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 13:17:50 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(S3)
  

• DIMENSION
  32
  

• GRAM
  32 0
  4
  0 4
  0 -1 4
  1 0 1 4
  0 0 -1 -1 4
  0 0 0 1 0 4
  0 1 -1 0 0 0 4
  1 -1 0 0 -1 -2 0 4
  0 1 0 -1 -1 0 1 0 4
  -1 0 -1 -1 0 1 0 0 1 4
  1 1 0 -1 0 0 0 0 1 0 4
  -1 1 -1 0 1 1 1 -2 0 0 -1 4
  1 0 0 0 -1 -1 0 2 0 0 1 -2 4
  1 -1 1 1 -1 0 0 0 -1 -1 0 0 -1 4
  1 0 0 0 0 1 -1 0 1 1 -1 0 -1 -1 4
  0 0 0 0 1 -1 -1 0 -1 0 0 0 0 -1 0 4
  0 0 -1 0 1 -1 1 0 0 0 0 1 0 0 -1 0 4
  1 0 0 1 1 0 -1 0 -1 0 -1 1 -1 0 1 2 -1 4
  1 -1 1 0 1 1 -1 -1 0 0 0 0 -1 0 1 1 -1 2 4
  -1 0 0 0 1 2 -1 -2 0 1 0 1 -1 0 0 -1 -1 0 0 4
  2 0 1 0 -1 -1 0 1 0 -2 1 -1 0 1 0 1 -1 1 1 -2 4
  0 -1 -1 0 0 0 0 1 -1 1 -1 0 0 1 0 -1 2 -1 -1 -1 -1 4
  0 -2 0 1 -1 0 0 2 -1 0 -1 -1 0 1 0 -1 0 0 -1 0 0 1 4
  -1 1 1 0 1 0 -1 -2 0 -1 0 1 -1 0 0 0 0 0 0 1 -1 -1 -2 4
  0 -2 2 0 -1 1 0 0 0 0 0 -1 -1 2 0 -1 -1 -1 1 0 1 1 1 -1 4
  1 1 1 1 0 2 -1 -2 0 0 1 0 0 0 1 0 -1 0 1 1 0 -1 -2 2 0 4
  2 0 0 1 1 0 0 0 -2 -2 0 0 0 1 0 1 0 1 1 -1 2 0 0 0 0 1 4
  1 -1 1 1 0 -1 0 1 -2 -2 1 -1 1 2 -2 0 1 -1 -1 -1 1 1 1 0 1 0 2 4
  0 0 1 1 1 1 -1 -2 -1 -1 1 1 -1 1 -1 1 -1 1 1 2 0 -2 -1 2 0 2 1 1 4
  0 2 -1 0 0 0 1 -1 1 0 2 1 1 -1 -1 0 1 -1 -1 0 -1 -1 -2 1 -2 1 -1 0 1 4
  0 0 -2 -2 1 -2 1 1 0 0 1 0 1 0 -2 0 2 -1 -1 -1 0 1 0 -1 -1 -2 0 1 -1 1 4
  -2 -1 0 0 1 1 1 -1 0 1 -1 1 -1 0 -1 -1 1 -1 -1 2 -2 1 1 0 1 -1 -1 0 0 -1 0 4
  

• DET
  1
  

• MINIMAL_NORM
  4
  

• MINVECS
  

• KISSING_NUMBER
  146880
  

• DENSITY
  

• HERMITE_NUMBER
  4
  

• GROUP_ORDER
  2^16 3^4 5
  

• GROUP_GENERATORS
  13
  32 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 -1 0 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 0 0 0 1 -1 0 1 0 0
  0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 1 -1 0 1 -1 0 0
  0 0 1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 -1 0 -1 0 0 -1 0 1 0 0 0 0 0 0
  -1 0 -1 0 -1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 2 0 -1 0 1 1 0 1 1 -2 1 0 0
  0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 -1 1 2 1 2 1 1 -1 0 0 0 -1 1 0 0
  -1 1 0 0 1 -1 1 0 0 0 -1 1 1 1 1 2 -2 -2 3 2 3 2 3 1 -1 1 -1 1 -2 3 0 1
  0 0 -1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 -1 0 1 1 0 -1 1 -1 -1 0 -1
  0 -1 -1 1 0 1 -1 0 -1 1 1 0 0 -1 0 -2 2 1 -3 -2 -2 -3 -3 0 3 -2 1 -1 1 -2 0 -2
  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 -1 -1 0 -1 0 0 1 0 0 0 -1 -1 -1 -1 0 1 2 -1 2 -1 -1 -1 1 3 0 2 0 -2 2 0 -1
  -1 1 0 0 1 0 0 0 0 0 -1 0 1 1 1 0 0 -1 1 0 2 1 1 0 -1 0 -1 0 1 1 0 1
  1 0 0 1 1 0 -1 0 0 1 0 1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0
  1 1 0 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 1 0 1 0 0 0 1 1 0 1
  0 -1 0 0 -1 1 0 0 0 0 1 -1 -1 -1 0 -2 2 2 -3 -1 -3 -2 -3 -1 1 -1 1 0 1 -3 0 -2
  0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 1 0 -1 0 0 0 0
  -1 1 0 0 1 -1 1 0 0 0 -1 1 1 1 1 1 -1 -2 3 2 3 2 2 0 -2 1 -2 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 0 -1 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 -1 0 -1 1 0 -1 0 0
  0 -1 0 0 -1 1 -1 0 0 0 1 -1 -1 -1 -1 -1 2 3 -3 0 -3 -2 -2 0 3 -1 3 -1 -1 0 0 -1
  0 0 0 0 0 -1 1 0 0 -1 0 0 0 0 0 1 -1 -1 1 1 1 2 1 0 -1 1 -1 0 0 0 0 0
  0 1 0 0 1 0 0 0 0 1 -1 1 1 1 1 0 -1 -2 2 0 3 1 1 0 -2 0 -2 1 1 0 0 1
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 2 0 0 0 1 1 0 0 1 -2 0 0 -1
  0 0 0 -1 -1 1 -1 1 0 -1 0 -1 -1 0 0 -1 1 1 -1 -2 -2 -1 -1 -1 0 0 1 -1 2 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 0
  0 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 0 0 0 0 -1 1 0 -1 -1 1 1 -1 1 1 0 1
  0 1 0 -1 0 -1 0 1 0 -1 -1 0 0 1 0 1 -1 -1 2 1 1 1 2 0 -1 2 0 0 -1 2 0 2
  0 1 0 -1 0 -1 0 1 0 -1 -1 0 0 1 0 1 -1 0 2 1 1 1 2 0 0 2 0 0 -1 3 0 2
  0 0 0 -1 -1 0 -1 1 0 -1 0 -1 -1 0 -1 0 1 2 -1 0 -2 -1 0 0 2 1 2 -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 0 0 0 0 0 0 1 0 0
  0 1 -1 0 1 -1 0 0 0 1 -1 1 1 1 0 1 -1 -2 3 1 3 1 2 1 -1 0 -1 1 -1 2 -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 1 0 1 0 -1 1 0 0
  
  32 32
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
  0 1 0 -1 1 -1 -1 0 0 0 -1 0 1 1 0 0 0 0 0 -1 1 0 2 0 1 1 1 -2 0 3 -1 2
  0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 -1 2 2 2 2 1 1 -2 0 -1 1 -1 1 0 0
  -1 0 0 -1 0 0 0 1 0 -1 -1 -1 0 1 0 1 0 1 1 2 1 1 1 0 0 1 1 0 -2 4 -1 1
  -1 0 0 1 0 0 1 -1 0 0 1 0 1 -1 1 -1 1 1 -1 0 -1 0 -1 0 1 -1 0 0 2 -3 1 -2
  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 0 0 1 -1 1 0 0 0 -1 1 1 1 1 2 -2 -2 3 2 3 2 3 1 -1 1 -1 1 -2 3 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 -1 0 0 1 -2 1 -1 1 0 0 0 0 0 -2 2 1 -2 -2 -1 -4 -2 0 3 -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 -1 0 0 0 1 0 0 0 0 -1 1 1 -2 -2 -2 -2 -1 -1 2 0 1 -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
  1 0 0 1 1 0 -1 0 0 1 0 1 0 0 -1 0 0 -1 -1 -1 -1 -2 0 0 1 0 0 0 -1 -1 0 -1
  0 1 0 0 1 -1 0 0 0 0 -1 1 1 2 1 2 -3 -3 4 1 4 3 3 1 -3 1 -2 1 -1 3 0 3
  0 -1 0 0 -1 1 0 0 0 0 1 -1 -1 -1 0 -2 1 2 -2 -1 -2 -1 -3 -1 0 -1 1 0 1 -2 0 -1
  0 -1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 -1 1 1 -2 -1 -1 -1 -1 0 1 -1 1 -1 1 -2 0 -2
  -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 1 -1 -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 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 -1 -1 1 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -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 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 -1 2 2 2 2 1 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 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 -1 0 0 0 0 0 0 0 0 -1 1 1 -2 -2 -2 -2 -1 -1 2 0 1 -1 1 0 0 0
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 1 -2 -2 -2 -2 -1 -1 2 0 1 -1 1 -1 1 0
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 3 1 1 1 1 0 0 0 1 -2 1 0 -1
  
  32 32
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 -1 -2 -1 -1 -1 -1 0 0 0 0 1 -1 0 0
  1 1 0 0 0 -1 0 0 -1 0 0 1 1 0 1 0 -1 -2 1 -1 1 1 1 0 -1 0 -1 -1 2 0 0 2
  0 0 1 0 0 -1 2 0 0 -1 0 0 0 0 0 2 -1 -1 2 3 1 3 2 1 -1 1 -1 0 -1 1 0 -1
  0 0 -1 1 0 1 0 0 -1 1 0 1 1 0 1 0 1 -1 0 0 1 -2 -1 1 0 -1 -2 2 0 -2 0 -1
  -1 -1 1 -1 -1 0 0 0 1 -1 1 -1 -1 -1 -1 -1 1 3 -2 0 -3 0 -1 -1 1 0 3 -1 0 0 0 -1
  0 0 0 0 0 1 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
  -1 1 0 0 1 -1 1 0 0 0 -1 1 1 1 1 2 -2 -2 3 2 3 2 3 1 -1 1 -1 1 -2 3 0 1
  0 0 -1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 -1 0 1 1 0 -1 1 -1 -1 0 -1
  0 0 -1 0 0 0 -1 1 -1 0 0 0 0 0 0 -1 1 1 -1 0 -1 -2 -1 0 3 0 1 -1 -1 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 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 0 -1 0 0 -1 -1 1 0 -1 0 1 0 -1 1 0 0 1
  -1 1 0 0 1 0 0 0 0 0 -1 0 1 1 1 0 0 -1 1 0 2 1 1 0 -1 0 -1 0 1 1 0 1
  1 0 0 1 1 0 -1 0 0 1 0 1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0
  0 1 0 0 1 -1 0 0 0 0 -1 1 1 2 1 2 -2 -3 3 0 3 2 3 1 -2 1 -2 0 0 2 0 2
  0 -1 0 0 -1 1 0 0 0 0 1 -1 -1 -1 0 -2 2 2 -3 -1 -3 -2 -3 -1 1 -1 1 0 1 -3 0 -2
  0 -1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 -1 1 1 -2 0 -1 -1 -1 0 1 -1 1 0 0 -2 0 -2
  -1 0 0 1 1 0 0 -1 0 1 0 1 1 0 1 -1 0 -1 0 -1 1 0 -1 -1 -1 -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 -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 -1 1 0 0 0 0 0 -1 0 -1 1 0 -1 0 0
  0 0 0 -1 -1 0 -1 1 0 -1 0 -1 -1 0 -1 0 1 2 -1 0 -2 -1 0 0 2 1 2 -2 -1 2 0 1
  0 0 0 0 0 -1 1 0 0 -1 0 0 0 0 0 1 -1 -1 1 1 1 2 1 0 -1 1 -1 0 0 0 0 0
  0 0 0 1 1 1 0 -1 0 2 0 1 1 0 1 -1 0 -2 0 -2 2 0 -1 0 -2 -2 -2 1 3 -3 0 -1
  0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 -1 -1 -1 -2 -1 0 1 0 -1 1 0 -2 0 -1
  0 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 1 -1 1 0 0 0 0 2 -1 0 2 0 1
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 -1 1 1 1 1 1 1 0 0 -1 0 0 0 0 -1
  0 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 0 0 0 0 -1 1 0 -1 -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 -1 0 -1 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 -1 0 0 0 0 0 0 0 0 1 0 0 0
  0 0 0 -1 -1 0 -1 1 0 -1 0 -1 -1 0 -1 0 1 2 -1 0 -2 -1 0 0 2 1 2 -1 -1 2 0 1
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 1 0 1
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -2 -1 -1 -1 -1 1 0 1 -1 1 0 1 1
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 2 1 1 1 1 0 0 0 0 -1 1 0 -1
  
  32 32
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
  1 0 1 0 -1 0 1 0 0 -1 1 0 -1 -1 0 0 -1 0 -1 -1 -2 1 -1 -1 -1 0 0 -1 2 -2 1 0
  0 0 1 0 0 -1 2 0 0 -1 0 0 0 0 0 2 -1 -1 2 3 1 3 2 1 -1 1 -1 0 -1 1 0 -1
  0 -1 0 2 0 1 1 -1 0 1 1 1 0 -1 0 0 0 0 -1 1 0 -1 -1 1 0 -1 -1 2 -1 -3 1 -3
  0 0 0 -1 0 0 -1 1 0 0 0 0 -1 0 -1 0 0 1 0 0 -1 -1 0 0 1 0 2 0 -2 2 -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
  -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 -1 0 -1 -1 -1 -1 1 0 1 0 0 0 0 -1
  0 0 -1 1 1 0 -1 0 0 1 0 1 1 0 0 -1 1 0 -1 -1 0 -2 -1 0 1 0 -1 1 0 -2 0 -1
  -1 0 0 0 0 -1 1 0 1 -1 0 0 0 0 0 1 -1 0 1 2 0 2 1 0 0 1 0 0 -1 1 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 -1 0 0 0 -1 1 0 0 0 0 0 -1 0 0 -1 -1 1 0 -1 0 1 0 -1 1 0 0 1
  -1 1 0 0 1 0 1 0 0 0 -1 0 1 1 1 1 -1 -1 2 1 3 2 2 1 -1 0 -1 0 0 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 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 1 0 1 -1 0 1 0 1 1 0 1 0 -1 -2 1 0 2 1 0 0 -2 -1 -2 2 1 -2 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 -1 -1 0 0 1 0 -1 0 -1 -1 0 -1 1 0 2 0 2 -1 0 1 1 2 1 2 -1 -3 3 0 1
  0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 -1 1 0 0 0
  0 0 0 1 1 1 0 -1 0 2 0 1 1 0 1 -1 0 -2 0 -1 2 0 -1 0 -2 -2 -2 2 2 -3 0 -1
  0 0 -1 1 1 0 -1 -1 0 1 0 1 1 0 0 -1 1 0 -1 -1 0 -2 0 0 1 0 -1 1 0 -2 0 -1
  0 0 1 -1 -1 0 1 1 0 -1 0 -1 -1 0 0 1 -1 0 1 1 0 2 1 1 -1 0 1 -1 0 2 0 1
  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 0 0 0 0 0 0 -1
  0 0 1 -1 -1 0 1 1 0 -1 0 -1 -1 0 0 1 -1 0 1 1 0 2 1 0 -1 1 1 -1 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 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 0 1 0 -1 0 -1 -1 0 -1 1 0 2 0 1 -1 0 1 1 2 1 2 -1 -2 3 0 1
  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 1 0 1
  0 1 -1 0 1 -1 -1 0 0 1 -1 1 1 1 0 0 -1 -2 2 -1 2 0 1 0 -1 0 -1 1 0 1 -1 2
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 3 1 1 1 1 0 0 0 1 -2 1 0 -1
  
  32 32
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
  1 -1 0 -1 -1 1 -2 1 0 0 0 -1 -2 -1 -2 -2 2 3 -3 -2 -4 -4 -3 -1 3 0 3 -1 -1 0 0 0
  0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 2 1 1 1 1 0 0 0 0 -1 1 0 -1
  0 -1 1 0 0 0 0 0 0 -1 1 0 -1 0 -1 0 0 1 -1 0 -2 0 0 -1 0 1 1 -1 -1 0 0 -1
  0 0 -1 1 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 1 0 -1 -1 1 1 -1 0 2 -1 -1 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
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 -1 0 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 -1 0 0 1 -2 1 -1 1 0 0 0 0 0 -2 2 1 -2 -2 -1 -4 -2 0 3 -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 -1 -1 0 -1 1 -2 1 0 1 0 -1 -1 -1 -1 -2 2 3 -3 -1 -2 -4 -3 0 4 -1 3 0 -1 1 0 0
  -1 1 0 0 1 0 0 0 0 0 -1 0 1 1 1 0 0 -1 2 0 2 1 1 0 -1 0 -1 0 1 1 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 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 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 1 -1 -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 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 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 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 1 0 0 0 0 0 0 0 0 1 0 0 0 2 1 1 1 1 1 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 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 -1 0 0 0 0 0 0 0 0 -1 0 0 0 -2 -1 -1 -1 -1 0 0 0 0 1 0 0 1
  0 1 -1 0 1 -1 -1 0 0 1 -1 1 1 1 0 0 -1 -2 2 -1 2 0 1 0 -1 0 -1 1 0 1 -1 2
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 3 1 1 1 1 0 0 0 1 -2 1 0 -1
  
  32 32
  0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
  -1 0 1 -1 0 -1 1 0 1 -2 0 -1 0 1 0 1 -1 1 0 1 0 3 1 -1 -1 2 1 -2 0 2 0 1
  0 0 1 0 0 -1 2 0 0 -1 0 0 0 0 0 2 -1 -1 2 3 1 3 2 1 -1 1 -1 0 -1 1 0 -1
  -1 -1 1 -1 -1 1 0 0 1 -1 0 -2 -1 -1 -1 -1 2 4 -3 1 -2 0 -1 -1 2 0 3 -1 0 1 0 -2
  -1 1 -1 1 1 0 0 0 -1 1 0 1 2 1 2 0 0 -2 2 0 3 0 0 1 -1 -1 -2 1 1 -1 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
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 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 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 1 -1 0 0 0 0 0 1 -1 0 1 2 0 2 1 0 0 1 0 0 -1 1 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 -1 0 0 0 -1 1 0 0 0 0 0 -1 0 0 -1 -1 1 0 -1 0 1 0 -1 1 0 0 1
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  1 0 0 0 1 0 -1 0 0 1 -1 1 0 1 -1 0 -1 -2 1 -1 1 -1 1 0 -1 0 0 0 -1 1 -1 1
  -1 -1 0 -1 0 -1 1 0 1 -1 0 -1 -1 0 -1 1 0 2 0 3 -1 1 1 0 1 1 2 0 -3 3 -1 -1
  0 1 0 0 1 -1 0 0 0 0 -1 1 1 1 1 1 -2 -3 3 0 3 2 2 0 -3 1 -2 1 0 1 -1 2
  1 0 -1 0 -2 1 -1 1 -2 0 1 -1 -1 -1 0 -2 3 2 -2 -2 -3 -4 -3 0 3 -1 1 -1 1 -2 1 0
  0 -1 0 1 0 1 0 0 1 0 1 0 0 -1 -1 0 1 2 -3 1 -2 -1 -1 1 3 -1 2 -1 -1 -1 1 -3
  0 -1 2 -2 -1 0 1 0 1 -2 0 -1 -2 0 -1 1 -1 2 -1 1 -2 2 0 -2 -2 2 1 0 -1 1 0 0
  0 0 -1 0 0 0 -1 0 -1 1 0 0 0 0 0 -1 1 1 -1 0 0 -2 -1 0 2 -1 1 0 -1 1 -1 0
  0 -1 1 -1 0 0 1 0 1 -1 0 -1 -1 0 -1 1 0 2 -1 2 -1 1 0 0 0 1 1 0 -2 1 0 -1
  1 -1 1 -1 0 1 -1 0 1 0 0 -1 -2 -1 -2 -1 1 2 -3 -1 -2 -1 -1 -1 1 0 2 -1 0 0 0 -1
  -1 1 0 0 1 -1 2 0 1 0 -1 1 1 1 0 3 -2 -3 5 4 4 4 4 2 -3 1 -2 2 -2 2 -1 0
  1 0 1 -1 -1 0 0 0 0 -1 0 -1 -1 0 0 -1 0 1 -1 -2 -2 0 -1 -2 -1 1 0 -1 2 -1 1 1
  1 0 -2 1 -1 1 -2 1 -2 1 1 0 0 -1 0 -2 3 2 -3 -2 -2 -5 -3 1 5 -2 1 -1 0 -1 0 0
  1 1 -2 3 0 1 0 -1 -2 2 1 2 2 -1 2 -1 1 -2 0 -2 1 -3 -2 2 1 -2 -4 2 2 -6 2 -1
  -1 0 1 -2 0 -1 0 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 2 0 2 2 0 0 1 3 -1 -2 5 -1 1
  2 0 -1 1 -2 2 -2 1 -2 1 1 0 -1 -2 0 -3 3 1 -3 -4 -3 -5 -4 0 3 -2 0 -1 3 -4 2 0
  0 0 1 -2 0 0 0 1 1 -1 -1 -1 -1 1 -1 1 -1 0 1 1 0 2 2 0 -1 1 2 -1 -1 4 -1 1
  1 1 1 -1 0 -1 1 -1 0 -1 0 0 0 1 1 1 -2 -2 2 -1 1 3 2 -1 -4 1 -2 0 2 0 0 2
  2 1 -1 0 -1 0 -1 0 -2 1 0 1 0 0 1 -1 0 -2 1 -3 0 -2 -1 0 -1 -1 -2 1 2 -2 0 2
  0 0 1 -2 0 -1 1 0 1 -1 -1 0 -1 1 -1 2 -2 -1 3 2 1 3 3 0 -3 2 0 1 -2 3 -1 1
  -1 -1 0 -1 1 -1 0 0 1 0 -1 0 0 1 -1 1 -1 0 1 2 1 1 2 0 0 1 2 0 -3 4 -2 0
  0 0 0 0 0 -1 0 -1 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 1 0 0 0 0 -1 1 0 1 1 0 1 0 0 -2 2 0 2 0 0 1 -1 -1 -2 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
  -1 0 0 1 0 -1 1 0 0 0 0 1 1 1 1 2 -1 -1 2 3 2 1 2 2 0 1 0 0 -3 2 1 0
  0 0 0 0 1 -1 0 -1 1 1 -1 0 0 0 -1 0 -1 0 0 1 1 1 1 0 0 0 0 1 -1 1 -1 -1
  0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 -1 0
  1 -1 0 1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 -1 0 -1 -1 -1 1 1 -1 1 0 -1 -1 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 -1 0 0 0 0 0 0 0 0
  -1 0 0 -1 0 -1 1 0 1 -1 0 0 0 1 0 1 -1 0 2 2 1 2 2 0 -2 2 0 1 -2 2 -1 1
  0 0 0 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -1 -1 1 0 1 0 0 0 1
  -1 1 0 -1 1 -2 1 0 1 -1 -2 0 1 2 0 3 -2 -2 4 3 4 4 5 1 -2 3 -1 0 -2 5 -1 2
  -1 0 1 0 0 -1 2 0 0 -1 0 0 0 0 0 2 -1 -1 2 3 2 3 2 0 -2 2 -1 0 -1 1 0 0
  0 0 -1 2 1 0 0 0 0 1 0 1 1 0 0 0 0 -1 0 0 1 -1 0 1 1 0 -1 0 0 -1 1 -1
  -1 0 0 -1 -1 0 1 0 0 -1 0 -1 0 0 1 0 1 2 0 1 -1 0 0 0 1 0 1 0 0 1 0 0
  0 0 1 0 0 -1 1 -1 1 -1 1 0 0 0 0 1 -2 -1 1 0 0 3 1 -1 -3 1 -1 0 1 -1 0 0
  0 0 -1 0 0 1 -1 1 -1 0 0 -1 0 0 0 -2 2 2 -2 -1 -1 -3 -2 0 3 -1 1 -1 0 0 0 0
  0 1 1 0 1 -1 1 -1 0 0 -1 1 1 1 1 2 -2 -3 3 1 3 3 3 0 -3 1 -2 1 0 1 0 1
  0 -1 0 1 0 1 0 0 0 1 1 0 0 -1 0 -1 2 1 -3 0 -2 -2 -3 0 2 -2 1 0 1 -3 0 -3
  0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 1 -1 -2 2 1 2 2 1 1 -3 0 -2 1 1 -1 0 0
  0 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 1 2 -1 1 -2 0 -1 -1 1 0 2 -1 0 1 0 0
  1 0 0 0 0 0 -1 0 0 0 0 0 -1 -1 -1 -1 1 1 -2 -1 -2 -1 -1 -1 2 0 1 -1 1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 1 0 0 1 1 2 0 1 -1 -2 2 0 0
  0 0 -1 0 0 1 -2 1 0 1 -1 -1 0 0 0 -2 2 2 -2 -1 -1 -3 -2 0 3 -1 2 0 0 1 0 0
  0 0 0 0 0 0 1 0 -1 0 0 0 0 0 1 0 -1 -2 2 0 2 1 0 0 -3 0 -2 1 1 -1 0 1
  0 0 0 -1 -1 1 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -1 -1 0 0 1 0 0 0 1
  0 0 0 1 1 -1 0 -1 0 1 0 1 1 0 0 0 0 -1 0 0 1 0 1 1 1 -1 0 -1 0 0 0 -1
  0 0 -1 0 1 0 -1 0 0 1 -1 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 1 0 0 1 -1 1 -1 0
  0 0 0 1 1 -1 0 -1 0 1 0 1 1 0 0 0 0 -1 0 0 1 0 1 0 1 0 0 -1 0 0 0 -1
  0 -1 -1 1 0 1 -1 0 0 1 1 0 0 -1 0 -2 2 2 -3 -1 -2 -3 -3 0 3 -2 2 0 0 -2 0 -2
  0 -1 -1 1 0 1 0 0 0 1 1 0 0 -1 0 -2 1 1 -2 -1 -1 -2 -3 0 1 -2 0 1 1 -3 0 -2
  0 -1 -1 1 0 1 -1 0 0 1 1 0 0 -1 -1 -2 3 3 -4 -1 -3 -4 -3 0 5 -2 2 -1 0 -2 0 -3
  0 0 0 1 0 0 1 -1 0 0 1 1 1 0 1 0 0 -1 0 -1 0 0 0 0 -1 0 -2 0 2 -3 1 -1
  0 -1 0 0 -1 1 0 1 0 -1 1 -1 -1 -1 0 -1 1 2 -2 -1 -2 -1 -2 0 1 0 1 -1 1 -1 1 0
  -1 0 0 -1 1 -1 1 0 1 0 -1 0 0 1 -1 2 -2 -1 3 3 3 3 3 1 -2 1 0 1 -3 4 -2 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^5220*12 x^5124*24 x^5112*4 x^5064*24 x^5040*16 x^4968*4 x^4944*96 x^4932*36 x^4920*12 x^4872*12 x^4869*64 x^4860*384 x^4848*48 x^4824*288 x^4773*192 x^4740*24 (5760x)
  
  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^5193*2 x^5124*30 x^5076*20 x^5028*6 x^4857*90 x^4833*532 x^4824*480 x^4752*20 x^4740*60 (4608x)
  
  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^5544*8 x^5400*16 x^5208*48 x^5160*48 x^5076*128 x^5064*96 x^4908*384 x^4896*384 x^4752*128 (360x)
  
  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 -1 0 0 -1 1 0
  x^5076*16 x^4992*6 x^4944*18 x^4917*144 x^4896*8 x^4884*288 x^4860*96 x^4845*288 x^4836*144 x^4833*96 x^4824*120 x^4725*16 (46080x)
  
  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 1 0
  x^5157*2 x^5148*2 x^5040*12 x^5004*6 x^4968*36 x^4944*72 x^4941*30 x^4917*216 x^4908*36 x^4869*12 x^4848*36 x^4845*432 x^4824*144 x^4773*144 x^4725*24 x^4701*36 (15360x)
  
  1 32
  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 1 -1 0 0 0
  x^5304*16 x^5208*32 x^5160*24 x^5124*64 x^5112*48 x^4992*128 x^4968*256 x^4944*384 x^4908*128 x^4872*32 x^4740*128 (1080x)
  
  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 -1 0 0 0
  x^5688*8 x^5304*120 x^5160*120 x^5112*160 x^5028*192 x^5004*640 (72x)
  
  1 32
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 -1 0 0 -1 -1 -1 0 -1 1 1 -1 0 0
  x^5832*2 x^5448*18 x^5148*128 x^5064*324 x^4968*96 x^4920*288 x^4896*384 (120x)
  
  
  

• 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
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe