We analyzed hyperbolic discs of three different hyperbolic radii to test our conjecture. The hyperbolic radii used were 1/2, 1, and 2. We then compared the eigenvalue counting function N(t) with its prediction for Hyperbolic Discs given by N'(t) = area/4pi*t - perimeter/4pi*sqrt(t) + 1/6, using the Hyperbolic area and perimeter. These are given by 2pi*(cosh(r)-1) and 2pi*sinh(r), respectively.
Note that the predicted counting function for the disc with hyperbolic radius 2 does not seem to match as well as the other two discs. This is because the error for each eigenvalue decayed at an extremely unsteady rate with successive refinements, making it difficult to predict the true eigenvalues. We suspect this is due to the relatively large area of the disc, because while the hyperbolic area of 2pi*(cosh(2)-1) is not excessive, in order to simulate the problem in MATLAB we had to use a Euclidean disc of radius (e^4-1)/2 and solve for the Eigenvalue of the Laplacian with a scalar.
Here N'(t) = (Area/4pi)*t - (Perimeter/4pi)*t^1/2 + 1/6.
Difference Graphs and Scatterplots for the Hyperbolic Discs
Calculated and Predicted Eigenvalue Spectrums for the Hyperbolic Discs
| Hyperbolic Disc of Radius 1/2 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 23.78011796 | 23.54557582 | 23.48544792 | 23.47026225 | 23.46645279 | 23.46549942 | 23.46517986 | |
| 60.7257011 | 59.24266162 | 58.86080858 | 58.76428029 | 58.74006096 | 58.73399949 | 58.73196778 | |
| 60.83533281 | 59.27307034 | 58.86878286 | 58.76630638 | 58.74056999 | 58.73412693 | 58.73196732 | |
| 111.2646812 | 106.258452 | 104.9622131 | 104.6336275 | 104.5511017 | 104.5304411 | 104.523516 | |
| 111.3907379 | 106.2902105 | 104.9700335 | 104.6355531 | 104.5515797 | 104.5305603 | 104.5235149 | |
| 130.9963796 | 124.4801902 | 122.789935 | 122.3609101 | 122.2531071 | 122.2261142 | 122.2170666 | |
| 176.2027091 | 164.3679641 | 161.2742668 | 160.488744 | 160.2914017 | 160.2419951 | 160.2254348 | |
| 176.9805681 | 164.537371 | 161.3165711 | 160.4993441 | 160.2940536 | 160.2426582 | 160.2254313 | |
| 218.3873769 | 202.3814782 | 198.267288 | 197.2264393 | 196.9651308 | 196.8997168 | 196.8777911 | |
| 220.5725726 | 203.1320872 | 198.4729759 | 197.2791567 | 196.9783982 | 196.9030396 | 196.8777806 | |
| 257.7408971 | 233.8438379 | 227.5851886 | 225.9949807 | 225.5953655 | 225.4953091 | 225.4617718 | |
| 259.3848863 | 234.2144929 | 227.677774 | 226.0181179 | 225.6011459 | 225.4967537 | 225.4617631 | |
| 327.8397975 | 294.2675139 | 285.4386297 | 283.1808545 | 282.6121376 | 282.4696401 | 282.4218773 | |
| 333.2978433 | 295.5223455 | 285.7466277 | 283.2574945 | 282.6312657 | 282.4744193 | 282.421847 | |
| 352.8307086 | 313.5720771 | 303.3529276 | 300.7554317 | 300.1002307 | 299.9352515 | 299.8799532 | |
| 357.2988937 | 314.8555401 | 303.7409134 | 300.9184551 | 300.2100632 | 300.0329231 | 299.9735486 | |
| 362.4125175 | 316.1801395 | 304.0637814 | 300.9970818 | 300.2290948 | 300.0375873 | 299.9733971 | |
| 463.0626022 | 400.6675087 | 384.1940196 | 379.9379078 | 378.8599602 | 378.5894452 | 378.4987729 | |
| 464.229896 | 401.0721492 | 384.2811949 | 379.9578319 | 378.8648134 | 378.5906506 | 378.4987556 | |
| 477.9108465 | 408.7997245 | 389.9289847 | 385.1592554 | 383.9670947 | 383.6691171 | 383.5692398 | |
| 483.1841743 | 409.7106265 | 390.1628285 | 385.2226773 | 383.9833454 | 383.6732064 | 383.5692528 | |
| 512.836036 | 438.8387656 | 420.2327111 | 415.5624977 | 414.3923101 | 414.0995162 | 414.0013764 | |
| 522.6505827 | 442.6549411 | 421.3515112 | 415.8534806 | 414.465791 | 414.1179338 | 414.0013376 | |
| 596.4823444 | 511.894047 | 485.5157208 | 478.4927182 | 476.7014889 | 476.2512613 | 476.1003522 | |
| 625.5900582 | 516.9852919 | 486.5370649 | 478.72427 | 476.7577771 | 476.265232 | 476.1001388 | |
| 632.1792927 | 523.077975 | 494.3980616 | 487.2130718 | 485.4166959 | 484.9675058 | 484.8169446 | |
| 640.6835833 | 523.7815485 | 494.5437717 | 487.2518793 | 485.4265781 | 484.9699871 | 484.8169452 | |
| 708.1322523 | 583.1928502 | 550.2644341 | 541.9064044 | 539.8056309 | 539.2795597 | 539.1032291 | |
| 716.5866356 | 585.967932 | 551.1983838 | 542.1617299 | 539.8709324 | 539.2959775 | 539.1032619 | |
| 758.4741016 | 606.5872551 | 568.9086682 | 559.5855778 | 557.2655558 | 556.6862017 | 556.4920115 | |
| 764.7119001 | 633.940989 | 592.0325375 | 581.1280269 | 578.3702832 | 577.6786306 | 577.4467998 | |
| 797.9028988 | 635.3793922 | 592.2884106 | 581.1895789 | 578.385515 | 577.6824273 | 577.4467636 | |
| 820.7747985 | 658.8953042 | 615.7715117 | 604.8133042 | 602.0604849 | 601.3713133 | 601.1403141 | |
| 834.0855252 | 661.9368795 | 616.4357324 | 604.9753471 | 602.1008316 | 601.3813928 | 601.1402485 | |
| 924.2145629 | 745.7899892 | 693.091504 | 679.5265596 | 676.1091031 | 675.2527897 | 674.9657673 | |
| 932.935056 | 746.6256649 | 693.3328659 | 679.6047965 | 676.1299603 | 675.2580877 | 674.9658501 | |
| 950.7706723 | 767.8312302 | 708.3287112 | 692.7586879 | 688.8265113 | 687.8407543 | 687.5103445 | |
| 990.3063733 | 769.8134033 | 708.5758254 | 692.8325064 | 688.8460124 | 687.8456965 | 687.5104067 | |
| 1005.907722 | 785.2993353 | 728.8578024 | 714.7790947 | 711.260313 | 710.3804567 | 710.085543 | |
| 1045.013781 | 790.3430236 | 730.7326215 | 715.2960835 | 711.392758 | 710.4137739 | 710.0856343 | |
| 1048.340001 | 813.0870348 | 749.0534292 | 732.7495513 | 728.6468497 | 727.6191372 | 727.2746645 | |
| 1076.317638 | 816.6206724 | 749.7888471 | 732.9122912 | 728.6859787 | 727.6288173 | 727.2744739 | |
| 1119.199357 | 915.9552961 | 834.8138627 | 813.442423 | 808.023759 | 806.6638336 | 806.2080085 | |
| 1188.520896 | 919.4899813 | 835.3734774 | 813.5648398 | 808.0533757 | 806.671181 | 806.2078916 | |
| 1210.510681 | 927.4140855 | 848.2865065 | 828.1526725 | 823.0750976 | 821.8019819 | 821.3752541 | |
| 1227.14659 | 928.0457314 | 848.8176248 | 828.3111227 | 823.1160888 | 821.8123113 | 821.3753061 | |
| 1234.19019 | 981.8601911 | 893.9814003 | 870.8811966 | 865.0214543 | 863.5510737 | 863.0582258 | |
| 1304.826144 | 987.0386936 | 894.7966345 | 871.0231429 | 865.0529774 | 863.5587024 | 863.0578456 | |
| 1349.711842 | 994.3786078 | 904.3372138 | 882.0944446 | 876.549879 | 875.1637636 | 874.6991601 | |
| 1361.051135 | 998.2005404 | 906.0499518 | 882.6468136 | 876.697106 | 875.2011633 | 874.6997474 | |
| 1382.825149 | 1019.676666 | 924.4172967 | 900.1452371 | 894.0806737 | 892.5659657 | 892.0582601 | |
| 1396.760227 | 1075.734351 | 971.1512248 | 943.0590544 | 935.8799727 | 934.0741165 | 933.4688226 | |
| 1455.038633 | 1089.749554 | 973.465408 | 943.5109305 | 935.9840288 | 934.0995564 | 933.4679116 | |
| 1489.838462 | 1124.004989 | 1015.906931 | 987.7342115 | 980.5523027 | 978.745762 | 978.1402388 | |
| 1526.91067 | 1133.516672 | 1017.701262 | 988.0973557 | 980.6366316 | 978.7664228 | 978.1395591 | |
| 1540.127538 | 1173.007477 | 1050.636335 | 1019.010096 | 1011.025051 | 1009.0239 | 1008.353147 | |
| 1598.228146 | 1182.928014 | 1052.6875 | 1019.454733 | 1011.132099 | 1009.050415 | 1008.352669 | |
| 1608.963531 | 1219.043443 | 1093.474686 | 1061.087676 | 1052.918897 | 1050.870565 | 1050.183997 | |
| 1650.88391 | 1220.591093 | 1093.999452 | 1061.335515 | 1052.989677 | 1050.888831 | 1050.184661 | |
| 1709.506981 | 1258.537015 | 1119.259146 | 1081.92357 | 1072.419682 | 1070.030925 | 1069.230252 | |
| 1750.807679 | 1261.78447 | 1121.388073 | 1082.387872 | 1072.5293 | 1070.057899 | 1069.229526 | |
| 1788.822828 | 1267.846307 | 1128.152324 | 1095.834561 | 1087.803759 | 1085.798799 | 1085.126769 | |
| 1817.268102 | 1271.322207 | 1134.498702 | 1097.599325 | 1088.254091 | 1085.911923 | 1085.126867 | |
| 1876.614171 | 1350.701268 | 1197.154172 | 1158.274824 | 1148.406204 | 1145.923347 | 1145.091133 | |
| 1924.543839 | 1351.207731 | 1198.792497 | 1158.738231 | 1148.522474 | 1145.952368 | 1145.09091 | |
| 1950.857398 | 1383.778821 | 1219.61938 | 1177.277601 | 1166.608846 | 1163.937115 | 1163.041594 | |
| 2015.102583 | 1398.634286 | 1223.088875 | 1178.008233 | 1166.780168 | 1163.979187 | 1163.040343 | |
| 2038.046679 | 1458.833787 | 1279.094042 | 1230.074268 | 1217.615216 | 1214.486895 | 1213.438332 | |
| 2046.057823 | 1464.777443 | 1279.80591 | 1230.220809 | 1217.650909 | 1214.495768 | 1213.438215 | |
| 2141.938575 | 1466.969891 | 1295.141722 | 1251.292539 | 1240.12861 | 1237.32056 | 1236.379347 | |
| 2208.892443 | 1471.055584 | 1297.506415 | 1251.902824 | 1240.280744 | 1237.358525 | 1236.379045 | |
| 2233.815028 | 1522.255708 | 1349.543529 | 1304.524415 | 1293.077398 | 1290.201285 | 1289.237258 | |
| 2255.590486 | 1551.671265 | 1356.595536 | 1306.394369 | 1293.556712 | 1290.3219 | 1289.237644 | |
| 0 | 1572.869406 | 1375.5942 | 1323.635653 | 1310.824992 | 1307.643771 | 1306.577478 | |
| 0 | 1592.195204 | 1391.087432 | 1339.730984 | 1326.554184 | 1323.205876 | 1322.083577 | |
| 0 | 1599.800093 | 1391.749613 | 1339.809499 | 1326.580311 | 1323.213473 | 1322.084963 | |
| 0 | 1624.852786 | 1404.026525 | 1346.208025 | 1331.783414 | 1328.212346 | 1327.015382 | |
| 0 | 1631.129515 | 1405.686266 | 1346.543466 | 1331.861427 | 1328.231573 | 1327.014905 | |
| 0 | 1674.969525 | 1449.495243 | 1387.236771 | 1371.366358 | 1367.381177 | 1366.045409 | |
| 0 | 1684.677275 | 1450.485163 | 1387.371532 | 1371.3984 | 1367.389233 | 1366.045424 | |
| 0 | 1735.68056 | 1511.278151 | 1453.009979 | 1438.132473 | 1434.385851 | 1433.130043 | |
| 0 | 1748.888023 | 1516.112432 | 1454.243317 | 1438.439318 | 1434.462407 | 1433.129411 | |
| 0 | 1823.625282 | 1588.974815 | 1524.115833 | 1506.28235 | 1501.733207 | 1500.208407 | |
| 0 | 1835.198823 | 1590.03624 | 1524.211044 | 1506.318405 | 1501.742849 | 1500.209197 | |
| 0 | 1849.103701 | 1592.096336 | 1526.19598 | 1509.818609 | 1505.671509 | 1504.281469 | |
| 0 | 1859.216638 | 1593.7351 | 1526.394991 | 1509.872022 | 1505.686141 | 1504.283101 | |
| 0 | 1881.693011 | 1606.917686 | 1532.823239 | 1514.851533 | 1510.441868 | 1508.963819 | |
| 0 | 1890.750991 | 1608.420598 | 1533.29408 | 1514.967321 | 1510.470388 | 1508.963088 | |
| 0 | 1895.193274 | 1625.578402 | 1553.471964 | 1533.650267 | 1528.675631 | 1527.008214 | |
| 0 | 1905.705998 | 1631.347215 | 1553.917012 | 1533.758976 | 1528.702692 | 1527.007908 | |
| 0 | 1920.211941 | 1633.636677 | 1560.455949 | 1544.445102 | 1540.459018 | 1539.122948 | |
| 0 | 1932.290954 | 1639.85541 | 1564.529725 | 1545.483573 | 1540.719588 | 1539.122777 | |
| 0 | 2039.960639 | 1745.82345 | 1667.108409 | 1647.035581 | 1641.985069 | 1640.292219 | |
| 0 | 2051.216531 | 1746.907975 | 1667.564294 | 1647.166154 | 1642.018785 | 1640.293471 | |
| 0 | 2115.849714 | 1799.763175 | 1712.824361 | 1690.182288 | 1684.434212 | 1682.50755 | |
| 0 | 2130.003314 | 1801.242268 | 1713.064971 | 1690.240789 | 1684.448777 | 1682.507388 | |
| 0 | 2146.581408 | 1823.044909 | 1729.284039 | 1704.570482 | 1698.366682 | 1696.287269 | |
| 0 | 2151.854891 | 1824.444523 | 1729.384844 | 1704.602986 | 1698.375225 | 1696.28778 | |
| 0 | 2161.983476 | 1829.444874 | 1735.804668 | 1713.165202 | 1707.12845 | 1705.105028 | |
| 0 | 2175.280667 | 1831.676983 | 1736.488627 | 1713.2227 | 1707.337821 | 1705.365305 | |
| 0 | 2197.977896 | 1846.429262 | 1759.293382 | 1737.453376 | 1731.967575 | 1730.128823 | |
| 0 | 2206.884995 | 1848.155257 | 1760.015498 | 1737.647695 | 1732.016903 | 1730.129553 | |
| 0 | 2225.011922 | 1898.572727 | 1812.378209 | 1790.197275 | 1784.600996 | 1782.725213 | |
| 0 | 2284.674792 | 1910.086369 | 1815.190346 | 1790.92934 | 1784.786585 | 1782.727633 | |
| 0 | 2297.632244 | 1932.145363 | 1832.783022 | 1808.162483 | 1802.084038 | 1800.046642 | |
| 0 | 0 | 1991.675688 | 1892.010048 | 1866.37669 | 1859.907008 | 1857.738475 | |
| 0 | 0 | 1997.888535 | 1893.401 | 1866.711348 | 1859.989715 | 1857.736732 | |
| 0 | 0 | 2018.643365 | 1910.645069 | 1883.101074 | 1876.172993 | 1873.850812 | |
| 0 | 0 | 2020.54227 | 1911.120813 | 1883.225993 | 1876.204648 | 1873.851206 | |
| 0 | 0 | 2034.039722 | 1915.045568 | 1884.249132 | 1876.464205 | 1873.854823 | |
| 0 | 0 | 2036.207838 | 1915.550178 | 1884.354695 | 1876.48905 | 1873.852613 | |
| 0 | 0 | 2065.395356 | 1950.21988 | 1921.558896 | 1914.418197 | 1912.02475 | |
| 0 | 0 | 2068.555079 | 1950.810444 | 1921.690896 | 1914.450298 | 1912.023367 | |
| 0 | 0 | 2112.827008 | 2003.953196 | 1976.060887 | 1969.022684 | 1966.663593 | |
| 0 | 0 | 2121.515 | 2006.023279 | 1976.568599 | 1969.148954 | 1966.662008 | |
| 0 | 0 | 2195.078849 | 2077.800901 | 2047.489268 | 2039.851544 | 2037.291503 | |
| 0 | 0 | 2198.703458 | 2078.45964 | 2047.688595 | 2039.905748 | 2037.297063 | |
| 0 | 0 | 2233.290272 | 2107.88118 | 2071.900598 | 2062.743077 | 2059.673624 | |
| 0 | 0 | 2243.344311 | 2108.432847 | 2071.99926 | 2062.766205 | 2059.671435 | |
| 0 | 0 | 2247.165682 | 2112.004267 | 2082.043879 | 2074.577149 | 2072.074422 | |
| 0 | 0 | 2253.460289 | 2118.070866 | 2083.579179 | 2074.960913 | 2072.072209 | |
| 0 | 0 | 2256.736046 | 2121.157049 | 2085.942437 | 2077.130394 | 2074.176739 | |
| 0 | 0 | 2260.015193 | 2121.797311 | 2086.098047 | 2077.168755 | 2074.1758 | |
| 0 | 0 | 2264.549961 | 2129.383428 | 2096.446153 | 2088.133015 | 2085.346586 | |
| 0 | 0 | 2266.149707 | 2130.10309 | 2096.587821 | 2088.165153 | 2085.342011 | |
| 0 | 0 | 0 | 2175.950187 | 2139.927533 | 2130.982228 | 2127.983907 | |
| 0 | 0 | 0 | 2176.102196 | 2139.999318 | 2131.003487 | 2127.98823 | |
| 0 | 0 | 0 | 2262.436054 | 2226.037343 | 2216.840386 | 2213.757714 | |
| 0 | 0 | 0 | 2262.851359 | 2226.12524 | 2216.862082 | 2213.757221 | |
| 0 | 0 | 0 | 0 | 2268.465561 | 2257.410004 | 2253.70436 | |
| 0 | 0 | 0 | 0 | 2268.488387 | 2257.416086 | 2253.704829 | |
| 0 | 0 | 0 | 0 | 2297.718173 | 2287.020882 | 2283.435323 | |
| 0 | 0 | 0 | 0 | 2297.89935 | 2287.065043 | 2283.433558 |
| Hyperbolic Disc of Radius 1 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 6.205400223 | 6.137725287 | 6.119430891 | 6.114684294 | 6.11348352 | 6.113182319 | 6.113078003 | |
| 15.43605282 | 14.89382987 | 14.7477731 | 14.71019955 | 14.70072447 | 14.69835001 | 14.69752767 | |
| 15.54153488 | 14.92452216 | 14.75651272 | 14.71247972 | 14.70130128 | 14.69849467 | 14.69752265 | |
| 28.13693839 | 26.20245618 | 25.66001373 | 25.51771152 | 25.48159698 | 25.47253104 | 25.46939122 | |
| 28.23768569 | 26.21936518 | 25.66473476 | 25.51895206 | 25.48191122 | 25.47260984 | 25.46938848 | |
| 34.44886152 | 31.78531873 | 31.05708336 | 30.86504416 | 30.81618475 | 30.80391023 | 30.79965918 | |
| 44.41366378 | 40.00488654 | 38.74029438 | 38.40402111 | 38.31825971 | 38.29670247 | 38.28923653 | |
| 45.17638322 | 40.19740503 | 38.78967371 | 38.41645946 | 38.32137653 | 38.29748222 | 38.28920687 | |
| 57.66400425 | 51.54334865 | 49.83689969 | 49.38672416 | 49.27217168 | 49.24339171 | 49.2334243 | |
| 60.26817203 | 52.26758605 | 50.04576409 | 49.44157981 | 49.28606913 | 49.24687786 | 49.23330469 | |
| 64.59752597 | 56.49670924 | 53.98698599 | 53.30503275 | 53.13002797 | 53.08596632 | 53.07070639 | |
| 67.20388725 | 56.96703409 | 54.09065757 | 53.3300149 | 53.13621584 | 53.0875098 | 53.07064137 | |
| 86.49350633 | 74.86850511 | 71.22040466 | 70.17251761 | 69.86387559 | 69.78233184 | 69.75409069 | |
| 88.47914958 | 75.26671636 | 71.30989125 | 70.19081907 | 69.86748161 | 69.78318291 | 69.75398763 | |
| 91.53796917 | 76.38691341 | 71.60840516 | 70.32241652 | 70.0271742 | 69.95648155 | 69.93199847 | |
| 94.3167812 | 76.77685027 | 71.65955567 | 70.33544964 | 70.03150432 | 69.95762568 | 69.9320392 | |
| 101.4836928 | 81.66036054 | 76.8936807 | 75.64103229 | 75.3222156 | 75.24211905 | 75.21437911 | |
| 111.7612866 | 98.15938124 | 91.08206087 | 89.01896574 | 88.47833824 | 88.34145698 | 88.29405071 | |
| 121.8203737 | 98.75197334 | 91.18295252 | 89.04089351 | 88.48365504 | 88.34277687 | 88.29398635 | |
| 128.373676 | 102.9244248 | 95.47086669 | 93.49590399 | 92.98973069 | 92.86225473 | 92.81810581 | |
| 132.1854653 | 103.0596667 | 95.52555262 | 93.51258491 | 92.9941228 | 92.86336701 | 92.81808219 | |
| 140.8240223 | 113.7275504 | 106.2091983 | 104.2009748 | 103.6871887 | 103.5579019 | 103.5131258 | |
| 145.7324529 | 116.1910053 | 107.0049503 | 104.4232187 | 103.7444742 | 103.5723362 | 103.5127194 | |
| 157.9385632 | 123.3221943 | 112.8892562 | 109.7666983 | 108.9395463 | 108.7293917 | 108.6566087 | |
| 163.8468964 | 125.1207995 | 113.2341089 | 109.8389461 | 108.9565481 | 108.7335731 | 108.6563499 | |
| 174.1105232 | 133.9404265 | 122.1414491 | 118.9368035 | 118.1075442 | 117.8981016 | 117.8255651 | |
| 182.8701774 | 134.5944355 | 122.2979342 | 118.9775778 | 118.1178675 | 117.9006912 | 117.8254763 | |
| 187.0831649 | 152.1879045 | 137.2189721 | 132.4885857 | 131.2401583 | 130.9230501 | 130.8132256 | |
| 200.8790277 | 152.5764821 | 137.3881959 | 132.5382671 | 131.2525972 | 130.9261541 | 130.8130966 | |
| 207.1150984 | 153.3156591 | 139.1111874 | 135.4048531 | 134.4305003 | 134.1832638 | 134.097638 | |
| 211.1270417 | 153.9017862 | 139.3847844 | 135.5071038 | 134.4594861 | 134.1907497 | 134.0976778 | |
| 222.0983732 | 160.4774258 | 145.1597294 | 140.8477406 | 139.7397081 | 139.4614528 | 139.3650843 | |
| 240.0200736 | 169.8226031 | 151.6320271 | 146.6413476 | 145.3431314 | 145.0147883 | 144.9010728 | |
| 243.5857577 | 170.1727003 | 151.7109403 | 146.6628492 | 145.3488161 | 145.0162329 | 144.901049 | |
| 251.5219544 | 185.5134082 | 163.8204552 | 157.1292623 | 155.3503465 | 154.8976732 | 154.7408983 | |
| 266.3559606 | 185.7248108 | 164.0937419 | 157.2081625 | 155.3704427 | 154.9027153 | 154.7407267 | |
| 275.3100005 | 194.157763 | 174.6898291 | 168.9906548 | 167.4510345 | 167.0564532 | 166.9197973 | |
| 284.7641051 | 195.4360033 | 175.0513552 | 169.0905228 | 167.4766796 | 167.0629084 | 166.9196065 | |
| 300.0269476 | 203.980649 | 183.7872406 | 176.5623091 | 174.6520094 | 174.1681581 | 174.0005852 | |
| 306.3098935 | 209.6798563 | 183.9014866 | 176.5971234 | 174.6617314 | 174.1706521 | 174.000576 | |
| 315.0520895 | 211.2127834 | 185.1398252 | 179.4538539 | 178.0189478 | 177.6569945 | 177.5316388 | |
| 317.2823617 | 215.2823837 | 188.1342139 | 180.3264641 | 178.2433383 | 177.7134713 | 177.5299617 | |
| 338.367714 | 219.1110432 | 192.8897302 | 183.7337886 | 181.2674949 | 180.6379815 | 180.4199613 | |
| 347.2053144 | 222.9017412 | 193.2835955 | 183.825085 | 181.2897688 | 180.643514 | 180.4196957 | |
| 370.1745045 | 241.326727 | 213.1865182 | 204.9714103 | 202.7179021 | 202.1342369 | 201.9320953 | |
| 379.4201948 | 243.5047775 | 213.8769263 | 205.1522745 | 202.7622946 | 202.1452196 | 201.9315072 | |
| 390.5070295 | 253.3435606 | 219.139329 | 208.7207361 | 206.0078978 | 205.3236367 | 205.0866556 | |
| 398.2004449 | 256.1839213 | 219.390394 | 208.8106823 | 206.0320094 | 205.3297491 | 205.0865343 | |
| 407.0967329 | 256.4652259 | 224.6173873 | 212.3305493 | 208.9851571 | 208.1296921 | 207.8334178 | |
| 421.8320532 | 263.1518445 | 224.9719858 | 212.3976071 | 209.0014006 | 208.1337287 | 207.8332267 | |
| 441.9306228 | 264.9282831 | 230.9195864 | 221.5145464 | 218.8908841 | 218.2225233 | 217.991049 | |
| 465.4578955 | 265.2058697 | 231.3885772 | 221.6043745 | 218.93749 | 218.2359683 | 217.9930093 | |
| 470.2874724 | 281.1941978 | 238.688754 | 227.1689267 | 224.2321875 | 223.502976 | 223.2504272 | |
| 482.2263938 | 292.9323934 | 254.2784514 | 242.5912909 | 238.4886933 | 237.3594148 | 236.9683102 | |
| 491.5608628 | 294.7536111 | 254.8001959 | 242.7238581 | 238.5002042 | 237.3617713 | 236.9674963 | |
| 520.2685919 | 296.1445433 | 258.1501864 | 242.9981346 | 239.3733723 | 238.4535997 | 238.1350536 | |
| 536.0203238 | 302.7651453 | 258.4350702 | 243.0602862 | 239.400169 | 238.4599522 | 238.1343257 | |
| 538.4907656 | 309.063224 | 259.1779932 | 243.9382371 | 240.2547261 | 239.3842171 | 239.0827326 | |
| 544.4474358 | 310.8142147 | 259.6894606 | 244.0443629 | 240.2946171 | 239.3944325 | 239.0826704 | |
| 584.5613496 | 325.6198464 | 279.3576102 | 265.7448514 | 262.011746 | 261.0476243 | 260.7137188 | |
| 586.7357533 | 328.6869134 | 280.3219881 | 266.0221358 | 262.0847075 | 261.0661739 | 260.7134239 | |
| 0 | 329.6545282 | 289.2184008 | 275.4349461 | 269.7713708 | 268.3129469 | 267.807849 | |
| 0 | 336.2280575 | 295.3109269 | 275.553901 | 269.8078721 | 268.3223744 | 267.8079 | |
| 0 | 347.9225157 | 295.5500124 | 275.9374207 | 272.4673546 | 271.5902794 | 271.2865208 | |
| 0 | 351.416146 | 295.8583546 | 277.8219454 | 272.959994 | 271.7145993 | 271.2832801 | |
| 0 | 352.8793681 | 297.2670531 | 279.6421236 | 274.7936111 | 273.5365263 | 273.1011585 | |
| 0 | 361.1363693 | 297.3108417 | 279.7086443 | 274.8118495 | 273.5412445 | 273.1011942 | |
| 0 | 369.2285059 | 303.2071779 | 284.7082564 | 279.960669 | 278.7668785 | 278.3534315 | |
| 0 | 371.5788443 | 303.2799712 | 284.7430153 | 279.9738088 | 278.7705722 | 278.3538537 | |
| 0 | 384.2335604 | 330.9893931 | 310.0690946 | 302.8617032 | 300.9921669 | 300.3446879 | |
| 0 | 393.343784 | 332.6675187 | 310.1788272 | 302.8772799 | 300.9953592 | 300.3435911 | |
| 0 | 400.6097036 | 335.2460332 | 312.5573382 | 307.4488563 | 306.1217285 | 305.6621027 | |
| 0 | 403.434298 | 336.3615577 | 312.9804536 | 307.5529098 | 306.1475394 | 305.6608156 | |
| 0 | 410.0097415 | 341.2140223 | 318.52456 | 312.1855337 | 310.5442714 | 309.9758508 | |
| 0 | 414.9074961 | 341.5528206 | 318.6594841 | 312.2227543 | 310.5537318 | 309.9756971 | |
| 0 | 415.8271628 | 347.793379 | 327.959195 | 321.8231127 | 320.2437468 | 319.6967629 | |
| 0 | 421.0226932 | 349.2223857 | 328.2413893 | 321.8805904 | 320.2576788 | 319.6956137 | |
| 0 | 436.874449 | 352.3205251 | 329.0584105 | 323.5189582 | 322.1067083 | 321.617602 | |
| 0 | 440.6077257 | 352.7217737 | 329.3977577 | 323.6929642 | 322.157897 | 321.6262551 | |
| 0 | 450.579407 | 359.7256187 | 335.3631636 | 328.9667705 | 327.4061221 | 326.8656206 | |
| 0 | 455.3322063 | 378.0732115 | 346.7704569 | 337.7249778 | 335.3786905 | 334.5660977 | |
| 0 | 457.2147903 | 379.039334 | 346.8666148 | 337.7488114 | 335.3845723 | 334.5657623 | |
| 0 | 471.2436374 | 386.8636004 | 359.7156024 | 351.5819886 | 349.4672307 | 348.7348237 | |
| 0 | 478.8780075 | 388.0575074 | 359.8131065 | 351.6027498 | 349.4721814 | 348.7342988 | |
| 0 | 481.265308 | 388.6100214 | 362.1594645 | 355.229576 | 353.4257413 | 352.8010168 | |
| 0 | 488.5736216 | 389.239421 | 362.4474366 | 355.3073797 | 353.4455642 | 352.8007592 | |
| 0 | 502.1571645 | 404.937973 | 374.1197056 | 365.8931678 | 363.8047431 | 363.0814562 | |
| 0 | 508.202025 | 405.134085 | 374.2088561 | 365.9239327 | 363.813062 | 363.0820014 | |
| 0 | 513.2972104 | 411.2214285 | 384.2664149 | 374.3520859 | 371.4641694 | 370.4639935 | |
| 0 | 515.3726909 | 412.9662127 | 385.0392492 | 374.4360215 | 371.4859248 | 370.4642139 | |
| 0 | 521.6699064 | 420.8676136 | 385.5069994 | 376.8409634 | 374.9002751 | 374.228154 | |
| 0 | 522.6745835 | 423.6196331 | 385.7355686 | 377.0690504 | 374.9596646 | 374.2291182 | |
| 0 | 529.180018 | 424.8357977 | 394.2272055 | 387.1788436 | 385.3940638 | 384.7759386 | |
| 0 | 545.5118067 | 431.9606865 | 398.0137997 | 388.1815564 | 385.6471016 | 384.7693405 | |
| 0 | 552.306743 | 439.2154901 | 403.162452 | 392.9375537 | 390.2787658 | 389.3579443 | |
| 0 | 563.091663 | 439.9409158 | 403.3593443 | 392.9918391 | 390.2926649 | 389.3578564 | |
| 0 | 567.2610214 | 446.7779679 | 414.3156776 | 405.2906532 | 402.9222904 | 402.1020522 | |
| 0 | 571.7762774 | 447.1441472 | 414.575042 | 405.3696824 | 402.9426018 | 402.1020278 | |
| 0 | 580.6041537 | 462.1088095 | 422.6662425 | 412.0918142 | 409.2630404 | 408.2833474 | |
| 0 | 0 | 462.8298815 | 422.9145285 | 412.1550018 | 409.2740201 | 408.276246 | |
| 0 | 0 | 471.7757652 | 426.364827 | 412.8210627 | 409.4134602 | 408.2333007 | |
| 0 | 0 | 473.9159591 | 426.7231921 | 412.8715026 | 409.4284313 | 408.2359879 | |
| 0 | 0 | 477.1244522 | 442.3929818 | 432.5697609 | 429.9814024 | 429.0849727 | |
| 0 | 0 | 480.3773856 | 443.312518 | 432.8022571 | 430.0392329 | 429.0823111 | |
| 0 | 0 | 492.5535913 | 448.9178283 | 436.2794662 | 432.9748962 | 431.8304202 | |
| 0 | 0 | 492.9971836 | 449.2435254 | 436.3501572 | 432.9919571 | 431.8289073 | |
| 0 | 0 | 494.3354321 | 458.7247096 | 448.6264081 | 445.9165242 | 444.9780066 | |
| 0 | 0 | 496.9625077 | 459.2732477 | 448.8847824 | 446.0118999 | 445.0169307 | |
| 0 | 0 | 509.4160399 | 467.0309614 | 453.0719535 | 448.7528059 | 447.2569497 | |
| 0 | 0 | 510.0918749 | 468.8766 | 453.1179252 | 448.7644053 | 447.2566451 | |
| 0 | 0 | 513.3712641 | 469.1732197 | 454.2791577 | 451.2438032 | 450.1925649 | |
| 0 | 0 | 522.9030915 | 469.5809201 | 457.591564 | 454.5850802 | 453.5438407 | |
| 0 | 0 | 524.3641222 | 469.7300124 | 457.6724617 | 454.6066252 | 453.54483 | |
| 0 | 0 | 524.8378654 | 474.2395954 | 460.5109122 | 457.0630602 | 455.8689611 | |
| 0 | 0 | 526.2488967 | 474.4009803 | 460.5600241 | 457.0763687 | 455.8698697 | |
| 0 | 0 | 548.2623003 | 497.1740478 | 481.606803 | 477.5419509 | 476.1341653 | |
| 0 | 0 | 549.9971027 | 497.3392851 | 481.674505 | 477.5603841 | 476.1355352 | |
| 0 | 0 | 551.0299644 | 503.6287099 | 490.7357233 | 487.3361222 | 486.1587339 | |
| 0 | 0 | 551.6360697 | 503.994029 | 490.8365969 | 487.3621003 | 486.1587734 | |
| 0 | 0 | 570.72446 | 514.8581104 | 495.1365611 | 489.9371954 | 488.1364922 | |
| 0 | 0 | 571.8078441 | 515.0410161 | 495.1640281 | 489.944603 | 488.1369526 | |
| 0 | 0 | 576.12305 | 524.5278339 | 510.6510208 | 506.6983609 | 505.3294309 | |
| 0 | 0 | 576.9686173 | 524.7791924 | 510.7050693 | 506.7163271 | 505.3349008 | |
| 0 | 0 | 578.1060951 | 525.9900857 | 512.2029429 | 508.4191749 | 507.1087375 | |
| 0 | 0 | 580.5285812 | 526.684532 | 512.4671738 | 508.438842 | 507.0437045 | |
| 0 | 0 | 582.7108591 | 529.6452975 | 512.6537666 | 508.700155 | 507.3308955 | |
| 0 | 0 | 0 | 529.8098324 | 512.6987801 | 508.8004848 | 507.4503831 | |
| 0 | 0 | 0 | 534.9181742 | 522.2713601 | 519.0965326 | 517.9969904 | |
| 0 | 0 | 0 | 541.9298318 | 524.1425703 | 519.5664544 | 517.9816022 | |
| 0 | 0 | 0 | 547.6391429 | 528.9088798 | 523.9715695 | 522.2616243 | |
| 0 | 0 | 0 | 548.0515944 | 528.9792556 | 523.9863786 | 522.2571889 | |
| 0 | 0 | 0 | 562.365738 | 538.9816606 | 532.8034383 | 530.6637264 | |
| 0 | 0 | 0 | 562.6204366 | 539.0527109 | 532.8220929 | 530.6642347 | |
| 0 | 0 | 0 | 567.4879035 | 551.201846 | 546.9121208 | 545.4264546 | |
| 0 | 0 | 0 | 567.8341894 | 551.3326663 | 546.9472172 | 545.4283989 | |
| 0 | 0 | 0 | 581.879463 | 563.4125009 | 558.3704142 | 556.6241816 | |
| 0 | 0 | 0 | 582.0096093 | 563.453199 | 558.382083 | 556.6257967 | |
| 0 | 0 | 0 | 0 | 569.324418 | 564.3560378 | 562.6353321 | |
| 0 | 0 | 0 | 0 | 569.4023178 | 564.3762636 | 562.6355837 | |
| 0 | 0 | 0 | 0 | 578.1931446 | 572.2523315 | 570.1948419 | |
| 0 | 0 | 0 | 0 | 578.2488539 | 572.2634148 | 570.1904698 | |
| 0 | 0 | 0 | 0 | 578.3484645 | 573.8016961 | 572.2270078 | |
| 0 | 0 | 0 | 0 | 578.7345606 | 573.8962634 | 572.2206095 | |
| 0 | 0 | 0 | 0 | 584.6652872 | 577.3654717 | 574.837317 | |
| 0 | 0 | 0 | 0 | 584.7486612 | 577.37908 | 574.8267632 |
| Hyperbolic Disc of Radius 2 | |||||||
|---|---|---|---|---|---|---|---|
| Refinement | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | Prediction | |
| 1.830040495 | 1.773376586 | 1.768345572 | 1.767640092 | 1.767365929 | 1.767282572 | 1.767246156 | |
| 4.311288071 | 3.860118418 | 3.756242746 | 3.731875479 | 3.725125614 | 3.723331846 | 3.722682625 | |
| 4.566986835 | 3.935063271 | 3.778405344 | 3.737608856 | 3.726556089 | 3.723688744 | 3.722684317 | |
| 7.763774475 | 6.425167455 | 6.05131993 | 5.945336279 | 5.915305251 | 5.907349559 | 5.904482422 | |
| 8.265150526 | 6.631158786 | 6.101419611 | 5.957250731 | 5.91820321 | 5.908067691 | 5.904514538 | |
| 11.50209121 | 8.90564381 | 8.19503111 | 8.006407169 | 7.954179156 | 7.940371649 | 7.935409527 | |
| 11.64507105 | 9.715188295 | 8.737186449 | 8.431765729 | 8.345396938 | 8.32265343 | 8.314518686 | |
| 13.73527483 | 9.88022443 | 8.76378822 | 8.438310175 | 8.347056623 | 8.32307111 | 8.314523531 | |
| 17.18263289 | 13.34983162 | 11.75731206 | 11.18382867 | 11.01172572 | 10.96557759 | 10.94864827 | |
| 20.11198056 | 13.69216028 | 11.85621998 | 11.20922419 | 11.01815994 | 10.96719132 | 10.94866955 | |
| 21.45134093 | 14.84724275 | 13.01853658 | 12.53260572 | 12.40088326 | 12.36600112 | 12.35338141 | |
| 22.77889486 | 15.48333951 | 13.2147779 | 12.58573314 | 12.41432645 | 12.36936708 | 12.35343649 | |
| 26.35726762 | 17.212424 | 15.22276455 | 14.23848918 | 13.9213703 | 13.8345694 | 13.80185638 | |
| 29.75947481 | 18.13762057 | 15.39607147 | 14.26261185 | 13.92572746 | 13.83555874 | 13.80260421 | |
| 32.53295615 | 21.21762334 | 18.468304 | 17.38716378 | 17.069552 | 16.92545001 | 16.80577155 | |
| 34.16965808 | 22.25606405 | 18.55669264 | 17.42046196 | 17.074541 | 16.92664836 | 16.81619833 | |
| 37.75893481 | 22.67646428 | 19.16935242 | 17.60032685 | 17.08977632 | 17.00861477 | 16.99317209 | |
| 41.27789509 | 24.27955225 | 19.37150448 | 17.62123837 | 17.0991789 | 17.01106422 | 16.99327391 | |
| 43.00203126 | 25.56064454 | 20.85300105 | 19.5346326 | 19.17005738 | 19.07251935 | 19.03689259 | |
| 51.81157893 | 28.44893309 | 23.46677018 | 21.25346052 | 20.45972421 | 20.23579079 | 20.1477846 | |
| 51.99432738 | 30.37652848 | 23.85776633 | 21.31836339 | 20.47200947 | 20.23852548 | 20.14957549 | |
| 58.09612735 | 31.47676185 | 24.44453102 | 22.56704665 | 22.02474173 | 21.87759832 | 21.8228076 | |
| 61.86580401 | 33.09994838 | 24.61645565 | 22.60308664 | 22.03364479 | 21.87983843 | 21.82292223 | |
| 65.19410348 | 36.40564766 | 28.15792013 | 25.26121509 | 24.0992604 | 23.76554296 | 23.63107989 | |
| 68.58834074 | 37.80248053 | 28.80277467 | 25.32438327 | 24.10926667 | 23.76777574 | 23.63429059 | |
| 75.28325136 | 38.42987513 | 28.95052732 | 26.76074503 | 26.14925009 | 25.98168355 | 25.91640752 | |
| 79.86517561 | 40.08193282 | 29.52036795 | 26.95610819 | 26.20314044 | 25.9954839 | 25.91843338 | |
| 82.02304113 | 41.07080997 | 31.0533837 | 28.09443994 | 27.21858804 | 26.97902834 | 26.88883574 | |
| 91.72095826 | 44.14678137 | 31.41768788 | 28.17921223 | 27.23984625 | 26.98444989 | 26.88908411 | |
| 96.70272942 | 46.93587646 | 33.35525855 | 29.61607438 | 27.98415195 | 27.51130499 | 27.31840621 | |
| 100.4543542 | 50.09266284 | 33.98808416 | 29.67929839 | 28.00067411 | 27.51565155 | 27.31856162 | |
| 102.2087908 | 50.80769049 | 37.54729523 | 33.9866687 | 32.12246006 | 31.47476648 | 31.11281089 | |
| 115.43112 | 51.38739767 | 37.93092925 | 34.01651717 | 32.1438564 | 31.47891364 | 31.12992325 | |
| 116.4643822 | 52.91668741 | 38.08012353 | 34.27239029 | 32.6896454 | 32.32002082 | 32.20740023 | |
| 122.7374918 | 55.3933393 | 38.92268384 | 34.41506355 | 32.70766167 | 32.32530032 | 32.21496392 | |
| 129.5207152 | 57.70459518 | 39.0951314 | 34.56907504 | 33.42299325 | 33.11701289 | 33.00524918 | |
| 131.6382715 | 59.95449678 | 39.57432317 | 34.73197758 | 33.46545224 | 33.12790127 | 33.00556923 | |
| 0 | 63.63177715 | 41.31310124 | 36.83213038 | 35.54902989 | 35.19842245 | 35.06659779 | |
| 0 | 64.24627959 | 43.06855871 | 39.35608518 | 36.52477914 | 35.65506105 | 35.26945022 | |
| 0 | 65.83837127 | 46.24271345 | 39.50670321 | 36.54145555 | 35.65816272 | 35.28341578 | |
| 0 | 70.47821884 | 46.30514913 | 40.35004044 | 38.44505613 | 37.90160337 | 37.68276405 | |
| 0 | 72.22148217 | 46.67943349 | 40.40719562 | 38.46474282 | 37.90721117 | 37.68468521 | |
| 0 | 73.9633081 | 48.56966907 | 42.71633534 | 40.96655874 | 40.04911351 | 39.0378507 | |
| 0 | 74.87214009 | 49.55256328 | 42.81718878 | 40.99246653 | 40.05643748 | 39.07055125 | |
| 0 | 76.70012715 | 50.708837 | 44.80894657 | 41.17871162 | 40.47964456 | 40.31181753 | |
| 0 | 78.07199896 | 53.14750866 | 44.96426647 | 41.21451831 | 40.48696586 | 40.312921 | |
| 0 | 83.41682354 | 54.64772431 | 46.89230369 | 44.48008367 | 43.72312111 | 43.37695603 | |
| 0 | 84.82812751 | 54.94922485 | 47.09414128 | 44.51764135 | 43.73316949 | 43.38976186 | |
| 0 | 87.85116842 | 55.19060302 | 47.18055435 | 45.10894361 | 44.60522146 | 43.96653928 | |
| 0 | 89.87956409 | 55.35587516 | 47.50319751 | 45.26939232 | 44.6442697 | 43.99811761 | |
| 0 | 93.67116537 | 59.69059492 | 50.56296147 | 46.11205493 | 44.66437779 | 44.40135149 | |
| 0 | 95.77990578 | 60.00590138 | 50.85940839 | 46.14447117 | 44.66954136 | 44.44338853 | |
| 0 | 96.05634627 | 60.84767608 | 51.28052893 | 48.77878709 | 48.07349504 | 47.79659509 | |
| 0 | 96.99631611 | 64.12255615 | 51.52279796 | 48.83744447 | 48.08842084 | 47.79867868 | |
| 0 | 98.8265566 | 64.62149225 | 54.3012464 | 50.82593652 | 49.49197821 | 48.66098678 | |
| 0 | 105.4362603 | 65.45665911 | 54.45884307 | 50.85473751 | 49.49982054 | 48.68361508 | |
| 0 | 107.0252362 | 67.11581186 | 56.73791991 | 51.32130608 | 49.79312033 | 49.19253016 | |
| 0 | 107.6140546 | 67.90454751 | 57.12935969 | 51.3493825 | 49.79848353 | 49.22973368 | |
| 0 | 112.6358195 | 70.59705048 | 57.90549871 | 55.06704967 | 54.26419358 | 49.84535643 | |
| 0 | 116.4771711 | 70.9133018 | 57.9780735 | 55.15176053 | 54.29158922 | 50.3808632 | |
| 0 | 119.3011569 | 71.85840697 | 60.09859158 | 56.78333037 | 54.5400193 | 53.91527113 | |
| 0 | 120.8116132 | 73.11744749 | 60.41636355 | 56.84948659 | 54.55037016 | 53.94753994 | |
| 0 | 122.758284 | 73.80572026 | 60.97595617 | 56.90162976 | 55.91405498 | 55.59809048 | |
| 0 | 125.5293329 | 75.2364732 | 62.04115255 | 56.95436816 | 55.9301816 | 55.67198275 | |
| 0 | 128.0331412 | 77.36453745 | 62.0920286 | 57.29334908 | 56.10145219 | 55.70218065 | |
| 0 | 131.7433523 | 81.58111294 | 63.31790614 | 57.4718674 | 56.11340755 | 55.70757811 | |
| 0 | 0 | 82.0279711 | 63.73817888 | 57.52071999 | 56.36695402 | 56.10406764 | |
| 0 | 0 | 82.89884518 | 68.96253349 | 62.56525841 | 59.81011719 | 57.72595349 | |
| 0 | 0 | 84.35059697 | 69.20078787 | 62.61596581 | 59.81696547 | 57.74755929 | |
| 0 | 0 | 84.97817403 | 69.93008835 | 64.41591796 | 62.65679575 | 57.96185092 | |
| 0 | 0 | 86.85093526 | 70.06846318 | 64.47266841 | 62.67167202 | 61.08903141 | |
| 0 | 0 | 87.33523737 | 70.33297757 | 65.19346326 | 63.99945834 | 61.81692621 | |
| 0 | 0 | 87.65704179 | 70.37260734 | 65.2501533 | 64.00914826 | 61.83270222 | |
| 0 | 0 | 90.70708145 | 70.45213019 | 65.49408931 | 64.16727619 | 63.61236512 | |
| 0 | 0 | 91.60384867 | 70.99586922 | 65.56514807 | 64.18502331 | 63.63812407 | |
| 0 | 0 | 93.2387125 | 73.47668189 | 68.62893564 | 65.29591061 | 63.68247238 | |
| 0 | 0 | 95.21485815 | 74.74949292 | 68.68263816 | 65.31018187 | 63.71478531 | |
| 0 | 0 | 97.17218647 | 77.12641942 | 69.44947247 | 68.28481242 | 64.38902613 | |
| 0 | 0 | 98.11754205 | 77.81081333 | 69.83130506 | 68.3837132 | 65.44183313 | |
| 0 | 0 | 99.37460491 | 78.95618984 | 71.72071227 | 69.46513858 | 67.30181824 | |
| 0 | 0 | 100.5538723 | 79.09844915 | 71.73358757 | 69.47187977 | 67.36451343 | |
| 0 | 0 | 101.4291223 | 79.87565392 | 74.11656975 | 71.00848695 | 68.06290044 | |
| 0 | 0 | 103.168827 | 79.99706892 | 74.17364521 | 71.02147743 | 68.07652415 | |
| 0 | 0 | 107.1919259 | 81.53507693 | 74.97105782 | 72.35037851 | 68.44350989 | |
| 0 | 0 | 108.0485891 | 82.16036005 | 75.06806603 | 72.3686154 | 68.46949528 | |
| 0 | 0 | 108.3673252 | 84.56485223 | 75.88995877 | 74.28278477 | 70.60871778 | |
| 0 | 0 | 108.5958596 | 85.38979064 | 76.02766623 | 74.31507356 | 70.70977328 | |
| 0 | 0 | 111.5260999 | 87.98979261 | 79.29204247 | 76.50912762 | 73.91731918 | |
| 0 | 0 | 113.2497263 | 88.05964671 | 79.37356595 | 76.52897105 | 73.93165484 | |
| 0 | 0 | 113.5435478 | 88.27975005 | 81.65064138 | 76.94574857 | 75.14375496 | |
| 0 | 0 | 115.322743 | 88.30006044 | 81.72662416 | 76.96030605 | 75.19977331 | |
| 0 | 0 | 117.3104193 | 90.55457681 | 82.23826061 | 80.50869856 | 78.54556954 | |
| 0 | 0 | 119.0296527 | 90.71137191 | 82.39388751 | 80.56621529 | 79.4521296 | |
| 0 | 0 | 120.0629584 | 91.15116272 | 83.25221036 | 80.96003557 | 79.5190585 | |
| 0 | 0 | 124.3073188 | 91.88914681 | 83.29631938 | 80.9709555 | 80.02294377 | |
| 0 | 0 | 126.4941982 | 92.55436182 | 84.54698868 | 82.63756533 | 80.05150306 | |
| 0 | 0 | 126.8523164 | 94.2327901 | 86.79337591 | 83.09837378 | 80.05454698 | |
| 0 | 0 | 127.1381639 | 94.7684525 | 86.93112892 | 83.12174513 | 80.10819545 | |
| 0 | 0 | 129.2181962 | 97.04960081 | 87.23353498 | 83.81889559 | 81.98966395 | |
| 0 | 0 | 130.4761121 | 97.95658781 | 87.34336194 | 83.83347982 | 81.99746372 | |
| 0 | 0 | 132.3273835 | 98.404528 | 88.61628334 | 84.66480548 | 82.03967626 | |
| 0 | 0 | 134.3646145 | 101.0630473 | 88.73227676 | 84.70269661 | 82.09918779 | |
| 0 | 0 | 135.1505476 | 102.0584414 | 92.7245393 | 89.49262422 | 82.74664992 | |
| 0 | 0 | 0 | 102.8235524 | 92.77787353 | 89.50703624 | 83.51302452 | |
| 0 | 0 | 0 | 103.4902071 | 95.31916148 | 89.82468258 | 87.78084163 | |
| 0 | 0 | 0 | 105.8638958 | 95.40532521 | 89.84059959 | 87.92790316 | |
| 0 | 0 | 0 | 106.6930232 | 95.48082366 | 91.36947436 | 88.98902802 | |
| 0 | 0 | 0 | 107.3994698 | 95.55801208 | 91.38978399 | 89.125532 | |
| 0 | 0 | 0 | 107.8163674 | 95.94677105 | 92.97524545 | 91.94546374 | |
| 0 | 0 | 0 | 108.0328308 | 96.06969369 | 93.00276993 | 91.98289951 | |
| 0 | 0 | 0 | 108.2292184 | 98.08954192 | 95.30864639 | 92.0465307 | |
| 0 | 0 | 0 | 109.8655061 | 98.15535738 | 95.33975847 | 93.7769051 | |
| 0 | 0 | 0 | 110.8614701 | 99.41326915 | 96.1087675 | 94.25774136 | |
| 0 | 0 | 0 | 113.9171082 | 100.1755912 | 96.13280632 | 94.44762627 | |
| 0 | 0 | 0 | 113.9598465 | 102.5557271 | 97.08653516 | 94.4484714 | |
| 0 | 0 | 0 | 116.0958822 | 102.6249479 | 97.28458651 | 94.76788655 | |
| 0 | 0 | 0 | 118.2992632 | 103.4742627 | 98.94909512 | 96.48467463 | |
| 0 | 0 | 0 | 118.4384344 | 103.5771955 | 98.9675061 | 96.49659508 | |
| 0 | 0 | 0 | 118.6800309 | 104.2143123 | 99.17655748 | 96.89472321 | |
| 0 | 0 | 0 | 118.8623757 | 104.2870336 | 99.21015711 | 96.96099089 | |
| 0 | 0 | 0 | 121.4949018 | 108.6251698 | 102.9596834 | 98.35184626 | |
| 0 | 0 | 0 | 121.7423659 | 108.7636091 | 102.9864079 | 98.50429179 | |
| 0 | 0 | 0 | 122.3285304 | 109.8628073 | 105.6548328 | 103.3063545 | |
| 0 | 0 | 0 | 125.7789074 | 109.9463487 | 105.7025332 | 103.436968 | |
| 0 | 0 | 0 | 126.2306148 | 111.4251865 | 106.236504 | 103.5105377 | |
| 0 | 0 | 0 | 126.2725278 | 111.5470381 | 106.2632627 | 103.5351999 | |
| 0 | 0 | 0 | 126.4646499 | 112.7526945 | 107.2405747 | 103.9689952 | |
| 0 | 0 | 0 | 127.5390428 | 112.7675195 | 107.2534192 | 104.1484415 | |
| 0 | 0 | 0 | 129.5265384 | 113.2145426 | 108.3634709 | 106.2089351 | |
| 0 | 0 | 0 | 129.6009026 | 113.3234785 | 108.3727859 | 106.310155 | |
| 0 | 0 | 0 | 129.7116363 | 115.1660313 | 110.0521708 | 107.2794525 | |
| 0 | 0 | 0 | 133.6085747 | 115.405932 | 110.0680921 | 107.8533256 | |
| 0 | 0 | 0 | 134.0394223 | 117.7127459 | 111.9218948 | 108.7390444 | |
| 0 | 0 | 0 | 134.3905791 | 119.6555367 | 112.0266389 | 108.7520137 |