Three triangles were created by choosing angles arbitrarily. The first two angles chosen were then joined to a side of length 1, with the third angle opposite the length 1 side. All sides were given Dirichlet Boundary Conditions, and the first approximately 150 Eigenvalues of the Laplacian operator on the Spectrum were generated using the finite element solver built into MATLAB. The solver uses an auto-generated mesh that is refined for successively more accurate estimations for the Eigenvalues.
The three Euclidean Triangles analyzed had angle measures of [pi/20,pi/5,3pi/4],[pi/4,pi/5,11pi/20], and [2pi/7,pi/7,4pi/7], respectively.
Here N'(t) = (Area/4pi)*t - (Perimeter/4pi)*t^1/2 + Sum(pi/theta-theta/pi).
Difference Graphs and Scatterplots for the three triangles
Calculated and Predicted Eigenvalue Spectrums for the Three Triangles
| Triangle 1 | ||||||||
|---|---|---|---|---|---|---|---|---|
| Theta1: pi/20 | Theta 2: pi/5 | Theta 3: 3pi/4 | ||||||
| Refinement | ||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | Predicted Value | |
| 1072.42869 | 894.715377 | 847.0646162 | 835.0103063 | 831.9710627 | 831.2070514 | 831.0153835 | 830.9516972 | |
| 1752.024482 | 1314.325506 | 1187.889619 | 1156.577205 | 1148.766499 | 1146.812803 | 1146.32398 | 1146.161556 | |
| 3263.926327 | 1768.853095 | 1534.930077 | 1479.226535 | 1465.528372 | 1462.117007 | 1461.264807 | 1460.981643 | |
| 0 | 2230.306281 | 1888.622216 | 1808.107814 | 1788.339188 | 1783.418934 | 1782.190172 | 1781.781886 | |
| 0 | 2688.532443 | 2250.283704 | 2143.268744 | 2116.903353 | 2110.336845 | 2108.696659 | 2108.151667 | |
| 0 | 3181.728035 | 2625.202769 | 2487.682877 | 2453.714159 | 2445.246717 | 2443.130867 | 2442.427825 | |
| 0 | 3519.207717 | 3000.041672 | 2842.524088 | 2801.579634 | 2791.265095 | 2788.680594 | 2787.821831 | |
| 0 | 3845.422667 | 3161.725843 | 3011.67762 | 2976.290628 | 2967.538816 | 2965.354289 | 2964.628427 | |
| 0 | 4286.572238 | 3486.818541 | 3262.458083 | 3206.518758 | 3192.554266 | 3189.064252 | 3187.904611 | |
| 0 | 4696.276975 | 3897.478242 | 3667.471655 | 3603.90291 | 3587.579235 | 3583.473883 | 3582.10978 | |
| 0 | 5132.945195 | 4013.079942 | 3732.892977 | 3669.425286 | 3654.001306 | 3650.167837 | 3648.894074 | |
| 0 | 5763.731635 | 4475.031585 | 4124.17359 | 4037.026679 | 4015.288832 | 4009.857186 | 4008.052389 | |
| 0 | 6161.626999 | 4826.454882 | 4420.523353 | 4316.26905 | 4290.064299 | 4283.503731 | 4281.323823 | |
| 0 | 6321.942868 | 5016.148007 | 4589.869631 | 4484.403884 | 4458.096107 | 4451.521523 | 4449.336958 | |
| 0 | 7175.033177 | 5586.060169 | 5069.157988 | 4923.83873 | 4886.515676 | 4877.163467 | 4874.055968 | |
| 0 | 7373.815023 | 5743.745255 | 5111.238001 | 4974.369349 | 4941.735664 | 4933.637841 | 4930.947142 | |
| 0 | 7884.480226 | 6196.141492 | 5587.706681 | 5429.710318 | 5389.448763 | 5379.325919 | 5375.962358 | |
| 0 | 8518.642038 | 6482.510963 | 5728.984556 | 5544.899866 | 5500.039632 | 5488.910303 | 5485.212313 | |
| 0 | 9102.594649 | 6848.700268 | 6125.915556 | 5942.053678 | 5895.446131 | 5883.741143 | 5879.851876 | |
| 0 | 9709.302018 | 6983.183764 | 6254.495322 | 6059.855967 | 6010.716366 | 5998.417437 | 5994.330819 | |
| 0 | 10412.55315 | 7559.62502 | 6619.540666 | 6416.991271 | 6368.5126 | 6356.499457 | 6352.507798 | |
| 0 | 10916.00224 | 7574.289324 | 6709.382669 | 6490.975582 | 6436.220837 | 6422.522747 | 6417.971224 | |
| 0 | 11246.81981 | 8114.643126 | 7058.44366 | 6789.269792 | 6722.960866 | 6706.46897 | 6700.989137 | |
| 0 | 12242.44818 | 8296.19318 | 7292.612429 | 7038.505835 | 6974.882026 | 6958.965989 | 6953.677499 | |
| 0 | 12418.48696 | 8667.979794 | 7625.47219 | 7344.821509 | 7271.736803 | 7253.317909 | 7247.197783 | |
| 0 | 13411.7314 | 9107.706296 | 7857.08912 | 7570.955136 | 7502.166368 | 7485.043578 | 7479.354115 | |
| 0 | 16242.0096 | 9209.643889 | 7954.865994 | 7664.062879 | 7594.038141 | 7576.75545 | 7571.012855 | |
| 0 | 17720.93242 | 9856.742452 | 8409.613483 | 8032.141824 | 7938.162415 | 7914.710236 | 7906.917679 | |
| 0 | 17960.79339 | 10004.63106 | 8592.670554 | 8238.690385 | 8150.725795 | 8128.769918 | 8121.474543 | |
| 0 | 0 | 10368.20269 | 8947.486835 | 8612.249518 | 8527.937741 | 8506.659158 | 8499.588832 | |
| 0 | 0 | 10848.38489 | 9125.229134 | 8687.174254 | 8579.226228 | 8552.483457 | 8543.597522 | |
| 0 | 0 | 11017.04405 | 9307.307605 | 8887.926793 | 8784.167457 | 8758.298329 | 8749.702682 | |
| 0 | 0 | 11773.46172 | 9857.139493 | 9351.888162 | 9225.937017 | 9194.498561 | 9184.052369 | |
| 0 | 0 | 11923.4838 | 10019.45818 | 9548.978807 | 9432.230038 | 9403.099871 | 9393.420664 | |
| 0 | 0 | 12184.83713 | 10135.7616 | 9616.871797 | 9487.367787 | 9454.999019 | 9444.243709 | |
| 0 | 0 | 12748.74198 | 10598.70214 | 10034.34804 | 9892.914391 | 9857.54607 | 9845.794086 | |
| 0 | 0 | 12841.97869 | 10761.60631 | 10231.36078 | 10099.02163 | 10065.95931 | 10054.97355 | |
| 0 | 0 | 13348.3889 | 11110.32757 | 10482.93252 | 10324.62249 | 10285.13219 | 10272.01057 | |
| 0 | 0 | 13906.27785 | 11371.99803 | 10737.5831 | 10577.66963 | 10537.60684 | 10524.295 | |
| 0 | 0 | 14042.24195 | 11463.63948 | 10877.45301 | 10736.50084 | 10701.3706 | 10689.69772 | |
| 0 | 0 | 14281.6623 | 11732.56695 | 11085.52139 | 10923.93191 | 10883.52153 | 10870.0942 | |
| 0 | 0 | 15010.94298 | 12185.35723 | 11442.91788 | 11261.46072 | 11216.44583 | 11201.48854 | |
| 0 | 0 | 15117.24032 | 12368.03904 | 11593.00175 | 11406.96503 | 11361.07325 | 11345.8246 | |
| 0 | 0 | 15487.93191 | 12492.4888 | 11768.84194 | 11586.98862 | 11541.43246 | 11526.29532 | |
| 0 | 0 | 15787.55707 | 12984.82459 | 12162.41197 | 11954.38291 | 11902.54658 | 11885.3227 | |
| 0 | 0 | 16152.05041 | 13053.38938 | 12281.30606 | 12080.59041 | 12029.97275 | 12013.1538 | |
| 0 | 0 | 16586.42312 | 13366.62451 | 12508.34126 | 12302.27913 | 12251.10224 | 12234.09748 | |
| 0 | 0 | 17105.30707 | 13699.08781 | 12883.80897 | 12679.95477 | 12627.00942 | 12609.41704 | |
| 0 | 0 | 17456.66113 | 13892.30406 | 12964.02567 | 12745.12814 | 12692.88008 | 12675.51939 | |
| 0 | 0 | 17618.65294 | 14290.75739 | 13247.12191 | 12995.0895 | 12933.1422 | 12912.5587 | |
| 0 | 0 | 18073.91303 | 14308.15214 | 13395.48935 | 13165.44444 | 13107.86773 | 13088.73646 | |
| 0 | 0 | 18653.57661 | 14800.89371 | 13757.34579 | 13497.52693 | 13432.73018 | 13411.19989 | |
| 0 | 0 | 19119.50839 | 15086.14768 | 14076.69457 | 13786.34334 | 13713.9438 | 13689.88729 | |
| 0 | 0 | 19227.78247 | 15235.52367 | 14163.375 | 13921.01925 | 13859.54347 | 13839.11666 | |
| 0 | 0 | 19662.10526 | 15510.92729 | 14444.28882 | 14210.58151 | 14153.97122 | 14135.16108 | |
| 0 | 0 | 19898.73049 | 15743.07606 | 14581.90484 | 14293.07374 | 14221.12168 | 14197.21386 | |
| 0 | 0 | 20380.03404 | 16191.642 | 14949.01825 | 14624.93176 | 14543.81043 | 14516.85589 | |
| 0 | 0 | 21081.16564 | 16443.09705 | 15147.00149 | 14842.88694 | 14767.70802 | 14742.728 | |
| 0 | 0 | 21199.17032 | 16710.84709 | 15425.40252 | 15104.64227 | 15024.64799 | 14998.06795 | |
| 0 | 0 | 21405.67452 | 16928.51248 | 15742.92964 | 15424.74338 | 15341.14938 | 15313.37325 | |
| 0 | 0 | 22052.36272 | 17155.75079 | 15848.07011 | 15524.39269 | 15446.29194 | 15420.34107 | |
| 0 | 0 | 22429.99776 | 17471.99566 | 16040.60641 | 15703.55664 | 15620.75116 | 15593.23703 | |
| 0 | 0 | 22795.22648 | 17750.86664 | 16305.6517 | 15945.8856 | 15856.20701 | 15826.40912 | |
| 0 | 0 | 23053.65682 | 18010.11831 | 16643.67599 | 16285.61963 | 16192.41922 | 16161.45111 | |
| 0 | 0 | 23499.50577 | 18355.17267 | 16815.99682 | 16453.72548 | 16366.80917 | 16337.92911 | |
| 0 | 0 | 23952.11587 | 18678.33843 | 17088.96645 | 16692.3655 | 16593.34366 | 16560.44125 | |
| 0 | 0 | 24234.05084 | 18817.57 | 17207.03693 | 16808.88747 | 16709.90306 | 16677.01309 | |
| 0 | 0 | 24471.51982 | 18954.60769 | 17393.9496 | 17022.26211 | 16930.12777 | 16899.51389 | |
| 0 | 0 | 24781.28439 | 19349.39105 | 17656.65641 | 17224.60263 | 17116.64859 | 17080.77823 | |
| 0 | 0 | 25263.34338 | 19870.05402 | 18078.67311 | 17642.01552 | 17533.24907 | 17497.10877 | |
| 0 | 0 | 25671.2415 | 19983.91826 | 18153.95253 | 17700.87541 | 17589.1275 | 17551.99654 | |
| 0 | 0 | 26298.859 | 20156.46814 | 18426.99423 | 17993.24372 | 17884.69295 | 17848.62432 | |
| 0 | 0 | 26498.0399 | 20532.20469 | 18605.91522 | 18120.12236 | 17998.71729 | 17958.37751 | |
| 0 | 0 | 26810.00303 | 20797.21378 | 19016.24735 | 18554.44746 | 18438.2619 | 18399.65643 | |
| 0 | 0 | 27229.58641 | 21037.22465 | 19108.32177 | 18626.80136 | 18502.40307 | 18461.06872 | |
| 0 | 0 | 27780.28311 | 21314.31718 | 19193.57901 | 18716.52981 | 18603.78846 | 18566.32741 | |
| 0 | 0 | 28034.51724 | 21650.30716 | 19597.39539 | 19072.26283 | 18939.75758 | 18895.72949 | |
| 0 | 0 | 28299.25201 | 22010.89419 | 19928.74417 | 19430.24086 | 19307.8998 | 19267.249 | |
| 0 | 0 | 28445.49128 | 22170.9087 | 20049.13747 | 19527.45612 | 19398.06263 | 19355.06849 | |
| 0 | 0 | 28812.45407 | 22543.36008 | 20233.1643 | 19639.66018 | 19493.64759 | 19445.13136 | |
| 0 | 0 | 0 | 22813.63972 | 20546.23016 | 19999.42157 | 19861.8782 | 19816.17608 | |
| 0 | 0 | 0 | 22927.7007 | 20727.49413 | 20155.82356 | 20013.09804 | 19965.67401 | |
| 0 | 0 | 0 | 23387.18683 | 21035.21699 | 20463.60912 | 20321.83796 | 20274.73105 | |
| 0 | 0 | 0 | 23709.95563 | 21231.10114 | 20594.19758 | 20433.66792 | 20380.32804 | |
| 0 | 0 | 0 | 24025.71421 | 21575.49969 | 20967.05688 | 20815.75021 | 20765.47489 | |
| 0 | 0 | 0 | 24112.53847 | 21676.21152 | 21110.49688 | 20967.06983 | 20919.41271 | |
| 0 | 0 | 0 | 24642.84025 | 22012.90312 | 21379.76555 | 21228.87399 | 21178.73661 | |
| 0 | 0 | 0 | 24737.58258 | 22072.35689 | 21445.12068 | 21290.30549 | 21238.86438 | |
| 0 | 0 | 0 | 25153.57415 | 22376.85694 | 21662.41089 | 21484.56892 | 21425.4766 | |
| 0 | 0 | 0 | 25333.07817 | 22657.20072 | 21989.70837 | 21823.23192 | 21767.91607 | |
| 0 | 0 | 0 | 25764.80899 | 23101.30888 | 22378.40347 | 22190.97092 | 22128.6919 | |
| 0 | 0 | 0 | 25821.74774 | 23142.78244 | 22428.6568 | 22260.95261 | 22205.22882 | |
| 0 | 0 | 0 | 26119.89295 | 23362.5066 | 22649.19218 | 22461.67087 | 22399.36235 | |
| 0 | 0 | 0 | 26516.58396 | 23500.14417 | 22913.86541 | 22772.27352 | 22725.22617 | |
| 0 | 0 | 0 | 26794.15754 | 23727.2929 | 22991.04018 | 22810.25508 | 22750.18484 | |
| 0 | 0 | 0 | 27027.36142 | 24119.38853 | 23390.62347 | 23204.23912 | 23142.30838 | |
| 0 | 0 | 0 | 27241.10353 | 24259.52928 | 23464.27725 | 23266.7726 | 23201.14687 | |
| 0 | 0 | 0 | 27949.86564 | 24422.51978 | 23629.59659 | 23437.57123 | 23373.76613 | |
| 0 | 0 | 0 | 28143.4557 | 24809.54371 | 23977.53438 | 23774.26658 | 23706.72592 | |
| 0 | 0 | 0 | 28161.12372 | 25070.10217 | 24282.21634 | 24084.80256 | 24019.20704 | |
| 0 | 0 | 0 | 28315.55062 | 25247.80413 | 24471.37531 | 24263.73584 | 24194.74257 | |
| 0 | 0 | 0 | 28630.73923 | 25334.4203 | 24536.77024 | 24340.1875 | 24274.8681 | |
| 0 | 0 | 0 | 0 | 25590.22539 | 24668.02968 | 24451.94392 | 24380.14418 | |
| 0 | 0 | 0 | 0 | 25956.85742 | 25033.54391 | 24805.28868 | 24729.44533 | |
| 0 | 0 | 0 | 0 | 26106.01468 | 25263.41587 | 25051.57993 | 24981.19229 | |
| 0 | 0 | 0 | 0 | 26457.7508 | 25576.69197 | 25352.6321 | 25278.18276 | |
| 0 | 0 | 0 | 0 | 26697.87461 | 25667.54344 | 25418.20105 | 25335.35098 | |
| 0 | 0 | 0 | 0 | 26948.16773 | 26064.13923 | 25817.4959 | 25735.54266 | |
| 0 | 0 | 0 | 0 | 27076.97816 | 26102.58129 | 25881.15008 | 25807.57417 | |
| 0 | 0 | 0 | 0 | 27276.21136 | 26318.94161 | 26082.99668 | 26004.59824 | |
| 0 | 0 | 0 | 0 | 27596.59045 | 26641.5507 | 26402.31028 | 26322.81683 | |
| 0 | 0 | 0 | 0 | 27745.34914 | 26788.46412 | 26511.82336 | 26419.90274 | |
| 0 | 0 | 0 | 0 | 27942.92472 | 26866.57326 | 26645.84197 | 26572.49864 | |
| 0 | 0 | 0 | 0 | 28387.61221 | 27272.48046 | 26995.88116 | 26903.97431 | |
| 0 | 0 | 0 | 0 | 28615.33642 | 27563.80322 | 27298.25549 | 27210.0208 | |
| 0 | 0 | 0 | 0 | 28841.24212 | 27810.94465 | 27546.36056 | 27458.44606 | |
| 0 | 0 | 0 | 0 | 28902.97912 | 27875.86032 | 27609.60349 | 27521.13318 | |
| 0 | 0 | 0 | 0 | 0 | 27926.19775 | 27643.62345 | 27549.73128 | |
| 0 | 0 | 0 | 0 | 0 | 28434.44442 | 28136.37844 | 28037.33878 | |
| 0 | 0 | 0 | 0 | 0 | 28689.80124 | 28427.76076 | 28340.69144 | |
| 0 | 0 | 0 | 0 | 0 | 28761.2133 | 28477.4169 | 28383.11865 | |
| 0 | 0 | 0 | 0 | 0 | 28977.38329 | 28696.14774 | 28602.70039 | |
| 0 | 0 | 0 | 0 | 0 | 0 | 28755.99101 | 0 |
| Triangle 2 | |||||||
|---|---|---|---|---|---|---|---|
| Theta 1: pi/4 | Theta2: pi/5 | Theta 3: 11pi/20 | |||||
| Refinement | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Predicted Eigenvalues | |
| 131.5532909 | 126.2811458 | 124.9494091 | 124.6152152 | 124.5315473 | 124.5106201 | 124.5036968 | |
| 260.0524717 | 242.1102643 | 237.5922175 | 236.4610908 | 236.178109 | 236.1073443 | 236.0839331 | |
| 372.4204893 | 336.8368989 | 327.9204584 | 325.6955192 | 325.1393767 | 325.0003325 | 324.9543323 | |
| 479.0017775 | 421.7355147 | 407.1484863 | 403.4977124 | 402.5841945 | 402.3557189 | 402.280132 | |
| 581.6970994 | 501.5423642 | 481.4521916 | 476.4552961 | 475.2073542 | 474.8954156 | 474.7922165 | |
| 769.9349547 | 641.3373012 | 608.2383635 | 600.0249581 | 597.9746627 | 597.4621854 | 597.2926417 | |
| 796.7752404 | 670.7182356 | 638.5049748 | 630.5044471 | 628.5075305 | 628.0084468 | 627.8433341 | |
| 962.9509216 | 769.4256936 | 720.9506707 | 709.0870504 | 706.1364522 | 705.3996713 | 705.1559209 | |
| 1094.227841 | 873.1959959 | 816.2738373 | 802.2781221 | 798.7933703 | 797.9229458 | 797.634982 | |
| 1220.039405 | 951.4561963 | 883.3433775 | 866.7154368 | 862.5836902 | 861.5521877 | 861.2109341 | |
| 1365.04921 | 1066.250775 | 978.71076 | 957.123957 | 951.7532128 | 950.4120911 | 949.9684058 | |
| 1465.145273 | 1121.656738 | 1033.536472 | 1012.330477 | 1007.078393 | 1005.76834 | 1005.334933 | |
| 1638.272355 | 1243.257961 | 1131.42201 | 1104.169063 | 1097.406502 | 1095.718878 | 1095.160558 | |
| 1676.055851 | 1306.836039 | 1196.692613 | 1169.479224 | 1162.698224 | 1161.004118 | 1160.443654 | |
| 1878.553544 | 1393.332525 | 1254.957917 | 1221.389258 | 1213.065989 | 1210.989294 | 1210.302258 | |
| 2117.227753 | 1497.790893 | 1331.361965 | 1291.985297 | 1282.296249 | 1279.883545 | 1279.085347 | |
| 2143.64957 | 1601.875487 | 1432.355645 | 1390.849082 | 1380.531343 | 1377.955177 | 1377.1029 | |
| 2266.990975 | 1707.307279 | 1525.606749 | 1480.347941 | 1469.096015 | 1466.287582 | 1465.358464 | |
| 2396.216829 | 1751.776892 | 1550.981877 | 1503.085957 | 1491.261687 | 1488.314225 | 1487.339111 | |
| 2655.401586 | 1903.884117 | 1660.755958 | 1602.267648 | 1587.843861 | 1584.250194 | 1583.061295 | |
| 2997.890544 | 1967.688225 | 1730.481505 | 1672.657833 | 1658.288044 | 1654.700111 | 1653.51311 | |
| 3087.186157 | 2067.471011 | 1791.884091 | 1725.209315 | 1708.741988 | 1704.637675 | 1703.279839 | |
| 3164.058939 | 2143.289597 | 1863.645679 | 1795.137817 | 1778.194764 | 1773.970899 | 1772.573511 | |
| 3319.104572 | 2269.10879 | 1960.984046 | 1885.254918 | 1866.463155 | 1861.773694 | 1860.222272 | |
| 3798.02082 | 2340.739906 | 2015.111295 | 1935.260104 | 1915.500765 | 1910.573331 | 1908.943181 | |
| 4890.809042 | 2481.976151 | 2123.449578 | 2036.750983 | 2015.376277 | 2010.050493 | 2008.288555 | |
| 2997.890544 | 2532.303029 | 2152.859 | 2059.401395 | 2036.318032 | 2030.565852 | 2028.66285 | |
| 3087.186157 | 2669.549827 | 2268.355481 | 2166.45206 | 2141.150481 | 2134.837944 | 2132.749558 | |
| 3164.058939 | 2762.990991 | 2361.143603 | 2262.27797 | 2237.636447 | 2231.475088 | 2229.436717 | |
| 3319.104572 | 2875.447334 | 2415.970015 | 2301.793984 | 2273.634525 | 2266.622994 | 2264.303359 | |
| 3798.02082 | 2930.895479 | 2460.659962 | 2345.60676 | 2317.139423 | 2310.040421 | 2307.691848 | |
| 4890.809042 | 3055.914144 | 2544.490347 | 2418.078252 | 2387.005115 | 2379.272754 | 2376.714645 | |
| 0 | 3172.332138 | 2635.554631 | 2501.589409 | 2468.282776 | 2459.968301 | 2457.217611 | |
| 0 | 3278.074627 | 2714.064629 | 2568.463209 | 2532.241093 | 2523.198564 | 2520.20701 | |
| 0 | 3444.955369 | 2824.077619 | 2674.172663 | 2637.467137 | 2628.33598 | 2625.315105 | |
| 0 | 3457.264553 | 2848.738953 | 2693.987122 | 2655.655313 | 2646.096237 | 2642.933794 | |
| 0 | 3615.353305 | 2953.811947 | 2788.16392 | 2747.356087 | 2737.192731 | 2733.830372 | |
| 0 | 3631.351587 | 3000.822289 | 2840.098911 | 2800.081325 | 2790.087295 | 2786.780955 | |
| 0 | 3803.426679 | 3117.313591 | 2942.199401 | 2898.602109 | 2887.710559 | 2884.10729 | |
| 0 | 3935.847179 | 3191.027434 | 2996.245459 | 2948.070529 | 2936.066087 | 2932.094639 | |
| 0 | 3960.88923 | 3240.010524 | 3049.701977 | 3002.675601 | 2990.963208 | 2987.088379 | |
| 0 | 4189.03461 | 3351.348365 | 3132.876779 | 3079.152364 | 3065.788736 | 3061.367626 | |
| 0 | 4246.11024 | 3427.110759 | 3205.893722 | 3150.65505 | 3136.86424 | 3132.301805 | |
| 0 | 4363.894372 | 3498.589123 | 3273.733146 | 3217.510607 | 3203.433193 | 3198.77594 | |
| 0 | 4428.716574 | 3561.292431 | 3332.151896 | 3275.094114 | 3260.856688 | 3256.146498 | |
| 0 | 4555.096295 | 3667.660259 | 3427.372392 | 3368.255598 | 3353.535095 | 3348.665088 | |
| 0 | 4689.322911 | 3688.040986 | 3435.914182 | 3374.659965 | 3359.490119 | 3354.471455 | |
| 0 | 4805.536295 | 3785.508176 | 3521.653402 | 3457.114707 | 3441.086514 | 3435.783882 | |
| 0 | 4994.176589 | 3911.885592 | 3622.012209 | 3550.733225 | 3533.003167 | 3527.137504 | |
| 0 | 5042.838312 | 3972.971964 | 3698.814231 | 3631.247746 | 3614.401904 | 3608.828768 | |
| 0 | 5222.740344 | 4087.807009 | 3768.958271 | 3689.978928 | 3670.320683 | 3663.817115 | |
| 0 | 5341.099022 | 4160.704576 | 3851.041871 | 3775.583758 | 3756.82889 | 3750.624189 | |
| 0 | 5348.545393 | 4223.004256 | 3897.971653 | 3816.927566 | 3796.761305 | 3790.08967 | |
| 0 | 5409.644096 | 4239.634298 | 3929.355524 | 3853.468705 | 3834.569161 | 3828.316595 | |
| 0 | 5620.369858 | 4393.119843 | 4058.771138 | 3971.172132 | 3949.429757 | 3942.236693 | |
| 0 | 5768.426836 | 4420.699419 | 4064.003002 | 3981.786892 | 3961.26282 | 3954.47281 | |
| 0 | 5813.767138 | 4516.090549 | 4158.818963 | 4071.951462 | 4050.424561 | 4043.302784 | |
| 0 | 6004.701885 | 4665.767083 | 4272.125012 | 4176.73444 | 4153.074076 | 4145.246482 | |
| 0 | 6095.022462 | 4685.023496 | 4290.950569 | 4193.288001 | 4168.965136 | 4160.918365 | |
| 0 | 6193.965544 | 4762.593049 | 4347.531421 | 4246.617586 | 4221.619477 | 4213.349314 | |
| 0 | 6261.496504 | 4896.574592 | 4467.169074 | 4359.772789 | 4333.006117 | 4324.150857 | |
| 0 | 6381.870768 | 4938.157913 | 4518.550489 | 4414.58661 | 4388.611968 | 4380.018738 | |
| 0 | 6534.86748 | 5040.141697 | 4592.780809 | 4483.212166 | 4456.068551 | 4447.088587 | |
| 0 | 6602.697267 | 5074.93562 | 4637.280588 | 4532.400975 | 4506.42015 | 4497.824873 | |
| 0 | 6685.932807 | 5178.512449 | 4732.965695 | 4623.792545 | 4596.659612 | 4587.683181 | |
| 0 | 6806.043765 | 5256.488838 | 4771.388703 | 4653.275722 | 4624.011393 | 4614.32983 | |
| 0 | 6897.677531 | 5367.504505 | 4861.958092 | 4739.21479 | 4708.801361 | 4698.739639 | |
| 0 | 7132.719249 | 5439.950434 | 4933.905457 | 4809.967381 | 4779.192861 | 4769.011679 | |
| 0 | 7214.572544 | 5514.302915 | 5013.785183 | 4887.660748 | 4855.952463 | 4845.462362 | |
| 0 | 7360.961019 | 5631.38555 | 5072.214399 | 4938.471674 | 4905.538769 | 4894.643525 | |
| 0 | 7500.005129 | 5764.057308 | 5188.202798 | 5044.829115 | 5009.175811 | 4997.380573 | |
| 0 | 7601.602616 | 5801.112792 | 5222.852366 | 5079.498339 | 5043.887416 | 5032.106199 | |
| 0 | 7699.782989 | 5820.999679 | 5244.076448 | 5104.572246 | 5069.945119 | 5058.489373 | |
| 0 | 7789.184838 | 5944.589186 | 5329.076408 | 5179.56423 | 5142.478613 | 5130.209521 | |
| 0 | 7968.554804 | 5974.754447 | 5393.938796 | 5251.475889 | 5216.037486 | 5204.313345 | |
| 0 | 8067.107009 | 6058.080799 | 5468.092997 | 5323.971765 | 5288.13055 | 5276.273146 | |
| 0 | 8202.657242 | 6218.334822 | 5558.723036 | 5399.863501 | 5360.609718 | 5347.623329 | |
| 0 | 8373.896903 | 6296.664328 | 5643.409762 | 5481.762644 | 5441.548904 | 5428.24493 | |
| 0 | 8482.227992 | 6352.061757 | 5686.010819 | 5525.475604 | 5485.798705 | 5472.672336 | |
| 0 | 8603.331351 | 6480.553233 | 5774.806858 | 5602.723374 | 5560.072091 | 5545.961701 | |
| 0 | 8636.949982 | 6608.504186 | 5863.701514 | 5675.846471 | 5628.910641 | 5613.382788 | |
| 0 | 8805.406224 | 6648.091363 | 5902.091957 | 5722.280672 | 5677.795293 | 5663.078126 | |
| 0 | 8874.783307 | 6731.39831 | 5995.899221 | 5807.121454 | 5759.99938 | 5744.409911 | |
| 0 | 0 | 6778.837843 | 6039.603479 | 5863.445717 | 5819.677268 | 5805.197285 | |
| 0 | 0 | 6840.922081 | 6100.424991 | 5919.840776 | 5874.950275 | 5860.099081 | |
| 0 | 0 | 6997.473226 | 6195.875709 | 6000.651023 | 5952.253029 | 5936.241446 | |
| 0 | 0 | 7091.86226 | 6272.083831 | 6073.224731 | 6024.140509 | 6007.9019 | |
| 0 | 0 | 7130.529013 | 6310.992973 | 6111.623748 | 6062.244311 | 6045.908036 | |
| 0 | 0 | 7221.644002 | 6384.092175 | 6179.709826 | 6129.04412 | 6112.282306 | |
| 0 | 0 | 7337.763832 | 6460.586495 | 6244.75251 | 6191.042548 | 6173.273598 | |
| 0 | 0 | 7404.872877 | 6530.05044 | 6310.934555 | 6256.293217 | 6238.216138 | |
| 0 | 0 | 7537.237093 | 6616.347095 | 6391.686516 | 6336.08038 | 6317.684116 | |
| 0 | 0 | 7626.341664 | 6694.652252 | 6471.821707 | 6416.870845 | 6398.691366 | |
| 0 | 0 | 7751.052017 | 6756.730722 | 6511.373943 | 6450.719671 | 6430.653325 | |
| 0 | 0 | 7786.728993 | 6827.475965 | 6588.881673 | 6529.244744 | 6509.514967 | |
| 0 | 0 | 7869.124707 | 6886.26778 | 6645.040614 | 6585.321141 | 6565.564056 | |
| 0 | 0 | 7919.11749 | 6945.458485 | 6708.694776 | 6649.734554 | 6630.228652 | |
| 0 | 0 | 7971.842549 | 6973.782902 | 6735.27851 | 6676.915016 | 6657.606532 | |
| 0 | 0 | 8149.584861 | 7099.552189 | 6846.944071 | 6784.369665 | 6763.668078 | |
| 0 | 0 | 8206.504158 | 7201.601956 | 6949.723903 | 6886.660143 | 6865.796662 | |
| 0 | 0 | 8272.514446 | 7224.894076 | 6971.159939 | 6908.632245 | 6887.946111 | |
| 0 | 0 | 8419.103847 | 7300.187587 | 7028.496332 | 6961.465042 | 6939.288976 | |
| 0 | 0 | 8563.583178 | 7436.662281 | 7155.359259 | 7084.360561 | 7060.871952 | |
| 0 | 0 | 8649.976558 | 7476.17612 | 7191.349462 | 7122.097117 | 7099.186257 | |
| 0 | 0 | 8669.32286 | 7509.342849 | 7228.608327 | 7159.247849 | 7136.301215 | |
| 0 | 0 | 8777.918815 | 7598.434423 | 7299.933533 | 7225.179224 | 7200.44814 | |
| 0 | 0 | 8846.128423 | 7661.620328 | 7366.690369 | 7293.323209 | 7269.051038 | |
| 0 | 0 | 8939.605583 | 7714.619495 | 7421.835175 | 7349.324153 | 7325.33522 | |
| 0 | 0 | 0 | 7782.614711 | 7473.713911 | 7397.828072 | 7372.722643 | |
| 0 | 0 | 0 | 7896.824514 | 7581.854572 | 7503.624727 | 7477.743827 | |
| 0 | 0 | 0 | 7913.2233 | 7614.472005 | 7540.834194 | 7516.472483 | |
| 0 | 0 | 0 | 8050.862871 | 7728.820284 | 7648.052786 | 7621.33235 | |
| 0 | 0 | 0 | 8107.096873 | 7766.496088 | 7683.175299 | 7655.610154 | |
| 0 | 0 | 0 | 8138.244606 | 7811.705186 | 7731.029389 | 7704.33929 | |
| 0 | 0 | 0 | 8198.030508 | 7868.444601 | 7786.682959 | 7759.633629 | |
| 0 | 0 | 0 | 8281.854146 | 7946.366568 | 7863.760095 | 7836.431267 | |
| 0 | 0 | 0 | 8398.744441 | 8046.341491 | 7959.371358 | 7930.598895 | |
| 0 | 0 | 0 | 8470.084578 | 8109.243012 | 8019.246507 | 7989.472824 | |
| 0 | 0 | 0 | 8532.347386 | 8168.695926 | 8078.283018 | 8048.371576 | |
| 0 | 0 | 0 | 8571.673183 | 8199.980182 | 8107.625426 | 8077.071559 | |
| 0 | 0 | 0 | 8670.274349 | 8314.203847 | 8226.512579 | 8197.501541 | |
| 0 | 0 | 0 | 8734.161084 | 8345.234368 | 8249.386963 | 8217.677618 | |
| 0 | 0 | 0 | 8793.265539 | 8404.609591 | 8309.083156 | 8277.479998 | |
| 0 | 0 | 0 | 8879.443972 | 8492.864098 | 8396.26627 | 8364.308662 | |
| 0 | 0 | 0 | 8936.751916 | 8559.182969 | 8466.641158 | 8436.025408 | |
| 0 | 0 | 0 | 0 | 8599.554464 | 8499.788044 | 8466.782165 | |
| 0 | 0 | 0 | 0 | 8668.876944 | 8569.687973 | 8536.873132 | |
| 0 | 0 | 0 | 0 | 8748.13337 | 8648.016251 | 8614.89435 | |
| 0 | 0 | 0 | 0 | 8834.406461 | 8728.917727 | 8694.018726 | |
| 0 | 0 | 0 | 0 | 8905.399619 | 8802.658194 | 8768.66809 | |
| 0 | 0 | 0 | 0 | 8929.467911 | 8815.557419 | 8777.872235 | |
| 0 | 0 | 0 | 0 | 0 | 8914.126878 |
| Triangle 3 | |||||||
|---|---|---|---|---|---|---|---|
| Theta 1: 2pi/7 | Theta 2: pi/7 | Theta 3: 4pi/7 | |||||
| Refinements | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Predicted Eigenvalues | |
| 181.5687491 | 169.9770171 | 167.0553166 | 166.3201954 | 166.1358705 | 166.0897393 | 166.0745604 | |
| 342.7253922 | 304.9422537 | 295.5861958 | 293.2470584 | 292.6613944 | 292.5148682 | 292.4666558 | |
| 521.0187471 | 449.0851738 | 430.8209275 | 426.2623902 | 425.122259 | 424.8371156 | 424.7432931 | |
| 621.5765055 | 530.6958487 | 506.970009 | 501.0249259 | 499.536819 | 499.1645753 | 499.0420937 | |
| 800.5617495 | 654.6549209 | 616.9155117 | 607.5413152 | 605.2013039 | 604.6164341 | 604.4239908 | |
| 968.2202804 | 772.9684349 | 721.4039804 | 708.7294426 | 705.5734572 | 704.7850965 | 704.5256974 | |
| 1208.550068 | 921.9376229 | 845.2633765 | 826.333406 | 821.6154219 | 820.4365558 | 820.0486665 | |
| 1314.452366 | 997.4797444 | 910.2600593 | 889.4682178 | 884.3378461 | 883.0593587 | 882.6386904 | |
| 1510.853305 | 1146.305606 | 1036.34916 | 1009.834325 | 1003.2732 | 1001.636879 | 1001.09847 | |
| 1711.856697 | 1267.669913 | 1119.291739 | 1084.347409 | 1075.746184 | 1073.603792 | 1072.898867 | |
| 1962.438146 | 1310.495362 | 1171.407418 | 1138.248524 | 1130.06285 | 1128.022514 | 1127.351169 | |
| 2099.927633 | 1516.116442 | 1342.988814 | 1301.163753 | 1290.815145 | 1288.234427 | 1287.385278 | |
| 2246.535017 | 1615.603842 | 1407.967944 | 1357.552942 | 1345.069068 | 1341.955078 | 1340.930464 | |
| 2481.504155 | 1721.606733 | 1494.810858 | 1440.365712 | 1426.948601 | 1423.606172 | 1422.506393 | |
| 2749.772818 | 1822.934823 | 1593.033576 | 1536.537472 | 1522.531429 | 1519.036913 | 1517.887091 | |
| 0 | 2022.72116 | 1738.271302 | 1667.950876 | 1650.389277 | 1645.997581 | 1644.552554 | |
| 0 | 2029.377553 | 1743.688461 | 1673.948698 | 1656.807257 | 1652.541935 | 1651.13849 | |
| 0 | 2244.034257 | 1894.301985 | 1806.110302 | 1784.395955 | 1778.990662 | 1777.212126 | |
| 0 | 2271.103528 | 1932.504855 | 1850.729296 | 1830.572246 | 1825.551285 | 1823.899209 | |
| 0 | 2560.907766 | 2130.133862 | 2021.587608 | 1994.392303 | 1987.587403 | 1985.348346 | |
| 0 | 2562.684711 | 2151.043392 | 2049.466575 | 2024.451303 | 2018.22419 | 2016.175246 | |
| 0 | 2780.860663 | 2263.810728 | 2140.858616 | 2111.148219 | 2103.790407 | 2101.369421 | |
| 0 | 2879.493226 | 2367.990462 | 2241.812492 | 2210.823466 | 2203.113195 | 2200.576238 | |
| 0 | 3047.485582 | 2501.440513 | 2366.372596 | 2333.116351 | 2324.830598 | 2322.104288 | |
| 0 | 3153.734822 | 2563.922436 | 2410.087605 | 2371.596099 | 2361.975085 | 2358.809425 | |
| 0 | 3275.202317 | 2667.35034 | 2502.177821 | 2461.16049 | 2451.014189 | 2447.675691 | |
| 0 | 3368.679265 | 2677.74264 | 2518.676132 | 2481.038849 | 2471.689562 | 2468.61331 | |
| 0 | 3624.743713 | 2903.219749 | 2717.430501 | 2672.008615 | 2660.723336 | 2657.010072 | |
| 0 | 3674.595429 | 2940.987914 | 2757.992225 | 2713.06164 | 2701.884782 | 2698.207193 | |
| 0 | 3733.016185 | 3020.625414 | 2825.662048 | 2775.998724 | 2763.520924 | 2759.415278 | |
| 0 | 3996.536341 | 3157.660376 | 2933.678889 | 2879.183869 | 2865.678545 | 2861.234807 | |
| 0 | 4024.574681 | 3183.26053 | 2972.066835 | 2920.334907 | 2907.474383 | 2903.242808 | |
| 0 | 4274.553759 | 3370.720181 | 3131.867351 | 3073.44995 | 3058.936554 | 3054.161124 | |
| 0 | 4449.480868 | 3474.869545 | 3219.731155 | 3157.244143 | 3141.708022 | 3136.596079 | |
| 0 | 4496.177242 | 3540.326775 | 3284.406508 | 3219.731145 | 3203.457548 | 3198.102948 | |
| 0 | 4601.646198 | 3622.984916 | 3351.677802 | 3285.137538 | 3268.607811 | 3263.168936 | |
| 0 | 4908.707885 | 3756.788235 | 3440.298916 | 3362.528044 | 3343.28591 | 3336.954555 | |
| 0 | 4970.799 | 3852.157964 | 3534.213946 | 3456.976023 | 3437.923916 | 3431.655087 | |
| 0 | 5143.629069 | 3878.274894 | 3564.330803 | 3490.141405 | 3471.75563 | 3465.706048 | |
| 0 | 5234.318706 | 4107.888266 | 3762.605917 | 3675.803292 | 3653.967818 | 3646.78316 | |
| 0 | 5333.500671 | 4147.007839 | 3808.063588 | 3720.078623 | 3697.820001 | 3690.496113 | |
| 0 | 5485.951718 | 4217.85023 | 3846.714217 | 3759.130802 | 3737.73777 | 3730.698692 | |
| 0 | 5754.984793 | 4389.643056 | 3939.845145 | 3835.082259 | 3809.556313 | 3801.157357 | |
| 0 | 5927.717944 | 4471.294734 | 4061.647553 | 3962.697199 | 3938.212506 | 3930.15616 | |
| 0 | 6081.602864 | 4496.252231 | 4088.284443 | 3989.96707 | 3965.598954 | 3957.580967 | |
| 0 | 6109.206073 | 4751.962328 | 4306.266515 | 4194.080767 | 4165.68534 | 4156.342223 | |
| 0 | 6210.155127 | 4771.101946 | 4325.674931 | 4215.467843 | 4188.094533 | 4179.087729 | |
| 0 | 6353.296218 | 4853.202038 | 4380.785296 | 4263.549526 | 4234.502014 | 4224.944337 | |
| 0 | 6433.760081 | 4987.397166 | 4449.335411 | 4324.676561 | 4294.449643 | 4284.503899 | |
| 0 | 6677.034867 | 5037.999203 | 4535.158629 | 4415.432399 | 4385.821968 | 4376.07907 | |
| 0 | 6815.865541 | 5204.23222 | 4668.972703 | 4538.512158 | 4506.16705 | 4495.524345 | |
| 0 | 7001.886854 | 5333.567963 | 4773.521333 | 4637.572422 | 4603.874441 | 4592.786592 | |
| 0 | 7065.664663 | 5386.771835 | 4824.32981 | 4688.497829 | 4654.937238 | 4643.894595 | |
| 0 | 7093.570553 | 5454.187476 | 4890.465655 | 4746.996511 | 4710.605199 | 4698.631146 | |
| 0 | 7300.730604 | 5636.423922 | 4989.115769 | 4830.330008 | 4791.347464 | 4778.520803 | |
| 0 | 7417.299884 | 5705.383535 | 5071.987549 | 4916.191358 | 4877.77958 | 4865.140721 | |
| 0 | 7488.874199 | 5736.968981 | 5107.822495 | 4959.25443 | 4922.482742 | 4910.383532 | |
| 0 | 7697.181734 | 6000.349259 | 5292.509126 | 5121.758043 | 5079.646205 | 5065.789894 | |
| 0 | 7894.562717 | 6075.930779 | 5379.68607 | 5212.250793 | 5170.89075 | 5157.281807 | |
| 0 | 8212.671178 | 6128.522485 | 5423.994261 | 5252.855 | 5210.455268 | 5196.504229 | |
| 0 | 8246.065927 | 6203.165972 | 5504.636033 | 5326.513368 | 5280.666602 | 5265.581365 | |
| 0 | 8451.509535 | 6396.27695 | 5613.171056 | 5414.527813 | 5365.918437 | 5349.924202 | |
| 0 | 8530.651197 | 6474.916047 | 5702.977555 | 5514.437177 | 5467.971689 | 5452.68287 | |
| 0 | 8724.478465 | 6554.664818 | 5735.967557 | 5540.549612 | 5492.699538 | 5476.955141 | |
| 0 | 9035.474501 | 6747.236691 | 5861.279844 | 5654.547752 | 5604.161109 | 5587.582089 | |
| 0 | 9174.776531 | 6782.702497 | 5932.430041 | 5731.537197 | 5681.815068 | 5665.454697 | |
| 0 | 9266.621494 | 6945.791169 | 6073.158032 | 5860.507099 | 5807.911978 | 5790.60629 | |
| 0 | 9562.54209 | 7054.249167 | 6162.347009 | 5934.475745 | 5875.939848 | 5856.679429 | |
| 0 | 9792.760493 | 7139.035454 | 6227.530021 | 6005.997244 | 5951.005339 | 5932.911023 | |
| 0 | 9937.942428 | 7241.016265 | 6275.494172 | 6036.536817 | 5977.955093 | 5958.679596 | |
| 0 | 10193.99557 | 7392.004427 | 6358.985877 | 6098.533121 | 6036.134381 | 6015.602948 | |
| 0 | 10390.05472 | 7503.847376 | 6433.874902 | 6187.954059 | 6127.711359 | 6107.889341 | |
| 0 | 10544.57012 | 7575.128317 | 6541.3102 | 6296.393495 | 6235.850208 | 6215.929287 | |
| 0 | 10756.19485 | 7672.165726 | 6599.368403 | 6348.132021 | 6286.423362 | 6266.118992 | |
| 0 | 0 | 7904.086384 | 6819.238304 | 6553.703897 | 6487.971046 | 6466.342571 | |
| 0 | 0 | 7947.329121 | 6855.938831 | 6579.071266 | 6508.611277 | 6485.427403 | |
| 0 | 0 | 8070.455082 | 6936.207739 | 6656.996438 | 6587.195772 | 6564.228839 | |
| 0 | 0 | 8110.565766 | 6975.535192 | 6694.238792 | 6622.316307 | 6598.651219 | |
| 0 | 0 | 8316.777947 | 7022.59471 | 6712.445019 | 6641.179701 | 6617.730845 | |
| 0 | 0 | 8362.90574 | 7140.517076 | 6846.615809 | 6773.95633 | 6750.048745 | |
| 0 | 0 | 8545.15631 | 7286.750024 | 6981.357238 | 6906.052105 | 6881.274004 | |
| 0 | 0 | 8605.799742 | 7314.392294 | 7006.379598 | 6930.743278 | 6905.856205 | |
| 0 | 0 | 8811.701608 | 7523.580421 | 7195.585885 | 7114.740103 | 7088.138929 | |
| 0 | 0 | 8860.733374 | 7534.118551 | 7217.741221 | 7139.205168 | 7113.363978 | |
| 0 | 0 | 8927.4222 | 7593.160308 | 7268.784696 | 7186.834234 | 7159.869581 | |
| 0 | 0 | 9052.146153 | 7682.027287 | 7338.713499 | 7251.25347 | 7222.475971 | |
| 0 | 0 | 9224.620955 | 7753.507711 | 7382.650545 | 7293.834235 | 7264.61047 | |
| 0 | 0 | 9276.893015 | 7884.615256 | 7534.229879 | 7445.214185 | 7415.924817 | |
| 0 | 0 | 9468.769689 | 7902.969179 | 7540.363499 | 7455.021959 | 7426.941519 | |
| 0 | 0 | 9626.327849 | 8089.297123 | 7706.52785 | 7611.471049 | 7580.193939 | |
| 0 | 0 | 9741.041316 | 8124.302289 | 7736.274168 | 7642.342701 | 7611.435866 | |
| 0 | 0 | 9812.891102 | 8254.501689 | 7877.697213 | 7784.292071 | 7753.558416 | |
| 0 | 0 | 9915.774813 | 8306.075924 | 7916.247242 | 7820.982663 | 7789.637185 | |
| 0 | 0 | 9974.355278 | 8379.757782 | 7989.327593 | 7888.064345 | 7854.74509 | |
| 0 | 0 | 10186.98633 | 8524.4596 | 8081.984415 | 7971.62886 | 7935.317909 | |
| 0 | 0 | 10247.83102 | 8535.125812 | 8120.480038 | 8021.015522 | 7988.288114 | |
| 0 | 0 | 10404.77819 | 8686.341357 | 8268.984466 | 8165.940215 | 8132.034946 | |
| 0 | 0 | 10561.5824 | 8747.516396 | 8296.964801 | 8187.531257 | 8151.523681 | |
| 0 | 0 | 10733.74188 | 8837.75096 | 8375.76064 | 8265.384953 | 8229.067377 | |
| 0 | 0 | 0 | 8941.798782 | 8488.570526 | 8377.290799 | 8340.675761 | |
| 0 | 0 | 0 | 9068.410549 | 8609.333926 | 8496.115486 | 8458.862543 | |
| 0 | 0 | 0 | 9120.650831 | 8663.542966 | 8550.07905 | 8512.745336 | |
| 0 | 0 | 0 | 9213.151743 | 8743.064347 | 8620.232309 | 8579.816145 | |
| 0 | 0 | 0 | 9338.885743 | 8830.596137 | 8704.870985 | 8663.502882 | |
| 0 | 0 | 0 | 9404.13082 | 8899.321525 | 8778.843453 | 8739.201828 | |
| 0 | 0 | 0 | 9445.016639 | 8933.30877 | 8807.901733 | 8766.638302 | |
| 0 | 0 | 0 | 9539.854099 | 9010.708741 | 8883.347753 | 8841.441402 | |
| 0 | 0 | 0 | 9579.7055 | 9045.768102 | 8917.792559 | 8875.683997 | |
| 0 | 0 | 0 | 9771.389904 | 9236.461633 | 9103.147955 | 9059.282954 | |
| 0 | 0 | 0 | 9790.539537 | 9256.530462 | 9128.158986 | 9085.920148 | |
| 0 | 0 | 0 | 9976.592331 | 9425.607956 | 9289.979469 | 9245.352812 | |
| 0 | 0 | 0 | 10048.44476 | 9504.2607 | 9366.140586 | 9320.694095 | |
| 0 | 0 | 0 | 10112.37127 | 9531.927538 | 9384.564823 | 9336.077183 | |
| 0 | 0 | 0 | 10243.60307 | 9633.417682 | 9482.748495 | 9433.172906 | |
| 0 | 0 | 0 | 10252.65548 | 9670.045692 | 9528.190182 | 9481.514611 | |
| 0 | 0 | 0 | 10310.30756 | 9704.953468 | 9560.404709 | 9512.842962 | |
| 0 | 0 | 0 | 10445.80118 | 9805.495231 | 9651.330166 | 9600.604308 | |
| 0 | 0 | 0 | 10470.02038 | 9864.894279 | 9717.282819 | 9668.713333 | |
| 0 | 0 | 0 | 10676.73531 | 10057.91087 | 9904.907953 | 9854.564482 | |
| 0 | 0 | 0 | 10731.59288 | 10084.94731 | 9927.501209 | 9875.695773 | |
| 0 | 0 | 0 | 0 | 10269.93499 | 10106.13863 | 10052.24373 | |
| 0 | 0 | 0 | 0 | 10284.31263 | 10125.30169 | 10072.98136 | |
| 0 | 0 | 0 | 0 | 10356.02968 | 10191.5097 | 10137.37671 | |
| 0 | 0 | 0 | 0 | 10392.79056 | 10226.55853 | 10171.8622 | |
| 0 | 0 | 0 | 0 | 10480.24889 | 10303.73171 | 10245.6512 | |
| 0 | 0 | 0 | 0 | 10533.77486 | 10356.62704 | 10298.33903 | |
| 0 | 0 | 0 | 0 | 10645.31442 | 10469.17648 | 10411.22075 | |
| 0 | 0 | 0 | 0 | 10733.54873 | 10559.2044 | 10501.83884 | |
| 0 | 0 | 0 | 0 | 10820.93667 | 10643.77969 | 10585.48866 | |
| 0 | 0 | 0 | 0 | 0 | 10719.25734 | ||
| 0 | 0 | 0 | 0 | 0 | 10756.37147 |