Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-4 -D5 &K=Q(sqrt(-1)) &Hdim=8 V=K^8 &HNeighbourhood at <5,-2+w> contains 6 classes: mass of the neighbourhood is 1037/4756340736 Steinitz class <1,w>: &Hlattice (#1 <- #5) 2 -w 2 -w 1 2 -w 1 1 2 -w 1 1 1 2 -w 1 1 1 1 2 0 1 1 1 1 1 2 -w 1 1 1+w 1 1+w 1+w 3 |Aut| = 2^15*3^2*5*7 #short vectors: 0 224 4096 31200 &Hlattice (#2 <- #6) 2 -w 2 0 0 2 -1 1-w 0 2 0 0 1+w 0 2 0 0 -1-w 0 -1 2 0 0 1 0 1 -1 3 w -w -1+w 1-w w -w w 3 |Aut| = 2^21*3^2 #short vectors: 0 224 4096 31200 &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 |Aut| = 2^23*3^2*5*7 #short vectors: 32 480 4480 29152 &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 -w -1 1 2 |Aut| = 2^21*3^3*5 #short vectors: 16 352 4288 30176 &Hlattice (#5 <- #3) 1 0 1 0 0 2 0 0 -1 2 0 0 1 -1 2 0 0 -1 1 -1 2 0 0 1-w -1+w 1-w -1+w 2 0 0 1 -1 1 -1 1 3 |Aut| = 2^20*3^2*5 #short vectors: 8 288 4192 30688 &Hlattice (#6 <- #4) 1 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 0 -1-w 1+w -1-w 1+w -1-w 0 3 |Aut| = 2^13*3^4*5*7 #short vectors: 4 256 4144 30944 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 46456 24640 64 896 7168 18432 45056 27000 0 1024 8192 16384 16384 0 5496 14336 28672 32768 24576 15360 1536 7032 24576 24576 32768 20480 512 4096 15224 24576 41472 20160 288 2016 12096 21624 classes of Z-lattices with respect to the trace form (scaled by 1/2) &Dim=16 V=Q^16 &Genus of the trace-forms: det= 1 = 1 2-adic symbol: 1^16_0 -1-adic symbol: +^16 -^0 level(of 2-scaled form)=4, weight=8 a_0,..,a_4 determine modular form &Gram (#1 <- H1,H2) 2 1 2 1 0 2 1 0 0 2 1 1 0 0 2 1 1 0 0 1 2 1 1 0 0 1 1 2 1 1 0 0 1 1 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 0 0 0 2 1 0 1 0 0 0 0 0 0 0 0 0 3 1 1 0 0 1 1 1 1 0 0 0 -1 1 3 1 1 0 1 0 0 0 0 1 -1 1 0 1 0 3 0 1 0 0 0 0 0 0 1 -1 1 0 0 1 1 3 |Aut| = 2^29*3^4*5^2*7^2 #short vectors: 0 224 4096 31200 &Gram (#2 <- H3) 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 |Aut| = 2^31*3^6*5^3*7^2*11*13 #short vectors: 32 480 4480 29152 &Gram (#3 <- H4) 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 0 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 1 -1 0 1 -1 2 0 0 0 0 0 0 0 0 1 -1 1 0 -1 1 -1 2 |Aut| = 2^29*3^7*5^3*7^2 #short vectors: 16 352 4288 30176 &Gram (#4 <- H5) 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 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 3 |Aut| = 2^28*3^6*5^2*7*11 #short vectors: 8 288 4192 30688 &Gram (#5 <- H6) 1 0 1 0 0 2 0 0 1 2 0 0 -1 -1 2 0 0 1 1 0 2 0 0 -1 0 0 -1 2 0 0 1 1 0 1 0 2 0 0 -1 -1 0 -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 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 -1 -1 0 -1 0 -1 1 0 1 0 0 3 0 0 1 1 -1 1 0 1 -1 -1 0 0 0 -1 3 0 0 -1 -1 0 -1 0 -1 1 0 0 1 1 1 0 3 |Aut| = 2^24*3^8*5^2*7^2 #short vectors: 4 256 4144 30944