Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-3 -D7 &K=Q(sqrt(-3)) &Hdim=10 V=K^10 &HNeighbourhood at <3,1+w> contains 6 classes: mass of the neighbourhood is 8899/31345665638400 Steinitz class <1,w>: &Hlattice (#1 <-- #4) 2 1 2 0 -1+w 2 0 w 1 2 1-w 1-w -1 -1 2 0 0 0 0 0 2 0 0 0 0 0 w 2 0 0 0 0 0 1 0 2 0 0 0 0 0 -1+w 1 0 2 0 w 1 1 0 -w -1 0 -1 3 |Aut| = 2^15*3^9*5^2 #short vectors: 0 540 21120 &Hlattice (#2 <-- #6) 2 0 2 w 0 2 -1+w 0 w 2 0 0 0 0 2 0 0 1 1-w 0 2 0 0 0 -w -1+w 1-w 2 0 1 0 0 0 0 0 3 1 0 0 -w -1 0 1 0 3 -1 0 0 0 -1+w 1-w 1 -1-w -w 3 |Aut| = 2^17*3^5*5^2*7 #short vectors: 0 540 21120 &Hlattice (#3 <-- #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| = 2^18*3^14*5^2*7 #short vectors: 60 1620 25980 &Hlattice (#4 <-- #2) 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 0 0 0 2 0 0 0 0 1 1 1 0 2 0 0 0 0 1-w 1-w 1-w 1 -w 2 |Aut| = 2^16*3^12*5*7 #short vectors: 24 972 23064 &Hlattice (#5 <-- #5) 1 0 1 0 0 2 0 0 -w 2 0 0 1 0 2 0 0 -w 1 -w 2 0 0 1-w w 1-w w 2 0 0 -w 0 -w 1 1-w 2 0 0 -w 0 -w 1 1-w 1 2 0 0 1-w w 0 0 1 0 0 2 |Aut| = 2^17*3^8*5^2*7 #short vectors: 12 756 22092 &Hlattice (#6 <-- #3) 1 0 2 0 -1+w 2 0 w 1 2 0 w 1 1 2 0 w 1 1 1 2 0 w 1 1 1 1 2 0 w 1 1 1 1 1 2 0 w 1 1 1 1 1 1 2 0 1 0 0 0 0 0 0 0 3 |Aut| = 2^9*3^13*5*7 #short vectors: 6 648 21606 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 6560 19440 0 80 0 3200 6720 19520 0 0 480 2560 0 0 1440 20160 0 7680 6048 0 112 3296 9072 10752 0 12960 0 1120 3680 11520 5670 13122 1 252 2187 8048 classes of Z-lattices with respect to the trace form &Dim=20 V=Q^20 &Genus of the trace-forms: det= 59049 = 3^10 2-adic symbol: 1^20_II 3-adic symbol: 1^10 3^10 -1-adic symbol: +^20 -^0 level=3, weight=10 a_0,..,a_6 determine modular form &Gram (#1 <- H1) 4 2 4 2 2 4 1 2 2 4 2 2 2 0 4 1 -1 1 1 -1 4 2 1 0 -1 2 -1 4 1 -1 -1 0 0 0 0 4 2 0 1 1 1 2 0 2 4 2 1 0 -1 1 -1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 -1 1 4 2 0 0 1 0 2 0 2 2 1 -1 -1 0 6 2 0 0 -1 0 0 2 1 1 2 0 0 0 1 6 2 2 0 0 2 -1 2 0 0 1 2 0 0 -1 -1 6 2 2 2 0 2 -1 2 -1 0 1 1 -2 0 0 2 2 6 2 0 0 -1 0 0 2 1 1 2 0 -1 -2 1 2 1 1 6 2 0 0 -1 0 0 2 1 1 2 2 2 0 -1 2 2 1 2 6 2 0 2 1 0 2 0 1 2 1 -1 -2 0 3 1 -1 2 2 0 6 |Aut| = 2^16*3^9*5^2 #short vectors: 0 0 0 540 0 21120 &Gram (#2 <- H2) 4 2 4 1 -1 4 2 1 -1 4 1 -1 0 1 4 1 -1 0 1 0 4 2 1 1 0 1 -1 4 2 1 1 0 -1 1 0 4 1 -1 2 0 0 0 1 1 4 2 1 0 2 1 1 0 0 1 4 1 -1 2 0 0 0 1 1 2 0 4 1 2 0 1 -1 -1 0 0 0 1 1 4 1 -1 2 0 0 0 1 1 2 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 2 1 -1 -2 -1 0 2 0 -1 1 1 0 0 6 2 1 -1 1 1 0 2 0 0 0 1 0 1 0 0 6 1 2 1 -1 0 -2 2 1 1 0 1 1 1 -1 1 0 6 2 1 -1 1 0 1 0 2 0 0 0 1 1 -2 0 2 0 6 2 1 -1 1 2 1 0 1 0 1 0 1 0 1 0 1 1 2 6 1 2 1 -1 0 -2 2 1 -1 -1 1 1 -1 0 2 1 2 -1 0 6 |Aut| = 2^18*3^5*5^2*7 #short vectors: 0 0 0 540 0 21120 &Gram (#3 <- H3) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^28*3^14*5^2*7 #short vectors: 0 60 0 1620 0 25980 &Gram (#4 <- H4) 2 1 2 0 0 2 0 0 -1 2 0 0 0 0 2 0 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 0 0 4 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 2 2 4 0 0 0 0 0 0 0 0 2 2 2 4 0 0 0 0 0 0 0 0 -1 -2 -2 0 4 0 0 0 0 0 0 0 0 1 2 2 2 0 4 0 0 0 0 0 0 0 0 -1 1 -1 1 1 0 4 0 0 0 0 0 0 0 0 1 2 2 2 0 2 0 4 0 0 0 0 0 0 0 0 -2 -1 0 -2 0 -1 0 -1 4 0 0 0 0 0 0 0 0 -2 0 -1 -2 0 -1 1 -1 2 4 0 0 0 0 0 0 0 0 -2 0 0 -1 -1 -1 0 1 1 1 4 0 0 0 0 0 0 0 0 -2 0 0 0 -1 0 0 1 0 0 2 4 |Aut| = 2^21*3^12*5*7 #short vectors: 0 24 0 972 0 23064 &Gram (#5 <- H5) 2 1 2 0 0 2 0 0 1 2 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -2 0 4 0 0 0 0 -2 0 0 4 0 0 0 0 -2 0 0 2 4 0 0 0 0 -2 2 0 0 0 4 0 0 0 0 2 0 -2 0 0 -2 4 0 0 0 0 2 -1 -1 -1 -1 -1 1 4 0 0 0 0 1 -1 1 -1 -1 -1 0 -1 4 0 0 0 0 -1 2 0 0 0 1 0 -2 1 4 0 0 0 0 -1 1 1 -1 0 1 -1 -2 0 2 4 0 0 0 0 1 -1 -1 0 1 -1 1 2 0 -2 -2 4 0 0 0 0 1 0 -1 -1 -1 0 1 -1 0 0 0 0 4 0 0 0 0 -1 1 0 1 1 1 0 1 -2 -1 0 0 -2 4 0 0 0 0 1 0 -1 -1 -1 0 0 -1 0 0 0 0 2 -2 4 0 0 0 0 1 0 -1 -1 -1 0 0 2 0 0 0 0 -1 1 -2 4 |Aut| = 2^20*3^8*5^2*7 #short vectors: 0 12 0 756 0 22092 &Gram (#6 <- H6) 2 1 2 0 0 4 0 0 2 4 0 0 2 2 4 0 0 -1 -2 -2 4 0 0 -1 1 1 -2 4 0 0 1 -1 1 -1 -1 4 0 0 2 1 0 1 -2 -1 4 0 0 2 0 1 1 -2 0 2 4 0 0 -2 0 0 -1 2 0 -2 -2 4 0 0 2 0 0 1 -2 0 2 2 -1 4 0 0 2 2 2 -2 1 1 0 0 0 0 4 0 0 2 0 0 1 -2 0 2 2 -2 2 1 4 0 0 -2 0 0 -1 2 0 -2 -2 2 -2 0 -2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 0 0 -1 1 -1 -1 0 0 -1 -2 2 -1 1 -1 2 1 6 0 0 -2 -2 0 0 1 0 -2 -1 0 -2 -2 -2 0 -2 -2 6 0 0 -2 0 0 1 0 -1 0 0 2 0 0 0 2 0 2 -1 6 0 0 -2 0 0 1 0 -1 0 0 0 -1 -2 -1 0 0 -2 1 1 6 |Aut| = 2^11*3^13*5*7 #short vectors: 0 6 0 648 0 21606