The Lattice L8(P^2)
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 13:11:46 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^2)
-
DIMENSION
32
-
DET
1
-
GRAM
32 0
4
2 4
2 2 4
2 2 2 4
2 1 1 0 4
2 2 1 2 1 4
2 2 2 2 1 2 4
2 2 2 2 1 2 2 4
1 1 1 2 1 2 1 1 4
1 1 2 2 0 2 1 2 1 4
1 2 2 2 1 2 2 2 2 2 4
1 1 2 1 1 2 1 2 2 2 2 4
1 1 1 1 0 1 1 1 1 1 1 2 4
1 1 1 1 1 1 0 1 1 1 1 2 2 4
2 1 1 2 1 1 1 1 1 1 0 1 1 2 4
1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 4
1 1 1 2 1 1 1 1 2 1 1 2 2 2 2 1 4
2 1 1 0 2 1 1 1 0 1 0 1 2 1 2 1 1 4
0 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 1 4
1 1 1 1 1 1 0 1 2 1 2 2 2 2 1 2 2 1 1 4
1 1 1 1 0 1 1 1 1 1 1 2 2 2 2 1 2 1 1 2 4
1 0 2 1 1 0 1 1 1 1 1 2 2 2 1 1 2 1 2 2 2 4
1 2 1 1 0 2 2 2 1 1 1 2 2 1 1 1 1 1 2 1 2 1 4
2 2 1 1 1 2 2 1 1 1 1 1 2 1 1 2 1 2 1 1 1 1 2 4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 1 4
1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 3 1 1 1 2 1 1 1 1 1 4
1 2 1 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 1 1 1 1 1 1 2 4
1 1 1 1 1 2 1 1 2 1 1 2 2 2 1 1 2 1 2 2 2 2 2 2 2 1 1 4
1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 3 1 1 1 2 1 1 1 2 1 3 2 1 4
1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 4
1 2 1 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 1 1 1 1 1 1 2 3 1 2 1 4
0 0 0 0 0 1 0 0 1 0 0 2 2 2 1 1 2 1 2 2 2 2 2 1 2 1 1 2 1 1 1 4
-
MINIMAL_NORM
2
-
HERMITE_NUMBER
2
-
HERMITIAN_GROUP_ORDER
2^20 * 3^2 * 5
-
HERMITIAN_GROUP_GENERATORS
11
32 32
-1 3 -2 1 2 -3 3 0 0 2 -2 4 4 -1 2 0 -4 -3 -2 -1 -1 -2 -5 0 3 0 0 1 0 0 0 3
-2 4 -3 1 2 -3 4 1 0 2 -3 5 5 -1 3 0 -5 -4 -3 -1 -2 -1 -6 0 4 0 0 1 0 0 0 3
-3 5 -4 2 4 -4 5 1 0 3 -4 7 7 -1 3 0 -7 -5 -4 -2 -2 -2 -8 0 6 0 0 1 0 0 0 4
-3 5 -4 3 4 -5 5 1 0 3 -4 7 7 -1 3 0 -7 -5 -4 -2 -2 -3 -8 0 6 0 0 2 0 0 0 4
-1 1 0 -1 1 0 1 0 0 1 -1 1 2 -1 2 0 -1 -2 -1 0 -1 0 -2 0 1 0 0 0 0 0 0 1
3 -4 2 0 -4 2 -2 -2 0 -2 2 -3 -7 1 -4 0 5 5 4 3 2 1 6 0 -5 0 0 -1 0 0 0 -4
3 -6 4 -1 -6 6 -4 -3 0 -4 3 -6 -10 2 -6 0 9 8 5 4 3 3 10 0 -7 0 0 -3 0 0 0 -7
-2 3 -2 1 2 -3 3 1 0 2 -2 4 4 -1 2 0 -4 -3 -2 -1 -1 -2 -5 0 3 0 0 1 0 0 0 3
-4 8 -5 0 7 -7 7 3 1 6 -5 8 13 -3 8 0 -11 -11 -6 -4 -4 -4 -13 0 9 0 0 3 0 0 0 8
-1 1 -2 3 1 -3 3 0 0 1 -2 4 1 1 -1 0 -3 0 -1 0 0 -2 -3 0 2 0 0 1 0 0 0 1
-2 3 -2 0 2 -2 3 1 0 2 -2 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 0 0 1 0 0 0 2
-4 8 -5 0 7 -7 7 3 0 6 -5 9 13 -3 8 0 -11 -11 -6 -4 -4 -4 -13 0 9 0 0 3 0 0 0 8
-4 8 -5 0 7 -7 7 3 0 6 -5 8 14 -3 8 0 -11 -11 -6 -4 -4 -4 -13 0 9 0 0 3 0 0 0 8
-5 10 -7 1 8 -9 8 3 0 7 -6 11 15 -3 9 0 -13 -12 -8 -5 -5 -4 -15 0 11 0 0 4 0 0 0 9
-3 5 -4 2 4 -5 5 1 0 3 -4 7 7 -1 4 0 -7 -5 -4 -2 -2 -3 -8 0 6 0 0 2 0 0 0 4
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 1 -4 -4 -3 -1 -2 -1 -5 0 4 0 0 1 0 0 0 2
-4 8 -5 0 7 -7 7 3 0 6 -5 8 13 -3 8 0 -10 -11 -6 -4 -4 -4 -13 0 9 0 0 3 0 0 0 8
1 -2 1 0 -2 1 0 -1 0 -1 0 -1 -3 1 -2 0 2 3 2 2 1 0 2 0 -2 0 0 -1 0 0 0 -2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -2 -1 -2 -1 -5 0 4 0 0 1 0 0 0 2
-4 8 -5 0 7 -7 7 3 0 6 -5 8 13 -3 8 0 -11 -11 -6 -3 -4 -4 -13 0 9 0 0 3 0 0 0 8
-4 8 -5 0 7 -7 7 3 0 6 -5 8 13 -3 8 0 -11 -11 -6 -4 -3 -4 -13 0 9 0 0 3 0 0 0 8
-4 7 -4 0 6 -5 6 2 0 5 -5 7 11 -2 6 0 -9 -9 -5 -3 -3 -3 -11 0 8 0 0 2 0 0 0 6
1 -2 1 0 -2 1 0 -1 0 -1 0 -1 -3 1 -2 0 2 2 2 2 1 0 3 0 -2 0 0 -1 0 0 0 -2
1 -2 1 0 -2 1 0 -1 0 -1 0 -1 -3 1 -2 0 2 2 2 2 1 0 2 1 -2 0 0 -1 0 0 0 -2
1 -2 1 0 -2 1 0 -1 0 -1 0 -1 -3 1 -2 0 2 2 2 2 1 0 2 0 -1 0 0 -1 0 0 0 -2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 1 0 1 0 0 0 2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 0 1 1 0 0 0 2
2 -2 1 -2 -2 2 -1 -1 0 0 1 -3 -3 0 -1 0 3 1 3 2 1 1 3 0 -3 0 0 -1 0 0 0 -2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 0 0 1 1 0 0 2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 0 0 1 0 1 0 2
-2 3 -2 0 2 -2 3 1 0 2 -3 4 5 -1 3 0 -4 -4 -3 -1 -2 -1 -5 0 4 0 0 1 0 0 1 2
1 0 0 -1 0 -1 1 0 0 1 -1 0 0 0 0 0 0 -1 1 1 0 -1 0 0 0 0 0 0 0 0 0 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 3 -1 -1 3 -1 1 1 0 2 -1 2 6 -2 4 0 -3 -5 -3 -2 -2 0 -4 0 3 0 0 1 0 0 0 3
1 -2 2 -2 -3 4 -3 -1 0 -2 2 -3 -4 0 -1 0 4 3 2 1 1 3 4 0 -3 0 0 -1 0 0 0 -3
-2 3 -2 0 2 -2 2 1 0 2 -1 3 4 -1 3 0 -3 -3 -3 -2 -2 0 -4 0 3 0 0 1 0 0 0 3
4 -8 5 0 -6 6 -6 -3 0 -5 4 -7 -12 3 -8 0 10 10 6 4 4 2 12 0 -8 0 0 -3 0 0 0 -7
-1 1 -1 1 1 -2 1 0 0 1 0 2 2 0 1 0 -2 -1 -2 -1 -1 -1 -2 0 2 0 0 1 0 0 0 2
0 -1 0 1 -1 1 -1 -1 0 -1 1 0 -2 1 -1 0 1 2 0 0 0 1 2 0 -1 0 0 0 0 0 0 -1
-1 0 0 0 -1 1 0 0 0 -1 0 1 0 1 0 0 0 1 -1 0 -1 1 0 0 1 0 0 0 0 0 0 -1
7 -13 7 0 -12 10 -9 -6 0 -8 8 -13 -23 6 -14 0 18 19 10 8 6 6 22 -1 -15 -1 0 -5 0 0 0 -13
-3 5 -3 -1 3 -3 3 2 0 3 -2 5 8 -2 6 0 -6 -6 -4 -3 -3 -1 -8 0 6 0 0 2 0 0 0 4
0 -3 2 0 -2 3 -3 -1 0 -2 2 -3 -4 1 -2 0 4 4 1 1 1 2 5 0 -3 0 0 -1 0 0 0 -3
5 -10 6 -1 -10 9 -8 -4 0 -7 6 -10 -17 4 -10 0 14 14 8 6 5 5 16 0 -11 0 0 -4 0 0 0 -11
5 -9 5 -1 -9 8 -7 -4 0 -6 5 -9 -15 4 -9 0 13 12 7 5 4 5 15 0 -10 0 0 -4 0 0 0 -10
3 -6 4 0 -6 5 -5 -3 0 -4 3 -6 -11 3 -7 0 9 9 5 4 3 3 11 0 -7 0 0 -3 0 0 0 -7
3 -4 2 0 -4 3 -3 -2 0 -2 2 -4 -8 2 -5 0 6 6 4 3 2 2 7 0 -5 0 0 -2 0 0 0 -4
-1 0 0 2 2 -1 0 0 0 1 -1 0 1 0 -1 0 -1 0 0 0 1 -1 0 0 0 0 1 0 0 -1 -1 1
3 -6 3 0 -6 5 -4 -3 0 -4 3 -5 -11 3 -7 0 9 9 5 4 3 3 10 0 -7 0 0 -3 0 0 0 -7
2 -2 1 -1 -2 2 -2 -1 0 -1 1 -2 -3 1 -2 0 3 2 2 1 1 1 3 0 -2 0 0 -1 0 0 0 -2
5 -9 5 0 -9 7 -7 -4 0 -6 5 -8 -16 4 -10 0 13 13 7 5 4 4 15 0 -10 0 0 -3 0 0 0 -10
2 -6 3 1 -5 5 -4 -3 0 -4 2 -5 -10 3 -7 0 8 9 4 4 3 3 10 0 -6 0 0 -3 0 0 0 -7
3 -6 3 1 -6 5 -4 -3 0 -4 2 -5 -11 3 -7 0 8 9 5 5 3 3 10 0 -7 0 0 -3 0 0 0 -7
3 -6 3 0 -7 6 -5 -3 0 -5 3 -5 -12 3 -7 0 9 10 5 4 3 4 11 0 -7 0 0 -3 0 0 0 -8
3 -6 3 0 -6 5 -4 -3 0 -4 3 -5 -10 3 -6 0 8 8 4 4 2 3 10 0 -6 0 0 -2 0 0 0 -7
3 -6 3 0 -5 5 -5 -3 -1 -4 4 -5 -9 2 -5 0 8 7 4 3 2 3 10 0 -6 0 0 -2 0 0 0 -6
1 -3 1 1 -3 2 -1 -2 0 -2 0 -1 -6 2 -4 0 4 5 2 3 1 1 5 0 -3 0 0 -1 0 0 0 -4
-4 6 -4 4 7 -7 5 2 1 5 -5 6 9 -1 3 0 -9 -6 -4 -3 -1 -4 -9 0 6 0 0 2 0 -1 -1 7
-1 1 -1 2 1 -2 1 0 0 1 -1 2 0 1 -1 0 -1 0 -1 0 0 -1 -1 1 1 0 0 0 -1 0 0 1
2 -5 2 2 -5 3 -3 -3 0 -4 2 -2 -9 3 -6 0 6 8 3 3 2 2 8 0 -4 0 0 -2 0 0 0 -6
-2 1 -1 2 1 0 0 -1 -1 0 -1 2 0 1 0 0 0 0 -2 0 -1 1 1 0 1 0 -1 0 0 1 0 -1
3 -4 2 0 -4 3 -3 -2 0 -2 2 -4 -7 2 -5 1 6 6 3 2 2 2 7 -1 -5 -1 0 -1 0 0 0 -4
-1 1 -1 2 1 -2 1 0 0 1 -1 2 0 1 -1 -1 -1 0 -1 0 0 -1 -1 1 1 0 0 0 0 0 0 1
3 -5 2 1 -5 3 -3 -3 0 -3 2 -4 -10 3 -7 0 7 8 4 4 3 2 9 0 -6 0 0 -2 0 0 0 -6
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
-3 6 -3 0 5 -4 4 2 0 3 -3 6 10 -2 6 0 -8 -8 -5 -3 -3 -2 -9 0 7 0 0 2 0 0 0 5
-3 6 -3 1 5 -4 4 2 0 3 -4 6 9 -2 5 0 -8 -7 -4 -3 -2 -2 -9 0 6 0 0 2 0 0 0 5
1 -1 0 2 -1 0 0 -1 0 -1 0 0 -2 1 -2 0 0 2 1 1 1 0 1 0 -1 0 0 0 0 0 0 -1
-4 9 -6 1 8 -8 7 3 0 6 -5 10 14 -3 8 0 -12 -11 -7 -5 -4 -4 -14 0 10 0 0 3 0 0 0 9
2 -2 1 -1 -3 3 -2 -1 0 -2 2 -2 -4 1 -2 0 3 3 2 1 1 2 3 0 -2 0 0 -1 0 0 0 -3
-1 3 -2 1 2 -2 2 1 0 1 -2 4 4 -1 2 0 -4 -3 -2 -1 -1 -1 -5 0 3 0 0 1 0 0 0 2
1 -1 0 1 -1 0 0 0 0 -1 0 0 -2 1 -2 0 0 2 1 1 1 0 1 0 -1 0 0 0 0 0 0 -1
2 -2 1 -2 -3 3 -2 -1 0 -2 2 -2 -3 0 -1 0 3 2 2 1 1 2 3 0 -2 0 1 -1 0 0 0 -3
1 -2 1 0 -2 3 -2 -1 0 -2 1 -2 -3 1 -2 0 2 3 2 1 1 2 3 0 -2 0 0 -1 0 0 0 -3
-3 6 -4 1 5 -4 4 2 0 3 -3 6 9 -2 5 0 -8 -7 -4 -3 -2 -2 -9 0 6 0 0 2 0 0 0 5
3 -5 3 -1 -5 5 -4 -2 0 -4 3 -5 -9 2 -5 0 7 7 5 3 3 3 8 0 -6 0 0 -2 0 0 0 -6
2 -3 2 -1 -3 3 -3 -1 0 -2 2 -4 -5 1 -3 0 5 4 3 2 2 2 5 0 -4 0 0 -1 0 0 0 -4
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 -1 0 1 -1 0 -1 -1 0 -1 1 0 -2 1 -1 0 1 2 0 0 0 1 2 0 -1 0 0 0 0 0 0 -1
-2 4 -3 1 3 -3 3 1 0 2 -2 4 5 0 3 0 -5 -4 -3 -1 -2 -1 -5 0 4 0 0 1 -1 0 0 3
1 -1 0 1 -1 0 0 -1 0 -1 0 0 -2 1 -2 0 1 2 1 1 1 0 1 0 -1 0 0 0 0 0 0 -1
-4 8 -5 0 7 -6 5 3 0 5 -4 8 13 -3 8 0 -10 -10 -7 -5 -4 -2 -12 0 9 0 0 3 0 0 0 7
0 1 -1 1 1 -2 1 0 0 1 -1 2 1 0 0 0 -2 -1 0 0 0 -1 -2 0 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0
4 -8 5 0 -7 7 -7 -3 0 -6 5 -8 -13 3 -8 0 11 11 6 4 4 4 13 0 -9 0 0 -3 0 0 0 -8
0 0 0 1 0 0 0 0 0 0 -1 0 -1 0 -1 0 0 1 1 1 1 0 0 0 -1 0 0 0 0 0 0 0
5 -8 5 -1 -8 7 -7 -3 0 -6 5 -8 -14 3 -8 0 11 11 7 5 4 4 13 0 -9 0 0 -3 0 0 0 -9
-2 4 -2 -1 3 -2 2 2 0 2 -2 4 7 -2 5 0 -5 -6 -3 -2 -2 -1 -7 1 5 1 0 1 -1 0 0 3
1 -1 0 2 -1 0 -1 -1 0 -1 0 0 -3 1 -3 0 1 3 1 1 1 0 2 0 -1 0 0 0 0 0 0 -1
-4 9 -5 -2 7 -4 5 3 0 5 -4 7 15 -4 10 1 -10 -12 -7 -5 -5 -1 -12 -2 9 -1 0 3 1 0 0 7
0 -1 0 2 0 0 0 -1 -1 -1 0 1 -1 1 -1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 -1
1 0 0 -1 -2 1 -1 0 0 -1 1 0 -1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 -1
-7 12 -7 0 11 -8 8 5 0 7 -7 12 21 -5 13 1 -16 -17 -10 -7 -6 -4 -19 0 14 0 0 4 0 0 0 11
0 1 -1 2 3 -3 1 1 0 2 -1 1 3 -1 0 0 -3 -2 0 -1 1 -2 -3 0 1 0 1 1 0 -1 -1 3
-4 6 -4 0 4 -3 4 1 -1 2 -3 8 9 -1 7 0 -7 -8 -7 -3 -5 0 -8 0 8 0 -1 2 0 2 1 3
2 -3 2 -1 -3 3 -3 -1 0 -2 2 -4 -6 1 -3 0 5 4 3 2 2 2 5 0 -4 0 0 -1 0 0 0 -3
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
2 -3 2 1 -3 2 -2 -1 0 -2 1 -3 -6 1 -4 0 4 5 3 2 2 1 5 0 -4 0 0 -1 0 0 0 -3
2 -3 2 0 -3 2 -2 -1 0 -2 2 -3 -5 1 -3 0 4 4 2 2 1 1 5 0 -3 0 0 -1 0 0 0 -3
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
3 -5 3 -1 -4 5 -4 -2 0 -3 3 -6 -8 1 -4 0 7 6 4 3 2 3 8 0 -6 0 0 -2 0 0 0 -5
-1 3 -2 1 4 -4 3 2 0 3 -2 3 6 -2 3 0 -5 -5 -2 -2 -1 -3 -6 0 3 0 0 2 0 0 0 5
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 -6 3 2 -4 3 -3 -2 0 -3 2 -5 -10 3 -7 0 7 8 5 4 3 1 9 0 -7 0 -1 -2 0 0 0 -5
0 1 -1 1 2 -3 1 1 0 2 0 1 2 -1 1 0 -2 -2 -1 -1 0 -2 -2 0 1 0 0 1 0 0 0 3
2 -4 2 1 -3 2 -2 -1 0 -2 2 -3 -6 1 -4 0 4 5 3 2 2 1 5 0 -4 0 0 -1 0 0 0 -3
2 -3 1 1 -2 1 -1 -1 0 -1 1 -2 -4 1 -3 0 3 3 2 2 1 0 4 0 -3 0 0 -1 0 0 0 -2
1 -3 1 2 -2 1 -1 -1 0 -2 1 -1 -4 2 -3 0 2 4 1 1 1 0 4 0 -2 0 0 -1 0 0 0 -2
4 -7 3 1 -6 4 -4 -2 0 -4 3 -6 -11 3 -7 0 8 9 5 4 3 2 10 0 -7 0 0 -2 0 0 0 -6
2 -4 2 0 -3 3 -2 -1 0 -2 1 -4 -6 2 -4 0 5 5 3 3 2 1 6 0 -4 0 0 -2 0 0 0 -4
2 -4 2 1 -3 2 -2 -1 0 -2 1 -3 -6 1 -4 0 4 5 3 2 2 1 5 0 -4 0 0 -1 1 0 0 -3
1 -2 1 -1 -2 2 -1 0 0 -1 1 -2 -3 1 -1 0 3 2 1 1 0 1 3 0 -2 0 0 -1 0 0 0 -2
1 -2 1 1 -1 1 -1 -1 0 -1 1 -2 -3 1 -2 0 2 3 1 1 1 0 3 0 -2 0 0 -1 0 0 0 -1
4 -7 4 -1 -6 6 -5 -2 0 -4 4 -8 -11 2 -6 0 9 8 6 4 3 3 11 0 -8 0 0 -3 0 0 0 -6
0 -1 0 2 0 -1 1 0 0 0 -1 1 -1 1 -1 0 -1 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0
-1 2 -2 1 2 -3 3 1 0 2 -2 3 4 0 2 0 -4 -3 -2 -1 -1 -2 -4 0 3 0 0 1 0 0 0 2
0 0 -1 1 0 -1 1 0 0 0 0 1 0 1 0 0 -1 0 -1 0 -1 0 0 0 1 0 0 0 0 0 0 0
0 0 0 1 1 -1 1 0 0 1 -1 0 1 0 0 0 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 1
3 -4 2 1 -3 2 -2 -2 0 -2 2 -4 -7 2 -5 0 5 6 3 2 2 1 7 -1 -5 -1 0 -1 1 0 0 -3
-1 3 -1 -2 3 -2 2 2 0 3 -1 1 6 -2 5 0 -4 -6 -2 -2 -2 -1 -5 0 3 0 0 1 0 0 0 4
4 -9 4 4 -7 3 -4 -3 0 -5 3 -6 -16 5 -11 -1 9 13 7 6 5 1 12 2 -9 1 0 -3 -1 0 0 -7
0 1 -1 0 0 -1 1 1 1 1 -1 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1
1 -2 1 1 0 0 0 0 0 0 0 -2 -2 1 -2 0 1 1 1 1 1 -1 2 0 -2 0 0 0 0 0 0 0
7 -12 6 2 -11 7 -7 -5 0 -7 6 -11 -22 6 -14 -1 15 18 10 8 6 4 19 0 -14 0 0 -4 0 0 0 -11
1 -2 1 -1 -3 3 -2 -1 0 -2 2 -2 -4 1 -1 0 3 3 1 1 0 2 4 0 -2 0 -1 -1 0 1 1 -3
4 -6 3 2 -4 2 -3 -1 1 -2 2 -7 -10 2 -8 0 6 9 7 4 5 0 8 0 -8 0 1 -2 0 -2 -1 -3
-1 2 -2 1 2 -3 3 1 0 2 -2 3 4 0 2 0 -4 -3 -2 -1 -2 -2 -4 0 3 0 0 1 0 0 0 3
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
5 -8 5 -1 -8 7 -6 -3 0 -5 5 -9 -14 3 -8 0 11 11 7 5 4 4 13 0 -10 0 0 -3 0 0 0 -8
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
3 -6 4 -1 -5 6 -5 -2 0 -4 3 -6 -9 1 -5 1 8 7 5 3 3 3 9 0 -7 0 0 -2 0 0 0 -6
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 1 0 0 0 0 0 0 0 0 -1 0 -1 0 0 1 1 0 1 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 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -3 2 -1 -2 2 -2 -1 0 -1 2 -4 -4 1 -2 0 4 3 2 2 1 1 5 0 -4 0 0 -1 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 1 0
5 -8 5 -2 -8 7 -6 -3 0 -5 5 -9 -14 3 -8 0 12 11 7 5 4 4 13 0 -10 0 0 -3 0 0 0 -8
-3 5 -3 1 6 -5 4 2 0 4 -3 5 9 -2 5 0 -7 -7 -5 -3 -2 -3 -8 0 6 0 0 2 0 0 0 6
2 -3 2 -1 -2 2 -2 -1 0 -1 2 -4 -5 1 -3 0 4 3 3 2 2 1 5 0 -4 0 0 -1 0 0 0 -2
0 0 0 1 0 0 0 0 0 0 -1 0 -1 0 -1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
-2 5 -3 1 5 -5 4 2 1 4 -3 4 8 -2 4 0 -7 -6 -3 -3 -1 -3 -8 0 5 0 0 2 0 -1 0 6
2 -3 2 0 -2 2 -2 -1 0 -1 1 -4 -5 1 -4 0 4 4 3 2 2 1 5 0 -4 0 0 -1 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 1 0 0 0 0 0
0 0 0 0 0 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
1 -1 0 4 1 -3 1 0 1 1 -1 -1 -2 1 -4 0 -1 3 3 1 3 -3 0 0 -2 0 1 0 0 -2 -1 2
-2 2 -1 1 4 -3 2 2 0 2 -2 3 6 -2 3 0 -5 -5 -2 -2 0 -3 -6 1 4 1 0 1 0 0 0 4
3 -3 2 -2 -4 4 -3 -2 0 -2 3 -5 -6 1 -3 1 6 5 3 2 1 3 7 -2 -5 -1 0 -1 1 0 0 -4
0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 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 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
2 -3 2 0 -2 2 -1 -1 0 -1 1 -3 -4 1 -3 0 3 3 3 2 2 0 3 0 -3 0 0 -1 0 0 0 -2
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
3 -5 2 3 -4 1 -2 -2 0 -3 2 -3 -9 3 -7 0 5 8 4 3 3 0 7 0 -5 0 0 -1 0 0 0 -4
1 -2 2 -2 -1 3 -2 0 0 -1 1 -3 -1 -1 0 0 3 0 2 1 1 1 2 0 -2 1 0 -1 0 0 0 -2
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32 32
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32 32
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32 32
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32 32
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-
HERMITIAN_STRUCTURE
4
32 32
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32 32
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32 32
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32 32
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-4 8 -5 1 6 -7 6 3 0 5 -4 8 11 -2 7 0 -10 -9 -6 -4 -4 -3 -12 0 8 0 -1 3 0 0 0 8
-1 3 -1 -3 1 0 1 1 -1 1 0 2 5 -2 5 0 -2 -5 -3 -2 -3 1 -4 0 3 0 0 1 0 1 0 2
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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