The Lattice Turyn2A10
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 13:27:25 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS (elementary divisors)
KISSING_NUMBER
MINIMAL_NORM
GROUP_NAME
GROUP_ORDER
GROUP_GENERATORS
REFERENCES
NOTES
LAST_LINE
-
NAME
Turyn2A10
-
DIMENSION
48
-
GRAM
48 48
12 6 6 6 6 4 4 4 4 6 6 4 4
-4 6 -4 -3 -3 -5 -1 -3 -1 -3 -1 0 0 -1 -3 -2 4 -2 1 3 0
-2 2 0 1 -1 1 2 3 2 -1 0 2 1 -1 6 12 6 6 6 -2 -2 -2 -2
4 4 4 2 -6 6 -6 0 -3 -3 0 -2 0 -1 1 2 0 1 1 -2 3 -2 -3
3 3 0 3 1 -1 -2 0 1 2 3 3 -1 0 1 -6 6 6 12 6 6 4 4 4
4 4 6 6 6 -6 4 -4 2 0 -3 2 0 -1 -2 -1 1 -1 -1 -2 -1 1
-1 -2 5 3 3 5 3 1 0 1 3 1 2 1 2 -2 1 -4 6 6 6 12 6 -2
-2 -2 -2 2 4 2 6 -4 2 -6 -2 -3 -5 -3 -3 0 -2 0 2 -1 -1
-1 -5 1 -1 0 1 0 -2 3 0 -1 -3 -1 1 0 1 0 -2 -1 0 -3 6 6
6 6 12 4 -2 -2 -2 6 2 0 4 -2 2 -2 0 -1 -3 0 -3 -1 -1 0
2 0 -2 -2 -4 3 3 -1 3 2 0 3 3 1 -2 -1 1 3 -1 -2 -2 2 4
-2 4 -2 4 -2 4 12 6 6 6 6 4 0 4 -2 2 0 -1 1 -1 1 -1 -3
-1 -2 -2 -1 -4 -2 -2 3 0 3 1 0 1 0 1 3 2 1 1 2 -2 -2 0
2 1 3 4 -2 4 -2 -2 6 12 6 6 4 4 2 4 -4 4 2 1 2 0 3 2
-2 -3 -2 -2 -1 -1 -1 1 1 -1 1 3 1 2 2 1 1 3 1 1 1 1 0
3 -1 1 2 4 -2 4 -2 -2 6 6 12 6 2 6 6 2 0 0 0 -1 0 -1 1
1 -1 -1 -3 -2 0 -3 -2 2 0 -2 2 1 -1 1 0 0 2 2 3 1 1 0
1 3 0 -2 2 4 -2 4 -2 -2 6 6 6 12 2 4 2 0 -2 4 -2 -2 -1
-3 -1 -1 -1 -1 -1 -3 -3 -2 -4 2 2 -4 2 0 -2 -1 -2 -2 2 2
2 3 -2 0 -3 2 1 -2 1 6 4 4 2 6 6 4 2 2 12 6 2 2 -2 6
0 -3 -2 -1 0 -3 -2 -1 -1 2 -3 -3 -2 -2 3 0 0 0 0 1 1 0
1 1 0 3 3 0 -1 -1 2 3 0 6 4 6 4 2 4 4 6 4 6 12 6 6 -6
2 -6 -2 -3 -2 -1 1 2 -1 0 0 0 -3 -2 -1 3 -3 2 1 -1 1 1
2 4 1 3 2 3 3 1 2 0 -2 -1 4 4 6 2 0 0 2 6 2 2 6 12 0
-4 0 -4 1 -3 -1 0 2 2 0 -1 3 1 -1 -3 1 2 -2 1 3 -1 2 1
2 2 1 2 4 2 2 3 1 0 -2 -1 4 2 6 6 4 4 4 2 0 2 6 0 12
-6 0 -4 0 1 -2 2 2 0 -3 -3 -2 1 -2 -1 -3 0 0 0 2 2 1 5
4 2 -1 -2 -2 2 1 -1 3 -3 0 -2 -4 -6 -6 -4 -2 -2 -4 0 -2
-2 -6 -4 -6 12 -4 6 -2 0 2 1 -2 -2 1 0 -1 -2 0 0 3 -3 1
0 -4 -3 -1 -1 -3 -3 -1 0 -2 -3 -3 -2 0 3 -1 3 6 6 4 2 2
2 4 0 4 6 2 0 0 -4 12 -2 -1 -1 -1 0 -4 -1 -1 2 2 -3 2 2
0 1 -3 -3 2 2 1 1 -3 0 1 2 4 0 3 2 0 -1 3 -4 -4 -6 -4
-6 -2 0 2 0 -2 0 -6 -4 -4 6 -2 12 1 6 4 3 2 -3 -2 -2 -1
0 1 1 2 -3 4 -3 -1 3 2 0 1 -3 -1 -2 -2 0 -2 -1 0 0 3 3
-3 0 2 -2 0 -1 1 -1 -2 -3 -2 1 0 -2 -1 1 12 6 6 6 6 4 4
4 4 6 6 4 4 -4 6 -4 3 3 5 1 3 1 3 1 0 0 1 3 2 -4 2 -1
-3 -3 0 -3 -1 1 2 0 -1 -2 -3 -3 1 0 -1 6 6 12 6 6 6 -2
-2 -2 -2 4 4 4 2 -6 6 -6 0 3 3 0 2 0 1 -1 -2 0 -1 -1 2
-3 2 3 -5 -3 -3 -5 -3 -1 0 -1 -3 -1 -2 -1 -2 2 -1 4 6 6
12 6 6 4 4 4 4 4 6 6 6 -6 4 -4 -2 0 3 -2 0 1 2 1 -1 1
1 2 1 -1 1 2 -1 0 2 -3 0 1 3 1 -1 0 -1 0 2 1 0 3 6 6
6 12 6 -2 -2 -2 -2 2 4 2 6 -4 2 -6 2 3 5 3 3 0 2 0 -2
1 1 1 5 -1 1 0 -3 -2 0 -3 -3 -1 2 1 -1 -3 1 2 2 -2 -4 2
6 6 6 6 12 4 -2 -2 -2 6 2 0 4 -2 2 -2 0 1 3 0 3 1 1 0
-2 0 2 2 4 -3 -3 1 -1 0 -1 0 -1 -3 -2 -1 -1 -2 2 2 0 -2
-1 -3 4 -2 4 -2 4 12 6 6 6 6 4 0 4 -2 2 0 1 -1 1 -1 1
3 1 2 2 1 4 2 2 -3 0 -3 -3 -1 -2 -2 -1 -1 -3 -1 -1 -1 -1
0 -3 1 -1 -2 4 -2 4 -2 -2 6 12 6 6 4 4 2 4 -4 4 2 -1 -2
0 -3 -2 2 3 2 2 1 1 1 -1 -1 1 -1 -1 1 -1 0 0 -2 -2 -3
-1 -1 0 -1 -3 0 2 -2 4 -2 4 -2 -2 6 6 12 6 2 6 6 2 0 0
0 1 0 1 -1 -1 1 1 3 2 0 3 2 -2 0 2 -2 0 2 1 2 2 -2 -2
-2 -3 2 0 3 -2 -1 2 -1 4 -2 4 -2 -2 6 6 6 12 2 4 2 0 -2
4 -2 2 1 3 1 1 1 1 1 3 3 2 4 -2 -2 4 -2 0 0 -1 -1 0 -1
-1 0 -3 -3 0 1 1 -2 -3 0 6 4 4 2 6 6 4 2 2 12 6 2 2 -2
6 0 3 2 1 0 3 2 1 1 -2 3 3 2 2 -3 0 0 -1 1 -1 -1 -2 -4
-1 -3 -2 -3 -3 -1 -2 0 2 1 6 4 6 4 2 4 4 6 4 6 12 6 6
-6 2 -6 2 3 2 1 -1 -2 1 0 0 0 3 2 1 -3 3 -2 -3 1 -2 -1
-2 -2 -1 -2 -4 -2 -2 -3 -1 0 2 1 4 4 6 2 0 0 2 6 2 2 6
12 0 -4 0 -4 -1 3 1 0 -2 -2 0 1 -3 -1 1 3 -1 -2 2 -1 -2
-2 -1 -5 -4 -2 1 2 2 -2 -1 1 -3 3 0 2 4 2 6 6 4 4 4 2
0 2 6 0 12 -6 0 -4 0 -1 2 -2 -2 0 3 3 2 -1 2 1 3 0 0 0
4 3 1 1 3 3 1 0 2 3 3 2 0 -3 1 -3 -4 -6 -6 -4 -2 -2 -4
0 -2 -2 -6 -4 -6 12 -4 6 2 0 -2 -1 2 2 -1 0 1 2 0 0 -3
3 -1 0 -2 -2 -1 -1 3 0 -1 -2 -4 0 -3 -2 0 1 -3 4 6 6 4
2 2 2 4 0 4 6 2 0 0 -4 12 -2 1 1 1 0 4 1 1 -2 -2 3 -2
-2 0 -1 3 3 1 -3 -2 0 -1 3 1 2 2 0 2 1 0 0 -3 -3 -4 -6
-4 -6 -2 0 2 0 -2 0 -6 -4 -4 6 -2 12 -1 -6 -4 -3 -2 3 2
2 1 0 -1 -1 -2 3 -4 3 3 3 5 1 3 1 3 1 0 0 1 3 2 -4 2
-1 3 0 -2 2 0 1 -1 1 2 3 2 -1 0 2 1 -1 12 6 6 6 6 4 4
4 4 6 6 4 4 -4 6 -4 0 3 3 0 2 0 1 -1 -2 0 -1 -1 2 -3 2
3 3 3 0 3 1 -1 -2 0 1 2 3 3 -1 0 1 -6 6 12 6 6 6 -2 -2
-2 -2 4 4 4 2 -6 6 -6 -2 0 3 -2 0 1 2 1 -1 1 1 2 1 -1
1 2 5 3 3 5 3 1 0 1 3 1 2 1 2 -2 1 -4 6 6 12 6 6 4 4
4 4 4 6 6 6 -6 4 -4 2 3 5 3 3 0 2 0 -2 1 1 1 5 -1 1 0
1 0 -2 3 0 -1 -3 -1 1 0 1 0 -2 -1 0 -3 6 6 6 12 6 -2 -2
-2 -2 2 4 2 6 -4 2 -6 0 1 3 0 3 1 1 0 -2 0 2 2 4 -3 -3
1 3 2 0 3 3 1 -2 -1 1 3 -1 -2 -2 2 4 -2 6 6 6 6 12 4
-2 -2 -2 6 2 0 4 -2 2 -2 1 -1 1 -1 1 3 1 2 2 1 4 2 2
-3 0 -3 1 0 1 0 1 3 2 1 1 2 -2 -2 0 2 1 3 4 -2 4 -2 4
12 6 6 6 6 4 0 4 -2 2 0 -1 -2 0 -3 -2 2 3 2 2 1 1 1 -1
-1 1 -1 3 1 2 2 1 1 3 1 1 1 1 0 3 -1 1 2 4 -2 4 -2 -2
6 12 6 6 4 4 2 4 -4 4 2 1 0 1 -1 -1 1 1 3 2 0 3 2 -2
0 2 -2 1 -1 1 0 0 2 2 3 1 1 0 1 3 0 -2 2 4 -2 4 -2 -2
6 6 12 6 2 6 6 2 0 0 0 2 1 3 1 1 1 1 1 3 3 2 4 -2 -2
4 -2 0 -2 -1 -2 -2 2 2 2 3 -2 0 -3 2 1 -2 1 4 -2 4 -2
-2 6 6 6 12 2 4 2 0 -2 4 -2 3 2 1 0 3 2 1 1 -2 3 3 2
2 -3 0 0 0 0 1 1 0 1 1 0 3 3 0 -1 -1 2 3 0 6 4 4 2 6
6 4 2 2 12 6 2 2 -2 6 0 2 3 2 1 -1 -2 1 0 0 0 3 2 1
-3 3 -2 1 -1 1 1 2 4 1 3 2 3 3 1 2 0 -2 -1 6 4 6 4 2
4 4 6 4 6 12 6 6 -6 2 -6 -1 3 1 0 -2 -2 0 1 -3 -1 1 3
-1 -2 2 -1 3 -1 2 1 2 2 1 2 4 2 2 3 1 0 -2 -1 4 4 6 2
0 0 2 6 2 2 6 12 0 -4 0 -4 0 -1 2 -2 -2 0 3 3 2 -1 2 1
3 0 0 0 2 2 1 5 4 2 -1 -2 -2 2 1 -1 3 -3 0 -2 4 2 6 6
4 4 4 2 0 2 6 0 12 -6 0 -4 2 0 -2 -1 2 2 -1 0 1 2 0 0
-3 3 -1 0 -4 -3 -1 -1 -3 -3 -1 0 -2 -3 -3 -2 0 3 -1 3 -4
-6 -6 -4 -2 -2 -4 0 -2 -2 -6 -4 -6 12 -4 6 1 1 1 0 4 1 1
-2 -2 3 -2 -2 0 -1 3 3 2 2 1 1 -3 0 1 2 4 0 3 2 0 -1 3
-4 6 6 4 2 2 2 4 0 4 6 2 0 0 -4 12 -2 -1 -6 -4 -3 -2 3
2 2 1 0 -1 -1 -2 3 -4 3 -1 3 2 0 1 -3 -1 -2 -2 0 -2 -1
0 0 3 3 -4 -6 -4 -6 -2 0 2 0 -2 0 -6 -4 -4 6 -2 12
-
DIVISORS (elementary divisors)
5^24
-
KISSING_NUMBER
1965600
-
MINIMAL_NORM
12
-
GROUP_NAME
(2.Alt7xC3xPSL2(7)).2
-
GROUP_ORDER
5080320 = 2^8 * 3^4 * 5 * 7^2 */ >;
-
GROUP_GENERATORS
#5
48 48
1 0 1 0 -2 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 2 -2 2 -1 -2 0 -1 0 -2 1 0 -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 0 0 0 0 0 2 -1 3 -1 -3 0 -1 0 -2 2 -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 1 -1 2 0 -2 0 -1 0 -1 1 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 1 -1 1 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 -1 2 -2 1 0 1 1 -1 1 -1 0
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 0 0 0 0 0 0 1 0 0 -1 1 0 -1 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 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 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 0 0 0 0 0 0 0 2 0 0 -1 1 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 1 -1 1 -1 2 0 -1 0 -1 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 0 0 0 0 0 0 0 0 0 0 1 0 1 -2 1 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 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 -1 2 -1 -2 0 -1 0 -1 2 -1
-1 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 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 1 0 0 0 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 0 0 0 0 0 0 0 0 2 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 0 0 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 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 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 -2 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 2 -2 2 -1 -2 0 -1 0 -2 1 0 -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 0 0
0 0 0 2 -1 3 -1 -3 0 -1 0 -2 2 -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 1 -1 2 0 -2 0 -1 0 -1 1 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 1 -1 1 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 -1 2 -2 1 0 1 1 -1 1 -1 0 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 0 0 0 0 0 0 1 0 0 -1 1 0 -1 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 -1 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 0 0
0 0 0 0 0 2 0 0 -1 1 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 1 -1 1 -1 2 0 -1 0 -1 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 0 0 0 0 0 0
0 0 0 0 1 0 1 -2 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 -1 2 -1 -2 0 -1 0 -1 2 -1 -1 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 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 1 0 0 0 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 0 0 0 0 0 0
0 0 2 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -2 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 2 -2 2 -1 -2 0
-1 0 -2 1 0 -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 0 0 0 0 0 2 -1 3 -1 -3
0 -1 0 -2 2 -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 1 -1 2
0 -2 0 -1 0 -1 1 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 1 -1
1 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 -1
2 -2 1 0 1 1 -1 1 -1 0 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 0 0 0 0 0 0 1
0 0 -1 1 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 -1 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 0 0 0 0 0 0 0 2 0 0
-1 1 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 1 -1 1
-1 2 0 -1 0 -1 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 0 0 0 0 0 0 0 0 0 0 1 0 1
-2 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 2 -1
-2 0 -1 0 -1 2 -1 -1 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
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
1 0 0 0 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 0 0 0 0 0 0 0 0 2 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 0
0 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 0 0 0 0 0 0
48 48
-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 -2 1 -2 2 2 1 1 0 1 -2 1 1 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 -2 2 -3 2 2 1 2 0 1 -2 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 -2 2 -2 2 1 1 1 0 1 -1 0 1 0 1 0 1 0 0 0 0 0
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0 0 -1 1 -1 1 1 1 1 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0
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0 1 -1 1 -1 0 -1 0 1 -1 1 -1 -1 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 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
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0 1 -1 1 -1 0 -1 0 1 -1 1 0 -2 -1 -1 -1 -1 0 0 0 0 0
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0 0 0 -1 -1 0 1 -1 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0
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0 0 -2 1 -2 1 2 0 1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
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0 -1 1 -1 1 1 0 1 1 0 -1 1 -1 -1 0 0 0 0 0 0 0 0 0
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0 -2 2 -2 1 1 1 1 0 1 -1 0 1 1 1 0 1 0 0 0 0 0 0 0
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2 -1 2 -1 -2 0 -1 0 -1 2 -1 -1 -1 -1 -1 -1 0 0 0 0 0
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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 0
0 1 -1 1 -1 -1 0 0 -1 -1 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 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 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 2 2 1 1 0
1 -2 1 1 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 -2 2 -3 2 2 1 2 0
1 -2 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 -2 2 -2 2 1 1 1 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 0 0 0 0 0 0 0 -1 1 -1 1 1 1 1 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
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-1 1 -1 -1 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 -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 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 0 -1 0 1
-1 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 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1 -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 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 1 0 1
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 -2 1 2 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 -1 1 -1 1 1 0 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 -2 2 -2 1 1 1 1
0 1 -1 0 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 0 0 0 0 0 2 -1 2 -1 -2 0
-1 0 -1 2 -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 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 0 0 1 -1 1 -1 -1
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-1 -2 0 -2 3 -1 -2 0 0 -1 -2 -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 0 0 0 0 1 -1 2
-1 -2 0 -1 -1 0 2 -1 -1 0 0 -1 -1 0 0 1 0 0 0 1 0 -1
-1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-3 3 -3 2 1 2 1 -1 2 -1 0 2 1 1 0 2 1 -1 2 -1 0 -1
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 -1 2 -1 1 0 2 1 -1 0 -1 0 1 1 1 0 1 0 0 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 -2 3 -3 1 1 1 2 -1 1 -1 0 2 1 1 0 1 0 -1 0
0 1 0 0 -1 0 -1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 -2 2 -3 1 1 2 0 -1 1 -2 0 3 2 1 2 2 2 -1
3 -1 -2 0 -1 -1 -1 1 0 -1 -1 0 -1 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 2 -1 1 -1 2 0 -1 1 0 -1 1 1 1 -1
0 2 -2 3 -1 -1 -1 0 0 -2 1 0 -2 -2 -1 -1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 1 1 -1 0 -1 0
1 1 2 0 0 2 -3 3 -1 -1 -1 -1 0 -2 1 0 -1 -1 -1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 -1 -3 1 0 -2
-1 0 0 0 0 1 -1 0 0 -1 0 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 2 -1 -1 -1 0
1 -1 2 -1 -2 0 0 -1 -1 -1 0 -1 1 1 0 1 0 0 -1 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 1 -4 2 3
0 2 1 2 -1 0 2 0 0 1 0 0 1 -1 0 0 1 0 -1 1 -1 0 1
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1
-1 0 -2 -1 0 1 -1 1 2 0 0 0 1 -1 2 0 -1 0 0 0 -1 1
0 -2 -2 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
0 -1 1 1 1 1 0 0 -1 1 0 -1 -1 0 0 -1 2 -2 1 1 1 1 0
1 -1 0 1 0 1 0 1 -3 2 -4 2 3 0 1 2 2 -2 1 1 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 2 0 -1 0 0
-1 -1 0 1 -1 -1 0 0 0 -3 3 -4 2 3 1 2 1 2 -2 0 2 0
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 -1 0 1 -1 -1 -1 0 0 0 0 -2 0 2 -1 0 2 1 0 -1
0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
1 1 0 1 0 0 -1 1 0 -1 0 0 0 -2 2 -4 2 3 1 1 0 2 -3
1 2 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
0 1 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 -3 1 2 0 0 1 1 -1
0 2 1 0 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 -1 -1 1 -1 -1 0 0 0 2 -2 1 -1 -1 -1 -1 1
-1 1 0 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 -1 2 -1 0 -1 0 0 -1 0 0 -1 -1 0 0 -1 1 -2 1 -2 0
-2 -1 1 0 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 1 0 0 0 0 0 0 0 0 -1 0 0 0 2 -2 3 -1
-2 -1 -2 2 -1 2 -1 -3 -1 -2 -1 -1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 -1 1 1 0 1 1 0 0
-1 0 0 1 -2 1 2 0 1 0 -2 -1 -1 -1 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 -1 3 -1 -2 0 -1 -1 -1 1 0 -1 -1
0 -1 -1 -1 0 -2 0 2 -1 0 1 1 -1 1 1 1 0 2 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 2 -2 3 -1 -1 -1 0 0 -2 1 0
-2 -2 -1 -1 -1 -1 1 -2 1 1 0 0 1 2 0 0 0 0 -1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -3 3 -1 -1 -1 -1 0
-2 1 0 -1 -1 -1 0 -1 -2 0 -2 1 2 0 0 2 1 0 -1 0 0 -1
1 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 0 0 0 0 0 1 0 -1 0 0 1 -1 -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 -1 0 -1 1 1
0 1 0 0 -1 0 1 0 0 1 0 3 -2 5 -2 -3 -1 -2 0 -3 2 0
-3 -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 1 0 -1 1 -1 0 1 1 1 0 1 -2 2 -3 1 2 0 2 1 1
-2 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
-1 2 0 -1 0 0 0 -1 1 0 -2 -2 -1 -1 -1 2 -2 3 -2 -2 -2
-2 0 -1 2 -1 -1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 2 -2 1 1 1 1 0 1 -1 0 1 0 1 0 1
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REFERENCES
G. Nebe: Turyn's Construction applied to extremal 16-dimensional 5-modular lattice
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NOTES
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe