Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-15 &K=Q(sqrt(-5)) &Hdim=5 V=K^5 &HNeighbourhood at <2,-1+w> contains 98 classes: mass of the neighbourhood is 587/256 Steinitz class <2,-1+w>: &Hlattice (#1 <- #51) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 1+w 4 1 0 1 -1 -1 -1/2 3/2 3/2+1/2w 3/2-1/2w 1/2 0 2 |Aut| = 2^5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#2 <- #52) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 1+w 4 3/2-1/2w -1-w 2 3/2+1/2w 2 1/2w 2 3/2-1/2w -1/2-1/2w 1 1/2-1/2w 2 |Aut| = 2^5*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#3 <- #53) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -1-w 4 -1 1/2-1/2w 1 1 -1/2+1/2w -1/2 1 -1/2-1/2w 1/2-1/2w 1/2 -1/2 3/2 |Aut| = 2^5*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#4 <- #54) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -1-w 4 -1 0 1 1 0 -1/2 1 0 1/2-1/2w -1/2 1/2 1 |Aut| = 2^5*3^2*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#5 <- #55) <1> <1> <1> <1> <2,-1+w> 3 1 3 -1+w -1+w 4 0 1 -1 4 1/2+1/2w 1/2+1/2w 3/2-1/2w -1/2+1/2w 3/2 |Aut| = 2^5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#6 <- #56) <1> <1> <1> <1> <2,-1+w> 3 1 3 0 -1+w 4 -w 1 -1 4 -1 -1/2-1/2w -2 0 2 |Aut| = 2^5*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#7 <- #57) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -1+w 4 0 -1/2-1/2w 1 1 0 -1/2 1 -1 0 1/2 -1/2 1 |Aut| = 2^5*3^2*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#8 <- #58) <1> <1> <1> <2,-1+w> <1> 3 0 4 1-w 2 4 -1/2-1/2w -1/2+1/2w 0 3/2 0 -w -1 1 6 |Aut| = 2^5*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#9 <- #75) <1> <1> <1> <1> <2,-1+w> 3 1+w 4 w 2+w 4 1 2 2-w 4 -1/2-1/2w -3/2-1/2w -2 -1-w 2 |Aut| = 2^3*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#10 <- #76) <1> <1> <1> <1> <2,-1+w> 3 w 3 1-w -1 4 1-w -1-w 1-w 6 3/2+1/2w 1/2-1/2w w -3/2+1/2w 2 |Aut| = 2^3*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#11 <- #87) <1> <1> <1> <1> <2,-1+w> 3 -1-w 3 -1 1 3 0 1 -w 3 -1/2-1/2w 1 -1/2+1/2w -1/2-1/2w 3/2 |Aut| = 2^4 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#12 <- #88) <1> <1> <1> <1> <2,-1+w> 3 1+w 3 -1 -1 3 1 0 -1-w 3 3/2-1/2w -1/2-1/2w 0 1 2 |Aut| = 2^4 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#13 <- #89) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -w 3 -1 1/2-1/2w 1 1 -1/2+1/2w -1/2 1 -1 1/2-1/2w 1/2 -1/2 1 |Aut| = 2^4*3*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#14 <- #90) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -w 3 -1 -1/2-1/2w 1 1 1/2+1/2w -1/2 1 -1 -1/2-1/2w 1/2 -1/2 1 |Aut| = 2^4*3*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#15 <- #94) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -w 4 0 1/2+1/2w 1 1/2-1/2w 1 0 1 1/2-1/2w 2 -1/2w 1/2 2 |Aut| = 2^3*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#16 <- #95) <1> <1> <1> <2,-1+w> <1> 3 1 3 1-w 1 4 1 1/2+1/2w 1/2+1/2w 1 w 1 -2+w 0 5 |Aut| = 2^3*3 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Hlattice (#17 <- #4) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 1 2 0 0 1/2 1 1 0 1 1 0 0 1/2 1 |Aut| = 2^8*3^2 #short vectors: 0 26 4 72 96 336 100 1370 1248 2954 3264 4948 6432 8400 12004 &Hlattice (#18 <- #5) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 1 2 0 1 0 2 0 1-w 1-w -w 6 |Aut| = 2^8*3 #short vectors: 0 26 4 72 96 336 100 1370 1248 2954 3264 4948 6432 8400 12004 &Hlattice (#19 <- #28) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 2 0 0 1 2 0 -w -w 0 6 |Aut| = 2^5*3*5 #short vectors: 0 22 4 80 80 360 164 1322 1200 2902 3200 5044 6480 8440 12004 &Hlattice (#20 <- #27) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 -1 2 0 0 -1 3 0 0 1 -1-w 3 |Aut| = 2^5*3 #short vectors: 0 14 20 32 176 216 436 1098 1488 2414 3584 4724 6192 8200 12404 &Hlattice (#21 <- #39) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 0 2 0 0 1/2 0 1/2-1/2w 0 1 -1/2-1/2w 0 0 0 1 |Aut| = 2^5*3^2 #short vectors: 0 14 4 96 48 408 292 1226 1104 2798 3072 5236 6576 8520 12004 &Hlattice (#22 <- #40) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 0 2 0 0 1/2 0 1/2-1/2w 0 1 1/2-1/2w 0 0 0 1 |Aut| = 2^6*3^2 #short vectors: 0 14 4 96 48 408 292 1226 1104 2798 3072 5236 6576 8520 12004 &Hlattice (#23 <- #43) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 0 2 0 0 1/2 0 -1/2-1/2w 0 1 -1/2-1/2w 0 0 0 1 |Aut| = 2^6*3^2 #short vectors: 0 14 4 96 48 408 292 1226 1104 2798 3072 5236 6576 8520 12004 &Hlattice (#24 <- #47) <1> <1> <2,-1+w> <1> <1> 2 1 2 0 0 1/2 0 0 0 2 -w -w 0 -1 4 |Aut| = 2^5*3^2 #short vectors: 0 14 4 96 48 408 292 1226 1104 2798 3072 5236 6576 8520 12004 &Hlattice (#25 <- #31) <1> <1> <1> <1> <2,-1+w> 2 1 2 1 0 2 1-w -w 1 5 1/2-1/2w 1 1/2-1/2w 1 2 |Aut| = 2^5*3 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#26 <- #32) <1> <1> <1> <1> <2,-1+w> 2 1 2 1 1 2 1-w -w -w 5 -1/2-1/2w -1/2-1/2w -1/2-1/2w 3/2-1/2w 3/2 |Aut| = 2^5*3 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#27 <- #35) <1> <1> <1> <1> <2,-1+w> 2 1 2 1 1 2 1-w 0 0 5 1/2-1/2w 1/2-1/2w 1/2-1/2w 1 3/2 |Aut| = 2^5*3 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#28 <- #36) <1> <1> <1> <1> <2,-1+w> 2 0 3 -1 1 4 1 1-w -1-w 4 -1/2-1/2w -1/2+1/2w 1/2+1/2w -1 2 |Aut| = 2^5*3 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#29 <- #77) <1> <1> <1> <2,-1+w> <1> 2 0 3 -1 -1 3 -1/2-1/2w 1 -1/2+1/2w 3/2 1-w 1-w w 1 6 |Aut| = 2^4*3^2 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#30 <- #80) <1> <1> <1> <1> <2,-1+w> 2 1 2 0 0 2 0 -1 -1 3 1/2-1/2w 1/2-1/2w 0 -1 3/2 |Aut| = 2^4*3^2 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Hlattice (#31 <- #10) <2,-1+w> <2,-1+w> <2,-1+w> <2,-1+w> <2,-1+w> 1/2 0 1/2 0 0 1/2 0 0 0 1/2 0 0 0 0 1/2 |Aut| = 2^8*3*5 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Hlattice (#32 <- #11) <2,-1+w> <1> <2,-1+w> <2,-1+w> <1> 1/2 0 2 0 0 1/2 0 0 0 1/2 0 -w 0 0 3 |Aut| = 2^7*3 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Hlattice (#33 <- #14) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 2 0 1-w -1 4 0 -1 1 -1-w 4 |Aut| = 2^7 #short vectors: 0 10 4 104 32 432 356 1178 1056 2746 3008 5332 6624 8560 12004 &Hlattice (#34 <- #15) <1> <2,-1+w> <1> <1> <1> 2 0 1/2 0 0 2 1 0 0 4 1-w 0 -1 1 4 |Aut| = 2^8 #short vectors: 0 10 4 104 32 432 356 1178 1056 2746 3008 5332 6624 8560 12004 &Hlattice (#35 <- #18) <1> <1> <2,-1+w> <1> <1> 2 0 2 0 0 1/2 -w 0 0 3 0 -w 0 0 3 |Aut| = 2^8 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Hlattice (#36 <- #19) <1> <2,-1+w> <2,-1+w> <2,-1+w> <1> 2 0 1/2 1 0 1 1 0 1/2 1 -w 0 1/2-1/2w -1/2-1/2w 4 |Aut| = 2^8*3 #short vectors: 0 10 4 104 32 432 356 1178 1056 2746 3008 5332 6624 8560 12004 &Hlattice (#37 <- #37) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 -w 4 0 -1 0 5 0 1 1+w -1+w 5 |Aut| = 2^5*3 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Hlattice (#38 <- #60) <1> <1> <1> <1> <2,-1+w> 2 w 3 0 0 3 0 0 1+w 3 0 0 -3/2+1/2w 1/2+1/2w 3/2 |Aut| = 2^5*3 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Hlattice (#39 <- #81) <1> <1> <1> <1> <2,-1+w> 2 0 2 0 -1 2 0 0 -1 3 1/2-1/2w 1 0 -1/2-1/2w 2 |Aut| = 2^3*3 #short vectors: 0 8 20 44 152 252 532 1026 1416 2336 3488 4868 6264 8260 12404 &Hlattice (#40 <- #82) <1> <1> <1> <1> <2,-1+w> 2 0 3 1 1 3 -w -1 -1 4 1/2-1/2w -1 -1/2-1/2w 3/2+1/2w 3/2 |Aut| = 2^3*3 #short vectors: 0 8 20 44 152 252 532 1026 1416 2336 3488 4868 6264 8260 12404 &Hlattice (#41 <- #26) <1> <1> <2,-1+w> <1> <1> 2 1 3 1 1 1 -w 1-w 1/2-1/2w 5 1-w -w 1/2-1/2w 2 5 |Aut| = 2^5 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#42 <- #38) <1> <1> <2,-1+w> <1> <1> 3 0 4 0 0 1 1-w -w 1/2-1/2w 5 w 1+w -1/2-1/2w -2 5 |Aut| = 2^5*3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#43 <- #41) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 1 3 0 0 1+w 3 0 -1-w -1-w -1 4 |Aut| = 2^5 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#44 <- #42) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 3 0 -1 w 3 0 -1-w -1 w 4 |Aut| = 2^6 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#45 <- #44) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 0 2 0 0 1/2 -1/2-1/2w 1 0 3/2 1 -1/2-1/2w 0 -1/2 3/2 |Aut| = 2^6 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#46 <- #48) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 3 0 0 1+w 3 0 -w -1 -1 4 |Aut| = 2^5 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#47 <- #59) <1> <1> <2,-1+w> <1> <1> 2 1 3 1 1 1 1 0 0 4 -w 0 1/2-1/2w -2 5 |Aut| = 2^5 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#48 <- #71) <1> <1> <1> <1> <2,-1+w> 2 0 3 0 1+w 3 0 1-w -1-w 3 1/2-1/2w 0 0 0 1 |Aut| = 2^4*3^2 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#49 <- #73) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 0 3 -1/2-1/2w 0 1 0 3/2-1/2w 0 3/2 0 3/2+1/2w 0 1/2+1/2w 3/2 |Aut| = 2^4*3^2 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#50 <- #84) <1> <1> <1> <1> <2,-1+w> 2 1 2 0 0 4 -w 0 -w 5 1/2-1/2w 1/2-1/2w -1 1 3/2 |Aut| = 2^3*3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#51 <- #85) <1> <1> <1> <1> <2,-1+w> 2 1 2 1 0 3 -w -w 0 4 -1/2-1/2w -1/2-1/2w 1 3/2-1/2w 2 |Aut| = 2^3*3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#52 <- #86) <1> <1> <1> <1> <2,-1+w> 2 -1 3 0 1+w 4 1 -1-w -2-w 5 -1/2-1/2w 3/2+1/2w 1/2-1/2w -1 2 |Aut| = 2^3*3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#53 <- #97) <1> <1> <1> <1> <2,-1+w> 2 -1 3 -1 1+w 4 0 -1+w 2 4 0 1/2+1/2w 1 1/2-1/2w 1 |Aut| = 2^3*3^2 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#54 <- #98) <1> <1> <1> <1> <2,-1+w> 2 -1 3 0 -1 3 0 -1 1+w 4 -1 1/2+1/2w 0 1/2-1/2w 3/2 |Aut| = 2^3*3^2 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Hlattice (#55 <- #29) <1> <1> <1> <1> <2,-1+w> 2 0 2 1 -1 3 -1-w 0 0 5 0 1/2-1/2w -1 -1 3/2 |Aut| = 2^5 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#56 <- #30) <1> <1> <1> <2,-1+w> <1> 2 0 3 1 1 3 0 1 1 1 -w w 1 1/2+1/2w 5 |Aut| = 2^5 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#57 <- #33) <1> <1> <1> <1> <2,-1+w> 2 1 3 1 w 6 1-w -w w 6 -1/2-1/2w 1/2-1/2w -3/2-1/2w 1 3/2 |Aut| = 2^5 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#58 <- #34) <1> <1> <1> <1> <2,-1+w> 3 -1 3 w 0 4 1-w -1-w -2 6 0 3/2+1/2w 1/2-1/2w -3/2+1/2w 2 |Aut| = 2^5 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#59 <- #65) <1> <1> <1> <1> <2,-1+w> 2 0 2 -w -1 4 1-w 0 2+w 5 1/2-1/2w -1 2 1 2 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#60 <- #66) <1> <1> <1> <1> <2,-1+w> 2 0 3 0 1-w 3 -w -1 0 4 0 -1/2+1/2w -1 0 1 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#61 <- #69) <1> <1> <1> <1> <2,-1+w> 2 0 2 0 0 3 -w -1 0 4 1/2-1/2w 0 -1 1 3/2 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#62 <- #70) <1> <1> <1> <1> <2,-1+w> 2 1 3 0 -1 4 -w -1-w -1+w 5 1/2-1/2w -1 1/2-1/2w 1 2 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#63 <- #78) <1> <1> <1> <1> <2,-1+w> 2 1 3 1 1 3 -w -w -1-w 4 -1/2-1/2w -1/2-1/2w -1 3/2-1/2w 3/2 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#64 <- #79) <1> <1> <1> <1> <2,-1+w> 2 0 2 -w 0 4 0 -1 w 5 1/2-1/2w 1/2-1/2w 1 -3/2+1/2w 2 |Aut| = 2^4 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Hlattice (#65 <- #45) <2,-1+w> <1> <1> <1> <1> 1 0 4 1/2-1/2w 1+w 4 -1/2-1/2w -1 2 6 0 -2-w -1 w 7 |Aut| = 2^5*3^2 #short vectors: 0 2 4 120 0 480 484 1082 960 2642 2880 5524 6720 8640 12004 &Hlattice (#66 <- #46) <2,-1+w> <1> <1> <1> <1> 1/2 0 3 0 0 3 0 -1-w -1 3 0 -1+w w -1-w 4 |Aut| = 2^5 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#67 <- #49) <2,-1+w> <1> <1> <1> <1> 1/2 0 3 0 0 3 0 -w w 4 0 1+w -1 -1+w 4 |Aut| = 2^6 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#68 <- #50) <2,-1+w> <1> <1> <1> <1> 1/2 0 4 0 -1+w 4 0 2+w 1-w 4 0 -2w -2+w -2-w 6 |Aut| = 2^6*3*5 #short vectors: 0 2 4 120 0 480 484 1082 960 2642 2880 5524 6720 8640 12004 &Hlattice (#69 <- #61) <2,-1+w> <1> <1> <2,-1+w> <2,-1+w> 1/2 0 4 0 2-w 4 0 1/2+1/2w -1/2+1/2w 1 0 -1/2+1/2w -1/2+1/2w 1/2 1 |Aut| = 2^5*3*5 #short vectors: 0 2 4 120 0 480 484 1082 960 2642 2880 5524 6720 8640 12004 &Hlattice (#70 <- #62) <2,-1+w> <1> <1> <2,-1+w> <2,-1+w> 1/2 0 3 0 1 3 0 -1/2+1/2w 1/2+1/2w 1 0 -1/2+1/2w 0 1/2 1 |Aut| = 2^5*3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#71 <- #72) <1> <1> <1> <1> <2,-1+w> 3 w 3 -1 0 3 -1-w -1 w 4 1 0 -1 -1/2+1/2w 1 |Aut| = 2^4 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#72 <- #74) <1> <1> <1> <1> <2,-1+w> 2 1-w 4 1 1 4 1 1 2-w 5 1/2-1/2w 2 1/2-1/2w 2 2 |Aut| = 2^4 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#73 <- #83) <1> <1> <2,-1+w> <1> <1> 2 1 3 0 -1/2-1/2w 3/2 1 0 3/2-1/2w 6 1-w 1-w 3/2+1/2w 1+w 6 |Aut| = 2^3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#74 <- #91) <1> <1> <1> <1> <2,-1+w> 3 1-w 4 0 -w 4 -1 -1-w 2-w 4 -1 0 -1/2+1/2w -1 3/2 |Aut| = 2^3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#75 <- #92) <1> <1> <1> <1> <2,-1+w> 2 -1 3 0 1-w 3 0 -1-w 1-w 4 0 3/2-1/2w 3/2+1/2w 1/2+1/2w 2 |Aut| = 2^3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#76 <- #93) <1> <1> <1> <1> <2,-1+w> 2 1 3 -w 0 4 1 -1-w -1+w 4 -1/2-1/2w 0 2 -1/2-1/2w 2 |Aut| = 2^3*3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#77 <- #96) <1> <1> <1> <1> <2,-1+w> 3 -1-w 3 w -1 4 1 -1 -1 4 1 -1/2+1/2w 0 1/2-1/2w 1 |Aut| = 2^3*3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Hlattice (#78 <- #1) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1/2 |Aut| = 2^8*3 #short vectors: 8 26 52 104 216 336 468 858 1560 2314 2944 3796 6240 9680 11284 &Hlattice (#79 <- #6) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 2 0 0 0 -1/2+1/2w 1 |Aut| = 2^6*3^2 #short vectors: 6 18 44 96 186 336 540 858 1482 2274 3024 4148 6288 9360 11564 &Hlattice (#80 <- #7) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 2 0 0 0 -1/2-1/2w 1 |Aut| = 2^6*3^2 #short vectors: 6 18 44 96 186 336 540 858 1482 2274 3024 4148 6288 9360 11564 &Hlattice (#81 <- #2) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 1 0 0 1/2 0 0 0 1/2 0 0 0 0 1/2 |Aut| = 2^7*3 #short vectors: 4 10 36 88 156 336 612 858 1404 2234 3104 4500 6336 9040 11844 &Hlattice (#82 <- #3) <1> <1> <1> <2,-1+w> <1> 1 0 1 0 0 2 0 0 0 1/2 0 0 -w 0 3 |Aut| = 2^7 #short vectors: 4 10 36 88 156 336 612 858 1404 2234 3104 4500 6336 9040 11844 &Hlattice (#83 <- #25) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 3 0 0 1+w 3 0 0 -3/2+1/2w 1/2+1/2w 3/2 |Aut| = 2^5*3 #short vectors: 4 10 36 88 156 336 612 858 1404 2234 3104 4500 6336 9040 11844 &Hlattice (#84 <- #8) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 0 2 0 0 -1 2 0 1/2-1/2w -1 0 3/2 |Aut| = 2^6*3 #short vectors: 2 14 28 56 174 264 492 1002 1470 2350 3376 4564 6240 8600 12124 &Hlattice (#85 <- #9) <1> <1> <1> <2,-1+w> <1> 1 0 2 0 1 2 0 1 0 1 0 1-w 1-w 1/2-1/2w 5 |Aut| = 2^6*3 #short vectors: 2 14 28 56 174 264 492 1002 1470 2350 3376 4564 6240 8600 12124 &Hlattice (#86 <- #12) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 2 0 0 1/2 0 0 0 1/2 0 1/2-1/2w 0 0 1 |Aut| = 2^6*3 #short vectors: 2 10 28 64 158 288 556 954 1422 2298 3312 4660 6288 8640 12124 &Hlattice (#87 <- #13) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 2 0 0 1/2 0 0 0 1/2 0 -1/2-1/2w 0 0 1 |Aut| = 2^6*3 #short vectors: 2 10 28 64 158 288 556 954 1422 2298 3312 4660 6288 8640 12124 &Hlattice (#88 <- #16) <1> <1> <1> <2,-1+w> <1> 1 0 2 0 1 3 0 1 1 1 0 1-w 1 1/2-1/2w 4 |Aut| = 2^6*3 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#89 <- #17) <1> <1> <1> <1> <2,-1+w> 2 -1 3 0 -1 3 1-w -1+w 0 4 -1 0 1 -1/2-1/2w 1 |Aut| = 2^6*3 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#90 <- #20) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 -1 3 0 1-w -1+w 4 0 -1/2-1/2w 1/2+1/2w 3/2-1/2w 3/2 |Aut| = 2^6 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#91 <- #21) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 0 2 0 1 -1 3 0 1/2-1/2w -1 1 3/2 |Aut| = 2^6 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#92 <- #22) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 0 2 0 0 -w 3 0 1/2-1/2w 0 0 1 |Aut| = 2^6*3 #short vectors: 2 10 28 64 158 288 556 954 1422 2298 3312 4660 6288 8640 12124 &Hlattice (#93 <- #23) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 0 2 0 0 -w 3 0 -1/2-1/2w 0 0 1 |Aut| = 2^6*3 #short vectors: 2 10 28 64 158 288 556 954 1422 2298 3312 4660 6288 8640 12124 &Hlattice (#94 <- #24) <1> <2,-1+w> <1> <2,-1+w> <2,-1+w> 1 0 1/2 0 0 3 0 0 3/2-1/2w 3/2 0 0 3/2+1/2w 1/2+1/2w 3/2 |Aut| = 2^4*3 #short vectors: 2 2 28 80 126 336 684 858 1326 2194 3184 4852 6384 8720 12124 &Hlattice (#95 <- #63) <1> <1> <2,-1+w> <1> <1> 1 0 2 0 0 1 0 0 -1/2-1/2w 4 0 -w 1 -2+w 5 |Aut| = 2^4*3 #short vectors: 2 2 28 80 126 336 684 858 1326 2194 3184 4852 6384 8720 12124 &Hlattice (#96 <- #64) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 1 3 0 0 -1-w 3 0 0 -1/2+1/2w -1/2-1/2w 1 |Aut| = 2^4*3 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#97 <- #67) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 1 2 0 -w -w 4 0 -1 -1 1/2-1/2w 3/2 |Aut| = 2^4*3 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Hlattice (#98 <- #68) <1> <1> <2,-1+w> <1> <1> 1 0 2 0 0 1 0 0 1/2-1/2w 4 0 -w 1/2+1/2w -2 5 |Aut| = 2^4*3 #short vectors: 2 2 28 80 126 336 684 858 1326 2194 3184 4852 6384 8720 12124 classes of Z-lattices with respect to the trace form (scaled by 1/2) &Dim=10 V=Q^10 &Genus of the trace-forms: det= 3125 = 5^5 2-adic symbol: 1^-10_2 5-adic symbol: 1^-5 5^-5 -1-adic symbol: +^10 -^0 level(of 2-scaled form)=20, weight=5 a_0,..,a_15 determine modular form &Gram (#1 <- H1,H2,H3,H4,H5,H6,H7,H8) 3 1 3 1 -1 3 1 1 -1 3 1 -1 1 -1 3 1 0 1 0 1 4 1 1 0 1 0 2 4 1 1 0 0 0 1 2 4 0 0 1 -1 0 1 -1 1 4 0 -1 1 0 0 1 -1 -2 1 4 |Aut| = 2^5*3^2*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Gram (#2 <- H9,H10) 3 1 3 1 -1 3 1 1 0 3 0 1 -1 -1 3 0 0 0 0 0 3 0 0 0 0 0 1 3 1 0 0 -1 0 1 0 4 1 0 0 -1 0 0 -1 0 4 1 0 1 -1 1 1 0 0 1 4 |Aut| = 2^5*3^2 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Gram (#3 <- H11,H12,H13,H14,H15,H16) 3 1 3 0 -1 3 1 1 -1 3 0 1 -1 1 3 1 1 -1 1 0 3 0 -1 1 0 0 -1 3 1 1 -1 1 1 1 -1 3 0 0 1 -1 0 -1 0 -1 3 0 -1 1 -1 0 -1 0 0 0 3 |Aut| = 2^4*3*5 #short vectors: 0 0 20 60 120 300 660 930 1320 2232 3360 5060 6360 8340 12404 &Gram (#4 <- H17,H18) 2 0 2 0 1 2 0 1 0 2 0 1 0 0 2 1 0 0 0 0 3 0 -1 0 -1 0 0 6 0 -1 -1 0 0 0 -2 6 0 -1 -1 0 0 0 -2 1 6 0 1 1 0 0 0 2 -1 -1 6 |Aut| = 2^15*3^3 #short vectors: 0 26 4 72 96 336 100 1370 1248 2954 3264 4948 6432 8400 12004 &Gram (#5 <- H19) 2 0 2 0 -1 2 0 -1 0 2 0 1 -1 0 2 1 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 -1 4 0 0 0 0 0 0 1 1 4 0 0 0 0 0 0 -1 -1 1 4 |Aut| = 2^10*3^2*5^2 #short vectors: 0 22 4 80 80 360 164 1322 1200 2902 3200 5044 6480 8440 12004 &Gram (#6 <- H20) 2 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 3 0 1 -1 1 -1 3 1 0 0 0 0 0 3 0 -1 0 -1 0 -1 0 5 0 1 0 1 -1 0 0 -2 5 0 1 -1 0 -1 0 0 -1 -1 5 |Aut| = 2^10*3^2 #short vectors: 0 14 20 32 176 216 436 1098 1488 2414 3584 4724 6192 8200 12404 &Gram (#7 <- H21,H22,H23,H24) 2 1 2 0 0 2 0 0 0 2 0 0 0 1 2 0 0 1 0 0 3 0 0 0 -1 0 0 4 0 0 0 1 0 0 1 4 1 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 -1 4 |Aut| = 2^9*3^4 #short vectors: 0 14 4 96 48 408 292 1226 1104 2798 3072 5236 6576 8520 12004 &Gram (#8 <- H25,H26,H27,H28) 2 1 2 1 0 2 1 0 1 3 1 0 1 0 3 0 0 0 -1 0 3 0 0 0 0 1 -1 3 1 0 1 1 1 -1 1 5 1 1 0 0 0 1 -1 1 5 1 0 1 1 1 -1 1 0 1 5 |Aut| = 2^8*3^2 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Gram (#9 <- H29,H30) 2 1 2 0 0 2 0 0 -1 2 1 0 -1 1 3 0 0 0 0 0 3 1 1 -1 1 1 1 5 1 0 -1 0 1 -1 2 5 1 1 1 0 0 -1 0 0 5 1 0 -1 0 1 1 1 1 1 5 |Aut| = 2^7*3^4 #short vectors: 0 12 20 36 168 228 468 1074 1464 2388 3552 4772 6216 8220 12404 &Gram (#10 <- H31,H32,H35) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 1 3 1 0 0 0 0 0 3 0 0 -1 0 0 0 0 3 0 0 0 -1 0 0 0 0 3 0 1 0 0 0 0 0 0 0 3 |Aut| = 2^13*3*5 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Gram (#11 <- H33,H34,H36) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 -1 0 0 0 3 0 0 -1 1 1 0 4 1 0 0 1 -1 0 0 4 1 0 -1 0 -1 0 0 1 4 1 0 -1 -1 0 0 0 0 1 4 |Aut| = 2^13*3 #short vectors: 0 10 4 104 32 432 356 1178 1056 2746 3008 5332 6624 8560 12004 &Gram (#12 <- H37,H38) 2 0 2 0 1 2 0 0 0 2 0 -1 0 0 3 0 1 0 0 0 3 0 0 0 -1 0 0 3 1 0 0 0 0 0 0 3 0 0 0 0 1 1 0 0 4 0 0 0 0 1 1 0 0 -1 4 |Aut| = 2^9*3^2 #short vectors: 0 10 20 40 160 240 500 1050 1440 2362 3520 4820 6240 8240 12404 &Gram (#13 <- H39,H40) 2 0 2 0 -1 2 1 -1 1 3 0 1 0 -1 3 0 0 0 -1 0 3 1 0 0 1 -1 -1 4 1 -1 0 0 -1 1 -1 5 0 1 0 0 0 1 -1 0 5 0 -1 0 0 0 -1 1 0 0 5 |Aut| = 2^5*3^2 #short vectors: 0 8 20 44 152 252 532 1026 1416 2336 3488 4868 6264 8260 12404 &Gram (#14 <- H41) 2 0 2 0 0 2 1 1 0 3 1 -1 0 0 3 0 0 0 -1 0 3 0 0 0 0 -1 0 3 1 -1 1 0 1 0 0 4 1 0 -1 0 1 -1 1 0 5 1 0 -1 0 0 -1 -1 0 1 5 |Aut| = 2^10 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#15 <- H42,H47) 2 0 2 1 1 3 1 1 0 3 1 1 0 1 4 1 1 0 1 1 4 0 -1 0 0 -2 0 5 0 -1 0 0 -2 0 0 5 1 0 0 0 0 2 1 1 5 1 1 1 1 0 2 1 1 2 5 |Aut| = 2^9*3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#16 <- H43,H44,H45,H46) 2 0 2 0 0 2 0 0 1 3 0 -1 0 -1 3 0 0 -1 0 0 3 0 1 0 0 0 1 3 1 0 0 0 0 0 0 3 0 0 1 1 -1 0 1 0 4 0 -1 0 1 0 -1 -1 0 0 4 |Aut| = 2^9 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#17 <- H48,H49) 2 1 2 0 0 3 0 0 1 3 0 0 1 -1 3 0 0 0 -1 1 3 0 0 0 1 0 1 3 0 0 0 0 -1 1 1 3 1 1 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 2 4 |Aut| = 2^7*3^3*5 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#18 <- H50,H52,H53,H54) 2 1 2 1 0 3 1 0 0 3 1 0 0 0 3 1 0 0 1 0 4 1 1 0 1 1 -1 4 1 1 1 1 0 -1 2 4 0 0 0 -1 0 -1 -1 -1 5 0 0 0 1 0 1 1 1 0 5 |Aut| = 2^4*3^3 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#19 <- H51) 2 1 2 1 0 3 1 0 0 3 0 0 1 -1 3 0 0 -1 1 0 3 0 0 0 0 -1 -1 3 0 0 0 0 -1 -1 0 3 0 0 0 0 0 0 -1 1 4 0 0 0 0 0 0 -1 1 -1 4 |Aut| = 2^6*3^2 #short vectors: 0 6 20 48 144 264 564 1002 1392 2310 3456 4916 6288 8280 12404 &Gram (#20 <- H55,H56,H57,H58) 2 0 2 1 -1 3 1 1 0 3 0 0 -1 1 3 1 1 0 1 1 4 1 0 1 0 -1 -1 4 0 1 0 0 -1 -1 1 4 1 0 0 0 1 1 -1 1 5 0 -1 0 -1 -1 -1 -1 1 1 5 |Aut| = 2^8 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Gram (#21 <- H59,H60,H61,H62) 2 0 2 1 -1 3 1 0 1 3 1 0 1 0 3 0 0 -1 -1 0 3 0 0 1 0 1 -1 3 1 0 0 0 0 0 0 4 1 0 1 0 0 1 -1 1 5 1 -1 0 1 1 1 -1 -1 -1 5 |Aut| = 2^6 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Gram (#22 <- H63,H64) 2 0 2 1 1 3 0 1 1 3 1 0 0 1 3 0 0 0 0 0 3 1 0 0 -1 1 -1 4 1 0 0 -1 1 1 0 4 0 0 0 1 1 -1 -1 0 4 0 0 0 1 1 1 0 -1 0 4 |Aut| = 2^7 #short vectors: 0 4 20 52 136 276 596 978 1368 2284 3424 4964 6312 8300 12404 &Gram (#23 <- H65,H68,H69) 2 1 3 0 0 4 0 0 -2 4 0 0 -2 2 4 0 0 2 0 -2 4 0 0 -1 2 0 1 4 0 0 -1 1 2 0 -1 4 0 0 -1 -1 1 -1 -2 2 4 0 0 1 -2 -1 1 -2 0 2 4 |Aut| = 2^9*3^2*5^2 #short vectors: 0 2 4 120 0 480 484 1082 960 2642 2880 5524 6720 8640 12004 &Gram (#24 <- H66,H67,H70) 2 1 3 0 0 3 0 0 -1 3 0 0 0 1 3 0 0 1 0 -1 3 0 0 0 1 0 1 3 0 0 -1 0 -1 0 -1 3 0 0 0 1 0 1 0 1 3 0 0 -1 0 -1 0 1 0 -1 3 |Aut| = 2^9*3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Gram (#25 <- H71,H72) 2 1 3 1 1 3 0 1 -1 3 0 -1 1 -1 3 0 0 0 0 -1 3 0 0 0 -1 0 0 3 0 0 1 -1 0 -1 -1 4 0 1 0 1 0 1 1 -2 4 1 0 0 0 0 0 0 -1 -1 4 |Aut| = 2^7 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Gram (#26 <- H73) 2 1 3 1 0 3 1 0 1 3 1 1 1 0 3 0 0 1 0 1 3 0 0 1 0 1 0 3 0 -1 1 0 -1 -1 1 4 0 0 1 1 -1 -1 1 1 4 0 1 0 1 0 -1 1 1 2 5 |Aut| = 2^6 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Gram (#27 <- H74,H75,H76,H77) 2 1 3 1 0 3 0 -1 1 3 1 0 1 1 3 0 -1 0 1 0 3 0 0 1 1 0 0 3 0 0 0 -1 -1 0 0 3 0 1 1 -1 -1 0 1 0 4 0 0 0 0 0 1 1 -1 1 4 |Aut| = 2^4*3 #short vectors: 0 2 20 56 128 288 628 954 1344 2258 3392 5012 6336 8320 12404 &Gram (#28 <- H78) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 -1 3 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^16*3^2 #short vectors: 8 26 52 104 216 336 468 858 1560 2314 2944 3796 6240 9680 11284 &Gram (#29 <- H79,H80) 1 0 1 0 0 1 0 0 0 2 0 0 0 1 2 0 0 0 1 0 4 0 0 0 1 0 -1 4 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^11*3^4 #short vectors: 6 18 44 96 186 336 540 858 1482 2274 3024 4148 6288 9360 11564 &Gram (#30 <- H81,H82) 1 0 1 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 1 3 0 0 0 -1 0 0 3 0 0 1 0 0 0 0 3 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^13*3 #short vectors: 4 10 36 88 156 336 612 858 1404 2234 3104 4500 6336 9040 11844 &Gram (#31 <- H83) 1 0 1 0 0 2 0 0 1 2 0 0 1 1 3 0 0 1 0 1 3 0 0 0 0 1 1 4 0 0 0 0 1 1 -1 4 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^10*3^2 #short vectors: 4 10 36 88 156 336 612 858 1404 2234 3104 4500 6336 9040 11844 &Gram (#32 <- H84,H85) 1 0 2 0 0 2 0 0 -1 2 0 0 1 -1 2 0 -1 1 0 1 4 0 -1 1 -1 1 1 5 0 -1 1 0 0 1 2 5 0 -1 1 0 0 1 2 0 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^11*3^2 #short vectors: 2 14 28 56 174 264 492 1002 1470 2350 3376 4564 6240 8600 12124 &Gram (#33 <- H86,H87,H92,H93) 1 0 2 0 -1 2 0 0 0 2 0 0 0 0 2 0 0 0 0 1 3 0 0 0 1 0 0 3 0 1 -1 0 0 0 0 4 0 1 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^10*3^2 #short vectors: 2 10 28 64 158 288 556 954 1422 2298 3312 4660 6288 8640 12124 &Gram (#34 <- H88,H89,H90,H91) 1 0 2 0 0 2 0 1 -1 3 0 -1 1 0 3 0 -1 0 0 1 4 0 -1 0 0 1 -1 4 0 0 -1 1 0 1 1 4 0 0 0 1 0 1 1 1 4 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^10*3 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124 &Gram (#35 <- H94) 1 0 2 0 1 3 0 0 0 3 0 0 0 1 3 0 0 0 1 -1 3 0 0 0 0 -1 1 3 0 0 0 0 1 0 1 3 0 0 0 0 0 -1 1 1 3 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^8*3*5 #short vectors: 2 2 28 80 126 336 684 858 1326 2194 3184 4852 6384 8720 12124 &Gram (#36 <- H95,H98) 1 0 2 0 -1 3 0 -1 1 3 0 1 -1 0 3 0 1 0 0 1 3 0 -1 0 0 0 0 3 0 1 0 -1 0 1 0 3 0 0 1 -1 0 -1 -1 1 5 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^7*3*5 #short vectors: 2 2 28 80 126 336 684 858 1326 2194 3184 4852 6384 8720 12124 &Gram (#37 <- H96,H97) 1 0 2 0 -1 2 0 -1 0 3 0 1 -1 -1 3 0 0 0 -1 1 3 0 0 0 1 -1 0 3 0 0 0 0 0 -1 -1 4 0 0 0 0 0 -1 -1 -1 4 0 0 0 0 0 0 0 0 0 5 |Aut| = 2^7*3^2 #short vectors: 2 6 28 72 142 312 620 906 1374 2246 3248 4756 6336 8680 12124