Output of /home/aschiem/bin/hn --invar -t --shells-27 --herm_lll3 0.8 &K=Q(sqrt(-163)) &Hdim=2 V=K^2 &HNeighbourhood at <2,2w> contains 8 classes: mass of the neighbourhood is 27/8 Steinitz class <1,w>: &Hlattice (#1 <- #8) 7 -3+2w 24 |Aut| = 2 #short vectors: 0 0 0 0 0 0 4 4 4 4 4 4 0 4 0 4 0 4 0 8 8 8 4 12 0 8 8 &Hlattice (#2 <- #5) 6 2+w 8 |Aut| = 2 #short vectors: 0 0 0 0 0 4 0 4 4 0 0 8 4 0 4 8 4 4 8 0 0 4 4 8 4 8 4 &Hlattice (#3 <- #6) 6 1-w 7 |Aut| = 2 #short vectors: 0 0 0 0 0 4 4 0 0 0 4 8 0 8 4 4 4 4 4 4 4 8 4 8 0 0 4 &Hlattice (#4 <- #7) 5 2-2w 33 |Aut| = 2 #short vectors: 0 0 0 0 4 0 0 0 4 8 0 0 4 4 4 4 0 12 0 12 4 4 0 4 12 8 8 &Hlattice (#5 <- #2) 4 2-w 11 |Aut| = 2 #short vectors: 0 0 0 4 0 0 0 4 0 0 4 4 4 4 0 4 4 8 0 12 8 4 8 12 4 4 8 &Hlattice (#6 <- #4) 3 w 14 |Aut| = 2 #short vectors: 0 0 4 0 0 4 0 0 0 0 0 4 0 4 12 4 4 4 8 0 4 4 4 12 4 4 4 &Hlattice (#7 <- #3) 2 1-w 21 |Aut| = 2^2 #short vectors: 0 4 0 4 0 0 0 4 0 8 0 0 0 0 0 4 0 4 0 8 8 8 0 8 8 16 8 &Hlattice (#8 <- #1) 1 0 1 |Aut| = 2^3 #short vectors: 4 4 0 4 8 0 0 4 4 8 0 0 8 0 0 4 8 4 0 8 0 0 0 0 12 8 0 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 1 1 2 0 1 1 0 1 0 1 0 1 2 1 0 1 1 0 1 1 2 0 0 2 0 1 2 1 0 0 0 0 1 1 1 1 1 0 1 1 2 2 0 1 0 0 0 2 2 0 0 0 0 1 1 0 0 0 0 4 0 2 0 classes of Z-lattices with respect to the trace form one representative of each class &Dim=4 V=Q^4 &Genus of the trace-forms: det= 26569 = 163^2 2-adic symbol: 1^4_II 163-adic symbol: 1^2 163^2 -1-adic symbol: +^4 -^0 level=163, weight=2 a_0,..,a_54 determine modular form 8-classes of trace forms &Gram (#1 <- H1) 14 0 14 6 5 16 5 -6 0 16 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 4 0 4 0 4 0 4 0 0 0 4 0 0 0 4 0 0 0 4 0 0 0 8 0 8 0 8 0 4 0 12 0 0 0 8 0 8 &Gram (#2 <- H2) 12 0 12 5 -2 16 2 5 0 16 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 4 0 0 0 0 0 8 0 4 0 0 0 4 0 8 0 4 0 4 0 8 0 0 0 0 0 4 0 4 0 8 0 4 0 8 0 4 &Gram (#3 <- H3) 12 0 12 1 2 14 2 -1 0 14 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 4 0 8 0 0 0 8 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 8 0 4 0 8 0 0 0 0 0 4 &Gram (#4 <- H4) 10 0 10 1 -4 18 4 1 0 18 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 8 0 0 0 0 0 4 0 4 0 4 0 4 0 0 0 12 0 0 0 12 0 4 0 4 0 0 0 4 0 12 0 8 0 8 &Gram (#5 <- H5) 8 0 8 3 2 22 2 -3 0 22 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 4 0 4 0 4 0 0 0 4 0 4 0 8 0 0 0 12 0 8 0 4 0 8 0 12 0 4 0 4 0 8 &Gram (#6 <- H6) 6 0 6 1 -2 28 2 1 0 28 |Aut| = 2^2 #short vectors: 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 12 0 4 0 4 0 4 0 8 0 0 0 4 0 4 0 4 0 12 0 4 0 4 0 4 &Gram (#7 <- H7) 4 0 4 1 -2 42 2 1 0 42 |Aut| = 2^3 #short vectors: 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 0 8 0 8 0 8 0 0 0 8 0 8 0 16 0 8 &Gram (#8 <- H8) 2 0 2 1 0 82 0 1 0 82 |Aut| = 2^5 #short vectors: 0 4 0 4 0 0 0 4 0 8 0 0 0 0 0 4 0 4 0 8 0 0 0 0 0 8 0 0 0 0 0 4 0 8 0 4 0 0 0 8 0 0 0 0 0 0 0 0 0 12 0 8 0 0