The Lattice LL32'
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:11:38 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMAL_NORM
HERMITE_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
LL32'
-
DIMENSION
32
-
DET
1
-
GRAM
32 0
4
2 4
1 1 4
2 2 0 4
2 2 1 2 4
2 2 2 2 2 4
2 2 1 2 2 2 4
2 1 2 2 2 2 2 4
2 2 1 2 2 2 2 2 4
2 2 2 1 2 2 2 2 2 4
2 2 1 2 2 2 2 2 2 2 4
2 1 1 2 2 2 2 2 2 2 2 4
2 1 1 2 1 2 1 2 2 1 1 2 4
1 2 2 1 1 2 1 1 2 2 2 1 1 4
2 2 1 2 2 2 2 2 2 2 2 1 2 1 4
2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 4
2 1 2 1 2 2 2 2 2 2 2 2 1 1 1 2 4
1 2 2 1 2 2 2 1 1 2 1 1 0 2 1 1 1 4
2 2 2 1 2 2 2 2 2 2 2 0 1 2 2 2 2 2 4
2 1 1 2 2 2 1 2 1 1 1 2 2 0 2 2 1 1 1 4
2 1 1 2 2 2 1 2 1 1 2 2 2 1 1 2 1 1 1 2 4
2 2 2 1 1 2 1 1 1 2 2 1 1 2 1 1 1 2 2 1 2 4
1 2 2 1 2 2 2 2 2 2 1 1 1 1 2 1 2 2 2 1 0 1 4
2 1 2 1 1 2 2 2 1 2 1 1 1 1 1 1 2 2 2 1 1 2 2 4
2 2 1 2 2 2 2 2 1 2 1 1 1 1 2 2 1 2 2 2 1 1 2 2 4
2 2 2 1 1 2 2 1 1 2 1 1 1 2 1 1 1 2 2 1 1 2 1 2 2 4
2 2 1 1 2 2 2 1 1 2 1 2 1 1 1 1 2 2 1 1 1 1 2 2 2 2 4
2 2 2 1 2 2 2 2 1 2 1 1 1 1 2 1 2 2 2 2 1 1 2 2 2 2 2 4
1 2 2 1 2 2 1 1 2 2 1 1 1 2 1 1 1 2 2 1 1 2 2 1 1 2 1 1 4
1 1 2 1 2 2 2 2 1 2 1 1 0 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 2 4
2 2 1 1 2 2 2 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 1 1 2 2 2 2 1 1 4
2 2 1 2 2 1 2 2 2 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 4
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
4
-
HERMITIAN_GROUP_ORDER
2^8 * 3^4 * 5^3
-
HERMITIAN_GROUP_GENERATORS
4
32 32
5 1 6 0 6 1 7 -2 0 -2 0 1 1 4 -6 -2 -7 -3 4 0 0 -2 -1 -1 2 -4 2 2 -2 -1 -8 -5
-2 -2 -1 0 -2 0 -1 0 0 1 0 0 0 -1 1 0 1 0 1 0 0 1 0 -1 1 0 1 1 1 -1 1 2
1 0 2 0 2 1 2 -1 0 -1 0 1 1 1 -2 -1 -2 -1 2 0 -1 0 -1 -1 1 -1 1 1 -1 0 -3 -1
2 1 3 0 3 0 3 -1 0 -1 0 2 0 2 -3 -1 -4 -2 3 0 0 -1 0 0 1 -2 1 1 -1 -1 -4 -3
3 0 4 0 4 1 5 -1 0 -2 0 1 0 3 -4 -1 -5 -3 3 0 -1 0 -1 -1 2 -3 2 2 -1 -1 -6 -3
-3 -1 -2 0 -2 0 -3 0 0 1 0 1 0 -2 2 0 2 1 1 0 0 1 0 0 0 1 0 0 0 0 2 2
7 2 8 0 8 2 9 -2 0 -3 0 2 1 5 -8 -2 -10 -4 5 0 -1 -2 -1 -1 2 -5 2 2 -3 -1 -10 -7
6 2 7 0 8 2 8 -2 0 -3 0 2 1 5 -8 -2 -9 -4 5 0 -1 -2 -1 -1 2 -4 2 2 -3 -1 -10 -6
7 2 7 -1 8 2 9 -2 0 -3 0 1 1 6 -8 -2 -9 -4 4 1 -1 -2 -1 -1 2 -5 2 2 -3 -1 -10 -6
0 -1 1 0 1 1 1 0 0 -1 0 1 0 0 -1 0 -2 -1 2 -1 -1 1 -1 -1 1 -1 2 2 0 -1 -2 0
8 3 9 -1 9 2 11 -3 0 -4 0 3 1 6 -9 -3 -11 -5 6 0 0 -3 -1 -1 3 -6 2 2 -3 -1 -12 -8
5 2 6 0 6 1 7 -2 0 -3 0 3 0 4 -6 -2 -8 -4 5 0 0 -2 -1 0 2 -4 2 2 -2 -1 -8 -6
-1 0 -1 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 -1 1 0 0 1 1 -1 0 0 0 1 0 0 -1 -1 -1 -1 2 0 0 0 0 -1 1 -1 1 1 0 -1 -1 0
2 1 2 -1 3 1 3 0 0 -1 0 0 1 2 -3 0 -3 -1 1 0 -1 0 -1 -1 1 -2 1 1 -1 0 -4 -2
3 1 4 0 4 1 4 -1 0 -3 -1 4 -1 3 -3 -1 -6 -3 5 -1 0 -1 -1 0 1 -3 2 2 -1 -1 -6 -4
8 3 9 0 9 2 10 -3 0 -4 -1 4 0 6 -8 -3 -11 -5 7 0 0 -3 -1 -1 2 -5 2 2 -4 -1 -12 -8
-3 -3 0 1 -2 0 -1 0 1 1 1 -1 0 -2 1 0 1 0 0 0 -1 2 -1 -1 1 0 2 1 1 -1 2 2
5 0 6 0 6 2 7 -2 0 -2 0 1 1 4 -6 -2 -7 -3 4 0 -1 -1 -1 -2 2 -4 2 2 -2 -1 -8 -4
2 1 3 0 3 0 3 -1 0 -1 0 2 0 2 -3 -1 -4 -2 3 0 0 -1 -1 0 1 -2 1 1 -1 0 -4 -3
2 1 3 0 3 0 3 -1 0 -2 0 2 0 2 -3 -1 -4 -2 3 0 0 -1 0 0 1 -2 1 1 -1 0 -4 -3
0 -1 1 0 0 0 1 -1 0 0 1 0 1 0 -1 -1 -1 0 1 0 0 0 0 -1 1 -1 1 1 0 0 -1 0
-1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 -1 -1 1 0 1 1 0 -1 -1 1
-1 0 1 1 0 0 -1 -1 0 0 0 2 0 -1 0 0 -1 0 2 -1 0 0 0 0 0 0 0 1 -1 0 0 0
-3 -2 -1 1 -2 0 -3 0 0 1 0 1 -1 -2 2 1 1 0 1 -1 0 1 0 0 0 1 1 1 1 -1 2 2
-5 -3 -3 1 -5 -1 -6 0 1 2 1 0 0 -5 4 1 4 2 -1 -1 0 2 0 0 0 2 0 1 2 0 6 4
-6 -3 -3 2 -6 -1 -6 0 1 2 0 1 -2 -5 5 1 4 1 1 -1 1 2 0 0 0 2 1 1 2 -1 6 4
3 1 4 0 4 1 4 -1 0 -1 0 1 1 2 -4 -1 -5 -2 3 0 -1 -1 -1 -1 1 -2 1 1 -2 0 -5 -3
-4 -3 -3 0 -3 0 -3 1 0 1 0 -1 0 -2 3 0 4 1 -1 0 -1 3 -1 -1 1 1 1 1 2 -1 3 4
2 0 4 1 3 1 3 -1 0 -1 0 1 0 1 -3 -1 -4 -2 3 0 -1 0 -1 -1 1 -2 2 1 -1 -1 -4 -2
0 -2 1 1 0 1 1 -1 0 1 0 0 0 0 -1 -1 -1 -1 2 0 0 0 0 -1 1 -1 1 1 0 -1 -1 0
11 4 11 -1 12 2 14 -3 -1 -5 0 2 2 9 -12 -3 -13 -6 6 1 -1 -4 -1 -1 3 -7 2 2 -4 -1 -15 -10
32 32
6 2 5 -1 6 1 7 -1 0 -3 -1 2 0 5 -5 -2 -6 -3 3 0 0 -2 -1 -1 2 -3 1 1 -2 -1 -8 -5
11 4 11 0 11 2 13 -3 0 -5 -1 3 0 8 -10 -3 -13 -6 6 0 0 -4 -1 -1 2 -6 2 2 -4 -1 -14 -10
-4 -2 -3 1 -5 -1 -5 0 1 3 0 -1 -1 -4 4 1 5 2 -2 0 1 1 1 0 -1 3 -1 -1 1 0 6 4
9 3 8 -1 9 1 11 -2 0 -4 0 1 1 7 -8 -3 -9 -4 3 1 0 -3 -1 -1 2 -5 1 1 -3 0 -11 -8
9 4 8 -1 9 1 9 -3 0 -4 0 3 1 6 -8 -2 -10 -4 4 0 0 -4 0 0 1 -4 0 1 -4 1 -10 -8
10 3 9 -1 10 2 12 -2 0 -3 0 0 2 7 -10 -3 -10 -4 3 1 -1 -3 -1 -2 2 -5 1 1 -4 0 -12 -8
8 3 7 -1 8 1 10 -2 0 -3 0 1 1 6 -8 -2 -9 -4 3 1 0 -3 0 -1 1 -4 1 1 -3 0 -10 -7
-1 0 0 0 -1 -1 -1 0 1 0 0 1 -1 -1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
3 1 4 0 3 0 4 -1 1 -2 0 1 0 2 -3 -1 -4 -2 1 0 0 -1 -1 0 1 -2 1 1 -1 0 -4 -3
5 2 6 0 5 0 6 -2 1 -2 0 2 0 3 -5 -1 -7 -3 3 0 0 -2 -1 0 1 -3 1 1 -2 0 -6 -5
9 3 9 -1 10 2 12 -2 0 -4 0 1 1 7 -9 -3 -10 -5 4 1 -1 -3 -2 -1 2 -5 2 1 -3 -1 -12 -8
8 3 8 -1 8 1 10 -3 0 -3 0 2 1 6 -8 -3 -9 -4 4 1 0 -3 -1 -1 2 -5 1 1 -3 0 -10 -7
2 0 3 0 1 0 3 -1 1 -1 0 1 0 1 -2 -2 -2 -1 2 0 1 -1 -1 -1 2 -2 1 1 0 -1 -3 -2
0 0 1 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0
6 1 7 0 6 1 8 -2 1 -3 0 2 0 4 -6 -2 -8 -4 4 0 0 -2 -1 -1 2 -4 2 2 -2 -1 -8 -6
7 2 7 -1 8 1 9 -2 1 -3 1 0 2 5 -8 -2 -8 -3 2 1 -1 -2 -1 -1 2 -4 1 1 -3 0 -9 -6
7 3 6 -1 7 1 8 -2 0 -2 0 1 1 5 -7 -2 -7 -3 2 1 0 -3 0 0 1 -3 0 0 -3 0 -8 -6
4 2 3 0 3 0 3 -1 0 -1 0 1 0 2 -3 0 -4 -1 1 0 0 -2 1 0 -1 -1 -1 0 -2 1 -3 -3
2 1 2 0 2 0 2 0 1 -1 0 0 0 1 -2 0 -2 -1 0 0 0 -1 0 0 0 0 0 0 -1 0 -2 -2
2 0 2 0 2 0 2 -1 1 -1 0 1 0 1 -2 -1 -2 -1 1 0 0 0 0 -1 1 -1 0 1 -1 0 -2 -2
5 2 4 -1 5 1 5 -1 0 -2 0 1 1 3 -4 -2 -4 -1 2 0 0 -2 -1 -1 1 -2 0 0 -2 0 -6 -4
6 2 6 0 6 1 7 -1 0 -2 -1 1 0 4 -5 -2 -6 -3 3 0 0 -2 -1 -1 1 -3 1 0 -2 -1 -7 -5
4 1 5 1 3 0 4 -2 1 -1 0 2 -1 2 -4 -1 -6 -3 3 0 1 -2 1 0 0 -2 1 1 -2 0 -4 -4
-1 0 -2 0 -2 -1 -2 1 0 1 -1 1 -1 -1 2 0 2 1 0 0 1 0 1 0 -1 2 -1 -1 0 0 2 1
4 1 4 0 4 0 5 -1 1 -2 0 1 0 3 -4 -1 -5 -2 2 0 0 -1 0 -1 1 -2 1 1 -2 0 -5 -4
1 0 0 0 0 0 1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0
12 5 10 -1 11 2 13 -3 -1 -4 -1 3 1 9 -11 -3 -13 -5 6 1 0 -5 0 -1 1 -6 1 1 -5 0 -14 -10
2 1 1 0 1 0 1 -1 0 -1 -1 3 -1 1 -1 0 -2 -1 2 -1 1 -1 1 0 0 0 -1 1 -1 0 -2 -2
3 1 3 0 2 0 2 -1 1 -1 0 0 0 1 -2 0 -3 -1 0 0 0 -1 0 0 0 -1 0 0 -1 1 -2 -2
5 3 3 -1 4 0 4 -1 0 -1 0 0 1 3 -4 0 -4 -1 0 1 0 -2 1 0 -1 -1 -1 -1 -3 2 -4 -4
5 2 4 -1 5 1 6 -1 0 -2 0 0 1 4 -5 -1 -5 -2 1 0 0 -2 0 -1 1 -2 0 1 -2 0 -6 -4
1 1 1 0 1 0 1 -1 0 -1 -1 2 -1 1 0 -1 -1 -1 2 0 1 -1 0 0 0 0 0 0 -1 0 -2 -1
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 2 4 0 5 1 5 -1 -1 -2 -1 1 0 4 -4 -1 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -6 -4
-6 -3 -6 1 -6 -1 -8 2 1 3 0 -2 -1 -5 6 2 7 3 -4 -1 0 3 1 0 -1 4 -1 0 2 0 8 6
9 3 7 -1 9 2 10 -2 -1 -3 -1 1 1 7 -8 -2 -9 -4 4 1 0 -3 0 -1 1 -4 1 0 -4 0 -11 -7
4 2 3 0 4 1 4 -1 -1 -1 -2 2 0 3 -3 -1 -4 -2 3 0 0 -1 0 0 0 -2 0 0 -2 0 -5 -3
3 0 2 0 3 1 3 0 0 0 0 -3 1 2 -3 0 -2 -1 -1 1 -1 0 0 -1 0 -1 1 0 -1 0 -3 -1
1 0 0 0 1 0 1 0 -1 0 -1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
-1 0 -1 0 -1 0 -2 1 0 0 -1 1 -1 -1 2 1 1 0 0 -1 0 1 0 0 0 1 0 0 0 0 1 1
4 2 3 0 4 1 3 -1 -1 -1 -1 2 0 3 -3 -1 -4 -2 3 0 0 -2 0 0 0 -1 0 0 -2 0 -5 -3
1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 -1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
6 2 6 0 6 1 7 -2 0 -1 0 0 1 4 -6 -2 -6 -3 2 1 0 -2 0 -1 1 -3 1 0 -3 0 -7 -5
6 2 6 0 6 1 6 -2 0 -2 0 1 1 4 -6 -1 -7 -3 3 0 0 -2 0 -1 1 -3 1 1 -3 0 -7 -5
1 0 0 0 1 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0
4 0 3 0 3 1 4 -1 -1 -1 -1 1 0 3 -3 -1 -4 -2 3 0 0 -1 0 -1 1 -2 1 1 -1 -1 -5 -2
5 1 5 0 6 1 7 -1 0 -1 0 -1 1 4 -6 -1 -6 -3 2 1 -1 -1 -1 -1 1 -3 2 1 -2 -1 -7 -4
-5 -1 -6 0 -5 -1 -7 2 0 3 0 -2 0 -4 5 2 7 3 -4 0 0 2 1 1 -2 4 -2 -1 1 1 7 5
1 0 0 0 1 0 1 0 0 0 -1 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0
-4 -1 -5 0 -4 -1 -6 2 0 1 -1 0 -1 -3 5 2 5 2 -2 -1 0 2 0 1 -1 3 -1 0 2 0 5 4
4 1 4 0 4 1 5 -1 0 -1 -1 0 0 3 -4 -1 -4 -2 2 1 0 -1 0 -1 1 -2 1 0 -2 -1 -5 -3
1 0 2 1 1 0 1 -1 1 0 0 0 0 0 -1 0 -2 -1 1 0 0 0 0 0 0 -1 1 0 -1 0 -1 -1
1 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
4 2 2 -1 4 1 3 0 -1 -1 -1 0 1 3 -3 0 -3 -1 0 0 -1 -1 0 0 0 -1 -1 0 -2 1 -4 -2
0 0 -2 -1 0 0 -1 1 0 0 0 -2 1 0 1 1 2 1 -3 0 -1 1 0 0 0 1 -1 0 0 1 1 1
6 2 4 -1 6 1 7 0 -1 -2 -1 -1 1 5 -5 -1 -5 -2 1 1 -1 -1 -1 -1 1 -3 1 0 -2 0 -7 -4
1 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
7 3 5 -1 7 1 7 -1 -1 -2 0 -1 2 5 -6 -1 -6 -2 0 1 -1 -2 0 0 0 -3 0 0 -3 1 -7 -5
-5 -2 -5 1 -6 -1 -7 1 0 2 -1 0 -2 -4 6 2 6 2 -2 -1 1 2 1 1 -1 3 -1 0 2 0 7 5
5 2 4 0 5 1 4 -1 0 -1 -1 1 0 3 -4 -1 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -5 -4
-4 -1 -5 0 -4 -1 -6 2 0 2 -1 -1 -1 -3 5 2 5 2 -3 0 0 2 1 1 -2 3 -1 -1 1 1 6 4
2 1 1 0 2 0 2 0 -1 -1 -1 0 0 2 -1 0 -1 -1 0 0 0 0 0 0 0 -1 0 0 0 0 -2 -1
-1 -1 -1 1 -1 0 -2 0 0 0 -1 2 -1 -1 2 0 1 0 1 -1 0 1 0 0 0 1 0 0 0 0 1 1
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 3 3 -1 4 1 4 -1 0 -2 0 1 1 3 -4 -1 -4 -1 1 0 0 -2 0 0 1 -2 -1 0 -2 1 -5 -4
2 0 0 -1 2 1 2 1 -1 -1 -1 -1 1 2 -1 0 0 0 -1 0 -2 1 -1 -1 1 -1 0 0 0 0 -2 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 3 0 4 1 5 0 0 -1 0 -1 1 3 -4 -2 -3 -1 1 1 -1 -1 -1 -1 1 -2 1 0 -1 -1 -5 -3
6 2 4 -1 7 2 7 0 -1 -2 0 -2 2 5 -6 -1 -5 -2 0 1 -2 -1 -1 -1 1 -3 1 0 -2 0 -7 -4
4 2 2 -1 4 1 4 0 -1 -2 0 1 1 3 -3 -1 -3 -1 1 0 -1 -1 -1 0 1 -2 0 0 -1 0 -5 -3
2 0 1 0 2 1 3 1 -1 -1 -1 0 0 2 -1 -1 -1 -1 1 0 -1 0 -1 -1 1 -1 1 0 0 -1 -3 -1
-2 -1 -3 0 -2 0 -3 1 0 1 0 -1 0 -2 3 0 4 2 -2 0 0 1 0 0 0 2 -1 -1 1 0 3 2
5 1 2 -1 4 1 5 0 -1 -1 0 -1 1 4 -4 -1 -3 -1 0 1 -1 -1 0 -1 1 -2 0 0 -1 0 -5 -3
2 1 0 -1 2 0 2 1 0 0 1 -3 2 1 -2 0 0 1 -3 1 -1 0 0 0 0 0 -1 -1 -1 1 -1 -1
0 -1 -1 0 0 0 0 1 0 1 1 -3 1 0 0 0 2 1 -3 1 -1 1 0 -1 0 1 0 -1 0 0 1 1
4 1 4 0 5 1 5 -1 0 -1 0 -1 1 3 -4 -1 -4 -2 1 1 -1 -1 -1 -1 1 -2 1 0 -2 0 -5 -3
0 0 -2 -1 0 0 -1 1 0 0 0 -2 1 0 1 1 2 2 -3 0 -1 1 0 0 0 1 -1 -1 0 1 1 1
11 4 9 -1 11 2 12 -2 -1 -4 0 1 2 8 -10 -3 -11 -4 4 1 -1 -4 -1 -1 2 -6 1 1 -4 0 -13 -9
4 1 3 0 4 1 5 0 -1 -1 0 -1 1 3 -4 -1 -3 -1 1 1 -1 -1 -1 -1 1 -2 1 0 -1 -1 -5 -3
-7 -3 -8 0 -7 -1 -8 3 0 3 0 -3 0 -5 7 2 10 4 -5 0 -1 4 0 0 -1 4 -1 -1 3 0 9 7
4 2 2 -1 4 1 4 0 -1 -2 -1 1 1 4 -3 -1 -3 -1 1 0 -1 -1 -1 0 1 -2 0 0 -1 0 -5 -3
4 2 2 -1 4 1 4 0 -1 -2 -1 1 1 3 -3 -1 -3 -1 2 0 -1 -1 -1 0 1 -2 0 0 -1 0 -5 -3
9 2 8 0 9 2 11 -2 -1 -3 0 0 2 7 -9 -3 -9 -4 4 1 -1 -3 -1 -2 2 -5 2 1 -3 -1 -11 -7
2 0 2 0 3 1 4 0 0 0 0 -2 1 2 -3 -1 -2 -1 0 1 -1 0 -1 -1 1 -1 1 0 -1 -1 -3 -1
0 0 -2 -1 0 0 -1 1 0 0 0 -1 1 0 0 1 1 1 -2 0 -1 1 0 0 0 1 -1 0 0 1 1 1
2 1 0 -1 2 1 2 1 -1 -1 -1 0 1 2 -1 -1 0 0 0 0 -1 0 -1 -1 1 -1 0 0 0 0 -3 -1
-2 -1 -4 -1 -2 0 -2 2 -1 0 -1 -1 0 0 3 1 4 1 -2 0 -1 2 -1 0 0 1 0 0 2 0 2 3
6 2 5 0 5 1 7 -1 -1 -3 -1 2 0 5 -5 -2 -6 -3 4 0 0 -2 -1 -1 2 -4 2 1 -1 -1 -8 -5
9 3 7 -1 9 2 10 -2 -1 -4 -1 2 1 7 -8 -2 -9 -4 4 0 -1 -2 -1 -1 2 -5 1 1 -3 0 -11 -7
3 1 2 -1 3 1 4 0 0 -1 0 -1 1 3 -3 -1 -2 -1 0 1 -1 0 -1 -1 1 -2 1 0 -1 0 -4 -2
7 2 5 -1 7 2 8 -1 -1 -3 -1 1 1 6 -6 -2 -6 -3 3 0 -1 -2 -1 -1 2 -4 1 1 -2 -1 -9 -5
2 0 1 0 2 1 2 0 0 0 0 -1 1 1 -2 -1 -1 0 0 0 -1 0 -1 -1 1 -1 0 0 0 0 -2 -1
0 -1 -1 0 0 1 1 1 -1 0 -1 0 0 1 0 -1 1 0 1 0 -1 1 -1 -1 1 -1 1 0 1 -1 -1 1
6 3 5 -1 6 1 6 -1 0 -3 0 1 1 4 -5 -1 -6 -2 2 0 -1 -2 -1 0 1 -3 1 0 -2 0 -7 -5
-2 -1 -3 0 -3 0 -3 1 0 1 0 -1 0 -2 3 0 4 2 -2 0 0 1 0 0 0 2 -1 -1 1 0 3 3
-
HERMITIAN_STRUCTURE
4
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0
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 0 0 0 0 0 0
0 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 0 0 0 0 0
0 0 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 0 0 0 0
0 0 0 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 0 0 0
0 0 0 0 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 0 0
0 0 0 0 0 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 0
0 0 0 0 0 0 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
0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
32 32
10 2 11 0 11 3 14 -2 0 -4 0 0 1 8 -11 -3 -13 -6 5 1 -1 -3 -2 -2 3 -7 4 2 -3 -2 -14 -9
6 2 5 -1 6 2 7 -1 -1 -3 -1 2 0 5 -5 -1 -7 -3 3 0 0 -2 0 -1 1 -3 1 1 -2 -1 -8 -5
-6 -2 -5 0 -6 -1 -7 1 1 3 1 -2 0 -5 6 2 6 3 -4 0 0 2 0 1 -1 3 -1 -1 2 1 8 5
5 2 5 0 5 2 6 -1 -1 -2 -1 1 0 4 -5 -1 -6 -3 3 0 0 -2 0 -1 1 -3 1 1 -2 -1 -7 -4
-1 -1 -1 1 -2 0 -2 0 0 1 0 0 -1 -1 1 1 0 0 0 0 1 0 2 0 -1 1 0 0 0 0 2 1
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 0 -3 -1 0 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
3 1 3 0 3 1 3 -1 0 -2 0 2 0 2 -3 0 -5 -2 2 -1 0 -1 0 0 1 -2 0 2 -1 0 -4 -3
-2 -1 -2 0 -2 0 -2 1 0 1 0 -2 0 -1 2 1 2 1 -2 0 0 1 0 0 0 1 0 0 1 0 2 2
5 1 3 -1 5 2 6 0 -1 -1 0 -2 2 4 -5 -1 -4 -1 0 1 -1 -1 0 -2 1 -2 0 0 -2 0 -6 -3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-6 -3 -5 1 -6 0 -6 2 0 2 -1 0 -2 -4 6 1 6 2 -1 -1 1 2 0 0 0 3 0 0 3 -2 6 5
0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
5 2 4 -1 6 2 7 0 -1 -2 -1 -1 1 5 -5 -1 -5 -3 1 1 -1 -1 -1 -1 1 -3 1 0 -2 0 -7 -4
-3 -1 -3 0 -3 0 -3 1 0 2 0 -2 0 -2 3 1 4 2 -3 1 0 1 0 0 -1 2 -1 -1 1 0 4 3
3 0 2 0 3 2 4 -1 -1 -1 -1 1 0 3 -3 -1 -4 -2 3 0 0 -1 0 -1 1 -2 1 1 -1 -1 -5 -2
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
1 1 1 0 1 0 0 -1 0 0 1 0 1 0 -1 1 -2 0 -1 0 0 -1 1 1 -1 0 -1 0 -1 1 0 -1
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 0 0 0 0
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 0 -1 1 0 -1 0 -3 -2
-3 -2 -1 1 -2 0 -2 1 1 1 0 -2 -1 -2 2 1 2 0 -2 0 0 2 0 0 0 1 1 0 1 -1 3 2
1 0 2 0 2 1 2 0 0 -1 0 0 0 1 -1 0 -2 -1 0 0 -1 0 -1 0 1 -1 1 0 0 -1 -2 -1
4 2 2 -1 3 1 3 -1 -1 -1 0 1 1 3 -3 0 -4 -1 1 0 0 -2 1 0 0 -1 -1 0 -2 1 -4 -3
3 1 4 0 4 1 4 -1 1 -1 1 -1 1 2 -4 0 -5 -2 0 0 -1 -1 -1 0 1 -2 1 1 -1 0 -4 -3
4 2 4 0 4 1 4 -1 0 -2 0 1 0 3 -4 0 -6 -2 2 0 0 -2 0 0 0 -2 1 1 -2 0 -5 -4
-2 -1 0 1 -2 0 -2 0 1 0 0 1 -1 -2 2 1 0 0 0 -1 0 1 -1 0 0 0 1 1 1 0 2 1
5 2 5 0 5 1 6 -1 0 -2 0 1 0 4 -5 0 -7 -3 2 0 0 -2 0 0 0 -3 1 1 -2 0 -6 -5
3 1 3 0 3 1 3 -1 0 -1 0 1 0 2 -3 0 -5 -2 2 0 0 -1 0 0 0 -2 1 1 -1 0 -4 -3
1 1 1 0 0 0 0 -1 0 0 0 1 0 0 0 0 -1 0 0 0 1 -1 1 0 0 0 -1 -1 -1 1 0 -1
-4 -1 -3 1 -5 -1 -6 0 1 2 1 0 -1 -4 4 2 3 2 -2 -1 1 1 1 1 -1 2 -1 0 1 1 6 3
5 2 5 0 5 1 6 -1 0 -2 0 1 0 4 -5 -1 -7 -3 2 1 0 -2 0 0 0 -3 1 1 -2 0 -6 -5
-3 -3 -2 0 -3 0 -2 1 1 1 1 -3 0 -2 2 1 3 1 -3 0 0 2 0 -1 1 1 1 1 2 -1 3 3
32 32
0 0 0 0 -1 0 -1 1 0 0 0 1 -1 -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 1 0
-3 0 -3 -1 -3 -1 -4 2 1 1 1 -1 0 -3 3 1 3 2 -3 0 0 1 0 1 -1 2 -1 -1 1 1 5 2
-1 0 0 1 -1 0 -1 0 0 1 0 1 0 -1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
5 3 4 -1 5 1 5 0 0 -2 0 1 0 3 -4 -1 -5 -2 1 0 0 -2 0 0 0 -2 0 0 -2 0 -5 -5
6 3 6 -1 7 1 7 -1 0 -2 0 1 1 4 -6 -2 -7 -3 2 0 0 -2 0 0 1 -3 0 0 -3 0 -7 -6
4 2 4 0 4 1 4 -1 0 -1 0 2 0 2 -4 -2 -5 -2 3 0 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
0 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 1 0
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 -1 -2 -1 0 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
1 1 2 0 1 0 1 0 1 0 0 1 -1 0 -1 -1 -2 -1 1 0 1 -1 0 0 0 0 0 0 -1 0 -1 -2
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 -1 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
5 2 4 -1 5 1 5 0 0 -1 1 -1 1 3 -5 -1 -5 -1 0 1 -1 -2 0 0 0 -2 0 0 -2 0 -5 -4
4 2 4 0 4 1 4 -1 0 0 0 1 0 2 -4 -1 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
-4 -2 -3 1 -5 0 -5 1 1 2 0 1 -2 -4 4 0 4 1 0 -1 1 1 0 0 0 2 0 0 2 -1 5 3
6 3 6 0 6 1 6 -1 0 -2 0 2 0 4 -6 -2 -8 -3 4 1 0 -3 0 0 0 -3 1 0 -3 0 -7 -6
1 -1 2 0 1 1 2 0 1 0 1 -1 0 0 -2 -1 -2 -1 0 0 0 0 0 -1 1 -1 1 1 0 -1 -1 -1
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 -1 -2 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 4 8 -1 10 2 11 -1 -1 -3 -1 1 2 7 -9 -3 -10 -4 4 1 -1 -3 -1 -1 1 -5 1 0 -4 0 -11 -8
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 3 0 3 1 3 -1 0 -1 0 2 0 1 -3 -1 -4 -2 2 -1 0 -1 0 0 1 -2 0 1 -1 0 -3 -3
8 4 7 -1 8 2 8 -1 -1 -3 0 2 1 5 -7 -2 -8 -3 3 0 -1 -3 -1 0 1 -4 0 0 -3 0 -9 -7
5 3 3 -1 4 1 4 0 -1 -2 0 2 1 3 -4 -1 -5 -1 2 0 -1 -2 0 0 0 -2 -1 0 -2 1 -5 -4
-1 0 0 0 -1 0 0 0 1 1 0 0 0 -1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
-2 -1 -2 1 -3 0 -3 1 0 1 -1 1 -1 -2 3 0 2 1 0 -1 0 1 0 0 -1 1 0 0 1 0 3 2
3 1 3 0 3 1 4 0 0 -1 0 0 0 2 -3 -1 -4 -2 1 0 0 -1 0 0 0 -2 1 0 -1 0 -3 -3
-5 -1 -5 1 -6 -1 -7 2 -1 2 -1 2 -2 -4 6 1 5 2 0 -1 1 1 1 1 -2 3 -1 -1 2 0 7 4
-2 -1 -2 0 -2 0 -2 1 0 2 0 -1 0 -2 2 0 2 1 -1 0 0 1 0 0 -1 1 0 -1 1 0 3 2
-2 -1 -2 0 -2 0 -3 1 0 1 0 0 0 -2 2 0 2 1 -1 -1 0 1 0 0 0 1 0 0 1 0 3 2
0 2 1 0 1 0 0 0 0 -1 -1 4 -1 0 0 -1 -2 -1 3 -1 1 -1 0 1 0 0 -1 0 -1 0 -1 -2
4 2 4 0 5 1 5 -1 -1 -1 0 1 1 3 -4 -2 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -5 -4
3 1 3 0 3 0 3 0 0 -1 0 1 0 2 -3 -1 -4 -2 2 0 0 -1 0 0 0 -2 1 0 -1 0 -3 -3
-1 1 0 0 -1 -1 -2 1 1 1 1 -1 0 -2 1 1 1 1 -3 0 0 0 0 1 -1 1 -1 -1 0 1 3 0
32 32
4 1 5 0 5 2 6 0 0 -2 0 0 0 3 -5 -1 -6 -3 2 0 -1 -1 -1 -1 1 -3 2 1 -1 -1 -6 -4
2 1 2 -1 2 1 2 0 0 -1 0 1 0 1 -2 0 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
-3 -2 -2 1 -3 0 -3 0 1 2 1 -1 0 -3 2 0 2 1 -1 0 0 1 0 0 0 1 0 0 1 0 4 2
2 2 2 -1 2 1 2 0 0 -1 0 0 0 1 -2 0 -2 -1 0 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
4 2 4 0 3 1 4 -1 0 -1 0 1 0 2 -4 -1 -5 -2 2 0 1 -2 1 0 0 -2 0 0 -2 0 -4 -4
4 2 4 0 4 1 4 -1 0 -1 0 1 0 2 -4 -1 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
2 1 2 0 2 1 1 0 0 -1 0 1 0 1 -2 0 -3 -1 1 -1 0 -1 0 0 0 -1 0 1 -1 0 -2 -2
0 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 0 0 0 0 0 0
7 3 6 -1 7 2 8 -1 -1 -2 0 0 1 5 -7 -2 -7 -3 2 1 0 -3 0 -1 1 -3 0 0 -3 0 -8 -6
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
0 0 0 0 0 1 0 1 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
2 1 2 0 2 1 2 0 0 0 0 -1 0 1 -2 0 -2 -1 0 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 2 4 0 4 1 4 -1 0 -1 0 1 0 2 -4 -1 -5 -2 2 1 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
3 0 3 0 3 2 4 -1 0 -1 0 0 0 2 -4 -1 -4 -2 2 0 0 -1 0 -1 1 -2 1 1 -1 -1 -4 -2
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 -1 -2 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 -1 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
4 2 4 0 4 1 4 -1 0 -1 0 1 1 2 -4 -1 -5 -2 2 0 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
2 1 2 0 2 1 2 0 0 -1 0 1 0 1 -2 -1 -3 -1 1 0 0 -1 0 0 0 -1 0 0 -1 0 -2 -2
0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 0 -2 -1 0 0 -1 0 0 0 0 -1 0 0 -1 0 -2 -2
2 1 2 0 2 1 2 0 0 -1 0 1 0 1 -2 0 -3 -1 1 0 -1 -1 0 0 0 -1 0 0 -1 0 -2 -2
2 1 2 0 1 1 2 -1 0 0 0 1 0 1 -2 -1 -3 -1 2 0 1 -2 0 0 0 -1 0 0 -1 0 -2 -2
-3 -1 -2 1 -3 0 -4 1 1 1 0 0 -1 -3 3 1 2 1 -1 -1 0 1 0 0 -1 2 0 0 1 0 4 2
2 1 2 0 2 1 2 0 0 -1 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 -1 -1 1 0 -1 0 -2 -2
-3 -1 -2 1 -3 0 -4 1 0 1 0 1 -1 -3 3 1 2 1 0 -1 0 1 0 0 -1 1 0 0 1 0 4 2
2 1 2 0 2 1 2 0 0 0 0 0 0 1 -2 0 -3 -1 1 0 0 -1 0 0 -1 -1 0 0 -1 0 -2 -2
0 0 0 0 0 1 -1 0 0 0 0 1 0 -1 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
5 3 6 0 5 1 6 -2 0 -2 0 3 0 3 -5 -2 -7 -3 4 0 1 -3 0 0 1 -3 0 0 -3 0 -6 -6
4 2 4 0 4 1 4 -1 0 -1 1 0 1 2 -4 -1 -5 -1 1 0 0 -2 0 0 0 -2 0 0 -2 0 -4 -4
5 2 5 0 5 1 5 -1 0 -2 0 2 0 3 -5 -1 -7 -3 3 0 0 -2 0 0 0 -3 1 1 -2 0 -6 -5
-2 -1 -1 0 -2 0 -2 1 1 1 1 -2 0 -2 1 1 2 1 -3 0 0 1 0 0 0 1 0 0 1 0 3 1
-
PROPERTIES
Unimodular=1
-
REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
-
NOTES
Called LAMBDA_32' in Bachoc-Nebe
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe