The region examined here is the Spherical Equilateral Right triangle under Dirichlet Boundary conditions. Side lengths are 1. This triangle was one of our test cases to determine the accuracy of MATLAB's finite element solver in spherical space and whether we could accurately assume that we could treat the remainder of the error as a portion of the geometric series. This is because this triangle is one of the regions for which the eigenvalue spectrum is known: the ith distinct eigenvalue is equal to 12+2(i-1)(7+2(i-1)), and has multiplicity i. It confirmed both that the MATLAB solver was very accurate, and that our estimate of the remaining error resulted in even more accurate values. Together with our other known cases, this triangle also helped us to determine that the accuracy of the built in solver begins to deteriorate after the first approximately 250 eigenvalues.
Here are the counting graphs for the eigenvalue
spectrum, using the true values since the spectrum is known. The first approximately 1250
values were used here.
Here are the difference graphs for the eigenvalue
spectrum, using the true values since the spectrum is known. The first approximately 1250
values were used here.
Below is the Eigenvalue spectrum for the Spherical Equilateral Right
triangle. These are the calculated and predicted eigenvalues, accompanied by their true values.
| Spherical Right Equilateral Triangle | ||||||||
|---|---|---|---|---|---|---|---|---|
| Refinement | ||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Predicted | True Value | |
| 12.16832943 | 12.04264031 | 12.0107194 | 12.00268508 | 12.00067169 | 12.00016795 | 12.00000027 | 12 | |
| 30.92847859 | 30.23553915 | 30.05924852 | 30.01484436 | 30.00371368 | 30.00092862 | 30.00000154 | 30 | |
| 31.10817657 | 30.28024859 | 30.07042777 | 30.01764039 | 30.00441283 | 30.00110342 | 30.0000018 | 30 | |
| 58.89555531 | 56.7339216 | 56.18445186 | 56.0461979 | 56.01155625 | 56.00288957 | 56.00000467 | 56 | |
| 59.60545031 | 56.9107846 | 56.22872605 | 56.05727643 | 56.0143269 | 56.00358233 | 56.00000575 | 56 | |
| 59.87165637 | 56.97753347 | 56.24542756 | 56.06145643 | 56.01537241 | 56.00384375 | 56.00000617 | 56 | |
| 97.16553893 | 91.81109473 | 90.45516235 | 90.11402124 | 90.02852459 | 90.00713265 | 90.00001185 | 90 | |
| 98.88887626 | 92.23472201 | 90.56025705 | 90.14023011 | 90.03507204 | 90.00876917 | 90.00001365 | 90 | |
| 99.74518871 | 92.45300409 | 90.61500466 | 90.15393232 | 90.03849892 | 90.009626 | 90.00001498 | 90 | |
| 100.1208093 | 92.55272129 | 90.64036196 | 90.16033022 | 90.040104 | 90.01002774 | 90.00001615 | 90 | |
| 146.5160578 | 135.6736273 | 132.9242088 | 132.2316375 | 132.0579592 | 132.0144937 | 132.0000252 | 132 | |
| 150.396585 | 136.6381668 | 133.162406 | 132.2909241 | 132.0727605 | 132.0181925 | 132.0000283 | 132 | |
| 151.8003386 | 136.9913554 | 133.2514386 | 132.3132341 | 132.0783416 | 132.0195881 | 132.0000306 | 132 | |
| 152.7219799 | 137.2375397 | 133.3146057 | 132.3292106 | 132.0823526 | 132.0205922 | 132.0000324 | 132 | |
| 154.2562291 | 137.5812818 | 133.3955685 | 132.3490457 | 132.08728 | 132.0218217 | 132.0000338 | 132 | |
| 209.8452718 | 188.9625641 | 183.7424285 | 182.4360188 | 182.1090486 | 182.027266 | 182.0000427 | 182 | |
| 215.5270294 | 190.4451412 | 184.1138887 | 182.5289008 | 182.1322696 | 182.0330712 | 182.0000508 | 182 | |
| 217.9216295 | 191.1473197 | 184.2916981 | 182.5734324 | 182.1434048 | 182.035855 | 182.0000546 | 182 | |
| 219.6365374 | 191.6068374 | 184.4090894 | 182.602986 | 182.1508105 | 182.0377078 | 182.000059 | 182 | |
| 221.5470387 | 192.1535037 | 184.5496542 | 182.6384313 | 182.1596953 | 182.0399308 | 182.0000632 | 182 | |
| 224.9730984 | 192.8072074 | 184.6974653 | 182.6744831 | 182.1686547 | 182.0421674 | 182.0000644 | 182 | |
| 285.8697669 | 251.5330442 | 242.8892147 | 240.723271 | 240.180915 | 240.045237 | 240.0000735 | 240 | |
| 294.9869808 | 253.9099551 | 243.4817917 | 240.8711334 | 240.2178539 | 240.0544696 | 240.0000833 | 240 | |
| 300.6125471 | 255.5097422 | 243.8823654 | 240.971304 | 240.2429019 | 240.0607322 | 240.0000928 | 240 | |
| 303.9000771 | 256.6030206 | 244.1596423 | 241.0407176 | 240.2602611 | 240.0650724 | 240.0000994 | 240 | |
| 308.6994311 | 257.6188972 | 244.4004996 | 241.1002031 | 240.2750923 | 240.0687781 | 240.0001016 | 240 | |
| 313.3610857 | 258.722834 | 244.6655585 | 241.165938 | 240.2915036 | 240.0728801 | 240.0001053 | 240 | |
| 315.6556743 | 259.1945856 | 244.7762824 | 241.1930884 | 240.2982551 | 240.0745656 | 240.0001062 | 240 | |
| 377.1752132 | 324.1895844 | 310.5646367 | 307.1432508 | 306.2860086 | 306.0715183 | 306.0001202 | 306 | |
| 393.583655 | 327.9903958 | 311.4786634 | 307.3692117 | 306.3423239 | 306.0855852 | 306.0001238 | 306 | |
| 400.0517694 | 330.4465249 | 312.111723 | 307.5285078 | 306.3822122 | 306.0955614 | 306.0001431 | 306 | |
| 402.5185491 | 332.4574666 | 312.6002264 | 307.6494391 | 306.4123752 | 306.1030983 | 306.0001484 | 306 | |
| 406.292866 | 332.9404826 | 312.7634199 | 307.6930636 | 306.4234594 | 306.1058804 | 306.0001542 | 306 | |
| 411.687984 | 334.5584778 | 313.1438758 | 307.7860223 | 306.4465562 | 306.1116457 | 306.0001592 | 306 | |
| 418.9730439 | 336.4970018 | 313.5835102 | 307.8933161 | 306.4732197 | 306.1183018 | 306.000163 | 306 | |
| 430.7204422 | 337.0666135 | 313.6719156 | 307.9132699 | 306.4781099 | 306.1195194 | 306.000167 | 306 | |
| 491.8077795 | 408.4055189 | 387.0977316 | 381.7755156 | 380.4440347 | 380.1110236 | 380.0001688 | 380 | |
| 496.9099078 | 414.3922856 | 388.5050989 | 382.1213288 | 380.530094 | 380.1325128 | 380.0001732 | 380 | |
| 512.7054999 | 416.9713718 | 389.2423056 | 382.310118 | 380.5775528 | 380.1443934 | 380.0002062 | 380 | |
| 518.5323187 | 418.4070016 | 389.7442224 | 382.4442792 | 380.6116458 | 380.1529523 | 380.0002125 | 380 | |
| 521.3600585 | 420.9901817 | 390.2150354 | 382.5517598 | 380.6378713 | 380.1594669 | 380.0002129 | 380 | |
| 532.7464694 | 424.1083807 | 391.0511427 | 382.7635171 | 380.6909808 | 380.1727569 | 380.000219 | 380 | |
| 539.7732361 | 425.2756987 | 391.2051254 | 382.7929143 | 380.6977983 | 380.1744286 | 380.000254 | 380 | |
| 554.4369168 | 426.5258823 | 391.6864998 | 382.9233289 | 380.7309859 | 380.1827605 | 380.0002656 | 380 | |
| 562.7489759 | 428.141522 | 391.8846012 | 382.9601416 | 380.739424 | 380.1848239 | 380.0002709 | 380 | |
| 619.9041543 | 502.0255484 | 471.9700807 | 464.4921926 | 462.6231624 | 462.1558056 | 462.0002266 | 462 | |
| 640.9017982 | 510.7164179 | 474.0029141 | 464.9910963 | 462.7472892 | 462.1867987 | 462.000235 | 462 | |
| 652.6430731 | 515.2580691 | 475.2887068 | 465.3208557 | 462.8302413 | 462.207569 | 462.0002981 | 462 | |
| 657.6724004 | 519.2867054 | 476.2778224 | 465.5659546 | 462.8913624 | 462.2228388 | 462.0003039 | 462 | |
| 661.0329873 | 522.0433668 | 476.97604 | 465.7387859 | 462.93444 | 462.2336 | 462.0003053 | 462 | |
| 678.3458585 | 525.098955 | 477.7262024 | 465.9233662 | 462.980365 | 462.2450685 | 462.0003081 | 462 | |
| 685.0848504 | 526.7353983 | 477.9331644 | 465.9739376 | 462.9931496 | 462.2482763 | 462.0003092 | 462 | |
| 699.7968408 | 529.2370197 | 478.7911654 | 466.1956041 | 463.0488478 | 462.2622154 | 462.0003274 | 462 | |
| 714.9483397 | 530.4594106 | 478.9890898 | 466.2353199 | 463.0582178 | 462.264526 | 462.0003281 | 462 | |
| 734.6033839 | 533.0751952 | 479.6721898 | 466.4030451 | 463.0998018 | 462.2748936 | 462.0003667 | 462 | |
| 753.623366 | 607.6586177 | 565.9044679 | 555.4783325 | 552.8699335 | 552.2175171 | 552.0003453 | 552 | |
| 785.0139688 | 616.9525915 | 568.2660787 | 556.0675661 | 553.0171258 | 552.2543083 | 552.0003851 | 552 | |
| 790.6582838 | 625.8980313 | 570.3611823 | 556.5831811 | 553.1455167 | 552.2863715 | 552.0003869 | 552 | |
| 815.9635539 | 630.9685466 | 571.7107144 | 556.9240132 | 553.2309358 | 552.3077398 | 552.0004112 | 552 | |
| 829.8350029 | 637.2532804 | 573.2936595 | 557.3126894 | 553.327573 | 552.331864 | 552.0004192 | 552 | |
| 845.5707089 | 638.8346217 | 573.701333 | 557.4211634 | 553.355176 | 552.3387958 | 552.0004327 | 552 | |
| 856.5884465 | 642.4156836 | 574.4607284 | 557.5970218 | 553.3982143 | 552.3495 | 552.000445 | 552 | |
| 884.7004889 | 645.0323671 | 575.2862725 | 557.8133033 | 553.4528449 | 552.3631883 | 552.0004556 | 552 | |
| 903.5438483 | 648.0584133 | 576.0658076 | 558.0061067 | 553.5009398 | 552.3752072 | 552.0004702 | 552 | |
| 929.8132655 | 651.2318335 | 576.593845 | 558.1265734 | 553.5304296 | 552.3825449 | 552.0004709 | 552 | |
| 935.0324134 | 653.1520476 | 577.2702858 | 558.299646 | 553.5737482 | 552.3933713 | 552.000481 | 552 | |
| 951.9217088 | 728.4651789 | 669.4776588 | 654.8646942 | 651.2161774 | 650.3040609 | 650.0004418 | 650 | |
| 958.9666729 | 742.7091014 | 673.0657339 | 655.7520233 | 651.4372289 | 650.3592714 | 650.0004483 | 650 | |
| 996.0809802 | 747.8230787 | 674.4534626 | 656.1141544 | 651.5288911 | 650.3822608 | 650.0004838 | 650 | |
| 1029.396911 | 754.3605455 | 676.2224938 | 656.5541889 | 651.6386123 | 650.4096673 | 650.0005379 | 650 | |
| 1037.405113 | 762.1948517 | 678.5136408 | 657.1374746 | 651.7849542 | 650.446283 | 650.0005698 | 650 | |
| 1061.601577 | 766.985072 | 679.4341319 | 657.3618422 | 651.8407964 | 650.4602314 | 650.0005784 | 650 | |
| 1070.687268 | 773.4227124 | 680.937476 | 657.7219022 | 651.9297613 | 650.4824063 | 650.0005846 | 650 | |
| 1093.290237 | 776.4215143 | 681.4946163 | 657.8485669 | 651.9606513 | 650.4900826 | 650.0006207 | 650 | |
| 1109.99435 | 782.2108579 | 682.8046436 | 658.1567049 | 652.0363692 | 650.508928 | 650.000639 | 650 | |
| 1151.939334 | 784.0849142 | 683.6485597 | 658.3940032 | 652.0972967 | 650.5242604 | 650.0006753 | 650 | |
| 1180.202107 | 786.2370317 | 684.526181 | 658.58508 | 652.1435619 | 650.535739 | 650.0006784 | 650 | |
| 1197.484159 | 789.7596777 | 684.6442026 | 658.6719518 | 652.1687006 | 650.5422331 | 650.0008258 | 650 | |
| 1224.033964 | 861.6767398 | 781.9736009 | 762.470469 | 757.6165303 | 756.4040813 | 756.0004299 | 756 | |
| 1239.169686 | 884.0644704 | 787.1829691 | 763.7400848 | 757.9318758 | 756.4827912 | 756.0004896 | 756 | |
| 1255.48831 | 885.9412567 | 788.4253999 | 764.1033225 | 758.0260986 | 756.5065633 | 756.0005844 | 756 | |
| 1269.856489 | 893.9818052 | 791.0660726 | 764.7808747 | 758.1963111 | 756.5491656 | 756.0006469 | 756 | |
| 1306.208467 | 902.2589784 | 793.2891942 | 765.3543472 | 758.3409268 | 756.5853962 | 756.0007059 | 756 | |
| 1308.957773 | 908.4790535 | 794.8640344 | 765.7378767 | 758.4360093 | 756.6091135 | 756.0007509 | 756 | |
| 1347.802629 | 919.142321 | 797.1386621 | 766.2648894 | 758.5649809 | 756.6411782 | 756.000796 | 756 | |
| 1362.754634 | 919.7703535 | 797.5049379 | 766.3619313 | 758.5895929 | 756.6473576 | 756.0008397 | 756 | |
| 1392.28707 | 928.0491466 | 799.4507456 | 766.8191725 | 758.7018809 | 756.6753001 | 756.0008752 | 756 | |
| 1410.491865 | 930.1267511 | 799.951079 | 766.98005 | 758.7442533 | 756.6860287 | 756.0009011 | 756 | |
| 1448.290425 | 937.3817682 | 801.5068498 | 767.3626389 | 758.8399696 | 756.7099696 | 756.0009498 | 756 | |
| 1509.31387 | 945.1075088 | 803.0181757 | 767.6726357 | 758.9129311 | 756.7279169 | 756.000989 | 756 | |
| 1545.297744 | 947.7433474 | 803.9488579 | 767.9110743 | 758.9728679 | 756.7429325 | 756.0010273 | 756 | |
| 1564.433623 | 1001.022778 | 902.7149103 | 878.179047 | 872.0453357 | 870.5113986 | 870.0007922 | 870 | |
| 1595.057682 | 1030.224667 | 910.0637037 | 880.0001164 | 872.4993765 | 870.6248322 | 870.0008244 | 870 | |
| 1609.022337 | 1040.907082 | 912.3156311 | 880.5461844 | 872.6351085 | 870.6587133 | 870.0008314 | 870 | |
| 1682.477563 | 1057.41829 | 917.3984849 | 881.8226905 | 872.9539062 | 870.7383876 | 870.0008468 | 870 | |
| 1687.07829 | 1059.227886 | 918.2292976 | 882.0987825 | 873.0277076 | 870.7571396 | 870.000855 | 870 | |
| 1721.568757 | 1076.23798 | 922.271107 | 883.0493226 | 873.2610779 | 870.8152072 | 870.0008885 | 870 | |
| 1747.302674 | 1078.870905 | 923.577123 | 883.4226333 | 873.3574034 | 870.8394837 | 870.000901 | 870 | |
| 1763.297241 | 1088.021479 | 925.4398312 | 883.8143262 | 873.4502896 | 870.8623825 | 870.0009379 | 870 | |
| 1821.008649 | 1093.18218 | 926.9433946 | 884.1639611 | 873.5362785 | 870.8837954 | 870.0010426 | 870 | |
| 1858.18282 | 1098.844748 | 927.188755 | 884.2679823 | 873.5649937 | 870.8911406 | 870.0010868 | 870 | |
| 1873.403171 | 1101.487039 | 928.9936198 | 884.6807397 | 873.6654544 | 870.916081 | 870.0011088 | 870 | |
| 1905.235291 | 1109.262338 | 931.1987411 | 885.3039162 | 873.8258814 | 870.9564807 | 870.0013286 | 870 | |
| 1941.757591 | 1111.212731 | 932.3313378 | 885.5290066 | 873.8763612 | 870.9687102 | 870.0013344 | 870 | |
| 2008.322841 | 1121.880362 | 933.329797 | 885.758156 | 873.9358886 | 870.9837848 | 870.0013359 | 870 | |
| 2097.660828 | 1168.878817 | 1035.369506 | 1002.790741 | 994.6951028 | 992.6736443 | 992.0007552 | 992 | |
| 2134.16773 | 1201.657871 | 1044.221796 | 1005.027454 | 995.2556633 | 992.8138861 | 992.000974 | 992 | |
| 2185.558921 | 1208.546567 | 1045.967051 | 1005.439585 | 995.3571567 | 992.8391506 | 992.0009784 | 992 | |
| 0 | 1231.067205 | 1052.540412 | 1007.123459 | 995.780023 | 992.9449744 | 992.0009914 | 992 | |
| 0 | 1238.712982 | 1054.063028 | 1007.46504 | 995.8636543 | 992.9657868 | 992.0010842 | 992 | |
| 0 | 1257.829072 | 1059.556028 | 1008.87762 | 996.218847 | 993.0547066 | 992.0011153 | 992 | |
| 0 | 1260.171306 | 1060.394441 | 1009.098358 | 996.2745637 | 993.0686687 | 992.001133 | 992 | |
| 0 | 1272.590787 | 1063.861958 | 1009.905635 | 996.4713185 | 993.1175218 | 992.0011647 | 992 | |
| 0 | 1273.92353 | 1064.932973 | 1010.232881 | 996.5575808 | 993.1393716 | 992.0011883 | 992 | |
| 0 | 1281.36455 | 1066.432002 | 1010.565491 | 996.638514 | 993.1594767 | 992.0012629 | 992 | |
| 0 | 1287.597309 | 1066.830107 | 1010.611357 | 996.6464511 | 993.1612463 | 992.0013987 | 992 | |
| 0 | 1292.566423 | 1069.860035 | 1011.350591 | 996.829231 | 993.206801 | 992.0014493 | 992 | |
| 0 | 1304.197035 | 1072.563925 | 1012.038294 | 997.000333 | 993.2495224 | 992.001474 | 992 | |
| 0 | 1306.977545 | 1073.04094 | 1012.202256 | 997.047178 | 993.2615933 | 992.0015125 | 992 | |
| 0 | 1311.535841 | 1074.697047 | 1012.56969 | 997.1348951 | 993.2832856 | 992.0015417 | 992 | |
| 0 | 1334.256991 | 1175.194125 | 1135.291663 | 1125.323299 | 1122.830894 | 1122.000896 | 1122 | |
| 0 | 1377.359728 | 1186.96828 | 1138.25221 | 1126.064129 | 1123.016149 | 1122.001021 | 1122 | |
| 0 | 1402.186941 | 1190.941261 | 1139.097982 | 1126.266773 | 1123.066261 | 1122.001166 | 1122 | |
| 0 | 1419.996584 | 1197.36048 | 1140.81977 | 1126.704364 | 1123.176106 | 1122.001196 | 1122 | |
| 0 | 1431.241158 | 1200.58683 | 1141.567405 | 1126.887235 | 1123.221564 | 1122.001239 | 1122 | |
| 0 | 1451.874526 | 1206.186288 | 1143.027958 | 1127.25621 | 1123.31405 | 1122.001256 | 1122 | |
| 0 | 1465.682113 | 1210.032958 | 1143.858767 | 1127.454078 | 1123.362873 | 1122.00136 | 1122 | |
| 0 | 1467.661111 | 1211.636429 | 1144.410719 | 1127.602985 | 1123.400804 | 1122.001427 | 1122 | |
| 0 | 1476.635521 | 1214.79513 | 1145.078939 | 1127.760161 | 1123.439446 | 1122.001558 | 1122 | |
| 0 | 1487.328709 | 1216.70803 | 1145.559918 | 1127.882114 | 1123.470076 | 1122.00159 | 1122 | |
| 0 | 1490.07658 | 1218.031267 | 1145.860383 | 1127.953904 | 1123.487809 | 1122.001644 | 1122 | |
| 0 | 1496.871631 | 1218.914337 | 1146.165156 | 1128.03672 | 1123.508925 | 1122.001724 | 1122 | |
| 0 | 1502.5264 | 1222.419169 | 1147.043536 | 1128.253995 | 1123.563072 | 1122.001743 | 1122 | |
| 0 | 1509.128844 | 1225.116187 | 1147.640652 | 1128.398511 | 1123.598913 | 1122.001811 | 1122 | |
| 0 | 1510.76189 | 1226.011025 | 1147.961888 | 1128.484316 | 1123.620694 | 1122.002011 | 1122 | |
| 0 | 1523.057342 | 1228.271611 | 1148.597618 | 1128.648324 | 1123.662007 | 1122.002196 | 1122 | |
| 0 | 1535.05964 | 1327.545614 | 1276.797719 | 1264.194969 | 1261.048516 | 1260.000334 | 1260 | |
| 0 | 1574.300501 | 1339.842914 | 1279.976721 | 1264.996259 | 1261.249264 | 1260.001125 | 1260 | |
| 0 | 1602.709419 | 1346.102206 | 1281.378605 | 1265.335443 | 1261.333323 | 1260.001147 | 1260 | |
| 0 | 1626.445262 | 1352.443352 | 1283.084036 | 1265.771309 | 1261.442927 | 1260.001638 | 1260 | |
| 0 | 1637.335945 | 1358.845466 | 1284.676852 | 1266.164758 | 1261.540916 | 1260.001763 | 1260 | |
| 0 | 1657.454877 | 1362.28619 | 1285.581023 | 1266.397887 | 1261.599711 | 1260.001854 | 1260 | |
| 0 | 1659.648828 | 1368.140259 | 1287.023737 | 1266.754863 | 1261.688682 | 1260.001902 | 1260 | |
| 0 | 1674.323943 | 1371.363902 | 1287.851879 | 1266.963739 | 1261.741034 | 1260.00199 | 1260 | |
| 0 | 1687.444261 | 1374.8898 | 1288.819001 | 1267.206773 | 1261.801803 | 1260.00211 | 1260 | |
| 0 | 1697.899902 | 1379.052109 | 1289.54405 | 1267.359371 | 1261.838188 | 1260.002125 | 1260 | |
| 0 | 1707.187897 | 1379.524103 | 1289.694262 | 1267.415591 | 1261.853404 | 1260.002157 | 1260 | |
| 0 | 1720.737889 | 1381.206524 | 1290.222763 | 1267.549904 | 1261.887139 | 1260.002224 | 1260 | |
| 0 | 1723.92469 | 1383.342341 | 1290.742155 | 1267.680851 | 1261.920005 | 1260.002286 | 1260 | |
| 0 | 1729.465429 | 1387.425532 | 1291.760061 | 1267.929511 | 1261.981715 | 1260.002374 | 1260 | |
| 0 | 1734.027938 | 1389.51475 | 1292.311467 | 1268.069575 | 1262.016887 | 1260.002528 | 1260 | |
| 0 | 1743.459157 | 1391.938944 | 1292.856423 | 1268.200112 | 1262.049133 | 1260.002536 | 1260 | |
| 0 | 1750.584458 | 1395.219145 | 1293.740145 | 1268.426656 | 1262.10615 | 1260.002634 | 1260 | |
| 0 | 1757.520275 | 1489.973122 | 1426.890241 | 1411.217312 | 1407.30407 | 1406.000817 | 1406 | |
| 0 | 1793.357747 | 1503.849676 | 1430.49379 | 1412.127607 | 1407.532262 | 1406.001053 | 1406 | |
| 0 | 1837.895485 | 1514.565506 | 1432.844809 | 1412.692324 | 1407.671961 | 1406.001185 | 1406 | |
| 0 | 1848.178174 | 1519.246094 | 1434.319656 | 1413.081625 | 1407.770589 | 1406.00124 | 1406 | |
| 0 | 1868.273375 | 1529.470328 | 1436.625061 | 1413.638817 | 1407.908656 | 1406.001299 | 1406 | |
| 0 | 1875.175056 | 1530.01022 | 1437.076903 | 1413.774807 | 1407.944118 | 1406.001457 | 1406 | |
| 0 | 1887.473817 | 1540.964113 | 1439.611522 | 1414.392115 | 1408.097391 | 1406.001759 | 1406 | |
| 0 | 1898.594374 | 1542.885179 | 1440.154345 | 1414.531873 | 1408.132599 | 1406.00203 | 1406 | |
| 0 | 1921.861738 | 1548.205081 | 1441.58916 | 1414.897931 | 1408.224598 | 1406.002046 | 1406 | |
| 0 | 1924.258732 | 1550.765067 | 1442.14613 | 1415.028174 | 1408.25648 | 1406.002224 | 1406 | |
| 0 | 1935.725651 | 1552.332725 | 1442.451306 | 1415.097213 | 1408.273267 | 1406.002365 | 1406 | |
| 0 | 1947.696977 | 1557.25443 | 1443.635145 | 1415.384572 | 1408.344503 | 1406.002453 | 1406 | |
| 0 | 1952.875789 | 1559.250872 | 1444.168278 | 1415.532104 | 1408.382491 | 1406.002577 | 1406 | |
| 0 | 1962.079564 | 1560.534943 | 1444.557351 | 1415.632597 | 1408.407765 | 1406.002595 | 1406 | |
| 0 | 1969.975354 | 1566.562149 | 1445.872405 | 1415.94154 | 1408.483699 | 1406.002688 | 1406 | |
| 0 | 1974.92446 | 1567.266649 | 1446.152202 | 1416.022743 | 1408.504759 | 1406.002813 | 1406 | |
| 0 | 1990.005018 | 1571.669978 | 1447.183493 | 1416.269879 | 1408.565784 | 1406.003225 | 1406 | |
| 0 | 1992.575453 | 1575.118375 | 1448.082467 | 1416.501429 | 1408.624161 | 1406.003239 | 1406 | |
| 0 | 2013.549814 | 1662.850023 | 1585.529437 | 1566.372543 | 1561.592605 | 1560.000157 | 1560 | |
| 0 | 2025.64583 | 1680.474733 | 1590.193961 | 1567.554704 | 1561.889177 | 1560.000694 | 1560 | |
| 0 | 2089.643478 | 1694.88731 | 1593.236122 | 1568.275557 | 1562.066864 | 1560.001492 | 1560 | |
| 0 | 2096.572396 | 1698.266982 | 1594.452819 | 1568.60903 | 1562.152117 | 1560.001506 | 1560 | |
| 0 | 2109.87425 | 1710.349164 | 1597.446488 | 1569.350941 | 1562.337147 | 1560.001621 | 1560 | |
| 0 | 2126.652535 | 1711.438953 | 1597.744473 | 1569.431915 | 1562.357842 | 1560.001623 | 1560 | |
| 0 | 2132.1253 | 1720.868125 | 1600.241693 | 1570.061499 | 1562.515547 | 1560.00183 | 1560 | |
| 0 | 2135.268092 | 1725.988985 | 1601.438848 | 1570.349627 | 1562.58677 | 1560.00213 | 1560 | |
| 0 | 2146.612722 | 1733.820705 | 1603.433294 | 1570.85613 | 1562.713978 | 1560.002186 | 1560 | |
| 0 | 2165.919071 | 1734.945318 | 1603.710243 | 1570.922503 | 1562.730407 | 1560.002444 | 1560 | |
| 0 | 2172.821459 | 1740.346383 | 1604.91964 | 1571.203889 | 1562.7992 | 1560.002476 | 1560 | |
| 0 | 2202.855521 | 1743.092113 | 1605.512202 | 1571.353366 | 1562.836775 | 1560.002723 | 1560 | |
| 0 | 2206.964947 | 1747.191838 | 1606.236323 | 1571.52696 | 1562.879973 | 1560.002785 | 1560 | |
| 0 | 2218.271129 | 1748.67584 | 1606.951508 | 1571.715766 | 1562.927547 | 1560.003073 | 1560 | |
| 0 | 2219.611986 | 1753.656553 | 1608.16408 | 1572.016933 | 1563.002719 | 1560.003275 | 1560 | |
| 0 | 2231.673303 | 1757.730645 | 1609.321936 | 1572.303068 | 1563.073797 | 1560.003479 | 1560 | |
| 0 | 0 | 1759.6315 | 1609.801297 | 1572.42892 | 1563.105869 | 1560.003675 | 1560 | |
| 0 | 0 | 1763.721818 | 1610.457597 | 1572.571386 | 1563.140111 | 1560.003702 | 1560 | |
| 0 | 0 | 1767.458675 | 1611.910267 | 1572.970305 | 1563.24209 | 1560.003829 | 1560 | |
| 0 | 0 | 1846.533727 | 1752.886494 | 1729.708047 | 1723.92628 | 1721.999445 | 1722 | |
| 0 | 0 | 1867.610602 | 1758.311026 | 1731.07525 | 1724.268812 | 1722.000789 | 1722 | |
| 0 | 0 | 1885.525597 | 1762.131013 | 1731.982764 | 1724.492689 | 1722.001491 | 1722 | |
| 0 | 0 | 1886.72463 | 1762.98721 | 1732.243032 | 1724.560764 | 1722.001685 | 1722 | |
| 0 | 0 | 1902.722575 | 1767.121033 | 1733.274569 | 1724.818351 | 1722.002213 | 1722 | |
| 0 | 0 | 1905.936872 | 1767.791287 | 1733.431767 | 1724.856958 | 1722.002331 | 1722 | |
| 0 | 0 | 1915.652831 | 1770.304572 | 1734.06527 | 1725.01572 | 1722.002342 | 1722 | |
| 0 | 0 | 1924.071114 | 1772.446527 | 1734.592502 | 1725.146799 | 1722.002578 | 1722 | |
| 0 | 0 | 1927.452903 | 1773.509493 | 1734.890959 | 1725.223834 | 1722.002634 | 1722 | |
| 0 | 0 | 1935.264998 | 1775.319834 | 1735.321148 | 1725.329774 | 1722.003011 | 1722 | |
| 0 | 0 | 1939.120682 | 1776.389969 | 1735.583415 | 1725.394764 | 1722.003131 | 1722 | |
| 0 | 0 | 1942.109403 | 1776.793073 | 1735.676647 | 1725.417879 | 1722.003156 | 1722 | |
| 0 | 0 | 1945.117635 | 1777.784067 | 1735.928229 | 1725.480818 | 1722.003236 | 1722 | |
| 0 | 0 | 1948.904337 | 1778.493084 | 1736.092351 | 1725.521195 | 1722.003368 | 1722 | |
| 0 | 0 | 1952.267287 | 1779.0745 | 1736.249576 | 1725.561487 | 1722.003503 | 1722 | |
| 0 | 0 | 1960.370937 | 1781.345171 | 1736.803977 | 1725.698909 | 1722.003525 | 1722 | |
| 0 | 0 | 1963.272858 | 1781.818263 | 1736.903068 | 1725.722499 | 1722.003543 | 1722 | |
| 0 | 0 | 1964.311016 | 1782.609514 | 1737.134345 | 1725.782311 | 1722.00371 | 1722 | |
| 0 | 0 | 1969.703939 | 1783.541446 | 1737.341297 | 1725.83247 | 1722.003915 | 1722 | |
| 0 | 0 | 1977.624078 | 1785.783107 | 1737.910205 | 1725.975091 | 1722.005909 | 1722 | |
| 0 | 0 | 2042.452578 | 1929.236422 | 1901.287806 | 1894.320752 | 1891.999277 | 1892 | |
| 0 | 0 | 2062.029111 | 1934.648589 | 1902.674674 | 1894.669645 | 1892.000137 | 1892 | |
| 0 | 0 | 2087.552945 | 1940.559037 | 1904.097288 | 1895.021292 | 1892.001164 | 1892 | |
| 0 | 0 | 2091.649279 | 1941.24074 | 1904.282028 | 1895.069322 | 1892.001198 | 1892 | |
| 0 | 0 | 2106.417778 | 1945.436268 | 1905.346728 | 1895.335999 | 1892.001607 | 1892 | |
| 0 | 0 | 2112.088804 | 1946.864149 | 1905.699384 | 1895.423828 | 1892.001928 | 1892 | |
| 0 | 0 | 2121.977839 | 1949.22734 | 1906.283461 | 1895.569517 | 1892.002502 | 1892 | |
| 0 | 0 | 2134.216848 | 1952.446003 | 1907.085952 | 1895.76973 | 1892.00266 | 1892 | |
| 0 | 0 | 2136.6724 | 1953.236373 | 1907.310735 | 1895.828051 | 1892.002752 | 1892 | |
| 0 | 0 | 2148.043283 | 1956.072455 | 1907.987808 | 1895.994877 | 1892.002832 | 1892 | |
| 0 | 0 | 2149.645897 | 1956.473672 | 1908.122285 | 1896.03082 | 1892.002864 | 1892 | |
| 0 | 0 | 2157.604701 | 1958.515346 | 1908.577671 | 1896.140998 | 1892.003134 | 1892 | |
| 0 | 0 | 2160.745432 | 1958.861559 | 1908.698984 | 1896.173358 | 1892.003372 | 1892 | |
| 0 | 0 | 2163.952317 | 1959.90159 | 1908.915806 | 1896.225469 | 1892.003423 | 1892 | |
| 0 | 0 | 2166.281923 | 1960.200748 | 1909.04693 | 1896.261604 | 1892.003697 | 1892 | |
| 0 | 0 | 2172.771723 | 1961.717756 | 1909.386381 | 1896.34397 | 1892.003914 | 1892 | |
| 0 | 0 | 2178.703589 | 1963.902603 | 1909.956727 | 1896.487747 | 1892.004286 | 1892 | |
| 0 | 0 | 2182.716127 | 1964.567975 | 1910.10898 | 1896.52468 | 1892.004987 | 1892 | |
| 0 | 0 | 2185.583124 | 1965.199666 | 1910.247117 | 1896.5585 | 1892.005713 | 1892 | |
| 0 | 0 | 2192.923015 | 1966.842598 | 1910.630475 | 1896.652251 | 1892.005775 | 1892 | |
| 0 | 0 | 2200.43718 | 1968.878433 | 1911.18431 | 1896.793678 | 1892.005897 | 1892 | |
| 0 | 0 | 0 | 2113.689918 | 2080.894777 | 2072.722113 | 2069.999227 | 2070 | |
| 0 | 0 | 0 | 2121.136393 | 2082.778795 | 2073.194647 | 2070.00118 | 2070 | |
| 0 | 0 | 0 | 2127.422 | 2084.326423 | 2073.57924 | 2070.001261 | 2070 | |
| 0 | 0 | 0 | 2128.073185 | 2084.482029 | 2073.619101 | 2070.001652 | 2070 | |
| 0 | 0 | 0 | 2132.139761 | 2085.530109 | 2073.882563 | 2070.001769 | 2070 | |
| 0 | 0 | 0 | 2135.355 | 2086.288546 | 2074.069246 | 2070.001791 | 2070 | |
| 0 | 0 | 0 | 2137.216674 | 2086.771195 | 2074.191016 | 2070.002577 | 2070 | |
| 0 | 0 | 0 | 2141.212206 | 2087.781602 | 2074.444335 | 2070.002868 | 2070 | |
| 0 | 0 | 0 | 2142.406523 | 2088.059436 | 2074.512334 | 2070.003125 | 2070 | |
| 0 | 0 | 0 | 2145.079288 | 2088.732304 | 2074.680713 | 2070.003308 | 2070 | |
| 0 | 0 | 0 | 2145.983005 | 2088.991503 | 2074.747931 | 2070.003317 | 2070 | |
| 0 | 0 | 0 | 2149.272537 | 2089.755759 | 2074.93477 | 2070.003378 | 2070 | |
| 0 | 0 | 0 | 2149.456098 | 2089.855027 | 2074.962661 | 2070.003413 | 2070 | |
| 0 | 0 | 0 | 2150.04214 | 2089.969361 | 2074.989651 | 2070.003602 | 2070 | |
| 0 | 0 | 0 | 2151.570735 | 2090.37976 | 2075.093567 | 2070.00385 | 2070 | |
| 0 | 0 | 0 | 2152.155155 | 2090.488242 | 2075.119643 | 2070.004046 | 2070 | |
| 0 | 0 | 0 | 2153.650416 | 2090.868894 | 2075.214522 | 2070.004341 | 2070 | |
| 0 | 0 | 0 | 2156.843121 | 2091.674581 | 2075.414966 | 2070.004718 | 2070 | |
| 0 | 0 | 0 | 2157.108195 | 2091.730069 | 2075.429424 | 2070.005204 | 2070 | |
| 0 | 0 | 0 | 2157.970701 | 2091.922816 | 2075.475912 | 2070.005393 | 2070 | |
| 0 | 0 | 0 | 2159.760452 | 2092.344659 | 2075.579798 | 2070.005408 | 2070 | |
| 0 | 0 | 0 | 2162.276608 | 2093.024086 | 2075.753094 | 2070.006629 | 2070 |