The Lattice L7(P^3)
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 13:11:12 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DIVISORS
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
L7(P^3)
-
DIMENSION
28
-
DIVISORS
2^2
-
GRAM
28 0
4
-2 4
-2 0 4
-2 2 2 4
-2 2 0 0 4
-1 -1 0 0 1 4
-2 0 2 2 0 1 4
0 1 1 1 -1 -1 -1 4
0 -1 -1 -1 1 1 -1 -2 4
-1 -1 2 0 0 1 0 0 0 4
1 1 0 0 0 -1 -2 1 -1 0 4
-1 -1 0 0 0 1 0 0 2 0 -2 4
-1 2 1 1 0 -2 1 1 -2 -1 0 -1 4
1 -2 -1 -1 -2 1 -1 0 1 1 0 1 -2 4
1 0 0 1 -1 -1 -1 0 0 1 1 -1 0 0 4
1 -2 0 -1 -1 0 -1 -1 1 2 0 0 -1 1 2 4
1 0 -2 -1 1 1 -2 -1 1 0 1 0 -1 1 1 1 4
1 0 0 -1 -1 -2 0 1 -1 -1 0 -1 1 -1 -1 -1 -2 4
0 1 1 1 -1 -2 0 2 -1 0 0 0 1 -1 0 -1 -2 2 4
1 -1 -1 -2 -1 0 -1 1 0 0 -1 1 0 1 -1 0 0 1 1 4
1 -2 0 0 -1 0 0 -1 1 0 0 1 -1 1 1 2 1 -1 -1 -1 4
-2 2 1 1 2 1 1 0 -1 0 1 -1 1 -1 -1 -2 0 -1 -1 -1 -2 4
-2 2 1 1 2 1 1 0 -1 0 1 -1 1 -1 -1 -2 0 -1 -1 -1 -2 3 4
0 1 0 1 1 -1 -1 1 0 -1 1 0 0 -1 1 0 1 -1 0 -1 1 0 0 4
1 -1 -1 -2 -1 0 -1 1 0 0 -1 1 0 1 -1 0 0 1 1 3 -1 -1 -1 -1 4
-1 -1 1 1 -1 0 2 -1 0 0 -1 1 0 0 0 1 -1 0 0 -1 2 -1 -1 0 -1 4
1 1 -1 -1 1 0 -2 1 0 0 1 -1 0 0 0 -1 1 0 0 1 -2 1 1 0 1 -3 4
1 1 -1 -1 1 0 -2 1 0 0 1 -1 0 0 0 -1 1 0 0 1 -2 1 1 0 1 -3 3 4
-
MINIMAL_NORM
2
-
KISSING_NUMBER
3*24
-
HERMITIAN_GROUP_ORDER
2^17 * 3^4
-
HERMITIAN_GROUP_GENERATORS
5
28 28
-10 -18 -5 13 5 -1 -10 -5 -4 -3 1 -3 3 0 -1 0 -1 2 2 1 0 0 0 -1 1 -1 1 1
9 15 6 -11 -2 2 6 2 1 1 -2 3 -2 2 2 0 0 -1 -1 -1 0 0 0 1 -1 1 -1 -1
2 3 0 -1 -1 0 2 1 1 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
2 3 2 -1 1 1 0 -1 -1 -1 -1 1 0 2 1 1 0 1 0 0 0 0 0 0 0 0 0 0
9 15 6 -11 -2 2 7 3 2 1 -1 3 -2 2 2 0 0 -1 -1 -1 0 0 0 1 -1 1 -1 -1
0 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 0 -1 0 0 2 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
-1 -4 -2 3 1 0 -3 -1 -1 0 -1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
0 3 2 -3 -2 0 2 1 1 0 1 0 -1 -1 0 -1 1 -1 -1 0 0 -1 -1 0 0 0 0 0
2 4 1 -2 -2 0 2 1 1 1 0 1 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
0 -1 -1 1 0 -1 0 0 0 1 0 0 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0
0 0 -1 0 -1 0 1 1 1 1 1 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0
4 5 2 -2 0 1 -1 0 0 1 -2 0 0 1 0 -1 -1 -1 -1 0 0 0 0 0 0 1 -1 -1
-6 -7 -3 4 -1 -1 -2 -1 -1 -1 1 -1 0 -2 -1 1 1 1 1 0 0 0 0 0 0 -1 1 1
-2 -5 1 6 3 0 -7 -4 -3 -2 -1 -1 1 1 0 0 -1 1 0 1 0 0 0 -1 1 0 0 0
-3 -5 -1 5 0 -1 -4 -1 0 0 0 -2 0 -2 -1 -1 0 0 -1 1 0 0 0 -1 1 0 0 0
0 0 3 1 2 2 -4 -3 -3 -3 -1 0 0 2 1 1 -1 1 1 0 0 0 0 0 0 0 0 0
-1 -1 -2 -1 -1 -1 2 1 1 1 1 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0
1 1 0 -1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -5 -1 3 1 0 -3 -1 -1 -1 0 -1 1 0 -1 0 0 0 1 0 -1 0 0 0 0 0 0 0
-5 -9 -3 8 2 -1 -5 -2 -1 -1 1 -2 1 -1 -1 0 0 1 0 1 0 0 0 -1 1 -1 0 0
4 8 3 -6 -1 1 4 1 0 0 -1 2 -1 2 1 1 0 0 0 -1 0 0 0 1 -1 0 0 0
7 11 3 -8 -2 1 6 3 2 2 -1 2 -1 1 1 0 0 -1 -1 -1 0 0 0 1 -1 1 -1 0
0 -2 1 2 3 1 -2 -2 -2 -2 0 1 1 2 1 1 0 1 1 0 -1 0 0 0 0 0 0 0
-2 -4 -2 2 0 0 -2 0 0 0 0 -1 1 -1 -1 0 0 0 1 0 0 0 1 0 0 0 0 0
-1 -2 -2 3 0 -1 0 0 1 1 1 -1 0 -1 -1 0 0 0 -1 1 0 0 0 0 1 0 0 0
1 1 2 -1 1 2 -2 -2 -2 -1 -1 1 1 2 1 0 -1 1 1 0 0 0 0 1 -1 0 0 0
-1 -3 1 2 3 1 -4 -2 -3 -2 -1 0 1 2 1 0 -1 1 1 0 0 0 0 0 0 0 0 0
28 28
-10 -17 -6 12 4 -2 -8 -3 -3 -2 1 -3 2 -1 -1 0 0 2 1 1 0 0 0 -1 1 -1 1 1
9 15 4 -11 -4 1 8 4 4 3 -1 2 -2 0 1 -1 0 -2 -2 -1 0 0 0 1 -1 1 -1 -1
2 3 2 -1 0 1 0 -1 -1 -1 0 1 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0
3 4 2 -2 1 1 2 0 0 -1 0 1 0 2 1 1 -1 0 0 0 0 0 0 0 0 0 0 0
8 14 6 -10 -3 2 5 2 2 1 -2 2 -2 1 1 0 0 -1 -1 -1 0 0 0 1 -1 1 -1 -1
0 -1 1 1 2 1 -1 -1 -1 -1 0 0 1 2 0 1 0 1 1 0 0 0 0 0 0 0 0 0
2 3 2 -1 0 1 1 0 0 -1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 -3 -2 3 2 0 -2 -1 -1 0 0 0 1 1 0 1 -1 1 1 0 0 1 1 0 0 0 0 0
1 4 3 -3 0 1 1 -1 -1 -1 0 1 -1 1 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0
0 0 -1 -1 -1 -1 2 1 1 1 1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 0 1 1 1 0 -1 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0
1 3 2 -2 0 1 1 -1 -1 -1 0 1 -1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0
4 8 1 -6 -4 1 5 2 2 2 0 2 -1 -1 0 0 0 -1 -1 -1 0 0 0 1 -1 0 0 0
-4 -8 -4 6 2 -2 -3 0 0 1 1 -2 1 -1 -1 -1 0 0 0 1 0 0 0 -1 1 0 0 0
-4 -6 -3 3 1 -1 0 -1 -1 -1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 -1 1 1
-5 -7 -2 3 1 0 -2 -2 -2 -2 1 0 1 0 0 1 0 1 2 0 0 0 0 0 0 -1 1 1
-1 -1 0 0 0 0 -1 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 -2 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 3 0 -2 -1 -1 3 1 1 1 1 1 -1 -1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
-1 -3 -2 2 0 -1 0 0 0 1 1 0 0 -1 -1 0 1 0 0 0 -1 0 0 0 0 0 0 0
-5 -6 0 3 2 0 -3 -2 -3 -4 0 0 0 1 1 2 0 1 2 0 0 0 0 -1 0 -1 1 1
7 11 3 -7 -3 1 5 3 3 3 -1 1 -1 0 0 -1 0 -1 -2 0 0 0 0 1 -1 1 -1 -1
7 11 3 -7 -3 1 5 3 3 3 -1 1 -1 0 0 -1 0 -1 -2 -1 0 0 0 1 0 1 -1 -1
0 -2 1 2 3 1 -3 -2 -2 -2 -1 0 1 2 1 1 -1 1 1 0 -1 0 0 0 0 0 0 0
-1 -2 -3 1 -1 -1 1 1 1 2 1 0 0 -2 -1 0 1 0 0 0 0 0 1 0 0 0 0 0
0 1 2 -1 0 1 0 -1 -1 -2 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1
0 -1 -2 1 0 -1 0 1 1 2 0 -1 0 -1 -1 -1 0 0 -1 0 0 0 0 0 0 1 0 0
0 -1 -2 1 0 -1 0 1 1 2 0 -1 0 -1 -1 -1 0 0 -1 0 0 0 0 0 0 0 -1 0
28 28
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 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
-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 -1 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
-1 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 -1 0 1 1 -1 0 1 0 1 1 1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0
-2 -3 -1 1 1 -1 -1 1 0 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0
0 0 -1 -1 -1 -1 3 2 2 2 1 0 0 -1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0
1 0 1 1 2 1 -1 -1 -1 -1 0 0 1 2 0 1 0 1 1 0 0 0 0 0 0 0 0 0
-1 -2 1 1 2 1 -3 -2 -2 -2 -1 0 1 2 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 -1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -3 -3 2 -1 -1 1 2 2 2 1 -1 1 -2 -1 -1 1 0 -1 0 0 0 0 0 0 0 0 0
0 0 -1 -1 -1 -1 3 2 2 1 1 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0
0 -2 -1 2 2 0 -1 0 0 0 0 0 1 1 0 0 0 1 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 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 -1 -1 -1 2 1 1 1 1 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0
-1 -3 -1 2 1 0 -2 -1 0 0 0 -1 1 0 0 -1 -1 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 1 0 0 0 0 0 0 0
0 0 1 1 1 1 -2 -1 -1 -1 -1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0
0 0 1 1 1 1 -2 -1 -1 -1 -1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0
0 -1 0 2 0 0 -2 -1 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
4 8 2 -8 -3 1 6 2 2 1 0 2 -1 0 1 0 0 -1 0 -1 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 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 1
28 28
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 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 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 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 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 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 2 2 -1 -1 0 -1 -1 -1 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 -2 0 -1 0 1 1 1 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 2 0 0 0 -1 -1 -1 -1 -1 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 2 -1 0 0 -1 -1 -1 -1 -1 0 -1 1 1 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 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
1 1 -2 -1 -2 -2 4 3 3 3 1 0 0 -2 -1 -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 1 0 0 0 0 0 0 0 0
1 1 0 -1 -1 -1 1 1 1 1 0 0 -1 -1 0 -1 0 -1 -1 0 0 0 0 0 0 0 -1 0
-5 -6 -1 4 2 1 -3 -3 -3 -3 1 0 1 1 0 2 0 2 2 0 0 0 0 0 0 -1 1 1
1 2 1 -1 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 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
-1 -2 -1 1 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 -2 0 2 2 1 -2 -1 -1 -1 0 0 1 1 0 1 0 1 1 0 -1 0 0 0 0 0 0 0
1 1 0 0 0 1 -1 0 0 0 -1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0
28 28
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 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
-1 1 0 -1 -1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 0 1 1 1 -1 -1 -1 -1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0
-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
3 5 2 -4 -1 0 4 2 1 0 0 1 -1 0 0 1 1 -1 0 -1 0 0 0 0 0 0 0 0
-2 -3 -1 2 0 0 -2 -1 0 0 0 -1 0 -1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0
0 -2 0 2 2 1 -2 -1 -1 0 0 0 1 1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0
1 0 -1 0 1 -1 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -3 -2 1 -1 -1 0 1 1 1 0 -1 0 -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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 0 2 2 1 -2 -1 -1 -1 0 0 1 1 1 0 -1 1 0 0 0 0 0 0 0 0 0 0
1 -1 0 1 2 1 -1 -1 -1 0 0 1 1 1 1 0 -1 1 0 0 0 0 0 0 0 0 0 0
0 -1 -1 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
1 2 1 -2 -1 0 1 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
0 0 -1 0 -2 -1 1 2 2 2 0 -1 0 -2 -1 -1 1 -1 -1 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 1 0 0 0 0 0 0 0 0 0 0 0
1 2 -1 -2 -2 -1 3 2 2 2 0 0 -1 -2 0 -1 0 -1 -1 0 1 0 0 0 0 0 0 0
-1 -1 0 1 1 0 -1 -1 -1 -1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0
-1 -1 0 1 1 0 -1 -1 -1 -1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0
0 0 0 1 0 -1 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 1 0 0 0
-3 -6 -2 4 1 -1 -3 0 0 0 0 -2 1 -1 -1 -1 1 0 0 0 0 0 0 -1 1 0 0 0
1 1 -1 -1 -1 -1 2 2 2 2 0 0 0 -1 0 -1 0 -1 -1 0 0 0 0 0 0 1 0 0
-1 -1 1 1 1 1 -2 -2 -2 -2 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0
-1 -1 1 1 1 1 -2 -2 -2 -2 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1
-
HERMITIAN_STRUCTURE
4
28 28
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 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 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 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 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 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 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 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 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 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 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 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 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 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
28 28
-2 -2 -1 2 0 0 -1 -1 -1 -1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 -1 0 1
2 2 1 -1 0 0 1 1 1 1 0 0 0 0 0 -1 0 -1 -1 0 -1 -1 0 0 0 1 0 -1
-1 -1 1 0 0 0 -2 -1 -1 -1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 6 3 -4 0 0 3 1 1 0 0 1 -1 1 1 0 0 -1 -1 0 -1 -1 0 0 0 1 0 -1
1 2 0 -3 -1 -1 4 2 2 1 1 0 -1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
1 1 0 -1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 -2 -1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0
-2 -3 -1 2 1 -1 -1 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0
-1 -1 1 0 0 0 -2 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 1 0 0 -2 -1 -1 -1 -1 -1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -3 -1 3 1 0 -2 -1 -1 0 0 0 1 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0
0 0 -1 0 -1 0 0 1 1 1 0 -1 0 -1 -1 0 0 0 0 0 1 1 0 0 0 0 0 0
-4 -5 -1 3 1 0 -2 -1 -1 -2 0 -1 1 1 0 1 0 1 1 0 0 0 0 0 0 -1 0 1
-4 -4 -1 2 0 0 -2 -1 -1 -2 0 -1 0 0 0 1 0 1 1 0 0 0 0 0 0 -1 0 1
0 1 -2 -1 -2 -2 4 3 3 2 1 -1 -1 -2 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0
1 1 0 0 -1 0 0 0 0 1 0 1 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0
-2 -4 -1 3 1 0 -3 -1 -1 0 0 0 1 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0
0 0 -2 -1 -2 -1 2 2 2 2 1 0 0 -2 -1 -1 1 -1 0 0 0 0 0 0 -1 0 0 0
-3 -3 -2 2 0 0 -1 -1 -1 -1 0 0 0 0 0 2 0 2 1 0 1 1 1 0 0 -1 0 1
3 4 2 -3 0 0 2 1 1 1 0 0 0 0 0 -1 0 -2 -1 0 -1 -1 -1 0 0 1 0 -1
3 2 2 -1 1 0 0 0 0 0 -1 0 0 1 0 0 0 -1 0 0 -1 0 0 0 0 1 0 -1
-2 -4 -1 4 2 0 -3 -2 -1 -1 0 -1 1 1 0 0 -1 1 0 1 0 0 0 0 0 0 0 0
-2 -5 -3 4 1 -1 -2 0 0 1 1 -1 1 -1 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0
-5 -7 -3 4 1 0 -2 -2 -2 -1 1 0 1 0 0 1 0 2 1 0 0 0 0 0 0 -1 1 1
2 2 1 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1
-1 -1 1 1 1 0 -1 -1 -1 -2 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0
28 28
4 7 3 -5 -2 0 3 2 2 2 0 0 -1 -1 0 -2 0 -2 -2 0 0 -1 -1 0 0 0 -1 -1
-3 -6 -3 4 2 0 -1 -1 -1 -1 1 0 1 1 0 2 0 2 2 0 0 1 1 0 0 0 1 1
-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 -2 0 0 0 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-4 -9 -3 7 4 0 -5 -3 -3 -2 0 0 2 2 0 2 -1 3 2 0 0 1 1 0 0 0 1 1
1 1 2 0 2 1 -2 -2 -2 -2 -1 1 0 2 1 1 -1 1 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 0 0 0 0 0 0 0 0 0 0 0
-2 -3 0 3 1 0 -3 -1 -1 -1 0 -1 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0
1 2 0 -2 -1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0
-2 -2 0 1 0 0 -2 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 -1 0 0 2 0 0 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 -2 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 -1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0
0 3 2 -3 -2 0 1 0 0 0 0 0 -1 -1 0 -1 1 -1 -1 0 0 -1 -1 0 0 0 0 0
2 3 -2 -3 -3 -2 5 4 4 4 1 -1 -1 -3 -1 -2 1 -2 -2 0 0 0 0 0 0 0 -1 -1
1 1 1 -1 0 0 -1 0 0 0 -1 -1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 -1
0 -1 0 1 1 0 -1 -1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 2 1 -2 -2 0 1 1 1 0 0 0 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 1 1 1 0 -1 0 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0
-4 -8 -1 7 2 -1 -7 -2 -1 -1 -1 -3 1 -1 -1 -1 0 0 0 1 0 0 0 -1 1 0 0 0
2 3 0 -2 -1 0 1 1 1 2 0 0 0 -1 0 -2 0 -1 -1 0 0 0 -1 0 0 0 -1 -1
-2 -5 -1 4 3 0 -1 -2 -2 -2 1 1 1 2 0 2 0 2 1 0 -1 0 0 0 0 0 1 1
-1 -2 -1 2 1 0 0 -1 -1 -1 0 1 0 1 0 2 0 2 1 0 1 1 1 0 0 0 1 1
-4 -10 -4 9 4 -1 -6 -2 -2 0 1 -2 2 0 -1 -1 -1 1 0 1 0 0 0 -1 1 0 0 0
-1 -1 1 0 0 -1 -1 1 0 -1 -1 -1 -1 -1 0 0 1 -1 0 0 0 0 0 -1 0 0 0 0
1 1 -1 -1 -1 0 1 1 1 1 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 0
2 2 1 -1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0
-4 -6 -1 4 2 0 -2 -2 -2 -2 1 0 1 1 0 2 0 2 1 0 0 0 0 0 0 -1 1 1
28 28
-1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0
1 0 -1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0
-1 -1 0 1 0 0 -2 -1 -1 -1 -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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 -1 0 0 -1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 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 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -3 0 4 2 1 -4 -3 -2 -1 0 0 1 1 0 0 -1 1 0 1 0 0 0 0 0 0 0 0
1 3 0 -4 -2 -1 4 2 1 1 1 1 -1 -1 0 0 1 -1 0 -1 0 0 0 0 0 0 0 0
-2 -2 1 1 0 0 -3 -1 -1 -2 -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 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 2 1 1 -2 -1 -1 -1 -1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0
0 1 2 -1 0 1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
-3 -3 -2 1 -1 -1 1 1 1 0 1 -1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 -1 0 0
-3 -3 0 1 0 0 -2 -1 -1 -2 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0
-1 -2 -2 1 0 -1 1 1 1 1 1 -1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 4 1 -2 -2 0 2 1 1 1 0 1 -1 -1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
-1 -1 -1 1 -1 0 -1 0 0 1 0 0 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0
-1 -3 -1 3 0 0 -3 -1 0 1 0 -1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0
-2 -2 -1 1 0 0 -1 -1 -1 -1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 -1 0 0
1 -1 0 1 2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 -1 0 0 0 1 0 0
2 1 1 0 1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
-4 -9 -4 8 3 -1 -5 -2 -1 0 1 -2 2 0 -1 -1 -1 1 0 1 0 0 0 -1 1 0 0 0
-3 -7 -2 6 2 -1 -5 -1 -1 0 0 -2 1 -1 -1 -1 0 0 0 1 0 0 0 -1 0 0 0 0
-1 -1 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
4 4 1 -2 0 0 2 2 2 2 0 0 0 0 0 -1 0 -1 -1 0 0 0 0 0 0 1 -1 -1
-2 -4 -1 3 2 0 -1 -1 -1 -1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0
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PROPERTIES
Modular=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