Output of /home/aschiem/bin/hn --invar -t --shells-5 -D5 --no_reduce &K=Q(sqrt(-1)) &Hdim=10 V=K^10 &HNeighbourhood at <2,-1+w> contains 25 classes: mass of the neighbourhood is 523807/456608710656 Steinitz class <1,w>: &Hlattice (#1 <-- #5) 2 1+w 2 1+w 1 2 1+w 1 1 2 1+w 1 1 1 2 1+w 1 1 1 1 2 1+w 1 1 1 1 1 2 1+w 1 1 1 1 1 1 2 1+w 1 1 1 1 1 1 1 2 1 0 0 0 0 0 0 0 0 5 |Aut| = 2^27*3^4*5^2*7 #short vectors: 0 760 0 77560 524288 &Hlattice (#2 <-- #7) 2 1+w 2 1+w 1 2 1+w 1 1 2 1+w 1 1 1 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 0 1+w 2 0 0 0 0 0 0 1+w 1 2 1 0 0 0 0 0 0 0 0 3 |Aut| = 2^25*3^4*5^2 #short vectors: 0 504 2048 73464 516096 &Hlattice (#3 <-- #9) 2 1+w 2 1+w 1 2 1+w 1 1 2 1+w 1 1 1 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 1+w 1 1 1 1 1 1-w 1-w 3 1 0 0 0 0 -1+w 0 0 0 4 |Aut| = 2^25*3^3*5 #short vectors: 0 376 3072 71416 512000 &Hlattice (#4 <-- #18) 2 0 2 0 1 2 0 1 1 2 0 1 1 1 2 w 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 1 0 w w w 0 0 0 2 0 1 1 1 1 1 1-w 1-w -w 3 |Aut| = 2^17*3^5*5*7 #short vectors: 0 312 3584 70392 509952 &Hlattice (#5 <-- #10) 2 1+w 2 1+w 1 2 0 0 0 2 0 0 0 1-w 2 0 0 0 0 0 2 0 0 0 0 0 1 2 1 0 0 -1+w -1 0 0 3 1+w 1 1 1 1+w -1 -1 0 3 0 0 0 0 1 0 0 0 0 3 |Aut| = 2^25*3^2 #short vectors: 0 248 4096 69368 507904 &Hlattice (#6 <-- #15) 2 0 2 0 1 2 0 1 1 2 0 1 1 1 2 0 1 1 1 1 2 0 1 1 1 1 1 2 1+w 0 0 0 0 0 0 2 1+w 1-w 1-w 1-w 1-w 1-w 1-w 1 3 1 0 0 0 0 0 0 1-w 0 3 |Aut| = 2^19*3^2*5*7 #short vectors: 0 248 4096 69368 507904 &Hlattice (#7 <-- #19) 2 1 2 1 1 2 1 1 1 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 -w -w -w 0 0 0 2 1 1 1 1 1 1-w 1-w w 3 -1+w -1+w -1+w -1+w w 0 0 -w -1+w 3 |Aut| = 2^17*3^3*5 #short vectors: 0 184 4608 68344 505856 &Hlattice (#8 <-- #23) 2 1 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 -1 -1 -1 -1 -1 -1 0 1 2 w w w w w w w 1-w -w 3 |Aut| = 2^11*3^4*5^2*7 #short vectors: 0 184 4608 68344 505856 &Hlattice (#9 <-- #24) 2 w 2 w 1 2 w 1 1 2 w 1 1 1 2 w 1 1 1 1 2 w 1 1 1 1 1 2 w 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 -w 0 0 0 0 0 0 -w 1 3 |Aut| = 2^11*3^4*5^2*7 #short vectors: 0 184 4608 68344 505856 &Hlattice (#10 <-- #16) 2 0 2 0 1-w 2 0 0 0 2 0 0 0 0 2 1 -1+w -1 0 -1+w 3 1+w 1 1+w 0 0 0 3 1+w 0 0 0 1 0 1 3 0 0 1 -1+w 0 0 0 0 3 -w w w 1 0 1-w 0 -w 0 3 |Aut| = 2^23*3*5 #short vectors: 0 120 5120 67320 503808 &Hlattice (#11 <-- #17) 2 0 2 0 1 2 0 1 1 2 0 0 -w -w 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 -1+w -1+w -1+w -w 0 0 3 -1-w 1 1 1 w -1 -1 -1-w 3 1 0 -1+w -1+w -1-w 0 0 1 -1+w 3 |Aut| = 2^19*3^2 #short vectors: 0 120 5120 67320 503808 &Hlattice (#12 <-- #20) 2 1 2 0 0 2 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 1 1 1 2 -w -w -1 0 0 0 0 2 -1-w 0 -1+w 0 0 0 0 1-w 3 0 -w 1 1-w 1-w 1-w 1-w 0 -1-w 3 |Aut| = 2^11*3^4*5^2 #short vectors: 0 120 5120 67320 503808 &Hlattice (#13 <-- #25) 2 -1 2 0 0 2 0 0 1 2 0 0 0 0 2 -w 0 0 0 0 2 -w 0 0 0 0 1 2 0 0 1 1 -w 0 0 2 -1-w w -1 -1 0 0 0 -1 3 -1 1 1 1 -1-w 0 0 1 -w 3 |Aut| = 2^10*3^4*5^2 #short vectors: 0 120 5120 67320 503808 &Hlattice (#14 <-- #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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 |Aut| = 2^28*3^4*5^2*7 #short vectors: 40 760 9120 77560 497648 &Hlattice (#15 <-- #2) 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 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1+w 2 0 0 0 0 0 0 0 1+w 1 2 |Aut| = 2^26*3^4*5^2 #short vectors: 24 504 7520 73464 500112 &Hlattice (#16 <-- #3) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 0 1-w 1-w 1-w 2 0 0 0 0 1 1 1 1+w 2 0 0 0 0 0 0 0 1 0 3 |Aut| = 2^26*3^3*5 #short vectors: 16 376 6720 71416 501344 &Hlattice (#17 <-- #11) 1 0 1 0 0 1 0 0 0 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 1 0 w w 2 0 0 0 0 1 1 1 -w 2 0 0 0 -1-w -1+w -1+w -1+w 0 -1+w 3 |Aut| = 2^18*3^5*5*7 #short vectors: 12 312 6320 70392 501960 &Hlattice (#18 <-- #4) 1 0 1 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 1 1 2 0 0 1 1 1 1 2 0 0 1 1 1 1 1 2 0 0 1-w 1-w 1-w 1-w 1-w 1-w 2 0 0 0 0 0 0 0 0 1 4 |Aut| = 2^27*3^2*5*7 #short vectors: 8 504 3872 73464 510768 &Hlattice (#19 <-- #6) 1 0 1 0 0 2 0 0 1 2 0 0 0 0 2 0 0 1-w 1-w 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1+w 2 0 0 0 0 0 0 0 1+w 1 2 |Aut| = 2^26*3^4*5^2 #short vectors: 8 504 3872 73464 510768 &Hlattice (#20 <-- #8) 1 0 1 0 0 2 0 0 1 2 0 0 1-w 1-w 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 0 0 0 0 1 -1+w 0 0 3 0 0 1 1 1+w 1 1-w 1-w 0 3 |Aut| = 2^26*3^2 #short vectors: 8 248 5920 69368 502576 &Hlattice (#21 <-- #13) 1 0 1 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 1 1 2 0 0 1 1 1 1 2 0 0 1 1 1 1 1 2 0 0 0 w w w w w 2 0 0 0 0 0 0 0 0 1 2 |Aut| = 2^20*3^5*5^2*7 #short vectors: 8 504 3872 73464 510768 &Hlattice (#22 <-- #14) 1 0 1 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 1 1 2 0 0 1 1 1 1 2 0 0 1 1 1 1 1 2 0 0 0 -w -w -w -w -w 2 0 0 -1+w -1+w -1+w -1+w -1+w -1+w -w 3 |Aut| = 2^20*3^2*5*7 #short vectors: 8 248 5920 69368 502576 &Hlattice (#23 <-- #12) 1 0 2 0 1+w 2 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 1 1 1 2 0 0 -1 0 0 0 0 2 0 1 0 0 0 0 0 1-w 3 0 1+w 1 1-w 1-w 1-w 1-w 0 0 3 |Aut| = 2^18*3^3*5 #short vectors: 4 184 5520 68344 503192 &Hlattice (#24 <-- #21) 1 0 2 0 0 2 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 1 1 1 2 0 1 -1 0 0 0 0 2 0 w 0 1 1 1 1 w 2 0 1+w 1 w w w w w 1 3 |Aut| = 2^12*3^4*5^2*7 #short vectors: 4 184 5520 68344 503192 &Hlattice (#25 <-- #22) 1 0 2 0 0 2 0 1 0 2 0 1 0 1 2 0 0 1 0 0 2 0 1 0 1 1 0 2 0 -w 0 -w -w -w -w 2 0 0 0 0 0 -1 0 -w 2 0 -1+w -1 -1+w -1+w -1 -1+w -1-w 1 3 |Aut| = 2^12*3^4*5^2*7 #short vectors: 4 184 5520 68344 503192 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 91 420 420 0 0 0 0 0 0 0 0 0 0 1 0 0 0 90 0 0 0 0 0 0 0 15 46 465 0 450 0 0 0 0 0 0 0 0 0 1 15 0 0 30 0 0 0 0 0 0 1 31 44 256 390 0 256 0 0 0 0 0 0 0 1 1 0 12 0 30 0 0 0 0 0 0 0 63 70 0 378 441 0 0 0 0 0 0 0 0 0 1 0 0 0 6 0 63 0 0 0 2 26 0 125 128 512 0 0 72 128 0 0 0 0 2 0 1 1 25 0 0 0 0 0 0 0 0 56 70 129 56 256 256 0 140 0 0 0 0 0 0 1 0 0 1 1 56 0 0 0 0 1 7 30 6 248 128 128 0 180 0 256 0 0 0 1 0 0 0 0 6 31 0 0 0 0 0 0 0 45 210 46 255 0 0 210 210 0 0 0 0 0 0 0 0 0 0 45 1 0 0 0 0 0 45 210 255 46 0 0 210 210 0 0 0 0 0 0 0 0 0 0 1 45 0 0 0 0 30 0 0 0 0 17 960 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 2 4 48 0 0 36 137 256 512 0 0 0 0 0 0 1 0 2 24 0 0 0 0 0 0 0 0 0 30 30 0 225 255 452 0 0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 30 15 15 0 225 226 481 0 0 0 0 0 0 0 0 0 0 15 15 2 0 0 0 0 0 0 0 0 0 0 0 0 90 420 420 0 90 0 0 0 0 0 0 0 0 2 30 0 0 0 0 0 0 0 0 0 0 15 45 450 0 0 30 450 0 0 0 0 0 0 2 2 0 60 0 0 0 0 0 0 0 0 1 30 43 256 12 0 360 0 0 256 0 0 0 0 0 2 0 0 126 0 0 0 0 0 0 0 0 63 69 0 0 0 6 378 378 0 0 2 0 112 0 140 256 0 0 0 0 0 0 0 1 0 56 0 59 70 70 128 128 0 0 0 0 60 0 0 450 0 0 0 0 0 0 0 0 0 30 0 0 225 32 225 0 0 0 0 0 0 0 4 0 50 0 0 0 0 72 128 0 0 0 2 24 0 1 1 100 0 128 512 0 0 0 0 0 240 0 270 0 0 0 0 0 0 0 0 0 0 120 135 0 0 122 135 0 0 0 0 0 0 0 0 2 112 0 0 0 140 0 0 0 0 0 56 1 0 70 1 128 0 256 256 0 0 0 2 0 12 62 0 0 0 180 256 0 0 0 1 6 0 0 30 0 0 217 128 128 0 0 0 0 0 0 0 90 2 0 0 0 420 0 0 0 0 0 0 0 0 45 210 45 210 0 0 0 0 0 0 0 2 90 0 0 0 420 0 0 0 0 0 0 0 0 45 210 210 45 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=20 V=Q^20 &Genus of the trace-forms: det= 1 = 1 2-adic symbol: 1^20_4 -1-adic symbol: +^20 -^0 level(of 2-scaled form)=4, weight=10 a_0,..,a_5 determine modular form 18-classes of trace forms &Gram (#1 <- H1) 2 1 2 1 1 2 1 0 1 2 1 1 1 0 2 1 1 1 0 1 2 1 1 1 0 1 1 2 1 1 1 0 1 1 1 2 1 1 1 0 1 1 1 1 2 1 1 1 0 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 5 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 5 |Aut| = 2^37*3^8*5^4*7^2*11*13*17*19 #short vectors: 0 760 0 77560 524288 &Gram (#2 <- H2) 2 1 2 1 1 2 1 0 1 2 1 1 1 0 2 1 1 1 0 1 2 1 1 1 0 1 1 2 1 1 1 0 1 1 1 2 1 1 1 0 1 1 1 1 2 1 1 1 0 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 1 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 -1 1 2 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 3 |Aut| = 2^35*3^10*5^4*7^2*11 #short vectors: 0 504 2048 73464 516096 &Gram (#3 <- H3) 2 1 2 1 1 2 1 0 1 2 1 1 1 0 2 1 1 1 0 1 2 1 1 1 0 1 1 2 1 1 1 0 1 1 1 2 1 1 1 0 1 1 1 1 2 1 1 1 0 1 1 1 1 1 2 1 0 0 1 0 0 0 0 0 0 2 1 1 1 0 1 1 1 1 1 1 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 1 0 0 1 0 0 0 0 0 0 1 0 0 0 3 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 4 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 4 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 4 1 0 0 0 0 0 0 0 0 0 1 1 0 -1 1 0 1 1 1 5 |Aut| = 2^35*3^7*5^3*7^2*11 #short vectors: 0 376 3072 71416 512000 &Gram (#4 <- H4) 2 1 2 1 1 2 1 0 1 2 1 0 0 1 2 1 1 0 0 0 2 1 1 1 1 0 1 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 1 0 0 -1 2 0 0 0 0 0 0 0 1 -1 0 -1 0 2 0 0 0 0 0 0 0 1 -1 0 -1 0 1 2 0 0 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 0 1 2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 1 0 0 -1 0 0 0 -1 0 0 0 1 1 4 1 1 0 0 0 1 1 -1 1 0 1 0 -1 -1 0 0 1 1 4 1 1 0 0 0 1 1 -1 0 1 0 0 0 0 0 0 0 1 2 4 |Aut| = 2^30*3^10*5^3*7^2 #short vectors: 0 312 3584 70392 509952 &Gram (#5 <- H5,H6) 2 1 2 1 1 2 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 -1 0 -1 2 0 0 0 -1 -1 -1 0 2 0 0 0 1 1 1 0 -1 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 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 1 1 2 1 0 0 1 0 1 -1 0 0 0 0 0 0 0 3 1 1 1 1 0 1 -1 -1 0 0 0 0 0 0 1 3 1 1 0 1 1 1 0 -1 1 0 1 0 0 0 1 1 3 1 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 0 3 1 1 0 -1 -1 -1 0 1 -1 1 0 1 0 1 0 0 0 0 3 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 3 |Aut| = 2^35*3^5*5^2*7^2 #short vectors: 0 248 4096 69368 507904 &Gram (#6 <- H7) 2 1 2 1 1 2 1 1 0 2 1 0 0 0 2 1 0 0 0 1 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 0 0 0 2 0 0 0 0 0 0 0 0 0 -1 2 1 0 0 0 1 1 0 -1 0 0 0 3 1 0 1 0 0 1 0 0 0 0 0 0 3 1 0 0 0 1 1 0 0 0 0 0 0 1 3 1 1 0 1 0 0 0 0 0 -1 1 0 0 1 3 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 3 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 3 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 3 0 1 0 1 -1 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 3 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 4 |Aut| = 2^30*3^7*5^3 #short vectors: 0 184 4608 68344 505856 &Gram (#7 <- H8,H9) 2 1 2 1 1 2 1 0 0 2 1 1 1 0 2 1 1 1 0 1 2 1 1 1 0 1 1 2 1 0 0 1 0 0 0 2 1 0 0 1 0 0 0 1 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 1 2 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 1 1 1 2 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 3 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 3 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 3 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 3 |Aut| = 2^20*3^8*5^4*7^2 #short vectors: 0 184 4608 68344 505856 &Gram (#8 <- H10,H11) 2 1 2 1 1 2 1 0 1 2 0 0 0 0 2 0 0 0 0 -1 2 0 0 0 0 -1 1 2 0 0 0 0 -1 0 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 2 1 0 1 1 -1 0 0 0 0 0 0 3 0 0 0 0 1 -1 -1 0 0 1 0 0 3 1 1 1 0 -1 1 0 0 0 0 0 1 -1 3 1 0 0 1 1 0 -1 -1 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 3 1 0 0 0 -1 0 0 1 0 0 0 1 0 1 0 1 3 1 0 0 0 1 0 0 -1 0 0 -1 0 0 0 1 1 0 3 0 0 0 0 1 0 -1 -1 0 0 1 0 1 0 1 1 0 0 3 1 0 1 1 1 0 0 0 1 -1 0 0 0 0 1 0 0 1 0 3 |Aut| = 2^33*3^6*5 #short vectors: 0 120 5120 67320 503808 &Gram (#9 <- H12,H13) 2 1 2 1 1 2 1 0 0 2 1 0 0 1 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 0 0 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 1 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 1 0 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 1 1 0 0 -1 -1 0 -1 0 0 1 0 0 0 3 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 3 1 0 0 1 1 0 0 1 0 -1 -1 0 -1 0 -1 0 0 3 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 3 1 0 1 1 1 0 0 -1 0 0 0 0 0 -1 0 1 0 0 0 3 |Aut| = 2^20*3^8*5^4 #short vectors: 0 120 5120 67320 503808 &Gram (#10 <- H14) 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |Aut| = 2^38*3^8*5^4*7^2*11*13*17*19 #short vectors: 40 760 9120 77560 497648 &Gram (#11 <- H15) 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 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 1 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 2 |Aut| = 2^36*3^10*5^4*7^2*11 #short vectors: 24 504 7520 73464 500112 &Gram (#12 <- H16) 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 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 0 -1 -1 -1 0 2 0 0 0 0 0 0 0 0 1 1 1 0 -1 2 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 2 0 0 0 0 0 0 0 0 -1 -1 -1 0 1 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 -1 0 1 0 3 0 0 0 0 0 0 0 0 -1 0 -1 1 0 0 -1 1 0 -1 0 3 |Aut| = 2^36*3^7*5^3*7^2*11 #short vectors: 16 376 6720 71416 501344 &Gram (#13 <- H17) 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 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 1 0 1 2 0 0 0 0 0 0 0 0 1 0 0 1 2 0 0 0 0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 -1 -1 -1 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 -1 2 0 0 0 0 0 0 -1 0 1 1 0 0 0 0 -1 0 0 0 -1 3 |Aut| = 2^31*3^10*5^3*7^2 #short vectors: 12 312 6320 70392 501960 &Gram (#14 <- H18) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 0 -1 0 -1 2 0 0 0 0 -1 -1 -1 0 2 0 0 0 0 1 1 1 0 -1 2 0 0 0 0 1 1 1 0 -1 1 2 0 0 0 0 1 1 1 0 -1 1 1 2 0 0 0 0 1 1 1 0 -1 1 1 1 2 0 0 0 0 1 1 1 0 -1 1 1 1 1 2 0 0 0 0 1 1 1 0 -1 1 1 1 1 1 2 0 0 0 0 -1 -1 -1 0 1 -1 -1 -1 -1 -1 -1 2 0 0 0 0 1 1 1 0 -1 1 1 1 1 1 1 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 4 0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 -1 2 4 |Aut| = 2^37*3^7*5^3*7^2*11*13 #short vectors: 8 504 3872 73464 510768 &Gram (#15 <- H19,H21) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 0 1 1 0 2 0 0 0 0 1 0 0 0 2 0 0 0 0 -1 -1 -1 0 0 2 0 0 0 0 -1 -1 -1 0 0 1 2 0 0 0 0 1 1 0 1 1 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 1 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 2 |Aut| = 2^36*3^11*5^4*7^2 #short vectors: 8 504 3872 73464 510768 &Gram (#16 <- H20,H22) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 0 0 -1 0 -1 2 0 0 0 0 -1 -1 -1 0 2 0 0 0 0 -1 -1 -1 0 1 2 0 0 0 0 -1 -1 -1 0 1 1 2 0 0 0 0 -1 -1 -1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 3 0 0 0 0 1 0 1 -1 0 0 0 -1 -1 0 0 -1 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 3 0 0 0 0 1 0 1 -1 0 -1 0 0 0 0 0 -1 1 -1 3 0 0 0 0 0 0 -1 1 0 0 0 0 1 -1 0 0 -1 0 -1 3 |Aut| = 2^36*3^5*5^2*7^2 #short vectors: 8 248 5920 69368 502576 &Gram (#17 <- H23) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 1 2 0 0 1 0 -1 2 0 0 1 0 0 1 2 0 0 1 0 0 1 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 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 1 2 0 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 0 2 0 0 1 -1 -1 0 0 0 0 1 1 1 1 -1 0 3 0 0 1 0 -1 1 1 1 0 0 0 0 0 0 0 0 3 0 0 -1 0 1 -1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 3 0 0 -1 0 0 0 0 -1 -1 0 0 0 0 0 -1 -1 0 0 3 0 0 1 0 0 0 1 0 -1 0 0 0 0 -1 0 1 0 -1 0 3 |Aut| = 2^31*3^7*5^3 #short vectors: 4 184 5520 68344 503192 &Gram (#18 <- H24,H25) 1 0 1 0 0 2 0 0 1 2 0 0 1 0 2 0 0 -1 0 -1 2 0 0 -1 0 -1 1 2 0 0 1 1 0 0 0 2 0 0 -1 0 -1 1 1 0 2 0 0 1 1 0 0 0 1 0 2 0 0 -1 -1 0 0 0 -1 0 -1 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 1 0 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 2 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -1 -1 2 0 0 -1 0 0 1 0 -1 0 -1 1 1 0 1 -1 -1 1 3 0 0 1 0 0 0 -1 1 0 1 -1 0 -1 0 0 0 0 -1 3 0 0 -1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 -1 3 |Aut| = 2^21*3^8*5^4*7^2 #short vectors: 4 184 5520 68344 503192