Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-7 -D6 --herm_lll3 0.8 &K=Q(sqrt(-2)) &Hdim=7 V=K^7 &HNeighbourhood at <2,w> contains 38 classes: mass of the neighbourhood is 5833/573440 Steinitz class <1,w>: &Hlattice (#1 <- #17) 2 1 2 0 0 2 0 1 1 2 0 1 1 1 2 0 1 1 1 1 2 -w 0 w w w w 3 |Aut| = 2^10*3^4*5*7 #short vectors: 0 126 56 882 7056 17948 42912 &Hlattice (#2 <- #18) 2 0 2 1 1 2 1 1 1 2 1 1 1 1 2 0 -1 0 0 0 3 -w -w -w -w -w 1 3 |Aut| = 2^10*3^2*5 #short vectors: 0 62 184 1266 6288 17564 43424 &Hlattice (#3 <- #25) 2 1-w 2 0 0 2 0 0 -1 2 0 0 0 1 2 0 0 0 0 -1 2 0 0 0 1 1+w -1-w 3 |Aut| = 2^9*3^3*5 #short vectors: 0 54 200 1314 6192 17516 43488 &Hlattice (#4 <- #26) 2 1+w 2 0 0 2 0 0 0 2 0 0 0 -1 2 0 0 1 0 -1 2 0 0 1+w 0 1 w 3 |Aut| = 2^9*3^3*5 #short vectors: 0 54 200 1314 6192 17516 43488 &Hlattice (#5 <- #33) 2 -1 2 -1 1 2 -1 1 1 2 -1 1 1 1 2 w -w -w -w -w 3 -1 0 0 -w 0 1 3 |Aut| = 2^5*3^2*5*7 #short vectors: 0 42 224 1386 6048 17444 43584 &Hlattice (#6 <- #37) 2 1 2 0 1 2 0 1 1 2 0 1 1 1 2 -1+w w 0 0 0 3 0 w w w w 1 3 |Aut| = 2^5*3^2*5*7 #short vectors: 0 42 224 1386 6048 17444 43584 &Hlattice (#7 <- #15) 2 w 2 0 0 2 -w -1 -1 3 0 0 1+w -1-w 3 -w -1 0 1+w -1 3 1 0 0 -1+w 0 1+w 3 |Aut| = 2^8*3^2 #short vectors: 0 30 248 1458 5904 17372 43680 &Hlattice (#8 <- #16) 2 -w 2 0 0 2 -w 1 -1 3 -w 1 0 1+w 3 0 0 -1-w 1+w 1 3 1 w 1 -1 -1+w -1+w 3 |Aut| = 2^8*3^2 #short vectors: 0 30 248 1458 5904 17372 43680 &Hlattice (#9 <- #19) 2 0 2 0 0 2 1 0 0 2 -w w 0 0 3 0 1 -w 1 -w 3 -1 w 1 0 1-w w 3 |Aut| = 2^10*3^2 #short vectors: 0 30 248 1458 5904 17372 43680 &Hlattice (#10 <- #20) 2 0 2 0 0 2 0 1 0 2 -1 1 -1-w 1 3 -1 0 0 0 0 3 -w 0 -w 0 1+w 1 3 |Aut| = 2^10*3 #short vectors: 0 30 248 1458 5904 17372 43680 &Hlattice (#11 <- #34) 2 -1 2 0 0 2 0 -1 0 2 0 0 1 0 2 0 0 -1+w -1 -1+w 3 0 0 w 0 0 1 3 |Aut| = 2^5*3^2*5 #short vectors: 0 26 256 1482 5856 17348 43712 &Hlattice (#12 <- #38) 2 0 2 0 -1 2 0 0 -1 2 1 0 w -w 3 0 0 0 -1+w -1 3 -1-w 0 0 -1 -1-w 1+w 3 |Aut| = 2^5*3^2*5 #short vectors: 0 26 256 1482 5856 17348 43712 &Hlattice (#13 <- #27) 2 0 2 0 0 2 0 0 -1 2 1-w w 0 0 3 w -1 0 -1 -1+w 3 -1 -1 0 1 0 w 3 |Aut| = 2^8*3 #short vectors: 0 22 264 1506 5808 17324 43744 &Hlattice (#14 <- #31) 2 1 2 0 0 2 0 0 1 2 1-w -w -1 -1 3 -w -w 0 0 1 3 -w 0 0 0 1-w 0 3 |Aut| = 2^5*3^3 #short vectors: 0 18 272 1530 5760 17300 43776 &Hlattice (#15 <- #32) 2 -1 2 0 0 2 w -w 0 3 -1 1 -w w 3 -w w 1 -1 w 3 -1 -w 0 1 0 -1 3 |Aut| = 2^5*3^4 #short vectors: 0 18 272 1530 5760 17300 43776 &Hlattice (#16 <- #35) 2 1 2 0 0 2 -1+w w 0 3 0 w 0 1 3 0 1 -w 0 -w 3 w w 1 1 1 w 3 |Aut| = 2^5*3^4 #short vectors: 0 18 272 1530 5760 17300 43776 &Hlattice (#17 <- #36) 2 0 2 1 0 2 0 0 0 2 0 1-w 0 1 3 -1+w 0 -1+w -1 0 3 w 0 0 0 0 1 3 |Aut| = 2^5*3^3 #short vectors: 0 18 272 1530 5760 17300 43776 &Hlattice (#18 <- #28) 2 0 2 0 0 2 0 0 -1 3 0 -w -w 1 3 -w 1 1 0 w 3 1 w 0 1 -1 w 3 |Aut| = 2^8*3 #short vectors: 0 14 280 1554 5712 17276 43808 &Hlattice (#19 <- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 |Aut| = 2^11*3^2*5*7 #short vectors: 14 98 476 1834 5936 16660 41568 &Hlattice (#20 <- #2) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 1+w 2 |Aut| = 2^12*3^2*5 #short vectors: 10 74 420 1754 5872 16836 42208 &Hlattice (#21 <- #3) 1 0 1 0 0 1 0 0 0 2 0 0 0 -w 2 0 0 0 1 w 2 0 0 0 0 1 0 2 |Aut| = 2^12*3^3 #short vectors: 6 66 332 1578 6000 17108 42720 &Hlattice (#22 <- #4) 1 0 1 0 0 1 0 0 0 2 0 0 0 1 2 0 0 0 w w 2 0 0 0 1+w 1+w 1-w 3 |Aut| = 2^11*3^2 #short vectors: 6 50 364 1674 5808 17012 42848 &Hlattice (#23 <- #7) 1 0 1 0 0 1 0 0 0 2 0 0 0 1+w 2 0 0 0 0 0 2 0 0 0 0 0 1+w 2 |Aut| = 2^13*3^3 #short vectors: 6 66 332 1578 6000 17108 42720 &Hlattice (#24 <- #13) 1 0 1 0 0 2 0 0 -1 2 0 0 0 1 2 0 0 0 0 -1 2 0 0 0 1 1+w -1-w 3 |Aut| = 2^8*3^2*5 #short vectors: 4 38 336 1634 5776 17100 43168 &Hlattice (#25 <- #14) 1 0 1 0 0 2 0 0 0 2 0 0 0 -1 2 0 0 1 0 -1 2 0 0 1+w 0 1 w 3 |Aut| = 2^8*3^2*5 #short vectors: 4 38 336 1634 5776 17100 43168 &Hlattice (#26 <- #5) 1 0 2 0 w 2 0 w 1 2 0 w 1 1 2 0 w 1 1 1 2 0 1 0 0 0 0 3 |Aut| = 2^11*3^2*5 #short vectors: 2 74 212 1306 6320 17476 43104 &Hlattice (#27 <- #6) 1 0 2 0 -w 2 0 -w 1 2 0 -w 1 1 2 0 -w 1 1 1 2 0 1-w 1+w 1+w 1+w 1+w 4 |Aut| = 2^11*3^2*5 #short vectors: 2 74 148 1946 3888 21316 42336 &Hlattice (#28 <- #8) 1 0 2 0 w 2 0 w 1 2 0 1 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1+w 2 |Aut| = 2^13*3^3 #short vectors: 2 74 148 1946 3888 21316 42336 &Hlattice (#29 <- #9) 1 0 2 0 -w 2 0 -w 1 2 0 0 0 0 2 0 0 0 0 1+w 2 0 1-w 1+w 1+w 0 0 3 |Aut| = 2^12*3^2 #short vectors: 2 58 244 1402 6128 17380 43232 &Hlattice (#30 <- #10) 1 0 2 0 w 2 0 w 1 2 0 0 0 0 2 0 1 0 0 w 3 0 -w -1 -1 1+w 1-w 3 |Aut| = 2^11*3 #short vectors: 2 42 276 1498 5936 17284 43360 &Hlattice (#31 <- #11) 1 0 2 0 0 2 0 0 -w 2 0 1 1+w -1+w 3 0 -w 1 w 1-w 3 0 w 0 1 0 -1 3 |Aut| = 2^12 #short vectors: 2 26 308 1594 5744 17188 43488 &Hlattice (#32 <- #12) 1 0 2 0 0 2 0 w 0 2 0 1 0 -w 3 0 w -w 1 0 3 0 1 1 -w 1-w 0 3 |Aut| = 2^13*3 #short vectors: 2 26 308 1594 5744 17188 43488 &Hlattice (#33 <- #21) 1 0 2 0 0 2 0 -1 0 2 0 0 1 -1 2 0 0 0 0 0 2 0 0 1-w 0 1 -1-w 4 |Aut| = 2^9*3^4*5 #short vectors: 2 74 148 1946 3888 21316 42336 &Hlattice (#34 <- #22) 1 0 2 0 0 2 0 0 -1 2 0 1 0 -1 2 0 0 0 1 0 2 0 -w 0 0 1 1+w 4 |Aut| = 2^9*3^4*5 #short vectors: 2 74 148 1946 3888 21316 42336 &Hlattice (#35 <- #23) 1 0 2 0 0 2 0 0 0 2 0 0 0 1 2 0 0 1 -1+w -1 3 0 1-w 0 0 -1 0 3 |Aut| = 2^8*3^2 #short vectors: 2 26 308 1594 5744 17188 43488 &Hlattice (#36 <- #24) 1 0 2 0 1-w 2 0 0 0 2 0 0 0 1+w 2 0 0 0 0 0 2 0 0 0 0 0 1+w 2 |Aut| = 2^14*3^4 #short vectors: 2 74 148 1946 3888 21316 42336 &Hlattice (#37 <- #29) 1 0 2 0 1 2 0 1 1 2 0 -1 -1 -1 2 0 0 0 0 0 2 0 1-w 1-w 1-w -1+w -1 3 |Aut| = 2^7*3^2*5 #short vectors: 2 34 292 1546 5840 17236 43424 &Hlattice (#38 <- #30) 1 0 2 0 0 2 0 -1 0 2 0 0 0 0 2 0 0 1 -1 0 2 0 0 -1+w 0 1 -1 3 |Aut| = 2^7*3^2*5 #short vectors: 2 34 292 1546 5840 17236 43424 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 63 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 32 32 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 15 0 0 0 0 0 0 0 0 0 0 7 0 0 0 7 35 0 0 0 35 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 7 0 0 7 0 0 35 0 0 21 35 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 21 0 0 0 3 8 0 3 25 0 0 8 0 21 24 24 0 0 0 0 0 0 1 0 3 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 3 0 0 8 25 3 0 0 0 8 21 0 0 24 24 0 0 0 0 1 0 0 3 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 51 0 0 48 0 0 0 0 12 0 0 0 0 0 0 0 3 0 0 0 0 0 12 0 0 0 0 0 0 0 2 0 0 0 0 0 0 17 0 32 32 16 0 0 0 0 12 0 0 0 0 0 0 0 1 0 0 0 2 12 0 0 0 0 0 0 0 0 0 0 0 5 3 5 0 0 15 0 15 30 30 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 3 0 0 0 0 3 5 0 5 0 15 15 0 30 10 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 3 0 0 0 0 0 0 0 7 7 4 4 16 16 7 16 0 0 16 24 0 0 0 0 0 1 1 0 0 0 1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 18 6 18 0 9 3 27 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 3 0 0 0 0 0 0 27 0 0 0 0 0 0 27 0 27 9 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 27 0 0 0 0 0 9 27 0 27 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 9 0 0 6 18 18 27 3 9 0 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0 1 3 0 0 24 24 8 8 24 27 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 21 35 35 0 0 0 7 7 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 0 0 6 10 0 60 10 0 0 0 0 5 5 30 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 6 0 12 6 9 0 0 18 0 3 0 18 27 27 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 1 6 1 9 0 24 24 0 3 0 3 21 18 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 12 18 0 3 0 0 0 0 0 36 0 54 0 0 0 0 3 0 0 0 0 1 0 0 0 15 0 0 0 0 0 15 0 0 0 0 0 0 0 0 15 0 1 15 0 0 0 0 0 0 0 2 0 30 0 30 2 0 0 0 1 0 0 0 15 0 0 0 0 15 0 0 0 0 0 0 0 0 15 0 15 1 0 0 0 0 0 0 0 0 2 30 0 2 30 2 2 0 0 0 0 0 0 30 30 0 0 0 0 0 0 0 0 1 0 15 0 0 0 0 15 1 0 15 15 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 1 0 0 15 0 0 0 1 15 15 0 15 0 0 12 12 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 36 9 6 0 54 0 0 0 0 9 0 0 0 0 8 8 0 0 0 0 0 0 0 0 48 0 0 0 0 0 0 1 0 6 6 0 0 6 0 1 6 36 0 0 0 0 0 0 0 0 0 4 0 0 0 0 16 16 0 4 0 0 0 0 0 0 0 24 0 1 1 7 0 0 0 1 1 0 6 7 6 0 0 0 0 0 16 16 0 0 0 0 0 0 0 0 0 16 0 0 32 0 0 0 0 16 0 0 1 4 1 0 0 0 0 1 0 4 10 9 0 0 32 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 32 0 0 6 0 0 0 0 0 0 0 0 0 54 1 0 0 0 1 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 36 0 0 27 0 0 0 0 0 0 27 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36 0 27 0 0 0 0 0 27 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 16 16 0 16 0 0 16 0 0 0 0 0 0 6 6 0 1 0 0 0 18 0 0 0 19 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 54 0 0 0 54 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 12 0 0 20 0 20 0 0 0 0 0 0 15 1 0 0 0 0 15 0 0 0 1 15 0 0 15 0 0 0 0 0 12 0 0 0 0 12 0 0 20 0 20 0 0 0 0 0 0 0 1 15 0 0 0 0 15 0 0 1 0 15 0 15 0 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=14 V=Q^14 &Genus of the trace-forms: det= 128 = 2^7 2-adic symbol: [1^7 2^7]_6 -1-adic symbol: +^14 -^0 level(of 2-scaled form)=8, weight=7 a_0,..,a_7 determine modular form 24-classes of trace forms &begin_block &Gram (#1 <- H1) 2 1 2 1 0 2 1 0 0 2 1 0 1 0 2 1 1 0 0 0 2 1 1 0 0 0 1 2 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 0 -1 1 3 0 0 0 0 0 0 0 1 1 1 3 0 0 0 0 0 0 0 -1 -1 1 -1 3 0 0 0 0 0 0 0 -1 -1 1 -1 1 3 0 0 0 0 0 0 0 -1 -1 1 -1 1 1 3 |Aut| = 2^20*3^8*5^2*7^2 #short vectors: 0 126 56 882 7056 17948 42912 &Gram (#2 <- H2) 2 1 2 1 0 2 1 0 0 2 1 0 0 1 2 1 0 0 1 1 2 1 0 1 0 0 1 3 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 -1 3 0 0 0 0 0 0 1 -1 -1 -1 3 0 0 0 0 0 0 -1 1 -1 1 -1 3 0 0 0 0 0 0 1 -1 1 -1 1 -1 3 0 0 0 0 0 0 1 -1 1 -1 1 -1 1 3 |Aut| = 2^20*3^4*5^2 #short vectors: 0 62 184 1266 6288 17564 43424 &Gram (#3 <- H3,H4) 2 1 2 1 0 2 1 0 0 2 0 0 0 0 2 0 0 0 0 -1 2 0 0 0 0 -1 0 2 0 0 0 0 1 -1 0 2 0 0 0 0 -1 0 1 0 2 0 0 0 0 -1 0 0 0 1 3 0 0 0 0 -1 0 0 -1 0 1 3 0 0 0 0 1 0 0 1 0 -1 -1 3 0 0 0 0 -1 0 0 -1 0 1 1 -1 3 0 0 0 0 -1 1 1 -1 0 0 0 0 0 3 |Aut| = 2^16*3^6*5^2 #short vectors: 0 54 200 1314 6192 17516 43488 &Gram (#4 <- H5,H6) 2 1 2 1 0 2 1 0 1 2 1 0 1 1 2 1 1 0 0 0 2 1 0 0 1 0 0 3 1 0 0 0 0 1 1 3 1 1 0 0 0 1 0 0 3 1 1 0 0 0 1 0 0 1 3 1 1 0 0 0 1 0 0 1 1 3 1 0 1 1 1 0 1 1 0 0 0 3 1 0 1 1 1 0 1 1 0 0 0 1 3 1 1 0 0 0 1 0 0 1 1 1 0 0 3 |Aut| = 2^9*3^4*5^2*7^2 #short vectors: 0 42 224 1386 6048 17444 43584 &Gram (#5 <- H7,H8) 2 0 2 0 -1 2 0 1 -1 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 0 0 0 3 0 0 0 0 0 0 0 0 0 1 3 0 1 0 1 -1 0 -1 0 0 0 -1 3 0 0 0 0 1 1 0 0 0 1 1 0 3 1 1 0 1 -1 0 0 -1 1 0 1 1 0 4 |Aut| = 2^15*3^4 #short vectors: 0 30 248 1458 5904 17372 43680 &Gram (#6 <- H9,H10) 2 1 2 1 1 2 1 1 0 2 0 0 0 0 2 0 0 0 0 0 2 1 1 1 0 1 -1 3 1 1 0 1 0 1 0 3 1 1 0 1 0 -1 1 0 3 1 0 0 0 -1 0 0 0 0 3 0 0 0 0 0 0 -1 0 0 0 3 0 0 0 0 0 0 1 0 0 0 -1 3 0 0 0 0 0 0 0 0 0 1 1 -1 3 1 1 0 1 0 1 0 1 0 1 1 -1 1 4 |Aut| = 2^19*3^3 #short vectors: 0 30 248 1458 5904 17372 43680 &Gram (#7 <- H11,H12) 2 1 2 0 0 2 0 0 1 2 0 0 -1 0 2 0 0 -1 0 1 2 1 0 1 0 0 -1 3 1 1 1 0 -1 -1 1 3 1 1 -1 -1 0 0 0 0 3 1 1 1 0 -1 -1 1 1 0 3 1 1 1 0 0 -1 1 1 0 1 4 1 1 1 0 0 -1 1 1 0 1 2 4 1 1 1 0 0 -1 1 1 0 1 2 2 4 1 1 1 0 0 -1 1 1 0 1 2 2 2 4 |Aut| = 2^9*3^4*5^2 #short vectors: 0 26 256 1482 5856 17348 43712 &Gram (#8 <- H13) 2 0 2 0 0 2 0 0 -1 2 0 0 1 0 2 0 0 0 0 0 2 1 1 1 -1 0 0 3 0 -1 1 0 1 1 0 3 0 0 -1 0 0 0 -1 0 3 0 0 1 0 0 0 1 0 -1 3 1 -1 1 0 1 0 0 1 0 0 3 1 1 1 -1 0 0 1 0 0 0 0 4 1 1 1 -1 0 0 1 0 0 0 0 2 4 1 1 1 -1 0 0 1 0 0 0 0 2 2 4 |Aut| = 2^16*3^2 #short vectors: 0 22 264 1506 5808 17324 43744 &Gram (#9 <- H14,H15,H16,H17) 2 1 2 0 0 2 0 0 1 2 0 0 0 0 2 0 0 0 0 -1 2 1 1 1 1 -1 1 3 1 1 -1 0 0 0 0 3 1 1 -1 0 0 0 0 1 3 1 0 -1 -1 0 0 0 1 1 3 1 1 0 0 -1 1 1 1 1 0 3 0 0 1 1 0 0 1 0 0 -1 1 3 1 0 0 0 0 0 0 0 0 1 0 -1 3 1 1 0 0 0 0 1 1 1 0 1 1 0 3 |Aut| = 2^8*3^7 #short vectors: 0 18 272 1530 5760 17300 43776 &Gram (#10 <- H18) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 -1 -1 -1 1 3 1 -1 -1 0 0 1 3 1 1 1 0 0 -1 0 3 1 0 0 -1 1 1 1 0 3 1 0 -1 -1 0 1 1 0 1 3 1 -1 0 0 1 1 1 0 1 1 3 1 1 0 0 -1 -1 0 1 0 0 0 3 0 0 -1 0 1 1 0 0 0 0 0 0 3 0 1 0 -1 0 0 0 0 1 1 0 0 -1 3 |Aut| = 2^17*3*7 #short vectors: 0 14 280 1554 5712 17276 43808 &Gram (#11 <- H19) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^22*3^4*5^2*7^2 #short vectors: 14 98 476 1834 5936 16660 41568 &Gram (#12 <- H20) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 1 1 2 0 0 0 0 0 -1 -1 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^23*3^4*5^2 #short vectors: 10 74 420 1754 5872 16836 42208 &Gram (#13 <- H21,H23) 1 0 1 0 0 1 0 0 0 2 0 0 0 1 2 0 0 0 -1 0 2 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 -1 -1 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^23*3^6 #short vectors: 6 66 332 1578 6000 17108 42720 &Gram (#14 <- H22) 1 0 1 0 0 1 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 1 1 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 1 0 1 1 0 1 1 0 0 3 |Aut| = 2^22*3^4 #short vectors: 6 50 364 1674 5808 17012 42848 &Gram (#15 <- H24,H25) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 0 2 0 0 1 -1 0 2 0 0 -1 0 1 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 1 0 0 1 0 0 0 3 0 0 -1 0 0 0 1 0 0 -1 3 0 0 1 -1 -1 1 0 0 0 0 0 3 0 0 1 0 0 1 0 0 0 1 -1 0 3 0 0 -1 0 0 -1 0 0 0 -1 1 0 -1 3 |Aut| = 2^15*3^4*5^2 #short vectors: 4 38 336 1634 5776 17100 43168 &Gram (#16 <- H26) 1 0 2 0 0 2 0 0 1 2 0 0 1 1 2 0 0 -1 0 -1 2 0 0 -1 -1 -1 0 2 0 0 -1 -1 -1 0 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 1 1 1 -1 3 |Aut| = 2^22*3^4*5^2 #short vectors: 2 74 212 1306 6320 17476 43104 &Gram (#17 <- H27) 1 0 2 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 0 1 2 0 0 -1 -1 -1 0 2 0 0 1 1 1 0 -1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 -1 -1 -1 0 1 -1 0 1 1 1 1 4 |Aut| = 2^22*3^4*5^2 #short vectors: 2 74 148 1946 3888 21316 42336 &Gram (#18 <- H28,H36) 1 0 2 0 1 2 0 1 0 2 0 1 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 -1 0 2 0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 -1 -1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^24*3^7 #short vectors: 2 74 148 1946 3888 21316 42336 &Gram (#19 <- H29) 1 0 2 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 1 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 1 2 0 0 0 0 0 0 1 0 -1 2 0 0 0 0 0 0 0 0 0 0 2 0 -1 -1 0 -1 0 0 0 0 0 0 3 0 1 1 1 0 1 0 0 0 0 0 -1 3 0 1 -1 -1 0 -1 0 0 0 0 0 0 0 3 |Aut| = 2^23*3^4 #short vectors: 2 58 244 1402 6128 17380 43232 &Gram (#20 <- H30) 1 0 2 0 0 2 0 0 1 2 0 0 -1 -1 2 0 0 -1 -1 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 -1 0 0 0 0 0 0 1 1 3 0 0 1 1 0 -1 1 0 0 0 0 3 0 0 -1 -1 0 1 -1 0 0 0 1 -1 3 0 0 1 0 -1 0 -1 0 0 0 0 0 0 3 |Aut| = 2^22*3^2 #short vectors: 2 42 276 1498 5936 17284 43360 &Gram (#21 <- H31,H32) 1 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 1 0 0 -1 -1 3 0 -1 -1 0 -1 0 0 0 -1 3 0 1 1 0 -1 0 0 0 0 0 3 0 0 -1 -1 0 0 -1 0 0 1 0 3 0 0 1 -1 0 0 -1 0 0 -1 0 0 3 0 -1 -1 0 1 0 0 0 0 0 -1 0 0 3 |Aut| = 2^23*3 #short vectors: 2 26 308 1594 5744 17188 43488 &Gram (#22 <- H33,H34) 1 0 2 0 -1 2 0 -1 0 2 0 -1 0 0 2 0 -1 1 0 0 2 0 -1 1 0 1 0 2 0 0 0 0 0 0 0 2 0 -1 0 0 1 0 1 0 4 0 -1 0 0 1 0 1 0 0 4 0 -1 1 0 1 0 1 0 0 0 4 0 -1 0 0 1 0 1 0 2 0 0 4 0 -1 0 0 1 0 1 0 2 0 0 2 4 0 -1 0 0 1 0 1 0 2 0 0 2 2 4 |Aut| = 2^17*3^8*5^2 #short vectors: 2 74 148 1946 3888 21316 42336 &Gram (#23 <- H35) 1 0 2 0 -1 2 0 1 0 2 0 0 0 0 2 0 0 0 0 -1 2 0 0 0 0 1 0 2 0 0 0 0 0 0 0 2 0 1 -1 0 1 0 1 0 3 0 -1 0 -1 1 0 1 0 0 3 0 -1 1 0 -1 1 0 0 -1 0 3 0 1 0 1 -1 1 0 0 0 -1 0 3 0 -1 0 -1 1 -1 0 0 0 1 0 -1 3 0 1 0 1 -1 0 -1 0 0 -1 0 1 -1 3 |Aut| = 2^17*3^4 #short vectors: 2 26 308 1594 5744 17188 43488 &Gram (#24 <- H37,H38) 1 0 2 0 -1 2 0 -1 0 2 0 1 0 -1 2 0 1 -1 0 0 2 0 0 0 0 0 0 2 0 1 -1 -1 0 0 0 3 0 -1 1 0 0 -1 0 0 3 0 1 -1 0 0 1 0 0 -1 3 0 1 0 -1 1 0 0 0 -1 1 3 0 -1 1 0 0 -1 0 0 1 -1 -1 3 0 -1 0 1 -1 0 0 0 1 -1 -1 1 3 0 1 -1 -1 0 0 0 1 0 0 0 0 0 3 |Aut| = 2^13*3^4*5^2 #short vectors: 2 34 292 1546 5840 17236 43424 &end_block