Output of hn --only_even &K=Q(sqrt(-5)) &Hdim=4 V=K^4 &HNeighbourhood at <2,-1+w> (even classes) contains 13 classes: mass of the neighbourhood is 13/192 Steinitz class <1,w>: &Hlattice (#1 <- #1) 4 1-w 4 -w -w 4 -1+w -2-w 1 4 |Aut| = 2^4*3^2 #short vectors: 0 0 0 120 &Hlattice (#2 <- #2) <2,-1+w> <1> <1> <2,-1+w> 1 1/2-1/2w 4 1/2-1/2w 1-w 4 1/2-1/2w 3/2+1/2w 1 3 |Aut| = 2^4*3*5 #short vectors: 0 0 0 120 &Hlattice (#3 <- #13) <1> <1> <2,-1+w> <2,-1+w> 4 2+w 4 -1+w 1+w 2 -2 -1+w 1+1/2w 2 |Aut| = 2^5*3*5 #short vectors: 0 0 0 120 &Hlattice (#4 <- #7) 2 0 2 -1+w w 6 w 1-w -w 6 |Aut| = 2^7*3 #short vectors: 0 24 0 24 0 288 &Hlattice (#5 <- #9) <1> <1> <2,-1+w> <2,-1+w> 2 1 2 1 1 1 1 1 1/2 1 |Aut| = 2^7*3^2 #short vectors: 0 24 0 24 0 288 &Hlattice (#6 <- #12) <1> <1> <2,-1+w> <2,-1+w> 2 -1 2 0 -1/2-1/2w 2 1 -1/2-1/2w 1+1/2w 2 |Aut| = 2^4*3*5 #short vectors: 0 20 0 40 &Hlattice (#7 <- #5) <1> <1> <2,-1+w> <2,-1+w> 2 0 2 0 -1/2+1/2w 1 1/2+1/2w 0 0 1 |Aut| = 2^4*3^2 #short vectors: 0 12 0 72 &Hlattice (#8 <- #6) <2,-1+w> <2,-1+w> <2,-1+w> <2,-1+w> 2 1/2-1/2w 2 1/2 1/2 2 -1/2+1/2w -1+1/2w -1/2+1/2w 2 |Aut| = 2^4*3^2 #short vectors: 0 12 0 72 &Hlattice (#9 <- #10) <1> <1> <2,-1+w> <2,-1+w> 2 0 2 1/2-1/2w 0 1 0 1/2-1/2w 0 1 |Aut| = 2^5*3^2 #short vectors: 0 12 0 72 &Hlattice (#10 <- #11) <1> <1> <2,-1+w> <2,-1+w> 2 0 2 0 1/2+1/2w 1 -1/2-1/2w 0 0 1 |Aut| = 2^5*3^2 #short vectors: 0 12 0 72 &Hlattice (#11 <- #3) <1> <1> <2,-1+w> <2,-1+w> 2 0 4 1 1/2+1/2w 1 -1/2-1/2w 2 -1/2w 2 |Aut| = 2^6 #short vectors: 0 8 0 88 &Hlattice (#12 <- #4) <1> <1> <2,-1+w> <2,-1+w> 2 -1 4 1 -1/2+1/2w 1 0 1/2+1/2w 1/2 1 |Aut| = 2^7*3 #short vectors: 0 8 0 88 &Hlattice (#13 <- #8) 2 0 2 1+w 1 4 -1 1-w 0 4 |Aut| = 2^7 #short vectors: 0 8 0 88 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 6 0 0 0 0 0 0 0 0 9 0 0 10 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 1 8 0 0 0 0 6 0 0 0 0 0 3 0 0 0 0 0 0 0 3 9 0 0 0 5 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 9 0 0 0 0 0 0 0 6 0 0 0 0 9 0 0 0 0 0 0 0 0 6 0 0 0 0 0 9 0 0 0 0 0 0 6 0 0 0 0 0 9 4 0 0 1 0 0 4 4 0 0 0 1 1 0 8 0 0 1 0 0 0 0 0 6 0 0 0 0 4 0 1 0 0 0 4 4 2 0 0