Output of /home/aschiem/bin/hn --invar -t --shells-11 --herm_lll3 0.8

&K=Q(sqrt(-67))
&Hdim=2      V=K^2
&HNeighbourhood at <2,2w> contains 4 classes:
mass of the neighbourhood is 11/8
  Steinitz class <1,w>:
&Hlattice (#1 <- #2)
       4 
     2-w        5 
  |Aut| = 2
  #short vectors:
    0    0    0    4    4    4    4    8    4    4    4


&Hlattice (#2 <- #4)
       3 
     1-w        6 
  |Aut| = 2
  #short vectors:
    0    0    4    0    0    8    4    4    4    4    8


&Hlattice (#3 <- #3)
       2 
      -w        9 
  |Aut| = 2^2
  #short vectors:
    0    4    0    4    0    0    0    4    8   16    0


&Hlattice (#4 <- #1)
       1 
       0        1 
  |Aut| = 2^3
  #short vectors:
    4    4    0    4    8    0    0    4    4    8    0



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  1   3   1   1 
  3   2   1   0 
  2   2   1   1 
  4   0   2   0 


classes of Z-lattices with respect to the trace form
one representative of each class
&Dim=4      V=Q^4

&Genus of the trace-forms:
det= 4489 = 67^2
   2-adic symbol:  1^4_II 
  67-adic symbol:  1^2 67^2 
  -1-adic symbol:  +^4 -^0 
level=67, weight=2
a_0,..,a_22 determine modular form

4-classes of trace forms

&Gram (#1 <- H1)
  8 
  0   8 
  3   2  10 
  2  -3   0  10 
  |Aut| = 2^2
  #short vectors:
    0    0    0    0    0    0    0    4    0    4    0    4    0    4    0    8    0    4    0    4    0    4

&Gram (#2 <- H2)
  6 
  0   6 
  1   2  12 
  2  -1   0  12 
  |Aut| = 2^2
  #short vectors:
    0    0    0    0    0    4    0    0    0    0    0    8    0    4    0    4    0    4    0    4    0    8

&Gram (#3 <- H3)
  4 
  0   4 
  1  -2  18 
  2  -1   1  18 
  |Aut| = 2^3
  #short vectors:
    0    0    0    4    0    0    0    4    0    0    0    0    0    0    0    4    0    8    0   16    0    0

&Gram (#4 <- H4)
  2 
  0   2 
  1   0  34 
  0   1   0  34 
  |Aut| = 2^5
  #short vectors:
    0    4    0    4    0    0    0    4    0    8    0    0    0    0    0    4    0    4    0    8    0    0

<end>