The Lattice GAMMA64{1}
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 Mon May 20 16:59:11 CEST 2019
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GRAM
BASIS
PROPERTIES
NOTES
REFERENCES
LAST_LINE
-
NAME
GAMMA64{1}
-
DIMENSION
64
-
DIVISORS
1^12, 2^32, 4^20
-
MINIMAL_NORM
12
-
KISSING_NUMBER
4 257 792
-
GRAM
64 64
12 -6 2 4 -2 2 4 -4 -4 4 6 -4 2 6 -6 -6 -2 -2 0 4 -4 -2 0 0 2 0 -4 0 -2 0 -2 0 -2 -4 -2 2 0 -2 4 2 0 0 0 -2 -5 -2 -1 -4 1 2 4 -5 4 0 -5 -2 1 1 -1 5 2 0 1 2
-6 12 -4 -6 0 -4 -2 -2 -2 -6 0 6 2 0 6 0 2 2 -2 -4 4 2 -4 -2 -2 -2 2 2 -2 2 -2 4 -2 4 0 -2 0 2 -4 -2 -2 2 2 2 3 0 1 0 0 -5 -3 1 -6 0 1 1 -3 -1 2 -3 -4 -2 -5 2
2 -4 12 -2 -4 0 -2 -2 6 6 -4 2 2 4 2 0 -2 2 0 0 0 -2 4 -2 2 0 0 0 4 0 4 0 0 0 2 2 0 2 -4 0 2 2 -2 4 -5 2 -1 4 2 -1 -1 1 4 4 1 -1 1 3 0 -1 0 6 -3 2
4 -6 -2 12 -2 2 4 4 -4 0 2 -4 2 -2 -2 2 2 -2 0 4 -4 -2 4 4 2 4 0 0 2 0 2 -4 2 0 -2 -2 0 -2 4 2 4 -4 -4 -4 1 2 1 0 -3 4 4 -5 2 -2 -1 -2 3 -3 -1 5 0 0 5 0
-2 0 -4 -2 12 4 2 -2 -2 2 4 2 -6 -4 -2 4 0 0 2 -4 4 4 -4 4 -4 -2 2 -2 0 -2 0 2 4 0 -2 0 2 0 0 -2 -6 4 6 -4 3 -2 3 0 -2 -3 -1 1 -4 0 1 1 -1 1 0 -5 -2 0 1 -2
2 -4 0 2 4 12 -2 2 2 6 0 2 2 0 -6 0 0 0 -2 4 -4 -4 4 0 4 2 -2 -2 4 2 4 2 0 0 -2 0 -2 -4 4 -2 -2 4 -2 -2 1 -2 1 -2 -4 1 5 1 2 2 -3 -1 3 5 -2 -1 0 4 -1 -2
4 -2 -2 4 2 -2 12 -4 -4 0 6 0 -2 2 -2 2 -2 2 0 -4 4 2 -4 0 -2 -4 0 0 -2 0 -2 -4 -2 -4 -2 2 0 2 0 2 -4 -4 4 -6 -1 0 3 2 -1 -2 0 -3 -2 -2 1 2 1 -5 1 5 -4 -4 3 -2
-4 -2 -2 4 -2 2 -4 12 0 -4 -6 0 2 -2 -2 2 2 -2 0 4 -4 -2 4 0 2 4 0 0 2 0 2 0 2 4 2 -2 0 -2 4 -2 4 0 -4 2 1 2 -3 2 -1 4 2 3 2 -2 1 2 3 1 1 -1 4 2 5 0
-4 -2 6 -4 -2 2 -4 0 12 4 -6 0 -2 -2 2 2 -2 2 0 0 0 -2 4 -2 2 0 0 -2 2 0 2 -2 -2 0 2 2 -2 0 -2 0 0 0 -2 4 1 0 -1 2 -1 0 -2 3 4 2 3 0 1 1 -1 -3 2 4 -3 -4
4 -6 6 0 2 6 0 -4 4 12 2 0 -2 2 -2 -2 -2 2 0 0 0 -2 4 2 2 0 0 0 4 0 4 -2 0 -4 0 2 -2 0 0 2 0 2 -2 -2 -3 -2 1 0 -1 0 0 1 2 4 -1 -2 1 5 -3 -1 0 2 -3 0
6 0 -4 2 4 0 6 -6 -6 2 12 -2 -2 0 -2 -4 -2 -2 2 0 0 2 -4 4 -2 -2 -2 2 -4 -2 -4 -2 0 -4 -2 2 2 0 0 2 -2 0 4 -4 1 -2 3 -4 0 -3 -1 -5 -4 0 -3 -1 -1 -1 -2 1 -2 -4 1 0
-4 6 2 -4 2 2 0 0 0 0 -2 12 2 2 2 2 0 4 -2 -4 4 0 0 -4 0 -2 2 2 4 2 4 4 0 4 0 0 0 2 -4 -4 -4 4 2 0 1 2 1 4 -1 -6 -2 3 -4 2 1 2 -1 1 1 -3 -4 4 -5 2
2 2 2 2 -6 2 -2 2 -2 -2 -2 2 12 6 0 -2 0 0 -2 4 -4 -4 4 -4 4 2 -2 0 0 2 0 2 -4 4 -2 0 -2 -2 2 -2 2 2 -4 4 -2 2 -2 -2 -1 -1 5 -2 2 2 -2 -1 2 2 1 2 -2 2 0 2
6 0 4 -2 -4 0 2 -2 -2 2 0 2 6 12 -2 -4 -2 2 -2 0 0 -2 0 -4 2 -2 -2 0 -2 2 -2 2 -6 0 0 2 -2 0 2 0 -2 2 0 2 -7 -2 -3 0 2 -1 3 1 2 2 -1 1 1 3 2 3 0 0 -1 4
-6 6 2 -2 -2 -6 -2 -2 2 -2 -2 2 0 -2 12 2 2 2 0 -4 4 2 0 2 -2 0 4 2 0 0 0 0 0 4 2 -2 0 4 -6 0 2 0 0 2 2 2 2 4 -1 -3 -5 0 -4 0 4 -1 -2 -2 1 -4 -2 0 -4 2
-6 0 0 2 4 0 2 2 2 -2 -4 2 -2 -4 2 12 2 2 0 -4 4 2 0 2 -2 0 4 -2 2 0 2 0 2 4 0 -2 0 2 -2 -2 -2 0 2 0 3 2 1 6 -2 -1 -1 1 0 0 5 1 1 -3 2 -1 -4 2 3 -2
-2 2 -2 2 0 0 -2 2 -2 -2 -2 0 0 -2 2 2 12 2 -6 -4 4 2 -4 0 -2 -2 6 2 0 -2 4 0 6 0 -4 -2 0 2 2 2 -2 2 -6 0 3 -1 -1 1 -4 6 -2 -4 -1 -1 -4 0 -2 -2 -2 1 -2 0 -1 -1
-2 2 2 -2 0 0 2 -2 2 2 -2 4 0 2 2 2 2 12 0 -4 4 4 -4 0 -4 -6 0 -2 4 -2 4 0 -2 0 0 4 -2 2 0 4 -4 -2 -4 -4 0 1 2 3 -4 1 -3 4 1 3 2 0 -2 -4 4 3 -5 -2 -6 3
0 -2 0 0 2 -2 0 0 0 0 2 -2 -2 -2 0 0 -6 0 12 4 -4 0 0 4 -4 2 -4 -2 0 -2 -4 0 -2 2 4 0 0 -2 0 0 2 -2 2 -2 -2 1 0 1 2 -3 1 2 1 1 2 0 0 -2 2 -1 3 -2 0 1
4 -4 0 4 -4 4 -4 4 0 0 0 -4 4 0 -4 -4 -4 -4 4 16 -8 -4 8 4 4 8 -8 -4 0 4 0 4 -4 4 4 -4 0 -4 4 0 8 0 0 0 -4 0 -2 -2 2 4 4 -2 6 2 0 0 4 2 2 2 4 0 2 0
-4 4 0 -4 4 -4 4 -4 0 0 0 4 -4 0 4 4 4 4 -4 -8 16 4 -4 0 -4 -4 4 0 -4 0 4 0 4 0 -4 0 0 8 -4 0 -4 4 4 0 0 0 0 4 0 -2 -6 0 -4 0 4 4 -4 -4 0 -2 -6 -2 -2 -4
-2 2 -2 -2 4 -4 2 -2 -2 -2 2 0 -4 -2 2 2 2 4 0 -4 4 12 -4 4 -4 -6 4 -2 0 -6 0 0 2 0 0 4 2 2 0 4 -4 -2 4 -4 2 1 2 1 -2 3 -5 -2 -1 1 2 0 -2 -2 2 1 -3 -2 2 3
0 -4 4 4 -4 4 -4 4 4 4 -4 0 4 0 0 0 -4 -4 0 8 -4 -4 16 2 8 8 0 -2 4 4 4 0 -2 4 2 -4 -2 -2 0 -2 8 0 0 2 -2 2 -2 2 0 0 4 0 4 2 4 0 4 6 0 -2 2 4 2 0
0 -2 -2 4 4 0 0 0 -2 2 4 -4 -4 -4 2 2 0 0 4 4 0 4 2 16 0 4 0 -4 2 -2 2 2 4 0 4 -2 4 -2 2 4 6 0 4 -6 -1 0 4 -1 -3 0 1 -1 2 0 1 -3 -1 -1 0 -3 -2 -3 3 3
2 -2 2 2 -4 4 -2 2 2 2 -2 0 4 2 -2 -2 -2 -4 -4 4 -4 -4 8 0 12 6 0 -2 4 2 4 0 -2 0 0 0 -2 -2 0 0 4 2 0 2 -2 -1 -2 -3 0 1 7 -2 3 1 -2 -2 2 6 -4 1 1 4 0 1
0 -2 0 4 -2 2 -4 4 0 0 -2 -2 2 -2 0 0 -2 -6 2 8 -4 -6 8 4 6 12 -2 -2 2 4 2 2 0 4 2 -6 0 -2 0 -2 8 2 0 2 -1 0 -3 0 2 1 5 -2 2 0 2 -2 2 2 -2 -2 3 2 1 0
-4 2 0 0 2 -2 0 0 0 0 -2 2 -2 -2 4 4 6 0 -4 -8 4 4 0 0 0 -2 12 2 2 -2 2 -2 4 0 -2 0 0 2 -2 0 -2 0 0 0 2 1 0 3 -2 1 -1 -2 -3 -1 0 0 -2 0 -2 -1 -3 2 2 1
0 2 0 0 -2 -2 0 0 -2 0 2 2 0 0 2 -2 2 -2 -2 -4 0 -2 -2 -4 -2 -2 2 12 -4 0 -4 0 2 0 0 0 -2 4 -4 0 0 2 0 4 3 1 0 2 0 -3 -4 -1 -2 -2 -4 0 -2 1 -3 1 0 0 0 1
-2 -2 4 2 0 4 -2 2 2 4 -4 4 0 -2 0 2 0 4 0 0 -4 0 4 2 4 2 2 -4 16 0 8 -2 2 0 2 0 2 -4 -2 0 2 -4 -6 -6 -1 2 2 3 -2 3 4 3 0 4 -1 -4 1 3 1 1 0 3 -3 5
0 2 0 0 -2 2 0 0 0 0 -2 2 2 2 0 0 -2 -2 -2 4 0 -6 4 -2 2 4 -2 0 0 12 0 4 -4 2 2 -6 -2 0 -2 -4 4 0 2 0 -3 0 1 4 2 -1 3 2 0 -2 2 2 2 2 2 0 -1 0 -3 -2
-2 -2 4 2 0 4 -2 2 2 4 -4 4 0 -2 0 2 4 4 -4 0 4 0 4 2 4 2 2 -4 8 0 16 -2 6 0 -2 0 2 0 -2 0 2 0 -6 -2 1 2 2 1 0 3 2 1 0 4 1 0 -1 1 -3 -1 -4 5 -5 -1
0 4 0 -4 2 2 -4 0 -2 -2 -2 4 2 2 0 0 0 0 0 4 0 0 0 2 0 2 -2 0 -2 4 -2 16 0 4 4 -4 -2 2 0 -2 2 8 8 0 -4 -2 -1 -1 0 -2 1 2 4 -2 -2 1 0 2 3 -4 0 1 -2 3
-2 -2 0 2 4 0 -2 2 -2 0 0 0 -4 -6 0 2 6 -2 -2 -4 4 2 -2 4 -2 0 4 2 2 -4 6 0 16 -4 -4 0 4 2 -2 0 2 2 0 0 4 1 3 -2 -1 1 0 0 -2 -2 -3 -2 -3 -2 -4 -2 -2 2 3 -1
-4 4 0 0 0 0 -4 4 0 -4 -4 4 4 0 4 4 0 0 2 4 0 0 4 0 0 4 0 0 0 2 0 4 -4 16 0 -4 0 0 -2 -4 0 4 0 6 2 2 -2 6 0 -2 0 -2 0 2 4 2 0 2 4 -2 0 4 -2 2
-2 0 2 -2 -2 -2 -2 2 2 0 -2 0 -2 0 2 0 -4 0 4 4 -4 0 2 4 0 2 -2 0 2 2 -2 4 -4 0 12 -2 0 0 -2 0 6 -2 4 -2 -5 1 0 4 2 -1 -2 5 2 0 2 0 2 1 3 -3 4 -2 0 3
2 -2 2 -2 0 0 2 -2 2 2 2 0 0 2 -2 -2 -2 4 0 -4 0 4 -4 -2 0 -6 0 0 0 -6 0 -4 0 -4 -2 12 0 0 0 2 -4 -2 0 0 2 1 0 -3 -2 1 -1 0 1 1 -2 -2 -2 -2 -2 3 -1 2 0 1
0 0 0 0 2 -2 0 0 -2 -2 2 0 -2 -2 0 0 0 -2 0 0 0 2 -2 4 -2 0 0 -2 2 -2 2 -2 4 0 0 0 12 -4 0 -2 0 -2 0 0 2 3 3 -2 2 -2 -1 -2 -2 0 -1 1 -1 -2 1 -4 0 2 3 -1
-2 2 2 -2 0 -4 2 -2 0 0 0 2 -2 0 4 2 2 2 -2 -4 8 2 -2 -2 -2 -2 2 4 -4 0 0 2 2 0 0 0 -4 12 -6 2 0 4 4 4 -1 -1 0 4 0 -1 -6 1 -2 0 4 2 -2 -1 1 1 -4 0 -2 1
4 -4 -4 4 0 4 0 4 -2 0 0 -4 2 2 -6 -2 2 0 0 4 -4 0 0 2 0 0 -2 -4 -2 -2 -2 0 -2 -2 -2 0 0 -6 16 2 -2 0 -4 -4 -3 -1 -2 -4 -3 6 1 0 4 -2 -3 0 3 0 0 0 3 -2 4 -1
2 -2 0 2 -2 -2 2 -2 0 2 2 -4 -2 0 0 -2 2 4 0 0 0 4 -2 4 0 -2 0 0 0 -4 0 -2 0 -4 0 2 -2 2 2 12 0 -2 -2 -4 -1 -1 2 -2 -1 4 -1 -1 2 2 -2 -3 -2 -1 0 7 -2 -4 0 3
0 -2 2 4 -6 -2 -4 4 0 0 -2 -4 2 -2 2 -2 -2 -4 2 8 -4 -4 8 6 4 8 -2 0 2 4 2 2 2 0 6 -4 0 0 -2 0 16 -2 0 0 -3 2 1 0 2 1 3 1 4 -2 1 -1 3 1 2 -1 2 0 3 2
0 2 2 -4 4 4 -4 0 0 2 0 4 2 2 0 0 2 -2 -2 0 4 -2 0 0 2 2 0 2 -4 0 0 8 2 4 -2 -2 -2 4 0 -2 -2 16 4 6 -3 -3 -2 -2 -2 -4 -1 -2 1 1 -2 1 0 6 -3 -5 -2 3 -3 0
0 2 -2 -4 6 -2 4 -4 -2 -2 4 2 -4 0 0 2 -6 -4 2 0 4 4 0 4 0 0 0 0 -6 2 -6 8 0 0 4 0 0 4 -4 -2 0 4 20 -2 -1 -1 2 2 1 -7 -2 1 -1 -3 3 1 -1 -1 2 -2 -3 -1 5 0
-2 2 4 -4 -4 -2 -6 2 4 -2 -4 0 4 2 2 0 0 -4 -2 0 0 -4 2 -6 2 2 0 4 -6 0 -2 0 0 6 -2 0 0 4 -4 -4 0 6 -2 20 0 1 -4 -1 3 -5 -1 -2 0 2 3 3 1 4 -1 -4 2 5 -3 0
-5 3 -5 1 3 1 -1 1 1 -3 1 1 -2 -7 2 3 3 0 -2 -4 0 2 -2 -1 -2 -1 2 3 -1 -3 1 -4 4 2 -5 2 2 -1 -3 -1 -3 -3 -1 0 18 1 3 -2 -3 -1 -3 -3 -3 -3 1 -1 -3 -3 -2 -1 -2 3 2 -3
-2 0 2 2 -2 -2 0 2 0 -2 -2 2 2 -2 2 2 -1 1 1 0 0 1 2 0 -1 0 1 1 2 0 2 -2 1 2 1 1 3 -1 -1 -1 2 -3 -1 1 1 12 0 3 2 -2 -2 0 1 -1 0 -1 -1 -4 2 0 -1 3 1 0
-1 1 -1 1 3 1 3 -3 -1 1 3 1 -2 -3 2 1 -1 2 0 -2 0 2 -2 4 -2 -3 0 0 2 1 2 -1 3 -2 0 0 3 0 -2 2 1 -2 2 -4 3 0 16 0 -2 -5 3 2 -4 -1 1 -1 1 0 3 1 -6 1 -2 2
-4 0 4 0 0 -2 2 2 2 0 -4 4 -2 0 4 6 1 3 1 -2 4 1 2 -1 -3 0 3 2 3 4 1 -1 -2 6 4 -3 -2 4 -4 -2 0 -2 2 -1 -2 3 0 20 1 2 -5 4 -2 1 7 1 0 0 4 -1 -2 2 -1 2
1 0 2 -3 -2 -4 -1 -1 -1 -1 0 -1 -1 2 -1 -2 -4 -4 2 2 0 -2 0 -3 0 2 -2 0 -2 2 0 0 -1 0 2 -2 2 0 -3 -1 2 -2 1 3 -3 2 -2 1 16 1 -1 3 -2 2 1 1 0 2 2 -1 4 0 0 -1
2 -5 -1 4 -3 1 -2 4 0 0 -3 -6 -1 -1 -3 -1 6 1 -3 4 -2 3 0 0 1 1 1 -3 3 -1 3 -2 1 -2 -1 1 -2 -1 6 4 1 -4 -7 -5 -1 -2 -5 2 1 20 0 -2 5 1 -2 -3 0 0 -2 5 4 0 2 -2
4 -3 -1 4 -1 5 0 2 -2 0 -1 -2 5 3 -5 -1 -2 -3 1 4 -6 -5 4 1 7 5 -1 -4 4 3 2 1 0 0 -2 -1 -1 -6 1 -1 3 -1 -2 -1 -3 -2 3 -5 -1 0 20 -1 2 1 -5 -2 1 3 0 5 1 3 2 1
-5 1 1 -5 1 1 -3 3 3 1 -5 3 -2 1 0 1 -4 4 2 -2 0 -2 0 -1 -2 -2 -2 -1 3 2 1 2 0 -2 5 0 -2 1 0 -1 1 -2 1 -2 -3 0 2 4 3 -2 -1 20 -2 1 5 0 -3 1 4 -3 0 0 -1 3
4 -6 4 2 -4 2 -2 2 4 2 -4 -4 2 2 -4 0 -1 1 1 6 -4 -1 4 2 3 2 -3 -2 0 0 0 4 -2 0 2 1 -2 -2 4 2 4 1 -1 0 -3 1 -4 -2 -2 5 2 -2 16 -2 -2 0 1 -1 -1 3 3 2 3 -1
0 0 4 -2 0 2 -2 -2 2 4 0 2 2 2 0 0 -1 3 1 2 0 1 2 0 1 0 -1 -2 4 -2 4 -2 -2 2 0 1 0 0 -2 2 -2 1 -3 2 -3 -1 -1 1 2 1 1 1 -2 12 1 -2 0 4 2 2 -2 1 -3 2
-5 1 1 -1 1 -3 1 1 3 -1 -3 1 -2 -1 4 5 -4 2 2 0 4 2 4 1 -2 2 0 -4 -1 2 1 -2 -3 4 2 -2 -1 4 -3 -2 1 -2 3 3 1 0 1 7 1 -2 -5 5 -2 1 16 3 2 -1 4 -4 -2 0 -1 2
-2 1 -1 -2 1 -1 2 2 0 -2 -1 2 -1 1 -1 1 0 0 0 0 4 0 0 -3 -2 -2 0 0 -4 2 0 1 -2 2 0 -2 1 2 0 -3 -1 1 1 3 -1 -1 -1 1 1 -3 -2 0 0 -2 3 12 4 0 2 -3 1 -1 0 -4
1 -3 1 3 -1 3 1 3 1 1 -1 -1 2 1 -2 1 -2 -2 0 4 -4 -2 4 -1 2 2 -2 -2 1 2 -1 0 -3 0 2 -2 -1 -2 3 -2 3 0 -1 1 -3 -1 1 0 0 0 1 -3 1 0 2 4 12 3 3 -1 3 0 1 -1
1 -1 3 -3 1 5 -5 1 1 5 -1 1 2 3 -2 -3 -2 -4 -2 2 -4 -2 6 -1 6 2 0 1 3 2 1 2 -2 2 1 -2 -2 -1 0 -1 1 6 -1 4 -3 -4 0 0 2 0 3 1 -1 4 -1 0 3 18 -1 -5 2 3 -2 4
-1 2 0 -1 0 -2 1 1 -1 -3 -2 1 1 2 1 2 -2 4 2 2 0 2 0 0 -4 -2 -2 -3 1 2 -3 3 -4 4 3 -2 1 1 0 0 2 -3 2 -1 -2 2 3 4 2 -2 0 4 -1 2 4 2 3 -1 16 1 0 -1 1 4
5 -3 -1 5 -5 -1 5 -1 -3 -1 1 -3 2 3 -4 -1 1 3 -1 2 -2 1 -2 -3 1 -2 -1 1 1 0 -1 -4 -2 -2 -3 3 -4 1 0 7 -1 -5 -2 -4 -1 0 1 -1 -1 5 5 -3 3 2 -4 -3 -1 -5 1 20 -4 -4 3 3
2 -4 0 0 -2 0 -4 4 2 0 -2 -4 -2 0 -2 -4 -2 -5 3 4 -6 -3 2 -2 1 3 -3 0 0 -1 -4 0 -2 0 4 -1 0 -4 3 -2 2 -2 -3 2 -2 -1 -6 -2 4 4 1 0 3 -2 -2 1 3 2 0 -4 16 1 1 -2
0 -2 6 0 0 4 -4 2 4 2 -4 4 2 0 0 2 0 -2 -2 0 -2 -2 4 -3 4 2 2 0 3 0 5 1 2 4 -2 2 2 0 -2 -4 0 3 -1 5 3 3 1 2 0 0 3 0 2 1 0 -1 0 3 -1 -4 1 16 -1 0
1 -5 -3 5 1 -1 3 5 -3 -3 1 -5 0 -1 -4 3 -1 -6 0 2 -2 2 2 3 0 1 2 0 -3 -3 -5 -2 3 -2 0 0 3 -2 4 0 3 -3 5 -3 2 1 -2 -1 0 2 2 -1 3 -3 -1 0 1 -2 1 3 1 -1 20 -2
2 2 2 0 -2 -2 -2 0 -4 0 0 2 2 4 2 -2 -1 3 1 0 -4 3 0 3 1 0 1 1 5 -2 -1 3 -1 2 3 1 -1 1 -1 3 2 0 0 0 -3 0 2 2 -1 -2 1 3 -1 2 2 -4 -1 4 4 3 -2 0 -2 18
-
BASIS
64 64
1 0 0 0 0 0 0 0 0 1 0 1 2 1 1 0 3 1 0 1 0 0 1 1 0 1 1 0 3 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 3 2 2 1 1 3 2 3 2 3 2 0 2 1 0
0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 2 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 2 1 1 3 1 2 0 2 3 1 1 2
0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 2 1 1 0 1 0 0 0 0 1 1 2 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 3 0 3 0 1 0 0 0 0 1 3 2 1 1
0 0 0 1 0 0 0 0 0 0 1 0 3 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 2 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 2 1 2 0 3 3 1 2 3 2 1 3 0 2
0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 3 0 0 2 0 2 0 0 0 2 2 0 0
0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 2 1 0 1 0 0 1 0 0 0 1 0 2 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 3 1 2 2 0 2 2 1 2 1 3 1 1 2
0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 2 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 2 1 3 2 1 1 1 3 0 3 1 2
0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 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 1 0 1 0 0 1 0 3 1 3 0 2 0 2 2 2 2 0 0 2 0 0
0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 2 2 2 2 0 2 0 2 0 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 3 3 0 0 2 0 2 2 0 2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 3 3 1 0 0 0 2 2 2 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 3 1 2 0 0 2 2 0 2 2 0 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 2 0 0 0 0 2 2 2 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 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 1 1 0 1 1 3 1 3 0 2 0 0 0 0 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 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 1 1 0 1 1 1 1 3 0 0 0 0 0 0 2 2 2 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 2 0 0 0 0 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 2 0 2 2 2 0 2 2 0 2 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 3 1 1 0 0 0 0 0 0 2 2 2 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 0 0 0 2 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 3 0 0 0 0 0 0 0 2 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 1 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 2 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 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 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 2 0 0 0 2 2 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 2 2 0 0 0 0 0 0 0 2 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 1 1 0 2 2 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0
0 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 2 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 2 2 0 0 0 0 0 0 0 2 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 2 2 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 0 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 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 2 1 0 0 2 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 0 0 0 2 0 0 0 0 2 2 2 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 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 0 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 0 2 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 2 0 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 0 0 2 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 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 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 0 0 0 0 0 0 0 0 2 2 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 0 0 0 0 0 0 0 0 0 2 0 2 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
-
PROPERTIES
INTEGRAL =1
-
NOTES
A sandwiched Barnes Wall lattice constructed as a sublattice
of Gamma643 using BASIS. GRAM gives a reduced Gram matrix, not compatible
with the automorphism group of Gamma643
-
REFERENCES
Hu/Nebe
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe