The Lattice LAMBDA(C2)
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 13:17:31 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(C2)
-
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 0 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 4
2 2 0 0 -1 1 0 2 0 -2 -1 -1 -1 0 -1 1 -2 4
-1 0 -1 1 0 0 -1 -1 1 -1 -1 -2 0 0 -2 1 -1 0 4
-1 0 0 1 0 0 -1 0 0 0 0 0 -1 -1 -1 0 -1 0 1 4
1 1 2 -1 0 -1 0 2 -1 1 1 0 1 1 1 -1 2 0 -1 -1 4
0 -2 0 1 2 0 1 -1 -1 -1 0 -1 0 0 0 1 -1 0 1 0 -1 4
-1 -1 -1 0 0 0 0 -2 -2 0 2 0 1 1 1 0 1 -1 0 -1 0 2 4
2 0 -2 0 -1 2 1 0 -1 -1 -1 0 0 0 0 0 1 1 0 -1 0 0 0 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 2 -1 -1 0 1 0 1 0 4
-2 0 -1 -1 -1 -1 -1 -2 0 -2 -1 -1 -1 0 -1 1 -1 0 1 0 -1 0 1 0 -2 4
0 -1 1 -1 0 -1 1 0 -1 1 2 1 0 1 2 -1 1 -1 -2 0 1 0 1 -1 0 0 4
-1 -2 1 1 2 0 0 -1 1 -1 -1 -1 -1 0 -2 0 -1 -1 1 1 -1 1 0 -1 -2 1 0 4
0 1 1 -1 0 -1 0 1 1 -1 -2 -2 -1 0 -2 0 -1 1 1 0 1 0 -1 0 -2 1 -1 1 4
0 -1 2 1 2 -1 0 1 1 -1 -1 -1 0 0 -1 1 -1 0 1 0 0 1 -1 -1 -2 0 0 2 1 4
1 0 0 0 0 0 1 1 -1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 -1 0 0 1 1 4
-1 -1 -1 -1 0 -1 1 -2 0 0 0 0 0 0 0 0 0 -1 1 0 -1 1 1 0 0 1 0 0 0 0 1 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^17 3
-
GROUP_GENERATORS
12
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 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
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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 1 -1 1 1 -1 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 -1 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 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 -1 1 1 -1 1 1 -1 1 -1 0 0 0 0 0 -1 0 1 0 0 -2 2 0 0 0 0 0 0 0 0 0
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1 0 1 -1 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
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0 -1 1 0 -1 0 0 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0
-1 -1 1 0 0 1 0 0 -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0
0 1 0 -1 1 0 0 0 -2 2 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0
0 -1 0 1 0 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0
0 -2 0 1 -2 0 0 2 -1 0 0 -1 1 -1 -1 0 1 0 0 -1 0 1 -1 -1 -1 0 0 0 0 -1 -1 1
-1 -2 0 2 -1 -1 0 1 -2 1 1 -1 0 0 -1 0 -1 0 0 -2 0 0 -2 0 -1 0 0 0 0 -2 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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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
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0 -1 1 -1 -1 1 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 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 -1 1 0 -1 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
-1 -1 -1 2 0 -1 1 1 -3 2 0 -1 -1 0 -1 0 -2 0 0 -1 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 1 0 0 0 0 0 0 0 0 0 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 -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 2 -1 0 0 0 0 0 0 0 0 0
1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 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 0 0 0 0 0 0
0 -1 1 0 -1 0 0 0 -1 1 0 0 -1 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 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 -1 1 0 -1 0 0 -1 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 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 0 -1 0 0 -2 2 1 -1 -1 1 -1 0 -1 0 -1 -1 0 0 -1 1 -1 0 -1 0 -1 0 1 0
-1 -1 0 1 -2 0 -1 -1 -2 1 2 -2 0 0 -2 0 0 0 -2 -2 0 2 -4 0 0 0 0 0 0 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 1 0 0 0 0 0 0 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 -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 -1 1 -1 -1 1 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 0 0 0 0 1 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 -1 0 -1 -1 0 0 1 -1 0 0 -1 0 1 0 -1 0 0 2 -2 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 0 -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 0 0
1 0 -1 0 -2 0 0 0 0 -1 0 1 0 0 0 1 1 -1 0 0 1 2 -1 -1 0 -1 0 1 1 0 -1 0
0 1 -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 0 -1
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 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 -1 0 0 -3 1 -1 0 -1 -1 1 -1 1 -1 -1 0 1 -1 -1 -1 1 3 -3 -1 -1 -1 0 0 0 0 -1 1
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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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32 32
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
-1 1 -1 1 2 -1 2 0 0 1 0 0 -1 0 1 -1 -1 1 1 0 0 -2 1 1 1 1 0 0 0 1 1 -1
0 2 -1 -1 2 0 2 -1 -1 1 -1 1 -2 0 1 0 -1 0 2 0 0 -2 2 0 1 0 0 0 0 2 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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32 32
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32 32
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32 32
1 4 -2 -1 4 -1 2 -1 2 -2 -2 2 -1 0 3 -2 0 0 2 2 0 -2 4 0 1 0 0 0 0 2 0 -2
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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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32 32
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-
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^5184*10 x^5148*12 x^5136*6 x^5088*12 x^5052*20 x^5040*4 x^5028*32 x^5004*8 x^4980*16 x^4968*32 x^4956*48 x^4944*48 x^4932*16 x^4929*32 x^4920*8 x^4896*80 x^4893*64 x^4884*32 x^4872*8 x^4869*128 x^4860*160 x^4848*16 x^4845*96 x^4836*144 x^4833*16 x^4824*32 x^4812*40 x^4800*32 x^4785*16 x^4764*8 x^4740*16 x^4725*32 x^4692*16 (1536x)
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^5052*2 x^5016*4 x^5004*2 x^4992*4 x^4980*8 x^4977*16 x^4968*12 x^4956*4 x^4953*16 x^4941*12 x^4932*32 x^4929*16 x^4920*20 x^4917*4 x^4908*4 x^4905*16 x^4896*148 x^4893*48 x^4884*72 x^4881*8 x^4872*16 x^4869*144 x^4860*24 x^4857*24 x^4848*8 x^4845*182 x^4836*96 x^4824*104 x^4821*34 x^4812*32 x^4809*32 x^4797*24 x^4788*8 x^4785*32 x^4776*16 x^4764*16 (12288x)
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^5040*4 x^5016*4 x^5004*4 x^4992*2 x^4956*20 x^4953*24 x^4944*18 x^4929*8 x^4920*32 x^4908*36 x^4905*16 x^4896*20 x^4884*54 x^4872*4 x^4869*32 x^4860*4 x^4857*8 x^4848*44 x^4845*160 x^4836*64 x^4833*24 x^4824*32 x^4821*144 x^4812*304 x^4809*32 x^4800*24 x^4797*16 x^4788*10 x^4785*24 x^4773*16 x^4761*24 x^4740*8 x^4725*16 x^4692*8 (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 0 0 0
x^5040*2 x^5028*2 x^5016*2 x^5004*4 x^4980*12 x^4968*2 x^4956*4 x^4953*8 x^4944*4 x^4932*18 x^4929*12 x^4920*24 x^4917*16 x^4908*12 x^4905*16 x^4896*102 x^4893*64 x^4884*16 x^4881*16 x^4872*136 x^4869*64 x^4860*16 x^4857*48 x^4848*12 x^4845*224 x^4836*32 x^4833*16 x^4824*144 x^4821*16 x^4812*32 x^4809*12 x^4800*32 x^4797*24 x^4788*8 x^4776*32 x^4773*32 x^4761*8 x^4737*4 x^4725*8 x^4713*4 (6144x)
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 -1 0 0
x^5256*8 x^5208*4 x^5160*8 x^5112*16 x^5076*16 x^5064*16 x^5016*12 x^4980*16 x^4968*72 x^4920*32 x^4896*128 x^4884*80 x^4872*208 x^4860*192 x^4812*128 x^4800*64 x^4788*144 x^4764*64 x^4692*32 (384x)
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^5088*2 x^5040*2 x^4968*4 x^4956*4 x^4944*40 x^4929*8 x^4920*20 x^4917*16 x^4908*88 x^4905*8 x^4896*8 x^4893*16 x^4884*24 x^4881*32 x^4872*48 x^4869*160 x^4860*28 x^4857*56 x^4848*28 x^4845*112 x^4836*56 x^4833*48 x^4824*32 x^4812*136 x^4809*24 x^4800*24 x^4797*112 x^4788*16 x^4785*16 x^4776*32 x^4773*32 x^4740*8 (6144x)
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^5496*4 x^5400*4 x^5304*12 x^5208*44 x^5172*32 x^5148*64 x^5112*8 x^5064*48 x^5052*32 x^5040*64 x^5004*80 x^4956*192 x^4944*64 x^4932*128 x^4920*128 x^4908*112 x^4872*32 x^4848*64 x^4773*128 (192x)
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^5352*8 x^5304*80 x^5208*32 x^5160*16 x^5124*128 x^5112*16 x^5064*64 x^5040*64 x^5016*128 x^4992*64 x^4968*128 x^4944*192 x^4896*64 x^4848*256 (48x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
x^5100*4 x^5088*2 x^5076*4 x^5016*4 x^5004*8 x^4992*2 x^4980*6 x^4956*36 x^4944*32 x^4932*32 x^4929*16 x^4908*8 x^4905*16 x^4896*14 x^4893*8 x^4884*58 x^4872*68 x^4869*16 x^4860*16 x^4857*16 x^4848*62 x^4845*176 x^4836*176 x^4833*8 x^4824*32 x^4821*64 x^4812*80 x^4809*32 x^4800*56 x^4797*96 x^4788*4 x^4785*24 x^4773*8 x^4749*8 x^4740*24 x^4737*8 x^4713*8 x^4701*8 (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 1 0 0 0 0 0 0 0 0 0
x^5244*8 x^5232*6 x^5184*10 x^5148*12 x^5136*8 x^5100*4 x^5088*8 x^5052*12 x^5028*64 x^5004*8 x^4980*32 x^4956*52 x^4944*64 x^4920*8 x^4917*64 x^4896*104 x^4893*128 x^4884*128 x^4872*88 x^4860*24 x^4848*96 x^4845*32 x^4836*16 x^4824*32 x^4812*8 x^4800*32 x^4797*96 x^4785*32 x^4740*64 (1536x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 0 0 0 0 0 0
x^5064*4 x^5028*4 x^5004*4 x^4992*2 x^4956*8 x^4953*8 x^4929*24 x^4920*12 x^4908*4 x^4896*10 x^4893*8 x^4884*88 x^4881*32 x^4869*16 x^4860*8 x^4857*176 x^4848*72 x^4845*96 x^4836*164 x^4833*72 x^4812*40 x^4809*64 x^4800*64 x^4797*32 x^4785*120 x^4773*88 x^4749*8 x^4740*4 x^4701*8 (3072x)
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 -1 0 -1 0 0 0
x^5100*2 x^5040*4 x^5004*2 x^4968*14 x^4944*24 x^4941*48 x^4932*40 x^4920*20 x^4917*16 x^4908*4 x^4905*16 x^4896*160 x^4893*16 x^4884*48 x^4881*16 x^4872*82 x^4869*144 x^4860*20 x^4857*20 x^4848*4 x^4845*112 x^4836*96 x^4833*8 x^4824*112 x^4821*16 x^4809*44 x^4797*64 x^4788*16 x^4785*36 x^4773*32 x^4761*4 (6144x)
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 0 -1 0 0 0
x^5004*4 x^4992*6 x^4980*8 x^4977*16 x^4956*16 x^4944*38 x^4932*80 x^4929*32 x^4908*44 x^4905*16 x^4896*92 x^4893*96 x^4884*48 x^4881*16 x^4872*64 x^4869*176 x^4860*8 x^4857*32 x^4845*112 x^4836*40 x^4833*16 x^4824*8 x^4821*16 x^4812*88 x^4809*48 x^4800*48 x^4797*32 x^4788*8 x^4785*16 x^4773*16 (12288x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 -1 0 0 0 -1 -1 0 0
x^5148*16 x^5112*8 x^5064*4 x^5040*32 x^5016*44 x^5004*24 x^4980*64 x^4968*80 x^4929*256 x^4920*16 x^4908*72 x^4872*32 x^4860*48 x^4848*128 x^4833*192 x^4824*64 x^4812*32 x^4809*64 x^4785*32 x^4761*32 (768x)
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^5400*4 x^5304*12 x^5256*8 x^5244*16 x^5208*44 x^5172*16 x^5112*76 x^5076*16 x^5064*8 x^5052*48 x^5028*16 x^5016*32 x^5004*88 x^4992*64 x^4980*32 x^4968*64 x^4956*64 x^4944*64 x^4932*144 x^4920*16 x^4908*120 x^4884*64 x^4872*16 x^4860*80 x^4773*128 (384x)
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^5304*16 x^5268*64 x^5208*32 x^5160*24 x^5112*48 x^5028*128 x^5004*256 x^4968*32 x^4944*256 x^4896*256 x^4740*128 (48x)
1 32
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 -1 0
x^4908*48 x^4905*24 x^4896*110 x^4893*48 x^4884*48 x^4872*24 x^4869*144 x^4860*80 x^4857*48 x^4848*162 x^4845*144 x^4836*96 x^4824*96 x^4821*48 x^4812*96 x^4809*24 (8192x)
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 0 0 -1 1 0 0 0 0
x^5112*6 x^5100*20 x^5064*6 x^5028*32 x^5016*6 x^5004*16 x^4977*128 x^4968*38 x^4953*32 x^4944*96 x^4920*8 x^4908*52 x^4905*128 x^4884*32 x^4881*64 x^4872*48 x^4860*128 x^4857*64 x^4848*128 x^4824*32 x^4800*32 x^4776*16 x^4764*32 x^4761*32 x^4740*32 x^4737*16 x^4713*16 (1536x)
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^5400*8 x^5208*56 x^5184*64 x^5160*24 x^5112*32 x^5100*96 x^5088*64 x^5040*64 x^5028*64 x^5016*16 x^5004*96 x^4980*32 x^4968*32 x^4944*32 x^4920*32 x^4908*64 x^4896*288 x^4884*32 x^4824*16 x^4788*128 (96x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 -1 0 0
x^5112*2 x^5064*2 x^4968*10 x^4929*32 x^4920*12 x^4908*48 x^4905*64 x^4884*32 x^4872*44 x^4860*48 x^4857*48 x^4848*160 x^4836*32 x^4824*138 x^4812*24 x^4809*336 x^4800*96 x^4764*80 x^4740*32 (1536x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 -1 -1 1 0 0 -1 0 0
x^5040*6 x^5028*12 x^4968*24 x^4944*48 x^4932*108 x^4920*24 x^4908*24 x^4896*2 x^4893*192 x^4872*96 x^4869*192 x^4860*176 x^4848*48 x^4812*96 x^4800*48 x^4785*96 x^4740*48 (1024x)
1 32
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 0 0 0 0
x^5304*8 x^5208*32 x^5148*32 x^5112*48 x^5076*32 x^5040*32 x^4956*32 x^4944*128 x^4920*64 x^4908*160 x^4896*224 x^4872*64 x^4860*160 x^4848*64 x^4812*32 x^4701*128 (192x)
1 32
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
x^5304*24 x^5256*16 x^5232*32 x^5208*32 x^5184*32 x^5160*24 x^5112*56 x^5088*32 x^5064*32 x^5040*32 x^5016*32 x^4992*128 x^4968*128 x^4956*128 x^4920*128 x^4884*128 x^4872*64 x^4824*64 x^4800*128 (96x)
1 32
0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 -1 0 1 0 0 -1 1 0 0 -1 0 0 1 0 0 0
x^5268*4 x^5172*12 x^5124*8 x^5112*32 x^5040*32 x^5028*8 x^4980*4 x^4953*80 x^4944*4 x^4932*192 x^4929*72 x^4908*16 x^4905*80 x^4881*96 x^4872*48 x^4857*176 x^4833*8 x^4824*128 x^4812*64 x^4809*32 x^4785*16 x^4773*128 (1536x)
1 32
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
x^5400*4 x^5304*12 x^5208*36 x^5112*60 x^5100*16 x^5088*64 x^5064*8 x^5028*32 x^4968*16 x^4956*64 x^4944*192 x^4932*32 x^4920*112 x^4908*352 x^4884*64 x^4824*32 x^4812*16 x^4740*128 (192x)
1 32
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
x^5592*8 x^5400*40 x^5352*8 x^5304*16 x^5256*48 x^5232*64 x^5208*32 x^5184*128 x^5160*64 x^5136*64 x^5112*96 x^5064*64 x^5016*32 x^4992*128 x^4968*320 x^4884*128 (24x)
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 0 0 0 0 0 0 0 0
x^5496*48 x^5352*24 x^5304*48 x^5256*96 x^5208*96 x^5184*192 x^5160*24 x^5136*192 x^4992*384 x^4968*8 x^4896*128 (8x)
1 32
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 1 0 0 0 0 0 0
x^5208*4 x^5172*16 x^5160*4 x^5112*4 x^5076*16 x^5064*12 x^5004*32 x^4968*8 x^4956*16 x^4944*64 x^4932*128 x^4920*48 x^4893*64 x^4872*360 x^4869*128 x^4824*128 x^4812*64 x^4788*64 x^4764*16 x^4749*64 (384x)
1 32
0 0 0 0 0 0 0 0 1 -2 1 -1 1 -2 1 -2 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*64 x^5100*32 x^5088*32 x^5064*80 x^5040*32 x^5028*128 x^5016*48 x^5004*160 x^4968*16 x^4920*256 x^4908*64 x^4884*32 x^4872*32 x^4848*128 x^4788*32 (96x)
1 32
0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 -1 1 0 1 0 0 0 1 0 0 0 0 0 0
x^5160*48 x^4980*192 x^4968*8 x^4896*512 x^4872*96 x^4836*384 (16x)
1 32
0 0 0 0 0 0 0 1 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
x^5400*16 x^5352*8 x^5304*32 x^5256*16 x^5208*48 x^5184*64 x^5160*16 x^5136*64 x^5112*96 x^5064*112 x^5040*128 x^5016*64 x^4944*256 x^4884*256 x^4824*64 (24x)
1 32
0 0 0 0 0 0 1 -1 -1 1 0 0 0 0 -1 1 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
x^5208*2 x^5112*4 x^5016*6 x^5004*8 x^4968*8 x^4932*16 x^4929*32 x^4920*16 x^4908*48 x^4905*64 x^4872*100 x^4860*32 x^4857*64 x^4848*160 x^4824*80 x^4812*8 x^4809*160 x^4800*64 x^4785*256 x^4776*32 x^4764*64 x^4740*16 (768x)
1 32
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
x^5208*24 x^5160*24 x^5100*64 x^5052*128 x^5028*128 x^5016*8 x^4992*128 x^4968*64 x^4920*32 x^4896*128 x^4884*128 x^4872*64 x^4848*256 x^4812*64 (96x)
1 32
0 0 0 0 1 0 0 0 -2 2 -1 -1 0 1 -2 1 0 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 0 0
x^5160*8 x^5112*32 x^5064*16 x^5016*8 x^4908*128 x^4896*32 x^4884*64 x^4872*16 x^4860*128 x^4848*224 x^4836*128 x^4824*136 x^4812*192 x^4776*64 x^4740*64 (384x)
1 32
0 0 0 0 1 0 0 0 -1 1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 0 0 0
x^5304*8 x^5256*16 x^5208*56 x^5172*64 x^5160*8 x^5112*72 x^5016*8 x^4992*128 x^4968*64 x^4956*128 x^4920*160 x^4908*128 x^4896*128 x^4872*16 x^4860*128 x^4692*128 (96x)
1 32
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
x^5400*40 x^5352*8 x^5304*16 x^5208*88 x^5172*128 x^5160*96 x^5112*64 x^5064*80 x^5016*144 x^4968*64 x^4884*128 x^4872*256 x^4848*128 (24x)
-
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