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 13:11:40 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
-2 0 4
-2 0 0 4
1 -2 0 0 4
1 1 -1 -1 1 4
-1 1 1 0 -2 0 4
-1 1 0 0 -2 0 0 4
0 1 0 0 -2 -1 0 0 4
-1 1 0 0 -2 0 0 2 0 4
-2 0 2 0 0 -1 0 0 0 1 4
-1 -1 1 1 1 0 -1 0 0 1 1 4
-1 -1 1 1 0 -2 -1 0 1 1 2 2 4
1 1 -1 -1 0 2 1 0 -1 -1 -2 -2 -2 4
-2 0 0 2 0 -1 1 0 -1 0 0 1 0 0 4
0 1 1 -1 1 2 -1 0 -1 0 0 0 -1 1 -1 4
1 1 0 -2 0 2 0 1 0 0 -1 -1 -2 1 -2 1 4
-1 -1 2 0 1 0 0 1 -1 0 1 2 1 -1 0 0 0 4
1 1 0 -2 -1 0 0 1 1 0 -1 -1 0 1 -2 0 2 0 4
1 1 -2 0 0 2 0 -1 0 0 -1 -1 -1 2 0 1 0 -2 0 4
-2 0 1 1 0 0 1 1 -1 1 1 1 1 0 2 0 -1 1 -1 0 4
-1 -1 0 2 0 -1 1 0 -1 0 1 1 1 -1 2 -1 -2 0 -2 0 1 4
-1 2 -1 0 -1 0 0 0 1 1 1 0 1 0 0 0 -1 -1 0 1 0 0 4
1 -1 0 0 2 0 0 -2 0 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 4
1 -2 1 0 1 0 1 -1 -1 -1 -1 1 0 0 0 0 0 1 0 -1 0 1 -2 1 4
1 -2 -1 0 1 -1 -1 -1 0 0 1 1 1 -2 0 -2 -1 0 -1 -1 -1 1 0 0 0 4
1 -1 0 0 2 1 -2 0 0 -1 0 1 1 0 -1 1 0 1 0 0 0 0 0 1 0 0 4
1 0 0 -2 1 0 0 -1 -1 -1 0 -1 0 1 -1 0 1 0 2 0 -1 -1 0 1 0 0 0 4
1 -2 1 0 2 0 0 -1 -1 -2 -1 1 0 0 0 0 0 2 0 -1 0 0 -2 2 2 0 1 1 4
-1 1 -1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 2 0 1 0 -1 -1 0 0 -1 4
-2 1 1 1 -2 -1 1 2 0 2 1 1 1 -1 1 0 -1 1 0 -1 1 1 1 -1 0 -1 -1 -1 -1 0 4
-1 -1 1 1 1 0 -1 1 -1 0 1 2 1 -1 1 1 -1 2 -1 -1 1 1 -1 -1 1 0 1 -1 1 0 1 4
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
4
-
HERMITIAN_GROUP_ORDER
2^20 * 3^4 * 5
-
HERMITIAN_GROUP_GENERATORS
4
32 32
1 1 0 0 1 -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 -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 0 1 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
-2 -2 0 0 -4 2 -2 -1 -1 -1 0 0 0 0 0 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 0 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
1 1 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 0 0 0 0 0
-3 -1 -1 -1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 1 -1 1 -1 1 1 0 -1 0 0 0 1 1 0 0 0 0 0 0 -1 0 1 1 0 1 1 1 0
-1 0 0 -1 -1 2 -1 1 -1 -1 0 0 1 -1 0 -1 -1 0 0 0 0 0 0 1 0 -1 -1 0 -1 -1 -1 0
0 0 0 0 2 0 1 0 1 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 -1 1 0 0 -1 -1 0 0 1 -1 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 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 -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 0 0
-1 -1 -1 0 0 0 1 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 -1 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 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 -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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 -1 -1 1 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 -1 -1 1 -1 1 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 -2 1 -2 0 -1 -1 1 0 0 0 1 -1 0 0 0 0 0 0 0 1 1 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 1 0 0 0 0 0 0
-3 -2 -1 -1 -1 0 0 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 2 0 1 2 1 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -1 1 -1 -1 -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 0 0
2 1 0 1 3 -2 2 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0
-1 0 0 -1 1 2 0 1 0 -1 -1 0 1 -1 0 -1 -1 0 0 0 0 0 0 0 0 -1 -1 0 -1 -1 0 0
-2 -1 -1 0 -1 -1 0 -2 0 1 0 0 -1 1 -1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1
32 32
0 0 0 0 0 0 0 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
1 0 -1 1 -3 0 -1 0 -1 -1 2 0 0 0 1 1 0 1 0 0 0 -1 0 1 1 0 0 0 0 0 -1 -1
0 0 -1 0 1 0 0 -1 1 1 0 -1 0 0 1 1 0 1 1 -1 0 1 0 -1 0 0 0 0 0 0 0 -1
0 1 2 -1 2 0 0 1 0 0 -1 0 0 0 -1 -2 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 1 -1 1 1 0 0 0 0 0 0 0 0 0 0
6 2 0 3 -4 1 -3 -2 0 -1 3 -1 0 0 3 2 1 3 1 -2 2 1 1 0 1 0 -1 0 0 0 -1 -1
2 2 0 0 0 -1 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
2 -1 1 2 0 0 0 -2 1 1 0 -1 -1 0 1 1 1 1 1 -1 0 1 1 -1 -1 0 0 0 0 1 0 0
-4 -1 -1 -2 1 0 0 2 0 0 0 0 0 0 -1 -1 -1 -1 -1 2 -1 -1 -1 1 1 0 0 0 0 -1 0 0
2 0 0 2 -3 0 -1 0 -1 -1 2 0 0 0 2 1 1 1 0 0 0 -1 1 0 1 0 0 0 0 0 -1 -1
-1 -1 -1 0 0 1 0 -1 1 1 0 -1 0 0 1 1 0 0 1 -1 0 1 0 -1 0 0 0 0 1 0 0 -1
0 -1 0 0 1 2 -1 0 1 0 0 -1 0 -1 1 0 0 0 1 -1 1 1 1 -1 0 -1 -1 0 0 -1 0 -1
-6 -3 0 -3 1 2 0 1 0 0 -2 0 0 -1 -1 -2 -1 -2 0 1 -1 0 0 0 0 -1 0 0 0 -1 0 0
0 0 -1 0 1 -1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 1 -1 2 -1 1 1 0 0 -2 1 0 0 -2 -1 0 -1 -1 1 0 0 0 0 -1 0 0 0 0 0 1 0
5 1 0 3 -4 1 -3 -2 0 -1 2 -1 0 0 3 2 1 3 1 -2 2 1 1 0 1 0 -1 1 -1 0 -1 -1
4 2 0 2 -1 -1 0 -1 -1 0 2 0 0 0 1 1 0 1 1 -1 0 0 0 0 0 0 0 -1 0 1 -1 0
1 -1 0 1 -1 1 -1 -3 1 1 0 -1 -1 0 1 1 1 1 2 -2 1 2 1 -1 -1 0 0 0 0 0 0 0
-2 -2 -2 0 1 0 1 0 1 1 1 0 -1 0 0 1 -1 0 1 -1 -1 0 0 0 0 -1 0 0 0 0 -1 0
1 1 0 0 -1 -1 0 1 -1 -1 1 1 0 0 0 0 0 0 -1 1 0 -1 0 1 1 0 0 0 0 0 0 0
-1 0 1 -1 -2 0 -1 0 -1 -1 -1 1 0 0 -1 -1 0 0 -1 1 0 0 0 1 0 0 0 0 -1 0 0 0
-1 0 2 -2 4 1 2 2 0 0 -3 0 1 -2 -1 -2 -1 -2 -1 1 -1 0 0 -1 -1 -1 0 0 0 0 1 0
-1 -1 -2 1 -4 1 -2 0 0 -1 2 0 -1 0 1 1 0 1 0 0 1 -1 0 1 2 0 0 1 0 -1 -1 -1
-1 0 0 0 -5 2 -4 0 -1 -1 1 0 -1 0 0 -1 -1 1 0 0 1 0 0 2 2 0 0 1 -1 -1 -1 0
1 1 0 -1 4 1 1 1 1 0 -1 0 1 -1 0 -1 -1 0 0 -1 0 1 0 -1 -1 -2 -1 0 -1 -1 0 0
0 0 0 0 2 0 1 1 1 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 1 0 0 0
-3 -2 0 -1 -1 2 -1 -1 0 0 -1 -1 0 -1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0
-3 -2 -1 -1 -1 0 1 -2 -1 1 -1 0 0 0 -1 0 0 -1 1 -1 -1 0 0 0 -1 0 1 -1 1 1 0 1
-1 -1 1 -1 1 1 -1 -2 1 1 -2 -1 -1 0 -1 -1 0 0 1 -1 1 2 1 -1 -1 0 0 0 0 0 1 1
-1 -1 0 0 -2 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
2 -1 0 2 -2 2 -2 -1 1 0 1 -1 -1 0 2 1 0 2 1 -2 1 1 1 0 0 -1 -1 1 -1 -1 -1 -1
1 -1 1 0 3 1 0 -2 2 1 -2 -1 0 0 0 0 1 0 1 -2 1 3 1 -2 -2 -1 -1 0 0 0 1 0
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
3 0 1 1 2 1 -1 -1 2 1 0 -1 -1 0 1 0 0 1 1 -2 1 2 1 -1 -1 -1 -1 0 0 0 0 0
0 0 0 0 1 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-3 -2 0 -1 -1 0 1 0 -1 0 -1 0 0 -1 0 0 0 -1 0 1 -1 -1 0 0 0 0 1 0 0 0 0 0
-3 0 -1 -1 0 -1 1 2 -1 -1 0 1 1 0 -1 0 0 -1 -1 2 -1 -2 -1 1 1 1 0 0 0 0 0 0
-3 0 -1 -1 -2 -1 1 1 -2 -1 0 1 1 0 -1 0 0 -1 -1 2 -1 -2 -1 1 1 1 2 0 0 0 0 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 -1 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
-1 -1 0 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 -1 0 0 0 0 0 1 -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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 2 -1 0 0 2 1 1 0 -1 1 0 1 0 1 0 -1 1 1 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 1 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 -1 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 -1 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 1 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 -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 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 -2 1 0 -1 2 -1 -1 0 0 -1 -1 0 -1 1 0 0 0 1 -1 0 1 1 0 -1 -1 0 0 0 0 0 0
0 -1 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 0 -1 0 0 0
-1 -2 0 0 0 2 -1 -1 1 1 0 -2 0 0 1 0 0 0 1 -1 0 1 1 -1 0 0 0 0 1 0 0 0
0 0 0 0 1 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
3 0 1 1 1 1 -1 -1 2 1 0 -1 -1 0 1 0 0 1 1 -2 1 2 1 -1 -1 -1 -1 1 0 0 0 0
0 -1 1 0 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
-5 -1 -1 -3 3 -1 2 2 0 0 -2 1 0 -1 -2 -1 -1 -2 -1 2 -1 -1 -1 0 0 0 1 0 0 0 1 0
2 1 0 2 -3 -1 -1 -1 -1 0 2 0 0 1 1 1 1 1 0 0 0 -1 0 1 1 1 0 0 0 1 0 0
0 1 0 0 1 -2 1 1 0 0 0 1 0 1 -1 0 0 0 -1 1 0 -1 -1 1 0 1 0 0 -1 0 0 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
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
-1 -1 0 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 -1 0 0 0 -1 -1 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 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
-2 -1 1 -1 1 1 0 1 0 0 -1 0 0 0 -1 -1 -1 -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
1 0 -1 1 -1 1 0 -1 0 0 1 0 0 0 1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 -1 1 1 0 -1 0 0 1 1 0 1 1 -1 0 1 0 0 0 0 0 0 0 0 0 0
3 1 -1 2 -1 -1 0 -1 0 0 2 0 0 1 1 1 1 1 0 -1 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 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
1 0 0 1 -1 -1 0 -1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 1 -1 0 1 0 0 1 0 0 0 0 -1 0 0 -1 1 0 -1 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 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
-1 0 1 -1 1 0 1 2 -1 -1 -1 1 1 0 -1 -1 -1 -1 -1 1 -1 -1 -1 1 0 0 0 0 -1 0 0 0
-3 -2 -2 -1 2 1 1 -1 2 1 -1 -1 0 0 0 1 0 0 1 -1 0 1 0 -1 -1 0 0 0 1 0 1 0
2 0 1 2 -3 0 -2 -2 0 1 1 -1 -1 1 1 1 1 1 1 -1 1 1 1 0 0 1 0 0 1 1 0 0
1 0 0 1 0 1 -1 2 1 -1 1 0 0 0 1 1 -1 1 0 0 1 0 0 0 1 0 -1 1 -1 -1 -1 -1
-
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
-1 0 -1 -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 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 -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
2 1 1 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 -1 0 0 -1 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
-2 -1 0 -1 -3 1 -2 -1 -1 -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 1 0 -1 1 -1 -1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 0 0 -1 1 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
1 1 0 0 3 -1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 0 -3 2 -2 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
-1 -1 0 0 0 1 0 0 0 0 -1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 -1 0 0 1 -1 -1 1 1 0 0 0 0 0 -1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0
-1 -1 0 0 2 0 2 2 0 0 -1 0 1 -1 0 0 0 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0
-2 -1 0 -1 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
2 1 1 1 -1 1 -1 1 -1 -1 1 1 0 0 0 -1 -1 0 0 0 0 0 0 1 0 -1 -1 0 -1 -1 -1 0
-2 -2 0 -1 -4 1 -2 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 -3 0 -3 -2 1 0 1 -1 -2 1 1 1 1 2 0 -1 2 1 1 0 1 1 0 1 0 0 0 0
0 -1 -2 1 1 0 1 0 1 0 1 0 0 0 1 2 0 0 1 -1 0 0 0 -1 0 0 0 0 1 0 0 -1
-1 -1 -1 0 3 -1 2 1 2 1 0 0 -1 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0
0 0 0 0 -2 2 -2 1 0 -1 1 0 0 -1 1 0 -1 1 0 0 0 0 0 1 1 -1 -1 1 -1 -1 -1 -1
0 -1 0 1 -2 2 -2 1 0 -1 1 0 0 0 1 0 -1 1 0 0 0 0 0 1 1 -1 -1 1 -1 -1 -1 -1
1 1 2 0 -3 1 -1 0 -3 -2 -1 1 1 -1 -1 -2 0 -1 -1 1 0 -1 0 1 0 0 0 0 -1 0 0 1
0 0 1 0 3 0 2 0 0 1 -1 -1 1 -1 0 0 0 -1 1 0 -1 0 0 -1 -1 0 0 -1 1 1 1 0
1 1 0 0 0 -1 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
1 0 0 1 -4 -1 -1 -2 -2 0 1 1 -1 1 0 0 1 0 0 0 0 -1 0 1 0 1 1 0 0 1 0 1
-4 0 0 -3 4 -1 3 2 -1 0 -3 1 1 -1 -3 -2 -1 -3 -1 2 -1 -1 -1 0 -1 0 1 -1 0 0 1 1
1 -1 0 0 2 1 1 0 1 0 -1 -1 1 -1 1 1 0 0 1 -1 0 1 1 -1 -1 -1 -1 0 0 0 0 0
-1 0 0 -1 3 -1 2 2 0 0 -1 0 1 -1 0 0 0 -1 -1 1 -1 -1 0 -1 0 0 0 0 0 0 0 0
2 1 -1 1 -1 -1 0 1 -1 -1 2 1 0 0 1 1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 -1
0 1 0 0 0 -1 1 1 -1 -1 0 1 1 0 0 0 0 0 -1 1 -1 -1 -1 1 0 0 0 0 -1 0 0 0
0 -1 0 1 -2 2 -1 -1 0 0 1 -1 0 0 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 1 0 0 0
0 -1 -1 1 -3 0 0 0 -1 -1 1 1 0 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 -1 0
32 32
1 1 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
-2 -1 -1 -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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 0 4 -2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
2 2 0 1 4 -2 2 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
-1 -1 0 0 -2 1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
-1 -1 0 0 -3 1 -2 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 0 0 -1 1 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
-1 -1 -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 0 0 0
0 0 -1 0 1 -1 1 -1 1 1 0 -1 0 0 1 1 1 0 0 0 0 0 0 -1 0 1 1 0 1 1 1 0
2 1 -1 1 -2 -1 0 1 -1 -1 2 1 0 0 1 1 0 1 0 0 0 -1 0 1 1 0 0 0 -1 0 -2 0
-5 -2 -2 -2 -2 -1 1 1 -1 -1 0 1 0 0 -1 0 0 -1 -1 2 -1 -2 -1 1 1 1 2 0 0 0 0 0
-5 -1 0 -3 2 1 1 3 -1 -1 -2 1 1 -1 -2 -2 -2 -2 -1 2 -1 -1 -1 1 0 -1 0 0 -1 -2 0 0
-1 -1 0 -1 -1 2 -1 1 -1 -1 -1 0 1 -1 0 -1 -1 0 0 0 0 0 0 1 0 -1 -1 0 -1 -1 -1 0
0 1 0 0 1 -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
3 2 0 2 2 -1 0 0 2 1 1 0 -1 1 0 1 0 1 0 -1 1 1 0 -1 0 0 -1 1 0 0 0 0
2 1 -1 1 -1 -1 0 1 -1 -1 2 1 0 0 1 1 0 1 0 0 0 -1 0 0 1 0 0 0 -1 0 -1 -1
-4 0 -1 -2 0 -1 2 2 -2 -1 0 2 1 0 -2 -1 -1 -2 -1 2 -2 -2 -2 1 0 0 1 -1 0 0 0 0
-3 1 1 -3 4 -2 4 3 -2 -1 -3 2 2 -1 -3 -2 -1 -3 -2 3 -2 -2 -2 1 -1 0 1 -1 -1 0 1 1
-6 -2 -1 -4 4 -1 3 2 -1 0 -3 1 1 -1 -3 -2 -1 -3 -1 2 -2 -1 -1 0 -1 -1 1 -1 0 0 1 1
0 -1 1 0 -4 0 -1 -2 -2 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 1 -1 1 1 0 0 1 0 1
0 0 0 1 -3 0 -1 0 -1 -1 1 0 0 0 1 0 1 0 0 1 0 -1 0 1 1 1 1 0 0 0 0 0
1 1 1 0 1 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
-1 -1 -1 0 -2 0 -1 -1 0 1 1 0 -1 1 0 1 0 1 1 -1 0 1 0 1 0 0 0 0 0 0 -1 0
6 2 0 3 -2 -1 -1 -3 1 1 2 -1 -1 1 2 2 2 2 1 -2 2 1 1 -1 0 1 0 0 1 1 0 0
-2 -1 0 -1 2 -1 2 1 0 0 -1 0 0 -1 0 0 0 -1 0 1 -1 -1 0 -1 0 0 1 0 0 0 0 0
-2 1 0 -1 0 -1 1 2 -1 0 0 1 0 0 -1 -1 -1 -1 -1 2 -1 -2 -1 1 1 1 1 0 0 0 0 0
2 2 1 0 -2 -1 -1 1 -2 -1 1 1 0 0 0 -1 0 1 -1 1 0 -1 0 1 1 0 0 0 -1 0 -1 0
-5 -1 0 -3 4 -1 3 2 -1 0 -3 1 1 0 -3 -2 -1 -3 -1 2 -2 -1 -1 0 -1 0 1 -1 0 0 1 1
0 -1 -1 1 -5 2 -3 -1 -1 -1 2 0 0 0 2 1 0 1 1 -1 0 0 0 1 1 0 0 0 0 0 -1 -1
1 0 -2 1 -2 0 -1 -1 0 0 2 -1 0 0 2 2 0 2 1 -1 0 0 0 0 1 0 0 0 0 0 -1 -1
32 32
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
-1 -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
-1 -1 -1 -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
1 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 1 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 1 0 0 1 -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 1 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
-1 -1 0 0 -2 1 -1 -1 -1 -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 1 0 1 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
-1 -1 0 0 -1 1 -1 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
-1 -1 -1 0 1 -1 1 -1 1 1 -1 -1 0 0 0 1 1 0 0 0 0 0 0 -1 0 1 1 0 1 1 1 0
2 1 0 1 -2 0 -1 1 -1 -1 2 0 0 0 1 0 0 0 0 0 0 -1 0 1 1 0 0 0 0 0 -1 0
-3 -1 -1 -1 -1 -1 1 2 -1 -1 0 1 0 0 -1 0 0 -1 -1 2 -1 -2 -1 1 1 1 1 0 0 0 0 0
-3 0 0 -2 1 0 1 2 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 1 0 0 0 0 -1 -1 0 0
1 0 1 0 -1 2 -1 1 -1 -1 0 0 1 -1 0 -1 -1 0 0 0 0 0 0 1 0 -1 -1 0 -1 -1 -1 0
-2 -1 0 -1 -3 1 -2 -1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
3 1 0 2 0 0 -2 -2 2 1 1 -1 -2 1 1 1 0 2 1 -2 2 2 1 -1 0 0 -1 1 0 0 0 0
2 1 -1 1 -1 -1 0 1 -1 -1 2 1 0 0 1 1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 -1
-2 0 -1 -1 2 -1 2 2 0 0 0 1 0 0 -1 0 -1 -1 -1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0
-1 1 1 -1 1 0 1 2 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 0 0 0 0 -1 0 0 0
-5 -2 0 -3 2 1 1 3 -1 -1 -2 1 1 -1 -2 -2 -2 -2 -1 2 -2 -1 -1 1 0 -1 0 0 -1 -1 0 0
1 0 1 1 -4 0 -1 -2 -2 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 1 0 1 1 0 0 1 0 1
-1 0 0 0 0 -1 1 0 -1 0 0 0 1 0 0 0 1 -1 0 1 -1 -1 -1 0 0 1 1 -1 1 1 1 0
1 1 1 0 -1 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 -1 1 -2 0 -1 -1 0 1 2 0 -1 1 1 1 0 1 1 -1 0 0 0 1 0 0 0 0 0 0 -1 0
1 1 0 0 2 -2 2 -1 0 1 -1 0 0 0 -1 0 1 -1 0 0 0 0 0 -1 -1 0 1 -1 1 1 1 1
-2 -1 0 -1 0 0 1 1 -1 -1 -1 0 1 -1 0 0 0 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 1 1 0 0 0 0 0 0
2 2 1 0 -2 -1 -1 1 -2 -1 1 1 0 0 0 -1 0 0 -1 1 0 -1 0 1 1 0 0 0 -1 0 -1 0
-2 0 0 -1 1 0 1 2 -1 -1 -1 1 1 0 -1 -1 -1 -1 -1 1 -1 -1 -1 1 0 0 0 0 -1 -1 0 0
0 -1 -1 1 -3 2 -2 -1 0 0 2 -1 0 0 2 1 0 1 1 -1 0 0 0 0 1 0 0 0 1 0 -1 -1
1 0 -1 1 -3 0 -1 0 -1 -1 2 0 0 0 1 1 0 1 0 0 0 -1 0 1 1 0 0 0 0 0 -1 -1
-
PROPERTIES
Unimodular=1
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REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
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NOTES
Called LAMBDA_32'' in Bachoc-Nebe
As Z-lattice isometric to the Barnes-Wall lattice.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe