Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-4

&K=Q(sqrt(-23))
&Hdim=2      V=K^2
&HNeighbourhood at <2,-1+w> contains 9 classes:
mass of the neighbourhood is 11/8
  Steinitz class <1,w>:
&Hlattice (#1 <-- #8)
      13 
    3-6w       16 
  |Aut| = 2^2*3
  #short vectors:
    0    0   12   12


&Hlattice (#2 <-- #7)
       5 
    2-2w        5 
  |Aut| = 2^2
  #short vectors:
    0    4    4    8


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


  Steinitz class <2,w>:
&Hlattice (#4 <-- #6)
     <1>    <2,w> 
       2 
-1/2+1/2w        1 
  |Aut| = 2^2*3
  #short vectors:
    0    6    0    6


&Hlattice (#5 <-- #4)
     <1>    <2,w> 
       5 
    -2-w      5/2 
  |Aut| = 2^3
  #short vectors:
    0    4    4    8


&Hlattice (#6 <-- #5)
     <1>    <2,w> 
       1 
       0      1/2 
  |Aut| = 2^2
  #short vectors:
    2    2    6    8


  Steinitz class <2,-1+w>:
&Hlattice (#7 <-- #9)
     <1> <2,-1+w> 
       2 
    1/2w        1 
  |Aut| = 2^2*3
  #short vectors:
    0    6    0    6


&Hlattice (#8 <-- #3)
     <1> <2,-1+w> 
       5 
    -3+w      5/2 
  |Aut| = 2^3
  #short vectors:
    0    4    4    8


&Hlattice (#9 <-- #2)
     <1> <2,-1+w> 
       1 
       0      1/2 
  |Aut| = 2^2
  #short vectors:
    2    2    6    8



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   0   0   0   0   0   0   3 
  0   0   0   0   0   0   1   1   1 
  0   0   0   0   0   0   0   1   2 
  0   3   0   0   0   0   0   0   0 
  0   2   1   0   0   0   0   0   0 
  1   1   1   0   0   0   0   0   0 
  0   0   0   0   0   3   0   0   0 
  0   0   0   0   1   2   0   0   0 
  0   0   0   1   1   1   0   0   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= 529 = 23^2
   2-adic symbol:  1^4_II 
  23-adic symbol:  1^2 23^2 
  -1-adic symbol:  +^4 -^0 
level=23, weight=2
a_0,..,a_8 determine modular form

&Gram (#1 <- H1)
  6 
  3   6 
  2   2   6 
  0   2   3   6 
  |Aut| = 2^3*3
  #short vectors:
    0    0    0    0    0   12    0   12

&Gram (#2 <- H2,H5,H8)
  4 
  0   4 
  0  -1   6 
  1   0   0   6 
  |Aut| = 2^3
  #short vectors:
    0    0    0    4    0    4    0    8

&Gram (#3 <- H3)
  2 
  0   2 
  1   0  12 
  0   1   0  12 
  |Aut| = 2^5
  #short vectors:
    0    4    0    4    0    0    0    4

&Gram (#4 <- H4,H7)
  4 
  2   4 
  1   1   8 
  1   0   4   8 
  |Aut| = 2^2*3
  #short vectors:
    0    0    0    6    0    0    0    6

&Gram (#5 <- H6,H9)
  2 
  0   4 
  0  -1   6 
  1   0   0  12 
  |Aut| = 2^3
  #short vectors:
    0    2    0    2    0    6    0    8

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