Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-5 --herm_lll3 0.8 -D6

&K=Q(sqrt(-2))
&Hdim=5      V=K^5
&HNeighbourhood at <3,-1+w> contains 7 classes:
mass of the neighbourhood is 19/5120
  Steinitz class <1,w>:
&Hlattice (#1 <-- #4)
       2 
      -1        2 
       1       -1        2 
      -1        1       -1        2 
      -w      1+w     -1-w      1+w        3 
  |Aut| = 2^5*3^2*5
  #short vectors:
    0   30  200  570 1392


&Hlattice (#2 <-- #6)
       2 
      -1        2 
       1       -1        2 
      -1        1       -1        2 
      -w        1       -1        1        3 
  |Aut| = 2^5*3^2*5
  #short vectors:
    0   30  200  570 1392


&Hlattice (#3 <-- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
       0        0        0        0        1 
  |Aut| = 2^8*3*5
  #short vectors:
   10   50  180  530 1312


&Hlattice (#4 <-- #2)
       1 
       0        1 
       0        0        1 
       0        0        0        2 
       0        0        0      1-w        2 
  |Aut| = 2^8*3^2
  #short vectors:
    6   42  188  546 1344


&Hlattice (#5 <-- #3)
       1 
       0        2 
       0       -1        2 
       0        w       -w        2 
       0       -1        1      1+w        3 
  |Aut| = 2^8*3
  #short vectors:
    2   34  196  562 1376


&Hlattice (#6 <-- #5)
       1 
       0        2 
       0      1+w        2 
       0        0        0        2 
       0        0        0      1-w        2 
  |Aut| = 2^10*3^2
  #short vectors:
    2   50  100  722 1440


&Hlattice (#7 <-- #7)
       1 
       0        2 
       0        1        2 
       0        w        w        2 
       0        0        0       -1        2 
  |Aut| = 2^9*3^2
  #short vectors:
    2   50  100  722 1440



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
 15  46   0  20  30   0  10 
 30  15   6   0  60  10   0 
 16   0  25  40  40   0   0 
  0  32  24  13  48   4   0 
 32  16   8  16  41   0   8 
 64   0   0  16   0   9  32 
  0  32   0   0  48  16  25 


classes of Z-lattices with respect to the trace form (scaled by 1/2)
one representative of each class
&Dim=10      V=Q^10

&Genus of the trace-forms:
det= 32 = 2^5
   2-adic symbol:  [1^5 2^5]_2 
  -1-adic symbol:  +^10 -^0 
level(of 2-scaled form)=8, weight=5
a_0,..,a_5 determine modular form

5-classes of trace forms

&Gram (#1 <- H1,H2)
  2 
  1   2 
  1   1   2 
  1   1   1   2 
  1   0   0   0   2 
  1   1   0   0   1   3 
  1   0   1   1   0   0   3 
  1   1   0   0   1   1   0   3 
  1   1   0   0   1   1   0   1   3 
  1   1   0   1   0   1   0   1   1   3 
  |Aut| = 2^9*3^4*5^2
  #short vectors:
    0   30  200  570 1392

&Gram (#2 <- H3)
  1 
  0   1 
  0   0   1 
  0   0   0   1 
  0   0   0   0   1 
  0   0   0   0   0   2 
  0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   0   2 
  |Aut| = 2^16*3^2*5^2
  #short vectors:
   10   50  180  530 1312

&Gram (#3 <- H4)
  1 
  0   1 
  0   0   1 
  0   0   0   2 
  0   0   0   1   2 
  0   0   0  -1  -1   2 
  0   0   0   1   1   0   2 
  0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   0   2 
  |Aut| = 2^15*3^4
  #short vectors:
    6   42  188  546 1344

&Gram (#4 <- H5)
  1 
  0   2 
  0  -1   2 
  0   1  -1   2 
  0   1   0   1   2 
  0   0   0   0   0   2 
  0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   2 
  0   1  -1   0   0   1   0  -1   1   3 
  |Aut| = 2^16*3^2
  #short vectors:
    2   34  196  562 1376

&Gram (#5 <- H6,H7)
  1 
  0   2 
  0   1   2 
  0  -1   0   2 
  0  -1   0   0   2 
  0   0   0   0   0   2 
  0   0   0   0   0   1   2 
  0   0   0   0   0  -1  -1   2 
  0   0   0   0   0   1   1   0   2 
  0   0   0   0   0   0   0   0   0   2 
  |Aut| = 2^17*3^4
  #short vectors:
    2   50  100  722 1440

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