x Cubed functions
and the cube root
Mathematical tables are accepted without question. Many contain mistakes due to the low order of resolution, typically set at four decimal places. There seems to be no order and logic in the tables when there is great beauty in the tables when one cares to look. The test for any table is to choose any number from the table and reverse the operation. In the cube root tables, multiply the decimal number by itself, and then again, so D x D = d, then d x D = X, which should equal the original whole number. The difference is the introduced acceptable error. The accuracy of the following tables is 0.000 000 1.
One of the most striking properties about mathematical tables is the fact that sequences are replicated in each column. There are about a dozen such replications. Cubic tables generally give the cubes of the numbers from 1 to 10 only. In the listing below, the cubes start at 0.010 and in graduations of 0.001 increase to illustrate more clearly the replication of the entire table. In the first block of numbers from 0.010 to 1.000 the decimals start with a sequence to the integer that is replicated. Note the first horizontal row, the numbers 1,8,27,64,125,216,343,512,729,(next number is 010) appear. Then again in the second vertical column is the same sequence of numbers, 1,8,27,64,125,216,343,512,729, and 010. In the main sequence (from 1 to 10), the same sequence appear again in this second column, starting each block.
This strange nature of repetitions in the mathematical table gave Newton the basic concept to discover logarithms. Today, many do not know how to use logarithms, or the slide rule, for the hand held calculator and computer complete the calculations that much faster with better accuracy, though the costs exceed the gains. Many young adults cannot add, subtract, multiply or divide without a calculator or cash-register. If one purchases goods to the value of $22.67 cents, what change is expected from $50 ? If one cannot work that out mentally in five seconds, it is a sorry state of affairs. Reliance on calculators kills the beauty in the mathematics. Using logarithms, to determine the cube root of a number, simply divide the logarithm by three and look-up the antilog table to ascertain the value. Very few computers have an antilog instruction, making the LOG instruction useless.
Note : Although every care has been taken, typographical errors may exist in the following table.
0.00 to 10.00 in 0.01 steps
Grid reference system 0.95 = 0.9 then .x5 .... thus 0.95 x 0.95 x 0.95 = 0.857375
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 0.0 | 0. | 0.000001 | 0.000008 | 0.000027 | 0.000064 | 0.000125 | 0.000216 | 0.000343 | 0.000512 | 0.000729 |
| 0.1 | 0.001 | 0.001331 | 0.001728 | 0.002197 | 0.002744 | 0.003375 | 0.004096 | 0.004913 | 0.005832 | 0.006859 |
| 0.2 | 0.08 | 0.009261 | 0.010648 | 0.012167 | 0.013824 | 0.015625 | 0.017576 | 0.019683 | 0.021952 | 0.024389 |
| 0.3 | 0.027 | 0.029791 | 0.032768 | 0.035937 | 0.039304 | 0.042875 | 0.046656 | 0.050653 | 0.054872 | 0.059319 |
| 0.4 | 0.064 | 0.068921 | 0.074088 | 0.079507 | 0.085184 | 0.091125 | 0.097336 | 0.103823 | 0.110592 | 0.117649 |
| 0.5 | 0.125 | 0.132651 | 0.140608 | 0.148877 | 0.157464 | 0.166375 | 0.175616 | 0.185193 | 0.195112 | 0.205379 |
| 0.6 | 0.216 | 0.226981 | 0.238326 | 0.250047 | 0.262144 | 0.274625 | 0.287496 | 0.300763 | 0.314432 | 0.328509 |
| 0.7 | 0.314 | 0.357911 | 0.373246 | 0.389017 | 0.405224 | 0.421875 | 0.438976 | 0.456533 | 0.474552 | 0.493039 |
| 0.8 | 0.512 | 0.531441 | 0.551368 | 0.571787 | 0.592704 | 0.614125 | 0.636056 | 0.658503 | 0.681472 | 0.704969 |
| 0.9 | 0.729 | 0.753571 | 0.778688 | 0.804357 | 0.830584 | 0.857375 | 0.888736 | 0.912673 | 0.941192 | 0.970299 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 1.0 | 1. | 1.030301 | 1.061208 | 1.092727 | 1.124864 | 1.157625 | 1.191016 | 1.225043 | 1.259712 | 1.295029 |
| 1.1 | 1.331 | 1.367631 | 1.404928 | 1.442897 | 1.481544 | 1.520875 | 1.560896 | 1.601613 | 1.643032 | 1.685159 |
| 1.2 | 1.728 | 1.771561 | 1.815848 | 1.860867 | 1.906624 | 1.953125 | 2.000376 | 2.048383 | 2.097152 | 2.146689 |
| 1.3 | 2.744 | 2.248091 | 2.299968 | 2.352637 | 2.406104 | 2.460375 | 2.515456 | 2.571353 | 2.628072 | 2.685619 |
| 1.4 | 2.744 | 2.803221 | 2.863288 | 2.924207 | 2.985984 | 3.048625 | 3.112136 | 3.176523 | 3.241792 | 3.307949 |
| 1.5 | 3.375 | 3.442951 | 3.511808 | 3.581577 | 3.652264 | 3.723875 | 3.796416 | 3.869893 | 3.944312 | 4.019679 |
| 1.6 | 4.096 | 4.173281 | 4.251528 | 4.330747 | 4.410944 | 4.492125 | 4.574296 | 4.657463 | 4.741632 | 4.826809 |
| 1.7 | 4.913 | 5.000211 | 5.088448 | 5.177717 | 5.268024 | 5.359375 | 5.451776 | 5.545233 | 5.639752 | 5.735339 |
| 1.8 | 5.832 | 5.929741 | 6.028568 | 6.128487 | 6.229504 | 6.331625 | 6.434856 | 6.539203 | 6.644672 | 6.751269 |
| 1.9 | 6.859 | 6.967871 | 7.077888 | 7.189057 | 7.301384 | 7.414875 | 7.529536 | 7.645373 | 7.762392 | 7.880599 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 2.0 | 8. | 8.120601 | 8.242408 | 8.365427 | 8.489664 | 8.615125 | 8.741816 | 8.869743 | 8.998912 | 9.129329 |
| 2.1 | 9.261 | 9.393931 | 9.528128 | 9.663597 | 9.800344 | 9.938375 | 10.077696 | 10.218313 | 10.360232 | 10.503459 |
| 2.2 | 10.648 | 10.793861 | 10.941048 | 11.089567 | 11.239424 | 11.390625 | 11.543176 | 11.697083 | 11.852352 | 12.008989 |
| 2.3 | 12.167 | 12.326391 | 12.487168 | 12.649337 | 12.812904 | 12.977875 | 13.144256 | 13.312053 | 13.481272 | 13.651919 |
| 2.4 | 13.824 | 13.997521 | 14.172488 | 14.348907 | 14.526784 | 14.706125 | 14.886936 | 15.069223 | 15.252992 | 15.438249 |
| 2.5 | 15.625 | 15.813251 | 16.003008 | 16.194277 | 16.387064 | 16.581375 | 16.777216 | 16.974593 | 17.173512 | 17.373979 |
| 2.6 | 17.576 | 17.779581 | 17.984728 | 18.191447 | 18.399744 | 18.609625 | 18.821096 | 19.034163 | 19.248832 | 19.465109 |
| 2.7 | 19.683 | 19.902511 | 20.123648 | 20.346417 | 20.570824 | 20.796875 | 21.024576 | 21.253933 | 21.484952 | 21.717639 |
| 2.8 | 21.952 | 22.188041 | 22.425768 | 22.665187 | 22.906304 | 23.149125 | 23.393656 | 23.639903 | 23.887872 | 24.137569 |
| 2.9 | 24.389 | 24.642171 | 24.897088 | 25.153757 | 25.412184 | 25.672375 | 25.934336 | 26.198073 | 26.463592 | 26.730899 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 3.0 | 27. | 27.270901 | 27.543608 | 27.818127 | 28.094464 | 28.372625 | 28.652616 | 28.934443 | 29.218112 | 29.503629 |
| 3.1 | 29.791 | 30.080231 | 30.371328 | 30.664297 | 30.959144 | 31.255875 | 31.554496 | 31.855013 | 32.157432 | 32.461759 |
| 3.2 | 32.768 | 33.076161 | 33.386248 | 33.698267 | 34.012224 | 34.328125 | 34.645976 | 34.965783 | 35.287552 | 35.611289 |
| 3.3 | 35.937 | 36.264691 | 36.594368 | 36.926037 | 37.259704 | 37.595375 | 37.933056 | 38.272753 | 38.614472 | 38.958219 |
| 3.4 | 39.304 | 39.651821 | 40.001688 | 40.353607 | 40.707584 | 41.063625 | 41.421736 | 41.781923 | 42.144192 | 42.508549 |
| 3.5 | 42.875 | 43.243551 | 43.614208 | 43.986977 | 44.361864 | 44.738875 | 45.118016 | 45.499293 | 45.882712 | 46.268279 |
| 3.6 | 46.656 | 47.045881 | 47.437928 | 47.832147 | 48.228544 | 48.627125 | 49.027896 | 49.430863 | 49.836032 | 50.243409 |
| 3.7 | 50.653 | 51.064811 | 51.478848 | 51.895117 | 52.313624 | 52.734375 | 53.157376 | 53.582633 | 54.010152 | 54.439939 |
| 3.8 | 54.872 | 55.306341 | 55.742968 | 56.181887 | 56.623104 | 57.066625 | 57.512456 | 57.960603 | 58.411072 | 58.863869 |
| 3.9 | 59.319 | 59.776471 | 60.236288 | 60.698457 | 61.162984 | 61.629875 | 62.099136 | 62.570773 | 63.044792 | 63.521199 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 4.0 | 64. | 64.481201 | 64.964808 | 65.450827 | 65.939264 | 66.430125 | 66.923416 | 67.419143 | 67.917312 | 68.417929 |
| 4.1 | 68.921 | 69.426531 | 69.934528 | 70.444997 | 70.957944 | 71.473375 | 71.991296 | 72.511713 | 73.034632 | 73.560059 |
| 4.2 | 74.088 | 74.618461 | 75.151448 | 75.686967 | 76.225024 | 76.765625 | 77.308776 | 77.854483 | 78.402752 | 78.953589 |
| 4.3 | 79.507 | 80.062991 | 80.621568 | 81.182737 | 81.746504 | 82.312875 | 82.881856 | 83.453453 | 84.027672 | 84.606519 |
| 4.4 | 85.184 | 85.766121 | 86.350888 | 86.938307 | 87.528384 | 88.121125 | 88.716536 | 89.314623 | 89.915392 | 90.518849 |
| 4.5 | 91.125 | 91.733851 | 92.345408 | 92.959677 | 93.576664 | 94.196375 | 94.818816 | 95.443993 | 96.071912 | 96.702579 |
| 4.6 | 97.336 | 97.972181 | 98.611128 | 99.252847 | 99.897344 | 100.544625 | 101.194696 | 101.847463 | 102.503232 | 103.161709 |
| 4.7 | 103.823 | 104.487111 | 105.154048 | 105.823817 | 106.496424 | 107.171875 | 107.850176 | 108.531333 | 109.215352 | 109.902239 |
| 4.8 | 110.592 | 111.284641 | 111.980168 | 112.678587 | 113.379904 | 114.084125 | 114.791256 | 115.501303 | 116.214272 | 116.930169 |
| 4.9 | 117.649 | 118.370771 | 119.095488 | 119.823157 | 120.553784 | 121.287375 | 122.023936 | 122.763473 | 123.505992 | 124.251499 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 5.0 | 125 | 125.751501 | 126.506008 | 127.263527 | 128.024064 | 128.787625 | 129.554216 | 130.323843 | 131.096512 | 131.872229 |
| 5.1 | 132.651 | 133.432831 | 134.217728 | 136.005697 | 135.796744 | 136.590875 | 137.388096 | 138.188413 | 138.991832 | 139.789359 |
| 5.2 | 140.608 | 141.420761 | 142.236648 | 143.055667 | 143.877824 | 144.703125 | 145.531576 | 146.363183 | 147.197952 | 148.035889 |
| 5.3 | 148.877 | 149.721291 | 150.568768 | 151.419437 | 152.273304 | 153.130375 | 153.990656 | 154.854153 | 155.720872 | 156.590819 |
| 5.4 | 157.464 | 158.340421 | 159.220088 | 160.103007 | 160.989184 | 161.878625 | 162.771336 | 163.667323 | 164.566592 | 165.469149 |
| 5.5 | 166.375 | 167.284151 | 168.196608 | 169.112377 | 170.031464 | 170.953875 | 171.879616 | 172.808693 | 173.741112 | 174.676879 |
| 5.6 | 175.616 | 176.558481 | 177.504328 | 178.453547 | 179.406144 | 180.362125 | 181.321496 | 182.284263 | 183.250432 | 184.220009 |
| 5.7 | 185.193 | 186.169411 | 187.149248 | 188.132517 | 189.119224 | 190.109375 | 191.102976 | 192.100033 | 193.100552 | 194.104539 |
| 5.8 | 195.112 | 196.122941 | 197.137368 | 198.155287 | 199.176704 | 200.201625 | 201.230056 | 202.262003 | 203.297472 | 204.336469 |
| 5.9 | 205.979 | 206.425071 | 207.474688 | 208.527857 | 209.584584 | 210.644875 | 211.708736 | 212.776173 | 213.847192 | 214.921799 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 6.0 | 216. | 217.081801 | 218.167208 | 219.256227 | 220.348864 | 221.445125 | 222.545016 | 223.648543 | 224.755712 | 225.866529 |
| 6.1 | 226.981 | 228.099131 | 229.220928 | 230.346397 | 231.475544 | 232.608375 | 233.744896 | 234.885113 | 236.029032 | 237.176659 |
| 6.2 | 238.328 | 239.483061 | 240.641848 | 241.804367 | 242.970624 | 244.140625 | 245.314376 | 246.491883 | 247.673152 | 248.858189 |
| 6.3 | 250.047 | 251.239591 | 252.435968 | 253.636137 | 254.840104 | 256.047875 | 257.259456 | 258.474853 | 259.694072 | 260.917119 |
| 6.4 | 262.144 | 263.374721 | 264.609288 | 265.847707 | 267.089984 | 268.336125 | 269.586136 | 270.840023 | 272.097792 | 273.359449 |
| 6.5 | 274.625 | 275.894451 | 277.167808 | 277.445077 | 279.726264 | 281.011375 | 282.300416 | 283.593393 | 284.890312 | 286.191179 |
| 6.6 | 287.496 | 288.804781 | 290.117528 | 291.434247 | 292.754944 | 294.079625 | 295.408296 | 296.740963 | 298.077632 | 299.418309 |
| 6.7 | 300.763 | 302.111711 | 303.464448 | 304.821217 | 306.182024 | 307.546875 | 308.915776 | 310.288733 | 311.665752 | 313.946838 |
| 6.8 | 314.432 | 315.821241 | 317.214568 | 318.611987 | 320.013504 | 321.419125 | 322.828856 | 324.242703 | 325.660672 | 327.082769 |
| 6.9 | 328.509 | 329.939371 | 331.373888 | 332.812557 | 334.255384 | 335.702375 | 337.153536 | 338.608873 | 340.068392 | 341.532099 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 7.0 | 343. | 344.472101 | 345.948408 | 347.428927 | 348.913664 | 350.402625 | 351.895816 | 353.393243 | 354.894912 | 356.400829 |
| 7.1 | 357.911 | 359.425431 | 360.944128 | 362.467097 | 363.994344 | 365.525875 | 367.061696 | 368.601813 | 370.146232 | 371.694959 |
| 7.2 | 373.248 | 374.805361 | 376.367048 | 377.933067 | 379.503424 | 381.078125 | 382.657176 | 384.240583 | 385.828352 | 387.420489 |
| 7.3 | 389.017 | 390.617891 | 392.223168 | 393.832837 | 395.446904 | 397.065375 | 398.688256 | 400.315553 | 401.947272 | 403.583419 |
| 7.4 | 405.224 | 406.869021 | 408.518488 | 410.172407 | 411.830784 | 413.493625 | 415.160936 | 416.832723 | 418.508992 | 420.189749 |
| 7.5 | 421.875 | 423.564751 | 425.259008 | 426.957777 | 428.661064 | 430.368875 | 432.081216 | 433.798093 | 435.519512 | 437.245479 |
| 7.6 | 438.976 | 440.711081 | 442.450728 | 444.194947 | 445.943744 | 447.697125 | 449.455096 | 451.217663 | 452.984832 | 454.756609 |
| 7.7 | 456.533 | 458.314011 | 460.099648 | 461.889917 | 463.684824 | 465.484375 | 467.288576 | 469.097433 | 470.910952 | 472.729139 |
| 7.8 | 474.552 | 476.379541 | 478.211768 | 480.048687 | 481.890304 | 483.736625 | 485.587656 | 487.443403 | 489.303872 | 491.169069 |
| 7.9 | 493.039 | 494.913671 | 496.793088 | 498.677257 | 500.566184 | 502.459875 | 504.358336 | 506.261573 | 508.169592 | 510.082399 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 8.0 | 512. | 513.922401 | 515.849608 | 517.781627 | 519.718464 | 521.660125 | 523.606616 | 525.557943 | 527.514112 | 529.475129 |
| 8.1 | 531.441 | 533.411731 | 535.387328 | 537.367797 | 539.353144 | 541.343375 | 543.338513 | 547.343432 | 549.343432 | 549.353259 |
| 8.2 | 551.368 | 553.387661 | 555.412248 | 557.441767 | 559.476224 | 561.515625 | 563.559976 | 565.609283 | 567.663552 | 569.722789 |
| 8.3 | 571.787 | 573.856191 | 575.930368 | 578.009537 | 580.093704 | 582.182875 | 584.277056 | 586.376253 | 588.480472 | 590.589719 |
| 8.4 | 592.704 | 594.823321 | 596.947688 | 599.077107 | 601.211584 | 603.351125 | 605.495736 | 607.645423 | 609.800192 | 611.960049 |
| 8.5 | 614.125 | 616.295051 | 618.470208 | 620.650477 | 622.835864 | 625.026375 | 627.222016 | 629.422793 | 631.638712 | 633.839779 |
| 8.6 | 636.056 | 638.277381 | 640.503928 | 642.735647 | 644.972544 | 647.214625 | 649.461896 | 651.714363 | 653.972032 | 656.234909 |
| 8.7 | 658.503 | 660.776311 | 663.054848 | 665.338617 | 667.627624 | 669.921875 | 672.221376 | 674.526133 | 676.836152 | 679.151439 |
| 8.8 | 681.472 | 683.797841 | 686.128968 | 688.465387 | 690.807104 | 693.154125 | 695.506456 | 697.864103 | 700.227072 | 702.595369 |
| 8.9 | 704.969 | 707.347971 | 709.732288 | 712.121957 | 714.516984 | 716.917375 | 719.323136 | 721.734273 | 724.150792 | 726.572699 |
| # | .x0 | .x1 | .x2 | .x3 | .x4 | .x5 | .x6 | .x7 | .x8 | .x9 |
| 9.0 | 729. | 731.432701 | 733.870808 | 736.314327 | 738.763264 | 741.217625 | 743.677416 | 746.142643 | 748.613312 | 751.089429 |
| 9.1 | 753.571 | 756.058031 | 758.550528 | 761.048497 | 763.551944 | 766.060875 | 768.575296 | 771.095213 | 773.620632 | 776.151559 |
| 9.2 | 778.688 | 781.229961 | 783.777448 | 768.330467 | 788.889024 | 791.453125 | 794.022776 | 796.597983 | 799.178752 | 801.765089 |
| 9.3 | 804.357 | 806.954491 | 809.557568 | 812.166237 | 814.780504 | 817.400375 | 820.025856 | 822.656953 | 825.293672 | 827.936019 |
| 9.4 | 830.584 | 833.237621 | 835.896888 | 838.561807 | 841.232384 | 843.908625 | 846.590536 | 849.278123 | 851.971392 | 854.670349 |
| 9.5 | 857.375 | 860.085351 | 862.801408 | 865.523177 | 868.250664 | 870.983875 | 873.722816 | 876.467493 | 879.217912 | 881.974079 |
| 9.6 | 884.796 | 887.503681 | 890.277128 | 893.056347 | 895.841344 | 898.632125 | 901.428696 | 904.231063 | 907.039232 | 909.853209 |
| 9.7 | 912.673 | 915.498611 | 918.330048 | 921.167317 | 924.010424 | 926.859375 | 929.714176 | 932.574833 | 935.441352 | 938.313739 |
| 9.8 | 941.192 | 944.076141 | 946.966168 | 949.862087 | 952.763904 | 955.671625 | 958.585256 | 961.504803 | 964.430272 | 967.361669 |
| 9.9 | 970.299 | 973.242271 | 976.191488 | 979.146657 | 982.107784 | 985.074875 | 988.047936 | 991.026973 | 994.011992 | 997.002999 |
| 10.0 | 1000. |
NOTE: The following program runs in most BASIC languages. (Note: Microsoft's QBasic has such a low order of mathematical accuracy, (even in high precision mode) that it is scientifically very poor, especially when loops are concerned. Other system bugs cause major formatting problems. Fixing these bugs only becomes important if the counter on line 15 is pushed from 8 to the value 10. )The program uses a fast method of determining the square root of numbers between 1 and 999. It requires a printer, unless all the LPRINT instructions are changed to PRINT instructions. Some basics use %, while others attach the # symbol to the variable name in order to return the 16 bit floating point precision needed for the number (ie. 29.00000000889598 not 29 or 29.000001).
Cube Roots| 50 | 3.684031499 | 100 | 4.641588834 | 150 | 5.313292846 | 200 | 5.848035477 | ||
| 1 | 1 | 51 | 3.70842977 | 101 | 4.657009508 | 151 | 5.325074022 | 201 | 5.857766003 |
| 2 | 1.259921051 | 52 | 3.732511157 | 102 | 4.672328729 | 152 | 5.336803298 | 202 | 5.867464309 |
| 3 | 1.442249571 | 53 | 3.756285755 | 103 | 4.687548148 | 153 | 5.348481242 | 203 | 5.877130660 |
| 4 | 1.587401052 | 54 | 3.77976315 | 104 | 4.702669376 | 154 | 5.360108412 | 204 | 5.886765317 |
| 5 | 1.709975947 | 55 | 3.802952461 | 105 | 4.71769399 | 155 | 5.371685355 | 205 | 5.89636854 |
| 6 | 1.817120593 | 56 | 3.825862366 | 106 | 4.732623492 | 156 | 5.383212613 | 206 | 5.905940584 |
| 7 | 1.912931183 | 57 | 3.848501132 | 107 | 4.747459399 | 157 | 5.394690713 | 207 | 5.9154817 |
| 8 | 2. | 58 | 3.870876641 | 108 | 4.762203156 | 158 | 5.406120176 | 208 | 5.924992137 |
| 9 | 2.080083824 | 59 | 3.892996416 | 109 | 4.776856182 | 159 | 5.417501515 | 209 | 5.934472141 |
| 10 | 2.154434691 | 60 | 3.914867642 | 110 | 4.791419858 | 160 | 5.428835234 | 210 | 5.943921953 |
| 11 | 2.223980092 | 61 | 3.936497184 | 111 | 4.805895534 | 161 | 5.440121826 | 211 | 5.953341814 |
| 12 | 2.289428586 | 62 | 3.95789161 | 112 | 4.820284529 | 162 | 5.451361779 | 212 | 5.962731958 |
| 13 | 2.351334688 | 63 | 3.979057208 | 113 | 4.834588128 | 163 | 5.462555572 | 213 | 5.97209262 |
| 14 | 2.410142265 | 64 | 4. | 114 | 4.848807586 | 164 | 5.473703675 | 214 | 5.98142403 |
| 15 | 2.466212075 | 65 | 4.020725759 | 115 | 4.862944132 | 165 | 5.484806553 | 215 | 5.990726415 |
| 16 | 2.5198421 | 66 | 4.041240021 | 116 | 4.876998962 | 166 | 5.495864661 | 216 | 6. |
| 17 | 2.571281591 | 67 | 4.061548101 | 117 | 4.890973247 | 167 | 5.506878447 | 217 | 6.009245007 |
| 18 | 2.620741395 | 68 | 4.081655102 | 118 | 4.904868132 | 168 | 5.517848353 | 218 | 6.018461655 |
| 19 | 2.668401649 | 69 | 4.10156593 | 119 | 4.918684735 | 169 | 5.528774814 | 219 | 6.027650161 |
| 20 | 2.714417617 | 70 | 4.1212853 | 120 | 4.932424149 | 170 | 5.539658257 | 220 | 6.036810737 |
| 21 | 2.758924177 | 71 | 4.14081775 | 121 | 4.946087444 | 171 | 5.550499103 | 221 | 6.045943597 |
| 22 | 2.802039331 | 72 | 4.160167647 | 122 | 4.959675664 | 172 | 5.561297767 | 222 | 6.055048947 |
| 23 | 2.84386798 | 73 | 4.179339197 | 123 | 4.973189834 | 173 | 5.572054656 | 223 | 6.064126995 |
| 24 | 2.884499141 | 74 | 4.198336454 | 124 | 4.986630953 | 174 | 5.582770172 | 224 | 6.073177944 |
| 25 | 2.924017739 | 75 | 4.217163327 | 125 | 5. | 175 | 5.593444711 | 225 | 6.082201996 |
| 26 | 2.962496069 | 76 | 4.235823585 | 126 | 5.013297935 | 176 | 5.604078662 | 226 | 6.091199349 |
| 27 | 3. | 77 | 4.254320866 | 127 | 5.026525696 | 177 | 5.614672409 | 227 | 6.100170201 |
| 28 | 3.036588972 | 78 | 4.272658682 | 128 | 5.0396842 | 178 | 5.625226329 | 228 | 6.109114745 |
| 29 | 3.072316826 | 79 | 4.290840428 | 129 | 5.052774348 | 179 | 5.635740795 | 229 | 6.118033173 |
| 30 | 3.107232506 | 80 | 4.308869381 | 130 | 5.06579702 | 180 | 5.646216174 | 230 | 6.126925676 |
| 31 | 3.141380656 | 81 | 4.326748711 | 131 | 5.078753079 | 181 | 5.656652826 | 231 | 6.13579244 |
| 32 | 3.174802104 | 82 | 4.344481486 | 132 | 5.09164337 | 182 | 5.667051109 | 232 | 6.144633652 |
| 33 | 3.20753433 | 83 | 4.362070672 | 133 | 5.104468723 | 183 | 5.677411371 | 233 | 6.153449494 |
| 34 | 3.239611802 | 84 | 4.37951914 | 134 | 5.117229947 | 184 | 5.68773396 | 234 | 6.162240148 |
| 35 | 3.27106631 | 85 | 4.396829672 | 135 | 5.129927841 | 185 | 5.698019216 | 235 | 6.171005793 |
| 36 | 3.301927249 | 86 | 4.414004963 | 136 | 5.142563182 | 186 | 5.708267474 | 236 | 6.179746606 |
| 37 | 3.332221852 | 87 | 4.431047622 | 137 | 5.155136736 | 187 | 5.718479065 | 237 | 6.188462763 |
| 38 | 3.361975407 | 88 | 4.447960182 | 138 | 5.167649253 | 188 | 5.728654316 | 238 | 6.197154434 |
| 39 | 3.391211444 | 89 | 4.464745096 | 139 | 5.180101468 | 189 | 5.738793549 | 239 | 6.205821795 |
| 40 | 3.419951894 | 90 | 4.481404747 | 140 | 5.192494102 | 190 | 5.748897079 | 240 | 6.214465012 |
| 41 | 3.448217241 | 91 | 4.497941446 | 141 | 5.204827864 | 191 | 5.758965221 | 241 | 6.223084254 |
| 42 | 3.476026645 | 92 | 4.514357436 | 142 | 5.217103447 | 192 | 5.768998281 | 242 | 6.231679685 |
| 43 | 3.503398061 | 93 | 4.530654897 | 143 | 5.229321532 | 193 | 5.778996566 | 243 | 6.24025147 |
| 44 | 3.530348336 | 94 | 4.546835944 | 144 | 5.241482789 | 194 | 5.788960373 | 244 | 6.24879977 |
| 45 | 3.556893305 | 95 | 4.562902636 | 145 | 5.253587873 | 195 | 5.798889998 | 245 | 6.257324746 |
| 46 | 3.583047872 | 96 | 4.578856971 | 146 | 5.265637429 | 196 | 5.808785734 | 246 | 6.265826557 |
| 47 | 3.608826082 | 97 | 4.594700893 | 147 | 5.277632088 | 197 | 5.818647868 | 247 | 6.274305358 |
| 48 | 3.634241186 | 98 | 4.610436293 | 148 | 5.289572473 | 198 | 5.828476684 | 248 | 6.282761305 |
| 49 | 3.659305711 | 99 | 4.62606501 | 149 | 5.301459193 | 199 | 5.838272461 | 249 | 6.291194552 |
250 to 499
| 250 | 6.29960525 | 300 | 6.694329501 | 350 | 7.047298732 | 400 | 7.368062998 | 450 | 7.663094324 |
| 251 | 6.307993549 | 301 | 6.701759396 | 351 | 7.054004064 | 401 | 7.374197941 | 451 | 7.668766491 |
| 252 | 6.316359598 | 302 | 6.709172853 | 352 | 7.060696671 | 402 | 7.380322693 | 452 | 7.674430279 |
| 253 | 6.324703544 | 303 | 6.716569962 | 353 | 7.067376615 | 403 | 7.386437296 | 453 | 7.68008572 |
| 254 | 6.333025532 | 304 | 6.723950814 | 354 | 7.074043956 | 404 | 7.392541792 | 454 | 7.685732844 |
| 255 | 6.341325705 | 305 | 6.731315498 | 355 | 7.080698752 | 405 | 7.398636223 | 455 | 7.691371681 |
| 256 | 6.349604207 | 306 | 6.738664101 | 356 | 7.087341062 | 406 | 7.404720631 | 456 | 7.697002263 |
| 257 | 6.35786118 | 307 | 6.745996712 | 357 | 7.093970945 | 407 | 7.410795056 | 457 | 7.702624619 |
| 258 | 6.366096761 | 308 | 6.753313417 | 358 | 7.100588459 | 408 | 7.416859539 | 458 | 7.708238779 |
| 259 | 6.374311088 | 309 | 6.760614302 | 359 | 7.107193662 | 409 | 7.422914121 | 459 | 7.713844772 |
| 260 | 6.382504299 | 310 | 6.767899453 | 360 | 7.113786609 | 410 | 7.428958842 | 460 | 7.71944263 |
| 261 | 6.390676529 | 311 | 6.775168953 | 361 | 7.120367359 | 411 | 7.434993742 | 461 | 7.72503238 |
| 262 | 6.398827911 | 312 | 6.782422887 | 362 | 7.126935968 | 412 | 7.441018861 | 462 | 7.730614053 |
| 263 | 6.406958578 | 313 | 6.789661337 | 363 | 7.13349249 | 413 | 7.447034239 | 463 | 7.736187677 |
| 264 | 6.41506866 | 314 | 6.796884386 | 364 | 7.140036982 | 414 | 7.453039914 | 464 | 7.741753282 |
| 265 | 6.423158289 | 315 | 6.804092116 | 365 | 7.146569499 | 415 | 7.459035926 | 465 | 7.747310895 |
| 266 | 6.431227592 | 316 | 6.811284607 | 366 | 7.153090096 | 416 | 7.465022314 | 466 | 7.752860547 |
| 267 | 6.439276696 | 317 | 6.818461942 | 367 | 7.159598825 | 417 | 7.470999116 | 467 | 7.758402265 |
| 268 | 6.447305728 | 318 | 6.825624197 | 368 | 7.166095743 | 418 | 7.47696637 | 468 | 7.763936077 |
| 269 | 6.455314811 | 319 | 6.832771453 | 369 | 7.172580901 | 419 | 7.482924115 | 469 | 7.769462012 |
| 270 | 6.463304071 | 320 | 6.839903787 | 370 | 7.179054353 | 420 | 7.488872388 | 470 | 7.774980098 |
| 271 | 6.471273627 | 321 | 6.847021278 | 371 | 7.185516151 | 421 | 7.494811226 | 471 | 7.780490362 |
| 272 | 6.479223603 | 322 | 6.854124002 | 372 | 7.191966349 | 422 | 7.500740668 | 472 | 7.785992832 |
| 273 | 6.487154117 | 323 | 6.861212036 | 373 | 7.198404997 | 423 | 7.50666075 | 473 | 7.791487536 |
| 274 | 6.495065289 | 324 | 6.868285456 | 374 | 7.204832148 | 424 | 7.512571509 | 474 | 7.79697451 |
| 275 | 6.502957235 | 325 | 6.875344336 | 375 | 7.211247852 | 425 | 7.518472982 | 475 | 7.802453754 |
| 276 | 6.510830072 | 326 | 6.882388751 | 376 | 7.217652161 | 426 | 7.524365204 | 476 | 7.807925322 |
| 277 | 6.518683916 | 327 | 6.889418775 | 377 | 7.224045124 | 427 | 7.530248213 | 477 | 7.813389233 |
| 278 | 6.52651888 | 328 | 6.896434481 | 378 | 7.230426793 | 428 | 7.536122044 | 478 | 7.818845512 |
| 279 | 6.534335078 | 329 | 6.903435942 | 379 | 7.236797216 | 429 | 7.541986733 | 479 | 7.824294186 |
| 280 | 6.542132621 | 330 | 6.910423231 | 380 | 7.243156444 | 430 | 7.547842315 | 480 | 7.829735283 |
| 281 | 6.549911621 | 331 | 6.917396417 | 381 | 7.249504525 | 431 | 7.553688826 | 481 | 7.835168827 |
| 282 | 6.557672187 | 332 | 6.924355573 | 382 | 7.255841507 | 432 | 7.5595263 | 482 | 7.840594846 |
| 283 | 6.565414428 | 333 | 6.931300769 | 383 | 7.26216744 | 433 | 7.565354773 | 483 | 7.846013366 |
| 284 | 6.543138452 | 334 | 6.938232074 | 384 | 7.268482372 | 434 | 7.571174279 | 484 | 7.851424411 |
| 285 | 6.580844366 | 335 | 6.945149559 | 385 | 7.274786349 | 435 | 7.576984852 | 485 | 7.856828008 |
| 286 | 6.588532275 | 336 | 6.95205329 | 386 | 7.28107942 | 436 | 7.582786527 | 486 | 7.862224183 |
| 287 | 6.596202285 | 337 | 6.958943338 | 387 | 7.287361632 | 437 | 7.588579338 | 487 | 7.867612961 |
| 288 | 6.603854498 | 338 | 6.965819768 | 388 | 7.29363303 | 438 | 7.594363319 | 488 | 7.872994367 |
| 289 | 6.611489019 | 339 | 6.972682649 | 389 | 7.299893663 | 439 | 7.600138502 | 489 | 7.878368426 |
| 290 | 6.619105949 | 340 | 6.979532047 | 390 | 7.306143575 | 440 | 7.605904922 | 490 | 7.883735164 |
| 291 | 6.626705388 | 341 | 6.986368028 | 391 | 7.312382812 | 441 | 7.611662612 | 491 | 7.889094605 |
| 292 | 6.634287437 | 342 | 6.993190658 | 392 | 7.318611421 | 442 | 7.617411603 | 492 | 7.894446773 |
| 293 | 6.641852196 | 343 | 7. | 393 | 7.324829445 | 443 | 7.623151931 | 493 | 7.899791695 |
| 294 | 6.649399762 | 344 | 7.006796121 | 394 | 7.331036931 | 444 | 7.628883626 | 494 | 7.905129394 |
| 295 | 6.656930232 | 345 | 7.013579084 | 395 | 7.337233922 | 445 | 7.634606722 | 495 | 7.910459894 |
| 296 | 6.664443703 | 346 | 7.020348952 | 396 | 7.343420463 | 446 | 7.64032125 | 496 | 7.91578322 |
| 297 | 6.671940272 | 347 | 7.027105789 | 397 | 7.349596597 | 447 | 7.646027243 | 497 | 7.921099396 |
| 298 | 6.679420032 | 348 | 7.033849656 | 398 | 7.355762369 | 448 | 7.651724732 | 498 | 7.926408445 |
| 299 | 6.686883077 | 349 | 7.040580617 | 399 | 7.361917822 | 449 | 7.657413748 | 499 | 7.931710392 |
500 to 749
| 500 | 7.93700526 | 550 | 8.93212707 | 600 | 8.434326654 | 650 | 8.662391054 | 700 | 8.879040018 |
| 501 | 7.942293074 | 551 | 8.198175283 | 601 | 8.43900979 | 651 | 8.66683103 | 701 | 8.88326612 |
| 502 | 7.947573855 | 552 | 8.2031386 | 602 | 8.443687734 | 652 | 8.671266461 | 702 | 8.887488205 |
| 503 | 7.952847628 | 553 | 8.208082453 | 603 | 8.448360501 | 653 | 8.675697359 | 703 | 8.891706283 |
| 504 | 7.958114416 | 554 | 8.213027083 | 604 | 8.453028101 | 654 | 8.680123736 | 704 | 8.895920362 |
| 505 | 7.963374242 | 555 | 8.217965765 | 605 | 8.457690559 | 655 | 8.684545603 | 705 | 8.900130453 |
| 506 | 7.768627129 | 556 | 8.222898518 | 606 | 8.462347878 | 656 | 8.688962972 | 706 | 8.904336565 |
| 507 | 7.9738731 | 557 | 8.227825362 | 607 | 8.467000077 | 657 | 8.693375854 | 707 | 8.908538706 |
| 508 | 7.979112177 | 558 | 8.232746311 | 608 | 8.471647169 | 658 | 8.69778426 | 708 | 8.912736887 |
| 509 | 7.984344383 | 559 | 8.237661385 | 609 | 8.476289168 | 659 | 8.702188202 | 709 | 8.916931116 |
| 510 | 7.98956975 | 560 | 8.2425706 | 610 | 8.480926089 | 660 | 8.706587691 | 710 | 8.921121405 |
| 511 | 7.994788273 | 561 | 8.247473974 | 611 | 8.485557945 | 661 | 8.710982739 | 711 | 8.92530776 |
| 512 | 8. | 562 | 8.252371525 | 612 | 8.490184749 | 662 | 8.715373356 | 712 | 9.929490191 |
| 513 | 8.005204946 | 563 | 8.25726327 | 613 | 8.494806517 | 663 | 8.719759553 | 713 | 8.933668709 |
| 514 | 8.010403133 | 564 | 8.262149226 | 614 | 8.49942326 | 664 | 8.724141343 | 714 | 8.937843321 |
| 515 | 8.015594582 | 565 | 8.26702941 | 615 | 8.504034993 | 665 | 8.728518735 | 715 | 8.942014037 |
| 516 | 8.020779315 | 566 | 8.271903839 | 616 | 8.508641731 | 666 | 8.732891742 | 716 | 8.946180866 |
| 517 | 8.025957353 | 567 | 8.27677253 | 617 | 8.513243485 | 667 | 8.737260372 | 717 | 8.950343817 |
| 518 | 8.031128719 | 568 | 8.281635499 | 618 | 8.517840269 | 668 | 8.741624639 | 718 | 8.9545029 |
| 519 | 8.036293433 | 569 | 8.286492764 | 619 | 8.522432098 | 669 | 8.745984552 | 719 | 8.958658121 |
| 520 | 8.041451518 | 570 | 8.291344342 | 620 | 8.527018983 | 670 | 8.750340123 | 720 | 8.962809494 |
| 521 | 8.046602993 | 571 | 8.296190249 | 621 | 8.53160094 | 671 | 8.754691362 | 721 | 8.966957023 |
| 522 | 8.051747882 | 572 | 8.301030501 | 622 | 8.53617798 | 672 | 8.75903828 | 722 | 8.971100719 |
| 523 | 8.056806203 | 573 | 8.305865114 | 623 | 8.540750117 | 673 | 8.763380888 | 723 | 8.975240591 |
| 524 | 8.062017979 | 574 | 8.310694108 | 624 | 8.545317364 | 674 | 8.767719196 | 724 | 8.979376646 |
| 525 | 8.06714323 | 575 | 8.315517494 | 625 | 8.549879733 | 675 | 8.772053215 | 725 | 8.983508896 |
| 526 | 8.072261978 | 576 | 8.320335292 | 626 | 8.554437239 | 676 | 8.776382956 | 726 | 8.987637347 |
| 527 | 8.077374242 | 577 | 8.325145518 | 627 | 8.558989895 | 677 | 8.780708429 | 727 | 8.99176201 |
| 528 | 8.082480042 | 578 | 8.329954186 | 628 | 8.563537712 | 678 | 8.785029643 | 728 | 8.995882891 |
| 529 | 8.087579399 | 579 | 8.334755313 | 629 | 8.568080704 | 679 | 8.789346612 | 729 | 9. |
| 530 | 8.092672335 | 580 | 8.339550915 | 630 | 8.572618883 | 680 | 8.793659345 | 730 | 9.004113347 |
| 531 | 8.097758868 | 581 | 8.344341009 | 631 | 8.577152262 | 681 | 8.797967851 | 731 | 9.008222938 |
| 532 | 8.102839019 | 582 | 8.349125610 | 632 | 8.581680855 | 682 | 8.802272141 | 732 | 9.012328783 |
| 533 | 8.107912809 | 583 | 8.353904732 | 633 | 8.586204672 | 683 | 8.806572226 | 733 | 9.01643089 |
| 534 | 8.112980255 | 584 | 8.358678393 | 634 | 8.590723728 | 684 | 8.810868115 | 734 | 9.020529268 |
| 535 | 8.118041379 | 585 | 8.363446608 | 635 | 8.595238034 | 685 | 8.81515982 | 735 | 9.024623926 |
| 536 | 8.123096201 | 586 | 8.368209392 | 636 | 8.599747604 | 686 | 8.819447349 | 736 | 9.028714871 |
| 537 | 8.12814474 | 587 | 8.372966760 | 637 | 8.604252449 | 687 | 8.823730715 | 737 | 9.032802113 |
| 538 | 8.133187014 | 588 | 8.377718728 | 638 | 8.608752582 | 688 | 8.828009925 | 738 | 9.036885658 |
| 538 | 8.138223044 | 589 | 8.382465313 | 639 | 8.613248015 | 689 | 8.832285 | 739 | 9.040965516 |
| 540 | 8.14325285 | 590 | 8.387206527 | 640 | 8.617738761 | 690 | 8.836555923 | 740 | 9.045041697 |
| 541 | 8.14827645 | 591 | 8.391942387 | 641 | 8.622224831 | 691 | 8.84082273 | 741 | 9.049114206 |
| 542 | 8.153293863 | 592 | 8.396672908 | 642 | 8.626706237 | 692 | 8.845085422 | 742 | 9.053183053 |
| 543 | 8.158305108 | 593 | 8.401398104 | 643 | 8.631182992 | 693 | 8.849344009 | 743 | 9.057248245 |
| 544 | 8.163310204 | 594 | 8.406117992 | 644 | 8.635655109 | 694 | 8.853598503 | 744 | 9.061309792 |
| 545 | 8.168309171 | 595 | 8.410832586 | 645 | 8.640122598 | 695 | 8.857848911 | 745 | 9.065367702 |
| 546 | 8.173302026 | 596 | 8.415541899 | 646 | 8.644585471 | 696 | 8.862095244 | 746 | 9.069421981 |
| 547 | 8.178288789 | 597 | 8.420245948 | 647 | 8.649043743 | 697 | 8.866337511 | 747 | 9.073472639 |
| 548 | 8.183269477 | 598 | 8.424944747 | 648 | 8.653497422 | 698 | 8.870575723 | 748 | 9.077519684 |
| 549 | 8.18824411 | 599 | 8.429638311 | 649 | 8.657946522 | 699 | 8.874809888 | 749 | 9.081563123 |
750 to 1000
| 750 | 9.085602965 | 800 | 9.283177668 | 850 | 9.472682372 | 900 | 9.654893847 | 950 | 9.830475725 |
| 751 | 9.089639217 | 801 | 9.287044048 | 851 | 9.476395693 | 901 | 9.658468409 | 951 | 9.833923806 |
| 752 | 9.093671888 | 802 | 9.290907211 | 852 | 9.480106107 | 902 | 9.662040329 | 952 | 9.837369469 |
| 753 | 9.097700985 | 803 | 9.294767165 | 853 | 9.483813618 | 903 | 9.665609609 | 953 | 9.840812721 |
| 754 | 9.101726517 | 804 | 9.298623915 | 854 | 7.487518234 | 904 | 9.669176254 | 954 | 9.844253565 |
| 755 | 9.105748492 | 805 | 9.302477469 | 855 | 9.491219959 | 905 | 9.672740271 | 955 | 9.847692005 |
| 756 | 9.109766916 | 806 | 9.306327832 | 856 | 9.494918797 | 906 | 9.676301664 | 956 | 9.851128046 |
| 757 | 9.113781798 | 807 | 9.310175013 | 857 | 9.498614756 | 907 | 9.679860436 | 957 | 9.854561692 |
| 758 | 9.117793147 | 808 | 9.314019016 | 858 | 9.502307842 | 908 | 9.683416593 | 958 | 9.857992945 |
| 759 | 9.121800968 | 809 | 9.317859848 | 859 | 9.505998059 | 909 | 9.686970142 | 959 | 9.861421813 |
| 760 | 9.125805271 | 810 | 9.321697519 | 860 | 9.509685414 | 910 | 9.690521084 | 960 | 9.864848298 |
| 761 | 9.129806063 | 811 | 9.32553203 | 861 | 9.51336991 | 911 | 9.694069426 | 961 | 9.868272404 |
| 762 | 9.133803352 | 812 | 9.329363391 | 862 | 9.517051555 | 912 | 9.697615172 | 962 | 9.871694135 |
| 763 | 9.137797144 | 813 | 9.333191608 | 863 | 9.520730354 | 913 | 9.701158327 | 963 | 9.875113496 |
| 764 | 9.14178745 | 814 | 9.337016686 | 864 | 9.524406312 | 914 | 9.704698897 | 964 | 9.87853049 |
| 765 | 9.145774274 | 815 | 9.340838635 | 865 | 9.528079434 | 915 | 9.708236884 | 965 | 9.881945122 |
| 766 | 9.149757625 | 816 | 9.344657457 | 866 | 9.531749728 | 916 | 9.71172294 | 966 | 9.885357397 |
| 767 | 9.153737512 | 817 | 9.348473161 | 867 | 9.535417195 | 917 | 9.715305132 | 967 | 9.888767317 |
| 768 | 9.157713941 | 818 | 9.352285752 | 868 | 9.539081846 | 918 | 9.718835404 | 968 | 9.892174887 |
| 769 | 9.161686919 | 819 | 9.356095238 | 869 | 9.542743681 | 919 | 9.722363113 | 969 | 9.895580111 |
| 770 | 9.165656455 | 820 | 9.359901623 | 870 | 9.54640271 | 920 | 9.725888263 | 970 | 9.898982993 |
| 771 | 9.169622555 | 821 | 9.363704916 | 871 | 9.550058935 | 921 | 9.729410859 | 971 | 9.902383536 |
| 772 | 9.173585227 | 822 | 9.367505121 | 872 | 9.553712363 | 922 | 9.732930907 | 972 | 9.905781747 |
| 773 | 9.177544479 | 823 | 9.371302246 | 873 | 9.557362998 | 923 | 9.736448409 | 973 | 9.09177627 |
| 774 | 9.181500317 | 824 | 9.375096296 | 874 | 9.561010847 | 924 | 9.739963374 | 974 | 9.912571182 |
| 775 | 9.185452751 | 825 | 9.378887277 | 875 | 9.564655914 | 925 | 9.743475802 | 975 | 9.915962414 |
| 776 | 9.189401784 | 826 | 9.382675197 | 876 | 9.568298205 | 926 | 9.7469857 | 976 | 9.919351328 |
| 777 | 9.193347428 | 827 | 9.38646006 | 877 | 9.571937725 | 927 | 9.750493072 | 977 | 9.922737928 |
| 778 | 9.197289687 | 828 | 9.390241873 | 878 | 9.575574481 | 928 | 9.753997922 | 978 | 9.926122219 |
| 779 | 9.20122857 | 829 | 9.394020643 | 879 | 9.579208475 | 929 | 9.757500256 | 979 | 9.929504203 |
| 780 | 9.205164083 | 830 | 9.397796375 | 880 | 9.582839715 | 930 | 9.761000077 | 980 | 9.932883884 |
| 781 | 9.209096234 | 831 | 9.401569075 | 881 | 9.586468204 | 931 | 9.76449739 | 981 | 9.936261268 |
| 782 | 9.21302503 | 832 | 9.405338751 | 882 | 9.590093948 | 932 | 9.7679922 | 982 | 9.939636356 |
| 783 | 9.216950477 | 833 | 9.409105407 | 883 | 9.593716954 | 933 | 9.771484511 | 983 | 9.943009155 |
| 784 | 9.220872585 | 834 | 9.412869049 | 884 | 9.597337225 | 934 | 9.774974327 | 984 | 9.946379667 |
| 785 | 9.224791358 | 835 | 9.416629684 | 885 | 9.600954766 | 935 | 9.778461653 | 985 | 9.949747986 |
| 786 | 9.228706805 | 836 | 9.420387319 | 886 | 9.604569584 | 936 | 9.781946494 | 986 | 9.953113846 |
| 787 | 9.232618931 | 837 | 9.424141958 | 887 | 9.608181682 | 937 | 9.785428853 | 987 | 9.956477521 |
| 788 | 9.236527746 | 838 | 9.427893607 | 888 | 9.611791067 | 938 | 9.788908735 | 988 | 9.959838925 |
| 789 | 9.240433255 | 839 | 9.431642272 | 889 | 9.615397744 | 939 | 9.792386146 | 989 | 9.963198062 |
| 790 | 9.244335465 | 840 | 9.435387961 | 890 | 9.619001717 | 940 | 9.795861088 | 990 | 9.966554934 |
| 791 | 9.248234385 | 841 | 9.439130677 | 891 | 9.62260299 | 941 | 9.799333565 | 991 | 9.969909548 |
| 792 | 9.252130019 | 842 | 9.442870429 | 892 | 9.62620157 | 942 | 9.802803584 | 992 | 9.973261905 |
| 793 | 9.256022375 | 843 | 9.44660722 | 893 | 9.629797463 | 943 | 9.80627115 | 993 | 9.97661201 |
| 794 | 9.259911461 | 844 | 9.450341057 | 894 | 9.633390671 | 944 | 9.809736264 | 994 | 9.979959867 |
| 795 | 9.263797282 | 845 | 9.454071946 | 895 | 9.636981201 | 945 | 9.813198931 | 995 | 9.983305479 |
| 796 | 9.267679846 | 846 | 9.457799893 | 896 | 9.640569057 | 946 | 9.816659157 | 996 | 9.986648849 |
| 797 | 9.27155916 | 847 | 9.461524903 | 897 | 9.644154244 | 947 | 9.820116945 | 997 | 9.989989983 |
| 798 | 9.27543523 | 848 | 9.465246983 | 898 | 9.647736769 | 948 | 9.823572299 | 998 | 9.993328884 |
| 799 | 9.279308065 | 849 | 9.468966137 | 899 | 9.651316635 | 949 | 9.827025225 | 999 | 9.996665555 |
| 1000 | 10. |
============ end of appendix 3 ==========
