Parameters: D = 352, A = 280, B = 631, X = 8756.
This page records the compact basis and Gram matrix for the lattice obtained from the primitive isotropic vector
w = (0,280,281,...,631;8756) in II_{353,1}.
Reference: A Lorentzian Construction in Dimension 88 and Infinitely Many Further Ranks.
We use the ambient basis [g, delta_1, ..., delta_352, h] of II_{353,1}, 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}.
Download: conway-lattice-D352-basis.txt
b_1 = 1:1, 2:84546 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 = 352:9387, 353:1 b_352 = 352:-8125, 354:1
Download: conway-lattice-D352-gram.txt
14296052320 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.
Download: conway-lattice-D352.sage