The Lattice LAMBDA(G3)
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 13:17:41 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(G3)
-
DIMENSION
32
-
GRAM
32 0
4
0 4
0 0 4
0 -1 -1 4
-1 0 1 1 4
1 -1 0 1 0 4
-1 1 0 0 1 -1 4
1 0 -1 0 -1 1 0 4
0 1 1 -1 1 -1 1 -1 4
0 1 0 0 1 1 1 0 1 4
0 -1 1 0 0 -1 -1 -2 1 0 4
-1 0 -1 -1 0 -1 1 0 0 -1 -1 4
-1 -1 0 0 -1 0 -1 -1 -1 -1 1 0 4
1 0 -1 1 -1 0 -1 -1 -1 0 1 -1 0 4
-1 2 0 -1 1 0 1 1 1 1 -2 1 -1 -2 4
1 0 1 1 1 1 0 0 0 0 0 -1 1 -1 0 4
1 2 1 -1 0 -1 0 0 1 1 1 -1 0 0 0 1 4
-1 1 1 -1 0 -1 0 0 0 1 1 0 0 0 1 -1 2 4
0 1 1 0 1 1 -1 0 0 0 -1 -1 -1 -1 1 1 0 -1 4
0 1 0 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 1 1 0 4
0 0 0 0 -1 -1 1 0 -1 -1 0 2 0 1 -1 -1 0 1 -2 0 4
-1 0 -1 2 0 1 -1 0 -1 -1 -1 -1 1 1 0 0 -1 -1 1 0 -1 4
0 -1 -2 0 -1 -1 0 0 -2 -1 0 2 1 1 -1 -1 -1 0 -2 0 2 -1 4
0 1 0 -1 -1 -1 -1 0 0 -2 0 0 2 0 0 1 1 0 0 2 0 1 0 4
1 -1 -1 2 0 -1 0 0 -1 -1 1 0 0 2 -2 0 0 0 -2 0 2 0 2 0 4
0 1 0 -1 -1 0 0 0 -1 0 0 0 2 0 0 0 1 1 -1 1 1 0 1 2 0 4
-1 1 1 -1 0 1 0 0 0 2 0 -1 1 -1 1 0 1 1 1 -1 -1 0 -1 0 -2 2 4
0 1 -1 -1 -1 -1 0 2 -1 -1 -1 1 1 -1 1 0 1 1 -1 1 1 0 1 2 0 2 0 4
1 -1 1 0 0 0 -1 -1 1 -1 1 -1 -1 1 -1 0 -1 -1 1 1 -1 0 -1 0 0 -2 -2 -2 4
0 1 -1 1 0 -1 1 1 -1 -1 -1 0 1 0 0 1 1 0 -1 1 1 1 1 2 2 2 0 2 -2 4
0 -1 1 0 2 -1 0 0 0 0 1 -1 0 -1 0 1 1 1 0 1 -1 -1 0 0 1 0 0 0 0 1 4
1 0 0 1 -1 0 -1 -1 -1 -1 1 -1 2 2 -2 1 1 0 -1 1 1 1 1 2 2 2 0 0 0 2 0 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^15 3^2
-
GROUP_GENERATORS
12
32 32
1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -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 0 0
0 -1 1 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 2 0 -1 -1 0 0 -1 0 -2 0 -1 2 -1 1
0 1 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 1 1 0 1 -1 3 0 1 -2 1 -1
-1 -1 1 1 -1 0 1 -1 0 0 -1 0 -1 0 1 0 1 -1 0 1 -1 0 0 1 3 0 1 1 -1 -3 0 0
0 -2 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 1 0 0 0 2 -1 -1 -1 -1 2 0 2 0 -1 -1 -2 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 1 -1 0 -1 -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 1 1 0 0 -1 1 -1 1 -1 0 0 0 0 0 1 0 0 -1 -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 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 -1 1 0 1 -1 0 0 1 1 1 1 1 1 -1 -1 -1 -2 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 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 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -1 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 0 1 0 0 -1 -1 0 -1 -1 -1 1 -1 1 0 2
0 1 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 1 -1 -2 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 -1 -1 1 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 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 1 1 -1 0 -1 -1 0 0
0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 2 1 0 1 -1 3 0 1 -2 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 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 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 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 -1 0 -1 -1 0 -2 0 -2 0 0 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 0 0 0 0 0 0 0 1
32 32
1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -1 1
0 -1 0 0 0 0 0 0 0 1 1 0 0 1 1 -1 0 0 1 -1 0 -1 0 0 -3 0 -2 0 0 3 0 1
0 -1 1 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 -1 -1 -1 0 0 -2 0 -2 0 0 3 -1 1
0 1 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 1 1 0 1 -1 3 0 1 -2 1 -1
0 -1 0 0 1 -1 -1 0 0 0 0 -1 1 0 1 0 0 0 0 1 0 -1 0 -1 0 0 0 -1 0 2 -2 -1
0 -2 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 1 0 0 0 2 -1 -1 -1 -1 2 0 2 0 -1 -1 -2 0
0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -3 1 -2 -1 1 4 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 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 -1 1 0 1 -1 0 0 1 1 1 1 1 1 -1 -1 -1 -2 0 -1
0 1 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 1 0 0 -1 0 1 2 1 1 0 0 1 0 0 -2 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 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -1 1
0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 1 1 -1 -1 -1 0 0 -2 0 -2 0 0 3 -1 1
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 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 1 0 -1 -1 1 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 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 0 0 1 -1 0 0 0 0 0
0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 2 1 0 1 -1 3 0 1 -2 1 -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 1 1 -1 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 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 1 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 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 0 0 1
32 32
1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -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 0 0
0 1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 -1 1 0 -1 0 -1 0 0 0 1 0 1 1
0 1 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 1 1 0 1 -1 3 0 1 -2 1 -1
0 -1 -1 0 1 -1 -1 0 -1 0 1 0 0 0 1 0 0 0 0 0 1 -1 -1 -1 -2 0 0 -1 1 3 -1 0
0 -2 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 1 0 0 0 2 -1 -1 -1 -1 2 0 2 0 -1 -1 -2 0
0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -3 1 -2 -1 1 4 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 0 0 0 0 0 0 0 -1 1 1 0 0 -1 1 -1 1 -1 0 -1 1 0 0 1 -1 0 -1 -1 1 1 0 0
0 -1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 -1 0 -1 -1 0 0 0 0 2 -1 0
0 1 0 0 0 0 0 0 0 1 0 0 0 -1 -1 0 0 0 0 -1 1 1 1 1 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 -1 0 -1 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 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 0 0 -1 0 0 -2 -1 -1 0 0 3 -1 1
0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 1 2 -1 0 -1 0 0 -2 0 -2 0 0 3 -1 1
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 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 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 1 0 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 -1 0 1 1 -1 0 -1 -1 0 0
0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -2 1 1 2 1 0 1 -1 3 0 1 -2 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 1 1 -1 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 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 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 2 -1 0 -1 0 0 -2 0 -2 0 0 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 0 0 0 0 0 0 0 1
32 32
-1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 1 -1 0 0 -1 -1 -1 -1 2 1 0 1 0 -2 0 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 1 -1 1 0 0 0 -3 0 -2 0 0 2 1 1
0 1 -1 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 0 1 0 -1 0 1 0 2 0 1 -2 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
0 2 0 1 -1 0 1 0 0 -1 -1 0 0 0 0 1 0 -1 -1 1 0 1 0 1 3 0 2 0 -1 -5 2 -1
0 -1 0 0 0 -1 0 0 0 -1 -1 0 0 0 0 1 0 0 0 1 -1 0 -1 -1 2 1 1 0 -1 -2 -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 -1 0 0 0 0 0 -1 0 -1 -1 0 0 0 0 0 0 0 0 1 -1 -1 -1 -1 2 -1 2 2 0 0 -1 0
0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 -1 0 0 0 -1 0 -1 -1 1 -2 0 -2 -1 0 2 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 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 1 1 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 1 1 -1 0 -1 -1 -1 0 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 0 1 1 1 0 0 1 0 0 -1 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 -1 -1 0 1 2 1 0 1 0 1 0 1 -2 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 0 -1 0 0 0 0 -2 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 0 0 0 0 0 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 0 0 0 0 0 0 0 0
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 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 1 -1 0 0 0 3 0 2 0 0 -2 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
32 32
1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 1 -1 0 0 0 0 -2 0 -2 0 0 2 0 1
0 -2 0 0 0 0 0 0 0 1 1 0 0 1 1 -1 0 0 2 0 0 -2 -1 0 -2 0 -2 0 -1 3 -1 1
0 1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 -1 1 0 -1 0 -1 0 0 0 1 0 1 1
0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0
-1 1 0 0 -1 0 1 0 0 0 -1 0 -1 -1 -1 1 0 0 0 0 -1 1 0 1 3 1 0 0 -1 -4 1 0
0 -1 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 1 0 0 0 1 -1 0 -1 -1 2 1 1 0 -1 -2 -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 -1 0 0 0 0 0 -1 0 -1 -1 0 0 1 1 0 0 0 0 1 -1 -1 -1 -1 2 -1 2 2 0 0 -1 0
0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 -1 0 0 0 -1 0 -1 -1 1 -2 0 -2 -1 0 2 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 1 0 1 1 -1 0 -1 -1 -1 0 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -1 0 1 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 1 0 0 -1 1 1 0 -1 -2 -1 0 -1 0 -1 0 -1 2 -1 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 -1 0 0 0 0 -2 0 -2 0 0 2 0 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 0 1 0 0 -1 -1 0 -1 -1 -1 1 -1 1 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 -1 -1 0 1 -1 1 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 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 0 0 0 0 1 1 -1 -1 1 0 1 0 0 2 0 2 0 0 -2 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 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 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 0 0 1
32 32
-1 -2 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 2 0 -2 -3 -2 -1 1 1 -2 1 -1 1 -2 2
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 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 0 -1 0 0 2 -1 0
0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0
1 -1 0 -1 1 0 0 0 -1 2 2 -1 0 -1 0 -1 0 1 1 -1 1 1 1 1 -3 0 -3 -2 0 4 -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 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 1 0 0 0 0 -1 0 0 0 -1 0 -1 -1 1 -2 0 -2 -1 0 2 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 1 0 1 1 -1 0 -1 -1 -1 0 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 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 -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 -1 0 0 0 0 1 0 -1
0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 -1 0 0 2 -1 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 0 1 0 0 -1 -1 0 -1 -1 -1 1 -1 1 0 2
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 1 1 0 0 1 -1 2 1 0 -2 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 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 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 0 0 1 0 0 1 0 1 0 0 -2 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 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 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 0 -1 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 1
32 32
1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 0 0 0 0 0 -1 0 -1 0 0 2 -1 0
0 -1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 -2 0 -1 0 0 2 0 0
0 1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 -1 1 0 -1 0 -1 0 0 0 1 0 1 1
0 1 0 1 0 0 0 0 0 -1 -1 0 0 0 0 0 1 -1 -1 0 0 0 0 0 1 0 1 0 0 -2 1 0
-1 1 0 1 -1 0 1 -1 0 -1 -2 1 0 0 0 0 0 -1 0 1 -2 -1 -2 0 5 0 2 2 -1 -5 1 1
0 -2 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 0 0 0 1 1 -2 -2 -2 -1 2 1 0 0 -2 -1 -2 1
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 1 0 0 -1 1 0 1 -1 -1 0 1 1 0 1 0 0 0 -1 1 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 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 0 0 0 0 0 0 0 0 -1 -1 -1 0 0 0 -1 -1 0 1 1 1 -1 0 0 0 0 -1 1 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 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 0 0 0 0 0 0 1 1 0 0 0 0 -1 -1 1 2 -1 -1 -2 -1 0 -2 0 -3 0 -1 3 -1 2
0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 -1 0 0 2 -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 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 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 1 -1 -1 0 0 1 0 0 1 0 1 0 0 -2 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 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 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 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 0 0 1
32 32
-1 -2 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 2 0 -2 -3 -2 -1 1 1 -2 1 -1 1 -2 2
0 -1 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 1 0 0 -1 -1 0 -1 0 -1 0 -1 1 0 1
0 1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 -1 1 0 -1 0 -1 0 0 0 1 0 1 1
0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0
0 2 0 0 -1 0 0 0 0 0 0 1 -1 -1 -1 1 -1 0 -1 0 0 2 0 0 1 0 1 0 0 -2 2 0
0 -2 0 0 0 -1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 -1 -1 -1 -1 1 1 0 0 -1 0 -2 0
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -1 -2 0 0 -1 1 3 0 -1
0 -2 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 1 1 -1 -2 -1 -1 1 -1 1 2 0 2 -2 0
0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 1 -1 1 -1 -1 0 0 0 -1 1 1 0 0 -1 0 -1 0 0
0 -1 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 0 0 0 1 -1 -1 -1 -1 1 0 1 0 -1 0 -1 0
0 1 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 0 0 0 -1 0 0 1 0 1 2 0 1 0 0 -3 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 -1 -1 -1 0 0 0 -1 0 -1 1 -1 1
0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 0 -1 -1 -1 0 0 0 -1 0 -1 1 -1 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
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 -1 0 1 2 1 0 0 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 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 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 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 0 0 1
32 32
1 3 0 0 0 1 0 1 0 1 1 0 0 -2 -2 0 0 1 -1 -2 2 3 3 2 -3 0 -1 -2 2 1 2 -2
1 1 0 0 0 1 -1 0 0 2 2 0 0 -1 -1 -1 -1 1 0 -1 2 1 1 0 -5 -1 -2 -1 1 5 1 0
0 -1 0 0 0 -1 0 1 0 0 1 -1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 -1 -1 -1 0 -1 0
-1 -2 0 0 0 0 0 -1 0 -1 -1 0 0 1 1 0 1 0 1 1 -2 -2 -1 0 3 1 0 0 -1 0 -2 -1
-1 -1 0 0 -1 0 1 0 1 -1 -1 1 -1 1 0 1 0 0 1 1 -2 0 -1 0 4 1 1 1 -2 -4 0 1
-1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 1 0 0 2 1 0 -1
0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 1 1 0 0 1 1 0 0 -1 -2 -2 0 0
1 0 -1 -1 2 0 -1 1 -1 1 2 -1 1 -1 0 -1 0 1 0 -2 2 0 1 0 -6 0 -3 -3 2 6 -1 0
1 1 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -1 1 -1 1 0 0 2 2 1 0 0 -1 1 0 0 -1 1 0
0 1 0 0 0 1 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 -1
0 -1 0 0 0 -1 0 0 1 -1 -1 0 0 1 0 1 -1 1 1 1 -1 -1 -1 -1 2 0 1 1 -1 -1 -1 0
0 1 -1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 -1 -1 0 1 0 -1 0 0 0 0 0 0 -2 1 1
-1 -1 0 0 0 -1 0 0 0 -1 -1 0 0 1 1 1 1 -1 0 1 -1 -1 -1 -2 2 1 1 1 0 -1 -1 0
0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 1 1 -1 -1 -1 0 0 2 0 -1
0 2 -1 0 0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 -1 -1 1 1 0 0 -1 0 0 0 1 -1 2 1
-1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 -1 0 0 0 0 0 2 -2 -1 0 0 0 0
1 1 0 0 0 0 0 1 1 1 1 0 0 0 -2 0 -2 2 1 -1 1 1 1 0 -4 0 -2 -1 0 3 1 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 -2 1 1 0 -1 -1 -1 -1 -1 0 -1 1 -1 1 0 1
0 -1 0 0 0 0 0 0 -1 1 1 1 0 0 0 -1 0 1 1 -1 -1 -1 -1 0 -1 0 -1 0 1 3 -1 1
0 0 0 0 0 0 0 0 1 0 0 1 0 1 -1 0 -2 1 1 0 -1 -1 -1 -1 -1 -1 0 2 -1 1 0 2
0 0 0 0 0 0 0 0 -1 1 1 -1 0 -1 1 -1 0 -1 0 0 1 0 0 1 -1 0 -2 -1 -1 0 0 0
-1 -2 0 0 0 0 0 -1 0 -1 -1 0 0 1 1 0 1 0 0 1 -2 -2 -1 -1 2 0 1 1 0 1 -2 0
0 1 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 -1 -1 0 0 0 -1 0 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 -1 -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 0 0 0 0 0 0 1 0 0 -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 0 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 -1 0 0 1 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 -1 -2 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 1 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 0 0 0 -1 0 -1 -1 -1 1 0 0
0 0 0 0 0 -1 1 1 1 -1 -1 1 0 1 -1 1 -1 1 1 0 -2 0 -1 0 2 1 0 0 -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 0 0 0 0 0 1 0 -1
32 32
-1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 -1 -1 -1 1 -1 0 1 1 0 1
0 -2 0 0 0 0 0 0 0 1 1 0 0 1 1 -1 0 0 1 0 0 -1 0 0 -2 0 -1 0 0 3 -1 0
0 -1 0 -1 0 0 -1 0 0 1 1 0 0 1 0 0 -1 1 1 0 0 -1 -1 -1 -2 0 -2 -1 -1 4 -1 0
0 -1 -1 -1 2 -1 0 1 -1 -1 0 -1 1 0 1 0 1 0 0 0 0 -1 -1 0 0 1 -1 -2 0 0 -2 0
0 -3 0 -1 1 -1 -1 0 0 0 1 -1 0 1 2 0 0 0 1 1 0 -2 -1 -1 -1 0 -1 -1 -1 4 -3 0
-1 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -1 0 -1 0 0 0 3 1 1 0 0 -3 0 -1
1 0 0 0 0 0 0 0 0 1 1 0 -1 0 -1 0 -1 1 0 -1 1 1 1 2 -3 0 -1 -1 0 2 1 -1
0 2 0 0 0 1 0 0 0 0 0 0 0 -1 -1 0 0 0 -1 -1 0 1 1 0 0 1 0 0 2 0 1 -1
0 -3 0 0 0 0 0 -1 0 0 1 0 0 2 1 -1 -1 1 2 0 -1 -3 -2 -1 -2 -1 -1 1 -1 5 -2 1
0 -2 0 0 0 0 0 -1 0 0 0 0 0 1 1 -1 0 0 1 0 -1 -2 -1 0 0 0 -1 0 -1 2 -1 0
0 -2 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 1 1 0 -1 -1 -1 0 -1 0 1 -1 1 -1 1
1 2 0 0 0 0 0 1 0 1 1 0 0 -1 -1 0 -1 0 -1 -1 2 2 1 1 -2 -1 0 0 1 0 2 0
0 1 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 1 -1 -1 0 1 1 0 0 0 0 0 0 0 -2 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 -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 -1 0 0 0 0 0 0 0 1 0 1 1 0 -1
-1 -1 0 0 0 0 -1 0 0 0 0 0 0 1 1 0 1 -1 0 0 0 -1 -1 -1 -1 1 -1 0 0 1 0 0
0 -3 0 0 0 0 -1 -1 0 1 1 1 0 2 1 -1 -1 1 2 0 -1 -3 -2 -2 -3 0 -2 1 0 6 -2 1
1 -1 0 0 0 0 0 -1 0 0 0 1 0 1 0 0 -1 1 0 1 -1 -1 -1 -1 0 -1 1 1 0 2 -1 0
-1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 -1 0 0 0 0 0 0 1 1 0 -1 0 -1 0 0
1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 -1 2 1 0 0 -1 0
1 1 0 0 0 0 0 1 0 1 1 0 0 0 -1 0 -1 1 0 -1 1 1 1 1 -3 0 -2 -1 0 1 1 0
-1 1 0 0 0 0 1 0 0 -2 -2 0 0 0 0 1 1 -1 -1 1 -1 0 0 0 4 0 3 1 0 -5 0 0
1 2 0 0 0 0 0 1 0 1 1 0 0 -2 -1 0 0 0 -1 -1 2 3 2 1 -2 0 -1 -1 1 -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 -1 -1 0 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 -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 1 -1 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 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 0 0 0 0 -1 0 1 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 -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 -1 1 -1 0 0 0 0 0
0 -1 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 1 0 -1 -1 -1 0 0 0 0 0 2 -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 -1 0 -1 -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 2 1 1 -2 1 1 -1 1 0 -1 1 -1 0 -1 0 0 -1 -1 0 0 2 1 1 1 -1 2 2 0 -3 3 0
-2 1 2 1 -2 1 1 -1 1 -2 -3 1 -1 1 0 1 1 -2 -1 2 -3 0 0 0 7 0 4 3 -1 -7 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 0 1 1 -1 1 1 -1 1 -1 -2 1 0 1 0 0 1 -1 0 1 -2 0 0 0 4 0 2 2 -1 -4 1 0
1 1 0 0 0 1 0 0 0 1 1 0 0 -1 -1 0 -1 1 0 -1 1 1 1 1 -2 0 -1 -1 1 2 1 -1
0 1 0 0 0 0 0 0 1 -1 -1 0 0 0 -1 1 0 0 -1 1 0 1 1 -1 1 0 2 0 0 -1 0 -1
1 1 0 0 0 0 0 1 0 1 1 0 0 -1 -1 0 -1 1 0 -1 1 1 1 1 -2 0 -1 -1 0 1 1 0
0 1 0 0 0 0 1 0 0 -1 -1 0 0 -1 0 0 1 -1 -1 1 -1 1 0 1 4 0 2 0 -1 -5 0 0
1 1 0 0 0 0 0 0 0 1 0 0 0 -1 -1 0 0 0 -1 0 1 2 1 1 0 0 1 -1 1 0 1 -2
-1 -1 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 1 -1 0 1 -1 -1 -1 -1 2 0 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 0 0 0 0 0 0 0
0 -1 -1 -1 2 -1 -1 1 -1 0 1 -1 1 0 1 0 0 0 0 0 1 -1 -1 -1 -2 0 -1 -1 1 3 -2 0
1 1 0 0 0 0 0 0 0 1 1 0 0 0 -1 0 -1 1 0 -1 1 1 1 0 -3 -1 -1 0 1 2 1 0
1 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 1 2 1 1 0 0 1 -1 0 -1 1 -1
0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 -1 -1 1 0 1 0 0 2 0 2 0 0 -2 0 -1
-1 2 1 1 -2 1 1 -1 1 -1 -2 1 -2 0 -1 1 1 -2 -2 1 -1 2 1 1 4 -1 4 3 0 -6 3 0
-1 2 1 1 -2 1 1 -1 1 -1 -2 1 -2 0 -1 1 0 -1 -2 1 -1 2 1 1 4 -1 4 3 0 -6 3 0
-1 0 1 1 -2 1 1 -1 1 0 -1 1 -1 1 0 0 0 -1 1 0 -1 0 0 1 2 0 1 2 -1 -3 2 1
-1 0 1 1 -2 1 1 -1 1 0 -1 1 -1 1 0 0 0 -1 0 1 -1 0 0 0 1 -1 1 3 -1 -3 2 2
-1 2 1 1 -2 1 1 -1 1 -1 -2 1 -1 0 -1 1 0 -1 -1 1 -1 1 1 0 4 -1 3 3 0 -5 2 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 1 1 -1 0 0 0 0 -2 0 -2 0 0 2 0 1
1 -2 -1 -1 2 -1 -1 1 -1 1 2 -1 1 0 1 -1 0 1 1 -1 2 -1 0 -1 -5 0 -3 -2 1 6 -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 -1 -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 -1 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 -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 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 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 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 -1 -1 0 1 0 1 0 1
-1 -1 0 0 0 0 0 0 0 -1 -1 0 0 1 1 0 1 -1 0 1 -1 -1 -1 -1 2 0 1 1 -1 -2 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 -1 -1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 -1 -1 0 0 0 0 -1 0 -1 1 -1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -1 -1 0 0 1 1 0 0 0 0 0 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
-1 1 1 1 -1 0 0 0 1 -1 -2 0 0 0 0 1 1 -1 -1 1 -1 1 1 0 3 1 1 0 -1 -4 1 -1
0 -2 0 0 0 -1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 -1 -1 -1 -1 1 1 0 0 -1 0 -2 0
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -1 -2 0 0 -1 1 3 0 -1
0 -2 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 1 1 -1 -2 -1 -1 1 -1 1 2 0 2 -2 0
0 1 0 0 0 0 0 0 0 -1 -1 -1 0 -1 0 0 0 0 -1 0 0 0 0 1 1 0 0 -1 -1 -2 0 0
0 0 0 0 0 0 0 0 0 -1 -1 0 1 0 0 0 0 0 0 1 -1 -1 -1 -1 2 0 1 0 -1 -1 -1 0
0 2 0 0 0 0 0 0 0 -1 -1 0 -1 -1 -1 1 0 0 -2 0 0 2 1 1 2 0 2 0 0 -4 1 0
0 -1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 -1 1 1 0 0 -1 0 0 -1 0 0 0 0 2 0 0
0 1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 -1 0 1 1 0 0 1 0 2 0 1 -2 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 -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 1 -1 -1 1 0 1 0 0 3 0 2 0 0 -3 0 -1
0 1 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 -1 -1 1 -1 0 0 0 3 -1 2 1 -1 -3 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 1 0 1 1 0 2 -1 2 1 0 -2 0 0
0 -2 1 0 0 0 0 0 0 1 1 0 0 1 1 -1 0 0 2 0 -1 -1 0 0 -2 0 -3 0 -2 2 -1 1
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 1 0 0 0 0 0 -1 -1
0 -2 1 0 0 0 0 0 0 1 1 0 0 1 1 -1 0 0 1 0 0 -1 0 0 -1 0 -1 0 0 3 -1 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 -1 0 -1 1 1 -1 0 0 0 0 -2 0 -2 0 0 2 0 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 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 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 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 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 0
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
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 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 -1
0 2 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 1 1 -1 -2 1 0 2 1 0 3 0 2 0 0 -4 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 0 -1 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^5304*18 x^5208*24 x^5112*62 x^5064*48 x^5040*96 x^5028*288 x^5016*48 x^4992*32 x^4932*96 x^4920*16 x^4884*272 x^4872*96 x^4824*96 x^4788*48 (96x)
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*2 x^5004*2 x^4968*6 x^4956*2 x^4944*6 x^4941*4 x^4908*12 x^4905*16 x^4896*50 x^4893*72 x^4884*48 x^4872*24 x^4869*20 x^4860*56 x^4857*108 x^4848*12 x^4845*72 x^4836*114 x^4833*74 x^4824*18 x^4821*100 x^4812*72 x^4809*18 x^4800*48 x^4797*12 x^4788*48 x^4785*54 x^4776*24 x^4773*96 x^4752*24 x^4725*24 x^4689*2 (3072x)
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 -1
x^5304*12 x^5256*48 x^5208*12 x^5184*96 x^5112*72 x^5088*64 x^5064*48 x^5040*96 x^5016*104 x^4968*48 x^4920*192 x^4884*192 x^4836*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 1 -1 -1 -1 1 1 1 1 0 1
x^5124*8 x^5112*6 x^5064*10 x^5040*16 x^5028*40 x^5016*6 x^5004*4 x^4992*8 x^4968*34 x^4965*128 x^4956*32 x^4932*64 x^4920*16 x^4908*16 x^4905*128 x^4896*16 x^4893*96 x^4884*48 x^4872*80 x^4860*36 x^4857*192 x^4848*48 x^4836*16 x^4812*16 x^4800*16 x^4788*32 x^4776*32 x^4761*32 x^4728*32 x^4713*32 (1152x)
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 0 -1 -1 0 0 0 1 0 0
x^5124*8 x^5112*8 x^5088*8 x^5076*48 x^5064*4 x^5028*72 x^5016*12 x^4992*24 x^4980*16 x^4968*32 x^4956*32 x^4944*32 x^4929*256 x^4917*128 x^4896*64 x^4872*16 x^4860*128 x^4848*16 x^4836*64 x^4833*64 x^4824*64 x^4800*16 x^4764*32 x^4761*64 x^4740*32 (576x)
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 0 -1 0 0 -1 0 1 0 0
x^5400*2 x^5304*2 x^5256*4 x^5208*16 x^5160*16 x^5124*48 x^5088*8 x^5076*24 x^5040*16 x^5028*24 x^5016*48 x^5004*56 x^4992*8 x^4980*8 x^4956*128 x^4944*16 x^4932*8 x^4908*64 x^4896*192 x^4893*64 x^4884*16 x^4872*32 x^4860*200 x^4836*32 x^4833*64 x^4812*48 x^4788*32 x^4761*32 x^4713*32 (576x)
1 32
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
x^5028*2 x^5016*4 x^5004*2 x^4992*4 x^4980*4 x^4965*16 x^4956*26 x^4944*8 x^4941*8 x^4929*8 x^4920*40 x^4917*68 x^4908*72 x^4905*36 x^4896*28 x^4893*60 x^4884*46 x^4881*12 x^4872*100 x^4869*76 x^4860*24 x^4857*136 x^4845*92 x^4836*20 x^4833*16 x^4824*4 x^4821*36 x^4812*72 x^4809*40 x^4797*12 x^4788*80 x^4785*32 x^4776*8 x^4761*18 x^4752*8 x^4737*16 x^4713*6 (9216x)
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 0 0 0 0 0 0 0 0 0
x^5400*8 x^5304*24 x^5256*24 x^5208*24 x^5172*96 x^5124*72 x^5076*96 x^5064*8 x^5016*96 x^5004*32 x^4980*48 x^4968*96 x^4956*384 x^4932*8 x^4860*96 x^4833*128 (96x)
1 32
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 1 1
x^5052*2 x^5040*8 x^5028*4 x^5016*2 x^5004*8 x^4980*20 x^4968*18 x^4965*16 x^4956*8 x^4944*38 x^4941*24 x^4932*44 x^4929*8 x^4920*20 x^4917*16 x^4908*8 x^4905*36 x^4896*46 x^4893*80 x^4881*12 x^4872*72 x^4869*44 x^4860*42 x^4857*84 x^4848*108 x^4845*68 x^4836*20 x^4833*32 x^4824*48 x^4821*32 x^4812*90 x^4809*20 x^4800*40 x^4788*6 x^4785*64 x^4776*20 x^4764*2 x^4740*10 x^4728*12 x^4725*8 (9216x)
1 32
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 -1 -1 0 0
x^5400*8 x^5352*32 x^5304*32 x^5256*48 x^5232*32 x^5208*64 x^5160*24 x^5136*96 x^5112*64 x^5088*32 x^5064*32 x^5016*16 x^4992*192 x^4968*16 x^4944*288 x^4932*128 x^4920*8 x^4812*128 (72x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 -2 0 -1 0 1 2 0 1
x^5076*6 x^4980*10 x^4968*2 x^4932*12 x^4920*44 x^4917*16 x^4908*8 x^4896*72 x^4893*16 x^4884*18 x^4872*66 x^4869*32 x^4848*32 x^4845*64 x^4836*88 x^4833*128 x^4824*64 x^4821*48 x^4812*104 x^4809*200 x^4800*8 x^4797*16 x^4788*18 x^4785*8 x^4776*88 x^4761*32 x^4740*8 x^4728*16 x^4713*16 (2304x)
1 32
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 -1 0 1 1 0 0
x^5220*2 x^5028*4 x^5004*8 x^4980*84 x^4968*4 x^4941*16 x^4932*34 x^4920*40 x^4908*24 x^4884*6 x^4872*24 x^4869*16 x^4860*240 x^4848*96 x^4836*96 x^4833*8 x^4824*196 x^4821*48 x^4812*72 x^4797*48 x^4788*30 x^4764*24 x^4761*88 x^4713*24 x^4689*8 (768x)
1 32
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 1 -1 -1 0 1 -1 -1
x^5100*8 x^5088*2 x^5076*16 x^5052*8 x^5040*2 x^5016*8 x^5004*24 x^4992*44 x^4980*32 x^4968*24 x^4965*64 x^4956*96 x^4944*8 x^4932*32 x^4929*32 x^4917*64 x^4908*8 x^4905*64 x^4896*8 x^4893*64 x^4884*56 x^4881*32 x^4872*32 x^4857*64 x^4848*160 x^4845*32 x^4833*32 x^4821*48 x^4812*32 x^4797*16 x^4785*32 x^4752*32 x^4737*32 x^4728*32 (2304x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 1 1 0 0 0 1 0 1 0 0 -1
x^5400*4 x^5304*12 x^5208*36 x^5112*124 x^5064*8 x^5040*48 x^4992*96 x^4980*96 x^4968*20 x^4944*96 x^4932*208 x^4896*112 x^4884*192 x^4872*12 x^4836*48 x^4752*128 (192x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 1 1 0 0 0 0 1 0 1 0 0 -1
x^5304*48 x^5220*32 x^5124*96 x^5112*24 x^5064*16 x^5028*16 x^5004*192 x^4980*48 x^4968*96 x^4956*128 x^4920*224 x^4872*96 x^4824*96 x^4785*128 (96x)
1 32
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 0 0 0 0 0
x^5304*8 x^5208*32 x^5172*64 x^5112*48 x^5052*128 x^5004*64 x^4968*128 x^4920*384 x^4908*128 x^4860*128 x^4713*128 (72x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 -1 -1 0 -1 0 0 -1 0 0 1 -1 0
x^5232*2 x^5208*8 x^5196*16 x^5184*2 x^5160*8 x^5136*4 x^5124*4 x^5100*8 x^5088*8 x^5076*36 x^5052*8 x^5040*8 x^5028*32 x^5004*48 x^4992*32 x^4980*4 x^4968*24 x^4965*64 x^4956*48 x^4944*80 x^4932*32 x^4917*64 x^4908*80 x^4896*32 x^4893*64 x^4884*12 x^4872*128 x^4860*64 x^4857*64 x^4848*48 x^4836*56 x^4824*8 x^4812*16 x^4809*32 x^4785*32 x^4761*32 x^4752*32 (2304x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 -1 0 0 0 0 0 -1 1 1 0 0 1 0 0 -1
x^5136*6 x^5124*12 x^5088*26 x^5076*12 x^4968*24 x^4920*120 x^4908*96 x^4896*48 x^4872*64 x^4869*192 x^4857*96 x^4836*256 x^4824*96 x^4821*48 x^4812*96 x^4797*48 (768x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 -1 0 1 0 0 0 -1 2 0 1 0 1 0 -1 -1
x^5004*10 x^4992*2 x^4944*6 x^4941*4 x^4932*10 x^4920*8 x^4917*12 x^4908*24 x^4905*12 x^4896*82 x^4893*12 x^4881*36 x^4872*12 x^4869*100 x^4860*34 x^4857*60 x^4848*42 x^4845*24 x^4836*18 x^4833*88 x^4824*96 x^4821*64 x^4812*84 x^4809*12 x^4800*144 x^4797*24 x^4788*16 x^4785*72 x^4776*12 x^4773*48 x^4761*24 x^4740*24 x^4728*24 (3072x)
1 32
0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -1 0 -1 -1 1 0 1 1 1 0 0 1
x^5400*32 x^5304*24 x^5220*32 x^5172*192 x^5076*96 x^5064*32 x^5004*320 x^4872*384 x^4833*128 (24x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 0 0 0 0 0 0 -1 -2 -1 0 1 0 1 0 2
x^5088*24 x^5076*144 x^5064*12 x^5028*8 x^5016*12 x^5004*32 x^4992*24 x^4977*256 x^4920*112 x^4908*48 x^4884*56 x^4845*192 x^4836*192 x^4785*96 x^4689*32 (192x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 0 0 0 0 0 0 -1 -1 0 0 1 0 1 0 1
x^5112*6 x^5028*8 x^5004*24 x^4992*48 x^4968*108 x^4932*32 x^4920*118 x^4905*256 x^4884*8 x^4869*192 x^4860*216 x^4833*32 x^4809*96 x^4800*96 (192x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 0 -1 0 0 0 1 0 0 0 1
x^5088*2 x^4968*48 x^4944*54 x^4920*120 x^4905*192 x^4896*24 x^4872*64 x^4869*192 x^4860*96 x^4836*160 x^4824*96 x^4785*96 x^4776*96 (768x)
1 32
0 0 0 0 0 0 0 0 1 -1 0 -1 -1 -1 0 1 1 -1 -1 1 1 2 2 0 1 0 2 0 0 -2 0 -1
x^5208*4 x^5172*8 x^5124*8 x^5112*20 x^5076*16 x^5052*16 x^5028*8 x^5004*16 x^4980*8 x^4944*80 x^4941*64 x^4920*64 x^4908*64 x^4896*80 x^4872*64 x^4860*256 x^4857*48 x^4848*64 x^4845*64 x^4836*64 x^4833*16 x^4812*64 x^4800*64 x^4788*16 x^4725*64 (1152x)
1 32
0 0 0 0 0 0 0 0 1 -1 0 -1 1 0 1 0 1 -1 0 1 1 1 1 -1 1 0 1 0 0 -1 0 -1
x^5352*4 x^5256*4 x^5196*16 x^5172*24 x^5124*16 x^5112*16 x^5088*16 x^5076*8 x^5028*32 x^5004*16 x^4992*16 x^4980*16 x^4968*80 x^4956*64 x^4944*8 x^4932*64 x^4920*16 x^4917*64 x^4908*48 x^4896*152 x^4884*64 x^4872*112 x^4860*80 x^4848*16 x^4845*64 x^4836*16 x^4833*64 x^4824*16 x^4797*64 x^4740*64 (1152x)
1 32
0 0 0 0 1 -2 0 1 -1 -1 -1 0 0 0 0 1 0 0 -1 1 -1 0 -1 0 2 1 1 -1 -1 -3 -1 0
x^4980*12 x^4968*12 x^4920*14 x^4905*16 x^4896*16 x^4884*2 x^4881*24 x^4872*108 x^4860*48 x^4857*164 x^4836*108 x^4833*326 x^4824*12 x^4812*30 x^4809*120 x^4788*48 x^4785*56 x^4776*54 x^4752*40 x^4737*24 x^4713*6 (3072x)
1 32
0 0 0 0 1 -1 -1 0 -1 0 0 -1 0 -1 1 0 1 -1 -1 0 1 0 0 0 0 0 0 -1 0 0 -1 0
x^5028*6 x^4992*14 x^4980*6 x^4977*4 x^4965*24 x^4956*14 x^4944*36 x^4941*6 x^4932*48 x^4929*12 x^4920*14 x^4917*60 x^4908*60 x^4905*18 x^4896*50 x^4893*108 x^4884*44 x^4872*36 x^4869*88 x^4860*72 x^4857*24 x^4848*60 x^4845*60 x^4836*6 x^4833*44 x^4824*54 x^4821*66 x^4812*6 x^4809*48 x^4800*42 x^4788*46 x^4785*6 x^4776*18 x^4773*36 x^4761*4 (24576x)
1 32
0 0 0 0 1 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 -1 -1 0 0 0 1 2 -1 0
x^4992*6 x^4941*24 x^4920*24 x^4908*36 x^4896*48 x^4893*48 x^4884*24 x^4881*12 x^4872*80 x^4869*144 x^4860*90 x^4857*36 x^4848*78 x^4845*144 x^4836*62 x^4833*72 x^4824*48 x^4821*24 x^4812*36 x^4809*12 x^4800*72 x^4788*96 x^4752*12 x^4737*12 (6144x)
1 32
0 1 0 0 0 -1 0 1 0 -1 -1 0 0 -1 0 1 0 0 -1 0 0 1 0 0 2 1 1 -1 0 -3 0 0
x^5220*32 x^5112*24 x^5100*192 x^5028*96 x^4992*256 x^4956*256 x^4857*128 x^4821*256 (96x)
1 32
0 1 0 0 0 -1 0 1 0 -1 -1 0 0 -1 0 1 1 -1 -2 1 0 2 0 0 3 1 2 -1 0 -4 0 -1
x^5220*32 x^5160*24 x^5004*192 x^4980*48 x^4944*48 x^4920*320 x^4908*192 x^4884*32 x^4821*256 x^4776*96 (96x)
-
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