The Lattice LAMBDA(C3)
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 13:17:33 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(C3)
-
DIMENSION
32
-
GRAM
32 0
4
0 4
0 0 4
0 0 0 4
0 -2 -2 2 4
2 0 2 2 0 4
2 -2 0 -2 0 0 4
2 2 -2 0 0 0 0 4
0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 -2 2 4
0 0 0 0 0 0 0 0 -2 2 2 4
0 0 0 0 0 0 0 0 -2 2 2 2 4
-1 1 0 2 1 0 -2 0 0 0 1 1 -1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 4
1 -1 0 -2 -1 0 2 0 0 -2 -1 -1 -1 -2 -2 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 4
-1 2 0 0 -1 0 -2 0 0 0 0 0 -1 1 1 -1 1 4
1 0 0 -2 -1 -1 2 0 0 2 1 1 1 -1 1 0 0 -1 4
0 1 1 1 -1 1 -1 0 2 0 -1 -1 0 0 -2 0 -2 -1 0 4
-1 -1 -2 0 2 -2 0 0 -1 1 2 1 1 1 1 -1 2 0 0 -2 4
0 -2 0 -1 1 -1 2 -1 1 -1 -1 0 -1 0 -1 1 0 -1 0 -1 1 4
-1 1 0 0 0 -1 -1 0 1 -1 0 -1 -2 2 0 -1 0 2 -1 -1 1 1 4
1 0 -1 2 2 1 -1 1 0 0 1 1 0 2 0 -1 0 0 -1 0 1 0 1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 2 0 1 -1 1 -1 -1 0 4
-2 -1 1 1 1 0 -1 -2 -2 0 1 1 1 1 1 -1 1 0 -1 -1 1 0 0 0 0 4
1 -1 1 1 0 2 0 -1 -1 1 0 1 1 -1 1 0 1 0 0 0 -1 -1 -2 0 2 0 4
-1 0 -2 0 1 -2 -1 1 1 -1 -1 0 -1 1 -1 0 -1 0 -1 0 1 1 1 1 -2 0 -2 4
1 -1 1 0 0 1 1 -1 1 -1 -1 -1 0 -1 -1 1 -1 -1 0 1 -1 1 0 1 0 -1 1 -1 4
-1 -1 0 1 1 0 0 -1 -1 -1 1 1 -1 2 0 0 0 0 -1 -1 1 1 1 1 -1 2 -1 1 -1 4
0 -2 -1 -1 1 -1 1 -1 1 1 0 0 0 -1 -1 1 0 -1 1 0 1 1 -1 0 1 -1 1 0 1 -1 4
0 1 0 1 0 0 -1 0 1 0 0 -1 0 1 -1 -1 -1 0 0 2 0 -1 0 0 -1 0 -1 0 0 0 0 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^18
-
GROUP_GENERATORS
15
32 32
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0 -1 -1 -1 -1 1 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 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 -1 -1 0 -1 1 -1 -1 0 0 -1 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 0 -1 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 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 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 -1 -1 -1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 -1 1 -1 -1 1 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 0 0 0 0 1 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 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
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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 1 0 0 0 0 0
0 0 0 0 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
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1 -1 -1 -1 0 0 -1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0
2 -1 0 1 0 -1 -1 0 0 0 0 1 1 1 -1 0 -1 1 0 0 1 -1 0 -2 -1 0 -1 -1 1 0 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
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2 0 0 1 0 -2 1 0 0 0 0 1 1 0 -1 -1 -1 1 -1 1 0 -1 1 -1 -1 1 0 -1 0 0 1 -1
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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32 32
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32 32
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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 -1 0 0 0
1 0 -1 0 -1 1 0 -1 1 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 2 1 -1 1 0 1 0 0
0 -1 -1 -1 0 1 -1 -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
1 0 1 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 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 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 -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 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 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -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
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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-6 1 1 0 1 2 1 0 -1 0 1 -1 -2 -2 1 2 2 -2 2 -2 -2 2 0 4 1 -2 2 2 -2 -2 -2 4
2 0 0 1 -1 -1 0 1 0 0 -1 1 1 1 0 -1 -1 1 -1 1 1 -1 0 -2 -1 1 -1 -1 1 1 2 -2
-1 0 0 1 0 0 1 0 -1 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -2 0 0
1 0 0 -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 1 1 0 0
0 1 -1 -1 0 1 -1 -1 0 0 0 0 -1 0 1 0 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 -1 0 0 0 0 -1 0 0 0 1 0 1 0 -1 -1 0 -1 1 1 -1 0 -2 -1 1 -1 -1 1 0 1 -2
0 -1 1 0 0 0 0 1 0 1 0 0 1 0 -1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
-2 1 1 0 1 0 1 0 0 1 0 -1 0 -1 0 1 0 0 0 -1 -1 1 0 2 1 -1 1 1 -1 0 -1 2
0 -1 -1 0 -1 1 -1 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 -1 0 1 -1 0 0 -1 0 1 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
2 0 -1 0 -1 0 -1 0 0 0 0 1 0 1 0 -1 -1 0 -1 1 1 0 0 -2 -1 1 -1 -1 1 0 1 -2
0 0 -1 1 -2 1 0 0 -1 1 -1 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 0 0 0 0 0 0 0 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 0 0 0 0 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 -1 0 0 0 0
-1 0 1 1 0 -1 1 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
-3 0 -1 -1 -1 3 0 0 -1 0 0 -1 -1 -1 0 0 0 -1 1 -1 0 2 0 2 1 -1 1 1 -1 -1 -1 2
3 -1 -1 0 -1 -1 -1 0 0 0 -1 1 1 1 0 -1 -1 1 -1 1 1 -1 0 -2 -1 1 -1 -1 1 1 1 -2
0 0 0 0 0 0 0 0 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 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 1 1 1 0 0 1 -1 0 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 0 -2 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
-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 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 0 0 0 0 0 0
1 1 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 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 -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
1 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 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 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 -1 0 1 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 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 -1 0 0 -1 0 0 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
-1 -1 0 0 0 1 -1 1 1 -1 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 -1 1 -1 1 0 0 1 -1 0 0 1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 -1 0 0 0 1 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 1 0 -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 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0
0 -1 1 0 1 -1 -1 1 0 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 0 0 0 0 0 1 -2 0 0 0 0 1 0 1 0 1 0 0 0 -1 1 0 0 0 0 0 0 0 0
0 2 1 0 1 -1 1 -1 1 -1 0 0 -1 0 1 0 1 0 0 0 0 0 -2 1 0 0 0 0 0 0 0 0
-1 0 1 0 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -2 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
-1 1 1 0 1 1 1 0 -1 1 0 -1 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 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0 0
-1 1 2 0 1 -1 1 0 0 -1 0 -1 -1 0 1 0 1 0 0 0 0 0 -2 2 0 -1 0 0 -1 0 0 0
1 0 0 -1 0 0 -1 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0
-1 1 2 1 1 -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0
2 0 -1 0 -1 0 0 0 0 1 -1 0 2 1 -1 0 -2 1 -1 0 1 0 1 -1 0 1 0 -1 0 1 1 -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^5097*8 x^5040*4 x^5016*2 x^5004*4 x^5001*16 x^4989*8 x^4980*12 x^4977*8 x^4968*24 x^4965*8 x^4956*4 x^4944*44 x^4932*28 x^4929*24 x^4920*10 x^4908*8 x^4905*136 x^4896*88 x^4893*48 x^4884*56 x^4881*56 x^4872*16 x^4860*48 x^4857*104 x^4848*32 x^4845*40 x^4836*28 x^4833*48 x^4824*84 x^4821*64 x^4812*56 x^4809*32 x^4800*24 x^4797*8 x^4788*12 x^4785*16 x^4776*16 x^4773*16 (8192x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
x^5100*4 x^5088*4 x^4992*6 x^4968*64 x^4956*8 x^4944*18 x^4941*32 x^4932*4 x^4929*64 x^4920*8 x^4908*48 x^4896*4 x^4884*16 x^4881*16 x^4872*48 x^4869*112 x^4860*32 x^4848*16 x^4845*144 x^4836*268 x^4833*64 x^4824*64 x^4821*64 x^4812*68 x^4788*16 x^4785*16 x^4773*32 (1024x)
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^5076*4 x^5064*2 x^5004*4 x^4992*8 x^4944*18 x^4932*24 x^4929*56 x^4920*24 x^4908*72 x^4905*40 x^4896*10 x^4881*36 x^4872*24 x^4860*180 x^4857*176 x^4848*8 x^4833*84 x^4824*118 x^4821*24 x^4812*144 x^4809*8 x^4800*64 x^4788*16 x^4785*24 x^4776*16 x^4773*32 x^4761*4 x^4752*8 x^4749*8 x^4737*4 (4096x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
x^5097*32 x^5076*20 x^5064*32 x^5040*4 x^5028*16 x^5016*32 x^5004*176 x^5001*128 x^4977*48 x^4968*80 x^4929*128 x^4905*32 x^4884*128 x^4881*16 x^4836*64 x^4833*8 x^4812*64 x^4785*80 x^4773*128 x^4737*16 x^4665*8 (1024x)
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 0 0
x^5268*8 x^5172*16 x^5160*4 x^5112*8 x^5076*8 x^5064*12 x^5028*8 x^5016*4 x^5004*32 x^4992*16 x^4968*8 x^4956*8 x^4944*32 x^4941*32 x^4932*8 x^4920*76 x^4896*224 x^4884*160 x^4872*88 x^4869*32 x^4860*128 x^4845*32 x^4836*64 x^4821*96 x^4812*32 x^4797*64 x^4788*32 x^4764*8 (1024x)
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 0 0 0 0
x^5208*4 x^5172*16 x^5160*4 x^5112*4 x^5076*16 x^5064*12 x^5016*36 x^4980*32 x^4968*12 x^4944*32 x^4920*40 x^4908*48 x^4896*40 x^4884*176 x^4872*72 x^4869*64 x^4860*32 x^4848*136 x^4845*96 x^4836*96 x^4824*44 x^4821*32 x^4812*64 x^4800*64 x^4776*4 x^4773*32 x^4749*32 (1024x)
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 0 0
x^5304*8 x^5208*32 x^5172*64 x^5112*48 x^5100*16 x^5064*64 x^5016*32 x^5004*32 x^4980*320 x^4968*128 x^4932*32 x^4920*64 x^4872*128 x^4824*96 x^4812*48 x^4725*128 (128x)
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 0 0 0 0 0 0
x^5304*24 x^5268*32 x^5208*32 x^5184*64 x^5172*32 x^5160*16 x^5148*16 x^5112*16 x^5100*32 x^5064*32 x^5040*128 x^5028*160 x^5004*64 x^4968*160 x^4956*96 x^4908*32 x^4884*64 x^4860*112 x^4749*128 (128x)
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 1 0 0 0 0 0 0 0
x^5496*16 x^5400*16 x^5352*8 x^5304*48 x^5208*80 x^5160*144 x^5148*128 x^5112*32 x^5088*64 x^5040*128 x^4992*128 x^4944*128 x^4908*256 x^4848*64 (32x)
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^5064*4 x^5028*8 x^5016*4 x^4932*8 x^4929*32 x^4920*6 x^4908*12 x^4905*32 x^4896*40 x^4893*40 x^4884*32 x^4881*32 x^4872*22 x^4869*32 x^4857*32 x^4848*40 x^4845*40 x^4836*80 x^4833*224 x^4824*178 x^4821*16 x^4812*132 x^4800*48 x^4797*16 x^4788*16 x^4785*32 x^4776*34 x^4773*16 x^4749*24 x^4725*8 (2048x)
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 0 0 -1 0 0 0 0
x^5052*2 x^5037*2 x^5004*4 x^4992*8 x^4968*2 x^4965*2 x^4920*8 x^4917*8 x^4908*12 x^4905*16 x^4896*16 x^4884*32 x^4881*16 x^4872*50 x^4869*20 x^4860*40 x^4857*16 x^4848*64 x^4845*184 x^4836*64 x^4833*48 x^4824*96 x^4821*192 x^4812*122 x^4809*32 x^4800*32 x^4797*48 x^4788*16 x^4776*16 x^4773*32 x^4764*8 x^4749*12 x^4725*12 x^4716*8 (4096x)
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 0 0 0 -1
x^5016*2 x^5013*8 x^4980*4 x^4968*6 x^4953*16 x^4932*8 x^4929*32 x^4920*6 x^4917*8 x^4905*64 x^4896*64 x^4884*60 x^4881*64 x^4872*134 x^4869*16 x^4860*80 x^4857*128 x^4848*64 x^4845*48 x^4836*32 x^4833*96 x^4824*148 x^4821*16 x^4812*48 x^4809*16 x^4800*40 x^4797*8 x^4773*16 x^4725*8 (4096x)
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 -1 0 0 0 -1
x^5112*8 x^5028*4 x^5004*32 x^4977*16 x^4953*8 x^4932*12 x^4905*120 x^4893*64 x^4884*16 x^4881*32 x^4872*56 x^4869*32 x^4860*256 x^4857*128 x^4848*4 x^4845*96 x^4836*68 x^4833*152 x^4821*64 x^4812*16 x^4809*40 x^4800*16 (4096x)
1 32
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 0 -1 0 1 0 0 0
x^5028*2 x^4989*8 x^4980*4 x^4977*16 x^4968*4 x^4965*8 x^4956*4 x^4944*4 x^4920*28 x^4917*12 x^4908*24 x^4905*64 x^4896*4 x^4893*24 x^4884*50 x^4881*96 x^4872*16 x^4869*74 x^4860*64 x^4857*64 x^4848*40 x^4845*74 x^4836*36 x^4833*160 x^4824*96 x^4821*28 x^4812*36 x^4809*80 x^4800*36 x^4797*16 x^4776*8 x^4773*44 x^4764*16 (8192x)
1 32
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
x^5136*2 x^5088*2 x^5040*2 x^5028*4 x^5025*16 x^5004*4 x^4992*16 x^4977*16 x^4968*12 x^4965*32 x^4956*24 x^4944*10 x^4932*12 x^4929*16 x^4920*16 x^4917*32 x^4908*16 x^4881*8 x^4872*124 x^4869*128 x^4860*16 x^4857*32 x^4848*24 x^4845*32 x^4836*164 x^4833*24 x^4824*16 x^4821*144 x^4812*52 x^4809*16 x^4800*8 x^4788*24 x^4785*40 x^4776*16 x^4773*64 x^4761*8 x^4752*24 x^4749*16 x^4740*12 x^4737*8 x^4665*8 (2048x)
1 32
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
x^5196*10 x^5184*8 x^5148*6 x^5100*16 x^5088*16 x^5064*16 x^5040*16 x^5037*2 x^5016*4 x^5013*8 x^5004*8 x^4965*2 x^4956*4 x^4941*32 x^4932*32 x^4920*8 x^4917*8 x^4896*16 x^4893*356 x^4872*16 x^4869*224 x^4860*8 x^4848*32 x^4845*136 x^4824*96 x^4800*32 x^4797*56 x^4773*72 (2048x)
1 32
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 0 0
x^5496*8 x^5304*24 x^5208*32 x^5160*24 x^5112*16 x^5100*64 x^5064*112 x^5016*48 x^5004*64 x^4992*64 x^4968*16 x^4956*128 x^4944*128 x^4932*64 x^4908*64 x^4896*64 x^4872*128 x^4860*64 x^4824*128 (128x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
x^5400*4 x^5304*20 x^5208*36 x^5172*16 x^5160*8 x^5148*8 x^5112*12 x^5088*64 x^5076*48 x^5064*8 x^5016*16 x^5004*32 x^4956*120 x^4932*192 x^4920*144 x^4908*96 x^4896*64 x^4884*64 x^4872*64 x^4860*64 x^4848*32 x^4749*128 (256x)
1 32
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
x^5148*4 x^5124*4 x^5088*2 x^5040*2 x^5028*6 x^5016*4 x^4992*18 x^4989*32 x^4956*18 x^4944*8 x^4932*46 x^4929*16 x^4920*16 x^4908*16 x^4896*26 x^4893*64 x^4881*32 x^4872*44 x^4860*186 x^4848*24 x^4845*208 x^4836*56 x^4833*48 x^4824*40 x^4821*96 x^4812*64 x^4809*16 x^4800*16 x^4797*48 x^4788*8 x^4785*32 x^4776*16 x^4764*8 x^4737*16 (2048x)
1 32
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 1 0 0 -1
x^4929*16 x^4905*64 x^4896*48 x^4893*32 x^4884*16 x^4881*112 x^4872*52 x^4869*32 x^4860*128 x^4857*64 x^4848*80 x^4845*64 x^4836*112 x^4833*112 x^4824*68 x^4821*128 x^4812*32 x^4809*64 x^4785*16 (8192x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
x^5040*2 x^4980*4 x^4968*8 x^4956*8 x^4932*8 x^4929*16 x^4920*8 x^4908*8 x^4905*96 x^4896*16 x^4884*144 x^4881*64 x^4872*112 x^4869*32 x^4860*48 x^4857*64 x^4848*2 x^4845*16 x^4836*192 x^4833*104 x^4812*48 x^4797*16 x^4788*8 x^4785*88 x^4773*64 x^4764*64 (2048x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 1 0 0
x^5028*4 x^5001*16 x^4992*16 x^4980*4 x^4968*32 x^4944*4 x^4941*16 x^4932*28 x^4929*32 x^4920*4 x^4917*8 x^4908*16 x^4905*64 x^4896*68 x^4893*48 x^4884*52 x^4881*88 x^4872*84 x^4869*40 x^4857*72 x^4845*32 x^4836*72 x^4833*88 x^4824*160 x^4821*48 x^4812*48 x^4809*32 x^4800*16 x^4788*8 x^4785*24 x^4764*16 (8192x)
1 32
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
x^5592*8 x^5400*8 x^5304*32 x^5160*120 x^5136*64 x^5112*64 x^5088*64 x^5076*128 x^5064*64 x^5028*128 x^5016*48 x^4932*64 x^4908*128 x^4872*256 x^4836*64 (32x)
1 32
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 0 0 1 1 0
x^5100*4 x^5076*4 x^5064*4 x^5025*8 x^5016*20 x^5004*16 x^4992*4 x^4941*16 x^4929*32 x^4908*4 x^4905*56 x^4896*24 x^4893*32 x^4884*8 x^4881*136 x^4872*8 x^4869*32 x^4860*216 x^4857*64 x^4848*56 x^4845*96 x^4836*32 x^4833*72 x^4824*64 x^4821*16 x^4809*8 x^4797*64 x^4788*8 x^4785*120 x^4752*16 (2048x)
1 32
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5304*16 x^5208*40 x^5196*64 x^5160*32 x^5112*24 x^5064*8 x^5028*64 x^5016*64 x^5004*128 x^4968*256 x^4956*32 x^4920*80 x^4896*64 x^4884*192 x^4872*16 x^4812*32 x^4716*128 (128x)
1 32
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
x^5304*16 x^5208*32 x^5160*24 x^5112*48 x^5100*64 x^5016*16 x^4992*64 x^4980*128 x^4968*128 x^4932*64 x^4920*384 x^4908*64 x^4848*64 x^4824*16 x^4764*128 (128x)
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 -1 0 0 0 1 1 0 0 0
x^5136*6 x^5100*16 x^5064*40 x^5040*2 x^4992*22 x^4956*32 x^4944*2 x^4932*68 x^4908*16 x^4896*108 x^4893*32 x^4884*16 x^4872*16 x^4869*160 x^4860*216 x^4848*20 x^4845*64 x^4836*44 x^4833*32 x^4824*32 x^4821*64 x^4812*64 x^4809*32 x^4800*8 x^4785*32 x^4773*64 x^4761*16 x^4737*16 (1024x)
1 32
0 0 0 0 0 0 0 0 0 1 -1 -1 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5400*8 x^5208*56 x^5160*24 x^5112*32 x^5076*128 x^5064*64 x^5028*64 x^4992*64 x^4980*128 x^4968*32 x^4944*64 x^4932*64 x^4872*256 x^4836*128 x^4812*128 (32x)
1 32
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
x^5352*8 x^5304*80 x^5208*32 x^5160*32 x^5148*128 x^5112*16 x^5088*64 x^5064*32 x^5040*192 x^5016*128 x^4968*16 x^4896*256 x^4872*256 (16x)
1 32
0 0 0 0 0 0 0 0 1 0 -1 -1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 -1 1 0 0
x^5256*8 x^5208*4 x^5160*8 x^5124*16 x^5112*16 x^5064*16 x^5016*12 x^4968*40 x^4944*64 x^4932*64 x^4896*32 x^4884*192 x^4872*144 x^4860*256 x^4848*64 x^4836*32 x^4824*128 x^4788*96 x^4752*32 x^4740*16 (256x)
1 32
0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0
x^5256*16 x^5160*16 x^5136*32 x^5076*64 x^5064*32 x^5016*16 x^4992*64 x^4968*40 x^4932*128 x^4920*128 x^4872*144 x^4848*160 x^4824*16 x^4800*256 x^4740*128 (64x)
1 32
0 0 0 0 0 0 0 1 -2 1 0 0 0 1 0 0 -1 1 0 1 1 0 0 -1 -2 0 0 -1 1 0 1 -1
x^5028*16 x^5004*32 x^4992*16 x^4944*32 x^4932*32 x^4920*4 x^4896*112 x^4893*32 x^4884*32 x^4881*96 x^4872*12 x^4869*64 x^4860*128 x^4857*192 x^4848*112 x^4845*32 x^4836*96 x^4833*96 x^4824*104 (4096x)
1 32
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
x^5592*4 x^5400*8 x^5304*16 x^5208*52 x^5160*24 x^5136*32 x^5112*128 x^5088*32 x^5076*192 x^5064*16 x^5028*128 x^5016*16 x^4992*32 x^4968*16 x^4944*32 x^4932*64 x^4896*256 x^4872*128 x^4836*64 (32x)
1 32
0 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 -1 0 0 0 -1 0 0 0 -1 -1 0 1 0 1 0 0 0
x^5064*8 x^5016*4 x^4968*40 x^4908*32 x^4884*64 x^4872*96 x^4860*64 x^4848*288 x^4845*192 x^4824*324 x^4797*64 x^4776*64 (512x)
1 32
0 0 0 0 0 0 1 -1 0 0 -1 0 0 0 0 0 1 0 0 0 -1 -1 0 1 1 0 -1 1 0 0 0 0
x^5160*24 x^5112*32 x^4944*128 x^4932*128 x^4920*32 x^4872*704 x^4860*128 x^4788*64 (128x)
1 32
0 0 0 0 0 0 1 -1 0 0 -1 0 1 0 0 1 0 0 0 0 0 -1 1 1 0 0 0 0 -1 0 0 0
x^5112*32 x^5100*16 x^5040*32 x^5028*80 x^5016*8 x^4968*368 x^4932*16 x^4917*64 x^4908*16 x^4872*32 x^4869*128 x^4848*128 x^4824*192 x^4800*64 x^4725*64 (512x)
1 32
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
x^5208*24 x^5160*24 x^5016*136 x^4992*128 x^4968*160 x^4932*128 x^4920*64 x^4908*128 x^4872*32 x^4836*128 x^4824*256 x^4776*32 (64x)
1 32
0 0 0 0 0 1 -1 0 -2 1 0 0 0 0 0 0 -1 0 0 0 1 1 0 -1 -1 -1 0 0 0 0 0 0
x^5160*48 x^5076*64 x^5028*128 x^5004*128 x^4968*72 x^4920*32 x^4872*384 x^4824*256 x^4788*128 (64x)
1 32
0 0 0 0 1 0 0 -1 0 0 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0
x^5160*8 x^5112*32 x^5064*16 x^4968*16 x^4884*128 x^4872*16 x^4848*128 x^4836*384 x^4824*256 x^4800*256 (64x)
1 32
0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5160*56 x^5028*256 x^4992*256 x^4920*256 x^4872*32 x^4848*128 x^4824*256 (32x)
1 32
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 0
x^5544*8 x^5208*16 x^5160*16 x^5064*96 x^5052*128 x^5016*16 x^4968*64 x^4932*256 x^4920*192 x^4896*128 x^4848*256 x^4824*64 (32x)
1 32
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
x^5544*8 x^5304*48 x^5208*32 x^5196*128 x^5160*64 x^5112*16 x^5064*64 x^5040*128 x^5016*96 x^4992*64 x^4968*16 x^4944*64 x^4896*128 x^4872*256 x^4776*128 (16x)
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PROPERTIES
Unimodular=1
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REFERENCES
H. Koch, B. B. Venkov,
\"Uber ganzzahlige unimodulare euklidische Gitter.
Journal f\"ur die reine und angewandte Mathematik 398 (1989), 144-168
H. Koch, B.B. Venkov, \"Uber gerade unimodulare
Gitter der Dimension 32, III
Mathem. Nachr. 152 (1991), 191-213
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NOTES
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe