Output of /home/aschiem/bin/hn --invar -t --shells_all --herm_lll3 0.8

&K=Q(sqrt(-10))
&Hdim=4      V=K^4
&HNeighbourhood at <3,3w> contains 83 classes:
mass of the neighbourhood is 1027/96
  Steinitz class <1,w>:
&Hlattice (#1 <- #47)
     <1>      <1>    <2,w>    <2,w> 
       4 
    -1-w        4 
      -1    -1/2w        1 
  1+1/2w       -1        0      3/2 
  |Aut| = 2^3
  #short vectors:
    0    0    0   16   12   52


&Hlattice (#2 <- #49)
     <1>      <1>    <2,w>    <2,w> 
       4 
      -1        4 
       0       -1        1 
    1/2w    -1/2w      1/2      3/2 
  |Aut| = 2^3
  #short vectors:
    0    0    0   16   12   52


&Hlattice (#3 <- #46)
   <2,w>    <2,w>      <1>      <1> 
       1 
     1/2        1 
       1        1        5 
  1-1/2w    -1/2w        1        6 
  |Aut| = 2^3*3
  #short vectors:
    0    0    0   12   12   72


&Hlattice (#4 <- #48)
     <1>    <2,w>      <1>    <2,w> 
       4 
       0        1 
    -1-w        1        5 
  1-1/2w     -1/2     1/2w      3/2 
  |Aut| = 2^3*3
  #short vectors:
    0    0    0   12   12   72


&Hlattice (#5 <- #80)
     <1>    <2,w>      <1>    <2,w> 
       4 
      -1        1 
     2-w     1/2w        5 
  1+1/2w        0     1/2w      3/2 
  |Aut| = 2^3
  #short vectors:
    0    0    0   12   24   36


&Hlattice (#6 <- #81)
       4 
       2        5 
     1+w        0        5 
    -2+w     -1+w        w        6 
  |Aut| = 2^3
  #short vectors:
    0    0    0   12   24   36


&Hlattice (#7 <- #67)
       4 
       0        4 
     2-w        1        5 
     1-w     -1+w        2        6 
  |Aut| = 2^4
  #short vectors:
    0    0    0    8   32   32


&Hlattice (#8 <- #70)
       5 
    -1+w        6 
       0      3+w        7 
    -2+w      3-w     -2-w        7 
  |Aut| = 2^4
  #short vectors:
    0    0    0    8   32   32   64


&Hlattice (#9 <- #71)
       4 
      -1        4 
    -2+w        2        5 
    -1-w       -1     -2+w        5 
  |Aut| = 2^2
  #short vectors:
    0    0    0    8   32


&Hlattice (#10 <- #72)
       4 
       2        5 
      -w     -2-w        5 
     1+w       -1       -2        6 
  |Aut| = 2^4
  #short vectors:
    0    0    0    8   32   32


&Hlattice (#11 <- #75)
       4 
       2        5 
       2        0        5 
     1-w       -w      2-w        5 
  |Aut| = 2^3
  #short vectors:
    0    0    0    8   32   32


&Hlattice (#12 <- #102)
       4 
       1        4 
      -1      2-w        5 
    -2-w        1      1+w        5 
  |Aut| = 2^2
  #short vectors:
    0    0    0    8   32


&Hlattice (#13 <- #50)
       3 
       0        3 
      -w       -1        4 
      -1       -w        0        4 
  |Aut| = 2^4
  #short vectors:
    0    0    8    8


&Hlattice (#14 <- #68)
     <1>      <1>    <2,w>    <2,w> 
       3 
      -1        3 
   -1/2w        1      3/2 
       0        0     -1/2      3/2 
  |Aut| = 2^2
  #short vectors:
    0    0    8    8   16   32


&Hlattice (#15 <- #69)
     <1>      <1>    <2,w>    <2,w> 
       3 
       1        3 
 -1-1/2w        0      3/2 
       0        0      1/2      3/2 
  |Aut| = 2^4
  #short vectors:
    0    0    8    8   16   32


&Hlattice (#16 <- #73)
     <1>      <1>    <2,w>    <2,w> 
       3 
      -1        3 
 -1+1/2w        0      3/2 
       0   1-1/2w     -1/2      3/2 
  |Aut| = 2^4
  #short vectors:
    0    0    8    8   16   32


&Hlattice (#17 <- #74)
       3 
       0        3 
     1-w        0        4 
       0     -1+w        0        4 
  |Aut| = 2^3
  #short vectors:
    0    0    8    8


&Hlattice (#18 <- #94)
       3 
       0        3 
       1       -1        3 
      -1       -1        w        5 
  |Aut| = 2^2
  #short vectors:
    0    0    8    8   16


&Hlattice (#19 <- #64)
     <1>    <2,w>      <1>    <2,w> 
       3 
       1        1 
    -1-w    -1/2w        5 
      -1     -1/2   1-1/2w      3/2 
  |Aut| = 2^2
  #short vectors:
    0    0    6    6   20   42


&Hlattice (#20 <- #65)
     <1>    <2,w>      <1>    <2,w> 
       3 
      -1        1 
    -1+w    -1/2w        5 
      -1      1/2   1+1/2w      3/2 
  |Aut| = 2^2
  #short vectors:
    0    0    6    6   20   42


&Hlattice (#21 <- #51)
       3 
      -1        4 
       w        0        4 
      -1      2+w        1        5 
  |Aut| = 2^3
  #short vectors:
    0    0    4    8   24


&Hlattice (#22 <- #95)
       3 
       0        3 
       1       -1        4 
      -1       -1     -1+w        4 
  |Aut| = 2^2
  #short vectors:
    0    0    4    8


&Hlattice (#23 <- #96)
       4 
       w        4 
       1        1        4 
       2       -1      2+w        5 
  |Aut| = 2
  #short vectors:
    0    0    4    8   24


&Hlattice (#24 <- #97)
     <1>      <1>    <2,w>    <2,w> 
       3 
      -1        4 
  1+1/2w       -1      3/2 
       1       -1      1/2        2 
  |Aut| = 2^3
  #short vectors:
    0    0    4    8   24   32   52   88


&Hlattice (#25 <- #98)
       4 
    -1+w        5 
      -w       -2        5 
      -2        2       -w        5 
  |Aut| = 2^3
  #short vectors:
    0    0    4    8   24


&Hlattice (#26 <- #99)
       3 
      -1        4 
       1      1+w        4 
       w       -2        w        5 
  |Aut| = 2
  #short vectors:
    0    0    4    8   24


&Hlattice (#27 <- #100)
       3 
      -1        4 
       0     -1-w        4 
      -w        w       -2        5 
  |Aut| = 2
  #short vectors:
    0    0    4    8   24


&Hlattice (#28 <- #101)
       4 
     1-w        4 
       2        w        5 
     1+w       -2     -1+w        6 
  |Aut| = 2^2
  #short vectors:
    0    0    4    8   24   32


&Hlattice (#29 <- #86)
       5 
    -1-w        5 
       0       -1        5 
       2        0     -2-w        5 
  |Aut| = 2^2
  #short vectors:
    0    0    2    6   28


&Hlattice (#30 <- #87)
       4 
       1        4 
      -w       -1        4 
      -w        1        1        5 
  |Aut| = 2^2
  #short vectors:
    0    0    2   10   24


&Hlattice (#31 <- #88)
     <1>    <2,w>      <1>    <2,w> 
       4 
   -1/2w        1 
    -1-w        1        5 
      -1        0        1      3/2 
  |Aut| = 2^2
  #short vectors:
    0    0    2   10   24   34


&Hlattice (#32 <- #89)
   <2,w>      <1>      <1>    <2,w> 
       1 
  1-1/2w        5 
      -1     -2-w        5 
       0       -1        1      3/2 
  |Aut| = 2^2
  #short vectors:
    0    0    2    6   28   42


&Hlattice (#33 <- #5)
       2 
       1        2 
       0        1        2 
      -w        0      1+w       11 
  |Aut| = 2^7*3
  #short vectors:
    0   24    0   24    0   96    0   24    0  152  128


&Hlattice (#34 <- #6)
   <2,w>    <2,w>    <2,w>    <2,w> 
     1/2 
       0      1/2 
       0        0      1/2 
       0        0        0      1/2 
  |Aut| = 2^7*3
  #short vectors:
    0    8


&Hlattice (#35 <- #7)
     <1>    <2,w>    <2,w>      <1> 
       2 
       0      1/2 
       0        0      1/2 
     1-w        0        0        6 
  |Aut| = 2^6
  #short vectors:
    0    8    0   24    4   48


&Hlattice (#36 <- #11)
       2 
       0        2 
       w        1        6 
       1        1        1        7 
  |Aut| = 2^6
  #short vectors:
    0    8    0   24    0   48   64


&Hlattice (#37 <- #13)
     <1>    <2,w>    <2,w>      <1> 
       2 
       1        1 
       1      1/2        1 
     1-w   1-1/2w    -1/2w        7 
  |Aut| = 2^7*3
  #short vectors:
    0    8    0   24    0   32  128


&Hlattice (#38 <- #38)
       2 
       1        3 
       1       -1        3 
     1-w       -w        1        7 
  |Aut| = 2^3*3
  #short vectors:
    0    8   12   12   12    8   56


&Hlattice (#39 <- #40)
       2 
       0        3 
       1       -1        3 
       0     -1+w      1-w        6 
  |Aut| = 2^3*3
  #short vectors:
    0    8   12   12   12    8


&Hlattice (#40 <- #43)
     <1>    <2,w>      <1>    <2,w> 
       2 
       0      1/2 
       1        0        3 
       0        0   1-1/2w      3/2 
  |Aut| = 2^3*3
  #short vectors:
    0    8    6   12   26    8


&Hlattice (#41 <- #45)
   <2,w>      <1>      <1>    <2,w> 
     1/2 
       0        2 
       0        1        3 
       0        0  -1-1/2w      3/2 
  |Aut| = 2^3*3
  #short vectors:
    0    8    6   12   26    8


&Hlattice (#42 <- #61)
       2 
       0        4 
       1       -w        4 
      -1     -1-w        1        5 
  |Aut| = 2^3*3
  #short vectors:
    0    6    0   12   24


&Hlattice (#43 <- #15)
       2 
       1        3 
      -1       -1        3 
      -w     -1-w        0        8 
  |Aut| = 2^4
  #short vectors:
    0    4   16    8    0   24   64   72


&Hlattice (#44 <- #16)
   <2,w>    <2,w>      <1>      <1> 
     1/2 
       0      1/2 
       0        0        3 
       0        0      1-w        4 
  |Aut| = 2^4
  #short vectors:
    0    4    4    8


&Hlattice (#45 <- #17)
     <1>      <1>    <2,w>    <2,w> 
       2 
      -1        4 
      -1        1        1 
       1  -1+1/2w     -1/2      3/2 
  |Aut| = 2^4
  #short vectors:
    0    4    0   24    0   56


&Hlattice (#46 <- #18)
     <1>      <1>    <2,w>    <2,w> 
       2 
       0        2 
       0    -1/2w      3/2 
   -1/2w        0        0      3/2 
  |Aut| = 2^5
  #short vectors:
    0    4    8    8   16   40


&Hlattice (#47 <- #19)
     <1>      <1>    <2,w>    <2,w> 
       2 
       0        2 
   -1/2w        0      3/2 
       0   1-1/2w        0        2 
  |Aut| = 2^4
  #short vectors:
    0    4    4   16    8   40   52   88


&Hlattice (#48 <- #21)
       2 
       0        4 
       1     -1-w        5 
      -w        1       -1        6 
  |Aut| = 2^4
  #short vectors:
    0    4    0   16   16   40


&Hlattice (#49 <- #27)
       2 
      -1        5 
       0        2        5 
       w       -1       -1        6 
  |Aut| = 2^5
  #short vectors:
    0    4    0    8   32   40


&Hlattice (#50 <- #32)
       2 
       0        3 
       0      1-w        4 
     1-w        0        0        6 
  |Aut| = 2^4
  #short vectors:
    0    4    4    8   24   40


&Hlattice (#51 <- #39)
       2 
      -1        3 
      -1        1        3 
      -1      1-w        0        5 
  |Aut| = 2^3
  #short vectors:
    0    4   12    8   12


&Hlattice (#52 <- #41)
       3 
       1        3 
       0        1        3 
    -1+w     -1+w       -1        6 
  |Aut| = 2^3
  #short vectors:
    0    4   12    8   12   20


&Hlattice (#53 <- #42)
   <2,w>      <1>      <1>    <2,w> 
     1/2 
       0        3 
       0       -1        3 
       0  -1+1/2w        1      3/2 
  |Aut| = 2^3
  #short vectors:
    0    4    6    8   26   20


&Hlattice (#54 <- #44)
   <2,w>      <1>      <1>    <2,w> 
     1/2 
       0        3 
       0       -1        3 
       0  -1-1/2w        1      3/2 
  |Aut| = 2^3
  #short vectors:
    0    4    6    8   26   20


&Hlattice (#55 <- #84)
       2 
       0        2 
      -1        0        3 
      -w        1      1+w        7 
  |Aut| = 2^3
  #short vectors:
    0    4    8    4   24   36   48


&Hlattice (#56 <- #85)
       2 
       0        2 
       0       -1        3 
       1        0      1-w        5 
  |Aut| = 2^3
  #short vectors:
    0    4    8    4   24


&Hlattice (#57 <- #22)
   <2,w>      <1>      <1>    <2,w> 
     1/2 
       0        3 
       0        0        4 
       0        1     1/2w        1 
  |Aut| = 2^3*3
  #short vectors:
    0    2    6   12


&Hlattice (#58 <- #23)
   <2,w>      <1>      <1>    <2,w> 
     1/2 
       0        3 
       0      1-w        5 
       0     1/2w       -1      3/2 
  |Aut| = 2^3
  #short vectors:
    0    2    6    8   22   28


&Hlattice (#59 <- #28)
       2 
       0        3 
       1       -1        5 
       w       -1        0        6 
  |Aut| = 2^3
  #short vectors:
    0    2    4    8   24   36


&Hlattice (#60 <- #29)
       4 
     2+w        4 
     2-w     -1-w        5 
      -1       -1     -1-w        5 
  |Aut| = 2^3
  #short vectors:
    0    2    4    8   24


&Hlattice (#61 <- #54)
       2 
       1        3 
       0        1        4 
      -1        w        2        6 
  |Aut| = 2^3
  #short vectors:
    0    2    8    8   16   36


&Hlattice (#62 <- #55)
       4 
       w        4 
     1-w       -1        5 
       0        1        2        5 
  |Aut| = 2^3
  #short vectors:
    0    2    0    8   32


&Hlattice (#63 <- #58)
   <2,w>      <1>    <2,w>      <1> 
       1 
   -1/2w        4 
     1/2     1/2w        1 
       1       -1        0        5 
  |Aut| = 2^3*3
  #short vectors:
    0    2    0   12   24


&Hlattice (#64 <- #59)
       2 
       1        3 
       0        1        4 
       0      1-w     -1-w        6 
  |Aut| = 2^3
  #short vectors:
    0    2    8    8   16   28


&Hlattice (#65 <- #60)
     <1>    <2,w>      <1>    <2,w> 
       2 
       0        1 
       1  -1-1/2w        5 
       1      1/2     1/2w      3/2 
  |Aut| = 2^3
  #short vectors:
    0    2    0   16   16   44


&Hlattice (#66 <- #62)
       4 
     1-w        4 
       1        1        4 
     2+w     -2+w        1        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6   10   20


&Hlattice (#67 <- #63)
       3 
       1        4 
      -1      1-w        4 
       1      1-w        2        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6   10   20


&Hlattice (#68 <- #90)
       2 
       0        3 
       1        1        4 
      -1     -1+w       -2        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6    6   24


&Hlattice (#69 <- #91)
       2 
       0        3 
       1        1        4 
       0       -w        2        5 
  |Aut| = 2^2
  #short vectors:
    0    2    6    6   24


&Hlattice (#70 <- #92)
       4 
    -1+w        4 
       1        0        4 
     1-w       -2     -1-w        5 
  |Aut| = 2^2
  #short vectors:
    0    2    2   10   28


&Hlattice (#71 <- #93)
       4 
     2+w        5 
     1-w     -2-w        5 
      -2     -2+w       -w        5 
  |Aut| = 2^2
  #short vectors:
    0    2    2   10   28


&Hlattice (#72 <- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
  |Aut| = 2^7*3
  #short vectors:
    8


&Hlattice (#73 <- #2)
     <1>      <1>    <2,w>    <2,w> 
       1 
       0        1 
       0        0      1/2 
       0        0        0      1/2 
  |Aut| = 2^6
  #short vectors:
    4    8


&Hlattice (#74 <- #3)
       1 
       0        1 
       0        0        2 
       0        0      1-w        6 
  |Aut| = 2^6
  #short vectors:
    4    8   16   24   24   48


&Hlattice (#75 <- #14)
       1 
       0        1 
       0        0        3 
       0        0      1-w        4 
  |Aut| = 2^4
  #short vectors:
    4    4    4   24


&Hlattice (#76 <- #8)
     <1>      <1>    <2,w>    <2,w> 
       1 
       0        2 
       0        0      1/2 
       0    -1/2w        0      3/2 
  |Aut| = 2^4
  #short vectors:
    2    4   12   16   22   40


&Hlattice (#77 <- #9)
     <1>      <1>    <2,w>    <2,w> 
       1 
       0        2 
       0        0      1/2 
       0   1-1/2w        0        2 
  |Aut| = 2^4
  #short vectors:
    2    4    8   16   30   40   64   88


&Hlattice (#78 <- #24)
       1 
       0        2 
       0        0        3 
       0        1        w        4 
  |Aut| = 2^3*3
  #short vectors:
    2    6   14   12


&Hlattice (#79 <- #25)
       1 
       0        3 
       0       -w        4 
       0       -1        1        4 
  |Aut| = 2^3
  #short vectors:
    2    2    6   16


&Hlattice (#80 <- #34)
     <1>    <2,w>    <2,w>      <1> 
       1 
       0        1 
       0      1/2        1 
       0   1-1/2w    -1/2w        5 
  |Aut| = 2^3*3
  #short vectors:
    2    0    2   12   36


&Hlattice (#81 <- #35)
       1 
       0        4 
       0     -1-w        4 
       0      2-w      1+w        5 
  |Aut| = 2^3
  #short vectors:
    2    0    2   16   36


&Hlattice (#82 <- #36)
     <1>    <2,w>    <2,w>      <1> 
       1 
       0        1 
       0      1/2        1 
       0   1-1/2w   1-1/2w        5 
  |Aut| = 2^3*3
  #short vectors:
    2    0    2   12   36


&Hlattice (#83 <- #37)
       1 
       0        3 
       0        1        4 
       0     -1+w        w        5 
  |Aut| = 2^3
  #short vectors:
    2    0    2   16   36





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= 10000 = 2^4 *5^4
   2-adic symbol:  [1^4 2^4]_0 
   5-adic symbol:  1^4 5^4 
  -1-adic symbol:  +^8 -^0 
level(of 2-scaled form)=40, weight=4
a_0,..,a_24 determine modular form

54 classes of trace forms

&begin_block

&Gram (#1 <- H1,H2)
  4 
  1   4 
  1   2   4 
  1  -1  -1   4 
  1   0   0  -1   4 
  1   0   0  -1   2   4 
  1   2   2  -1   1   1   5 
  0   0   2   0  -1  -1   2   5 
  |Aut| = 2^5
  #short vectors:
    0    0    0   16   12   52   36   96  132  172  224  232  308  436  660  648  832  840 1088 1400 1524 1640 1924 2272

&Gram (#2 <- H3,H4)
  4 
  2   4 
  0   0   4 
  0   0   2   4 
  1   0  -2   0   5 
  1   0  -2   0   0   5 
  2   0  -2   0   2   2   6 
  2   0  -2   0   2   2   1   6 
  |Aut| = 2^5*3^2
  #short vectors:
    0    0    0   12   12   72   36   72  132  152  224  264  308  456  660  696  832  720 1088 1380 1524 1680 1924 2304

&Gram (#3 <- H5,H6)
  4 
  2   4 
  0   0   4 
  0   0  -2   4 
  2   0   1  -1   5 
  2   2  -1   1   2   5 
  1   0  -2   2   0   1   5 
  2   2  -2   2   0   2   0   6 
  |Aut| = 2^6
  #short vectors:
    0    0    0   12   24   36   56   80  136  172  224  224  296  452  632  744  768  904  992 1420 1512 1736 1912 2240

&Gram (#4 <- H7,H11)
  4 
  0   4 
  0   0   4 
  0   0   0   4 
  2  -1   1   2   5 
  1   2  -2  -1  -1   5 
  2   1   1  -2   0   1   5 
  1  -2  -2   1   1   0  -1   5 
  |Aut| = 2^7
  #short vectors:
    0    0    0    8   32   32   64   88   96  192  192  256  352  416  640  664  768  960 1088 1400 1504 1600 1856 2336

&Gram (#5 <- H8,H9,H10,H12)
  4 
  1   4 
  0   1   4 
  1   0  -1   4 
  1   2   2   1   5 
  2  -1   1   0   1   5 
  1   1   2  -2   0   1   5 
  2  -1  -1   2   0   2   0   5 
  |Aut| = 2^4
  #short vectors:
    0    0    0    8   32   32   64   88   96  192  192  256  352  416  640  664  768  960 1088 1400 1504 1600 1856 2336

&Gram (#6 <- H13,H17)
  3 
  0   3 
  0   0   3 
  0   0   0   3 
  0  -1   1   0   4 
  1   0   0  -1   0   4 
  1   0   0   1   0   0   4 
  0  -1  -1   0   0   0   0   4 
  |Aut| = 2^7
  #short vectors:
    0    0    8    8   16   32   40   88  144  192  208  256  336  416  664  664  736  960  992 1400 1456 1600 1912 2336

&Gram (#7 <- H14,H15,H16,H18)
  3 
  1   3 
  0  -1   3 
  1   0   1   3 
  1   0   1   1   5 
  0  -1   1   1  -1   5 
  1   1   0   1  -1   0   5 
  1   1  -1   0   0   1  -1   5 
  |Aut| = 2^4
  #short vectors:
    0    0    8    8   16   32   40   88  144  192  208  256  336  416  664  664  736  960  992 1400 1456 1600 1912 2336

&Gram (#8 <- H19,H20)
  3 
  1   3 
  0   0   3 
  1   1  -1   4 
  1   1   1   0   4 
  1  -1   0  -1  -1   5 
  1   1  -1   0   1   0   5 
  1   1  -1   0   1   0   0   5 
  |Aut| = 2^3
  #short vectors:
    0    0    6    6   20   42   46   76  132  182  204  272  340  426  658  688  744  900 1016 1390 1468 1620 1898 2352

&Gram (#9 <- H21)
  3 
  0   3 
  1  -1   4 
  1   1   0   4 
  0   0   0   0   4 
  0   0   0   0   0   4 
  1   0   2   2   1  -1   5 
  1   0   2   2  -1  -1   2   5 
  |Aut| = 2^6
  #short vectors:
    0    0    4    8   24   32   52   88  120  192  200  256  344  416  652  664  752  960 1040 1400 1480 1600 1884 2336

&Gram (#10 <- H22,H24,H25,H28)
  3 
  0   3 
  1  -1   4 
  1   1  -1   4 
  1  -1   1   0   4 
  1   1   0   1   1   4 
  0   1   1  -1  -1   1   5 
  1   0   1   1  -1  -1   0   5 
  |Aut| = 2^3
  #short vectors:
    0    0    4    8   24   32   52   88  120  192  200  256  344  416  652  664  752  960 1040 1400 1480 1600 1884 2336

&Gram (#11 <- H23)
  3 
  1   3 
  1   1   4 
  1   0  -1   4 
  0  -1   1   0   4 
  0  -1  -2   2   1   5 
  1   0   0  -1   0  -1   5 
  0   1   0   0   1   1   1   5 
  |Aut| = 2^2
  #short vectors:
    0    0    4    8   24   32   52   88  120  192  200  256  344  416  652  664  752  960 1040 1400 1480 1600 1884 2336

&Gram (#12 <- H26,H27)
  3 
  0   3 
  1   1   4 
  1   0  -1   4 
  1  -1   0   1   4 
  0   1   1   0   1   4 
  0   1   1  -1   1   2   5 
  1   0  -1   2   1   1   0   5 
  |Aut| = 2^2
  #short vectors:
    0    0    4    8   24   32   52   88  120  192  200  256  344  416  652  664  752  960 1040 1400 1480 1600 1884 2336

&Gram (#13 <- H29,H32)
  3 
  1   4 
  0   0   4 
  0   0   0   4 
  1   1   2  -1   5 
  0   1   2   2   0   5 
  1  -1  -2   0   0   0   5 
  1   1   0   0   0   2   1   5 
  |Aut| = 2^3
  #short vectors:
    0    0    2    6   28   42   58   76  108  182  196  272  348  426  646  688  760  900 1064 1390 1492 1620 1870 2352

&Gram (#14 <- H30,H31)
  3 
  1   4 
  1  -1   4 
  0  -1  -1   4 
  1   1   1   0   4 
  0   0   0   0   0   4 
  0  -1  -1   2   1   2   5 
  1   0   0   0   1   0   2   5 
  |Aut| = 2^3
  #short vectors:
    0    0    2   10   24   34   54   84  128  182  212  240  320  434  642  704  760  932 1016 1410 1496 1668 1898 2288

&Gram (#15 <- H33)
  2 
  1   2 
  1   0   2 
  1   0   0   2 
  0   0   0   0  10 
  0   0   0   0   0  10 
  0   0   0   0   0   0  10 
  1   0   1   0   5   5  -5  11 
  |Aut| = 2^14*3^2
  #short vectors:
    0   24    0   24    0   96    0   24    0  152  128  288  512  384  768  792 1024  504 1664 1320 1536 1632 1792 2208

&Gram (#16 <- H34)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  0   0   0   0   5 
  0   0   0   0   0   5 
  0   0   0   0   0   0   5 
  0   0   0   0   0   0   0   5 
  |Aut| = 2^14*3^2
  #short vectors:
    0    8    0   24    8   32   64   24  192   72  256  288  192  640  416  792 1024  680 1280 1320 1216 2592 1600 2208

&Gram (#17 <- H35)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  0   0   0   0   5 
  0   0   0   0   0   5 
  1   0   0   1   0   0   6 
  1   0   0  -1   0   0   0   6 
  |Aut| = 2^12
  #short vectors:
    0    8    0   24    4   48   32   88   96  152  192  288  352  464  592  536 1024  776 1472 1320 1376 1856 1696 2336

&Gram (#18 <- H36)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  0   1   1   0   6 
  0   1  -1   0   0   6 
  1   1  -1  -1   0   1   7 
  1   1   1   1   1   0   0   7 
  |Aut| = 2^12
  #short vectors:
    0    8    0   24    0   48   64   88    0  152  320  288  256  464  768  536  768  776 1344 1320 1792 1856 1728 2336

&Gram (#19 <- H37)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  1   1  -1   1   7 
  1   1  -1  -1   1   7 
  1   1  -1  -1   1   2   7 
  1   1  -1  -1   1   2   2   7 
  |Aut| = 2^14*3^2
  #short vectors:
    0    8    0   24    0   32  128   24    0   72  512  288    0  640  768  792  512  680 1024 1320 2048 2592 1664 2208

&Gram (#20 <- H38,H39)
  2 
  0   2 
  0  -1   2 
  1   1  -1   3 
  0   0   0  -1   6 
  1   0   0   1  -3   7 
  0  -1   0   0  -2   1   8 
  0  -1   0   0  -2   1  -2   8 
  |Aut| = 2^5*3^2
  #short vectors:
    0    8   12   12   12    8   56   72   84  192  248  264  324  424  720  696  656 1016 1072 1380 1556 1776 1808 2304

&Gram (#21 <- H40,H41)
  2 
  0   2 
  0   1   2 
  0  -1  -1   3 
  0   1   0   0   5 
  0   0   0   0   0   5 
  0  -1   0   1  -2   0   8 
  0  -1  -1   0   1   0   3   8 
  |Aut| = 2^5*3^2
  #short vectors:
    0    8    6   12   26    8   58   72   96  192  172  264  384  424  614  696  808 1016 1208 1380 1384 1776 1750 2304

&Gram (#22 <- H42)
  2 
  1   2 
  1   0   4 
  0   0   0   4 
  0   0   0   2   4 
  1   0  -1   1   2   5 
  0   0   0   2   2   1   8 
  0   0   0   0  -2  -1  -4   8 
  |Aut| = 2^6*3^2
  #short vectors:
    0    6    0   12   24   48   48   72   72  182  176  264  392  408  672  696  832  846 1232 1380 1512 1608 1840 2304

&Gram (#23 <- H43)
  2 
  0   2 
  1   1   3 
  1   1   1   3 
  0   0   1   1   6 
  0   0   1  -1   0   6 
  0   0  -1   0   2  -3   8 
  0   0   0   1  -2  -3   0   8 
  |Aut| = 2^9
  #short vectors:
    0    4   16    8    0   24   64   72   64  172  320  336  256  456  768  568  576  932 1056 1320 1664 1824 1760 2464

&Gram (#24 <- H44)
  2 
  0   2 
  0   0   3 
  0   0   0   3 
  0   0   1   1   4 
  0   0  -1   1   0   4 
  0   0   0   0   0   0   5 
  0   0   0   0   0   0   0   5 
  |Aut| = 2^9
  #short vectors:
    0    4    4    8   28   24   68   72   88  172  168  336  376  456  556  568  880  932 1328 1320 1320 1824 1644 2464

&Gram (#25 <- H45)
  2 
  0   2 
  1   1   4 
  1   1   1   4 
  0   0  -1   1   4 
  0   0   1   1   0   4 
  0   0  -1   0   2  -2   7 
  0   0   1   0  -2   2  -2   7 
  |Aut| = 2^9
  #short vectors:
    0    4    0   24    0   56   16  104  128  172  224  208  320  424  688  632  896  804 1184 1400 1536 1632 1936 2208

&Gram (#26 <- H46)
  2 
  0   2 
  0   1   3 
  1   0   0   3 
  0   0   0   0   4 
  0   0   0   0   0   4 
  0   0   0   0   0   2   6 
  0   0   0   0   2   0   0   6 
  |Aut| = 2^10
  #short vectors:
    0    4    8    8   16   40   40   56  144  172  208  256  336  440  664  792  736  868  992 1400 1456 1728 1912 2272

&Gram (#27 <- H47)
  2 
  0   2 
  1   0   3 
  0  -1   0   4 
  0   1   0  -2   4 
  0   0   0   0   0   4 
  0   0   0   0   0   2   6 
  0   0   0   1   1   0   0   6 
  |Aut| = 2^8
  #short vectors:
    0    4    4   16    8   40   52   88   72  172  264  272  296  440  716  600  752  868 1168 1360 1624 1728 1820 2336

&Gram (#28 <- H48)
  2 
  0   2 
  0   1   4 
  0  -1  -2   4 
  1   0  -1  -1   5 
  1   0  -1  -1   0   5 
  0   0   1   1  -1  -1   6 
  0   0   0   0  -1  -1   0   6 
  |Aut| = 2^8
  #short vectors:
    0    4    0   16   16   40   64   88   48  172  256  272  304  440  704  600  768  868 1216 1360 1648 1728 1792 2336

&Gram (#29 <- H49)
  2 
  0   2 
  0   0   4 
  0   0   0   4 
  1   0  -2  -2   5 
  0   1  -2   2   0   5 
  0   0  -2   0   1   1   6 
  0   0   0  -2   1  -1   0   6 
  |Aut| = 2^10
  #short vectors:
    0    4    0    8   32   40   64   56   96  172  192  256  352  440  640  792  768  868 1088 1400 1504 1728 1856 2272

&Gram (#30 <- H50)
  2 
  0   2 
  0   0   3 
  0   0   0   3 
  0   0   1   1   4 
  0   0  -1   1   0   4 
  1   1   0   0   0   0   6 
  1  -1   0   0   0   0   0   6 
  |Aut| = 2^9
  #short vectors:
    0    4    4    8   24   40   52   56  120  172  200  256  344  440  652  792  752  868 1040 1400 1480 1728 1884 2272

&Gram (#31 <- H51,H52)
  2 
  0   2 
  1   1   3 
  0   1   1   3 
  0   1   0   1   5 
  0   0  -1  -1  -1   6 
  0  -1   0   0   0  -3   7 
  1   0   1  -1  -2  -2   1   8 
  |Aut| = 2^5
  #short vectors:
    0    4   12    8   12   20   56   80   84  192  248  296  324  420  720  616  656  988 1072 1360 1556 1688 1808 2400

&Gram (#32 <- H53,H54)
  2 
  0   2 
  0  -1   3 
  0   0  -1   3 
  0  -1   0  -1   5 
  0   0   0  -1   2   5 
  0   0   0   0   0   0   5 
  0   1  -1   1   0   2   0   7 
  |Aut| = 2^5
  #short vectors:
    0    4    6    8   26   20   58   80   96  192  172  296  384  420  614  616  808  988 1208 1360 1384 1688 1750 2400

&Gram (#33 <- H55,H56)
  2 
  0   2 
  0  -1   3 
  1   0   0   3 
  1   0  -1   1   5 
  0   1  -1  -1   0   5 
  0  -1   1   1  -2  -1   7 
  1   0  -1   1   1  -2   0   7 
  |Aut| = 2^6
  #short vectors:
    0    4    8    4   24   36   48   64  104  192  176  288  392  404  672  712  736  924 1088 1380 1448 1592 1856 2368

&Gram (#34 <- H57)
  2 
  0   3 
  0  -1   3 
  0   1  -1   3 
  0   0   0   0   4 
  0   0   0   0  -1   4 
  0   0   0   0  -1  -1   4 
  0   0   0   0   0   0   0   5 
  |Aut| = 2^6*3^2
  #short vectors:
    0    2    6   12   14   32   46   72  156  162  220  264  300  472  602  696  808  890 1064 1380 1396 1848 1834 2304

&Gram (#35 <- H58)
  2 
  0   3 
  0  -1   3 
  0  -1   1   3 
  0   0   0   0   4 
  0  -1  -1   0  -1   5 
  0  -1  -1   0   1   2   5 
  0   0   0   0   0   0   0   5 
  |Aut| = 2^6
  #short vectors:
    0    2    6    8   22   28   54   80  116  182  188  296  356  436  610  616  808  946 1160 1360 1388 1712 1778 2400

&Gram (#36 <- H59,H60)
  2 
  0   3 
  0  -1   3 
  0   1  -1   4 
  0   1  -1   2   4 
  1  -1   1   0  -1   5 
  1   1  -1   0   1   1   5 
  0   1   1   0   0   0   0   6 
  |Aut| = 2^5
  #short vectors:
    0    2    4    8   24   36   52   72  120  182  200  256  344  428  652  728  752  914 1040 1400 1480 1664 1884 2304

&Gram (#37 <- H61)
  2 
  1   3 
  1   1   3 
  0  -1   1   4 
  0   1   1   0   4 
  1   0   0   1  -2   6 
  1   0   0   1  -2   1   6 
  0   1  -1   0   0   2   2   8 
  |Aut| = 2^6
  #short vectors:
    0    2    8    8   16   36   40   72  144  182  208  256  336  428  664  728  736  914  992 1400 1456 1664 1912 2304

&Gram (#38 <- H62)
  2 
  0   4 
  0   2   4 
  0   0   0   4 
  1  -2   0   1   5 
  1   2   0   1  -1   5 
  0  -1  -2   1  -1  -1   5 
  1   0   0  -1  -1  -1   1   7 
  |Aut| = 2^6
  #short vectors:
    0    2    0    8   32   36   64   72   96  182  192  256  352  428  640  728  768  914 1088 1400 1504 1664 1856 2304

&Gram (#39 <- H63)
  2 
  0   4 
  0   2   4 
  0   0   0   4 
  0   0   0   1   4 
  1  -2   0   1  -1   5 
  1   2   2  -1   1   0   5 
  1   0   0   1  -1   2  -1   7 
  |Aut| = 2^6*3^2
  #short vectors:
    0    2    0   12   24   32   80   72   72  162  272  264  264  472  672  696  704  890 1072 1380 1640 1848 1808 2304

&Gram (#40 <- H64)
  2 
  1   3 
  1   1   3 
  0   1  -1   4 
  0   1   1   0   4 
  0  -1  -1  -1   1   6 
  0  -1  -1   1   1   2   6 
  0   1  -1   0   0   2  -2   8 
  |Aut| = 2^6
  #short vectors:
    0    2    8    8   16   28   64   80   80  182  256  296  304  436  704  616  672  946 1072 1360 1584 1712 1808 2400

&Gram (#41 <- H65)
  2 
  1   4 
  1   1   4 
  0  -1  -1   4 
  0   1   1  -2   4 
  0   1  -1   0   0   4 
  1   0   1   1   1  -2   5 
  1   2  -1   1   1   1   1   8 
  |Aut| = 2^6
  #short vectors:
    0    2    0   16   16   44   40   96  112  182  208  232  336  420  664  648  832  882 1136 1400 1520 1616 1896 2272

&Gram (#42 <- H66,H67)
  2 
  1   3 
  0  -1   3 
  1   0   1   4 
  0   1   0   1   4 
  1   0   1   1  -1   5 
  1   1   0   2   1   2   6 
  1   0  -1   0   1  -1  -2   8 
  |Aut| = 2^3
  #short vectors:
    0    2    6   10   20   26   46   84  132  192  204  240  340  418  658  704  744  974 1016 1410 1468 1644 1898 2288

&Gram (#43 <- H68,H69)
  2 
  1   3 
  0   0   3 
  1   0  -1   4 
  0  -1   1   0   4 
  1   0  -1   2   1   5 
  0   1   0   1  -1   0   5 
  0   0  -1   1   1   1   2   7 
  |Aut| = 2^3
  #short vectors:
    0    2    6    6   24   34   50   76  112  192  188  272  368  410  662  688  744  942 1064 1390 1464 1596 1870 2352

&Gram (#44 <- H70,H71)
  2 
  0   3 
  1  -1   4 
  0  -1  -1   4 
  1   0   1  -1   4 
  1  -1   2   0   2   5 
  1   0   0   0   2   2   5 
  0  -1   0  -1   1   2   1   7 
  |Aut| = 2^3
  #short vectors:
    0    2    2   10   28   26   58   84  108  192  196  240  348  418  646  704  760  974 1064 1410 1492 1644 1870 2288

&Gram (#45 <- H72)
  1 
  0   1 
  0   0   1 
  0   0   0   1 
  0   0   0   0  10 
  0   0   0   0   0  10 
  0   0   0   0   0   0  10 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^14*3^2
  #short vectors:
    8   24   32   24   48   96   64   24  104  152  160  288  368  384  576  792  656  504  992 1320 1216 1632 1856 2208

&Gram (#46 <- H73)
  1 
  0   1 
  0   0   2 
  0   0   0   2 
  0   0   0   0   5 
  0   0   0   0   0   5 
  0   0   0   0   0   0  10 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^12
  #short vectors:
    4    8   16   24   28   48   64   88  148  152  208  288  280  464  496  536  840  776 1136 1320 1216 1856 1728 2336

&Gram (#47 <- H74)
  1 
  0   1 
  0   0   2 
  0   0   0   2 
  0   0  -1  -1   6 
  0   0   1  -1   0   6 
  0   0   0   0   0   0  10 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^12
  #short vectors:
    4    8   16   24   24   48   96   88   52  152  336  288  184  464  672  536  584  776 1008 1320 1632 1856 1760 2336

&Gram (#48 <- H75)
  1 
  0   1 
  0   0   3 
  0   0   0   3 
  0   0   1   1   4 
  0   0  -1   1   0   4 
  0   0   0   0   0   0  10 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^9
  #short vectors:
    4    4    4   24   48   56   84  104  108  172  216  208  272  424  556  632  760  804  992 1400 1448 1632 1884 2208

&Gram (#49 <- H76)
  1 
  0   2 
  0   0   2 
  0   1   0   3 
  0   0   0   0   4 
  0   0   0   0   0   5 
  0   0   0   0   2   0   6 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^8
  #short vectors:
    2    4   12   16   22   40   52   88  146  172  208  272  308  440  580  600  788  868 1064 1360 1336 1728 1820 2336

&Gram (#50 <- H77)
  1 
  0   2 
  0   0   2 
  0  -1   0   4 
  0  -1   0  -1   4 
  0   0   0   0   0   5 
  0   0   0   1   1   0   6 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^8
  #short vectors:
    2    4    8   16   30   40   64   88  122  172  200  272  316  440  568  600  804  868 1112 1360 1360 1728 1792 2336

&Gram (#51 <- H78)
  1 
  0   2 
  0   1   2 
  0   0   0   3 
  0  -1  -1   0   4 
  0   0   0  -1   0   7 
  0   0   0  -1   0  -3   7 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^6*3^2
  #short vectors:
    2    6   14   12   24   48   46   72  134  182  196  264  344  408  642  696  716  846  992 1380 1396 1608 1898 2304

&Gram (#52 <- H79)
  1 
  0   2 
  0   0   3 
  0   1  -1   4 
  0  -1   1  -1   4 
  0   0   0   1   1   4 
  0   1   0  -1  -2  -1   7 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^6
  #short vectors:
    2    2    6   16   32   44   62   96  126  182  212  232  304  420  610  648  748  882  992 1400 1452 1616 1898 2272

&Gram (#53 <- H80,H82)
  1 
  0   3 
  0   0   4 
  0   0  -2   4 
  0   1  -2   0   5 
  0  -1   2   0   0   5 
  0   1   2   0  -1   1   5 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^5*3^2
  #short vectors:
    2    0    2   12   36   72   70   72  122  152  220  264  284  456  594  696  764  720  992 1380 1480 1680 1898 2304

&Gram (#54 <- H81,H83)
  1 
  0   3 
  0   1   4 
  0   1  -1   4 
  0   0   1   1   4 
  0   0   1   1   2   4 
  0  -1  -1  -1  -2  -2   5 
  0   0   0   0   0   0   0  10 
  |Aut| = 2^5
  #short vectors:
    2    0    2   16   36   52   70   96  122  172  220  232  284  436  594  648  764  840  992 1400 1480 1640 1898 2272

&end_block
<end>