Output of /home/aschiem/bin/hn --invar -t --shells-5 --herm_lll3 0.8

&K=Q(sqrt(-31))
&Hdim=2      V=K^2
&HNeighbourhood at <2,-1+w> contains 9 classes:
mass of the neighbourhood is 15/8
  Steinitz class <1,w>:
&Hlattice (#1 <- #8)
       3 
    -1+w        3 
  |Aut| = 2^2
  #short vectors:
    0    0    8    4    4


&Hlattice (#2 <- #7)
   <2,w> <2,-1+w> 
     1/2 
       0      1/2 
  |Aut| = 2^2
  #short vectors:
    0    4    0    8    4


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


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


&Hlattice (#5 <- #6)
     <1>    <2,w> 
       3 
1/2+1/2w        1 
  |Aut| = 2^2
  #short vectors:
    0    2    4    6    4


&Hlattice (#6 <- #5)
     <1>    <2,w> 
       1 
       0      1/2 
  |Aut| = 2^2
  #short vectors:
    2    2    4    4    6


  Steinitz class <2,-1+w>:
&Hlattice (#7 <- #3)
   <2,w>    <2,w> 
     1/2 
       0      1/2 
  |Aut| = 2^3
  #short vectors:
    0    4    0    8    4


&Hlattice (#8 <- #9)
     <1> <2,-1+w> 
       2 
 -1+1/2w      3/2 
  |Aut| = 2^2
  #short vectors:
    0    2    4    6    4


&Hlattice (#9 <- #2)
     <1> <2,-1+w> 
       1 
       0      1/2 
  |Aut| = 2^2
  #short vectors:
    2    2    4    4    6



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   0   0   0   0   0   2   1 
  0   0   0   0   0   0   1   1   1 
  0   0   0   0   0   0   1   0   2 
  0   2   1   0   0   0   0   0   0 
  2   1   0   0   0   0   0   0   0 
  1   1   1   0   0   0   0   0   0 
  0   0   0   1   0   2   0   0   0 
  0   0   0   0   2   1   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= 961 = 31^2
   2-adic symbol:  1^4_II 
  31-adic symbol:  1^2 31^2 
  -1-adic symbol:  +^4 -^0 
level=31, weight=2
a_0,..,a_10 determine modular form

5-classes of trace forms

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

&Gram (#2 <- H2,H4,H7)
  4 
  0   4 
 -1   0   8 
  0  -1   0   8 
  |Aut| = 2^3
  #short vectors:
    0    0    0    4    0    0    0    8    0    4

&Gram (#3 <- H3)
  2 
  0   2 
  1   0  16 
  0   1   0  16 
  |Aut| = 2^5
  #short vectors:
    0    4    0    4    0    0    0    4    0    8

&Gram (#4 <- H5,H8)
  4 
  2   6 
  2  -1   8 
  1   2   3  10 
  |Aut| = 2^2
  #short vectors:
    0    0    0    2    0    4    0    6    0    4

&Gram (#5 <- H6,H9)
  2 
  0   4 
  0  -1   8 
  1   0   0  16 
  |Aut| = 2^3
  #short vectors:
    0    2    0    2    0    4    0    4    0    6

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