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 3 classes:
mass of the neighbourhood is 1/128
  Steinitz class <1,w>:
&Hlattice (#1 <-- #3)
       2 
       w        2 
      -w       -1        2 
     1+w        1       -1        3 
  |Aut| = 2^7*3
  #short vectors:
    0   32  128  240  512  896


&Hlattice (#2 <-- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
  |Aut| = 2^7*3
  #short vectors:
    8   32   96  240  496  896


&Hlattice (#3 <-- #2)
       1 
       0        1 
       0        0        2 
       0        0      1-w        2 
  |Aut| = 2^7*3
  #short vectors:
    4   32  112  240  504  896



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
 16   8  16 
  8  16  16 
 16  16   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 2^4]_0 
  -1-adic symbol:  +^8 -^0 
level(of 2-scaled form)=8, weight=4
a_0,..,a_4 determine modular form

&Gram (#1 <- H1)
  2 
  0   2 
  0  -1   2 
  0  -1   1   2 
  0  -1   0   1   2 
  0   0   0   0   0   2 
  0   0   0   0   0   0   2 
  1   1  -1   0   0   1   1   3 
  |Aut| = 2^14*3^2
  #short vectors:
    0   32  128  240

&Gram (#2 <- H2)
  1 
  0   1 
  0   0   1 
  0   0   0   1 
  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 
  |Aut| = 2^14*3^2
  #short vectors:
    8   32   96  240

&Gram (#3 <- H3)
  1 
  0   1 
  0   0   2 
  0   0   1   2 
  0   0  -1  -1   2 
  0   0   1   1   0   2 
  0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   2 
  |Aut| = 2^13*3^2
  #short vectors:
    4   32  112  240

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