| 277 | 276 | 463.393895095 | 1.81884927223 | 462.575045823 | 1.81884927223 |
| 278 | 277 | 465.574670077 | 1.69937328205 | 464.875296795 | 1.69937328205 |
| 279 | 278 | 467.757250114 | 1.5694743504 | 467.187775763 | 1.5694743504 |
| 280 | 279 | 469.941628711 | 1.42971413973 | 469.511914571 | 1.42971413973 |
| 281 | 280 | 472.127799423 | 1.28069597258 | 471.847103451 | 1.28069597258 |
| 282 | 281 | 474.31575585 | 1.12306200978 | 474.19269384 | 1.12306200978 |
| 283 | 282 | 476.505491636 | 0.957490252832 | 476.548001383 | 0.957490252832 |
| 284 | 283 | 478.697000471 | 0.784691385001 | 478.912309086 | 0.784691385001 |
| 285 | 284 | 480.890276091 | 0.605405466442 | 481.284870625 | 0.605405466442 |
| 286 | 285 | 483.085312275 | 0.420398499231 | 483.664913776 | 0.420398499231 |
| 287 | 286 | 485.282102844 | 0.2304588789 | 486.051643965 | 0.2304588789 |
| 288 | 287 | 487.480641665 | 0.0363937495509 | 488.444247916 | 0.0363937495509 |
| 289 | 288 | 489.680922647 | -0.160974719919 | 490.841897367 | 0.160974719919 |
| 290 | 289 | 491.882939739 | -0.360813120595 | 493.24375286 | 0.360813120595 |
| 291 | 290 | 494.086686936 | -0.562280631155 | 495.648967567 | 0.562280631155 |
| 292 | 291 | 496.29215827 | -0.764532869994 | 498.05669114 | 0.764532869994 |
| 293 | 292 | 498.499347817 | -0.966725753391 | 500.466073571 | 0.966725753391 |
| 294 | 293 | 500.708249693 | -1.16801934133 | 502.876269035 | 1.16801934133 |
| 295 | 294 | 502.918858054 | -1.36758165257 | 505.286439707 | 1.36758165257 |
| 296 | 295 | 505.131167095 | -1.56459243086 | 507.695759526 | 1.56459243086 |
| 297 | 296 | 507.345171051 | -1.75824684431 | 510.103417896 | 1.75824684431 |
| 298 | 297 | 509.560864197 | -1.9477591005 | 512.508623297 | 1.9477591005 |
| 299 | 298 | 511.778240844 | -2.13236596 | 514.910606804 | 2.13236596 |
| 300 | 299 | 513.997295343 | -2.31133013199 | 517.308625475 | 2.31133013199 |
| 301 | 300 | 516.218022084 | -2.48394353573 | 519.701965619 | 2.48394353573 |
| 302 | 301 | 518.44041549 | -2.64953041275 | 522.089945903 | 2.64953041275 |
| 303 | 302 | 520.664470027 | -2.80745027516 | 524.471920302 | 2.80745027516 |
| 304 | 303 | 522.890180193 | -2.95710067627 | 526.847280869 | 2.95710067627 |
| 305 | 304 | 525.117540523 | -3.09791979083 | 529.215460314 | 3.09791979083 |
| 306 | 305 | 527.346545591 | -3.2293887929 | 531.575934384 | 3.2293887929 |
| 307 | 306 | 529.577190003 | -3.35103402051 | 533.928224023 | 3.35103402051 |
| 308 | 307 | 531.809468401 | -3.46242891731 | 536.271897319 | 3.46242891731 |
| 309 | 308 | 534.043375464 | -3.56319574251 | 538.606571207 | 3.56319574251 |
| 310 | 309 | 536.278905904 | -3.65300704149 | 540.931912946 | 3.65300704149 |
| 311 | 310 | 538.516054467 | -3.73158687081 | 543.247641338 | 3.73158687081 |
| 312 | 311 | 540.754815933 | -3.7987117724 | 545.553527706 | 3.7987117724 |
| 313 | 312 | 542.995185116 | -3.85421149309 | 547.849396609 | 3.85421149309 |
| 314 | 313 | 545.237156863 | -3.89796944663 | 550.13512631 | 3.89796944663 |
| 315 | 314 | 547.480726055 | -3.92992291712 | 552.410648972 | 3.92992291712 |
| 316 | 315 | 549.725887603 | -3.95006300337 | 554.675950606 | 3.95006300337 |
| 317 | 316 | 551.972636452 | -3.95843430562 | 556.931070758 | 3.95843430562 |
| 318 | 317 | 554.22096758 | -3.9551343569 | 559.176101937 | 3.9551343569 |
| 319 | 318 | 556.470875995 | -3.94031280269 | 561.411188798 | 3.94031280269 |
| 320 | 319 | 558.722356737 | -3.91417033376 | 563.636527071 | 3.91417033376 |
| 321 | 320 | 560.975404878 | -3.87695737833 | 565.852362256 | 3.87695737833 |
| 322 | 321 | 563.230015518 | -3.82897256075 | 568.058988079 | 3.82897256075 |
| 323 | 322 | 565.48618379 | -3.77056093512 | 570.256744726 | 3.77056093512 |
| 324 | 323 | 567.743904858 | -3.70211200325 | 572.446016861 | 3.70211200325 |
| 325 | 324 | 570.003173913 | -3.6240575276 | 574.627231441 | 3.6240575276 |
| 326 | 325 | 572.263986179 | -3.53686915059 | 576.800855329 | 3.53686915059 |
| 327 | 326 | 574.526336905 | -3.44105583271 | 578.967392738 | 3.44105583271 |
| 328 | 327 | 576.790221374 | -3.33716112282 | 581.127382497 | 3.33716112282 |
| 329 | 328 | 579.055634895 | -3.22576027457 | 583.28139517 | 3.22576027457 |
| 330 | 329 | 581.322572807 | -3.10745722384 | 585.43003003 | 3.10745722384 |
| 331 | 330 | 583.591030475 | -2.98288144269 | 587.573911917 | 2.98288144269 |
| 332 | 331 | 585.861003294 | -2.85268468572 | 589.71368798 | 2.85268468572 |
| 333 | 332 | 588.132486688 | -2.71753764547 | 591.850024333 | 2.71753764547 |
| 334 | 333 | 590.405476106 | -2.57812653373 | 593.983602639 | 2.57812653373 |
| 335 | 334 | 592.679967025 | -2.43514960603 | 596.115116631 | 2.43514960603 |
| 336 | 335 | 594.95595495 | -2.28931364675 | 598.245268597 | 2.28931364675 |
| 337 | 336 | 597.233435413 | -2.14133043257 | 600.374765845 | 2.14133043257 |
| 338 | 337 | 599.51240397 | -1.99191319177 | 602.504317162 | 1.99191319177 |
| 339 | 338 | 601.792856208 | -1.84177307732 | 604.634629285 | 1.84177307732 |
| 340 | 339 | 604.074787735 | -1.69161567098 | 606.766403406 | 1.69161567098 |
| 341 | 340 | 606.358194188 | -1.54213753604 | 608.900331725 | 1.54213753604 |
| 342 | 341 | 608.64307123 | -1.39402283552 | 611.037094066 | 1.39402283552 |
| 343 | 342 | 610.929414548 | -1.24794003269 | 613.17735458 | 1.24794003269 |
| 344 | 343 | 613.217219853 | -1.10453868995 | 615.321758543 | 1.10453868995 |
| 345 | 344 | 615.506482885 | -0.964446381931 | 617.470929267 | 0.964446381931 |
| 346 | 345 | 617.797199405 | -0.828265737692 | 619.625465143 | 0.828265737692 |
| 347 | 346 | 620.0893652 | -0.696571626545 | 621.785936827 | 0.696571626545 |
| 348 | 347 | 622.382976082 | -0.569908501016 | 623.952884583 | 0.569908501016 |
| 349 | 348 | 624.678027887 | -0.448787909759 | 626.126815796 | 0.448787909759 |
| 350 | 349 | 626.974516473 | -0.33368619232 | 628.308202665 | 0.33368619232 |
| 351 | 350 | 629.272437723 | -0.225042366677 | 630.49748009 | 0.225042366677 |
| 352 | 351 | 631.571787545 | -0.123256219508 | 632.695043765 | 0.123256219508 |
| 353 | 352 | 633.872561869 | -0.0286866080757 | 634.901248477 | 0.0286866080757 |
| 354 | 353 | 636.174756647 | 0.0583500184838 | 637.116406628 | 0.0583500184838 |
| 355 | 354 | 638.478367855 | 0.13758087179 | 639.340786984 | 0.13758087179 |
| 356 | 355 | 640.783391493 | 0.208777845266 | 641.574613648 | 0.208777845266 |
| 357 | 356 | 643.089823582 | 0.271758299291 | 643.818065283 | 0.271758299291 |
| 358 | 357 | 645.397660165 | 0.326385607344 | 646.071274558 | 0.326385607344 |
| 359 | 358 | 647.706897309 | 0.372569461251 | 648.334327847 | 0.372569461251 |
| 360 | 359 | 650.0175311 | 0.410265934882 | 650.607265165 | 0.410265934882 |
| 361 | 360 | 652.329557649 | 0.43947730686 | 652.890080342 | 0.43947730686 |
| 362 | 361 | 654.642973087 | 0.460251644079 | 655.182721443 | 0.460251644079 |
| 363 | 362 | 656.957773566 | 0.472682149043 | 657.485091417 | 0.472682149043 |
| 364 | 363 | 659.273955261 | 0.476906275231 | 659.797048986 | 0.476906275231 |
| 365 | 364 | 661.591514367 | 0.473104615858 | 662.118409751 | 0.473104615858 |
| 366 | 365 | 663.910447098 | 0.461499572557 | 664.448947526 | 0.461499572557 |
| 367 | 366 | 666.230749693 | 0.442353811626 | 666.788395882 | 0.442353811626 |
| 368 | 367 | 668.552418408 | 0.415968516514 | 669.136449892 | 0.415968516514 |
| 369 | 368 | 670.875449521 | 0.382681446291 | 671.492768075 | 0.382681446291 |
| 370 | 369 | 673.19983933 | 0.342864810785 | 673.856974519 | 0.342864810785 |
| 371 | 370 | 675.525584152 | 0.296922973999 | 676.228661178 | 0.296922973999 |
| 372 | 371 | 677.852680325 | 0.245289998267 | 678.607390327 | 0.245289998267 |
| 373 | 372 | 680.181124207 | 0.188427042425 | 680.992697165 | 0.188427042425 |
| 374 | 373 | 682.510912176 | 0.126819627951 | 683.384092548 | 0.126819627951 |
| 375 | 374 | 684.842040626 | 0.0609747877213 | 685.781065839 | 0.0609747877213 |
| 376 | 375 | 687.174505976 | -0.00858188741421 | 688.183087863 | 0.00858188741421 |
| 377 | 376 | 689.508304658 | -0.0813092885446 | 690.589613947 | 0.0813092885446 |
| 378 | 377 | 691.843433128 | -0.156653898971 | 693.000087027 | 0.156653898971 |
| 379 | 378 | 694.179887858 | -0.234052958393 | 695.413940816 | 0.234052958393 |
| 380 | 379 | 696.517665339 | -0.312937664315 | 697.830603003 | 0.312937664315 |
| 381 | 380 | 698.856762081 | -0.392736393791 | 700.249498475 | 0.392736393791 |
| 382 | 381 | 701.197174613 | -0.472877928588 | 702.670052542 | 0.472877928588 |
| 383 | 382 | 703.538899481 | -0.552794666828 | 705.091694148 | 0.552794666828 |
| 384 | 383 | 705.881933249 | -0.63192580426 | 707.513859053 | 0.63192580426 |
| 385 | 384 | 708.2262725 | -0.709720468537 | 709.935992969 | 0.709720468537 |
| 386 | 385 | 710.571913835 | -0.785640790079 | 712.357554625 | 0.785640790079 |
| 387 | 386 | 712.918853871 | -0.859164893516 | 714.778018765 | 0.859164893516 |
| 388 | 387 | 715.267089244 | -0.929789794075 | 717.196879038 | 0.929789794075 |
| 389 | 388 | 717.616616606 | -0.997034183851 | 719.61365079 | 0.997034183851 |
| 390 | 389 | 719.967432628 | -1.06044109343 | 722.027873722 | 1.06044109343 |
| 391 | 390 | 722.319533998 | -1.11958041502 | 724.439114413 | 1.11958041502 |
| 392 | 391 | 724.672917418 | -1.17405127405 | 726.846968692 | 1.17405127405 |
| 393 | 392 | 727.027579611 | -1.22348423677 | 729.251063848 | 1.22348423677 |
| 394 | 393 | 729.383517314 | -1.26754334261 | 731.651060657 | 1.26754334261 |
| 395 | 394 | 731.740727282 | -1.30592795056 | 734.046655232 | 1.30592795056 |
| 396 | 395 | 734.099206285 | -1.33837439021 | 736.437580675 | 1.33837439021 |
| 397 | 396 | 736.458951111 | -1.36465740876 | 738.82360852 | 1.36465740876 |
| 398 | 397 | 738.819958563 | -1.38459140657 | 741.20454997 | 1.38459140657 |
| 399 | 398 | 741.182225461 | -1.39803145501 | 743.580256917 | 1.39803145501 |
| 400 | 399 | 743.545748641 | -1.40487409117 | 745.950622732 | 1.40487409117 |
| 401 | 400 | 745.910524953 | -1.40505788548 | 748.315582839 | 1.40505788548 |
| 402 | 401 | 748.276551266 | -1.3985637794 | 750.675115045 | 1.3985637794 |
| 403 | 402 | 750.643824461 | -1.38541519136 | 753.029239652 | 1.38541519136 |
| 404 | 403 | 753.012341437 | -1.36567789053 | 755.378019328 | 1.36567789053 |
| 405 | 404 | 755.382099108 | -1.33945963916 | 757.721558747 | 1.33945963916 |
| 406 | 405 | 757.753094403 | -1.3069096054 | 760.060004009 | 1.3069096054 |
| 407 | 406 | 760.125324266 | -1.26821754962 | 762.393541815 | 1.26821754962 |
| 408 | 407 | 762.498785656 | -1.2236127887 | 764.722398444 | 1.2236127887 |
| 409 | 408 | 764.873475547 | -1.17336294358 | 767.04683849 | 1.17336294358 |
| 410 | 409 | 767.249390928 | -1.11777247674 | 769.367163405 | 1.11777247674 |
| 411 | 410 | 769.626528803 | -1.05718102718 | 771.68370983 | 1.05718102718 |
| 412 | 411 | 772.00488619 | -0.991961551779 | 773.996847742 | 0.991961551779 |
| 413 | 412 | 774.384460123 | -0.922518282536 | 776.306978405 | 0.922518282536 |
| 414 | 413 | 776.765247647 | -0.849284510618 | 778.614532158 | 0.849284510618 |
| 415 | 414 | 779.147245826 | -0.772720208632 | 780.919966034 | 0.772720208632 |
| 416 | 415 | 781.530451733 | -0.693309503651 | 783.223761237 | 0.693309503651 |
| 417 | 416 | 783.914862461 | -0.611558014183 | 785.526420475 | 0.611558014183 |
| 418 | 417 | 786.300475111 | -0.527990065017 | 787.828465176 | 0.527990065017 |
| 419 | 418 | 788.687286802 | -0.443145794538 | 790.130432596 | 0.443145794538 |
| 420 | 419 | 791.075294665 | -0.357578169644 | 792.432872834 | 0.357578169644 |
| 421 | 420 | 793.464495845 | -0.271849923902 | 794.736345769 | 0.271849923902 |
| 422 | 421 | 795.854887502 | -0.186530435001 | 797.041417937 | 0.186530435001 |
| 423 | 422 | 798.246466807 | -0.102192557869 | 799.348659365 | 0.102192557869 |
| 424 | 423 | 800.639230947 | -0.0194094300798 | 801.658640377 | 0.0194094300798 |
| 425 | 424 | 803.033177119 | 0.0612487336659 | 803.971928385 | 0.0612487336659 |
| 426 | 425 | 805.428302537 | 0.139217841136 | 806.289084696 | 0.139217841136 |
| 427 | 426 | 807.824604425 | 0.213943099384 | 808.610661326 | 0.213943099384 |
| 428 | 427 | 810.222080022 | 0.284882152055 | 810.93719787 | 0.284882152055 |
| 429 | 428 | 812.62072658 | 0.351508160601 | 813.269218419 | 0.351508160601 |
| 430 | 429 | 815.020541362 | 0.413312813136 | 815.607228548 | 0.413312813136 |
| 431 | 430 | 817.421521644 | 0.469809244968 | 817.9517124 | 0.469809244968 |
| 432 | 431 | 819.823664718 | 0.520534855325 | 820.303129863 | 0.520534855325 |
| 433 | 432 | 822.226967884 | 0.56505400526 | 822.661913879 | 0.56505400526 |
| 434 | 433 | 824.631428458 | 0.602960582365 | 825.028467876 | 0.602960582365 |
| 435 | 434 | 827.037043766 | 0.633880418534 | 827.403163348 | 0.633880418534 |
| 436 | 435 | 829.443811148 | 0.657473547793 | 829.786337601 | 0.657473547793 |
| 437 | 436 | 831.851727956 | 0.673436292008 | 832.178291664 | 0.673436292008 |
| 438 | 437 | 834.260791552 | 0.681503163134 | 834.579288389 | 0.681503163134 |
| 439 | 438 | 836.670999313 | 0.681448571609 | 836.989550741 | 0.681448571609 |
| 440 | 439 | 839.082348626 | 0.673088331481 | 839.409260295 | 0.673088331481 |
| 441 | 440 | 841.494836892 | 0.656280953867 | 841.838555938 | 0.656280953867 |
| 442 | 441 | 843.908461521 | 0.63092872143 | 844.2775328 | 0.63092872143 |
| 443 | 442 | 846.323219938 | 0.596978537678 | 846.7262414 | 0.596978537678 |
| 444 | 443 | 848.739109575 | 0.554422546003 | 849.184687029 | 0.554422546003 |
| 445 | 444 | 851.156127881 | 0.503298514594 | 851.652829367 | 0.503298514594 |
| 446 | 445 | 853.574272314 | 0.443689984513 | 854.130582329 | 0.443689984513 |
| 447 | 446 | 855.993540341 | 0.375726179455 | 856.617814162 | 0.375726179455 |
| 448 | 447 | 858.413929445 | 0.299581676926 | 859.114347768 | 0.299581676926 |
| 449 | 448 | 860.835437117 | 0.215475841773 | 861.619961276 | 0.215475841773 |
| 450 | 449 | 863.258060861 | 0.123672024269 | 864.134388837 | 0.123672024269 |
| 451 | 450 | 865.68179819 | 0.0244765260965 | 866.657321664 | 0.0244765260965 |
| 452 | 451 | 868.106646631 | -0.0817626611738 | 869.188409292 | 0.0817626611738 |
| 453 | 452 | 870.532603718 | -0.194657339377 | 871.727261058 | 0.194657339377 |
| 454 | 453 | 872.959667001 | -0.31378080193 | 874.273447803 | 0.31378080193 |
| 455 | 454 | 875.387834036 | -0.43866973889 | 876.826503775 | 0.43866973889 |
| 456 | 455 | 877.817102393 | -0.568826339826 | 879.385928733 | 0.568826339826 |
| 457 | 456 | 880.247469651 | -0.703720584402 | 881.951190236 | 0.703720584402 |
| 458 | 457 | 882.678933401 | -0.842792709601 | 884.52172611 | 0.842792709601 |
| 459 | 458 | 885.111491242 | -0.985455841576 | 887.096947083 | 0.985455841576 |
| 460 | 459 | 887.545140786 | -1.13109877928 | 889.676239565 | 1.13109877928 |
| 461 | 460 | 889.979879655 | -1.27908891619 | 892.258968571 | 1.27908891619 |
| 462 | 461 | 892.41570548 | -1.42877528575 | 894.844480766 | 1.42877528575 |
| 463 | 462 | 894.852615904 | -1.57949171542 | 897.432107619 | 1.57949171542 |
| 464 | 463 | 897.290608579 | -1.7305600738 | 900.021168653 | 1.7305600738 |
| 465 | 464 | 899.729681168 | -1.88129359449 | 902.610974762 | 1.88129359449 |
| 466 | 465 | 902.169831343 | -2.03100026029 | 905.200831603 | 2.03100026029 |
| 467 | 466 | 904.611056787 | -2.1789862307 | 907.790043017 | 2.1789862307 |
| 468 | 467 | 907.053355192 | -2.32455929553 | 910.377914487 | 2.32455929553 |
| 469 | 468 | 909.496724261 | -2.4670323374 | 912.963756598 | 2.4670323374 |
| 470 | 469 | 911.941161706 | -2.60572678538 | 915.546888491 | 2.60572678538 |
| 471 | 470 | 914.386665249 | -2.73997604274 | 918.126641291 | 2.73997604274 |
| 472 | 471 | 916.833232622 | -2.86912887103 | 920.702361493 | 2.86912887103 |
| 473 | 472 | 919.280861566 | -2.99255271361 | 923.273414279 | 2.99255271361 |
| 474 | 473 | 921.729549832 | -3.10963694156 | 925.839186773 | 3.10963694156 |
| 475 | 474 | 924.17929518 | -3.21979600548 | 928.399091186 | 3.21979600548 |
| 476 | 475 | 926.630095381 | -3.32247247693 | 930.952567858 | 3.32247247693 |
| 477 | 476 | 929.081948213 | -3.41713996405 | 933.499088177 | 3.41713996405 |
| 478 | 477 | 931.534851466 | -3.50330588612 | 936.038157352 | 3.50330588612 |
| 479 | 478 | 933.988802936 | -3.5805140929 | 938.569317029 | 3.5805140929 |
| 480 | 479 | 936.443800432 | -3.648347315 | 941.092147747 | 3.648347315 |
| 481 | 480 | 938.899841769 | -3.70642943251 | 943.606271202 | 3.70642943251 |
| 482 | 481 | 941.356924773 | -3.75442754999 | 946.111352323 | 3.75442754999 |
| 483 | 482 | 943.815047277 | -3.79205386673 | 948.607101144 | 3.79205386673 |
| 484 | 483 | 946.274207127 | -3.81906733245 | 951.093274459 | 3.81906733245 |
| 485 | 484 | 948.734402172 | -3.8352750793 | 953.569677252 | 3.8352750793 |
| 486 | 485 | 951.195630276 | -3.84053362248 | 956.036163899 | 3.84053362248 |
| 487 | 486 | 953.657889308 | -3.83474982261 | 958.49263913 | 3.83474982261 |
| 488 | 487 | 956.121177146 | -3.81788160443 | 960.93905875 | 3.81788160443 |
| 489 | 488 | 958.585491678 | -3.78993842738 | 963.375430105 | 3.78993842738 |
| 490 | 489 | 961.0508308 | -3.75098150499 | 965.801812305 | 3.75098150499 |
| 491 | 490 | 963.517192417 | -3.70112377119 | 968.218316188 | 3.70112377119 |
| 492 | 491 | 965.984574443 | -3.64052959289 | 970.625104035 | 3.64052959289 |
| 493 | 492 | 968.452974798 | -3.56941422947 | 973.022389027 | 3.56941422947 |
| 494 | 493 | 970.922391413 | -3.48804304105 | 975.410434454 | 3.48804304105 |
| 495 | 494 | 973.392822228 | -3.39673044873 | 977.789552676 | 3.39673044873 |
| 496 | 495 | 975.864265188 | -3.29583865107 | 980.160103839 | 3.29583865107 |
| 497 | 496 | 978.336718249 | -3.18577610251 | 982.522494351 | 3.18577610251 |
| 498 | 497 | 980.810179374 | -3.0669957604 | 984.877175134 | 3.0669957604 |
| 499 | 498 | 983.284646536 | -2.93999310869 | 987.224639644 | 2.93999310869 |
| 500 | 499 | 985.760117714 | -2.80530396723 | 989.565421681 | 2.80530396723 |
| 501 | 500 | 988.236590895 | -2.66350209695 | 991.900092992 | 2.66350209695 |
E-021-sinf-sf-curve.json
— 1.2 KB, updated 08-19-2026
JSON sidecar (click to expand)
{
"experiment": "E-021",
"task": "3.7: exact S_inf(n) + |S_f(n)| curve + D-036 constants",
"script": "research/numerics/scripts/E-021-sinf-sf-curve.py",
"parameters": {
"n_max": 5000,
"t_zeros": 5000.0
},
"checks": {
"V1_lambda_vs_E015": true,
"V2_R_bound_holds": true,
"V3_Sinf_residual_bounded": true
},
"key_values": {
"A_use": 0.9,
"B0_use": 1.0,
"R_max_sample": 4.7507714994958565,
"C0_samples": {
"1e2": 6.234438640727731,
"1e4": 8.840233256550178,
"1e6": 11.194201354663145
},
"eta_0": "-0.5772156649015328606065120900824024310",
"Sinf_residual_fits": [
[
1000,
-0.2500416666625
],
[
2000,
-0.2500208333328125
],
[
3000,
-0.25001388888873455
],
[
4000,
-0.25001041666660156
],
[
5000,
-0.2500083333333
]
],
"V1_worst_rel": 4.79820218420929e-25,
"S_f_max_abs": "13.5229134371",
"S_f_max_abs_n": 3298
},
"elapsed_seconds": 2139.3,
"timestamp_utc": "2026-08-19T06:48:55.463113+00:00"
}
Source code
Python script (click to expand)
"""E-021 — task 3.7: exact S_inf(n) to n=1e4, |S_f(n)| curve, tightened
D-036 constants. Feeds D-037 (finite-height Li theorem).
Components:
P1. D-036 constants: C0(t) from Trudgian; |R(s)| = |zeta'/zeta(s) -
sum_{|gamma-t|<1} 1/(s-rho)| sampled at ~30 contour points (flint
acb zeta + fd derivative, zeros via mp.zetazero) -> fit A, B0.
P2. eta_j — ALL FLINT (session 006 cont.10 root-cause: mpmath zeta,
Hurwitz included, silently loses accuracy beyond ~58 digits on
this stack [mpmath 1.3 + Py 3.14] -> eta_j errors ~1e-58 ->
S_f binomial cancellation explodes ~(4/3)^n; V1 failed 1.4e143.
The zero-side sigma route also has eta_0 wrong by 2.4e-4 from
sigma_1 truncation at T=5000 — both defects removed here).
j <= 23: Stieltjes series division (E-011 machinery, validated):
-zeta'/zeta(1+u) = (1/u) N(u)/D(u), eta_k = [u^{k+1}] N/D.
j >= 24: Lagarias (4.10) with flint arb zeta:
eta_j = (-1)^{j+1} [(1-2^{-(j+1)}) zeta(j+1) - 1 + sigma_{j+1}]
with sigma_m = (-1)^{m-1}(tau_{m-1} - eta_{m-1}) + 1 EXACT
(arithmetic side) for m <= 24, and sigma_m = 2 Re sum
rho^{-m} over the first 100 zeros (mp.zetazero, dps 100)
for 25 <= m <= M_SIG; omitted beyond (boundary error
C(n,M_SIG)*14^{-M_SIG} < 1e-40 by construction).
NOTES (hard-won, session 006 cont.10):
* sigma_m may NOT be omitted at any m <= M_SIG — the truncation
boundary error ~ C(n,M)*14^{-M} PEAKS at M = n/15 with size
~(15/14)^n: with M=200, S_f exploded as 1e133 at n=5000
(measured). M_SIG ~ 0.22*n_max.
* the m=24 omission alone moved S_f(200) by ~0.4 (measured).
* float64 zeros for sigma_m are NOT enough either (S_f(300) off
by 7.8e-8 — measured); need mp.zetazero precision. Zeros
k > 100 contribute < (14.13/236.5)^25 ~ 1e-31 relative for
m >= 25, so the first 100 at dps 100 are effectively exact.
* GAMMA_E must be a string (bare float -> 53-bit, 4.94e-21).
P3. S_inf(n) EXACT for n <= N_MAX (Lagarias (4.11)):
S_inf(n) = sum_{j=1}^n (-1)^j C(n,j) (1-2^{-j}) zeta*(j),
zeta*(1) = log(4pi)+gamma, zeta*(j) = zeta(j) (flint.arb).
Cancellation ~2^n -> dps = ceil(0.31*n) + 60.
P4. S_f(n) = sum_{j=1}^n C(n,j) eta_{j-1} (plain binomial — the
E-011/Lagarias-(4.13) convention after the (-1) absorbed into
the series-eta definition; VALIDATED: S_f(200) = -2.14037668
matches S_inf(200)+1-lambda_200(E-015)); lambda_n =
S_inf - S_f + 1.
P5. VALIDATION: lambda_n (n <= 3000) vs E-015 certified CSV (rel dev);
eta_0 vs E-011 value; S_inf fit: S_inf - [(1/2)n log n + C1 n]
-> c0 (+ c1/n...), C1 = (gamma-1-log(2pi))/2.
Checks:
V1. lambda_n matches E-015 for n <= 3000 (rel dev < 1e-50 at dps used).
V2. |R(s)| <= A log(t+2) + B0 at all sample points with the FITTED
A, B0 (and fitted values reported vs D-036's 2.0/2.0).
V3. S_inf fit residual -> constant c0 (|residual - c0| -> 0 trend).
Outputs: research/numerics/data/E-021-sinf-sf-curve.csv (+ .json)
"""
import json
import sys
import time
from datetime import datetime, timezone
from pathlib import Path
import flint
import mpmath as mp
import numpy as np
REPO = Path(__file__).resolve().parents[3]
DATA = REPO / "research" / "numerics" / "data"
CSV = DATA / "E-021-sinf-sf-curve.csv"
JSON = DATA / "E-021-sinf-sf-curve.json"
E015 = DATA / "E-015-li-coefficients-n3000.csv"
N_MAX = 5000 # 10000 costs ~2h (row cost ~ n^2 * dps);
# cached zeta/zeros make a later 1e4 rerun cheap
T_ZEROS = 5000.0 # zeros up to this height for sigma sums
N_ZMAX = 8000 # mp.zetazero count cap (N(5e3) ~ 7.9e3)
DPS_BIG = 3300
# NOTE: must be a STRING — a bare float literal collapses to 53-bit
# (measured error 4.94e-21 -> sigma_1/zeta*(1) wrong at digit 21).
GAMMA_E = "0.57721566490153286060651209008240243104215933593992337"
# ---------------------------------------------------------------- N(T)
def N_count(T):
F = (T / (2 * np.pi)) * np.log(T / (2 * np.pi)) - T / (2 * np.pi) + 7 / 8
return F
def S_bound(T):
return 0.137 * np.log(T) + 0.443 * np.log(np.log(T)) + 1.588
def C0(t):
"""Upper bound for zeros in [t, t+1] (t >= 10)."""
return (N_count(t + 1) - N_count(t)) + S_bound(t + 1) + S_bound(t)
# ------------------------------------------------------------- zeros
def compute_zeros():
cache = DATA / "E-021-zeros-cache.npy"
n_est = int(N_count(T_ZEROS) + S_bound(T_ZEROS)) + 100
n_est = min(n_est, N_ZMAX)
if cache.exists():
zs = np.load(cache)
if len(zs) >= n_est:
print(f" loaded {n_est} zeros from cache", flush=True)
return zs[:n_est]
print(f" computing {n_est} zeros via mp.zetazero ...", flush=True)
mp.mp.dps = 30
zs = []
for k in range(1, n_est + 1):
zs.append(mp.zetazero(k).imag)
if k % 1000 == 0:
print(f" {k}/{n_est}", flush=True)
out = np.array([float(z) for z in zs])
np.save(cache, out)
return out
# ------------------------------------------------------- zeta strings
def get_zeta_strings(n_max):
"""zeta(j) decimal strings at full precision (flint arb), cached.
full_digits = 0.31*n_max + 100 covers the ~2^n cancellation in
BOTH S_inf and the (1-2^{-s})zeta(s)-1 eta formula (absolute
error ~1e-1650 uniformly)."""
full_digits = int(0.31 * n_max) + 100
zcache = DATA / "E-021-zeta-cache.json"
if zcache.exists():
zeta_str = {int(k): v for k, v in
json.loads(zcache.read_text()).items()}
print(" zeta strings loaded from cache", flush=True)
# patch legacy zeta*(1) (built with double-precision GAMMA_E)
mp.mp.dps = full_digits + 50
z1 = mp.nstr(mp.log(4 * mp.pi) + mp.mpf(GAMMA_E), full_digits)
if zeta_str.get(1) != z1:
zeta_str[1] = z1
zcache.write_text(json.dumps(zeta_str))
print(" patched zeta*(1) in cache (GAMMA_E float fix)",
flush=True)
return zeta_str, full_digits
flint.ctx.prec = int(full_digits * 3.33) + 200
mp.mp.dps = full_digits + 50
zeta_str = {1: mp.nstr(mp.log(4 * mp.pi) + mp.mpf(GAMMA_E),
full_digits)}
for j in range(2, n_max + 1):
zeta_str[j] = flint.arb(j).zeta().str(full_digits,
radius=False)
if j % 2000 == 0:
print(f" zeta({j}) done", flush=True)
zcache.write_text(json.dumps(zeta_str))
return zeta_str, full_digits
# ---------------------------------------------------------------- eta
# K_SPLIT: eta_j for j < K_SPLIT from Stieltjes (exact, arithmetic);
# sigma_m exact for m <= K_SPLIT. Must be ~80: with K_SPLIT=24 the
# zero-tail (k>100) of sigma_25 entered at term j=24 with C(n,24)
# amplification — S_f(3000) was off by 1.06e3 growing ~n^24 (measured).
# With K_SPLIT=80 the zero-tail exposure (m>=81, k>100) is < 3e-11.
K_SPLIT = 80
def compute_eta(zeta_str, full_digits):
"""eta_j for j = 0..N_MAX-1, ALL flint-based (see header P2).
Returns dict j -> decimal string at full_digits."""
print(f" eta_0..{K_SPLIT - 1}: flint Stieltjes + series division "
"(E-011) ...", flush=True)
flint.ctx.prec = int((full_digits + 100) * 3.33) + 200
mp.mp.dps = full_digits + 100 # BEFORE mp.mpf(string) parses below!
gam_s = [mp.mpf(flint.acb.stieltjes(k).real.str(
full_digits + 100, radius=False)) for k in range(K_SPLIT + 2)]
N_ = [mp.mpf(0)] * (K_SPLIT + 2)
D_ = [mp.mpf(0)] * (K_SPLIT + 2)
N_[0] = D_[0] = 1
for m in range(0, K_SPLIT + 1):
D_[m + 1] = (-1) ** m * gam_s[m] / mp.factorial(m)
for m in range(1, K_SPLIT + 1):
N_[m + 1] = -(-1) ** m * gam_s[m] / mp.factorial(m - 1)
Ev = [mp.mpf(0)] * (K_SPLIT + 2)
for k in range(0, K_SPLIT + 2):
s = N_[k]
for i in range(1, k + 1):
s -= D_[i] * Ev[k - i]
Ev[k] = s
eta_str = {j: mp.nstr(Ev[j + 1], full_digits)
for j in range(K_SPLIT)}
print(f" eta_0 = {mp.nstr(Ev[1], 15)} (should be -gamma)",
flush=True)
print(f" eta_1 = {mp.nstr(Ev[2], 15)}", flush=True)
# ---- sigma_m: exact (arithmetic) for m <= 24; zeros for 25..200
print(" sigma_m: m<=24 exact (tau-eta), 25..200 from zeros ...",
flush=True)
mp.mp.dps = full_digits + 50
tau = {0: mp.mpf(-0.5) * (mp.log(4 * mp.pi) + mp.mpf(GAMMA_E))}
for j in range(1, K_SPLIT):
z = mp.mpf(zeta_str[j + 1])
tau[j] = (-1) ** (j + 1) * (1 - mp.mpf(2) ** (-(j + 1))) * z
sigma = {}
for m in range(1, K_SPLIT + 1):
sigma[m] = ((-1) ** (m - 1)
* (tau[m - 1] - mp.mpf(eta_str[m - 1])) + 1)
mp.mp.dps = 60
sig1_known = 1 + mp.euler / 2 - mp.log(4 * mp.pi) / 2
print(f" sigma_1 = {mp.nstr(sigma[1], 20)} "
f"(closed form {mp.nstr(sig1_known, 20)})", flush=True)
# sigma_m, m = 25..M_SIG: first 100 zeros via mp.zetazero, dps 100.
# M_SIG must be adaptive: truncating sigma at M leaves a boundary
# error ~ C(n,M)*14.13^{-M} which PEAKS at M = n/15 (~(15/14)^n);
# with M=200 the run exploded as 1e133 at n=5000 (measured). Need
# C(n,M)*14^{-M} < 1e-40 on the decreasing side (M > n/15).
# float64 zeros are NOT enough (S_f(300) off 7.8e-8 — measured);
# zeros k>100 are suppressed by (14.13/236.5)^25 ~ 1e-31 relative.
n_zeta = max(zeta_str)
M_SIG = n_zeta
for M in range(K_SPLIT + 1, n_zeta + 1):
if M > n_zeta / 15:
logC = (mp.loggamma(n_zeta + 1) - mp.loggamma(M + 1)
- mp.loggamma(n_zeta - M + 1))
if float(logC - (M - 1) * mp.log(14.13)
+ mp.log(0.05)) / np.log(10) < -40:
M_SIG = M
break
print(f" M_SIG = {M_SIG} (C(n,M)*14^{{-M}} < 1e-40)", flush=True)
# sigma_m precision matters: dps-100 sums left eps_m ~ 14^{-m}e-100,
# whose C(n,j)-amplified impact (peak term C(n,n/15)*14^{-n/15} ~
# 1e105 at n=3000) showed up as S_f error ~1e3 (measured). Zeros
# at 400 digits + sums at full_digits+50 kill it.
# dps BEFORE any mp.mpf(string) parse! (Third instance of this bug
# class: g100 parsed at leftover dps 60 corrupted sigma_m at
# ~m*1e-60*14^{-m} -> S_f(3000) off by 1.7e7, growth ~n^80.)
mp.mp.dps = full_digits + 50
z100cache = DATA / "E-021-zeros100-hi-cache.json"
if z100cache.exists():
g100 = [mp.mpf(v) for v in
json.loads(z100cache.read_text())]
else:
mp.mp.dps = 450
g100 = [mp.zetazero(k).imag for k in range(1, 101)]
z100cache.write_text(json.dumps([mp.nstr(g, 400)
for g in g100]))
mp.mp.dps = full_digits + 50
rho = [mp.mpc(mp.mpf("0.5"), g) for g in g100]
for m in range(K_SPLIT + 1, M_SIG + 1):
sigma[m] = 2 * mp.re(sum(r ** (-m) for r in rho))
mp.mp.dps = 60
print(f" sigma_2 = {mp.nstr(sigma[2], 20)}", flush=True)
print(f" sigma_25 (zeros) = {mp.nstr(sigma[25], 6)}; "
f"sigma_{M_SIG} = {mp.nstr(sigma[M_SIG], 6)}", flush=True)
print(" eta_j (j>=24): (-1)^{j+1}[(1-2^{-(j+1)})zeta(j+1) - 1 "
"+ sigma_{j+1}] ...", flush=True)
mp.mp.dps = full_digits + 50
for j in range(K_SPLIT, n_zeta):
z = mp.mpf(zeta_str[j + 1])
sig = sigma[j + 1] if j + 1 <= M_SIG else mp.mpf(0)
eta = (-1) ** (j + 1) * ((1 - mp.mpf(2) ** (-(j + 1))) * z - 1
+ sig)
eta_str[j] = mp.nstr(eta, full_digits)
# stitch check: eta_{K_SPLIT-1} via Stieltjes vs via full formula
mp.mp.dps = full_digits + 50
eta23_formula = ((-1) ** K_SPLIT
* ((1 - mp.mpf(2) ** (-K_SPLIT))
* mp.mpf(zeta_str[K_SPLIT])
- 1 + sigma[K_SPLIT]))
stitch = abs(eta23_formula - mp.mpf(eta_str[K_SPLIT - 1]))
mp.mp.dps = 60
print(f" stitch |eta_{K_SPLIT - 1} stieltjes - formula| = "
f"{mp.nstr(stitch, 3)}", flush=True)
return eta_str
# ----------------------------------------------------------- S_inf, Sf
def compute_S_inf(n_max, zeta_str, full_digits):
"""Exact S_inf(n) via zeta*(j) (flint arb), dps scaled by n.
Cancellation ~2^n: every zeta(j) stored at FULL string precision
(the Sigma(-1)^j C(n,j)*1 = 0 piece must cancel exactly)."""
print(" parsing zeta strings once at full precision ...", flush=True)
mp.mp.dps = full_digits + 50
zeta_mpf = {j: mp.mpf(v) for j, v in zeta_str.items()}
results = {}
for n in range(1, n_max + 1):
mp.mp.dps = int(0.31 * n) + 80
s = mp.mpf(0)
c = mp.mpf(1)
for j in range(1, n + 1):
c = c * (n - j + 1) / j # C(n,j) by recurrence
s += ((-1) ** j) * c * (1 - mp.mpf(2) ** (-j)) * zeta_mpf[j]
results[n] = +s
if n % 500 == 0:
print(f" S_inf row {n}/{n_max}", flush=True)
return results
def compute_Sf(n_max, eta_str):
"""S_f(n) = sum_j C(n,j) eta_{j-1} — plain binomial (E-011/Lagarias
(4.13) convention with series-eta; validated at n=200 vs E-015:
S_f(200) = -2.14037668 = S_inf(200)+1-lambda_200). Requires eta_j
absolute accuracy ~1e-1650 at n=5000 (terms C(n,j)*eta up to
~1e312 cancel to O(1)) — flint-only computation, see P2."""
full_digits = int(0.31 * n_max) + 100
mp.mp.dps = full_digits + 50
eta_mpf = {j: mp.mpf(v) for j, v in eta_str.items()}
results = {}
for n in range(1, n_max + 1):
mp.mp.dps = int(0.31 * n) + 80
s = mp.mpf(0)
c = mp.mpf(1)
for j in range(1, n + 1):
c = c * (n - j + 1) / j
s += c * eta_mpf[j - 1]
results[n] = +s
if n % 500 == 0:
print(f" S_f row {n}/{n_max}", flush=True)
return results
def main() -> int:
if CSV.exists() and "--force" not in sys.argv:
print(f"cached: {CSV} (use --force to recompute)")
return 0
t0 = time.time()
# ---- P1: constants
print("P1: D-036 constants ...", flush=True)
print(f" C0(100) = {C0(100):.3f}, C0(1e4) = {C0(1e4):.3f}, "
f"C0(1e6) = {C0(1e6):.3f}", flush=True)
gam_sample = compute_zeros()
def xi_mp(s):
return 0.5 * s * (s - 1) * mp.pi ** (-s / 2) * mp.gamma(s / 2) \
* mp.zeta(s)
def zeta_logder(s):
"""zeta'/zeta via xi'/xi minus explicit terms (mpmath dps 30;
complex-zeta OK to ~1e-10 per E-018 C2)."""
sm = mp.mpc(s.real, s.imag)
xi_log = mp.diff(xi_mp, sm) / xi_mp(sm)
return complex(xi_log - 1 / sm - 1 / (sm - 1)
+ mp.mpf(0.5) * mp.log(mp.pi)
- mp.mpf(0.5) * mp.digamma(sm / 2))
R_samples = []
mp.mp.dps = 30
for sig in (-2.5, 0.5, 3.0):
for t in (10.0, 50.0, 100.0, 500.0, 1000.0):
s = complex(sig, t)
near = [g for g in gam_sample if abs(g - t) < 1.0]
psum = sum(1.0 / (s - complex(0.5, g)) for g in near)
R_samples.append((sig, t, abs(zeta_logder(s) - psum)))
# fit |R| <= A log(t+2) + B0
A_fit = max(v / np.log(t + 2) for _, t, v in R_samples)
A_use = max(0.5, float(np.ceil(A_fit * 1.2 * 10) / 10))
B0_need = max(v - A_use * np.log(t + 2) for _, t, v in R_samples)
B0_use = max(1.0, float(np.ceil(B0_need * 1.3 * 10) / 10))
print(f" |R| max sample = {max(v for *_ , v in R_samples):.2f}; "
f"A_use={A_use}, B0_use={B0_use}", flush=True)
# ---- P2: zeta strings + eta (all flint)
print("P2: zeta strings + eta_j (flint) ...", flush=True)
zeta_str, full_digits = get_zeta_strings(N_MAX)
eta_str = compute_eta(zeta_str, full_digits)
# ---- P3/P4: S_inf, S_f
print("P3: S_inf exact ...", flush=True)
S_inf = compute_S_inf(N_MAX, zeta_str, full_digits)
print("P4: S_f ...", flush=True)
S_f = compute_Sf(N_MAX, eta_str)
# ---- P5: validation + fit
print("P5: validation vs E-015 ...", flush=True)
e015 = {}
with E015.open() as f:
header = f.readline()
for line in f:
parts = line.strip().split(",")
if len(parts) >= 2 and parts[0].isdigit():
e015[int(parts[0])] = mp.mpf(parts[1])
worst = 0.0
mp.mp.dps = 100
for n in sorted(e015):
lam = S_inf[n] - S_f[n] + 1
dev = abs(lam - e015[n]) / abs(e015[n])
worst = max(worst, float(dev))
print(f" V1 worst rel dev vs E-015 (n<=3000): {worst:.2e}", flush=True)
C1 = (mp.mpf(GAMMA_E) - 1 - mp.log(2 * mp.pi)) / 2
fits = []
for n in (1000, 2000, 3000, 4000, 5000, 6000, 8000, 10000):
if n > N_MAX:
continue
mp.mp.dps = 100
resid = S_inf[n] - (mp.mpf(n) / 2) * mp.log(n) - C1 * n
fits.append((n, float(resid)))
print(f" S_inf residual (should -> c0): {fits}", flush=True)
# ---- write CSV
with CSV.open("w", encoding="utf-8", newline="") as f:
f.write("n,S_inf,S_f,lambda_n,abs_Sf\n")
for n in range(1, N_MAX + 1):
lam = S_inf[n] - S_f[n] + 1
f.write(f"{n},{mp.nstr(S_inf[n],12)},{mp.nstr(S_f[n],12)},"
f"{mp.nstr(lam,12)},{mp.nstr(abs(S_f[n]),12)}\n")
checks = {
# V1 floor is ~1e-24 (E-015 CSV holds 26 digits); 1e-15 still
# kills any macroscopic (convention/precision) bug — the bugs
# found in cont.10 produced 1e-8..1e143 deviations.
"V1_lambda_vs_E015": bool(worst < 1e-15),
"V2_R_bound_holds": bool(all(
v <= A_use * np.log(t + 2) + B0_use for _, t, v in R_samples)),
"V3_Sinf_residual_bounded": bool(
abs(fits[-1][1] - fits[-2][1]) < abs(fits[0][1] - fits[1][1])),
}
meta = {
"experiment": "E-021",
"task": "3.7: exact S_inf(n) + |S_f(n)| curve + D-036 constants",
"script": "research/numerics/scripts/E-021-sinf-sf-curve.py",
"parameters": {"n_max": N_MAX, "t_zeros": T_ZEROS},
"checks": checks,
"key_values": {
"A_use": A_use, "B0_use": B0_use,
"R_max_sample": max(v for *_, v in R_samples),
"C0_samples": {"1e2": C0(100), "1e4": C0(1e4), "1e6": C0(1e6)},
"eta_0": eta_str[0][:40],
"Sinf_residual_fits": fits,
"V1_worst_rel": worst,
"S_f_max_abs": mp.nstr(max(abs(S_f[n]) for n in S_f), 12),
"S_f_max_abs_n": int(max(S_f, key=lambda k: abs(S_f[k]))),
},
"elapsed_seconds": round(time.time() - t0, 1),
"timestamp_utc": datetime.now(timezone.utc).isoformat(),
}
JSON.write_text(json.dumps(meta, indent=2), encoding="utf-8")
ok = all(checks.values())
print(f"wrote {CSV.name}, {JSON.name} — "
f"{'ALL CHECKS PASS' if ok else 'CHECK FAILURE: ' + str(checks)}")
return 0 if ok else 1
if __name__ == "__main__":
raise SystemExit(main())