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 13:26:41 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DIVISORS
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  R28''
  

• DIMENSION
  28
  

• DIVISORS
  2^14
  

• GRAM
  28 0
  10
  0 10
  0 0 10
  -5 5 5 10
  0 -2 0 -1 4
  2 0 0 -1 0 4
  0 0 0 1 0 0 4
  1 1 -1 0 -2 2 2 4
  0 0 0 0 2 0 0 -1 4
  0 0 0 0 0 2 0 1 0 4
  0 0 0 0 0 0 2 1 0 0 4
  0 0 0 0 -1 1 1 2 -2 2 2 4
  0 -2 0 -1 2 0 0 -1 2 0 0 -1 4
  2 0 0 -1 0 2 0 1 0 2 0 1 0 4
  0 0 0 1 0 0 2 1 0 0 2 1 0 0 4
  1 1 -1 0 -1 1 1 2 -1 1 1 2 -2 2 2 4
  0 0 0 0 2 0 0 -1 2 0 0 -1 2 0 0 -1 4
  0 0 0 0 0 2 0 1 0 2 0 1 0 2 0 1 0 4
  0 0 0 0 0 0 2 1 0 0 2 1 0 0 2 1 0 0 4
  0 0 0 0 -1 1 1 2 -1 1 1 2 -1 1 1 2 -2 2 2 4
  0 0 0 0 2 0 0 -1 2 0 0 -1 2 0 0 -1 2 0 0 -1 4
  0 0 0 0 0 2 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 4
  0 0 0 0 0 0 2 1 0 0 2 1 0 0 2 1 0 0 2 1 0 0 4
  0 0 0 0 -1 1 1 2 -1 1 1 2 -1 1 1 2 -1 1 1 2 -2 2 2 4
  2 0 0 -1 -3 -1 -1 0 -3 -1 -1 0 -3 -1 -1 0 -3 -1 -1 0 -3 -1 -1 0 6
  0 2 0 1 1 -3 1 -2 1 -3 1 -2 1 -3 1 -2 1 -3 1 -2 1 -3 1 -2 0 6
  0 0 2 1 1 -1 -3 -2 1 -1 -3 -2 1 -1 -3 -2 1 -1 -3 -2 1 -1 -3 -2 0 0 6
  -1 1 1 2 3 -1 -1 -3 3 -1 -1 -3 3 -1 -1 -3 3 -1 -1 -3 3 -1 -1 -3 -3 3 3 6
  

• MINIMAL_NORM
  4
  

• KISSING_NUMBER
  1512
  

• HERMITIAN_GROUP_ORDER
  2 * 3^6 * (7!)
  

• HERMITIAN_GROUP_GENERATORS
  4
  28 28
  0 0 0 1 2 0 -1 1 0 0 1 -2 1 0 -1 1 1 0 0 0 1 1 0 0 1 1 0 -3
  0 -1 -1 1 -1 2 0 -1 1 1 1 0 -1 1 0 -1 0 1 0 0 -1 1 0 0 -1 4 3 -3
  -1 1 0 -1 0 1 2 -1 1 -2 0 2 0 1 1 -1 0 0 1 0 -1 1 2 -2 2 -2 2 1
  -1 0 0 -1 -1 1 1 0 2 -1 -1 3 -1 1 1 -1 0 0 0 1 -1 0 1 0 2 0 1 3
  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 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 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 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 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 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 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 -1 0 0 0 -1 0 0 -1 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
  0 0 0 0 0 0 -1 0 1 -1 -1 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 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 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 -1 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 -1 -1 1
  0 0 0 0 0 0 -1 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 -1 1 0 -1
  0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 -1
  1 0 0 2 1 -1 -2 1 0 0 0 -1 2 -1 -2 1 0 0 0 -1 0 0 0 -1 -1 0 -2 -3
  0 -1 -2 2 -1 2 1 -3 0 1 1 -1 -1 3 1 -3 0 1 1 -1 0 1 1 -1 -2 4 5 -7
  -2 2 1 -2 2 0 0 1 1 -1 0 1 2 0 1 1 1 -1 0 1 1 -1 0 1 5 -3 -1 3
  -2 0 0 -1 0 2 1 -1 1 0 0 1 0 2 1 0 1 0 0 1 1 0 0 1 3 2 2 0
  0 0 0 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 1 -1 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 -1 1 2 -1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  28 28
  1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 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 1 -1 0 -1 0 0
  0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 -1 0
  0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 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 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 0 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 0 0 0 0 0 0 0 -1 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 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 -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 1 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 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 1
  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 -1 -1 1
  0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1
  0 0 0 0 0 0 0 0 -1 0 0 -1 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 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 0 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
  28 28
  1 0 0 0 -1 -1 0 0 -1 -1 -1 1 -1 -1 0 0 0 0 0 0 -1 0 1 -2 -2 -2 -1 2
  0 1 0 0 1 -1 0 0 0 -1 0 -1 1 -1 0 0 0 0 0 0 1 0 1 0 1 -3 -1 0
  0 0 1 0 1 -1 -2 2 1 0 -2 1 1 -1 -2 2 0 0 0 0 1 -2 -1 2 1 0 -4 2
  0 0 0 1 1 0 -1 0 0 1 0 -2 1 0 -1 0 0 0 0 0 2 -1 -1 2 0 1 -1 -3
  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 1 1 -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 1 -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 1 0 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -1 -2 -1 1 -2 -1 0 0 0 -2 -1 1 -1 -1 0 0 0 -1 0 0 0 -3 -2 0 2
  0 2 1 -1 2 -1 1 0 0 -1 0 0 2 -2 0 1 0 -1 0 0 0 -1 0 0 2 -5 -2 2
  1 -1 1 1 2 -3 -3 4 0 0 -1 0 1 -2 -3 3 0 0 -1 0 0 0 -1 0 0 0 -5 2
  1 0 0 2 3 -1 -2 2 0 0 0 -1 2 -1 -2 1 0 0 0 -1 0 0 0 -1 0 0 -2 -3
  0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 0 0 -1
  0 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 -1
  0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 -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 0 1 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 0 0 0 0 0
  0 0 0 0 0 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 1 -1 0 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 1 0 0 1 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 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1
  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 1 -1
  0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 0 1
  0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1
  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 1
  0 0 0 0 0 -2 -1 1 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 1 -1 -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 -1 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1
  28 28
  0 0 0 -1 -1 0 1 0 0 0 0 1 -1 0 0 1 -1 -1 0 0 -1 0 0 0 0 -1 0 4
  0 1 1 -1 1 -2 -1 2 0 -1 -1 1 0 -2 -1 1 1 -1 0 0 0 -1 0 0 1 -4 -4 4
  1 -1 0 1 -1 0 -1 0 -1 1 0 -1 -1 1 -1 -1 1 -1 -2 2 0 0 -1 0 -3 3 -1 -2
  1 0 0 1 0 -1 -1 0 -1 0 0 -1 -1 0 0 -2 1 0 -1 0 0 0 0 -1 -3 0 -1 -3
  1 0 0 2 2 -1 -2 1 0 0 0 -1 3 -1 -2 2 0 0 0 -1 0 0 0 -1 0 0 -2 -3
  0 -1 -2 2 -1 3 1 -3 0 1 1 -1 -1 3 0 -2 0 1 1 -1 0 1 1 -1 -2 5 5 -7
  -2 2 1 -2 2 0 1 1 1 -1 0 1 1 1 2 0 1 -1 0 1 1 -1 0 1 5 -3 0 3
  -2 0 0 -1 0 2 1 0 1 0 0 1 -1 2 1 0 1 0 0 1 1 0 0 1 3 2 2 1
  1 0 0 2 2 -1 -2 1 0 0 0 -1 2 -1 -2 1 0 0 0 -1 -1 0 0 -1 -1 0 -2 -3
  0 -1 -2 2 -1 3 1 -3 0 1 1 -1 -1 3 1 -3 0 1 1 -1 0 0 1 -1 -2 4 5 -7
  -2 2 1 -2 2 0 1 1 1 -1 0 1 2 0 1 1 1 -1 0 1 1 -1 -1 1 5 -3 -1 3
  -2 0 0 -1 0 2 1 0 1 0 0 1 0 2 1 0 1 0 0 1 1 0 0 0 3 2 2 0
  1 0 0 2 2 -1 -2 1 0 0 0 -1 2 -1 -2 1 -1 0 0 -1 0 0 0 -1 -1 0 -2 -3
  0 -1 -2 2 -1 3 1 -3 0 1 1 -1 -1 3 1 -3 0 0 1 -1 0 1 1 -1 -2 4 5 -7
  -2 2 1 -2 2 0 1 1 1 -1 0 1 2 0 1 1 1 -1 -1 1 1 -1 0 1 5 -3 -1 3
  -2 0 0 -1 0 2 1 0 1 0 0 1 0 2 1 0 1 0 0 0 1 0 0 1 3 2 2 0
  1 0 0 2 3 -1 -2 2 0 0 0 -1 2 -1 -2 1 0 0 0 -1 0 0 0 -1 0 0 -2 -3
  0 -1 -2 2 -1 3 0 -2 0 1 1 -1 -1 3 1 -3 0 1 1 -1 0 1 1 -1 -2 5 5 -7
  -2 2 1 -2 1 1 2 0 1 -1 0 1 2 0 1 1 1 -1 0 1 1 -1 0 1 5 -3 0 3
  -2 0 0 -1 -1 2 1 0 1 0 0 1 0 2 1 0 1 0 0 1 1 0 0 1 3 2 2 1
  1 0 0 2 2 -1 -2 1 1 0 0 0 2 -1 -2 1 0 0 0 -1 0 0 0 -1 0 0 -2 -3
  0 -1 -2 2 -1 3 1 -3 0 1 0 0 -1 3 1 -3 0 1 1 -1 0 1 1 -1 -2 5 5 -7
  -2 2 1 -2 2 0 1 1 0 0 1 0 2 0 1 1 1 -1 0 1 1 -1 0 1 5 -3 0 3
  -2 0 0 -1 0 2 1 0 0 0 0 1 0 2 1 0 1 0 0 1 1 0 0 1 3 2 2 1
  0 0 0 -3 -4 0 3 -2 -1 0 0 1 -4 0 3 -2 -1 0 0 1 -1 0 0 1 -2 -2 2 6
  0 3 3 -3 3 -5 -1 4 0 -2 -1 1 3 -5 -1 4 0 -2 -1 1 0 -2 -1 1 4 -10 -8 10
  3 -3 0 3 -1 -2 -4 2 -1 1 -1 -1 -1 -2 -4 2 -1 1 -1 -1 -1 1 -1 -1 -6 4 -4 -2
  3 0 0 3 2 -3 -3 1 -1 0 0 -2 2 -3 -3 1 -1 0 0 -2 -1 0 0 -2 -4 -2 -4 -4
  

• HERMITIAN_STRUCTURE
  4
  28 28
  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 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 0 0 0 0
  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 0 0
  0 0 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
  28 28
  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
  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 -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 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 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 -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 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 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 -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 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 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 -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 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 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 -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 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 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 -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 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 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 -1 -1 1
  28 28
  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 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
  -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 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 0 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 -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 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 0 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 -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 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 0 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 -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 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 0 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 -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 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 0 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 -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 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 0
  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 -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 1 0 -1
  28 28
  -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
  -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 -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 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 -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 -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 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 -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 -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 -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 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 -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 -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 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 -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 -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 -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 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 -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 -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 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 -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 -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 -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
  

• PROPERTIES
  Modular=1
  

• REFERENCES
  C. Bachoc, Voisinage au sens de Kneser pour les r\'eseaux quaternioniens.
  Comment. Math. Helvetici 70 (1995), 350-374.
  
  Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
  over the Hurwitz order
  

• NOTES
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe