Conway lattice in rank 856

Parameters: D = 856, A = 8617, B = 9472, X = 264718.

This page records the compact basis and Gram matrix for the lattice obtained from the primitive isotropic vector w = (0,8617,8618,...,9472;264718) in II_{857,1}.

Reference: A Lorentzian Construction in Dimension 88 and Infinitely Many Further Ranks.

Ambient basis

We use the ambient basis [g, delta_1, ..., delta_856, h] of II_{857,1}, where g=(1/2,...,1/2,-1/2), delta_j=e_{j+1}-e_{j+2} for j=1,...,D, and h=e_{D+1}+e_{D+2}.

Explicit basis of the quotient lattice

Download: conway-lattice-D856-basis.txt

b_1 = 1:1, 2:4003405
b_2 = 2:1, 3:2, 4:-3
b_3 = 4:-1, 5:1
b_4 = 5:-1, 6:1
b_5 = 6:-1, 7:1
b_6 = 7:-1, 8:1
b_7 = 8:-1, 9:1
b_8 = 9:-1, 10:1
b_9 = 10:-1, 11:1
b_10 = 11:-1, 12:1
b_11 = 12:-1, 13:1
b_12 = 13:-1, 14:1
b_13 = 14:-1, 15:1
b_14 = 15:-1, 16:1
b_15 = 16:-1, 17:1
b_16 = 17:-1, 18:1
b_17 = 18:-1, 19:1
b_18 = 19:-1, 20:1
b_19 = 20:-1, 21:1
b_20 = 21:-1, 22:1
b_21 = 22:-1, 23:1
b_22 = 23:-1, 24:1
b_23 = 24:-1, 25:1
b_24 = 25:-1, 26:1
b_25 = 26:-1, 27:1
b_26 = 27:-1, 28:1
b_27 = 28:-1, 29:1
b_28 = 29:-1, 30:1
b_29 = 30:-1, 31:1
b_30 = 31:-1, 32:1
b_31 = 32:-1, 33:1
b_32 = 33:-1, 34:1
b_33 = 34:-1, 35:1
b_34 = 35:-1, 36:1
b_35 = 36:-1, 37:1
b_36 = 37:-1, 38:1
b_37 = 38:-1, 39:1
b_38 = 39:-1, 40:1
b_39 = 40:-1, 41:1
b_40 = 41:-1, 42:1
b_41 = 42:-1, 43:1
b_42 = 43:-1, 44:1
b_43 = 44:-1, 45:1
b_44 = 45:-1, 46:1
b_45 = 46:-1, 47:1
b_46 = 47:-1, 48:1
b_47 = 48:-1, 49:1
b_48 = 49:-1, 50:1
b_49 = 50:-1, 51:1
b_50 = 51:-1, 52:1
b_51 = 52:-1, 53:1
b_52 = 53:-1, 54:1
b_53 = 54:-1, 55:1
b_54 = 55:-1, 56:1
b_55 = 56:-1, 57:1
b_56 = 57:-1, 58:1
b_57 = 58:-1, 59:1
b_58 = 59:-1, 60:1
b_59 = 60:-1, 61:1
b_60 = 61:-1, 62:1
b_61 = 62:-1, 63:1
b_62 = 63:-1, 64:1
b_63 = 64:-1, 65:1
b_64 = 65:-1, 66:1
b_65 = 66:-1, 67:1
b_66 = 67:-1, 68:1
b_67 = 68:-1, 69:1
b_68 = 69:-1, 70:1
b_69 = 70:-1, 71:1
b_70 = 71:-1, 72:1
b_71 = 72:-1, 73:1
b_72 = 73:-1, 74:1
b_73 = 74:-1, 75:1
b_74 = 75:-1, 76:1
b_75 = 76:-1, 77:1
b_76 = 77:-1, 78:1
b_77 = 78:-1, 79:1
b_78 = 79:-1, 80:1
b_79 = 80:-1, 81:1
b_80 = 81:-1, 82:1
b_81 = 82:-1, 83:1
b_82 = 83:-1, 84:1
b_83 = 84:-1, 85:1
b_84 = 85:-1, 86:1
b_85 = 86:-1, 87:1
b_86 = 87:-1, 88:1
b_87 = 88:-1, 89:1
b_88 = 89:-1, 90:1
b_89 = 90:-1, 91:1
b_90 = 91:-1, 92:1
b_91 = 92:-1, 93:1
b_92 = 93:-1, 94:1
b_93 = 94:-1, 95:1
b_94 = 95:-1, 96:1
b_95 = 96:-1, 97:1
b_96 = 97:-1, 98:1
b_97 = 98:-1, 99:1
b_98 = 99:-1, 100:1
b_99 = 100:-1, 101:1
b_100 = 101:-1, 102:1
b_101 = 102:-1, 103:1
b_102 = 103:-1, 104:1
b_103 = 104:-1, 105:1
b_104 = 105:-1, 106:1
b_105 = 106:-1, 107:1
b_106 = 107:-1, 108:1
b_107 = 108:-1, 109:1
b_108 = 109:-1, 110:1
b_109 = 110:-1, 111:1
b_110 = 111:-1, 112:1
b_111 = 112:-1, 113:1
b_112 = 113:-1, 114:1
b_113 = 114:-1, 115:1
b_114 = 115:-1, 116:1
b_115 = 116:-1, 117:1
b_116 = 117:-1, 118:1
b_117 = 118:-1, 119:1
b_118 = 119:-1, 120:1
b_119 = 120:-1, 121:1
b_120 = 121:-1, 122:1
b_121 = 122:-1, 123:1
b_122 = 123:-1, 124:1
b_123 = 124:-1, 125:1
b_124 = 125:-1, 126:1
b_125 = 126:-1, 127:1
b_126 = 127:-1, 128:1
b_127 = 128:-1, 129:1
b_128 = 129:-1, 130:1
b_129 = 130:-1, 131:1
b_130 = 131:-1, 132:1
b_131 = 132:-1, 133:1
b_132 = 133:-1, 134:1
b_133 = 134:-1, 135:1
b_134 = 135:-1, 136:1
b_135 = 136:-1, 137:1
b_136 = 137:-1, 138:1
b_137 = 138:-1, 139:1
b_138 = 139:-1, 140:1
b_139 = 140:-1, 141:1
b_140 = 141:-1, 142:1
b_141 = 142:-1, 143:1
b_142 = 143:-1, 144:1
b_143 = 144:-1, 145:1
b_144 = 145:-1, 146:1
b_145 = 146:-1, 147:1
b_146 = 147:-1, 148:1
b_147 = 148:-1, 149:1
b_148 = 149:-1, 150:1
b_149 = 150:-1, 151:1
b_150 = 151:-1, 152:1
b_151 = 152:-1, 153:1
b_152 = 153:-1, 154:1
b_153 = 154:-1, 155:1
b_154 = 155:-1, 156:1
b_155 = 156:-1, 157:1
b_156 = 157:-1, 158:1
b_157 = 158:-1, 159:1
b_158 = 159:-1, 160:1
b_159 = 160:-1, 161:1
b_160 = 161:-1, 162:1
b_161 = 162:-1, 163:1
b_162 = 163:-1, 164:1
b_163 = 164:-1, 165:1
b_164 = 165:-1, 166:1
b_165 = 166:-1, 167:1
b_166 = 167:-1, 168:1
b_167 = 168:-1, 169:1
b_168 = 169:-1, 170:1
b_169 = 170:-1, 171:1
b_170 = 171:-1, 172:1
b_171 = 172:-1, 173:1
b_172 = 173:-1, 174:1
b_173 = 174:-1, 175:1
b_174 = 175:-1, 176:1
b_175 = 176:-1, 177:1
b_176 = 177:-1, 178:1
b_177 = 178:-1, 179:1
b_178 = 179:-1, 180:1
b_179 = 180:-1, 181:1
b_180 = 181:-1, 182:1
b_181 = 182:-1, 183:1
b_182 = 183:-1, 184:1
b_183 = 184:-1, 185:1
b_184 = 185:-1, 186:1
b_185 = 186:-1, 187:1
b_186 = 187:-1, 188:1
b_187 = 188:-1, 189:1
b_188 = 189:-1, 190:1
b_189 = 190:-1, 191:1
b_190 = 191:-1, 192:1
b_191 = 192:-1, 193:1
b_192 = 193:-1, 194:1
b_193 = 194:-1, 195:1
b_194 = 195:-1, 196:1
b_195 = 196:-1, 197:1
b_196 = 197:-1, 198:1
b_197 = 198:-1, 199:1
b_198 = 199:-1, 200:1
b_199 = 200:-1, 201:1
b_200 = 201:-1, 202:1
b_201 = 202:-1, 203:1
b_202 = 203:-1, 204:1
b_203 = 204:-1, 205:1
b_204 = 205:-1, 206:1
b_205 = 206:-1, 207:1
b_206 = 207:-1, 208:1
b_207 = 208:-1, 209:1
b_208 = 209:-1, 210:1
b_209 = 210:-1, 211:1
b_210 = 211:-1, 212:1
b_211 = 212:-1, 213:1
b_212 = 213:-1, 214:1
b_213 = 214:-1, 215:1
b_214 = 215:-1, 216:1
b_215 = 216:-1, 217:1
b_216 = 217:-1, 218:1
b_217 = 218:-1, 219:1
b_218 = 219:-1, 220:1
b_219 = 220:-1, 221:1
b_220 = 221:-1, 222:1
b_221 = 222:-1, 223:1
b_222 = 223:-1, 224:1
b_223 = 224:-1, 225:1
b_224 = 225:-1, 226:1
b_225 = 226:-1, 227:1
b_226 = 227:-1, 228:1
b_227 = 228:-1, 229:1
b_228 = 229:-1, 230:1
b_229 = 230:-1, 231:1
b_230 = 231:-1, 232:1
b_231 = 232:-1, 233:1
b_232 = 233:-1, 234:1
b_233 = 234:-1, 235:1
b_234 = 235:-1, 236:1
b_235 = 236:-1, 237:1
b_236 = 237:-1, 238:1
b_237 = 238:-1, 239:1
b_238 = 239:-1, 240:1
b_239 = 240:-1, 241:1
b_240 = 241:-1, 242:1
b_241 = 242:-1, 243:1
b_242 = 243:-1, 244:1
b_243 = 244:-1, 245:1
b_244 = 245:-1, 246:1
b_245 = 246:-1, 247:1
b_246 = 247:-1, 248:1
b_247 = 248:-1, 249:1
b_248 = 249:-1, 250:1
b_249 = 250:-1, 251:1
b_250 = 251:-1, 252:1
b_251 = 252:-1, 253:1
b_252 = 253:-1, 254:1
b_253 = 254:-1, 255:1
b_254 = 255:-1, 256:1
b_255 = 256:-1, 257:1
b_256 = 257:-1, 258:1
b_257 = 258:-1, 259:1
b_258 = 259:-1, 260:1
b_259 = 260:-1, 261:1
b_260 = 261:-1, 262:1
b_261 = 262:-1, 263:1
b_262 = 263:-1, 264:1
b_263 = 264:-1, 265:1
b_264 = 265:-1, 266:1
b_265 = 266:-1, 267:1
b_266 = 267:-1, 268:1
b_267 = 268:-1, 269:1
b_268 = 269:-1, 270:1
b_269 = 270:-1, 271:1
b_270 = 271:-1, 272:1
b_271 = 272:-1, 273:1
b_272 = 273:-1, 274:1
b_273 = 274:-1, 275:1
b_274 = 275:-1, 276:1
b_275 = 276:-1, 277:1
b_276 = 277:-1, 278:1
b_277 = 278:-1, 279:1
b_278 = 279:-1, 280:1
b_279 = 280:-1, 281:1
b_280 = 281:-1, 282:1
b_281 = 282:-1, 283:1
b_282 = 283:-1, 284:1
b_283 = 284:-1, 285:1
b_284 = 285:-1, 286:1
b_285 = 286:-1, 287:1
b_286 = 287:-1, 288:1
b_287 = 288:-1, 289:1
b_288 = 289:-1, 290:1
b_289 = 290:-1, 291:1
b_290 = 291:-1, 292:1
b_291 = 292:-1, 293:1
b_292 = 293:-1, 294:1
b_293 = 294:-1, 295:1
b_294 = 295:-1, 296:1
b_295 = 296:-1, 297:1
b_296 = 297:-1, 298:1
b_297 = 298:-1, 299:1
b_298 = 299:-1, 300:1
b_299 = 300:-1, 301:1
b_300 = 301:-1, 302:1
b_301 = 302:-1, 303:1
b_302 = 303:-1, 304:1
b_303 = 304:-1, 305:1
b_304 = 305:-1, 306:1
b_305 = 306:-1, 307:1
b_306 = 307:-1, 308:1
b_307 = 308:-1, 309:1
b_308 = 309:-1, 310:1
b_309 = 310:-1, 311:1
b_310 = 311:-1, 312:1
b_311 = 312:-1, 313:1
b_312 = 313:-1, 314:1
b_313 = 314:-1, 315:1
b_314 = 315:-1, 316:1
b_315 = 316:-1, 317:1
b_316 = 317:-1, 318:1
b_317 = 318:-1, 319:1
b_318 = 319:-1, 320:1
b_319 = 320:-1, 321:1
b_320 = 321:-1, 322:1
b_321 = 322:-1, 323:1
b_322 = 323:-1, 324:1
b_323 = 324:-1, 325:1
b_324 = 325:-1, 326:1
b_325 = 326:-1, 327:1
b_326 = 327:-1, 328:1
b_327 = 328:-1, 329:1
b_328 = 329:-1, 330:1
b_329 = 330:-1, 331:1
b_330 = 331:-1, 332:1
b_331 = 332:-1, 333:1
b_332 = 333:-1, 334:1
b_333 = 334:-1, 335:1
b_334 = 335:-1, 336:1
b_335 = 336:-1, 337:1
b_336 = 337:-1, 338:1
b_337 = 338:-1, 339:1
b_338 = 339:-1, 340:1
b_339 = 340:-1, 341:1
b_340 = 341:-1, 342:1
b_341 = 342:-1, 343:1
b_342 = 343:-1, 344:1
b_343 = 344:-1, 345:1
b_344 = 345:-1, 346:1
b_345 = 346:-1, 347:1
b_346 = 347:-1, 348:1
b_347 = 348:-1, 349:1
b_348 = 349:-1, 350:1
b_349 = 350:-1, 351:1
b_350 = 351:-1, 352:1
b_351 = 352:-1, 353:1
b_352 = 353:-1, 354:1
b_353 = 354:-1, 355:1
b_354 = 355:-1, 356:1
b_355 = 356:-1, 357:1
b_356 = 357:-1, 358:1
b_357 = 358:-1, 359:1
b_358 = 359:-1, 360:1
b_359 = 360:-1, 361:1
b_360 = 361:-1, 362:1
b_361 = 362:-1, 363:1
b_362 = 363:-1, 364:1
b_363 = 364:-1, 365:1
b_364 = 365:-1, 366:1
b_365 = 366:-1, 367:1
b_366 = 367:-1, 368:1
b_367 = 368:-1, 369:1
b_368 = 369:-1, 370:1
b_369 = 370:-1, 371:1
b_370 = 371:-1, 372:1
b_371 = 372:-1, 373:1
b_372 = 373:-1, 374:1
b_373 = 374:-1, 375:1
b_374 = 375:-1, 376:1
b_375 = 376:-1, 377:1
b_376 = 377:-1, 378:1
b_377 = 378:-1, 379:1
b_378 = 379:-1, 380:1
b_379 = 380:-1, 381:1
b_380 = 381:-1, 382:1
b_381 = 382:-1, 383:1
b_382 = 383:-1, 384:1
b_383 = 384:-1, 385:1
b_384 = 385:-1, 386:1
b_385 = 386:-1, 387:1
b_386 = 387:-1, 388:1
b_387 = 388:-1, 389:1
b_388 = 389:-1, 390:1
b_389 = 390:-1, 391:1
b_390 = 391:-1, 392:1
b_391 = 392:-1, 393:1
b_392 = 393:-1, 394:1
b_393 = 394:-1, 395:1
b_394 = 395:-1, 396:1
b_395 = 396:-1, 397:1
b_396 = 397:-1, 398:1
b_397 = 398:-1, 399:1
b_398 = 399:-1, 400:1
b_399 = 400:-1, 401:1
b_400 = 401:-1, 402:1
b_401 = 402:-1, 403:1
b_402 = 403:-1, 404:1
b_403 = 404:-1, 405:1
b_404 = 405:-1, 406:1
b_405 = 406:-1, 407:1
b_406 = 407:-1, 408:1
b_407 = 408:-1, 409:1
b_408 = 409:-1, 410:1
b_409 = 410:-1, 411:1
b_410 = 411:-1, 412:1
b_411 = 412:-1, 413:1
b_412 = 413:-1, 414:1
b_413 = 414:-1, 415:1
b_414 = 415:-1, 416:1
b_415 = 416:-1, 417:1
b_416 = 417:-1, 418:1
b_417 = 418:-1, 419:1
b_418 = 419:-1, 420:1
b_419 = 420:-1, 421:1
b_420 = 421:-1, 422:1
b_421 = 422:-1, 423:1
b_422 = 423:-1, 424:1
b_423 = 424:-1, 425:1
b_424 = 425:-1, 426:1
b_425 = 426:-1, 427:1
b_426 = 427:-1, 428:1
b_427 = 428:-1, 429:1
b_428 = 429:-1, 430:1
b_429 = 430:-1, 431:1
b_430 = 431:-1, 432:1
b_431 = 432:-1, 433:1
b_432 = 433:-1, 434:1
b_433 = 434:-1, 435:1
b_434 = 435:-1, 436:1
b_435 = 436:-1, 437:1
b_436 = 437:-1, 438:1
b_437 = 438:-1, 439:1
b_438 = 439:-1, 440:1
b_439 = 440:-1, 441:1
b_440 = 441:-1, 442:1
b_441 = 442:-1, 443:1
b_442 = 443:-1, 444:1
b_443 = 444:-1, 445:1
b_444 = 445:-1, 446:1
b_445 = 446:-1, 447:1
b_446 = 447:-1, 448:1
b_447 = 448:-1, 449:1
b_448 = 449:-1, 450:1
b_449 = 450:-1, 451:1
b_450 = 451:-1, 452:1
b_451 = 452:-1, 453:1
b_452 = 453:-1, 454:1
b_453 = 454:-1, 455:1
b_454 = 455:-1, 456:1
b_455 = 456:-1, 457:1
b_456 = 457:-1, 458:1
b_457 = 458:-1, 459:1
b_458 = 459:-1, 460:1
b_459 = 460:-1, 461:1
b_460 = 461:-1, 462:1
b_461 = 462:-1, 463:1
b_462 = 463:-1, 464:1
b_463 = 464:-1, 465:1
b_464 = 465:-1, 466:1
b_465 = 466:-1, 467:1
b_466 = 467:-1, 468:1
b_467 = 468:-1, 469:1
b_468 = 469:-1, 470:1
b_469 = 470:-1, 471:1
b_470 = 471:-1, 472:1
b_471 = 472:-1, 473:1
b_472 = 473:-1, 474:1
b_473 = 474:-1, 475:1
b_474 = 475:-1, 476:1
b_475 = 476:-1, 477:1
b_476 = 477:-1, 478:1
b_477 = 478:-1, 479:1
b_478 = 479:-1, 480:1
b_479 = 480:-1, 481:1
b_480 = 481:-1, 482:1
b_481 = 482:-1, 483:1
b_482 = 483:-1, 484:1
b_483 = 484:-1, 485:1
b_484 = 485:-1, 486:1
b_485 = 486:-1, 487:1
b_486 = 487:-1, 488:1
b_487 = 488:-1, 489:1
b_488 = 489:-1, 490:1
b_489 = 490:-1, 491:1
b_490 = 491:-1, 492:1
b_491 = 492:-1, 493:1
b_492 = 493:-1, 494:1
b_493 = 494:-1, 495:1
b_494 = 495:-1, 496:1
b_495 = 496:-1, 497:1
b_496 = 497:-1, 498:1
b_497 = 498:-1, 499:1
b_498 = 499:-1, 500:1
b_499 = 500:-1, 501:1
b_500 = 501:-1, 502:1
b_501 = 502:-1, 503:1
b_502 = 503:-1, 504:1
b_503 = 504:-1, 505:1
b_504 = 505:-1, 506:1
b_505 = 506:-1, 507:1
b_506 = 507:-1, 508:1
b_507 = 508:-1, 509:1
b_508 = 509:-1, 510:1
b_509 = 510:-1, 511:1
b_510 = 511:-1, 512:1
b_511 = 512:-1, 513:1
b_512 = 513:-1, 514:1
b_513 = 514:-1, 515:1
b_514 = 515:-1, 516:1
b_515 = 516:-1, 517:1
b_516 = 517:-1, 518:1
b_517 = 518:-1, 519:1
b_518 = 519:-1, 520:1
b_519 = 520:-1, 521:1
b_520 = 521:-1, 522:1
b_521 = 522:-1, 523:1
b_522 = 523:-1, 524:1
b_523 = 524:-1, 525:1
b_524 = 525:-1, 526:1
b_525 = 526:-1, 527:1
b_526 = 527:-1, 528:1
b_527 = 528:-1, 529:1
b_528 = 529:-1, 530:1
b_529 = 530:-1, 531:1
b_530 = 531:-1, 532:1
b_531 = 532:-1, 533:1
b_532 = 533:-1, 534:1
b_533 = 534:-1, 535:1
b_534 = 535:-1, 536:1
b_535 = 536:-1, 537:1
b_536 = 537:-1, 538:1
b_537 = 538:-1, 539:1
b_538 = 539:-1, 540:1
b_539 = 540:-1, 541:1
b_540 = 541:-1, 542:1
b_541 = 542:-1, 543:1
b_542 = 543:-1, 544:1
b_543 = 544:-1, 545:1
b_544 = 545:-1, 546:1
b_545 = 546:-1, 547:1
b_546 = 547:-1, 548:1
b_547 = 548:-1, 549:1
b_548 = 549:-1, 550:1
b_549 = 550:-1, 551:1
b_550 = 551:-1, 552:1
b_551 = 552:-1, 553:1
b_552 = 553:-1, 554:1
b_553 = 554:-1, 555:1
b_554 = 555:-1, 556:1
b_555 = 556:-1, 557:1
b_556 = 557:-1, 558:1
b_557 = 558:-1, 559:1
b_558 = 559:-1, 560:1
b_559 = 560:-1, 561:1
b_560 = 561:-1, 562:1
b_561 = 562:-1, 563:1
b_562 = 563:-1, 564:1
b_563 = 564:-1, 565:1
b_564 = 565:-1, 566:1
b_565 = 566:-1, 567:1
b_566 = 567:-1, 568:1
b_567 = 568:-1, 569:1
b_568 = 569:-1, 570:1
b_569 = 570:-1, 571:1
b_570 = 571:-1, 572:1
b_571 = 572:-1, 573:1
b_572 = 573:-1, 574:1
b_573 = 574:-1, 575:1
b_574 = 575:-1, 576:1
b_575 = 576:-1, 577:1
b_576 = 577:-1, 578:1
b_577 = 578:-1, 579:1
b_578 = 579:-1, 580:1
b_579 = 580:-1, 581:1
b_580 = 581:-1, 582:1
b_581 = 582:-1, 583:1
b_582 = 583:-1, 584:1
b_583 = 584:-1, 585:1
b_584 = 585:-1, 586:1
b_585 = 586:-1, 587:1
b_586 = 587:-1, 588:1
b_587 = 588:-1, 589:1
b_588 = 589:-1, 590:1
b_589 = 590:-1, 591:1
b_590 = 591:-1, 592:1
b_591 = 592:-1, 593:1
b_592 = 593:-1, 594:1
b_593 = 594:-1, 595:1
b_594 = 595:-1, 596:1
b_595 = 596:-1, 597:1
b_596 = 597:-1, 598:1
b_597 = 598:-1, 599:1
b_598 = 599:-1, 600:1
b_599 = 600:-1, 601:1
b_600 = 601:-1, 602:1
b_601 = 602:-1, 603:1
b_602 = 603:-1, 604:1
b_603 = 604:-1, 605:1
b_604 = 605:-1, 606:1
b_605 = 606:-1, 607:1
b_606 = 607:-1, 608:1
b_607 = 608:-1, 609:1
b_608 = 609:-1, 610:1
b_609 = 610:-1, 611:1
b_610 = 611:-1, 612:1
b_611 = 612:-1, 613:1
b_612 = 613:-1, 614:1
b_613 = 614:-1, 615:1
b_614 = 615:-1, 616:1
b_615 = 616:-1, 617:1
b_616 = 617:-1, 618:1
b_617 = 618:-1, 619:1
b_618 = 619:-1, 620:1
b_619 = 620:-1, 621:1
b_620 = 621:-1, 622:1
b_621 = 622:-1, 623:1
b_622 = 623:-1, 624:1
b_623 = 624:-1, 625:1
b_624 = 625:-1, 626:1
b_625 = 626:-1, 627:1
b_626 = 627:-1, 628:1
b_627 = 628:-1, 629:1
b_628 = 629:-1, 630:1
b_629 = 630:-1, 631:1
b_630 = 631:-1, 632:1
b_631 = 632:-1, 633:1
b_632 = 633:-1, 634:1
b_633 = 634:-1, 635:1
b_634 = 635:-1, 636:1
b_635 = 636:-1, 637:1
b_636 = 637:-1, 638:1
b_637 = 638:-1, 639:1
b_638 = 639:-1, 640:1
b_639 = 640:-1, 641:1
b_640 = 641:-1, 642:1
b_641 = 642:-1, 643:1
b_642 = 643:-1, 644:1
b_643 = 644:-1, 645:1
b_644 = 645:-1, 646:1
b_645 = 646:-1, 647:1
b_646 = 647:-1, 648:1
b_647 = 648:-1, 649:1
b_648 = 649:-1, 650:1
b_649 = 650:-1, 651:1
b_650 = 651:-1, 652:1
b_651 = 652:-1, 653:1
b_652 = 653:-1, 654:1
b_653 = 654:-1, 655:1
b_654 = 655:-1, 656:1
b_655 = 656:-1, 657:1
b_656 = 657:-1, 658:1
b_657 = 658:-1, 659:1
b_658 = 659:-1, 660:1
b_659 = 660:-1, 661:1
b_660 = 661:-1, 662:1
b_661 = 662:-1, 663:1
b_662 = 663:-1, 664:1
b_663 = 664:-1, 665:1
b_664 = 665:-1, 666:1
b_665 = 666:-1, 667:1
b_666 = 667:-1, 668:1
b_667 = 668:-1, 669:1
b_668 = 669:-1, 670:1
b_669 = 670:-1, 671:1
b_670 = 671:-1, 672:1
b_671 = 672:-1, 673:1
b_672 = 673:-1, 674:1
b_673 = 674:-1, 675:1
b_674 = 675:-1, 676:1
b_675 = 676:-1, 677:1
b_676 = 677:-1, 678:1
b_677 = 678:-1, 679:1
b_678 = 679:-1, 680:1
b_679 = 680:-1, 681:1
b_680 = 681:-1, 682:1
b_681 = 682:-1, 683:1
b_682 = 683:-1, 684:1
b_683 = 684:-1, 685:1
b_684 = 685:-1, 686:1
b_685 = 686:-1, 687:1
b_686 = 687:-1, 688:1
b_687 = 688:-1, 689:1
b_688 = 689:-1, 690:1
b_689 = 690:-1, 691:1
b_690 = 691:-1, 692:1
b_691 = 692:-1, 693:1
b_692 = 693:-1, 694:1
b_693 = 694:-1, 695:1
b_694 = 695:-1, 696:1
b_695 = 696:-1, 697:1
b_696 = 697:-1, 698:1
b_697 = 698:-1, 699:1
b_698 = 699:-1, 700:1
b_699 = 700:-1, 701:1
b_700 = 701:-1, 702:1
b_701 = 702:-1, 703:1
b_702 = 703:-1, 704:1
b_703 = 704:-1, 705:1
b_704 = 705:-1, 706:1
b_705 = 706:-1, 707:1
b_706 = 707:-1, 708:1
b_707 = 708:-1, 709:1
b_708 = 709:-1, 710:1
b_709 = 710:-1, 711:1
b_710 = 711:-1, 712:1
b_711 = 712:-1, 713:1
b_712 = 713:-1, 714:1
b_713 = 714:-1, 715:1
b_714 = 715:-1, 716:1
b_715 = 716:-1, 717:1
b_716 = 717:-1, 718:1
b_717 = 718:-1, 719:1
b_718 = 719:-1, 720:1
b_719 = 720:-1, 721:1
b_720 = 721:-1, 722:1
b_721 = 722:-1, 723:1
b_722 = 723:-1, 724:1
b_723 = 724:-1, 725:1
b_724 = 725:-1, 726:1
b_725 = 726:-1, 727:1
b_726 = 727:-1, 728:1
b_727 = 728:-1, 729:1
b_728 = 729:-1, 730:1
b_729 = 730:-1, 731:1
b_730 = 731:-1, 732:1
b_731 = 732:-1, 733:1
b_732 = 733:-1, 734:1
b_733 = 734:-1, 735:1
b_734 = 735:-1, 736:1
b_735 = 736:-1, 737:1
b_736 = 737:-1, 738:1
b_737 = 738:-1, 739:1
b_738 = 739:-1, 740:1
b_739 = 740:-1, 741:1
b_740 = 741:-1, 742:1
b_741 = 742:-1, 743:1
b_742 = 743:-1, 744:1
b_743 = 744:-1, 745:1
b_744 = 745:-1, 746:1
b_745 = 746:-1, 747:1
b_746 = 747:-1, 748:1
b_747 = 748:-1, 749:1
b_748 = 749:-1, 750:1
b_749 = 750:-1, 751:1
b_750 = 751:-1, 752:1
b_751 = 752:-1, 753:1
b_752 = 753:-1, 754:1
b_753 = 754:-1, 755:1
b_754 = 755:-1, 756:1
b_755 = 756:-1, 757:1
b_756 = 757:-1, 758:1
b_757 = 758:-1, 759:1
b_758 = 759:-1, 760:1
b_759 = 760:-1, 761:1
b_760 = 761:-1, 762:1
b_761 = 762:-1, 763:1
b_762 = 763:-1, 764:1
b_763 = 764:-1, 765:1
b_764 = 765:-1, 766:1
b_765 = 766:-1, 767:1
b_766 = 767:-1, 768:1
b_767 = 768:-1, 769:1
b_768 = 769:-1, 770:1
b_769 = 770:-1, 771:1
b_770 = 771:-1, 772:1
b_771 = 772:-1, 773:1
b_772 = 773:-1, 774:1
b_773 = 774:-1, 775:1
b_774 = 775:-1, 776:1
b_775 = 776:-1, 777:1
b_776 = 777:-1, 778:1
b_777 = 778:-1, 779:1
b_778 = 779:-1, 780:1
b_779 = 780:-1, 781:1
b_780 = 781:-1, 782:1
b_781 = 782:-1, 783:1
b_782 = 783:-1, 784:1
b_783 = 784:-1, 785:1
b_784 = 785:-1, 786:1
b_785 = 786:-1, 787:1
b_786 = 787:-1, 788:1
b_787 = 788:-1, 789:1
b_788 = 789:-1, 790:1
b_789 = 790:-1, 791:1
b_790 = 791:-1, 792:1
b_791 = 792:-1, 793:1
b_792 = 793:-1, 794:1
b_793 = 794:-1, 795:1
b_794 = 795:-1, 796:1
b_795 = 796:-1, 797:1
b_796 = 797:-1, 798:1
b_797 = 798:-1, 799:1
b_798 = 799:-1, 800:1
b_799 = 800:-1, 801:1
b_800 = 801:-1, 802:1
b_801 = 802:-1, 803:1
b_802 = 803:-1, 804:1
b_803 = 804:-1, 805:1
b_804 = 805:-1, 806:1
b_805 = 806:-1, 807:1
b_806 = 807:-1, 808:1
b_807 = 808:-1, 809:1
b_808 = 809:-1, 810:1
b_809 = 810:-1, 811:1
b_810 = 811:-1, 812:1
b_811 = 812:-1, 813:1
b_812 = 813:-1, 814:1
b_813 = 814:-1, 815:1
b_814 = 815:-1, 816:1
b_815 = 816:-1, 817:1
b_816 = 817:-1, 818:1
b_817 = 818:-1, 819:1
b_818 = 819:-1, 820:1
b_819 = 820:-1, 821:1
b_820 = 821:-1, 822:1
b_821 = 822:-1, 823:1
b_822 = 823:-1, 824:1
b_823 = 824:-1, 825:1
b_824 = 825:-1, 826:1
b_825 = 826:-1, 827:1
b_826 = 827:-1, 828:1
b_827 = 828:-1, 829:1
b_828 = 829:-1, 830:1
b_829 = 830:-1, 831:1
b_830 = 831:-1, 832:1
b_831 = 832:-1, 833:1
b_832 = 833:-1, 834:1
b_833 = 834:-1, 835:1
b_834 = 835:-1, 836:1
b_835 = 836:-1, 837:1
b_836 = 837:-1, 838:1
b_837 = 838:-1, 839:1
b_838 = 839:-1, 840:1
b_839 = 840:-1, 841:1
b_840 = 841:-1, 842:1
b_841 = 842:-1, 843:1
b_842 = 843:-1, 844:1
b_843 = 844:-1, 845:1
b_844 = 845:-1, 846:1
b_845 = 846:-1, 847:1
b_846 = 847:-1, 848:1
b_847 = 848:-1, 849:1
b_848 = 849:-1, 850:1
b_849 = 850:-1, 851:1
b_850 = 851:-1, 852:1
b_851 = 852:-1, 853:1
b_852 = 853:-1, 854:1
b_853 = 854:-1, 855:1
b_854 = 855:-1, 856:1
b_855 = 856:274190, 857:1
b_856 = 856:-255246, 858:1

Gram matrix

Download: conway-lattice-D856-gram.txt

32054503188264 0 0 0 0 0 0 0
0 36 11 -3 0 0 0 0
0 11 6 -4 1 0 0 0
0 -3 -4 6 -4 1 0 0
0 0 1 -4 6 -4 1 0
0 0 0 1 -4 6 -4 1
0 0 0 0 1 -4 6 -4
0 0 0 0 0 1 -4 6

Shown above: the upper-left 8×8 block. The full Gram matrix is in the text file.

SageMath script

Download: conway-lattice-D856.sage