Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-9

&K=Q(sqrt(-5))
&Hdim=3      V=K^3
&HNeighbourhood at <3,-1+w> contains 6 classes:
mass of the neighbourhood is 5/16
  Steinitz class <2,-1+w>:
&Hlattice (#1 <-- #2)
<2,-1+w>      <1>      <1> 
     1/2 
       0        2 
       0       -w        3 
  |Aut| = 2^4
  #short vectors:
    0    6   12   12   48   56   60  102  112


&Hlattice (#2 <-- #3)
     <1>      <1> <2,-1+w> 
       2 
       1        2 
1/2-1/2w        1      3/2 
  |Aut| = 2^2*3
  #short vectors:
    0    6   12   12   48   56   60  102  112


&Hlattice (#3 <-- #4)
<2,-1+w> <2,-1+w> <2,-1+w> 
     1/2 
       0      1/2 
       0        0      1/2 
  |Aut| = 2^4*3
  #short vectors:
    0    6   12   12   48   56   60  102  112


&Hlattice (#4 <-- #1)
     <1>      <1> <2,-1+w> 
       1 
       0        1 
       0        0      1/2 
  |Aut| = 2^4
  #short vectors:
    4    6   12   28   28   24   60  102  140


&Hlattice (#5 <-- #5)
     <1>      <1> <2,-1+w> 
       1 
       0        2 
       0 -1/2-1/2w        1 
  |Aut| = 2^3*3
  #short vectors:
    2    6   12   20   38   40   60  102  126


&Hlattice (#6 <-- #6)
     <1>      <1> <2,-1+w> 
       1 
       0        2 
       0 -1/2+1/2w        1 
  |Aut| = 2^3*3
  #short vectors:
    2    6   12   20   38   40   60  102  126



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


classes of Z-lattices with respect to the trace form (scaled by 1/2)
&Dim=6      V=Q^6

&Genus of the trace-forms:
det= 125 = 5^3
   2-adic symbol:  1^-6_6 
   5-adic symbol:  1^-3 5^-3 
  -1-adic symbol:  +^6 -^0 
level(of 2-scaled form)=20, weight=3
a_0,..,a_9 determine modular form

&Gram (#1 <- H1,H3)
  2 
  0   2 
  0   0   2 
  0   0   1   3 
  1   0   0   0   3 
  0   1   0   0   0   3 
  |Aut| = 2^7*3
  #short vectors:
    0    6   12   12   48   56   60  102  112

&Gram (#2 <- H2)
  2 
  1   2 
  1   0   3 
  1   1   1   3 
  0   0   1   1   4 
  0   0   1   1  -1   4 
  |Aut| = 2^4*3^2
  #short vectors:
    0    6   12   12   48   56   60  102  112

&Gram (#3 <- H4)
  1 
  0   1 
  0   0   2 
  0   0  -1   3 
  0   0   0   0   5 
  0   0   0   0   0   5 
  |Aut| = 2^8
  #short vectors:
    4    6   12   28   28   24   60  102  140

&Gram (#4 <- H5,H6)
  1 
  0   2 
  0  -1   2 
  0   1   0   4 
  0  -1   0   1   4 
  0   0   0   0   0   5 
  |Aut| = 2^5*3^2
  #short vectors:
    2    6   12   20   38   40   60  102  126

<end>