We analyzed hyperbolic equilateral triangles of different angle measures to test our conjecture. The angles chosen were pi/4,pi/5,pi/6, and pi/7. Unlike Euclidean and Spherical space, we do not have a region where the eigenvalue spectrum is known to use as a test case for accuracy in Hyperbolic space. These served as an important check because every one has a high number of multiplicity 2 eigenvalues: we can look at the difference of these pairs to get some idea of our accuracy.
Note that the predicted counting function for the triangles with theta = pi/6 and pi/7 does not seem to match as well as the other two discs. This is because the error for each eigenvalue decayed at an unsteady rate with successive refinements, making it difficult to predict the true eigenvalues. Looking at their eigenvalue charts below, we can see that the 95th and 96th eigenvalues for theta = pi/6 are 892.8237929 and 893.9625554. Given the large number of eigenvalues for this region that have multiplicity 2 and the average distance between eigenvalues, these values are likely supposed to converge to one eigenvalue of multiplicity 2, but due to the relatively unstable rate of decay in the error of the eigenvalues, our method of estimating the remaining area is not as accurate for this region as we would like. The 112th and 113th eigenvalues of the triangle with theta = pi/7, 927.8018455 and 926.2621529, demonstrate the same problem. This is likely because, although these triangles have greater hyperbolic area than the previous two triangles, they correspond to and were solved on Euclidean regions that are much smaller than the regions of the first two triangles.
Here N'(t) = (pi-3*theta)*t - (Perimeter/4pi)*t^1/2 + 3*(pi/theta-theta/pi).
Difference Graphs and Scatterplots for the Hyperbolic Discs
Calculated and Predicted Eigenvalue Spectrums for the Hyperbolic Discs
| Hyperbolic Equilateral Triangle with theta = pi/4 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| Initial Value | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 34.245116 | 33.072305 | 32.773973 | 32.698793 | 32.679941 | 32.675223 | 32.673641 | |
| 81.057826 | 75.554336 | 74.140225 | 73.783252 | 73.693699 | 73.671286 | 73.663771 | |
| 83.005795 | 76.048684 | 74.261462 | 73.813363 | 73.701212 | 73.673163 | 73.663758 | |
| 141.34308 | 126.10076 | 121.88203 | 120.80486 | 120.53413 | 120.46635 | 120.44362 | |
| 165.28768 | 143.56755 | 137.85311 | 136.41959 | 136.0609 | 135.9712 | 135.94112 | |
| 167.07772 | 143.87184 | 137.92098 | 136.43674 | 136.06523 | 135.97228 | 135.94111 | |
| 236.62515 | 202.01952 | 192.71723 | 190.33459 | 189.73444 | 189.58407 | 189.53365 | |
| 250.83052 | 207.10859 | 193.97642 | 190.64648 | 189.81218 | 189.60349 | 189.53352 | |
| 289.92495 | 234.72144 | 219.52275 | 215.72002 | 214.76919 | 214.53141 | 214.45168 | |
| 299.92523 | 243.31526 | 227.53743 | 223.65862 | 222.69281 | 222.45154 | 222.37064 | |
| 374.92876 | 298.27693 | 277.7362 | 271.86969 | 270.32848 | 269.93852 | 269.80777 | |
| 392.18579 | 309.04744 | 284.81899 | 278.7294 | 277.26609 | 276.90416 | 276.78281 | |
| 417.91624 | 311.97077 | 285.20647 | 278.89404 | 277.31201 | 276.91594 | 276.78314 | |
| 475.74879 | 363.03656 | 331.50009 | 323.58208 | 321.60757 | 321.11429 | 320.9489 | |
| 485.34215 | 365.9015 | 332.24285 | 323.77525 | 321.65648 | 321.12656 | 320.94888 | |
| 560.1232 | 416.06005 | 381.21513 | 372.0132 | 369.59415 | 368.97837 | 368.77191 | |
| 616.84212 | 434.7641 | 385.99722 | 373.11837 | 369.86124 | 369.04452 | 368.77068 | |
| 647.55929 | 438.92793 | 390.59639 | 378.51935 | 375.6058 | 374.88751 | 374.64667 | |
| 740.41463 | 461.94289 | 411.24428 | 398.73054 | 395.6155 | 394.83719 | 394.57623 | |
| 773.52788 | 517.3705 | 459.90996 | 445.09351 | 441.38466 | 440.45722 | 440.14626 | |
| 838.15543 | 528.25805 | 462.18979 | 445.65303 | 441.52437 | 440.49216 | 440.14607 | |
| 890.87431 | 555.53964 | 497.30648 | 481.09548 | 476.68352 | 475.55184 | 475.1724 | |
| 971.79388 | 591.8834 | 511.92079 | 492.01755 | 487.32217 | 486.17174 | 485.78601 | |
| 1023.7479 | 600.77103 | 515.56172 | 493.20095 | 487.63958 | 486.25244 | 485.78735 | |
| 1101.0997 | 615.94102 | 540.87692 | 522.12688 | 517.4504 | 516.28144 | 515.8895 | |
| 1150.6638 | 640.08557 | 547.99922 | 523.94013 | 517.90525 | 516.39523 | 515.88894 | |
| 1325.2456 | 694.68815 | 604.27014 | 577.94685 | 571.2027 | 569.5085 | 568.94045 | |
| 1356.5537 | 723.55133 | 619.92631 | 592.61076 | 585.75924 | 584.04456 | 583.46965 | |
| 1503.0624 | 735.22212 | 632.4204 | 608.06804 | 601.98634 | 600.46145 | 599.95017 | |
| 1710.6649 | 768.92229 | 646.38783 | 611.66228 | 602.88394 | 600.68567 | 599.94861 | |
| 1873.8787 | 798.26547 | 670.51629 | 636.65712 | 628.30121 | 626.22274 | 625.52585 | |
| 2196.4643 | 808.50585 | 689.74123 | 658.62516 | 650.48477 | 648.40296 | 647.70495 | |
| 2228.0092 | 826.81804 | 702.32076 | 668.54692 | 660.09019 | 657.9759 | 657.267 | |
| 2603.2076 | 862.55351 | 710.88763 | 670.25394 | 660.46739 | 658.06663 | 657.26168 | |
| 0 | 893.31731 | 771.69929 | 736.27846 | 726.30524 | 723.68728 | 722.8095 | |
| 0 | 950.5091 | 783.63753 | 738.10898 | 726.63958 | 723.76282 | 722.79827 | |
| 0 | 973.85467 | 799.7231 | 749.83718 | 737.73639 | 734.79338 | 733.80662 | |
| 0 | 980.61282 | 818.6887 | 773.41331 | 761.93631 | 759.0966 | 758.14447 | |
| 0 | 992.18818 | 821.08362 | 773.46322 | 761.98812 | 759.11225 | 758.148 | |
| 0 | 1044.2913 | 870.4162 | 821.92648 | 809.82558 | 806.79229 | 805.77526 | |
| 0 | 1050.0346 | 873.09022 | 823.79969 | 810.43554 | 806.95424 | 805.787 | |
| 0 | 1081.2085 | 894.49197 | 832.44687 | 817.61458 | 814.0479 | 812.85203 | |
| 0 | 1106.8456 | 895.61684 | 839.63531 | 825.75841 | 822.28863 | 821.12525 | |
| 0 | 1131.9337 | 944.70158 | 894.29676 | 880.85528 | 877.41169 | 876.25709 | |
| 0 | 1205.1482 | 979.55348 | 902.30735 | 882.76906 | 877.88388 | 876.24593 | |
| 0 | 1227.6517 | 992.3643 | 924.30118 | 907.66452 | 903.5435 | 902.16176 | |
| 0 | 1233.9794 | 1005.1765 | 941.37293 | 924.3526 | 920.04643 | 918.60262 | |
| 0 | 1246.6779 | 1010.3748 | 941.65424 | 924.39814 | 920.06443 | 918.61138 | |
| 0 | 1297.8002 | 1046.8102 | 972.5162 | 954.19149 | 949.6401 | 948.11407 | |
| 0 | 1318.6728 | 1080.4944 | 1010.3939 | 992.42351 | 987.89802 | 986.38067 | |
| 0 | 1354.7196 | 1094.4087 | 1016.2598 | 993.84106 | 988.24751 | 986.37205 | |
| 0 | 1383.7921 | 1109.9637 | 1021.7293 | 1003.0811 | 998.45952 | 996.90995 | |
| 0 | 1414.3004 | 1112.7898 | 1026.5522 | 1004.3769 | 998.78764 | 996.91362 | |
| 0 | 1437.9314 | 1149.3253 | 1066.5757 | 1043.5816 | 1037.7062 | 1035.7362 | |
| 0 | 1495.5973 | 1192.1514 | 1093.9103 | 1072.0039 | 1066.7032 | 1064.9259 | |
| 0 | 1520.3575 | 1203.1535 | 1100.9187 | 1074.0063 | 1067.2169 | 1064.9405 | |
| 0 | 1534.5537 | 1227.014 | 1126.5935 | 1101.477 | 1095.1933 | 1093.0864 | |
| 0 | 1560.0457 | 1233.8386 | 1141.7214 | 1117.3213 | 1111.0876 | 1108.9975 | |
| 0 | 1580.7558 | 1248.4652 | 1158.6962 | 1136.576 | 1131.0617 | 1129.2128 | |
| 0 | 1614.9079 | 1288.038 | 1169.106 | 1139.1178 | 1131.6914 | 1129.2014 | |
| 0 | 1648.1076 | 1309.9163 | 1215.5617 | 1190.1142 | 1183.4227 | 1181.1791 | |
| 0 | 1721.4764 | 1339.7402 | 1224.9462 | 1192.3701 | 1183.9651 | 1181.147 | |
| 0 | 1725.1257 | 1357.8936 | 1227.3355 | 1196.1305 | 1188.6799 | 1186.1818 | |
| 0 | 1776.74 | 1365.0614 | 1241.7149 | 1213.155 | 1206.1584 | 1203.8125 | |
| 0 | 1800.8407 | 1387.8048 | 1276.2531 | 1247.6038 | 1240.0058 | 1237.4583 | |
| 0 | 1833.1129 | 1419.6602 | 1282.2923 | 1248.557 | 1240.1935 | 1237.3893 | |
| 0 | 1851.5585 | 1448.2093 | 1300.0757 | 1262.0565 | 1252.9862 | 1249.945 | |
| 0 | 1901.7477 | 1470.9484 | 1349.9158 | 1316.0315 | 1307.4478 | 1304.5698 | |
| 0 | 1917.0936 | 1481.9114 | 1351.9923 | 1316.7192 | 1307.626 | 1304.5771 | |
| 0 | 1970.877 | 1491.3052 | 1355.3215 | 1323.0247 | 1314.5359 | 1311.6897 | |
| 0 | 2008.4181 | 1515.1906 | 1378.0663 | 1344.1977 | 1335.7875 | 1332.9676 | |
| 0 | 2059.5286 | 1558.7833 | 1389.2811 | 1346.4361 | 1336.296 | 1332.8961 | |
| 0 | 2092.6713 | 1566.4744 | 1427.5045 | 1388.0232 | 1377.4594 | 1373.9175 | |
| 0 | 2119.1171 | 1617.0794 | 1458.6057 | 1418.2526 | 1408.6226 | 1405.3938 | |
| 0 | 2177.2842 | 1630.4023 | 1461.7521 | 1419.677 | 1409.0976 | 1405.5504 | |
| 0 | 2217.8214 | 1642.3571 | 1464.4009 | 1420.7856 | 1409.7243 | 1406.0156 | |
| 0 | 2261.3475 | 1672.9173 | 1504.3587 | 1462.7402 | 1452.1716 | 1448.6281 | |
| 0 | 2299.6396 | 1690.2255 | 1510.7265 | 1463.9095 | 1452.4253 | 1448.5748 | |
| 0 | 2315.4797 | 1705.2292 | 1518.1443 | 1472.7513 | 1461.7393 | 1458.0471 | |
| 0 | 2339.9251 | 1734.7149 | 1571.3676 | 1529.8704 | 1519.0693 | 1515.4478 | |
| 0 | 2383.9978 | 1745.1599 | 1584.1854 | 1532.9702 | 1519.8277 | 1515.4212 | |
| 0 | 2446.4915 | 1780.9523 | 1588.3326 | 1544.145 | 1532.0237 | 1527.9596 | |
| 0 | 0 | 1783.853 | 1593.2995 | 1544.2693 | 1532.1361 | 1528.068 | |
| 0 | 0 | 1824.7055 | 1624.1069 | 1565.3226 | 1551.8586 | 1547.3443 | |
| 0 | 0 | 1838.5904 | 1630.9177 | 1581.8046 | 1569.588 | 1565.4919 | |
| 0 | 0 | 1877.3022 | 1666.2289 | 1617.9089 | 1604.8704 | 1600.4987 | |
| 0 | 0 | 1912.3614 | 1681.4475 | 1620.4482 | 1605.4085 | 1600.3658 | |
| 0 | 0 | 1941.3155 | 1720.0397 | 1658.0248 | 1643.3083 | 1638.374 | |
| 0 | 0 | 1961.8561 | 1727.441 | 1671.7535 | 1657.874 | 1653.2203 | |
| 0 | 0 | 1967.0574 | 1729.3795 | 1672.5457 | 1658.1018 | 1653.2589 | |
| 0 | 0 | 1993.1997 | 1770.9578 | 1714.264 | 1700.0859 | 1695.3321 | |
| 0 | 0 | 2004.4568 | 1778.3178 | 1716.0399 | 1700.521 | 1695.3177 | |
| 0 | 0 | 2026.9763 | 1798.3846 | 1739.9349 | 1724.613 | 1719.4757 | |
| 0 | 0 | 2034.2718 | 1823.8485 | 1771.8399 | 1757.4896 | 1752.6781 | |
| 0 | 0 | 2099.4018 | 1844.521 | 1776.2363 | 1759.8906 | 1754.4101 | |
| 0 | 0 | 2104.3512 | 1848.7746 | 1779.059 | 1760.9787 | 1754.9166 | |
| 0 | 0 | 2112.7674 | 1861.2045 | 1794.6101 | 1778.0172 | 1772.4538 | |
| 0 | 0 | 2146.6771 | 1885.6552 | 1815.3019 | 1798.8471 | 1793.33 | |
| 0 | 0 | 2187.8105 | 1888.587 | 1817.2715 | 1799.3784 | 1793.379 | |
| 0 | 0 | 2216.2791 | 1932.3699 | 1868.501 | 1851.0683 | 1845.2233 | |
| 0 | 0 | 2238.4703 | 1948.5109 | 1872.0182 | 1854.5863 | 1848.7416 | |
| 0 | 0 | 2253.9191 | 1960.5235 | 1876.78 | 1855.9333 | 1848.9436 | |
| 0 | 0 | 2294.2722 | 2002.0858 | 1928.4762 | 1910.0222 | 1903.8348 | |
| 0 | 0 | 2302.3 | 2008.0973 | 1930.1179 | 1910.4179 | 1903.8127 | |
| 0 | 0 | 2325.2941 | 2034.3899 | 1959.7162 | 1941.0253 | 1934.7584 | |
| 0 | 0 | 2339.2608 | 2054.175 | 1982.9549 | 1964.2761 | 1958.0133 | |
| 0 | 0 | 2345.4831 | 2062.6212 | 1988.8286 | 1969.7557 | 1963.3608 | |
| 0 | 0 | 2385.9948 | 2078.9348 | 1993.3422 | 1970.7256 | 1963.1425 | |
| 0 | 0 | 2436.2245 | 2113.8913 | 2028.6311 | 2007.2249 | 2000.0476 | |
| 0 | 0 | 2437.3952 | 2130.2274 | 2042.9957 | 2021.5025 | 2014.2961 | |
| 0 | 0 | 2466.9266 | 2133.2212 | 2043.719 | 2021.7694 | 2014.4099 | |
| 0 | 0 | 2484.9187 | 2136.5649 | 2056.0123 | 2035.3592 | 2028.4344 | |
| 0 | 0 | 0 | 2165.8656 | 2075.5295 | 2054.0104 | 2046.7953 | |
| 0 | 0 | 0 | 2182.6679 | 2079.9001 | 2055.0679 | 2046.7419 | |
| 0 | 0 | 0 | 2208.0201 | 2118.2175 | 2094.1868 | 2086.1296 | |
| 0 | 0 | 0 | 2243.8287 | 2149.7443 | 2127.0063 | 2119.3825 | |
| 0 | 0 | 0 | 2251.1667 | 2151.2685 | 2127.4315 | 2119.4392 | |
| 0 | 0 | 0 | 2264.1381 | 2166.3751 | 2141.4205 | 2133.0535 | |
| 0 | 0 | 0 | 2298.5188 | 2203.9465 | 2179.1253 | 2170.803 | |
| 0 | 0 | 0 | 2335.2313 | 2244.3413 | 2220.6573 | 2212.7163 | |
| 0 | 0 | 0 | 2338.076 | 2245.4029 | 2220.959 | 2212.7632 | |
| 0 | 0 | 0 | 2355.1207 | 2251.4237 | 2226.6166 | 2218.299 | |
| 0 | 0 | 0 | 2356.0938 | 2257.7372 | 2228.6076 | 2218.8407 | |
| 0 | 0 | 0 | 2395.1247 | 2269.2909 | 2242.2516 | 2233.1856 | |
| 0 | 0 | 0 | 2401.9371 | 2311.3123 | 2286.8914 | 2278.7033 | |
| 0 | 0 | 0 | 2437.3026 | 2322.2239 | 2293.506 | 2283.8772 | |
| 0 | 0 | 0 | 2444.9384 | 2324.5201 | 2294.2894 | 2284.1534 | |
| 0 | 0 | 0 | 2449.0291 | 2338.3168 | 2311.1186 | 2301.9993 | |
| 0 | 0 | 0 | 2472.6667 | 2342.2932 | 2311.9897 | 2301.8292 | |
| 0 | 0 | 0 | 0 | 2394.4399 | 2367.1919 | 2358.0559 | |
| 0 | 0 | 0 | 0 | 2399.7065 | 2371.182 | 2361.618 | |
| 0 | 0 | 0 | 0 | 2406.1589 | 2372.4781 | 2361.1853 | |
| 0 | 0 | 0 | 0 | 2454.9257 | 2425.3923 | 2415.4901 | |
| 0 | 0 | 0 | 0 | 2459.9229 | 2429.3694 | 2419.1251 | |
| 0 | 0 | 0 | 0 | 2461.6313 | 2429.7532 | 2419.0648 | |
| 0 | 0 | 0 | 0 | 0 | 2487.3263 |
| Hyperbolic Equilateral Triangle with theta = pi/5 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| Initial Value | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 24.20135759 | 22.67462615 | 22.29100237 | 22.1946015 | 22.17045166 | 22.16441009 | 22.16234795 | |
| 57.07838819 | 51.11459958 | 49.54731326 | 49.1498132 | 49.04998582 | 49.0249952 | 49.01646529 | |
| 61.82470724 | 52.20381002 | 49.81017384 | 49.21493132 | 49.06622843 | 49.02905357 | 49.01636488 | |
| 101.3462835 | 84.81314031 | 79.74073825 | 78.40918614 | 78.07233423 | 77.98786709 | 77.95903637 | |
| 123.4341247 | 98.46557633 | 91.93041982 | 90.34133716 | 89.94676254 | 89.84826759 | 89.81464883 | |
| 128.3398794 | 99.69765419 | 92.24732127 | 90.42150486 | 89.96687383 | 89.85330001 | 89.81453446 | |
| 169.9316703 | 135.4899174 | 125.7527738 | 123.2040048 | 122.556312 | 122.3936288 | 122.338101 | |
| 196.3602644 | 143.6597209 | 127.7095579 | 123.6835951 | 122.6755755 | 122.4234059 | 122.3373342 | |
| 216.2070315 | 161.4685366 | 143.7151138 | 139.2688291 | 138.1626585 | 137.8864676 | 137.7921968 | |
| 260.2856909 | 174.0063747 | 154.8404948 | 150.2347553 | 149.093148 | 148.8082565 | 148.711016 | |
| 312.6536789 | 201.0699719 | 182.1396033 | 177.5008437 | 176.3349944 | 176.0298608 | 175.9257112 | |
| 335.9493529 | 215.5624307 | 185.789996 | 178.4063869 | 176.5659974 | 176.1135127 | 175.9590685 | |
| 382.1343051 | 217.5122292 | 186.8316015 | 178.7094397 | 176.656677 | 176.14737 | 175.9735309 | |
| 498.6772716 | 250.6824227 | 220.0171466 | 211.8941613 | 209.8360913 | 209.3193611 | 209.1429883 | |
| 542.3484053 | 258.3509148 | 222.0958993 | 212.4012729 | 209.9616204 | 209.3506573 | 209.1421205 | |
| 772.7365437 | 284.8525964 | 247.0746046 | 236.5787053 | 233.669926 | 232.9219774 | 232.6666841 | |
| 807.4265698 | 305.0314458 | 254.7520591 | 242.933839 | 240.2270646 | 239.5669509 | 239.3416378 | |
| 855.8514216 | 313.1919651 | 258.3369005 | 244.0861797 | 240.5318703 | 239.6441555 | 239.3411565 | |
| 1186.705541 | 321.3605973 | 274.939908 | 261.6455953 | 258.2324971 | 257.3736886 | 257.0805561 | |
| 1403.620598 | 349.7202572 | 300.5237011 | 286.1335156 | 282.3765963 | 281.4270103 | 281.1028932 | |
| 0 | 370.8599885 | 304.9952707 | 287.118074 | 282.6164035 | 281.4866368 | 281.1010195 | |
| 0 | 393.7190899 | 326.9495444 | 309.3485716 | 304.6212758 | 303.4002114 | 302.9834321 | |
| 0 | 414.4785611 | 339.2592357 | 318.1118622 | 312.8052653 | 311.5175571 | 311.0780306 | |
| 0 | 426.9649934 | 340.9500439 | 318.2128551 | 312.8745048 | 311.538021 | 311.0818461 | |
| 0 | 435.2006923 | 362.3220965 | 343.1566992 | 338.2682602 | 337.0372264 | 336.6170442 | |
| 0 | 452.6352893 | 370.5152078 | 345.3503549 | 338.8167381 | 337.1742181 | 336.6135855 | |
| 0 | 486.064327 | 388.2557553 | 363.223417 | 356.8436923 | 355.2261648 | 354.6740629 | |
| 0 | 508.3676747 | 410.5591935 | 384.7466859 | 378.0223615 | 376.1363171 | 375.4925637 | |
| 0 | 519.5062513 | 415.082278 | 385.7095471 | 378.5138289 | 376.8868037 | 376.3314599 | |
| 0 | 549.9661354 | 426.5479795 | 388.9222489 | 379.4640966 | 377.1222673 | 376.3229432 | |
| 0 | 567.7024355 | 456.1332937 | 420.9740923 | 412.2114937 | 410.0199888 | 409.2719741 | |
| 0 | 593.0195427 | 464.7182034 | 433.1883201 | 424.4684626 | 422.2290063 | 421.4646248 | |
| 0 | 610.2202869 | 468.808263 | 433.8239463 | 424.640312 | 422.2742031 | 421.4665919 | |
| 0 | 624.491877 | 487.1444584 | 445.5377803 | 435.8224357 | 433.46677 | 432.6627233 | |
| 0 | 634.8504568 | 498.8573524 | 462.6128161 | 452.4922899 | 449.7762637 | 448.8492171 | |
| 0 | 646.6399787 | 505.8096328 | 463.5331406 | 452.6275561 | 449.8171088 | 448.8578339 | |
| 0 | 699.2687296 | 532.6736633 | 474.1336599 | 460.9560774 | 457.9217082 | 456.8860032 | |
| 0 | 710.3408687 | 552.7636076 | 506.0369883 | 493.8066107 | 490.7041331 | 489.6451811 | |
| 0 | 716.734875 | 557.764183 | 507.5914728 | 494.2113771 | 490.8067389 | 489.644652 | |
| 0 | 747.946302 | 577.5901549 | 534.330159 | 522.0305272 | 518.7179127 | 517.5872358 | |
| 0 | 763.4712948 | 595.7668428 | 538.0694264 | 523.0702201 | 519.2662585 | 517.9678728 | |
| 0 | 787.6685047 | 604.1310254 | 548.3463154 | 533.8170696 | 530.1028451 | 528.8350889 | |
| 0 | 806.3215516 | 612.02426 | 549.454285 | 533.9372526 | 530.1415792 | 528.8460224 | |
| 0 | 823.9728213 | 628.6470457 | 566.4941997 | 551.3855344 | 547.6212591 | 546.3364192 | |
| 0 | 828.8799236 | 650.9360401 | 571.0785934 | 552.3345277 | 547.8435008 | 546.3106027 | |
| 0 | 846.577234 | 654.7754647 | 588.8244784 | 571.2088812 | 566.6667664 | 565.1164308 | |
| 0 | 878.5675015 | 672.5407074 | 609.7537989 | 593.3275614 | 589.1572729 | 587.7338507 | |
| 0 | 913.783697 | 692.9288967 | 615.9715829 | 594.7730067 | 589.5102827 | 587.7139853 | |
| 0 | 937.6232984 | 708.8564167 | 643.5323373 | 627.705817 | 623.4426351 | 621.9875061 | |
| 0 | 951.0719001 | 724.1146023 | 649.4101974 | 629.4850141 | 623.9832047 | 622.1053017 | |
| 0 | 994.2053295 | 737.3760826 | 653.2431504 | 630.3174531 | 624.6887177 | 622.7674917 | |
| 0 | 1035.226233 | 760.6763127 | 668.2650896 | 643.2067631 | 637.176313 | 635.1179718 | |
| 0 | 1047.534102 | 765.9086328 | 675.8904121 | 653.5413419 | 647.9451728 | 646.0350624 | |
| 0 | 1069.930657 | 776.5607462 | 679.9448875 | 654.5427214 | 648.196046 | 646.0297693 | |
| 0 | 1096.7167 | 802.7037936 | 706.9037888 | 684.0039119 | 678.3955305 | 676.4812518 | |
| 0 | 1138.799919 | 809.36746 | 710.4887791 | 685.3732424 | 678.7580509 | 676.5001231 | |
| 0 | 1167.007023 | 833.161981 | 719.5498551 | 692.1844261 | 685.7563644 | 683.5623086 | |
| 0 | 1185.457416 | 839.7167274 | 752.5070266 | 728.2732845 | 721.728806 | 719.4950143 | |
| 0 | 1213.446964 | 858.4307154 | 763.2754429 | 741.1104878 | 735.2388356 | 733.2346961 | |
| 0 | 1244.024734 | 865.7472339 | 767.1076466 | 741.9270098 | 735.5017058 | 733.3085912 | |
| 0 | 1291.731013 | 893.1364177 | 776.8770231 | 745.9267333 | 737.9775243 | 735.2642636 | |
| 0 | 1325.100595 | 900.4283859 | 780.2391855 | 746.5887324 | 738.2781994 | 735.4416098 | |
| 0 | 1379.775956 | 916.1164333 | 788.6421878 | 748.5560768 | 738.6988084 | 735.3342799 | |
| 0 | 1403.536307 | 940.8616011 | 813.1043334 | 783.5766027 | 776.0884271 | 773.5325283 | |
| 0 | 0 | 961.4601174 | 818.6964128 | 784.7845808 | 776.3708709 | 773.4990645 | |
| 0 | 0 | 973.5870312 | 839.6740608 | 805.8003129 | 797.3969888 | 794.5287274 | |
| 0 | 0 | 981.3718973 | 858.0916151 | 823.0666635 | 814.1856705 | 811.1543689 | |
| 0 | 0 | 996.229621 | 870.1805095 | 837.2410513 | 828.7554888 | 825.8591573 | |
| 0 | 0 | 1010.941187 | 877.1764359 | 839.3855453 | 829.3033806 | 825.8620895 | |
| 0 | 0 | 1015.030791 | 883.248207 | 854.9800206 | 847.4768264 | 844.9158014 | |
| 0 | 0 | 1045.881686 | 898.4563262 | 860.1289831 | 848.9855948 | 845.1820819 | |
| 0 | 0 | 1069.533062 | 910.6079962 | 863.4243819 | 852.5382593 | 848.8225575 | |
| 0 | 0 | 1084.112718 | 920.1128315 | 869.4952939 | 857.9444552 | 854.0018695 | |
| 0 | 0 | 1092.350485 | 934.9249449 | 899.1537906 | 888.9068103 | 885.4092636 | |
| 0 | 0 | 1113.439275 | 941.5868412 | 899.5593505 | 888.9419668 | 885.3179923 | |
| 0 | 0 | 1121.25773 | 948.9137386 | 904.3924668 | 894.2464849 | 890.7834114 | |
| 0 | 0 | 1135.51077 | 975.666667 | 930.5534236 | 918.5300785 | 914.4262146 | |
| 0 | 0 | 1155.04471 | 989.0405221 | 946.4401419 | 935.5379519 | 931.8167659 | |
| 0 | 0 | 1164.285085 | 996.1498484 | 947.8597997 | 935.8658405 | 931.7720069 | |
| 0 | 0 | 1202.491096 | 1015.905995 | 976.4456362 | 965.6415994 | 961.9539155 | |
| 0 | 0 | 1207.224352 | 1029.913437 | 979.7029964 | 966.2165385 | 961.6132783 | |
| 0 | 0 | 1238.346776 | 1040.081412 | 986.1630754 | 971.1323451 | 966.0019867 | |
| 0 | 0 | 1244.514616 | 1048.70345 | 992.8264155 | 980.5957481 | 976.4211201 | |
| 0 | 0 | 1254.14993 | 1060.741224 | 996.7928535 | 981.5976703 | 976.4111801 | |
| 0 | 0 | 1271.212027 | 1067.538709 | 1019.291439 | 1006.501785 | 1002.13636 | |
| 0 | 0 | 1280.258838 | 1078.284343 | 1029.69215 | 1016.909723 | 1012.546765 | |
| 0 | 0 | 1295.905909 | 1092.428772 | 1033.049432 | 1017.62008 | 1012.353662 | |
| 0 | 0 | 1320.794073 | 1106.181428 | 1053.572246 | 1040.010768 | 1035.381902 | |
| 0 | 0 | 1332.740587 | 1112.882368 | 1054.100679 | 1040.267139 | 1035.545412 | |
| 0 | 0 | 1356.011243 | 1121.510702 | 1061.387633 | 1046.238627 | 1041.067898 | |
| 0 | 0 | 1370.398491 | 1156.168893 | 1094.403472 | 1079.509307 | 1074.425561 | |
| 0 | 0 | 1380.034971 | 1160.233718 | 1108.759002 | 1094.660389 | 1089.848185 | |
| 0 | 0 | 1397.514237 | 1178.416197 | 1116.467121 | 1096.734192 | 1089.998857 | |
| 0 | 0 | 1424.340219 | 1186.116272 | 1124.811022 | 1109.888461 | 1104.795023 | |
| 0 | 0 | 1436.464918 | 1205.278265 | 1128.928688 | 1111.078046 | 1104.985182 | |
| 0 | 0 | 1451.266169 | 1216.308258 | 1133.300461 | 1111.964269 | 1104.681702 | |
| 0 | 0 | 1485.712372 | 1220.874662 | 1147.177029 | 1128.522575 | 1122.15535 | |
| 0 | 0 | 0 | 1230.877996 | 1169.212135 | 1153.323822 | 1147.90075 | |
| 0 | 0 | 0 | 1245.518586 | 1172.532496 | 1154.046321 | 1147.736534 | |
| 0 | 0 | 0 | 1254.395813 | 1181.607725 | 1165.168996 | 1159.558053 | |
| 0 | 0 | 0 | 1270.449589 | 1207.094251 | 1191.389343 | 1186.028872 | |
| 0 | 0 | 0 | 1286.822328 | 1213.110518 | 1193.22298 | 1186.434873 | |
| 0 | 0 | 0 | 1299.185515 | 1222.083817 | 1202.439757 | 1195.734755 | |
| 0 | 0 | 0 | 1304.253618 | 1224.069407 | 1202.724112 | 1195.438437 | |
| 0 | 0 | 0 | 1319.61945 | 1247.000231 | 1227.610881 | 1220.992818 | |
| 0 | 0 | 0 | 1323.58853 | 1255.58397 | 1236.454741 | 1229.925464 | |
| 0 | 0 | 0 | 1347.689223 | 1267.453765 | 1245.051006 | 1237.404393 | |
| 0 | 0 | 0 | 1372.957001 | 1271.947954 | 1246.889859 | 1238.336914 | |
| 0 | 0 | 0 | 1376.65953 | 1277.966863 | 1257.11628 | 1249.999463 | |
| 0 | 0 | 0 | 1395.570464 | 1286.000342 | 1259.143479 | 1249.976571 | |
| 0 | 0 | 0 | 1400.674724 | 1318.827211 | 1297.068919 | 1289.642277 | |
| 0 | 0 | 0 | 1408.888858 | 1336.05253 | 1315.835786 | 1308.935313 | |
| 0 | 0 | 0 | 1433.787483 | 1340.784724 | 1319.744227 | 1312.562587 | |
| 0 | 0 | 0 | 1440.405287 | 1346.871817 | 1321.600771 | 1312.97514 | |
| 0 | 0 | 0 | 1444.611809 | 1361.956919 | 1340.08673 | 1332.621895 | |
| 0 | 0 | 0 | 1448.796426 | 1363.873854 | 1340.603365 | 1332.660574 | |
| 0 | 0 | 0 | 1473.019072 | 1382.434081 | 1352.763452 | 1342.636136 | |
| 0 | 0 | 0 | 1494.344629 | 1390.959594 | 1368.591773 | 1360.957085 | |
| 0 | 0 | 0 | 0 | 1398.66548 | 1374.783888 | 1366.632513 | |
| 0 | 0 | 0 | 0 | 1405.891812 | 1379.572122 | 1370.588563 | |
| 0 | 0 | 0 | 0 | 1413.671758 | 1381.701183 | 1370.788838 | |
| 0 | 0 | 0 | 0 | 1435.357305 | 1409.864292 | 1401.162899 | |
| 0 | 0 | 0 | 0 | 1443.668975 | 1415.473008 | 1405.849031 | |
| 0 | 0 | 0 | 0 | 1447.449219 | 1416.018259 | 1405.290098 | |
| 0 | 0 | 0 | 0 | 1473.336103 | 1448.745779 | 1440.352496 | |
| 0 | 0 | 0 | 0 | 1478.447616 | 1451.081014 | 1441.740118 | |
| 0 | 0 | 0 | 0 | 1489.012299 | 1455.01448 | 1443.410187 | |
| 0 | 0 | 0 | 0 | 0 | 1494.20755 | ||
| 0 | 0 | 0 | 0 | 0 | 1498.239929 |
| Hyperbolic Equilateral Triangle with theta = pi/6 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| Initial Value | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 20.52070282 | 19.276066 | 18.94070771 | 18.85552671 | 18.83413106 | 18.82877472 | 18.82690475 | |
| 48.4173302 | 43.08296502 | 41.65066095 | 41.28194461 | 41.18899032 | 41.16569936 | 41.15756818 | |
| 48.84583958 | 43.87381854 | 41.85882021 | 41.33431093 | 41.20209664 | 41.16897677 | 41.1574142 | |
| 86.88755162 | 70.532283 | 66.02564763 | 64.77122494 | 64.44834021 | 64.36702457 | 64.33863624 | |
| 111.1584364 | 83.80811383 | 77.20804722 | 75.50772786 | 75.08230606 | 74.9759986 | 74.9388853 | |
| 131.9812101 | 85.23902748 | 77.46080933 | 75.56720799 | 75.0970707 | 74.97968521 | 74.93870443 | |
| 159.0932646 | 113.4576936 | 104.2715082 | 101.7101387 | 101.0418013 | 100.8726789 | 100.8136362 | |
| 191.5960718 | 120.0232161 | 106.2032888 | 102.1909308 | 101.1614559 | 100.9025526 | 100.8121661 | |
| 236.1204616 | 135.0708133 | 118.412475 | 113.9511898 | 112.8373582 | 112.5592996 | 112.4622257 | |
| 256.300395 | 150.7844353 | 131.7960009 | 126.9342449 | 125.7204483 | 125.4169882 | 125.3110464 | |
| 344.4190962 | 166.2944095 | 149.5750233 | 144.7856655 | 143.4211024 | 143.0598675 | 142.9337558 | |
| 369.090164 | 182.4182923 | 154.3860266 | 145.9551513 | 143.7024834 | 143.1293108 | 142.9292089 | |
| 542.529277 | 186.5283301 | 157.336084 | 148.6142843 | 146.6530658 | 146.1878951 | 146.0254981 | |
| 610.574925 | 213.7494156 | 184.8641793 | 175.8356285 | 173.4938362 | 172.9018135 | 172.6951308 | |
| 724.7794324 | 217.0689487 | 186.4588297 | 176.379338 | 173.6399839 | 172.9390134 | 172.6942956 | |
| 854.042396 | 250.4919992 | 203.8246551 | 190.918346 | 187.4421699 | 186.5599155 | 186.2519092 | |
| 1031.090141 | 260.7300535 | 213.3190174 | 201.0088296 | 198.1968445 | 197.511254 | 197.2719055 | |
| 0 | 272.3553692 | 219.1100443 | 202.8050776 | 198.6660048 | 197.6297462 | 197.267975 | |
| 0 | 276.0618679 | 231.896539 | 218.1588674 | 214.457329 | 213.5084222 | 213.1771466 | |
| 0 | 290.9778537 | 247.1357968 | 233.8193558 | 230.107522 | 229.1478122 | 228.8127651 | |
| 0 | 326.7651861 | 261.3428637 | 237.1548204 | 230.9124488 | 229.3468928 | 228.8003371 | |
| 0 | 337.2203783 | 270.8031688 | 251.9288649 | 246.483147 | 245.0269872 | 244.5186232 | |
| 0 | 361.0522238 | 284.3095748 | 261.5829923 | 255.7423513 | 254.2820666 | 253.7722625 | |
| 0 | 375.1955802 | 289.2019955 | 262.178434 | 255.8179443 | 254.2986725 | 253.7682752 | |
| 0 | 383.1840534 | 309.3140391 | 288.5560785 | 283.132992 | 281.7522745 | 281.2702482 | |
| 0 | 401.227892 | 314.156785 | 290.9290228 | 283.7984321 | 281.9226249 | 281.2677565 | |
| 0 | 433.4025728 | 324.2706314 | 296.6884686 | 288.9281714 | 286.9122628 | 286.2084832 | |
| 0 | 463.1801088 | 345.3018016 | 310.2536045 | 302.6284894 | 300.8419364 | 300.2182278 | |
| 0 | 472.7269641 | 349.3031341 | 315.9171016 | 304.4029285 | 301.3002896 | 300.2171185 | |
| 0 | 495.3585933 | 364.1475543 | 319.9189156 | 310.7839081 | 308.6698632 | 307.9318229 | |
| 0 | 521.6077482 | 383.5127774 | 349.0092535 | 338.715739 | 335.9885298 | 335.0364261 | |
| 0 | 533.6190532 | 391.8239324 | 359.5952567 | 350.8597941 | 348.5228908 | 347.7070479 | |
| 0 | 540.2997751 | 397.3806598 | 361.8599827 | 351.5120727 | 348.6937513 | 347.709839 | |
| 0 | 584.4736486 | 412.5972254 | 373.7730114 | 362.9189145 | 359.8170284 | 358.7341201 | |
| 0 | 610.6684049 | 424.5408396 | 378.0085046 | 363.6048977 | 359.9478795 | 358.6711674 | |
| 0 | 652.2136848 | 440.7994203 | 380.6180821 | 368.5788071 | 365.7998834 | 364.8297254 | |
| 0 | 660.5825782 | 455.9190571 | 388.3034044 | 371.5690556 | 367.9332551 | 366.6639504 | |
| 0 | 704.841619 | 461.3863784 | 415.4030539 | 402.6370492 | 399.3493041 | 398.2015101 | |
| 0 | 713.2097111 | 472.4846339 | 420.4098952 | 404.265447 | 399.7841041 | 398.2196097 | |
| 0 | 755.6448952 | 475.5413011 | 438.3225586 | 425.842803 | 421.4848001 | 419.9633653 | |
| 0 | 771.2825191 | 508.0291907 | 443.5702788 | 428.1740343 | 424.8190434 | 423.6477729 | |
| 0 | 798.8906913 | 521.8380534 | 453.7415251 | 433.3901662 | 428.6875185 | 427.0457638 | |
| 0 | 823.9560886 | 523.9260288 | 457.4293216 | 434.8704419 | 429.1922361 | 427.2099015 | |
| 0 | 847.3861606 | 545.4953362 | 476.055436 | 457.9688512 | 452.6988871 | 450.8590749 | |
| 0 | 879.8800919 | 554.2676137 | 476.7427845 | 458.3065309 | 454.1871474 | 452.7490177 | |
| 0 | 906.2547963 | 561.2896265 | 478.3880541 | 458.966057 | 454.3556866 | 452.7461471 | |
| 0 | 950.3645962 | 567.9909896 | 501.672313 | 482.7695832 | 477.7664716 | 476.0198211 | |
| 0 | 1010.981595 | 573.774917 | 511.8580449 | 485.0187968 | 478.2707126 | 475.9148698 | |
| 0 | 1023.200726 | 606.5114669 | 523.1537867 | 508.5637363 | 504.7665882 | 503.440955 | |
| 0 | 0 | 616.4216796 | 540.8630045 | 514.0663437 | 506.0942738 | 503.3111218 | |
| 0 | 0 | 637.6897197 | 546.8317576 | 517.5094997 | 509.1890908 | 506.2843292 | |
| 0 | 0 | 639.4072151 | 552.2082227 | 523.290383 | 517.4974681 | 515.4750872 | |
| 0 | 0 | 648.4737167 | 553.5841525 | 530.5393244 | 524.8188319 | 522.8217345 | |
| 0 | 0 | 662.4670449 | 562.8553565 | 532.9260693 | 525.4173308 | 522.7959337 | |
| 0 | 0 | 674.8859648 | 587.1924699 | 564.30047 | 557.0953138 | 554.5799013 | |
| 0 | 0 | 697.6424181 | 591.8908994 | 564.8171084 | 558.7062026 | 556.5728069 | |
| 0 | 0 | 702.7841754 | 604.102707 | 568.1843662 | 559.4512216 | 556.4023687 | |
| 0 | 0 | 705.9763729 | 614.0519215 | 587.0709965 | 577.8033066 | 574.5678371 | |
| 0 | 0 | 723.0143741 | 627.9978288 | 601.5875787 | 594.6848805 | 592.2750599 | |
| 0 | 0 | 750.8373843 | 634.9320344 | 605.1478481 | 595.85654 | 592.612825 | |
| 0 | 0 | 759.6048256 | 643.0822495 | 606.3052395 | 598.5914069 | 595.8984089 | |
| 0 | 0 | 772.4751159 | 653.3403979 | 608.8958675 | 599.3028719 | 595.9538339 | |
| 0 | 0 | 777.9868433 | 658.2495458 | 611.3746819 | 600.3960184 | 596.563226 | |
| 0 | 0 | 793.9154384 | 675.1260884 | 643.9288862 | 635.1820145 | 632.1283692 | |
| 0 | 0 | 809.7199016 | 677.1118325 | 644.5912368 | 635.3022429 | 632.0593359 | |
| 0 | 0 | 818.9954345 | 699.0168705 | 665.0994799 | 655.9554567 | 652.7631607 | |
| 0 | 0 | 830.9122767 | 706.3132687 | 669.7400203 | 659.5581065 | 656.0034696 | |
| 0 | 0 | 855.4689286 | 717.9440955 | 674.6830215 | 662.871303 | 658.7476803 | |
| 0 | 0 | 864.6697408 | 726.2849062 | 678.034369 | 663.8616625 | 658.9137887 | |
| 0 | 0 | 876.0645486 | 738.0990965 | 694.3579553 | 684.9452723 | 681.6591838 | |
| 0 | 0 | 904.3657862 | 753.308704 | 701.0243038 | 686.6761805 | 681.6670664 | |
| 0 | 0 | 912.4604795 | 763.9053099 | 709.2047218 | 697.6119446 | 693.5647571 | |
| 0 | 0 | 916.7033075 | 767.0959896 | 716.1174466 | 704.1760497 | 700.0071547 | |
| 0 | 0 | 928.4285809 | 773.9064562 | 735.390097 | 725.0496522 | 721.4396701 | |
| 0 | 0 | 949.1182202 | 780.5886902 | 737.0888601 | 725.3023294 | 721.1875001 | |
| 0 | 0 | 954.2752334 | 797.0500898 | 748.5228317 | 732.5150404 | 726.9265148 | |
| 0 | 0 | 978.8674105 | 805.1287917 | 758.0589467 | 746.9790591 | 743.110928 | |
| 0 | 0 | 995.8801247 | 810.4418025 | 769.4219066 | 756.7185105 | 752.2835917 | |
| 0 | 0 | 1003.64491 | 833.97105 | 773.4648896 | 757.6266205 | 752.0972774 | |
| 0 | 0 | 1013.921672 | 848.6283556 | 783.7503121 | 769.2691962 | 764.2136526 | |
| 0 | 0 | 1033.677235 | 858.8928077 | 788.3464963 | 770.2617366 | 763.9481147 | |
| 0 | 0 | 1042.249942 | 867.3041282 | 799.0907337 | 780.3492548 | 773.8063638 | |
| 0 | 0 | 0 | 876.8070905 | 823.8557815 | 810.1893271 | 805.4181923 | |
| 0 | 0 | 0 | 882.4453647 | 827.0082813 | 814.1130348 | 809.6111385 | |
| 0 | 0 | 0 | 889.5622555 | 831.2453212 | 815.5927256 | 810.1282034 | |
| 0 | 0 | 0 | 895.7304035 | 835.8939447 | 821.5376157 | 816.5256369 | |
| 0 | 0 | 0 | 914.4640849 | 845.2038175 | 823.1436653 | 815.4421828 | |
| 0 | 0 | 0 | 926.1561389 | 859.546156 | 843.1991488 | 837.4921986 | |
| 0 | 0 | 0 | 930.6790676 | 876.8530111 | 861.604588 | 856.2811677 | |
| 0 | 0 | 0 | 944.563336 | 883.7772994 | 862.0608499 | 854.4793585 | |
| 0 | 0 | 0 | 959.409212 | 886.3563976 | 869.7769954 | 863.9889131 | |
| 0 | 0 | 0 | 970.2170065 | 892.4186011 | 870.2108343 | 862.4578176 | |
| 0 | 0 | 0 | 979.8459759 | 898.8112784 | 880.0194722 | 873.4590113 | |
| 0 | 0 | 0 | 988.3751783 | 916.073409 | 895.0549385 | 887.7171204 | |
| 0 | 0 | 0 | 1000.947966 | 919.0069713 | 899.5992706 | 892.8237929 | |
| 0 | 0 | 0 | 1014.078532 | 921.5695262 | 901.1064709 | 893.9625554 | |
| 0 | 0 | 0 | 1023.762417 | 936.2526821 | 912.8061802 | 904.6207052 | |
| 0 | 0 | 0 | 1028.828925 | 961.2911111 | 945.2434052 | 939.640945 | |
| 0 | 0 | 0 | 1034.174479 | 965.9850623 | 947.7347547 | 941.3633379 | |
| 0 | 0 | 0 | 0 | 972.7529462 | 950.419778 | 942.6229821 | |
| 0 | 0 | 0 | 0 | 983.3538377 | 952.3179352 | 941.482903 | |
| 0 | 0 | 0 | 0 | 993.7089109 | 973.2625698 | 966.1244895 | |
| 0 | 0 | 0 | 0 | 1002.525099 | 974.2892384 | 964.4317369 | |
| 0 | 0 | 0 | 0 | 1005.286541 | 979.8456562 | 970.9639166 | |
| 0 | 0 | 0 | 0 | 1017.431034 | 996.7823743 | 989.573662 | |
| 0 | 0 | 0 | 0 | 1021.4459 | 998.2811103 | 990.1939845 | |
| 0 | 0 | 0 | 0 | 1035.990919 | 1010.841078 | 1002.060945 | |
| 0 | 0 | 0 | 0 | 1038.621673 | 1011.27337 | 1001.725726 | |
| 0 | 0 | 0 | 0 | 1041.591149 | 1018.573748 | 1010.538078 | |
| 0 | 0 | 0 | 0 | 0 | 1022.579213 |
| Hyperbolic Equilateral Triangle with theta = pi/7 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| Initial Value | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 19.07752764 | 17.77011736 | 17.38280555 | 17.28240424 | 17.25707587 | 17.25072904 | 17.24866782 | |
| 46.01618233 | 39.77731372 | 38.03700084 | 37.57938916 | 37.46339364 | 37.43429076 | 37.42483919 | |
| 48.75360665 | 41.13093229 | 38.36733273 | 37.66107506 | 37.48375218 | 37.43937633 | 37.42496465 | |
| 84.22545401 | 65.5820281 | 60.00145029 | 58.39603528 | 57.98005796 | 57.87515269 | 57.84108324 | |
| 123.8612105 | 78.80769287 | 70.46606441 | 68.45180466 | 67.95773933 | 67.83485235 | 67.79494309 | |
| 151.0652561 | 80.28869569 | 70.93761307 | 68.58507014 | 67.9921485 | 67.84352544 | 67.79525804 | |
| 232.6074291 | 105.2894873 | 94.69848167 | 91.64494287 | 90.8250057 | 90.61549932 | 90.54745921 | |
| 269.9510597 | 115.4590653 | 97.36724214 | 92.26867788 | 90.97712291 | 90.65327183 | 90.54809669 | |
| 373.3668185 | 129.0666565 | 107.8520066 | 102.0195063 | 100.5855878 | 100.2296811 | 100.1140955 | |
| 536.9974204 | 144.8638785 | 122.2691552 | 116.2458516 | 114.7376943 | 114.3603055 | 114.2377432 | |
| 616.2121237 | 153.2212551 | 134.6099955 | 129.026257 | 127.4159673 | 126.9899155 | 126.8515493 | |
| 864.005848 | 175.2506757 | 141.5415837 | 130.6419827 | 127.8020447 | 127.0851196 | 126.8522882 | |
| 0 | 176.8885263 | 144.5943694 | 134.7088393 | 132.4188457 | 131.8687862 | 131.6901468 | |
| 0 | 199.97012 | 169.8308405 | 159.0610393 | 156.0692087 | 155.3113894 | 155.065277 | |
| 0 | 209.8356538 | 170.7073202 | 159.2735682 | 156.1552776 | 155.3351748 | 155.068835 | |
| 0 | 237.4016088 | 185.1640007 | 169.4200141 | 165.2564165 | 164.2154474 | 163.8773781 | |
| 0 | 252.9361911 | 196.4034637 | 181.0356327 | 177.6168081 | 176.788945 | 176.520085 | |
| 0 | 263.7557753 | 203.887528 | 183.4638682 | 178.2605755 | 176.9521774 | 176.5272569 | |
| 0 | 270.2641071 | 215.6004211 | 198.4770113 | 193.8828288 | 192.7067613 | 192.324817 | |
| 0 | 278.2047826 | 222.2825728 | 209.0688804 | 205.1661106 | 204.1145207 | 203.7730022 | |
| 0 | 319.8205043 | 243.5864101 | 213.7903399 | 206.2507485 | 204.3779642 | 203.7697515 | |
| 0 | 322.0297665 | 248.0638679 | 224.2505781 | 217.2881419 | 215.4326282 | 214.8300244 | |
| 0 | 346.2807632 | 264.5428253 | 235.7447106 | 228.4756323 | 226.6444126 | 226.0496985 | |
| 0 | 368.3830841 | 270.2732386 | 236.6772936 | 228.5622032 | 226.6554473 | 226.0362018 | |
| 0 | 378.2916167 | 284.3690667 | 263.3876447 | 256.7146285 | 254.5797109 | 253.8863667 | |
| 0 | 411.1953926 | 289.9499216 | 264.3196414 | 257.4650683 | 255.6810501 | 255.1016654 | |
| 0 | 422.1593454 | 299.7107007 | 266.9396917 | 257.9893951 | 255.791874 | 255.0781984 | |
| 0 | 464.1029258 | 321.3003418 | 275.5184163 | 265.5536714 | 263.4106835 | 262.7147184 | |
| 0 | 508.6492768 | 322.3555779 | 282.02225 | 267.6932287 | 263.9710553 | 262.7622277 | |
| 0 | 519.6138615 | 343.3332174 | 290.2318461 | 279.0797718 | 276.4376987 | 275.5796487 | |
| 0 | 563.7433907 | 346.3693532 | 311.910015 | 299.853749 | 296.4129682 | 295.2955268 | |
| 0 | 576.0671027 | 365.7770019 | 325.282194 | 315.4654321 | 312.8639533 | 312.0190869 | |
| 0 | 655.6817723 | 370.6355906 | 328.8921631 | 317.0954376 | 313.3964561 | 312.1951604 | |
| 0 | 671.1977013 | 386.3494639 | 335.6409758 | 320.3020305 | 316.1669739 | 314.8240567 | |
| 0 | 723.7496372 | 396.8739971 | 338.8105011 | 320.4157921 | 316.2714515 | 314.9255193 | |
| 0 | 741.2365168 | 412.377211 | 350.0531568 | 331.1612375 | 327.0899313 | 325.7677181 | |
| 0 | 804.5060943 | 417.7590056 | 350.1486569 | 336.8929771 | 333.7048804 | 332.6695016 | |
| 0 | 842.7599134 | 430.0306271 | 371.3096937 | 356.6673452 | 352.7018184 | 351.4139584 | |
| 0 | 853.1297773 | 435.3860695 | 379.0177392 | 358.9313716 | 353.2755915 | 351.4387983 | |
| 0 | 915.7533814 | 447.9606367 | 392.1849722 | 379.3173127 | 374.8789122 | 373.4374799 | |
| 0 | 1014.213738 | 481.1451495 | 401.6383993 | 379.9440503 | 375.086835 | 373.5093867 | |
| 0 | 0 | 484.0203289 | 410.419721 | 385.3513639 | 379.3444811 | 377.3936624 | |
| 0 | 0 | 488.0179081 | 414.529147 | 386.8326879 | 379.9651887 | 377.7348729 | |
| 0 | 0 | 501.8526668 | 427.1336082 | 406.2461476 | 400.6106228 | 398.7804077 | |
| 0 | 0 | 519.5302515 | 435.1300524 | 414.7924565 | 409.9630464 | 408.3946283 | |
| 0 | 0 | 521.978051 | 439.7820521 | 416.4662972 | 410.4152328 | 408.4500656 | |
| 0 | 0 | 528.9900654 | 453.0930575 | 429.111999 | 422.4705601 | 420.3136604 | |
| 0 | 0 | 534.307408 | 454.9364986 | 429.8148045 | 422.8154243 | 420.5422783 | |
| 0 | 0 | 567.4981104 | 472.0539637 | 449.0732801 | 444.2394498 | 442.6695962 | |
| 0 | 0 | 579.9510702 | 490.1075718 | 454.9617907 | 445.5809852 | 442.5344382 | |
| 0 | 0 | 582.8515145 | 496.2388125 | 457.529135 | 446.625692 | 443.0846473 | |
| 0 | 0 | 600.6835431 | 500.6841905 | 470.5543347 | 463.3315137 | 460.9858022 | |
| 0 | 0 | 606.7521397 | 503.4818563 | 476.2898254 | 469.8775303 | 467.7950483 | |
| 0 | 0 | 620.8473151 | 512.5832873 | 478.9437769 | 470.4985457 | 467.7558395 | |
| 0 | 0 | 631.652006 | 523.4912817 | 500.8483169 | 494.9790568 | 493.072933 | |
| 0 | 0 | 656.3122266 | 540.3079576 | 506.8848022 | 496.7151201 | 493.4123745 | |
| 0 | 0 | 663.9379028 | 547.9509526 | 508.2769552 | 498.7354459 | 495.6367082 | |
| 0 | 0 | 671.4627163 | 555.2228244 | 513.6744072 | 500.2919505 | 495.9458116 | |
| 0 | 0 | 683.3032323 | 571.1613415 | 535.4723644 | 526.887474 | 524.0994115 | |
| 0 | 0 | 696.391079 | 573.8682178 | 539.6788924 | 528.2784372 | 524.5759809 | |
| 0 | 0 | 716.1681389 | 586.4186929 | 541.4259914 | 531.7079884 | 528.5519319 | |
| 0 | 0 | 729.1157267 | 595.2997134 | 545.1427302 | 533.199604 | 529.3209078 | |
| 0 | 0 | 737.4627193 | 601.0879428 | 550.4915385 | 539.5104978 | 535.9442522 | |
| 0 | 0 | 764.3493508 | 603.8241834 | 572.6550405 | 565.4470619 | 563.1061706 | |
| 0 | 0 | 767.3551762 | 620.8073947 | 580.8250636 | 567.4742538 | 563.1383927 | |
| 0 | 0 | 773.8852381 | 630.826814 | 590.1421529 | 573.7980213 | 568.4900374 | |
| 0 | 0 | 780.3225033 | 638.5736199 | 592.9023415 | 581.8159402 | 578.2154774 | |
| 0 | 0 | 801.5212216 | 654.3349915 | 600.6260841 | 587.2220481 | 582.8689011 | |
| 0 | 0 | 821.4792454 | 665.7087872 | 601.3891326 | 587.4155081 | 582.8773793 | |
| 0 | 0 | 837.1477752 | 672.1297716 | 616.9644215 | 604.4309872 | 600.3605803 | |
| 0 | 0 | 857.1871162 | 679.9120704 | 624.4539085 | 606.366396 | 600.4922249 | |
| 0 | 0 | 862.7383872 | 709.8982711 | 640.2908416 | 627.3311516 | 623.1223122 | |
| 0 | 0 | 872.1030093 | 713.8503622 | 642.1828529 | 628.497328 | 624.0527635 | |
| 0 | 0 | 876.6084002 | 725.4784493 | 655.1343244 | 643.2345054 | 639.3698737 | |
| 0 | 0 | 887.2645284 | 730.6260325 | 658.5028412 | 644.0909014 | 639.4104236 | |
| 0 | 0 | 905.0335154 | 739.8336261 | 669.4750433 | 652.1401909 | 646.5104566 | |
| 0 | 0 | 924.2074368 | 763.7778834 | 674.4298564 | 658.5259332 | 653.360913 | |
| 0 | 0 | 931.5746772 | 768.9266356 | 683.0029257 | 660.2102344 | 652.8079911 | |
| 0 | 0 | 953.2369423 | 784.3298674 | 692.7070099 | 679.5365406 | 675.2592476 | |
| 0 | 0 | 968.3783855 | 787.1771072 | 701.4669299 | 682.4249657 | 676.2408231 | |
| 0 | 0 | 971.1363679 | 792.566876 | 703.4391284 | 685.8412813 | 680.1261358 | |
| 0 | 0 | 997.45201 | 794.5042035 | 707.2928713 | 686.0033671 | 679.0893047 | |
| 0 | 0 | 1004.704137 | 813.8296198 | 729.7946829 | 711.8683172 | 706.0464807 | |
| 0 | 0 | 1031.337149 | 829.3497857 | 736.7099798 | 724.6794112 | 720.7723168 | |
| 0 | 0 | 1040.981224 | 838.1240881 | 746.6437673 | 727.7360164 | 721.5954615 | |
| 0 | 0 | 0 | 852.623889 | 752.5880686 | 731.4686749 | 724.6098583 | |
| 0 | 0 | 0 | 858.3776995 | 756.7499017 | 734.8892171 | 727.7896559 | |
| 0 | 0 | 0 | 858.8086703 | 761.2633747 | 736.8762321 | 728.9561686 | |
| 0 | 0 | 0 | 871.8463332 | 776.7435246 | 751.8171226 | 743.721927 | |
| 0 | 0 | 0 | 883.1108758 | 781.2727372 | 753.3517113 | 744.28397 | |
| 0 | 0 | 0 | 891.7432023 | 803.7180623 | 786.2819017 | 780.6192662 | |
| 0 | 0 | 0 | 905.2148921 | 807.1559025 | 788.4959989 | 782.4359358 | |
| 0 | 0 | 0 | 912.4063451 | 808.6390166 | 789.0216847 | 782.6506835 | |
| 0 | 0 | 0 | 923.1188288 | 815.1446254 | 791.145208 | 783.3510636 | |
| 0 | 0 | 0 | 929.3631683 | 816.4828913 | 792.9210708 | 785.2690421 | |
| 0 | 0 | 0 | 946.4851424 | 822.0665742 | 795.4429547 | 786.7965642 | |
| 0 | 0 | 0 | 965.2923564 | 837.306622 | 814.1143069 | 806.5822802 | |
| 0 | 0 | 0 | 967.4134208 | 843.1888396 | 821.1899481 | 814.0455023 | |
| 0 | 0 | 0 | 975.3625612 | 867.293245 | 828.1299682 | 815.4111497 | |
| 0 | 0 | 0 | 984.9226719 | 868.8054481 | 842.1384257 | 833.4779395 | |
| 0 | 0 | 0 | 992.8796011 | 879.3385048 | 850.1220494 | 840.6335995 | |
| 0 | 0 | 0 | 998.3772331 | 880.0634787 | 852.8237508 | 843.9772706 | |
| 0 | 0 | 0 | 1010.465759 | 887.6873666 | 855.5321447 | 845.0892894 | |
| 0 | 0 | 0 | 1030.357591 | 907.1838317 | 880.9274705 | 872.4003523 | |
| 0 | 0 | 0 | 1043.388316 | 909.8795588 | 886.2165856 | 878.5317061 | |
| 0 | 0 | 0 | 0 | 919.8489463 | 888.0615795 | 877.7381903 | |
| 0 | 0 | 0 | 0 | 927.2325993 | 903.063587 | 895.2143643 | |
| 0 | 0 | 0 | 0 | 928.9405008 | 903.3169289 | 894.9953178 | |
| 0 | 0 | 0 | 0 | 938.7560925 | 907.0998288 | 896.8190171 | |
| 0 | 0 | 0 | 0 | 949.1726385 | 910.9090444 | 898.4824103 | |
| 0 | 0 | 0 | 0 | 954.0982762 | 921.3778281 | 910.7514078 | |
| 0 | 0 | 0 | 0 | 962.871837 | 936.3992017 | 927.8018455 | |
| 0 | 0 | 0 | 0 | 974.5870109 | 938.10892 | 926.2621529 | |
| 0 | 0 | 0 | 0 | 979.8181263 | 947.9276985 | 937.5708388 | |
| 0 | 0 | 0 | 0 | 990.7266593 | 952.4519872 | 940.0217554 | |
| 0 | 0 | 0 | 0 | 999.5307191 | 956.710682 | 942.8042798 | |
| 0 | 0 | 0 | 0 | 1007.476105 | 958.4158686 | 942.4828748 | |
| 0 | 0 | 0 | 0 | 1023.401073 | 995.7568157 | 986.7789589 | |
| 0 | 0 | 0 | 0 | 1024.806147 | 999.8345257 | 991.7246445 | |
| 0 | 0 | 0 | 0 | 1035.768342 | 1003.807625 | 993.4279385 | |
| 0 | 0 | 0 | 0 | 1041.893615 | 1006.017657 | 994.3664407 | |
| 0 | 0 | 0 | 0 | 0 | 1012.378156 | ||
| 0 | 0 | 0 | 0 | 0 | 1018.615515 | ||
| 0 | 0 | 0 | 0 | 0 | 1020.344274 | ||
| 0 | 0 | 0 | 0 | 0 | 1031.424008 | ||
| 0 | 0 | 0 | 0 | 0 | 1035.555741 |