The Lattice MxA8
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 13:11:29 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
KISSING_NUMBER
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
HERMITE_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
MxA8
-
DIMENSION
32
-
KISSING_NUMBER
864
-
GRAM
32 0
14
0 14
0 0 14
-7 7 7 14
6 -2 -2 -6 36
2 6 -2 2 0 36
2 2 6 2 0 0 36
0 4 4 6 -18 18 18 36
8 0 2 -2 16 2 2 -3 16
0 8 2 4 -2 16 6 11 0 16
-2 -2 8 4 -2 -6 16 7 0 0 16
-6 4 4 8 -13 5 9 16 -8 8 8 16
2 0 2 0 11 -5 1 -5 10 0 2 -3 12
0 2 0 0 5 11 5 5 0 10 2 5 0 12
-2 0 2 2 -1 -5 11 1 -2 -2 10 5 0 0 12
-2 2 0 2 -6 6 10 11 -7 5 5 10 -6 6 6 12
-5 -7 -3 -3 3 -7 -7 -9 -3 -7 -1 -3 0 -2 0 -2 8
7 -5 -1 -5 7 3 -1 1 7 -3 -1 -5 2 0 -2 -2 0 8
3 1 -5 -7 7 1 3 -5 1 1 -3 -5 0 2 0 0 0 0 8
8 0 2 -5 6 2 8 3 6 2 2 -3 2 2 0 0 -4 4 4 8
1 1 -1 0 -7 3 -1 4 -1 -1 -5 -3 -4 -4 -4 -2 -2 0 0 0 8
-1 1 1 2 -3 -7 -1 -2 1 -1 -1 1 4 -4 0 -2 0 -2 -2 -2 0 8
1 -1 1 0 1 1 -7 -2 5 1 -1 -3 4 0 -4 -6 0 2 -2 0 0 0 8
-1 -1 1 1 3 -5 -5 -7 4 -2 2 -1 6 -2 2 -4 2 0 -2 -2 -4 4 4 8
2 -2 -2 -2 -4 4 -2 3 -3 -1 -5 -1 -5 -1 -3 2 0 2 0 0 4 0 -2 -4 8
2 2 2 2 -4 -4 0 1 1 -3 1 1 1 -5 3 0 -2 0 -2 0 0 4 -2 2 0 8
2 -2 2 -2 2 0 -4 -1 5 -1 -3 -5 3 -3 -5 -6 0 2 0 2 2 2 4 2 0 0 8
0 0 4 2 1 -5 -3 -4 4 -4 2 -3 3 -5 1 -5 0 0 -2 0 0 2 2 4 -4 4 4 8
0 -2 0 -1 -10 -16 -4 -5 -5 -7 1 0 -1 -7 1 -2 2 -2 -2 -2 0 4 0 2 0 4 0 2 12
2 0 0 -1 16 -10 0 -11 7 -5 1 -6 7 -1 1 -4 2 2 2 2 -4 0 0 2 -4 0 0 2 0 12
0 0 0 -1 4 0 -10 -15 -1 -1 -5 -6 -1 -1 -1 -4 2 -2 2 -2 0 0 0 2 0 0 0 2 0 0 12
1 1 1 0 15 1 5 -10 5 1 1 -5 3 3 3 -1 0 0 4 2 -2 -2 -2 0 -2 -2 -2 0 -6 6 6 12
-
DIVISORS (elementary divisors)
2^16
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
2.83
-
HERMITIAN_GROUP_ORDER
2^8 * 3^4 * 5 * 7
-
HERMITIAN_GROUP_GENERATORS
3
32 32
1 -1 -1 1 -1 1 2 -1 -2 2 1 -6 0 0 -1 1 1 -3 -4 2 -1 0 -1 2 0 1 -1 -1 -3 3 1 -5
1 0 0 1 -2 1 1 -3 3 -1 -5 4 0 -1 0 1 5 -3 -2 6 -1 -2 1 0 1 -1 -2 3 1 -2 -4 3
0 0 1 -1 -1 0 -1 1 1 4 2 -2 1 -1 -1 1 1 1 2 -4 1 -2 -3 2 2 0 0 1 2 2 -1 1
0 0 1 0 -1 1 -1 -1 5 -1 -2 5 0 -1 0 0 2 -1 3 0 -1 -1 0 -2 2 -2 -1 3 4 -2 -3 4
2 0 -3 3 -7 2 5 -7 2 -5 -5 8 -2 1 -1 -3 6 -2 -3 9 -5 1 4 -4 0 1 1 1 -7 4 0 -1
0 -1 0 3 0 -2 -2 -3 2 -3 3 2 3 -3 -4 5 -4 3 6 -3 -1 -1 0 -4 -3 1 2 -3 -3 -7 -1 1
3 -3 -1 3 -3 5 -2 -3 0 -3 -1 -2 2 2 0 -1 1 -7 -1 5 -3 3 -2 -2 0 -2 -2 3 4 -3 -10 7
0 -3 0 2 2 3 -2 -3 -3 0 5 -6 4 -2 -1 3 -6 -1 2 -2 0 3 -1 -4 -2 0 -1 -1 1 -4 -4 -2
1 -1 -1 2 -4 1 2 -3 2 -2 -1 1 0 -1 -2 1 1 -2 1 2 -5 1 2 -3 1 -1 -1 2 -4 2 0 -2
0 0 1 0 0 -2 -1 -1 2 1 0 1 2 -2 -1 3 -1 2 3 -4 0 -3 -1 -1 0 0 1 0 0 -4 -2 2
0 -1 0 0 -1 2 -2 -1 -1 1 3 -3 1 0 0 -1 -3 0 1 -2 -1 2 -3 -1 0 -1 0 0 2 0 -4 2
-1 0 1 -1 1 1 -1 -2 0 1 2 0 1 -1 1 0 -3 3 2 -4 1 1 -1 -3 -1 0 1 -1 2 -2 -2 0
0 0 0 0 -4 1 3 -3 2 -2 -2 3 -1 -1 0 0 0 1 2 -1 -5 2 4 -5 1 -1 0 2 -4 4 2 -3
0 0 0 0 -1 -1 0 -3 1 0 1 1 1 -1 0 0 -2 2 1 -3 -1 -1 -1 -3 -1 1 2 -2 -3 -2 -1 -1
0 0 0 0 -2 2 -2 -1 0 -1 1 -1 -1 1 0 -2 -1 0 0 1 -2 3 -2 -1 -1 -1 0 0 2 -1 -5 5
0 0 0 0 0 2 -1 -3 -1 0 2 -1 0 1 1 -2 -1 1 -1 0 1 2 -2 -2 -2 1 1 -2 1 -2 -4 1
-1 1 0 -1 1 -1 0 1 -1 -1 1 2 -1 1 1 -2 -2 3 1 -2 1 1 1 -1 -1 1 2 -2 -1 1 3 -1
0 -1 -1 1 0 1 1 -1 -2 0 3 -4 0 0 -1 0 -2 -1 -1 0 -1 2 0 -1 -1 1 0 -2 -3 2 2 -5
1 0 -1 1 -1 0 1 -1 -2 -1 -2 0 0 1 0 0 2 -1 -3 4 0 0 1 1 -1 1 0 0 -2 0 -1 1
1 -1 -1 1 -1 1 1 -1 -3 2 1 -5 1 0 -1 1 1 -2 -3 2 0 0 -1 2 0 1 -1 0 -2 2 -1 -2
1 -1 0 1 1 0 -1 2 1 -1 -1 -1 1 0 -1 2 1 -4 0 2 0 -1 0 2 1 -1 -2 2 2 -2 -1 2
0 1 1 -1 -1 0 1 0 3 0 -2 3 -1 0 1 0 2 1 2 -2 -1 0 2 -2 1 -1 0 2 1 1 1 0
-1 0 1 -1 1 -2 -1 2 0 2 3 -3 1 -2 -1 2 -4 2 3 -6 -1 -1 -1 0 1 -1 0 0 -1 0 2 -2
-1 1 1 -1 -1 -1 0 0 2 0 1 2 -1 -1 0 0 -2 4 4 -5 -2 1 1 -3 0 -1 1 0 -1 1 2 -1
0 0 0 0 1 0 0 1 0 1 1 -2 0 1 0 0 1 -1 -1 0 2 -1 -1 2 0 1 0 -1 1 0 1 -1
0 0 0 0 -1 1 1 -1 0 1 -1 0 -1 0 0 0 2 0 -1 2 0 1 1 0 0 0 -1 1 0 2 0 -1
0 0 0 0 0 -1 0 1 0 1 1 0 1 -1 -1 2 0 1 2 -2 0 -1 1 0 1 0 0 1 -1 1 2 -1
0 0 0 0 -1 0 0 0 1 0 -1 2 0 -1 -1 1 1 0 1 1 -1 0 1 0 1 -1 -1 2 0 1 0 1
-1 1 1 -3 3 0 0 4 -3 4 1 -5 -1 1 2 -1 0 0 -3 -2 3 0 -1 4 1 0 -1 0 3 3 2 -2
1 0 -2 1 -4 3 4 -4 0 -2 -4 3 -2 1 1 -3 5 -3 -5 8 -3 2 3 -2 1 0 -1 2 -3 5 0 -2
0 2 1 -1 0 -4 -1 4 3 1 -2 3 -1 0 -1 1 3 2 2 -2 1 -4 -1 4 1 0 1 0 1 -1 2 4
2 0 -1 2 -4 0 0 -1 4 -3 -4 5 -1 1 -1 -1 5 -3 0 5 -3 -1 0 0 1 -1 0 2 0 -1 -3 6
32 32
1 0 0 0 0 -1 -1 2 0 2 0 -2 0 0 0 0 1 -1 0 0 0 -1 -1 2 2 -1 -1 2 1 0 -1 2
0 1 0 0 0 -1 1 0 0 0 -2 2 0 0 0 0 1 1 0 0 0 -1 1 0 0 1 1 0 -1 0 1 0
0 0 1 0 0 -1 -1 0 2 0 0 2 0 0 0 0 -1 1 2 -2 0 -1 -1 0 0 -1 1 0 1 -2 -1 2
0 0 0 1 -1 0 1 -2 2 -2 -2 4 0 0 0 0 0 1 1 0 -1 0 1 -2 -1 0 1 0 -1 -1 0 0
0 0 0 0 2 2 0 0 -3 0 3 -4 0 0 0 0 -1 -1 -2 1 1 2 0 0 -1 1 -1 -2 0 2 1 -3
0 0 0 0 -2 2 0 0 1 0 -1 -2 0 0 0 0 2 -3 -1 3 -2 1 0 0 2 -2 -3 4 0 1 -2 1
0 0 0 0 2 -2 0 4 -3 4 1 -4 0 0 0 0 1 0 -1 -1 2 -2 -1 4 2 1 0 0 1 1 1 1
0 0 0 0 0 -2 -2 4 1 3 0 -2 0 0 0 0 1 -1 1 -1 0 -2 -2 3 3 -2 -1 3 2 -1 -2 4
0 0 0 0 2 0 -1 2 -2 2 3 -4 0 0 0 0 -1 0 -1 -1 2 0 -1 2 0 1 0 -2 1 1 1 -1
0 0 0 0 -1 1 1 0 -1 1 -1 -2 0 0 0 0 2 -2 -2 3 -1 1 1 0 1 0 -2 2 -1 2 0 -1
0 0 0 0 1 -2 0 2 -1 2 0 0 0 0 0 0 1 1 0 -1 1 -2 0 2 1 1 1 0 0 0 1 1
0 0 0 0 -1 -1 0 1 1 1 -2 1 0 0 0 0 2 -1 0 1 -1 -1 0 1 2 -1 -1 3 0 0 -1 2
0 0 0 0 2 0 -1 2 -3 2 3 -4 1 0 0 0 -1 0 -1 -1 2 0 -1 2 0 1 0 -2 1 1 1 -1
0 0 0 0 -1 1 1 0 -1 0 -1 -2 0 1 0 0 2 -2 -2 3 -1 1 1 0 1 0 -2 2 -1 2 0 -1
0 0 0 0 1 -2 0 2 -1 2 -1 0 0 0 1 0 1 1 0 -1 1 -2 0 2 1 1 1 0 0 0 1 1
0 0 0 0 -1 -1 0 1 1 1 -2 0 0 0 0 1 2 -1 0 1 -1 -1 0 1 2 -1 -1 3 0 0 -1 2
0 0 0 0 0 1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 0 -1 0 0 0 -1
0 0 0 0 0 0 -1 1 0 1 1 -2 0 0 0 0 0 0 0 0 0 0 -1 1 1 -1 -1 1 1 0 -1 1
0 0 0 0 1 0 0 1 -2 1 1 -2 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 -1 0 1 1 -1
0 0 0 0 1 -1 -1 2 -1 2 1 -2 0 0 0 0 0 0 0 0 1 -1 -1 2 1 0 0 0 1 0 0 1
0 0 0 0 0 0 0 -1 1 -1 0 2 0 0 0 0 -1 1 1 -1 1 0 0 -1 -1 0 1 -1 0 -1 0 0
0 0 0 0 1 0 -1 1 -1 1 2 -2 0 0 0 0 -1 0 0 -1 1 1 -1 1 0 0 0 -1 1 0 0 0
0 0 0 0 0 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 -1 1 0 1 2 -1 -1 1 0 -1 -1 1 1 -2
0 0 0 0 1 0 0 1 -2 1 1 -2 0 0 0 0 0 0 -1 0 1 0 0 2 0 1 0 -1 0 1 1 -1
0 0 0 0 -2 1 0 -2 3 -2 -1 2 0 0 0 0 0 -1 1 1 -2 1 0 -2 1 -2 -1 2 0 -1 -2 1
0 0 0 0 1 -2 -2 2 1 2 1 0 0 0 0 0 -1 1 2 -3 1 -2 -2 2 1 0 1 0 2 -2 -1 3
0 0 0 0 1 1 -1 0 -1 0 3 -2 0 0 0 0 -2 0 0 -1 1 1 -1 0 -1 0 1 -2 1 0 0 -1
0 0 0 0 2 -1 -1 1 -1 1 2 0 0 0 0 0 -2 2 1 -3 2 -1 -1 1 -1 1 2 -2 1 -1 1 0
0 0 0 0 0 -1 0 0 1 0 -1 2 0 0 0 0 0 1 1 -1 0 -1 0 0 0 0 1 0 1 -1 0 1
0 0 0 0 1 0 0 0 -1 0 1 0 0 0 0 0 -1 1 0 -1 1 0 0 0 -1 1 1 -2 0 1 1 -1
0 0 0 0 -1 1 1 -2 1 -2 -1 2 0 0 0 0 0 0 0 1 -1 1 1 -2 -1 0 0 0 -1 0 1 -1
0 0 0 0 0 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 -1 1 0 1 1 -1 -1 1 0 -1 -1 1 1 -1
32 32
-2 1 2 -1 3 -4 -4 6 -1 2 2 -2 0 0 -1 2 -3 4 5 -5 3 -2 -2 5 0 0 1 -1 3 -3 0 5
-2 0 1 -3 2 -1 2 2 -2 1 0 -2 -1 -1 1 0 -4 2 0 -5 -1 1 3 -1 0 1 0 -1 -2 3 5 -5
-1 0 -2 1 0 -2 1 -2 0 0 -1 2 1 -2 -2 2 -1 1 -2 3 0 -3 0 1 -1 1 1 -1 -3 -2 1 -1
-1 1 -1 -2 -2 0 4 -3 0 0 -2 1 -1 -1 0 -1 0 1 -4 1 -3 0 2 -2 0 1 0 0 -5 3 3 -5
0 0 1 0 0 -1 -6 1 -2 -1 9 -3 1 -2 -3 2 -7 4 7 -8 -2 3 -2 -4 -3 1 4 -4 -1 -4 -4 6
-1 1 1 -2 6 -6 -5 11 -5 7 6 -15 3 -2 -1 4 -3 0 -1 -6 3 -4 -6 8 -1 1 0 -4 2 -5 2 2
-1 0 0 0 5 0 0 -1 -10 4 2 -5 1 0 1 -2 -3 4 -3 0 5 1 -1 2 -3 3 0 -2 0 -2 -3 -2
-1 1 0 -1 5 -5 1 4 -6 10 1 -9 1 -1 2 0 1 3 -4 -2 6 -5 -3 7 0 3 -1 -2 -2 0 4 -7
-1 1 1 -1 0 -3 -3 3 -1 2 3 -3 0 -2 -2 2 -3 3 3 -4 -1 -1 -2 2 0 0 1 -1 -1 -2 -1 4
-1 0 0 -1 3 -3 0 3 -2 2 0 -3 2 -2 0 2 -2 0 -1 -2 1 -3 0 2 0 1 0 -1 -1 -2 3 -2
0 0 -1 1 0 0 0 -3 -1 1 0 1 0 0 0 -2 0 1 -2 2 1 -1 -2 0 -1 1 1 -1 -1 -2 -3 0
0 0 -1 0 0 0 3 -3 0 1 -2 1 0 0 2 -2 1 0 -3 1 0 -1 1 -2 0 1 0 0 -3 1 2 -6
0 0 0 0 -2 0 0 -2 2 -1 1 1 0 -2 -1 1 -2 0 2 -2 -4 1 1 -4 1 -1 0 1 -3 0 0 -1
0 0 0 0 2 -2 -2 2 -1 3 2 -3 2 -1 0 1 0 0 0 -2 2 -3 -3 2 0 1 1 -1 1 -3 -1 1
0 0 0 0 0 2 0 -2 -2 0 2 -1 -1 1 1 -3 -2 2 0 -2 0 3 -1 -2 -1 0 1 -1 0 1 -2 -1
0 0 0 0 2 0 0 0 -2 2 1 -1 0 1 2 -2 0 2 0 -2 3 0 -1 0 -1 1 1 -1 1 0 0 -2
2 -1 -1 2 -3 3 0 -4 3 -3 0 3 0 1 0 -1 2 -3 0 3 -2 2 0 -4 0 -1 0 1 0 0 -3 1
0 1 1 0 1 -3 -4 4 0 3 3 -3 0 0 -1 1 0 2 3 -3 2 -2 -4 4 0 0 1 -1 2 -3 -2 5
0 -1 1 0 3 1 -2 2 -3 0 3 -3 1 0 0 1 -3 0 2 -3 2 2 0 0 -1 0 0 -1 3 -1 -1 1
-1 0 1 0 4 -3 -3 4 -3 3 3 -3 1 -1 -1 2 -3 3 3 -4 4 -2 -2 4 -1 1 1 -2 2 -3 0 2
0 0 0 0 1 0 1 2 -2 1 -2 -2 0 0 0 1 2 -1 -2 3 1 0 1 3 0 0 -2 1 1 1 1 0
0 0 0 0 -3 2 3 -4 3 -4 -4 6 -1 0 1 -1 0 0 1 1 -4 2 4 -5 1 -2 -1 3 -2 2 1 -2
0 0 0 0 -1 -2 -1 2 3 1 -1 0 0 -1 -1 1 1 -2 0 1 -1 -3 -2 3 2 -1 -1 1 0 -1 0 2
0 0 0 0 -3 1 0 -2 4 -3 -1 3 -1 0 0 -1 -1 -1 1 0 -4 1 0 -3 1 -2 0 1 -1 0 -1 1
0 0 1 0 1 0 -1 2 0 0 0 -1 0 1 0 0 0 0 2 -1 1 0 -1 2 0 -1 -1 1 3 -1 -1 2
-1 1 1 -2 -1 0 1 0 1 0 -1 1 -1 0 0 0 -1 2 1 -3 -1 0 1 0 1 -1 0 1 0 2 1 0
-1 0 0 0 1 -2 -1 2 0 1 1 -1 1 -1 -1 2 -2 1 1 -1 1 -2 -1 2 0 0 0 -1 0 -1 2 0
-1 1 0 -1 -1 -1 0 0 1 0 0 1 0 -1 -1 1 -1 2 0 -1 -1 -1 0 0 0 0 1 -1 -1 0 1 1
0 0 0 0 -2 2 3 -3 4 -3 -5 8 -2 2 1 -2 3 -1 0 3 0 0 3 -1 2 -1 -1 3 1 3 1 -1
0 0 0 0 -2 1 0 -3 0 -1 3 2 -1 -1 -1 0 -2 3 3 -3 -2 3 2 -5 -1 1 2 -1 -3 2 0 -1
0 0 0 0 -1 1 -1 1 2 -5 -1 2 1 0 -2 2 -1 -2 1 1 -3 1 1 -1 0 -2 0 1 2 -2 -1 5
0 0 0 0 0 1 -2 0 -3 -2 3 -2 1 -1 -2 1 -3 1 1 -1 -2 3 0 -2 -2 0 1 -1 0 -2 -3 4
-
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
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 0
-1 1 1 -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
-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 -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 1 1 -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 -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 -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 1 1 -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 -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 -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 1 1 -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 -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 -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 1 1 -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 -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 -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 1 1 -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 -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 -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 1 1 -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 -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 -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 1 1 -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 -1 0 1 -1
32 32
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 -1 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
-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 -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 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 -1 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 -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 -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 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 -1 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 -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 -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 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 -1 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 -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 -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 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 -1 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 -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 -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 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 -1 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 -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 -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 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 -1 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 -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 -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 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 -1 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 -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 -1 1
32 32
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 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 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
-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 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 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 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 -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 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 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 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 -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 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 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 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 -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 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 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 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 -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 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 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 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 -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 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 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 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 -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 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 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 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 -1 0 0 -1
-
PROPERTIES
Modular=1
UnimodularHermitian=1
-
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