The Lattice D2(1+i)^4
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 13:11:30 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
D2(1+i)^4
-
DIMENSION
32
-
KISSING_NUMBER
960
-
GRAM
32 32
6 0 0 -3 1 -1 1 -1 2 0 0 -1 0 0 0 0 4 -2 0 -3 2 0 0 -1 0 0 0 0 2 2 0 0
0 6 0 3 1 1 1 1 0 2 0 1 0 0 0 0 2 4 0 1 0 2 0 1 0 0 0 0 -2 2 0 2
0 0 6 3 -1 -1 1 1 0 0 2 1 0 0 0 0 0 0 4 3 0 0 2 1 0 0 0 0 0 0 2 0
-3 3 3 6 0 0 0 1 -1 1 1 2 0 0 0 0 -1 3 1 4 -1 1 1 2 0 0 0 0 -2 0 2 2
1 1 -1 0 6 0 0 -3 0 0 0 1 1 -1 -1 -1 0 0 -2 0 2 0 0 -1 0 0 0 1 -2 0 0 2
-1 1 -1 0 0 6 0 3 0 0 -2 -1 1 1 -1 -1 0 0 -2 -2 0 2 0 1 0 0 -2 -1 0 -2 -2 -2
1 1 1 0 0 0 6 3 0 2 0 1 1 1 1 1 2 2 0 0 0 0 2 1 0 2 0 1 0 2 -2 0
-1 1 1 1 -3 3 3 6 -1 1 -1 0 0 2 0 1 0 2 0 0 -1 1 1 2 -1 1 -1 0 0 0 -2 -2
2 0 0 -1 0 0 0 -1 6 0 0 -3 2 -2 0 -2 2 -2 0 -2 0 0 0 0 2 0 0 -1 2 0 0 -1
0 2 0 1 0 0 2 1 0 6 0 3 2 2 0 0 2 2 0 0 0 0 0 0 0 2 0 1 0 2 0 1
0 0 2 1 0 -2 0 -1 0 0 6 3 0 0 2 2 0 0 2 2 0 0 0 0 0 0 2 1 0 0 2 1
-1 1 1 2 1 -1 1 0 -3 3 3 6 0 2 0 2 0 2 0 2 0 0 0 0 -1 1 1 2 -1 1 1 2
0 0 0 0 1 1 1 0 2 2 0 0 4 0 0 -2 2 0 0 -1 0 0 0 0 2 2 0 0 0 0 0 0
0 0 0 0 -1 1 1 2 -2 2 0 2 0 4 0 2 0 2 0 1 0 0 0 0 -2 2 0 2 0 0 0 0
0 0 0 0 -1 -1 1 0 0 0 2 0 0 0 4 2 0 0 2 1 0 0 0 0 0 0 2 0 0 0 0 0
0 0 0 0 -1 -1 1 1 -2 0 2 2 -2 2 2 4 -1 1 1 2 0 0 0 0 -2 0 2 2 0 0 0 0
4 2 0 -1 0 0 2 0 2 2 0 0 2 0 0 -1 8 0 0 -4 2 2 0 0 2 2 0 0 2 2 0 0
-2 4 0 3 0 0 2 2 -2 2 0 2 0 2 0 1 0 8 0 4 -2 2 0 2 -2 2 0 2 -2 2 0 2
0 0 4 1 -2 -2 0 0 0 0 2 0 0 0 2 1 0 0 8 4 0 0 2 0 0 0 2 0 0 0 2 0
-3 1 3 4 0 -2 0 0 -2 0 2 2 -1 1 1 2 -4 4 4 8 -2 0 2 2 -2 0 2 2 -2 0 2 2
2 0 0 -1 2 0 0 -1 0 0 0 0 0 0 0 0 2 -2 0 -2 4 0 0 -2 0 0 0 0 0 0 0 0
0 2 0 1 0 2 0 1 0 0 0 0 0 0 0 0 2 2 0 0 0 4 0 2 0 0 0 0 0 0 0 0
0 0 2 1 0 0 2 1 0 0 0 0 0 0 0 0 0 0 2 2 0 0 4 2 0 0 0 0 0 0 0 0
-1 1 1 2 -1 1 1 2 0 0 0 0 0 0 0 0 0 2 0 2 -2 2 2 4 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 2 0 0 -1 2 -2 0 -2 2 -2 0 -2 0 0 0 0 4 0 0 -2 0 0 0 0
0 0 0 0 0 0 2 1 0 2 0 1 2 2 0 0 2 2 0 0 0 0 0 0 0 4 0 2 0 0 0 0
0 0 0 0 0 -2 0 -1 0 0 2 1 0 0 2 2 0 0 2 2 0 0 0 0 0 0 4 2 0 0 0 0
0 0 0 0 1 -1 1 0 -1 1 1 2 0 2 0 2 0 2 0 2 0 0 0 0 -2 2 2 4 0 0 0 0
2 -2 0 -2 -2 0 0 0 2 0 0 -1 0 0 0 0 2 -2 0 -2 0 0 0 0 0 0 0 0 4 0 0 -2
2 2 0 0 0 -2 2 0 0 2 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 4 0 2
0 0 2 2 0 -2 -2 -2 0 0 2 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 4 2
0 2 0 2 2 -2 0 -2 -1 1 1 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 -2 2 2 4
-
DIVISORS (elementary divisors)
2^16
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
2.83
-
HERMITIAN_GROUP_ORDER
2^24 * 3^2 * 5
-
HERMITIAN_GROUP_GENERATORS
10
32 32
0 -1 -1 3 0 1 1 -3 0 0 1 -1 1 1 -2 2 0 0 2 -2 0 -1 -1 2 -2 0 0 -1 -1 1 -1 -1
0 -2 -2 1 0 2 2 -1 1 0 0 1 -3 1 0 -2 2 0 0 2 0 -1 -1 0 0 -1 1 -1 -2 1 2 -3
-1 2 -1 -1 1 -2 1 1 0 -1 0 1 -1 3 2 -4 0 -2 0 2 0 1 -1 0 1 -1 -2 1 1 0 0 -1
-2 1 0 -3 2 -1 0 3 1 -1 -1 2 -3 2 3 -4 2 -2 -2 4 -1 1 0 -2 1 0 0 -1 0 1 2 -2
0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0 -1 0 1 -1 -1 1 1 -1
1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 1 -1 0 1 0 -1 0 1
1 -1 -1 2 -1 1 1 -2 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0 0 -1 -1 1 -1 0 0 -1
1 0 -1 1 -1 0 1 -1 0 0 0 0 0 0 0 0 -1 1 1 -1 0 0 0 0 1 -1 -1 1 0 -1 0 0
2 -1 -2 3 -1 0 2 -2 0 0 1 0 0 1 -1 -1 -1 0 2 -1 1 0 -2 2 0 -1 -1 1 -1 -1 -1 -1
-1 1 -1 -1 2 -1 0 2 1 -1 -1 2 -2 2 2 -3 2 -2 -1 3 -2 1 0 -2 0 0 0 -1 0 1 2 -3
0 2 1 -1 0 -2 -1 2 -1 0 0 0 1 0 1 -1 -1 -1 -1 1 0 2 1 -2 1 0 -1 1 3 -2 -2 3
-2 2 1 -2 2 -2 -2 3 0 -1 -1 1 0 1 2 -1 1 -2 -2 2 -2 2 2 -3 0 1 0 -1 2 1 0 0
0 0 0 0 2 -1 -1 2 0 0 0 0 -1 1 1 -1 0 0 0 0 -1 1 0 -1 1 0 0 0 1 0 0 0
0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 1 -1 0 1 0 0 0 1 0 0
0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 0
0 0 0 0 -1 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 1
-1 -1 0 1 2 0 -1 0 1 0 0 0 -1 2 0 1 1 0 1 -1 -1 0 0 0 0 0 0 -1 0 1 -1 0
1 -2 -1 1 -1 3 1 -2 0 1 0 0 -2 -2 -1 1 1 1 0 1 0 -1 0 0 0 1 1 -1 -2 1 1 -2
0 0 -2 1 1 0 2 0 0 0 1 0 -3 3 1 -5 0 -1 1 1 0 0 -1 0 1 -1 0 1 0 1 1 -2
0 0 -1 -1 0 1 1 1 0 0 0 1 -3 0 2 -4 1 -1 -1 3 0 0 0 -1 1 0 0 1 -1 1 2 -2
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 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 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 2 -2 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 -1 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0
0 0 0 0 1 -2 -1 2 0 0 0 0 0 1 1 -1 0 0 0 0 0 1 0 -1 1 -1 -1 1 1 -1 -1 1
0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 1 -1 0 1 0 -1 0 1 0 -1
0 0 0 0 1 0 -1 2 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 1 -1 1 0 0 1 1 0 0 1
0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0
0 1 1 0 0 -1 -1 0 0 0 0 0 1 0 0 1 -1 0 1 -2 0 0 0 1 0 0 -1 1 1 -1 -2 2
0 -1 -1 2 0 1 1 -2 0 0 0 0 0 0 -1 1 1 0 1 0 0 -1 -1 1 -1 0 0 -1 -1 1 0 -2
-2 1 1 -2 2 -1 -1 2 0 0 0 0 -1 1 1 -1 1 -2 -1 2 -1 1 0 -1 0 1 0 -1 1 1 0 0
-1 -1 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 2 -1 -1 2 -1 0 0 -1 -1 1 1 -2 -1 2 1 -2
32 32
-1 0 1 -1 1 0 -2 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 -1 1
1 -1 0 1 -2 2 1 -3 0 0 0 0 1 -1 -1 1 0 0 0 0 0 0 0 0 -1 0 0 0 -2 1 0 -1
0 -1 -1 1 1 1 1 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 -1 1 1 -2 -1 2 2 -3
1 -1 -1 1 -1 2 2 -2 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 1 -1 -2 1 2 -2
-1 0 3 -3 1 0 -3 3 0 1 -1 0 -1 -1 2 0 0 1 -1 0 0 0 1 -1 2 0 0 1 2 -1 -1 4
3 -1 0 3 -3 1 0 -3 -2 1 1 -2 3 -3 -2 4 -2 1 1 -2 1 0 0 1 0 1 -1 1 0 -1 -3 2
0 -3 -1 3 0 3 1 -3 0 1 1 -2 -1 -1 -2 2 0 1 1 -2 0 -1 0 1 -1 1 2 -1 -2 3 1 -2
3 -3 -3 5 -3 3 3 -5 -1 1 2 -2 1 -2 -3 2 -1 1 2 -2 1 -1 -1 2 -1 0 0 1 -3 1 0 -2
-1 1 2 -2 0 -1 -2 1 0 0 -1 0 1 -1 0 2 0 0 -1 0 0 1 1 -1 0 1 0 0 1 0 -1 2
1 -1 0 2 -1 1 1 -3 -1 1 1 -2 1 -1 -2 2 -1 1 1 -2 0 0 0 1 -1 0 0 0 -1 0 -1 0
-1 -1 0 0 2 0 -1 1 1 0 0 0 -1 1 0 0 1 0 0 0 -1 0 1 -1 -1 1 1 -2 -1 2 1 -2
1 -2 -1 2 0 2 1 -2 0 1 1 -1 -1 0 -1 0 0 1 1 -1 0 -1 0 1 -1 0 1 -1 -2 1 1 -2
0 0 2 0 0 0 -2 0 -1 1 0 -2 2 -2 -1 4 -1 1 0 -2 0 0 1 0 0 1 0 0 1 0 -2 3
2 -2 -2 4 -2 2 2 -4 -1 1 2 -2 1 -1 -3 2 -1 1 2 -2 1 -1 -1 2 -1 0 0 0 -2 0 -1 -1
-2 0 0 0 2 0 0 0 1 -1 0 0 -1 2 0 0 1 -1 0 0 -1 0 0 0 -1 1 1 -2 -1 3 1 -3
0 -2 -2 2 0 2 2 -2 1 0 1 0 -2 1 -1 -1 1 0 1 0 0 -1 -1 1 -1 0 1 -1 -3 2 2 -4
-2 0 2 -1 2 1 -2 0 0 0 0 -1 0 -1 -1 3 1 -1 -1 0 -2 0 1 -1 -2 3 2 -3 0 3 0 0
2 -3 -1 3 -3 4 2 -4 0 1 1 -1 0 -2 -2 1 0 2 1 -2 1 -2 0 1 -1 -1 1 1 -3 0 0 0
-1 -1 -2 1 1 1 3 -2 1 -1 0 1 -1 2 -1 -1 2 -1 0 2 0 -1 -2 1 -2 0 1 -3 -3 3 3 -6
1 -2 -2 1 -1 2 3 -1 1 0 0 1 -2 1 0 -3 1 1 0 1 1 -1 -1 0 0 -2 1 0 -3 0 3 -3
-2 1 1 -2 2 -1 -1 2 0 0 0 0 -1 1 1 -1 1 -2 -1 2 -1 1 0 -1 0 1 0 -1 1 1 0 0
0 -1 1 0 0 1 -1 0 0 0 0 0 0 -1 0 1 1 0 -1 0 -1 0 1 -1 -1 1 1 -1 -1 1 0 0
0 -1 -1 0 0 1 1 0 0 0 0 0 -1 0 0 -1 1 0 -1 2 0 0 0 -1 0 0 1 -1 -1 1 2 -2
1 -1 0 0 -1 1 0 0 0 0 0 0 0 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 1 0 -1 0 1 0
-2 2 2 -2 2 -2 -2 2 0 -1 -1 0 1 1 1 1 0 -1 -1 0 -1 1 1 -1 0 1 0 -1 2 1 0 1
0 -2 0 2 0 2 0 -2 0 1 1 -2 0 -1 -2 3 0 1 1 -2 0 -1 0 1 -1 1 1 -1 -1 1 -1 1
-2 0 0 -2 2 0 0 2 2 -1 -1 2 -3 2 2 -3 2 -1 -1 2 -1 0 0 -1 0 0 1 -1 -2 2 3 -3
0 -2 0 0 0 2 0 0 1 1 0 0 -2 -1 0 0 1 1 0 0 0 -1 0 0 0 0 1 0 -2 0 1 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 -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 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 1 0 -1 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 1 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
32 32
3 -2 0 2 -3 2 0 -2 -1 2 1 -2 2 -4 -3 4 -1 2 1 -2 1 -1 0 1 0 0 0 1 -1 -2 -2 3
2 1 -2 2 -2 -1 2 -2 -1 0 1 0 1 1 -1 -2 -1 0 1 0 1 0 -1 1 0 -1 -1 1 0 -2 -1 -1
0 0 1 2 0 0 -1 -2 -1 0 1 -2 3 0 -2 4 -1 0 1 -2 0 0 0 1 -1 1 0 -1 1 1 -3 1
0 0 -2 3 0 0 2 -3 0 -1 1 0 0 3 -1 -1 0 -1 1 0 0 0 -1 1 -1 0 0 -1 -1 2 0 -4
2 -2 0 2 -1 1 -1 -1 -1 2 1 -2 0 -2 -1 2 -1 2 1 -2 1 -1 0 1 1 0 -1 2 0 -1 -2 2
2 0 -2 2 -2 1 2 -3 -1 0 1 0 1 -1 -1 0 -1 0 1 0 1 0 -1 1 -1 0 -1 0 -1 0 0 -2
0 0 0 2 1 0 0 -1 -1 0 1 -2 1 0 -2 2 -1 0 1 -2 0 0 0 1 -1 2 1 -2 1 1 -1 0
0 0 -2 2 0 1 2 -2 0 -1 1 0 0 1 -1 -1 0 -1 1 0 0 0 -1 1 -2 1 1 -2 -1 2 1 -3
1 1 0 0 -1 -1 0 -1 0 0 0 0 2 -1 -1 2 -1 0 0 0 1 0 0 1 0 0 -1 0 0 -1 -1 0
-1 1 0 0 1 0 1 -1 0 0 0 0 0 1 -1 0 0 -1 0 0 0 0 -1 1 -1 1 1 -2 0 1 1 -2
-1 1 2 -2 2 -2 -2 3 0 0 0 0 0 1 1 0 0 0 -1 0 -1 1 1 -1 1 0 0 0 2 -1 -1 2
-1 0 1 0 2 0 -1 1 0 0 0 0 -1 1 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 1 1 0 0
0 0 0 0 0 1 1 -2 0 0 0 0 0 0 -1 1 0 0 0 0 1 -1 -1 2 -1 1 1 -2 -1 1 1 -2
0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 1 0
0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 1 0 0 0 -1 0 0 0 -1 0 0
0 0 0 0 1 -1 0 2 0 0 0 0 -1 1 1 -2 0 0 0 0 -1 1 0 -1 1 -1 0 1 1 -1 0 1
2 -1 -1 2 -2 2 2 -3 -1 1 1 -1 1 -2 -3 2 0 1 1 -1 1 -2 -1 2 -1 0 1 -1 -2 -1 0 -1
0 1 -1 0 0 -1 1 1 0 -1 0 1 -1 2 1 -4 0 0 0 1 1 0 -1 0 1 -1 0 1 1 -1 1 -1
0 1 1 0 -1 -1 0 -1 -1 0 0 -1 3 0 -1 2 -1 0 1 -1 1 0 -1 2 0 -1 -1 1 2 -2 -3 3
-1 1 0 0 1 -2 0 1 0 -1 0 0 0 3 1 -2 0 -1 0 1 0 1 -1 0 1 -1 -1 1 2 0 -1 0
2 -2 0 2 -2 2 0 -2 -1 2 1 -2 1 -3 -2 3 -1 2 1 -2 1 -1 0 1 0 0 0 1 -1 -1 -2 2
2 0 -2 2 -2 0 2 -2 -1 0 1 0 1 0 -1 -1 -1 0 1 0 1 0 -1 1 0 -1 -1 1 -1 -1 0 -2
0 0 0 2 0 0 0 -2 -1 0 1 -2 2 0 -2 3 -1 0 1 -2 0 0 0 1 -1 1 0 -1 1 1 -2 0
0 0 -2 2 0 0 2 -2 0 -1 1 0 0 2 -1 -1 0 -1 1 0 0 0 -1 1 -1 0 0 -1 -1 2 1 -4
0 0 0 0 0 1 1 -2 0 0 0 0 0 0 -1 1 0 0 0 0 0 -1 0 1 -1 1 1 -2 -1 1 1 -2
0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 -1 -1 1 0 0 1 0 0 0 1 0
0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 -1 1 0 -1 0 0 0 -1 0 0
0 0 0 0 1 -1 0 2 0 0 0 0 -1 1 1 -2 0 0 0 0 0 0 -1 0 1 -1 0 1 1 -1 0 1
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 -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 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 1 -1 0 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 0 0 0 1 0 0 1 0 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 -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 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 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 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 1 0 -1 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 -1 0 0 -1 1 1 -1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 -1 0 0 0 1 -1 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 -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 0 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 -1 -1 1 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 1 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 1 -1 0 0 -1 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 1 -1 -1 2 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 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 1 2 -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 1 -1 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 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 -1 -1 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 1 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 1 0 1 -1 -2 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 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 -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 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 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
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 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 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 1 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 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 -1 0 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 -1 1 -1 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 -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 -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 -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 -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 -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 0 0 1 -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 0 0 1 -1 -2 2 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 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 -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 1 0 0 1 -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 1 0 1 -1 -2 2 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 1 1 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 -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
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 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 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 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
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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 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 -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 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 -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 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 -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 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 -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 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 -1 1 0 -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
-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 -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 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 -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 -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 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 -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 -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 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 -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 -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 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 -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 -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 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 -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 -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 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 -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 -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 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 -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 -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 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