Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-6 -D5

&K=Q(sqrt(-2))
&Hdim=4      V=K^4
&HNeighbourhood at <3,-1+w> contains 2 classes:
(same result with neighbours above 2 and --only_even and with neighbours above 5=<5,5w>,
 thus the local factor at 2 is trivial (also for all lattices whose localization at 2 splits
 such a sublattice as an orthogonal component)
mass of the neighbourhood is 1/1536
  Steinitz class <1,w>:
&Hlattice (#1 <-- #1)
       2 
       1        2 
       0        w        2 
       0        w        1        2 
  |Aut| = 2^8*3^2
  #short vectors:
    0   48    0  624    0 1344


&Hlattice (#2 <-- #2)
       2 
    -1-w        2 
       0        0        2 
       0        0     -1-w        2 
  |Aut| = 2^9*3^2
  #short vectors:
    0   48    0  624    0 1344



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
 24  16 
 32   8 


classes of Z-lattices with respect to the trace form (scaled by 1/2)
&Dim=8      V=Q^8

&Genus of the trace-forms:
det= 16 = 2^4
   2-adic symbol:  1^4_II 2^4_II 
  -1-adic symbol:  +^8 -^0 
level=2, weight=4
a_0,..,a_2 determine modular form

&Gram (#1 <- H1,H2)
  2 
  1   2 
  1   0   2 
  1   0   0   2 
  0   0   0   0   2 
  0   0   0   0  -1   2 
  0   0   0   0   1  -1   2 
  0   0   0   0   1  -1   0   2 
  |Aut| = 2^15*3^4
  #short vectors:
    0   48

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