The Lattice P_48n

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)

Last modified Mon Nov 2 21:58:37 EST 1998

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  P_48n
  
• DIMENSION
  48
  
• DET
  1
  
• GRAM
  48 0
  6
  3 6
  3 1 6
  -2 1 -3 6
  1 2 2 -2 6
  -1 1 0 -1 3 6
  -1 -1 1 -2 -1 1 6
  0 1 1 -1 3 0 1 6
  -2 0 -2 3 0 0 -3 0 6
  1 2 2 0 3 0 -1 3 2 6
  -2 0 -2 3 0 -1 0 2 2 0 6
  1 -1 0 0 1 1 0 -1 -1 -1 1 6
  2 0 2 -2 2 -1 -1 0 -2 1 -2 2 6
  -1 -1 1 -2 1 2 3 2 0 1 0 1 -1 6
  0 2 -1 3 -1 -1 -2 0 3 1 2 -2 -3 -2 6
  -2 -2 -1 -1 -2 -1 2 1 0 -1 1 -1 -2 1 1 6
  -2 -3 0 0 -1 0 -1 -2 2 0 -1 0 -1 0 0 0 6
  1 2 0 -1 3 1 -2 2 0 2 0 0 1 -1 1 1 -2 6
  0 -2 1 0 1 -1 0 1 -1 0 1 3 3 1 -2 -1 -1 -1 6
  1 -1 1 -3 -1 1 3 -1 -3 -2 -3 -1 0 1 -2 0 -1 -1 0 6
  3 3 1 0 2 1 0 0 -1 0 1 2 1 -1 0 -2 -2 0 1 0 6
  0 1 2 -2 0 -1 0 0 -1 1 -3 -4 0 -1 1 2 1 1 -2 1 -2 8
  -1 1 1 -1 3 3 0 0 1 1 0 1 1 1 -1 0 1 1 0 -1 2 1 6
  1 2 -1 0 1 2 -2 -2 1 -1 0 1 -1 -1 1 -1 0 2 -2 0 2 -1 2 6
  -3 0 -2 3 1 2 -2 -1 4 0 1 1 -1 1 1 -1 2 -1 1 -2 0 -1 3 1 8
  -2 1 -2 1 1 1 0 1 0 -1 1 -2 -1 0 0 -1 -2 0 0 1 0 0 0 1 2 6
  0 0 -2 -1 -1 1 2 -1 -2 -1 -1 1 0 0 -1 2 -1 1 -1 1 0 0 0 1 -2 -1 6
  1 -1 1 0 1 -1 -3 -1 1 1 -1 1 2 -2 1 -2 2 0 2 -1 0 0 0 0 1 -1 -1 6
  -2 0 1 2 0 2 1 1 2 2 0 -2 -3 2 1 -1 2 -2 -1 0 -2 0 0 -1 2 1 -2 -1 8
  -3 -3 -1 -1 -1 1 1 -1 0 -1 -1 0 -1 1 0 3 3 0 -1 0 -3 2 1 -1 1 -1 1 0 0 6
  -1 -2 1 -2 1 2 2 1 -1 -1 0 2 1 3 -3 0 1 -2 2 1 0 -1 2 -1 1 0 -1 -1 1 1 6
  2 1 0 -2 2 2 -1 -1 -1 0 -1 1 1 -1 0 -1 -1 2 -1 1 1 0 0 2 -2 0 1 1 -2 0 0 6
  -3 -3 0 -2 -1 1 2 -1 1 -1 0 0 0 2 -1 2 3 -2 0 1 -2 1 2 0 1 -1 1 0 0 3 3 0 8
  0 0 -1 2 -1 1 1 -2 0 -1 1 1 -1 0 0 -2 0 -2 0 1 2 -3 0 0 1 0 0 -1 1 -1 0 0 -1 6
  -1 1 1 -1 3 2 -1 1 0 2 0 -1 0 0 0 0 1 2 -1 -2 0 2 2 1 0 1 0 0 1 1 0 1 0 -2 6
  -2 -2 -3 2 -1 -2 -2 0 1 -1 2 0 0 -2 1 0 0 0 2 -1 -1 -1 -2 0 0 2 0 2 -1 0 -1 0 0 -1 0 6
  -3 0 -3 1 2 1 -2 2 3 0 3 -1 -1 -1 1 1 0 2 -1 -3 -1 0 2 1 2 2 0 0 -1 1 0 0 1 -2 2 2 8
  -3 0 -3 3 -2 1 0 -2 1 -2 1 -1 -2 -2 1 0 1 -1 -2 -1 -1 0 0 1 1 1 1 -1 1 1 -1 0 1 1 0 1 2 6
  2 -1 -1 0 -3 -3 1 -1 -3 -3 1 1 0 -2 0 1 -2 -1 1 2 1 -1 -3 0 -4 0 2 0 -3 -1 -1 1 -1 1 -3 2 -2 0 8
  1 -1 0 1 -2 -2 -1 0 0 0 -1 -1 -1 -1 0 0 0 0 0 1 -1 0 -3 -1 -2 -1 -1 0 1 -1 -2 -1 -3 0 -2 1 -2 0 2 6
  0 -2 0 -1 1 0 1 2 -2 -1 0 1 0 1 -2 0 -1 0 2 1 -1 -1 -2 -2 -1 1 0 0 0 0 1 0 -2 0 -1 1 0 -1 2 2 6
  -2 -1 -1 1 -1 -1 2 2 -1 0 1 -2 -1 1 -1 0 -1 -1 0 1 -2 0 -2 -3 -1 2 -1 -2 2 0 0 -2 -1 1 -1 1 0 1 1 2 2 6
  -2 -3 -3 0 0 2 -1 -1 2 -1 -1 0 -1 0 0 1 1 1 0 1 -2 -1 0 0 2 0 1 1 0 2 0 1 0 1 -1 1 2 1 -1 1 2 0 8
  -3 -1 -1 2 1 0 1 2 0 0 4 2 0 1 0 0 0 -1 3 -2 0 -2 0 -1 2 2 -1 0 1 0 2 -1 1 0 1 2 1 1 0 -2 1 1 -2 8
  1 -1 0 1 -3 -4 -2 -3 -1 -1 -1 0 1 -3 1 0 1 -1 0 -1 -1 1 -3 0 -2 -1 0 2 -2 0 -2 0 -1 -1 0 2 -2 0 2 1 -1 -1 -2 0 8
  2 -1 1 -2 1 -1 -2 1 1 1 -1 0 1 1 -1 0 1 0 1 0 0 0 0 0 0 -1 -1 1 0 -1 1 0 0 -1 0 0 0 -3 0 1 1 -1 1 -2 0 6
  -3 -1 -1 1 0 2 2 -1 0 -1 1 1 0 0 0 1 0 0 0 0 0 -1 2 0 1 0 1 -1 0 2 1 0 2 1 0 0 1 2 -1 -2 -1 0 1 1 -1 -3 6
  -1 -1 -2 1 -2 -2 1 -1 0 0 1 0 -1 0 1 2 0 0 0 0 -1 1 -1 -1 0 0 2 0 -1 1 -2 0 0 1 -1 1 -1 0 2 0 0 1 1 0 1 -1 0 6
  
• DIVISORS
  1
  
• MINIMAL_NORM
  6
  
• KISSING_NUMBER
  52416000
  
• HERMITE_NUMBER
  6
  
• SUBGROUP_ORDER
  2^7 *3^2*5*7*13
  
• SUBGROUP_NAME
  (SL_2(13) otimes SL_2(5)).2^2
  
• SUBGROUP_GENERATORS
  5
  48 48
  -3 1 -1 1 3 -1 3 -1 4 -2 -1 1 -2 -2 0 -1 0 1 3 -2 0 1 -1 0 -3 2 1 1 -1 1 1 0 0 0 0 -3 -2 -1 0 0 -1 1 0 -1 0 1 -1 -1
  -3 1 -2 -2 -1 0 2 2 4 -2 1 1 0 -1 -2 -2 -2 1 1 -1 1 3 -2 1 0 -1 0 2 1 1 0 0 0 1 1 -2 -1 -1 1 0 0 0 0 -1 1 0 0 -1
  2 1 -3 -1 3 0 3 0 3 -2 2 0 0 -1 -1 0 0 0 2 -1 -2 1 0 0 -1 1 0 1 0 1 0 -1 0 1 1 -1 -2 0 0 1 -1 0 0 -1 1 0 0 -1
  1 -3 1 2 -2 0 0 2 0 -1 1 0 1 1 0 -2 -1 1 -2 1 1 1 0 0 2 -1 1 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 2 -1 -5 -5 3 0 4 1 0 2 0 4 1 -2 0 -1 -1 -1 0 1 2 -2 2 3 -3 -2 1 2 0 -2 0 -1 2 1 1 1 0 2 0 1 -1 0 -1 2 -1 1 0
  1 2 -2 -2 -1 2 0 1 -1 1 1 -1 3 2 -3 2 -2 -1 -2 1 0 1 -2 2 2 -4 -4 2 2 0 -1 -2 0 2 1 2 2 1 2 0 1 -2 0 0 1 -1 1 1
  1 2 -2 -1 1 1 1 -1 0 1 1 0 0 -1 -1 2 0 -1 1 0 -2 0 0 1 -1 0 -2 1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 0 1 -4 -4 0 1 3 3 -1 1 2 0 -2 1 -3 0 0 1 -1 0 1 1 0 1 1 2 -1 0 0 -1 2 -1 0 0 -1 -1 -1 0 0 0 1 0 -1 1 0 0 -1
  -1 0 1 -1 -1 0 -1 0 0 0 0 1 0 0 1 -1 1 1 0 0 1 0 0 -1 0 1 1 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 2 0 -4 -3 1 1 2 3 -1 1 2 0 -2 0 -1 1 0 2 -1 0 1 0 0 0 1 1 0 0 0 -1 1 -1 0 0 -1 -1 -1 0 0 0 1 0 -1 1 0 0 -1
  2 -2 0 2 -1 -1 1 2 0 -1 -1 0 0 0 0 -1 -1 1 -1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 2 -1 2 2 1 1 0 -1 0 -1 -1 2 1 -1 3 0 -1 -1 1 -1 -1 -1 1 0 -2 -3 1 0 0 0 -1 0 1 1 1 1 1 1 0 0 -1 0 0 0 0 0 1
  1 -2 2 2 0 1 0 2 0 -1 0 -1 1 1 0 0 1 -1 -1 0 0 0 0 0 1 0 1 -1 -1 0 -1 1 -1 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0
  -1 3 -1 -2 1 0 0 -2 0 1 0 1 -1 -1 0 1 1 0 1 0 -1 -1 1 -1 -2 1 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 -1 0 0 1 0 2 1 -1 2 0 2 0 0 0 0 -1 0 1 -1 1 0 1 1 -1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 0 0 -1 1 -1 0 0
  1 0 1 1 0 -2 -2 -1 -1 1 -2 1 -2 -1 2 1 2 -1 1 1 -1 -2 3 -1 -2 2 1 -2 -1 -1 0 1 0 -1 -1 0 0 0 -2 -1 1 1 0 1 -1 0 0 0
  -3 5 -1 -5 1 0 -1 -2 -2 2 -1 1 0 -1 1 2 0 -1 1 0 -1 -2 -1 0 0 -1 -2 0 1 0 1 -2 0 1 0 1 1 1 1 1 0 -1 0 0 0 0 0 1
  1 0 0 -1 -4 1 -1 3 0 0 0 0 2 1 -1 1 0 -1 -1 1 1 1 0 1 2 -2 -1 0 1 -1 -2 1 0 1 1 1 1 0 0 -1 2 0 0 0 1 -1 1 0
  3 -4 2 4 -1 1 1 2 -1 -1 1 -2 2 2 0 -1 1 0 -2 0 0 0 1 0 2 0 1 -1 -1 0 -1 2 -1 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0
  2 -1 -1 1 1 2 1 -2 -1 1 2 -2 1 1 -1 1 0 0 0 -1 0 1 -1 1 0 0 -1 1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 -1 -1 -1 -3 2 2 3 2 -1 2 -1 3 1 -2 -2 -2 1 -1 -1 2 3 -3 2 2 -2 -1 2 1 1 0 0 -1 1 1 -1 0 0 2 0 0 -1 0 -1 1 0 0 0
  -3 2 0 -4 -1 -1 -1 0 1 0 0 1 -2 -2 1 -1 1 -1 3 -1 -1 0 1 0 -1 1 2 -1 0 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 1 0 0 0 0 0 -1
  -1 2 -1 -4 -4 2 -1 3 -1 1 1 -1 4 2 -2 1 -1 -1 -2 1 1 1 -2 2 3 -4 -3 1 2 0 -1 -1 -1 2 1 2 2 1 2 0 1 -2 0 0 1 -1 1 1
  0 2 -3 -2 -2 2 0 0 -1 1 1 -2 4 3 -3 2 -2 1 -2 0 3 2 -4 2 2 -4 -4 3 3 0 0 -2 1 2 1 1 2 1 2 0 2 -2 0 0 1 -1 1 1
  -1 0 0 -3 -4 3 -3 2 -3 2 3 -1 5 3 -1 0 -1 -1 -4 2 2 1 -2 1 4 -4 -2 0 2 0 -1 -1 -1 0 0 2 2 1 2 0 1 -2 0 0 1 -1 1 1
  2 -4 0 -1 -5 3 -1 2 -1 1 4 -2 4 3 -2 -2 -2 1 -4 0 3 3 -2 1 4 -2 0 1 2 0 -1 0 0 0 0 1 1 0 1 0 1 -1 0 0 1 -1 1 0
  -2 3 0 1 0 0 -1 -1 -2 2 -3 0 0 0 -1 4 0 -2 0 1 0 -1 -1 2 -1 -2 -3 1 0 -1 0 0 0 1 0 1 2 0 0 -1 1 0 0 1 -1 0 0 1
  0 3 0 -1 2 2 -1 1 -1 0 2 -1 4 1 0 3 1 -3 -1 2 -2 -1 -1 1 2 -2 -1 0 0 0 0 -1 -1 1 1 2 0 1 1 1 0 -1 0 -1 1 -1 0 1
  3 -3 -3 -1 -1 2 4 0 3 -1 4 0 2 0 -1 -2 -2 2 0 -1 0 3 -1 1 1 0 0 2 1 1 0 -1 0 0 1 -1 -1 0 0 1 0 0 -1 -1 1 0 0 -1
  -4 6 2 -2 0 -2 -3 -2 -4 3 -4 1 -2 -1 1 3 2 -2 1 1 -1 -4 1 0 -1 -1 -2 -2 0 -1 0 0 0 0 -1 2 2 0 0 -1 1 0 1 1 -1 0 0 1
  1 1 -1 0 2 1 2 0 -1 0 -1 -1 1 0 0 1 0 -1 0 -1 -2 -1 0 1 0 -1 -2 0 0 0 0 -1 0 1 0 1 1 0 1 1 -1 -1 0 0 0 0 0 1
  2 1 -1 2 3 0 1 -1 1 -1 -2 0 -1 0 -1 2 0 0 1 -1 -1 0 0 0 -2 1 -1 1 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 2 -1 0 5 -1 0 -3 -3 1 -2 -1 -1 0 0 3 0 -1 0 -1 -2 -2 0 0 -1 0 -2 0 0 0 1 -2 1 1 -1 2 1 1 0 1 -1 -1 0 1 -1 0 0 1
  2 -3 0 2 -1 2 0 1 -2 1 1 -1 2 2 -1 0 -2 0 -3 1 1 1 -1 1 2 -2 -2 1 0 0 0 -1 0 0 1 1 1 1 1 0 0 -1 0 0 0 0 0 1
  1 0 -1 -2 -3 1 0 2 0 0 1 -1 2 1 -2 0 -1 0 -1 0 1 1 -1 1 2 -2 -1 1 2 0 -1 0 0 1 1 1 1 0 1 0 1 -1 0 0 1 -1 1 0
  3 -7 2 3 -3 2 2 2 0 -1 2 -3 3 2 0 -3 -1 2 -3 -1 2 2 -1 1 4 -1 2 0 0 0 0 2 -1 -1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0
  -3 1 3 1 -2 -3 -2 1 -3 1 -5 1 -2 0 1 0 1 0 0 0 1 -2 1 0 0 0 0 -2 0 -1 -1 2 1 0 -1 1 2 -1 0 -1 0 0 1 1 -1 0 0 0
  -1 2 2 1 0 -3 -2 -1 -3 1 -3 1 -2 1 1 1 1 0 0 1 0 -2 1 -1 0 0 0 -1 0 -1 0 1 1 0 0 1 2 0 0 0 0 0 1 1 -1 0 0 0
  1 -3 2 5 2 -1 2 -1 1 -1 -1 -1 -1 0 1 -1 0 1 0 -1 0 0 0 0 -1 2 2 0 -2 0 2 1 0 -1 0 -1 -1 0 -1 0 -1 1 0 0 -1 1 -1 0
  -3 -3 4 1 -2 -3 1 -2 3 -1 -1 2 -5 -2 3 -5 2 4 3 -2 2 0 2 -3 -2 5 6 -2 -2 0 1 3 -1 -3 -2 -3 -2 -1 -2 -1 -1 3 0 0 -1 2 -1 -2
  -5 2 5 -2 -5 -1 -2 1 0 1 -3 2 -2 -1 2 -2 2 0 1 0 1 -2 2 -1 0 1 2 -3 -1 -1 -1 3 -1 -1 -1 0 1 -1 0 -1 0 2 1 1 0 1 0 0
  1 -5 1 -1 -3 1 0 1 1 0 4 0 1 0 1 -3 -1 1 -1 0 1 2 0 0 2 1 3 0 0 0 0 1 -1 -1 0 -1 -1 0 -1 0 0 1 -1 -1 0 0 0 -1
  -5 4 5 0 -5 1 -5 0 -5 4 -3 1 1 1 2 3 4 -3 0 2 1 -3 1 1 0 -1 -1 -3 -1 -2 -2 2 -1 -1 -2 2 3 -1 0 -2 2 1 1 1 -1 0 0 1
  2 1 0 -2 -1 1 -1 2 -1 0 1 -1 2 1 -1 1 -1 -1 -2 1 -1 -1 0 0 3 -2 -1 0 1 0 0 0 0 1 1 2 1 1 1 1 0 -1 0 0 1 -1 1 1
  2 -2 0 2 2 -2 -2 -2 0 -1 -1 0 -2 0 1 0 0 1 0 0 1 -1 1 -2 -2 2 2 0 0 0 1 0 1 -1 0 -1 -1 0 -2 0 0 1 0 1 -1 0 0 0
  -5 -4 5 1 -3 -3 0 0 2 -1 -4 2 -4 -1 4 -6 1 3 1 -2 3 -1 3 -3 -2 4 5 -3 -2 0 0 3 -1 -3 -2 -2 -1 -1 -1 -1 -1 2 0 1 -1 2 -1 -1
  4 0 -2 0 -2 3 0 4 -2 0 2 -1 4 2 -2 2 -1 -2 -3 2 -2 1 0 2 3 -4 -4 1 1 -1 -2 -1 0 2 2 3 1 1 1 0 1 -2 0 0 1 -1 1 1
  3 1 -3 -2 -1 3 -3 0 -1 2 3 0 3 0 -1 4 -1 -3 -1 2 -1 1 -1 2 0 -1 -2 2 1 0 0 -2 0 1 1 0 0 1 -1 0 2 0 -1 0 0 -1 1 1
  48 48
  -10 7 3 -8 -6 0 -3 0 1 2 -1 3 -2 -3 1 -1 2 0 3 -1 2 -1 -1 0 -1 1 1 -1 0 0 0 1 -1 0 -2 -1 0 -1 0 -1 1 2 1 0 0 1 0 0
  -9 4 3 -5 -7 1 0 2 0 1 -2 2 0 -2 1 -2 1 0 1 -2 2 0 -1 1 1 -1 0 -1 0 -1 -1 2 -1 0 -1 0 1 -2 1 -1 1 1 1 0 0 1 0 0
  -4 4 1 -5 -5 0 -3 2 -1 2 -2 1 -1 -1 -1 0 -1 -1 0 0 1 -1 0 1 1 -2 -2 0 1 0 -1 0 0 1 0 1 1 0 1 -1 1 0 1 1 0 0 1 1
  -1 -3 3 0 -3 0 -1 2 1 -1 1 1 1 1 1 -3 0 1 -2 0 2 1 0 -1 1 1 3 -1 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 0 -1 -4 4 1 3 0 0 3 -3 5 2 -2 0 -2 -1 -3 0 1 2 -2 3 4 -4 -2 1 1 0 -1 0 -1 1 1 2 1 0 1 0 1 -1 0 0 1 -1 1 1
  4 -3 -1 2 3 3 1 1 -1 -1 4 -4 5 2 0 1 -1 -2 -3 2 -2 0 0 1 3 -3 -1 0 0 0 0 -1 -1 0 1 2 0 1 1 1 0 -2 -1 -1 1 -1 0 1
  -1 4 -2 -1 3 -1 -1 -1 -1 1 -3 1 -2 -2 0 3 0 -2 2 0 -2 -2 1 0 -2 0 -2 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 2 1 -3 -5 0 -1 2 1 1 -2 2 0 -1 -1 0 -1 -1 0 -1 2 1 -1 2 0 -1 -1 0 1 0 -1 1 0 1 0 0 1 -1 0 -1 1 1 1 1 0 0 1 0
  3 -4 1 4 -1 0 2 1 1 -2 1 -1 2 2 0 -2 0 2 -2 0 1 1 0 0 1 0 1 0 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 2 -2 -6 0 -1 2 1 0 -1 1 0 0 -1 -2 -1 1 -1 -1 3 1 -1 1 1 -1 0 0 1 0 -1 1 0 0 0 0 1 -1 0 -1 1 1 1 1 0 0 1 0
  0 0 0 0 0 0 1 0 1 0 -1 1 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 0 0 0 0 0 0 0 0 0
  2 -1 0 -2 2 2 -2 0 1 0 4 -1 2 1 0 0 -1 -1 -2 2 -1 0 0 -1 1 0 1 0 0 1 1 -2 -1 0 0 1 -1 2 0 1 0 -1 -1 -1 1 -1 0 1
  5 -7 0 -1 -2 2 -1 3 2 -1 4 -2 2 2 -2 -3 -4 1 -4 1 2 3 -1 0 4 -2 1 1 1 1 0 -1 -1 0 1 1 -1 2 0 0 0 -1 -1 0 1 -1 1 1
  0 3 -2 0 3 -1 0 -1 0 0 -2 1 -1 -1 0 2 0 -1 1 0 -2 -1 1 0 -2 0 -2 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -6 2 5 2 -4 -2 2 0 -1 0 -5 2 -4 -2 2 -3 4 2 3 -3 1 -2 2 -1 -2 3 2 -3 -2 -1 -1 4 0 -2 -2 -1 1 -3 0 -1 -1 2 2 1 -1 2 -1 -1
  1 -3 1 4 3 -5 3 -2 3 -2 -4 2 -7 -3 2 -4 0 3 3 -2 -1 -1 4 -3 -4 5 4 -1 -2 1 1 2 1 -2 -1 -3 -2 -1 -2 0 -2 2 0 1 -1 2 -1 -2
  5 5 -5 3 6 1 0 -3 -5 2 1 -2 3 2 -2 8 1 -3 0 3 -4 -2 -1 2 0 -3 -6 2 1 -1 0 -3 2 2 2 2 2 1 1 1 1 -2 0 -1 0 -2 0 1
  2 -7 3 2 -3 0 3 1 3 -2 1 -1 -1 0 1 -6 -1 3 -1 -2 2 2 1 -1 1 2 4 -1 -1 1 0 2 -1 -2 -1 -1 -1 -1 -1 0 -1 1 0 1 0 1 0 -1
  3 -6 1 -3 -3 3 -3 3 2 0 5 -1 3 2 -1 -3 -3 0 -4 1 2 3 -1 0 3 -1 2 0 1 1 0 -1 -2 0 0 1 -1 2 0 0 0 -1 -1 0 1 -1 1 1
  -1 1 0 -1 1 0 -2 -1 -2 1 0 -1 0 0 1 1 1 -1 1 0 0 -1 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
  -6 4 2 -6 -4 3 -1 2 1 1 2 0 3 -1 0 0 0 -2 0 0 0 0 -2 2 2 -2 0 0 0 0 0 0 -2 1 0 1 0 0 1 0 1 0 0 -1 1 0 0 1
  -3 3 0 0 -2 -2 1 -1 -2 1 -4 1 -4 -2 0 0 1 1 3 -2 0 -1 1 0 -1 0 -1 0 0 -1 -1 2 1 0 -1 -1 1 -2 0 -1 0 1 1 1 -1 1 0 -1
  5 -2 -2 2 3 2 3 1 0 -1 2 -3 3 1 -1 1 -2 -1 -2 1 -3 0 0 1 3 -3 -2 1 0 0 0 -1 0 1 2 2 0 1 1 1 0 -2 -1 -1 1 -1 0 1
  -1 2 -1 2 2 2 3 -2 -3 1 1 -2 3 1 1 2 2 -1 0 0 -2 -1 -1 1 1 -1 -2 0 -1 -1 0 0 0 0 0 1 1 -1 1 1 0 -1 0 -1 0 0 -1 0
  5 -6 0 3 0 3 2 3 0 -2 4 -3 5 3 0 -2 -2 0 -4 1 -1 2 0 1 4 -3 0 0 0 0 0 0 -1 0 2 2 0 1 1 1 0 -2 -1 -1 1 -1 0 1
  -1 -1 -1 1 -1 1 2 2 -2 0 -1 -1 2 1 0 0 -1 -1 -1 -1 0 1 -1 2 2 -3 -2 0 0 -1 -1 1 0 1 1 1 1 -1 1 0 0 -1 0 0 0 0 0 0
  3 -2 -2 2 5 1 2 -3 0 0 2 -1 0 -1 1 1 1 0 1 0 -2 0 0 -1 -1 2 1 0 -1 0 1 -1 0 -1 -1 -1 -1 0 -1 1 -1 0 -1 -1 0 0 -1 -1
  1 1 1 1 -1 2 -1 0 -4 2 1 -2 2 2 -1 2 2 -1 -1 1 0 -1 -1 1 2 -2 -2 -1 0 -1 -1 0 0 0 0 2 2 0 1 0 0 -1 1 0 0 -1 0 1
  -1 3 1 -1 -2 -1 -4 2 -3 1 -2 1 1 1 0 2 0 -2 -2 2 0 -2 1 0 1 -2 -2 -1 1 -1 -1 0 1 1 1 2 2 0 1 0 1 -1 1 1 0 -1 1 1
  6 -1 -2 8 8 -3 2 -4 -3 0 -3 -1 -4 0 1 3 2 0 2 1 -4 -3 4 -2 -3 2 -1 -1 -2 -1 0 0 2 -1 0 0 0 0 -1 0 -1 0 0 0 -1 0 -1 -1
  3 4 -5 -2 5 1 -2 0 -2 1 1 -1 3 1 -2 6 -2 -4 -1 3 -3 -1 -1 2 1 -4 -5 2 2 0 0 -3 1 3 2 2 1 2 1 1 1 -2 -1 -1 1 -2 1 2
  0 0 0 0 1 0 0 -2 -1 0 1 -2 0 1 0 0 1 1 0 0 1 -1 0 -1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  10 -2 -7 6 9 1 2 -3 -5 1 1 -4 3 3 -2 6 -1 -2 -2 2 -4 -1 0 1 1 -3 -6 2 1 -1 0 -3 2 1 2 2 1 2 1 1 0 -3 -1 -1 0 -2 0 1
  3 -1 0 -1 3 2 -1 0 1 -1 4 -2 3 1 0 1 0 -1 -1 1 -1 0 -1 0 1 0 1 0 0 1 1 -2 -1 0 0 1 -1 2 0 1 0 -1 -1 -1 1 -1 0 1
  0 1 -2 1 0 1 3 1 -1 0 -1 -1 1 0 -1 1 -1 -1 0 0 -2 0 0 2 1 -3 -3 1 0 -1 -1 0 0 1 1 1 1 -1 1 0 0 -1 0 0 0 0 0 0
  4 -3 -1 4 1 2 0 0 -3 1 2 -2 3 3 -1 2 1 -1 -2 1 0 1 -1 1 1 -1 -1 0 0 -1 -1 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 -1 0 0
  7 -2 -5 5 5 2 5 -1 0 -1 1 -2 3 1 -1 4 0 -1 0 0 -3 1 -1 2 0 -1 -3 2 0 -1 0 -1 1 1 2 0 0 0 0 1 0 -1 -1 -1 0 -1 0 0
  3 -2 -3 2 4 1 1 -2 -1 0 3 -2 3 2 -1 2 -1 0 -2 1 0 1 -2 0 1 -1 -1 2 1 0 1 -2 0 0 1 0 0 1 1 1 0 -2 -1 -1 0 -1 0 0
  -8 7 2 -4 0 -3 -3 -4 -1 3 -3 3 -5 -3 2 1 4 0 5 -1 1 -3 0 -2 -4 4 2 -2 -1 0 1 1 0 -1 -3 -2 0 -1 -1 -1 0 2 1 0 -1 1 -1 -1
  -4 1 4 -5 -6 -2 -6 1 3 0 2 3 -1 0 1 -3 1 1 0 1 4 1 0 -2 -1 3 5 -1 1 1 0 1 -1 -1 -1 -2 -1 0 -1 -1 1 2 1 1 0 0 1 -1
  0 1 -1 -5 -3 2 -3 1 1 1 4 0 3 1 -1 1 -1 -1 -1 1 2 2 -2 1 1 -1 0 1 2 1 0 -1 -1 1 0 0 0 1 0 0 1 0 0 0 1 -1 1 0
  -2 2 1 1 1 -4 -2 -1 0 0 -4 2 -4 -1 0 1 1 0 2 -1 1 -1 1 -1 -3 2 1 -1 0 0 0 1 1 0 -1 -1 0 -1 -1 -1 0 1 1 1 -1 0 0 -1
  11 -14 2 6 2 1 2 1 5 -5 7 -4 2 3 1 -6 -1 4 -3 1 1 3 2 -3 2 3 7 -1 -1 2 1 1 -2 -3 0 -1 -3 2 -2 1 -2 0 -2 0 1 0 0 -1
  -1 1 1 1 0 1 -2 1 -4 2 -1 0 2 2 0 2 0 -3 -2 1 0 -1 0 1 1 -2 -2 -1 0 -1 -1 0 0 0 0 2 2 0 1 0 0 -1 1 0 0 -1 0 1
  -4 4 0 1 1 -4 0 -3 -2 1 -6 3 -6 -2 1 1 2 1 4 -2 0 -2 1 -1 -4 3 0 0 -1 -1 0 1 2 0 -1 -2 1 -2 -1 0 -1 2 1 1 -2 1 -1 -1
  2 1 -4 -5 -1 2 0 0 3 0 5 0 3 0 -2 1 -2 0 0 0 0 3 -3 2 1 -1 -1 3 2 1 1 -2 0 2 1 -1 -1 1 0 1 1 0 -1 -1 1 -1 1 0
  12 -11 -3 8 4 3 5 2 1 -3 4 -5 4 3 -2 -1 -3 1 -4 0 -1 3 0 1 3 -1 0 2 0 1 0 -1 0 0 2 1 -1 1 0 1 -1 -2 -2 -1 1 -1 0 0
  -1 -2 3 1 1 -4 2 -2 3 -2 -3 2 -7 -3 2 -5 1 4 3 -3 0 -1 3 -4 -3 5 5 -2 -2 1 1 2 0 -2 -2 -2 -2 -1 -2 0 -2 2 0 1 -1 2 -1 -2
  48 48
  4 -6 -1 2 1 0 3 0 3 -2 3 -1 0 1 -1 -4 -3 3 -2 -1 1 3 -1 -1 1 1 2 2 0 2 1 -1 0 0 1 -1 -2 1 0 1 -1 -1 -1 0 0 1 0 -1
  3 -8 1 -3 -6 1 1 2 5 -2 4 -1 0 1 -1 -8 -4 5 -3 -2 4 4 0 -2 3 1 4 1 1 2 0 0 -1 -1 0 -1 -2 1 0 0 0 0 -1 1 1 1 1 -1
  1 -3 1 3 -1 2 1 1 0 0 3 -1 2 1 0 -1 1 0 -1 1 0 1 0 0 1 0 1 0 -1 0 -1 1 -1 -1 0 0 -1 0 0 -1 0 0 0 -1 0 0 -1 -1
  -2 5 1 -1 2 -2 -2 -1 -3 1 -4 0 -3 -1 1 2 2 -1 2 0 -2 -4 2 -1 -1 0 -1 -2 -1 -1 0 0 1 0 -1 1 1 0 0 0 0 0 1 1 0 0 0 1
  4 -1 0 1 -2 0 -1 1 2 -1 -1 1 -1 0 -1 0 0 0 0 1 0 0 2 -1 -1 1 0 0 0 0 -2 0 1 0 1 0 0 0 -1 -1 1 1 0 1 0 0 1 0
  1 -2 2 -1 -5 0 -2 1 1 0 0 0 0 1 -1 -1 -1 1 -1 0 3 1 0 0 1 0 1 0 1 0 -1 1 0 0 0 0 1 0 -1 -1 1 1 0 1 0 0 1 0
  -6 5 -2 -4 -3 1 0 0 -1 2 0 1 2 -1 -1 2 -1 -1 1 -1 1 1 -3 3 0 -2 -3 2 2 0 0 0 0 2 0 -1 1 -1 1 0 1 0 0 -1 0 0 0 0
  1 2 -3 1 0 1 2 1 0 0 -1 0 1 -1 -1 2 0 -2 1 0 -2 0 1 2 -1 -1 -3 1 0 0 -2 0 1 1 1 0 0 -1 0 0 1 0 0 0 0 0 0 0
  -1 2 1 1 1 -3 -2 -1 -3 1 -4 1 -4 -1 1 1 2 -1 2 0 -1 -3 3 -1 -2 1 0 -2 -1 -1 -1 1 1 -1 -1 0 1 -1 -1 -1 0 1 1 1 -1 0 0 0
  0 4 -1 1 1 -2 -2 -2 -3 2 -4 2 -3 -1 1 3 2 -2 2 1 -2 -3 3 -1 -3 1 -2 -1 -1 -1 -2 0 2 0 0 0 1 -1 -1 -1 1 1 1 1 -1 0 0 0
  0 5 -4 -1 4 -1 1 0 -1 0 -3 1 -2 -3 -1 3 -1 -2 2 0 -4 -2 1 1 -2 -1 -4 1 0 0 0 -2 2 2 1 0 0 0 0 1 0 -1 0 0 0 0 0 1
  -1 7 -1 2 4 -4 -1 -2 -3 1 -7 2 -4 -1 -1 5 1 -1 2 1 -2 -4 1 -1 -3 0 -4 0 0 -1 0 -1 3 2 1 1 2 0 0 0 0 -1 1 1 -1 0 0 1
  -3 2 4 0 0 -3 -2 -1 1 0 -4 3 -4 -1 1 -1 2 1 1 0 1 -2 1 -3 -2 3 2 -2 -1 0 0 1 0 -1 -1 0 0 0 0 -1 -1 1 1 1 -1 1 0 0
  -5 6 0 1 -1 -1 0 -1 -3 2 -4 1 0 -1 0 4 2 -2 2 0 0 -2 0 2 -2 -1 -3 0 0 -1 -1 1 1 1 0 0 2 -2 0 -1 1 1 1 0 -1 0 -1 0
  5 -5 -2 -2 -1 1 0 2 1 -1 4 -2 1 1 -1 -3 -3 1 -2 0 0 2 0 0 3 -1 1 1 1 1 0 -1 0 0 1 0 -1 1 0 1 0 -1 -1 0 1 -1 1 0
  1 2 -7 -4 0 5 2 1 -2 2 5 -2 7 1 -3 4 -3 -3 -2 0 -1 3 -5 5 3 -5 -6 4 3 0 0 -3 0 3 2 1 1 0 2 2 1 -3 -1 -2 1 -2 1 1
  -1 -1 4 6 0 -2 -2 0 -4 1 -4 0 -2 1 2 1 3 -1 0 2 0 -3 3 -1 -1 0 1 -3 -2 -2 -1 3 0 -2 -1 1 2 -1 -1 -2 0 1 1 1 -1 0 -1 0
  6 -4 -3 -4 -4 3 0 2 4 -1 5 0 3 1 -2 -2 -3 1 -2 0 1 4 -1 0 2 0 0 2 2 1 -1 -2 0 1 2 0 -1 1 0 1 1 -1 -1 0 1 -1 2 0
  0 8 -1 4 8 -2 1 -3 -3 1 -6 1 -3 -2 0 7 4 -3 4 1 -5 -5 1 0 -4 1 -4 -1 -2 -1 0 -1 2 1 0 1 1 0 0 0 -1 0 1 0 -1 0 -1 1
  -2 -1 0 -3 -2 2 0 -1 3 0 4 0 2 0 0 -1 0 1 1 -1 2 3 -3 1 0 1 2 1 1 1 1 0 -2 0 -1 -2 -1 0 0 0 0 1 -1 -1 0 0 0 -1
  5 -5 -2 1 1 0 3 0 3 -2 1 -1 -1 0 -3 -3 -5 3 -2 -2 1 3 -2 0 1 0 0 3 1 2 1 -2 1 1 1 -1 -1 1 0 1 -1 -1 -1 1 0 1 1 0
  5 -9 -2 -1 -3 7 3 2 4 -1 10 -3 7 3 -1 -4 -2 2 -4 0 2 6 -3 1 4 -1 2 2 1 1 0 -1 -3 -1 0 0 -2 1 1 0 0 -1 -2 -2 2 -1 0 -1
  2 -4 1 0 -4 1 0 1 1 0 0 0 0 1 -2 -2 -2 2 -2 -1 3 2 -1 0 1 0 0 1 1 0 -1 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 1 0
  6 -8 0 0 -2 0 0 -1 3 -1 3 -1 -1 1 -1 -4 -3 4 -2 -1 3 3 0 -2 1 2 3 1 1 1 1 -1 0 -1 0 -1 -1 1 -1 0 0 0 -1 1 0 0 1 -1
  0 1 4 0 -4 -1 -4 1 -3 1 -4 -1 -1 2 0 1 3 0 0 1 2 -3 2 -1 1 -1 0 -3 0 -2 -2 2 0 -1 -1 2 3 0 0 -2 1 1 1 2 0 -1 1 1
  3 -1 -1 -4 -1 2 -1 0 3 -1 3 -1 2 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 -1 -1 0 0 0 -1 1 0 0 1 1 -1 0 1 -1 1 0
  -3 5 -3 -4 -1 0 -1 -2 -2 3 -1 1 1 0 -1 3 -2 -1 0 0 1 0 -3 2 0 -2 -4 2 2 0 1 -2 1 2 1 0 2 0 1 1 1 -1 0 0 0 0 1 1
  2 0 3 6 4 -4 -1 -1 -3 0 -6 1 -5 0 3 1 4 -1 2 2 -3 -5 5 -3 -2 2 1 -4 -3 -2 -1 2 1 -2 0 1 1 0 -1 -1 -1 1 1 1 -1 0 -1 0
  -1 2 4 4 0 -1 -4 -1 -5 2 -3 -1 -2 0 3 3 5 -3 2 2 -2 -5 5 -1 -2 1 1 -4 -3 -2 -2 3 0 -2 -2 1 1 -1 -2 -2 1 2 1 1 -1 0 -1 0
  -1 3 0 -3 -3 1 -3 2 -2 1 1 0 3 2 -1 2 0 -2 -2 2 1 0 -1 1 2 -3 -2 0 2 -1 -1 0 0 1 1 2 2 0 1 0 1 -1 1 0 1 -2 1 1
  -2 -1 2 4 1 -2 2 0 1 -1 -3 1 -2 -1 0 0 1 1 1 -1 1 0 0 0 -2 2 1 0 -1 0 0 2 0 0 -1 -1 0 -1 -1 -1 -1 1 0 0 -1 1 -1 -1
  3 -1 -2 -3 1 -1 -1 -1 3 -1 1 2 -2 -1 0 -1 -2 1 0 0 0 1 0 -2 -1 2 1 1 1 1 1 -2 1 1 1 -1 -1 1 -1 1 0 0 -1 0 0 0 1 0
  -7 3 3 -1 -2 -2 -3 -1 -3 3 -3 2 -2 -1 1 1 2 -1 1 1 2 -2 0 0 -1 0 0 -2 0 -1 0 2 -1 -1 -2 0 2 -1 0 -2 0 1 1 0 -1 0 -1 0
  -6 6 2 -1 0 -2 -2 -2 -2 1 -4 1 -2 -1 0 2 1 0 2 -1 1 -2 -2 1 -2 0 -1 0 0 0 1 0 1 1 -1 -1 2 -1 0 0 0 1 1 1 -1 1 0 1
  8 -5 -2 1 -1 3 0 2 2 -1 4 -1 3 1 -1 0 -2 -1 -3 2 -1 2 1 0 2 -1 0 1 0 0 -1 -1 0 0 2 1 -1 1 -1 0 1 0 -1 0 1 -1 1 0
  4 0 -1 3 9 -3 1 -2 1 -2 -2 1 -4 -2 2 1 1 -1 2 1 -5 -3 4 -3 -3 3 1 -2 -2 0 1 -1 1 -1 0 0 -2 1 -1 1 -2 0 0 0 0 0 -1 0
  2 -1 -1 -1 -1 0 1 3 3 -2 0 1 -1 -1 -1 -2 -1 0 0 0 -1 1 2 0 0 0 0 0 0 0 -1 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 1 0
  -4 1 3 -2 -4 -1 -1 0 -1 1 -3 1 -3 -1 1 -2 1 2 1 -2 2 -1 1 -1 0 1 1 -2 0 -1 0 2 0 -1 -2 0 1 -1 0 -1 0 1 1 1 0 1 0 0
  1 6 -8 -3 7 3 3 -2 -1 1 3 -1 4 -1 -2 6 -2 -3 1 0 -4 1 -5 4 0 -3 -6 4 2 1 2 -5 1 4 2 0 0 1 2 3 0 -3 -1 -2 1 -1 0 1
  1 1 -2 2 4 2 2 -1 -1 0 2 -1 2 0 1 2 1 -2 1 0 -3 0 0 1 -1 0 -1 0 -1 0 0 -1 0 0 0 0 -1 0 0 1 0 -1 0 -1 0 0 -1 0
  -1 9 -5 -1 3 3 1 0 -2 1 1 0 5 0 -1 8 2 -5 2 2 -4 -1 -2 4 -1 -3 -6 2 1 -1 -1 -2 1 3 2 1 1 0 1 1 2 -1 0 -2 1 -1 0 1
  -3 4 1 0 1 0 -1 0 -1 0 -2 1 0 -1 2 2 3 -2 2 0 -2 -2 2 0 -2 1 0 -2 -1 -1 -1 1 0 0 -1 0 0 -1 0 0 0 1 1 0 0 0 -1 0
  0 1 -1 0 0 -1 0 -1 0 0 -2 1 -1 0 -1 2 0 0 2 -2 1 1 -2 2 -2 1 -1 1 1 0 0 0 1 1 0 -1 1 -1 -1 0 0 1 0 0 -1 0 1 0
  -3 9 1 2 3 -3 -2 -2 -4 2 -8 2 -4 -3 2 6 5 -3 4 2 -4 -7 4 -1 -4 1 -3 -3 -2 -2 -1 1 2 0 -1 1 2 -1 -1 -1 1 1 1 1 -1 0 -1 1
  3 -1 0 4 7 -1 0 -2 -2 0 1 -1 0 1 2 2 2 -1 -1 2 -3 -2 1 -2 0 1 1 -1 -2 -1 2 -1 0 -1 0 1 -1 1 0 1 -1 -1 0 -1 0 -1 -1 0
  -1 1 0 4 4 0 2 -1 -1 0 -2 0 -1 -1 0 2 1 -2 1 0 -2 -1 0 1 -2 0 -1 0 -2 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 -1 1 -1 0
  -8 5 2 -7 -5 -2 -3 1 1 1 -3 3 -3 -2 -1 -1 -1 1 2 -2 3 0 -2 0 0 0 0 0 2 0 0 1 0 1 -1 -1 1 -1 1 -1 0 1 1 0 0 0 1 0
  2 7 -8 -4 5 2 -1 -3 -4 3 0 0 3 0 -1 8 -1 -4 1 1 -4 -1 -3 3 -1 -3 -7 3 2 -1 1 -5 2 4 2 1 2 1 1 2 1 -2 -1 -1 0 -2 1 2
  48 48
  5 -1 -2 1 3 -1 1 -2 3 -2 0 -1 -2 -1 -1 0 -1 1 1 0 -1 0 1 -1 -1 1 1 1 0 1 1 -1 1 0 1 -1 -1 0 -1 1 0 1 -1 1 0 0 1 0
  4 -1 -1 4 5 -1 1 -2 -1 0 -2 -1 -2 0 -1 2 0 -1 0 0 -2 -1 1 0 -1 0 -1 0 -1 0 0 -1 1 0 0 1 0 0 0 0 -1 0 0 1 -1 0 0 0
  8 -4 -4 -5 -5 6 0 5 5 -2 7 -3 6 2 -4 -1 -4 0 -3 1 1 5 -2 2 5 -4 -1 3 3 1 -1 -2 -1 2 3 1 -1 2 1 1 2 -1 -2 0 3 -2 3 1
  -6 1 8 11 2 -6 0 -3 -7 2 -11 1 -7 0 3 1 6 1 2 -1 1 -6 4 -2 -4 3 1 -5 -4 -2 -1 5 1 -3 -4 1 3 -3 -1 -3 -2 2 3 2 -3 2 -3 -1
  2 1 -4 -5 -2 3 0 2 1 0 2 0 3 0 -2 1 -3 -2 -1 0 -1 2 -1 2 2 -3 -3 2 2 0 -1 -2 0 2 2 1 0 1 1 1 1 -1 -1 0 1 -1 1 1
  -2 4 -3 -6 -3 2 -3 2 -2 2 1 1 3 1 -1 2 -2 -3 -2 2 -1 0 0 1 2 -4 -4 1 2 -1 -2 -2 0 2 2 2 1 1 2 0 2 -2 0 0 1 -1 1 1
  2 -4 -1 -4 -2 3 0 4 5 -2 8 1 3 0 0 -4 -2 0 -2 1 -1 4 0 -1 2 1 3 1 0 1 0 -1 -2 0 1 -1 -4 2 0 1 0 -1 -1 -2 2 0 1 -1
  1 -2 -4 -2 -1 2 3 1 3 -1 3 1 2 -1 -1 -1 -3 0 0 -2 0 4 -2 2 0 0 -1 3 1 1 0 -1 0 1 1 -2 -2 0 0 1 0 0 -1 -1 0 0 0 -1
  -11 9 6 1 -1 -3 -3 -1 -6 3 -8 1 -2 0 2 3 5 -2 2 1 1 -6 1 0 -1 -2 -2 -4 -1 -2 -1 3 0 -1 -2 2 4 -2 2 -2 0 1 3 1 -1 0 -2 1
  2 1 -2 -3 -1 2 -2 2 0 0 2 -1 3 1 -2 2 -1 -2 -1 1 0 1 -1 2 2 -3 -2 1 2 0 -1 -1 0 1 1 1 0 1 1 0 1 0 0 0 1 -2 1 1
  -8 6 6 5 2 -5 0 -2 -4 1 -9 4 -7 -3 4 1 6 -1 4 -1 -2 -6 5 -3 -5 4 1 -5 -4 -2 -1 4 1 -2 -3 0 1 -3 -1 -1 -2 2 3 1 -2 2 -3 -1
  -4 3 4 -2 -4 -2 -2 2 1 -1 -3 3 -3 -2 1 -2 1 0 1 0 0 -2 3 -2 -1 2 2 -2 -1 0 -1 2 0 0 0 0 0 -1 -1 0 0 1 1 1 0 1 0 0
  9 -7 -3 -2 -2 2 1 2 6 -3 5 -1 2 1 -3 -3 -4 3 -2 -1 2 5 -2 0 2 1 2 3 2 2 1 -2 0 1 2 -1 -2 2 -1 1 0 0 -2 0 1 -1 2 0
  -2 -3 0 -7 -6 3 0 7 6 -3 5 2 3 -1 0 -6 -4 0 -2 0 0 4 0 0 3 -1 2 1 1 1 -1 0 -2 1 2 -1 -3 1 1 1 0 -1 -1 -1 2 0 1 0
  -9 9 4 5 1 -2 0 -4 -7 4 -8 0 -3 -1 1 5 6 -2 4 -1 0 -5 0 2 -3 -1 -3 -3 -2 -2 -1 3 1 -1 -3 1 4 -4 1 -2 0 2 3 1 -2 1 -2 0
  -6 9 -3 -9 -3 4 -2 1 -1 3 4 1 5 -1 -1 4 0 -4 1 1 -1 1 -5 4 2 -4 -4 2 2 0 0 -2 -1 3 1 0 1 0 2 1 2 -1 0 -2 1 -1 1 1
  0 1 -1 -3 -3 4 -2 3 -2 1 4 -3 7 3 -2 2 -1 -2 -3 2 2 1 -3 3 4 -5 -3 1 3 0 -1 -1 -1 1 1 2 2 1 2 0 2 -2 0 -1 2 -2 1 2
  1 5 -3 -4 1 0 -2 -2 -2 2 -1 0 0 -1 -1 4 -1 -3 1 0 -2 -1 -1 2 0 -2 -3 1 1 0 0 -2 1 2 1 1 1 0 0 1 1 0 0 1 -1 -1 1 1
  -4 1 1 -2 -6 0 2 2 3 -1 -2 3 -1 -2 0 -2 0 2 2 -3 2 2 -1 1 -1 2 1 1 0 0 0 2 0 1 0 -2 0 -2 -1 0 0 2 0 0 0 1 0 -1
  2 -2 -2 -3 0 1 1 0 3 -1 4 0 1 0 1 -2 -1 1 0 0 -1 2 0 -1 1 1 2 1 0 0 1 -1 -1 0 1 -1 -2 1 0 1 0 0 -1 -1 1 0 1 -1
  1 3 -2 0 5 -1 0 -3 0 0 -1 1 -2 -1 -1 3 0 -1 1 0 -2 -1 0 -1 -2 1 -1 1 0 0 1 -2 1 1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0
  5 3 -8 -6 -1 9 0 2 -2 3 8 -5 11 3 -5 7 -3 -5 -3 2 -1 4 -8 8 6 -9 -8 5 4 0 0 -5 -1 4 3 3 2 2 3 1 3 -3 -2 -2 2 -3 3 3
  3 2 -3 -8 -3 7 -4 5 0 1 7 -2 9 3 -3 3 -3 -5 -5 4 -1 2 -3 3 6 -7 -4 2 3 0 -1 -4 -2 3 3 4 1 3 3 1 2 -3 -1 -1 3 -3 2 3
  -5 9 3 -3 2 -4 -5 -3 -3 2 -6 2 -5 -2 2 3 3 -3 3 1 -2 -6 3 -2 -3 1 0 -3 -1 -1 0 0 1 0 -1 1 2 -1 0 0 0 1 2 2 -1 0 0 1
  -8 2 4 2 -4 2 1 3 -4 2 -3 0 3 1 1 1 3 -2 0 0 1 -1 -1 3 2 -3 -2 -2 -1 -2 -2 3 -2 0 -1 2 3 -2 2 -2 0 0 1 -1 0 0 -2 0
  -2 -3 2 4 2 -3 2 -2 0 0 -4 3 -5 -2 4 -2 2 1 3 -2 -1 -1 3 -2 -4 5 3 -2 -3 -1 0 2 0 -2 -2 -2 -1 -1 -2 -1 -2 2 0 0 -2 2 -2 -2
  0 7 -3 -4 4 0 -3 -2 -2 2 2 1 1 -1 0 5 1 -4 1 2 -4 -2 -1 1 -1 0 -2 1 0 0 1 -3 1 2 1 0 0 1 0 2 1 -1 0 -1 0 -1 1 1
  0 4 -1 1 -1 2 0 -2 -3 2 -1 -2 3 1 -1 5 2 -1 1 0 1 -1 -2 3 0 -2 -3 1 1 -1 0 0 1 1 0 1 3 -1 0 0 2 1 0 0 0 -1 0 1
  -2 -3 3 1 -6 0 -1 5 -1 0 -2 0 1 2 1 -3 0 0 -2 1 2 0 3 0 2 -2 0 -2 0 -1 -3 3 -1 -1 0 1 1 0 1 -2 1 0 1 1 1 0 0 0
  -2 -2 -1 -7 -8 7 -1 5 1 1 9 -2 9 2 -2 -2 -3 -1 -4 1 3 5 -5 4 6 -5 -1 2 3 1 -1 -1 -3 1 1 1 0 1 2 0 2 -2 -1 -2 2 -1 1 1
  -1 -2 -2 -6 -6 3 0 5 5 -2 4 2 3 0 -1 -4 -4 1 -2 0 2 4 -1 0 2 -1 0 2 2 1 -1 -1 -1 1 2 -1 -2 1 1 0 1 -1 -1 -1 2 0 1 0
  -6 12 -2 -5 2 -3 -2 -4 -2 2 -6 3 -5 -4 1 4 2 -2 5 0 -3 -5 2 -1 -4 0 -3 -1 0 -1 0 -1 2 1 0 0 1 -1 0 0 1 1 1 1 -1 1 0 1
  -6 9 -1 -9 -5 4 -3 3 0 2 3 1 5 0 -1 3 2 -3 1 1 0 0 -3 2 2 -3 -3 0 2 -1 -1 -1 -1 2 1 1 1 0 3 0 2 -1 1 -2 2 -2 1 1
  -1 -3 5 8 5 -5 1 -1 -1 -2 -6 1 -7 -1 3 -3 3 2 1 0 -2 -4 6 -5 -3 4 4 -4 -4 -1 0 3 0 -3 -2 0 -1 -1 -1 -1 -3 1 1 1 -1 2 -2 -1
  3 2 -6 -7 -1 3 -3 1 -1 2 3 0 4 1 -3 4 -4 -3 -2 1 0 2 -3 3 2 -4 -5 3 4 0 -1 -4 1 3 2 1 1 2 1 1 2 -2 -1 0 1 -2 2 2
  -8 6 4 3 1 -6 0 -5 -3 2 -9 4 -7 -3 3 2 4 1 5 -3 1 -4 1 -1 -6 5 1 -2 -2 -1 1 3 2 -1 -3 -2 2 -3 -2 -1 -1 3 2 1 -3 2 -2 -1
  -4 3 2 1 1 0 -1 -2 -5 3 -2 0 1 1 2 2 2 -2 -1 1 0 -3 0 0 0 -1 -2 -2 -1 -1 0 0 0 -1 -1 2 2 0 1 0 0 -1 1 0 -1 0 -2 1
  -5 4 3 3 1 -4 -2 -3 -5 3 -6 1 -4 0 1 2 3 0 1 0 1 -4 1 -1 -3 1 -1 -2 -1 -1 0 1 1 -1 -2 1 2 -1 0 -2 0 0 2 1 -2 1 -1 0
  -1 4 3 5 4 -4 0 -5 -1 0 -5 2 -6 -3 4 2 6 0 5 0 -3 -5 4 -3 -6 6 3 -3 -4 -1 1 2 1 -2 -2 -2 0 -2 -3 0 -1 3 1 1 -2 2 -1 -1
  3 -1 -1 4 3 -2 1 -3 -2 0 -2 -2 -1 1 0 2 0 1 0 0 0 -1 0 0 -1 0 -1 1 0 0 1 0 1 0 0 0 1 0 -1 0 0 0 0 1 -1 0 0 0
  -1 -2 0 3 -1 -1 3 0 1 -1 -2 1 -2 -2 2 -2 0 1 2 -1 -1 0 2 0 -2 2 1 0 -2 0 0 2 0 -1 0 -2 -1 -1 -2 0 0 1 -1 0 -1 2 -1 -1
  7 -14 2 8 1 -1 3 1 2 -3 2 -1 -1 2 2 -6 -1 4 -3 -1 1 3 3 -3 0 4 5 -1 -2 0 0 2 -1 -3 -1 -1 -3 1 -2 -1 -2 0 -1 0 -1 1 -1 -2
  -9 8 1 -2 -2 -2 -3 -2 -6 4 -4 1 0 0 2 3 2 -2 1 2 0 -4 0 1 0 -3 -3 -1 0 -2 0 1 0 0 0 1 3 -1 1 -1 2 0 1 0 -1 0 -1 1
  -7 4 2 0 -4 -2 2 1 0 0 -5 5 -4 -3 1 -1 3 1 4 -4 1 0 1 0 -4 4 0 -1 -1 -1 -2 3 1 0 -2 -2 0 -3 -1 -1 -1 2 2 0 -1 2 -1 -2
  1 -4 3 3 0 -3 0 -3 1 -1 -2 -1 -5 0 0 -3 1 5 2 -3 4 0 0 -2 -2 4 4 -1 0 1 1 2 1 -2 -3 -2 0 -1 -2 -1 -1 2 0 1 -1 1 0 -1
  0 0 -2 -4 -3 1 0 2 2 -1 0 0 2 0 0 -1 -2 0 0 0 1 1 -1 1 2 -2 -1 1 2 0 0 0 0 1 2 -1 1 0 1 1 1 0 -1 0 1 -1 1 1
  -2 -2 4 -2 -5 2 -3 3 -1 1 3 0 2 2 0 -3 0 0 -3 1 2 1 0 -1 3 -1 2 -2 0 0 -1 1 -2 -1 -1 2 0 1 1 -1 0 -1 1 0 1 0 0 0
  -4 7 2 2 4 -1 -2 -1 -5 2 -3 1 -1 -2 3 5 5 -5 3 2 -5 -5 2 1 -2 0 -1 -3 -3 -2 0 1 0 0 -1 1 1 -1 -1 0 0 1 1 -1 -1 0 -1 1
  48 48
  -4 0 1 0 -4 0 3 2 2 -1 -2 1 -1 -1 -1 -3 0 2 1 -3 2 2 -1 1 0 0 0 0 0 0 -1 2 0 0 0 -1 0 -2 1 -1 0 1 1 0 0 1 0 -1
  -1 -2 1 0 -3 0 1 1 1 0 0 1 0 0 0 -2 0 1 0 -2 2 2 -1 1 0 1 1 0 0 0 0 1 0 0 0 -1 0 -1 0 0 0 1 1 0 0 0 0 -1
  -2 5 -3 1 1 2 1 -1 -3 2 0 0 2 0 -1 4 2 -2 1 0 -1 0 -2 2 -1 -1 -4 1 0 -1 -1 -1 1 1 0 0 1 -1 1 0 1 -1 1 -1 0 0 0 0
  1 0 1 -3 -1 1 -2 2 0 0 2 0 2 0 1 0 0 -2 -1 2 -1 -1 1 0 2 -1 1 -1 0 0 0 0 -1 0 1 1 0 1 0 1 0 0 0 0 1 -1 0 1
  0 -3 0 -2 -4 1 -1 0 0 1 2 0 0 1 -1 -2 -1 2 -1 -2 3 3 -2 0 1 1 1 1 1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 1 -1
  1 -3 0 1 0 0 0 0 0 0 1 0 0 1 0 -1 0 1 0 -1 1 2 -1 0 0 1 1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 -1
  0 -2 1 4 4 -2 1 -2 1 -1 0 0 -1 0 1 -1 0 1 0 0 0 0 0 -1 -2 2 2 0 -1 1 1 0 0 -1 -1 -1 -1 0 -1 0 -1 0 0 0 -1 1 -1 -1
  1 -8 3 2 -2 -2 0 -1 1 -1 1 -1 -2 1 0 -6 -3 4 -3 -2 4 2 0 -2 1 2 4 0 0 1 1 1 0 -2 -1 -1 -1 0 -1 0 -1 0 0 1 -1 1 0 -1
  3 1 -4 -4 -1 3 -1 1 -2 1 3 -1 4 1 -1 3 -1 -2 -1 1 -1 1 -2 2 3 -3 -3 2 2 -1 0 -2 0 2 2 1 1 1 1 1 1 -1 -1 -1 1 -2 1 1
  0 -1 -2 -4 -4 3 0 2 0 0 4 -1 4 1 -1 -1 -2 0 -2 -1 2 3 -3 2 3 -2 -1 2 2 0 0 -1 0 1 1 0 0 0 1 1 1 -1 0 -1 1 -1 1 0
  1 -3 1 -3 2 -2 -2 -1 3 -1 2 1 -2 -1 1 -3 -2 1 -1 1 0 0 1 -3 0 2 4 0 0 1 2 -1 -1 -1 0 -1 -2 2 -1 1 -1 0 -1 0 0 0 0 0
  -3 3 0 -6 -3 1 -1 2 2 0 1 1 0 -1 -1 -1 0 0 1 0 0 1 -1 0 1 -1 0 0 1 0 -1 0 -1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0
  0 3 -2 -4 -4 3 -1 2 0 1 2 -1 3 1 -3 2 -1 -1 -1 0 1 2 -3 3 2 -3 -3 2 2 0 -1 -1 0 2 1 1 1 0 1 0 2 -1 0 0 1 -1 2 1
  4 -3 -4 2 4 1 4 -2 1 -1 3 -2 1 0 -2 0 -2 2 0 -2 0 3 -3 1 0 0 -1 3 1 1 1 -2 1 1 0 -1 -1 0 0 1 -1 -1 -1 -1 0 0 0 -1
  -3 3 2 -1 0 -2 -2 0 -1 0 -2 2 -2 -1 2 0 2 -1 1 1 -1 -3 3 -2 -1 1 1 -2 -1 -1 0 1 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 -1 0
  0 1 0 3 4 -3 -1 -2 -2 0 -2 1 -2 0 2 1 1 -1 0 2 -2 -3 3 -2 -2 1 0 -1 -1 -1 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 0
  -2 7 -2 -2 1 2 -2 -1 -5 3 -1 0 2 0 1 6 3 -4 2 2 -3 -3 0 1 0 -2 -4 -1 0 -2 -1 -1 0 1 0 2 2 0 1 0 1 -1 0 -1 0 -1 0 1
  -4 1 3 -2 -5 -1 -3 1 -1 1 -2 1 -2 0 1 -2 1 0 0 0 2 -1 2 -1 0 0 1 -2 0 -1 -1 2 0 -1 -1 0 1 -1 0 -1 1 1 1 1 0 0 0 0
  3 -2 -2 -2 0 1 1 1 2 -1 3 -1 1 0 -2 -1 -3 1 -2 0 0 2 -1 0 2 -1 0 2 1 1 0 -1 0 1 1 0 -1 1 0 1 0 -1 -1 0 1 0 1 0
  0 -3 2 5 1 -2 3 0 2 -2 -3 0 -3 -1 1 -3 0 2 1 -2 0 0 2 -1 -2 2 2 -1 -2 1 0 2 0 -1 -1 -1 -1 -1 -1 -1 -1 1 0 1 -1 2 -1 -1
  0 -2 1 -2 -3 0 0 1 2 0 1 1 0 0 0 -2 0 1 0 -1 1 2 -1 0 1 1 2 0 0 0 0 1 -1 0 0 -1 0 0 0 0 0 1 0 0 0 0 1 -1
  0 4 -1 5 3 -1 0 -2 -5 2 -4 1 -1 0 2 5 3 -3 1 1 -3 -4 3 0 -3 1 -3 -1 -2 -2 -1 0 2 0 0 1 1 -1 -1 0 1 0 1 0 -1 0 -1 0
  4 0 -4 -4 -3 4 -2 1 -1 2 5 0 5 2 -1 3 0 -2 -1 1 0 3 -3 2 2 -1 -2 2 2 -1 -1 -2 0 2 1 0 1 1 0 1 2 -1 -1 -1 1 -2 2 0
  -5 1 2 -4 -5 -1 0 1 3 0 -2 3 -3 -2 1 -3 1 2 3 -2 2 1 0 -1 -1 2 2 -1 0 0 0 2 -1 0 -1 -2 0 -1 0 -1 0 2 0 0 0 1 0 -1
  5 0 -5 -3 -1 4 -1 0 -3 2 5 -1 5 2 -1 4 0 -2 -1 1 -1 2 -2 2 2 -2 -3 2 2 -1 -1 -2 0 2 1 1 1 1 0 1 1 -1 -1 -1 1 -2 1 0
  3 -7 1 1 0 -2 0 -2 3 -1 1 0 -3 0 0 -4 -3 4 -1 -2 3 2 0 -2 -1 3 4 1 0 2 2 0 0 -1 -1 -2 -2 1 -2 0 -1 1 -1 1 -1 1 0 -1
  -3 -4 4 1 -2 -3 1 2 5 -3 -1 2 -3 -1 2 -6 0 3 1 -1 2 1 2 -2 -1 3 5 -2 -1 1 0 3 -1 -2 -1 -2 -2 -1 -1 -1 -1 2 0 0 0 1 -1 -2
  -2 4 -1 -5 -4 1 -1 2 1 0 0 1 0 -1 -1 0 0 0 1 0 0 0 0 0 1 -1 -1 0 1 0 -1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0
  1 -3 0 3 1 2 1 1 -2 0 2 -1 3 1 1 0 0 -1 -1 0 0 1 -1 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 -1 0 0 -1 0
  2 4 -2 0 3 1 -3 -2 -4 2 0 0 1 1 1 5 2 -3 0 3 -3 -3 2 -1 -1 -1 -3 -1 0 -2 -1 -2 1 0 0 2 1 1 0 0 1 -1 0 0 0 -1 0 1
  4 -4 -2 0 2 1 1 0 1 -1 3 -1 1 1 -2 -1 -3 1 -2 -1 0 3 -2 0 1 0 0 2 1 1 0 -2 0 1 0 0 -1 1 0 1 -1 -2 -1 0 0 0 1 0
  -4 2 0 -3 0 -1 1 1 3 -1 -2 2 -3 -2 -1 -2 -2 1 1 -2 0 1 -1 0 -1 0 0 1 0 1 1 -1 0 1 0 -1 -1 0 1 0 -1 0 0 0 0 1 0 0
  -1 3 -2 -2 3 0 0 -1 1 0 1 1 0 -1 0 2 0 -1 1 1 -2 0 -1 0 -1 0 -1 1 0 0 1 -2 -1 1 0 0 -1 1 0 0 0 -1 -1 -1 0 0 0 0
  3 -4 0 0 0 3 0 2 2 -1 5 -2 4 1 0 -1 0 -1 -1 1 0 2 -1 1 2 -1 2 0 0 1 0 0 -2 -1 0 0 -1 1 0 0 0 0 -1 -1 1 -1 0 0
  1 1 -2 0 4 0 -2 -3 -3 2 1 0 0 1 1 3 1 -1 0 1 -1 -1 0 -1 -1 1 -1 0 0 -1 1 -2 1 0 -1 0 0 1 0 1 0 -1 0 -1 0 -1 0 0
  0 -3 3 -2 -1 -2 -1 1 4 -2 -1 1 -4 -2 1 -4 -2 2 0 0 0 -1 3 -3 0 2 4 -1 -1 1 1 1 -1 -1 0 -1 -2 1 -1 0 -1 1 -1 1 0 1 0 0
  5 -6 1 -1 -1 -1 -4 -1 1 0 2 0 -1 2 0 -2 -2 2 -3 1 2 1 1 -3 1 2 3 0 1 0 1 -1 0 -1 0 0 -1 2 -1 0 0 0 -1 1 0 -1 1 0
  -2 2 2 1 1 0 -1 0 -1 1 -1 0 1 0 1 2 1 -2 0 2 -1 -2 0 1 0 -1 0 -1 -1 0 1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 1
  -7 0 5 -2 -2 -5 1 1 7 -3 -4 4 -7 -5 2 -7 -1 3 3 -2 1 -1 3 -3 -3 4 6 -2 -2 2 1 3 -1 -2 -1 -3 -3 -1 -2 -1 -1 3 0 1 -1 3 -1 -1
  -3 4 2 3 0 -1 1 0 -3 1 -6 0 -2 -2 1 2 2 -2 2 0 -2 -4 2 1 -1 -1 -2 -2 -2 -1 -1 2 1 0 0 1 2 -2 0 -1 0 1 1 1 -1 1 -1 1
  -2 -4 3 3 0 -2 1 -1 1 -1 -2 0 -4 -1 0 -4 -1 3 0 -2 2 0 1 -2 -1 2 3 -1 -1 1 0 2 0 -2 -2 -1 -1 -1 -1 -1 -2 1 0 1 -1 2 -1 -1
  3 -5 3 6 2 -1 1 -1 0 -1 0 -2 -1 0 1 -2 0 1 -1 0 0 -1 2 -1 -1 2 3 -1 -2 1 1 1 0 -2 -1 0 -1 0 -2 0 -1 0 0 1 -1 1 -1 0
  7 -7 -2 3 0 2 1 2 0 -2 3 -3 3 3 -1 -1 -2 1 -3 1 0 2 1 0 3 -2 0 1 1 0 -1 0 0 0 1 1 0 1 0 0 0 -1 -2 0 1 -1 0 0
  -4 3 1 -4 3 -4 -3 -3 0 1 -1 2 -4 -2 1 0 -1 0 1 0 0 -2 0 -2 -2 2 2 0 0 1 2 -1 0 0 -1 -1 -1 1 -1 1 -1 0 0 0 -1 1 0 0
  -3 6 1 -2 1 -1 -1 0 0 0 -2 1 -1 -1 0 2 2 -1 1 1 -1 -3 1 -1 -1 0 -1 -1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
  2 -5 -1 2 -1 1 4 1 2 -2 1 -1 0 0 -1 -3 -1 3 0 -3 1 3 -1 0 1 1 1 1 0 0 0 1 0 0 0 -1 -1 -1 0 0 -1 0 -1 -1 0 0 0 -1
  2 1 1 -2 1 1 -3 1 0 0 3 0 2 1 1 1 1 -2 -1 3 -2 -1 1 -1 1 0 1 -1 0 0 0 -1 -1 0 0 1 0 2 0 1 0 -1 0 0 1 -1 0 1
  -1 1 1 0 1 -2 0 0 1 -1 -1 1 -2 -1 2 -1 1 0 1 1 -1 -2 3 -2 -1 1 2 -1 -1 0 0 1 0 -1 0 0 -1 0 -1 0 0 1 0 0 0 0 -1 -1
  
• PROPERTIES
  Uniodular=1
  
• REFERENCES
  G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
  
• NOTES
  G. Nebe's recently discovered extremal unimodular 48-dim. lattice.
  CycloQuaternionic lattice of type Delta2 otimes Delta2
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

[ AT&T Labs Research | Our People | Our Work | History | Find ]