The Lattice M80
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 13:19:33 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
M80
-
DIMENSION
80
-
GRAM
80 0
8
-4 8
-4 0 8
-2 -2 0 8
-4 2 0 4 8
-4 2 0 0 0 8
-4 0 0 2 2 2 8
-4 0 4 4 2 2 0 8
-4 2 0 0 4 4 2 2 8
-4 4 0 -2 0 4 4 0 4 8
-4 4 0 -2 2 2 4 0 2 4 8
-4 0 0 2 4 4 4 2 4 2 4 8
2 -4 -2 0 -2 2 0 0 0 -2 -2 2 8
-4 2 0 4 4 0 2 2 0 0 2 2 -2 8
2 -4 2 2 -2 -2 0 2 -4 -4 -2 -2 0 0 8
-2 -2 2 2 0 2 2 2 2 2 0 2 0 0 0 8
-2 -2 0 2 2 2 2 2 2 0 2 4 2 2 0 0 8
0 -2 -2 4 2 0 2 0 0 0 0 2 0 2 0 0 4 8
0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 -2 2 4 8
-2 0 0 4 2 2 0 4 2 0 0 2 0 2 0 2 2 2 2 8
0 -2 2 -2 -2 0 2 -2 0 2 0 0 0 -2 0 2 0 0 -2 -4 8
0 -2 -2 4 2 0 2 0 0 0 0 2 0 2 0 2 2 4 2 0 0 8
2 2 -4 0 0 0 -2 -2 0 0 -2 -2 0 0 -2 -2 -2 0 2 -2 0 2 8
2 0 -4 -2 -2 2 0 -2 2 2 0 0 2 -2 -2 0 0 0 0 -2 2 0 4 8
-2 2 2 0 0 2 -2 2 2 2 0 0 -2 0 -2 2 0 0 2 0 0 2 2 0 8
2 0 -4 2 2 -2 0 -2 -2 -2 0 0 0 2 0 -2 0 2 2 -2 -2 4 4 0 0 8
0 -2 2 -2 -2 0 2 -2 0 2 0 0 0 -2 0 2 0 0 -2 -4 4 2 0 0 2 0 8
2 -4 2 -2 -2 -2 0 -2 0 0 -2 0 2 -4 0 2 0 0 -2 -2 4 0 -2 0 0 -2 4 8
0 2 2 -4 -2 0 -2 0 0 0 0 -2 0 -2 0 0 -4 -4 -2 -2 0 -4 0 0 0 -2 0 0 8
1 -3 1 -1 0 1 -1 1 1 -1 0 2 2 -2 1 -1 3 1 0 0 0 -1 -2 0 1 -1 2 2 -1 10
-3 3 1 1 0 1 1 3 1 3 2 0 -2 2 -1 -1 1 1 2 2 -2 -1 0 0 3 -1 0 -2 -1 2 10
-3 3 1 1 0 1 1 3 1 3 2 0 -2 2 -1 3 -1 -1 0 2 0 1 0 0 1 -1 -2 -2 1 -6 2 10
-1 3 -3 -1 2 3 1 -1 3 3 2 2 0 0 -3 -3 1 1 2 0 -2 -1 2 2 1 1 0 -2 -1 2 2 -2 10
2 -2 0 -1 -2 0 0 0 0 0 -2 -2 0 -2 2 2 -1 -1 -3 -1 1 -2 -1 1 -1 -1 0 0 1 -1 -1 1 0 10
-2 -2 2 1 2 2 0 2 2 0 0 2 2 0 0 0 3 1 1 1 1 2 -1 -1 1 -1 2 2 -1 5 1 -1 0 -5 12
0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 0 0 2 4 2 -2 2 2 0 2 2 -2 -2 -2 0 2 2 0 -3 1 8
-2 -2 0 2 2 2 2 2 2 0 2 4 2 2 0 2 4 2 0 2 0 2 -2 0 0 0 0 0 -2 3 -1 -1 -1 -3 3 0 8
1 1 -3 -1 2 -1 -1 -1 3 1 0 0 0 0 -3 1 -1 -1 0 0 0 1 2 2 -1 1 -2 0 1 -2 -2 2 -2 1 -1 2 -1 10
-4 0 4 2 2 2 0 4 2 0 0 2 0 2 0 4 0 0 0 2 0 0 -2 -2 2 -2 0 0 2 0 0 2 -2 0 2 0 2 0 8
0 -2 2 -2 -2 0 2 0 0 0 0 0 2 -2 2 2 0 -4 -4 -2 2 -2 -2 0 -2 -2 2 2 2 0 -2 0 -2 3 -1 -4 0 0 0 8
0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 -2 2 2 4 2 -2 2 2 0 2 2 -2 -2 -4 0 2 0 2 -3 1 4 0 0 -2 -4 8
3 -1 -1 1 -2 -3 -3 -1 -3 -3 -4 -4 0 0 1 -3 -1 1 2 0 -2 -1 2 0 1 1 0 0 -1 0 2 -2 2 -1 -1 0 -1 -4 -2 -2 2 10
-4 4 2 2 4 1 0 2 2 2 2 2 -3 2 -3 2 -1 -1 3 2 -2 0 0 -2 4 0 0 -1 -1 0 3 0 3 -3 0 3 -1 -1 3 -1 3 0 12
-3 4 2 -2 0 2 0 1 2 3 2 -1 -2 0 -2 0 -1 -1 0 -1 -1 -1 0 -1 4 -1 1 -1 2 1 3 1 1 -1 0 2 0 -1 2 0 0 -1 3 10
2 0 -4 0 0 0 0 -2 0 0 0 0 1 0 -1 0 0 2 0 1 0 0 2 2 -2 1 -2 -1 0 0 0 0 -1 1 -1 1 1 3 -2 -2 0 -1 -4 -2 8
-4 0 5 0 2 1 2 1 1 0 1 1 0 0 1 0 0 -2 -2 0 0 0 -3 -5 1 -1 3 2 1 3 -1 -3 -1 -5 6 -1 3 -3 3 2 -1 -1 3 4 -4 14
3 -2 -3 -2 -3 0 0 -4 -2 -1 -1 -2 3 -1 0 -2 -1 -1 -2 -2 0 -1 1 3 -2 1 1 0 -1 3 0 -4 1 -1 2 -1 2 -3 -3 0 -1 3 -3 0 2 2 12
-2 -2 1 4 0 1 4 3 -1 0 1 1 1 2 4 2 1 2 -2 0 1 4 0 -1 1 2 2 -1 -1 -2 0 2 -1 -1 2 -2 2 -3 1 0 -1 1 -1 0 -1 3 0 12
4 -3 -1 1 -1 -4 -1 -2 -4 -4 -2 -1 0 -1 3 0 0 1 -1 1 -1 -1 -2 -2 -3 0 -1 1 -2 0 -1 -1 -2 3 -3 1 -3 0 -2 1 1 2 -1 -4 1 -4 -2 -2 12
-1 3 2 -2 0 0 -1 1 0 0 1 0 -2 0 0 0 -3 -4 -3 1 -1 -4 -1 -2 -1 -2 -3 -2 3 -1 -2 2 -1 2 -5 -1 0 1 0 2 -2 -2 -1 1 1 -1 -2 -4 1 12
-4 4 2 -2 0 4 0 2 2 4 4 2 -1 1 -2 -1 2 -1 1 2 -2 -2 -2 0 2 -2 0 -1 -1 3 4 0 3 -4 3 2 1 -2 1 -2 3 -1 4 4 -3 4 1 -1 -3 -1 12
3 -1 -4 2 2 -1 -1 0 0 -3 -1 1 1 0 1 -1 1 1 0 2 -2 0 2 2 -4 2 -4 -2 -2 -1 -3 0 0 3 -3 1 0 3 -2 0 2 -1 -2 -4 4 -6 -2 -2 5 3 -4 12
2 0 0 -2 -1 -1 -2 0 -1 0 0 -2 0 -3 1 -3 -1 0 0 0 -2 -2 -2 -2 0 0 0 1 1 4 2 -2 3 0 3 -1 -1 -2 -2 -2 1 2 -1 1 0 2 2 0 0 -1 3 -2 10
-3 -1 2 4 4 0 3 2 0 -1 1 2 -2 3 2 -1 3 2 1 2 -2 2 -2 -4 0 2 0 -2 -3 2 2 -2 1 -1 4 0 2 -3 0 0 1 1 1 -1 -2 5 1 3 0 -2 1 -2 1 12
-3 3 2 0 1 1 1 0 1 3 1 -1 -3 1 -2 -1 -1 1 2 -2 2 2 2 0 4 0 2 -1 -1 -1 2 0 1 -2 2 1 -2 -1 1 -2 1 0 3 4 -3 3 0 2 -4 -3 3 -5 0 2 10
-1 1 -2 2 1 3 1 0 1 1 1 1 -1 2 0 -1 2 3 4 0 0 2 2 2 2 2 0 -3 -2 1 2 -2 4 -1 1 1 0 -2 0 -3 3 1 2 1 -1 -1 1 3 -3 -5 2 -1 0 2 4 10
4 -3 0 -2 -5 -1 -1 -2 -3 -1 -3 -3 1 -3 3 0 -3 0 -3 -1 3 -2 -1 1 -3 -3 1 2 2 1 -3 -1 -3 2 -1 -1 -1 -1 -1 0 -2 0 -6 -1 2 -2 2 -1 3 3 -2 2 1 -5 -2 -2 12
-3 1 3 0 1 0 1 3 2 1 2 1 -2 1 1 2 0 -2 -2 -1 0 1 -1 -1 2 0 2 0 1 -2 0 2 -2 -1 0 -1 1 1 3 2 -1 -1 2 2 -4 3 -3 4 -2 -1 2 -2 -2 1 2 0 -3 10
2 -1 -3 2 1 -2 -1 0 0 -2 -2 -1 2 1 0 -2 0 1 2 3 -2 0 2 0 -2 1 -2 0 -1 -1 1 -1 1 -1 0 1 -1 2 -1 -2 1 2 0 -3 2 -2 -1 -1 1 -2 -2 3 0 -1 -2 0 0 -3 10
3 0 -2 0 0 -2 -4 -1 -2 -3 -2 -2 -1 0 0 -1 -2 0 1 2 -3 0 1 -1 -1 1 -3 -1 1 -2 -2 0 -1 2 -2 0 -2 3 0 -3 1 1 -2 -4 3 -4 -2 -3 3 2 -3 4 1 -1 -3 -2 1 -2 3 10
-4 2 4 2 3 1 0 3 1 1 0 0 -2 1 0 1 1 1 2 -1 0 2 0 -3 3 1 2 0 0 0 2 2 -1 -2 4 2 0 -1 4 -1 1 -1 4 4 -3 5 -3 2 -3 -3 3 -4 1 2 4 1 -4 3 -3 -3 12
3 1 -4 1 -1 -1 -3 -2 -3 -2 -1 -3 0 0 0 0 -1 0 3 2 -3 0 3 1 1 3 -3 -2 -1 -3 0 0 1 -1 -2 3 -1 0 -2 -2 3 3 3 -2 2 -3 2 0 2 -2 -1 2 0 0 -2 2 -3 -2 3 3 -1 14
2 0 -4 0 1 -1 0 -2 1 -1 0 0 1 0 -1 -3 0 2 1 1 -2 1 1 0 -2 2 -2 -1 -1 -1 -2 -2 0 -1 -2 0 1 3 -2 -2 1 1 -3 0 2 0 0 0 0 0 -1 2 1 -1 0 0 1 0 3 2 -3 -2 10
-2 -2 2 4 3 -1 2 2 1 -1 0 2 -1 2 1 1 4 4 3 1 1 2 -1 0 1 0 1 1 -3 2 3 0 1 -1 3 1 1 -3 2 0 1 1 3 -1 -2 0 -1 1 1 -4 -1 0 -2 4 1 3 -3 0 0 -3 3 1 -5 12
-1 3 2 -1 2 0 -3 0 0 0 1 -1 -3 -1 -1 0 -1 -2 1 -2 0 1 2 -1 5 1 1 0 -1 1 0 -1 1 -3 3 3 -1 -1 0 -2 3 0 6 3 -2 3 0 0 -1 -1 3 -2 1 1 4 1 -4 2 -3 -1 6 5 -4 1 14
-2 4 2 -3 -2 2 0 0 0 3 2 0 -2 -1 -2 -2 -1 -2 -1 -1 2 -3 0 1 0 -3 0 -1 1 -2 1 1 0 0 -3 -2 -1 -2 -2 0 1 -1 -1 1 0 -1 -1 -2 -2 4 3 0 0 -2 2 -1 2 0 -2 0 -2 -4 1 -4 -2 12
1 -3 2 -2 -1 -2 1 0 -1 -1 1 1 2 -1 2 0 0 0 -2 0 1 -3 -5 -2 -3 -3 1 3 2 4 -1 -2 0 2 1 -4 1 -1 2 2 -4 0 -2 -2 0 1 0 -1 3 2 -1 0 3 -1 -3 -3 4 -2 1 1 -3 -4 0 0 -4 -2 12
-3 1 4 2 2 1 -1 4 2 1 -1 0 -3 1 1 0 0 0 2 3 -2 1 -2 -3 2 -2 0 0 0 1 1 0 -1 -4 4 1 1 -1 2 -2 2 0 3 2 -4 6 -2 1 -4 -1 5 -4 2 3 3 1 -1 3 -1 -1 5 -3 0 0 2 1 -2 12
0 2 0 -2 1 -1 0 -2 1 1 2 -1 -3 -1 -1 -2 0 -1 0 -2 2 0 2 1 2 1 1 0 -2 0 0 -1 2 0 -1 0 -1 0 -2 -1 2 0 2 1 -1 1 1 0 -1 0 1 0 0 1 3 2 -2 1 -1 -1 1 3 -1 2 6 0 -2 0 10
0 1 -2 1 1 1 1 -2 -1 -1 1 1 1 1 0 -1 0 2 2 2 -1 0 1 -1 -2 1 -1 -1 -1 -2 0 0 1 0 0 1 -2 -1 0 -1 0 0 1 -1 2 -1 -1 0 3 -1 -1 3 -1 0 0 1 0 -3 4 2 -1 2 2 0 -1 0 1 -3 -1 10
4 -2 -2 -3 -5 -1 -2 -3 -3 -1 -2 -2 4 -3 -1 -1 -1 -2 -2 0 -1 -2 0 1 -1 -1 1 3 0 1 -1 -3 1 0 -2 -1 -2 -1 -3 1 0 2 -1 -1 0 -1 3 -3 3 0 1 0 1 -4 -3 -3 3 -3 3 2 -6 2 1 -4 -2 1 2 -3 -2 1 12
-1 1 2 -1 0 0 -1 2 0 0 1 0 -1 0 1 -2 1 -2 -1 0 0 -2 0 -1 1 -1 0 -1 -1 2 1 -2 2 -2 1 -2 1 -2 0 0 1 2 2 0 -2 2 1 1 -1 1 3 -1 1 2 1 1 -2 3 -1 -1 1 2 -2 1 5 0 0 2 5 -3 -1 10
2 -1 -3 0 1 -2 -1 -1 0 -1 0 0 0 1 -1 -1 1 0 1 1 -3 0 0 1 -1 2 -2 -1 -1 1 -1 -1 3 0 0 1 1 1 -2 0 1 2 0 -2 0 -1 3 -1 1 -1 0 1 1 3 -2 0 -3 0 0 1 -4 3 0 1 -1 -3 0 -1 0 -3 2 1 10
2 2 -1 -2 -3 0 -2 -2 -2 0 -2 -3 -1 -1 0 -1 -4 -3 -1 -2 1 -2 4 2 1 0 0 -1 2 -3 -1 1 0 1 -4 0 -3 -1 -2 1 0 2 0 1 0 -3 0 -1 1 4 -2 2 -2 -4 0 -1 3 -1 -1 1 -2 2 -1 -3 1 3 -2 -2 1 1 2 0 -2 10
2 -2 -3 -1 1 -2 2 -4 0 -1 2 2 2 -1 -1 -2 2 1 0 -2 1 1 -1 1 -2 2 1 2 -3 3 0 -3 2 -2 2 -1 1 0 -3 0 0 0 -1 -3 1 0 4 -1 2 -3 -1 -1 2 1 -1 1 -2 -2 0 -1 -2 1 0 3 0 -3 2 -3 3 0 1 1 3 -3 12
1 -1 2 0 1 -3 -3 0 -1 -3 -3 -2 -1 0 0 1 -2 -1 0 -2 2 0 2 0 0 0 0 1 3 -1 -4 0 -4 0 0 0 1 2 2 1 -2 0 -1 -1 1 0 -1 -2 -1 3 -5 1 -3 -1 -1 -4 1 0 -1 2 1 -1 -1 0 1 0 0 0 -1 -2 -2 -1 0 2 -3 10
-3 4 0 -1 0 2 3 0 0 4 4 1 -1 1 -1 -1 1 1 1 0 0 -1 0 0 -1 0 0 -2 0 -1 3 2 1 -2 0 1 0 -1 0 0 0 -2 1 3 1 1 0 0 -1 0 4 -1 0 0 2 1 -1 0 -1 -3 3 1 -1 1 1 2 -1 0 1 2 -2 2 -2 -1 0 -3 10
-1 -1 -1 4 4 -1 2 1 0 -2 0 2 1 3 1 -1 2 3 1 0 -1 3 1 0 -1 2 -1 -1 -2 -1 -2 -2 1 -2 0 0 2 0 0 -1 0 0 1 -1 0 1 -1 3 -1 -2 -2 2 -2 2 1 1 -3 0 2 0 0 0 2 2 0 -1 -1 0 -1 1 -1 -1 1 -1 0 2 -1 10
3 -4 -2 3 -2 0 1 1 -1 0 -3 0 1 -1 3 2 1 2 -1 3 1 1 0 1 -2 0 -1 1 -4 1 1 1 -2 4 -1 1 -1 1 -3 0 1 0 -4 -4 4 -5 0 1 5 0 -2 5 0 0 -3 0 4 -3 2 1 -3 0 0 0 -3 -1 0 -1 -1 1 1 -1 0 0 0 -3 0 -3 14
-4 0 1 1 0 3 5 2 2 4 2 2 1 2 0 3 2 0 -2 -1 1 3 0 0 2 0 4 0 0 0 3 2 0 1 2 -2 2 0 2 3 -2 -2 0 2 -1 2 -1 4 -3 -2 0 -3 -2 2 1 0 -2 3 -1 -3 2 -3 -1 0 -2 -1 0 -1 -2 -1 -1 -1 -2 -1 -2 -1 1 1 -2 12
-
DET
1
-
MINIMAL_NORM
8
-
KISSING_NUMBER
1250172000
-
DENSITY
-
HERMITE_NUMBER
8
-
SUBGROUP_ORDER
2^11 * 3^4 * 5^2
-
SUBGROUP_NAME
(SL2(5) otimes C3).2 otimes 2^5.S6
-
SUBGROUP_GENERATORS
8
80 80
-2 0 -1 -1 -1 -1 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 0 0 0 0 0 0
0 0 0 0 0 0 0 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 1 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 0 0 0 0 0 0 0
0 0 0 0 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 0 1 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 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 -1 -1 1 1 1 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 0 0 0 0 0 0 0 0
0 0 0 0 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 0 1 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0
0 0 0 0 0 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 1 0 -1 -1 0 2 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 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 2 1 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 0 0 0 0 0 0
0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 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 1 1 0 1 2 1 1 0 0 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 1 1 1 0 -1 0 -1 0 1 -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 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 1 0 -1 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 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 -1 -1 1 1 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 0 0 0 0 0 0 0
0 0 0 0 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 0 1 4 0 0 -2 -2 0 3 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 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 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 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 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
-2 -1 -1 -2 0 0 1 1 0 -1 -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 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 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 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 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 2 0 0 -1 -1 0 2 1 0 0 0 0 0 0 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 0 0 0 0 0 0
0 0 0 0 0 0 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 -1 -1 1 1 1 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 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 1 0 1 1 -1 -1 -2 0 0 0 0 0 0 0 0 1 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 0 0 0
0 0 0 0 0 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 -1 -3 1 0 1 1 -1 -2 -2 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 -3 1 0 1 1 -1 -1 -2 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 0 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 -4 2 0 2 2 -2 -1 -3 0 0 0 0 0 0 0 0 2 1 1 -2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 4 -3 -5 2 0 3 3 -2 -4 -4 0 0 0 0 0 0 0 0 3 2 1 -3 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 2 6 -1 0 -3 -3 1 3 3 0 0 0 0 -2 1 -1 -1 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0
5 -72 38 119 -32 7 -66 -61 39 63 79 -6 0 -1 2 -22 1 3 -5 -51 -42 -37 42 -25 -3 -19 -5 -1 1 4 -8 14 -7 -5 -5 -3 1 3 4 6 0 -5 0 -4 0 0 0 0 0 0 0 0
0 0 0 0 0 -3 2 2 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
5 -79 40 129 -33 9 -70 -66 40 67 86 -7 -1 -2 1 -24 1 3 -5 -55 -46 -41 46 -27 -3 -21 -5 -1 1 5 -9 16 -8 -5 -5 -4 1 4 4 6 0 -5 0 -4 0 0 0 0 0 0 0 0
0 0 0 0 0 -3 2 2 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
-5 74 -38 -118 30 -9 66 61 -39 -63 -80 7 0 1 -2 22 -1 -3 5 51 42 37 -42 25 3 19 5 1 -1 -4 8 -14 8 6 6 3 0 -3 -4 -6 0 4 0 4 0 0 0 0 0 0 0 0
0 0 0 0 0 3 -2 -2 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
-5 73 -38 -124 33 -7 68 63 -39 -65 -82 6 1 2 -1 23 -2 -2 6 51 43 37 -43 25 4 20 5 1 -1 -5 9 -14 8 5 5 3 0 -3 -5 -6 1 4 0 4 0 0 0 0 0 0 0 0
0 0 0 0 0 3 -2 -2 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
-175 1734 -970 -2913 582 -227 1666 1531 -821 -1608 -1949 254 -59 34 -33 601 -57 45 127 1024 881 755 -876 517 34 390 116 10 -70 -75 153 -278 106 163 140 77 47 -53 -135 -162 60 94 38 64 -37 20 -22 6 -32 -3 1 -26
31 5 27 2 -2 34 -33 -32 1 6 -15 12 6 -7 -5 -1 3 -3 -2 2 1 -3 3 -1 2 -2 1 -1
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PROPERTIES
Unimodular=1
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REFERENCES
C. Bachoc, G. Nebe: Extremal lattices of minimum 8 related to the Mathieu group M22, submitted
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NOTES
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe