Acceleration..

rudeonline · 11-13-2007

I was thinking about acceleration. If you speed up from 50km/h to 60km/h does this "cost" the same amount of energie like speeding up from 200km/h to 210 km/h?

And what for 2000km/h to 2010km/h?

Jay-qu · 11-13-2007

The bottom line is no, it will be different. But there are varying reasons for the answer.

Firstly it will depend on your vehicle. Often frictional resistance is proportional to v^2 meaning the faster you go the more resistance you encouter, requiring more force to accelerate you the same amount.

But say your in a space-ship the differences you mention would be minimised. There is a slight difference that is a direct consequence of Special relativity and that is that as your increase your velocity your mass will increase, needing more force to keep you accelerating at the same rate. Note that this effect is absolutely minuscule on the scale you outline in your post.

rudeonline · 11-13-2007

I was thinking about a spaceship, using solar energy to accelerate.

Say at some point you travel with 20.000km/h, you can switch of your engine and the same speed will remain.

To speed up 10km/h more, you just switch on your engine and accelerate 10km/h. No big deal..

Then, if aaceleration will cost all the time the same amount of energy, I mean all kinds of speed could been seen as a zeropoint of acceleraton and you just need a little bit of energy to speed up 10km/h, would it then be possible to accelerate to the lightspeed if you would use solar energy to speed up?

Boerseun · 11-13-2007

As far as your spaceship is concerned, you're not moving at all. Until you define your velocity in terms of movement relative to some arbitrary vantage point like, say, Earth. So, travelling at 99% the velocity of light will be identical to travelling at 10km/h.

Matter of fact, we are already moving at 99.9% the speed of light. But only in relation to very far-off galaxies, which, according to them, are standing perfectly still.

What you're proposing is exactly the reason why Einstein came up with Relativity.

Qfwfq · 11-13-2007

For a given mass, kinetic energy is proportional to velocity squared in the non-relativistic approximation.

$60^2-50^2=1100$

$210^2-200^2=4100$

It's almost 4 times as much, and for a reason: in the second case the initial velocity is 4 times than in the first case. The first order term of $\Delta E$ is exactly 4 times as much while the second order term is the same.

$\Delta E=2v\Delta v + (\Delta v)^2$

CraigD · 11-13-2007

Quote:

Originally Posted by rudeonline

I was thinking about acceleration. If you speed up from 50km/h to 60km/h does this "cost" the same amount of energie like speeding up from 200km/h to 210 km/h?

And what for 2000km/h to 2010km/h?

Short answer: yes, a given change in velocity – “delta V” – requires about the same amount of energy and reaction mass (more on “reaction mass” later), assuming your rocket’s mass is about the same in both cases. (This isn’t a very good assumption, though, since rockets become less massive as they expel reaction mass - more on that later, too)

At the same time Qfwfq’s post explaining that a ship accelerating from 200 to 210 ship gains about 4 times as much kinetic energy as the same ship (net mass, rockets, etc) accelerating from 50 to 60 is correct, and perfectly simple mechanics.

So, the rocket science paradox question of the day: huh? How can that be?

The answer comes from realizing that a rocket isn’t only a spaceship-accelerating machine, but a reaction mass (the gas and particles in its exhaust) accelerating machine. If you calculate the change of kinetic energy of the ship and its reaction mass, you find it matches (allowing for various engineering inefficiencies) the energy of the chemical or other energy sources used to accelerate them. As a rocket expels reaction mass, it becomes less massive, so requires less power (energy used per unit time) to experience the same acceleration

As a rocket’s velocity relative to some stationary (unaccelerating) observation point increases, more of this energy is in the form of change in ship velocity, less in exhaust, so the rocket appears to become more “efficient” as it’s velocity nears that of its exhaust, peaking when the expelled reaction mass appears stationary relative to the observation point.

It can be helpful to just crank out some numbers and look at them Here’s a mass 100 rocket with an acceleration of 10 and an exhaust velocity of 1000 (you can use any units you like – kgs, m/s/s, and m/s are not too far from accurate for a small rocket):

Code:

Ship                                  Exhaust                 Total
------------------------------------- ----------------------- ---------------- 
                Kinetic                 Kinetic                 Kinetic
Speed    Mass    Energy   %    Change    Energy   %    Change    Energy Change
------------------------------------- ----------------------- ----------------
   10   99.01      4950   0.01   4950    485198   0.99 485198    490149 490149
   20   98.03     19606   0.02  14655    955936   0.98 470738    975542 485394
   30   97.06     43677   0.03  24071   1412550   0.97 456614   1456227 480685
   40   96.10     76878   0.04  33202   1855370   0.96 442820   1932248 476022
   50   95.15    118933   0.05  42055   2284719   0.95 429349   2403652 471404
   60   94.20    169568   0.06  50635   2700915   0.94 416196   2870483 466831
   70   93.27    228516   0.07  58948   3104268   0.93 403354   3332784 462302
   80   92.35    295515   0.08  66999   3495087   0.92 390818   3790601 457817
   90   91.43    370308   0.09  74793   3873669   0.91 378582   4243977 453375
  100   90.53    452643   0.10  82336   4240310   0.90 366641   4692954 448977
  110   89.63    542276   0.11  89632   4595299   0.89 354989   5137575 444621
  120   88.74    638963   0.11  96688   4938920   0.89 343620   5577883 440308
  130   87.87    742470   0.12 103506   5271449   0.88 332530   6013919 436036
  140   87.00    852564   0.13 110094   5593162   0.87 321712   6445725 431806
  150   86.13    969018   0.14 116454   5904324   0.86 311162   6873342 427617
  160   85.28   1091611   0.15 122593   6205200   0.85 300875   7296811 423468
  170   84.44   1220125   0.16 128514   6496045   0.84 290846   7716171 419360
  180   83.60   1354348   0.17 134223   6777114   0.83 281069   8131462 415292
  190   82.77   1494071   0.17 139722   7048654   0.83 271540   8542725 411263
  200   81.95   1639089   0.18 145018   7310909   0.82 262254   8949998 407273
  210   81.14   1789204   0.19 150115   7564115   0.81 253207   9353319 403321
  220   80.34   1944219   0.20 155015   7808509   0.80 244393   9752727 399408
  230   79.54   2103944   0.21 159725   8044317   0.79 235809  10148261 395533
  240   78.76   2268190   0.22 164247   8271766   0.78 227449  10539957 391696
  250   77.98   2436776   0.22 168586   8491076   0.78 219310  10927853 387896
  260   77.20   2609522   0.23 172746   8702463   0.77 211387  11311985 384132
  270   76.44   2786252   0.24 176730   8906138   0.76 203675  11692391 380406
  280   75.68   2966795   0.25 180543   9102310   0.75 196172  12069106 376715
  290   74.93   3150984   0.25 184188   9291182   0.75 188872  12442166 373060
  300   74.19   3338653   0.26 187669   9472953   0.74 181771  12811606 369441
  310   73.46   3529643   0.27 190990   9647819   0.73 174866  13177462 365856
  320   72.73   3723797   0.28 194154   9815972   0.72 168153  13539769 362307
  330   72.01   3920961   0.28 197164   9977599   0.72 161627  13898560 358791
  340   71.30   4120986   0.29 200025  10132885   0.71 155286  14253870 355310
  350   70.59   4323724   0.30 202739  10282009   0.70 149124  14605733 351863
  360   69.89   4529034   0.30 205309  10425149   0.70 143140  14954182 348449
  370   69.20   4736774   0.31 207740  10562477   0.69 137328  15299251 345068
  380   68.52   4946807   0.32 210034  10694164   0.68 131686  15640971 341720
  390   67.84   5159001   0.32 212194  10820374   0.68 126211  15979376 338405
  400   67.17   5373225   0.33 214224  10941272   0.67 120898  16314497 335121
  410   66.50   5589351   0.34 216126  11057016   0.66 115744  16646367 331870
  420   65.84   5807255   0.34 217904  11167762   0.66 110746  16975017 328650
  430   65.19   6026815   0.35 219560  11273663   0.65 105901  17300478 325461
  440   64.54   6247912   0.35 221097  11374869   0.65 101206  17622781 322303
  450   63.91   6470431   0.36 222519  11471526   0.64  96657  17941957 319176
  460   63.27   6694258   0.37 223827  11563777   0.63  92252  18258036 316079
  470   62.65   6919284   0.37 225026  11651764   0.63  87987  18571048 313012
  480   62.03   7145400   0.38 226116  11735623   0.62  83859  18881023 309975
  490   61.41   7372501   0.38 227101  11815490   0.62  79866  19187991 306967
  500   60.80   7600485   0.39 227984  11891494   0.61  76005  19491980 303989
  510   60.20   7829252   0.40 228767  11963767   0.60  72272  19793019 301039
  520   59.61   8058705   0.40 229453  12032433   0.60  68666  20091138 298118
  530   59.02   8288748   0.41 230043  12097615   0.59  65183  20386363 295226
  540   58.43   8519289   0.41 230541  12159436   0.59  61820  20678725 292361
  550   57.85   8750237   0.42 230948  12218012   0.58  58576  20968249 289524
  560   57.28   8981505   0.42 231268  12273459   0.58  55447  21254964 286715
  570   56.71   9213007   0.43 231502  12325890   0.57  52431  21538897 283933
  580   56.15   9444660   0.43 231652  12375415   0.57  49526  21820075 281178
  590   55.60   9676381   0.44 231722  12422143   0.56  46728  22098525 278450
  600   55.04   9908093   0.44 231712  12466179   0.56  44036  22374272 275748
  610   54.50  10139718   0.45 231625  12507627   0.55  41447  22647344 273072
  620   53.96  10371181   0.45 231463  12546586   0.55  38959  22917767 270422
  630   53.43  10602409   0.46 231228  12583156   0.54  36570  23185565 267798
  640   52.90  10833331   0.46 230922  12617433   0.54  34277  23450765 265200
  650   52.37  11063879   0.47 230548  12649512   0.53  32079  23713391 262626
  660   51.85  11293985   0.47 230106  12679484   0.53  29972  23973469 260078
  670   51.34  11523584   0.48 229599  12707440   0.52  27955  24231023 257554
  680   50.83  11752612   0.48 229029  12733466   0.52  26027  24486079 255055
  690   50.33  11981009   0.48 228397  12757650   0.52  24183  24738659 252580
  700   49.83  12208714   0.49 227705  12780074   0.51  22424  24988788 250129
  710   49.34  12435669   0.49 226955  12800820   0.51  20747  25236490 247702
  720   48.85  12661819   0.50 226149  12819970   0.50  19149  25481788 245298
  730   48.37  12887107   0.50 225289  12837599   0.50  17629  25724706 242918
  740   47.89  13111482   0.50 224375  12853785   0.50  16186  25965267 240561
  750   47.41  13334892   0.51 223410  12868601   0.49  14817  26203493 238226
  760   46.94  13557287   0.51 222395  12882121   0.49  13520  26439408 235915
  770   46.48  13778618   0.52 221332  12894415   0.48  12294  26673033 233625
  780   46.02  13998840   0.52 220222  12905551   0.48  11136  26904391 231358
  790   45.56  14217907   0.52 219066  12915598   0.48  10047  27133504 229113
  800   45.11  14435774   0.53 217867  12924620   0.47   9022  27360394 226890
  810   44.67  14652400   0.53 216626  12932682   0.47   8062  27585082 224688
  820   44.22  14867743   0.53 215343  12939846   0.47   7164  27807590 222508
  830   43.79  15081765   0.54 214021  12946173   0.46   6327  28027938 220348
  840   43.35  15294426   0.54 212661  12951722   0.46   5549  28246148 218210
  850   42.92  15505690   0.54 211264  12956551   0.46   4829  28462241 216092
  860   42.50  15715520   0.55 209831  12960716   0.45   4165  28676236 213995
  870   42.08  15923883   0.55 208363  12964271   0.45   3555  28888155 211919
  880   41.66  16130746   0.55 206863  12967271   0.45   3000  29098017 209862
  890   41.25  16336076   0.56 205330  12969766   0.44   2495  29305842 207826
  900   40.84  16539843   0.56 203767  12971808   0.44   2042  29511651 205809
  910   40.43  16742017   0.56 202174  12973446   0.44   1638  29715463 203811
  920   40.03  16942569   0.57 200552  12974727   0.43   1281  29917296 201834
  930   39.64  17141473   0.57 198904  12975698   0.43    971  30117171 199875
  940   39.25  17338702   0.57 197229  12976404   0.43    706  30315106 197935
  950   38.86  17534230   0.57 195529  12976890   0.43    486  30511120 196014
  960   38.47  17728034   0.58 193804  12977198   0.42    308  30705232 194112
  970   38.09  17920091   0.58 192057  12977369   0.42    171  30897461 192228
  980   37.71  18110378   0.58 190287  12977445   0.42     75  31087823 190363
  990   37.34  18298875   0.59 188497  12977463   0.41     19  31276338 188515
 1000   36.97  18485561   0.59 186686  12977463   0.41      0  31463024 186686
 1010   36.61  18670416   0.59 184856  12977482   0.41     18  31647898 184874
 1020   36.24  18853423   0.59 183007  12977554   0.41     72  31830978 183080
 1030   35.88  19034565   0.59 181141  12977716   0.41    161  32012281 181303
 1040   35.53  19213824   0.60 179259  12978000   0.40    284  32191824 179543
 1050   35.18  19391185   0.60 177361  12978440   0.40    440  32369625 177801
 1060   34.83  19566634   0.60 175448  12979067   0.40    627  32545700 176075
 1070   34.48  19740155   0.60 173522  12979911   0.40    845  32720067 174366
 1080   34.14  19911737   0.61 171582  12981004   0.39   1093  32892741 172674
 1090   33.80  20081366   0.61 169629  12982373   0.39   1369  33063739 170998
 1100   33.47  20249032   0.61 167665  12984046   0.39   1673  33233078 169339
 1110   33.14  20414722   0.61 165690  12986051   0.39   2005  33400773 167695
 1120   32.81  20578428   0.61 163705  12988414   0.39   2362  33566841 166068
 1130   32.49  20740139   0.61 161711  12991159   0.39   2745  33731297 164456
 1140   32.16  20899846   0.62 159708  12994311   0.38   3152  33894157 162860
 1150   31.85  21057543   0.62 157697  12997893   0.38   3583  34055436 161279
 1160   31.53  21213221   0.62 155678  13001929   0.38   4036  34215150 159714
 1170   31.22  21366874   0.62 153653  13006440   0.38   4511  34373314 158164
 1180   30.91  21518496   0.62 151622  13011447   0.38   5007  34529943 156629
 1190   30.60  21668081   0.62 149585  13016971   0.38   5524  34685052 155109
 1200   30.30  21815624   0.63 147543  13023031   0.37   6060  34838655 153603
 1210   30.00  21961122   0.63 145497  13029646   0.37   6615  34990767 152112
 1220   29.70  22104570   0.63 143448  13036834   0.37   7188  35141403 150636
 1230   29.41  22245965   0.63 141395  13044612   0.37   7779  35290577 149174
 1240   29.12  22385305   0.63 139340  13052998   0.37   8386  35438303 147726
 1250   28.83  22522589   0.63 137283  13062007   0.37   9009  35584596 146292
 1260   28.54  22657814   0.63 135225  13071655   0.37   9648  35729468 144872
 1270   28.26  22790979   0.64 133165  13081956   0.36  10301  35872934 143466
 1280   27.98  22922084   0.64 131105  13092924   0.36  10969  36015008 142074
 1290   27.70  23051129   0.64 129045  13104574   0.36  11650  36155703 140695
 1300   27.43  23178115   0.64 126986  13116917   0.36  12343  36295032 139329
 1310   27.16  23303043   0.64 124927  13129967   0.36  13049  36433009 137977
 1320   26.89  23425913   0.64 122870  13143734   0.36  13767  36569647 136638
 1330   26.62  23546728   0.64 120815  13158230   0.36  14496  36704959 135311
 1340   26.36  23665491   0.64 118762  13173466   0.36  15236  36838957 133998
 1350   26.10  23782203   0.64 116712  13189451   0.36  15985  36971654 132698
 1360   25.84  23896868   0.64 114665  13206196   0.36  16744  37103064 131410
 1370   25.58  24009490   0.64 112622  13223708   0.36  17512  37233198 130134
 1380   25.33  24120072   0.65 110582  13241997   0.35  18289  37362069 128871
 1390   25.08  24228618   0.65 108547  13261070   0.35  19073  37489689 127620
 1400   24.83  24335134   0.65 106516  13280936   0.35  19865  37616070 126381
 1410   24.59  24439624   0.65 104490  13301600   0.35  20664  37741225 125155
 1420   24.34  24542094   0.65 102470  13323070   0.35  21470  37865164 123940
 1430   24.10  24642549   0.65 100455  13345352   0.35  22282  37987901 122737
 1440   23.86  24740995   0.65  98446  13368451   0.35  23099  38109446 121545
 1450   23.63  24837439   0.65  96444  13392373   0.35  23922  38229812 120366
 1460   23.39  24931887   0.65  94448  13417123   0.35  24749  38349009 119197
 1470   23.16  25024346   0.65  92459  13442704   0.35  25581  38467050 118040
 1480   22.93  25114823   0.65  90477  13469121   0.35  26417  38583944 116894
 1490   22.70  25203325   0.65  88503  13496378   0.35  27257  38699704 115760
 1500   22.48  25289862   0.65  86536  13524478   0.35  28100  38814340 114636
 1510   22.26  25374439   0.65  84578  13553424   0.35  28946  38927863 113523
 1520   22.04  25457067   0.65  82627  13583218   0.35  29794  39040285 112421
 1530   21.82  25537753   0.65  80686  13613862   0.35  30644  39151615 111330
 1540   21.60  25616505   0.65  78753  13645359   0.35  31497  39261864 110249
 1550   21.39  25693334   0.65  76829  13677710   0.35  32351  39371044 109179
 1560   21.18  25768248   0.65  74914  13710915   0.35  33206  39479163 108119
 1570   20.97  25841256   0.65  73008  13744977   0.35  34062  39586233 107070
 1580   20.76  25912369   0.65  71113  13779895   0.35  34918  39692264 106031
 1590   20.55  25981596   0.65  69227  13815669   0.35  35775  39797265 105001
 1600   20.35  26048947   0.65  67351  13852301   0.35  36631  39901247 103982
 1610   20.15  26114432   0.65  65485  13889788   0.35  37488  40004220 102973
 1620   19.95  26178061   0.65  63630  13928132   0.35  38343  40106193 101973
 1630   19.75  26239846   0.65  61785  13967330   0.35  39198  40207176 100983
 1640   19.56  26299797   0.65  59951  14007382   0.35  40052  40307179 100003
 1650   19.36  26357925   0.65  58128  14048286   0.35  40904  40406212  99032
 1660   19.17  26414241   0.65  56316  14090042   0.35  41755  40504282  98071
 1670   18.98  26468756   0.65  54515  14132646   0.35  42604  40601401  97119
 1680   18.79  26521481   0.65  52725  14176096   0.35  43451  40697577  96176
 1690   18.61  26572428   0.65  50947  14220391   0.35  44295  40792820  95242
 1700   18.42  26621609   0.65  49181  14265528   0.35  45137  40887138  94318
 1710   18.24  26669035   0.65  47426  14311505   0.35  45976  40980540  93402
 1720   18.06  26714719   0.65  45683  14358317   0.35  46812  41073035  92496
 1730   17.88  26758671   0.65  43953  14405962   0.35  47645  41164633  91598
 1740   17.70  26800905   0.65  42234  14454436   0.35  48475  41255342  90708
 1750   17.53  26841432   0.65  40527  14503737   0.35  49301  41345169  89828
 1760   17.36  26880266   0.65  38833  14553860   0.35  50123  41434125  88956
 1770   17.18  26917417   0.65  37151  14604801   0.35  50941  41522218  88092
 1780   17.01  26952898   0.65  35482  14656556   0.35  51755  41609455  87237
 1790   16.85  26986723   0.65  33825  14709121   0.35  52565  41695845  86390
 1800   16.68  27018904   0.65  32181  14762492   0.35  53371  41781396  85552
 1810   16.51  27049454   0.65  30549  14816664   0.35  54172  41866117  84721
 1820   16.35  27078385   0.65  28931  14871631   0.35  54968  41950016  83899
 1830   16.19  27105710   0.64  27325  14927390   0.36  55759  42033100  83084
 1840   16.03  27131442   0.64  25732  14983935   0.36  56545  42115377  82277
 1850   15.87  27155594   0.64  24152  15041262   0.36  57326  42196856  81479
 1860   15.71  27178180   0.64  22586  15099364   0.36  58102  42277544  80688
 1870   15.56  27199212   0.64  21032  15158236   0.36  58872  42357448  79904
 1880   15.40  27218703   0.64  19491  15217873   0.36  59637  42436577  79129
 1890   15.25  27236667   0.64  17964  15278270   0.36  60396  42514937  78360
 1900   15.10  27253117   0.64  16450  15339419   0.36  61150  42592537  77600
 1910   14.95  27268067   0.64  14949  15401316   0.36  61897  42669383  76846
 1920   14.80  27281528   0.64  13462  15463955   0.36  62639  42745483  76100
 1930   14.65  27293516   0.64  11987  15527329   0.36  63374  42820845  75361
 1940   14.51  27304042   0.64  10527  15591432   0.36  64103  42895475  74630
 1950   14.37  27313122   0.64   9079  15656258   0.36  64826  42969380  73905
 1960   14.22  27320767   0.63   7645  15721801   0.37  65543  43042568  73188
 1970   14.08  27326991   0.63   6225  15788053   0.37  66253  43115045  72477
 1980   13.94  27331809   0.63   4817  15855009   0.37  66956  43186818  71774
 1990   13.81  27335233   0.63   3424  15922662   0.37  67653  43257895  71077
 2000   13.67  27337276   0.63   2043  15991005   0.37  68343  43328282  70387
 2010   13.53  27337953   0.63    677  16060032   0.37  69027  43397985  69703
 2020   13.40  27337276   0.63   -677  16129735   0.37  69703  43467011  69027
 2030   13.27  27335260   0.63  -2017  16200108   0.37  70373  43535368  68356
 2040   13.14  27331917   0.63  -3343  16271144   0.37  71036  43603061  67693
 2050   13.01  27327261   0.63  -4656  16342835   0.37  71691  43670096  67036
 2060   12.88  27321305   0.62  -5955  16415175   0.38  72340  43736481  66385
 2070   12.75  27314064   0.62  -7241  16488157   0.38  72982  43802221  65740
 2080   12.62  27305550   0.62  -8514  16561773   0.38  73616  43867323  65102
 2090   12.50  27295777   0.62  -9773  16636016   0.38  74243  43931793  64470
 2100   12.37  27284758   0.62 -11019  16710879   0.38  74863  43995636  63844
 2110   12.25  27272506   0.62 -12252  16786354   0.38  75476  44058860  63224
 2120   12.13  27259035   0.62 -13471  16862435   0.38  76081  44121471  62610
 2130   12.01  27244359   0.62 -14676  16939114   0.38  76679  44183473  62002
 2140   11.89  27228490   0.62 -15869  17016383   0.38  77269  44244873  61400
 2150   11.77  27211442   0.61 -17048  17094235   0.39  77852  44305677  60804
 2160   11.66  27193228   0.61 -18214  17172663   0.39  78428  44365891  60214
 2170   11.54  27173862   0.61 -19367  17251658   0.39  78996  44425520  59629
 2180   11.43  27153356   0.61 -20506  17331215   0.39  79556  44484570  59050
 2190   11.31  27131723   0.61 -21633  17411324   0.39  80109  44543047  58477
 2200   11.20  27108977   0.61 -22746  17491979   0.39  80655  44600956  57909
 2210   11.09  27085131   0.61 -23846  17573171   0.39  81193  44658303  57347
 2220   10.98  27060198   0.61 -24933  17654895   0.39  81723  44715093  56790
 2230   10.87  27034191   0.60 -26007  17737140   0.40  82246  44771331  56239
 2240   10.76  27007122   0.60 -27068  17819901   0.40  82761  44827024  55693
 2250   10.66  26979006   0.60 -28117  17903170   0.40  83269  44882176  55152
 2260   10.55  26949853   0.60 -29152  17986938   0.40  83768  44936792  54616
 2270   10.45  26919679   0.60 -30175  18071199   0.40  84261  44990878  54086
 2280   10.34  26888494   0.60 -31185  18155945   0.40  84746  45044438  53561
 2290   10.24  26856312   0.60 -32182  18241167   0.40  85223  45097479  53041
 2300   10.14  26823146   0.59 -33166  18326859   0.41  85692  45150005  52526
 2310   10.04  26789007   0.59 -34138  18413013   0.41  86154  45202021  52016
 2320    9.94  26753910   0.59 -35098  18499622   0.41  86608  45253531  51511
 2330    9.84  26717865   0.59 -36044  18586676   0.41  87055  45304542  51010
 2340    9.75  26680886   0.59 -36979  18674170   0.41  87494  45355057  50515
 2350    9.65  26642986   0.59 -37901  18762096   0.41  87925  45405081  50025
 2360    9.55  26604175   0.59 -38810  18850445   0.41  88349  45454620  49539
 2370    9.46  26564467   0.58 -39708  18939211   0.42  88766  45503678  49058
 2380    9.37  26523874   0.58 -40593  19028386   0.42  89175  45552260  48582
 2390    9.27  26482408   0.58 -41466  19117962   0.42  89576  45600370  48110
 2400    9.18  26440081   0.58 -42327  19207931   0.42  89970  45648012  47643
 2410    9.09  26396905   0.58 -43176  19298287   0.42  90356  45695192  47180
 2420    9.00  26352892   0.58 -44013  19389022   0.42  90735  45741914  46722
 2430    8.91  26308054   0.57 -44838  19480128   0.43  91106  45788182  46268
 2440    8.82  26262403   0.57 -45651  19571599   0.43  91470  45834001  45819
 2450    8.74  26215950   0.57 -46453  19663426   0.43  91827  45879375  45374
 2460    8.65  26168707   0.57 -47243  19755601   0.43  92176  45924309  44933
 2470    8.56  26120686   0.57 -48021  19848119   0.43  92518  45968806  44497
 2480    8.48  26071899   0.57 -48787  19940972   0.43  92852  46012871  44065
 2490    8.39  26022357   0.57 -49542  20034151   0.43  93180  46056508  43637
 2500    8.31  25972071   0.56 -50286  20127651   0.44  93499  46099721  43213
 2510    8.23  25921052   0.56 -51018  20221463   0.44  93812  46142515  42794
 2520    8.15  25869313   0.56 -51739  20315580   0.44  94118  46184893  42378
 2530    8.07  25816864   0.56 -52449  20409996   0.44  94416  46226860  41967
 2540    7.99  25763716   0.56 -53148  20504703   0.44  94707  46268419  41559
 2550    7.91  25709880   0.56 -53836  20599695   0.44  94991  46309575  41156
 2560    7.83  25655368   0.55 -54512  20694963   0.45  95268  46350331  40756
 2570    7.75  25600190   0.55 -55178  20790501   0.45  95538  46390691  40360
 2580    7.68  25544357   0.55 -55833  20886302   0.45  95801  46430659  39968
 2590    7.60  25487881   0.55 -56477  20982358   0.45  96057  46470239  39580
 2600    7.52  25430770   0.55 -57110  21078664   0.45  96306  46509435  39196
 2610    7.45  25373038   0.55 -57733  21175212   0.45  96548  46548250  38815
 2620    7.38  25314692   0.54 -58345  21271996   0.46  96783  46586688  38438
 2630    7.30  25255746   0.54 -58947  21369007   0.46  97012  46624753  38065
 2640    7.23  25196208   0.54 -59538  21466240   0.46  97233  46662448  37695
 2650    7.16  25136089   0.54 -60119  21563689   0.46  97448  46699777  37329
 2660    7.09  25075399   0.54 -60690  21661345   0.46  97656  46736744  36967
 2670    7.02  25014149   0.53 -61250  21759203   0.47  97858  46773352  36608
 2680    6.95  24952348   0.53 -61801  21857256   0.47  98053  46809604  36252
 2690    6.88  24890007   0.53 -62341  21955497   0.47  98241  46845504  35900
 2700    6.81  24827135   0.53 -62872  22053920   0.47  98423  46881056  35552
 2710    6.74  24763743   0.53 -63392  22152519   0.47  98598  46916262  35206
 2720    6.68  24699840   0.53 -63903  22251286   0.47  98767  46951126  34864
 2730    6.61  24635436   0.52 -64404  22350216   0.48  98930  46985652  34526
 2740    6.55  24570541   0.52 -64895  22449302   0.48  99086  47019842  34190
 2750    6.48  24505163   0.52 -65377  22548538   0.48  99236  47053701  33858
 2760    6.42  24439314   0.52 -65850  22647917   0.48  99379  47087231  33530
 2770    6.35  24373001   0.52 -66313  22747434   0.48  99517  47120435  33204
 2780    6.29  24306235   0.52 -66766  22847082   0.48  99648  47153316  32882
 2790    6.23  24239024   0.51 -67211  22946854   0.49  99773  47185878  32562
 2800    6.17  24171378   0.51 -67646  23046746   0.49  99892  47218124  32246
 2810    6.11  24103306   0.51 -68072  23146751   0.49 100005  47250057  31933
 2820    6.04  24034817   0.51 -68489  23246863   0.49 100112  47281680  31623
 2830    5.98  23965919   0.51 -68897  23347076   0.49 100213  47312995  31316
 2840    5.93  23896623   0.50 -69297  23447384   0.50 100308  47344007  31011
 2850    5.87  23826936   0.50 -69687  23547781   0.50 100397  47374717  30710
 2860    5.81  23756867   0.50 -70069  23648262   0.50 100481  47405129  30412
 2870    5.75  23686425   0.50 -70442  23748820   0.50 100559  47435246  30117
 2880    5.69  23615619   0.50 -70806  23849451   0.50 100631  47465070  29824
 2890    5.64  23544456   0.50 -71162  23950148   0.50 100697  47494604  29535
 2900    5.58  23472946   0.49 -71510  24050906   0.51 100758  47523852  29248
 2910    5.53  23401097   0.49 -71849  24151719   0.51 100813  47552816  28964
 2920    5.47  23328916   0.49 -72181  24252582   0.51 100863  47581498  28682
 2930    5.42  23256413   0.49 -72503  24353489   0.51 100907  47609902  28404
 2940    5.36  23183595   0.49 -72818  24454435   0.51 100946  47638030  28128
 2950    5.31  23110470   0.48 -73125  24555415   0.52 100980  47665884  27855
 2960    5.26  23037046   0.48 -73424  24656423   0.52 101008  47693469  27584
 2970    5.21  22963331   0.48 -73715  24757454   0.52 101031  47720785  27316
 2980    5.16  22889333   0.48 -73998  24858503   0.52 101049  47747836  27051
 2990    5.10  22815060   0.48 -74273  24959564   0.52 101061  47774624  26788
 3000    5.05  22740519   0.48 -74541  25060633   0.52 101069  47801152  26528
 3010    5.00  22665718   0.47 -74801  25161704   0.53 101071  47827423  26270
 3020    4.95  22590665   0.47 -75054  25262773   0.53 101069  47853438  26015
 3030    4.90  22515366   0.47 -75299  25363835   0.53 101062  47879201  25763
 3040    4.86  22439829   0.47 -75537  25464884   0.53 101049  47904713  25512
 3050    4.81  22364062   0.47 -75767  25565916   0.53 101032  47929978  25265
 3060    4.76  22288071   0.46 -75991  25666926   0.54 101010  47954997  25019
 3070    4.71  22211864   0.46 -76207  25767909   0.54 100983  47979773  24776
 3080    4.67  22135448   0.46 -76416  25868861   0.54 100952  48004309  24536
 3090    4.62  22058830   0.46 -76618  25969776   0.54 100916  48028606  24297
 3100    4.57  21982016   0.46 -76814  26070651   0.54 100875  48052667  24061
 3110    4.53  21905014   0.46 -77002  26171481   0.54 100830  48076495  23828
 3120    4.48  21827830   0.45 -77184  26272260   0.55 100780  48100091  23596
 3130    4.44  21750472   0.45 -77358  26372986   0.55 100725  48123458  23367
 3140    4.40  21672945   0.45 -77527  26473653   0.55 100667  48146598  23140
 3150    4.35  21595257   0.45 -77689  26574256   0.55 100604  48169513  22915
 3160    4.31  21517413   0.45 -77844  26674793   0.55 100536  48192206  22693
 3170    4.27  21439420   0.44 -77993  26775258   0.56 100465  48214678  22472
 3180    4.22  21361285   0.44 -78135  26875647   0.56 100389  48236932  22254
 3190    4.18  21283014   0.44 -78271  26975956   0.56 100309  48258970  22038
 3200    4.14  21204613   0.44 -78401  27076180   0.56 100225  48280793  21824
 3210    4.10  21126088   0.44 -78525  27176317   0.56 100137  48302405  21612
 3220    4.06  21047445   0.44 -78643  27276362   0.56 100045  48323807  21402
 3230    4.02  20968691   0.43 -78754  27376310   0.57  99948  48345001  21194
 3240    3.98  20889831   0.43 -78860  27476159   0.57  99848  48365989  20988
 3250    3.94  20810871   0.43 -78960  27575903   0.57  99744  48386774  20784
 3260    3.90  20731816   0.43 -79054  27675540   0.57  99637  48407356  20582
 3270    3.86  20652674   0.43 -79143  27775065   0.57  99525  48427738  20382
 3280    3.82  20573448   0.42 -79225  27874475   0.58  99410  48447923  20184
 3290    3.79  20494146   0.42 -79302  27973765   0.58  99291  48467911  19988
 3300    3.75  20414772   0.42 -79374  28072933   0.58  99168  48487706  19794
 3310    3.71  20335332   0.42 -79440  28171975   0.58  99042  48507308  19602
 3320    3.68  20255832   0.42 -79501  28270888   0.58  98912  48526719  19412
 3330    3.64  20176276   0.42 -79556  28369667   0.58  98779  48545942  19223
 3340    3.60  20096670   0.41 -79606  28468309   0.59  98642  48564979  19036
 3350    3.57  20017019   0.41 -79651  28566811   0.59  98502  48583830  18851
 3360    3.53  19937329   0.41 -79690  28665170   0.59  98359  48602498  18668
 3370    3.50  19857604   0.41 -79725  28763381   0.59  98212  48620985  18487
 3380    3.46  19777849   0.41 -79754  28861443   0.59  98062  48639293  18307
 3390    3.43  19698071   0.40 -79779  28959352   0.60  97908  48657422  18130
 3400    3.39  19618272   0.40 -79799  29057103   0.60  97752  48675376  17953
 3410    3.36  19538459   0.40 -79813  29154696   0.60  97592  48693155  17779
 3420    3.33  19458635   0.40 -79823  29252125   0.60  97430  48710761  17606
 3430    3.29  19378807   0.40 -79829  29349389   0.60  97264  48728196  17435
 3440    3.26  19298978   0.40 -79829  29446484   0.60  97095  48745462  17266
 3450    3.23  19219153   0.39 -79825  29543408   0.61  96923  48762560  17098
 3460    3.20  19139336   0.39 -79817  29640156   0.61  96749  48779492  16932
 3470    3.17  19059533   0.39 -79803  29736727   0.61  96571  48796260  16768
 3480    3.13  18979747   0.39 -79786  29833118   0.61  96391  48812865  16605
 3490    3.10  18899983   0.39 -79764  29929326   0.61  96208  48829308  16443
 3500    3.07  18820245   0.39 -79738  30025347   0.61  96022  48845592  16284
 3510    3.04  18740537   0.38 -79707  30121180   0.62  95833  48861718  16126
 3520    3.01  18660865   0.38 -79673  30216822   0.62  95642  48877687  15969
 3530    2.98  18581230   0.38 -79634  30312270   0.62  95448  48893500  15814
 3540    2.95  18501639   0.38 -79591  30407521   0.62  95251  48909161  15660
 3550    2.92  18422095   0.38 -79544  30502574   0.62  95052  48924669  15508
 3560    2.89  18342602   0.37 -79493  30597424   0.63  94851  48940026  15357
 3570    2.87  18263163   0.37 -79439  30692071   0.63  94647  48955234  15208
 3580    2.84  18183783   0.37 -79380  30786511   0.63  94440  48970295  15060
 3590    2.81  18104466   0.37 -79317  30880743   0.63  94232  48985209  14914
 3600    2.78  18025215   0.37 -79251  30974763   0.63  94020  48999978  14769
 3610    2.75  17946033   0.37 -79181  31068570   0.63  93807  49014604  14626
 3620    2.73  17866926   0.36 -79108  31162162   0.64  93591  49029088  14484
 3630    2.70  17787896   0.36 -79030  31255535   0.64  93373  49043431  14343
 3640    2.67  17708946   0.36 -78950  31348688   0.64  93153  49057634  14204
 3650    2.65  17630081   0.36 -78865  31441619   0.64  92931  49071700  14066
 3660    2.62  17551303   0.36 -78778  31534326   0.64  92707  49085629  13929
 3670    2.59  17472617   0.36 -78686  31626806   0.64  92480  49099423  13794
 3680    2.57  17394025   0.35 -78592  31719057   0.65  92252  49113082  13660
 3690    2.54  17315531   0.35 -78494  31811079   0.65  92021  49126609  13527
 3700    2.52  17237138   0.35 -78393  31902867   0.65  91789  49140005  13396
 3710    2.49  17158849   0.35 -78289  31994422   0.65  91554  49153271  13265
 3720    2.47  17080667   0.35 -78181  32085740   0.65  91318  49166407  13137
 3730    2.44  17002596   0.35 -78071  32176820   0.65  91080  49179416  13009
 3740    2.42  16924639   0.34 -77957  32267660   0.66  90840  49192299  12883
 3750    2.40  16846798   0.34 -77841  32358258   0.66  90598  49205056  12757
 3760    2.37  16769077   0.34 -77721  32448613   0.66  90355  49217690  12634
 3770    2.35  16691478   0.34 -77599  32538723   0.66  90110  49230200  12511
 3780    2.33  16614004   0.34 -77474  32628585   0.66  89863  49242590  12389
 3790    2.30  16536659   0.34 -77346  32718200   0.66  89614  49254858  12269
 3800    2.28  16459444   0.33 -77215  32807564   0.67  89364  49267008  12150
 3810    2.26  16382363   0.33 -77081  32896677   0.67  89113  49279040  12032
 3820    2.23  16305418   0.33 -76945  32985536   0.67  88859  49290955  11915
 3830    2.21  16228613   0.33 -76806  33074141   0.67  88605  49302754  11799
 3840    2.19  16151948   0.33 -76664  33162489   0.67  88348  49314438  11684
 3850    2.17  16075428   0.33 -76520  33250580   0.67  88091  49326009  11571
 3860    2.15  15999055   0.32 -76373  33338412   0.68  87832  49337467  11458
 3870    2.13  15922831   0.32 -76224  33425983   0.68  87571  49348814  11347
 3880    2.11  15846758   0.32 -76073  33513293   0.68  87310  49360051  11237
 3890    2.08  15770839   0.32 -75919  33600340   0.68  87046  49371179  11128
 3900    2.06  15695077   0.32 -75763  33687122   0.68  86782  49382198  11020
 3910    2.04  15619473   0.32 -75604  33773638   0.68  86516  49393111  10913
 3920    2.02  15544030   0.31 -75443  33859888   0.69  86250  49403917  10806
 3930    2.00  15468750   0.31 -75280  33945869   0.69  85982  49414619  10701
 3940    1.98  15393635   0.31 -75115  34031582   0.69  85712  49425216  10598
 3950    1.96  15318687   0.31 -74947  34117024   0.69  85442  49435711  10495
 3960    1.94  15243909   0.31 -74778  34202194   0.69  85171  49446104  10393
 3970    1.92  15169303   0.31 -74606  34287092   0.69  84898  49456395  10292
 3980    1.91  15094870   0.31 -74433  34371717   0.69  84624  49466587  10192
 3990    1.89  15020613   0.30 -74257  34456066   0.70  84350  49476679  10093
 4000    1.87  14946533   0.30 -74080  34540141   0.70  84074  49486674   9995
 4010    1.85  14872633   0.30 -73900  34623938   0.70  83798  49496571   9897
 4020    1.83  14798914   0.30 -73719  34707459   0.70  83520  49506373   9801
 4030    1.81  14725378   0.30 -73536  34790700   0.70  83242  49516079   9706
 4040    1.80  14652028   0.30 -73351  34873663   0.70  82963  49525691   9612
 4050    1.78  14578863   0.29 -73164  34956345   0.71  82682  49535209   9518
 4060    1.76  14505888   0.29 -72976  35038747   0.71  82401  49544635   9426
 4070    1.74  14433102   0.29 -72785  35120867   0.71  82120  49553969   9334
 4080    1.73  14360509   0.29 -72594  35202704   0.71  81837  49563213   9244
 4090    1.71  14288109   0.29 -72400  35284258   0.71  81554  49572367   9154
 4100    1.69  14215904   0.29 -72205  35365528   0.71  81270  49581431   9065
 4110    1.67  14143895   0.29 -72009  35446513   0.71  80985  49590408   8977
 4120    1.66  14072085   0.28 -71810  35527213   0.72  80700  49599298   8890
 4130    1.64  14000474   0.28 -71611  35607627   0.72  80414  49608101   8803
 4140    1.63  13929064   0.28 -71410  35687754   0.72  80127  49616819   8718
 4150    1.61  13857857   0.28 -71207  35767594   0.72  79840  49625452   8633
 4160    1.59  13786854   0.28 -71003  35847147   0.72  79552  49634001   8549
 4170    1.58  13716056   0.28 -70798  35926411   0.72  79264  49642467   8466
 4180    1.56  13645465   0.27 -70591  36005386   0.73  78975  49650850   8384
 4190    1.55  13575081   0.27 -70383  36084071   0.73  78686  49659153   8302
 4200    1.53  13504907   0.27 -70174  36162467   0.73  78396  49667374   8222
 4210    1.52  13434943   0.27 -69964  36240573   0.73  78106  49675516   8142
 4220    1.50  13365191   0.27 -69752  36318388   0.73  77815  49683579   8063
 4230    1.49  13295652   0.27 -69539  36395911   0.73  77524  49691563   7984
 4240    1.47  13226326   0.27 -69325  36473143   0.73  77232  49699470   7907
 4250    1.46  13157216   0.26 -69110  36550083   0.74  76940  49707299   7830
 4260    1.44  13088322   0.26 -68894  36626731   0.74  76648  49715053   7754
 4270    1.43  13019645   0.26 -68677  36703086   0.74  76355  49722732   7678
 4280    1.41  12951187   0.26 -68459  36779149   0.74  76062  49730335   7604
 4290    1.40  12882947   0.26 -68239  36854918   0.74  75769  49737865   7530
 4300    1.39  12814929   0.26 -68019  36930394   0.74  75476  49745322   7457
 4310    1.37  12747131   0.26 -67798  37005576   0.74  75182  49752706   7384
 4320    1.36  12679555   0.25 -67576  37080464   0.75  74888  49760019   7313
 4330    1.35  12612203   0.25 -67352  37155058   0.75  74594  49767261   7242
 4340    1.33  12545074   0.25 -67128  37229357   0.75  74300  49774432   7171
 4350    1.32  12478171   0.25 -66904  37303362   0.75  74005  49781533   7101
 4360    1.31  12411493   0.25 -66678  37377073   0.75  73711  49788566   7032
 4370    1.29  12345041   0.25 -66452  37450489   0.75  73416  49795530   6964
 4380    1.28  12278816   0.25 -66224  37523610   0.75  73121  49802426   6896
 4390    1.27  12212820   0.25 -65997  37596436   0.75  72826  49809256   6829
 4400    1.25  12147052   0.24 -65768  37668967   0.76  72531  49816019   6763
 4410    1.24  12081514   0.24 -65539  37741203   0.76  72236  49822716   6697
 4420    1.23  12016205   0.24 -65308  37813143   0.76  71941  49829348   6632
 4430    1.22  11951127   0.24 -65078  37884789   0.76  71646  49835916   6568
 4440    1.21  11886281   0.24 -64846  37956139   0.76  71350  49842420   6504
 4450    1.19  11821666   0.24 -64615  38027195   0.76  71055  49848861   6441
 4460    1.18  11757284   0.24 -64382  38097955   0.76  70760  49855239   6378
 4470    1.17  11693135   0.23 -64149  38168420   0.77  70465  49861555   6316
 4480    1.16  11629220   0.23 -63915  38238590   0.77  70170  49867810   6255
 4490    1.15  11565538   0.23 -63681  38308466   0.77  69875  49874004   6194
 4500    1.14  11502092   0.23 -63447  38378046   0.77  69581  49880138   6134
 4510    1.12  11438880   0.23 -63212  38447332   0.77  69286  49886212   6074
 4520    1.11  11375904   0.23 -62976  38516324   0.77  68991  49892228   6015
 4530    1.10  11313164   0.23 -62740  38585020   0.77  68697  49898185   5957
 4540    1.09  11250660   0.23 -62504  38653423   0.77  68403  49904083   5899
 4550    1.08  11188393   0.22 -62267  38721532   0.78  68109  49909925   5842
 4560    1.07  11126364   0.22 -62030  38789346   0.78  67815  49915710   5785
 4570    1.06  11064571   0.22 -61792  38856867   0.78  67521  49921438   5729
 4580    1.05  11003017   0.22 -61555  38924095   0.78  67227  49927111   5673
 4590    1.04  10941700   0.22 -61316  38991029   0.78  66934  49932729   5618
 4600    1.03  10880622   0.22 -61078  39057670   0.78  66641  49938292   5563
 4610    1.02  10819783   0.22 -60839  39124019   0.78  66348  49943802   5509
 4620    1.01  10759182   0.22 -60600  39190075   0.78  66056  49949257   5456
 4630    1.00  10698821   0.21 -60361  39255839   0.79  65764  49954660   5403
 4640    0.99  10638699   0.21 -60122  39321311   0.79  65472  49960010   5350
 4650    0.98  10578817   0.21 -59882  39386491   0.79  65180  49965308   5298
 4660    0.97  10519174   0.21 -59643  39451380   0.79  64889  49970554   5247
 4670    0.96  10459772   0.21 -59403  39515978   0.79  64598  49975750   5196
 4680    0.95  10400609   0.21 -59163  39580286   0.79  64308  49980895   5145
 4690    0.94  10341687   0.21 -58922  39644303   0.79  64017  49985990   5095
 4700    0.93  10283005   0.21 -58682  39708031   0.79  63728  49991036   5046
 4710    0.92  10224563   0.20 -58442  39771469   0.80  63438  49996033   4997
 4720    0.91  10166362   0.20 -58201  39834618   0.80  63149  50000981   4948
 4730    0.90  10108402   0.20 -57961  39897479   0.80  62861  50005880   4900
 4740    0.89  10050682   0.20 -57720  39960051   0.80  62572  50010733   4852
 4750    0.89   9993202   0.20 -57479  40022336   0.80  62285  50015538   4805
 4760    0.88   9935964   0.20 -57239  40084333   0.80  61997  50020296   4758
 4770    0.87   9878965   0.20 -56998  40146043   0.80  61710  50025009   4712
 4780    0.86   9822208   0.20 -56757  40207467   0.80  61424  50029675   4666
 4790    0.85   9765691   0.20 -56517  40268605   0.80  61138  50034296   4621
 4800    0.84   9709415   0.19 -56276  40329457   0.81  60852  50038872   4576
 4810    0.83   9653379   0.19 -56036  40390025   0.81  60567  50043404   4532
 4820    0.83   9597584   0.19 -55795  40450308   0.81  60283  50047892   4488
 4830    0.82   9542029   0.19 -55555  40510307   0.81  59999  50052336   4444
 4840    0.81   9486714   0.19 -55315  40570022   0.81  59716  50056736   4401
 4850    0.80   9431640   0.19 -55075  40629455   0.81  59433  50061094   4358
 4860    0.79   9376805   0.19 -54835  40688605   0.81  59150  50065410   4316
 4870    0.79   9322210   0.19 -54595  40747474   0.81  58868  50069684   4274
 4880    0.78   9267855   0.19 -54355  40806061   0.81  58587  50073916   4232
 4890    0.77   9213740   0.18 -54115  40864367   0.82  58307  50078107   4191
 4900    0.76   9159864   0.18 -53876  40922394   0.82  58026  50082258   4150
 4910    0.76   9106227   0.18 -53637  40980141   0.82  57747  50086368   4110
 4920    0.75   9052829   0.18 -53398  41037609   0.82  57468  50090438   4070
 4930    0.74   8999670   0.18 -53159  41094799   0.82  57190  50094468   4031
 4940    0.73   8946749   0.18 -52921  41151711   0.82  56912  50098460   3991
 4950    0.73   8894067   0.18 -52682  41208345   0.82  56635  50102412   3953
 4960    0.72   8841622   0.18 -52444  41264704   0.82  56358  50106326   3914
 4970    0.71   8789416   0.18 -52207  41320787   0.82  56083  50110202   3876
 4980    0.70   8737447   0.17 -51969  41376594   0.83  55807  50114041   3838
 4990    0.70   8685715   0.17 -51732  41432127   0.83  55533  50117842   3801
 5000    0.69   8634220   0.17 -51495  41487386   0.83  55259  50121606   3764
 5010    0.68   8582962   0.17 -51258  41542372   0.83  54986  50125334   3728
 5020    0.68   8531940   0.17 -51022  41597085   0.83  54713  50129025   3691
 5030    0.67   8481154   0.17 -50786  41651526   0.83  54441  50132681   3655
 5040    0.66   8430604   0.17 -50550  41705696   0.83  54170  50136300   3620
 5050    0.66   8380289   0.17 -50315  41759596   0.83  53900  50139885   3585
 5060    0.65   8330209   0.17 -50080  41813226   0.83  53630  50143435   3550
 5070    0.64   8280364   0.17 -49845  41866587   0.83  53361  50146951   3515
 5080    0.64   8230753   0.16 -49611  41919679   0.84  53092  50150432   3481
 5090    0.63   8181375   0.16 -49377  41972504   0.84  52825  50153879   3447
 5100    0.63   8132231   0.16 -49144  42025062   0.84  52558  50157293   3414
 5110    0.62   8083321   0.16 -48911  42077353   0.84  52292  50160674   3381
 5120    0.61   8034642   0.16 -48678  42129379   0.84  52026  50164022   3348
 5130    0.61   7986196   0.16 -48446  42181141   0.84  51761  50167337   3315
 5140    0.60   7937982   0.16 -48214  42232638   0.84  51497  50170620   3283
 5150    0.59   7889999   0.16 -47983  42283872   0.84  51234  50173871   3251
 5160    0.59   7842247   0.16 -47752  42334844   0.84  50972  50177091   3220
 5170    0.58   7794726   0.16 -47521  42385553   0.84  50710  50180279   3188
 5180    0.58   7747434   0.15 -47292  42436002   0.85  50449  50183437   3157
 5190    0.57   7700372   0.15 -47062  42486191   0.85  50189  50186563   3127
 5200    0.57   7653539   0.15 -46833  42536120   0.85  49929  50189659   3096
 5210    0.56   7606935   0.15 -46604  42585791   0.85  49670  50192726   3066
 5220    0.55   7560559   0.15 -46376  42635203   0.85  49413  50195762   3036
 5230    0.55   7514410   0.15 -46149  42684359   0.85  49156  50198769   3007
 5240    0.54   7468488   0.15 -45922  42733258   0.85  48899  50201746   2978
 5250    0.54   7422793   0.15 -45695  42781902   0.85  48644  50204695   2949
 5260    0.53   7377324   0.15 -45469  42830291   0.85  48389  50207615   2920
 5270    0.53   7332081   0.15 -45243  42878426   0.85  48135  50210507   2892
 5280    0.52   7287062   0.15 -45018  42926308   0.85  47882  50213370   2863
 5290    0.52   7242268   0.14 -44794  42973937   0.86  47630  50216206   2836
 5300    0.51   7197698   0.14 -44570  43021316   0.86  47378  50219014   2808
 5310    0.51   7153352   0.14 -44347  43068443   0.86  47128  50221795   2781
 5320    0.50   7109228   0.14 -44124  43115321   0.86  46878  50224548   2754
 5330    0.50   7065326   0.14 -43902  43161950   0.86  46629  50227275   2727
 5340    0.49   7021646   0.14 -43680  43208330   0.86  46381  50229976   2701
 5350    0.49   6978187   0.14 -43459  43254463   0.86  46133  50232650   2674
 5360    0.48   6934948   0.14 -43238  43300350   0.86  45887  50235298   2648
 5370    0.48   6891930   0.14 -43018  43345991   0.86  45641  50237921   2623
 5380    0.47   6849131   0.14 -42799  43391387   0.86  45396  50240518   2597
 5390    0.47   6806550   0.14 -42580  43436539   0.86  45152  50243090   2572
 5400    0.46   6764188   0.13 -42362  43481448   0.87  44909  50245637   2547
 5410    0.46   6722043   0.13 -42145  43526115   0.87  44667  50248159   2522
 5420    0.45   6680116   0.13 -41928  43570540   0.87  44425  50250656   2498
 5430    0.45   6638404   0.13 -41711  43614725   0.87  44185  50253129   2473
 5440    0.45   6596909   0.13 -41496  43658670   0.87  43945  50255578   2449
 5450    0.44   6555628   0.13 -41281  43702376   0.87  43706  50258004   2425
 5460    0.44   6514562   0.13 -41066  43745844   0.87  43468  50260406   2402
 5470    0.43   6473709   0.13 -40852  43789075   0.87  43231  50262784   2378
 5480    0.43   6433070   0.13 -40639  43832069   0.87  42995  50265139   2355
 5490    0.42   6392644   0.13 -40427  43874828   0.87  42759  50267472   2332
 5500    0.42   6352429   0.13 -40215  43917353   0.87  42525  50269782   2310
 5510    0.42   6312425   0.13 -40004  43959644   0.87  42291  50272069   2287
 5520    0.41   6272632   0.12 -39793  44001702   0.88  42058  50274334   2265
 5530    0.41   6233049   0.12 -39583  44043528   0.88  41826  50276577   2243
 5540    0.40   6193676   0.12 -39374  44085123   0.88  41595  50278798   2221
 5550    0.40   6154511   0.12 -39165  44126487   0.88  41365  50280998   2200
 5560    0.40   6115553   0.12 -38957  44167623   0.88  41135  50283176   2178
 5570    0.39   6076804   0.12 -38750  44208530   0.88  40907  50285333   2157
 5580    0.39   6038260   0.12 -38543  44249209   0.88  40679  50287470   2136
 5590    0.38   5999923   0.12 -38337  44289662   0.88  40453  50289585   2115
 5600    0.38   5961791   0.12 -38132  44329889   0.88  40227  50291680   2095
 5610    0.38   5923863   0.12 -37928  44369891   0.88  40002  50293754   2074
 5620    0.37   5886140   0.12 -37724  44409669   0.88  39778  50295808   2054
 5630    0.37   5848619   0.12 -37520  44449223   0.88  39555  50297843   2034
 5640    0.37   5811301   0.12 -37318  44488556   0.88  39332  50299857   2015
 5650    0.36   5774185   0.11 -37116  44527667   0.89  39111  50301852   1995
 5660    0.36   5737270   0.11 -36915  44566557   0.89  38891  50303828   1976
 5670    0.35   5700556   0.11 -36715  44605228   0.89  38671  50305784   1956
 5680    0.35   5664041   0.11 -36515  44643681   0.89  38452  50307721   1937
 5690    0.35   5627725   0.11 -36316  44681915   0.89  38234  50309640   1918
 5700    0.34   5591607   0.11 -36118  44719932   0.89  38017  50311540   1900
 5710    0.34   5555687   0.11 -35920  44757734   0.89  37801  50313421   1881
 5720    0.34   5519964   0.11 -35723  44795320   0.89  37586  50315284   1863
 5730    0.33   5484437   0.11 -35527  44832692   0.89  37372  50317129   1845
 5740    0.33   5449106   0.11 -35331  44869850   0.89  37158  50318956   1827
 5750    0.33   5413969   0.11 -35137  44906796   0.89  36946  50320765   1809
 5760    0.32   5379026   0.11 -34943  44943531   0.89  36734  50322557   1792
 5770    0.32   5344277   0.11 -34749  44980054   0.89  36524  50324331   1774
 5780    0.32   5309720   0.11 -34557  45016368   0.89  36314  50326088   1757
 5790    0.31   5275355   0.10 -34365  45052473   0.90  36105  50327828   1740
 5800    0.31   5241181   0.10 -34174  45088370   0.90  35897  50329551   1723
 5810    0.31   5207198   0.10 -33983  45124059   0.90  35690  50331258   1706
 5820    0.31   5173404   0.10 -33794  45159543   0.90  35483  50332947   1690
 5830    0.30   5139800   0.10 -33605  45194821   0.90  35278  50334620   1673
 5840    0.30   5106383   0.10 -33416  45229894   0.90  35073  50336277   1657
 5850    0.30   5073154   0.10 -33229  45264764   0.90  34870  50337918   1641
 5860    0.29   5040112   0.10 -33042  45299431   0.90  34667  50339543   1625
 5870    0.29   5007256   0.10 -32856  45333896   0.90  34465  50341152   1609
 5880    0.29   4974585   0.10 -32671  45368161   0.90  34264  50342746   1593
 5890    0.28   4942099   0.10 -32486  45402225   0.90  34064  50344324   1578
 5900    0.28   4909797   0.10 -32302  45436090   0.90  33865  50345886   1563
 5910    0.28   4877677   0.10 -32119  45469757   0.90  33667  50347434   1547
 5920    0.28   4845740   0.10 -31937  45503226   0.90  33469  50348966   1532
 5930    0.27   4813985   0.10 -31755  45536499   0.90  33273  50350484   1518
 5940    0.27   4782411   0.09 -31574  45569576   0.91  33077  50351987   1503
 5950    0.27   4751016   0.09 -31394  45602458   0.91  32882  50353475   1488
 5960    0.27   4719802   0.09 -31215  45635147   0.91  32688  50354948   1474
 5970    0.26   4688766   0.09 -31036  45667642   0.91  32495  50356408   1459
 5980    0.26   4657907   0.09 -30858  45699946   0.91  32303  50357853   1445
 5990    0.26   4627226   0.09 -30681  45732058   0.91  32112  50359284   1431
 6000    0.26   4596722   0.09 -30504  45763979   0.91  31922  50360701   1417
 6010    0.25   4566393   0.09 -30329  45795711   0.91  31732  50362105   1403
 6020    0.25   4536239   0.09 -30154  45827255   0.91  31544  50363494   1390
 6030    0.25   4506260   0.09 -29980  45858611   0.91  31356  50364871   1376
 6040    0.25   4476454   0.09 -29806  45889780   0.91  31169  50366234   1363
 6050    0.24   4446821   0.09 -29633  45920763   0.91  30983  50367583   1350
 6060    0.24   4417359   0.09 -29461  45951560   0.91  30798  50368920   1337
 6070    0.24   4388070   0.09 -29290  45982174   0.91  30613  50370243   1324
 6080    0.24   4358950   0.09 -29119  46012604   0.91  30430  50371554   1311
 6090    0.23   4330001   0.09 -28950  46042851   0.91  30247  50372852   1298
 6100    0.23   4301220   0.09 -28780  46072917   0.91  30066  50374137   1285
 6110    0.23   4272608   0.08 -28612  46102802   0.92  29885  50375410   1273
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 8300    0.03    892043   0.02  -6751  49597728   0.98   6900  50489771    150
 8310    0.03    885341   0.02  -6703  49604578   0.98   6851  50489919    148
 8320    0.03    878686   0.02  -6655  49611380   0.98   6802  50490066    147
 8330    0.03    872079   0.02  -6607  49618133   0.98   6753  50490211    145
 8340    0.02    865519   0.02  -6560  49624837   0.98   6704  50490355    144
 8350    0.02    859005   0.02  -6513  49631492   0.98   6656  50490498    143
 8360    0.02    852539   0.02  -6467  49638100   0.98   6608  50490639    141
 8370    0.02    846118   0.02  -6420  49644660   0.98   6560  50490779    140
 8380    0.02    839744   0.02  -6374  49651173   0.98   6513  50490917    138
 8390    0.02    833415   0.02  -6329  49657639   0.98   6466  50491054    137
 8400    0.02    827132   0.02  -6283  49664058   0.98   6419  50491190    136
 8410    0.02    820893   0.02  -6238  49670431   0.98   6373  50491324    134
 8420    0.02    814700   0.02  -6194  49676758   0.98   6327  50491457    133
 8430    0.02    808550   0.02  -6149  49683039   0.98   6281  50491589    132
 8440    0.02    802445   0.02  -6105  49689274   0.98   6236  50491720    131
 8450    0.02    796384   0.02  -6061  49695465   0.98   6190  50491849    129
 8460    0.02    790366   0.02  -6018  49701610   0.98   6146  50491977    128
 8470    0.02    784392   0.02  -5974  49707712   0.98   6101  50492104    127
 8480    0.02    778461   0.02  -5931  49713768   0.98   6057  50492229    126
 8490    0.02    772572   0.02  -5889  49719781   0.98   6013  50492354    124
 8500    0.02    766726   0.02  -5846  49725751   0.98   5969  50492477    123
 8510    0.02    760922   0.02  -5804  49731677   0.98   5926  50492599    122
 8520    0.02    755160   0.01  -5762  49737560   0.99   5883  50492719    121
 8530    0.02    749439   0.01  -5721  49743400   0.99   5840  50492839    120
 8540    0.02    743760   0.01  -5679  49749198   0.99   5798  50492957    118
 8550    0.02    738121   0.01  -5638  49754953   0.99   5756  50493074    117
 8560    0.02    732524   0.01  -5598  49760667   0.99   5714  50493190    116
 8570    0.02    726966   0.01  -5557  49766339   0.99   5672  50493305    115
 8580    0.02    721449   0.01  -5517  49771970   0.99   5631  50493419    114
 8590    0.02    715972   0.01  -5477  49777560   0.99   5590  50493532    113
 8600    0.02    710535   0.01  -5437  49783109   0.99   5549  50493644    112
 8610    0.02    705137   0.01  -5398  49788617   0.99   5509  50493754    111
 8620    0.02    699778   0.01  -5359  49794085   0.99   5468  50493864    109
 8630    0.02    694458   0.01  -5320  49799514   0.99   5428  50493972    108
 8640    0.02    689177   0.01  -5281  49804903   0.99   5389  50494079    107
 8650    0.02    683934   0.01  -5243  49810252   0.99   5349  50494186    106
 8660    0.02    678729   0.01  -5205  49815562   0.99   5310  50494291    105
 8670    0.02    673561   0.01  -5167  49820834   0.99   5271  50494395    104
 8680    0.02    668432   0.01  -5130  49826067   0.99   5233  50494498    103
 8690    0.02    663339   0.01  -5092  49831261   0.99   5195  50494601    102
 8700    0.02    658284   0.01  -5055  49836418   0.99   5157  50494702    101
 8710    0.02    653266   0.01  -5018  49841536   0.99   5119  50494802    100
 8720    0.02    648284   0.01  -4982  49846618   0.99   5081  50494901     99
 8730    0.02    643338   0.01  -4946  49851662   0.99   5044  50495000     98
 8740    0.02    638428   0.01  -4910  49856669   0.99   5007  50495097     97
 8750    0.02    633555   0.01  -4874  49861639   0.99   4970  50495193     96
 8760    0.02    628716   0.01  -4838  49866572   0.99   4934  50495289     95
 8770    0.02    623914   0.01  -4803  49871470   0.99   4897  50495383     95
 8780    0.02    619146   0.01  -4768  49876331   0.99   4861  50495477     94
 8790    0.02    614413   0.01  -4733  49881157   0.99   4826  50495570     93
 8800    0.02    609714   0.01  -4698  49885947   0.99   4790  50495661     92
 8810    0.02    605050   0.01  -4664  49890702   0.99   4755  50495752     91
 8820    0.02    600420   0.01  -4630  49895422   0.99   4720  50495842     90
 8830    0.02    595825   0.01  -4596  49900107   0.99   4685  50495931     89
 8840    0.02    591262   0.01  -4562  49904758   0.99   4651  50496020     88
 8850    0.01    586733   0.01  -4529  49909374   0.99   4616  50496107     87
 8860    0.01    582238   0.01  -4496  49913956   0.99   4582  50496194     87
 8870    0.01    577775   0.01  -4463  49918504   0.99   4548  50496279     86
 8880    0.01    573345   0.01  -4430  49923019   0.99   4515  50496364     85
 8890    0.01    568948   0.01  -4397  49927501   0.99   4481  50496448     84
 8900    0.01    564582   0.01  -4365  49931949   0.99   4448  50496532     83
 8910    0.01    560249   0.01  -4333  49936365   0.99   4415  50496614     82
 8920    0.01    555948   0.01  -4301  49940748   0.99   4383  50496696     82
 8930    0.01    551679   0.01  -4270  49945098   0.99   4350  50496777     81
 8940    0.01    547440   0.01  -4238  49949416   0.99   4318  50496857     80
 8950    0.01    543233   0.01  -4207  49953702   0.99   4286  50496936     79
 8960    0.01    539058   0.01  -4176  49957957   0.99   4254  50497014     79
 8970    0.01    534912   0.01  -4145  49962180   0.99   4223  50497092     78
 8980    0.01    530798   0.01  -4115  49966371   0.99   4192  50497169     77
 8990    0.01    526713   0.01  -4084  49970532   0.99   4161  50497245     76
 9000    0.01    522659   0.01  -4054  49974662   0.99   4130  50497321     75
 9010    0.01    518635   0.01  -4024  49978761   0.99   4099  50497396     75
 9020    0.01    514640   0.01  -3995  49982829   0.99   4069  50497470     74
 9030    0.01    510675   0.01  -3965  49986867   0.99   4038  50497543     73
 9040    0.01    506740   0.01  -3936  49990876   0.99   4008  50497615     73
 9050    0.01    502833   0.01  -3907  49994854   0.99   3978  50497687     72
 9060    0.01    498955   0.01  -3878  49998803   0.99   3949  50497759     71
 9070    0.01    495106   0.01  -3849  50002723   0.99   3920  50497829     70
 9080    0.01    491286   0.01  -3821  50006613   0.99   3890  50497899     70
 9090    0.01    487494   0.01  -3792  50010474   0.99   3861  50497968     69
 9100    0.01    483730   0.01  -3764  50014307   0.99   3833  50498036     68
 9110    0.01    479993   0.01  -3736  50018111   0.99   3804  50498104     68
 9120    0.01    476285   0.01  -3708  50021886   0.99   3776  50498171     67
 9130    0.01    472604   0.01  -3681  50025634   0.99   3747  50498238     66
 9140    0.01    468950   0.01  -3654  50029353   0.99   3719  50498304     66
 9150    0.01    465324   0.01  -3627  50033045   0.99   3692  50498369     65
 9160    0.01    461724   0.01  -3600  50036709   0.99   3664  50498433     65
 9170    0.01    458151   0.01  -3573  50040346   0.99   3637  50498497     64
 9180    0.01    454605   0.01  -3546  50043956   0.99   3610  50498561     63
 9190    0.01    451085   0.01  -3520  50047538   0.99   3583  50498623     63
 9200    0.01    447591   0.01  -3494  50051094   0.99   3556  50498685     62
 9210    0.01    444124   0.01  -3468  50054623   0.99   3529  50498747     61
 9220    0.01    440682   0.01  -3442  50058126   0.99   3503  50498808     61
 9230    0.01    437266   0.01  -3416  50061602   0.99   3476  50498868     60
 9240    0.01    433875   0.01  -3391  50065053   0.99   3450  50498928     60
 9250    0.01    430509   0.01  -3365  50068477   0.99   3425  50498987     59
 9260    0.01    427169   0.01  -3340  50071876   0.99   3399  50499045     59
 9270    0.01    423854   0.01  -3315  50075250   0.99   3373  50499103     58
 9280    0.01    420563   0.01  -3291  50078598   0.99   3348  50499161     57
 9290    0.01    417297   0.01  -3266  50081921   0.99   3323  50499218     57
 9300    0.01    414055   0.01  -3242  50085219   0.99   3298  50499274     56
 9310    0.01    410838   0.01  -3217  50088492   0.99   3273  50499330     56
 9320    0.01    407644   0.01  -3193  50091740   0.99   3249  50499385     55
 9330    0.01    404475   0.01  -3170  50094965   0.99   3224  50499440     55
 9340    0.01    401329   0.01  -3146  50098165   0.99   3200  50499494     54
 9350    0.01    398207   0.01  -3122  50101340   0.99   3176  50499547     54
 9360    0.01    395108   0.01  -3099  50104492   0.99   3152  50499600     53
 9370    0.01    392032   0.01  -3076  50107621   0.99   3128  50499653     53
 9380    0.01    388980   0.01  -3053  50110725   0.99   3105  50499705     52
 9390    0.01    385950   0.01  -3030  50113806   0.99   3081  50499757     52
 9400    0.01    382943   0.01  -3007  50116864   0.99   3058  50499808     51
 9410    0.01    379959   0.01  -2984  50119899   0.99   3035  50499858     51
 9420    0.01    376997   0.01  -2962  50122911   0.99   3012  50499908     50
 9430    0.01    374057   0.01  -2940  50125901   0.99   2989  50499958     50
 9440    0.01    371139   0.01  -2918  50128867   0.99   2967  50500007     49
 9450    0.01    368244   0.01  -2896  50131812   0.99   2944  50500055     49
 9460    0.01    365370   0.01  -2874  50134734   0.99   2922  50500104     48
 9470    0.01    362518   0.01  -2852  50137634   0.99   2900  50500151     48
 9480    0.01    359687   0.01  -2831  50140512   0.99   2878  50500198     47
 9490    0.01    356877   0.01  -2810  50143368   0.99   2856  50500245     47
 9500    0.01    354089   0.01  -2788  50146203   0.99   2835  50500292     46
 9510    0.01    351321   0.01  -2767  50149016   0.99   2813  50500337     46
 9520    0.01    348575   0.01  -2747  50151808   0.99   2792  50500383     45
 9530    0.01    345849   0.01  -2726  50154579   0.99   2771  50500428     45
 9540    0.01    343144   0.01  -2705  50157328   0.99   2750  50500472     45
 9550    0.01    340459   0.01  -2685  50160057   0.99   2729  50500516     44
 9560    0.01    337794   0.01  -2665  50162766   0.99   2708  50500560     44
 9570    0.01    335150   0.01  -2644  50165453   0.99   2688  50500603     43
 9580    0.01    332525   0.01  -2624  50168120   0.99   2667  50500646     43
 9590    0.01    329921   0.01  -2605  50170768   0.99   2647  50500688     42
 9600    0.01    327336   0.01  -2585  50173394   0.99   2627  50500730     42
 9610    0.01    324771   0.01  -2565  50176001   0.99   2607  50500772     42
 9620    0.01    322225   0.01  -2546  50178589   0.99   2587  50500813     41
 9630    0.01    319698   0.01  -2527  50181156   0.99   2567  50500854     41
 9640    0.01    317190   0.01  -2508  50183704   0.99   2548  50500894     40
 9650    0.01    314702   0.01  -2489  50186233   0.99   2529  50500934     40
 9660    0.01    312232   0.01  -2470  50188742   0.99   2509  50500974     40
 9670    0.01    309781   0.01  -2451  50191232   0.99   2490  50501013     39
 9680    0.01    307348   0.01  -2432  50193703   0.99   2471  50501052     39
 9690    0.01    304934   0.01  -2414  50196156   0.99   2452  50501090     38
 9700    0.01    302539   0.01  -2396  50198590   0.99   2434  50501128     38
 9710    0.01    300161   0.01  -2377  50201005   0.99   2415  50501166     38
 9720    0.01    297802   0.01  -2359  50203402   0.99   2397  50501203     37
 9730    0.01    295460   0.01  -2342  50205780   0.99   2378  50501240     37
 9740    0.01    293136   0.01  -2324  50208140   0.99   2360  50501277     37
 9750    0.01    290830   0.01  -2306  50210483   0.99   2342  50501313     36
 9760    0.01    288542   0.01  -2289  50212807   0.99   2324  50501349     36
 9770    0.01    286271   0.01  -2271  50215114   0.99   2307  50501385     36
 9780    0.01    284017   0.01  -2254  50217403   0.99   2289  50501420     35
 9790    0.01    281780   0.01  -2237  50219674   0.99   2272  50501455     35
 9800    0.01    279561   0.01  -2220  50221929   0.99   2254  50501489     35
 9810    0.01    277358   0.01  -2203  50224166   0.99   2237  50501523     34
 9820    0.01    275172   0.01  -2186  50226385   0.99   2220  50501557     34
 9830    0.01    273002   0.01  -2169  50228588   0.99   2203  50501591     34
 9840    0.01    270850   0.01  -2153  50230774   0.99   2186  50501624     33
 9850    0.01    268713   0.01  -2136  50232943   0.99   2169  50501657     33
 9860    0.01    266593   0.01  -2120  50235096   0.99   2153  50501689     33
 9870    0.01    264489   0.01  -2104  50237232   0.99   2136  50501722     32
 9880    0.01    262402   0.01  -2088  50239352   0.99   2120  50501754     32
 9890    0.01    260330   0.01  -2072  50241455   0.99   2103  50501785     32
 9900    0.01    258274   0.01  -2056  50243543   0.99   2087  50501816     31
 9910    0.01    256233   0.01  -2040  50245614   0.99   2071  50501847     31
 9920    0.01    254209   0.01  -2025  50247669   0.99   2055  50501878     31
 9930    0.01    252200   0.00  -2009  50249709   1.00   2040  50501909     30
 9940    0.01    250206   0.00  -1994  50251733   1.00   2024  50501939     30
 9950    0.01    248227   0.00  -1979  50253741   1.00   2008  50501968     30
 9960    0.00    246264   0.00  -1963  50255734   1.00   1993  50501998     30
 9970    0.00    244315   0.00  -1948  50257712   1.00   1978  50502027     29
 9980    0.00    242382   0.00  -1933  50259674   1.00   1962  50502056     29
 9990    0.00    240463   0.00  -1919  50261622   1.00   1947  50502085     29
10000    0.00    238559   0.00  -1904  50263554   1.00   1932  50502113     28

Note the “magic velocity” of 1000, the same as the exhaust velocity, where all of the rocket’s power contributes to its kinetic energy, none to the exhaust’s. From the point of view of the observation point, the exhaust at this moment appears to be stationary.