Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-12 --herm_lll3 0.8

&K=Q(sqrt(-6))
&Hdim=3      V=K^3
&HNeighbourhood at <2,w> contains 7 classes:
mass of the neighbourhood is 23/48
  Steinitz class <2,w>:
&Hlattice (#1 <- #6)
     <1>      <1>    <2,w> 
       3 
     1-w        3 
    1/2w       -1        1 
  |Aut| = 2^2*3
  #short vectors:
    0    0   12   24   24   38   60   42   80  144   84  150


&Hlattice (#2 <- #7)
     <1>      <1>    <2,w> 
       3 
     1-w        3 
      -1    -1/2w        1 
  |Aut| = 2^2*3
  #short vectors:
    0    0   12   24   24   38   60   42   80  144   84  150


&Hlattice (#3 <- #2)
   <2,w>    <2,w>    <2,w> 
     1/2 
       0      1/2 
       0        0      1/2 
  |Aut| = 2^4*3
  #short vectors:
    0    6    6   12   36   20   72   78   56  168   84  126


&Hlattice (#4 <- #3)
   <2,w>      <1>      <1> 
     1/2 
       0        2 
       0      1+w        4 
  |Aut| = 2^4
  #short vectors:
    0    6    2   28   12   44   56   62   88  136  124  110


&Hlattice (#5 <- #1)
     <1>      <1>    <2,w> 
       1 
       0        1 
       0        0      1/2 
  |Aut| = 2^4
  #short vectors:
    4    6   10   20   20   28   56   46   68  136  100  150


&Hlattice (#6 <- #4)
     <1>      <1>    <2,w> 
       1 
       0        2 
       0     1/2w        1 
  |Aut| = 2^3*3
  #short vectors:
    2    6   12    8   12   56   88   30   38  136  108  162


&Hlattice (#7 <- #5)
     <1>      <1>    <2,w> 
       1 
       0        3 
       0  -1+1/2w        1 
  |Aut| = 2^3
  #short vectors:
    2    2   12   24   20   36   56   38   78  136   92  154



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


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

&Genus of the trace-forms:
det= 216 = 2^3 *3^3
   2-adic symbol:  [1^-3 2^3]_4 
   3-adic symbol:  1^-3 3^3 
  -1-adic symbol:  +^6 -^0 
level(of 2-scaled form)=24, weight=3
a_0,..,a_12 determine modular form

&Gram (#1 <- H1,H2)
  3 
  1   3 
  1   1   3 
  1   1   1   3 
  0   1   1   1   3 
  0   1   1   1   0   3 
  |Aut| = 2^3*3^2
  #short vectors:
    0    0   12   24   24   38   60   42   80  144   84  150

&Gram (#2 <- H3)
  2 
  0   2 
  0   0   2 
  0   0   0   3 
  0   0   0   0   3 
  0   0   0   0   0   3 
  |Aut| = 2^8*3^2
  #short vectors:
    0    6    6   12   36   20   72   78   56  168   84  126

&Gram (#3 <- H4)
  2 
  0   2 
  0   0   2 
  0   0   0   3 
  0  -1   1   0   4 
  0  -1  -1   0   0   4 
  |Aut| = 2^8
  #short vectors:
    0    6    2   28   12   44   56   62   88  136  124  110

&Gram (#4 <- H5)
  1 
  0   1 
  0   0   2 
  0   0   0   3 
  0   0   0   0   6 
  0   0   0   0   0   6 
  |Aut| = 2^8
  #short vectors:
    4    6   10   20   20   28   56   46   68  136  100  150

&Gram (#5 <- H6)
  1 
  0   2 
  0  -1   2 
  0   0   0   4 
  0   0   0  -2   4 
  0   0   0   0   0   6 
  |Aut| = 2^6*3^2
  #short vectors:
    2    6   12    8   12   56   88   30   38  136  108  162

&Gram (#6 <- H7)
  1 
  0   2 
  0  -1   3 
  0   1   0   3 
  0   0   1  -1   4 
  0   0   0   0   0   6 
  |Aut| = 2^6
  #short vectors:
    2    2   12   24   20   36   56   38   78  136   92  154

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