The Lattice D4(1-w)^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 13:11:27 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
D4(1-w)^2
-
DIMENSION
32
-
KISSING_NUMBER
864
-
GRAM
32 0
4
0 4
0 0 4
-2 2 2 4
-3 1 1 3 10
-1 -3 1 -1 0 10
-1 -1 -3 -1 0 0 10
0 -2 -2 -3 -5 5 5 10
-3 -1 1 1 4 4 2 2 8
1 -3 -1 -3 -4 4 2 4 0 8
-1 1 -3 -1 -2 -2 4 4 0 0 8
2 0 -2 -3 -6 0 0 4 -4 4 4 8
-3 -1 1 2 6 0 0 -4 4 -2 -2 -6 8
1 -3 1 -2 0 6 -2 2 2 4 -4 0 0 8
-1 -1 -3 -2 0 2 6 4 2 4 4 2 0 0 8
1 -1 -1 -3 -2 4 2 6 2 4 2 4 -4 4 4 8
2 2 0 0 -1 -3 -3 -3 -1 -1 -1 0 0 0 -2 -1 8
-2 2 0 2 3 -1 -1 -1 1 -1 1 0 0 0 0 1 0 8
0 0 2 2 3 1 -1 -3 1 -1 -1 -2 2 0 0 -1 0 0 8
-2 0 0 2 4 0 2 -1 1 -1 1 -1 1 -1 1 0 -4 4 4 8
2 2 2 1 -1 -3 -3 -3 -2 -2 -2 0 -1 -1 -3 -1 4 0 0 -2 8
-2 2 0 1 3 -1 -1 -1 2 -2 2 0 1 -1 1 1 0 4 0 2 0 8
-2 0 2 3 3 1 -1 -3 2 -2 -2 -4 3 -1 -1 -3 0 0 4 2 0 0 8
-3 1 -1 2 4 0 2 -1 2 -2 2 -2 2 -2 2 -1 -2 2 2 4 -4 4 4 8
1 1 1 1 0 -6 -4 -6 -4 -4 -2 -1 1 -3 -5 -5 2 0 0 0 4 0 0 -2 8
-1 1 1 1 6 0 -2 -2 4 -4 0 -3 3 1 -1 1 0 2 2 2 0 4 0 2 0 8
-1 -1 1 1 4 2 0 -4 2 0 -4 -5 5 1 1 -3 0 -2 2 0 0 0 4 2 0 0 8
-2 0 0 1 6 2 4 0 5 -1 1 -4 4 0 4 1 -2 0 2 2 -2 2 2 4 -4 4 4 8
0 -2 0 0 0 0 -2 -1 0 0 -2 -2 2 2 -2 -2 0 0 0 0 0 -2 0 -2 2 0 0 -2 8
2 0 2 0 0 0 0 1 0 0 -2 0 -2 2 -2 2 0 0 0 0 2 0 -2 -2 0 2 -2 0 0 8
0 -2 0 -2 2 0 0 -1 2 2 0 0 2 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 0 0 8
0 0 2 0 1 -1 1 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 0 0 2 0 2 -4 4 4 8
-
DIVISORS (elementary divisors)
2^16
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
2.83
-
HERMITIAN_GROUP_ORDER
2^8*3^8
-
HERMITIAN_GROUP_GENERATORS
5
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
1 1 -1 0 0 -1 -2 1 3 -1 -1 1 0 2 2 -2 0 -1 0 1 0 0 0 0 2 -3 -2 2 -1 1 1 -1
0 0 -1 2 2 -2 -1 3 1 2 0 1 -2 2 0 -2 0 0 1 -1 0 0 0 0 3 0 0 2 -1 0 0 -1
2 -1 0 2 1 0 0 -1 0 0 3 -1 0 0 0 2 -1 0 0 -1 0 0 0 0 -1 1 3 -4 0 0 -1 1
1 -2 -1 3 1 -1 1 0 0 0 1 2 0 0 -2 2 -1 1 1 -2 0 0 0 0 0 1 3 -1 0 0 -1 0
1 -1 -2 2 1 -2 -1 1 2 0 0 1 -1 1 0 0 -1 0 1 -1 0 0 0 0 1 -1 1 0 -1 1 0 -1
1 -1 0 2 2 0 0 1 -1 2 1 -1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 2 1 -2 0 -1 -1 1
1 -1 0 0 -1 1 2 -3 0 -1 1 1 1 -1 -2 2 -1 1 0 -1 0 0 0 0 -2 1 2 -2 1 0 -1 1
0 -1 1 0 0 1 2 -1 -1 0 0 1 0 -1 -1 0 0 1 0 -1 0 0 0 0 -1 2 1 -1 1 -1 -1 1
1 1 -2 1 0 -1 -3 2 2 0 -1 0 0 1 1 -1 0 -1 0 1 0 0 0 0 2 -3 -2 3 -1 1 1 -1
0 -1 -1 3 2 -3 -1 4 1 1 -1 2 -1 1 0 -1 0 0 1 -1 0 0 0 0 2 0 1 1 -1 0 0 -1
3 -2 -1 3 2 -1 -1 0 1 0 2 0 0 0 0 1 -1 0 0 -1 0 0 0 0 -1 0 2 -3 0 0 -1 1
1 -3 -1 3 1 -2 1 0 1 -1 0 3 0 0 -1 1 -1 1 1 -2 0 0 0 0 -1 1 3 -2 0 0 -1 0
1 -3 -2 4 2 -3 -3 5 2 1 -2 1 -1 0 0 0 0 0 1 -1 0 0 -1 1 3 -2 0 3 -1 0 0 -1
1 -1 2 0 1 -1 2 1 0 0 -1 3 0 -1 0 0 0 1 0 -1 0 -1 0 1 -1 3 3 -3 1 -1 -1 1
-1 -1 0 -2 0 -2 0 -1 3 -2 0 3 0 0 -1 0 -1 1 1 -1 1 -1 -1 1 -2 -1 2 -1 0 1 0 -1
-2 1 3 -4 -2 0 3 -3 1 -3 -1 4 0 0 0 -1 0 1 0 0 0 -1 0 0 -3 2 2 -2 1 0 0 0
-2 0 1 -2 -2 2 1 -2 -2 -1 -1 -1 0 -1 2 -1 1 0 -1 1 0 0 0 0 -2 2 -1 -1 1 0 0 1
1 -1 -1 0 -1 -1 -1 0 3 -3 -2 3 0 2 1 -3 0 0 0 1 0 0 0 0 0 -3 -2 3 -1 1 1 -1
-1 2 0 -2 1 0 -2 2 0 2 0 -3 -3 2 2 -3 1 -1 0 1 0 0 0 0 3 -1 -3 3 0 -1 0 1
1 1 0 -1 1 -1 -2 1 2 0 1 -1 -1 3 1 -2 0 -1 0 1 0 0 0 0 2 -3 -2 2 -1 0 0 0
-2 2 2 -4 -3 2 1 -2 -1 -2 -2 0 1 -1 1 -1 1 0 -1 2 0 0 0 0 -2 0 -2 1 1 0 1 0
0 0 -2 0 -1 -2 -1 0 4 -3 -2 4 1 2 0 -1 -1 0 1 0 0 0 0 0 1 -4 -1 3 -1 2 1 -2
0 2 0 0 1 0 -3 2 0 2 1 -4 -2 2 3 -3 1 -2 -1 2 0 0 0 0 2 -1 -3 1 -1 0 1 0
2 0 -2 2 1 -1 -2 0 2 0 2 -1 0 2 1 0 -1 -1 0 0 0 0 0 0 1 -2 0 -1 -1 1 0 0
-2 0 0 -2 -3 0 1 -2 0 -3 -3 3 2 -2 -1 1 0 1 0 1 0 0 0 -1 -3 0 0 1 0 1 1 -1
2 -2 -2 2 1 -2 -1 0 3 -3 0 3 2 1 0 1 -2 0 1 -1 1 0 -1 1 -1 -3 1 -1 -1 1 0 -1
0 2 0 -2 -1 2 -1 -2 0 0 0 -3 -1 1 3 -3 1 -2 -2 3 0 1 1 -1 0 -1 -4 1 0 0 0 1
2 0 0 0 1 1 0 -2 0 0 3 -3 0 1 2 0 -1 -1 -1 0 1 0 0 1 -1 0 0 -4 0 0 -1 1
32 32
0 -1 0 0 0 -1 0 0 1 -1 -1 2 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 1 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
-1 1 1 -2 -1 1 1 -2 0 -1 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
0 1 1 -1 0 1 1 -1 -1 0 1 -1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
0 2 3 0 3 -1 1 3 -2 2 3 -2 -1 1 1 1 0 0 0 -1 0 -1 0 1 1 3 4 -5 1 -1 -1 1
-5 3 3 -6 -3 4 4 -5 -3 1 1 -4 -3 0 2 -3 1 0 -1 1 0 0 1 -1 -2 5 -1 -3 1 0 0 1
-1 -2 -2 4 -2 -2 1 1 -1 0 -2 2 0 -2 -3 3 0 1 1 -1 -1 0 0 -1 -1 2 3 1 0 0 1 -1
-3 1 -2 -1 -4 2 1 -2 -1 1 -2 -1 -2 0 -1 -2 1 0 0 1 -1 1 1 -2 1 1 -3 5 0 0 1 0
-3 4 2 -2 -1 2 2 0 -3 3 1 -3 -3 1 1 -2 1 0 0 0 -1 0 1 -1 2 4 0 0 1 -1 0 1
-4 -1 0 -2 -4 1 2 -4 -1 -2 -2 1 0 -2 -1 0 0 1 0 0 0 0 0 -1 -4 2 0 0 0 1 1 -1
2 -2 -5 6 0 -2 -3 4 2 0 -3 3 0 1 -2 0 0 0 1 0 -1 1 0 -1 4 -4 -2 8 -1 0 1 -1
0 -2 -4 1 -2 0 -2 -1 2 -2 -3 2 1 0 -1 -1 0 0 0 1 0 1 0 -1 0 -4 -4 6 -1 1 1 -1
0 2 3 0 2 0 1 2 -2 2 2 -2 -1 0 1 1 0 0 0 -1 0 -1 0 1 1 3 3 -4 1 -1 -1 1
-5 3 3 -6 -3 3 3 -4 -2 0 0 -2 -2 0 2 -3 1 0 -1 1 0 0 1 -1 -2 4 -1 -2 1 0 0 1
-1 -2 -2 4 -1 -2 0 2 0 0 -2 2 -1 -1 -2 1 0 1 1 -1 -1 0 0 -1 0 1 2 2 0 0 1 -1
-3 1 -2 -1 -3 1 0 -1 0 0 -2 0 -2 1 0 -3 1 0 0 1 -1 1 1 -2 1 0 -3 5 0 0 1 0
0 1 2 -3 -1 2 2 -4 -1 -2 1 0 2 -1 0 0 0 0 -1 1 1 0 0 0 -5 1 0 -4 1 0 0 1
0 2 -1 -1 0 1 -2 0 1 0 1 -2 1 2 0 0 0 -1 0 1 0 1 0 0 3 -5 -4 4 -1 1 1 -1
-1 2 2 -1 0 2 1 0 -3 2 1 -4 -1 1 3 -2 1 -1 -1 1 0 0 1 0 1 3 -2 -2 0 -1 0 1
1 1 -1 2 2 0 -2 3 -1 3 2 -4 0 1 1 1 0 -1 0 0 0 0 0 1 4 -1 -1 0 -1 0 0 0
1 1 1 -2 -1 1 1 -3 1 -2 0 1 2 0 0 0 0 0 -1 1 0 0 0 0 -2 -1 -1 -1 0 0 0 0
0 2 -1 0 1 0 -2 1 1 1 1 -1 0 2 0 0 0 -1 0 1 0 0 0 0 3 -3 -2 3 0 0 0 0
0 1 2 0 0 2 1 -1 -2 1 2 -3 0 0 2 0 1 -1 -1 1 0 0 0 0 0 2 0 -3 0 0 0 0
1 0 -1 3 2 0 -1 2 -1 2 2 -2 0 0 0 2 0 -1 0 0 0 0 0 0 2 0 1 -1 0 0 0 0
5 -1 -1 2 4 -2 -4 3 3 0 1 0 2 1 1 1 -1 -1 0 0 1 0 -1 2 2 -5 -1 0 -1 0 -1 0
0 4 1 0 3 0 -1 5 -1 4 1 -2 -3 3 2 -3 1 -1 0 0 -1 0 1 0 6 1 -1 2 1 -2 -1 2
0 -1 4 0 2 -1 3 -1 -1 0 3 0 0 -2 0 3 -1 1 0 -2 1 -2 -1 2 -4 5 7 -10 1 0 -1 0
-1 0 1 3 1 -2 2 3 -1 1 0 2 -2 0 -1 1 0 1 1 -2 -1 -1 0 0 1 4 5 -2 1 -1 0 0
0 2 1 -1 1 -1 -2 3 1 1 0 -1 -1 2 2 -3 0 -1 0 1 0 0 0 0 2 -1 -1 1 -1 0 0 0
-2 1 0 -1 0 -1 1 1 0 1 -1 1 -1 1 -1 -1 0 0 1 -1 0 0 0 0 1 1 0 1 0 -1 0 0
1 -1 -1 3 1 -2 -1 1 1 0 1 1 0 1 0 1 -1 0 0 -1 0 0 0 0 0 0 2 -1 0 0 -1 0
0 -1 -2 2 -1 -1 1 -1 1 -1 -1 3 1 0 -2 2 -1 1 1 -2 0 0 0 0 0 0 1 1 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 -1 0 0 0 0 0 0 0 0 0 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
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
1 1 -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 1 2 -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
1 0 0 2 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
2 0 -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 1 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 -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 0 0 0 0 0
0 -1 0 2 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
1 1 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 1 -1 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
1 0 1 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
1 -1 -1 3 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 -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
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
-1 1 0 -2 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 1 1 -2 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 -1 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 -2 -1 2 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 -2 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 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
-1 0 0 -1 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 -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 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 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 0 0 0 0 1 0 0 0 0
-1 2 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 1 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 1 0 0
1 0 -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 1 0
1 -1 -2 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 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
-2 0 1 -1 -1 1 1 -2 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 -1 2 0 0 0 0
-1 1 -1 -1 0 1 0 0 -1 1 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0
0 1 0 -2 1 0 -1 1 0 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 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 1 -1 0 1 0 0 0 0
0 -1 0 0 0 -1 0 1 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 -1 0 1 -1 -1 1 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 -1 0 -1 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
-1 -1 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 -1 1 -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
-1 0 -1 -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
-1 1 1 -3 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
2 -1 -2 5 2 -3 -3 6 2 2 -1 2 -2 1 0 -1 0 0 1 -1 -1 0 0 0 5 -1 1 4 -1 0 0 -1
-2 0 3 -1 0 -1 3 0 -3 1 1 0 0 -2 -1 1 0 1 0 -1 0 -1 0 0 -4 6 5 -6 1 -1 -1 1
1 -4 -2 3 0 -3 -1 0 3 -4 -2 6 1 0 -2 1 -1 1 1 -1 0 0 -1 0 -2 -3 2 2 0 1 0 -1
-3 -1 1 -2 -3 0 3 -4 -1 -3 -2 3 1 -1 -1 0 0 1 0 0 0 0 0 -1 -5 2 1 -1 1 0 0 0
1 1 0 1 -1 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 1 0 0 0 0
-2 1 1 -1 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 -1 1 1 -1 0 0 0 0
1 -2 -1 3 0 0 -1 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 1 0 0 0 0
-1 -1 -1 1 0 0 0 -1 0 -1 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 1 -1 0 1 -1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 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 -1 -1 0 0 0 0 0 0
0 -1 -1 1 -1 1 0 -1 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -2 2 0 0 0 0
-1 0 0 -1 0 1 0 -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
1 -1 -2 1 -1 -1 -2 0 2 -2 -1 1 1 1 0 -1 0 -1 0 2 0 1 0 -1 -1 -4 -2 3 -1 1 1 -1
2 -1 -1 3 3 -3 -2 4 2 1 0 1 0 1 -1 1 -1 0 2 -2 0 0 -1 1 3 -3 1 1 -1 0 0 -1
1 0 1 -1 1 1 0 -2 -1 1 3 -3 1 0 1 1 -1 -1 -1 0 1 0 0 1 -2 1 0 -5 0 0 -1 1
1 -1 1 1 2 -1 1 0 0 1 2 0 1 -1 -1 3 -2 1 1 -3 1 -1 -1 2 -1 2 4 -6 0 0 -1 0
32 32
0 -2 1 0 0 -1 1 -2 1 -2 1 2 1 -1 -1 2 -1 1 0 -1 1 -1 -1 1 -3 0 3 -3 0 1 0 -1
1 1 1 -2 2 1 -1 0 -1 2 3 -4 0 0 1 0 0 -1 -1 1 1 0 0 1 0 0 0 -3 0 0 -1 1
-3 2 2 -4 -2 3 3 -4 -3 0 1 -2 0 -1 0 0 1 0 -1 1 0 0 1 -1 -3 3 0 -3 1 0 0 1
-1 3 2 -3 1 2 1 0 -3 3 2 -4 -1 0 1 -1 1 -1 -1 1 0 0 1 0 0 3 0 -3 1 -1 -1 2
0 5 2 -3 0 4 1 -1 -3 3 2 -5 -1 1 2 -2 1 -2 -2 2 -1 1 2 -1 2 2 -3 -1 1 -1 0 2
-4 2 -1 -1 -4 1 0 -1 0 -1 -3 1 -1 1 0 -2 2 -1 0 2 -2 1 1 -3 2 -1 -4 7 -1 1 2 -2
3 -2 -2 7 3 -3 -3 7 1 2 -1 1 -1 1 0 0 0 0 1 -2 -1 0 -1 1 5 -1 1 3 -1 -1 0 0
1 -3 -5 6 0 -3 -4 4 3 -1 -3 3 0 1 -1 0 0 0 2 -1 -1 1 -1 -1 4 -5 -2 8 -2 1 1 -2
-1 2 -2 1 -1 0 -2 3 1 0 -3 1 -1 2 0 -3 1 -1 1 1 -1 1 0 -1 4 -3 -4 7 -1 0 2 -1
-1 -3 -1 3 -1 -3 1 1 2 -2 -2 5 1 -1 -3 3 -1 2 2 -3 0 -1 -1 1 0 0 3 1 -1 1 1 -3
4 -3 -4 5 2 -3 -4 3 3 -1 0 1 2 1 0 1 -2 0 1 -1 1 0 -1 1 1 -4 0 1 -2 1 0 -1
1 -4 -2 2 -1 -2 0 -2 2 -3 0 3 3 -2 -2 4 -2 2 1 -2 1 -1 -1 1 -3 -1 3 -2 -1 2 0 -2
-1 4 3 -3 0 3 2 0 -3 3 1 -4 -2 1 2 -3 1 -1 -1 1 0 0 1 0 1 4 -2 -2 1 -2 0 2
-4 2 0 -3 -5 2 2 -4 0 -2 -3 2 0 0 -1 -1 1 0 0 1 -1 1 1 -2 0 -1 -4 6 0 1 2 -2
1 -1 -2 5 1 -3 -3 6 2 1 -2 2 -1 2 0 -1 0 0 1 -1 -1 0 0 0 6 -2 -1 6 -2 0 1 -2
0 -1 -4 3 -2 -1 -3 1 3 -2 -3 3 1 1 -1 0 0 0 1 0 -1 1 0 -1 4 -6 -4 9 -2 2 2 -3
0 1 2 -3 1 0 0 -1 0 0 2 -2 0 0 1 0 -1 0 0 0 2 -1 -1 2 -2 0 1 -4 0 0 0 0
0 2 -1 -1 1 1 -1 1 0 2 0 -2 -1 1 1 -2 0 -1 0 0 0 1 1 0 3 -1 -3 2 0 0 0 0
-1 2 2 -1 0 1 2 -1 -2 2 2 -2 -1 0 0 0 0 0 -1 0 0 -1 1 0 -1 4 2 -4 0 0 0 0
1 1 -1 2 1 0 0 2 0 2 0 0 -1 1 0 -1 0 0 0 -1 -1 0 1 0 3 1 0 1 0 0 0 0
-2 1 3 -4 0 2 1 -2 -2 0 1 -2 -1 -1 2 -1 1 0 -1 1 1 -1 0 1 -2 2 0 -3 1 0 0 1
0 1 -1 -2 -1 1 -1 0 1 -1 -1 0 0 1 1 -3 0 0 0 1 0 1 1 -1 1 -2 -3 3 -1 1 1 -1
-2 3 1 -2 1 0 0 2 -1 2 0 -2 -3 2 1 -3 1 -1 0 1 -1 0 1 -1 2 1 -1 1 0 -1 0 1
1 2 -1 0 1 -1 -2 3 1 1 0 -1 -1 3 1 -3 0 -1 0 1 -1 1 1 -1 3 -2 -2 3 -1 0 0 0
0 0 3 -3 0 2 3 -3 -2 0 1 -1 0 -2 1 0 0 1 -1 0 1 -1 0 1 -4 4 2 -6 2 -1 -1 2
0 3 0 -3 -2 3 0 -3 0 -1 0 -1 1 1 1 -2 0 -1 -1 2 0 1 1 -1 0 -2 -4 2 0 1 1 0
-3 3 3 -3 -1 1 1 1 -1 1 -1 -1 -3 2 2 -4 2 -1 -1 2 -1 0 1 -1 2 2 -2 2 0 -1 1 0
0 3 0 0 0 1 -2 2 0 1 0 -2 -1 3 2 -3 1 -2 -1 2 -1 1 1 -1 4 -2 -4 4 -1 0 1 0
0 0 0 2 1 -1 1 2 0 1 -1 2 -1 0 -1 0 0 0 1 -1 0 0 0 0 1 1 1 1 1 -1 0 0
-2 0 2 -2 -2 2 3 -4 -2 -1 1 0 1 -2 -1 2 0 1 0 -1 0 0 0 0 -3 2 2 -3 1 1 0 0
0 -2 -2 2 -2 -1 0 0 2 -3 -3 4 1 0 -1 0 -1 1 1 -1 0 0 0 0 0 -2 -1 3 -1 1 2 -2
-2 0 0 -2 -3 2 1 -3 -1 -2 -1 0 1 -1 0 0 0 1 0 0 0 0 0 0 -2 0 -1 0 0 1 1 0
-
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
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-
PROPERTIES
Modular=1
UnimodularHermitian=1
-
REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe