Generator points of E(Q)/2E(Q) on E : y^2=x^3+(n^2-6n-3)x^2+16nx (-500 <= n <= -1)
(using Cremona's mwrank.exe)

This curve is birationally equivalent to

  (x+y+z)(1/x+1/y+1/z)=n

Ranks of some of the curve are not completely determined yet.
("x" in front of "n")

   n |rank| (xp, yp, zp), height
-----+---+----------------------------------------------------------------------
  -1 | 0 |
  -2 | 0 |
  -3 | 0 |
  -4 | 1 | (64, -640, 1), 1.1705
  -5 | 0 |
  -6 | 0 |
  -7 | 0 |
  -8 | 0 |
  -9 | 0 |
 -10 | 1 | (-8, -104, 1), 1.58
 -11 | 1 | (100, -1680, 1), 1.8679
 -12 | 1 | (48, -496, 27), 2.9355
 -13 | 0 |
 -14 | 0 |
 -15 | 0 |
 -16 | 0 |
 -17 | 0 |
 -18 | 1 | (-6, -171, 8), 1.0649
 -19 | 1 | (484, -14960, 1), 2.9608
 -20 | 1 | (144, -3696, 1), 2.0019
 -21 | 0 |
 -22 | 1 | (896, 19648, 343), 5.4893
 -23 | 0 |
 -24 | 0 |
 -25 | 1 | (2500, -143000, 1), 2.712
 -26 | 0 |
 -27 | 0 |
 -28 | 2 | (-16, -496, 1), 2.1368
     |   | (12288, -460288, 27), 4.2539
 -29 | 1 | (242, -7755, 8), 4.1382
 -30 | 1 | (-756, -27180, 343), 5.4912
 -31 | 1 | (196, -7168, 1), 1.9552
 -32 | 1 | (5780, -204204, 125), 4.3495
 -33 | 0 |
 -34 | 0 |
 -35 | 0 |
 -36 | 1 | (18928, 746096, 343), 6.8257
 -37 | 0 |
 -38 | 0 |
 -39 | 1 | (64, -2720, 1), 2.6836
 -40 | 1 | (32, 1376, 1), 2.3439
 -41 | 0 |
 -42 | 1 | (-32856, -927368, 27), 7.6639
 -43 | 1 | (1887876, 129335536, 729), 8.4583
 -44 | 1 | (256, -12672, 1), 2.5563
 -45 | 0 |
 -46 | 0 |
 -47 | 0 |
 -48 | 1 | (704, -23744, 1331), 3.831
 -49 | 0 |
 -50 | 1 | (89100, -4758300, 1331), 5.2143
 -51 | 1 | (7396, -750608, 1), 6.6564
 -52 | 2 | (-1, -62, 1), 3.6863
     |   | (67280, -4008496, 125), 5.2029
 -53 | 0 |
 -54 | 1 | (36, -2052, 1), 1.9724
 -55 | 0 |
 -56 | 1 | (2268, -131076, 343), 6.7702
 -57 | 0 |
 -58 | 1 | (-2052855000, -117940167800, 5000211), 15.0715
 -59 | 2 | (1444, -104880, 1), 3.4165
     |   | (3364, -285360, 1), 4.1437
x -60 | 0-2 |
 -61 | 1 | (28938650, 2190541865, 17576), 14.1665
 -62 | 0 |
 -63 | 0 |
 -64 | 0 |
 -65 | 0 |
 -66 | 0 |
 -67 | 1 | (16428, -1217744, 27), 4.8959
 -68 | 0 |
 -69 | 1 | (3468, -252280, 27), 3.8419
 -70 | 2 | (648, 50040, 1), 5.2289
     |   | (10, 665, 8), 4.4589
 -71 | 0 |
 -72 | 1 | (-84, -8532, 343), 4.5198
x -73 | 0-2 |
 -74 | 0 |
 -75 | 0 |
 -76 | 2 | (18845008, -2293095056, 2197), 12.1983
     |   | (400, -32560, 1), 2.9726
 -77 | 0 |
 -78 | 1 | (-12990877176, -1063298090184, 1647212741), 13.5095
 -79 | 0 |
 -80 | 0 |
 -81 | 0 |
 -82 | 0 |
 -83 | 0 |
 -84 | 1 | (236992, -21520640, 343), 5.9326
 -85 | 1 | (-60, -5480, 27), 3.6766
 -86 | 1 | (96160712, 42542055789, 512), 13.331
 -87 | 0 |
x -88 |   |
 -89 | 1 | (100, -9240, 1), 2.1175
 -90 | 0 |
 -91 | 1 | (-7, -665, 1), 2.833
 -92 | 1 | (66660617744, -10537038516432, 4173281), 14.8107
 -93 | 0 |
 -94 | 0 |
 -95 | 1 | (484, -48576, 1), 2.8587
 -96 | 1 | (35208152148, 3448011074516, 4716275733), 18.125
 -97 | 0 |
 -98 | 0 |
 -99 | 0 |
 -100 | 1 | (10543167251152, -1079242332937648, 861985991413), 18.0515
 -101 | 2 | (38332, -4002216, 343), 7.3004
      |   | (12, -1016, 27), 4.229
 -102 | 1 | (-1507038, -157673121, 17576), 8.7197
 -103 | 2 | (12996, -1372256, 729), 6.5157
      |   | (20, -608, 125), 3.9891
 -104 | 1 | (7396, -1014972, 1), 5.6478
 -105 | 1 | (-518940, -30892275, 64), 10.474
 -106 | 0 |
 -107 | 1 | (345845, -42150747, 125), 10.4792
 -108 | 2 | (-36, -3996, 1), 2.3914
      |   | (646912, -77072512, 343), 9.7474
 -109 | 1 | (1682, -189805, 8), 5.1226
 -110 | 0 |
 -111 | 0 |
 -112 | 1 | (-300352, -34362944, 2197), 7.3188
 -113 | 1 | (66631303840, -11485214672793, 4096000), 19.208
 -114 | 0 |
 -115 | 2 | (180, 21360, 1), 3.1112
      |   | (153228, -21444688, 27), 6.497
 -116 | 1 | (400, -48240, 1), 3.3058
 -117 | 0 |
x -118 | 0-2 |
 -119 | 0 |
 -120 | 1 | (-18816, -2259712, 27), 6.9995
 -121 | 0 |
 -122 | 2 | (-128, -15936, 1), 3.7059
      |   | (1469412, -185318196, 4913), 8.4918
 -123 | 1 | (16820, -2126512, 125), 7.1159
 -124 | 1 | (646416, -84286000, 729), 6.5227
 -125 | 1 | (3364, -472584, 1), 4.3818
 -126 | 0 |
 -127 | 1 | (42284, -5489728, 1331), 6.9686
 -128 | 1 | (1862295186089404, 262639143582600444, 679383257671), 24.3311
 -129 | 1 | (2116, -295688, 1), 6.2389
 -130 | 2 | (-682328, -90517000, 6859), 10.2223
      |   | (79380, 24730020, 1), 9.1193
 -131 | 1 | (1764, -247632, 1), 4.0449
 -132 | 1 | (93104, -12578608, 1331), 5.3424
 -133 | 1 | (-473458614804, -70575730626744, 831379493827), 16.8258
 -134 | 1 | (104188, -14381604, 343), 7.0542
 -135 | 1 | (252, -31968, 343), 3.4768
x -136 | 0-2 |
 -137 | 1 | (29877156, 7353162008, 729), 11.1328
 -138 | 1 | (-5595450, -747174345, 2744), 9.4977
 -139 | 2 | (98283, -15159655, 27), 8.3669
      |   | (43732, -6193936, 2197), 6.8294
x -140 | 0-2 |
 -141 | 1 | (3950628, 608081160, 1331), 9.9179
 -142 | 0 |
 -143 | 1 | (7220, -1054272, 125), 4.6723
 -144 | 0 |
 -145 | 0 |
 -146 | 1 | (2692868, 406014924, 4913), 9.0976
 -147 | 1 | (3, -109, 27), 6.0869
 -148 | 2 | (-714420, -93351636, 125), 10.713
      |   | (1684108617040, 301855601429936, 180362125), 16.6004
 -149 | 1 | (1596587436, 280497978360, 205379), 14.1524
 -150 | 0 |
 -151 | 1 | (9409, -1712147, 1), 7.3904
 -152 | 1 | (30260236, 5101718292, 6859), 9.872
 -153 | 1 | (612, -41832, 4913), 5.3528
 -154 | 1 | (56, 8792, 1), 3.1582
 -155 | 1 | (14558408, 3363789507, 512), 12.0638
 -156 | 1 | (73721480348594190000, -11853428056711568477200, 125464824978676659), 31.4178
 -157 | 0 |
 -158 | 0 |
 -159 | 0 |
 -160 | 0 |
 -161 | 0 |
 -162 | 0 |
 -163 | 1 | (547118270465858, 90730317458383933, 16190436763592), 25.928
 -164 | 2 | (23104, -5216640, 1), 4.6816
      |   | (2088968, -373431135, 512), 9.4398
 -165 | 1 | (-7535360, -595395520, 343), 8.7862
 -166 | 1 | (9226822472, 742013097400, 76711450249), 14.7364
 -167 | 1 | (144, -24528, 1), 3.737
 -168 | 1 | (1332396, 224727516, 389017), 11.4
 -169 | 1 | (114244, -43324840, 1), 4.3019
 -170 | 1 | (-577368, -99148536, 1331), 8.1903
 -171 | 1 | (637, 91931, 2197), 9.2688
 -172 | 2 | (-505141, -90146602, 226981), 12.8684
      |   | (1489664, -265351552, 1331), 7.0172
 -173 | 0 |
 -174 | 0 |
 -175 | 0 |
 -176 | 0 |
 -177 | 0 |
x -178 | 0-2 |
 -179 | 0 |
 -180 | 2 | (-48, -8784, 1), 2.4303
      |   | (9851472, -1807327152, 50653), 10.68
 -181 | 2 | (68644, -21975512, 1), 7.633
      |   | (96100, -34641880, 1), 6.658
 -182 | 1 | (-59763816, -11091733352, 5000211), 12.8455
 -183 | 1 | (3288781467972, 613448307261152, 14832537993), 19.3899
x -184 | 0-2 |
 -185 | 0 |
 -186 | 1 | (17956, -4159628, 1), 5.0882
 -187 | 0 |
 -188 | 1 | (671744, -127755264, 68921), 8.2791
 -189 | 0 |
 -190 | 2 | (47432, 8173880, 117649), 10.3218
      |   | (39690, 8153145, 8), 9.471
 -191 | 1 | (676, -132288, 1), 3.4179
 -192 | 1 | (755318954936765891431092060, -230224801955810996475855818468, 13759843824727599693375), 43.5834
x -193 | 0-2 |
 -194 | 0 |
 -195 | 0 |
 -196 | 1 | (2888693392, 460801009904, 13027640977), 17.626
 -197 | 1 | (81559363396, 69838399738008, 117649), 16.145
 -198 | 1 | (2213072169408306405000, 570164413294608578897400, 85161350807660681), 29.9312
 -199 | 2 | (33708, -6911200, 27), 5.1578
      |   | (37004, -7465760, 1331), 6.3687
 -200 | 0 |
 -201 | 1 | (583182762516898820, 36150970000491755224, 6847580693068258625), 28.0388
 -202 | 0 |
 -203 | 1 | (99304336460, -152507671354704, 42875), 18.7255
 -204 | 1 | (799071495376, 214618969621232, 27270901), 17.2749
 -205 | 1 | (-878140, -187079240, 571787), 10.7838
 -206 | 1 | (2018068, 426113364, 2197), 8.4224
 -207 | 0 |
 -208 | 2 | (4762880, 1368961024, 125), 11.1037
      |   | (12544, -2996224, 1), 3.3434
 -209 | 1 | (492804, -361375560, 1), 8.9003
 -210 | 2 | (-24, -5320, 27), 4.9994
      |   | (-9444708, -2017115316, 753571), 12.4664
x -211 | 0-2 |
x -212 | 0-2 |
x -213 | 0-2 |
 -214 | 0 |
 -215 | 0 |
 -216 | 0 |
 -217 | 1 | (7266381077817368, -1587046662621027401, 1444736517166592), 28.3257
x -218 | 0-2 |
 -219 | 0 |
 -220 | 2 | (-20, -5356, 125), 4.3821
      |   | (1024, -230656, 1), 3.8215
 -221 | 1 | (146068, -32719656, 2197), 8.7217
 -222 | 2 | (-4848120, -527268024, 125), 11.5367
      |   | (56316, -12192452, 59319), 10.5089
 -223 | 2 | (6724, -1616384, 1), 4.0752
      |   | (27380, -6199424, 125), 5.0514
 -224 | 0 |
 -225 | 1 | (47315196432523342567500, -9163814909479781492143000, 190074096188717948450307), 33.4125
 -226 | 0 |
 -227 | 0 |
 -228 | 2 | (-7884, -3808476, 389017), 10.7795
      |   | (240, -10864, 3375), 7.4425
 -229 | 0 |
 -230 | 0 |
 -231 | 1 | (19808800284, 4647433035232, 63521199), 16.087
x -232 | 1-3 | (-39200, -4960480, 1), 8.1947
 -233 | 0 |
 -234 | 1 | (120, 27432, 125), 4.1691
x -235 | 0-2 |
 -236 | 0 |
 -237 | 1 | (461216220140, -113877920252824, 136590875), 18.0165
 -238 | 1 | (-56, -13496, 1), 3.4267
 -239 | 1 | (20164, -5657280, 1), 4.8466
x -240 | 0-2 |
 -241 | 0 |
 -242 | 0 |
 -243 | 1 | (711957765660, -10342052331106672, 3375), 19.5322
 -244 | 0 |
 -245 | 0 |
 -246 | 1 | (97468, -24320036, 343), 7.8301
 -247 | 0 |
x -248 | 0-2 |
 -249 | 0 |
 -250 | 0 |
 -251 | 1 | (1156, -296208, 1), 4.16
 -252 | 1 | (60212939664, 16204698701488, 8120601), 14.1416
 -253 | 1 | (13162170022293820, 2389900835439375544, 105854023288566125), 24.0466
 -254 | 1 | (2215779934159116, 570197704005948660, 10851105871619), 24.4115
 -255 | 0 |
 -256 | 0 |
 -257 | 0 |
 -258 | 0 |
 -259 | 1 | (525532, -139202960, 343), 6.9415
x -260 | 0-2 |
 -261 | 0 |
 -262 | 1 | (2267523400, 180539053640, 34550415593), 14.9114
 -263 | 1 | (49284, -17074464, 1), 6.557
 -264 | 1 | (616340609436, 162943910373572, 202365391311), 20.986
 -265 | 0 |
 -266 | 1 | (-207576, -55984760, 19683), 9.5203
 -267 | 1 | (27911161431296892, -7566286809360937456, 46063660590423), 23.4035
 -268 | 2 | (-13328, -3650192, 4913), 8.5837
      |   | (20121304147330928, -28509837617160780592, 10403062487), 24.0473
 -269 | 1 | (1420794788, 856213500744, 4913), 14.712
 -270 | 2 | (72, 19656, 1), 2.9555
      |   | (-4024566, -1106009073, 941192), 12.6701
 -271 | 1 | (1369, -378473, 1), 8.087
 -272 | 0 |
 -273 | 1 | (7961898700, 283983337960, 136511322949), 15.1271
 -274 | 0 |
 -275 | 0 |
 -276 | 1 | (1223117085621202180382656, -325260864659845453335484672, 1969842675630924992704591), 36.0729
 -277 | 1 | (1992758, -557624389, 54872), 13.2954
 -278 | 1 | (226286201448, 63587572511373, 3036027392), 20.9276
 -279 | 1 | (196, -55328, 1), 4.1191
 -280 | 1 | (2847520, 812265440, 2197), 8.548
x -281 | 0-2 |
x -282 |   |
 -283 | 1 | (169983713940, 50747005808848, 23149125), 15.4885
 -284 | 2 | (898704, -890153040, 1), 8.6038
      |   | (192892, -55541940, 343), 6.2659
 -285 | 0 |
 -286 | 0 |
 -287 | 1 | (131044, -60781248, 1), 7.0892
 -288 | 1 | (224238003048, 65408055397803, 527514112), 17.293
 -289 | 0 |
 -290 | 0 |
x -291 | 0-2 |
 -292 | 1 | (272, -13936, 4913), 7.8153
 -293 | 1 | (586762348, 180836474952, 79507), 12.672
x -294 | 0-2 |
 -295 | 1 | (140645060054750524, -41305917090637737824, 75703608616538791), 27.9037
 -296 | 1 | (16904683652, -6395949503361, 314432), 15.6698
 -297 | 0 |
 -298 | 0 |
 -299 | 0 |
 -300 | 0 |
 -301 | 0 |
 -302 | 0 |
x -303 | 0-2 |
 -304 | 1 | (-64, -19648, 1), 3.5783
 -305 | 0 |
 -306 | 0 |
 -307 | 0 |
x -308 |   |
 -309 | 1 | (145906913729252, 45653896901903641, 251000770112), 22.8043
 -310 | 1 | (45017098820, 12149404554500, 227987153029), 15.8687
 -311 | 1 | (2, -561, 8), 5.1498
 -312 | 1 | (303314132804490247348, -79511150113147111030669, 1852884881832938635072), 33.2399
x -313 | 0-1 |
 -314 | 2 | (62500, -25231500, 1), 6.8411
      |   | (31684, -11518380, 1), 6.6476
 -315 | 1 | (-32448, -8502624, 1), 7.5113
 -316 | 2 | (-196, -62468, 1), 5.5773
      |   | (165888975155200, 54791284297387520, 22593183283), 19.3507
 -317 | 1 | (1959380, -673247976, 125), 7.9723
 -318 | 0 |
 -319 | 1 | (1444, -468160, 1), 3.8362
x -320 | 0-2 |
 -321 | 0 |
 -322 | 1 | (-83824200, -37655357480, 1564936281), 16.7512
 -323 | 0 |
 -324 | 1 | (300304, -191635600, 1), 6.7141
 -325 | 0 |
 -326 | 1 | (2554428174821968055446768136343287896, 902399088043295938151055986291293980603, 154160100685588614025425943320064), 55.5855
 -327 | 2 | (1182558238400, -481448219437024, 20796875), 18.4663
      |   | (10894232580, -3747018863456, 1157625), 15.9434
 -328 | 2 | (542944, 178883936, 103823), 9.3192
      |   | (956484, -316238419, 46656), 9.1768
 -329 | 1 | (49284, -19682520, 1), 5.1661
x -330 | 0-2 |
x -331 | 0-2 |
 -332 | 0 |
 -333 | 0 |
 -334 | 0 |
 -335 | 0 |
 -336 | 1 | (2544709374846253422677810104472, 866168547813136621789209767221769, 2663860337688680312405898752), 46.1738
x -337 | 0-2 |
x -338 | 0-2 |
 -339 | 2 | (1859, -625105, 1331), 8.673
      |   | (114244, -54931760, 1), 6.4642
 -340 | 2 | (80, 27440, 1), 3.6477
      |   | (35344, -13824016, 1), 6.3159
 -341 | 0 |
 -342 | 1 | (-588, -202356, 1), 4.8946
 -343 | 1 | (2548, -863968, 2197), 4.4968
 -344 | 1 | (8145316, 4053614685, 64), 12.8059
 -345 | 1 | (92080661167288260130860, 17859016807494222698451000, 1392479442125088453157861), 34.7195
 -346 | 0 |
x -347 | 0-2 |
x -348 | 0-1 |
 -349 | 1 | (62669648092, 24632162282120, 2048383), 17.066
 -350 | 0 |
 -351 | 1 | (7396, -2694208, 1), 4.5291
 -352 | 1 | (-2368456000000, -18623872259584000, 25949321221297193), 21.0126
 -353 | 1 | (3505087579820902965910248, -249090505004065964604920693, 75509412349333585583135232), 41.33
 -354 | 1 | (384, 137280, 1), 2.8627
 -355 | 1 | (49650919688535172, -17351916940284992653, 52604544192781888), 30.5437
 -356 | 3 | (258064, -160525968, 1), 7.8094
      |   | (4415349712, -2052247266384, 50653), 14.6076
      |   | (84872, -30483159, 512), 7.1826
 -357 | 1 | (2558312474976435012, 913595637245870112744, 924497180235202211), 26.8519
x -358 | 0-1 |
 -359 | 1 | (12100, -4577760, 1), 5.5747
 -360 | 1 | (-13380704, -4858540448, 300763), 12.2653
 -361 | 1 | (5936857857463772, -5761620357265333096, 7335308807), 23.4515
 -362 | 1 | (1175674382716706060, -412829849250602131524, 2011995844908162875), 28.752
 -363 | 1 | (174724, -97072976, 1), 4.4259
 -364 | 2 | (-96721, -18843490, 1), 7.5858
      |   | (9922832, -3668682160, 4913), 8.1471
 -365 | 1 | (940372707967644670215975558500, 349509850547830680581532897681864, 344467125588829445931640625), 44.1188
x -366 | 0-1 |
 -367 | 0 |
 -368 | 0 |
 -369 | 0 |
 -370 | 1 | (-7911025901205080, -3167045917043949640, 28263089785136543), 23.4291
 -371 | 0 |
x -372 | 0-2 |
 -373 | 1 | (2596607080, 753199750543, 24897088000), 18.5348
 -374 | 1 | (-30118, -11202675, 8), 5.888
 -375 | 0 |
 -376 | 2 | (23716, -9701692, 1), 7.2768
      |   | (4700, -486980, 103823), 8.964
 -377 | 0 |
 -378 | 1 | (-72, -27432, 1), 3.1641
x -379 | 0-2 |
x -380 | 0-2 |
 -381 | 1 | (100597222950, -38783602071235, 84027672), 20.3297
x -382 |   |
 -383 | 0 |
 -384 | 0 |
x -385 | 0-2 |
 -386 | 1 | (90589417170913412, -182451217690585205979, 23197894208), 27.6706
 -387 | 1 | (3265195615667864158973571944005576557403482, -1195552379897872513757885427992417842517738231, 9503604759659338539609458935137196705484328), 70.6727
 -388 | 2 | (-20, -8756, 125), 6.4299
      |   | (544444339487568, 218022838494658352, 72668325717), 20.086
 -389 | 0 |
 -390 | 0 |
 -391 | 0 |
x -392 | 0-2 |
 -393 | 0 |
x -394 |   |
 -395 | 1 | (1764, -705936, 1), 4.5315
 -396 | 1 | (9695136274863233202330736, 2570390009429964384703361072, 136031224116102606712396711), 38.4962
 -397 | 1 | (4628438, 1851358099, 54872), 13.9296
 -398 | 2 | (465124, -367981284, 1), 9.0031
      |   | (112148, -43771668, 148877), 8.7536
 -399 | 1 | (3319684, -6193925440, 1), 10.4448
 -400 | 1 | (7519032499419212395503090514636, 3033377795784906392815657732044916, 20148541273935685072498733299), 45.5352
x -401 | 0-2 |
 -402 | 0 |
 -403 | 2 | (10812672, 4583039552, 729), 11.7388
      |   | (1602756, -655014896, 729), 7.6071
 -404 | 0 |
 -405 | 1 | (2723220, 1181505528, 125), 8.2011
 -406 | 0 |
 -407 | 1 | (7368732, 3208326624, 343), 11.4344
x -408 |   |
 -409 | 0 |
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x -416 |   |
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      |   | (1291584, 546461056, 9261), 10.9582
x -421 | 0-1 |
 -422 | 0 |
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x -424 |   |
 -425 | 0 |
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      |   | (74880, 15035840, 1601613), 11.4326
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 -433 | 0 |
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x -435 | 0-2 |
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x -437 | 0-2 |
x -438 | 0-1 |
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x -451 | 1-3 | (2042492, -927545264, 12167), 11.051
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      |   | (3492113772, 1610469205064, 3176523), 12.7137
x -458 |   |
 -459 | 0 |
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      |   | (1846132203348784, 887980002994161904, 108599606011), 25.0276
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x -478 | 0-1 |
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      |   | (23276, -10543039, 85184), 8.2432
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x -488 | 0-1 |
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x -491 |   |
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x -493 | 0-2 |
 -494 | 0 |
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x -498 | 0-1 |
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