Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-8 --herm_lll3 0.8

&K=Q(sqrt(-6))
&Hdim=4      V=K^4
&HNeighbourhood at <2,w> (even classes) contains 7 classes:
mass of the neighbourhood is 23/480
  Steinitz class <2,w>:
&Hlattice (#1 <- #27)
   <2,w>      <1>    <2,w>    <2,w> 
       1 
  1-1/2w        4 
     1/2     1/2w        1 
     1/2        1        0        1 
  |Aut| = 2^4*3*5
  #short vectors:
    0    0    0   70    0  220    0  330


&Hlattice (#2 <- #28)
     <1>    <2,w>    <2,w>    <2,w> 
       4 
 -1-1/2w        1 
  1+1/2w     -1/2        1 
 -1-1/2w      1/2     -1/2        1 
  |Aut| = 2^4*3*5
  #short vectors:
    0    0    0   70    0  220    0  330


&Hlattice (#3 <- #19)
     <1>      <1>      <1>    <2,w> 
       2 
      -1        2 
       1        0        2 
       1       -1    -1/2w        2 
  |Aut| = 2^4*3*5
  #short vectors:
    0   20    0   30    0  160    0  410


&Hlattice (#4 <- #20)
     <1>      <1>      <1>    <2,w> 
       2 
       0        2 
       1        1        2 
       0   1+1/2w   1+1/2w        2 
  |Aut| = 2^4*3*5
  #short vectors:
    0   20    0   30    0  160    0  410


&Hlattice (#5 <- #7)
     <1>      <1>    <2,w>      <1> 
       2 
      -1        2 
       0       -1        1 
      -w       -1   1+1/2w        6 
  |Aut| = 2^5*3
  #short vectors:
    0   14    0   42    0  178    0  386


&Hlattice (#6 <- #12)
     <1>      <1>    <2,w>      <1> 
       2 
       0        2 
   -1/2w        0        1 
       0      1-w        0        4 
  |Aut| = 2^5*3
  #short vectors:
    0   10    0   50    0  190    0  370


&Hlattice (#7 <- #11)
     <1>      <1>      <1>    <2,w> 
       2 
      -w        4 
       1       -1        4 
       1     1/2w        1        1 
  |Aut| = 2^5*3
  #short vectors:
    0    6    0   58    0  202    0  354





classes of Z-lattices with respect to the trace form (scaled by 1/2)
one representative of each class
&Dim=8      V=Q^8

&Genus of the trace-forms:
det= 1296 = 2^4 *3^4
   2-adic symbol:  1^-4_II 2^-4_II 
   3-adic symbol:  1^-4 3^-4 
  -1-adic symbol:  +^8 -^0 
level=6, weight=4
a_0,..,a_8 determine modular form

&Gram (#1 <- H1,H2)
  4 
  2   4 
  2   0   4 
  2   2   0   4 
  2   1   2   0   4 
  2   0   2   0   2   4 
  2   1   2   0   1   2   4 
  2   1   0   2   1   0   1   4 
  |Aut| = 2^7*3^2*5^2
  #short vectors:
    0    0    0   70    0  220    0  330

&Gram (#2 <- H3,H4)
  2 
  1   2 
  1   0   2 
  1   1   0   2 
  1   0   0   0   6 
  1   0   0   1   2   6 
  1   0   0   1   2   0   6 
  1   0   0   1   2   0   0   6 
  |Aut| = 2^7*3^2*5^2
  #short vectors:
    0   20    0   30    0  160    0  410

&Gram (#3 <- H5)
  2 
  1   2 
  1   1   2 
  0   0   0   2 
  1   0   1   0   4 
  1   0   1  -1   1   6 
  1   0   1  -1   1   3   6 
  1   0   1   1   1   2  -1   6 
  |Aut| = 2^10*3^2
  #short vectors:
    0   14    0   42    0  178    0  386

&Gram (#4 <- H6)
  2 
  1   2 
  0   0   2 
  0   0   0   2 
  0   0  -1   1   4 
  0   0  -1   1   1   4 
  0   0   0   0   0   0   4 
  0   0   0   0   0   0   2   4 
  |Aut| = 2^10*3^2
  #short vectors:
    0   10    0   50    0  190    0  370

&Gram (#5 <- H7)
  2 
  0   2 
  0   0   2 
  1  -1   1   4 
  1  -1  -1   0   4 
  0   0   0   1   1   4 
  0   0   0   1   1   1   4 
  0   0   0  -1  -1  -1  -1   4 
  |Aut| = 2^10*3^2
  #short vectors:
    0    6    0   58    0  202    0  354

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