The Lattice CQ32
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 13:12:26 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
BACHER_POLYNOMIALS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
CQ32
-
DIMENSION
32
-
GRAM
32 0
6
3 6
3 3 6
3 1 1 6
2 2 1 3 6
2 2 3 1 2 6
3 2 1 2 3 2 6
2 1 1 3 1 1 0 6
3 1 3 3 3 3 3 2 6
1 1 1 3 3 3 1 2 3 6
3 1 3 3 2 2 2 2 3 2 6
1 3 3 2 3 2 0 0 2 2 2 6
2 2 2 3 2 1 2 3 2 1 2 1 6
2 1 1 1 -1 0 0 1 1 -1 1 0 1 6
3 1 2 1 0 1 1 0 2 0 1 1 0 0 6
3 2 2 1 2 2 2 0 2 0 2 2 2 1 2 6
3 1 0 3 2 1 3 2 2 2 3 -1 2 1 0 2 6
1 -1 1 3 2 1 0 2 2 2 3 2 2 -1 1 2 1 6
3 1 1 3 2 2 0 3 2 2 2 1 2 2 1 2 2 2 6
3 3 3 2 2 2 1 2 3 2 3 2 2 1 2 2 1 2 3 6
3 3 1 2 2 2 2 3 1 2 2 1 2 0 0 1 2 1 3 2 6
2 2 3 2 0 1 0 1 2 2 3 3 2 2 2 2 0 2 1 3 1 6
1 0 0 1 0 1 0 1 2 2 1 0 1 1 3 0 1 1 2 2 0 2 6
3 1 2 2 2 2 2 2 2 1 3 0 3 2 1 1 2 0 3 2 2 1 2 6
1 1 0 1 3 0 0 0 0 1 1 2 1 0 0 1 1 1 1 0 0 0 1 1 6
1 1 1 0 2 2 1 -1 2 1 1 2 0 0 1 3 1 2 2 2 1 0 1 0 1 6
1 1 1 2 2 1 0 3 1 2 3 1 3 1 -1 1 2 2 3 3 2 1 1 3 1 1 6
1 2 2 1 1 1 0 3 2 3 2 1 1 0 0 -1 1 0 0 2 1 2 1 1 1 -1 1 6
3 2 3 1 2 2 0 2 3 2 3 2 2 2 1 2 2 1 3 3 2 2 2 3 2 2 3 2 6
1 2 1 2 3 2 1 3 2 3 0 1 3 -1 1 0 1 1 2 2 2 0 2 2 1 0 2 2 2 6
1 1 2 1 2 2 1 2 3 3 3 2 1 -2 1 1 0 2 1 3 2 2 1 1 0 1 2 3 2 2 6
2 3 2 2 0 1 0 3 1 1 2 1 2 3 0 0 2 -1 2 2 2 2 1 2 1 -1 2 3 2 1 0 6
-
DIVISORS
2^16
-
MINIMAL_NORM
6
-
MINVECS
-
KISSING_NUMBER
261120
-
DENSITY
-
HERMITE_NUMBER
.424264068712E+01
-
GROUP_ORDER
29376= 2^6*3^3*17
-
GROUP_NAME
SL2(17) o tilde(S)3
-
GROUP_GENERATORS
4
32 32
-1 2 0 2 0 0 2 0 1 -2 -2 -2 -3 -2 -1 0 -1 2 1 -2 -1 2 0 1 0 0 1 0 2 0 0 1
0 3 -1 1 0 0 2 0 1 -2 -1 -3 -3 -3 -1 -1 -1 2 2 -3 -3 4 -1 1 0 1 1 -1 2 1 0 2
0 2 -1 0 0 0 1 0 0 0 -1 -1 -1 -1 0 -1 0 2 1 -1 -2 1 -1 1 0 0 0 -1 1 0 1 1
-1 1 1 3 3 1 4 1 -4 -3 -4 -3 -3 -2 -1 -1 -1 3 1 -3 -3 3 1 0 -2 1 0 0 5 -1 2 3
-1 1 1 4 1 1 5 0 -3 -5 -6 -3 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 1 1 5 0 2 3
1 1 -1 -3 -1 -1 -3 0 3 3 2 1 1 1 1 0 1 0 -1 1 1 -2 -1 1 1 -1 0 -1 -3 0 -1 -1
0 1 0 -1 -1 -1 -2 0 3 1 1 0 0 0 0 1 0 0 0 0 1 -1 0 1 1 -1 0 0 -2 0 -1 -1
1 2 -1 0 0 0 -2 -1 3 -1 2 -2 -1 -1 -1 0 -1 0 0 -2 0 1 0 0 0 1 1 0 -1 2 -1 0
0 1 0 1 0 0 1 0 0 -1 -2 -1 -2 -1 -1 0 0 2 0 -1 -1 1 0 1 0 0 0 0 1 0 1 1
0 0 1 1 1 0 2 0 -2 -1 -2 -1 -2 -1 -1 0 0 2 0 -1 -1 1 1 0 -1 0 0 0 2 0 1 2
1 1 -1 0 1 0 0 0 0 0 0 -1 0 -1 0 0 -1 1 0 -1 -1 0 0 0 -1 0 0 0 1 0 0 1
-1 2 0 3 1 1 5 0 -3 -4 -5 -3 -4 -3 -1 -2 0 4 2 -3 -4 5 -1 1 -1 1 1 0 5 0 2 3
0 2 0 1 2 1 2 0 -1 -4 -4 -2 -3 -2 -1 -2 1 3 2 -3 -3 4 0 1 -1 1 1 0 2 0 2 2
0 0 0 0 1 0 2 1 -2 1 -1 0 0 0 0 0 -1 1 0 0 -2 -1 0 0 -1 0 -1 -1 2 -1 1 2
-1 0 0 2 -1 0 4 0 -1 -2 -3 0 -3 -2 -1 0 -1 2 1 -1 -1 2 0 1 0 0 1 1 3 0 0 1
0 0 0 0 0 0 2 0 0 -2 -3 0 -2 -1 0 -1 1 2 1 -1 -1 2 -1 1 0 0 1 0 1 0 1 1
1 0 0 -1 1 -1 -1 1 0 2 1 0 1 0 0 1 -1 0 -1 0 0 -2 1 0 -1 0 -1 -1 0 -1 0 1
0 1 0 2 2 1 4 0 -3 -4 -4 -2 -3 -2 -1 -2 0 3 2 -3 -3 4 0 0 -2 1 1 1 4 0 2 2
0 2 0 2 2 1 2 0 -1 -3 -2 -3 -3 -2 -1 -1 -1 2 1 -3 -2 3 0 0 -1 1 1 0 3 0 1 2
1 1 -1 1 1 0 2 0 -1 -1 0 -2 -2 -2 -1 0 -2 1 1 -2 -2 2 0 0 -1 1 0 0 2 1 0 2
0 4 -1 1 1 1 0 -1 3 -4 -1 -4 -3 -3 -1 -2 0 2 2 -4 -2 5 -1 1 0 1 2 0 1 1 0 1
0 0 0 0 1 0 3 0 -2 -1 -2 0 -1 -1 0 -1 0 2 1 -1 -2 1 0 0 -1 0 0 0 2 0 1 2
-1 1 0 1 -1 0 3 0 0 -2 -3 0 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 1 2 0 0 1
-1 1 0 2 0 1 2 0 0 -3 -3 -1 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 1 2 0 0 1
-1 1 1 4 0 1 6 0 -3 -5 -7 -2 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 2 1 5 0 2 3
1 2 -1 0 1 0 2 1 -1 -1 -1 -2 -2 -2 -1 -1 -1 2 1 -2 -3 3 -1 1 -1 1 0 -1 2 0 1 2
0 1 0 2 2 1 3 0 -3 -3 -4 -2 -3 -2 -1 -1 0 3 1 -2 -3 3 0 1 -2 1 0 0 4 0 2 3
2 0 -1 -1 -1 -1 -2 -1 2 2 4 0 1 0 -1 2 -2 -1 -1 0 1 -2 1 -1 0 0 0 0 -2 2 -2 0
0 1 0 3 1 1 4 0 -2 -4 -5 -2 -4 -3 -2 -1 0 3 1 -2 -3 4 0 1 -1 1 1 0 4 0 2 3
-1 2 0 3 0 1 3 -1 0 -5 -4 -3 -5 -3 -2 -1 0 3 2 -3 -2 5 0 1 0 1 2 1 3 1 1 2
0 2 -1 1 -1 1 0 -2 3 -4 -2 -2 -3 -2 -1 -1 1 2 1 -2 0 4 -1 1 1 0 2 1 0 2 0 0
1 2 -1 0 1 0 0 0 0 1 1 -2 0 -1 0 0 -2 1 0 -2 -2 0 0 0 -1 1 0 -1 1 0 0 2
32 32
1 0 -1 -3 1 -1 -5 0 2 4 4 1 4 2 2 1 0 -2 -2 2 2 -4 0 0 0 -1 -2 -1 -3 -1 -1 -1
0 -1 0 0 0 0 0 -1 0 -1 -1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 -1 0 1 0 0 0 0
0 1 -1 -2 -1 -1 -2 -1 3 1 1 1 1 0 1 0 1 0 0 1 1 -1 -1 1 1 -1 0 0 -2 0 -1 -1
-1 -1 0 0 -1 0 -1 0 1 1 1 1 1 1 1 1 0 -1 -1 2 2 -2 0 0 1 -1 -1 0 -1 0 -1 -1
1 -2 0 -2 -1 -1 -4 0 2 3 4 2 3 2 1 2 0 -3 -2 3 3 -4 0 -1 1 -1 -1 0 -4 1 -2 -2
0 -1 0 -1 0 0 -1 -1 0 0 -1 2 1 1 1 0 2 0 0 1 1 -1 0 0 0 -1 0 1 -1 0 0 -1
2 -2 -1 -4 1 -1 -5 0 1 5 5 2 5 3 2 1 0 -3 -2 3 2 -5 0 -1 0 -1 -2 -1 -4 0 -1 -1
0 1 -1 -1 0 0 -1 0 1 1 1 0 1 0 1 -1 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 0 0 0
0 1 -1 -1 0 0 -3 -1 3 0 2 -1 1 0 1 0 0 -1 0 0 1 0 -1 0 1 0 0 0 -2 1 -1 -1
-1 0 0 2 0 1 1 -1 0 -3 -1 -1 -1 -1 0 0 0 0 1 -1 0 2 0 -1 0 0 1 1 1 1 0 0
0 -1 0 -3 1 -1 -2 1 0 3 2 2 3 2 2 0 1 -1 -1 2 1 -3 0 0 0 -1 -2 -1 -2 -1 0 -1
-1 0 0 0 -2 0 -1 -1 3 -2 -1 1 -1 0 0 0 2 0 0 1 2 1 -1 1 2 -1 1 1 -2 1 -1 -2
0 0 -1 -1 -1 0 -1 0 2 1 1 1 1 0 1 0 0 -1 0 1 1 -1 -1 0 1 -1 0 0 -1 0 -1 -1
-1 1 0 1 0 0 -2 -1 3 -1 2 -2 -1 -1 0 1 -1 -1 0 -1 2 1 0 0 1 0 1 1 -1 1 -2 -1
0 1 -1 0 2 1 2 1 -2 -2 -3 -1 -1 -1 0 -2 1 2 1 -1 -3 3 -1 1 -1 1 -1 -1 3 -1 2 2
2 0 -1 -2 2 0 -4 0 2 1 3 0 2 1 1 0 0 -2 -1 0 1 -1 0 -1 0 0 0 0 -3 0 -1 -1
1 -1 0 -1 3 0 0 1 -3 2 1 0 2 1 1 0 -1 0 -1 0 -1 -2 1 -1 -2 0 -2 -1 1 -1 1 2
1 -1 -1 -4 -1 -2 -5 1 3 6 7 3 5 3 2 2 -1 -4 -2 3 3 -6 0 -1 1 -1 -2 -1 -5 0 -3 -3
-1 0 0 0 -1 0 -3 -1 3 0 1 1 1 1 1 1 1 -1 -1 1 3 -2 0 0 1 -1 0 1 -2 0 -1 -2
-1 0 0 1 0 0 1 0 0 -2 -1 0 -1 -1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
1 -1 -1 -4 -1 -1 -6 -1 4 4 5 3 5 3 2 1 1 -3 -2 3 4 -5 0 -1 1 -2 -1 0 -5 0 -2 -3
-1 2 -1 1 0 1 0 -1 3 -4 0 -2 -2 -2 0 -1 0 0 2 -2 0 4 -1 0 1 0 2 1 0 1 -1 -1
-2 1 0 3 1 2 5 0 -2 -6 -6 -2 -4 -3 -1 -2 1 3 3 -3 -3 6 -1 1 -1 1 1 1 5 0 2 2
-1 0 0 -1 -1 0 -1 0 2 0 -1 1 0 0 1 0 2 0 0 1 1 0 -1 1 1 -1 0 0 -1 0 0 -1
0 -1 1 1 1 0 2 1 -3 0 -2 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 -1 0 2 -1 1 1
0 -1 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
-1 0 0 1 0 0 1 1 0 -1 -1 0 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0
-1 1 0 2 1 1 4 0 -3 -3 -3 -2 -2 -2 0 -2 0 2 2 -2 -3 4 -1 0 -1 1 0 0 4 0 2 2
0 1 0 0 1 0 -1 0 1 -1 0 -1 0 -1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 1 2 0 -1 -2 -3 0 -1 -1 0 -1 1 1 1 0 -1 2 -1 0 0 0 0 0 2 0 1 1
-1 0 0 0 1 1 1 0 -1 -2 -3 0 0 0 1 -2 2 1 1 0 -1 2 -1 0 0 0 0 0 1 -1 2 0
-2 2 0 2 0 1 3 -1 0 -4 -4 -2 -3 -2 0 -2 1 3 2 -2 -1 4 -1 1 0 0 1 1 3 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 0 -1 0 1 0 0 0 -1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 2 -2 -1 -2 -1 -2 -1 5 1 4 -1 0 -1 0 1 -2 -1 0 -1 1 0 -1 0 1 0 1 0 -2 2 -3 -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
1 0 0 1 0 0 -1 -1 1 -1 2 -1 0 0 -1 1 -1 -1 0 -1 1 0 1 -1 0 0 1 1 -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 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 -1 1 0 0 2 1 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 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0
1 1 -1 -2 0 0 -1 0 1 1 1 0 1 0 1 -1 1 0 0 0 -1 0 -1 0 0 0 0 -1 -1 0 0 0
2 -2 0 -2 0 -1 -3 0 1 3 3 2 3 2 0 2 0 -2 -2 2 2 -4 1 -1 0 -1 -1 0 -3 0 -1 -1
0 1 0 -1 0 0 -3 -1 3 0 1 0 1 1 1 0 1 -1 0 0 2 -1 0 0 1 -1 1 1 -3 0 -1 -2
1 1 -1 -1 -1 0 -2 -1 3 0 2 0 0 0 0 0 0 -1 0 0 1 0 -1 0 1 0 1 0 -2 1 -1 -1
2 0 -2 -3 -2 -1 -4 -1 4 3 4 2 3 1 1 1 0 -2 -1 2 2 -3 -1 0 1 -1 0 0 -4 1 -2 -2
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 0 1 0 0 -1 -1 1 -1 -1 -1 0 1 0 0 0 0 1 0 0 0 0 1 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 -1 1 2 0 0 2 0 -1 -2 -2 0 -2 -1 -1 1 0 0 0 0 0 1 1 0 0 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
1 0 0 -2 0 -1 -2 0 1 3 2 1 2 1 1 1 0 -1 -1 1 1 -3 0 0 0 -1 0 0 -2 -1 -1 -1
0 1 0 1 0 0 2 0 0 -1 -1 -1 -2 -1 -1 0 -1 1 1 -1 -1 1 0 0 0 0 1 0 1 0 0 1
-1 1 0 1 -1 0 -1 -1 3 -1 0 -1 -1 0 0 1 0 0 0 0 2 0 0 0 1 -1 1 1 -1 0 -1 -1
2 -1 0 -1 0 -1 -1 0 -1 3 2 1 2 1 0 1 -1 -1 -1 1 0 -3 1 -1 -1 0 -1 -1 -1 0 0 1
1 -2 0 0 0 0 1 0 -1 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 -1 0 0 0 0 0 1 0 0
1 -1 0 -1 -1 -1 -3 -1 3 1 3 1 1 1 0 2 0 -2 -1 1 3 -2 1 -1 1 -1 1 1 -4 1 -2 -2
0 0 1 1 0 -1 -1 0 0 2 3 -1 1 1 0 2 -2 -2 -1 0 1 -2 1 -1 0 0 0 0 -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 -1 0 0 0
0 0 0 1 -2 0 0 -1 2 -1 0 0 -1 0 -1 1 0 0 0 0 1 0 0 0 1 0 1 1 -1 1 -1 -1
0 0 0 0 -1 -1 1 0 0 1 1 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
1 0 0 -1 0 -1 -5 -1 3 3 5 0 3 2 1 2 -1 -3 -2 1 3 -4 1 -1 1 -1 0 0 -4 0 -2 -2
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 -1 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 -1 -1 0 0 1 1 1 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0
0 1 0 0 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 1 -1 0 1 0 0 0 0 1 0 0 0 0 0
0 -1 1 -1 -2 -1 -1 0 1 1 -1 2 0 1 0 1 2 0 -1 2 2 -2 0 1 1 -1 0 0 -2 0 0 -1
0 0 0 1 0 0 2 0 -2 0 -2 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 0 0 2 -1 1 1
1 -1 0 -3 -1 -1 -4 0 2 4 3 2 3 3 1 1 1 -2 -2 3 3 -4 0 0 1 -1 -1 -1 -4 0 -1 -2
-2 2 1 4 3 2 7 1 -5 -6 -8 -3 -5 -3 -1 -3 1 5 3 -4 -5 6 0 1 -2 1 1 0 7 -2 4 4
-1 1 1 2 -1 0 3 0 -1 -2 -3 -1 -3 -1 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 0 2 0 1 1
-2 1 1 3 -1 1 4 -1 -1 -5 -6 -1 -4 -2 -1 -1 2 3 2 -2 -1 4 0 1 0 0 2 1 3 0 2 1
0 0 0 0 -1 -1 0 0 1 1 1 0 0 0 0 1 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 -1 0
0 0 1 0 -1 -1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
-2 1 1 2 1 1 4 1 -3 -2 -5 -1 -3 -1 0 -1 1 3 1 -1 -2 2 0 1 -1 0 0 0 4 -2 2 2
0 1 0 0 0 0 0 0 1 0 1 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 -2 0 -1 -1 0 0 3 1 1 2 1 1 0 0 0 0 1 0 -2 0 0 0 -1 -1 -1 -1 -1 0 0
0 -2 1 -1 -1 -1 0 1 -2 4 -1 3 2 2 1 1 1 0 -2 3 1 -4 0 1 0 -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 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 1 0 0 5 1 -4 -1 -5 1 -2 -1 0 -1 1 3 1 0 -2 1 0 1 -1 0 0 0 4 -2 2 2
0 1 0 1 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0
-1 1 1 2 -1 0 3 0 0 -2 -3 -1 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 0 2 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 0 0 0 0 0 0 0 0 0 0
-2 1 1 2 -1 0 3 0 -1 -1 -3 -1 -2 -1 0 0 0 2 1 -1 -1 1 0 1 0 0 0 0 3 -1 1 1
-2 0 2 4 1 1 6 0 -4 -4 -6 -2 -4 -2 -1 -1 0 3 2 -2 -2 4 1 0 -1 0 1 1 5 -1 2 2
-1 1 0 1 -1 0 -1 -1 3 -1 0 -1 -1 0 0 1 0 0 0 0 2 0 0 0 1 -1 1 1 -1 0 -1 -1
0 -1 1 0 1 0 2 1 -3 -1 -4 1 -1 0 0 -1 2 2 0 0 -1 1 0 1 -1 0 -1 0 2 -1 2 1
0 -1 1 -1 -2 -1 -1 0 1 2 1 2 1 1 0 1 1 -1 -1 2 2 -2 0 0 1 -1 0 0 -2 0 -1 -2
-2 1 1 3 0 1 5 0 -2 -4 -6 -1 -4 -2 -1 -1 1 4 2 -2 -2 3 0 1 -1 0 1 1 4 -1 2 2
-2 2 1 3 0 1 3 -1 0 -5 -5 -2 -4 -2 -1 -1 1 3 2 -3 -1 4 0 1 0 0 2 1 3 0 1 1
-1 1 1 4 0 1 6 0 -3 -5 -6 -2 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 1 1 5 0 2 3
-1 1 1 2 1 1 5 0 -3 -4 -7 -1 -4 -2 -1 -2 2 4 2 -2 -3 4 0 1 -1 0 1 0 4 -1 3 3
-1 0 1 2 -1 0 3 0 -1 -2 -4 0 -3 -1 -1 0 1 2 1 -1 -1 2 0 1 0 0 1 0 2 0 1 1
-1 2 0 1 1 0 1 0 0 -1 0 -2 -1 -1 0 0 -1 1 1 -2 -1 1 0 0 -1 0 0 0 2 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^2916*6 x^2900*12 x^2880*6 x^2425*12 x^2415*12 x^2408*6 x^2407*6 x^2405*12 x^2401*24 x^2400*24 x^2399*12 x^2398*12 x^2397*16 x^2396*18 x^2395*36 x^2394*22 x^2393*12 x^2392*24 x^2391*38 x^2390*6 x^2389*12 x^2388*30 x^2387*6 x^2385*36
x^2384*12 x^2383*24 x^2382*24 x^2381*36 x^2380*48 x^2379*24 x^2378*24 x^2377*24 x^2376*12 x^2375*24 x^2374*12 x^2373*24 x^2372*24 x^2371*24 x^2370*36 x^2369*54 x^2368*30 x^2367*42 x^2366*12 x^2364*60 x^2362*36 x^2361*6 x^2360*12
x^2359*36 x^2358*36 x^2357*12 x^2356*12 x^2354*12 x^2353*12 x^2352*24 x^2351*12 x^2350*24 x^2349*40 x^2348*12 x^2347*12 x^2346*52 x^2344*12 x^2343*12 x^2342*6 x^2341*60 x^2340*12 x^2337*12 x^2336*24 x^2328*12 x^2324*12 x^2319*18 x^2313*2 x^2292*18 (2448x)
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^2985*6 x^2895*12 x^2787*6 x^2441*6 x^2419*12 x^2417*12 x^2413*12 x^2412*12 x^2411*12 x^2408*60 x^2404*12 x^2403*24 x^2402*12 x^2398*12 x^2396*12 x^2395*6 x^2394*26 x^2393*24 x^2392*30 x^2391*36 x^2390*24 x^2389*12 x^2388*24 x^2387*36
x^2386*24 x^2385*12 x^2383*12 x^2382*24 x^2381*72 x^2380*36 x^2379*12 x^2378*48 x^2377*48 x^2376*16 x^2375*48 x^2374*30 x^2373*36 x^2372*24 x^2371*24 x^2370*36 x^2369*24 x^2368*48 x^2367*36 x^2366*24 x^2362*6 x^2360*24 x^2359*12
x^2358*42 x^2357*24 x^2356*36 x^2355*12 x^2354*36 x^2352*36 x^2349*30 x^2347*12 x^2346*4 x^2345*12 x^2344*12 x^2343*16 x^2341*12 x^2340*12 x^2337*6 x^2335*18 x^2324*36 x^2323*6 x^2322*12 x^2321*12 x^2293*12 x^2286*4 x^2178*2 (2448x)
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 -1 -1
x^2960*2 x^2956*2 x^2942*4 x^2928*2 x^2927*2 x^2920*2 x^2910*2 x^2901*2 x^2900*2 x^2888*2 x^2854*2 x^2435*4 x^2428*2 x^2425*4 x^2422*8 x^2420*4 x^2419*2 x^2417*4 x^2415*6 x^2414*2 x^2413*4 x^2412*8 x^2411*6 x^2410*8 x^2409*6 x^2408*8
x^2407*4 x^2406*6 x^2405*16 x^2404*4 x^2403*10 x^2402*4 x^2401*18 x^2400*18 x^2399*10 x^2398*14 x^2397*18 x^2396*10 x^2395*14 x^2394*16 x^2393*16 x^2392*18 x^2391*16 x^2390*20 x^2389*22 x^2388*20 x^2387*26 x^2386*14 x^2385*10 x^2384*30
x^2383*26 x^2382*20 x^2381*34 x^2380*36 x^2379*10 x^2378*38 x^2377*30 x^2376*16 x^2375*26 x^2374*16 x^2373*28 x^2372*24 x^2371*38 x^2370*36 x^2369*24 x^2368*12 x^2367*38 x^2366*12 x^2365*22 x^2364*24 x^2363*14 x^2362*12 x^2361*20
x^2360*24 x^2359*22 x^2358*24 x^2357*20 x^2356*36 x^2355*14 x^2354*38 x^2353*24 x^2352*22 x^2351*22 x^2350*28 x^2349*6 x^2348*20 x^2347*18 x^2346*18 x^2345*12 x^2344*14 x^2343*16 x^2341*12 x^2340*12 x^2339*6 x^2338*10 x^2337*6 x^2336*2
x^2335*10 x^2334*4 x^2332*2 x^2331*8 x^2330*4 x^2328*4 x^2324*10 x^2322*4 x^2321*4 x^2320*6 x^2317*2 x^2315*2 x^2314*2 x^2311*2 x^2310*6 x^2308*8 x^2306*2 x^2305*2 x^2293*2 (14688x)
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 1 0 0 -1 -1
x^2979*2 x^2928*4 x^2927*4 x^2910*4 x^2905*2 x^2900*4 x^2884*4 x^2441*4 x^2431*4 x^2424*4 x^2421*4 x^2419*8 x^2417*4 x^2415*16 x^2414*4 x^2411*4 x^2410*4 x^2409*4 x^2408*16 x^2406*8 x^2405*20 x^2404*10 x^2403*12 x^2401*14 x^2400*12
x^2399*20 x^2398*20 x^2397*4 x^2396*8 x^2395*8 x^2394*18 x^2393*16 x^2392*12 x^2391*8 x^2390*12 x^2389*24 x^2388*28 x^2387*24 x^2386*24 x^2385*24 x^2384*28 x^2383*10 x^2382*20 x^2381*40 x^2380*20 x^2379*4 x^2378*28 x^2377*20 x^2376*16
x^2375*18 x^2374*8 x^2373*20 x^2372*24 x^2371*16 x^2370*26 x^2369*12 x^2368*42 x^2367*18 x^2366*20 x^2365*28 x^2364*40 x^2363*20 x^2362*56 x^2361*30 x^2360*40 x^2359*24 x^2358*16 x^2357*24 x^2356*20 x^2355*32 x^2354*40 x^2353*20
x^2352*20 x^2351*12 x^2350*16 x^2349*16 x^2348*16 x^2347*36 x^2346*10 x^2345*16 x^2344*16 x^2343*28 x^2342*8 x^2341*18 x^2340*12 x^2339*2 x^2338*8 x^2336*4 x^2335*8 x^2334*10 x^2332*4 x^2331*8 x^2330*8 x^2326*4 x^2324*8 x^2322*4 x^2320*8 x^2316*8 x^2313*4 x^2297*2 (7344x)
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 0 0 0 1 0 0 -1 -1
x^2985*4 x^2956*8 x^2940*2 x^2918*2 x^2911*4 x^2901*4 x^2474*2 x^2441*4 x^2439*4 x^2437*4 x^2424*4 x^2422*4 x^2417*4 x^2415*4 x^2414*16 x^2413*4 x^2410*8 x^2409*4 x^2408*4 x^2407*8 x^2406*4 x^2405*20 x^2404*4 x^2403*8 x^2402*14
x^2401*12 x^2400*8 x^2399*4 x^2398*28 x^2397*16 x^2396*18 x^2395*12 x^2394*10 x^2393*8 x^2392*8 x^2391*14 x^2390*20 x^2389*16 x^2388*16 x^2387*24 x^2386*20 x^2385*16 x^2384*22 x^2383*24 x^2382*20 x^2381*36 x^2380*8 x^2379*8 x^2378*44
x^2377*28 x^2376*16 x^2375*28 x^2374*40 x^2373*20 x^2372*32 x^2371*24 x^2370*60 x^2369*16 x^2368*24 x^2367*24 x^2366*28 x^2365*16 x^2364*16 x^2363*16 x^2362*32 x^2361*34 x^2360*24 x^2359*36 x^2358*16 x^2357*20 x^2356*8 x^2355*16
x^2354*32 x^2353*20 x^2352*24 x^2351*16 x^2350*24 x^2349*24 x^2348*16 x^2347*24 x^2346*4 x^2345*4 x^2344*12 x^2343*18 x^2342*8 x^2341*8 x^2340*20 x^2339*8 x^2338*12 x^2337*4 x^2336*8 x^2335*14 x^2333*4 x^2332*4 x^2331*4 x^2330*8 x^2329*4 x^2328*6 x^2324*8 x^2323*8 x^2322*6 x^2321*2 x^2320*4 x^2317*4 x^2315*4 x^2313*4 x^2311*2 x^2310*4 x^2308*4 x^2298*6 (7344x)
1 32
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
x^2979*4 x^2928*4 x^2919*4 x^2911*4 x^2910*2 x^2901*4 x^2854*2 x^2474*4 x^2439*8 x^2428*6 x^2425*4 x^2423*4 x^2422*8 x^2418*4 x^2417*4 x^2414*8 x^2413*4 x^2411*2 x^2410*12 x^2409*8 x^2408*8 x^2407*12 x^2406*12 x^2405*4 x^2404*8
x^2403*26 x^2401*12 x^2400*12 x^2399*8 x^2397*12 x^2396*18 x^2395*12 x^2394*4 x^2393*20 x^2392*12 x^2391*20 x^2390*26 x^2389*8 x^2388*12 x^2387*18 x^2386*8 x^2385*36 x^2384*34 x^2383*28 x^2382*22 x^2381*12 x^2380*36 x^2379*20
x^2378*24 x^2377*32 x^2376*28 x^2375*40 x^2374*16 x^2373*12 x^2371*32 x^2370*32 x^2369*12 x^2368*16 x^2367*32 x^2366*8 x^2365*16 x^2364*28 x^2363*24 x^2362*44 x^2361*24 x^2360*34 x^2359*12 x^2358*24 x^2357*40 x^2356*56 x^2355*20
x^2354*38 x^2353*20 x^2352*24 x^2351*20 x^2350*16 x^2349*8 x^2348*24 x^2347*16 x^2346*16 x^2345*16 x^2344*8 x^2343*12 x^2342*12 x^2341*8 x^2340*4 x^2339*12 x^2338*22 x^2337*8 x^2336*4 x^2335*8 x^2333*4 x^2329*8 x^2328*8 x^2326*8 x^2324*4 x^2323*2 x^2318*4 x^2315*4 x^2312*4 x^2311*4 x^2308*4 x^2291*2 x^2289*2 (7344x)
1 32
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
x^4266*2 x^4230*2 x^4179*4 x^2449*6 x^2442*18 x^2432*6 x^2423*12 x^2418*24 x^2416*6 x^2409*36 x^2408*30 x^2406*36 x^2404*6 x^2402*12 x^2400*18 x^2399*36 x^2398*12 x^2394*24 x^2393*24 x^2391*12 x^2390*24 x^2387*60 x^2386*24 x^2385*24
x^2384*30 x^2383*12 x^2382*24 x^2381*12 x^2380*36 x^2379*12 x^2377*18 x^2376*12 x^2375*24 x^2374*12 x^2373*6 x^2372*24 x^2371*30 x^2370*60 x^2369*48 x^2367*36 x^2366*36 x^2365*12 x^2364*12 x^2363*24 x^2362*12 x^2361*12 x^2360*24
x^2359*36 x^2358*60 x^2357*48 x^2355*12 x^2354*54 x^2353*12 x^2351*12 x^2350*12 x^2349*12 x^2348*54 x^2347*6 x^2346*12 x^2345*12 x^2344*6 x^2343*12 x^2341*24 x^2340*12 x^2338*24 x^2337*30 x^2335*12 x^2321*24 x^2320*12 x^2318*12 x^2312*12 x^2306*12 (2448x)
1 32
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 -1 -1
x^2960*4 x^2939*4 x^2937*4 x^2931*4 x^2920*2 x^2918*4 x^2876*2 x^2470*4 x^2445*2 x^2431*4 x^2430*12 x^2427*4 x^2424*4 x^2422*8 x^2421*8 x^2420*4 x^2418*4 x^2417*4 x^2416*4 x^2411*4 x^2410*2 x^2409*4 x^2408*26 x^2407*4 x^2406*12
x^2405*12 x^2404*8 x^2403*8 x^2402*8 x^2400*8 x^2399*4 x^2398*12 x^2397*16 x^2396*4 x^2395*20 x^2394*20 x^2393*12 x^2392*24 x^2391*12 x^2390*16 x^2389*24 x^2388*30 x^2387*12 x^2386*24 x^2385*20 x^2384*44 x^2383*20 x^2382*36 x^2381*26
x^2380*22 x^2379*24 x^2378*42 x^2377*28 x^2376*20 x^2375*24 x^2374*12 x^2373*44 x^2372*8 x^2371*16 x^2370*22 x^2369*32 x^2368*32 x^2367*8 x^2366*16 x^2365*44 x^2364*8 x^2363*12 x^2362*36 x^2361*30 x^2360*12 x^2359*28 x^2358*20
x^2357*20 x^2356*12 x^2355*24 x^2354*16 x^2353*24 x^2352*38 x^2351*12 x^2350*28 x^2349*28 x^2348*8 x^2347*8 x^2346*8 x^2345*12 x^2344*4 x^2343*16 x^2342*8 x^2341*20 x^2340*24 x^2339*16 x^2337*4 x^2335*4 x^2333*14 x^2332*8 x^2331*4 x^2328*12 x^2327*2 x^2326*12 x^2323*6 x^2321*4 x^2320*8 x^2316*2 x^2314*4 x^2308*4 x^2307*4 x^2295*4 (7344x)
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 0 -1 0 0 0 0 0
x^4284*4 x^4161*4 x^2478*2 x^2443*6 x^2434*12 x^2425*24 x^2423*12 x^2421*6 x^2420*24 x^2419*12 x^2418*12 x^2414*6 x^2409*6 x^2408*12 x^2404*12 x^2401*12 x^2400*12 x^2399*24 x^2398*12 x^2397*2 x^2395*12 x^2393*6 x^2391*12 x^2390*48 x^2388*12 x^2387*24 x^2385*24 x^2384*48 x^2383*6 x^2382*18 x^2381*48 x^2380*12 x^2379*24 x^2378*12 x^2377*24 x^2376*16 x^2375*12 x^2374*12 x^2373*24 x^2372*36 x^2371*24 x^2370*48 x^2369*24 x^2368*24 x^2367*24 x^2366*48 x^2364*12 x^2363*54 x^2362*36 x^2361*42 x^2359*36 x^2358*24 x^2357*30 x^2356*24 x^2355*12 x^2354*48 x^2353*24 x^2350*12 x^2349*16 x^2348*48 x^2347*24 x^2346*4 x^2343*48 x^2341*48 x^2340*6 x^2338*12 x^2337*30 x^2335*12 x^2334*12 x^2333*12 x^2331*24 x^2329*12 x^2324*12 x^2308*6 x^2286*2 (2448x)
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 0 0 1 0 0 -1 -1
x^2972*4 x^2942*4 x^2937*4 x^2928*4 x^2927*4 x^2924*4 x^2470*4 x^2446*4 x^2437*2 x^2434*4 x^2433*4 x^2431*4 x^2428*4 x^2422*4 x^2421*4 x^2419*4 x^2417*12 x^2416*8 x^2414*4 x^2411*16 x^2410*12 x^2409*8 x^2408*8 x^2405*16 x^2404*12 x^2403*20 x^2402*16 x^2401*8 x^2400*16 x^2399*4
x^2398*4 x^2397*20 x^2396*12 x^2395*32 x^2394*12 x^2393*12 x^2392*22 x^2391*16 x^2390*20 x^2389*8 x^2388*26 x^2387*24 x^2386*32 x^2385*12 x^2384*22 x^2383*30 x^2382*20 x^2381*36 x^2380*32 x^2379*16 x^2378*4 x^2377*32 x^2376*40 x^2375*24 x^2374*8 x^2373*22 x^2372*10 x^2371*24 x^2370*12 x^2369*30
x^2368*12 x^2367*28 x^2366*20 x^2365*32 x^2364*44 x^2363*12 x^2362*24 x^2361*24 x^2360*24 x^2359*40 x^2358*8 x^2357*24 x^2356*20 x^2355*24 x^2354*24 x^2353*8 x^2352*24 x^2351*4 x^2350*14 x^2349*24 x^2348*14 x^2347*36 x^2346*16 x^2345*10 x^2343*12 x^2342*4 x^2341*8 x^2340*14 x^2339*8 x^2338*4
x^2337*12 x^2336*6 x^2335*4 x^2334*4 x^2333*20 x^2332*4 x^2331*4 x^2330*4 x^2328*14 x^2326*4 x^2324*4 x^2322*4 x^2321*4 x^2320*4 x^2317*12 x^2316*2 x^2313*4 x^2308*8 x^2307*4 x^2265*2 (7344x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0
x^2956*4 x^2940*2 x^2930*2 x^2924*2 x^2919*2 x^2918*4 x^2910*2 x^2905*2 x^2895*4 x^2470*2 x^2442*2 x^2441*2 x^2434*2 x^2433*2 x^2428*4 x^2427*2 x^2424*2 x^2423*2 x^2422*2 x^2421*2 x^2420*4 x^2419*6 x^2418*2 x^2417*2 x^2416*2 x^2415*6 x^2414*4 x^2413*4 x^2412*6 x^2411*8 x^2410*6 x^2409*6 x^2408*10 x^2407*2
x^2406*6 x^2405*8 x^2404*6 x^2403*16 x^2402*14 x^2401*2 x^2400*4 x^2399*10 x^2398*16 x^2397*8 x^2396*12 x^2395*12 x^2394*10 x^2393*22 x^2392*22 x^2391*22 x^2390*8 x^2389*16 x^2388*20 x^2387*28 x^2386*20 x^2385*28 x^2384*18 x^2383*22
x^2382*18 x^2381*40 x^2380*30 x^2379*12 x^2378*24 x^2377*26 x^2376*28 x^2375*18 x^2374*16 x^2373*16 x^2372*38 x^2371*22 x^2370*44 x^2369*18 x^2368*20 x^2367*30 x^2366*22 x^2365*18 x^2364*18 x^2363*36 x^2362*30 x^2361*18 x^2360*18 x^2359*32 x^2358*14 x^2357*28 x^2356*24 x^2355*16 x^2354*20 x^2353*12
x^2352*34 x^2351*18 x^2350*24 x^2349*10 x^2348*24 x^2347*16 x^2346*14 x^2345*20 x^2344*4 x^2343*20 x^2342*16 x^2341*12 x^2340*10 x^2339*6 x^2338*10 x^2337*4 x^2336*12 x^2335*6 x^2334*6 x^2333*12 x^2332*10 x^2331*10 x^2329*2 x^2328*4 x^2327*2 x^2326*2 x^2325*4 x^2324*6 x^2323*2 x^2322*4 x^2321*4 x^2320*2 x^2319*4 x^2317*2 x^2310*2 x^2308*2 x^2306*2 x^2305*4 x^2297*2 (14688x)
1 32
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 1 -1 0
x^2990*2 x^2960*2 x^2927*8 x^2924*4 x^2920*4 x^2910*4 x^2453*2 x^2425*4 x^2424*4 x^2420*4 x^2417*8 x^2416*10 x^2415*4 x^2411*12 x^2410*16 x^2409*10 x^2408*16 x^2407*4 x^2406*8 x^2405*12 x^2404*12 x^2403*20 x^2402*8 x^2401*4 x^2400*16 x^2399*12 x^2398*24 x^2397*20 x^2396*20 x^2395*12
x^2394*8 x^2393*14 x^2392*28 x^2391*16 x^2390*14 x^2389*26 x^2388*20 x^2387*24 x^2386*20 x^2385*10 x^2384*24 x^2383*24 x^2382*16 x^2381*32 x^2380*32 x^2379*22 x^2378*30 x^2377*48 x^2376*28 x^2375*32 x^2374*16 x^2373*34 x^2372*12 x^2371*10 x^2370*34 x^2369*24 x^2368*38 x^2367*34 x^2366*24 x^2365*28
x^2364*28 x^2363*16 x^2362*20 x^2361*16 x^2360*24 x^2359*34 x^2358*32 x^2357*16 x^2356*36 x^2355*20 x^2354*20 x^2353*4 x^2352*28 x^2351*4 x^2350*16 x^2349*12 x^2348*8 x^2347*16 x^2346*8 x^2345*16 x^2344*8 x^2343*24 x^2342*10 x^2341*12 x^2339*4 x^2337*8 x^2336*8 x^2335*8 x^2333*12 x^2332*4
x^2328*4 x^2327*4 x^2325*4 x^2324*4 x^2321*4 x^2320*8 x^2317*4 x^2314*4 x^2308*4 (7344x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0
x^4326*2 x^4212*2 x^4161*4 x^2442*12 x^2434*18 x^2433*12 x^2428*12 x^2419*6 x^2417*12 x^2415*12 x^2414*24 x^2412*12 x^2409*12 x^2406*12 x^2405*12 x^2404*12 x^2403*12 x^2402*18 x^2399*12 x^2398*12 x^2397*6 x^2394*18 x^2393*12 x^2392*12 x^2390*30 x^2388*30 x^2387*24 x^2386*24 x^2385*12 x^2384*12
x^2383*36 x^2381*48 x^2380*12 x^2378*36 x^2377*24 x^2376*24 x^2375*48 x^2374*24 x^2373*48 x^2372*48 x^2371*12 x^2370*36 x^2369*36 x^2368*12 x^2367*60 x^2366*36 x^2365*6 x^2364*6 x^2363*12 x^2362*24 x^2360*12 x^2359*48 x^2357*36 x^2356*18 x^2355*42 x^2354*36 x^2351*24 x^2350*12 x^2348*48 x^2347*36
x^2345*12 x^2343*24 x^2341*24 x^2340*12 x^2339*24 x^2334*12 x^2333*12 x^2327*12 x^2326*18 x^2325*6 x^2324*24 x^2322*6 x^2316*12 x^2310*6 x^2289*6 (2448x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 1 0 0 -1 -1
x^2936*8 x^2925*4 x^2920*4 x^2888*2 x^2884*2 x^2876*4 x^2435*4 x^2431*4 x^2430*4 x^2425*8 x^2420*12 x^2419*4 x^2417*10 x^2416*4 x^2414*8 x^2413*8 x^2412*4 x^2411*8 x^2410*4 x^2409*4 x^2408*12 x^2406*16 x^2405*4 x^2404*8 x^2403*12 x^2402*12 x^2401*4 x^2400*12 x^2399*12 x^2398*20
x^2397*4 x^2396*14 x^2395*10 x^2394*20 x^2393*12 x^2392*12 x^2391*26 x^2390*20 x^2389*6 x^2388*20 x^2387*32 x^2386*12 x^2385*20 x^2384*40 x^2383*44 x^2382*20 x^2381*24 x^2380*22 x^2379*10 x^2378*16 x^2377*20 x^2376*46 x^2375*28 x^2374*24 x^2373*32 x^2372*12 x^2371*20 x^2370*34 x^2369*8 x^2368*12
x^2367*44 x^2366*20 x^2365*36 x^2364*26 x^2363*36 x^2362*4 x^2361*8 x^2360*20 x^2359*8 x^2358*16 x^2357*16 x^2356*16 x^2355*22 x^2354*24 x^2353*24 x^2352*20 x^2351*34 x^2350*20 x^2349*8 x^2348*16 x^2347*10 x^2346*8 x^2345*24 x^2344*8 x^2343*20 x^2342*14 x^2341*4 x^2340*16 x^2338*16 x^2337*16
x^2336*12 x^2335*4 x^2334*8 x^2333*12 x^2332*12 x^2331*18 x^2330*4 x^2329*4 x^2328*4 x^2325*4 x^2322*4 x^2321*4 x^2320*4 x^2316*4 x^2315*12 x^2314*4 x^2307*4 x^2301*2 x^2296*4 (7344x)
1 32
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 1 0 0 -1 -1
x^2990*6 x^2960*2 x^2956*4 x^2928*4 x^2919*4 x^2911*4 x^2457*2 x^2453*4 x^2449*4 x^2445*8 x^2443*4 x^2442*4 x^2439*4 x^2437*2 x^2434*8 x^2424*4 x^2423*4 x^2420*12 x^2419*4 x^2418*8
x^2416*4 x^2415*4 x^2414*4 x^2413*8 x^2411*4 x^2409*12 x^2408*6 x^2407*12 x^2406*4 x^2405*12 x^2404*4 x^2403*16 x^2402*16 x^2401*16 x^2400*22 x^2399*16 x^2398*36 x^2397*12 x^2396*4 x^2395*6 x^2394*12 x^2393*24 x^2392*32 x^2391*32 x^2389*24 x^2388*16 x^2387*46 x^2386*12 x^2385*12 x^2384*24
x^2383*14 x^2382*16 x^2381*24 x^2380*32 x^2379*4 x^2378*12 x^2377*28 x^2376*20 x^2375*30 x^2374*32 x^2373*28 x^2372*40 x^2371*28 x^2370*40 x^2369*28 x^2368*16 x^2367*16 x^2366*12 x^2365*32 x^2364*24 x^2363*8 x^2362*20 x^2361*6 x^2360*28 x^2359*30 x^2358*18 x^2357*12 x^2356*16 x^2355*32 x^2354*10
x^2353*16 x^2352*8 x^2351*20 x^2350*12 x^2349*12 x^2348*4 x^2347*12 x^2346*18 x^2345*12 x^2344*16 x^2343*20 x^2341*4 x^2340*16 x^2339*24 x^2338*20 x^2337*8 x^2335*12 x^2334*8 x^2333*4 x^2332*8 x^2331*4 x^2330*12 x^2324*10 x^2320*4 x^2319*4 x^2317*6 x^2315*6 x^2314*4 x^2311*4 x^2308*4 x^2293*4 (7344x)
1 32
0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^2972*6 x^2931*12 x^2910*6 x^2478*4 x^2446*6 x^2433*12 x^2431*12 x^2427*18 x^2420*18 x^2416*6 x^2415*6 x^2414*12 x^2413*12 x^2412*6 x^2411*18 x^2410*12 x^2407*12 x^2406*12 x^2405*12 x^2402*12 x^2400*24 x^2399*24 x^2398*36 x^2396*12 x^2395*12 x^2394*12 x^2393*36 x^2392*12 x^2391*4 x^2390*12 x^2388*24 x^2386*24 x^2385*12 x^2384*12 x^2383*42 x^2382*24 x^2381*24 x^2380*12 x^2379*12 x^2378*72 x^2377*48 x^2376*16 x^2375*24 x^2374*12 x^2373*12 x^2371*12 x^2369*24 x^2368*12 x^2367*72 x^2366*24 x^2365*12 x^2364*12 x^2363*42 x^2362*36 x^2361*12 x^2360*12 x^2359*12 x^2358*12 x^2357*36 x^2356*24 x^2355*48 x^2353*36 x^2352*30 x^2351*36 x^2349*16 x^2348*12 x^2347*18 x^2344*12 x^2343*8 x^2342*24 x^2340*50 x^2339*12 x^2338*12 x^2336*18 x^2335*12 x^2334*12 x^2331*12 x^2321*12 x^2317*12 x^2308*6 (2448x)
1 32
0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 0 -1 0 0
x^2990*2 x^2937*2 x^2931*2 x^2930*4 x^2927*6 x^2925*2 x^2920*2 x^2918*2 x^2880*2 x^2457*2 x^2441*2 x^2439*2 x^2434*2 x^2432*2 x^2425*2 x^2424*2 x^2423*4 x^2422*6 x^2421*2 x^2418*2 x^2417*6 x^2416*2 x^2415*2 x^2414*4 x^2413*6 x^2411*6
x^2410*14 x^2409*10 x^2408*14 x^2407*2 x^2406*10 x^2405*10 x^2404*6 x^2403*10 x^2402*10 x^2400*14 x^2399*8 x^2398*26 x^2397*20 x^2396*16 x^2395*10 x^2394*12 x^2393*6 x^2392*12 x^2391*28 x^2390*12 x^2389*22 x^2388*18 x^2387*20 x^2386*24
x^2385*22 x^2384*26 x^2383*32 x^2382*36 x^2381*36 x^2380*32 x^2379*20 x^2378*20 x^2377*24 x^2376*26 x^2375*16 x^2374*8 x^2373*32 x^2372*20 x^2371*24 x^2370*26 x^2369*30 x^2368*22 x^2367*32 x^2366*16 x^2365*20 x^2364*18 x^2363*16 x^2362*24 x^2361*26 x^2360*28 x^2359*34 x^2358*22 x^2357*20 x^2356*22 x^2355*14 x^2354*20 x^2353*24 x^2352*22 x^2351*18 x^2350*26 x^2349*20 x^2348*18 x^2347*12 x^2346*10 x^2345*16 x^2343*16 x^2342*16 x^2341*4 x^2340*12 x^2339*18 x^2338*12 x^2337*8 x^2336*4 x^2335*4 x^2334*4 x^2333*10 x^2332*6 x^2331*4 x^2330*10 x^2328*8 x^2327*4 x^2325*2 x^2324*8 x^2322*2 x^2321*10 x^2317*2 x^2316*4 x^2314*2 x^2313*2 x^2311*2 x^2308*2 x^2291*2 (14688x)
1 32
0 0 0 0 0 0 0 0 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 -1 0
x^2939*2 x^2936*4 x^2927*4 x^2925*4 x^2916*4 x^2910*4 x^2871*2 x^2439*4 x^2433*8 x^2425*8 x^2424*8 x^2423*8 x^2422*4 x^2419*4 x^2417*8 x^2415*8 x^2414*4 x^2412*12 x^2411*4 x^2410*8 x^2409*4 x^2408*8 x^2407*4 x^2406*14 x^2405*8 x^2404*8 x^2403*10 x^2402*4 x^2401*4 x^2400*8 x^2399*16 x^2398*20 x^2397*28
x^2396*10 x^2395*20 x^2394*8 x^2393*20 x^2392*14 x^2391*46 x^2390*16 x^2389*16 x^2387*28 x^2386*18 x^2385*12 x^2384*36 x^2383*52 x^2382*10 x^2381*40 x^2380*28 x^2379*18 x^2378*26 x^2377*32 x^2376*16 x^2375*34 x^2374*8 x^2373*24 x^2372*12 x^2371*36 x^2370*28 x^2369*24 x^2368*14 x^2367*14 x^2366*40 x^2365*22 x^2364*16 x^2363*20 x^2362*32 x^2361*28 x^2360*20 x^2359*28 x^2358*16 x^2357*16 x^2356*32 x^2355*12 x^2354*18 x^2353*16 x^2352*20 x^2351*20 x^2350*12 x^2349*4 x^2348*28 x^2347*4 x^2346*12 x^2345*28 x^2344*4 x^2343*20 x^2342*2 x^2341*12 x^2340*14 x^2338*8 x^2337*8 x^2336*12 x^2335*8 x^2334*4 x^2333*12 x^2332*4 x^2328*4 x^2325*2 x^2324*8 x^2323*4 x^2321*8 x^2316*16 x^2313*2 x^2312*4 x^2310*4 x^2308*4 x^2296*4 (7344x)
1 32
0 0 0 0 0 0 1 -1 -1 0 -1 1 0 0 0 0 0 1 1 0 0 -1 1 0 -1 -1 0 1 1 -1 0 0
x^4326*2 x^4284*2 x^4161*2 x^4149*2 x^2437*6 x^2431*6 x^2428*6 x^2421*6 x^2420*6 x^2419*6 x^2417*6 x^2415*6 x^2414*12 x^2412*6 x^2411*24 x^2410*18 x^2405*6 x^2404*18 x^2402*6 x^2400*6 x^2399*6 x^2398*18 x^2397*6 x^2395*12 x^2394*30 x^2393*12 x^2392*18 x^2390*6 x^2389*18 x^2388*18 x^2387*12 x^2386*24 x^2385*24 x^2384*12 x^2383*36 x^2382*36 x^2381*30 x^2380*30 x^2379*6 x^2378*6 x^2377*12 x^2376*12 x^2375*36 x^2374*18 x^2373*12 x^2372*48 x^2371*6 x^2370*36 x^2369*42 x^2368*42
x^2367*30 x^2366*12 x^2365*48 x^2364*18 x^2363*30 x^2361*18 x^2360*30 x^2359*24 x^2358*12 x^2357*24 x^2356*24 x^2355*24 x^2354*48 x^2353*6 x^2352*24 x^2351*12 x^2350*30 x^2349*24 x^2348*12 x^2347*30 x^2346*12 x^2345*24 x^2344*18 x^2343*12 x^2342*6 x^2341*12 x^2340*18 x^2339*6 x^2338*6 x^2337*24 x^2336*6 x^2335*6 x^2334*24 x^2333*6 x^2331*6 x^2330*12 x^2328*6 x^2324*6 x^2323*6 x^2322*12 x^2318*6 x^2313*12 x^2310*12 x^2296*6 (4896x)
1 32
0 0 0 0 1 0 -2 0 1 1 2 -1 1 0 0 1 -1 -2 0 0 1 0 0 -1 0 0 0 0 -1 0 -1 -1
x^4179*6 x^4077*2 x^2430*18 x^2412*18 x^2406*18 x^2398*36 x^2393*36 x^2389*18 x^2386*72 x^2385*36 x^2383*108 x^2382*36 x^2381*36 x^2380*36 x^2379*36 x^2378*36 x^2377*54 x^2374*36 x^2373*36 x^2372*36 x^2370*72 x^2369*36 x^2367*36 x^2366*36 x^2365*36 x^2361*18 x^2357*54 x^2356*36 x^2355*108 x^2354*72 x^2353*18 x^2347*18 x^2346*18 x^2345*18 x^2342*54 x^2341*18 x^2334*36 x^2328*18 x^2327*72 x^2326*36 (816x)
-
PROPERTIES
Modular=2
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REFERENCES
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
-
NOTES
Official name is (5+sqrt(17))/2 L_32,2(M_sqrt(17),infty,infty)
This lattice can be seen as a hermitian lattice over a maximal order in
the quaternion algebra over Q[sqrt(17)] ramified only at the infinite places.
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe