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 13:26:06 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
THETA_SERIES
LAST_LINE
-
NAME
Q32
-
DIMENSION
32
-
GRAM
32 32
6 0 -3 -3 0 0 0 0 2 -2 1 -2 -3 -3 2 1 3 3 -2 1 -2 -2 -2 -3 -3 1 -1 -1 2 2 0 1
0 6 -3 -3 0 0 0 0 -2 2 3 -2 -1 -1 2 -3 1 1 -2 -3 -2 -2 2 -1 -1 -1 1 -1 2 -2 2 1
-3 -3 6 3 0 0 0 0 1 -1 -3 1 2 2 -1 0 -2 -2 1 0 1 1 -1 2 1 1 -1 2 -2 -1 -2 0
-3 -3 3 6 0 0 0 0 -1 1 -2 1 3 3 -1 1 -3 -3 1 1 1 1 1 3 2 0 0 1 -2 1 0 -1
0 0 0 0 6 0 -3 -3 -2 2 -2 3 2 2 2 -3 2 2 1 2 3 3 -2 -1 -2 2 3 3 -2 1 0 3
0 0 0 0 0 6 3 3 2 -2 -2 1 -2 -2 2 -1 2 2 -3 -2 -1 -1 2 -3 0 2 -1 -1 0 1 2 -1
0 0 0 0 -3 3 6 3 3 -3 1 -1 -3 -3 -1 1 -1 -1 -1 -3 -2 -2 3 -2 1 1 -3 -2 0 1 2 -1
0 0 0 0 -3 3 3 6 3 -3 -1 -2 -3 -3 1 2 1 1 -2 -3 -1 -1 3 -1 1 1 -2 -3 2 0 0 -2
2 -2 1 -1 -2 2 3 3 6 -3 0 -2 -3 -3 0 2 1 1 -1 -1 -1 -1 0 -2 0 2 -3 -2 1 0 0 -1
-2 2 -1 1 2 -2 -3 -3 -3 6 1 1 3 3 0 -2 -1 -1 1 1 1 1 0 2 0 -2 2 1 0 -2 1 1
1 3 -3 -2 -2 -2 1 -1 0 1 6 -2 -1 -1 -1 0 -1 -1 0 -1 -2 -2 1 0 1 -1 -1 -1 2 -1 1 -1
-2 -2 1 1 3 1 -1 -2 -2 1 -2 6 2 2 -1 -1 0 0 2 2 3 3 -1 0 1 1 1 3 -2 1 -1 0
-3 -1 2 3 2 -2 -3 -3 -3 3 -1 2 6 3 0 -2 -2 -2 2 2 2 2 -1 3 0 0 3 2 -3 0 -1 0
-3 -1 2 3 2 -2 -3 -3 -3 3 -1 2 3 6 -1 -1 -2 -2 2 2 2 2 -1 3 1 -2 1 2 -1 -1 0 1
2 2 -1 -1 2 2 -1 1 0 0 -1 -1 0 -1 6 -2 3 3 -3 -1 -1 -1 0 -2 -3 2 1 -1 1 0 0 2
1 -3 0 1 -3 -1 1 2 2 -2 0 -1 -2 -1 -2 6 -1 -1 1 1 0 0 0 1 2 -1 -2 -2 1 0 -2 -2
3 1 -2 -3 2 2 -1 1 1 -1 -1 0 -2 -2 3 -1 6 3 -1 1 0 0 -1 -3 -2 2 1 0 1 0 1 2
3 1 -2 -3 2 2 -1 1 1 -1 -1 0 -2 -2 3 -1 3 6 -2 0 0 0 -1 -3 -3 1 1 -1 1 1 -1 1
-2 -2 1 1 1 -3 -1 -2 -1 1 0 2 2 2 -3 1 -1 -2 6 2 3 3 -1 2 2 0 2 2 -3 -1 -1 1
1 -3 0 1 2 -2 -3 -3 -1 1 -1 2 2 2 -1 1 1 0 2 6 2 2 -3 1 -1 -1 1 1 -1 1 -1 1
-2 -2 1 1 3 -1 -2 -1 -1 1 -2 3 2 2 -1 0 0 0 3 2 6 3 0 0 1 1 1 1 -1 0 -1 0
-2 -2 1 1 3 -1 -2 -1 -1 1 -2 3 2 2 -1 0 0 0 3 2 3 6 -1 1 0 0 3 2 -3 0 -1 1
-2 2 -1 1 -2 2 3 3 0 0 1 -1 -1 -1 0 0 -1 -1 -1 -3 0 -1 6 0 1 -1 -1 -3 1 0 3 -1
-3 -1 2 3 -1 -3 -2 -1 -2 2 0 0 3 3 -2 1 -3 -3 2 1 0 1 0 6 2 -2 1 1 -1 -1 -1 0
-3 -1 1 2 -2 0 1 1 0 0 1 1 0 1 -3 2 -2 -3 2 -1 1 0 1 2 6 0 -1 1 0 -2 0 -3
1 -1 1 0 2 2 1 1 2 -2 -1 1 0 -2 2 -1 2 1 0 -1 1 0 -1 -2 0 6 0 2 -1 1 -1 0
-1 1 -1 0 3 -1 -3 -2 -3 2 -1 1 3 1 1 -2 1 1 2 1 1 3 -1 1 -1 0 6 2 -3 0 0 2
-1 -1 2 1 3 -1 -2 -3 -2 1 -1 3 2 2 -1 -2 0 -1 2 1 1 2 -3 1 1 2 2 6 -2 0 -1 1
2 2 -2 -2 -2 0 0 2 1 0 2 -2 -3 -1 1 1 1 1 -3 -1 -1 -3 1 -1 0 -1 -3 -2 6 -1 0 -1
2 -2 -1 1 1 1 1 0 0 -2 -1 1 0 -1 0 0 0 1 -1 1 0 0 0 -1 -2 1 0 0 -1 6 0 0
0 2 -2 0 0 2 2 0 0 1 1 -1 -1 0 0 -2 1 -1 -1 -1 -1 -1 3 -1 0 -1 0 -1 0 0 6 1
1 1 0 -1 3 -1 -1 -2 -1 1 -1 0 0 1 2 -2 2 1 1 1 0 1 -1 0 -3 0 2 1 -1 0 1 6
-
DIVISORS
2^16
-
MINIMAL_NORM
6
-
MINVECS
-
KISSING_NUMBER
261120
-
DENSITY
-
HERMITE_NUMBER
.424264068712E+01
-
GROUP_ORDER
2^9 * 3^4 * 5
-
GROUP_GENERATORS
3
32 32
2 3 0 0 -1 2 -2 3 1 0 1 1 1 0 -1 1 -2 -1 -1 1 2 -1 -1 0 0 0 0 1 -2 0 0 2
-1 -2 -1 -1 1 -1 -1 1 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 1 0 0 0 -1 0 -1 0 0 0
-4 -2 -2 1 0 -1 0 -3 0 -1 -1 -1 0 -1 1 0 1 1 1 -1 -2 1 0 -1 0 0 -1 0 2 0 0 0
-3 -2 -1 0 0 -2 1 -2 0 0 -1 -1 -1 0 1 0 1 1 0 0 -1 0 1 -1 0 0 0 1 1 0 0 -1
-1 -2 -1 0 0 0 0 -1 0 0 0 -1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 1 -2 1 2 0 2 -2 1 1 -1 0 0 0 0 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 -1 0 1 0 1 -1 0 0 0 0 0 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 -1 0 0 1 1 -1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 3 1 0 -1 2 -2 3 0 0 1 1 1 0 -1 1 -2 -1 0 1 1 0 -1 -1 0 0 0 0 -1 0 0 2
-1 -2 -1 -1 1 -2 -1 1 1 0 0 0 0 1 0 0 0 0 -1 0 -1 -1 2 -1 0 0 0 1 -1 0 0 0
2 3 0 1 -1 1 -2 1 1 -1 0 1 1 0 -1 0 -1 0 0 0 1 0 0 0 0 0 -1 0 -1 0 0 1
1 -1 1 0 1 1 2 -2 -1 0 0 -1 0 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 -1 2 0 0 -1
-3 -3 -1 0 0 -3 0 -2 0 0 -1 0 -1 0 1 0 1 1 0 -1 -2 0 1 -1 0 1 0 0 1 0 1 -1
-2 -1 0 1 -1 -1 1 -3 0 0 0 -1 -1 0 1 0 2 1 0 -1 0 1 0 0 0 0 0 0 1 1 0 -1
-3 -4 -2 -2 0 -1 -1 1 -1 1 0 -1 0 0 0 0 0 0 -1 0 -1 -1 1 -1 0 1 -1 1 -1 0 0 1
2 3 0 2 0 1 1 0 1 -1 0 1 0 0 -1 0 0 -1 -1 0 2 0 -1 1 -1 -1 1 0 0 -1 -1 0
1 -1 1 0 0 1 0 1 -1 1 1 0 -1 -1 0 -1 0 -1 0 0 1 0 -1 1 0 0 1 -1 0 0 0 0
2 2 0 0 0 3 -2 2 0 0 1 0 2 0 -2 1 -1 -1 0 0 1 0 -1 0 0 0 -1 0 -1 0 0 2
2 1 2 2 -1 0 1 -2 0 0 0 1 -2 0 0 -1 1 0 0 -1 1 1 -1 1 0 0 2 -2 1 0 0 -1
1 1 1 2 0 0 1 -2 0 0 0 0 -1 -1 0 0 1 0 0 -1 1 1 -1 1 0 0 1 -1 1 0 0 -1
1 1 1 2 -1 1 1 -2 0 0 0 0 -1 0 0 0 1 0 1 -1 1 1 -1 1 -1 0 1 -1 1 0 0 -1
0 -2 1 -1 0 -2 3 -2 -1 1 -1 -1 0 1 0 0 2 1 -1 0 -1 1 1 0 1 1 1 -1 1 0 0 -1
-2 -3 -1 0 1 -2 1 0 -1 0 0 0 -1 0 0 -1 1 1 0 0 -1 -1 1 0 -1 0 0 0 0 -1 0 -1
-2 -2 -2 2 1 -3 2 -3 1 -1 -1 0 0 0 0 -1 3 1 -1 -2 -1 0 1 0 0 -1 0 0 1 -1 -1 -1
3 2 2 1 0 2 1 -1 0 0 0 0 -1 0 0 -1 0 -1 1 0 1 1 0 1 0 -1 1 -1 1 0 -1 -1
1 1 0 0 -1 2 -1 1 0 0 0 0 0 0 0 0 -1 -1 1 0 1 0 -1 0 0 0 0 0 0 0 0 1
0 -2 0 -1 0 -2 1 -1 0 1 -1 0 -1 1 0 -1 1 0 -1 0 -1 0 1 0 1 1 1 -1 0 0 0 -1
0 1 0 0 -1 1 0 -2 1 0 -1 -1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0
0 3 0 0 -1 1 -1 1 1 0 0 0 1 0 0 1 -1 0 0 1 1 0 0 0 0 0 -1 1 -1 1 0 1
0 1 0 0 -1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 -1 0 0 0 0 1 0 0 1 0
0 -2 1 -1 0 -1 0 1 -1 1 1 0 -2 0 1 -1 0 0 0 1 0 -1 1 0 0 0 1 0 -1 0 0 -1
-2 -3 -2 0 0 -2 1 -2 0 0 -1 -1 0 0 0 -1 2 1 -1 -1 -1 0 1 0 1 0 0 0 0 0 -1 0
32 32
0 -2 1 -1 1 1 0 1 -2 0 2 -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 0 1 1 -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 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
-1 0 -1 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
1 2 0 1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -2 1 0 0 0 0 0 0 0 0
-2 -2 -1 -1 2 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -2 -1 0 0 0 0 0 0 0 0 0 0
-3 -4 -1 -2 3 -2 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -3 -2 2 -1 0 0 0 0 0 0 0 0
-3 -3 -1 -1 2 -2 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -3 -1 1 -2 0 0 0 0 0 0 0 0
-2 -3 -1 -1 2 -1 -1 1 0 0 1 0 0 0 0 0 0 0 0 0 -2 -1 1 -1 0 0 0 0 0 0 0 0
2 2 0 1 -2 1 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 2 1 -1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 3 -1 2 -1 0 0 -1 2 -1 -1 1 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0
2 3 0 1 -2 1 1 -1 1 0 -1 0 1 0 0 0 0 0 0 0 2 1 -1 1 0 0 0 0 0 0 0 0
1 3 0 2 -2 1 0 -2 1 0 -1 0 -1 -1 0 0 0 0 0 0 2 1 -1 1 0 0 0 0 0 0 0 0
1 -1 1 -1 1 1 1 2 -2 1 1 -1 1 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
0 1 0 0 1 0 -1 0 1 -1 0 0 1 1 -1 1 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0
0 -1 -2 3 2 1 0 1 0 -2 2 1 0 -1 -1 -1 1 -1 0 -2 1 -1 -2 1 -2 -2 0 0 0 -2 -1 0
-1 -1 2 -2 0 -1 0 2 -2 1 1 0 0 0 1 1 -1 1 0 1 -1 0 -1 -1 1 1 0 0 0 1 2 0
-2 1 -2 3 -1 -1 -2 -1 2 -2 0 2 -1 -1 0 0 0 0 0 -1 1 -1 -1 0 -2 0 0 0 0 -1 1 0
1 0 -2 2 1 0 1 -1 1 -2 0 0 1 0 -1 -1 1 0 -1 -1 1 0 0 1 0 -1 0 0 0 -2 -1 0
0 3 -1 2 -1 -1 0 -1 2 -1 -1 1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0
0 3 -1 2 -2 0 -1 -1 2 -1 -1 1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0
-2 -2 -1 -1 1 -2 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -2 -1 1 -1 0 0 0 0 0 0 0 0
1 2 0 1 -2 1 0 -2 1 0 -1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
-2 1 -2 2 -1 -1 -1 -2 2 -1 -1 1 -1 0 0 0 1 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0
-2 -1 -1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 0 0 0 0 0 0 0
1 2 1 1 -2 0 1 0 0 0 0 1 -1 0 1 0 0 0 0 0 2 0 -2 1 -1 0 1 0 0 0 1 -1
-1 1 -1 1 -2 1 0 -1 1 0 0 0 -1 0 1 0 0 0 0 0 2 0 -1 1 -1 0 0 1 0 0 0 0
0 -2 0 -2 1 -1 1 1 -1 1 0 -1 0 1 0 0 0 0 -1 1 -1 0 2 -1 1 0 0 1 -1 0 -1 0
0 1 1 -1 0 1 0 0 0 0 0 -1 0 0 1 0 -1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0
-1 -2 -2 1 1 0 0 -1 0 -1 0 0 -1 -1 0 -1 1 -1 0 -1 0 -1 0 1 -1 -1 0 0 0 -1 -1 0
0 -2 0 1 1 0 1 0 -1 0 1 0 -1 -1 0 -1 1 0 0 -1 1 -1 -1 1 -1 -1 0 0 0 -1 0 -1
32 32
2 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0
0 -2 -2 -1 1 -1 2 -1 0 0 -2 -1 1 1 -1 -1 1 0 -1 0 -1 0 2 0 1 0 0 0 0 -1 -2 0
-2 0 -1 2 0 -1 -2 0 1 -2 1 2 -1 -1 0 0 0 0 0 -1 0 -1 -1 0 -2 0 0 0 0 -1 1 0
0 3 -1 3 -1 2 -2 -1 2 -2 1 1 -1 -1 0 0 0 -1 1 -1 2 0 -2 1 -2 -1 0 0 0 0 0 0
-3 -1 -2 1 0 -1 -1 -2 0 -1 -1 -1 1 -1 0 0 1 1 1 -1 -2 1 0 -1 0 0 -2 0 1 0 0 0
2 1 1 0 1 1 -2 2 0 0 1 1 0 0 -1 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 1
3 0 3 0 1 0 1 1 -1 1 1 1 -2 0 0 -1 0 -1 0 0 1 0 0 1 0 0 2 -2 0 0 0 -1
4 3 2 1 -1 3 -1 1 0 0 1 1 0 0 -1 0 -1 -1 0 0 2 1 -1 1 0 0 1 -1 0 0 0 1
3 3 3 2 0 2 -1 2 0 0 2 2 -1 -1 0 0 -1 -1 1 0 2 0 -2 1 -1 -1 1 -1 0 0 1 0
-3 0 -3 1 -1 0 0 -2 1 -1 -1 -1 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 -1 1 0 0 -1 0
3 1 1 -1 1 1 3 0 0 1 -1 -1 0 1 0 -1 0 -1 0 1 1 0 1 1 1 -1 1 0 0 0 -2 -1
-2 -2 -1 -1 1 -1 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 -2 0 1 -1 0 1 -1 0 0 0 0 0
-4 0 -3 1 0 0 -1 -3 1 -2 -1 -1 1 -1 0 1 1 1 1 -1 -1 0 0 0 -1 0 -2 1 1 0 0 0
-3 -1 -2 0 0 -1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 -1 0 0 1 0 0 0 0
0 1 -3 1 1 1 -2 0 2 -2 -1 0 4 0 -2 1 0 0 0 -1 -1 0 1 -1 0 -1 -2 1 0 -1 -1 2
4 4 3 0 -2 3 -1 3 0 1 2 1 0 1 0 1 -2 -1 0 1 3 0 -2 0 0 0 1 0 -1 1 1 1
2 1 0 1 0 1 0 0 0 0 0 0 2 0 -1 0 1 0 0 -1 0 1 0 0 1 -1 -1 0 0 0 -1 1
1 2 1 -1 -1 1 -2 1 0 1 -1 0 1 0 0 1 -2 0 1 1 -1 1 0 -1 1 1 -1 0 0 1 1 1
-1 0 1 0 -2 0 1 -2 -1 1 0 -1 -1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 -1
-1 1 0 1 -1 1 -1 0 0 0 1 0 0 -1 1 1 0 0 1 -1 1 0 -2 0 -1 -1 -1 1 0 1 1 0
0 2 1 0 -2 1 0 -1 -1 0 0 -1 1 0 0 1 0 1 1 0 0 2 -1 0 0 1 -1 0 1 1 1 0
-3 0 0 0 -1 0 -1 -1 -1 0 0 -1 0 -1 1 1 0 1 1 0 -1 1 -1 -1 0 1 -1 0 1 1 1 0
3 2 1 0 0 2 1 0 0 0 0 0 0 1 -1 0 0 -1 0 0 1 1 0 1 0 0 1 -1 0 0 -1 0
-3 -1 -2 0 -1 0 -1 -1 1 -1 0 0 -1 0 1 0 0 0 0 0 0 -1 0 0 -1 0 0 1 0 0 0 0
3 2 1 0 -1 2 0 1 0 0 1 0 -1 1 0 -1 -1 -1 0 1 2 0 0 1 0 0 1 0 -1 0 -1 0
2 1 0 2 1 1 0 -1 0 -1 0 0 1 -1 -1 -1 1 0 1 -1 0 1 0 1 0 -1 -1 -1 1 -1 -1 0
-4 -1 -2 -1 -1 -1 0 -3 0 0 -2 -2 1 0 1 1 1 2 1 0 -2 1 1 -1 1 1 -2 1 1 1 0 0
-4 -4 -3 1 1 -3 1 -3 0 -1 -1 -1 -1 -1 1 -2 2 1 0 -1 -2 0 1 0 0 0 -1 0 1 -1 -1 -1
3 0 0 0 1 1 2 1 0 0 0 0 1 1 -1 -1 0 -1 -1 0 1 0 0 1 0 -1 1 0 0 -1 -1 0
0 -1 2 -1 1 0 0 -1 -1 1 0 -1 -1 -1 1 0 0 0 1 0 -1 1 0 0 1 0 0 -1 1 1 1 -1
0 -1 0 1 1 -1 2 -1 0 0 0 0 -1 0 0 -1 2 0 0 -1 0 0 0 1 0 -1 1 -1 0 0 -1 -1
-3 -3 -1 0 0 -3 1 -2 0 0 -1 0 0 0 1 0 2 1 0 -1 -2 0 1 -1 0 0 0 0 1 0 0 -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^3996*8 x^2436*4 x^2411*12 x^2400*24 x^2398*12 x^2395*12 x^2393*6 x^2388*24 x^2385*12 x^2384*24 x^2380*12 x^2378*12 x^2376*18 x^2375*12 x^2373*12 x^2372*36 x^2371*36 x^2370*24 x^2369*24 x^2367*16 x^2365*84 x^2364*12 x^2360*24 x^2359*24 x^2358*12 x^2357*36 x^2356*12 x^2354*36 x^2353*12 x^2352*24 x^2351*12 x^2350*24 x^2349*72 x^2348*24 x^2347*12 x^2346*24 x^2345*48 x^2344*36 x^2343*36 x^2342*24 x^2341*12 x^2340*24 x^2339*12 x^2338*48 x^2337*12 x^2336*36 x^2335*12 x^2334*16 x^2333*24 x^2332*12 x^2331*12 x^2330*24 x^2329*12 x^2328*12 x^2327*12 x^2326*24 x^2325*14 x^2322*8 x^2320*12 x^2319*48 x^2317*36 x^2315*12 x^2313*12 x^2312*24 x^2310*12 x^2309*24 x^2306*12 x^2301*18 x^2298*6 x^2290*12 x^2286*8 x^2285*12 x^2279*12 x^2259*2 x^2250*4 (17280x)
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^4050*6 x^4038*2 x^2441*8 x^2421*8 x^2418*4 x^2410*8 x^2407*6 x^2400*4 x^2398*8 x^2395*4 x^2394*8 x^2393*12 x^2392*8 x^2388*4 x^2386*8 x^2385*8 x^2384*16 x^2383*4 x^2381*4 x^2380*24 x^2379*18 x^2378*14 x^2377*6 x^2376*28 x^2375*16 x^2374*40 x^2373*8 x^2372*16 x^2371*32 x^2370*4 x^2369*16 x^2368*28 x^2367*44 x^2366*12 x^2365*44 x^2364*14 x^2363*22 x^2362*20 x^2360*24 x^2359*24 x^2358*22 x^2357*16 x^2356*20 x^2355*28 x^2354*30 x^2353*12 x^2352*4 x^2351*18 x^2350*32 x^2349*44 x^2348*24 x^2347*24 x^2346*24 x^2345*42 x^2344*36 x^2343*60 x^2342*20 x^2341*4 x^2340*8 x^2339*12 x^2338*28 x^2337*24 x^2336*34 x^2335*24 x^2334*24 x^2333*20 x^2332*20 x^2331*20 x^2330*10 x^2329*10 x^2328*44 x^2327*4 x^2326*12 x^2325*4 x^2324*4 x^2322*8 x^2321*24 x^2320*12 x^2319*20 x^2318*20 x^2317*4 x^2316*8 x^2314*4 x^2313*18 x^2312*8 x^2311*4 x^2309*4 x^2307*4 x^2306*8 x^2296*8 x^2290*4 x^2285*4 x^2282*8 x^2279*4 (51840x)
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^3942*6 x^3870*2 x^2441*12 x^2439*2 x^2436*2 x^2430*4 x^2418*6 x^2405*6 x^2404*6 x^2396*12 x^2394*12 x^2393*12 x^2392*12 x^2386*12 x^2385*6 x^2379*24 x^2378*18 x^2377*12 x^2376*60 x^2375*12 x^2374*12 x^2373*36 x^2372*24 x^2371*36 x^2369*18 x^2368*12 x^2367*60 x^2366*6 x^2365*12 x^2364*36 x^2363*24 x^2360*6 x^2358*24 x^2357*36 x^2356*12 x^2355*12 x^2354*36 x^2353*36 x^2352*68 x^2351*12 x^2350*24 x^2349*48 x^2348*18 x^2347*42 x^2346*36 x^2345*12 x^2344*12 x^2342*30 x^2340*12 x^2339*24 x^2338*24 x^2336*48 x^2335*36 x^2334*24 x^2333*24 x^2332*24 x^2331*12 x^2329*12 x^2328*12 x^2327*12 x^2325*16 x^2322*4 x^2321*12 x^2320*18 x^2319*24 x^2316*30 x^2315*12 x^2314*12 x^2312*36 x^2311*12 x^2309*18 x^2307*24 x^2301*12 x^2290*12 x^2288*24 x^2284*12 (17280x)
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 1 0 0 0
x^3978*6 x^3906*2 x^2484*2 x^2426*6 x^2424*4 x^2421*12 x^2407*12 x^2405*12 x^2404*12 x^2398*12 x^2396*24 x^2394*6 x^2388*12 x^2387*24 x^2385*4 x^2384*24 x^2381*24 x^2380*24 x^2379*24 x^2378*24 x^2377*12 x^2376*24 x^2372*24 x^2369*24 x^2368*12 x^2367*48 x^2366*12 x^2365*12 x^2364*24 x^2362*12 x^2361*8 x^2360*42 x^2359*24 x^2358*24 x^2355*12 x^2354*36 x^2353*36 x^2352*24 x^2351*12 x^2350*36 x^2349*24 x^2347*36 x^2346*12 x^2345*48 x^2344*24 x^2343*36 x^2342*30 x^2341*24 x^2340*18 x^2339*24 x^2338*36 x^2337*12 x^2336*12 x^2334*36 x^2333*12 x^2332*6 x^2331*36 x^2330*18 x^2329*24 x^2328*12 x^2326*24 x^2324*12 x^2322*24 x^2321*12 x^2320*12 x^2319*24 x^2318*24 x^2317*12 x^2316*24 x^2313*24 x^2312*24 x^2311*12 x^2310*12 x^2309*36 x^2301*12 x^2296*12 x^2279*12 (17280x)
1 32
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
x^3942*6 x^3618*2 x^2430*36 x^2424*36 x^2412*18 x^2368*54 x^2367*108 x^2361*72 x^2352*72 x^2349*36 x^2348*108 x^2343*216 x^2338*216 x^2334*252 x^2301*216 x^2286*72 (960x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 1
x^3966*6 x^3954*2 x^2496*2 x^2426*2 x^2411*4 x^2410*8 x^2407*4 x^2398*16 x^2395*8 x^2388*16 x^2387*8 x^2385*8 x^2384*8 x^2383*16 x^2380*24 x^2379*16 x^2378*8 x^2377*8 x^2376*20 x^2374*32 x^2372*32 x^2371*8 x^2370*12 x^2369*8 x^2368*4 x^2367*40 x^2365*32 x^2364*12 x^2363*24 x^2362*12 x^2360*72 x^2359*40 x^2358*72 x^2357*16 x^2356*16 x^2355*48 x^2354*24 x^2353*4 x^2352*24 x^2351*24 x^2350*24 x^2349*56 x^2348*22 x^2347*24 x^2346*16 x^2345*24 x^2344*24 x^2343*40 x^2342*24 x^2341*4 x^2340*32 x^2339*32 x^2338*20 x^2337*8 x^2336*24 x^2335*28 x^2334*40 x^2333*16 x^2332*16 x^2331*16 x^2330*42 x^2329*20 x^2328*12 x^2326*16 x^2324*8 x^2322*4 x^2321*32 x^2320*8 x^2319*16 x^2318*16 x^2317*8 x^2315*8 x^2314*8 x^2313*24 x^2310*8 x^2307*8 x^2296*12 x^2288*8 x^2285*8 x^2284*16 x^2282*8 (25920x)
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PROPERTIES
INTEGRAL=1
MODULAR=2
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REFERENCES
H.-G. Quebbemann, Lattices with Theta Functions for G(sqrt(2)) and Linear Codes.
J. Algebra 105, pp. 443-450, 1987.
W. Plesken, B. Souvignier, Computing isometries of lattices.
J. Symb. Computation. (to appear)
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THETA_SERIES
1,0,0,261120,18947520,535818240,8320327680,83347937280,
622558664640,3614759362560,17694184734720,73337844372480,
272615629589760,898646461378560,2752654757806080,7687895624386560
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe