The Lattice LAMBDA(G4)
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 13:17:43 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(G4)
-
DIMENSION
32
-
GRAM
32 0
4
-1 4
0 1 4
0 -1 1 4
0 -1 -1 -1 4
-1 0 -1 0 -1 4
-1 1 0 0 -1 1 4
-1 0 -1 0 -1 1 2 4
0 2 0 -1 -1 1 1 1 4
0 -1 -1 -1 1 0 -1 -1 -1 4
1 0 0 0 0 0 0 1 1 -2 4
1 0 -1 -1 1 -1 -1 -1 -1 2 -2 4
-1 1 0 0 -1 0 1 1 1 -1 0 0 4
-1 0 0 1 -1 0 0 1 0 -1 0 0 2 4
1 0 0 -2 0 -1 -1 -1 0 1 -1 2 0 -1 4
-1 0 -1 -1 1 0 1 1 0 -1 0 0 1 1 0 4
0 0 0 1 -1 1 1 1 1 0 -1 0 1 1 0 -1 4
-2 1 -1 0 0 1 1 1 0 0 -2 1 1 1 0 1 2 4
-2 -1 0 0 0 1 0 1 0 0 -1 -1 1 1 0 1 1 1 4
0 1 0 -1 -1 1 -1 -1 1 0 -1 1 1 0 2 0 1 1 1 4
-2 1 1 -1 0 -1 0 0 0 -1 -1 0 1 1 1 2 -1 1 2 1 4
1 0 -1 -1 -1 1 0 0 0 1 -1 2 0 -1 2 -1 1 1 -1 2 -1 4
0 0 1 -1 -1 0 0 0 -1 0 -1 1 1 0 2 0 1 1 1 2 1 2 4
1 1 0 -1 0 0 -1 -1 0 1 -1 2 0 -1 2 -1 1 1 -1 2 -1 2 2 4
-1 0 0 2 0 -1 1 1 0 -1 1 -2 0 0 -2 0 0 0 0 -2 0 -2 -2 -2 4
0 1 0 0 -1 0 0 2 1 -1 1 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 4
-1 1 1 1 -1 1 2 0 0 0 -2 0 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 4
-1 2 1 1 -2 1 1 1 1 -1 -1 0 1 1 -1 -1 2 2 0 1 0 1 1 1 0 2 2 4
1 -1 0 -1 1 0 0 0 0 0 1 -1 -2 -2 0 1 -2 -2 0 -1 0 -1 -1 -1 0 0 0 -2 4
1 0 0 -1 0 1 1 0 0 0 -1 1 -1 -1 1 1 0 0 0 1 0 1 1 1 -2 0 2 0 2 4
-1 1 0 2 -1 0 1 2 1 -2 1 -1 2 2 -2 0 1 1 0 -1 0 -1 -1 -1 2 2 0 2 -2 -2 4
-1 0 1 2 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 -1 2 -2 2 0 0 0 0 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^16 3^2
-
GROUP_GENERATORS
14
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 -1 0 0 0 0 0 0 0 1 1 -1 1 -1 0 0 0 0 -1 -1 2 0 -1 0 0 0 -1 2 -2 2 -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 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 1 1 1 -2 -2 2 -1 2 1 0 -1 1 0 2 -4 -1 3 -1 -1 1 1 -2 4 -5 0 2
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 1 1 -1 1 -1 0 0 0 0 0 -1 1 0 -1 0 1 -1 0 1 -2 3 0 -1
0 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 1 -1 1 1 -1 1 1 0 0 0 -1 2 1 -1
0 0 0 0 0 0 0 0 -1 1 1 -1 1 -1 0 0 1 -1 0 -1 2 1 -2 0 0 -1 -1 2 -1 2 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
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 0 -1 0 -1 0 0 0 0 -2 1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 2 -2 0 -1 2 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 -1 2 1 -1 1 0 0 -1 0 -1 1 -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 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 0 0 0 0 -1 0 0 -1 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 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 -1 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 -1 0 0 0 0 -1 1 -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 -1 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
32 32
-1 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 -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 -1 0 1 -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 1 -1 -1 0 1 -1 1 0 -1 0 0 1 1 -1 0 1
0 0 0 -1 0 0 0 0 0 -1 -1 1 -1 1 0 0 0 0 0 1 -1 0 1 0 0 0 1 -1 2 -2 2 1
0 -1 0 0 -1 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 -1 1 0 -1 1 0 0 -1 0 -1 1 -1 0
0 0 0 0 0 -1 0 0 0 1 1 -1 0 0 0 0 -1 1 1 0 0 1 -1 0 -1 -1 0 1 0 1 1 0
0 0 0 0 0 0 -1 0 0 1 1 -1 1 -1 0 0 0 0 0 -1 1 0 -1 0 1 -1 0 1 -2 3 0 -1
0 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 1 -1 1 1 -1 1 1 0 0 0 -1 2 1 -1
0 0 0 0 0 0 0 0 -1 1 1 -1 1 -1 0 0 1 -1 0 -1 2 1 -2 0 0 -1 -1 2 -1 2 0 -1
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 1 -1 1 0 1 1 -1 -1 -1 -2 0
0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 -1 0 0 1 1 0
0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 -1 -1 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 -2 1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 2 -2 0 -1 2 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 -1 0 -1 0 0 -1 1 -1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 1 -1 -1 1 -1 1 -1 1 -1 0 1 1 -2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 1 1 -1 1 1 -1 0 1 -1 1 0 -1
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 -1 0 1 -1 1 0 -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 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
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 0 0 0 0 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 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 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 -1 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
32 32
-1 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 -1 -1 1 -1 -1 1 -1 0 0 -1 0 1 0 0 0
0 -1 0 0 0 0 0 0 0 1 1 -1 1 -1 0 0 0 0 -1 -1 2 0 -1 0 0 0 -1 2 -2 2 -1 0
0 0 -1 2 0 0 0 0 0 1 1 -1 1 -1 0 0 1 -1 -1 -2 3 0 -1 1 -1 0 -1 2 -1 1 -2 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 0 0 0 -1 0 1 0 0 -1 0 0 1 1 0 -1 0 0 0 -1 0 0 -1 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 0 0 -1 0 0 1 1 -1 1 -1 0 0 0 0 0 -1 1 0 -1 0 1 -1 0 1 -2 3 0 -1
0 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 1 -1 1 1 -1 1 1 0 0 0 -1 2 1 -1
0 0 0 0 0 0 0 0 -1 1 1 -1 1 -1 0 0 1 -1 0 -1 2 1 -2 0 0 -1 -1 2 -1 2 0 -1
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 0 -1 -1 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 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 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 1 -1 -1 0 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 1 -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 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 0 0 0 0 0 0 1 -1 1 -1 0 1 1 -2
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 -1 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 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 1 -1 1 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 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
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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 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
32 32
-1 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 -1 0 0 -1 0 0 0 0 0 -1 0 1 0 0 0
0 -1 0 0 0 0 0 0 0 1 1 -1 1 -1 0 0 0 0 0 -1 2 0 -2 1 0 0 -1 2 -2 2 -1 0
0 0 -1 2 0 0 0 0 0 1 1 -1 1 -1 0 0 1 -1 0 -2 3 0 -1 1 -1 0 -1 2 -1 1 -2 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 1 0 1 0 0 -1 0 0 0 0 0 0 -1 -1 0 1 -1 1 0 0 0 0 0 0 -1 -1 0
0 0 0 0 0 -1 0 0 0 1 1 -1 0 0 0 0 -1 1 0 1 -1 0 0 -1 -1 -1 0 1 0 1 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
0 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 0 -1 1 1 0 0 1 0 0 0 -1 2 1 -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 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 -1 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 -1 0 0 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 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 0 -1 1 0 -1 1 -1 0 0 0 0 0 0 0 0
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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
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0 0 0 0 0 -1 0 0 0 1 1 -1 0 0 0 0 -1 1 1 0 -1 0 0 0 -1 -1 0 1 0 1 1 0
0 0 0 0 0 0 -1 0 0 1 1 -1 1 -1 0 0 0 0 0 -1 1 0 -1 0 1 -1 0 1 -2 3 0 -1
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32 32
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 -1 -1 0 -1 0 0 -1 1 -1 1 -1 0
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32 32
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0 1 -1 2 2 1 1 0 0 0 -1 -1 0 1 1 -1 0 -1 -1 0 1 0 1 0 1 1 0 0 0 0 -1 -1
-1 -1 0 -1 -2 -1 -1 -1 -1 1 2 0 1 -2 -1 1 2 -1 1 -2 2 1 -3 1 0 -1 -2 2 -2 4 0 0
-1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 -1 0 0 0 -1 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 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
-2 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 -1 0 1 0 0 0
-2 -1 1 -1 -2 -2 -1 -1 -1 1 2 0 1 -2 -1 1 1 0 1 -1 0 1 -3 0 0 -2 -2 2 -2 5 1 -1
-2 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 -1 0 0 -1 0 0 0 0 0 -1 0 1 0 0 0
0 -1 1 -3 -2 -2 -1 -1 -1 1 2 0 0 -1 -1 1 0 1 2 0 -1 1 -2 0 0 -2 0 1 -1 3 3 0
-2 -1 1 -3 -2 0 -1 -1 -1 -1 0 2 0 -1 -1 1 2 -1 0 0 -1 0 -1 0 1 -1 -1 0 0 2 2 0
0 -1 1 -1 -2 0 -1 -1 -1 1 2 0 1 -2 -1 1 1 0 1 -2 2 1 -3 1 1 -1 -1 1 -3 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 -1 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 -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 -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 -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 -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
0 -1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 -1 0 0 1 0 -1 0 1
0 0 -1 2 1 1 0 1 1 0 -1 -1 0 0 0 -1 0 -1 -2 0 2 -1 1 0 0 0 0 0 -1 0 -2 -1
0 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 1 -1 -1 1 -1 2 0 -1
-1 0 0 -1 -1 0 0 0 -1 -1 0 2 0 -1 -1 1 2 -1 0 0 0 0 -1 0 -1 0 -1 0 1 -1 0 1
0 0 0 0 0 -1 0 0 0 1 1 -1 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 1 1 1
0 1 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 0
0 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 1 -1 1 1 -1 1 1 0 0 0 -1 2 1 -1
0 0 0 -1 0 -1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 -1 0 0 0 -1 -1 0 1 2 -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 1 0 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 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 1 1 1 1 -2 -3 1 -1 2 0 -1 -1 0 -1 2 -2 -1 3 0 1 1 1 -3 2 -3 0 0
-1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 -1 0 -1 2 0 -1
1 1 0 1 2 1 1 1 1 -2 -2 1 -1 2 1 -1 -1 0 0 1 -1 0 2 0 0 1 2 -2 2 -4 -1 0
-1 1 0 0 0 0 1 0 0 -2 -2 1 -1 1 0 0 1 0 0 1 -2 0 1 0 -1 2 0 -3 2 -3 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 -1 0 1 0 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
-1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 1 0 -1
0 0 0 0 1 0 0 1 0 -1 -1 0 0 1 0 -1 0 0 -1 1 0 0 1 0 0 0 1 -1 1 -1 0 0
-1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1
1 0 0 1 1 0 0 0 0 1 1 -1 1 0 0 0 0 0 0 -1 2 1 -1 1 0 0 0 1 -1 1 -1 0
0 0 0 1 1 1 0 0 1 -1 -1 0 0 0 0 -1 0 0 -1 0 1 0 1 0 1 1 1 -2 -1 0 -1 -1
1 0 0 0 1 1 0 1 1 -1 -1 1 -1 1 0 0 0 0 -1 1 0 0 2 0 0 1 2 -2 1 -3 0 1
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 -1 0 1 0 0 0 -1
0 -1 0 0 0 0 -1 0 0 2 1 -2 1 -1 0 0 0 0 -1 -1 2 0 -1 0 1 0 -1 1 -3 4 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 0 0 -1 1 0 0
0 -1 0 0 0 0 -1 0 0 2 1 -2 1 -1 0 0 0 0 -1 -1 2 0 -1 0 1 -1 -1 2 -3 4 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 -1 1 0 -1 1 -1 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 -1 1 0 -1 0 0 0 1
0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 1 -1 -1 1 -1 2 1 -1
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 -1 0 1 0 0 0 0
-
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^5448*4 x^5256*8 x^5208*20 x^5160*32 x^5100*64 x^5064*32 x^5040*128 x^5016*68 x^4968*52 x^4956*192 x^4932*64 x^4920*80 x^4896*64 x^4872*32 x^4836*64 x^4824*16 x^4776*256 x^4752*64 (144x)
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^5448*2 x^5256*8 x^5208*12 x^5160*4 x^5064*18 x^5016*12 x^5004*128 x^4992*128 x^4968*16 x^4956*64 x^4944*64 x^4932*64 x^4908*32 x^4872*144 x^4860*128 x^4836*64 x^4812*32 x^4800*64 x^4752*256 (144x)
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 -1 0 0
x^5832*2 x^5448*6 x^5208*48 x^5160*24 x^5148*128 x^5112*96 x^5064*96 x^5052*128 x^5016*112 x^4968*88 x^4860*128 x^4776*384 (12x)
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 1 0 0 0
x^5544*8 x^5064*144 x^5004*128 x^4968*128 x^4872*384 x^4824*192 x^4752*256 (24x)
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 -1 1 0 0 -1 1
x^5544*8 x^5448*12 x^5304*96 x^5292*128 x^5160*96 x^5112*32 x^5064*228 x^5016*96 x^4968*96 x^4920*192 x^4824*256 (12x)
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 -1 0 0 0 1 -1 1 1
x^5064*4 x^5061*8 x^5052*8 x^5016*6 x^5001*32 x^4968*18 x^4956*32 x^4953*32 x^4941*32 x^4932*16 x^4929*32 x^4920*20 x^4908*8 x^4905*32 x^4896*32 x^4893*48 x^4884*16 x^4881*192 x^4872*148 x^4869*16 x^4860*40 x^4848*16 x^4845*40 x^4836*176 x^4833*32 x^4824*50 x^4812*8 x^4809*32 x^4800*48 x^4797*16 x^4776*2 x^4773*24 x^4764*16 x^4725*8 (4608x)
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 0 0 0 0 0
x^5304*16 x^5208*40 x^5160*32 x^5112*24 x^5100*64 x^5064*8 x^5016*16 x^5004*96 x^4968*48 x^4956*128 x^4932*128 x^4920*224 x^4908*64 x^4896*128 x^4872*64 x^4860*32 x^4764*128 (288x)
1 32
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
x^5400*8 x^5304*32 x^5208*24 x^5196*64 x^5160*24 x^5124*64 x^5112*16 x^5100*96 x^5064*48 x^5016*64 x^4980*128 x^4968*128 x^4956*96 x^4944*128 x^4908*64 x^4884*128 x^4776*128 (288x)
1 32
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
x^5304*32 x^5208*32 x^5160*64 x^5136*64 x^5112*8 x^5076*64 x^5064*16 x^5028*16 x^5004*64 x^4980*72 x^4968*96 x^4956*32 x^4944*64 x^4932*160 x^4920*160 x^4896*96 x^4884*8 x^4848*32 x^4812*32 x^4749*128 (576x)
1 32
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 0 0 0 0 0 0 0
x^5208*48 x^5112*104 x^5004*96 x^4944*192 x^4932*48 x^4908*288 x^4896*192 x^4884*144 x^4725*128 (192x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 1 -1 -1 0 0 0 1 -1 0 0
x^5400*16 x^5304*16 x^5208*56 x^5160*8 x^5124*128 x^5112*24 x^5064*64 x^5052*64 x^5016*32 x^4992*128 x^4968*152 x^4932*128 x^4920*128 x^4872*8 x^4860*128 x^4824*160 (144x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 1 -1 -1 0 1 -1 1 -1 1 0
x^5160*8 x^5112*32 x^5064*16 x^4872*160 x^4860*256 x^4824*128 x^4812*256 x^4800*256 x^4740*128 (144x)
1 32
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 -2 2 -1 1 -1 1
x^5040*10 x^5013*16 x^5004*14 x^5001*8 x^4992*2 x^4989*16 x^4980*12 x^4968*4 x^4956*12 x^4953*8 x^4944*4 x^4941*24 x^4932*56 x^4929*80 x^4920*24 x^4917*80 x^4908*66 x^4896*60 x^4893*40 x^4884*40 x^4881*80 x^4872*64 x^4869*16 x^4860*8 x^4857*64 x^4848*4 x^4845*112 x^4836*4 x^4824*76 x^4812*48 x^4809*8 x^4800*68 x^4797*8 x^4785*40 x^4773*32 x^4764*4 x^4752*4 x^4740*16 x^4725*8 (18432x)
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 -1 0 -1 1 0 0 0 1
x^5208*6 x^5124*24 x^5112*2 x^5088*24 x^5076*64 x^5028*48 x^5004*192 x^4968*8 x^4956*192 x^4932*112 x^4908*12 x^4905*64 x^4869*96 x^4860*4 x^4848*192 x^4836*48 x^4812*96 x^4797*32 x^4764*24 (384x)
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 -1 0 0 1 0 -1 0 1
x^5208*2 x^5160*4 x^5136*4 x^5124*8 x^5112*12 x^5088*4 x^5076*16 x^5064*4 x^5040*64 x^5028*24 x^5016*4 x^4989*128 x^4968*40 x^4956*40 x^4944*4 x^4932*52 x^4929*192 x^4920*106 x^4908*16 x^4896*12 x^4893*32 x^4872*68 x^4869*32 x^4836*52 x^4824*40 x^4821*64 x^4812*32 x^4800*80 x^4797*64 x^4752*8 x^4740*16 x^4692*16 (2304x)
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 -1 -1 2 0 0 0 0
x^5112*2 x^5076*12 x^5052*2 x^5016*8 x^4956*36 x^4944*12 x^4932*24 x^4929*192 x^4920*6 x^4917*16 x^4908*6 x^4905*32 x^4896*60 x^4884*36 x^4872*40 x^4860*50 x^4848*96 x^4845*96 x^4812*54 x^4809*64 x^4800*68 x^4797*16 x^4785*192 x^4764*108 x^4752*12 (768x)
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 -1 0 1 0 0 0 0
x^5064*4 x^5016*4 x^4968*2 x^4932*12 x^4920*16 x^4908*16 x^4896*16 x^4884*24 x^4872*50 x^4860*64 x^4857*128 x^4848*32 x^4845*128 x^4836*84 x^4824*140 x^4821*32 x^4812*48 x^4809*64 x^4800*36 x^4797*32 x^4785*64 x^4773*160 x^4752*4 x^4740*80 (2304x)
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 1 0 0 0 1
x^5136*24 x^5124*8 x^5112*2 x^5076*32 x^5052*4 x^5016*6 x^4980*24 x^4968*8 x^4956*72 x^4944*192 x^4932*40 x^4908*16 x^4896*192 x^4872*32 x^4860*96 x^4836*48 x^4824*192 x^4812*60 x^4797*96 x^4725*96 (384x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 -1 0 -1 0 1 -1 1 -1 1 -1 1 0 -1 -1 2
x^5400*8 x^5304*120 x^5244*96 x^5208*24 x^5160*48 x^5112*56 x^5064*144 x^5040*128 x^5016*48 x^5004*32 x^4968*216 x^4932*128 x^4824*192 (48x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 -1 -1 0 -1 0 -1 0 0 0 1 1 -1
x^5160*2 x^5136*8 x^5088*8 x^5076*16 x^5064*2 x^5052*16 x^5040*32 x^5016*8 x^4980*64 x^4968*108 x^4956*32 x^4929*256 x^4920*16 x^4896*32 x^4884*32 x^4869*32 x^4860*32 x^4857*192 x^4836*64 x^4824*128 x^4800*64 x^4773*96 (1152x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 -1 -1 0 -1 0 -1 0 1 0 0 0 -1
x^5112*2 x^5064*8 x^5016*10 x^4956*24 x^4920*16 x^4908*48 x^4884*64 x^4872*80 x^4869*32 x^4860*64 x^4857*192 x^4848*96 x^4845*64 x^4824*4 x^4812*80 x^4800*64 x^4785*256 x^4776*64 x^4773*32 x^4764*8 x^4692*32 (1152x)
1 32
0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 0 0 0 0 1 0 0 0 0 -1 0 0 1 0 1 -1
x^5040*2 x^4992*6 x^4968*6 x^4956*6 x^4932*12 x^4929*24 x^4920*18 x^4908*14 x^4905*32 x^4896*72 x^4893*36 x^4884*84 x^4872*36 x^4869*36 x^4860*36 x^4857*24 x^4845*148 x^4836*24 x^4833*24 x^4824*156 x^4821*24 x^4812*120 x^4809*32 x^4800*54 x^4797*36 x^4785*24 x^4773*96 x^4752*6 x^4740*6 x^4728*16 x^4725*24 x^4692*6 (6144x)
1 32
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 -1 0 0 1 0 1 0
x^5004*2 x^4980*4 x^4968*4 x^4956*20 x^4953*16 x^4944*12 x^4941*4 x^4929*56 x^4920*4 x^4917*36 x^4908*66 x^4905*8 x^4896*112 x^4893*52 x^4884*24 x^4881*64 x^4869*10 x^4860*20 x^4857*96 x^4848*12 x^4845*140 x^4836*76 x^4833*8 x^4824*104 x^4821*24 x^4812*48 x^4809*16 x^4800*64 x^4797*8 x^4785*40 x^4776*12 x^4773*68 x^4725*10 (18432x)
1 32
0 0 0 0 0 0 0 0 1 -1 -1 0 -1 0 -1 0 0 0 0 0 0 0 1 0 0 1 0 -2 -1 0 0 0
x^5148*2 x^5100*12 x^5076*16 x^5061*2 x^5040*24 x^5004*14 x^4968*4 x^4941*80 x^4908*24 x^4905*32 x^4896*240 x^4893*72 x^4884*96 x^4872*24 x^4869*60 x^4848*48 x^4845*26 x^4824*96 x^4821*96 x^4800*96 x^4797*48 x^4773*48 x^4728*64 x^4629*16 (1536x)
1 32
0 0 0 0 0 0 0 0 1 -1 -1 0 -1 0 -1 0 0 0 0 0 0 0 1 1 0 1 1 -3 -1 -1 0 0
x^5004*2 x^4956*12 x^4920*6 x^4896*24 x^4893*30 x^4869*38 x^4860*54 x^4857*48 x^4848*24 x^4845*168 x^4836*24 x^4833*48 x^4824*246 x^4812*96 x^4800*144 x^4797*48 x^4776*24 x^4773*108 x^4764*24 x^4752*16 x^4749*48 x^4725*8 (3072x)
1 32
0 0 0 0 0 0 0 0 1 -1 -1 1 -1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 0 0
x^5100*18 x^5076*8 x^5061*4 x^5052*6 x^5040*24 x^5004*12 x^5001*48 x^4968*52 x^4956*48 x^4953*48 x^4944*24 x^4941*48 x^4932*120 x^4917*38 x^4896*144 x^4893*36 x^4884*96 x^4869*24 x^4857*48 x^4845*96 x^4836*48 x^4821*36 x^4809*16 x^4797*22 x^4785*48 x^4773*96 x^4728*32 (3072x)
1 32
0 0 0 0 0 0 0 1 -1 -1 0 1 0 0 0 -1 0 0 0 1 0 -1 0 0 0 -1 1 0 1 -1 0 -1
x^5292*2 x^5244*6 x^5196*24 x^5136*48 x^5100*24 x^5061*12 x^5040*72 x^5013*96 x^4956*12 x^4941*136 x^4920*12 x^4917*72 x^4893*414 x^4869*34 x^4848*48 x^4845*12 x^4824*96 x^4773*96 x^4749*24 (1536x)
1 32
0 0 0 0 0 0 0 1 0 -2 -1 1 0 0 0 0 0 0 0 0 -1 -1 0 0 -1 1 0 0 0 -2 -2 1
x^4977*16 x^4968*8 x^4932*16 x^4920*6 x^4893*24 x^4884*216 x^4881*96 x^4872*12 x^4869*8 x^4860*48 x^4857*240 x^4845*96 x^4833*32 x^4824*62 x^4821*48 x^4800*120 x^4797*48 x^4785*96 x^4752*16 x^4749*24 x^4725*8 (3072x)
1 32
0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 -1 -1 0 -1 1 0 1 1 -1 1 1 -1 0 0 0 1 1 -2
x^5160*24 x^5124*24 x^5112*8 x^4989*96 x^4977*8 x^4953*48 x^4941*64 x^4932*96 x^4929*96 x^4905*32 x^4881*192 x^4860*48 x^4857*144 x^4833*40 x^4824*192 x^4773*96 x^4752*20 x^4740*12 (3072x)
-
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
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe