The Lattice 2.Alt7SS3.2
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 13:14:59 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
MINIMAL_NORM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME
2.Alt7SS3.2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
12
2 12
-2 2 12
3 1 2 12
3 2 1 3 12
2 3 3 6 3 12
2 4 3 2 2 0 12
2 3 0 5 -1 4 0 12
3 1 3 6 0 2 6 6 12
6 3 -1 1 1 2 3 3 0 12
3 -1 0 1 0 -1 0 3 3 3 12
1 2 1 6 3 6 1 6 4 3 3 12
-2 2 3 4 3 3 0 2 1 -1 4 2 12
2 2 0 2 0 1 1 2 2 -1 3 0 6 12
2 4 6 2 1 3 1 2 2 0 1 1 3 3 12
6 1 2 4 3 2 1 1 3 3 6 3 1 3 4 12
4 3 3 -2 3 2 2 -2 -2 3 3 -3 3 3 5 6 12
0 1 3 1 1 2 -1 3 2 -2 4 3 0 0 2 3 0 12
-2 1 6 1 1 2 3 3 3 -2 0 3 1 1 2 2 2 6 12
2 2 4 1 0 2 0 1 2 0 3 0 2 3 6 6 6 3 2 12
3 1 3 2 2 3 3 2 4 4 1 4 0 0 1 2 0 3 4 1 12
0 3 -1 1 3 2 1 3 1 4 -1 3 0 2 1 0 0 2 1 3 2 12
-2 1 0 3 1 0 3 3 3 0 3 3 3 1 0 -1 -1 5 3 -1 3 4 12
3 2 4 5 3 4 2 2 3 3 3 6 2 3 5 6 3 3 4 3 4 3 1 12
-1 1 -1 -3 1 -1 1 -2 0 -1 -1 -2 -1 0 -2 0 1 -1 -2 -1 -4 0 -3 -3 12
0 3 2 1 1 1 1 2 2 2 -1 1 2 1 3 -2 -1 0 1 0 3 4 2 -1 -1 12
0 2 -2 0 -6 0 -1 2 0 1 -3 0 -3 0 1 0 -3 -2 -2 0 -1 0 -2 -3 1 1 12
-1 0 -2 0 -6 -3 0 2 1 1 -2 0 -4 -2 -2 -3 -6 0 0 -3 0 0 0 -3 1 1 6 12
3 1 1 3 3 3 2 4 4 2 5 3 2 2 1 6 3 6 3 3 2 3 3 3 -2 1 -3 -3 12
-2 -2 0 -1 -5 -2 -2 1 0 -2 -2 0 -3 -3 1 -3 -3 0 2 0 0 -1 1 -3 -3 2 4 6 -3 12
5 3 -1 1 2 1 -1 4 -2 6 3 1 2 2 0 2 3 1 0 1 1 1 -1 1 -2 0 -1 1 1 -2 12
-1 -2 -2 0 0 0 -2 -2 -3 2 0 0 1 1 1 1 1 -3 -3 1 -2 1 -1 -1 2 0 3 0 -3 1 -1 12
1 -6 0 -2 1 -4 -3 -3 0 -3 0 -3 -2 1 -2 2 -1 0 0 -1 1 -3 -3 -2 2 -2 1 1 -1 2 -1 2 12
3 -2 -3 1 -1 1 1 -1 -1 1 -2 -2 -4 -2 -3 0 1 -3 -1 -1 0 -2 0 -3 -2 -3 2 2 0 4 0 1 1 12
0 -1 -3 -2 -1 -1 -1 0 -1 2 -1 0 -4 -2 -3 -2 -2 0 -2 -2 -3 3 -2 -1 6 0 2 2 -2 1 1 3 0 0 12
0 -1 0 1 0 1 1 -1 2 -1 -1 1 1 -1 -2 -2 -1 -3 0 0 0 -1 -1 -1 2 0 0 1 -2 2 -3 1 1 3 0 12
2 -1 -4 1 0 -2 0 1 2 0 1 1 -2 1 -3 1 -1 -1 -1 0 -1 2 1 -1 1 -1 0 1 1 1 1 1 2 3 2 6 12
-2 -2 0 -1 1 1 0 -3 -3 -1 -3 0 -1 1 -2 -1 -1 -2 0 -1 -1 1 -3 -2 2 0 1 0 0 0 -2 1 3 1 1 4 3 12
0 -2 0 -1 0 -1 -1 1 1 -2 1 -1 2 1 -1 -1 1 0 3 0 0 -2 1 -2 1 3 0 -1 -1 1 0 -1 2 0 0 6 3 2 12
1 -3 1 1 0 -2 0 2 1 2 2 1 0 0 -1 2 0 1 1 1 2 0 2 1 -2 -3 0 1 1 1 3 1 4 2 -1 3 3 0 3 12
-
MINIMAL_NORM
12
-
GROUP_ORDER
2^6 * 3^3 * 5 * 7
-
GROUP_GENERATORS
5
40
-1 0 -2 -1 3 0 -2 0 3 5 -2 1 3 1 -1 -1 3 4 1 2 -2 -4 -1 -1 -3 2 0 2 -4 -2 -5 -2 0 1 2 -2 2 1 -2 2
2 0 1 -2 1 2 0 1 -2 -2 1 -3 0 -1 -1 0 -4 -4 1 2 1 -2 3 3 2 0 1 0 2 1 1 1 -1 -1 0 -1 1 0 0 0
1 1 0 1 -1 0 0 -1 -1 -1 2 -1 0 -1 1 -2 -2 -2 1 0 1 1 0 1 2 -1 0 -1 2 1 1 1 0 0 -1 -1 0 0 1 0
-4 0 -2 2 1 -3 -1 0 4 6 -3 4 2 2 0 -1 7 8 -2 -1 -2 -1 -5 -3 -4 1 -1 1 -5 -2 -5 -2 1 2 1 -1 1 0 0 1
-3 0 -1 1 0 -2 0 1 2 2 -2 3 1 1 0 0 5 5 -2 -1 -1 0 -3 -2 -3 1 -1 1 -3 -2 -2 -1 1 2 1 0 0 0 0 0
-4 0 -2 1 2 -3 -3 -1 6 7 -3 3 2 2 0 -2 6 7 -1 0 -2 -3 -3 -2 -3 1 0 1 -4 -2 -4 -2 0 2 1 -1 1 1 -1 1
-3 0 -1 3 -2 -4 1 1 1 2 -3 5 1 1 1 1 6 6 -3 -2 0 2 -4 -4 -3 0 -2 0 -3 -2 -2 -1 2 2 1 1 -1 -1 1 -1
5 1 2 -2 -2 5 3 1 -7 -7 4 -5 -1 -3 0 2 -9 -9 2 1 2 1 4 3 3 -1 0 -1 5 2 3 2 0 -3 0 0 0 -1 1 0
1 1 0 0 -2 1 2 1 -3 -1 0 0 1 -1 1 2 -2 -1 0 0 0 1 0 -1 -1 0 -2 0 0 -1 -1 0 2 0 1 0 0 -1 1 0
2 0 1 -1 0 1 1 1 -2 -3 1 -1 0 -1 -1 1 -2 -2 0 0 1 0 1 1 1 0 0 0 1 1 1 1 -1 -1 0 0 0 0 0 0
-6 0 -4 4 2 -5 -3 -2 7 10 -4 7 2 4 1 -3 11 11 -1 -1 -3 -2 -6 -6 -6 1 -1 2 -7 -4 -7 -4 2 3 2 -1 1 0 -1 1
-3 0 -1 2 1 -3 -2 -1 4 4 -2 3 0 2 0 -2 5 5 -1 -1 -1 -1 -3 -2 -2 0 0 0 -2 -1 -2 -1 0 1 0 0 0 0 0 0
-9 -1 -4 4 2 -7 -2 1 8 12 -7 9 3 5 0 -1 16 16 -5 -2 -4 -2 -8 -7 -9 2 -2 3 -10 -5 -9 -5 3 4 3 0 1 0 -1 0
-7 -1 -4 2 4 -4 -3 0 7 13 -6 6 3 5 0 -2 11 12 -2 1 -4 -5 -5 -5 -7 2 -1 3 -8 -4 -9 -5 2 3 3 -1 2 0 -2 1
2 1 0 -1 -1 2 1 1 -3 -3 2 -2 0 -2 0 0 -3 -4 1 1 1 0 2 2 1 0 0 0 2 0 1 1 1 -1 0 0 0 0 0 0
-3 0 -2 1 2 -2 -2 -1 4 6 -2 3 2 2 0 -2 5 6 0 0 -2 -2 -3 -2 -3 1 0 1 -4 -2 -4 -2 1 2 1 -1 1 0 -1 1
-7 -1 -4 3 3 -6 -4 -1 9 11 -5 7 3 4 0 -3 13 13 -2 -1 -3 -3 -6 -5 -6 2 0 2 -8 -4 -7 -4 1 4 2 -1 1 1 -2 1
2 1 0 0 0 2 -1 -2 -1 -2 3 -3 -1 -1 1 -2 -5 -5 3 1 1 0 2 2 3 -1 1 -1 3 1 2 1 -1 -1 -1 -1 0 0 0 1
4 1 2 0 -4 3 3 0 -6 -8 4 -4 -2 -3 1 1 -8 -8 1 -1 3 4 3 3 5 -2 0 -3 6 3 6 3 0 -2 -2 1 -2 -1 2 -1
-7 0 -4 4 2 -5 -4 -2 8 11 -4 7 2 4 1 -3 12 11 -1 -1 -3 -2 -6 -6 -6 1 -1 2 -7 -4 -7 -4 2 3 2 -1 1 0 -1 1
6 1 2 -3 -2 5 2 0 -6 -7 4 -6 0 -4 0 1 -12 -10 3 2 2 1 5 5 6 -1 0 -2 6 3 5 3 -1 -2 -2 -1 0 0 1 0
-1 0 0 0 1 0 -1 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 -1 0 0 0 0 0 0 0
-5 -1 -2 4 1 -5 -2 -1 5 6 -3 5 0 3 1 -2 8 8 -2 -2 -1 0 -5 -4 -3 0 0 0 -4 -2 -3 -2 0 2 0 0 0 0 0 0
-5 0 -3 3 2 -5 -4 -2 8 8 -3 5 1 3 0 -4 9 9 -1 -1 -2 -2 -5 -3 -3 1 0 0 -5 -2 -4 -2 0 3 0 -1 0 1 -1 1
1 0 1 -2 1 1 0 1 -1 -1 0 -1 0 0 0 1 -2 -2 0 1 0 -1 2 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0
8 1 4 -5 -3 8 6 4 -12 -12 5 -8 -1 -5 -1 5 -14 -13 1 2 3 2 7 6 5 -1 -1 0 7 3 5 4 0 -4 -1 0 0 -1 2 -1
4 0 3 -3 -1 4 3 2 -6 -6 2 -4 -1 -2 -1 3 -7 -7 0 1 2 1 4 3 2 -1 0 0 4 2 3 2 0 -3 0 1 0 -1 1 -1
10 1 5 -5 -4 8 6 3 -12 -15 6 -9 -2 -6 -1 5 -16 -16 2 1 4 4 8 7 7 -2 0 -2 9 5 8 5 -1 -5 -2 1 -1 -1 2 -1
-3 0 -2 1 2 -2 -2 -1 4 6 -2 2 2 2 0 -1 4 6 0 0 -2 -2 -3 -2 -3 1 0 1 -4 -2 -4 -2 0 2 1 -1 1 0 -1 1
9 1 4 -4 -4 8 5 1 -11 -14 7 -9 -3 -6 0 3 -16 -16 3 1 4 4 8 7 8 -2 1 -3 10 5 9 5 -1 -5 -3 1 -1 -1 2 -1
2 0 0 -1 0 2 1 1 -2 -2 1 -1 1 -1 -1 0 -1 -2 1 1 0 -1 1 1 0 1 0 1 0 0 -1 0 0 -1 1 -1 1 0 -1 1
-3 -1 0 1 0 -2 1 2 0 1 -2 3 -1 2 0 2 5 4 -3 -2 0 1 -2 -3 -3 0 -1 1 -2 -1 -1 -1 1 0 1 3 -1 -1 0 -1
7 1 3 -4 -2 7 4 1 -9 -9 5 -7 -1 -4 0 2 -13 -12 3 2 2 2 6 5 5 -1 0 -1 7 3 5 3 0 -3 -1 0 0 -1 1 0
-3 -1 -2 1 2 -3 -3 -2 6 7 -3 3 2 2 0 -2 5 7 0 0 -2 -2 -3 -2 -2 1 1 0 -4 -1 -3 -2 -1 2 0 -1 1 1 -1 1
1 0 1 -1 0 1 0 0 -1 -3 1 -1 -2 0 0 1 -2 -3 0 0 1 0 2 1 1 0 0 0 2 1 2 1 -1 -1 0 1 -1 0 0 0
-8 -1 -4 3 3 -7 -4 -1 10 13 -7 8 3 5 0 -2 14 15 -3 -1 -4 -3 -7 -6 -7 2 -1 2 -9 -4 -8 -5 1 4 2 -1 1 1 -1 1
-3 -1 -3 0 4 -2 -4 -2 6 9 -3 2 2 3 0 -3 4 6 2 2 -3 -5 -2 -1 -2 2 1 1 -4 -2 -5 -3 -1 2 1 -2 2 1 -2 2
-3 0 -1 1 1 -2 -1 -1 3 4 -2 2 0 2 0 -1 3 4 -1 0 -1 -1 -2 -1 -1 0 0 0 -1 0 -1 -1 0 1 0 0 0 0 0 0
-5 -1 -2 2 0 -4 0 1 4 6 -5 6 2 3 0 1 10 10 -4 -2 -2 0 -5 -5 -6 1 -2 2 -6 -3 -5 -3 2 2 2 0 0 0 0 0
-4 -1 -2 2 2 -4 -2 -1 5 7 -3 5 2 3 0 -2 8 8 -1 -1 -2 -1 -5 -4 -4 1 0 1 -5 -2 -5 -3 0 2 1 -1 1 0 -1 1
40
0 0 0 -1 1 1 0 1 0 0 0 -1 0 0 -1 1 0 -1 0 1 0 -1 1 0 -1 0 0 1 0 0 -1 0 0 -1 1 0 0 0 0 0
2 0 1 -2 1 2 0 1 -1 -2 1 -3 0 -1 -1 1 -3 -3 1 1 0 -1 3 2 1 0 1 0 1 1 1 1 -1 -1 0 0 0 1 -1 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 0 0 0 2 0 -2 -1 2 2 0 -1 0 1 -1 -2 0 0 1 1 0 -2 0 1 1 0 1 0 0 1 -1 0 -2 0 0 -2 1 1 0 1
-4 -1 -1 2 2 -3 -1 1 3 4 -2 3 0 3 -1 0 7 6 -2 -1 -1 -1 -3 -3 -3 1 0 1 -4 -1 -3 -2 0 1 1 1 0 0 -1 0
2 0 1 -2 0 2 1 2 -2 -3 1 -3 0 -1 -1 2 -3 -3 0 0 1 0 2 2 1 0 0 0 1 1 1 1 -1 -1 0 0 0 1 0 0
8 1 4 -4 -3 7 5 3 -11 -12 5 -8 -2 -5 -1 4 -14 -14 2 2 3 2 8 6 6 -1 0 -2 8 4 7 4 0 -4 -1 1 -1 -1 1 -1
3 0 1 -3 2 3 -1 0 -1 -1 1 -4 1 -1 -1 0 -5 -4 2 2 0 -2 3 3 2 0 1 1 2 1 0 1 -2 -1 0 -2 1 1 0 1
7 1 3 -4 -1 6 2 1 -7 -8 4 -7 -1 -4 -1 1 -12 -12 3 3 2 0 7 6 6 -1 1 -1 7 3 5 3 -1 -3 -1 -1 0 0 1 0
4 0 2 -4 0 4 2 2 -4 -5 2 -5 0 -2 -1 3 -7 -6 1 1 1 0 4 3 2 0 0 0 3 2 2 2 -1 -2 0 0 0 0 0 0
-7 -1 -3 3 3 -7 -5 -2 10 11 -6 7 1 5 0 -3 12 12 -2 -1 -3 -3 -5 -5 -5 1 0 1 -6 -3 -5 -3 0 3 1 0 0 1 -1 0
-6 -2 -2 1 5 -6 -5 0 10 10 -6 5 2 5 -2 -2 12 12 -3 -1 -3 -4 -5 -3 -5 2 1 2 -7 -2 -6 -3 -2 3 1 -1 1 2 -2 1
-1 0 1 1 0 -1 0 0 0 -1 0 0 -2 1 0 0 0 0 -1 -1 1 1 0 0 1 -1 0 -1 1 1 2 1 -1 0 -1 1 -1 0 1 -1
4 1 3 -1 -3 4 3 1 -7 -9 4 -5 -4 -3 0 2 -9 -10 1 0 3 3 5 4 5 -2 0 -2 7 3 7 4 0 -3 -2 2 -2 -1 2 -2
-4 -1 -2 1 2 -3 -2 0 5 6 -3 3 1 2 0 -1 6 6 -1 0 -2 -2 -2 -2 -3 1 0 1 -4 -2 -3 -2 0 2 1 0 0 1 -1 0
-5 -1 -2 2 2 -5 -3 0 7 7 -4 5 1 3 -1 -2 10 9 -2 -1 -2 -2 -4 -3 -4 1 0 1 -5 -2 -4 -2 0 2 1 0 0 1 -1 0
2 0 2 -1 -3 2 4 3 -6 -7 2 -2 -2 -2 0 4 -4 -5 -1 -1 2 3 3 1 1 -1 -1 -1 3 1 4 2 1 -2 0 3 -2 -1 1 -2
-10 -1 -6 5 6 -9 -9 -4 15 19 -7 9 3 7 1 -7 17 17 0 0 -5 -6 -8 -7 -7 2 1 2 -10 -5 -10 -6 0 5 2 -2 2 2 -3 2
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 0 0 0 0 0
-3 -1 -1 1 2 -3 -3 -1 5 5 -2 2 0 2 0 -2 4 4 0 0 -1 -2 -1 -1 -1 0 1 0 -2 -1 -1 -1 -1 1 0 0 0 1 -1 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 0 0 0 0 0
6 0 3 -4 0 6 1 0 -6 -7 5 -8 -2 -3 0 1 -13 -12 4 2 2 0 7 6 7 -1 2 -2 7 4 6 3 -2 -3 -2 0 0 0 0 0
2 0 1 0 1 1 -2 -2 -1 -1 2 -3 -2 0 1 -2 -5 -5 3 1 1 -1 3 2 4 -1 2 -2 4 2 3 1 -2 -1 -1 0 0 0 0 0
-3 -1 -1 0 2 -2 -2 0 4 4 -2 1 0 2 -1 -1 4 4 -1 0 -1 -2 -1 0 -1 1 1 0 -2 0 -1 -1 -1 1 0 0 0 1 -1 0
4 1 2 -1 -3 3 4 2 -7 -8 3 -2 -1 -3 0 2 -5 -7 0 0 2 3 3 2 2 -1 -1 0 4 1 3 2 2 -2 0 1 -1 -1 1 -1
2 0 1 -2 0 2 1 1 -2 -2 1 -2 0 -1 0 1 -4 -3 1 1 0 0 2 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 1 1 0 -1 -1 1 1 -1 0 1 2 1 -1 -1 0 1 -1 -1 -2 0 -1 1 -1 -1 -1 0 1 0 1 0 0 0 0 0
0 1 -1 0 0 0 -1 -1 1 3 -1 1 2 0 1 -1 0 1 1 1 -1 -1 -1 -1 -1 0 -1 1 -1 -1 -3 -1 1 1 1 -2 1 0 0 1
1 0 0 -2 2 1 -2 0 1 2 0 -2 1 0 -1 -1 -2 -1 2 2 -1 -3 2 2 1 1 1 0 0 0 -1 0 -1 0 0 -1 1 1 -1 1
-6 -1 -3 3 2 -5 -3 -1 7 10 -5 7 2 4 1 -2 11 11 -2 -1 -3 -2 -6 -6 -6 1 -1 2 -7 -4 -7 -4 1 3 2 -1 1 0 -1 1
-3 0 -1 1 1 -2 -1 0 3 4 -2 2 1 2 0 1 4 5 -1 -1 -1 0 -3 -3 -3 0 -1 1 -3 -1 -3 -1 0 1 1 0 0 0 0 0
-6 -1 -2 3 2 -5 -2 0 6 7 -4 6 0 4 0 -1 11 10 -3 -2 -2 -1 -5 -5 -6 1 -1 2 -6 -3 -5 -3 1 2 2 1 0 0 -1 0
-7 0 -2 6 -2 -6 1 1 3 5 -4 9 0 3 1 0 14 11 -5 -4 -1 3 -8 -8 -7 0 -3 2 -6 -4 -5 -3 4 2 2 2 -1 -2 1 -1
5 1 2 -2 -2 5 3 1 -7 -7 4 -5 -1 -3 0 2 -9 -9 2 1 2 1 4 3 3 -1 0 -1 5 2 3 2 0 -3 0 0 0 -1 1 0
0 0 -1 -1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 -1 -1 0 0 -1 1 0 1 -1 -1 -2 -1 1 0 1 -1 1 0 -1 1
4 0 3 -3 -1 4 4 3 -7 -7 2 -4 -1 -2 -1 3 -7 -7 -1 1 2 1 4 3 2 -1 0 0 4 2 3 2 0 -3 0 1 0 -1 1 -1
4 0 3 -3 -1 4 3 2 -6 -6 2 -4 -1 -2 -1 3 -7 -7 0 1 1 1 4 3 2 -1 0 0 4 2 3 2 0 -3 0 1 0 -1 1 -1
0 0 1 1 -3 0 4 3 -4 -4 0 1 -1 -1 0 3 1 0 -3 -2 1 3 -1 -1 -1 0 -2 0 0 0 1 1 2 -1 0 2 -1 -1 1 -1
3 0 2 -2 -1 3 3 2 -6 -6 2 -3 -1 -2 0 2 -6 -6 0 1 2 1 3 2 2 -1 0 0 4 1 3 2 0 -2 0 1 0 -1 1 -1
-4 -1 -1 2 2 -3 -1 0 3 6 -3 3 1 3 0 -1 6 7 -2 -1 -1 -1 -4 -3 -3 0 0 1 -3 -1 -4 -2 0 1 1 0 1 -1 0 0
40
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-7 -1 -3 5 2 -7 -3 -1 8 10 -5 9 1 5 0 -3 15 13 -3 -2 -3 -1 -7 -7 -7 1 -1 2 -8 -4 -7 -4 2 3 2 0 0 0 -1 0
7 1 3 -4 -1 6 2 0 -7 -8 5 -7 -1 -4 0 1 -13 -13 4 3 2 0 7 6 6 -1 1 -1 7 3 5 3 -1 -3 -1 -1 0 0 1 0
8 1 4 -3 -4 7 6 2 -12 -13 6 -7 -2 -5 0 4 -14 -14 2 1 4 4 6 5 6 -2 0 -2 8 4 7 4 0 -4 -1 1 -1 -2 2 -1
4 1 2 -1 -3 3 3 1 -6 -7 3 -3 -2 -3 0 1 -7 -8 1 1 2 2 4 3 4 -1 0 -2 5 2 5 2 1 -2 -1 1 -1 -1 1 -1
6 1 2 -2 -2 5 3 1 -8 -7 4 -5 -1 -3 0 2 -10 -10 3 2 2 1 5 3 4 -1 0 -1 5 2 3 2 0 -3 0 0 0 -1 1 0
8 1 4 -4 -2 7 3 0 -9 -11 6 -8 -3 -4 0 2 -15 -15 4 2 3 2 8 6 7 -2 1 -2 9 4 8 4 -1 -4 -2 1 -1 -1 1 -1
0 0 0 1 -1 0 2 1 -2 -1 0 1 0 0 0 1 1 1 -1 -1 0 2 -2 -1 -1 0 -1 0 -1 0 -1 0 1 0 0 0 0 -1 1 0
7 1 3 -4 -2 7 4 1 -9 -9 5 -7 -1 -4 0 3 -13 -12 3 2 2 2 6 5 5 -1 0 -1 6 3 5 3 0 -3 -1 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 0 0 0 0 0 0 0 0 0 0
-2 0 -2 1 3 -2 -4 -3 6 7 -2 2 2 2 0 -4 4 5 1 1 -2 -3 -3 -1 -1 1 1 1 -3 -1 -4 -2 -1 2 0 -3 2 1 -1 2
5 1 2 -1 -2 4 3 1 -7 -7 4 -4 -1 -3 0 1 -8 -8 2 1 2 2 3 3 4 -1 0 -1 4 2 3 2 0 -2 -1 0 0 -1 1 0
-2 0 -1 2 2 -2 -3 -3 4 5 -1 2 0 2 0 -4 3 3 1 1 -1 -2 -2 -1 0 0 1 0 -1 0 -2 -1 -1 1 0 -2 1 0 0 1
-2 0 -1 2 1 -2 -2 -2 4 4 -1 2 0 2 0 -2 4 4 0 -1 -1 0 -3 -2 -1 0 0 0 -2 0 -2 -1 -1 1 0 -1 0 0 0 1
0 0 1 1 -2 -1 2 2 -2 -1 -1 2 0 0 0 2 2 1 -2 -1 0 2 -1 -2 -2 0 -2 1 -1 -1 -1 0 2 0 1 1 -1 -1 1 -1
5 1 1 -2 -1 4 1 0 -4 -4 3 -4 1 -3 0 0 -7 -7 3 2 1 0 3 3 3 0 0 0 3 1 1 1 0 -1 0 -2 1 0 0 1
-2 0 -2 1 2 -3 -4 -2 6 7 -3 3 2 2 0 -3 5 5 1 1 -2 -3 -2 -2 -2 1 0 1 -3 -2 -4 -2 0 2 1 -2 1 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 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 1 1 -2 -1 4 1 0 -4 -5 3 -4 0 -3 0 0 -7 -8 3 2 1 0 4 3 3 0 0 0 4 1 2 2 0 -2 0 -1 0 0 0 1
0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 0 0
4 1 2 -1 -4 3 4 2 -6 -9 3 -3 -2 -3 0 3 -6 -7 0 -1 2 4 3 2 3 -1 -1 -2 4 2 5 3 1 -2 -1 2 -2 -1 1 -1
0 0 1 0 -1 0 1 0 -1 -2 0 0 -1 0 0 1 -1 -1 -1 -1 1 2 0 0 1 -1 0 -1 1 1 2 1 0 0 -1 1 -1 -1 1 -1
1 0 1 -1 0 0 1 2 -1 -1 -1 0 1 0 -1 2 0 0 -1 0 0 0 0 0 -1 0 -1 1 -1 0 -1 0 0 0 1 0 0 0 0 0
1 1 0 0 -2 1 0 -1 -1 -1 1 0 0 -1 1 0 -2 -2 1 0 0 1 1 0 1 0 -1 -1 1 0 1 0 1 0 0 0 0 0 0 0
-4 0 -1 5 -2 -4 0 -1 2 2 -1 5 -2 2 2 -1 7 5 -2 -3 0 3 -4 -5 -2 -1 -1 -1 -2 -1 0 -1 2 1 0 2 -2 -1 1 -1
0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 -1 0 1 -1 -1 -1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0
-7 -1 -3 4 1 -6 -2 -1 7 8 -4 7 1 4 1 -1 12 12 -3 -3 -2 0 -7 -6 -6 1 -1 1 -7 -3 -5 -3 1 3 1 1 0 0 -1 0
8 1 2 -4 0 7 1 -1 -7 -7 6 -9 -1 -4 0 -1 -15 -14 6 4 2 -1 7 7 8 -1 2 -2 8 4 5 3 -2 -3 -2 -2 1 0 0 1
-7 -1 -3 4 2 -6 -3 -1 7 9 -4 6 1 4 1 -2 11 11 -2 -2 -2 -1 -6 -5 -5 1 0 1 -6 -3 -5 -3 1 3 1 1 0 0 -1 0
-7 -1 -3 5 1 -7 -2 -1 8 8 -5 8 1 4 0 -2 14 13 -4 -3 -2 0 -8 -6 -6 1 -1 1 -7 -3 -5 -3 1 3 1 0 0 0 0 0
1 0 0 0 -1 0 0 0 0 -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
-1 0 -1 -1 2 0 -2 -1 3 3 0 -1 1 0 0 -1 0 1 1 1 -1 -2 0 1 0 1 1 0 -1 0 -1 -1 -1 1 0 -1 1 1 -1 1
4 0 1 -2 0 3 0 -1 -3 -4 3 -5 -1 -2 0 0 -8 -7 3 1 2 0 4 4 5 -1 2 -2 5 3 4 2 -2 -2 -2 0 0 0 0 0
-1 0 0 1 -2 -1 1 1 0 -1 -1 1 0 0 0 2 2 2 -2 -2 0 2 -1 -1 -1 0 -1 -1 -1 0 1 0 1 0 0 2 -1 0 0 -1
3 0 0 -3 2 3 -2 -2 0 0 2 -4 0 -1 0 -2 -7 -5 4 3 0 -3 4 4 4 0 2 -1 3 2 2 1 -2 -1 -1 -1 1 1 -1 1
2 0 0 -2 -1 2 1 0 -1 -2 1 -2 1 -2 0 1 -4 -2 1 0 0 1 1 2 2 0 0 -1 1 1 2 1 0 0 -1 0 0 0 0 0
8 1 3 -4 -2 7 2 0 -8 -11 7 -9 -3 -5 0 1 -15 -15 5 2 3 1 8 7 8 -1 2 -3 9 4 8 4 -2 -4 -2 1 -1 0 0 0
-4 -1 -2 1 3 -3 -4 -2 7 8 -3 3 1 3 0 -3 6 7 0 0 -2 -3 -3 -2 -2 1 1 0 -4 -1 -3 -2 -1 2 0 -1 1 1 -1 1
4 0 1 -4 2 4 -1 -1 -1 -3 3 -6 0 -2 -1 -1 -9 -7 3 3 1 -2 4 6 5 0 2 -1 4 3 3 2 -3 -1 -2 -2 1 1 0 1
40
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 -1 0 0 0 0 0 1 0 -2 -1 1 0 0 0 1 0 1 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 0
6 1 2 -3 -2 5 2 0 -6 -8 5 -6 -1 -4 0 1 -11 -10 3 1 2 2 5 5 6 -1 1 -2 6 3 5 3 -1 -2 -2 -1 0 0 1 0
-1 0 -1 2 -1 -2 0 0 1 1 -1 3 1 0 1 0 4 3 -1 -1 0 1 -2 -3 -2 0 -1 1 -2 -2 -2 -1 1 1 1 0 0 0 0 0
0 -1 0 0 2 -1 -2 -1 2 2 0 -1 -1 1 0 -2 -1 0 1 1 0 -2 1 1 2 0 2 -1 1 1 1 0 -2 0 -1 0 0 1 -1 0
3 0 1 -1 0 2 0 -1 -2 -3 2 -2 -1 -1 0 0 -4 -5 2 1 1 0 3 1 2 -1 1 0 3 1 2 1 -1 -2 0 0 0 0 0 0
3 0 1 -1 0 2 0 0 -3 -3 2 -3 -1 -1 0 0 -5 -5 2 1 1 0 3 2 3 0 1 -1 3 1 2 1 -1 -1 -1 0 0 0 0 0
-2 0 -1 1 0 -2 -1 -1 3 3 -2 3 1 1 1 0 4 4 -1 -1 -1 0 -2 -3 -3 0 -1 1 -2 -2 -2 -1 1 1 1 0 0 0 0 0
3 0 1 -1 -1 2 1 1 -3 -4 2 -2 0 -2 0 1 -3 -4 1 0 1 1 2 1 1 0 0 0 2 0 1 1 0 -1 0 0 0 0 0 0
1 0 0 -1 0 0 0 0 0 0 -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 0 0 0 0 0
-1 0 0 1 0 -2 -1 0 2 1 -1 2 0 1 0 -1 3 3 -1 -1 0 0 -2 -1 -1 0 0 0 -1 -1 -1 0 0 1 0 0 0 0 0 0
4 0 2 -2 0 3 0 -1 -3 -5 3 -4 -1 -2 0 0 -7 -7 2 1 2 0 4 3 4 -1 2 -1 5 2 4 2 -2 -2 -1 0 0 0 0 0
-5 0 -2 4 0 -5 -2 -1 5 6 -3 6 0 3 1 -2 9 8 -2 -2 -1 0 -5 -5 -4 0 -1 1 -4 -3 -4 -2 1 2 1 0 0 0 0 0
-5 0 -2 4 0 -5 -2 -1 5 6 -3 6 0 3 1 -2 10 8 -2 -2 -1 0 -5 -5 -4 0 -1 1 -4 -3 -4 -2 1 2 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 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
2 0 1 -1 -1 1 1 1 -2 -3 1 -1 0 -1 0 1 -2 -2 0 0 1 1 1 1 1 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 -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 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 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
8 1 3 -4 -3 8 5 2 -11 -12 6 -8 -2 -5 0 3 -14 -14 3 2 3 2 7 6 6 -1 0 -1 8 3 6 4 0 -4 -1 0 0 -1 1 0
4 0 1 -2 0 3 0 -1 -3 -4 3 -5 -1 -2 0 0 -8 -7 3 1 2 0 4 4 5 -1 2 -2 5 3 4 2 -2 -2 -2 0 0 0 0 0
3 0 1 -2 -1 3 2 1 -4 -4 1 -3 0 -2 0 2 -5 -5 1 1 1 0 3 2 2 0 0 0 3 1 2 1 0 -2 0 0 0 0 0 0
-2 0 -1 2 0 -2 -1 -1 2 2 -1 2 0 1 1 -1 3 3 0 -1 0 0 -2 -2 -1 0 0 0 -1 -1 -1 -1 0 1 0 0 0 0 0 0
0 0 0 1 -1 -1 0 0 0 -1 0 1 0 0 0 0 2 1 -1 -1 1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-4 -1 -1 2 2 -4 -2 0 5 6 -3 4 1 3 -1 -1 8 8 -2 -1 -2 -1 -4 -3 -4 1 0 1 -5 -2 -4 -2 0 2 1 0 0 1 -1 0
0 -1 0 -2 1 0 1 2 0 1 -2 0 2 0 -1 2 1 2 -1 0 -1 -1 0 0 -2 1 0 1 -2 -1 -2 -1 0 0 1 0 1 0 -1 0
0 0 1 -1 -2 1 3 2 -3 -2 -1 1 1 -1 0 4 0 0 -2 -1 0 2 0 -1 -2 0 -2 1 -1 -1 0 0 2 0 1 1 0 -1 1 -1
-8 -1 -3 4 1 -7 -2 0 8 10 -7 9 3 4 0 0 15 15 -5 -3 -3 0 -8 -7 -8 1 -2 2 -9 -4 -7 -4 2 4 2 0 0 0 0 0
2 0 1 -1 -1 1 1 1 -2 -4 1 -1 -1 -1 0 1 -2 -3 0 0 1 1 2 1 1 0 0 0 2 0 2 1 0 -1 0 1 -1 0 0 0
0 0 0 -1 0 1 0 0 0 -1 0 -1 0 -1 0 1 -1 -1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
-4 0 -2 2 1 -4 -2 -1 5 7 -4 5 1 3 1 -1 7 8 -2 -1 -2 -1 -4 -4 -4 0 -1 1 -4 -2 -4 -2 1 2 1 0 0 0 0 0
-5 -1 -2 1 2 -3 -1 1 4 7 -4 4 2 3 0 1 7 8 -2 0 -2 -2 -4 -4 -5 1 -1 2 -6 -3 -5 -3 1 2 2 0 1 0 -1 0
0 0 1 0 -1 0 1 1 -1 -2 1 -1 -1 -1 0 1 -1 -1 -1 -1 1 2 0 1 1 -1 0 -1 1 1 2 1 0 0 -1 1 -1 0 1 -1
0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 0 0
-5 -1 -2 1 2 -4 -2 1 6 7 -5 5 2 3 -1 1 10 10 -3 -1 -3 -2 -4 -4 -6 2 -1 2 -7 -3 -5 -3 1 2 2 1 0 1 -2 0
0 0 -1 -1 2 1 -1 0 1 2 0 -1 1 0 -1 -1 0 0 1 2 -1 -3 1 1 -1 1 1 1 -1 -1 -2 -1 0 0 1 -1 1 1 -1 1
0 0 -1 -1 2 1 -1 0 1 2 0 -1 1 0 0 -1 0 0 1 2 -1 -3 1 1 -1 1 1 1 -1 -1 -2 -1 0 0 1 -1 1 1 -1 1
-1 0 -1 0 3 0 -3 -2 3 4 0 -1 0 1 0 -3 0 0 2 2 -1 -3 1 1 1 0 2 0 0 0 -1 -1 -1 0 0 -1 1 1 -1 1
-6 -1 -3 1 4 -4 -3 0 8 11 -5 5 3 4 -1 -2 11 12 -2 0 -4 -4 -5 -4 -7 2 0 3 -8 -4 -8 -4 1 3 2 -1 2 1 -2 1
3 1 0 -3 1 3 -1 -1 -1 -1 2 -4 1 -2 0 -1 -7 -5 3 3 0 -2 3 4 3 0 1 0 3 1 1 1 -1 0 -1 -2 1 1 0 1
40
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 2 3 -3 -3 7 3 -1 -9 -10 7 -8 -2 -5 1 1 -16 -15 5 2 3 2 7 6 8 -2 1 -3 9 4 7 4 -1 -3 -2 -1 0 -1 2 0
11 1 5 -6 -4 8 4 1 -11 -15 7 -10 -2 -7 0 3 -19 -18 4 2 4 3 10 9 10 -2 1 -3 11 5 10 6 -2 -4 -3 0 -1 0 2 -1
9 1 2 -6 0 8 1 -1 -6 -8 6 -10 0 -5 0 0 -17 -14 6 4 2 -1 8 8 8 -1 2 -2 8 4 6 4 -3 -3 -2 -2 1 1 0 1
5 0 1 -4 1 4 0 -1 -2 -4 3 -6 1 -3 -1 0 -9 -7 3 2 1 -1 4 6 5 0 2 -1 4 3 3 2 -3 -1 -2 -2 1 1 0 1
11 2 3 -6 -3 10 4 0 -11 -13 8 -11 -1 -7 0 2 -20 -18 6 4 3 1 10 9 9 -1 1 -2 10 4 8 5 -1 -4 -2 -1 0 0 1 0
6 1 3 -2 -3 4 2 -1 -5 -9 5 -5 -2 -4 0 0 -10 -10 2 0 3 3 4 5 7 -2 1 -3 7 4 7 4 -2 -2 -3 -1 -1 0 2 0
0 1 0 1 -2 0 1 0 -1 -2 1 0 -1 -1 1 1 -1 -1 0 -1 1 2 0 -1 0 -1 -1 -1 1 0 2 1 1 0 0 1 -1 0 1 -1
6 1 3 -3 -3 4 3 1 -6 -9 4 -5 -1 -4 0 2 -10 -9 1 0 3 3 4 4 5 -2 0 -2 6 3 6 4 -1 -2 -2 0 -1 0 2 -1
0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0
5 1 3 -1 -3 4 4 2 -8 -9 4 -4 -2 -3 0 3 -7 -8 0 -1 3 4 3 2 3 -2 -1 -1 5 3 4 3 0 -3 -1 1 -1 -1 2 -1
9 1 4 -4 -4 8 6 2 -12 -14 7 -9 -2 -6 0 4 -16 -15 3 1 4 4 7 6 7 -2 0 -2 9 4 8 5 -1 -4 -2 1 -1 -1 2 -1
7 1 2 -5 0 6 1 0 -5 -6 4 -7 1 -4 -1 1 -12 -10 4 3 1 -1 6 6 5 0 1 -1 5 3 3 3 -2 -2 -1 -2 1 1 0 1
1 0 0 -2 2 1 -1 0 1 1 0 -1 1 0 -1 0 -1 0 1 1 -1 -2 1 1 0 1 1 0 -1 0 -1 0 -1 0 0 -1 1 1 -1 1
5 1 2 -2 -4 4 4 1 -7 -8 3 -4 -1 -4 1 3 -9 -8 1 0 2 3 4 3 4 -1 -1 -2 5 2 5 3 1 -2 -1 1 -1 -1 2 -1
8 1 4 -3 -4 6 5 2 -10 -14 6 -7 -3 -5 0 4 -12 -13 1 -1 4 5 6 5 6 -2 0 -2 8 4 8 5 -1 -4 -2 2 -2 -1 2 -1
5 1 2 -1 -2 3 1 -1 -4 -7 4 -4 -2 -3 0 0 -7 -8 2 0 2 2 4 4 5 -1 1 -2 5 3 5 3 -1 -2 -2 0 -1 0 1 0
5 1 3 -2 -2 4 3 1 -7 -9 4 -5 -2 -3 0 3 -9 -9 1 0 3 3 4 3 4 -2 0 -1 6 3 5 3 -1 -3 -1 1 -1 -1 2 -1
7 1 4 -2 -4 4 3 0 -7 -13 6 -6 -3 -5 0 2 -11 -12 2 -1 4 5 5 5 7 -2 1 -3 8 4 9 5 -2 -3 -3 1 -2 0 2 -1
8 1 4 -3 -3 6 4 1 -10 -13 6 -7 -3 -5 0 2 -13 -14 2 1 4 3 7 6 7 -2 1 -2 9 4 8 5 -1 -4 -2 1 -1 -1 2 -1
7 0 4 -4 -2 5 4 2 -8 -11 5 -7 -2 -4 -1 3 -12 -11 1 1 3 2 6 6 6 -1 1 -2 7 4 7 4 -2 -3 -2 1 -1 0 1 -1
-4 -1 -2 1 5 -3 -4 -2 7 8 -2 2 1 3 -1 -4 6 7 0 1 -2 -4 -3 -1 -2 1 2 1 -4 -1 -4 -2 -2 2 0 -2 2 1 -1 1
0 0 0 0 3 0 -3 -3 3 3 1 -2 0 1 0 -3 -2 0 2 1 0 -2 0 1 2 -1 2 -1 1 2 0 0 -3 0 -1 -2 1 1 0 1
13 1 6 -7 -4 11 7 3 -15 -19 9 -13 -3 -8 -1 5 -22 -21 4 2 5 4 11 10 10 -2 1 -3 12 6 11 7 -2 -6 -3 1 -1 -1 2 -1
-3 0 -1 1 1 -2 -2 -1 4 4 -2 3 0 2 0 -1 5 4 -1 -1 -1 -1 -2 -2 -2 0 0 1 -2 -1 -2 -1 0 1 0 0 0 0 0 0
0 0 -1 -1 2 0 -2 -1 2 4 0 -1 2 0 0 -2 -1 1 2 2 -1 -3 0 1 1 1 1 0 -1 0 -2 -1 -1 1 0 -2 2 1 -1 1
-4 0 -1 3 -1 -3 0 0 2 3 -2 4 -1 2 1 0 6 5 -2 -2 -1 1 -3 -4 -3 0 -1 0 -2 -2 -1 -1 2 1 1 2 -1 -1 0 -1
-3 0 -1 2 1 -2 -2 -1 3 4 -1 2 -1 2 1 -2 3 3 0 0 -1 -1 -2 -2 -1 0 0 0 -1 -1 -1 -1 0 1 0 0 0 0 0 0
3 1 1 -1 -1 2 1 0 -3 -5 3 -3 -1 -2 0 1 -5 -5 1 0 2 2 2 2 3 -1 0 -1 3 2 3 2 -1 -1 -1 0 -1 0 1 0
-2 0 -1 2 0 -2 -1 -1 2 3 -1 2 0 1 1 -2 3 3 0 0 -1 0 -2 -2 -1 0 0 0 -1 -1 -1 -1 1 1 0 0 0 0 0 0
-3 0 -2 2 2 -3 -3 -1 5 6 -2 3 1 2 0 -2 6 6 0 0 -2 -2 -3 -2 -3 1 0 1 -4 -2 -4 -2 0 2 1 -1 1 1 -1 1
-4 -1 -2 2 1 -3 -1 0 4 5 -3 4 1 2 0 -1 8 7 -2 -1 -2 -1 -3 -3 -4 1 0 1 -4 -2 -3 -2 1 1 1 1 0 0 -1 0
-6 -2 -2 1 3 -6 -3 1 8 8 -6 6 2 4 -1 0 12 12 -4 -2 -3 -2 -5 -4 -6 2 0 2 -7 -3 -5 -3 0 3 1 1 0 1 -2 0
-2 0 -2 2 2 -2 -4 -4 5 5 0 1 -1 2 1 -5 2 2 2 1 -1 -2 -1 0 1 0 2 -1 0 0 0 -1 -1 1 -1 -1 0 1 -1 1
-10 -1 -4 5 3 -8 -4 -1 11 14 -7 10 2 6 0 -3 18 17 -4 -2 -4 -2 -9 -8 -9 1 -1 3 -10 -5 -9 -5 2 4 2 0 1 0 -1 0
3 0 0 -2 2 2 -2 -2 0 0 2 -3 0 -1 0 -3 -5 -5 4 3 0 -3 3 3 3 0 2 0 3 1 1 1 -2 -1 -1 -2 1 1 -1 1
-11 -2 -6 5 7 -10 -8 -3 16 19 -8 10 3 8 0 -6 20 20 -2 -1 -5 -6 -10 -8 -9 2 1 3 -12 -5 -11 -6 -1 5 2 -2 2 2 -3 2
-5 -1 -3 1 3 -4 -3 -1 7 8 -4 5 2 3 0 -2 9 9 -1 0 -3 -3 -4 -3 -4 2 0 2 -6 -3 -5 -3 0 3 1 -1 1 1 -2 1
0 0 0 0 1 -1 -2 -1 2 1 0 0 0 0 0 -1 1 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 1 -1 0
-3 -1 -1 2 2 -4 -3 -1 5 4 -2 3 -1 2 0 -2 6 5 -1 -1 -1 -1 -2 -2 -2 0 1 0 -2 -1 -1 -1 -1 1 0 1 -1 1 -1 0
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PROPERTIES
INTEGRAL = 1
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REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
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NOTES
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URL (links to other sites for this lattice)
All the quaternionic matrix groups
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe