The Lattice Q32'
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 13:26:01 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_GENERATORS
BACHER_POLYNOMIALS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
Q32'
-
DIMENSION
32
-
GRAM
32 32
6 0 0 0 0 0 2 -1 -1 1 3 3 -2 2 -3 2 3 2 -2 -2 -2 1 -2 -1 2 0 -2 2 2 0 0 3
0 6 -3 3 3 -3 -2 2 -2 -2 2 2 3 -2 -1 2 2 -2 2 1 -2 -1 3 1 -1 2 1 -2 0 2 2 1
0 -3 6 -3 -2 2 -1 1 -1 -1 -3 -3 -2 -1 2 1 -3 3 -3 0 0 1 -1 1 0 0 0 0 -1 -2 -1 -2
0 3 -3 6 1 -1 1 -1 1 1 1 1 1 1 -3 -1 1 -1 1 1 0 -2 2 2 -1 0 -1 0 -1 2 1 1
0 3 -2 1 6 -3 -1 -1 -1 1 2 0 1 -2 0 1 1 -1 1 2 1 -2 0 1 -2 -1 1 -3 0 -1 3 1
0 -3 2 -1 -3 6 0 -1 0 1 -3 0 -3 2 -1 -1 -1 1 -1 0 -1 -1 -1 1 -1 -2 -2 3 1 -1 -1 1
2 -2 -1 1 -1 0 6 -1 3 3 2 0 0 3 -2 -2 1 0 0 0 2 2 -3 -1 0 -2 0 3 -1 -1 -2 1
-1 2 1 -1 -1 -1 -1 6 -2 -3 -1 -1 2 -1 1 1 0 -1 1 1 -1 2 1 -1 -1 1 2 0 -1 0 0 -1
-1 -2 -1 1 -1 0 3 -2 6 1 0 -2 -1 0 -1 -1 0 1 -1 1 2 1 0 1 1 0 1 1 -2 -1 0 -2
1 -2 -1 1 1 1 3 -3 1 6 0 0 0 3 -2 -3 1 -1 1 1 3 -1 -3 0 -1 -3 -2 2 1 0 0 2
3 2 -3 1 2 -3 2 -1 0 0 6 3 1 0 -2 1 3 -1 1 -2 -1 1 0 -1 2 1 1 0 0 1 0 2
3 2 -3 1 0 0 0 -1 -2 0 3 6 0 1 -2 1 3 -1 1 -3 -3 -1 0 -2 1 1 -2 1 3 2 0 3
-2 3 -2 1 1 -3 0 2 -1 0 1 0 6 -1 1 -1 0 -3 3 1 1 1 1 -1 -1 1 2 -1 -1 2 -1 0
2 -2 -1 1 -2 2 3 -1 0 3 0 1 -1 6 -2 -2 1 0 0 0 1 1 -3 -1 0 -3 -3 3 2 0 -2 3
-3 -1 2 -3 0 -1 -2 1 -1 -2 -2 -2 1 -2 6 0 -3 0 0 0 1 0 0 -1 0 0 1 -3 -1 -1 -1 -2
2 2 1 -1 1 -1 -2 1 -1 -3 1 1 -1 -2 0 6 1 2 -2 0 -2 0 1 1 1 2 1 -1 1 -1 2 0
3 2 -3 1 1 -1 1 0 0 1 3 3 0 1 -3 1 6 -1 1 -1 -1 0 1 -1 1 1 0 2 1 2 2 3
2 -2 3 -1 -1 1 0 -1 1 -1 -1 -1 -3 0 0 2 -1 6 -3 0 -1 0 -1 1 0 -1 -2 0 -1 -3 1 -1
-2 2 -3 1 1 -1 0 1 -1 1 1 1 3 0 0 -2 1 -3 6 1 0 -1 1 0 -2 0 1 0 -1 2 1 0
-2 1 0 1 2 0 0 1 1 1 -2 -3 1 0 0 0 -1 0 1 6 1 -1 0 3 -3 -2 0 0 -2 -1 2 0
-2 -2 0 0 1 -1 2 -1 2 3 -1 -3 1 1 1 -2 -1 -1 0 1 6 0 -2 -1 -1 -2 1 0 -1 -1 0 -1
1 -1 1 -2 -2 -1 2 2 1 -1 1 -1 1 1 0 0 0 0 -1 -1 0 6 -1 -2 2 1 2 1 0 -1 -3 -1
-2 3 -1 2 0 -1 -3 1 0 -3 0 0 1 -3 0 1 1 -1 1 0 -2 -1 6 2 1 3 2 -1 -2 3 2 -1
-1 1 1 2 1 1 -1 -1 1 0 -1 -2 -1 -1 -1 1 -1 1 0 3 -1 -2 2 6 -1 0 0 -1 -2 0 2 -1
2 -1 0 -1 -2 -1 0 -1 1 -1 2 1 -1 0 0 1 1 0 -2 -3 -1 2 1 -1 6 3 0 0 1 2 -1 0
0 2 0 0 -1 -2 -2 1 0 -3 1 1 1 -3 0 2 1 -1 0 -2 -2 1 3 0 3 6 2 -1 0 3 0 -2
-2 1 0 -1 1 -2 0 2 1 -2 1 -2 2 -3 1 1 0 -2 1 0 1 2 2 0 0 2 6 -1 -2 0 0 -2
2 -2 0 0 -3 3 3 0 1 2 0 1 -1 3 -3 -1 2 0 0 0 0 1 -1 -1 0 -1 -1 6 0 1 -1 2
2 0 -1 -1 0 1 -1 -1 -2 1 0 3 -1 2 -1 1 1 -1 -1 -2 -1 0 -2 -2 1 0 -2 0 6 0 -1 2
0 2 -2 2 -1 -1 -1 0 -1 0 1 2 2 0 -1 -1 2 -3 2 -1 -1 -1 3 0 2 3 0 1 0 6 0 1
0 2 -1 1 3 -1 -2 0 0 0 0 0 -1 -2 -1 2 2 1 1 2 0 -3 2 2 -1 0 0 -1 -1 0 6 0
3 1 -2 1 1 1 1 -1 -2 2 2 3 0 3 -2 0 3 -1 0 0 -1 -1 -1 -1 0 -2 -2 2 2 1 0 6
-
DIVISORS
2^16
-
MINIMAL_NORM
6
-
MINVECS
-
KISSING_NUMBER
261120
-
DENSITY
-
HERMITE_NUMBER
.424264068712E+01
-
GROUP_ORDER
2^14 3^4
-
GROUP_GENERATORS
5
32 32
-1 0 0 0 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 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 0 0 0 0 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 2 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 0 0 0 0 0
0 -1 1 1 0 0 -1 1 1 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 -1 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 0 0 0 0
1 0 -1 0 -1 0 0 0 -1 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 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 0 0 0 0 0 0
-1 2 -1 -1 -1 0 1 -1 -1 0 0 -1 -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 1 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 -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 -2 -1 1 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 -1 0 -1 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
-1 0 0 0 0 0 1 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 1 -1 -1 -1 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 1 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 2 -2 -1 -2 0 0 0 -1 2 1 -1 -1 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 -1 0 0 0 0 1 1 0 0 0 1 0 0 -1 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 0
1 -2 -2 1 -1 0 0 -1 -2 -1 -1 0 0 -2 0 0 1 0 0 1 1 1 -1 1 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0 -1 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 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 2 2 -1 1 0 0 1 2 1 0 1 0 2 0 0 -1 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0
-1 -1 1 0 2 0 1 0 0 -2 -1 1 0 1 -1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
-1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 -1 -1 0 0 0 0 0 1 -1 -1 0 1 0 1 0 0 0 -1 -1 0 0 0 0 0 0 0 -1 0 0 0
0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 -2 1 1 1 0 -1 0 1 -1 0 1 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 -1 0 0
0 1 0 0 -1 0 -1 0 0 0 1 1 -1 0 0 -1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0
-1 2 0 -1 -1 0 2 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0
-1 -2 0 1 2 0 1 0 0 -1 -1 0 0 -1 0 1 0 0 1 -1 0 1 0 0 0 0 -1 0 0 1 0 1
32 32
-1 -2 -1 2 0 1 0 1 -1 0 1 1 0 -2 1 0 1 2 0 1 1 2 -1 1 0 0 0 0 1 1 0 0
-1 2 0 0 -1 0 0 0 0 2 1 -1 -1 0 0 1 -1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0
2 -3 2 1 2 0 0 0 1 -3 -1 1 2 0 0 -1 1 -1 1 0 1 0 1 1 0 0 -1 0 1 -1 0 0
0 1 0 0 -1 0 0 0 0 1 1 0 -1 0 0 0 -1 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0
-1 1 -1 0 0 1 0 1 0 3 2 -1 -1 0 1 1 -1 1 -1 0 -1 0 0 -1 -1 1 0 0 0 1 0 0
1 -1 2 -1 2 0 0 0 2 -2 -1 0 2 2 -1 0 0 -1 1 -1 0 -1 1 0 0 0 -1 0 0 0 0 0
0 -1 0 0 1 0 -1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
0 0 2 0 1 -1 0 0 1 -1 -1 0 1 1 -1 0 0 -1 1 -1 -1 -1 0 0 1 -1 0 0 0 -1 0 0
0 1 -2 -1 -1 0 0 0 -1 1 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0
0 0 -1 0 -2 0 -1 0 -1 1 2 1 -1 0 1 -1 0 1 -1 2 1 0 0 0 -1 1 1 0 0 0 0 0
-1 0 -1 1 0 1 0 1 0 1 1 0 -1 -1 1 1 0 1 0 0 0 1 -1 0 0 0 0 0 0 1 0 0
-2 1 -1 0 -1 0 1 0 -1 1 0 0 -1 -1 0 1 0 1 0 0 0 1 -1 0 0 0 0 0 0 1 0 0
0 3 1 -1 -1 -1 -1 -1 1 1 0 0 -1 2 0 0 -1 -1 0 0 -1 -1 0 -1 0 0 1 0 -1 -1 0 0
0 0 0 0 -1 0 -1 0 0 0 1 1 0 0 0 -1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0
1 0 1 -1 1 -1 0 -1 1 -1 -2 0 1 1 -1 0 0 -2 0 -1 -1 -1 0 0 0 0 0 0 -1 -1 0 0
0 -3 -1 2 2 1 1 1 -1 -1 -1 0 1 -2 0 1 1 1 1 0 1 1 0 1 1 0 -1 0 1 0 -1 0
-3 2 -3 0 -4 1 1 0 -3 4 3 -2 -2 -1 1 1 0 2 -2 1 -1 1 -1 -1 -1 1 1 -1 0 1 1 0
0 0 1 -1 2 0 1 0 1 -1 -1 0 1 1 -1 0 0 0 0 -1 0 0 1 0 0 0 -1 0 0 0 0 0
-1 1 1 -1 1 0 0 0 1 0 0 0 0 2 -1 1 -1 -1 0 -1 -1 -1 0 -1 0 0 0 0 -1 0 0 0
0 0 1 -1 2 0 0 0 1 0 0 -1 1 2 -1 1 -1 -1 0 -1 -1 -1 1 -1 0 0 -1 0 -1 0 0 0
1 1 -1 0 -2 0 -1 0 -1 1 1 1 -1 0 1 -2 0 1 -1 2 1 -1 0 0 0 1 2 0 0 -1 0 0
0 0 -1 1 -2 0 -1 0 -1 0 1 0 -1 -2 1 -1 1 1 0 1 1 1 -1 1 0 -1 1 0 1 0 0 0
0 2 -1 -1 -3 0 1 -1 -1 2 1 -2 -1 0 0 1 -1 -1 -1 0 -1 0 1 -1 -1 0 0 -1 0 0 1 0
1 -2 0 0 2 1 0 1 1 0 1 -1 1 1 0 1 -1 -1 0 -1 0 0 2 0 -1 1 -2 0 0 0 0 0
0 -1 -2 2 -3 0 0 -1 -3 -1 0 1 -1 -4 1 -1 2 1 0 2 2 2 -2 2 1 -1 1 0 1 0 0 0
-1 -1 -2 2 -1 1 1 0 -3 0 0 0 -1 -3 1 0 1 1 0 1 1 2 -1 1 1 0 0 0 1 0 0 0
0 -1 -1 1 1 1 0 1 0 1 0 -1 0 0 1 1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 -2 1 -3 0 -1 0 -2 1 1 1 -1 -3 1 -1 1 2 0 2 2 1 -1 1 0 0 1 0 1 0 -1 0
-1 1 -1 1 -3 0 0 -1 -2 1 1 0 -1 -1 1 0 0 0 -1 1 0 1 -1 0 0 0 1 0 0 0 1 0
-2 2 -2 -1 -2 1 2 0 -2 3 2 -2 -1 0 0 1 -1 1 -2 0 -1 0 0 -1 -1 1 0 -1 0 1 1 0
-1 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 1 0 1 1 0 0 1 -1 0 0 0 0 0 0 1 0 1
32 32
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
2 1 2 -1 1 0 -1 0 2 -1 0 1 1 2 0 -2 0 -1 0 0 0 -1 1 0 0 0 0 0 0 -1 0 -1
-2 -2 -2 1 1 0 1 1 -1 1 -1 -1 0 -1 0 2 0 1 0 -2 -1 1 -1 1 0 0 0 0 0 1 0 1
3 0 1 -1 0 0 -1 0 1 -2 0 2 1 1 0 -2 0 -1 0 1 2 -1 1 1 0 0 0 0 0 -1 0 -1
2 5 3 -4 -1 0 -1 -1 4 2 1 -1 0 5 -1 0 -2 -3 -1 -1 -2 -2 2 -3 -2 0 0 -2 -2 0 1 -1
-1 -1 -1 1 1 1 1 1 -1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0
0 1 1 0 -1 -1 0 -1 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0 1 0 0 1 0
-2 0 -2 1 -2 0 1 0 -3 1 1 0 -1 -2 1 -1 1 2 -1 1 0 1 -1 1 0 0 1 0 1 0 0 0
0 1 0 0 -2 -1 0 -2 -1 -1 0 -1 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 -1 0 1 0 0 1 0
1 0 3 -1 3 0 0 0 3 -2 -1 1 1 3 -1 1 -1 -2 1 -1 0 -1 1 -1 0 0 -1 0 -1 0 0 0
3 2 2 -1 -2 -1 -2 -1 2 0 1 0 0 1 0 -1 0 -2 0 1 0 -1 1 -1 -1 -1 0 0 0 -1 0 -1
2 1 0 -1 0 1 -1 1 1 2 2 0 0 2 1 -1 -1 0 -1 1 0 -1 2 -1 -1 2 0 0 0 -1 0 -1
0 -3 2 2 4 -1 -1 1 2 -4 -2 2 1 -1 0 -1 1 0 2 -1 1 1 -1 2 1 -1 -1 2 1 0 -1 1
0 -5 1 3 4 0 1 1 -1 -5 -3 3 1 -3 -1 0 2 1 3 1 3 1 -1 2 3 -1 -1 1 1 0 -2 1
-2 -1 -1 1 1 1 0 1 0 1 0 -1 0 -1 0 1 0 1 0 -1 -1 1 -1 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0
1 2 1 -1 -1 0 0 -1 0 0 1 0 0 1 0 -1 0 -1 -1 1 0 -1 1 -1 0 0 0 0 0 -1 0 -1
0 -4 -3 2 0 0 1 1 -2 -1 -1 -1 0 -4 0 1 0 1 1 -1 1 2 -1 2 0 0 -1 0 1 1 0 2
1 2 2 -1 0 0 -1 0 2 0 1 1 0 2 0 -1 -1 -1 0 1 0 -1 1 -1 0 0 0 0 0 -1 0 -1
-1 -1 1 0 3 0 1 0 1 -2 -2 0 1 1 -1 1 0 -1 1 -2 -1 0 -1 0 1 -1 -1 0 -1 1 0 0
0 0 2 0 0 -1 0 -1 1 -2 -1 1 0 0 -1 0 0 -1 1 0 1 0 0 0 0 -1 0 0 0 0 0 1
-2 -3 0 3 2 -1 1 0 -2 -3 -2 1 0 -4 0 0 2 2 2 0 1 2 -2 2 2 -2 0 2 2 1 -1 1
0 -1 -2 1 -1 1 0 0 -2 0 1 0 0 -2 1 -1 1 1 -1 1 1 1 0 1 0 0 0 0 1 0 0 -1
1 -1 2 0 3 0 0 0 2 -2 -2 0 2 2 -1 1 0 -2 1 -2 -1 -1 0 0 1 -1 -1 0 -1 0 0 -1
0 -2 -1 2 0 0 0 -1 -2 -2 -1 0 0 -3 0 0 2 1 1 1 1 1 -1 1 1 -1 0 1 1 0 -1 0
0 2 0 -1 -1 -1 -1 -1 0 1 0 0 0 1 0 -1 0 0 -1 0 -1 -1 0 0 0 0 1 1 0 -1 0 -1
-1 5 0 -1 -5 -1 -1 -2 -1 3 2 -1 -2 0 1 -1 0 0 -2 1 -1 0 -1 -1 -1 -1 2 0 0 0 1 -1
-1 -2 -1 2 0 0 1 0 -2 -1 0 1 0 -2 1 0 1 1 0 1 1 1 -1 1 1 0 0 1 1 0 0 0
0 1 2 -1 2 0 0 0 1 0 -1 1 0 2 -1 0 0 0 1 0 0 -1 1 -1 1 1 0 0 -1 -1 -1 0
1 -2 0 1 2 0 -1 0 0 -2 -1 2 1 0 0 -1 1 0 0 1 1 0 0 1 1 0 0 1 0 -1 -1 -1
1 4 -1 -3 -3 1 1 -1 0 3 2 -2 -1 2 0 0 -2 -1 -2 0 -1 -1 2 -2 -2 1 0 -2 -1 0 1 -1
1 -2 1 1 3 1 0 1 1 -2 -1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 -1 0 0 0 -1 0
32 32
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
2 -5 -1 2 2 0 -1 2 0 -2 -1 2 0 -3 0 0 1 1 2 1 3 1 1 2 0 0 -1 0 1 0 -3 1
-1 0 3 1 1 -1 1 -2 0 -4 -3 1 1 -1 -2 0 2 -1 2 0 0 0 -2 0 3 -3 0 0 0 0 0 0
1 3 -3 -3 -4 2 0 1 -1 6 4 -1 -2 2 1 0 -2 1 -3 2 0 -1 3 -2 -3 3 1 -3 -1 0 0 -1
2 -4 3 1 7 0 -1 2 4 -4 -3 2 2 1 -1 0 0 -1 3 -2 1 0 1 1 1 0 -2 1 0 0 -2 1
-1 6 -1 -3 -5 0 0 -2 -1 4 2 -2 -1 2 0 0 -1 -1 -3 0 -2 -1 0 -2 -1 0 1 -1 -2 -1 2 -1
1 5 0 -3 -4 0 -1 -1 1 4 3 -1 -1 4 1 -1 -2 -1 -3 1 -2 -2 1 -2 -2 2 2 -1 -1 -1 2 -1
0 -5 1 3 3 -1 0 0 0 -5 -3 2 1 -3 -1 1 2 0 3 0 2 1 -1 2 2 -2 -1 1 1 0 -2 1
0 5 0 -3 -4 0 0 -1 0 4 3 -1 -1 4 1 -1 -2 -1 -3 1 -2 -2 1 -2 -2 2 2 -1 -1 -1 2 -1
0 5 -1 -3 -3 1 0 -1 0 4 3 -2 -1 3 1 -1 -2 0 -3 0 -2 -1 1 -2 -2 2 1 -1 -1 0 2 -1
3 -1 0 0 0 0 -2 1 2 1 1 0 0 1 1 0 -1 -1 0 0 0 0 1 0 -2 1 0 0 0 0 0 0
1 1 -2 -1 -2 0 -1 1 0 3 2 -1 -1 0 1 0 -1 1 -1 0 0 0 1 0 -2 1 0 0 0 0 0 0
1 -6 -2 4 1 0 -1 1 -2 -3 -1 2 0 -5 1 -1 2 2 2 2 3 2 -1 3 1 0 0 1 2 0 -2 1
-2 3 -4 -1 -4 2 1 0 -3 5 4 -2 -2 0 2 0 -1 2 -4 1 -1 1 0 -1 -2 2 1 -1 0 1 2 -1
-1 -3 2 3 3 -1 0 0 0 -5 -3 2 1 -3 -1 -1 2 1 3 0 2 1 -2 2 3 -2 0 2 2 0 -1 1
1 -4 2 2 4 -1 0 1 1 -4 -3 3 1 -2 -1 0 1 0 3 0 2 1 0 2 2 -2 -1 1 1 0 -2 1
2 1 0 -1 -1 0 -1 0 1 2 2 -1 0 2 1 0 -1 -1 -1 0 -1 -1 2 -1 -2 1 0 0 0 -1 0 -1
-1 -1 2 1 2 0 1 0 0 -2 -2 2 1 0 -1 0 1 0 1 0 0 0 -1 0 2 -1 0 0 0 0 0 0
1 -1 -1 0 -1 0 -2 1 1 2 2 0 0 0 1 0 -1 0 -1 0 0 0 1 0 -2 1 0 0 0 0 0 0
-1 -3 1 1 3 0 1 0 0 -3 -2 2 1 -1 -1 0 1 0 1 0 1 1 0 1 1 0 -1 0 0 0 -1 1
0 2 1 -1 1 1 0 0 1 1 1 0 0 3 1 -1 -1 0 -1 0 -1 -1 1 -1 0 1 1 0 0 0 1 -1
-1 -4 -1 4 0 0 0 0 -2 -3 0 0 0 -4 1 0 2 1 1 1 1 2 -3 2 1 -1 0 1 2 1 0 1
0 0 -1 0 -2 0 0 0 -1 2 1 -1 -1 -1 0 1 0 0 0 1 0 0 1 -1 -1 0 0 -1 0 0 -1 0
0 4 0 -3 -3 0 0 -1 0 3 1 0 -1 2 -1 0 -1 -1 -2 1 -1 -1 1 -2 -1 0 1 -2 -2 0 0 -1
-1 2 -2 0 -4 0 1 -1 -3 2 2 -2 -2 -2 1 0 0 1 -1 1 0 1 -1 0 -1 0 1 0 1 1 1 0
1 -2 0 1 -1 -1 0 0 -1 -1 0 0 0 -2 0 0 1 0 1 1 1 0 0 1 0 -1 0 0 1 0 -1 0
2 -1 3 1 2 -1 -2 0 3 -2 -1 1 1 1 0 0 0 -2 2 0 0 -1 0 0 1 -1 0 1 0 -1 -1 0
0 4 -1 -2 -5 0 0 -2 -1 4 3 -2 -1 2 1 0 -1 -1 -3 1 -2 -1 1 -2 -2 1 1 -1 -1 -1 2 -1
-1 -1 -3 1 0 0 1 1 -2 0 0 -1 -1 -3 1 0 0 2 0 -1 1 2 -1 2 0 0 -1 1 1 1 0 1
0 2 -3 -1 -5 0 0 -1 -3 4 3 -2 -2 -1 1 0 0 1 -2 2 0 0 1 -1 -2 1 1 -1 0 0 0 -1
0 0 3 -1 4 0 0 1 3 0 -1 1 1 3 -1 1 -1 -1 1 -2 -1 -1 2 -1 0 0 -1 0 -1 0 -1 0
0 1 -2 0 -1 1 0 0 -1 2 1 -1 -1 -1 1 0 0 1 -1 0 0 1 0 0 -1 1 0 0 0 0 0 0
32 32
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 3 -1 -1 -2 0 -1 0 0 2 1 -1 -1 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0 0 1 0 -1 0 0 -1
0 -4 0 2 1 0 1 0 -1 -3 -1 0 1 -2 0 0 2 0 1 0 1 1 0 1 0 0 -1 0 1 0 0 1
-1 4 0 -1 -2 0 -1 -1 0 2 1 -1 -1 1 0 0 0 0 -1 0 -1 -1 -2 -1 0 0 1 0 -1 0 0 -1
0 2 -1 -1 -1 0 -1 0 0 2 1 -1 -1 2 0 0 -1 0 -1 0 -1 -1 0 -1 0 0 1 0 -1 0 0 -1
-1 -4 1 2 2 0 1 1 0 -2 0 1 1 -2 0 0 1 1 1 0 1 1 0 1 0 0 -1 0 2 1 0 1
0 2 1 -1 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 2 1 -1 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 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
1 2 -1 -1 -1 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
1 0 0 0 0 0 -1 1 1 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 -1 -2 -2 0 0 -1 0 2 0 -1 -1 1 0 0 -1 0 -1 0 -1 -1 0 -1 0 0 1 0 -1 0 0 -1
0 0 1 0 1 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 -2 0 0 2 0 0 1 1 0 -1 0 1 1 0 1 0 -1 0 -1 -1 0 1 0 0 0 -1 0 -1 0 0 0
0 0 -1 0 0 0 0 1 0 1 1 -1 0 1 1 0 -1 0 -1 -1 -1 0 0 0 -1 1 0 1 0 0 1 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
-1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 4 2 -2 0 0 0 -1 2 1 1 -1 0 4 0 0 -1 -1 -1 -1 -2 -2 0 -2 0 0 1 0 -1 0 1 -1
-2 -1 -1 1 1 0 1 -1 -2 -1 -1 0 0 -1 0 0 1 1 0 0 0 1 -1 1 1 0 0 1 0 0 0 0
1 1 -1 -1 -2 0 1 -1 -1 0 0 0 -1 -1 0 0 0 0 0 1 1 1 1 0 -1 0 0 -1 0 0 0 0
0 0 -1 0 -1 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
0 -3 1 2 3 0 0 1 1 -3 -1 0 1 -1 0 0 1 0 2 -1 1 0 -1 1 1 0 -1 1 1 0 -1 1
1 -1 -1 0 0 0 1 0 -1 -1 -1 0 0 -2 0 0 0 0 1 0 1 1 0 1 0 0 -1 0 0 0 0 1
1 -1 -1 1 -1 0 0 0 -1 -1 -1 0 0 -2 0 0 0 0 1 0 1 1 -1 1 0 0 0 0 0 0 0 1
1 0 -1 -1 0 0 0 0 0 0 0 -1 0 1 0 0 -1 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0
0 0 1 0 0 0 1 -1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
1 -1 0 0 0 0 -1 1 1 1 1 1 0 0 0 0 -1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0
1 -1 0 1 1 1 0 0 0 -1 -1 0 1 -1 0 0 0 0 1 0 0 0 -1 0 1 0 0 0 0 0 0 0
-1 -1 0 1 1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 1 0 0 0 0
0 4 0 -3 -2 0 0 0 1 4 2 -1 -1 3 0 0 -2 0 -2 0 -2 -2 1 -2 -1 1 1 -1 -1 0 1 -1
-
BACHER_POLYNOMIALS
1 32
0 0 0 0 0 0 0 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
x^4320*2 x^4224*6 x^2544*6 x^2503*24 x^2484*12 x^2448*36 x^2434*48 x^2425*48 x^2424*18 x^2418*16 x^2412*24 x^2402*48 x^2397*64 x^2388*48 x^2387*72 x^2381*48 x^2378*96 x^2374*96 x^2373*48 x^2372*48 x^2370*72 x^2368*48 x^2366*48 x^2358*16 x^2356*72 x^2353*24 x^2351*48 x^2347*48 x^2346*48 x^2344*48 x^2341*48 x^2333*24 x^2332*48 x^2328*24 x^2311*48 x^2293*48 (6912x)
1 32
0 0 0 0 0 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
x^3044*12 x^3020*12 x^2508*4 x^2504*32 x^2503*32 x^2500*24 x^2452*24 x^2443*32 x^2441*16 x^2436*4 x^2434*64 x^2425*32 x^2417*32 x^2413*64 x^2412*32 x^2407*32 x^2406*32 x^2402*16 x^2400*64 x^2399*64 x^2397*32 x^2396*16 x^2394*32 x^2388*32 x^2385*16 x^2383*32 x^2378*64 x^2377*32 x^2374*48 x^2373*32 x^2370*80 x^2368*32 x^2366*32 x^2361*32 x^2356*32 x^2353*112 x^2352*16 x^2347*32 x^2346*16 x^2344*32 x^2331*64 x^2330*16 x^2317*16 x^2316*32 x^2262*16 (41472x)
1 32
0 0 0 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
x^4239*4 x^4077*4 x^2504*12 x^2443*12 x^2441*24 x^2425*24 x^2419*36 x^2417*12 x^2413*24 x^2407*48 x^2400*24 x^2399*60 x^2397*24 x^2396*24 x^2395*36 x^2394*48 x^2388*48 x^2387*36 x^2385*24 x^2384*36 x^2383*48 x^2381*48 x^2378*48 x^2376*24 x^2374*24 x^2373*24 x^2372*48 x^2370*24 x^2368*24 x^2366*24 x^2364*12 x^2361*24 x^2356*12 x^2355*12 x^2353*48 x^2351*12 x^2347*24 x^2346*24 x^2344*24 x^2341*12 x^2333*24 x^2332*24 x^2331*24 x^2330*60 x^2328*24 x^2319*24 x^2317*24 x^2316*24 x^2314*48 x^2312*60 x^2311*24 x^2307*12 x^2293*48 (20736x)
1 32
0 0 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
x^4239*4 x^4077*4 x^2504*12 x^2443*12 x^2441*24 x^2425*24 x^2419*36 x^2417*12 x^2413*24 x^2407*48 x^2400*24 x^2399*60 x^2397*24 x^2396*24 x^2395*36 x^2394*48 x^2388*48 x^2387*36 x^2385*24 x^2384*36 x^2383*48 x^2381*48 x^2378*48 x^2376*24 x^2374*24 x^2373*24 x^2372*48 x^2370*24 x^2368*24 x^2366*24 x^2364*12 x^2361*24 x^2356*12 x^2355*12 x^2353*48 x^2351*12 x^2347*24 x^2346*24 x^2344*24 x^2341*12 x^2333*24 x^2332*24 x^2331*24 x^2330*60 x^2328*24 x^2319*24 x^2317*24 x^2316*24 x^2314*48 x^2312*60 x^2311*24 x^2307*12 x^2293*48 (20736x)
1 32
0 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
x^4320*2 x^4224*6 x^2544*6 x^2503*24 x^2484*12 x^2448*36 x^2434*48 x^2425*48 x^2424*18 x^2418*16 x^2412*24 x^2402*48 x^2397*64 x^2388*48 x^2387*72 x^2381*48 x^2378*96 x^2374*96 x^2373*48 x^2372*48 x^2370*72 x^2368*48 x^2366*48 x^2358*16 x^2356*72 x^2353*24 x^2351*48 x^2347*48 x^2346*48 x^2344*48 x^2341*48 x^2333*24 x^2332*48 x^2328*24 x^2311*48 x^2293*48 (13824x)
1 32
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
x^4239*4 x^4077*4 x^2504*12 x^2443*12 x^2441*24 x^2425*24 x^2419*36 x^2417*12 x^2413*24 x^2407*48 x^2400*24 x^2399*60 x^2397*24 x^2396*24 x^2395*36 x^2394*48 x^2388*48 x^2387*36 x^2385*24 x^2384*36 x^2383*48 x^2381*48 x^2378*48 x^2376*24 x^2374*24 x^2373*24 x^2372*48 x^2370*24 x^2368*24 x^2366*24 x^2364*12 x^2361*24 x^2356*12 x^2355*12 x^2353*48 x^2351*12 x^2347*24 x^2346*24 x^2344*24 x^2341*12 x^2333*24 x^2332*24 x^2331*24 x^2330*60 x^2328*24 x^2319*24 x^2317*24 x^2316*24 x^2314*48 x^2312*60 x^2311*24 x^2307*12 x^2293*48 (13824x)
1 32
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
x^4320*2 x^4224*6 x^2544*6 x^2503*24 x^2484*12 x^2448*36 x^2434*48 x^2425*48 x^2424*18 x^2418*16 x^2412*24 x^2402*48 x^2397*64 x^2388*48 x^2387*72 x^2381*48 x^2378*96 x^2374*96 x^2373*48 x^2372*48 x^2370*72 x^2368*48 x^2366*48 x^2358*16 x^2356*72 x^2353*24 x^2351*48 x^2347*48 x^2346*48 x^2344*48 x^2341*48 x^2333*24 x^2332*48 x^2328*24 x^2311*48 x^2293*48 (6912x)
1 32
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
x^3942*6 x^3618*2 x^2484*18 x^2418*36 x^2406*108 x^2397*36 x^2377*108 x^2376*108 x^2361*216 x^2358*72 x^2332*216 x^2314*216 x^2312*108 x^2311*216 x^2304*54 (4608x)
1 32
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 -1 0 -1 0 0 0
x^3942*6 x^3618*2 x^2484*18 x^2418*36 x^2406*108 x^2397*36 x^2377*108 x^2376*108 x^2361*216 x^2358*72 x^2332*216 x^2314*216 x^2312*108 x^2311*216 x^2304*54 (768x)
1 32
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
x^3942*6 x^3618*2 x^2484*18 x^2418*36 x^2406*108 x^2397*36 x^2377*108 x^2376*108 x^2361*216 x^2358*72 x^2332*216 x^2314*216 x^2312*108 x^2311*216 x^2304*54 (768x)
-
PROPERTIES
Modular=1
-
REFERENCES
H.-G. Quebbemann, A construction of integral lattices,
Mathematika 31, pp. 137-140, 1984
W. Plesken, B. Souvignier, Computing isometries of lattices.
J. Symb. Computation. (to appear)
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe