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

&K=Q(sqrt(-1))
&Hdim=7      V=K^7
&HNeighbourhood at <5,-2+w> contains 4 classes:
mass of the neighbourhood is 61/148635648
  Steinitz class <1,w>:
&Hlattice (#1 <-- #4)
       2 
      -1        2 
       1       -1        2 
      -1        1       -1        2 
       1       -1        1       -1        2 
      -1        1       -1        1       -1        2 
       0     -1-w      1+w     -1-w      1+w     -1-w        3 
  |Aut| = 2^11*3^4*5*7
  #short vectors:
    0  252 3136 17388


&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 
  |Aut| = 2^18*3^2*5*7
  #short vectors:
   28  364 2912 16044


&Hlattice (#3 <-- #2)
       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       -w        1        2 
  |Aut| = 2^17*3^3*5
  #short vectors:
   12  300 3040 16812


&Hlattice (#4 <-- #3)
       1 
       0        2 
       0       -1        2 
       0        1       -1        2 
       0       -1        1       -1        2 
       0     -1+w      1-w     -1+w      1-w        2 
       0       -1        1       -1        1        1        3 
  |Aut| = 2^17*3^2*5
  #short vectors:
    4  268 3104 17196



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
9163 288 2016 8064 
4096 2891 5376 7168 
6144 1152 3787 8448 
8192 512 2816 8011 


classes of Z-lattices with respect to the trace form (scaled by 1/2)
&Dim=14      V=Q^14

&Genus of the trace-forms:
det= 1 = 1 
   2-adic symbol:  1^14_6 
  -1-adic symbol:  +^14 -^0 
level(of 2-scaled form)=4, weight=7
a_0,..,a_3 determine modular form

&Gram (#1 <- H1)
  2 
  1   2 
  1   1   2 
  1   0   1   2 
  1   1   1   0   2 
  1   0   0   0   0   2 
  1   0   0   0   0   1   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   1   0   2 
  0   0   0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0  -1  -1   0   2 
  1   0   1   1   1   0   0   1   1   1   0  -1   3 
  1   0   1   1   0   1   1   0   0   0   1   0   0   3 
  |Aut| = 2^21*3^8*5^2*7^2
  #short vectors:
    0  252 3136

&Gram (#2 <- H2)
  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 
  0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   0   0   0   1 
  |Aut| = 2^25*3^5*5^2*7^2*11*13
  #short vectors:
   28  364 2912

&Gram (#3 <- H3)
  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   2 
  0   0   0   0   0   0   1   2 
  0   0   0   0   0   0   1   1   2 
  0   0   0   0   0   0   1   1   0   2 
  0   0   0   0   0   0   1   1   0   1   2 
  0   0   0   0   0   0   1   0   0   0   1   2 
  0   0   0   0   0   0   1   0   0   0   1   1   2 
  0   0   0   0   0   0  -1   0   0   0  -1  -1  -1   2 
  |Aut| = 2^24*3^7*5^3*7
  #short vectors:
   12  300 3040

&Gram (#4 <- H4)
  1 
  0   1 
  0   0   2 
  0   0   1   2 
  0   0  -1  -1   2 
  0   0  -1  -1   0   2 
  0   0  -1   0   0   1   2 
  0   0   1   0   0  -1  -1   2 
  0   0   1   0   0  -1  -1   1   2 
  0   0  -1   0   0   1   1  -1  -1   2 
  0   0   1   0   0  -1  -1   1   1  -1   2 
  0   0   0   0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   0   0   0  -1   2 
  0   0  -1  -1   1   1   0   0   0   0   0  -1   1   3 
  |Aut| = 2^24*3^5*5^2*7*11
  #short vectors:
    4  268 3104

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