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

&K=Q(sqrt(-43))
&Hdim=3      V=K^3
&HNeighbourhood at <2,2w> contains 8 classes:
mass of the neighbourhood is 83/48
  Steinitz class <1,w>:
&Hlattice (#1 <- #4)
       3 
       1        4 
     1-w        2        5 
  |Aut| = 2
  #short vectors:
    0    0    2    6   18   18   24   24   30   30   66


&Hlattice (#2 <- #8)
       3 
     1+w        5 
     2-w     -2-w        5 
  |Aut| = 2^2*3
  #short vectors:
    0    6    2    0   24    6   12   18   60   12   60


&Hlattice (#3 <- #5)
       2 
      -1        4 
       1      1-w        4 
  |Aut| = 2^2
  #short vectors:
    0    2    4    8   10    0   28   30   66   34   44


&Hlattice (#4 <- #6)
       3 
       1        3 
    -1-w       -1        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6    4    8   10   28   30   28   44   80


&Hlattice (#5 <- #7)
       3 
      -1        3 
    -1-w        0        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6    4    8   10   28   30   28   44   80


&Hlattice (#6 <- #1)
       1 
       0        1 
       0        0        1 
  |Aut| = 2^4*3
  #short vectors:
    6   12    8    6   24   24    0   12   30   24   36


&Hlattice (#7 <- #2)
       1 
       0        3 
       0     -1+w        4 
  |Aut| = 2^2
  #short vectors:
    2    0    4   14   12   16   28   28   42   40   32


&Hlattice (#8 <- #3)
       1 
       0        2 
       0       -w        6 
  |Aut| = 2^3
  #short vectors:
    2    4    8    6    8   16   24   28   18   48   72



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  7   1   1   3   3   0   2   1 
  6   0   6   3   3   0   0   0 
  2   2   6   2   2   0   4   0 
  6   1   2   2   5   0   0   2 
  6   1   2   5   2   0   0   2 
  0   0   0   0   0   0  12   6 
  4   0   4   0   0   1   7   2 
  4   0   0   4   4   1   4   1 


classes of Z-lattices with respect to the trace form
one representative of each class
&Dim=6      V=Q^6

&Genus of the trace-forms:
det= 79507 = 43^3
   2-adic symbol:  1^-6_II 
  43-adic symbol:  1^-3 43^-3 
  -1-adic symbol:  +^6 -^0 
level=43, weight=3
a_0,..,a_22 determine modular form

7-classes of trace forms

&Gram (#1 <- H1)
  6 
  2   8 
  0   2   8 
  0  -2   3   8 
  2  -3   2   4  10 
  1   4   2   0   1  10 
  |Aut| = 2^2
  #short vectors:
    0    0    0    0    0    2    0    6    0   18    0   18    0   24    0   24    0   30    0   30    0   66

&Gram (#2 <- H2)
  4 
  2   4 
  0   0   6 
  2   2   3  10 
  1  -1   2   1  16 
  1   2  -2   0   6  16 
  |Aut| = 2^3*3
  #short vectors:
    0    0    0    6    0    2    0    0    0   24    0    6    0   12    0   18    0   60    0   12    0   60

&Gram (#3 <- H3)
  4 
  2   6 
  2   0   8 
  2   2  -1   8 
  2   1   0   0  10 
  1   3  -2  -1  -3  16 
  |Aut| = 2^3
  #short vectors:
    0    0    0    2    0    4    0    8    0   10    0    0    0   28    0   30    0   66    0   34    0   44

&Gram (#4 <- H4,H5)
  4 
  2   6 
  0   2   6 
  0   2   3  10 
  2  -1  -2   2  12 
  1  -1   0  -2  -4  14 
  |Aut| = 2^2
  #short vectors:
    0    0    0    2    0    6    0    4    0    8    0   10    0   28    0   30    0   28    0   44    0   80

&Gram (#5 <- H6)
  2 
  0   2 
  0   0   2 
  1   0   0  22 
  0   1   0   0  22 
  0   0   1   0   0  22 
  |Aut| = 2^7*3
  #short vectors:
    0    6    0   12    0    8    0    6    0   24    0   24    0    0    0   12    0   30    0   24    0   36

&Gram (#6 <- H7)
  2 
  0   6 
  0   0   6 
  0  -1  -2   8 
  0   2  -1   0   8 
  1   0   0   0   0  22 
  |Aut| = 2^4
  #short vectors:
    0    2    0    0    0    4    0   14    0   12    0   16    0   28    0   28    0   42    0   40    0   32

&Gram (#7 <- H8)
  2 
  0   4 
  0   0   4 
  0  -1   2  12 
  0   2  -1  -1  12 
  1   0   0   0   0  22 
  |Aut| = 2^5
  #short vectors:
    0    2    0    4    0    8    0    6    0    8    0   16    0   24    0   28    0   18    0   48    0   72

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