The Lattice Shimada_86

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 Wed Feb 7 18:11:08 EST 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIM
GRAM
GRAM_MATRIX (in Maple)
DET
PROPERTIES
MINIMAL_NORM
KISSING_NUMBER
GROUP_NAME
REMARKS
REFERENCES
LAST_LINE

• NAME
  Shimada_86
  
• DIM
  86
  
• GRAM
  86 86
  16
  8 8
  8 4 8
  8 4 4 8
  8 4 4 4 8
  8 4 4 4 4 8
  8 4 4 4 4 4 8
  8 4 4 4 4 4 4 8
  0 2 2 2 2 2 2 2 8
  8 4 4 4 4 4 4 4 0 8
  -8 4 4 4 4 4 4 4 0 4 8
  -4 2 4 4 4 4 2 2 4 4 4 8
  -8 4 4 4 4 4 4 4 0 4 4 2 8
  4 4 2 4 4 2 4 2 4 4 2 4 4 8
  4 4 4 4 2 2 2 4 4 2 2 4 4 4 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 8
  0 2 2 2 2 0 0 0 4 2 0 4 0 4 4 2 8
  4 4 4 2 4 4 2 2 4 2 2 4 4 4 4 4 4 8
  0 2 2 2 2 0 0 0 4 0 0 4 0 4 4 0 4 4 8
  4 4 2 4 4 4 2 2 4 2 2 4 2 4 4 2 4 4 4 8
  0 2 2 2 2 0 0 0 4 0 2 4 2 4 4 0 4 4 4 4 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 8
  0 2 2 2 2 0 0 0 4 0 0 3 0 3 3 0 4 3 4 3 4 2 2 2 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 8
  -8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 8
  -4 2 4 4 4 2 2 2 3 2 2 4 2 3 3 2 3 3 3 3 3 4 2 2 4 4 4 8
  -8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 8
  4 4 2 4 4 2 2 2 3 2 2 3 2 4 3 2 3 3 3 4 3 2 4 2 4 4 2 4 4 8
  4 4 4 4 2 2 2 2 3 2 2 3 2 3 4 2 3 3 3 3 3 2 2 4 4 2 2 4 4 4 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 8
  0 2 2 2 2 0 0 0 4 0 0 3 0 3 3 0 4 3 4 3 4 0 0 0 4 2 0 4 0 4 4 2 8
  4 4 4 2 4 2 2 2 3 2 2 3 2 3 3 2 3 4 3 3 3 4 2 2 4 2 2 4 4 4 4 4 4 8
  0 2 2 2 2 0 0 0 4 0 0 3 0 3 3 0 4 3 4 3 4 0 0 0 4 0 0 4 0 4 4 0 4 4 8
  4 4 2 4 4 2 2 2 3 2 2 3 2 4 3 2 3 3 3 4 3 4 2 2 4 2 2 4 2 4 4 2 4 4 4 8
  0 0 0 0 0 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 8
  -8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 8
  -4 2 2 2 2 2 4 4 3 2 2 1 2 2 2 2 0 1 0 1 0 4 2 2 1 2 2 2 2 1 1 2 0 2 0 2 2 4 4 8
  -8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 2 8
  4 2 2 2 2 4 2 4 3 2 2 2 2 1 2 2 0 2 0 2 0 2 4 2 1 2 2 1 2 2 1 2 0 1 0 1 2 4 2 4 4 8
  4 2 2 2 2 4 4 4 3 2 2 2 2 2 2 2 0 2 0 2 0 2 2 4 1 2 2 1 2 1 2 2 0 1 0 1 2 2 2 4 4 4 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 2 4 2 2 8
  0 0 0 0 0 2 2 2 4 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 4 0 4 4 2 8
  4 2 2 2 2 4 4 2 3 2 2 2 2 2 1 2 0 2 0 2 0 4 2 2 1 2 2 2 2 1 1 2 0 2 0 2 2 2 2 4 4 4 4 4 4 8
  0 0 0 0 0 2 2 2 4 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 4 4 0 4 4 8
  4 2 2 2 2 4 2 4 3 2 2 2 2 1 2 2 0 2 0 2 0 4 2 2 1 2 2 2 2 1 1 2 0 2 0 2 2 2 2 4 2 4 4 2 4 4 4 8
  0 1 1 1 1 0 0 0 2 1 1 3 1 3 3 1 4 3 4 3 4 1 1 1 4 0 0 2 0 2 2 0 2 2 2 2 4 1 1 2 1 2 2 1 2 2 2 2 8
  8 4 4 4 4 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 4 0 4 4 2 4 2 2 4 0 2 0 2 0 4 4 2 4 2 2 4 0 2 0 2 0 8
  4 2 2 2 2 2 2 2 0 2 2 1 2 1 2 4 3 2 0 2 0 2 2 2 0 4 2 2 2 2 1 2 1 1 0 1 2 4 2 2 2 2 1 2 1 1 0 1 2 4 8
  4 2 2 2 2 2 2 2 0 4 2 2 2 2 2 2 3 1 0 2 0 2 2 2 0 2 2 1 2 1 2 2 1 1 0 2 2 2 2 1 2 1 1 2 1 1 0 1 2 2 4 8
  4 2 2 2 2 2 2 2 0 4 2 2 2 2 1 4 3 2 0 1 0 2 2 2 0 4 2 2 2 2 1 2 1 1 0 1 2 2 2 1 2 1 2 2 1 1 0 2 2 2 4 4 8
  4 2 2 2 2 2 2 2 0 2 2 1 2 1 2 4 3 2 0 2 0 2 2 2 0 2 2 1 2 1 1 4 1 2 0 1 2 2 2 1 2 1 1 4 1 2 0 1 2 2 4 4 4 8
  0 0 0 0 0 0 0 0 0 2 0 1 0 1 1 2 4 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 4 4 4 4 8
  4 2 2 2 2 2 2 2 0 4 2 2 2 2 2 2 3 1 0 2 0 2 2 2 0 4 2 2 2 2 1 2 1 1 0 1 2 2 2 1 2 1 1 4 1 2 0 1 2 2 4 4 4 4 4 8
  0 1 1 1 1 1 1 1 4 0 1 3 1 3 3 0 2 3 4 3 4 0 0 0 2 1 0 2 0 2 2 1 4 2 2 2 4 1 0 2 0 2 2 1 4 2 2 2 4 1 2 2 2 2 2 2 8
  4 2 2 2 2 2 2 2 0 2 2 1 2 2 1 2 0 2 3 2 0 2 2 2 0 2 4 2 2 1 1 2 0 1 0 1 2 2 2 2 2 1 2 2 0 1 1 1 2 4 2 1 1 1 0 1 2 8
  4 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 0 1 3 2 0 2 2 2 0 2 4 2 2 1 1 2 0 1 0 1 2 2 2 1 2 1 1 2 0 1 1 2 2 2 1 2 2 2 0 1 2 4 8
  4 2 2 2 2 2 2 2 0 2 2 2 2 1 2 2 0 2 3 2 0 2 2 2 0 2 4 2 2 1 1 2 0 1 0 1 2 2 2 1 2 1 1 2 0 2 1 1 2 2 1 1 1 1 0 2 2 4 4 8
  0 1 1 1 1 1 1 1 4 1 1 3 1 3 3 1 4 3 2 3 4 0 0 0 2 0 1 2 1 2 2 0 2 2 2 2 4 0 0 2 0 2 2 0 2 2 4 2 4 1 2 2 2 2 2 2 4 2 2 2 8
  0 4 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 2 0 0 0 0 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 8
  0 0 0 0 0 2 0 0 1 2 2 4 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 1 0 2 1 0 2 1 1 1 2 0 1 1 1 0 1 1 2 1 1 1 2 2 8
  0 2 0 0 0 2 0 0 2 2 0 3 0 2 2 0 2 2 2 2 1 2 0 0 2 0 0 1 0 1 1 0 1 2 1 2 2 0 0 1 0 1 1 0 1 2 1 2 2 2 1 1 1 0 1 1 2 1 1 1 2 4 4 8
  0 0 0 0 0 2 0 0 1 2 2 4 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 1 2 0 1 1 2 1 2 0 1 2 1 0 2 1 2 1 1 1 2 0 4 4 8
  0 2 0 0 0 2 0 0 2 0 2 3 0 1 2 0 1 2 2 2 2 2 0 0 2 0 0 1 0 1 1 0 1 2 1 2 2 0 0 1 0 1 1 0 1 2 1 2 2 0 0 0 0 0 0 0 2 1 1 1 2 2 4 4 4 8
  2 1 2 2 2 1 2 2 3 1 1 2 2 3 3 2 3 3 3 3 3 2 1 1 2 2 2 4 1 2 2 1 2 2 2 2 4 2 2 4 1 2 2 1 2 2 2 2 4 2 4 2 2 2 2 2 4 4 2 2 4 1 2 2 2 2 8
  0 0 0 0 0 0 2 0 1 2 0 1 2 4 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 1 0 1 1 1 1 2 0 0 1 1 0 1 1 2 1 1 0 2 0 1 1 1 1 2 8
  0 0 0 0 0 0 2 0 1 2 0 1 2 4 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 1 0 1 1 2 1 2 0 0 1 1 0 2 2 2 1 2 0 2 0 1 1 2 1 2 4 8
  0 0 2 0 0 0 2 0 2 2 0 2 0 3 1 0 2 1 2 0 1 2 0 0 2 0 0 2 0 0 1 0 1 2 1 1 2 0 0 2 0 0 1 0 1 2 1 1 2 0 0 1 1 0 1 1 2 1 1 0 2 0 1 2 1 1 2 4 4 8
  2 2 1 2 2 2 1 2 3 1 2 3 1 2 3 2 3 3 3 4 3 2 1 1 2 1 1 2 1 2 2 1 2 2 2 4 4 1 1 2 1 2 2 1 2 2 2 4 4 1 2 2 2 2 2 2 4 2 2 2 4 1 2 2 2 4 4 2 2 2 8
  0 0 0 0 0 0 0 2 1 0 0 1 2 1 4 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 2 2 2 0 1 1 1 1 2 0 1 1 0 1 1 1 2 0 1 1 2 0 1 1 1 1 2 2 1 1 2 8
  2 2 2 2 1 2 2 1 3 2 2 3 1 3 2 2 3 3 3 3 3 2 1 1 2 1 1 2 1 2 2 1 2 2 2 2 4 1 1 2 2 2 2 2 2 4 2 2 4 1 2 2 2 2 2 2 4 2 2 2 4 1 2 2 2 2 4 2 2 4 4 2 8
  0 0 0 0 0 2 0 0 1 0 0 1 0 0 1 0 1 1 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 1 1 2 1 2 1 2 0 1 1 1 1 2 0 0 0 2 2 2 8
  2 2 1 2 2 1 2 2 3 2 2 3 2 4 3 2 3 3 3 2 3 1 2 1 2 2 1 2 2 4 2 1 2 2 2 2 4 1 1 2 1 2 2 1 2 2 2 2 4 1 2 2 4 2 2 2 4 2 2 2 4 1 2 2 2 2 4 2 2 2 4 2 4 2 8
  0 0 0 0 0 0 0 0 0 2 0 1 0 1 1 2 4 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 3 3 3 3 4 3 0 0 0 0 2 0 1 1 1 1 2 2 1 1 2 2 2 2 2 8
  0 1 1 1 1 1 1 1 4 0 1 3 1 3 3 0 2 3 4 3 4 1 1 1 4 0 0 2 0 2 2 0 2 2 2 2 4 0 0 2 0 2 2 0 2 2 2 2 4 0 0 0 0 0 0 0 4 2 2 2 4 1 2 2 2 4 4 2 2 2 4 2 4 2 4 2 8
  4 4 2 4 4 2 2 2 3 2 2 3 2 4 3 2 3 3 3 4 3 2 2 2 3 2 2 3 2 4 3 2 3 3 3 4 0 2 4 2 2 1 1 2 0 1 0 1 2 2 1 1 1 1 0 2 2 1 1 2 2 2 0 1 0 1 2 0 0 0 2 1 2 0 2 1 2 8
  0 0 0 0 0 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 2 1 2 2 0 2 2 2 2 4 1 2 2 2 2 2 2 4 2 2 2 4 0 2 2 2 2 4 4 2 2 4 4 4 4 4 4 4 2 8
  2 2 2 1 2 1 2 2 3 2 2 3 1 3 3 1 3 2 3 3 3 2 1 1 2 1 1 2 2 2 2 2 2 4 2 2 4 2 2 4 1 2 2 1 2 2 2 2 4 1 2 2 2 2 2 2 4 2 2 2 4 1 2 2 2 2 4 2 2 4 4 2 4 2 4 2 4 2 4 8
  0 1 1 1 1 1 1 1 4 1 1 3 1 3 3 1 4 3 2 3 4 1 1 1 4 0 0 2 0 2 2 0 2 2 2 2 4 0 0 2 0 2 2 0 2 2 2 2 4 0 2 2 2 2 4 2 4 0 0 0 4 1 2 2 2 2 4 2 2 2 4 2 4 2 4 2 4 2 4 4 8
  2 1 2 2 2 1 2 2 3 1 1 2 2 3 3 2 3 3 3 3 3 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 4 1 1 2 1 2 2 2 2 2 2 2 4 1 2 2 2 4 2 2 4 2 2 2 4 0 0 0 0 0 4 2 2 2 4 2 4 2 4 2 4 2 4 4 4 8
  0 0 0 0 0 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 2 0 2 2 1 4 2 2 2 4 0 2 2 2 2 2 2 4 2 2 2 4 1 4 2 2 2 4 2 2 2 4 2 4 2 4 2 4 0 4 4 4 4 8
  2 2 1 2 2 1 2 2 3 2 2 3 2 4 3 2 3 3 3 2 3 2 1 1 2 1 1 2 1 2 2 1 2 2 2 4 4 2 2 4 1 2 2 1 2 2 2 2 4 1 2 2 2 2 2 2 4 2 2 2 4 1 2 2 2 2 4 2 2 2 4 2 4 0 4 2 4 4 4 4 4 4 4 8
  0 0 0 0 0 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 0 2 2 0 2 2 4 2 4 0 2 2 2 2 4 2 4 2 2 2 4 0 2 2 4 2 4 2 4 2 4 2 4 2 4 2 4 0 4 4 4 4 4 4 8
  1 1 1 1 1 1 1 1 2 -1 -1 -1 1 1 1 1 1 2 1 2 1 1 1 1 2 -1 -1 -1 1 1 1 1 1 2 1 2 1 -1 -1 -1 1 1 1 1 1 2 1 2 1 1 0 1 0 2 1 0 2 0 0 0 2 1 -2 0 -2 0 1 1 1 1 3 1 3 2 2 1 3 1 2 1 3 4 2 1 2 10
  
• GRAM_MATRIX (in Maple)
  [[16, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 8, 8
  , 8, 0, 8, 8, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 8, 8, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0
  , 8, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2
  , 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 1], [8, 8, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4,
  4, 4, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 2, 4, 2, 4, 0, 4, 4, 2,
  4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 4, 0, 2, 0, 2,
  1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 4, 0, 2, 1, 1, 0, 2, 0, 1], [8, 4, 8, 4, 4, 4
  , 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4
  , 2, 4, 2, 2, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 1, 2
  , 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1
  , 0, 1], [8, 4, 4, 8, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 2, 4, 4,
  4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1,
  4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2,
  0, 1, 4, 0, 1, 1, 2, 0, 2, 0, 1], [8, 4, 4, 4, 8, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2
  , 4, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 2, 4, 2, 4, 0, 4, 4, 2, 4
  , 2, 2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2
  , 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 4, 0, 2, 1, 2, 0, 2, 0, 1], [8, 4, 4, 4, 4, 8,
  4, 4, 2, 4, 4, 4, 4, 2, 2, 4, 0, 4, 0, 4, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4,
  0, 2, 0, 2, 1, 4, 4, 2, 4, 4, 4, 4, 2, 4, 2, 4, 0, 4, 2, 2, 2, 2, 0, 2, 1, 2,
  2, 2, 1, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1,
  1, 1], [8, 4, 4, 4, 4, 4, 8, 4, 2, 4, 4, 2, 4, 4, 2, 4, 0, 2, 0, 2, 0, 4, 4, 4
  , 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 4, 4, 2, 4, 4, 2, 4, 2, 2, 0, 4
  , 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0
  , 1, 2, 1, 2, 1, 2, 1, 2, 1, 1], [8, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 2, 4, 2, 4,
  4, 0, 2, 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 4, 4,
  4, 4, 4, 2, 2, 2, 4, 0, 4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2,
  0, 0, 0, 2, 2, 1, 0, 2, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1], [0, 2, 2, 2, 2, 2, 2
  , 2, 8, 0, 0, 4, 0, 4, 4, 0, 4, 4, 4, 4, 4, 0, 0, 0, 4, 0, 0, 3, 0, 3, 3, 0, 4
  , 3, 4, 3, 2, 0, 0, 3, 0, 3, 3, 0, 4, 3, 4, 3, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0
  , 0, 4, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 3, 0, 4, 3, 2, 3, 4, 3, 2, 3, 2
  , 2], [8, 4, 4, 4, 4, 4, 4, 4, 0, 8, 4, 4, 4, 4, 2, 4, 2, 2, 0, 2, 0, 4, 4, 4,
  0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4,
  2, 4, 4, 2, 2, 4, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2,
  0, 2, 1, 2, 1, 1, 1, 2, 1, -1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 8, 4, 4, 2, 2,
  4, 0, 2, 0, 2, 2, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 2, 4,
  2, 2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1,
  0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 1, 2, 1, 1, 1, 2, 1, -1], [4, 2, 4, 4, 4, 4,
  2, 2, 4, 4, 4, 8, 2, 4, 4, 2, 4, 4, 4, 4, 4, 2, 2, 2, 3, 2, 2, 4, 2, 3, 3, 2,
  3, 3, 3, 3, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 3, 2, 1, 2, 2, 1, 1, 2, 3, 1,
  2, 2, 3, 0, 4, 3, 4, 3, 2, 1, 1, 2, 3, 1, 3, 1, 3, 1, 3, 3, 2, 3, 3, 2, 2, 3,
  2, -1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 8, 4, 4, 4, 0, 4, 0, 2, 2, 4, 4,
  4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1,
  4, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 1, 0, 2,
  0, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1], [4, 4, 2, 4, 4, 2, 4, 2, 4, 4, 2, 4, 4, 8, 4
  , 2, 4, 4, 4, 4, 4, 2, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 3, 3, 4, 2, 2, 2, 2, 2
  , 1, 2, 2, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 1, 1, 3
  , 4, 4, 3, 2, 1, 3, 0, 4, 1, 3, 4, 2, 3, 3, 3, 2, 4, 2, 1], [4, 4, 4, 4, 2, 2,
  2, 4, 4, 2, 2, 4, 4, 4, 8, 2, 4, 4, 4, 4, 4, 2, 2, 2, 3, 2, 2, 3, 2, 3, 4, 2,
  3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 3, 2, 2, 2, 1, 2, 1, 2, 3, 1,
  2, 2, 3, 2, 1, 2, 1, 2, 3, 1, 1, 1, 3, 4, 2, 1, 3, 1, 3, 3, 2, 3, 3, 3, 2, 3,
  2, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 8, 2, 4, 0, 2, 0, 4, 4, 4
  , 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4
  , 4, 2, 4, 4, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2
  , 0, 2, 1, 1, 1, 2, 1, 2, 1, 1], [0, 2, 2, 2, 2, 0, 0, 0, 4, 2, 0, 4, 0, 4, 4,
  2, 8, 4, 4, 4, 4, 0, 0, 0, 4, 0, 0, 3, 0, 3, 3, 0, 4, 3, 4, 3, 2, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 4, 0, 3, 3, 3, 3, 4, 3, 2, 0, 0, 0, 4, 2, 1, 2, 1, 1, 3,
  1, 1, 2, 3, 1, 3, 1, 3, 4, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1], [4, 4, 4, 2, 4, 4, 2
  , 2, 4, 2, 2, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3
  , 4, 3, 3, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 3, 2, 2, 1, 2, 2, 1, 1, 3, 2, 1
  , 2, 3, 2, 1, 2, 1, 2, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 3, 2, 2, 3, 3, 2, 3, 2
  , 2], [0, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 0, 0,
  4, 0, 0, 3, 0, 3, 3, 0, 4, 3, 4, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,
  0, 0, 0, 0, 0, 0, 4, 3, 3, 3, 2, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 3, 0,
  4, 3, 2, 3, 2, 3, 2, 3, 2, 1], [4, 4, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2
  , 4, 4, 4, 8, 4, 2, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 3, 3, 4, 2, 2, 2, 1, 2, 2
  , 2, 2, 1, 2, 1, 2, 3, 2, 2, 2, 1, 2, 1, 2, 3, 2, 2, 2, 3, 2, 1, 2, 1, 2, 3, 0
  , 0, 0, 4, 1, 3, 4, 2, 1, 3, 4, 2, 3, 3, 3, 2, 2, 2, 2], [0, 2, 2, 2, 2, 0, 0,
  0, 4, 0, 2, 4, 2, 4, 4, 0, 4, 4, 4, 4, 8, 0, 0, 0, 4, 0, 0, 3, 0, 3, 3, 0, 4,
  3, 4, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0,
  0, 4, 2, 1, 1, 1, 2, 3, 1, 1, 1, 3, 1, 3, 1, 3, 0, 4, 3, 2, 3, 4, 3, 2, 3, 2,
  1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 8, 4, 4, 2
  , 4, 4, 4, 4, 2, 2, 4, 0, 4, 0, 4, 1, 4, 4, 4, 4, 2, 2, 4, 0, 4, 0, 4, 1, 4, 2
  , 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0, 1
  , 2, 0, 2, 1, 1, 0, 2, 0, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4,
  0, 2, 0, 2, 0, 4, 8, 4, 2, 4, 4, 2, 4, 4, 2, 4, 0, 2, 0, 2, 1, 4, 4, 2, 4, 4,
  2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0,
  0, 0, 1, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1], [8, 4, 4, 4, 4, 4, 4, 4
  , 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 8, 2, 4, 4, 2, 4, 2, 4, 4, 0, 2
  , 0, 2, 1, 4, 4, 2, 4, 2, 4, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2
  , 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1
  ], [0, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 3, 0, 3, 3, 0, 4, 3, 4, 3, 4, 2, 2, 2, 8,
  0, 0, 4, 0, 4, 4, 0, 4, 4, 4, 4, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 4, 0, 0,
  0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 4,
  3, 0, 2, 4, 2, 0, 2, 0, 2], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0
  , 2, 0, 2, 0, 4, 4, 4, 0, 8, 4, 4, 4, 4, 2, 4, 2, 2, 0, 2, 1, 4, 4, 2, 4, 2, 2
  , 4, 0, 2, 0, 2, 0, 4, 4, 2, 4, 2, 0, 4, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0
  , 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, -1], [8, 4, 4, 4, 4, 4, 4, 4
  , 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 4, 0, 4, 8, 4, 4, 2, 2, 4, 0, 2
  , 0, 2, 1, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 2, 2, 2, 2, 0, 2, 0, 4, 4, 4
  , 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0,
  -1], [4, 2, 4, 4, 4, 2, 2, 2, 3, 2, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 2, 2, 4
  , 4, 4, 8, 2, 4, 4, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2
  , 1, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 1, 0, 1, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2
  , 3, 0, 2, 2, 2, 0, 2, 0, -1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4
  , 0, 2, 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 8, 4, 4, 4, 0, 4, 0, 2, 1, 4, 4, 2, 4, 2
  , 2, 4, 0, 2, 0, 2, 0, 4, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 0
  , 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1], [4, 4, 2, 4, 4, 2, 2,
  2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 3, 3, 4, 3, 2, 4, 2, 4, 4, 2, 4, 4, 8, 4, 2, 4,
  4, 4, 4, 2, 2, 2, 1, 2, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 1, 2, 1, 0, 2, 2, 1, 1,
  1, 2, 2, 0, 1, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 4, 0, 2, 2, 2, 0, 2, 0,
  1], [4, 4, 4, 4, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 4, 2, 3, 3, 3, 3, 3, 2, 2, 4, 4
  , 2, 2, 4, 4, 4, 8, 2, 4, 4, 4, 4, 2, 2, 2, 1, 2, 1, 2, 2, 0, 1, 0, 1, 2, 2, 1
  , 2, 1, 1, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2
  , 3, 0, 2, 2, 2, 0, 2, 0, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4,
  0, 2, 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 8, 2, 4, 0, 2, 1, 4, 4, 2, 4, 2,
  2, 4, 0, 2, 0, 2, 0, 4, 2, 2, 2, 4, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0,
  0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1], [0, 2, 2, 2, 2, 0, 0, 0
  , 4, 0, 0, 3, 0, 3, 3, 0, 4, 3, 4, 3, 4, 0, 0, 0, 4, 2, 0, 4, 0, 4, 4, 2, 8, 4
  , 4, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 1, 0, 1, 4, 0, 0, 0
  , 2, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 0, 2, 0, 1
  ], [4, 4, 4, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 4, 3, 3, 3, 4, 2, 2, 4,
  2, 2, 4, 4, 4, 4, 4, 4, 8, 4, 4, 2, 2, 2, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 1,
  1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2,
  3, 0, 4, 2, 2, 0, 2, 0, 2], [0, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 3, 0, 3, 3, 0, 4
  , 3, 4, 3, 4, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 2, 0, 0, 0, 0, 0, 0
  , 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 1, 2, 0, 0
  , 1, 2, 0, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 0, 2, 0, 1], [4, 4, 2, 4, 4, 2, 2, 2,
  3, 2, 2, 3, 2, 4, 3, 2, 3, 3, 3, 4, 3, 4, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2, 4, 4,
  4, 8, 2, 2, 2, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1,
  2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 4, 0, 2, 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 4, 0, 2],
  [0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1,
  1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 8, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 0, 2, 2,
  2, 2, 2, 2, 4, 2, 2, 2, 4, 0, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 0,
  4, 4, 4, 4, 4, 4, 4, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2
  , 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 8, 4, 4, 4, 4, 2, 4
  , 2, 2, 0, 2, 1, 4, 4, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0
  , 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 1, 1, 2, 0, -1], [8, 4, 4, 4, 4, 4, 4, 4, 0
  , 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0
  , 2, 0, 4, 8, 4, 4, 2, 2, 4, 0, 2, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0
  , 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 1, 2, 0, 1, 0, 2, 0, -1],
  [4, 2, 2, 2, 2, 2, 4, 4, 3, 2, 2, 1, 2, 2, 2, 2, 0, 1, 0, 1, 0, 4, 2, 2, 1, 2,
  2, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 4, 4, 8, 2, 4, 4, 2, 4, 4, 4, 4, 2, 2, 2, 1,
  1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 4, 1, 1, 2, 2, 1, 2, 0, 2, 0, 2, 2,
  2, 4, 2, 2, 2, 4, 2, -1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0,
  2, 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 2, 8, 4, 4,
  4, 0, 4, 0, 2, 1, 4, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0,
  0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1], [4, 2, 2, 2, 2, 4, 2, 4, 3
  , 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 4, 2, 1, 2, 2, 1, 2, 2, 1, 2, 0, 1, 0
  , 1, 2, 4, 2, 4, 4, 8, 4, 2, 4, 4, 4, 4, 2, 2, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2
  , 0, 2, 1, 1, 1, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1],
  [4, 2, 2, 2, 2, 4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 4, 1, 2,
  2, 1, 2, 1, 2, 2, 0, 1, 0, 1, 2, 2, 2, 4, 4, 4, 8, 2, 4, 4, 4, 4, 2, 2, 1, 1,
  2, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 0, 2, 1,
  2, 2, 2, 2, 2, 2, 2, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2
  , 0, 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 2, 4, 2, 2, 8
  , 2, 4, 0, 2, 1, 4, 2, 2, 2, 4, 0, 4, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
  , 1, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1], [0, 0, 0, 0, 0, 2, 2, 2, 4,
  0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 2, 2, 0, 4, 0, 4, 4, 2, 8, 4, 4, 4, 2, 0, 1, 1, 1, 1, 0, 1, 4, 0, 0, 0, 2,
  0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 4, 2, 2, 1], [4
  , 2, 2, 2, 2, 4, 4, 2, 3, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 4, 2, 2, 1, 2, 2
  , 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 8, 4, 4, 2, 2, 1, 1, 1
  , 2, 0, 2, 2, 1, 1, 2, 2, 0, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 4, 1, 2, 0, 2, 1, 2
  , 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 1, 0, 1, 1, 0, 0, 1,
  0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 4, 4, 0,
  4, 4, 8, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 4, 0, 1, 1, 2, 1, 2, 1, 2, 1,
  2, 1, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 4, 1], [4, 2, 2, 2, 2, 4, 2, 4, 3, 2
  , 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 4, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 0, 2, 0, 2
  , 2, 2, 2, 4, 2, 4, 4, 2, 4, 4, 4, 8, 2, 2, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0
  , 1, 2, 1, 2, 2, 1, 1, 1, 4, 1, 2, 1, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2], [0,
  1, 1, 1, 1, 0, 0, 0, 2, 1, 1, 3, 1, 3, 3, 1, 4, 3, 4, 3, 4, 1, 1, 1, 4, 0, 0,
  2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 8, 0, 2, 2, 2,
  2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4,
  4, 4, 4, 4, 4, 4, 1], [8, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0
  , 2, 0, 4, 4, 4, 0, 4, 4, 2, 4, 2, 2, 4, 0, 2, 0, 2, 0, 4, 4, 2, 4, 2, 2, 4, 0
  , 2, 0, 2, 0, 8, 4, 2, 2, 2, 0, 2, 1, 4, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1
  , 0, 1, 0, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1], [4, 2, 2, 2, 2, 2, 2, 2, 0, 2,
  2, 1, 2, 1, 2, 4, 3, 2, 0, 2, 0, 2, 2, 2, 0, 4, 2, 2, 2, 2, 1, 2, 1, 1, 0, 1,
  2, 4, 2, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 4, 8, 4, 4, 4, 4, 4, 2, 2, 1, 1, 2, 0,
  1, 1, 1, 0, 4, 0, 0, 0, 2, 1, 2, 1, 2, 3, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0], [4, 2
  , 2, 2, 2, 2, 2, 2, 0, 4, 2, 2, 2, 2, 2, 2, 3, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1
  , 2, 1, 2, 2, 1, 1, 0, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 2, 4, 8, 4, 4
  , 4, 4, 2, 1, 2, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 1, 2, 1, 2, 2, 2, 3, 0, 1, 2, 2
  , 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 2, 2, 2, 0, 4, 2, 2, 2, 2, 1, 4, 3, 2, 0,
  1, 0, 2, 2, 2, 0, 4, 2, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1,
  1, 0, 2, 2, 2, 4, 4, 8, 4, 4, 4, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2,
  0, 2, 1, 4, 3, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0], [4, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2
  , 1, 2, 1, 2, 4, 3, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2, 1, 1, 4, 1, 2, 0, 1, 2
  , 2, 2, 1, 2, 1, 1, 4, 1, 2, 0, 1, 2, 2, 4, 4, 4, 8, 4, 4, 2, 1, 2, 1, 2, 0, 0
  , 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 3, 0, 1, 2, 2, 2, 4, 2, 2, 2, 2], [0, 0,
  0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 1, 2, 4, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4, 4, 4,
  8, 4, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 4, 0, 0, 2, 2,
  4, 2, 2, 2, 4, 1], [4, 2, 2, 2, 2, 2, 2, 2, 0, 4, 2, 2, 2, 2, 2, 2, 3, 1, 0, 2
  , 0, 2, 2, 2, 0, 4, 2, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 1, 4, 1, 2
  , 0, 1, 2, 2, 4, 4, 4, 4, 4, 8, 2, 1, 1, 2, 2, 0, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1
  , 2, 1, 2, 3, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0], [0, 1, 1, 1, 1, 1, 1, 1, 4, 0, 1,
  3, 1, 3, 3, 0, 2, 3, 4, 3, 4, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 1, 4, 2, 2, 2, 4,
  1, 0, 2, 0, 2, 2, 1, 4, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 4, 1, 2,
  2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 0, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2], [4, 2, 2
  , 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 1, 2, 0, 2, 3, 2, 0, 2, 2, 2, 0, 2, 4, 2, 2
  , 1, 1, 2, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2, 0, 1, 1, 1, 2, 4, 2, 1, 1, 1, 0
  , 1, 2, 8, 4, 4, 2, 0, 1, 1, 1, 1, 4, 1, 1, 1, 2, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0
  , 2, 2, 2, 2, 0], [4, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 3, 2,
  0, 2, 2, 2, 0, 2, 4, 2, 2, 1, 1, 2, 0, 1, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 0, 1,
  1, 2, 2, 2, 1, 2, 2, 2, 0, 1, 2, 4, 8, 4, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1,
  2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0], [4, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2
  , 2, 1, 2, 2, 0, 2, 3, 2, 0, 2, 2, 2, 0, 2, 4, 2, 2, 1, 1, 2, 0, 1, 0, 1, 2, 2
  , 2, 1, 2, 1, 1, 2, 0, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 2, 4, 4, 8, 2, 0, 1, 1
  , 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0], [0, 1, 1,
  1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 3, 3, 1, 4, 3, 2, 3, 4, 0, 0, 0, 2, 0, 1, 2, 1,
  2, 2, 0, 2, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, 0, 2, 2, 4, 2, 4, 1, 2, 2, 2, 2, 2,
  2, 4, 2, 2, 2, 8, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 4,
  4, 4, 4, 4, 2], [0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2
  , 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
  , 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 8, 2, 4, 0, 2, 1, 0, 0, 0, 1, 0, 1
  , 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 4,
  0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,
  0, 1, 0, 2, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 8, 4,
  4, 4, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 0, 2, 2, 2, 0, 4, 2, 2, -2], [0, 2, 0,
  0, 0, 2, 0, 0, 2, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 1, 0,
  1, 1, 0, 1, 2, 1, 2, 2, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 1, 1, 1, 0, 1,
  1, 2, 1, 1, 1, 2, 4, 4, 8, 4, 4, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2,
  0, 2, 2, 2, 0], [0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 4, 0, 1, 1, 0, 1, 1, 1, 1, 1
  , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2
  , 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 0, 4, 4, 8, 4, 2, 1, 2, 1, 2, 1, 2
  , 1, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 4, -2], [0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 3
  , 0, 1, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 0
  , 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 2, 4, 4
  , 4, 8, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 2, 2, 0, 2, 2, 2, 0], [2, 1, 2,
  2, 2, 1, 2, 2, 3, 1, 1, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 1, 1, 2, 2, 2, 4, 1,
  2, 2, 1, 2, 2, 2, 2, 4, 2, 2, 4, 1, 2, 2, 1, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2,
  2, 4, 4, 2, 2, 4, 1, 2, 2, 2, 2, 8, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 4,
  4, 4, 4, 4, 1], [0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 2, 4, 1, 0, 1, 1, 1, 0, 1
  , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1
  , 1, 2, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 8, 4, 4, 2, 2, 2
  , 0, 2, 2, 2, 0, 4, 2, 2, 2, 2, 2, 2, 1], [0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1,
  2, 4, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,
  0, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 0, 2, 0, 1, 1,
  2, 1, 2, 4, 8, 4, 2, 1, 2, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 4, 1], [0, 0, 2, 0
  , 0, 0, 2, 0, 2, 2, 0, 2, 0, 3, 1, 0, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0
  , 1, 0, 1, 2, 1, 1, 2, 0, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 1, 0, 1, 1
  , 2, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 4, 4, 8, 2, 1, 4, 0, 2, 1, 2, 0, 2, 4, 2, 2
  , 2, 2, 2, 1], [2, 2, 1, 2, 2, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 2, 3, 3, 3, 4, 3,
  2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 4, 4, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2,
  4, 4, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 2, 2, 4, 4, 2, 2, 2, 8, 2, 4,
  2, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 3], [0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2
  , 1, 4, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0
  , 1, 2, 2, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1
  , 1, 2, 2, 1, 1, 2, 8, 2, 2, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2,
  1, 2, 2, 1, 3, 2, 2, 3, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2,
  2, 1, 2, 2, 2, 2, 4, 1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2,
  4, 2, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 8, 2, 4, 2, 4, 2, 4, 4, 4, 4,
  4, 4, 4, 3], [0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 4, 1, 0
  , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1
  , 2, 0, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 2, 2, 2, 8
  , 2, 2, 2, 0, 4, 2, 2, 2, 2, 0, 2, 2], [2, 2, 1, 2, 2, 1, 2, 2, 3, 2, 2, 3, 2,
  4, 3, 2, 3, 3, 3, 2, 3, 1, 2, 1, 2, 2, 1, 2, 2, 4, 2, 1, 2, 2, 2, 2, 4, 1, 1,
  2, 1, 2, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 2, 2,
  2, 4, 2, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2], [0, 0, 0, 0, 0
  , 0, 0, 0, 0, 2, 0, 1, 0, 1, 1, 2, 4, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
  , 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 3, 3, 3, 4, 3, 0
  , 0, 0, 0, 2, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 8, 2, 1, 4, 2, 2, 2, 2
  , 2, 2, 1], [0, 1, 1, 1, 1, 1, 1, 1, 4, 0, 1, 3, 1, 3, 3, 0, 2, 3, 4, 3, 4, 1,
  1, 1, 4, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2,
  4, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 1, 2, 2, 2, 4, 4, 2, 2, 2, 4, 2, 4, 2,
  4, 2, 8, 2, 4, 4, 4, 4, 4, 4, 4, 3], [4, 4, 2, 4, 4, 2, 2, 2, 3, 2, 2, 3, 2, 4
  , 3, 2, 3, 3, 3, 4, 3, 2, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 3, 3, 4, 0, 2, 4, 2
  , 2, 1, 1, 2, 0, 1, 0, 1, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 1, 0, 1
  , 2, 0, 0, 0, 2, 1, 2, 0, 2, 1, 2, 8, 2, 2, 2, 2, 0, 4, 0, 1], [0, 0, 0, 0, 0,
  1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 4, 0, 1, 2, 1, 2, 2, 0, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2, 4,
  2, 2, 2, 4, 0, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 8, 4, 4, 4, 4,
  4, 4, 2], [2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 3, 1, 3, 3, 1, 3, 2, 3, 3, 3, 2, 1
  , 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 1, 2, 2, 1, 2, 2, 2, 2, 4
  , 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 4, 2, 4
  , 2, 4, 2, 4, 8, 4, 4, 4, 4, 4, 1], [0, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 3,
  3, 1, 4, 3, 2, 3, 4, 1, 1, 1, 4, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 0, 0, 2,
  0, 2, 2, 0, 2, 2, 2, 2, 4, 0, 2, 2, 2, 2, 4, 2, 4, 0, 0, 0, 4, 1, 2, 2, 2, 2,
  4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 8, 4, 4, 4, 4, 3], [2, 1, 2, 2, 2, 1
  , 2, 2, 3, 1, 1, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2
  , 2, 2, 2, 2, 4, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 2, 4, 2, 2, 4, 2
  , 2, 2, 4, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 4, 8, 4, 4
  , 4, 4], [0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 2, 0, 2, 2, 1, 4, 2, 2, 2, 4,
  0, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 1, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4,
  2, 4, 0, 4, 4, 4, 4, 8, 4, 4, 2], [2, 2, 1, 2, 2, 1, 2, 2, 3, 2, 2, 3, 2, 4, 3
  , 2, 3, 3, 3, 2, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 2, 4, 1
  , 2, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 2, 2, 2, 4
  , 2, 2, 2, 4, 2, 4, 0, 4, 2, 4, 4, 4, 4, 4, 4, 4, 8, 4, 1], [0, 0, 0, 0, 0, 1,
  1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, 2, 2, 4, 2, 4, 0, 2, 2, 2, 2, 4, 2, 4, 2,
  2, 2, 4, 0, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 0, 4, 4, 4, 4, 4, 4,
  8, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2, -1, -1, -1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1
  , 1, 2, -1, -1, -1, 1, 1, 1, 1, 1, 2, 1, 2, 1, -1, -1, -1, 1, 1, 1, 1, 1, 2, 1
  , 2, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 2, 1, -2, 0, -2, 0, 1, 1, 1, 1, 3, 1,
  3, 2, 2, 1, 3, 1, 2, 1, 3, 4, 2, 1, 2, 10]];
  
• DET
  2^16*3
  
• PROPERTIES
  INTEGRAL=1
  
• MINIMAL_NORM
  8
  
• KISSING_NUMBER
  109421928
  
• GROUP_NAME
  U_8(2)
  
• REMARKS
  The normalized center density of this lattice exceeds the
  Minkowski-Hlawka bound.
  This lattice comes from the algebraic geometry of the
  cubic Fermat 6-fold in characteristic 2.
  The same construction for the cubic Fermat surface and
  the cubic Fermat 4-fold yields the root lattice of type E_6
  and the laminated lattice of rank 22.
  Thus this lattice can be regarded as a generalization of E_6
  and is expected to be a member of an infinite series of non-trivially
  dense lattices.
  The discriminant group (the quotient of the dual lattice by the lattice)
  is isomorphic to $Z/(2)^{\oplus 16}\oplus Z/(3)$.
  
• REFERENCES
  Ichiro Shimada (shimada@math.sci.hokudai.ac.jp),
  "Lattices of algebraic cycles on Fermat varieties in positive characteristics",
  Proc. London Math. Soc. (3) 82 (2001), no. 1, 131-172.
  Available from
  http://www.math.sci.hokudai.ac.jp/~shimada/preprints.html
  
• LAST_LINE
  
  
  

INDEX FILE | ABBREVIATIONS

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