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 3 classes:
mass of the neighbourhood is 61/35672555520
  Steinitz class <1,w>:
&Hlattice (#1 <-- #1)
       2 
       0        2 
      -1        0        2 
      -1       -w        1        2 
      -1       -w        1        1        2 
      -1       -w        1        1        1        2 
      -1       -w        1        1        1        1        2 
       w       -1       -w       -w       -w       -w       -w        2 
  |Aut| = 2^15*3^5*5^2*7
  #short vectors:
    0  480    0 61920


&Hlattice (#2 <-- #2)
       2 
      -1        2 
       0      1+w        2 
      -1        0        0        2 
      -1        0        0        1        2 
      -1        0        0        1        1        2 
       w        0        0       -w       -w       -w        2 
     1-w        w        1       -1       -1       -1       -w        4 
  |Aut| = 2^22*3^2*5*7
  #short vectors:
    0  480    0 61920


&Hlattice (#3 <-- #3)
       2 
     1-w        2 
      -w      1-w        2 
       1        1        1        2 
       0        0        0        0        2 
       0        0        0        0      1-w        2 
       0        0        0        0        1        1        2 
       0        0        0        0       -w      1-w      1-w        2 
  |Aut| = 2^21*3^4*5^2
  #short vectors:
    0  480    0 61920



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
42360 43200 12096 
40960 42360 14336 
36864 46080 14712 


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_II 
  -1-adic symbol:  +^16 -^0 
level=1, weight=8
a_0,..,a_0 determine modular form

&Gram (#1 <- H1,H3)
  2 
  0   2 
 -1   0   2 
 -1   0   1   2 
 -1   0   1   1   2 
 -1   0   1   1   1   2 
 -1   0   1   1   1   1   2 
  0  -1   0   0   0   0   0   2 
  0   0   0   0   0   0   0   1   2 
  0   0   0  -1  -1  -1  -1   0   0   2 
  0   0   0   0   0   0   0  -1  -1   0   2 
  0   1   0   0   0   0   0  -1  -1   0   1   2 
  0   1   0   0   0   0   0  -1  -1   0   1   1   2 
  0   1   0   0   0   0   0  -1  -1   0   1   1   1   2 
  0   1   0   0   0   0   0  -1  -1   0   1   1   1   1   2 
 -1   0   1   1   1   1   1   0   0  -1   0   0   0   0   0   2 
  |Aut| = 2^29*3^10*5^4*7^2

&Gram (#2 <- H2)
  2 
  1   2 
  1   0   2 
  1   0   0   2 
  1   0   1   0   2 
  1   0   1   0   1   2 
  1   0   1   0   1   1   2 
  1   0   1   0   1   1   1   2 
  1   0   1   0   1   1   1   1   2 
  1   0   1   0   1   1   1   1   1   2 
  1   0   1   0   1   1   1   1   1   1   2 
  1   0   1   0   1   1   1   1   1   1   1   2 
  1   0   1   0   1   1   1   1   1   1   1   1   2 
  0   0   1   0   0   0   0   0   0   0   0   0   0   2 
  1   1   0   0   0   0   0   0   0   0   0   0   1   0   4 
  1   0   0   1   0   0   0   0   0   0   0   0   0  -1   2   4 
  |Aut| = 2^30*3^6*5^3*7^2*11*13

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