Output of /home/aschiem/Pgm/Hn/hn.debug --invar -t --shells-4 -D5

&K=Q(sqrt(-3))
&Hdim=8      V=K^8
&HNeighbourhood at <3,1+w> contains 3 classes:
mass of the neighbourhood is 41/48372940800
  Steinitz class <1,w>:
&Hlattice (#1 <- #3)
       2 
     1-w        2 
      -w        0        2 
       1        0        0        2 
       1        0     -1+w        1        2 
     1-w        1        0      1-w      1-w        2 
       1        w        0        1        1        w        2 
     1-w        0        0      1-w      1-w        1      1-w        2 
  |Aut| = 2^14*3^6*5^2*7
  #short vectors:
    0  720 13440 97200


&Hlattice (#2 <- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
       0        0        0        0        1 
       0        0        0        0        0        1 
       0        0        0        0        0        0        1 
       0        0        0        0        0        0        0        1 
  |Aut| = 2^15*3^10*5*7
  #short vectors:
   48 1008 12144 92784


&Hlattice (#3 <- #2)
       1 
       0        1 
       0        0        2 
       0        0        1        2 
       0        0        1        1        2 
       0        0        1        1        1        2 
       0        0        0        0        0        0        2 
       0        0       -w      1-w      1-w      1-w        1        2 
  |Aut| = 2^12*3^9*5*7
  #short vectors:
   12  792 13116 96096



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
2240   0 1120 
  0 672 2688 
1512 112 1736 


classes of Z-lattices with respect to the trace form
&Dim=16      V=Q^16

&Genus of the trace-forms:
det= 6561 = 3^8
   2-adic symbol:  1^16_II 
   3-adic symbol:  1^8 3^8 
  -1-adic symbol:  +^16 -^0 
level=3, weight=8
a_0,..,a_4 determine modular form

&Gram (#1 <- H1)
  4 
  1   4 
 -1   0   4 
  2   0   0   4 
  2   0  -1   2   4 
  1   2   0   1   1   4 
  2   1   0   2   2   1   4 
  1   0   0   1   1   2   1   4 
  2  -1  -2   1   1  -1   1  -1   4 
  2   2   0   0   0   1   2   0   1   4 
  1   0   2   0   1   0   0   0  -1   0   4 
  1   0   0   2   1  -1   1  -1   2   0   0   4 
  1   0  -2   1   2  -1   1  -1   2   0  -1   2   4 
  2   1   0   2   2   2   2   1   1   2   0   1   1   4 
  1  -1   0   1   1  -1   2  -1   2   1   0   2   2   1   4 
  2   0   0   2   2   1   2   2   1   0   0   1   1   2   1   4 
  |Aut| = 2^15*3^6*5^2*7
  #short vectors:
    0    0    0  720

&Gram (#2 <- H2)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  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 
  1   0   0   0   0   0   0   0   2 
  0   1   0   0   0   0   0   0   0   2 
  0   0   1   0   0   0   0   0   0   0   2 
  0   0   0   1   0   0   0   0   0   0   0   2 
  0   0   0   0   1   0   0   0   0   0   0   0   2 
  0   0   0   0   0   1   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   1   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   2 
  |Aut| = 2^23*3^10*5*7
  #short vectors:
    0   48    0 1008

&Gram (#3 <- H3)
  2 
  1   2 
  0   0   2 
  0   0   1   2 
  0   0   0   0   4 
  0   0   0   0   2   4 
  0   0   0   0   2   2   4 
  0   0   0   0   2   2   2   4 
  0   0   0   0  -1  -2  -2   0   4 
  0   0   0   0   1   2   2   2   0   4 
  0   0   0   0  -1   1  -1   1   1   0   4 
  0   0   0   0   1   2   2   2   0   2   0   4 
  0   0   0   0  -2  -1   0  -2   0  -1   0  -1   4 
  0   0   0   0  -2   0  -1  -2   0  -1   1  -1   2   4 
  0   0   0   0  -2   0   0  -1  -1  -1   0   1   1   1   4 
  0   0   0   0  -2   0   0   0  -1   0   0   1   0   0   2   4 
  |Aut| = 2^15*3^9*5*7
  #short vectors:
    0   12    0  792

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