Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-8 -D5 &K=Q(sqrt(-11)) &Hdim=6 V=K^6 &HNeighbourhood at <3,-1+w> contains 39 classes: mass of the neighbourhood is 8075/101376 Steinitz class <1,w>: &Hlattice (#1 <-- #34) 3 -1 3 w 2-w 3 w 0 1 3 1 1 1 -1 3 0 0 0 1-w -2+w 3 |Aut| = 2^4*3*5 #short vectors: 0 0 100 444 1188 2908 6504 12564 &Hlattice (#2 <-- #24) 2 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 -w -w w -w w 4 |Aut| = 2^8*3^4*5 #short vectors: 0 72 0 324 864 3564 6624 14436 &Hlattice (#3 <-- #27) 2 0 2 0 1 2 0 -1 -1 2 0 1 1 -1 2 1-w -1+w 0 0 0 4 |Aut| = 2^8*3^4*5 #short vectors: 0 72 0 324 864 3564 6624 14436 &Hlattice (#4 <-- #32) 2 0 2 0 -1 2 0 0 0 2 -1 0 0 -1 2 -w -1 1 1-w -1+w 4 |Aut| = 2^9*3^2*5 #short vectors: 0 60 0 444 768 3288 7104 14124 &Hlattice (#5 <-- #28) 2 -w 2 0 0 2 0 0 0 2 0 0 0 -w 2 0 0 -w 0 0 2 |Aut| = 2^7*3^4 #short vectors: 0 36 36 468 900 3096 6984 13500 &Hlattice (#6 <-- #5) 2 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 1 -w w -w w 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 64 340 1120 3284 6304 13396 &Hlattice (#7 <-- #7) 2 0 2 0 -1 2 0 1 -1 2 -w 0 0 0 2 0 -w w 1-w 0 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 52 412 1012 3164 6664 13396 &Hlattice (#8 <-- #22) 2 1 2 1 1 2 -1 -1 -1 2 0 0 0 0 2 1-w 1-w 1-w -1+w 1 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 64 340 1120 3284 6304 13396 &Hlattice (#9 <-- #25) 2 1 2 -1 -1 2 1 1 -1 2 0 0 0 0 2 -w -w w -w 1-w 4 |Aut| = 2^6*3^2*5 #short vectors: 0 32 40 484 904 3044 7024 13396 &Hlattice (#10 <-- #29) 2 -1 2 1 -1 2 0 0 0 2 0 0 0 -w 2 -w -1+w 1-w 0 0 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 52 412 1012 3164 6664 13396 &Hlattice (#11 <-- #38) 2 -1 2 0 0 2 0 0 0 2 -1 1 0 1 2 0 0 w 1-w 1-w 4 |Aut| = 2^6*3^2*5 #short vectors: 0 32 40 484 904 3044 7024 13396 &Hlattice (#12 <-- #16) 2 0 2 0 0 2 0 0 -1 2 -1 w 1 -1 3 w -1 0 0 0 3 |Aut| = 2^9*3 #short vectors: 0 28 64 380 1088 3192 6464 13292 &Hlattice (#13 <-- #17) 2 0 2 0 -1 2 0 0 0 2 1-w 0 0 -1 3 1 -1 1 1-w -1+w 3 |Aut| = 2^9*3 #short vectors: 0 28 64 380 1088 3192 6464 13292 &Hlattice (#14 <-- #10) 2 0 2 0 0 2 0 0 -1 2 -1 1 0 0 2 -1+w 0 -1 1 1-w 3 |Aut| = 2^7*3^2 #short vectors: 0 24 64 420 1056 3100 6624 13188 &Hlattice (#15 <-- #21) 2 1 2 -1 0 2 -1 -1 0 3 0 0 1 -1-w 3 w w -w 1-w 0 4 |Aut| = 2^8*3^2 #short vectors: 0 24 96 228 1344 3420 5664 13188 &Hlattice (#16 <-- #30) 2 1 2 0 0 2 0 0 0 2 0 0 -w 0 2 1-w -w 0 1 0 3 |Aut| = 2^6*3^3 #short vectors: 0 24 84 300 1236 3300 6024 13188 &Hlattice (#17 <-- #13) 2 0 2 0 0 2 0 0 -1 2 -1+w 1 0 0 3 -w 0 -1 1 -1 3 |Aut| = 2^6*3 #short vectors: 0 16 88 356 1208 3156 6224 12980 &Hlattice (#18 <-- #18) 2 0 2 0 0 2 0 1-w 0 3 -1 1 1 -1+w 3 -1+w 0 1 1 1-w 3 |Aut| = 2^7*3 #short vectors: 0 16 80 404 1136 3076 6464 12980 &Hlattice (#19 <-- #20) 2 -1 2 0 0 2 0 0 -w 3 0 -1 1-w 1 3 1-w -1+w 0 1 0 3 |Aut| = 2^6*3 #short vectors: 0 16 88 356 1208 3156 6224 12980 &Hlattice (#20 <-- #31) 2 0 2 0 0 2 0 0 -1 2 -w 0 1 -1 3 -1+w 1-w 0 0 -1-w 4 |Aut| = 2^7*3 #short vectors: 0 16 80 404 1136 3076 6464 12980 &Hlattice (#21 <-- #14) 2 1 2 0 0 2 1 1 -1 3 1 1 -1 2-w 3 1-w -w 0 -w 1-w 3 |Aut| = 2^5*3^2 #short vectors: 0 12 100 324 1284 3184 6024 12876 &Hlattice (#22 <-- #23) 2 1 2 0 0 2 -1 -1 -1 3 0 0 -w 1 3 1-w -w 0 w 0 3 |Aut| = 2^4*3^2 #short vectors: 0 12 84 420 1140 3024 6504 12876 &Hlattice (#23 <-- #26) 2 0 2 0 0 2 0 1-w -1 3 0 1 1-w -1+w 3 -w 0 0 0 -1 3 |Aut| = 2^7*3 #short vectors: 0 12 96 348 1248 3144 6144 12876 &Hlattice (#24 <-- #35) 2 0 2 0 0 2 1-w 1 -1 3 1 0 1 -1+w 3 1 -1+w 1 -1+w 1 3 |Aut| = 2^7*5 #short vectors: 0 12 80 444 1104 2984 6624 12876 &Hlattice (#25 <-- #37) 2 0 2 0 0 2 -1 w 1 3 0 -1 w w 3 1 -1 1 0 1-w 4 |Aut| = 2^7*5 #short vectors: 0 12 80 444 1104 2984 6624 12876 &Hlattice (#26 <-- #39) 2 0 2 0 0 2 1 1 1 3 -w -w -1 -1-w 4 1 -w 0 1 1 4 |Aut| = 2^8*3*5 #short vectors: 0 12 64 540 960 2824 7104 12876 &Hlattice (#27 <-- #15) 2 0 2 1-w -1 3 -1 w -w 3 0 -1 1 -1+w 3 0 1 -1 1 1-w 3 |Aut| = 2^6*3 #short vectors: 0 8 88 436 1144 2972 6544 12772 &Hlattice (#28 <-- #19) 2 0 2 0 0 2 -w 0 0 3 0 1 -1+w 0 3 0 0 -w -1 -1 3 |Aut| = 2^6 #short vectors: 0 8 96 388 1216 3052 6304 12772 &Hlattice (#29 <-- #36) 2 1 3 -1+w -1+w 3 1-w 1-w -1 3 0 1-w 0 1 3 0 0 -1 -1 -1+w 3 |Aut| = 2^6*3 #short vectors: 0 8 88 436 1144 2972 6544 12772 &Hlattice (#30 <-- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 |Aut| = 2^10*3^2*5 #short vectors: 12 60 184 492 1296 2944 6000 11868 &Hlattice (#31 <-- #2) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 -w 2 |Aut| = 2^9*3^2 #short vectors: 8 36 156 516 1228 2840 6328 11996 &Hlattice (#32 <-- #3) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 1 2 0 0 w 1-w -w 3 |Aut| = 2^7*3*5 #short vectors: 4 24 128 420 1256 3012 6176 12436 &Hlattice (#33 <-- #6) 1 0 1 0 0 2 0 0 0 2 0 0 0 -w 2 0 0 -w 0 0 2 |Aut| = 2^8*3^2 #short vectors: 4 28 128 380 1288 3104 6016 12540 &Hlattice (#34 <-- #8) 1 0 1 0 0 2 0 0 0 2 0 0 -1 -1 2 0 0 1-w -1 w 3 |Aut| = 2^7*3*5 #short vectors: 4 24 128 420 1256 3012 6176 12436 &Hlattice (#35 <-- #11) 1 0 1 0 0 2 0 0 0 2 0 0 1 0 2 0 0 -w 1 1-w 3 |Aut| = 2^7*3^2 #short vectors: 4 16 128 500 1192 2828 6496 12228 &Hlattice (#36 <-- #4) 1 0 2 0 1 2 0 -1 -1 2 0 1 1 -1 3 0 -1+w -1+w 1-w -2+w 3 |Aut| = 2^5*3*5 #short vectors: 2 20 114 352 1286 3144 6020 12708 &Hlattice (#37 <-- #9) 1 0 2 0 0 2 0 -1 0 2 0 0 0 -w 3 0 0 1 1 -1 3 |Aut| = 2^5*3^2 #short vectors: 2 12 114 432 1222 2960 6340 12500 &Hlattice (#38 <-- #12) 1 0 2 0 -1 2 0 0 0 2 0 0 -1 -1 3 0 -w 0 1 -1 3 |Aut| = 2^5*3^2 #short vectors: 2 12 114 432 1222 2960 6340 12500 &Hlattice (#39 <-- #33) 1 0 3 0 -2+w 3 0 -w -1 3 0 1 -1-w 1 3 0 0 -1 1 1-w 3 |Aut| = 2^4*3*5*11 #short vectors: 2 0 114 552 1126 2684 6820 12188 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 30 0 12 12 0 20 120 60 0 0 0 0 0 0 0 30 10 10 0 0 0 27 40 0 0 216 36 0 0 0 0 0 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 72 0 0 0 36 0 0 0 0 135 0 0 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 6 0 0 0 0 0 16 80 96 30 0 0 0 0 0 0 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 0 36 0 0 54 36 0 0 0 0 6 0 108 0 0 0 0 0 0 0 0 0 0 108 0 0 0 9 0 0 0 0 0 0 0 1 6 0 0 0 30 0 20 0 0 0 15 0 0 0 135 30 60 0 0 0 30 0 0 0 15 0 0 0 0 0 10 0 0 12 0 0 0 0 0 0 10 15 20 1 0 0 5 0 0 30 60 0 10 0 0 0 30 0 80 0 0 0 0 0 90 0 0 0 3 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 20 1 30 0 55 30 10 0 90 60 0 0 0 45 0 0 0 0 0 0 2 0 0 0 0 0 0 0 20 0 0 0 0 12 10 1 0 0 0 0 6 45 0 60 0 0 0 30 0 15 0 120 0 0 0 30 0 0 15 0 0 0 0 0 0 0 20 0 0 0 0 0 0 10 0 10 30 20 1 0 0 30 10 0 15 60 0 0 0 20 60 0 90 0 0 0 0 0 0 5 0 0 3 0 0 0 0 0 0 0 1 2 0 1 20 20 60 0 0 0 30 0 0 0 0 0 15 30 0 40 0 45 0 0 90 0 0 0 0 0 0 0 10 0 0 0 0 0 2 0 0 0 0 16 8 16 16 0 0 2 0 0 0 64 4 64 80 0 0 0 0 12 0 0 0 48 0 0 0 0 0 0 32 0 0 0 0 0 0 2 0 16 0 0 0 0 24 32 0 4 2 16 16 64 48 0 0 64 12 0 0 0 0 48 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 22 4 0 0 24 24 3 0 0 0 0 48 0 54 3 0 0 0 18 36 0 0 36 72 0 4 0 0 0 0 0 16 0 0 0 0 1 0 0 24 0 0 0 0 0 3 0 0 32 16 72 0 24 12 96 0 24 0 0 0 0 0 12 0 0 0 0 0 0 48 0 0 0 0 2 0 0 1 6 9 0 0 6 0 18 0 0 12 7 36 0 108 0 36 12 54 0 0 0 36 0 0 0 0 0 18 0 3 0 0 0 0 0 0 0 1 0 4 0 4 1 0 0 6 8 9 2 12 28 4 18 8 24 56 18 0 6 0 12 93 12 0 0 2 4 0 0 16 0 16 0 0 0 0 0 0 0 0 0 4 4 2 0 20 1 2 0 48 0 16 56 16 16 6 12 0 3 24 42 60 0 0 8 0 0 0 0 24 0 0 0 0 0 0 0 0 4 9 0 0 0 2 8 8 6 4 31 1 28 24 32 32 12 12 3 0 24 84 6 0 2 0 0 4 0 12 16 0 0 0 0 0 0 4 12 0 4 0 0 4 16 1 0 0 0 2 37 8 0 16 64 0 12 30 0 18 96 0 0 0 0 0 0 0 16 0 24 0 18 0 0 0 0 0 2 0 0 0 0 0 0 0 12 6 48 12 36 12 18 12 36 0 0 0 0 108 0 0 0 0 0 6 0 18 2 18 0 18 0 0 0 0 0 3 0 2 4 6 6 0 0 0 1 24 24 42 6 6 24 0 0 18 0 36 54 54 0 0 3 0 0 3 6 18 6 0 0 0 0 0 0 6 0 4 0 0 0 3 0 0 4 12 24 0 36 6 48 0 0 3 24 0 0 120 38 0 0 12 0 0 0 0 24 0 0 32 0 0 0 0 0 0 0 0 0 0 0 5 20 0 0 10 50 20 0 0 80 40 0 1 16 10 20 40 0 0 0 0 0 20 0 0 0 0 32 0 0 0 0 0 20 0 10 0 0 0 0 10 0 0 40 20 0 20 0 0 5 16 0 1 100 50 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 30 0 0 0 6 96 0 40 0 120 0 0 0 0 0 0 0 0 0 32 48 0 0 0 2 0 0 0 0 0 1 0 6 12 1 0 6 0 12 30 0 72 19 0 12 6 8 69 20 0 0 0 0 0 4 0 24 12 0 32 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 28 16 31 7 24 24 20 5 2 0 32 72 23 0 0 0 2 0 4 8 12 16 0 16 0 0 0 0 0 0 1 6 0 0 0 0 0 0 4 24 9 12 12 0 48 0 30 3 2 55 96 8 0 0 0 0 6 0 0 0 24 8 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 110 120 0 0 0 96 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 16 0 0 48 0 0 0 0 0 0 0 0 0 0 0 0 11 29 0 28 24 72 0 32 96 0 0 0 0 0 0 0 2 0 0 0 0 20 0 0 0 0 40 0 0 0 40 0 0 0 0 0 60 0 0 0 10 2 15 45 10 20 0 100 0 0 0 0 0 2 0 0 8 0 8 0 0 0 0 0 24 0 0 48 0 0 0 0 0 0 0 0 72 0 0 14 12 28 18 2 48 72 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 20 40 0 40 60 0 0 0 0 0 0 5 0 10 10 2 55 60 60 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 0 0 0 0 0 24 0 0 36 0 0 72 24 0 18 33 1 6 8 0 76 36 24 0 0 0 0 0 0 0 2 0 0 0 0 10 0 10 0 30 20 40 0 30 20 0 0 0 0 0 60 0 1 0 15 10 5 0 36 40 35 0 12 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 18 24 0 18 12 0 18 0 0 36 72 18 0 6 0 1 15 9 21 28 48 6 36 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0 24 0 0 18 2 36 18 0 0 0 0 54 36 0 2 9 9 0 19 24 43 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 242 0 0 0 0 0 0 0 110 0 0 0 12 classes of Z-lattices with respect to the trace form &Dim=12 V=Q^12 &Genus of the trace-forms: det= 1771561 = 11^6 2-adic symbol: 1^12_II 11-adic symbol: 1^6 11^6 -1-adic symbol: +^12 -^0 level=11, weight=6 a_0,..,a_12 determine modular form &Gram (#1 <- H1) 6 3 6 2 -1 6 2 2 -2 6 2 3 1 -1 6 2 0 -1 3 -2 6 2 2 -2 1 0 2 6 2 3 1 2 2 0 1 6 2 2 0 2 -1 0 0 2 6 2 -1 2 0 1 2 0 1 -2 6 2 0 -1 0 0 2 1 -2 0 2 6 0 0 0 -1 2 -2 -2 -2 -2 0 2 6 |Aut| = 2^5*3*5 #short vectors: 0 0 0 0 0 100 0 444 0 1188 0 2908 &Gram (#2 <- H2,H3) 4 2 4 2 0 4 2 0 0 4 2 0 2 0 4 2 2 0 0 2 4 1 0 0 1 1 1 8 1 1 1 0 1 1 2 8 0 1 0 -1 0 1 -2 4 8 1 0 1 1 0 0 2 2 -2 8 1 0 1 0 1 0 2 2 -2 2 8 0 0 0 0 -1 -1 -4 -4 -2 2 2 8 |Aut| = 2^8*3^4*5 #short vectors: 0 0 0 72 0 0 0 324 0 864 0 3564 &Gram (#3 <- H4) 4 2 4 2 0 4 2 0 0 4 2 0 2 0 4 2 0 2 0 2 4 1 -1 0 1 0 2 8 1 2 -1 0 1 -1 -1 8 2 2 0 0 2 1 0 2 8 1 0 2 -1 1 2 -2 2 3 10 2 1 0 2 0 0 -2 -2 -2 -3 10 1 2 1 -1 0 0 2 -2 -2 -2 3 10 |Aut| = 2^10*3^2*5 #short vectors: 0 0 0 60 0 0 0 444 0 768 0 3288 &Gram (#4 <- H5) 4 2 4 1 0 4 0 1 -2 4 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -1 0 4 0 0 0 0 0 -1 2 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 -1 -1 4 0 0 0 0 0 0 0 0 1 0 -2 4 |Aut| = 2^10*3^4 #short vectors: 0 0 0 36 0 36 0 468 0 900 0 3096 &Gram (#5 <- H6,H8) 4 0 4 0 -2 4 0 2 -2 4 0 -2 2 -2 4 0 2 -2 2 -2 4 1 2 0 2 -2 0 6 2 -1 1 -1 1 -1 0 6 2 -1 0 0 0 0 0 2 6 2 0 1 0 0 0 1 2 0 6 2 0 0 -1 0 0 0 2 0 0 6 2 0 0 0 1 0 0 2 0 0 0 6 |Aut| = 2^6*3^2*5 #short vectors: 0 0 0 32 0 64 0 340 0 1120 0 3284 &Gram (#6 <- H7,H10) 4 2 4 1 1 4 0 -1 -2 4 0 0 0 0 4 0 0 0 0 2 4 0 0 0 0 -2 -2 4 0 0 0 0 -2 -2 2 4 0 0 0 0 -1 -2 0 0 6 0 0 0 0 -1 1 -1 -1 -1 6 0 0 0 0 -2 -1 2 2 1 1 6 0 0 0 0 2 0 0 -1 1 0 -2 6 |Aut| = 2^7*3^2*5 #short vectors: 0 0 0 32 0 52 0 412 0 1012 0 3164 &Gram (#7 <- H9,H11) 4 2 4 2 2 4 2 0 0 4 2 2 2 0 4 0 0 0 0 0 4 2 0 2 0 0 1 6 2 0 2 1 2 2 2 8 1 2 2 1 0 2 1 2 8 1 -1 -1 0 1 -2 0 -1 -2 8 2 1 0 0 2 -2 0 -1 -1 2 8 2 0 1 0 2 -2 1 0 -1 2 2 8 |Aut| = 2^6*3^2*5 #short vectors: 0 0 0 32 0 40 0 484 0 904 0 3044 &Gram (#8 <- H12,H13) 4 0 4 0 0 4 0 0 -2 4 0 0 -2 0 4 0 0 -2 0 0 4 2 -1 2 0 0 -2 6 1 -2 -2 0 2 0 0 6 2 0 1 -2 0 -1 1 1 8 0 2 -1 -1 2 1 -1 0 3 8 0 2 -1 2 -1 0 -1 -1 2 0 8 0 -2 -2 0 1 2 -1 2 -3 0 -1 8 |Aut| = 2^9*3 #short vectors: 0 0 0 28 0 64 0 380 0 1088 0 3192 &Gram (#9 <- H14) 4 2 4 2 0 4 0 0 0 4 0 0 0 2 4 0 0 0 2 2 4 1 0 1 -2 -2 -2 6 1 1 0 -2 0 0 2 6 0 1 0 2 0 0 -2 0 6 2 2 0 -1 -1 -1 1 1 0 6 2 0 2 -1 0 0 1 1 -1 2 6 2 2 0 0 1 0 0 1 0 0 2 6 |Aut| = 2^8*3^2 #short vectors: 0 0 0 24 0 64 0 420 0 1056 0 3100 &Gram (#10 <- H15) 4 2 4 2 0 4 2 0 0 4 2 2 0 0 6 2 0 0 2 -1 6 2 0 0 2 2 2 6 2 2 0 2 0 2 -1 6 1 1 1 0 2 -2 2 -1 8 0 0 -1 0 2 1 2 -2 3 8 0 1 0 -1 2 0 1 -2 -2 2 8 1 0 1 0 2 1 2 -2 -2 2 2 8 |Aut| = 2^9*3^2 #short vectors: 0 0 0 24 0 96 0 228 0 1344 0 3420 &Gram (#11 <- H16) 4 2 4 0 0 4 0 0 -2 4 0 0 -1 0 4 0 0 0 -1 2 4 0 0 0 0 0 0 4 0 0 0 0 0 0 2 4 1 -1 0 0 0 0 2 0 6 2 1 0 0 0 0 2 0 0 6 2 0 0 0 0 0 -1 -2 1 1 6 2 0 0 0 0 0 2 1 2 2 -1 6 |Aut| = 2^8*3^3 #short vectors: 0 0 0 24 0 84 0 300 0 1236 0 3300 &Gram (#12 <- H17,H19) 4 0 4 0 0 4 0 0 -2 4 0 0 -2 2 4 2 2 2 0 0 6 1 0 2 0 0 3 6 1 0 2 -2 -2 0 2 6 0 1 2 0 0 1 0 2 6 0 -2 1 0 0 -1 1 0 0 6 0 -2 1 -1 -1 0 0 1 0 2 6 0 2 0 1 0 2 0 0 1 0 -2 6 |Aut| = 2^6*3 #short vectors: 0 0 0 16 0 88 0 356 0 1208 0 3156 &Gram (#13 <- H18,H20) 4 0 4 0 0 4 0 0 -2 4 0 0 -2 0 4 2 -2 2 0 0 6 1 0 -2 2 0 -1 6 0 -1 -2 2 0 0 0 6 1 0 2 -2 0 2 0 0 6 2 0 -1 0 -1 -1 0 2 1 8 2 0 1 -1 -2 0 -1 1 2 2 8 2 0 0 1 -2 0 0 2 1 2 2 8 |Aut| = 2^7*3 #short vectors: 0 0 0 16 0 80 0 404 0 1136 0 3076 &Gram (#14 <- H21) 4 2 4 0 0 4 0 0 2 4 2 0 -2 0 6 2 0 -2 0 3 6 2 0 -2 -2 2 2 6 2 0 -2 -2 2 2 3 6 1 -1 0 0 0 2 2 0 6 2 1 0 0 0 2 2 0 0 6 0 0 1 2 -1 1 -2 0 0 0 6 0 0 2 1 -2 0 -2 0 0 0 0 6 |Aut| = 2^6*3^2 #short vectors: 0 0 0 12 0 100 0 324 0 1284 0 3184 &Gram (#15 <- H22) 4 2 4 0 0 4 0 0 2 4 2 0 2 0 6 2 2 2 0 2 6 2 2 0 0 -1 0 6 2 0 0 0 0 -1 2 6 1 -1 0 0 0 1 -1 2 6 2 1 0 0 0 2 0 2 0 6 0 0 -1 -2 1 1 -2 -2 0 0 6 0 0 1 -1 2 2 -2 -2 0 0 0 6 |Aut| = 2^5*3^2 #short vectors: 0 0 0 12 0 84 0 420 0 1140 0 3024 &Gram (#16 <- H23) 4 0 4 0 0 4 0 0 0 4 0 0 0 0 4 0 1 -2 2 0 6 0 -1 -2 2 0 0 6 2 0 2 0 1 0 0 6 0 2 1 2 -2 1 0 0 6 2 -2 -2 -1 0 0 1 0 -2 6 1 0 0 2 -2 0 0 -1 2 0 6 2 -2 0 0 -2 0 1 1 0 2 1 6 |Aut| = 2^8*3 #short vectors: 0 0 0 12 0 96 0 348 0 1248 0 3144 &Gram (#17 <- H24,H25) 4 0 4 0 0 4 0 0 0 4 0 0 0 0 4 0 0 0 0 0 4 2 -1 -2 0 2 0 6 2 0 0 1 -2 2 0 6 0 2 1 0 -2 -2 -2 0 6 1 2 0 -2 2 0 1 -1 0 6 0 0 2 -2 2 -1 0 -2 0 2 6 2 -2 2 2 1 -2 1 0 0 -1 1 8 |Aut| = 2^7*5 #short vectors: 0 0 0 12 0 80 0 444 0 1104 0 2984 &Gram (#18 <- H26) 4 0 4 0 0 4 2 2 2 6 2 -2 2 0 6 2 2 2 2 0 6 1 1 -2 1 0 -1 8 1 0 -2 -1 1 0 -1 8 0 1 -2 1 -2 0 -1 4 8 1 2 1 3 -1 1 3 -4 0 8 1 -2 -2 -2 1 -2 -2 4 0 -4 8 1 -2 0 1 2 -2 -2 3 0 -3 4 8 |Aut| = 2^9*3*5 #short vectors: 0 0 0 12 0 64 0 540 0 960 0 2824 &Gram (#19 <- H27,H29) 4 0 4 0 0 4 0 0 0 4 1 2 -2 2 6 0 2 2 0 0 6 0 -2 0 -2 -2 1 6 2 -1 0 0 0 -2 1 6 2 1 0 0 1 -1 0 0 6 0 -2 -2 0 0 -2 0 1 0 6 2 0 0 1 1 -2 -2 2 2 2 6 2 2 -1 2 3 2 0 0 1 0 1 8 |Aut| = 2^6*3 #short vectors: 0 0 0 8 0 88 0 436 0 1144 0 2972 &Gram (#20 <- H28) 4 0 4 0 0 4 0 0 0 4 0 -2 -2 2 6 2 -2 0 -2 0 6 0 2 -1 0 -2 -2 6 2 0 -2 0 1 0 -1 6 1 -2 0 0 0 0 0 1 6 2 0 2 0 -2 1 0 0 -1 6 0 1 0 2 1 -1 1 -2 0 -2 6 0 -2 0 -1 0 2 0 -2 0 2 -1 6 |Aut| = 2^7 #short vectors: 0 0 0 8 0 96 0 388 0 1216 0 3052 &Gram (#21 <- H30) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 1 0 0 0 0 0 6 0 1 0 0 0 0 0 6 0 0 1 0 0 0 0 0 6 0 0 0 1 0 0 0 0 0 6 0 0 0 0 1 0 0 0 0 0 6 0 0 0 0 0 1 0 0 0 0 0 6 |Aut| = 2^16*3^2*5 #short vectors: 0 12 0 60 0 184 0 492 0 1296 0 2944 &Gram (#22 <- H31) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -1 0 4 0 0 0 0 0 -1 2 4 1 0 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 0 6 0 0 1 0 0 0 0 0 0 0 6 0 0 0 1 0 0 0 0 0 0 0 6 |Aut| = 2^14*3^2 #short vectors: 0 8 0 36 0 156 0 516 0 1228 0 2840 &Gram (#23 <- H32,H34) 2 0 2 0 0 4 0 0 2 4 0 0 -2 0 4 0 0 2 0 -2 4 0 0 -1 -2 -1 1 6 0 0 1 -1 -2 2 0 6 0 0 -2 0 1 -2 1 0 6 0 0 -2 -1 0 0 0 -1 2 6 1 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 0 0 0 6 |Aut| = 2^9*3*5 #short vectors: 0 4 0 24 0 128 0 420 0 1256 0 3012 &Gram (#24 <- H33) 2 0 2 0 0 4 0 0 -2 4 0 0 -1 0 4 0 0 0 -1 2 4 0 0 0 0 0 0 4 0 0 0 0 0 0 2 4 0 0 0 0 0 0 -1 -1 4 0 0 0 0 0 0 1 0 -2 4 1 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 0 0 0 6 |Aut| = 2^12*3^2 #short vectors: 0 4 0 28 0 128 0 380 0 1288 0 3104 &Gram (#25 <- H35) 2 0 2 0 0 4 0 0 -2 4 0 0 0 0 4 0 0 0 0 2 4 0 0 1 -2 -2 0 6 0 0 2 -1 2 0 1 6 0 0 2 -2 1 2 1 1 6 0 0 -2 0 -1 1 1 -2 -2 6 1 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 0 0 0 6 |Aut| = 2^10*3^2 #short vectors: 0 4 0 16 0 128 0 500 0 1192 0 2828 &Gram (#26 <- H36) 2 0 4 0 2 4 0 -2 -2 4 0 2 2 -2 4 0 -2 -2 0 -2 6 0 -2 -2 0 -2 1 6 0 1 1 -1 1 1 0 6 0 1 0 0 0 -2 -1 0 6 0 0 1 0 0 -2 -1 0 0 6 0 0 0 0 1 -2 -1 0 0 0 6 1 0 0 0 0 0 0 0 0 0 0 6 |Aut| = 2^7*3*5 #short vectors: 0 2 0 20 0 114 0 352 0 1286 0 3144 &Gram (#27 <- H37,H38) 2 0 4 0 -2 4 0 0 0 4 0 0 0 -2 4 0 -2 2 2 -2 6 0 -2 2 2 -2 3 6 0 -1 0 2 0 0 2 6 0 1 -1 -2 2 -3 -1 -2 6 0 2 0 1 -1 1 -1 -1 -1 6 0 2 -2 1 0 -2 0 1 1 2 6 1 0 0 0 0 0 0 0 0 0 0 6 |Aut| = 2^6*3^2 #short vectors: 0 2 0 12 0 114 0 432 0 1222 0 2960 &Gram (#28 <- H39) 2 1 6 0 0 6 0 0 3 6 0 0 2 3 6 0 0 2 -1 1 6 0 0 0 -2 -3 2 6 0 0 3 2 0 2 2 6 0 0 2 2 -1 0 -1 0 6 0 0 -2 0 2 -1 -1 -3 0 6 0 0 0 0 2 2 -2 -2 0 2 6 0 0 -2 0 2 1 0 -2 -2 2 3 6 |Aut| = 2^6*3*5*11 #short vectors: 0 2 0 0 0 114 0 552 0 1126 0 2684