The Lattice M80

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  M80
  
• DIMENSION
  80
  
• GRAM
  80 0
  8
  -4 8
  -4 0 8
  -2 -2 0 8
  -4 2 0 4 8
  -4 2 0 0 0 8
  -4 0 0 2 2 2 8
  -4 0 4 4 2 2 0 8
  -4 2 0 0 4 4 2 2 8
  -4 4 0 -2 0 4 4 0 4 8
  -4 4 0 -2 2 2 4 0 2 4 8
  -4 0 0 2 4 4 4 2 4 2 4 8
  2 -4 -2 0 -2 2 0 0 0 -2 -2 2 8
  -4 2 0 4 4 0 2 2 0 0 2 2 -2 8
  2 -4 2 2 -2 -2 0 2 -4 -4 -2 -2 0 0 8
  -2 -2 2 2 0 2 2 2 2 2 0 2 0 0 0 8
  -2 -2 0 2 2 2 2 2 2 0 2 4 2 2 0 0 8
  0 -2 -2 4 2 0 2 0 0 0 0 2 0 2 0 0 4 8
  0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 -2 2 4 8
  -2 0 0 4 2 2 0 4 2 0 0 2 0 2 0 2 2 2 2 8
  0 -2 2 -2 -2 0 2 -2 0 2 0 0 0 -2 0 2 0 0 -2 -4 8
  0 -2 -2 4 2 0 2 0 0 0 0 2 0 2 0 2 2 4 2 0 0 8
  2 2 -4 0 0 0 -2 -2 0 0 -2 -2 0 0 -2 -2 -2 0 2 -2 0 2 8
  2 0 -4 -2 -2 2 0 -2 2 2 0 0 2 -2 -2 0 0 0 0 -2 2 0 4 8
  -2 2 2 0 0 2 -2 2 2 2 0 0 -2 0 -2 2 0 0 2 0 0 2 2 0 8
  2 0 -4 2 2 -2 0 -2 -2 -2 0 0 0 2 0 -2 0 2 2 -2 -2 4 4 0 0 8
  0 -2 2 -2 -2 0 2 -2 0 2 0 0 0 -2 0 2 0 0 -2 -4 4 2 0 0 2 0 8
  2 -4 2 -2 -2 -2 0 -2 0 0 -2 0 2 -4 0 2 0 0 -2 -2 4 0 -2 0 0 -2 4 8
  0 2 2 -4 -2 0 -2 0 0 0 0 -2 0 -2 0 0 -4 -4 -2 -2 0 -4 0 0 0 -2 0 0 8
  1 -3 1 -1 0 1 -1 1 1 -1 0 2 2 -2 1 -1 3 1 0 0 0 -1 -2 0 1 -1 2 2 -1 10
  -3 3 1 1 0 1 1 3 1 3 2 0 -2 2 -1 -1 1 1 2 2 -2 -1 0 0 3 -1 0 -2 -1 2 10
  -3 3 1 1 0 1 1 3 1 3 2 0 -2 2 -1 3 -1 -1 0 2 0 1 0 0 1 -1 -2 -2 1 -6 2 10
  -1 3 -3 -1 2 3 1 -1 3 3 2 2 0 0 -3 -3 1 1 2 0 -2 -1 2 2 1 1 0 -2 -1 2 2 -2 10
  2 -2 0 -1 -2 0 0 0 0 0 -2 -2 0 -2 2 2 -1 -1 -3 -1 1 -2 -1 1 -1 -1 0 0 1 -1 -1 1 0 10
  -2 -2 2 1 2 2 0 2 2 0 0 2 2 0 0 0 3 1 1 1 1 2 -1 -1 1 -1 2 2 -1 5 1 -1 0 -5 12
  0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 0 0 2 4 2 -2 2 2 0 2 2 -2 -2 -2 0 2 2 0 -3 1 8
  -2 -2 0 2 2 2 2 2 2 0 2 4 2 2 0 2 4 2 0 2 0 2 -2 0 0 0 0 0 -2 3 -1 -1 -1 -3 3 0 8
  1 1 -3 -1 2 -1 -1 -1 3 1 0 0 0 0 -3 1 -1 -1 0 0 0 1 2 2 -1 1 -2 0 1 -2 -2 2 -2 1 -1 2 -1 10
  -4 0 4 2 2 2 0 4 2 0 0 2 0 2 0 4 0 0 0 2 0 0 -2 -2 2 -2 0 0 2 0 0 2 -2 0 2 0 2 0 8
  0 -2 2 -2 -2 0 2 0 0 0 0 0 2 -2 2 2 0 -4 -4 -2 2 -2 -2 0 -2 -2 2 2 2 0 -2 0 -2 3 -1 -4 0 0 0 8
  0 2 -2 2 2 0 -2 0 0 0 0 0 -2 2 -2 -2 2 2 4 2 -2 2 2 0 2 2 -2 -2 -4 0 2 0 2 -3 1 4 0 0 -2 -4 8
  3 -1 -1 1 -2 -3 -3 -1 -3 -3 -4 -4 0 0 1 -3 -1 1 2 0 -2 -1 2 0 1 1 0 0 -1 0 2 -2 2 -1 -1 0 -1 -4 -2 -2 2 10
  -4 4 2 2 4 1 0 2 2 2 2 2 -3 2 -3 2 -1 -1 3 2 -2 0 0 -2 4 0 0 -1 -1 0 3 0 3 -3 0 3 -1 -1 3 -1 3 0 12
  -3 4 2 -2 0 2 0 1 2 3 2 -1 -2 0 -2 0 -1 -1 0 -1 -1 -1 0 -1 4 -1 1 -1 2 1 3 1 1 -1 0 2 0 -1 2 0 0 -1 3 10
  2 0 -4 0 0 0 0 -2 0 0 0 0 1 0 -1 0 0 2 0 1 0 0 2 2 -2 1 -2 -1 0 0 0 0 -1 1 -1 1 1 3 -2 -2 0 -1 -4 -2 8
  -4 0 5 0 2 1 2 1 1 0 1 1 0 0 1 0 0 -2 -2 0 0 0 -3 -5 1 -1 3 2 1 3 -1 -3 -1 -5 6 -1 3 -3 3 2 -1 -1 3 4 -4 14
  3 -2 -3 -2 -3 0 0 -4 -2 -1 -1 -2 3 -1 0 -2 -1 -1 -2 -2 0 -1 1 3 -2 1 1 0 -1 3 0 -4 1 -1 2 -1 2 -3 -3 0 -1 3 -3 0 2 2 12
  -2 -2 1 4 0 1 4 3 -1 0 1 1 1 2 4 2 1 2 -2 0 1 4 0 -1 1 2 2 -1 -1 -2 0 2 -1 -1 2 -2 2 -3 1 0 -1 1 -1 0 -1 3 0 12
  4 -3 -1 1 -1 -4 -1 -2 -4 -4 -2 -1 0 -1 3 0 0 1 -1 1 -1 -1 -2 -2 -3 0 -1 1 -2 0 -1 -1 -2 3 -3 1 -3 0 -2 1 1 2 -1 -4 1 -4 -2 -2 12
  -1 3 2 -2 0 0 -1 1 0 0 1 0 -2 0 0 0 -3 -4 -3 1 -1 -4 -1 -2 -1 -2 -3 -2 3 -1 -2 2 -1 2 -5 -1 0 1 0 2 -2 -2 -1 1 1 -1 -2 -4 1 12
  -4 4 2 -2 0 4 0 2 2 4 4 2 -1 1 -2 -1 2 -1 1 2 -2 -2 -2 0 2 -2 0 -1 -1 3 4 0 3 -4 3 2 1 -2 1 -2 3 -1 4 4 -3 4 1 -1 -3 -1 12
  3 -1 -4 2 2 -1 -1 0 0 -3 -1 1 1 0 1 -1 1 1 0 2 -2 0 2 2 -4 2 -4 -2 -2 -1 -3 0 0 3 -3 1 0 3 -2 0 2 -1 -2 -4 4 -6 -2 -2 5 3 -4 12
  2 0 0 -2 -1 -1 -2 0 -1 0 0 -2 0 -3 1 -3 -1 0 0 0 -2 -2 -2 -2 0 0 0 1 1 4 2 -2 3 0 3 -1 -1 -2 -2 -2 1 2 -1 1 0 2 2 0 0 -1 3 -2 10
  -3 -1 2 4 4 0 3 2 0 -1 1 2 -2 3 2 -1 3 2 1 2 -2 2 -2 -4 0 2 0 -2 -3 2 2 -2 1 -1 4 0 2 -3 0 0 1 1 1 -1 -2 5 1 3 0 -2 1 -2 1 12
  -3 3 2 0 1 1 1 0 1 3 1 -1 -3 1 -2 -1 -1 1 2 -2 2 2 2 0 4 0 2 -1 -1 -1 2 0 1 -2 2 1 -2 -1 1 -2 1 0 3 4 -3 3 0 2 -4 -3 3 -5 0 2 10
  -1 1 -2 2 1 3 1 0 1 1 1 1 -1 2 0 -1 2 3 4 0 0 2 2 2 2 2 0 -3 -2 1 2 -2 4 -1 1 1 0 -2 0 -3 3 1 2 1 -1 -1 1 3 -3 -5 2 -1 0 2 4 10
  4 -3 0 -2 -5 -1 -1 -2 -3 -1 -3 -3 1 -3 3 0 -3 0 -3 -1 3 -2 -1 1 -3 -3 1 2 2 1 -3 -1 -3 2 -1 -1 -1 -1 -1 0 -2 0 -6 -1 2 -2 2 -1 3 3 -2 2 1 -5 -2 -2 12
  -3 1 3 0 1 0 1 3 2 1 2 1 -2 1 1 2 0 -2 -2 -1 0 1 -1 -1 2 0 2 0 1 -2 0 2 -2 -1 0 -1 1 1 3 2 -1 -1 2 2 -4 3 -3 4 -2 -1 2 -2 -2 1 2 0 -3 10
  2 -1 -3 2 1 -2 -1 0 0 -2 -2 -1 2 1 0 -2 0 1 2 3 -2 0 2 0 -2 1 -2 0 -1 -1 1 -1 1 -1 0 1 -1 2 -1 -2 1 2 0 -3 2 -2 -1 -1 1 -2 -2 3 0 -1 -2 0 0 -3 10
  3 0 -2 0 0 -2 -4 -1 -2 -3 -2 -2 -1 0 0 -1 -2 0 1 2 -3 0 1 -1 -1 1 -3 -1 1 -2 -2 0 -1 2 -2 0 -2 3 0 -3 1 1 -2 -4 3 -4 -2 -3 3 2 -3 4 1 -1 -3 -2 1 -2 3 10
  -4 2 4 2 3 1 0 3 1 1 0 0 -2 1 0 1 1 1 2 -1 0 2 0 -3 3 1 2 0 0 0 2 2 -1 -2 4 2 0 -1 4 -1 1 -1 4 4 -3 5 -3 2 -3 -3 3 -4 1 2 4 1 -4 3 -3 -3 12
  3 1 -4 1 -1 -1 -3 -2 -3 -2 -1 -3 0 0 0 0 -1 0 3 2 -3 0 3 1 1 3 -3 -2 -1 -3 0 0 1 -1 -2 3 -1 0 -2 -2 3 3 3 -2 2 -3 2 0 2 -2 -1 2 0 0 -2 2 -3 -2 3 3 -1 14
  2 0 -4 0 1 -1 0 -2 1 -1 0 0 1 0 -1 -3 0 2 1 1 -2 1 1 0 -2 2 -2 -1 -1 -1 -2 -2 0 -1 -2 0 1 3 -2 -2 1 1 -3 0 2 0 0 0 0 0 -1 2 1 -1 0 0 1 0 3 2 -3 -2 10
  -2 -2 2 4 3 -1 2 2 1 -1 0 2 -1 2 1 1 4 4 3 1 1 2 -1 0 1 0 1 1 -3 2 3 0 1 -1 3 1 1 -3 2 0 1 1 3 -1 -2 0 -1 1 1 -4 -1 0 -2 4 1 3 -3 0 0 -3 3 1 -5 12
  -1 3 2 -1 2 0 -3 0 0 0 1 -1 -3 -1 -1 0 -1 -2 1 -2 0 1 2 -1 5 1 1 0 -1 1 0 -1 1 -3 3 3 -1 -1 0 -2 3 0 6 3 -2 3 0 0 -1 -1 3 -2 1 1 4 1 -4 2 -3 -1 6 5 -4 1 14
  -2 4 2 -3 -2 2 0 0 0 3 2 0 -2 -1 -2 -2 -1 -2 -1 -1 2 -3 0 1 0 -3 0 -1 1 -2 1 1 0 0 -3 -2 -1 -2 -2 0 1 -1 -1 1 0 -1 -1 -2 -2 4 3 0 0 -2 2 -1 2 0 -2 0 -2 -4 1 -4 -2 12
  1 -3 2 -2 -1 -2 1 0 -1 -1 1 1 2 -1 2 0 0 0 -2 0 1 -3 -5 -2 -3 -3 1 3 2 4 -1 -2 0 2 1 -4 1 -1 2 2 -4 0 -2 -2 0 1 0 -1 3 2 -1 0 3 -1 -3 -3 4 -2 1 1 -3 -4 0 0 -4 -2 12
  -3 1 4 2 2 1 -1 4 2 1 -1 0 -3 1 1 0 0 0 2 3 -2 1 -2 -3 2 -2 0 0 0 1 1 0 -1 -4 4 1 1 -1 2 -2 2 0 3 2 -4 6 -2 1 -4 -1 5 -4 2 3 3 1 -1 3 -1 -1 5 -3 0 0 2 1 -2 12
  0 2 0 -2 1 -1 0 -2 1 1 2 -1 -3 -1 -1 -2 0 -1 0 -2 2 0 2 1 2 1 1 0 -2 0 0 -1 2 0 -1 0 -1 0 -2 -1 2 0 2 1 -1 1 1 0 -1 0 1 0 0 1 3 2 -2 1 -1 -1 1 3 -1 2 6 0 -2 0 10
  0 1 -2 1 1 1 1 -2 -1 -1 1 1 1 1 0 -1 0 2 2 2 -1 0 1 -1 -2 1 -1 -1 -1 -2 0 0 1 0 0 1 -2 -1 0 -1 0 0 1 -1 2 -1 -1 0 3 -1 -1 3 -1 0 0 1 0 -3 4 2 -1 2 2 0 -1 0 1 -3 -1 10
  4 -2 -2 -3 -5 -1 -2 -3 -3 -1 -2 -2 4 -3 -1 -1 -1 -2 -2 0 -1 -2 0 1 -1 -1 1 3 0 1 -1 -3 1 0 -2 -1 -2 -1 -3 1 0 2 -1 -1 0 -1 3 -3 3 0 1 0 1 -4 -3 -3 3 -3 3 2 -6 2 1 -4 -2 1 2 -3 -2 1 12
  -1 1 2 -1 0 0 -1 2 0 0 1 0 -1 0 1 -2 1 -2 -1 0 0 -2 0 -1 1 -1 0 -1 -1 2 1 -2 2 -2 1 -2 1 -2 0 0 1 2 2 0 -2 2 1 1 -1 1 3 -1 1 2 1 1 -2 3 -1 -1 1 2 -2 1 5 0 0 2 5 -3 -1 10
  2 -1 -3 0 1 -2 -1 -1 0 -1 0 0 0 1 -1 -1 1 0 1 1 -3 0 0 1 -1 2 -2 -1 -1 1 -1 -1 3 0 0 1 1 1 -2 0 1 2 0 -2 0 -1 3 -1 1 -1 0 1 1 3 -2 0 -3 0 0 1 -4 3 0 1 -1 -3 0 -1 0 -3 2 1 10
  2 2 -1 -2 -3 0 -2 -2 -2 0 -2 -3 -1 -1 0 -1 -4 -3 -1 -2 1 -2 4 2 1 0 0 -1 2 -3 -1 1 0 1 -4 0 -3 -1 -2 1 0 2 0 1 0 -3 0 -1 1 4 -2 2 -2 -4 0 -1 3 -1 -1 1 -2 2 -1 -3 1 3 -2 -2 1 1 2 0 -2 10
  2 -2 -3 -1 1 -2 2 -4 0 -1 2 2 2 -1 -1 -2 2 1 0 -2 1 1 -1 1 -2 2 1 2 -3 3 0 -3 2 -2 2 -1 1 0 -3 0 0 0 -1 -3 1 0 4 -1 2 -3 -1 -1 2 1 -1 1 -2 -2 0 -1 -2 1 0 3 0 -3 2 -3 3 0 1 1 3 -3 12
  1 -1 2 0 1 -3 -3 0 -1 -3 -3 -2 -1 0 0 1 -2 -1 0 -2 2 0 2 0 0 0 0 1 3 -1 -4 0 -4 0 0 0 1 2 2 1 -2 0 -1 -1 1 0 -1 -2 -1 3 -5 1 -3 -1 -1 -4 1 0 -1 2 1 -1 -1 0 1 0 0 0 -1 -2 -2 -1 0 2 -3 10
  -3 4 0 -1 0 2 3 0 0 4 4 1 -1 1 -1 -1 1 1 1 0 0 -1 0 0 -1 0 0 -2 0 -1 3 2 1 -2 0 1 0 -1 0 0 0 -2 1 3 1 1 0 0 -1 0 4 -1 0 0 2 1 -1 0 -1 -3 3 1 -1 1 1 2 -1 0 1 2 -2 2 -2 -1 0 -3 10
  -1 -1 -1 4 4 -1 2 1 0 -2 0 2 1 3 1 -1 2 3 1 0 -1 3 1 0 -1 2 -1 -1 -2 -1 -2 -2 1 -2 0 0 2 0 0 -1 0 0 1 -1 0 1 -1 3 -1 -2 -2 2 -2 2 1 1 -3 0 2 0 0 0 2 2 0 -1 -1 0 -1 1 -1 -1 1 -1 0 2 -1 10
  3 -4 -2 3 -2 0 1 1 -1 0 -3 0 1 -1 3 2 1 2 -1 3 1 1 0 1 -2 0 -1 1 -4 1 1 1 -2 4 -1 1 -1 1 -3 0 1 0 -4 -4 4 -5 0 1 5 0 -2 5 0 0 -3 0 4 -3 2 1 -3 0 0 0 -3 -1 0 -1 -1 1 1 -1 0 0 0 -3 0 -3 14
  -4 0 1 1 0 3 5 2 2 4 2 2 1 2 0 3 2 0 -2 -1 1 3 0 0 2 0 4 0 0 0 3 2 0 1 2 -2 2 0 2 3 -2 -2 0 2 -1 2 -1 4 -3 -2 0 -3 -2 2 1 0 -2 3 -1 -3 2 -3 -1 0 -2 -1 0 -1 -2 -1 -1 -1 -2 -1 -2 -1 1 1 -2 12
  
  
• DET
  1
  
• MINIMAL_NORM
  8
  
• KISSING_NUMBER
  1250172000
  
• DENSITY
  
• HERMITE_NUMBER
  8
  
• SUBGROUP_ORDER
  2^11 * 3^4 * 5^2
  
• SUBGROUP_NAME
  (SL2(5) otimes C3).2 otimes 2^5.S6
  
• SUBGROUP_GENERATORS
  8
  80 80
  -2 0 -1 -1 -1 -1 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 0 0 0 0 0 0 0 0
  0 0 0 0 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 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 0 0 0 0 0 0
  0 0 0 0 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 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 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0
  0 0 0 0 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 -1 -1 1 1 1 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 0 0 0 0 0
  0 0 0 0 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 0 1 1 0 0 0 1 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 0 0 0 0 0 0
  0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 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 1 0 -1 -1 0 2 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 0 0 0 0 0
  0 0 0 0 0 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 2 1 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 0 0 0 0 0 0 0 0
  0 0 0 0 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 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 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 1 1 0 1 2 1 1 0 0 0 -1 0 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 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 1 1 0 0 1 1 1 0 -1 0 -1 0 1 -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 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 1 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 0 0 0 0 0 0 0
  0 0 0 0 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 -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 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 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 4 0 0 -2 -2 0 3 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 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 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 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
  -2 -1 -1 -2 0 0 1 1 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 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
  -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 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 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 2 0 0 -1 -1 0 2 1 0 0 0 0 0 0 0 0 -1 -1 -1 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 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 -1 -1 1 1 1 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 0 0 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 1 0 1 1 -1 -1 -2 0 0 0 0 0 0 0 0 1 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 0
  0 0 0 0 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 2 -1 -3 1 0 1 1 -1 -2 -2 0 0 0 0 0 0 0 0 2 1 1 -1 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 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 -3 1 0 1 1 -1 -1 -2 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 0
  0 0 0 0 0 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 -2 -4 2 0 2 2 -2 -1 -3 0 0 0 0 0 0 0 0 2 1 1 -2 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 0 0 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 4 -3 -5 2 0 3 3 -2 -4 -4 0 0 0 0 0 0 0 0 3 2 1 -3 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0
  3 0 2 6 -1 0 -3 -3 1 3 3 0 0 0 0 -2 1 -1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  5 -72 38 119 -32 7 -66 -61 39 63 79 -6 0 -1 2 -22 1 3 -5 -51 -42 -37 42 -25 -3 -19 -5 -1 1 4 -8 14 -7 -5 -5 -3 1 3 4 6 0 -5 0 -4 0 0 0 0 0 0 0 0
  0 0 0 0 0 -3 2 2 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
  5 -79 40 129 -33 9 -70 -66 40 67 86 -7 -1 -2 1 -24 1 3 -5 -55 -46 -41 46 -27 -3 -21 -5 -1 1 5 -9 16 -8 -5 -5 -4 1 4 4 6 0 -5 0 -4 0 0 0 0 0 0 0 0
  0 0 0 0 0 -3 2 2 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
  -5 74 -38 -118 30 -9 66 61 -39 -63 -80 7 0 1 -2 22 -1 -3 5 51 42 37 -42 25 3 19 5 1 -1 -4 8 -14 8 6 6 3 0 -3 -4 -6 0 4 0 4 0 0 0 0 0 0 0 0
  0 0 0 0 0 3 -2 -2 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
  -5 73 -38 -124 33 -7 68 63 -39 -65 -82 6 1 2 -1 23 -2 -2 6 51 43 37 -43 25 4 20 5 1 -1 -5 9 -14 8 5 5 3 0 -3 -5 -6 1 4 0 4 0 0 0 0 0 0 0 0
  0 0 0 0 0 3 -2 -2 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
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