The Lattice LAMBDA(C1)
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 13:17:30 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_GENERATORS
BACHER_POLYNOMIALS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
LAMBDA(C1)
-
DIMENSION
32
-
GRAM
32 0
4
-1 4
0 0 4
1 -1 1 4
-1 1 0 0 4
0 0 2 0 -1 4
0 1 1 1 1 0 4
-1 1 1 1 1 1 1 4
0 1 -1 0 0 -1 0 -1 4
-1 1 1 1 1 1 1 1 0 4
0 0 0 1 -1 1 -1 0 1 1 4
-1 1 0 -1 1 -1 1 0 0 -1 -1 4
-1 0 -1 0 -1 0 -2 0 1 1 2 -1 4
0 -2 1 1 0 1 0 0 -1 0 0 -1 -1 4
0 1 0 0 1 0 0 0 0 1 1 -1 0 0 4
0 0 0 1 1 -1 1 1 -1 -1 -2 1 -2 0 -1 4
-1 0 -1 -1 0 0 1 -1 1 1 0 0 0 0 -1 -1 4
0 1 -1 -1 0 -1 0 -2 2 0 1 1 1 -1 1 -2 1 4
-1 1 1 0 1 1 0 1 0 2 1 -1 0 1 2 -1 0 0 4
1 -1 0 0 0 0 1 -1 0 0 -1 -1 -2 1 -1 1 2 -1 0 4
-2 0 0 0 1 0 -1 2 -1 1 0 -1 1 1 1 0 0 -1 2 -1 4
0 -2 1 0 -1 1 -1 0 -1 -1 0 1 0 1 -1 0 -1 -1 -1 -1 0 4
-1 1 -1 -2 0 0 -2 0 0 0 0 -1 2 -1 1 -1 0 1 1 -1 2 -1 4
1 1 1 1 0 1 1 1 0 0 1 1 0 -1 1 0 -2 0 0 -2 -1 1 -1 4
0 0 -1 -1 -1 1 -1 -1 0 1 2 -1 1 0 0 -2 2 1 1 1 0 -1 1 -1 4
0 1 1 0 0 2 1 0 0 2 2 -1 0 0 2 -2 1 1 2 0 0 -1 0 1 2 4
1 -1 1 2 -1 0 -1 1 0 0 1 -1 1 1 0 0 -2 -1 1 -1 1 1 0 1 -1 -1 4
0 -1 1 1 1 0 2 0 -1 0 -2 1 -2 1 -2 2 1 -1 -1 2 -1 0 -2 -1 -1 -1 -1 4
1 0 1 2 -1 0 1 1 0 0 0 0 -1 0 -1 2 -1 -2 0 1 -1 0 -2 1 -1 -1 2 1 4
-1 0 -1 0 1 -1 0 -1 1 1 0 0 1 -1 -1 0 2 0 0 1 0 -1 0 -1 1 0 -1 1 0 4
1 -1 0 1 0 0 0 0 0 -2 0 1 -1 1 0 1 -2 -1 -1 -1 -1 2 -2 2 -2 -1 1 0 1 -1 4
0 -1 0 1 -1 1 0 1 -1 0 1 0 1 0 -1 0 0 -1 -2 -1 0 2 -1 1 0 0 0 0 0 0 1 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^21 3 7
-
GROUP_GENERATORS
12
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 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 1 -1 -1 0 0 0 0 -1 -1 -1 0 0 0 0
-1 1 0 -1 -1 -1 -1 1 0 1 0 -1 -1 0 0 0 0 1 -1 1 0 0 0 1 0 1 2 2 -1 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
1 -1 -1 1 1 0 0 -2 1 0 1 1 -1 1 -1 -1 0 -2 2 -2 0 0 2 0 -2 0 -3 0 2 -1 -2 1
-1 1 1 -1 -1 -1 -1 2 0 1 -1 -1 0 -1 1 1 1 1 -1 1 -1 0 0 0 2 1 3 2 -2 0 3 0
0 0 0 0 0 1 1 -1 0 0 0 0 0 -1 0 0 -1 0 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 -1 1 0 1 0 0 0 0 0 0 1 0 -1 0 1
0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 -1 -1 0 0 0 -1 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 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 -1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 -1 0 -1 0 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 0 0 0 0
-1 1 1 -1 -1 0 -1 2 -1 1 -1 -1 0 -1 1 1 0 3 -2 2 1 0 -2 0 2 0 3 1 -2 1 3 -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 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 1 -1 0 0 0 0 0 0 0 0 1 -1 0 0 0 -1 -1 0 0 0 -1 0 1 0 -1
0 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 0 -1 0 0 0 0 0 -1 -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 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 -1 2 -1 1 0 0 -1 0 0 0 0 2 -1 1 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 1 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 -1 -1 -1 -1 1 0 1 0 0 -1 0 0 0 0 0 0 1 -1 -1 0 1 0 0 2 1 -2 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 -1 0 -1 1 0 0 0 0 0 0 0 0 -2 1 -1 -1 0 1 0 0 1 0 1 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 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 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
1 -1 -1 1 0 0 0 0 0 0 1 1 -1 2 -1 -1 0 -1 1 -2 -1 0 2 0 -2 0 -3 -1 2 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 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
32 32
0 0 0 -1 -1 -1 -1 1 0 1 0 0 0 0 0 0 -1 1 -1 2 1 0 0 1 0 1 0 1 0 0 1 0
-1 1 1 0 -1 -1 0 1 0 0 -1 -1 0 -1 1 1 1 0 0 0 -1 0 0 0 2 0 2 1 -2 0 2 0
1 0 0 0 1 1 2 -3 1 -2 0 1 2 0 0 0 -1 -2 2 -1 1 0 -1 -1 0 0 -1 0 1 -1 -2 1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 1 0 1 1 0 -1 0 0 0 -1 0 1 0 0 0
0 0 -1 1 1 0 1 -2 1 -1 0 1 0 0 0 -2 -1 -2 1 0 1 0 1 0 0 0 -1 1 1 -1 -1 1
0 0 1 -1 -1 0 0 1 0 0 0 -1 0 0 1 2 1 0 1 -1 -2 0 -1 0 1 -1 1 0 -2 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
1 0 0 0 1 0 2 -2 1 -1 0 0 1 0 0 0 0 -2 2 -2 0 0 0 -1 1 -1 -1 0 1 -1 -1 1
-1 0 0 0 -1 0 0 1 0 1 0 0 -1 0 0 0 -1 1 -2 1 1 0 0 1 1 0 1 0 -1 1 1 -1
0 0 0 0 0 1 1 0 0 -1 -1 0 2 -1 1 1 0 0 1 0 0 0 -2 -1 1 0 1 0 -1 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 0 -1 0 -1 1 0 0 1 -1 0 0 -1 1 -2 1 -1 -1 0 2 0 0 0 0 1 0 -1 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 0 1 -1 -1 0 -1 3 -1 0 0 -1 0 1 1 2 1 2 0 0 -2 0 -2 0 0 -1 1 -1 -2 2 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 0 0
0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 1 0 0 -1 -1 0 1 0 0 0
0 0 0 0 0 1 0 1 -1 0 0 0 0 0 0 1 1 1 -1 0 0 0 -1 0 0 0 1 -1 -1 1 0 -1
-1 0 0 0 -1 -1 -1 1 0 1 0 0 -1 0 0 0 0 1 -1 1 0 0 1 1 0 1 1 1 -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 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 1 -1 0 0 0 0 0 0 1 0 1 -1 1 0 0 -1 0 0 0 1 -1 -1 1 0 -1
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 0 0 0 1 -1 1 0 -1 -1 0 -1 -1 -1 1 0 -1 0
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 0 0 0 1 -1 0 1 -1 -1 0 -1 -1 -1 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 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 -1 0 -1 1 0 0 0 1 1 0 0 -1 1 1 -1 0 1
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 1 0 0 0 -1 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 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 1 0 0 0 -1 1 0 1 1 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 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 -1 1 1 1 0 -1 0 0 0 1 0 0 -1 -2 -1 0 -1 1 2 0 1 0 -1 1 -1 0 2 0 0 0
0 0 0 0 -1 -1 -1 1 0 1 1 0 -2 1 0 -1 0 0 0 0 -1 0 1 1 -1 -1 -1 0 0 1 0 0
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 0 0 0 1 -1 0 0 -1 -1 0 -1 -1 -1 1 0 -1 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
1 0 -1 1 2 1 2 -3 1 -1 0 1 1 0 -1 -2 -2 -1 0 -1 3 1 1 -1 0 1 -3 0 4 -1 -1 0
0 -1 0 1 1 0 1 -2 0 0 1 1 -1 0 -2 -2 -1 -1 1 0 1 -1 2 0 -1 0 -2 -1 2 -1 0 1
0 0 0 1 1 0 0 -1 0 -1 0 0 0 0 0 0 1 -1 1 -1 -1 0 1 0 0 0 0 0 1 -1 -1 1
0 1 1 0 1 1 1 0 -1 -1 -1 -1 2 -1 1 2 1 1 0 0 0 1 -2 -1 2 -1 1 -1 -1 0 1 -1
0 -1 -1 1 0 0 0 -1 0 1 1 1 -2 1 -2 -2 -1 -1 1 0 0 -1 2 1 -2 0 -2 -1 1 0 -1 1
0 0 0 0 0 1 1 -1 0 0 1 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0
0 0 0 0 0 1 1 -1 0 0 0 0 0 -1 0 0 -1 0 0 0 2 0 -1 0 1 -1 0 0 0 0 0 0
0 0 0 0 1 0 1 -2 1 -1 -1 0 1 0 0 0 0 -1 1 -1 0 0 0 0 1 0 0 0 1 -1 -1 1
0 0 0 0 1 1 1 -1 0 0 0 0 1 -1 0 0 0 0 0 0 1 0 0 -1 1 0 0 0 1 -1 1 0
0 0 0 0 1 0 0 -1 0 -1 -1 0 2 0 0 0 0 0 1 0 0 0 -1 0 0 1 0 0 1 -1 -1 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 1 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 -2 0 0 1 1 -2 1 -2 -2 0 -1 2 0 0 -1 2 1 -3 0 -2 -1 2 -1 -2 2
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 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 -1 -1 -1 -1 1 0 1 0 0 -1 0 0 0 0 0 0 1 -1 -1 0 1 0 0 2 1 -2 0 1 1
0 0 0 0 -1 0 0 1 0 1 0 0 0 0 0 0 -1 1 -1 1 1 0 0 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 -1 1 0 0 -1 0 1 0 0 0 0 1 0 1 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 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 1 0 0 0 0 -1 0 1 0 -1 0 -1 0 1 0 1 0 -1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 1 0 0 0 0 2 -1 -1 -1 -1 2 0 1 2 2 1 0 0 -2 1 -1 -1 1 0 1 -1 -1 1 1 -1
0 0 0 0 0 -1 -1 0 0 0 0 0 -1 1 0 0 1 -1 1 -1 -2 0 1 1 -1 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 1
32 32
0 0 0 -1 -1 -1 -1 1 0 1 0 0 0 0 0 0 -1 1 -1 2 1 0 0 1 0 1 0 1 0 0 1 0
-1 0 1 0 -1 0 0 0 0 1 0 -1 -1 -1 0 0 0 1 0 1 1 -1 0 1 1 -2 0 0 -1 0 2 0
0 1 0 -1 0 0 1 0 0 0 0 -1 1 0 0 1 -1 1 -1 0 1 1 -1 -1 1 1 1 1 0 0 1 -1
0 0 0 0 1 0 0 -1 0 -1 -1 0 2 0 0 1 0 0 1 0 0 0 -1 0 0 1 0 0 1 -1 -1 1
0 -1 -1 1 1 0 0 -3 1 0 0 1 -1 0 -1 -2 0 -2 2 -1 1 -1 2 1 -1 0 -2 1 2 -2 -1 2
0 1 1 -1 -1 -1 0 2 0 1 0 -1 0 0 1 2 0 1 -1 0 -1 1 0 -1 2 0 2 1 -2 1 2 -1
0 0 0 0 0 1 1 -1 0 0 0 0 0 -1 0 0 -1 1 0 1 2 0 -1 0 0 -1 0 0 0 0 0 0
1 0 0 0 1 1 2 -3 1 -1 0 0 1 -1 0 1 0 -2 2 -2 1 0 -1 -1 1 -1 0 0 0 -1 -1 1
-1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 1 -1 1 1 0 0 1 1 0 0 0 1 0 0 0
0 0 0 0 1 1 1 -1 0 0 -1 0 2 -1 0 0 -1 1 0 1 2 0 -1 -1 1 0 0 0 1 -1 1 0
0 0 0 0 1 0 0 -1 0 -1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 -1 -1 1
-1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 1 0 0 0 -1 0 0 1 0 -1 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 0 0 0 0
0 1 1 -1 0 0 -1 2 -1 0 -1 -1 1 0 1 2 1 2 -1 0 -1 1 -2 -1 1 1 2 0 -1 1 1 -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 0 0
0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 1 -1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 1 -1 0 0 0 0 0 0 0 0 2 -1 1 1 0 -1 0 0 -1 0 -1 0 1 0 -1
-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 -1 2 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 -1 2 -1 1 0 0 -1 0 0 0 0 2 -1 1 0 0 0 0 0 0 0 0 0 1 1 -1
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 1 1 -1 1 -2 0 0 -1 -1 0 0 0 -1 0 0 -1 0
1 0 0 0 1 0 1 0 0 -1 0 0 1 1 0 1 1 -1 1 -2 -2 1 0 -1 0 0 0 -1 0 0 -1 0
0 0 0 0 -1 0 0 1 0 1 1 0 -1 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 -1 1 1 -1
0 0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 1 1 0 0 0 1 0 -1 0 1
0 0 0 0 0 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 1 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 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 -1 -1 1 0 0 -1 0 0 0 0 1 -1 1 -1 -2 0 0 1 0 0 -1 2 1 -2 0 -2 0 2 0 -1 1
0 0 0 0 0 -1 -1 0 0 0 0 0 -1 1 0 0 1 -1 1 -1 -2 0 1 1 -1 0 0 0 0 0 -1 1
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 1 0 0 1 -1 0 0 -1 -1 0 -1 0 -1 0 0 -1 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
0 0 -1 0 1 0 1 -2 1 -1 0 0 0 0 -1 -1 -1 -1 1 -1 1 0 1 0 0 1 -1 1 2 -1 -1 1
0 -1 0 1 1 0 1 -2 0 -1 0 0 0 0 -1 -1 0 -1 2 -1 0 0 1 0 -1 0 -2 -1 2 -1 -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
-1 1 1 -1 -1 0 0 2 -1 0 -1 -2 1 -1 1 3 1 2 0 1 -1 0 -3 0 2 -1 3 0 -4 1 2 -1
1 -1 -1 2 1 0 1 -3 1 -1 1 2 -1 1 -1 -2 0 -4 3 -2 -1 0 3 0 -2 0 -3 -1 2 -1 -3 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 -1 1 -1 1 0 0 0 0 0 0 0 0 -2 1 -1 0 0 1 0 1 0 0 1 0 -1 0 1
0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 1 -1 0 1 0 -1 0 1 -1 0 -1 0 1 0 -1
0 0 0 0 0 1 1 0 0 -1 -1 0 2 -1 1 1 0 0 1 0 0 0 -2 -1 1 0 1 0 -1 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 -1 -1 -1 -1 1 0 1 0 -1 -1 0 0 1 1 1 0 0 -1 0 0 1 0 0 1 1 -1 0 1 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 -1 2 1 0 0 -1 0 -1 1 2 -1 2 -1 -2 0 -2 2 -1 -1 0 2 0 -3 0 -3 -2 2 0 -3 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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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 1 0 1 -1 0 0 0 0 0 1 0 0 1 -1 1 0 0 -1 0 0 -1 0 -1 0 1 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 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 -1 0 -1 1 0 0 0 0 0 -1 0 0 -1 1 0 0 0 1 1 0 1 0 1 0 -1 0 1
0 0 0 0 0 0 -1 1 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 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 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 1 0 -1 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 0 0 0 0 0 0 0 0 0 1 0 0 0
-1 1 1 -1 -1 1 -1 3 -2 1 -1 -2 1 -1 1 2 1 4 -2 2 0 0 -3 0 1 -1 2 -1 -2 2 3 -2
0 0 0 0 -1 -1 -1 1 0 1 1 0 -2 1 -1 0 0 0 0 0 -1 0 1 1 -1 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 1
32 32
0 0 0 0 -1 -1 -1 1 0 1 0 0 -1 0 0 -1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0
1 -1 -1 2 2 0 1 -3 1 -1 1 2 0 1 -2 -3 -1 -2 1 -1 2 0 3 0 -2 1 -5 -1 5 -2 -2 1
0 0 0 0 1 1 1 -1 0 0 0 0 0 -1 -1 -1 -2 1 -1 1 2 0 0 -1 0 1 0 0 1 0 1 0
0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 1
0 0 1 0 1 0 0 0 0 -1 -1 0 2 0 1 1 1 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 0
0 0 -1 0 1 1 0 -1 0 0 1 0 -1 0 -1 -1 -1 0 -1 0 1 0 0 0 -1 1 0 0 1 0 -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 0 0 0 0 0 0 0
1 0 0 0 1 1 1 0 0 -1 0 0 1 0 0 1 0 0 0 -1 0 0 -1 -1 0 0 0 -1 0 0 -1 0
-1 0 0 0 0 -1 -1 0 1 0 -1 0 0 0 0 -1 0 0 0 1 0 0 1 1 0 1 0 1 1 -1 0 1
0 0 0 0 1 1 1 -1 0 0 -1 0 2 -1 0 0 -1 1 -1 1 2 0 -1 -1 1 1 0 0 1 -1 1 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 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 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 -1 0 0 0 0 -1 1 -1 -1 -1 0 0 0 0 0 1 0 -1 1 0 0 1 0 -1 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 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
-1 0 0 0 -1 -1 -1 1 0 1 0 0 -1 0 0 -1 0 1 0 1 0 0 1 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 -1 1 -1 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 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 1 1 -1 0 -1 0 0 1 0 0 1 0 0 0 -1 1 0 -1 -1 0 0 0 -1 0 0 -1 0
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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 1 1 1 -1 0 -1 0 0 1 0 0 0 0 0 2 -1 0 0 -1 -1 0 -1 -1 -1 1 0 -1 1
0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 1 -1 0 -1 -1 0 1 0 0 0 1 0 -1 0 0 0
0 0 0 -1 -1 0 0 1 0 0 1 0 0 0 1 1 0 0 -1 0 0 0 -1 0 0 0 1 1 -1 1 0 -1
0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 1 -1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0
0 -1 -1 1 -1 -1 -1 -1 1 1 1 2 -2 1 -1 -2 -1 -2 1 0 0 -1 3 1 -2 1 -2 1 1 0 -1 1
0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 1 0 1 0 0 0 0 -1 0 0 -1 0 0 1 0
-1 0 0 0 -1 -1 -1 1 0 1 0 0 -1 0 0 -1 -1 1 0 2 0 0 1 1 0 0 0 1 0 0 1 1
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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^5400*4 x^5304*12 x^5208*36 x^5112*124 x^5064*8 x^5052*48 x^4968*208 x^4956*48 x^4920*96 x^4908*96 x^4896*64 x^4884*192 x^4872*96 x^4860*64 x^4824*16 x^4716*128 (7168x)
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 1 0
x^5028*28 x^4992*28 x^4977*8 x^4932*168 x^4905*224 x^4896*56 x^4884*168 x^4857*168 x^4833*56 x^4788*168 x^4785*168 (16384x)
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^5052*24 x^5016*18 x^4968*96 x^4956*40 x^4920*166 x^4905*256 x^4857*192 x^4833*32 x^4824*288 x^4785*96 x^4716*32 (28672x)
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 1 0 0 0
x^5208*2 x^5064*14 x^4977*32 x^4968*42 x^4956*16 x^4860*126 x^4833*112 x^4824*406 x^4785*336 x^4764*42 x^4716*112 (8192x)
1 32
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 1 0 0 0 0
x^5160*8 x^5112*32 x^5064*16 x^4968*16 x^4932*128 x^4920*128 x^4872*272 x^4824*512 x^4788*128 (10752x)
1 32
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 0 0 0 0 0 1
x^5400*8 x^5208*120 x^5160*24 x^5112*96 x^5028*256 x^4968*96 x^4956*192 x^4920*256 x^4764*192 (896x)
1 32
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 1
x^5400*8 x^5352*24 x^5304*48 x^5208*168 x^5160*48 x^5064*176 x^5016*192 x^4992*256 x^4956*128 x^4824*192 (896x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -1 0 0 0 0 -1 0 0 0 0 0 1
x^5400*224 x^5352*56 x^5208*256 x^5064*448 x^4956*256 (32x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 -1 0 0 0 0 0 0
x^5400*64 x^5352*56 x^5208*192 x^5160*264 x^4968*280 x^4920*384 (224x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 -1 -1 0 0 -1 0 1 1 0 -1 0 0 0
x^5352*8 x^5208*96 x^5112*64 x^5016*384 x^4968*48 x^4872*384 x^4860*256 (224x)
-
PROPERTIES
Unimodular=1
-
REFERENCES
H. Koch, B. B. Venkov,
\"Uber ganzzahlige unimodulare euklidische Gitter.
Journal f\"ur die reine und angewandte Mathematik 398 (1989), 144-168
H. Koch, B.B. Venkov, \"Uber gerade unimodulare
Gitter der Dimension 32, III
Mathem. Nachr. 152 (1991), 191-213
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NOTES
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe