The Lattice GAMMA64{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 Di 9. Jun 19:37:27 CEST 2020
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GRAM
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
NOTES
REFERENCES
LAST_LINE
-
NAME
GAMMA64{3}
-
DIMENSION
64
-
DIVISORS
1^20, 2^32, 4^12
-
MINIMAL_NORM
8
-
KISSING_NUMBER
114048
-
GRAM
64 64
8 2 1 1 1 2 1 -1 1 1 1 2 1 4 1 1 1 2 2 2 4 1 0 2 1 2 1 -1 2 1 4 2 1 1 2 1 1 1 4
2 1 0 1 0 0 1 1 2 1 1 2 1 0 2 1 3 4 0 3 4 4 4 4 -4
2 8 1 1 -1 1 1 0 -1 -1 1 2 0 0 1 1 1 0 1 0 1 2 1 0 1 0 1 0 0 -1 0 -2 -1 -1 0 -1
1 -1 0 0 -1 2 1 2 0 1 -1 2 1 1 0 1 0 -2 1 3 1 0 -1 4 2 -2 0 -1
1 1 8 2 -1 1 -2 0 0 0 0 4 -1 0 0 0 0 1 1 1 -1 -1 -2 -1 -2 -1 -1 -1 0 1 0 1 0 0
0 -1 -1 -1 0 0 1 -1 0 -1 -1 2 -2 -1 0 0 0 1 -1 2 -1 -1 0 2 0 -1 -1 0 0 1
1 1 2 8 0 2 0 1 -1 0 -1 2 0 1 0 0 1 2 1 0 -1 -1 0 -2 -1 0 0 -1 0 1 0 -1 -2 0 0
1 -1 -1 0 0 -1 1 0 1 -1 -2 0 1 0 2 0 1 -2 1 2 2 1 2 1 -1 1 0 0 0
1 -1 -1 0 8 -2 1 -1 1 0 0 -2 -1 1 1 4 1 -1 -1 0 0 0 1 -1 0 1 -1 1 1 -1 1 0 1 1
0 1 -1 1 -1 -1 -2 -1 -1 0 0 -1 0 0 -1 1 0 1 -2 -1 3 -1 -1 0 2 0 2 3 0 2
2 1 1 2 -2 8 1 0 0 2 0 2 4 1 0 -1 -2 1 -1 0 0 -1 0 0 -1 0 1 -1 0 1 1 1 0 0 0 -1
1 -1 1 1 0 0 0 1 1 -2 1 1 0 2 0 1 -1 -2 1 0 2 3 0 1 -1 1 2 -2
1 1 -2 0 1 1 8 1 0 1 0 -1 1 1 0 0 1 0 1 0 1 1 2 1 2 1 1 1 0 -1 0 1 0 0 0 1 1 1
0 0 -1 1 0 1 1 -2 2 1 0 0 0 -1 1 -1 1 2 2 -1 -1 1 -1 0 0 -1
-1 0 0 1 -1 0 1 8 1 -1 0 0 0 1 -1 -1 -1 0 1 0 1 1 1 1 1 1 0 0 -1 -1 -1 1 0 0 1
0 0 -1 -1 0 -1 1 -1 1 1 -1 1 1 0 0 1 -1 0 -1 1 0 0 -2 -1 -2 -2 0 0 1
1 -1 0 -1 1 0 0 1 8 1 2 -1 0 0 1 0 -1 0 -1 -1 0 1 1 0 2 0 0 0 -1 -1 0 1 2 0 1 2
0 1 0 -1 2 0 1 -1 -1 1 -2 -1 0 0 -1 -1 2 -1 3 -2 0 -4 -1 0 0 1 -2 1
1 -1 0 0 0 2 1 -1 1 8 1 1 0 -1 0 -1 0 -1 -2 -2 0 1 1 1 1 1 -1 1 0 -1 2 1 0 0 1
2 0 1 0 -1 1 -1 0 -1 1 0 0 -1 -2 0 -1 -1 1 2 2 2 2 0 -2 1 0 2 2 0
1 1 0 -1 0 0 0 0 2 1 8 -1 0 0 -1 1 1 -1 1 1 0 0 1 1 0 1 1 -1 -1 -1 -1 0 1 1 0 1
1 1 1 -1 0 -1 -1 -2 0 1 0 0 -1 -1 0 -1 0 -1 2 -1 1 -3 1 0 0 1 0 0
2 2 4 2 -2 2 -1 0 -1 1 -1 8 1 0 -1 -1 1 0 1 2 1 1 -1 0 0 0 1 -1 0 1 1 0 -1 1 1
0 0 -1 1 0 0 -1 0 -1 -1 4 -1 0 1 -1 1 1 -1 2 -2 2 0 0 2 1 2 2 2 -2
1 0 -1 0 -1 4 1 0 0 0 0 1 8 2 1 1 -1 1 -1 1 0 0 1 1 0 1 2 0 0 0 1 1 1 1 -1 -1 1
0 1 0 0 -1 -1 0 0 -1 1 1 1 1 1 0 -2 -2 0 -1 3 0 0 1 1 1 2 -5
4 0 0 1 1 1 1 1 0 -1 0 0 2 8 2 2 2 4 1 4 2 0 -1 1 0 1 0 0 4 2 2 4 2 2 1 1 1 2 2
1 -1 1 0 1 1 0 1 4 2 2 1 2 -2 0 0 3 3 2 2 2 2 4 4 -5
1 1 0 0 1 0 0 -1 1 0 -1 -1 1 2 8 2 2 0 0 -2 1 1 0 0 1 2 1 1 2 -2 0 0 2 -2 1 1 1
2 0 1 1 -1 0 1 -1 0 -1 0 2 2 1 2 -2 0 -2 1 2 2 -2 2 0 0 0 0
1 1 0 0 4 -1 0 -1 0 -1 1 -1 1 2 2 8 2 -2 -1 0 1 1 0 0 1 2 1 1 2 -2 0 0 2 2 1 1
1 2 0 -1 -1 -1 0 1 -1 0 -1 0 -2 2 1 2 -6 -2 2 0 1 2 0 2 4 4 2 1
1 1 0 1 1 -2 1 -1 -1 0 1 1 -1 2 2 2 8 0 1 0 1 1 0 0 1 2 1 1 2 -2 0 0 -2 2 1 1 1
2 0 1 -1 -1 -2 -1 -1 2 1 0 2 -2 1 2 -2 0 -3 2 -1 0 2 0 0 0 2 2
2 0 1 2 -1 1 0 0 0 -1 -1 0 1 4 0 -2 0 8 1 2 1 -1 -1 1 -1 -1 -1 -1 2 4 1 2 -2 2
0 0 0 0 1 1 1 1 1 1 1 -1 0 2 2 2 0 0 1 2 0 -1 1 1 2 -1 -1 0 2 -4
2 1 1 1 -1 -1 1 1 -1 -2 1 1 -1 1 0 -1 1 1 8 2 2 1 1 1 1 1 0 0 1 2 -2 -1 -1 -1 0
0 0 0 2 2 0 1 1 -1 1 1 1 1 1 -1 0 0 0 2 -3 1 1 0 2 -1 -1 -2 0 0
2 0 1 0 0 0 0 0 -1 -2 1 2 1 4 -2 0 0 2 2 8 1 -1 -1 1 -1 -1 -1 -1 2 4 1 2 2 2 0
0 0 0 1 1 -1 1 -1 -1 1 1 2 2 2 -2 0 0 -1 0 0 2 -2 -1 4 -1 1 2 0 -5
4 1 -1 -1 0 0 1 1 0 0 0 1 0 2 1 1 1 1 2 1 8 2 0 4 2 4 2 -2 4 2 2 1 1 1 4 2 2 2
2 2 0 -1 -1 1 -1 1 1 1 1 1 4 2 -1 3 -1 4 0 0 4 3 3 4 4 -3
1 2 -1 -1 0 -1 1 1 1 1 0 1 0 0 1 1 1 -1 1 -1 2 8 4 2 2 2 2 0 0 -2 -1 -1 -1 -1
-2 0 0 -2 1 1 1 0 0 0 0 2 -1 1 1 1 2 2 1 -1 0 1 2 -1 -2 2 2 0 0 -1
0 1 -2 0 1 0 2 1 1 1 1 -1 1 -1 0 0 0 -1 1 -1 0 4 8 2 2 2 0 2 -2 -2 -1 -1 -1 -1
-2 0 0 -2 -1 -1 -1 0 0 0 0 -2 1 -1 -1 -1 -2 -2 1 -3 3 -1 3 -2 -2 -2 -2 -4 -4
1
2 0 -1 -2 -1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 4 2 2 8 0 0 0 0 2 2 1 1 1 1 2 0 4 2
1 1 1 0 0 0 0 0 1 -1 -1 -1 2 -2 0 1 -1 -1 -1 -2 0 2 0 0 2 -4
1 1 -2 -1 0 -1 2 1 2 1 0 0 0 0 1 1 1 -1 1 -1 2 2 2 0 8 4 2 2 0 -2 1 1 1 1 2 4 0
2 -1 -1 1 2 2 0 0 0 -1 -1 -1 -1 -2 -2 0 -1 2 3 2 -3 -2 0 2 0 -2 2
2 0 -1 0 1 0 1 1 0 1 1 0 1 1 2 2 2 -1 1 -1 4 2 2 0 4 8 4 0 2 -2 1 1 1 1 2 4 0 2
1 1 -1 -2 -2 0 0 0 1 1 1 1 2 2 -2 1 1 3 3 0 2 0 2 4 2 2
1 1 -1 0 -1 1 1 0 0 -1 1 1 2 0 1 1 1 -1 0 -1 2 2 0 0 2 4 8 -2 0 -2 0 1 1 1 0 2
2 2 2 2 0 -1 -1 1 -1 1 1 1 1 1 4 2 0 -1 -2 1 2 0 0 3 3 2 2 0
-1 0 -1 -1 1 -1 1 0 0 1 -1 -1 0 0 1 1 1 -1 0 -1 -2 0 2 0 2 0 -2 8 0 -2 0 1 1 1
0 -2 2 2 -2 -2 0 1 1 -1 1 -1 -1 -1 -1 -1 -4 -2 -2 -3 1 -2 1 0 -4 -1 -3 -2 0
1
2 0 0 0 1 0 0 -1 -1 0 -1 0 0 4 2 2 2 2 1 2 4 0 -2 2 0 2 0 0 8 4 1 2 2 2 2 2 2 4
1 1 -1 -1 -1 1 -1 1 0 2 2 2 2 4 -3 2 -3 3 -1 3 4 3 3 4 4 -2
1 -1 1 1 -1 1 -1 -1 -1 -1 -1 1 0 2 -2 -2 -2 4 2 4 2 -2 -2 2 -2 -2 -2 -2 4 8 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 -1 1 -2 2 4 0 0 0 0 -4
4 0 0 0 1 1 0 -1 0 2 -1 1 1 2 0 0 0 1 -2 1 2 -1 -1 1 1 1 0 0 1 0 8 4 2 2 4 2 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 2 -2 0 4 4 4 4 -3
2 -2 1 -1 0 1 1 1 1 1 0 0 1 4 0 0 0 2 -1 2 1 -1 -1 1 1 1 1 1 2 0 4 8 4 4 2 2 2
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 1 3 -2 -2 0 0 4 4 -2
1 -1 0 -2 1 0 0 0 2 0 1 -1 1 2 2 2 -2 -2 -1 2 1 -1 -1 1 1 1 1 1 2 0 2 4 8 0 2 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 1 2 1 -2 -2 2 2 4 0 -2
1 -1 0 0 1 0 0 0 0 0 1 1 1 2 -2 2 2 2 -1 2 1 -1 -1 1 1 1 1 1 2 0 2 4 0 8 2 2 2
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 1 -2 -1 -2 2 -2 2 4 4 0
2 0 0 0 0 0 0 1 1 1 0 1 -1 1 1 1 1 0 0 0 4 -2 -2 2 2 2 0 0 2 0 4 2 2 2 8 4 4 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 2 3 -1 -1 2 2 2 4 4 0
1 -1 -1 1 1 -1 1 0 2 2 1 0 -1 1 1 1 1 0 0 0 2 0 0 0 4 4 2 -2 2 0 2 2 2 2 4 8 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 1 -3 2 0 4 4 0 2
1 1 -1 -1 -1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 2 0 0 4 0 0 2 2 2 0 2 2 2 2 4 0 8 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 -1 0 1 1 -2 4 0 0 4 -2
1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 0 2 2 2 2 0 0 0 2 -2 -2 2 2 2 2 2 4 0 2 4 4 4 4 4
4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 1 0 -2 0 2 2 4 4 0
4 0 0 0 -1 1 0 -1 0 0 1 1 1 2 0 0 0 1 2 1 2 1 -1 1 -1 1 2 -2 1 0 0 0 0 0 0 0 0
0 8 4 2 0 2 0 0 2 2 4 2 2 4 2 2 2 -3 0 2 2 4 4 4 4 4 -3
2 0 0 0 -1 1 0 0 -1 -1 -1 0 0 1 1 -1 1 1 2 1 2 1 -1 1 -1 1 2 -2 1 0 0 0 0 0 0 0
0 0 4 8 2 2 0 2 2 0 4 2 4 0 4 2 2 0 -3 1 -1 3 2 0 0 0 0 1
1 -1 1 -1 -2 0 -1 -1 2 1 0 0 0 -1 1 -1 -1 1 0 -1 0 1 -1 1 1 -1 0 0 -1 0 0 0 0 0
0 0 0 0 2 2 8 0 4 -2 2 0 -2 -2 0 0 0 -2 2 2 -1 -2 2 0 -4 0 0 -2 -2 1
0 2 -1 1 -1 0 1 1 0 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 0 0 0 2 -2 -1 1 -1 0 0 0 0
0 0 0 0 0 0 2 0 8 2 2 2 -2 0 2 0 0 -2 -2 2 -2 2 2 -1 0 -2 0 0 -2 -2 -1
1 1 0 0 -1 0 0 -1 1 0 -1 0 -1 0 0 0 -2 1 1 -1 -1 0 0 0 2 -2 -1 1 -1 0 0 0 0 0 0
0 0 0 2 0 4 2 8 2 2 0 -2 0 -2 2 -2 -2 2 0 0 0 3 1 -4 2 2 -2 -2 1
0 2 -1 1 0 1 1 1 -1 -1 -2 -1 0 1 1 1 -1 1 -1 -1 1 0 0 0 0 0 1 -1 1 0 0 0 0 0 0
0 0 0 0 2 -2 2 2 8 0 -2 2 2 0 4 2 2 0 -2 0 2 1 3 0 2 2 0 0 1
0 0 -1 -1 0 1 1 1 -1 1 0 -1 0 1 -1 -1 -1 1 1 1 -1 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0
0 0 0 0 2 2 2 2 0 8 -2 2 2 0 0 -2 -2 0 0 2 0 1 1 -2 -2 -2 0 0 1
1 1 2 -2 -1 -2 -2 -1 1 0 1 4 -1 0 0 0 2 -1 1 1 1 2 -2 0 0 0 1 -1 1 0 0 0 0 0 0
0 0 0 2 0 0 -2 0 -2 -2 8 -2 0 2 -2 2 2 2 2 -4 2 -1 -1 2 2 2 2 2 -1
1 -1 -2 0 0 1 2 1 -2 0 0 -1 1 1 -1 -1 1 0 1 2 1 -1 1 1 -1 1 1 -1 0 0 0 0 0 0 0
0 0 0 2 4 -2 0 -2 2 2 -2 8 2 2 -2 2 0 0 0 0 1 -1 1 4 -2 -2 0 0 0
2 2 -1 1 0 1 1 1 -1 -1 0 0 1 4 0 0 0 2 1 2 1 1 -1 -1 -1 1 1 -1 2 0 0 0 0 0 0 0
0 0 4 2 -2 2 0 2 2 0 2 8 4 4 2 4 0 0 0 3 1 2 4 4 4 4 4 -4
1 1 0 0 -1 0 0 0 0 -2 -1 1 1 2 2 -2 2 2 1 2 1 1 -1 -1 -1 1 1 -1 2 0 0 0 0 0 0 0
0 0 2 4 0 0 -2 0 0 2 2 4 8 0 2 4 2 0 -3 2 -1 0 4 0 0 0 0 -2
1 1 0 2 1 2 0 0 0 0 -1 -1 1 2 2 2 -2 2 -1 -2 1 1 -1 -1 -1 1 1 -1 2 0 0 0 0 0 0
0 0 0 2 0 0 0 2 4 0 -2 -2 4 0 8 2 4 -2 0 1 0 3 4 0 4 4 4 4 -2
2 0 0 0 0 0 0 1 -1 -1 0 1 1 1 1 1 1 0 0 0 4 2 -2 2 -2 2 4 -4 2 0 0 0 0 0 0 0 0
0 4 4 0 -2 -2 2 -2 2 2 2 2 2 8 4 0 2 -4 1 -1 1 4 4 4 4 4 -2
1 1 1 1 1 1 -1 -1 -1 -1 -1 1 0 2 2 2 2 0 0 0 2 2 -2 -2 -2 2 2 -2 4 0 0 0 0 0 0
0 0 0 2 2 -2 -2 -2 2 -2 2 0 4 4 4 4 8 -2 0 -3 3 0 4 4 4 4 4 4 0
0 0 -1 -2 -2 -1 1 0 2 1 0 -1 -2 -2 -2 -6 -2 1 0 -1 -1 1 1 0 0 -2 0 -2 -3 0 0 0
-2 -2 -2 0 -2 -2 2 2 2 2 2 0 0 2 0 0 2 -2 0 -2 12 1 -2 1 0 -3 -1 0 -2 -4 -4
1
2 -2 2 1 -1 -2 -1 -1 -1 2 -1 2 -2 0 0 -2 0 2 2 0 3 -1 -3 1 -1 1 -1 -3 2 4 0 -2
-2 -2 2 2 -2 0 2 0 2 -2 0 -2 0 2 0 0 0 0 2 0 1 12 -1 3 0 2 4 0 0 2 2 -2
1 1 -1 2 3 1 1 1 3 2 2 -2 0 0 -2 2 -3 0 -3 0 -1 0 3 -1 2 1 -2 1 -3 -1 3 0 1 1 2
3 -1 -1 -3 -3 -1 2 0 0 2 -4 0 0 -3 1 -4 -3 -2 -1 16 1 1 -2 -1 -3 0 2 -2 0
3 3 -1 2 -1 0 2 0 -2 2 -1 2 -1 3 1 0 2 -1 1 2 4 1 -1 -1 3 3 1 -2 3 1 4 1 2 -2 3
4 0 1 0 1 -2 2 0 2 0 2 1 3 2 0 1 3 1 3 1 16 3 1 0 5 5 2 0 -2
4 1 0 1 -1 2 2 0 0 2 1 0 3 3 2 1 -1 1 1 -2 0 2 3 -1 2 3 2 1 -1 -2 2 3 1 -1 -1 1
1 0 2 -1 2 -1 3 1 1 -1 -1 1 -1 3 -1 0 0 0 1 3 16 3 -5 3 2 0 2 -2
0 0 2 2 0 3 -1 -2 -4 0 -3 0 0 2 2 2 0 1 0 -1 0 -1 -2 -2 -3 0 0 0 3 2 -2 -2 -2
-2 -1 -3 1 -2 2 3 0 0 1 3 1 -1 1 2 0 4 1 4 -3 2 -2 1 3 16 0 1 -2 -1 2 2
3 -1 0 1 2 0 -1 -1 -1 -2 1 2 0 2 -2 0 2 2 2 4 4 -2 -2 0 -2 2 0 -4 4 4 0 -2 -2 2
2 2 -2 0 4 2 -4 -2 -4 0 -2 2 4 4 4 0 4 4 -1 4 -1 0 -5 0 16 0 4 6 4 -3
4 4 -1 -1 0 1 1 -2 0 1 0 1 1 2 2 2 0 -1 -1 -1 3 2 -2 2 0 0 3 -1 3 0 4 0 2 -2 2
0 4 2 4 0 0 0 2 2 -2 2 -2 4 0 4 4 4 0 0 -3 5 3 1 0 16 10 4 6 -5
4 2 -1 1 2 -1 -1 -2 0 0 0 2 1 2 0 4 0 -1 -1 1 3 2 -2 0 2 2 3 -3 3 0 4 0 2 2 2 4
0 2 4 0 0 0 2 2 -2 2 -2 4 0 4 4 4 -2 0 0 5 2 -2 4 10 16 8 4 -3
4 -2 0 0 3 1 0 0 1 2 1 2 1 4 0 4 0 0 -2 2 4 0 -4 0 0 4 2 -2 4 0 4 4 4 4 4 4 0 4
4 0 -2 -2 -2 0 0 2 0 4 0 4 4 4 -4 2 2 2 0 -1 6 4 8 16 10 -4
4 0 0 0 0 2 0 0 -2 2 0 2 2 4 0 2 2 2 0 0 4 0 -4 2 -2 2 2 0 4 0 4 4 0 4 4 0 4 4
4 0 -2 -2 -2 0 0 2 0 4 0 4 4 4 -4 2 -2 0 2 2 4 6 4 10 16 -6
-4 -1 1 0 2 -2 -1 1 1 0 0 -2 -5 -5 0 1 2 -4 0 -5 -3 -1 1 -4 2 2 0 1 -2 -4 -3 -2
-2 0 0 2 -2 0 -3 1 1 -1 1 1 1 -1 0 -4 -2 -2 -2 0 1 -2 0 -2 -2 2 -3 -5 -3 -4
-6 18
-
GROUP_ORDER
1356127870648320=2^29 * 3^8 * 5 * 7 * 11
-
GROUP_NAME
2^{1+12}_+.GU(6,4)
-
GROUP_GENERATORS
5
64 64
1 1 -1 -2 0 2 -1 1 0 0 -1 0 0 -1 -2 0 2 1 2 1 0 2 -1 -1 -3 2 -2 0 -2 -2 0 2 0 -2 -2 2 1 3 -1 -4 1 2 1 -1 -1 0 2 -3 2 3 2 -2 0 0 0 0 -1 2 1 0 1 0 -1 0
0 0 0 1 1 -1 0 0 -1 0 -1 0 1 2 -1 -3 -1 1 1 1 1 -4 0 2 2 -2 1 0 3 -6 0 -5 2 1 -2 2 1 -2 -2 3 3 -2 -1 2 -1 1 -2 3 -6 -4 -2 6 1 0 1 -1 1 -1 0 0 -2 1 0 -1
-1 -2 -1 1 0 1 -1 0 1 -2 0 3 0 -4 1 1 2 1 2 1 4 -4 -3 3 0 -3 1 2 6 -7 0 0 2 1 -4 4 0 -6 1 0 0 -1 -3 2 2 -1 -1 2 -3 -2 -3 2 3 1 2 -1 1 0 -1 1 0 -1 0 -1
1 -1 -1 1 -1 -1 0 0 0 -1 0 2 0 -2 1 1 1 0 1 -1 0 -4 1 1 2 -1 -1 0 2 -1 -1 1 1 1 -1 1 0 -3 -1 0 1 0 -2 0 2 1 1 1 -2 0 0 3 2 0 1 -1 0 0 -1 1 0 0 0 -1
1 0 -1 0 -1 -1 1 0 0 1 0 1 -1 -1 1 2 0 0 -1 -1 -3 0 2 -1 2 1 -1 -2 -2 5 0 1 0 0 3 -4 -1 3 1 0 -1 0 0 -1 1 0 -1 1 0 0 3 1 0 -1 0 0 0 0 0 -1 0 -1 0 0
-1 1 -2 0 -1 1 -1 0 1 -1 -1 2 -1 0 -1 1 1 1 3 0 -1 -1 0 0 1 1 -3 -1 0 -4 0 2 1 0 -3 0 2 1 0 -3 1 0 -2 0 2 -1 1 -4 1 2 2 0 2 1 1 0 -1 2 1 1 1 0 -1 -1
3 -1 0 0 0 -1 1 0 -1 0 0 -1 0 -1 1 -1 -1 0 -2 0 -4 2 2 -1 0 2 0 -2 -1 4 -3 1 -1 1 6 -4 -3 3 -1 0 0 1 0 -2 0 3 2 -1 0 3 1 -1 -1 -2 0 1 0 0 0 1 0 -1 0 0
-2 1 0 1 1 0 0 -1 0 -1 0 1 0 4 -1 -2 -2 0 1 -1 2 -3 -1 1 1 0 -1 1 2 -5 1 -3 1 1 -4 3 3 -3 -2 3 3 -2 -1 2 -1 0 -1 3 -5 -4 -2 4 1 1 0 -1 0 -1 0 0 -1 1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 -1 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
1 0 -1 -1 -1 1 -1 1 1 0 0 0 0 -3 0 2 2 0 1 0 1 3 -2 0 -3 0 0 1 -2 1 0 5 -1 -1 -1 1 -1 1 2 -4 -2 1 0 -1 1 -1 1 -3 5 4 0 -5 -1 0 0 1 -1 2 1 1 1 -1 -1 1
-1 2 1 0 1 -1 0 0 -1 1 -1 -1 1 5 -2 -3 -2 1 0 0 0 -2 1 0 1 0 0 0 0 -4 0 -4 0 -1 -2 1 3 1 -2 4 3 -2 1 1 -2 0 -2 1 -5 -4 -1 5 0 0 0 0 0 -1 1 -1 -1 2 0 -1
0 -2 -3 1 0 1 -1 1 1 -2 0 4 0 -6 1 2 3 2 3 1 3 -2 -5 3 -2 0 0 1 5 -7 -1 4 2 0 -4 3 0 -5 1 -2 1 0 -4 2 2 0 1 0 -2 1 -5 0 3 1 2 -1 0 1 0 2 1 -2 -1 -1
0 2 0 -1 0 0 0 0 0 0 0 -1 0 3 -2 -1 -1 0 0 0 -3 2 2 -2 0 2 -2 -1 -3 1 0 0 -1 -1 1 -1 1 4 -1 -1 1 1 1 -1 -1 0 1 -4 2 2 3 -1 -1 0 -1 1 -1 1 1 0 0 1 0 0
0 2 0 -1 0 0 0 0 0 0 0 0 0 3 -2 -1 -1 0 1 -1 -1 0 1 -1 0 1 -2 0 -2 -1 1 -1 0 -1 -2 2 2 2 -2 0 2 0 1 0 -1 -1 0 -1 -1 -1 2 2 0 0 -1 0 -1 1 1 -1 0 1 0 -1
0 0 1 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 -1 -1 0 3 1 -1 0 -1 -2 1 2 -1 1 2 -1 0 0 -2 4 0 -2 0 0 -1 0 2 0 -1 -1 -1 2 1 -1 0 -1 -1 0 -1 0 0 0 0 -1 -1 0 1 1
0 1 -1 1 0 -2 1 0 0 1 0 1 0 2 0 0 -2 0 -1 -1 -3 -1 1 0 3 1 -1 -2 -1 1 0 -1 0 0 1 -3 1 2 0 4 1 -2 0 1 0 -1 -3 2 -4 -4 0 5 0 0 0 0 0 -1 1 -1 -1 0 0 -1
2 -2 2 0 1 -1 0 0 -1 0 1 -1 2 -1 0 -2 0 0 -2 1 3 1 -2 1 -2 -2 3 2 2 0 -1 -2 -1 -1 1 3 -2 -2 0 0 -1 1 2 0 -1 0 0 1 0 -1 -2 0 -1 -2 0 0 1 -1 -1 0 -1 0 1 1
0 1 1 -1 0 0 0 0 0 0 0 -1 0 1 0 0 0 -1 0 -1 0 -1 2 -1 0 -1 0 1 -1 2 1 -1 0 0 -1 2 1 -1 -2 0 1 1 1 -1 -1 0 1 1 0 0 2 0 0 0 -1 0 0 0 0 -1 0 1 1 0
3 -2 -1 0 0 -1 0 1 -1 -1 0 2 1 -4 1 0 1 2 0 1 1 -2 -1 1 -2 1 0 0 3 -3 -2 0 1 0 0 2 -1 -2 -2 0 2 1 -1 0 0 2 2 2 -4 0 -3 3 2 -1 1 -1 0 0 -1 1 0 -1 0 -1
0 1 -1 -1 0 0 0 1 0 0 0 1 0 0 -1 0 0 1 1 0 0 0 -1 0 -2 2 -1 0 -1 -2 0 2 -1 -2 -2 1 1 2 0 -1 1 1 0 0 0 0 1 -3 0 1 -1 1 0 0 0 0 -1 1 1 0 1 0 -1 -1
1 0 -2 -1 0 1 0 1 0 0 0 1 0 -2 0 1 1 1 1 0 -1 3 -2 -1 -3 3 -1 -1 -1 0 0 3 0 -1 0 -1 0 2 0 -2 1 1 0 0 -1 0 1 0 0 1 -1 -2 0 0 0 0 -1 1 1 0 1 -1 -1 0
1 1 0 -1 0 0 0 0 0 1 0 -1 0 1 -1 0 -1 0 0 0 -2 3 0 -1 -1 2 -1 -1 -3 2 0 1 -1 -1 1 -1 0 3 0 -2 0 1 1 -1 -1 0 1 -2 3 2 2 -3 -2 -1 -1 1 -1 1 1 0 0 0 0 1
2 2 0 -1 0 -1 1 0 -1 1 -1 -2 0 3 -2 -2 -2 1 -1 0 -6 2 4 -2 0 4 -2 -3 -4 3 -2 -1 -1 -1 5 -4 -1 7 -3 0 3 1 1 -2 -2 3 2 -2 0 2 3 0 -2 -2 -1 1 -1 1 1 0 0 1 0 0
2 1 0 -2 0 1 0 1 -1 1 0 -2 0 0 -1 0 0 0 -1 1 -3 5 1 -3 -3 3 -1 -1 -4 4 -1 2 -2 -2 3 -2 -1 6 -1 -2 0 2 2 -2 -2 1 2 -3 4 4 2 -5 -2 -1 -1 1 -1 1 1 0 1 0 0 1
1 1 -2 0 0 -1 1 1 0 0 0 1 0 0 0 0 -1 1 0 -1 -4 1 0 0 0 4 -2 -2 -2 1 -1 2 0 0 2 -3 0 3 0 0 2 0 -1 0 0 1 1 -1 -2 0 -1 3 0 0 0 0 -1 1 1 0 1 -1 -1 -1
0 1 -1 0 0 -1 1 0 0 0 0 1 0 3 -1 -1 -2 1 0 -1 -3 0 1 -1 1 3 -2 -2 -1 -1 0 -1 0 -1 0 -2 2 3 -1 2 3 -1 0 1 -1 0 -1 1 -4 -3 0 4 0 0 0 0 -1 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 -1 1 0 -1 1 1 -1 -1 -1 1 0 0 0 0 0 -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 0 0 0
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0 1 0 0 0 -1 1 0 0 0 0 0 0 1 0 -1 -1 0 0 -1 -2 -2 2 0 2 0 -1 -1 0 0 0 -1 0 0 0 -1 1 1 -1 2 1 -1 0 0 0 0 -1 1 -2 -2 1 3 0 0 0 0 0 0 0 -1 0 1 0 -1
2 0 0 -1 -1 -1 1 1 0 1 1 -1 0 -2 1 2 0 -1 -2 0 -2 3 1 -1 -2 2 0 -1 -4 6 -1 5 -3 -2 3 -3 -2 4 0 -1 -2 2 2 -3 0 1 2 -3 5 5 0 -4 -2 -1 -1 1 -1 1 1 0 2 -1 0 1
1 0 0 0 -1 -1 1 0 0 1 0 0 -1 0 1 1 -1 0 -1 0 -3 0 2 -1 1 2 -1 -2 -1 3 -1 1 -1 0 3 -4 -1 3 0 0 -1 1 0 -2 1 1 1 -2 1 2 2 0 0 -1 0 0 0 0 0 0 1 -1 0 0
1 0 0 -1 -1 0 0 1 0 1 1 -1 0 -2 1 3 1 -2 -2 0 0 4 0 -1 -2 1 0 0 -5 7 0 6 -3 -2 1 -2 -1 3 1 -2 -3 2 2 -3 0 0 2 -3 7 6 0 -6 -2 0 -1 1 -1 1 1 0 2 -1 0 2
0 2 0 -1 0 0 1 1 -1 1 0 -1 0 3 -1 0 -1 0 -1 -1 -2 1 2 -2 -1 3 -2 -1 -4 3 0 0 -1 -2 0 -1 2 4 -3 2 2 1 2 -2 -3 2 2 -1 0 2 0 0 -1 0 -1 0 -1 0 1 -1 1 1 0 0
0 0 2 -1 0 0 0 0 0 1 1 -2 0 0 1 1 0 -2 -2 0 1 3 0 -1 -2 0 1 1 -3 6 0 2 -3 -1 1 0 -1 1 0 -1 -3 2 3 -3 -1 0 2 -2 6 4 1 -6 -2 -1 -1 1 0 0 0 0 1 0 1 2
0 -1 -2 2 0 -1 1 0 0 -1 -1 3 -1 -1 1 0 -1 3 1 0 -5 -4 2 1 3 3 -1 -4 6 -5 -3 -2 3 2 4 -6 -1 0 -3 4 4 -2 -3 1 1 2 0 3 -9 -4 -2 7 4 0 2 -1 1 -1 0 1 0 -1 0 -3
0 1 -5 1 -2 -1 1 1 1 -1 0 5 -2 -2 1 4 0 2 2 -2 -7 -1 1 1 2 5 -4 -4 -1 0 -1 6 2 0 1 -6 0 3 0 0 2 -1 -4 0 3 0 1 -3 -2 2 -1 3 3 1 1 0 -2 2 2 1 2 -2 -1 -2
4 -3 0 -1 -1 1 -1 1 0 -1 1 -1 1 -9 2 2 4 -1 -1 2 2 4 -2 0 -4 -2 2 2 0 4 -2 7 -2 0 3 1 -5 -1 2 -6 -4 3 0 -2 2 1 3 -2 7 7 0 -8 -1 -1 0 1 0 2 -1 2 1 -1 -1 2
1 -1 4 -3 0 2 -1 0 0 0 2 -4 1 -1 -1 0 1 -2 -3 2 4 7 -1 -2 -6 -2 3 4 -3 6 0 2 -5 -3 3 3 -5 3 1 -6 -6 5 5 -5 -1 0 5 -7 13 9 3 -12 -4 -2 -2 2 0 1 -1 1 1 0 1 4
4 4 3 -1 1 -1 0 -1 0 2 0 -2 0 9 -2 -2 -3 -3 -1 -2 3 -2 2 -1 1 -2 1 2 -3 1 4 -5 -1 -1 -5 4 5 -1 -1 3 2 -1 4 1 -3 -3 -2 2 -1 -5 1 4 -2 1 -2 0 0 -2 1 -3 -2 3 1 0
2 -2 1 -1 -1 0 0 0 0 1 1 -2 0 -4 2 2 2 -2 -2 1 -1 4 1 -1 -1 -1 2 0 -2 8 -1 4 -3 0 5 -3 -4 2 2 -3 -6 2 2 -3 2 0 1 -3 8 5 3 -7 -2 -1 0 1 0 1 -1 1 1 -1 0 2
3 1 -2 -1 -1 -1 1 2 0 0 0 1 0 -2 0 1 0 2 0 0 -5 1 1 -1 -2 5 -3 -2 -3 1 -2 4 -1 -3 0 -2 1 5 -3 0 2 1 1 -2 -1 1 2 -3 0 3 0 0 0 -1 0 1 -2 2 2 0 2 0 0 -1
-3 1 2 -1 1 0 0 0 0 2 1 -1 1 3 0 1 0 -3 -1 -1 6 1 -3 0 -4 -1 3 3 -2 3 2 1 -3 -3 -4 4 2 -3 -1 2 0 1 4 -1 -4 -1 1 2 3 1 -4 -4 -2 0 -1 0 0 -2 1 -1 0 1 1 2
1 2 3 -3 1 0 0 1 -1 2 1 -4 2 3 -2 -1 -1 -2 -3 0 3 6 -1 -2 -7 1 2 3 -7 6 1 1 -5 -5 -1 4 0 4 -3 -1 0 4 7 -4 -6 1 4 -3 7 6 -1 -7 -5 -2 -3 2 -1 0 2 -1 0 2 1 3
1 1 2 -1 0 -1 0 1 -1 1 1 -3 2 1 -1 0 0 -2 -2 0 4 2 0 -1 -4 -1 1 3 -5 4 0 2 -3 -3 -3 5 1 0 -2 0 0 2 4 -2 -3 1 2 -2 5 4 -2 -4 -3 -1 -2 1 -1 0 1 0 0 2 1 2
-2 1 1 0 0 -1 0 0 0 1 1 0 1 2 0 2 0 -2 0 -2 6 -1 -2 0 -2 -2 1 3 -2 1 2 2 -1 -2 -7 6 4 -5 0 2 0 -1 2 1 -2 -2 -1 2 2 -1 -4 -2 -1 1 -1 0 -1 -1 1 -1 0 1 1 1
-1 2 3 0 3 2 -1 -2 -1 0 -2 -5 1 6 -4 -7 -2 0 1 1 -1 2 1 0 0 0 0 0 0 -4 0 -8 1 2 2 2 0 2 -2 0 3 -1 1 2 -3 1 -2 1 -2 -4 3 0 -2 -1 -1 1 1 0 0 0 -3 3 0 0
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PROPERTIES
INTEGRAL =1
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NOTES
A sandwiched Barnes Wall lattice
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REFERENCES
Hu/Nebe
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe