The Lattice D2(1+i)+MxD6
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 13:11:26 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)+MxD6
-
DIMENSION
32
-
KISSING_NUMBER
960
-
GRAM
32 0
6
0 6
0 0 6
-3 3 3 6
0 2 0 1 6
-2 0 0 1 0 6
0 0 0 1 0 0 6
-1 -1 -1 0 -3 3 3 6
0 0 2 1 3 -1 3 -1 18
0 0 0 -1 1 3 -1 -1 0 18
-2 0 0 1 -3 1 3 3 0 0 18
-1 1 -1 0 -2 4 0 3 -9 9 9 18
-3 1 -1 3 2 0 0 0 0 -4 -4 -4 8
-1 -3 3 1 0 2 2 2 4 0 0 0 0 8
1 -3 -3 -3 0 -2 2 0 4 0 0 -4 0 0 8
0 -4 0 -3 -2 0 2 2 4 0 4 0 -4 4 4 8
4 -4 0 -4 0 -2 0 -1 3 -1 -3 -5 -2 2 4 3 8
4 4 0 0 2 0 0 -1 1 3 -3 1 -2 -2 -2 -3 0 8
0 0 4 0 0 0 0 -1 3 3 3 1 -4 2 -2 3 0 0 8
0 4 4 4 1 1 1 0 2 2 2 3 -1 1 -5 -2 -4 4 4 8
2 0 -2 -2 0 0 -2 0 -2 2 -6 -1 2 -2 2 -2 2 2 -2 -2 8
0 2 0 2 0 0 2 2 -2 -2 0 3 2 2 -2 -2 -2 2 -2 2 0 8
2 0 2 0 2 -2 0 -2 6 0 -2 -3 -2 2 2 2 2 2 2 2 0 0 8
0 0 2 2 0 -2 2 0 3 -5 1 -2 0 4 0 2 0 0 0 2 -4 4 4 8
0 -2 0 0 -2 0 2 3 2 -8 -2 -7 2 2 2 2 2 -2 -2 -2 0 0 0 2 8
2 0 2 0 0 -2 2 -1 8 2 -2 -3 -2 2 2 2 2 2 2 2 0 0 4 2 0 8
0 -2 0 -2 -2 -2 -2 -1 2 2 2 -3 -2 -2 2 2 2 -2 2 -2 0 -4 0 -2 0 0 8
0 0 2 0 -1 -1 -1 -2 5 5 5 2 -4 0 0 2 0 0 4 2 -2 -2 2 0 -4 4 4 8
-1 1 -1 0 2 0 0 0 4 -2 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
-1 -1 -1 0 0 2 2 2 2 4 2 2 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 4
1 1 -1 0 0 -2 2 0 0 -2 4 0 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
1 -1 -1 -1 -2 0 2 2 -2 2 4 4 -2 0 2 2 0 0 0 0 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
2^16*3^3*5
-
HERMITIAN_GROUP_GENERATORS
10
32 32
1 0 0 0 1 -1 -1 1 1 -1 -1 1 -1 0 1 -1 0 -1 0 1 0 0 -1 0 0 -1 0 1 -1 1 0 0
0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 -1 0 0 1 -1 1 -1 -1 2 0 0 1 -1 -1 -1 0 0
0 0 1 0 0 0 1 -1 0 0 1 -1 -1 1 0 -1 -1 0 0 -1 1 0 0 0 -1 0 0 -1 1 -1 -2 2
0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 -1 -1 1 1 -2 1 -1 0 1 -1 1 1 -2 0 -1 -1 0
0 0 0 0 1 -1 -2 2 2 -1 -2 2 -2 -1 2 -1 1 -2 0 3 0 0 -2 1 0 -1 0 0 -2 2 2 -3
0 0 0 0 1 -1 0 2 1 0 0 2 0 0 1 -3 -1 1 3 -3 1 -2 -1 3 1 0 0 0 -1 0 -1 -1
0 0 0 0 1 -1 0 0 1 -1 1 0 -3 2 0 -3 -2 -1 0 -1 2 -1 -1 1 -1 1 1 -2 0 1 -1 1
0 0 0 0 0 -1 1 0 0 -1 1 1 -1 3 1 -4 -3 2 2 -4 1 -2 0 1 0 1 1 -1 1 0 -2 1
0 0 0 0 1 0 1 -1 2 0 1 -1 -2 1 0 -2 -1 -1 0 -1 2 0 -1 1 -1 -1 0 -1 1 -2 -3 4
0 0 0 0 0 2 0 -1 0 3 0 -1 1 -2 -2 2 2 -1 -1 1 0 1 0 1 2 -1 -1 1 1 -2 1 2
0 0 0 0 -1 1 2 -1 -1 1 3 -1 1 1 -1 0 -1 2 1 -3 1 -1 1 1 -1 2 1 -3 1 -2 -1 0
0 0 0 0 0 1 0 1 0 1 0 2 2 -1 -1 1 1 1 1 -1 0 -1 0 2 1 1 1 -1 -1 -1 2 -2
0 0 0 0 -1 0 0 0 -1 0 0 0 2 0 0 1 0 1 0 0 -1 0 1 -1 0 1 0 0 0 1 1 -2
0 0 0 0 0 -1 0 0 0 -1 0 0 -1 2 1 -1 -1 0 0 0 0 0 0 -1 -1 0 0 0 0 1 -1 0
0 0 0 0 0 0 -1 0 0 0 -1 0 0 -1 1 1 1 -1 -1 2 -1 1 0 -1 1 -1 -1 2 0 1 1 0
0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 0 1 0 -1 -1 1 0 1 0 -1 0 -1 -1 1 1 0 -1 2
0 0 0 0 0 -1 -1 0 0 -1 -1 0 -1 0 1 0 1 -1 -1 2 -1 1 0 -2 0 -1 -1 2 0 2 0 0
0 0 0 0 2 -1 -1 2 2 -1 -1 2 -1 0 1 -2 0 0 1 0 1 -1 -2 2 0 -1 1 0 -2 0 0 0
0 0 0 0 0 1 1 -2 0 1 1 -2 -1 0 -1 0 0 -1 0 0 1 1 0 0 0 -1 -1 0 2 -2 -2 4
0 0 0 0 1 0 1 0 1 0 1 0 -1 1 0 -2 -1 0 1 -1 2 -1 -1 2 -1 0 1 -2 0 -2 -2 2
0 0 0 0 0 0 0 0 0 0 -2 2 2 -1 1 0 1 1 1 0 -1 0 0 0 3 -2 -1 4 0 0 1 0
0 0 0 0 0 0 0 0 0 -2 0 2 0 3 1 -2 -2 2 1 -2 0 -1 0 0 -1 2 3 -2 -1 1 1 -2
0 0 0 0 0 0 0 0 2 -2 -2 2 -2 1 3 -2 0 -1 0 2 0 0 -1 0 -1 -2 1 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 -2 0 0 -1 2 1 0 -1 0 -1 1 0 0 0 -1 -3 1 2 -2 -1 1 0 -1
0 0 0 0 0 -2 0 0 0 -2 0 0 -2 2 2 -2 -2 0 0 0 0 0 0 -2 -1 0 0 0 0 2 -2 0
0 0 0 0 2 0 0 0 2 0 0 0 -2 0 0 -2 0 -2 0 0 2 0 -2 2 0 -1 0 0 0 -2 -2 4
0 0 0 0 -2 2 2 -4 -2 2 2 -4 0 0 -2 2 0 0 -2 0 0 2 2 -2 0 0 -1 0 4 -2 -2 4
0 0 0 0 0 2 2 -2 0 2 2 -2 0 0 -2 0 0 0 0 -2 2 0 0 2 0 0 0 -1 2 -4 -2 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 1 0 0 0
0 0 0 0 0 0 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 -1 0 1 -1 0 1 -1 0 1 -1 0 -1 0 1 0 0 -1 0 -1 1 1 -2 -1 1 0 -1
0 1 0 0 1 -1 -1 2 0 1 1 -1 0 0 0 -1 0 0 1 -1 1 -1 -1 2 0 0 -1 0 0 -1 -1 1
0 0 1 0 1 0 0 0 -1 0 1 -1 -1 1 0 -1 -1 0 0 -1 1 0 0 0 0 1 0 0 1 0 -1 1
0 0 0 1 1 -1 0 1 -1 1 1 -1 0 1 0 -1 -1 1 1 -2 1 -1 0 1 1 0 -1 1 1 -1 -1 1
0 0 0 0 -1 1 0 -1 0 1 1 -2 1 -1 -3 3 1 -1 -2 1 0 1 1 -1 -2 1 0 -2 0 0 1 0
0 0 0 0 0 -1 -1 1 0 1 -1 0 1 -2 0 3 2 -1 -1 3 -1 1 0 -1 1 -2 -2 2 -1 1 1 -2
0 0 0 0 1 0 -1 1 0 1 1 0 2 -2 -1 1 1 0 1 -1 0 0 0 1 1 1 -1 0 -1 0 0 0
0 0 0 0 1 -1 -1 1 1 0 -1 2 0 -2 1 0 1 -1 1 1 0 0 -1 1 2 -1 -1 1 -1 1 0 -1
0 0 0 0 3 -1 -1 1 1 -1 1 -1 -5 1 2 -4 -1 -3 0 1 3 0 -3 2 -1 1 0 -1 1 1 -3 2
0 0 0 0 1 2 0 1 1 2 0 -1 1 -3 -2 0 2 -1 1 -1 1 0 -1 4 0 -1 -1 1 0 -2 -1 4
0 0 0 0 0 0 3 -1 -2 2 3 -3 -1 3 -2 -2 -3 2 1 -5 3 -2 1 2 1 0 -1 1 4 -3 -2 4
0 0 0 0 0 0 1 2 0 2 1 0 2 1 -1 -2 -1 3 3 -5 1 -3 0 4 1 -1 -1 1 1 -4 -1 3
0 0 0 0 -1 0 1 -1 0 0 -1 1 2 0 0 1 0 1 0 0 -1 0 1 -1 1 -1 0 1 0 0 1 -1
0 0 0 0 0 0 0 -1 0 -1 0 1 -1 2 1 -1 -1 0 0 0 0 0 0 -1 0 1 1 -1 0 1 0 -1
0 0 0 0 -1 1 0 -1 1 -1 -1 1 0 -1 1 1 1 -1 -1 2 -1 1 0 -1 -1 0 1 -1 -1 1 1 -1
0 0 0 0 0 1 0 -1 0 -1 0 0 -1 0 0 1 0 -1 -1 1 0 1 0 -1 -1 1 1 -1 0 1 0 0
0 0 0 0 -1 1 0 -2 1 -2 -1 2 -1 0 1 0 1 -1 -1 2 -1 1 0 -2 -1 1 2 -2 -1 2 1 -2
0 0 0 0 1 -1 -2 2 1 0 1 0 -1 0 1 -2 0 0 1 0 1 -1 -2 2 -1 1 0 -2 -1 0 -1 0
0 0 0 0 1 1 0 0 -1 0 1 -2 -1 0 -1 0 0 -1 0 0 1 1 0 0 -1 1 0 0 1 0 -1 2
0 0 0 0 2 -1 -1 2 -1 1 2 -2 -1 1 0 -2 -1 0 1 -1 2 -1 -1 2 0 1 -1 0 1 -1 -2 2
0 0 0 0 0 0 -1 1 3 -2 -3 4 0 -2 3 -1 2 -1 1 3 -1 0 -2 1 0 -2 1 0 -3 1 1 -2
0 0 0 0 0 -1 0 1 1 0 1 2 0 3 2 -5 -3 3 4 -5 1 -3 -1 3 1 1 1 -2 0 -2 -1 0
0 0 0 0 1 -1 -1 1 1 -2 1 0 -5 3 3 -5 -2 -2 0 1 2 -1 -2 1 -3 2 2 -4 0 1 -2 0
0 0 0 0 0 -1 0 0 -1 -1 2 0 -2 5 2 -4 -4 2 1 -3 1 -2 0 0 -1 3 2 -3 1 0 -1 -1
0 0 0 0 0 -1 -1 -1 0 -1 -1 1 -1 -1 1 2 1 -2 -2 4 -1 2 0 -3 1 0 0 0 -1 3 1 -3
0 0 0 0 3 -1 -2 3 1 -1 0 1 -2 0 3 -4 0 -1 2 0 1 -1 -3 3 0 1 0 0 -1 0 -2 1
0 0 0 0 0 2 2 -3 0 0 0 -1 -2 -1 -2 0 0 -2 -1 0 2 1 0 1 0 0 1 0 2 0 -1 3
0 0 0 0 2 0 1 1 0 0 1 -1 -3 2 1 -5 -2 0 2 -3 3 -2 -2 4 0 0 0 1 2 -2 -3 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 1 0 0 0
0 0 0 0 0 0 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 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 1 1 -2 -1 1 1 -2 1 0 -3 3 0 0 -2 0 0 1 2 -2 -1 1 0 -1 1 0 1 0
0 0 0 0 0 0 -1 0 0 0 -1 0 0 -2 0 3 2 -2 -2 4 -1 2 0 -2 0 -1 -1 1 -1 2 1 -2
0 0 0 0 0 1 0 0 0 1 0 0 3 -3 -2 3 2 0 0 0 -1 1 1 0 1 0 -1 1 -1 0 1 0
0 0 0 0 1 0 -1 1 1 0 -1 1 0 -3 0 1 2 -2 0 2 0 1 -1 1 1 -1 -1 1 -1 1 0 0
0 0 0 0 1 -1 0 0 2 -1 -1 1 -3 0 2 -2 0 -2 0 2 1 0 -2 1 0 -1 0 0 0 1 -1 0
0 0 0 0 1 1 0 0 1 1 0 1 0 -1 0 -2 0 0 2 -2 1 -1 -1 3 1 0 0 0 0 -1 -1 2
0 0 0 0 -1 1 2 -2 0 0 2 -1 -2 2 -1 -2 -2 0 0 -2 2 -1 0 1 -1 1 1 -2 2 -1 -1 2
0 0 0 0 0 1 1 0 0 0 1 1 0 2 0 -3 -2 2 2 -4 1 -2 0 2 0 1 1 -1 1 -2 -1 2
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 2 -1 -1 2 1 -1 -1 2 -1 0 3 -3 0 0 2 0 1 -1 -2 2 1 -1 0 1 -1 0 -1 0
0 0 0 0 0 1 1 0 0 0 1 0 0 2 0 -3 -2 2 2 -4 1 -1 0 2 0 1 1 -1 1 -2 -1 2
0 0 0 0 0 -1 1 0 0 -1 0 0 -3 3 2 -3 -2 0 0 0 1 -1 0 0 -1 0 1 -1 1 0 -1 0
0 0 0 0 -1 0 1 0 -1 0 1 -1 0 3 0 -1 -2 2 0 -2 0 -1 1 0 -1 1 1 -1 1 -1 0 0
0 0 0 0 0 -1 -1 0 0 0 -1 0 0 -2 0 3 2 -2 -2 4 -1 2 0 -2 1 -1 -1 1 -1 2 1 -2
0 0 0 0 2 -1 -1 2 1 -1 -1 2 -1 0 3 -3 0 0 2 0 0 -1 -2 2 1 0 0 1 -1 0 -1 0
0 0 0 0 0 1 1 -2 1 0 0 0 -2 -1 -1 -1 0 -2 0 0 2 0 -1 2 0 0 1 -1 1 0 -1 2
0 0 0 0 1 0 1 0 1 -1 0 1 -3 2 2 -5 -2 0 2 -2 2 -2 -2 3 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 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 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 -1 1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 1 0 -1
0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 1 0 0 -1 1
0 0 0 0 1 -1 0 1 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -2 3 1 0 0 1
0 0 0 0 0 -1 0 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 -2 2 1 -1 -1 2
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 -1 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 -1 0 -1 0 -1 -1 1
0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 -1 -1 1 1 -1 0 1
0 0 0 0 -1 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 2 1 -3 0 0 0 -1
0 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 -1 0 0 1 -1
0 0 0 0 0 -1 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 0 -1 1
0 0 0 0 0 0 1 -1 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 -1 0 1
0 0 0 0 -1 0 0 -1 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 1
0 0 0 0 -1 1 1 -2 1 0 0 1 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 1 0 0 0
0 0 0 0 0 0 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 -1 0 -1 0 -1 0 0 0 1 0 1 1 0 0 0 1 -2 1 1 -2 0 1 0 -1 0 1 1 -2
0 1 0 0 1 -2 -1 2 0 -1 0 0 -2 2 2 -3 -1 0 1 -1 0 -1 -1 0 0 0 -1 1 0 1 -1 0
0 0 1 0 1 0 -1 0 0 0 -1 0 -1 -1 0 1 0 -1 -1 1 0 1 -1 0 1 0 0 1 0 1 1 0
0 0 0 1 1 -1 0 0 0 0 0 -1 -2 1 0 -1 -1 0 0 -1 1 0 -1 0 1 -1 -1 2 1 0 -1 2
0 0 0 0 1 0 0 0 -1 0 1 -1 0 1 0 -1 -1 1 1 -2 0 0 0 0 0 1 0 0 1 0 -1 1
0 0 0 0 0 1 0 0 0 0 0 -1 0 0 -1 1 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0 -1 1 0 -1 1 0 0 1 0 1 0 0 0 0 0 0 1 -1 -1 2 1 -1 0 1
0 0 0 0 0 0 0 1 0 1 0 -1 1 -1 -1 2 1 0 -1 1 0 0 0 0 0 -1 -1 1 0 -1 0 1
0 0 0 0 -1 1 0 0 -2 1 1 -1 3 1 1 0 -1 3 2 -2 -1 0 1 0 1 1 0 1 2 -1 0 0
0 0 0 0 -1 -1 0 0 -1 -1 0 -1 -2 4 1 -2 -3 1 0 -2 -1 0 1 -2 -2 1 1 -1 1 2 0 0
0 0 0 0 1 -1 -2 2 0 0 -2 1 0 -1 2 2 1 -1 -2 4 -1 0 -1 0 1 -2 -1 3 -1 1 3 -2
0 0 0 0 0 -1 -1 0 0 0 -1 -1 -1 0 -1 3 0 -1 -3 2 -1 1 0 -2 -1 -1 -1 1 0 1 1 1
0 0 0 0 0 0 2 -2 1 0 1 -1 -1 1 -2 -1 -1 0 0 -2 2 0 0 0 0 -1 0 0 1 -1 -2 3
0 0 0 0 0 2 0 -2 0 2 0 -1 2 -3 -3 5 2 -1 -2 2 0 2 0 0 1 0 0 0 0 -1 1 1
0 0 0 0 -2 2 2 -2 -1 1 2 -1 3 0 -1 1 0 2 1 -2 0 0 2 0 -1 1 1 -2 1 -2 -1 1
0 0 0 0 0 2 0 0 0 1 0 1 3 -3 -1 3 2 0 0 1 0 0 0 2 0 1 1 -1 -1 -1 1 -1
0 0 0 0 -2 2 0 -2 -1 1 0 0 3 -2 -1 4 2 0 -1 2 -2 2 2 -2 0 1 1 -2 0 0 2 -2
0 0 0 0 0 -2 -2 2 -1 -1 0 0 -1 2 3 -2 -1 1 1 0 -2 0 0 -2 0 1 -1 0 0 2 0 -2
0 0 0 0 2 0 -2 2 1 -1 -2 2 -1 -2 1 0 1 -2 0 2 0 0 -2 2 0 1 1 0 -2 2 2 -2
0 0 0 0 2 -2 -2 2 0 -1 -1 0 -3 1 2 -2 -1 -1 0 1 0 0 -2 0 1 0 -1 2 0 2 0 0
0 0 0 0 -2 1 1 -2 0 0 2 -2 1 0 -3 2 0 0 -1 -1 0 1 2 -2 -3 2 1 -4 0 0 -1 1
0 0 0 0 0 -1 -1 0 0 2 0 -2 1 -2 -1 4 2 -1 -2 3 -1 2 0 -2 1 -2 -3 2 0 -1 0 1
0 0 0 0 0 1 -1 0 -2 2 2 -2 3 -2 -1 2 1 1 1 -1 -1 1 1 0 1 2 -1 0 1 -1 -1 1
0 0 0 0 1 0 -1 0 0 2 0 0 1 -3 0 2 2 -1 0 2 0 1 -1 1 3 -1 -2 2 0 -1 0 0
0 0 0 0 0 1 1 0 0 1 1 0 2 -1 -1 0 1 1 1 -1 1 -1 0 2 1 0 0 0 0 -2 -1 1
0 0 0 0 -2 1 1 -2 -2 1 1 -2 2 1 -1 2 -1 2 0 -1 -1 1 2 -2 0 1 0 0 2 -1 0 1
0 0 0 0 0 -1 -1 2 0 -1 -1 2 0 1 3 -2 0 0 1 1 -1 -1 0 0 0 0 1 0 -1 1 1 -3
0 0 0 0 -1 0 -1 0 -1 0 -1 0 1 0 1 2 0 0 -1 2 -2 1 1 -2 0 0 0 1 0 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 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 -1 -1 1 0 -1 0 1 -1 -1 4 1 -3 -3 2 1 -3 0 -1 1 -1 0 0 0 0 2 -1 -1 1
0 1 0 0 0 0 1 -2 0 0 0 -1 -2 0 -2 1 0 -2 -2 1 1 1 0 -1 0 0 0 0 1 1 0 1
0 0 1 0 -2 1 0 -2 -1 1 0 -1 3 -1 -2 5 1 1 -2 1 -2 2 2 -3 0 0 0 0 0 0 2 -1
0 0 0 1 -1 2 1 -3 0 1 0 -1 2 -3 -4 5 2 -1 -2 1 0 2 1 -1 0 0 0 0 0 0 1 1
0 0 0 0 -1 0 1 -2 1 0 0 -1 -2 1 -1 0 -1 -1 -1 0 1 1 0 -1 -1 -1 0 -1 1 0 0 1
0 0 0 0 1 0 -1 0 1 1 -1 1 0 -3 -1 2 2 -2 -1 2 0 1 -1 1 2 -1 -1 1 -1 1 1 -1
0 0 0 0 -1 2 1 -2 0 1 2 -1 2 -1 -3 2 0 1 0 -2 1 0 1 1 -1 2 1 -3 0 -1 0 1
0 0 0 0 1 1 0 0 1 0 0 2 1 -2 -1 0 1 0 1 -1 1 -1 -1 3 1 1 1 -1 -1 0 0 0
0 0 0 0 -2 1 1 -1 0 1 1 -1 3 1 -1 1 -1 3 1 -3 -1 0 2 -1 0 0 0 0 1 -2 0 1
0 0 0 0 -1 -1 0 -1 -1 1 0 -1 -1 2 0 1 -1 0 -2 1 -1 1 1 -3 0 0 0 0 1 1 1 -1
0 0 0 0 0 0 -2 1 0 0 0 1 2 -2 1 3 2 0 -1 3 -2 1 0 -1 0 0 0 0 -2 1 2 -3
0 0 0 0 0 0 -1 -1 0 0 -1 1 0 -2 -1 4 2 -2 -3 4 -1 2 0 -2 0 0 0 0 -1 2 2 -2
0 0 0 0 1 1 1 -1 1 0 0 0 0 -2 -2 0 1 -2 0 0 2 0 -1 2 0 0 0 0 0 0 -1 2
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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
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32 32
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0 0 0 0 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
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0 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