The Lattice L8(P^8)
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 13:11:49 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
L8(P^8)
-
DIMENSION
32
-
DET
1
-
GRAM
32 0
4
2 4
2 2 4
1 1 2 4
1 1 2 3 4
1 1 2 2 2 4
2 1 3 2 2 2 4
2 2 2 2 2 2 2 4
2 2 2 2 2 2 2 3 4
2 2 2 2 2 2 2 3 3 4
1 1 2 2 2 2 2 2 2 2 4
2 1 3 2 2 2 3 2 2 2 2 4
2 2 2 2 2 2 2 2 2 2 2 2 4
2 2 2 2 2 2 2 2 2 2 2 2 3 4
1 1 2 2 2 2 2 2 2 2 2 2 2 2 4
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4
2 1 1 2 2 1 1 1 1 1 1 1 2 2 2 1 4
1 2 1 2 2 1 1 1 1 1 1 1 2 2 2 2 2 4
2 1 2 2 2 2 2 1 1 1 1 2 1 1 1 1 2 1 4
1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 1 4
1 1 2 3 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 4
1 1 2 3 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 3 4
1 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 1 1 1 2 2 2 4
1 1 2 2 2 3 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 4
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 4
1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 1 2 1 4
1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 1 4
2 1 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 1 2 2 2 2 2 2 1 1 4
2 1 1 2 2 1 1 2 2 2 2 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 4
1 2 1 2 2 1 1 2 2 2 1 1 1 1 1 2 1 2 1 1 2 1 2 1 1 2 1 1 2 4
2 1 2 2 2 2 2 3 2 3 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 1 1 2 2 1 4
2 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 3 1 2 2 1 1 1 1 2 1 1 2 2 1 1 4
-
MINIMAL_NORM
2
-
HERMITE_NUMBER
2
-
HERMITIAN_GROUP_ORDER
2^30 * 3^2 * 7
-
HERMITIAN_GROUP_GENERATORS
3
32 32
0 2 -1 2 -1 0 1 -1 0 -1 0 0 -1 0 1 0 0 -1 0 0 1 -2 0 0 0 -1 0 1 0 0 1 0
2 2 -1 -4 5 1 0 -1 -1 -1 0 0 0 -2 1 0 1 -1 -1 -1 1 4 0 0 -1 -1 0 -1 0 0 0 0
-2 2 -1 8 -7 0 1 -1 1 -1 0 1 0 1 2 0 0 -2 0 -1 1 -8 0 0 1 0 0 2 0 0 2 0
0 0 0 -3 2 0 0 -1 0 -1 1 0 0 0 0 -1 0 0 0 0 -1 3 -2 0 0 0 0 1 0 2 1 0
0 0 0 -3 2 0 0 -1 1 -1 1 0 0 -1 0 -1 1 0 0 -1 -1 3 -1 0 0 0 0 0 -2 2 2 1
0 0 0 1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0
0 0 0 2 -2 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 -2 0 0 0 0 0 1 0 0 0 1
2 0 -1 -5 5 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 0 0 0 5 0 0 -1 0 0 0 0 0 -1 0
2 0 -1 -4 4 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 4 0 0 -1 0 0 0 0 0 -1 0
2 0 0 -4 4 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0
-2 2 -1 8 -7 0 1 -1 1 -1 0 1 0 1 1 0 0 -2 0 0 1 -8 0 0 1 0 0 2 0 0 2 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 1 0 0 0 0
4 0 1 -7 8 1 -1 0 -2 0 0 -1 0 -3 0 1 1 0 -2 -1 1 7 0 1 -2 -2 0 -2 0 0 -2 1
-2 0 0 8 -8 0 0 0 1 0 0 0 0 2 0 1 -1 0 2 1 0 -8 0 -1 2 0 -1 3 0 0 1 -1
-2 2 -1 4 -4 0 1 -1 1 -1 0 1 0 0 0 -1 0 0 0 0 0 -4 0 0 1 0 0 2 0 0 2 0
0 1 0 -2 2 0 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 2 -1 0 0 -1 0 1 0 1 1 0
1 1 0 -3 3 1 0 -1 0 -1 1 0 0 -2 0 0 1 0 -1 -1 0 3 -1 0 0 -1 0 -1 -1 1 1 1
-2 2 -1 4 -4 0 1 -1 1 -2 0 1 -1 1 1 -1 0 -1 0 0 0 -4 -1 0 1 0 0 2 0 1 3 0
0 0 0 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 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0
0 0 0 1 -1 0 0 0 -1 0 0 0 0 1 0 0 -1 0 0 1 0 -1 -1 0 0 0 0 2 2 0 -1 -1
0 0 0 -5 3 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 1 3 0 0 -1 0 0 0 0 0 0 1
0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 1 0
-2 2 -1 4 -4 0 1 -1 1 -1 0 1 -2 1 0 -1 0 0 0 0 0 -4 0 0 1 0 0 3 0 0 2 0
-2 2 -1 3 -3 0 1 -1 1 -2 1 1 0 0 1 -1 1 -1 0 -1 0 -3 -1 0 1 0 0 1 -1 1 3 0
-2 2 -1 4 -4 0 1 0 1 -1 0 1 -1 0 0 -1 0 0 0 0 0 -4 0 0 1 0 0 2 0 0 2 0
-2 0 0 6 -6 -1 0 0 1 0 0 0 0 2 0 0 -1 0 2 1 0 -6 0 -1 1 0 0 3 0 0 1 -1
0 1 -1 -4 3 0 1 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 3 -1 0 0 0 0 1 0 1 1 0
1 1 -1 -9 7 0 0 -1 0 -1 1 0 0 -2 0 -1 1 0 0 -1 0 8 -1 0 -1 0 0 -1 -1 1 1 1
0 0 0 1 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0
0 1 0 -3 3 0 0 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 3 -1 0 0 -1 0 1 0 1 1 0
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
-2 2 -1 7 -6 0 1 -1 1 -1 0 1 0 1 1 0 0 -1 0 0 1 -7 0 0 1 0 0 1 0 0 2 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 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
0 0 0 -1 1 0 0 0 -1 0 -1 0 0 1 0 0 -1 0 0 1 0 1 0 0 0 0 0 1 2 0 -1 -1
2 0 -1 -7 7 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 0 0 0 7 0 0 -1 0 0 -1 0 0 -1 0
2 -2 1 -7 6 0 -1 1 -1 1 0 -1 0 -1 -1 0 -1 2 0 1 -1 7 0 0 -1 0 0 -1 0 0 -2 1
-2 2 -1 3 -3 0 1 -1 1 -1 0 1 -1 1 0 -1 0 0 0 0 0 -3 0 0 1 0 0 2 0 0 2 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 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 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 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 0 0 0 0 0
0 0 0 -5 4 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 1 4 0 0 -1 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
1 0 -1 -2 2 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 1 0 2 0 0 0 0 0 0 1 0 -1 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 1 0
0 0 0 -4 3 0 0 -1 1 -1 1 0 0 -1 0 -1 1 0 0 -1 -1 4 0 0 0 0 0 -1 -2 2 2 1
0 0 0 0 0 0 0 0 1 0 1 0 0 -1 0 0 1 0 0 -1 0 0 1 0 0 0 0 -1 -2 0 1 1
-4 0 -1 7 -8 -1 1 0 2 0 0 1 0 3 0 -1 -1 0 2 1 -1 -7 0 -1 2 2 0 3 0 0 2 -1
0 0 -1 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
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 -1 -1 1 0 0 -1 0 -1 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 1 1 0
4 0 -1 -11 11 0 0 0 -2 0 0 0 0 -3 0 0 1 0 -2 -1 0 11 0 1 -2 0 1 -3 0 0 -2 1
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
-1 0 0 5 -5 0 0 0 0 0 0 0 0 2 0 0 -1 0 1 1 0 -5 0 0 1 0 0 2 1 0 0 -1
-4 1 -1 7 -8 -1 1 -1 2 -1 0 1 0 3 0 -1 -1 0 2 1 -1 -7 0 -1 2 1 0 3 0 1 3 -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 1 0 0 0 0
0 0 0 -1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 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
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 -5 4 0 0 -1 0 -1 1 0 0 0 0 -1 0 0 0 0 -1 5 -2 0 0 0 0 0 0 2 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 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 -4 3 0 0 -1 1 -1 2 0 0 -1 0 -1 1 0 0 -1 -1 4 -1 0 0 0 0 -1 -2 2 2 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 0 0
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 -4 3 0 0 -1 1 -1 1 0 0 -1 0 -1 1 0 0 -1 -1 4 -1 0 0 0 0 -1 -1 2 2 1
0 0 0 0 0 0 0 0 1 0 1 0 0 -1 0 0 1 0 0 -1 0 0 0 0 0 0 0 -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 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
-
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
3 0 -1 -10 10 0 0 0 -1 -1 0 0 0 -3 0 -1 1 0 -2 -1 0 10 0 1 -2 0 1 -2 0 0 -1 1
2 1 -1 -6 6 0 1 0 -1 -1 0 0 -1 -2 0 -1 1 0 -2 -1 0 6 0 1 -1 0 1 -1 0 0 0 1
6 0 -1 -18 18 0 0 0 -3 0 0 0 0 -5 0 -1 2 0 -4 -2 0 18 0 2 -4 0 2 -5 0 0 -3 2
4 0 0 -13 13 0 0 0 -2 0 0 0 0 -4 0 -1 2 0 -4 -2 -1 14 0 2 -3 0 2 -4 0 0 -2 2
4 0 0 -7 9 0 0 0 -2 0 0 0 0 -3 0 -1 1 0 -4 -1 -1 9 0 2 -2 0 2 -3 0 0 -2 1
8 0 1 -20 21 1 -1 0 -4 0 0 -1 0 -7 0 0 3 0 -6 -3 1 20 0 4 -5 -2 2 -7 0 0 -4 3
4 0 -1 -13 13 0 0 0 -2 0 0 1 0 -4 0 -1 2 0 -4 -2 0 13 0 2 -3 0 2 -4 0 0 -2 2
4 0 0 -13 13 0 0 0 -2 -1 0 0 0 -4 0 -1 2 0 -4 -2 0 13 0 2 -3 0 2 -4 0 0 -1 2
4 0 0 -13 13 0 0 1 -2 -1 0 0 0 -4 0 -1 2 0 -4 -2 0 13 0 2 -3 0 2 -4 0 0 -2 2
4 0 0 -12 12 0 0 0 -1 -1 0 0 0 -4 0 -1 2 0 -4 -2 0 12 0 2 -3 0 2 -4 0 0 -1 2
4 0 0 -10 11 0 0 1 -3 1 -1 0 0 -3 0 0 1 0 -4 -1 1 10 0 2 -3 0 2 -3 2 -2 -4 1
6 0 -1 -19 19 0 -1 0 -3 0 0 0 0 -5 0 -1 2 0 -4 -2 0 19 0 2 -4 0 2 -5 0 0 -3 2
2 2 -1 -10 10 0 1 -1 -1 -1 0 1 -1 -4 0 -2 2 0 -4 -2 0 10 0 2 -2 0 2 -2 0 0 0 2
4 0 0 -12 12 0 0 0 -2 0 0 0 0 -4 0 -1 2 0 -4 -2 0 12 0 2 -3 0 2 -3 0 0 -2 2
6 -2 1 -19 18 0 -1 1 -3 1 0 -1 0 -5 -1 -1 1 2 -4 -1 -1 19 0 2 -4 0 2 -5 0 0 -4 3
4 0 0 -12 12 0 0 0 -2 0 0 0 0 -4 0 -1 2 0 -4 -2 0 12 0 2 -2 0 2 -4 0 0 -2 2
4 -2 1 -11 11 0 -1 1 -2 1 0 -1 0 -3 -1 -1 0 2 -2 0 -2 12 0 1 -2 0 1 -2 0 0 -3 1
2 0 0 -6 6 0 0 0 -1 0 0 0 -1 -2 0 -1 0 1 -2 -1 -1 7 0 1 -1 0 1 -1 0 0 -1 2
4 0 -1 -10 11 0 0 0 -2 0 0 0 0 -3 0 -1 1 0 -3 -1 -1 11 0 2 -2 0 1 -3 0 0 -2 1
6 -2 1 -20 19 0 -1 1 -3 1 0 -1 0 -5 -2 -1 2 2 -4 -1 -1 20 0 2 -4 0 2 -5 0 0 -4 2
4 0 0 -17 16 0 0 0 -2 0 0 0 0 -5 0 -1 3 0 -4 -3 0 17 0 2 -4 0 2 -5 0 0 -2 3
4 0 0 -19 17 0 0 0 -2 0 0 0 0 -5 0 -1 3 0 -4 -3 0 18 0 2 -4 0 2 -5 0 0 -2 3
4 0 0 -9 10 0 0 1 -2 1 0 0 0 -4 0 0 2 0 -4 -2 1 9 1 2 -3 0 2 -4 0 -2 -3 2
6 0 0 -19 19 0 0 0 -3 0 0 0 0 -6 0 -1 3 0 -6 -3 0 19 0 3 -4 0 2 -6 0 0 -3 3
4 0 0 -14 14 0 0 0 -2 0 0 0 0 -4 0 -2 2 0 -4 -2 0 14 0 2 -3 0 2 -4 0 0 -2 2
6 0 0 -14 15 1 0 0 -3 0 0 -1 0 -5 0 0 2 0 -4 -2 0 15 0 2 -3 -1 1 -5 0 0 -3 2
2 0 0 -5 5 0 0 0 -1 0 0 0 0 -2 0 -1 1 0 -2 -1 0 5 0 2 -1 0 1 -2 0 0 -1 1
4 0 0 -14 14 0 0 0 -2 0 0 0 0 -5 0 -1 2 0 -4 -2 0 14 0 2 -3 0 2 -4 0 0 -2 2
2 0 0 -1 3 0 0 1 -1 0 -1 0 0 -1 0 0 0 0 -2 0 0 2 1 1 -1 0 1 -1 1 -2 -2 0
2 0 0 -2 3 0 0 1 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 3 1 1 -1 0 1 -2 0 -1 -1 1
4 0 0 -13 13 0 0 -1 -1 -1 0 0 0 -4 0 -1 2 0 -4 -2 0 13 0 2 -3 0 2 -4 0 0 -1 2
2 0 0 -5 6 0 0 0 -1 0 0 0 0 -2 -1 -1 1 0 -2 0 -1 6 0 1 -1 0 1 -1 0 0 -1 0
32 32
-1 0 0 4 -4 0 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 -4 0 0 1 0 0 1 0 0 1 0
-2 -1 1 10 -10 0 0 0 1 1 0 0 0 3 0 1 -1 0 2 1 0 -10 0 -1 2 0 -1 2 0 0 1 -1
-2 0 0 7 -7 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 -7 0 0 2 0 0 1 0 0 1 0
0 0 0 -4 2 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 1 3 0 0 0 0 0 -1 0 0 0 1
0 0 0 -3 2 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 3 0 0 0 0 0 -1 0 0 0 1
2 0 0 -5 5 1 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 5 0 0 0 0 0 -2 0 0 -1 1
-2 0 0 6 -6 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 -6 0 0 2 0 0 1 0 0 1 0
0 0 0 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0
0 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 1 0 0 0 0 0 1 0
0 0 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 1 0
0 0 0 1 -1 0 0 0 1 0 1 0 0 -1 0 0 1 0 0 -1 0 -1 0 0 1 0 0 -1 -2 0 1 1
0 0 -1 1 -1 0 1 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 0 2 -2 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 -2 0 0 1 0 0 1 0 0 0 0
2 -2 1 -2 2 0 -1 1 -1 1 0 -1 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 -1 0 0 -2 0
0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 -1 0 -1 0 0 1 0 0 0 0 0 0 1
-4 0 0 14 -14 0 0 0 2 0 0 0 0 4 0 1 -2 0 4 2 0 -14 0 -2 4 0 -2 4 0 0 2 -2
0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 1
-2 0 0 4 -5 0 0 0 1 0 0 0 0 2 1 1 0 -1 2 -1 1 -5 0 -1 1 0 -1 1 0 0 1 0
0 0 0 -1 0 1 1 0 0 0 0 0 0 -1 0 0 1 0 -1 -1 0 1 0 0 0 0 0 -1 0 0 0 1
2 -2 1 -5 4 0 -1 1 -1 1 0 -1 0 -1 0 0 -1 2 0 0 -1 5 0 0 0 0 0 -1 0 0 -2 1
0 0 0 -5 3 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 1 3 0 0 0 0 0 -1 0 0 0 1
0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 0
0 0 0 -2 1 0 0 -1 1 -1 2 0 0 -1 0 -1 1 0 0 -1 -1 2 -1 0 1 0 0 -1 -2 2 2 1
-2 0 -1 3 -4 0 1 0 1 0 0 1 0 1 0 -1 0 0 0 0 -1 -3 0 -1 2 2 0 1 0 0 1 0
0 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 1 0 0 0 0 0 0 0
-4 0 0 6 -8 0 1 0 2 0 0 1 0 2 0 0 0 0 2 0 0 -7 0 -2 2 1 -1 2 0 0 2 0
2 0 1 1 0 2 -1 0 -1 0 0 -1 0 -1 0 2 0 0 0 0 1 -1 0 0 0 -2 -1 -1 0 0 -1 0
-2 2 -1 4 -4 0 1 -1 1 -1 0 1 -2 1 0 -1 0 0 0 0 0 -4 0 0 2 0 0 2 0 0 2 0
0 0 0 -1 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 -1 0 1 0 0 0 0 0 -1 -1 0 1 1
-2 0 0 1 -3 0 0 -1 1 0 1 0 0 1 0 0 0 0 2 0 0 -2 -1 -1 1 0 -1 1 0 1 2 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
2 -2 1 -8 6 0 -1 1 -1 1 0 -1 -1 -1 -1 0 0 2 0 0 -1 8 0 0 -1 0 0 -1 0 0 -2 1
32 32
1 1 -1 -6 6 0 1 0 -1 -1 0 0 -1 -2 0 -1 1 0 -2 -1 0 6 0 1 -1 0 1 -1 0 0 0 1
-1 0 0 4 -4 0 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 -4 0 0 1 0 0 1 0 0 1 0
2 0 -1 -5 5 0 1 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 5 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -6 5 0 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 6 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -4 4 0 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 5 0 1 -1 0 1 -2 0 0 -1 1
4 0 0 -11 11 0 0 0 -2 0 0 0 0 -4 0 0 2 0 -4 -2 0 11 0 2 -2 0 1 -4 0 0 -2 2
2 0 -1 -6 6 0 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 6 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -6 6 0 0 0 -2 0 0 0 0 -2 0 0 1 0 -2 -1 0 6 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -5 5 0 0 1 -2 0 0 0 0 -2 0 0 1 0 -2 -1 0 5 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -5 5 0 0 0 -1 -1 0 0 0 -2 0 0 1 0 -2 -1 0 5 0 1 -1 0 1 -2 0 0 0 1
2 0 0 -2 3 0 0 1 -1 1 -1 0 0 -2 0 1 1 0 -2 -1 1 2 1 1 -1 0 1 -2 0 -2 -2 1
4 0 -1 -11 11 0 0 0 -2 0 0 -1 0 -3 0 0 1 0 -2 -1 0 11 0 1 -2 0 1 -3 0 0 -2 1
0 2 -1 -2 2 0 1 -1 0 -1 0 1 -2 -1 0 -1 1 0 -2 -1 0 2 0 1 0 0 1 0 0 0 1 1
2 0 0 -5 5 0 0 0 -1 0 0 0 -1 -2 0 0 1 0 -2 -1 0 5 0 1 -1 0 1 -1 0 0 -1 1
4 -2 1 -12 11 0 -1 1 -2 1 0 -1 0 -3 -1 0 0 2 -2 -1 -1 12 0 1 -2 0 1 -3 0 0 -3 2
0 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 1 0 0 0 0 0 0 0
2 0 0 -6 6 0 0 0 -1 0 0 0 -1 -2 0 -1 0 1 -2 -1 -1 7 0 1 -1 0 1 -1 0 0 -1 1
0 0 0 -2 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 2 0 0 0 0 0 0 0 0 0 1
2 0 -1 -6 6 0 1 0 -1 0 0 0 0 -2 0 -1 1 0 -3 -1 -1 7 0 1 -1 1 1 -2 0 0 -1 1
4 -2 1 -12 11 0 -1 1 -2 1 0 -1 0 -3 -1 0 1 2 -2 -1 -1 12 0 1 -2 0 1 -3 0 0 -3 1
2 0 0 -11 9 0 0 0 -1 0 0 0 0 -3 0 0 2 0 -2 -2 0 10 0 1 -2 0 1 -3 0 0 -1 2
2 0 0 -7 6 0 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 6 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -5 5 0 0 0 0 0 1 0 0 -3 0 0 2 0 -2 -2 0 5 0 1 -1 0 1 -3 -2 0 0 2
0 0 -1 -4 3 -1 1 0 0 0 0 1 0 -1 0 -1 1 0 -2 -1 -1 4 0 0 0 2 1 -1 0 0 0 1
4 0 0 -12 12 0 0 0 -2 0 0 0 0 -4 0 -1 2 0 -4 -2 0 12 0 2 -3 0 2 -4 0 0 -2 2
0 0 0 -2 1 0 1 0 0 0 0 0 0 -1 0 0 1 0 -1 -1 0 2 0 0 0 0 0 -1 0 0 0 1
2 0 0 -4 4 1 0 0 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 4 0 1 -1 0 0 -2 0 0 -1 1
0 2 -1 -3 3 0 1 -1 0 -1 0 1 -1 -2 0 -1 1 0 -2 -1 0 3 0 1 0 0 1 -1 0 0 1 1
2 0 0 -2 3 0 0 1 -1 0 0 0 0 -2 0 0 1 0 -2 -1 0 3 1 1 -1 0 1 -2 -1 -1 -1 1
0 0 0 -1 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 -1 0 1 0 0 0 0 0 -1 -1 0 1 1
2 0 0 -6 6 0 0 0 -1 -1 0 0 0 -2 0 0 1 0 -2 -1 0 6 0 1 -1 0 1 -2 0 0 -1 1
2 0 0 -6 6 0 0 0 -1 0 0 0 -1 -2 -1 -1 1 1 -2 0 -1 7 0 1 -1 0 1 -1 0 0 -1 0
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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
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe