Output of /home/aschiem/bin/hn --invar -t --shells_all --herm_lll3 0.8 &K=Q(sqrt(-10)) &Hdim=4 V=K^4 &HNeighbourhood at <3,3w> contains 78 classes: mass of the neighbourhood is 79/8 Steinitz class <2,w>: &Hlattice (#1 <- #39) <1> <1> <2,w> <1> 4 -w 4 -1 -1/2w 1 1-w 1 0 5 |Aut| = 2^3*3 #short vectors: 0 0 0 26 8 &Hlattice (#2 <- #30) <1> <2,w> <1> <1> 4 -1 1 -1+w 1-1/2w 5 1-w 0 -1 5 |Aut| = 2^4 #short vectors: 0 0 0 22 16 &Hlattice (#3 <- #31) <1> <2,w> <1> <1> 4 -1 1 -1 -1/2w 5 -1-w 1 1+w 5 |Aut| = 2^4 #short vectors: 0 0 0 22 16 &Hlattice (#4 <- #40) <2,w> <1> <1> <1> 1 1 4 1 1-w 5 -1-1/2w -w 0 6 |Aut| = 2^3 #short vectors: 0 0 0 22 8 28 &Hlattice (#5 <- #36) <1> <1> <1> <2,w> 4 -1 4 1+w 0 5 -1 -1-1/2w 0 2 |Aut| = 2^2 #short vectors: 0 0 0 18 16 24 64 94 &Hlattice (#6 <- #87) <1> <1> <2,w> <1> 4 2 4 -1/2w 1-1/2w 3/2 1-w 0 1/2w 7 |Aut| = 2^2 #short vectors: 0 0 0 10 24 40 72 &Hlattice (#7 <- #50) <1> <1> <1> <2,w> 3 -1 3 0 -1 3 1/2w -1 1 3/2 |Aut| = 2^2 #short vectors: 0 0 8 6 12 48 &Hlattice (#8 <- #52) <1> <1> <1> <2,w> 3 -1 3 0 -1 3 -1/2w -1 1 3/2 |Aut| = 2^2 #short vectors: 0 0 8 6 12 48 &Hlattice (#9 <- #70) <1> <1> <1> <2,w> 3 1 3 1+w w 6 -1+1/2w 0 1+1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 8 6 12 48 &Hlattice (#10 <- #72) <1> <1> <2,w> <1> 3 1 3 -1-1/2w 0 3/2 -1+w w -1-1/2w 6 |Aut| = 2^2 #short vectors: 0 0 8 6 12 48 &Hlattice (#11 <- #88) <1> <1> <1> <2,w> 3 -1 3 0 -1 3 1+1/2w -1/2w -1 2 |Aut| = 2^2 #short vectors: 0 0 8 10 8 40 48 78 &Hlattice (#12 <- #65) <1> <1> <2,w> <1> 3 -1 4 -1 1 1 -w -1+w 1/2w 5 |Aut| = 2^2*3 #short vectors: 0 0 6 12 16 &Hlattice (#13 <- #66) <1> <1> <2,w> <1> 3 1 4 1 1 1 0 -1-w -1/2w 5 |Aut| = 2^2*3 #short vectors: 0 0 6 12 16 &Hlattice (#14 <- #91) <1> <2,w> <1> <1> 3 -1 1 -1 1 4 -w 1/2w 2+w 6 |Aut| = 2^2 #short vectors: 0 0 6 12 12 30 &Hlattice (#15 <- #92) <1> <2,w> <1> <1> 3 -1 1 -1 1 4 w -1/2w 2-w 6 |Aut| = 2^2 #short vectors: 0 0 6 12 12 30 &Hlattice (#16 <- #49) <1> <1> <1> <2,w> 3 0 4 0 w 5 1 -1-1/2w -1 3/2 |Aut| = 2^2 #short vectors: 0 0 4 6 20 48 &Hlattice (#17 <- #51) <1> <1> <1> <2,w> 3 0 4 0 w 5 1 -1+1/2w 1 3/2 |Aut| = 2^2 #short vectors: 0 0 4 6 20 48 &Hlattice (#18 <- #55) <1> <1> <1> <2,w> 4 1+w 4 2 0 4 1 1 1-1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 4 10 16 40 &Hlattice (#19 <- #56) <1> <1> <1> <2,w> 4 1-w 4 2 1+w 4 -1+1/2w -1 0 3/2 |Aut| = 2^2 #short vectors: 0 0 4 10 16 40 &Hlattice (#20 <- #57) <1> <1> <1> <2,w> 3 0 4 1 -1+w 4 1 -1 1+1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 4 10 16 40 &Hlattice (#21 <- #58) <1> <1> <1> <2,w> 3 1 4 0 1-w 4 1 1 1 3/2 |Aut| = 2^2 #short vectors: 0 0 4 10 16 40 &Hlattice (#22 <- #69) <1> <1> <1> <2,w> 3 w 4 -1 1 5 1 -1/2w 0 3/2 |Aut| = 2^2 #short vectors: 0 0 4 6 20 48 &Hlattice (#23 <- #71) <1> <1> <1> <2,w> 3 0 4 0 w 5 1 -1+1/2w 1+1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 4 6 20 48 &Hlattice (#24 <- #53) <1> <1> <1> <2,w> 4 2 4 1+w 2+w 5 -1 -1+1/2w 1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 2 12 20 30 &Hlattice (#25 <- #54) <1> <1> <1> <2,w> 4 2 4 2-w 1 5 -1-1/2w -1-1/2w -1/2w 3/2 |Aut| = 2^2 #short vectors: 0 0 2 12 20 30 &Hlattice (#26 <- #7) <1> <1> <2,w> <1> 2 1 2 1 1 1 1-w 1 1-1/2w 9 |Aut| = 2^5*3 #short vectors: 0 14 0 30 0 48 0 102 96 &Hlattice (#27 <- #26) <2,w> <1> <1> <1> 1/2 0 2 0 0 3 0 1 w 4 |Aut| = 2^3*3 #short vectors: 0 8 2 18 &Hlattice (#28 <- #37) <1> <1> <1> <2,w> 2 1 4 1 2+w 5 1 2 2-1/2w 2 |Aut| = 2^3*3 #short vectors: 0 8 0 18 24 24 48 54 &Hlattice (#29 <- #8) <1> <2,w> <2,w> <2,w> 2 0 1/2 0 0 1/2 -1/2w 0 0 3/2 |Aut| = 2^5 #short vectors: 0 6 4 14 20 24 &Hlattice (#30 <- #9) <1> <2,w> <2,w> <2,w> 2 0 1/2 0 0 1/2 1-1/2w 0 0 2 |Aut| = 2^5 #short vectors: 0 6 0 22 4 56 24 102 &Hlattice (#31 <- #11) <1> <2,w> <1> <1> 2 1 1 -1 -1 5 w 1/2w -1 6 |Aut| = 2^5*3 #short vectors: 0 6 0 14 32 32 &Hlattice (#32 <- #12) <1> <1> <1> <2,w> 2 0 2 1-w 0 6 0 -1/2w 0 3/2 |Aut| = 2^5 #short vectors: 0 6 4 14 16 40 &Hlattice (#33 <- #14) <1> <2,w> <1> <1> 2 1 1 1 0 5 -1+w 1/2w -2+w 7 |Aut| = 2^5 #short vectors: 0 6 0 14 32 24 32 &Hlattice (#34 <- #15) <1> <2,w> <1> <1> 2 1 1 1 1 4 1-w 1-1/2w 1-w 7 |Aut| = 2^5 #short vectors: 0 6 0 30 0 24 32 &Hlattice (#35 <- #59) <1> <1> <1> <2,w> 2 1 2 1 0 4 -1 0 -1+1/2w 3/2 |Aut| = 2^2*3 #short vectors: 0 6 6 12 16 30 &Hlattice (#36 <- #60) <1> <1> <1> <2,w> 2 1 2 1 1 4 -1 0 1/2w 3/2 |Aut| = 2^2*3 #short vectors: 0 6 6 12 16 30 &Hlattice (#37 <- #75) <1> <1> <2,w> <1> 2 -1 4 0 1 1 0 2+w 1+1/2w 5 |Aut| = 2^3*3 #short vectors: 0 6 0 14 20 &Hlattice (#38 <- #78) <1> <1> <2,w> <1> 2 1 4 0 -1 1 1 2+w -1/2w 5 |Aut| = 2^3*3 #short vectors: 0 6 0 14 20 &Hlattice (#39 <- #20) <1> <1> <1> <2,w> 2 1 3 0 -1 4 1 0 1-1/2w 3/2 |Aut| = 2^4 #short vectors: 0 4 8 10 16 24 &Hlattice (#40 <- #21) <1> <1> <1> <2,w> 3 0 4 1 2+w 4 1 -1+1/2w 1+1/2w 3/2 |Aut| = 2^4 #short vectors: 0 4 8 10 16 24 &Hlattice (#41 <- #24) <1> <1> <1> <2,w> 4 2 4 1+w 2 5 -1/2w 1-1/2w -1 2 |Aut| = 2^4 #short vectors: 0 4 0 22 16 12 64 86 &Hlattice (#42 <- #25) <1> <1> <1> <2,w> 4 -1+w 5 -1+w 1 5 -1 2 -1+1/2w 2 |Aut| = 2^4 #short vectors: 0 4 0 22 16 12 64 86 &Hlattice (#43 <- #27) <2,w> <1> <1> <1> 1/2 0 3 0 -1 4 0 -w 1 4 |Aut| = 2^3 #short vectors: 0 4 2 14 &Hlattice (#44 <- #38) <1> <1> <1> <2,w> 4 1-w 4 w -2 5 2-1/2w 2+1/2w -1-1/2w 2 |Aut| = 2^3 #short vectors: 0 4 0 14 24 36 48 62 &Hlattice (#45 <- #17) <1> <1> <1> <2,w> 3 -1 3 w -1-w 6 1 1 -1 3/2 |Aut| = 2^3 #short vectors: 0 2 8 6 16 40 &Hlattice (#46 <- #32) <1> <1> <1> <2,w> 2 0 3 0 1-w 4 -1/2w 0 0 3/2 |Aut| = 2^3 #short vectors: 0 2 8 6 16 40 &Hlattice (#47 <- #33) <1> <1> <2,w> <1> 4 1+w 4 -1 0 1 1+w 2 -1/2w 5 |Aut| = 2^3 #short vectors: 0 2 0 14 16 &Hlattice (#48 <- #34) <1> <1> <1> <2,w> 2 0 3 0 1-w 4 1-1/2w 0 0 2 |Aut| = 2^3 #short vectors: 0 2 4 14 16 24 60 86 &Hlattice (#49 <- #41) <2,w> <2,w> <2,w> <1> 1/2 0 1 0 1/2 1 0 1-1/2w -1/2w 5 |Aut| = 2^3*3 #short vectors: 0 2 2 6 30 &Hlattice (#50 <- #42) <2,w> <1> <1> <1> 1/2 0 4 0 -1-w 4 0 2-w 1+w 5 |Aut| = 2^3 #short vectors: 0 2 2 10 22 &Hlattice (#51 <- #45) <2,w> <2,w> <2,w> <1> 1/2 0 1 0 1/2 1 0 1-1/2w 0 5 |Aut| = 2^3*3 #short vectors: 0 2 2 6 30 &Hlattice (#52 <- #46) <2,w> <1> <1> <1> 1/2 0 3 0 1 4 0 -1+w w 5 |Aut| = 2^3 #short vectors: 0 2 2 10 22 &Hlattice (#53 <- #63) <1> <1> <1> <2,w> 4 w 4 2 -1 4 -1-1/2w -1+1/2w -1/2w 3/2 |Aut| = 2^2 #short vectors: 0 2 6 12 12 34 &Hlattice (#54 <- #64) <1> <1> <1> <2,w> 4 -w 4 2 -1 4 -1+1/2w -1-1/2w 1/2w 3/2 |Aut| = 2^2 #short vectors: 0 2 6 12 12 34 &Hlattice (#55 <- #73) <1> <1> <2,w> <1> 2 1 3 0 1 1 1 1+w 1/2w 5 |Aut| = 2^3*3 #short vectors: 0 2 12 6 12 &Hlattice (#56 <- #74) <1> <2,w> <1> <1> 3 0 1 1 -1/2w 4 -1 -1 -1-w 4 |Aut| = 2^3 #short vectors: 0 2 4 10 &Hlattice (#57 <- #76) <1> <1> <1> <2,w> 4 -2 4 1-w -2 5 1-1/2w -1+1/2w 1 3/2 |Aut| = 2^3 #short vectors: 0 2 0 18 12 40 &Hlattice (#58 <- #77) <1> <1> <1> <2,w> 4 -2 4 -1-w 2 5 1+1/2w -1-1/2w -1 3/2 |Aut| = 2^3 #short vectors: 0 2 0 18 12 40 &Hlattice (#59 <- #79) <1> <2,w> <1> <1> 3 0 1 -1 1 4 -1 1/2w 1+w 4 |Aut| = 2^3 #short vectors: 0 2 4 10 &Hlattice (#60 <- #80) <1> <1> <2,w> <1> 2 -1 3 0 -1 1 1 -1+w -1/2w 5 |Aut| = 2^3*3 #short vectors: 0 2 12 6 12 &Hlattice (#61 <- #81) <1> <2,w> <1> <1> 3 0 1 1 1 4 0 -1/2w 2 5 |Aut| = 2^3 #short vectors: 0 2 4 6 24 &Hlattice (#62 <- #82) <1> <1> <2,w> <1> 2 1 3 0 1 1 0 1-w -1/2w 5 |Aut| = 2^3 #short vectors: 0 2 12 6 8 &Hlattice (#63 <- #83) <1> <1> <2,w> <1> 2 1 3 0 1 1 0 1+w 1/2w 5 |Aut| = 2^3 #short vectors: 0 2 12 6 8 &Hlattice (#64 <- #84) <1> <2,w> <1> <1> 3 0 1 -1 -1 4 0 1/2w -2 5 |Aut| = 2^3 #short vectors: 0 2 4 6 24 &Hlattice (#65 <- #89) <1> <1> <1> <2,w> 2 -1 4 0 2 4 1 -1-1/2w -1/2w 3/2 |Aut| = 2^2 #short vectors: 0 2 2 12 20 34 &Hlattice (#66 <- #90) <1> <1> <1> <2,w> 2 1 4 1 2 4 1 1-1/2w 1 3/2 |Aut| = 2^2 #short vectors: 0 2 2 12 20 34 &Hlattice (#67 <- #1) <1> <1> <1> <2,w> 1 0 1 0 0 1 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 6 14 &Hlattice (#68 <- #4) <1> <1> <1> <2,w> 1 0 1 0 0 2 0 0 -1/2w 3/2 |Aut| = 2^5 #short vectors: 4 6 12 30 32 24 &Hlattice (#69 <- #5) <1> <1> <1> <2,w> 1 0 1 0 0 2 0 0 1-1/2w 2 |Aut| = 2^5 #short vectors: 4 6 8 22 48 56 48 102 &Hlattice (#70 <- #2) <1> <2,w> <2,w> <2,w> 1 0 1/2 0 0 1/2 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 2 6 &Hlattice (#71 <- #3) <1> <1> <2,w> <1> 1 0 2 0 0 1/2 0 1-w 0 6 |Aut| = 2^5 #short vectors: 2 6 12 14 26 40 &Hlattice (#72 <- #16) <1> <2,w> <1> <1> 1 0 1/2 0 0 3 0 0 1-w 4 |Aut| = 2^3 #short vectors: 2 2 8 14 &Hlattice (#73 <- #18) <1> <1> <1> <2,w> 1 0 3 0 0 4 0 1 1/2w 1 |Aut| = 2^3*3 #short vectors: 2 0 6 26 &Hlattice (#74 <- #19) <1> <1> <2,w> <1> 1 0 3 0 1 1 0 1 1-1/2w 5 |Aut| = 2^3 #short vectors: 2 0 6 22 24 &Hlattice (#75 <- #43) <1> <1> <1> <2,w> 1 0 3 0 -1 3 0 -1+1/2w 1 3/2 |Aut| = 2^3 #short vectors: 2 2 10 18 20 40 &Hlattice (#76 <- #44) <1> <1> <1> <2,w> 1 0 2 0 1 2 0 1-1/2w 1-1/2w 5/2 |Aut| = 2^3*3 #short vectors: 2 6 18 14 12 44 46 78 146 138 &Hlattice (#77 <- #47) <1> <1> <1> <2,w> 1 0 3 0 -1 3 0 -1-1/2w 1 3/2 |Aut| = 2^3 #short vectors: 2 2 10 18 20 40 &Hlattice (#78 <- #48) <1> <1> <1> <2,w> 1 0 2 0 1 3 0 0 -1-1/2w 3/2 |Aut| = 2^3*3 #short vectors: 2 6 18 14 12 44 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=8 V=Q^8 &Genus of the trace-forms: det= 10000 = 2^4 *5^4 2-adic symbol: [1^4 2^4]_4 5-adic symbol: 1^-4 5^-4 -1-adic symbol: +^8 -^0 level(of 2-scaled form)=40, weight=4 a_0,..,a_24 determine modular form 52-classes of trace forms &Gram (#1 <- H1) 4 2 4 2 0 4 2 2 0 4 0 0 0 0 4 0 0 0 0 1 4 1 1 -1 1 -1 1 5 1 1 -1 1 -1 1 0 5 |Aut| = 2^6*3^2 #short vectors: 0 0 0 26 8 8 48 150 120 168 240 240 344 424 480 454 896 1200 1232 1178 1656 1680 2032 2184 &Gram (#2 <- H2,H3) 4 2 4 2 2 4 2 0 0 4 0 0 0 0 4 1 2 1 0 1 5 1 0 -1 1 1 -1 5 1 0 -1 1 1 -1 0 5 |Aut| = 2^7 #short vectors: 0 0 0 22 16 4 64 118 144 148 256 232 304 468 448 614 832 1176 1088 1198 1648 1864 2048 2120 &Gram (#3 <- H4) 4 2 4 2 0 4 2 2 0 4 0 0 0 0 4 2 1 1 1 1 5 2 0 0 1 1 0 6 2 0 0 1 -1 2 3 6 |Aut| = 2^6 #short vectors: 0 0 0 22 8 28 48 126 120 148 240 272 344 444 480 502 896 1080 1232 1158 1656 1720 2032 2216 &Gram (#4 <- H5) 4 2 4 2 0 4 1 1 1 4 1 1 1 2 4 1 2 0 0 1 5 0 1 1 0 1 2 5 1 0 2 1 0 1 -1 5 |Aut| = 2^5 #short vectors: 0 0 0 18 16 24 64 94 144 128 256 264 304 488 448 662 832 1056 1088 1178 1648 1904 2048 2152 &Gram (#5 <- H6) 4 2 4 2 1 4 1 2 -1 5 1 -1 2 -2 5 1 0 1 1 2 5 2 1 0 2 -1 2 6 2 0 1 1 0 -1 -1 6 |Aut| = 2^5 #short vectors: 0 0 0 10 24 40 72 78 104 128 224 328 360 472 456 630 832 992 1184 1138 1640 1808 1992 2280 &Gram (#6 <- H7,H8) 3 1 3 0 1 3 0 0 -1 3 1 1 -1 0 5 1 1 -1 0 1 5 1 -1 -1 -1 1 -1 6 1 -1 -1 -1 -1 1 0 6 |Aut| = 2^3 #short vectors: 0 0 8 6 12 48 52 70 132 128 224 360 372 464 484 614 800 960 1136 1118 1588 1760 2020 2344 &Gram (#7 <- H9,H10) 3 1 3 1 0 3 0 0 0 3 0 1 -1 0 4 0 -1 -1 -1 0 5 1 1 1 0 0 -2 5 0 -1 -1 1 0 1 -2 5 |Aut| = 2^3 #short vectors: 0 0 8 6 12 48 52 70 132 128 224 360 372 464 484 614 800 960 1136 1118 1588 1760 2020 2344 &Gram (#8 <- H11) 3 1 3 0 1 3 1 0 1 3 1 1 -1 -1 6 1 -1 0 0 2 6 1 -1 -1 1 2 2 6 1 1 -1 -1 0 -2 -2 6 |Aut| = 2^5 #short vectors: 0 0 8 10 8 40 48 78 152 128 240 328 344 472 480 630 800 992 1088 1138 1592 1808 2048 2280 &Gram (#9 <- H12,H13) 3 1 3 1 1 3 1 -1 1 4 1 1 1 -1 5 0 0 0 -1 2 5 0 0 0 -1 2 0 5 0 0 0 -1 2 0 0 5 |Aut| = 2^3*3^2 #short vectors: 0 0 6 12 16 18 58 106 120 158 220 312 376 434 478 542 808 1140 1160 1148 1600 1700 2006 2296 &Gram (#10 <- H14,H15) 3 1 3 1 1 3 1 -1 1 4 1 1 1 -1 5 0 0 0 -1 2 5 1 -1 0 0 2 0 6 1 -1 0 2 -2 0 1 6 |Aut| = 2^3 #short vectors: 0 0 6 12 12 30 54 90 140 138 236 312 348 462 474 606 808 1052 1112 1148 1604 1788 2034 2264 &Gram (#11 <- H16,H17) 3 1 3 0 -1 4 1 0 -1 4 1 -1 -1 2 5 1 -1 -1 2 1 5 1 1 1 -1 1 -1 6 0 1 -2 -1 -1 1 1 6 |Aut| = 2^3 #short vectors: 0 0 4 6 20 48 64 70 108 128 216 360 380 464 472 614 816 960 1184 1118 1612 1760 1992 2344 &Gram (#12 <- H18,H19,H20,H21) 3 1 3 1 0 4 1 1 2 4 0 0 -1 0 4 0 1 -1 -1 1 5 1 0 0 -1 -1 -1 5 1 1 0 -1 -2 1 2 5 |Aut| = 2^2 #short vectors: 0 0 4 10 16 40 60 78 128 128 232 328 352 472 468 630 816 992 1136 1138 1616 1808 2020 2280 &Gram (#13 <- H22,H23) 3 0 3 0 -1 4 0 1 -1 4 0 0 -1 -1 4 1 -1 -1 -2 1 5 0 1 1 -1 0 -1 5 1 1 -2 -1 1 2 1 5 |Aut| = 2^3 #short vectors: 0 0 4 6 20 48 64 70 108 128 216 360 380 464 472 614 816 960 1184 1118 1612 1760 1992 2344 &Gram (#14 <- H24,H25) 3 1 4 1 2 4 1 2 0 4 0 -1 1 -1 5 1 0 -1 0 -2 5 1 0 -1 0 -2 0 5 0 1 1 -1 -1 1 1 5 |Aut| = 2^3 #short vectors: 0 0 2 12 20 30 66 90 116 138 228 312 356 462 462 606 824 1052 1160 1148 1628 1788 2006 2264 &Gram (#15 <- H26) 2 1 2 1 0 2 0 0 0 2 1 0 0 0 6 1 0 0 -1 1 9 1 0 0 -1 1 4 9 1 0 0 -1 1 4 -1 9 |Aut| = 2^10*3^2 #short vectors: 0 14 0 30 0 48 0 102 96 158 128 248 512 376 512 614 1088 950 1536 1158 1536 1576 2048 2088 &Gram (#16 <- H27) 2 0 2 0 1 2 0 0 0 3 0 -1 -1 0 4 0 0 0 0 0 5 0 0 0 -1 0 0 7 0 0 0 -1 0 0 -3 7 |Aut| = 2^6*3^2 #short vectors: 0 8 2 18 18 24 58 54 132 128 244 224 340 472 510 902 760 1016 1016 1218 1708 1936 2126 1992 &Gram (#17 <- H28) 2 1 2 0 0 2 1 0 0 4 1 0 -1 -1 5 1 0 1 -1 1 7 1 0 -1 -1 1 1 9 1 0 -1 -1 1 1 -1 9 |Aut| = 2^6*3^2 #short vectors: 0 8 0 18 24 24 48 54 168 128 176 224 392 472 416 902 896 1016 1104 1218 1512 1936 2096 1992 &Gram (#18 <- H29) 2 0 2 0 0 2 1 0 0 3 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 2 0 0 6 |Aut| = 2^10 #short vectors: 0 6 4 14 20 24 52 70 120 158 232 216 376 416 572 870 688 1086 944 1238 1768 1688 2204 2024 &Gram (#19 <- H30) 2 0 2 0 0 2 1 0 0 4 1 0 0 -1 4 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 -1 -1 0 0 6 |Aut| = 2^10 #short vectors: 0 6 0 22 4 56 24 102 88 158 224 232 408 384 616 678 832 958 1184 1198 1816 1496 2200 2088 &Gram (#20 <- H31) 2 0 2 0 0 2 1 1 -1 5 1 1 -1 0 5 0 0 0 1 1 6 0 0 0 1 1 1 6 0 0 0 1 1 1 1 6 |Aut| = 2^10*3^2 #short vectors: 0 6 0 14 32 32 0 102 192 198 0 216 608 328 384 742 1088 1134 1280 1238 1248 1320 2176 2088 &Gram (#21 <- H32) 2 0 2 0 0 2 0 1 0 3 0 0 0 0 4 1 0 -1 0 0 6 0 0 0 0 2 0 6 1 0 1 0 0 0 0 6 |Aut| = 2^10 #short vectors: 0 6 4 14 16 40 28 86 128 158 136 296 480 400 468 646 944 1022 1296 1158 1488 1592 2052 2216 &Gram (#22 <- H33) 2 0 2 0 0 2 0 0 0 4 1 -1 1 -2 5 0 0 0 2 -1 6 1 -1 0 -2 2 -1 7 1 -1 0 -2 2 -1 2 7 |Aut| = 2^10 #short vectors: 0 6 0 14 32 24 32 70 192 158 96 216 480 416 384 870 960 1086 1120 1238 1376 1688 2144 2024 &Gram (#23 <- H34) 2 0 2 0 0 2 1 1 1 4 0 0 0 0 4 0 0 0 0 -2 6 1 1 0 1 -2 1 7 1 1 0 1 2 -1 0 7 |Aut| = 2^10 #short vectors: 0 6 0 30 0 24 32 134 96 158 224 248 384 416 512 486 960 1086 1376 1158 1664 1688 2016 2152 &Gram (#24 <- H35,H36) 2 1 2 1 0 3 1 1 0 4 1 0 0 1 4 0 0 -1 1 0 5 1 0 0 2 2 2 9 1 1 1 -1 -1 -2 2 9 |Aut| = 2^3*3^2 #short vectors: 0 6 6 12 16 30 58 58 120 128 220 312 376 470 478 734 808 1002 1160 1148 1600 1892 2006 2200 &Gram (#25 <- H37,H38) 2 1 2 1 1 4 1 0 -1 4 1 0 -1 2 5 1 1 2 -1 1 5 1 0 1 0 1 0 8 1 0 1 0 1 0 -2 8 |Aut| = 2^5*3^2 #short vectors: 0 6 0 14 20 44 60 78 60 138 192 336 428 436 492 598 896 966 1376 1118 1644 1728 1948 2280 &Gram (#26 <- H39,H40) 2 0 2 1 -1 3 0 0 0 4 1 -1 0 -2 5 1 -1 1 -2 2 7 0 0 1 -1 0 -2 7 0 0 1 -1 0 -2 2 7 |Aut| = 2^7 #short vectors: 0 4 8 10 16 24 56 78 112 148 208 328 400 440 488 630 800 1076 1184 1138 1584 1760 1992 2280 &Gram (#27 <- H41,H42) 2 0 2 1 -1 4 1 1 -1 4 0 -1 -1 0 5 0 -1 0 1 2 5 0 1 -1 0 1 -2 7 1 0 0 0 -1 1 -1 7 |Aut| = 2^7 #short vectors: 0 4 0 22 16 12 64 86 144 128 256 232 304 492 448 742 832 1084 1088 1198 1648 1992 2048 2056 &Gram (#28 <- H43) 2 0 2 0 0 3 0 -1 -1 4 0 1 1 -1 4 0 0 0 1 1 4 0 0 0 0 0 0 5 0 -1 0 -1 -2 -1 0 7 |Aut| = 2^6 #short vectors: 0 4 2 14 18 36 58 62 132 128 244 256 340 468 510 822 760 988 1016 1198 1708 1848 2126 2088 &Gram (#29 <- H44) 2 0 2 1 0 4 1 0 0 4 0 0 1 1 4 1 1 1 -1 -2 5 0 -1 -1 -1 1 -1 7 1 1 0 0 -2 2 -1 7 |Aut| = 2^6 #short vectors: 0 4 0 14 24 36 48 62 168 128 176 256 392 468 416 822 896 988 1104 1198 1512 1848 2096 2088 &Gram (#30 <- H45) 2 0 3 0 -1 3 0 -1 -1 3 1 0 -1 1 6 1 1 0 0 -2 6 0 1 1 -1 2 -2 6 0 -1 1 1 0 0 0 6 |Aut| = 2^7 #short vectors: 0 2 8 6 16 40 56 70 112 138 208 360 400 448 488 614 800 1002 1184 1118 1584 1736 1992 2344 &Gram (#31 <- H46) 2 1 3 0 0 3 0 0 0 3 0 0 1 1 4 0 0 -1 1 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 2 6 |Aut| = 2^7 #short vectors: 0 2 8 6 16 40 56 70 112 138 208 360 400 448 488 614 800 1002 1184 1118 1584 1736 1992 2344 &Gram (#32 <- H47) 2 0 4 0 -2 4 0 1 -2 4 0 1 0 -1 4 0 1 0 1 0 4 1 0 0 1 -2 2 5 0 -1 2 -1 0 0 0 6 |Aut| = 2^7 #short vectors: 0 2 0 14 16 56 32 86 144 138 160 296 432 432 448 646 960 938 1248 1158 1520 1640 2080 2216 &Gram (#33 <- H48) 2 0 3 0 0 3 0 1 1 4 0 -1 1 0 4 1 0 0 0 0 4 1 0 0 0 0 -1 4 0 0 0 0 0 -1 -1 6 |Aut| = 2^7 #short vectors: 0 2 4 14 16 24 60 86 128 138 232 296 352 464 468 646 816 1066 1136 1158 1616 1832 2020 2216 &Gram (#34 <- H49,H51) 2 0 3 0 0 4 0 0 -2 4 0 -1 -2 0 5 0 1 2 0 0 5 0 1 2 -2 -1 1 5 0 0 0 0 0 0 0 5 |Aut| = 2^5*3^2 #short vectors: 0 2 2 6 30 36 70 78 72 158 196 320 424 412 522 662 760 1058 1160 1158 1696 1600 2042 2280 &Gram (#35 <- H50,H52) 2 0 3 0 1 4 0 1 -1 4 0 0 1 1 4 0 0 1 1 2 4 0 -1 -1 -1 -2 -2 5 0 0 0 0 0 0 0 5 |Aut| = 2^5 #short vectors: 0 2 2 10 22 40 62 70 112 138 228 288 368 448 514 742 760 1002 1064 1178 1704 1736 2098 2184 &Gram (#36 <- H53,H54) 2 1 3 0 -1 3 1 1 1 4 0 0 -1 -1 4 1 0 -1 -1 -1 6 1 1 -1 0 -1 3 6 0 1 0 0 1 0 2 7 |Aut| = 2^3 #short vectors: 0 2 6 12 12 34 54 74 140 128 236 312 348 474 474 670 808 1006 1112 1148 1604 1852 2034 2232 &Gram (#37 <- H55,H60) 2 1 3 1 0 3 1 0 1 3 1 0 1 1 5 1 1 0 0 1 5 1 1 0 0 1 0 5 0 1 -1 -1 1 -1 -1 8 |Aut| = 2^5*3^2 #short vectors: 0 2 12 6 12 36 24 78 180 158 152 320 452 412 464 662 848 1058 1104 1158 1428 1600 2096 2280 &Gram (#38 <- H56,H59) 2 1 3 0 1 4 0 1 -1 4 0 -1 -1 -1 4 0 1 1 1 -2 4 0 0 1 1 -2 0 6 1 1 0 0 -1 1 -2 7 |Aut| = 2^5 #short vectors: 0 2 4 10 20 40 40 70 172 138 168 288 412 448 432 742 880 1002 1104 1178 1484 1736 2096 2184 &Gram (#39 <- H57,H58) 2 1 4 1 -1 4 1 2 -1 4 1 0 2 0 5 1 1 -1 1 1 5 1 -1 0 -1 -1 2 6 1 2 1 0 0 1 -1 8 |Aut| = 2^5 #short vectors: 0 2 0 18 12 40 52 102 100 138 224 304 372 448 484 550 896 1002 1280 1138 1652 1736 2004 2248 &Gram (#40 <- H61,H64) 2 1 3 0 -1 4 0 1 -2 4 0 -1 2 0 5 0 1 -2 0 0 5 0 -1 2 -2 0 0 6 1 0 1 -1 0 0 3 7 |Aut| = 2^5 #short vectors: 0 2 4 6 24 40 68 70 88 138 200 360 408 448 476 614 816 1002 1232 1118 1608 1736 1964 2344 &Gram (#41 <- H62,H63) 2 1 3 1 0 3 1 0 1 3 0 1 -1 0 5 1 1 0 0 1 5 0 1 -1 0 0 1 5 0 -1 1 1 -2 1 -2 8 |Aut| = 2^5 #short vectors: 0 2 12 6 8 40 44 70 136 138 216 360 392 448 500 614 784 1002 1136 1118 1560 1736 2020 2344 &Gram (#42 <- H65,H66) 2 0 3 1 1 4 1 0 -1 4 0 0 -1 1 4 0 1 -1 0 2 5 1 0 -1 1 1 2 5 1 1 1 1 1 -1 0 7 |Aut| = 2^3 #short vectors: 0 2 2 12 20 34 66 74 116 128 228 312 356 474 462 670 824 1006 1160 1148 1628 1852 2006 2232 &Gram (#43 <- H67) 1 0 1 0 0 1 0 0 0 2 0 0 0 0 5 0 0 0 0 0 10 0 0 0 0 0 0 10 0 0 0 0 0 0 0 10 |Aut| = 2^10*3^2 #short vectors: 6 14 20 30 42 48 76 102 102 158 208 248 364 376 444 614 700 950 1016 1158 1528 1576 2084 2088 &Gram (#44 <- H68) 1 0 1 0 0 2 0 0 1 3 0 0 0 0 4 0 0 0 0 2 6 0 0 0 0 0 0 10 0 0 0 0 0 0 0 10 |Aut| = 2^10 #short vectors: 4 6 12 30 32 24 76 134 124 158 232 248 320 416 404 486 792 1086 1088 1158 1528 1688 2020 2152 &Gram (#45 <- H69) 1 0 1 0 0 2 0 0 -1 4 0 0 -1 -1 4 0 0 0 1 1 6 0 0 0 0 0 0 10 0 0 0 0 0 0 0 10 |Aut| = 2^10 #short vectors: 4 6 8 22 48 56 48 102 188 158 96 232 448 384 320 678 936 958 1072 1198 1288 1496 2144 2088 &Gram (#46 <- H70) 1 0 2 0 0 2 0 0 0 2 0 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 0 10 |Aut| = 2^10*3^2 #short vectors: 2 6 12 14 30 32 52 102 98 198 208 216 420 328 612 742 596 1134 872 1238 1768 1320 2268 2088 &Gram (#47 <- H71) 1 0 2 0 0 2 0 0 0 2 0 0 0 0 5 0 -1 0 -1 0 6 0 1 0 -1 0 0 6 0 0 0 0 0 0 0 10 |Aut| = 2^10 #short vectors: 2 6 12 14 26 40 60 86 106 158 208 296 396 400 508 646 724 1022 1064 1158 1616 1592 2084 2216 &Gram (#48 <- H72) 1 0 2 0 0 3 0 0 0 3 0 0 1 1 4 0 0 -1 1 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 0 10 |Aut| = 2^7 #short vectors: 2 2 8 14 26 56 64 86 122 138 232 296 348 432 488 646 740 938 1016 1158 1648 1640 2112 2216 &Gram (#49 <- H73) 1 0 3 0 -1 3 0 1 -1 3 0 0 0 0 4 0 0 0 0 -1 4 0 0 0 0 -1 -1 4 0 0 0 0 0 0 0 10 |Aut| = 2^6*3^2 #short vectors: 2 0 6 26 24 8 70 150 134 168 244 240 312 424 426 454 812 1200 1088 1178 1588 1680 2034 2184 &Gram (#50 <- H74) 1 0 3 0 -1 3 0 1 -1 3 0 0 0 0 4 0 1 1 0 -1 5 0 -1 -1 0 -1 -2 5 0 0 0 0 0 0 0 10 |Aut| = 2^6 #short vectors: 2 0 6 22 24 28 70 126 134 148 244 272 312 444 426 502 812 1080 1088 1158 1588 1720 2034 2216 &Gram (#51 <- H75,H77) 1 0 2 0 -1 3 0 0 -1 3 0 -1 0 -1 5 0 0 0 -1 2 5 0 1 -1 1 0 2 7 0 0 0 0 0 0 0 10 |Aut| = 2^5 #short vectors: 2 2 10 18 20 40 62 102 138 138 236 304 332 448 442 550 796 1002 1088 1138 1560 1736 2034 2248 &Gram (#52 <- H76,H78) 1 0 2 0 1 2 0 -1 -1 3 0 1 0 0 5 0 -1 0 1 -2 8 0 -1 -1 0 1 3 8 0 0 0 0 0 0 0 10 |Aut| = 2^5*3^2 #short vectors: 2 6 18 14 12 44 46 78 146 138 220 336 372 436 474 598 764 966 1088 1118 1504 1728 2034 2280