The Lattice F4S6.2
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 13:14:44 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME
F4S6.2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
6
1 6
3 1 6
1 3 1 6
1 2 1 1 6
3 2 3 1 2 6
2 3 1 3 1 1 6
2 1 1 1 3 1 2 6
1 2 1 1 2 2 1 1 6
1 3 1 3 1 1 3 1 1 6
1 1 1 2 3 1 1 3 1 1 6
1 1 1 1 3 1 1 3 1 1 3 6
0 1 0 -1 0 0 0 0 -1 0 0 -1 6
1 1 1 1 1 1 1 1 3 2 1 1 0 6
0 0 0 0 2 0 0 1 -2 1 1 1 1 -1 6
1 1 1 2 1 1 1 1 3 1 2 1 1 3 -1 6
1 3 1 3 1 1 3 1 1 3 1 1 0 1 -1 1 6
1 3 1 3 1 1 3 1 1 3 1 1 0 1 1 1 0 6
3 1 0 1 1 3 1 1 1 1 1 1 0 1 0 1 1 1 6
1 1 1 1 3 1 1 3 1 2 3 3 0 0 1 1 1 1 1 6
1 1 0 1 1 1 1 1 3 1 1 1 0 3 -1 3 1 0 1 0 6
0 0 0 0 0 1 0 0 -1 0 0 1 2 0 1 1 1 -1 0 0 0 6
-1 0 0 0 1 0 1 0 -1 0 0 0 1 0 3 0 -1 1 0 0 -1 1 6
1 1 1 1 3 1 1 3 1 1 3 3 -1 1 1 1 2 0 1 3 0 1 0 6
1 1 1 1 3 1 1 3 1 1 3 3 1 1 1 1 0 2 1 3 1 -1 0 0 6
1 1 0 1 3 1 1 3 1 0 3 3 -1 1 1 1 1 0 1 0 1 1 1 3 0 6
1 3 1 3 1 1 3 1 1 3 1 0 0 1 0 1 3 3 1 1 1 -1 0 1 1 0 6
1 3 1 3 1 1 3 1 1 3 1 0 0 1 0 1 3 0 0 1 2 0 0 1 0 1 3 6
0 0 0 0 1 0 0 0 -1 0 -1 0 2 0 3 1 -1 1 0 0 0 2 3 0 0 0 1 0 6
0 0 1 0 1 0 0 1 -1 0 0 0 1 0 3 0 -1 1 -1 0 -1 1 3 0 0 1 0 0 3 6
1 0 1 0 0 2 0 0 -2 -1 0 0 1 -1 2 -1 1 -1 1 -1 -1 3 1 1 -1 1 0 0 1 1 6
0 1 -1 0 0 0 1 0 -1 0 0 0 3 0 1 0 0 0 1 0 -1 1 1 -1 1 0 0 1 1 2 1 6
1 -1 1 -1 1 1 -1 0 -1 -1 0 0 1 1 3 0 -2 0 1 -1 0 1 3 0 0 1 -1 -1 3 3 1 1 6
0 0 -1 0 0 1 1 -1 -1 0 0 0 1 0 1 0 1 -1 1 0 0 3 2 1 -1 0 0 1 1 1 3 1 1 6
1 0 0 0 0 1 0 0 -1 0 0 0 1 0 1 0 1 -1 0 0 -1 3 1 1 -1 0 0 0 1 2 3 2 1 3 6
0 0 1 0 1 0 0 1 -1 0 0 1 1 0 3 0 -1 0 0 0 0 1 3 0 1 1 0 1 3 3 1 1 3 1 1 6
1 1 1 1 1 1 1 1 3 1 1 2 0 3 -1 3 1 1 1 1 3 0 0 1 1 1 2 1 0 0 -1 0 0 0 0 0 6
1 1 2 1 1 1 1 1 3 1 1 1 0 3 -1 3 1 1 0 1 0 0 1 1 1 1 1 0 0 0 -1 0 0 -1 0 0 3 6
1 1 1 1 1 1 1 1 3 1 1 1 0 3 -1 3 2 0 1 1 3 0 0 0 2 0 1 1 0 0 -1 0 0 0 0 0 3 3 6
3 1 3 1 1 3 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 -1 1 0 1 0 1 1 1 6
-
DIVISORS (elementary divisors)
1^24 6^16
-
MINIMAL_NORM
6
-
KISSING_NUMBER
2400
-
GROUP_ORDER
2^12 * 3^4 * 5
-
GROUP_GENERATORS
7
40
1 0 0 2 -1 2 1 -1 0 2 -1 -1 1 -1 0 0 -2 -2 -2 0 0 -1 0 2 1 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
0 1 1 1 -1 1 1 -1 0 2 -1 -2 0 -1 0 0 -2 -2 -1 0 0 0 0 2 2 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
0 1 1 2 -2 1 2 -2 0 2 -2 -2 1 -1 0 0 -3 -3 -1 1 0 -1 -1 2 3 4 0 -2 0 0 0 -1 0 0 1 0 1 -1 1 -2
1 1 1 1 -1 1 1 -1 0 2 -1 -2 0 -1 0 0 -2 -2 -1 0 0 0 0 2 2 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
0 0 1 0 -1 1 0 0 0 1 0 -2 0 -1 0 0 0 1 -1 0 0 -1 0 1 1 2 -2 0 1 -1 0 0 0 0 1 0 1 -1 1 -2
0 1 1 2 -2 1 2 -2 0 2 -2 -2 1 -1 0 0 -3 -3 -1 1 0 -1 0 2 3 4 0 -2 0 0 0 -1 0 0 1 0 1 -1 1 -2
1 1 0 1 -1 2 1 -1 0 2 -1 -2 0 -1 0 0 -2 -2 -2 0 0 0 0 2 2 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
1 1 0 1 -2 2 1 -1 0 2 0 -2 0 -1 0 0 -1 -2 -2 0 0 -1 0 2 2 2 -1 -2 1 0 0 0 0 0 0 0 1 -1 1 -2
0 -1 0 -1 1 1 -1 1 -1 0 1 0 0 -2 0 0 1 3 0 -2 2 -1 0 1 -1 -2 -2 2 0 0 0 0 0 0 1 0 0 2 0 -2
1 2 1 2 -2 1 2 -2 0 3 -2 -4 0 -1 0 0 -3 -4 -2 1 0 0 0 3 4 4 0 -4 0 0 0 0 0 0 0 0 2 -2 1 -2
0 1 2 1 -2 1 1 -1 0 1 -1 -3 0 -1 1 0 -1 -1 -1 1 0 -1 -1 1 2 4 -1 -2 1 -1 -1 0 0 1 1 0 1 -1 1 -2
2 -1 -2 -1 2 1 -2 2 0 0 3 1 -1 0 -1 0 3 3 -2 -1 0 0 1 -1 -4 -4 -1 0 0 -1 1 2 0 0 -2 2 0 0 0 0
-2 2 3 2 -4 0 3 -3 0 2 -4 -4 1 -1 1 0 -4 -4 0 3 0 -1 -2 2 6 8 0 -2 1 0 -1 -2 1 1 2 -2 1 -1 1 -2
1 3 2 3 -3 1 2 -2 0 4 -3 -5 -1 -1 0 1 -4 -6 -3 2 0 -1 0 3 5 6 1 -6 1 -1 0 1 0 1 0 0 2 -3 1 -2
0 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0
-1 5 5 5 -7 1 6 -6 0 6 -7 -8 1 -2 1 1 -9 -11 -2 5 0 -2 -2 5 11 14 2 -8 1 0 -1 -2 1 1 3 -2 2 -4 2 -4
1 1 0 1 -1 1 1 -1 0 2 -1 -2 0 -1 0 0 -2 -2 -1 0 0 0 0 2 2 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
1 1 1 1 -1 1 1 -1 0 2 -1 -2 0 -1 0 0 -2 -2 -2 0 0 0 0 2 2 2 0 -2 0 0 0 0 0 0 0 0 1 -1 1 -2
-1 3 3 4 -5 1 5 -5 0 4 -5 -5 2 -2 1 0 -7 -7 -1 3 0 -2 -2 4 8 10 0 -4 1 1 0 -3 1 0 3 -2 2 -2 2 -4
0 1 1 1 -2 1 2 -2 0 2 -1 -3 1 -1 0 0 -2 -2 -1 1 0 -1 -1 2 3 4 -1 -2 1 0 0 -1 0 0 1 0 1 -1 1 -2
1 -2 -2 -2 3 1 -3 3 -1 -1 3 2 -1 -1 -1 0 4 5 0 -3 1 0 1 -1 -4 -6 -2 3 0 0 0 1 0 0 -1 1 0 2 -1 0
0 0 0 0 -1 0 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 2 0 0 0 0 1 2 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 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 -2 1 2 -2 0 2 -1 -3 0 -1 0 0 -2 -2 -1 1 0 -1 -1 2 3 4 -1 -2 1 0 0 0 0 0 1 0 1 -1 1 -2
1 1 1 1 -1 1 0 0 0 2 0 -2 0 -1 0 0 -1 -1 -2 0 0 -1 0 1 1 2 -1 -2 1 -1 0 0 0 1 0 0 1 -1 1 -2
1 -1 -1 -1 1 1 -2 2 0 -1 2 1 -1 0 0 0 3 3 -1 -1 0 0 1 -1 -3 -3 -1 1 0 -1 0 2 0 0 -1 1 0 0 0 0
1 0 0 0 0 1 0 0 0 2 0 -1 0 -2 0 0 -1 0 -1 -2 0 0 0 2 1 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 -2
0 0 0 0 0 1 0 0 0 1 0 -1 0 -1 0 0 0 0 0 -1 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 -1
0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 2 2 0 0 0 0 0 0 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 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 2 3 2 -4 0 3 -3 0 2 -4 -4 1 -1 1 0 -4 -4 0 3 0 -1 -2 2 6 8 0 -2 1 0 0 -2 1 1 2 -2 1 -1 1 -2
0 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 -1 2 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 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 1 0 0 0 1 1 2 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 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 -1 1 1 -1 0 3 -1 -2 0 -2 -1 1 -2 -2 -2 0 0 -1 0 2 2 2 0 -2 0 0 1 0 1 0 0 0 1 -1 1 -2
1 3 2 3 -3 1 2 -2 0 4 -3 -4 0 -1 0 1 -5 -6 -3 2 0 -1 0 3 4 6 2 -6 0 -1 0 1 0 1 0 0 1 -3 2 -2
1 2 1 2 -2 1 1 -1 0 3 -2 -3 0 -1 0 1 -3 -4 -2 1 0 -1 0 2 3 4 1 -4 0 0 0 0 0 1 0 0 1 -2 1 -2
1 -1 -1 0 1 1 -1 1 0 0 1 1 0 0 -1 0 1 1 -1 -1 0 0 1 0 -2 -2 0 0 -1 0 0 1 0 0 -1 1 0 0 0 0
40
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 -1 -1 1 0 -1 1 0 -1 1 1 0 0 0 0 2 2 1 -1 0 0 0 -1 -1 -2 -1 2 0 0 0 0 0 0 0 0 0 1 -1 1
0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
-1 3 3 3 -4 0 4 -4 0 4 -4 -4 1 -1 0 0 -6 -7 0 2 0 -1 -1 3 7 8 1 -4 1 1 0 -2 0 0 2 -2 1 -2 1 -2
0 -1 0 -1 1 0 -1 1 0 0 1 1 0 -1 0 0 1 2 1 -2 0 0 0 0 -1 -2 -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 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
-1 2 2 2 -3 0 3 -3 0 2 -3 -3 1 0 0 0 -4 -4 0 2 -1 -1 -1 2 5 6 0 -2 1 0 0 -2 0 0 2 -1 1 -2 1 -1
0 0 0 0 0 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 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 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 0 -1 0 1 -1 -1 0 -1 -1 1 -1 0 -1 -1 1 2 0 1 -1 -2 1 2 2 -2 2 1 1 0 -2 0 0 2 -1 0 2 0 -1
-1 -1 0 -1 0 0 0 -1 -1 -1 0 0 1 -1 0 -1 1 3 2 -1 1 -1 -1 1 1 0 -3 4 1 1 0 -2 0 -1 2 -1 0 2 0 -1
2 -4 -4 -4 6 0 -6 6 0 -4 6 6 -2 2 -1 0 8 8 0 -4 0 2 3 -4 -10 -12 0 4 -1 -1 0 4 -2 0 -4 3 -2 2 -2 4
2 -2 -3 -2 4 0 -4 4 0 -1 4 3 -2 0 -2 0 5 5 -1 -3 0 1 2 -2 -6 -8 -1 2 0 -1 1 3 0 0 -3 2 0 1 -1 2
0 1 1 1 -1 0 1 -1 0 0 -1 -1 0 1 1 0 -1 -2 0 1 0 0 0 0 1 2 1 -2 0 0 0 0 -1 0 0 0 0 -1 0 0
2 -5 -5 -5 8 0 -8 8 -1 -5 8 8 -2 1 -2 -1 10 12 1 -6 1 2 3 -5 -13 -16 -2 7 -1 -1 0 4 -1 0 -4 3 -2 4 -2 4
0 0 0 1 0 0 0 0 0 1 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 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 1 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 0 1
-2 2 3 3 -4 0 4 -4 0 2 -4 -4 2 -1 1 -1 -5 -5 1 2 0 -1 -2 3 7 8 0 -2 1 1 -1 -3 0 0 3 -2 1 -1 1 -2
1 -1 -1 -1 2 1 -2 2 -1 0 2 1 -1 -1 -1 0 2 3 -1 -2 1 0 1 0 -3 -4 -1 1 0 -1 0 2 0 0 -1 1 0 1 0 0
3 -6 -5 -6 9 0 -9 8 -1 -6 9 8 -2 1 -1 -1 11 14 1 -7 1 2 3 -5 -14 -17 -3 9 -1 -1 0 4 -2 0 -4 3 -2 5 -2 3
1 0 -1 -1 1 0 -1 1 0 -1 2 1 -1 1 0 0 2 1 0 -1 0 1 1 -1 -2 -3 0 0 0 0 0 1 -1 0 -2 1 0 0 -1 1
0 -1 -1 0 1 0 0 0 0 0 1 1 1 0 -1 -1 0 1 1 -1 0 0 0 0 -1 -2 -1 2 0 1 1 -1 0 -1 0 0 0 1 0 0
-2 3 4 3 -5 0 4 -4 0 3 -5 -5 1 -1 1 0 -5 -6 0 3 0 -2 -2 3 8 10 0 -4 2 0 -1 -2 0 1 3 -2 1 -2 1 -2
0 0 -1 -1 1 0 0 0 -1 0 1 1 0 0 -1 0 0 1 1 -1 0 0 0 0 -1 -2 -1 2 0 1 1 -1 0 -1 0 0 0 1 0 0
0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
3 -2 -3 -2 5 0 -4 4 0 -2 5 4 -2 2 -1 0 5 4 -1 -3 0 2 3 -3 -8 -9 1 0 -1 -1 0 4 -2 0 -4 3 -1 0 -1 3
1 0 -1 -1 1 0 -1 1 0 -1 2 1 -1 1 0 0 2 1 0 -1 0 1 1 -1 -2 -3 0 0 0 0 0 1 -1 0 -1 1 0 0 -1 1
0 -1 0 -1 1 0 -1 1 0 -1 1 1 0 0 1 0 1 2 1 -1 0 0 0 -1 -2 -2 -1 2 0 0 0 0 -1 0 0 0 0 1 0 0
0 -1 -1 -2 2 -1 -2 2 0 -2 2 2 -1 1 0 0 3 3 1 -1 0 1 1 -2 -3 -4 0 2 0 0 0 1 -1 0 -1 1 -1 1 -1 2
2 -1 -2 -2 3 0 -3 3 0 -1 4 2 -2 1 -1 0 4 3 -1 -2 0 1 2 -2 -5 -6 0 0 0 -1 1 3 -1 0 -3 2 0 0 -1 2
1 -3 -2 -3 4 0 -4 4 0 -3 5 4 -1 0 0 -1 5 7 1 -4 1 1 1 -2 -7 -9 -2 5 0 0 0 2 -1 0 -2 1 -1 3 -1 1
1 -3 -2 -3 3 0 -4 3 0 -3 4 3 -1 0 0 -1 5 7 1 -3 1 1 1 -2 -5 -7 -2 5 0 0 0 1 -1 0 -1 1 -1 3 -1 1
1 0 -1 -1 1 0 -1 1 0 -1 2 1 -1 1 0 0 2 1 0 -1 0 0 1 -1 -2 -3 0 0 0 0 0 1 -1 0 -1 1 0 0 -1 1
0 -4 -3 -4 5 0 -4 4 -1 -4 5 5 -1 0 -1 -1 7 9 2 -4 1 1 1 -3 -7 -10 -3 7 0 0 0 1 0 -1 -1 1 -1 4 -2 2
1 -1 -2 -1 2 0 -2 2 0 -1 2 2 -1 1 -1 0 3 2 0 -1 -1 1 1 -2 -3 -4 0 1 0 0 0 1 0 0 -2 1 0 0 -1 2
0 2 2 2 -2 0 1 -1 0 2 -2 -3 -1 0 0 0 -2 -4 -1 2 0 0 0 1 3 4 1 -4 1 -1 -1 1 0 1 0 0 1 -2 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
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
0 0 0 1 0 0 1 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 1 0 1 -1 0 1 -1 0 0 -1 -1 0 1 0 0 -1 -2 0 2 0 0 0 0 1 2 1 -2 0 0 0 0 0 0 0 0 0 -1 0 1
0 1 0 0 0 0 1 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 -2 -1 -2 2 0 -2 2 -1 -2 2 2 0 -1 0 0 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -1 0
0 -1 -1 -1 1 -1 -1 1 0 -2 1 2 0 1 0 0 2 2 1 0 0 0 0 -2 -2 -2 0 2 0 0 0 0 0 0 0 0 -1 1 -1 2
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 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 5 -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 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 -1 -2 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 -1 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -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 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 -1 -1 0 0 0 1 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 1 0 -1 0
0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 -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 0 1 -1 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 -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 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 3 0 0 0 0 3 4 1 -2 0 0 0 -2 -3 -4 -1 4 0 0 0 0 0 0 0 0 -1 2 -1 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 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 -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 1 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 2 -2 -5 -6 0 2 0 -1 0 2 -1 0 -2 1 -1 1 -1 2
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 2 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 -1 0
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -2 5 -1 0
0 0 0 0 0 0 0 0 0 -1 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 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 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
-1 2 2 2 -3 0 3 -3 0 2 -3 -3 1 -1 1 0 -4 -4 0 2 0 -1 -1 2 5 6 0 -2 1 0 0 -2 1 0 2 -2 1 -1 1 -2
0 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 2 3 0 0 0 -1 0 0 0 0 -2 2 1 -1 0 0 0 0 1 0 0 0 0 0
-2 1 2 1 -3 0 4 -4 0 1 -3 -3 1 -1 1 0 -3 -3 1 2 0 -1 -2 2 6 6 -1 0 1 1 0 -3 1 -1 3 -2 1 0 0 -2
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 0 -1 0 2 0 0 -2 1 -1 1 -1 2
0 3 3 3 -4 0 3 -3 1 3 -4 -4 0 0 1 1 -4 -7 -2 3 -1 -1 0 2 6 8 2 -6 1 -1 -1 0 0 1 1 -1 1 -4 1 -1
1 -1 -1 -1 1 0 -1 0 0 -1 1 1 0 0 0 0 2 2 0 -1 0 0 1 0 -1 -2 -1 2 0 0 0 0 0 -1 0 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 -1 0 4 4 0 -2 0 1 2 -2 -5 -6 0 2 0 -1 0 2 0 0 -2 1 -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 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 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 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 -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
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
0 0 0 1 0 0 1 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 -2 -1 -2 2 0 -2 2 0 -2 2 3 0 0 0 0 3 4 1 -2 0 0 0 -2 -3 -4 -1 4 0 0 0 0 0 0 0 0 -1 2 -1 1
0 1 0 0 0 0 1 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 1 0 0 1 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 -1 -1 -1 1 -1 -1 1 0 -2 1 2 0 1 0 0 2 2 1 0 0 0 0 -2 -2 -2 0 2 0 0 0 0 0 0 0 0 -1 1 -1 2
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 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 -2 -1 -2 2 0 -2 2 -1 -2 2 2 0 -1 0 0 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -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 -1 1 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 -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 -1 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 -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 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 0 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -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 -1 1 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 -1 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -1 0
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -2 -2 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 -1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 -1 0 1 -1 0 0 -1 -1 0 1 0 0 -1 -2 0 2 0 0 0 0 1 2 1 -2 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 1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 -1 -2 2 2 0 0 0 -1 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -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
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 -1 0 4 4 0 -2 0 1 2 -2 -5 -6 0 2 -1 0 0 2 -1 0 -2 1 -1 1 -1 2
0 0 0 0 1 0 0 1 0 0 1 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 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 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 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -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 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 -1 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 -1 0 0 2 -1 0 -2 2 -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 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
-1 0 0 0 -1 0 2 -2 0 0 -1 -1 0 0 0 0 -1 -1 1 1 0 0 -1 1 2 2 0 0 0 1 0 -1 0 -1 1 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 -1 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 -1 0 0 2 0 0 -2 1 -1 1 -1 2
1 0 0 0 1 0 -1 1 0 0 1 0 -1 1 0 0 1 0 -1 0 0 0 1 -1 -2 -1 1 -2 0 -1 -1 2 -1 1 -1 1 0 -1 0 1
2 -2 -3 -2 4 0 -3 3 0 -2 4 4 -1 1 -1 0 4 4 0 -3 0 1 2 -2 -6 -8 0 2 -1 0 0 2 -1 -1 -2 2 -1 1 -1 2
2 -4 -4 -4 6 0 -6 6 0 -4 6 6 -2 2 -1 0 8 8 0 -4 0 2 3 -4 -10 -12 0 4 -2 -1 0 4 -1 0 -4 3 -2 2 -2 4
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 1 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -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 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
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
1 -1 -1 -1 1 0 -1 1 0 0 1 1 0 -1 0 0 1 2 0 -2 0 0 0 0 -1 -2 -1 2 0 0 0 0 0 0 0 0 0 1 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 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
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 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 0 0 0 0 0 0 0 0 0 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 -2 -4 4 0 -4 4 -2 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 5 -1 0
0 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 -1 2 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 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 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 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 4 -1 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 -1 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 -1 0 0 2 -1 0 -2 2 -1 1 -1 2
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -2 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 5 -1 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 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 0 0 0
1 1 0 1 -1 0 1 -1 0 0 -1 -1 0 1 0 0 -1 -2 -1 2 0 0 0 0 1 2 1 -2 0 0 0 0 0 0 0 0 0 -1 0 0
0 0 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 0 0 -1 6 10 2 -4 1 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 4 -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 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 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
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
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 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 -1 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 1 2 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 -1 0 0 0 0 0 0 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 -1 -1 0 2 -1 0 -2 2 -1 1 -1 2
2 -2 -3 -2 4 0 -3 3 0 -2 4 4 -1 1 -1 0 4 4 0 -3 0 1 2 -2 -6 -8 0 2 -1 0 0 2 -1 -1 -2 2 -1 1 -1 2
1 -2 -3 -2 3 0 -2 2 0 -2 3 3 -1 1 -1 0 4 4 0 -1 0 1 1 -2 -5 -6 0 2 -1 0 1 1 0 -1 -2 2 -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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 -1 0 1 -1 0 0 -1 -1 0 1 1 0 -1 -2 0 1 0 0 0 0 1 2 1 -2 0 0 -1 0 -1 0 0 0 0 -1 0 0
2 -2 -3 -2 4 0 -3 3 0 -2 4 4 -1 1 -1 0 4 4 0 -3 0 1 2 -2 -6 -8 0 2 -1 0 1 2 -1 -1 -3 2 -1 1 -1 2
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 -1 0 0 2 -1 0 -2 1 -1 1 -1 2
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -2 5 -1 0
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -2 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 5 -1 0
0 -4 -2 -4 4 0 -4 4 -1 -4 4 4 0 -1 0 -1 6 10 2 -4 2 0 0 -2 -6 -8 -4 8 0 0 0 0 0 0 0 0 -1 5 -2 0
1 -1 0 -1 1 0 -1 1 0 0 1 1 0 -1 0 0 1 2 0 -2 0 0 0 0 -1 -2 -1 2 0 0 0 0 0 0 0 0 0 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
0 0 0 1 0 0 1 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 1 0 1 -1 0 1 -1 0 0 -1 -1 0 1 0 0 -1 -2 0 2 0 0 0 0 1 2 1 -2 0 0 0 0 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 0 0 0 0 0 0 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 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 -1 -1 1 -1 -1 1 0 -2 1 2 0 1 0 0 2 2 1 0 0 0 0 -2 -2 -2 0 2 0 0 0 0 0 0 0 0 -1 1 -1 2
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 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 -2 -1 -2 2 0 -2 2 -1 -2 2 2 0 -1 0 0 3 5 1 -2 2 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -1 0
0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 -1 -2 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 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 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
2 0 -2 0 2 0 -1 2 1 0 2 2 -1 2 -1 1 1 -1 -2 0 -2 1 2 -2 -4 -4 2 -2 -1 -1 1 2 0 0 -3 2 0 -2 0 2
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 0 0 0 0 0 0 1 0 0
0 2 1 2 -2 0 2 -1 1 2 -1 -2 0 1 0 0 -3 -5 -1 2 -2 0 0 0 2 4 2 -4 1 -1 0 0 0 0 0 0 1 -3 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 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 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 3 0 0 0 0 3 4 1 -2 0 0 0 -2 -3 -4 -1 4 0 0 0 0 0 0 0 0 -1 2 -1 1
0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 -1 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 0 0
1 2 0 2 -2 0 2 -2 1 2 -2 -2 0 1 0 1 -3 -5 -2 2 -2 0 0 1 3 4 2 -4 0 0 1 0 0 0 -1 0 1 -3 1 0
-2 2 2 2 -4 0 4 -3 1 2 -3 -3 1 0 1 0 -4 -5 0 3 -1 -1 -2 1 5 7 1 -3 1 0 0 -2 1 0 2 -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 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 1 0 0 1 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 -1 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 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -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 1 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 2 1 2 -2 0 2 -1 1 2 -2 -2 0 1 1 1 -3 -5 -1 2 -2 0 0 0 2 4 2 -4 0 -1 0 0 0 0 0 0 1 -3 1 0
-1 6 4 6 -8 0 7 -6 2 6 -7 -7 1 0 1 1 -10 -14 -2 6 -2 -1 -1 4 11 14 4 -10 1 0 0 -2 1 0 2 -2 2 -6 2 -2
0 1 0 1 -1 -1 1 -1 1 0 -1 0 0 2 0 0 -1 -3 0 2 -2 1 0 -1 1 2 2 -2 0 0 0 0 0 0 -1 0 0 -2 0 2
1 3 2 4 -3 0 3 -2 2 4 -3 -3 0 1 0 1 -5 -9 -3 3 -2 0 1 1 4 6 4 -8 0 -1 0 1 0 1 -1 0 1 -5 1 0
-1 2 2 2 -4 0 3 -3 1 2 -3 -3 1 0 1 0 -4 -5 0 3 -1 -1 -1 1 5 7 1 -3 1 0 0 -2 0 0 2 -1 1 -2 1 -1
-1 0 0 0 -1 -1 2 -2 1 0 -1 0 1 0 0 0 -1 -1 1 1 -1 0 -1 0 2 2 0 1 0 1 1 -2 1 -1 1 -1 0 0 0 0
-1 6 5 6 -8 -1 7 -7 2 6 -8 -8 1 0 1 1 -10 -14 -2 7 -2 -1 -2 4 12 16 4 -10 1 0 0 -2 1 1 2 -2 2 -6 2 -2
-2 5 4 5 -7 0 7 -6 1 5 -7 -7 1 0 1 1 -9 -12 -1 6 -2 -1 -2 3 11 14 3 -8 1 0 0 -3 1 0 3 -2 2 -5 2 -2
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 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 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 2 0 0
0 0 0 0 0 -1 0 0 0 -1 0 1 0 1 0 0 0 0 1 1 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 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
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 -2 -1 -2 2 0 -2 2 0 -2 2 3 0 0 0 0 3 4 1 -2 0 0 0 -2 -3 -4 -1 4 0 0 0 0 0 0 0 0 -1 2 -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 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 -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 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 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 0 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 2 -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 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 -1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 -1 0 1 -1 0 0 -1 -1 0 1 0 0 -1 -2 0 2 0 0 0 0 1 2 1 -2 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 1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 0 0 0 3 5 1 -2 0 0 0 -1 -3 -4 -2 4 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 2 -2 -5 -6 0 2 0 -1 0 2 -1 0 -2 1 -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 1 0 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 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 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 -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 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 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 0 -1 0 2 -1 0 -2 2 -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 0 0 1 0 0 0 0 0 0 0 0 0
1 -2 -3 -2 3 0 -2 2 0 -2 3 3 0 1 -1 0 4 4 0 -1 0 1 1 -2 -5 -6 0 2 -1 0 1 1 0 -1 -2 2 -1 1 -1 2
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 0 -1 0 2 0 0 -2 1 -1 1 -1 2
1 0 0 0 1 0 -1 1 0 0 1 0 -1 1 0 0 1 0 -1 0 0 1 1 -1 -2 -1 1 -2 0 -1 0 2 -1 1 -2 1 0 -1 0 1
2 -2 -3 -2 4 0 -3 3 0 -2 4 4 -1 1 -1 0 4 4 0 -3 0 2 2 -2 -6 -8 0 2 -1 0 1 2 -1 -1 -3 2 -1 1 -1 2
1 -2 -2 -2 3 0 -3 3 0 -2 3 3 -1 1 0 0 4 4 0 -2 0 1 1 -2 -5 -6 0 2 0 0 0 2 -1 0 -2 1 -1 1 -1 2
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 0 2 -1 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 3 -1 0
0 -2 -1 -2 2 0 -2 2 0 -2 2 2 0 -1 0 0 3 5 1 -2 1 0 0 -1 -3 -4 -2 4 0 0 0 0 0 0 0 0 -1 2 0 0
0 -1 0 -1 1 0 -1 1 0 0 1 1 0 -1 0 0 1 2 1 -2 0 0 0 0 -1 -2 -1 2 0 0 0 0 0 0 0 0 0 1 0 0
-
PROPERTIES
INTEGRAL = 1
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
-
NOTES
-
URL (links to other sites for this lattice)
All the quaternionic matrix groups
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe