Output of /home/aschiem/bin/hn --invar -t --shells-14 --herm_lll3 0.8 &K=Q(sqrt(-43)) &Hdim=4 V=K^4 &HNeighbourhood at <2,2w> contains 69 classes: mass of the neighbourhood is 15355/1152 Steinitz class <1,w>: &Hlattice (#1 <- #60) 5 -2-w 6 3-w -2+w 6 0 3-w -3+w 7 |Aut| = 2^4*3 #short vectors: 0 0 0 0 24 48 96 48 24 120 192 336 192 528 &Hlattice (#2 <- #15) 4 2 4 0 1-w 4 -1+w 0 2 4 |Aut| = 2^3*3 #short vectors: 0 0 0 24 0 24 24 120 120 120 216 264 312 336 &Hlattice (#3 <- #13) 4 2 4 0 w 4 -1+w -1 -2 5 |Aut| = 2^2 #short vectors: 0 0 0 16 16 12 52 104 84 156 200 268 248 384 &Hlattice (#4 <- #18) 4 2 4 w 2 6 -1+w -2+w w 8 |Aut| = 2^2 #short vectors: 0 0 0 12 16 32 44 88 100 144 176 260 288 388 &Hlattice (#5 <- #21) 4 1 4 1-w -1 5 -w 1-w 1 5 |Aut| = 2^2 #short vectors: 0 0 0 12 16 32 44 88 100 144 176 260 288 388 &Hlattice (#6 <- #24) 4 2 4 2 1-w 5 1+w 2 2+w 5 |Aut| = 2^2*3 #short vectors: 0 0 0 12 24 12 48 96 96 180 168 240 264 372 &Hlattice (#7 <- #44) 4 -2+w 5 1+w 2-w 6 2-w -2 -2 6 |Aut| = 2^2 #short vectors: 0 0 0 12 8 52 40 80 104 108 184 280 312 404 &Hlattice (#8 <- #25) 4 2-w 5 -w 3-w 5 w -2 -1 5 |Aut| = 2^2 #short vectors: 0 0 0 8 20 40 44 76 104 148 156 252 300 396 &Hlattice (#9 <- #27) 4 -2 4 -1-w 2 5 -2+w 2-w -w 6 |Aut| = 2^2 #short vectors: 0 0 0 8 20 40 44 76 104 148 156 252 300 396 &Hlattice (#10 <- #46) 4 0 4 -1 2 5 1-2w -1 w 12 |Aut| = 2^2 #short vectors: 0 0 0 8 16 48 48 72 96 128 168 272 296 416 &Hlattice (#11 <- #56) 4 1-w 4 -2 -1 5 w -2 -1-w 5 |Aut| = 2^2 #short vectors: 0 0 0 8 20 32 68 76 64 140 188 292 236 444 &Hlattice (#12 <- #19) 4 -2 5 -2 0 5 1-w w -2+w 5 |Aut| = 2^2 #short vectors: 0 0 0 4 32 28 48 72 104 188 128 224 288 388 &Hlattice (#13 <- #8) 3 0 3 -1+w 0 4 0 -1+w 0 4 |Aut| = 2^3 #short vectors: 0 0 8 8 8 32 40 72 112 128 200 288 296 400 &Hlattice (#14 <- #30) 3 1 3 -1 1-w 5 -1+w 1 2 5 |Aut| = 2^2 #short vectors: 0 0 8 4 8 44 56 56 88 108 208 320 272 452 &Hlattice (#15 <- #47) 3 1 3 -1+w -1 5 -1 1-w 1+w 6 |Aut| = 2 #short vectors: 0 0 8 8 12 24 36 76 120 148 188 268 300 380 &Hlattice (#16 <- #59) 3 2-w 5 1 0 5 1+w -3+w 1 6 |Aut| = 2^4 #short vectors: 0 0 8 0 16 56 16 48 160 144 128 232 384 368 &Hlattice (#17 <- #62) 3 -1 3 0 1-w 5 w 0 -2 5 |Aut| = 2 #short vectors: 0 0 6 6 12 38 48 66 100 128 190 290 286 420 &Hlattice (#18 <- #31) 4 2 4 2-w 0 5 2-w 1-w 2 5 |Aut| = 2^2 #short vectors: 0 0 4 12 12 24 40 88 108 144 192 268 288 380 &Hlattice (#19 <- #33) 4 -2 4 -1-w w 5 -1-w 0 2 5 |Aut| = 2^2 #short vectors: 0 0 4 12 12 24 40 88 108 144 192 268 288 380 &Hlattice (#20 <- #45) 3 0 3 -1 0 4 2-w 1 -1+w 6 |Aut| = 2^2 #short vectors: 0 0 4 4 12 56 48 56 100 112 176 292 304 436 &Hlattice (#21 <- #55) 3 1 4 -w 1 5 1 -2+w w 5 |Aut| = 2^2 #short vectors: 0 0 4 4 20 36 52 64 96 148 168 272 280 420 &Hlattice (#22 <- #57) 3 1+w 6 1 3-w 7 -1+w 3 3-w 8 |Aut| = 2^2 #short vectors: 0 0 4 8 16 36 28 76 132 152 156 240 332 364 &Hlattice (#23 <- #58) 3 1-w 5 -1 -2 5 1 1+w -w 6 |Aut| = 2^2 #short vectors: 0 0 4 4 20 36 52 64 96 148 168 272 280 420 &Hlattice (#24 <- #61) 3 -1 4 -w -1 5 0 -1 2 5 |Aut| = 2 #short vectors: 0 0 4 8 20 24 36 80 120 168 160 240 304 368 &Hlattice (#25 <- #63) 3 1 4 1 -1+w 4 1-w -1 1 5 |Aut| = 2 #short vectors: 0 0 4 10 18 16 48 86 98 162 186 264 266 388 &Hlattice (#26 <- #69) 3 0 4 -1 -2+w 4 1+w -1 0 5 |Aut| = 2^2 #short vectors: 0 0 4 8 20 16 60 80 80 160 192 280 240 416 &Hlattice (#27 <- #64) 4 -1 4 -1+w 2 5 w -2 0 7 |Aut| = 2^2 #short vectors: 0 0 2 4 26 30 56 68 90 166 156 258 268 416 &Hlattice (#28 <- #65) 4 1-w 7 1+w 1 8 2 -1-w 3-2w 8 |Aut| = 2 #short vectors: 0 0 2 10 16 30 48 82 96 144 182 270 278 400 &Hlattice (#29 <- #66) 4 -w 4 1 -2 5 -2+w -2 -2 7 |Aut| = 2 #short vectors: 0 0 2 10 16 30 48 82 96 144 182 270 278 400 &Hlattice (#30 <- #4) 2 1 2 1 1 2 1-w 1 0 9 |Aut| = 2^4*3 #short vectors: 0 12 0 16 8 72 24 48 48 136 96 256 304 472 &Hlattice (#31 <- #7) 2 1 2 1 1 2 1-w 1 1 9 |Aut| = 2^4*3 #short vectors: 0 12 0 16 8 72 24 48 48 136 96 256 304 472 &Hlattice (#32 <- #20) 2 1 2 1-w 0 8 1-w 1-w 4 8 |Aut| = 2^3*3^2 #short vectors: 0 12 0 36 0 12 0 120 72 180 144 216 288 348 &Hlattice (#33 <- #5) 2 0 2 -w 0 6 0 -w 0 6 |Aut| = 2^5 #short vectors: 0 8 0 24 0 48 16 88 80 128 152 256 312 400 &Hlattice (#34 <- #23) 2 1 4 -1 -2 4 1 2-w -2 5 |Aut| = 2^3*3 #short vectors: 0 8 0 24 12 20 16 100 84 184 132 216 292 364 &Hlattice (#35 <- #26) 2 1 4 -1 -2 4 1 1+w -2 5 |Aut| = 2^3*3 #short vectors: 0 8 0 24 12 20 16 100 84 184 132 216 292 364 &Hlattice (#36 <- #29) 2 1 2 1 0 3 -w -w 0 8 |Aut| = 2^3*3 #short vectors: 0 8 12 12 12 8 40 64 60 184 168 276 232 436 &Hlattice (#37 <- #32) 2 1 3 1 -1 3 1-w 0 1-w 7 |Aut| = 2^3*3 #short vectors: 0 8 12 12 12 8 40 64 60 184 168 276 232 436 &Hlattice (#38 <- #37) 2 1 2 1-w 0 9 -w 1-w 4 11 |Aut| = 2^2*3 #short vectors: 0 6 6 12 10 30 56 64 42 142 184 306 224 472 &Hlattice (#39 <- #38) 2 1 2 1 1 4 1-w 1-w 1 9 |Aut| = 2^2*3 #short vectors: 0 6 0 18 10 36 44 82 54 142 166 276 254 436 &Hlattice (#40 <- #6) 2 0 2 1 -1 3 1 0 1-w 6 |Aut| = 2^4 #short vectors: 0 4 16 8 0 24 40 56 88 128 216 320 264 440 &Hlattice (#41 <- #9) 2 0 3 0 -1+w 4 -w 0 0 6 |Aut| = 2^3 #short vectors: 0 4 4 8 20 32 44 64 80 168 144 256 272 424 &Hlattice (#42 <- #12) 2 0 4 1 2-w 4 1-w 2 1 7 |Aut| = 2^3 #short vectors: 0 4 0 16 8 40 56 80 48 120 192 304 240 456 &Hlattice (#43 <- #14) 2 0 4 1 -2+w 4 1-w -w -2 9 |Aut| = 2^3 #short vectors: 0 4 0 20 4 40 32 92 84 124 180 272 292 400 &Hlattice (#44 <- #16) 2 0 4 1 1+w 4 1-w 2 2-w 8 |Aut| = 2^3 #short vectors: 0 4 0 20 4 40 32 92 84 124 180 272 292 400 &Hlattice (#45 <- #17) 2 0 3 1 1 4 -w -1 -1-w 7 |Aut| = 2^3 #short vectors: 0 4 4 8 24 24 40 68 88 188 132 236 276 404 &Hlattice (#46 <- #22) 2 1 3 -1 1 5 1-w 1-w -1 7 |Aut| = 2^3 #short vectors: 0 4 4 8 24 24 40 68 88 188 132 236 276 404 &Hlattice (#47 <- #28) 2 1 3 0 1-w 5 1-w 0 -2 7 |Aut| = 2^3 #short vectors: 0 4 8 4 24 20 48 56 80 188 144 256 256 428 &Hlattice (#48 <- #34) 2 0 4 1 2 5 1-w -1 1 7 |Aut| = 2^3 #short vectors: 0 4 0 12 24 28 32 80 96 188 120 216 296 380 &Hlattice (#49 <- #39) 4 -1 4 -1-w w 5 -1+w -2 -2 5 |Aut| = 2^2 #short vectors: 0 2 0 10 18 44 36 74 102 150 142 244 310 396 &Hlattice (#50 <- #40) 2 1 3 1 2-w 6 1-w 0 -2 9 |Aut| = 2^2 #short vectors: 0 2 6 10 12 30 36 74 104 148 174 266 294 396 &Hlattice (#51 <- #41) 2 0 4 0 -w 4 -w 1 -1 7 |Aut| = 2^2 #short vectors: 0 2 2 8 18 42 40 68 98 150 148 254 300 408 &Hlattice (#52 <- #42) 3 0 4 1 -2+w 5 2-w -2 2 6 |Aut| = 2^2 #short vectors: 0 2 2 10 16 34 52 74 76 144 174 278 262 428 &Hlattice (#53 <- #48) 2 0 3 -1 1 3 1 1-w -1 5 |Aut| = 2^2 #short vectors: 0 2 10 6 12 26 44 62 96 148 186 286 274 420 &Hlattice (#54 <- #49) 2 0 3 -1 -1 3 1 -w -1 5 |Aut| = 2^2 #short vectors: 0 2 10 6 12 26 44 62 96 148 186 286 274 420 &Hlattice (#55 <- #50) 2 1 3 -w 0 8 1-w 1-w 4 8 |Aut| = 2^2 #short vectors: 0 2 8 8 12 32 28 68 120 152 164 256 316 384 &Hlattice (#56 <- #51) 2 -1 6 -1 2+w 6 1-w -1 -2 7 |Aut| = 2^2 #short vectors: 0 2 2 8 18 42 40 68 98 150 148 254 300 408 &Hlattice (#57 <- #52) 3 0 4 -1 -1-w 5 1+w 2 -2 6 |Aut| = 2^2 #short vectors: 0 2 2 10 16 34 52 74 76 144 174 278 262 428 &Hlattice (#58 <- #53) 2 0 4 -1 w 4 -w -1 w 7 |Aut| = 2^2 #short vectors: 0 2 0 10 18 44 36 74 102 150 142 244 310 396 &Hlattice (#59 <- #54) 2 1 3 1 -w 6 -w -w 2 9 |Aut| = 2^2 #short vectors: 0 2 6 10 12 30 36 74 104 148 174 266 294 396 &Hlattice (#60 <- #67) 4 w 4 -1 -2 4 -2 -2+w 2-w 5 |Aut| = 2^2 #short vectors: 0 2 4 8 16 36 44 68 92 148 164 268 284 416 &Hlattice (#61 <- #68) 4 1-w 4 w -2 4 2 1+w 0 5 |Aut| = 2^2 #short vectors: 0 2 4 8 16 36 44 68 92 148 164 268 284 416 &Hlattice (#62 <- #1) 1 0 1 0 0 1 0 0 0 1 |Aut| = 2^7*3 #short vectors: 8 24 32 24 48 96 64 24 104 144 112 192 320 416 &Hlattice (#63 <- #2) 1 0 1 0 0 3 0 0 -1+w 4 |Aut| = 2^4 #short vectors: 4 4 4 24 44 40 68 112 124 160 172 192 292 320 &Hlattice (#64 <- #3) 1 0 1 0 0 2 0 0 -w 6 |Aut| = 2^5 #short vectors: 4 8 16 24 24 40 72 88 92 120 228 272 252 392 &Hlattice (#65 <- #10) 1 0 3 0 1 4 0 -w -2 5 |Aut| = 2^2 #short vectors: 2 0 2 12 30 54 64 84 116 126 178 246 302 380 &Hlattice (#66 <- #11) 1 0 2 0 0 7 0 -w -2-w 8 |Aut| = 2^3 #short vectors: 2 2 8 18 26 24 36 102 148 166 176 208 324 308 &Hlattice (#67 <- #35) 1 0 3 0 1 3 0 2-w 0 5 |Aut| = 2^3 #short vectors: 2 2 10 18 16 30 60 94 106 120 232 282 268 380 &Hlattice (#68 <- #36) 1 0 3 0 1 3 0 2-w 1 5 |Aut| = 2^3 #short vectors: 2 2 10 18 16 30 60 94 106 120 232 282 268 380 &Hlattice (#69 <- #43) 1 0 3 0 2-w 5 0 1+w -3+w 5 |Aut| = 2^3*3 #short vectors: 2 6 14 6 24 66 28 42 146 144 124 222 368 380 classes of Z-lattices with respect to the trace form one representative of each class &Dim=8 V=Q^8 &Genus of the trace-forms: det= 3418801 = 43^4 2-adic symbol: 1^8_II 43-adic symbol: 1^4 43^4 -1-adic symbol: +^8 -^0 level=43, weight=4 a_0,..,a_28 determine modular form 52-classes of trace forms &Gram (#1 <- H1) 10 5 10 0 -4 10 4 0 5 10 0 -4 0 0 10 4 4 0 0 -5 10 0 0 0 4 0 -4 10 0 0 4 0 -4 4 -5 10 |Aut| = 2^5*3 #short vectors: 0 0 0 0 0 0 0 0 0 24 0 48 0 96 0 48 0 24 0 120 0 192 0 336 0 192 0 528 &Gram (#2 <- H2) 8 4 8 0 -2 8 2 0 4 8 0 1 0 0 8 1 0 0 0 -4 8 0 0 0 -1 0 2 8 0 0 1 0 2 0 4 8 |Aut| = 2^4*3 #short vectors: 0 0 0 0 0 0 0 24 0 0 0 24 0 24 0 120 0 120 0 120 0 216 0 264 0 312 0 336 &Gram (#3 <- H3) 8 4 8 0 2 8 2 0 -4 8 0 1 0 0 8 0 0 0 -1 0 8 4 2 1 1 -2 -4 10 1 2 4 -2 4 2 -1 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 0 0 16 0 16 0 12 0 52 0 104 0 84 0 156 0 200 0 268 0 248 0 384 &Gram (#4 <- H4,H5) 8 4 8 2 -2 8 0 0 0 8 4 2 -2 3 10 1 1 2 -4 -2 10 1 0 2 -2 -1 -2 10 4 0 1 -4 1 2 5 12 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 12 0 16 0 32 0 44 0 88 0 100 0 144 0 176 0 260 0 288 0 388 &Gram (#5 <- H6) 8 4 8 0 0 8 0 0 4 8 4 1 0 2 10 3 4 -2 0 5 10 0 -2 4 1 0 -2 10 2 2 3 -1 0 0 -2 10 |Aut| = 2^3*3 #short vectors: 0 0 0 0 0 0 0 12 0 24 0 12 0 48 0 96 0 96 0 180 0 168 0 240 0 264 0 372 &Gram (#6 <- H7) 8 4 8 2 2 8 0 -2 -4 8 2 3 0 2 10 2 2 -1 -2 0 10 2 2 -1 3 4 -4 10 3 -1 4 0 -4 1 -2 12 |Aut| = 2^3 #short vectors: 0 0 0 0 0 0 0 12 0 8 0 52 0 40 0 80 0 104 0 108 0 184 0 280 0 312 0 404 &Gram (#7 <- H8,H9) 8 0 8 0 4 8 4 4 2 10 3 -2 -2 -2 10 0 4 3 4 -2 10 4 -4 0 -1 -1 -2 12 2 -1 -2 4 -2 4 4 12 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 8 0 20 0 40 0 44 0 76 0 104 0 148 0 156 0 252 0 300 0 396 &Gram (#8 <- H10) 8 2 8 0 0 8 0 0 -2 8 2 4 -3 -2 10 4 0 -2 -3 4 10 2 -3 4 0 -3 0 10 3 -2 2 -4 0 3 4 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 0 0 8 0 16 0 48 0 48 0 72 0 96 0 128 0 168 0 272 0 296 0 416 &Gram (#9 <- H11) 8 1 8 0 2 8 2 0 -1 8 4 2 2 0 10 0 2 2 -4 4 10 2 4 0 2 5 0 10 4 3 2 2 -1 1 3 12 |Aut| = 2^3 #short vectors: 0 0 0 0 0 0 0 8 0 20 0 32 0 68 0 76 0 64 0 140 0 188 0 292 0 236 0 444 &Gram (#10 <- H12) 8 0 8 4 -4 10 4 4 0 10 0 -4 3 0 10 4 0 4 1 0 10 1 2 0 3 -4 4 10 2 -1 0 1 4 4 0 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 0 0 4 0 32 0 28 0 48 0 72 0 104 0 188 0 128 0 224 0 288 0 388 &Gram (#11 <- H13) 6 0 6 0 0 6 0 0 0 6 1 0 2 0 8 0 -1 0 -2 0 8 2 0 -1 0 0 0 8 0 2 0 -1 0 0 0 8 |Aut| = 2^5 #short vectors: 0 0 0 0 0 8 0 8 0 8 0 32 0 40 0 72 0 112 0 128 0 200 0 288 0 296 0 400 &Gram (#12 <- H14) 6 2 6 0 0 6 0 0 2 6 1 -2 2 0 10 2 -1 0 -2 4 10 0 -2 -2 1 0 0 10 2 0 -1 2 0 0 4 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 8 0 4 0 8 0 44 0 56 0 56 0 88 0 108 0 208 0 320 0 272 0 452 &Gram (#13 <- H15) 6 2 6 2 0 6 0 -2 2 6 1 2 0 0 10 0 0 -2 -1 0 10 2 2 3 2 4 2 12 2 3 -2 -2 -2 4 0 12 |Aut| = 2^2 #short vectors: 0 0 0 0 0 8 0 8 0 12 0 24 0 36 0 76 0 120 0 148 0 188 0 268 0 300 0 380 &Gram (#14 <- H16) 6 0 6 0 0 6 0 0 0 6 3 -2 -2 0 10 2 0 3 -2 0 10 2 3 0 2 0 0 10 0 2 -2 3 0 -2 2 10 |Aut| = 2^5 #short vectors: 0 0 0 0 0 8 0 0 0 16 0 56 0 16 0 48 0 160 0 144 0 128 0 232 0 384 0 368 &Gram (#15 <- H17) 6 2 6 0 0 6 0 2 2 8 2 0 2 1 8 1 0 2 -2 0 10 0 -1 -2 0 2 -4 10 2 -2 -3 0 -2 -1 1 12 |Aut| = 2^2 #short vectors: 0 0 0 0 0 6 0 6 0 12 0 38 0 48 0 66 0 100 0 128 0 190 0 290 0 286 0 420 &Gram (#16 <- H18,H19) 6 2 6 2 -2 8 2 -2 4 8 0 -2 -1 2 10 2 0 0 3 4 10 0 1 2 0 -4 2 12 1 0 1 3 -2 4 0 12 |Aut| = 2^2 #short vectors: 0 0 0 0 0 4 0 12 0 12 0 24 0 40 0 88 0 108 0 144 0 192 0 268 0 288 0 380 &Gram (#17 <- H20) 6 0 6 2 0 8 0 -2 0 8 2 -2 -3 -2 10 2 -2 -2 -3 4 10 1 2 4 -4 1 0 12 2 -1 4 4 -2 -4 0 12 |Aut| = 2^3 #short vectors: 0 0 0 0 0 4 0 4 0 12 0 56 0 48 0 56 0 100 0 112 0 176 0 292 0 304 0 436 &Gram (#18 <- H21,H23) 6 0 6 2 2 8 2 2 2 8 2 -2 2 -3 10 2 -2 3 -2 4 10 1 0 2 -2 4 0 10 0 -1 2 -2 0 4 0 10 |Aut| = 2^2 #short vectors: 0 0 0 0 0 4 0 4 0 20 0 36 0 52 0 64 0 96 0 148 0 168 0 272 0 280 0 420 &Gram (#19 <- H22) 6 0 6 2 2 8 2 -2 0 8 2 -2 -1 2 8 2 2 2 1 0 8 3 2 4 2 -2 0 12 2 3 0 2 -2 4 2 12 |Aut| = 2^3 #short vectors: 0 0 0 0 0 4 0 8 0 16 0 36 0 28 0 76 0 132 0 152 0 156 0 240 0 332 0 364 &Gram (#20 <- H24) 6 0 6 2 -2 8 2 0 3 8 2 2 0 0 8 0 2 0 0 3 8 1 2 -2 2 0 -2 10 2 -1 0 -2 2 -2 0 10 |Aut| = 2^2 #short vectors: 0 0 0 0 0 4 0 8 0 20 0 24 0 36 0 80 0 120 0 168 0 160 0 240 0 304 0 368 &Gram (#21 <- H25) 6 2 6 2 2 8 2 2 -1 8 0 2 0 2 8 2 0 2 0 -3 8 1 0 -2 2 -2 0 10 0 1 2 -2 0 -2 2 10 |Aut| = 2^2 #short vectors: 0 0 0 0 0 4 0 10 0 18 0 16 0 48 0 86 0 98 0 162 0 186 0 264 0 266 0 388 &Gram (#22 <- H26) 6 0 6 2 0 8 0 2 3 8 0 -2 0 -2 8 2 0 2 0 3 8 3 0 2 2 2 2 10 0 -3 2 0 0 -2 0 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 4 0 8 0 20 0 16 0 60 0 80 0 80 0 160 0 192 0 280 0 240 0 416 &Gram (#23 <- H27) 6 0 8 0 -2 8 0 4 -4 10 0 4 -4 5 10 2 1 -4 4 0 10 2 4 -1 0 4 1 10 3 2 2 0 0 0 2 10 |Aut| = 2^3 #short vectors: 0 0 0 0 0 2 0 4 0 26 0 30 0 56 0 68 0 90 0 166 0 156 0 258 0 268 0 416 &Gram (#24 <- H28,H29) 6 2 8 2 1 8 2 0 -2 8 0 2 2 -4 8 2 2 0 -2 3 10 0 2 -2 1 -3 3 10 1 4 -2 2 2 0 2 12 |Aut| = 2 #short vectors: 0 0 0 0 0 2 0 10 0 16 0 30 0 48 0 82 0 96 0 144 0 182 0 270 0 278 0 400 &Gram (#25 <- H30,H31) 4 2 4 2 2 4 2 2 2 8 0 0 0 -3 8 1 2 2 2 -2 18 1 -1 1 1 -2 -5 18 2 2 1 2 -2 -4 -5 18 |Aut| = 2^4*3 #short vectors: 0 0 0 12 0 0 0 16 0 8 0 72 0 24 0 48 0 48 0 136 0 96 0 256 0 304 0 472 &Gram (#26 <- H32) 4 2 4 0 0 4 0 0 -2 4 1 0 -2 0 16 1 1 2 0 6 16 2 2 1 -1 0 1 16 2 2 0 1 0 1 -6 16 |Aut| = 2^4*3^2 #short vectors: 0 0 0 12 0 0 0 36 0 0 0 12 0 0 0 120 0 72 0 180 0 144 0 216 0 288 0 348 &Gram (#27 <- H33) 4 0 4 0 0 4 0 0 0 4 1 0 -2 0 12 0 -1 0 2 0 12 2 0 -1 0 1 0 12 0 2 0 -1 0 -1 0 12 |Aut| = 2^7 #short vectors: 0 0 0 8 0 0 0 24 0 0 0 48 0 16 0 88 0 80 0 128 0 152 0 256 0 312 0 400 &Gram (#28 <- H34,H35) 4 2 4 0 0 4 2 2 -2 8 2 0 2 -1 10 0 0 1 -3 -3 14 1 0 0 2 3 -2 16 0 1 0 2 2 -2 -6 16 |Aut| = 2^3*3 #short vectors: 0 0 0 8 0 0 0 24 0 12 0 20 0 16 0 100 0 84 0 184 0 132 0 216 0 292 0 364 &Gram (#29 <- H36,H37) 4 0 4 0 2 4 2 2 2 6 0 0 0 -1 12 1 0 0 1 -6 14 0 -1 -1 -1 4 -2 16 0 0 1 0 4 -2 -6 16 |Aut| = 2^3*3 #short vectors: 0 0 0 8 0 12 0 12 0 12 0 8 0 40 0 64 0 60 0 184 0 168 0 276 0 232 0 436 &Gram (#30 <- H38) 4 2 4 2 0 6 2 0 2 8 2 0 2 1 8 2 0 -1 2 0 12 1 0 3 -1 3 2 18 1 1 -2 2 -2 -1 4 18 |Aut| = 2^3*3 #short vectors: 0 0 0 6 0 6 0 12 0 10 0 30 0 56 0 64 0 42 0 142 0 184 0 306 0 224 0 472 &Gram (#31 <- H39) 4 2 4 2 2 8 2 0 4 8 2 2 1 0 10 0 0 2 3 4 10 1 -1 3 1 0 -4 20 2 1 -2 1 1 4 3 20 |Aut| = 2^3*3 #short vectors: 0 0 0 6 0 0 0 18 0 10 0 36 0 44 0 82 0 54 0 142 0 166 0 276 0 254 0 436 &Gram (#32 <- H40) 4 0 4 2 -2 6 2 2 0 6 2 0 1 0 12 0 -2 0 -1 0 12 1 -2 0 -1 6 -4 18 2 1 0 0 -4 5 -5 18 |Aut| = 2^5 #short vectors: 0 0 0 4 0 16 0 8 0 0 0 24 0 40 0 56 0 88 0 128 0 216 0 320 0 264 0 440 &Gram (#33 <- H41) 4 0 4 0 0 6 0 0 0 6 0 0 -1 -2 8 0 0 2 -1 0 8 1 -2 0 0 0 0 12 2 -1 0 0 0 0 1 12 |Aut| = 2^5 #short vectors: 0 0 0 4 0 4 0 8 0 20 0 32 0 44 0 64 0 80 0 168 0 144 0 256 0 272 0 424 &Gram (#34 <- H42) 4 0 4 2 0 8 0 0 3 8 0 -2 0 -2 8 0 0 2 0 3 8 1 2 -1 -4 0 0 14 2 1 2 0 1 4 1 14 |Aut| = 2^4 #short vectors: 0 0 0 4 0 0 0 16 0 8 0 40 0 56 0 80 0 48 0 120 0 192 0 304 0 240 0 456 &Gram (#35 <- H43,H44) 4 0 4 2 -2 8 2 0 0 8 0 0 2 -3 8 0 0 1 -2 0 8 2 1 1 0 0 4 14 1 2 -2 3 -4 -4 -1 16 |Aut| = 2^3 #short vectors: 0 0 0 4 0 0 0 20 0 4 0 40 0 32 0 92 0 84 0 124 0 180 0 272 0 292 0 400 &Gram (#36 <- H45,H46) 4 0 4 0 2 6 2 0 -2 8 2 0 -2 -1 10 2 0 -1 4 3 12 1 0 2 -2 -3 -2 14 0 1 1 -2 2 4 0 14 |Aut| = 2^3 #short vectors: 0 0 0 4 0 4 0 8 0 24 0 24 0 40 0 68 0 88 0 188 0 132 0 236 0 276 0 404 &Gram (#37 <- H47) 4 0 4 2 0 6 0 2 0 6 0 2 -1 2 10 2 0 0 -1 0 10 1 0 1 2 -4 0 14 0 1 -2 1 1 -4 0 14 |Aut| = 2^4 #short vectors: 0 0 0 4 0 8 0 4 0 24 0 20 0 48 0 56 0 80 0 188 0 144 0 256 0 256 0 428 &Gram (#38 <- H48) 4 0 4 0 2 8 2 0 0 8 2 -2 -4 -1 10 2 2 3 -2 0 10 1 0 2 3 2 0 14 0 1 -2 2 0 2 0 14 |Aut| = 2^4 #short vectors: 0 0 0 4 0 0 0 12 0 24 0 28 0 32 0 80 0 96 0 188 0 120 0 216 0 296 0 380 &Gram (#39 <- H49,H58) 4 2 8 0 2 8 0 0 -2 8 0 1 2 2 8 2 -2 -3 -2 0 10 2 4 4 -3 0 -2 10 1 1 2 2 -2 -2 1 14 |Aut| = 2^2 #short vectors: 0 0 0 2 0 0 0 10 0 18 0 44 0 36 0 74 0 102 0 150 0 142 0 244 0 310 0 396 &Gram (#40 <- H50,H59) 4 2 6 0 -2 6 2 0 2 8 0 0 -2 1 8 0 -2 3 4 2 12 2 -1 0 2 0 4 12 1 -1 2 0 -4 -2 -4 16 |Aut| = 2^2 #short vectors: 0 0 0 2 0 6 0 10 0 12 0 30 0 36 0 74 0 104 0 148 0 174 0 266 0 294 0 396 &Gram (#41 <- H51,H56) 4 0 6 2 2 8 0 -2 2 8 0 -2 -2 1 8 0 2 3 2 2 10 2 1 4 2 -4 -2 12 1 2 0 -2 -2 -4 2 14 |Aut| = 2^2 #short vectors: 0 0 0 2 0 2 0 8 0 18 0 42 0 40 0 68 0 98 0 150 0 148 0 254 0 300 0 408 &Gram (#42 <- H52,H57) 4 0 6 2 2 8 2 0 4 8 2 -2 0 -1 10 0 0 -3 -2 4 10 2 3 4 4 -2 -4 12 1 -2 -3 -3 0 4 -3 16 |Aut| = 2^2 #short vectors: 0 0 0 2 0 2 0 10 0 16 0 34 0 52 0 74 0 76 0 144 0 174 0 278 0 262 0 428 &Gram (#43 <- H53,H54) 4 2 6 2 0 6 0 -2 0 6 2 2 0 1 10 0 -2 1 0 0 10 0 1 2 -2 -4 -2 12 1 2 -1 -2 2 -4 -4 16 |Aut| = 2^2 #short vectors: 0 0 0 2 0 10 0 6 0 12 0 26 0 44 0 62 0 96 0 148 0 186 0 286 0 274 0 420 &Gram (#44 <- H55) 4 2 6 2 0 6 0 2 2 8 0 -2 0 -1 8 2 0 1 -1 4 12 0 1 0 3 -4 -4 12 1 0 3 2 0 4 4 16 |Aut| = 2^3 #short vectors: 0 0 0 2 0 8 0 8 0 12 0 32 0 28 0 68 0 120 0 152 0 164 0 256 0 316 0 384 &Gram (#45 <- H60,H61) 4 2 6 0 2 8 0 -2 -4 8 0 0 2 -1 8 2 2 3 0 4 10 2 -1 -2 2 -2 2 12 1 -2 -4 2 0 -2 -3 16 |Aut| = 2^2 #short vectors: 0 0 0 2 0 4 0 8 0 16 0 36 0 44 0 68 0 92 0 148 0 164 0 268 0 284 0 416 &Gram (#46 <- H62) 2 0 2 0 0 2 0 0 0 2 1 0 0 0 22 0 1 0 0 0 22 0 0 1 0 0 0 22 0 0 0 1 0 0 0 22 |Aut| = 2^11*3 #short vectors: 0 8 0 24 0 32 0 24 0 48 0 96 0 64 0 24 0 104 0 144 0 112 0 192 0 320 0 416 &Gram (#47 <- H63) 2 0 2 0 0 6 0 0 0 6 0 0 -1 -2 8 0 0 2 -1 0 8 1 0 0 0 0 0 22 0 1 0 0 0 0 0 22 |Aut| = 2^7 #short vectors: 0 4 0 4 0 4 0 24 0 44 0 40 0 68 0 112 0 124 0 160 0 172 0 192 0 292 0 320 &Gram (#48 <- H64) 2 0 2 0 0 4 0 0 0 4 0 0 -1 2 12 0 0 2 -1 -1 12 1 0 0 0 0 0 22 0 1 0 0 0 0 0 22 |Aut| = 2^8 #short vectors: 0 4 0 8 0 16 0 24 0 24 0 40 0 72 0 88 0 92 0 120 0 228 0 272 0 252 0 392 &Gram (#49 <- H65) 2 0 6 0 2 8 0 0 2 8 0 0 2 -3 8 0 2 -3 2 -4 10 0 1 4 2 0 1 10 1 0 0 0 0 0 0 22 |Aut| = 2^4 #short vectors: 0 2 0 0 0 2 0 12 0 30 0 54 0 64 0 84 0 116 0 126 0 178 0 246 0 302 0 380 &Gram (#50 <- H66) 2 0 4 0 2 6 0 2 2 8 0 2 0 -1 8 0 -2 -1 0 0 10 0 -1 -3 -3 -2 4 16 1 0 0 0 0 0 0 22 |Aut| = 2^5 #short vectors: 0 2 0 2 0 8 0 18 0 26 0 24 0 36 0 102 0 148 0 166 0 176 0 208 0 324 0 308 &Gram (#51 <- H67,H68) 2 0 4 0 2 6 0 0 2 6 0 0 2 3 10 0 2 -1 -2 2 12 0 -1 -2 0 -2 -5 14 1 0 0 0 0 0 0 22 |Aut| = 2^4 #short vectors: 0 2 0 2 0 10 0 18 0 16 0 30 0 60 0 94 0 106 0 120 0 232 0 282 0 268 0 380 &Gram (#52 <- H69) 2 0 4 0 2 4 0 0 0 6 0 2 2 3 10 0 1 -1 2 1 16 0 1 2 -2 0 6 16 1 0 0 0 0 0 0 22 |Aut| = 2^5*3 #short vectors: 0 2 0 6 0 14 0 6 0 24 0 66 0 28 0 42 0 146 0 144 0 124 0 222 0 368 0 380