The Lattice P42.1

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 Aug 16 13:40:32 EDT 1999

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIM
GRAM
PROPERTIES
MINIMAL_NORM
KISSING_NUMBER
THETA_SERIES
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
REFERENCES
LAST_LINE

• NAME
  P42.1
  
• DIM
  42
  
• GRAM
  42 0
  4
  -2 4
  -2 1 4
  -1 2 -1 4
  -2 1 2 -1 4
  -2 0 0 0 0 4
  -2 0 0 1 0 1 4
  -2 2 1 2 0 0 2 4
  1 -2 -2 -1 0 1 0 -1 4
  -2 0 1 -1 2 1 2 1 0 4
  -2 1 0 0 0 2 1 0 0 1 4
  -1 2 2 0 2 -1 0 1 -1 0 -1 4
  -2 0 1 -1 1 2 2 1 1 2 1 1 4
  -2 2 1 0 2 0 0 1 0 1 1 2 1 4
  -1 2 -1 2 0 1 0 0 -1 0 1 0 0 0 4
  -2 1 2 1 0 0 1 2 -2 1 1 0 0 1 0 4
  -2 1 2 1 0 0 1 2 -2 0 0 1 1 1 0 2 4
  -1 2 0 2 -1 0 0 1 -1 -1 1 0 0 1 1 1 1 4
  -2 2 0 1 0 2 1 1 0 0 2 1 2 1 2 0 1 1 4
  -2 0 0 0 1 1 2 0 0 2 2 0 1 1 1 1 0 0 1 4
  -2 0 1 -1 2 2 0 0 1 1 1 0 1 1 0 0 0 -1 1 1 4
  -2 1 0 2 0 2 1 1 0 0 1 0 1 0 2 1 1 1 2 1 1 5
  -2 1 2 -1 2 0 1 1 -1 2 1 1 1 2 -1 1 1 0 0 1 1 0 5
  -2 1 0 0 1 2 1 1 1 1 2 0 2 1 1 0 0 0 2 1 2 1 0 5
  -2 2 1 0 2 0 0 0 -1 1 2 1 0 2 1 1 0 1 1 2 1 1 1 2 6
  1 -1 0 -1 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 0 -1 0 5
  -1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 -1 2 1 -2 5
  -1 2 -1 1 1 1 0 0 0 0 1 1 0 1 2 -1 -1 0 2 1 1 0 0 2 1 -2 0 6
  1 -2 1 -1 -1 -1 0 0 0 0 -1 -1 0 -1 -2 1 1 0 -2 -1 -1 0 1 -1 -2 2 -1 -3 6
  -2 2 0 1 0 2 0 1 0 0 2 0 1 2 1 1 1 2 2 0 1 2 1 1 0 0 1 1 0 6
  -1 2 2 0 0 0 -1 1 -2 -1 1 1 0 1 0 1 2 1 1 -1 0 -1 0 1 1 1 1 0 0 1 6
  -2 1 0 0 0 2 2 1 0 2 2 0 2 1 1 1 0 1 2 2 1 1 0 2 1 0 -1 2 -1 2 -1 6
  -2 2 1 0 2 0 0 0 -1 1 2 1 0 2 1 1 0 1 1 2 1 0 1 2 3 1 1 1 -1 2 1 2 6
  1 0 -1 1 0 -2 -1 -1 -1 -1 -1 0 -2 0 1 0 0 0 -1 0 -1 -1 -1 -1 0 1 -1 1 -1 -1 0 -1 0 5
  1 -1 0 -1 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 0 -2 1 2 -3 -1 0 -2 0 0 -1 0 5
  1 -2 0 -2 1 -1 0 -2 1 0 -1 0 0 0 -2 -1 -1 -1 -2 0 0 -2 1 0 0 0 -1 0 1 -2 -2 -1 0 0 1 6
  -2 1 0 0 1 2 1 1 1 1 2 0 2 1 1 0 0 0 2 1 2 1 1 2 0 -1 2 1 -1 2 1 1 1 -1 -2 -1 5
  -2 0 1 1 0 2 2 2 0 1 0 0 2 0 0 1 2 0 1 0 1 2 0 2 0 0 1 -1 1 1 0 1 -1 -1 -1 -1 0 6
  -2 0 1 1 0 1 1 1 0 0 1 0 1 1 0 2 2 1 1 1 1 2 0 0 0 0 0 -1 0 2 0 1 0 0 0 -1 1 2 5
  -2 2 0 1 0 2 0 1 0 0 2 0 1 2 1 1 1 2 2 0 1 1 1 2 0 -1 1 2 -1 4 1 2 2 0 -2 -1 2 0 1 6
  1 -1 0 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 0 -1 -2 0 0 0 0 0 1 -1 0 0 -1 0 1 1 -2 1 0 -1 5
  -2 0 2 0 2 0 2 1 -1 2 0 1 1 0 0 1 1 -1 0 2 1 0 2 1 0 0 -1 1 1 -1 -1 1 1 0 -1 1 0 2 1 -1 0 6
  
• PROPERTIES
  INTEGRAL=1
  UNIMODULAR=1
  
• MINIMAL_NORM
  4
  
• KISSING_NUMBER
  44100
  
• THETA_SERIES
  1+44100*q^4+693504*q^5+42571200*q^6+907776000*q^7+13025848500*q^8+
  137700774400*q^9+O(q^10)
  
• SUBGROUP_ORDER
  (2^4*3^2*5^3*7)^2
  
• SUBGROUP_NAME
  U3(5)xU3(5)
  
• SUBGROUP_GENERATORS
  6
  42 42
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
  -1 -2 2 1 -1 -1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 -1 0 0 0
  -6 1 0 0 -1 -2 -1 -2 0 -1 -1 0 0 0 -1 0 -1 -1 0 1 -1 -1 0 2 -1 0 0 -1 0 1 -1 0 -1 0 1 -1 0 0 -1 0 0 0
  -5 -2 -1 -2 -2 -3 0 -2 0 2 -1 1 -3 0 0 0 -1 1 1 -1 -1 1 0 1 -1 -1 0 0 -1 0 1 0 0 -1 0 0 1 1 0 0 0 0
  3 -2 -4 -2 1 1 1 -2 1 4 0 4 -4 -2 -1 3 2 4 1 -2 0 2 2 1 -1 -1 0 0 -2 0 2 0 1 0 0 0 1 0 0 -1 1 1
  -6 -2 4 -1 -5 -3 1 -1 0 1 -2 -2 -2 2 1 -3 -2 -1 1 -1 -1 0 -1 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0
  3 0 0 0 0 1 1 -1 0 2 -1 1 -2 0 -1 0 0 1 1 0 0 1 0 1 0 -2 0 -1 0 1 1 0 0 1 1 0 1 0 0 0 0 1
  -4 0 -3 1 1 -2 -2 -1 -1 -1 0 1 1 -1 0 1 -1 -1 0 1 0 -1 0 0 0 1 -1 0 0 -1 0 0 -1 -2 -1 0 0 1 0 1 0 -1
  -6 -3 5 0 -4 -5 0 -1 1 0 -1 -2 -1 2 2 -2 -2 -1 0 0 -1 0 -1 0 0 0 0 0 -1 1 0 0 -1 -1 0 0 0 1 -1 1 -1 0
  -6 -1 5 0 -4 -3 0 0 0 -1 -1 -3 0 3 1 -3 -2 -2 0 0 -1 0 -2 0 1 0 0 0 0 1 -1 0 -1 0 0 0 0 0 -1 1 -1 0
  -1 2 1 0 -2 0 0 -1 0 0 -1 -1 0 0 0 -1 0 -1 0 0 0 -1 0 0 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 0
  -4 0 0 -3 -2 -1 0 2 0 0 1 -1 0 1 1 -1 -1 0 0 -1 0 1 -1 -2 0 1 1 1 0 -1 0 0 0 0 -1 1 -1 0 0 0 0 0
  -9 1 0 -5 -4 -3 0 -1 0 1 -1 -1 -3 1 -1 -2 -2 0 1 -1 -2 2 -1 0 -1 -1 2 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
  -3 -1 2 3 -1 -2 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -2 0 1 0 -2 -1 1 1 0 -1 0 1 1 -1 0 -1 -1 0 0 0 0 0 0 -1 -1
  0 -2 -4 0 2 0 -1 0 0 0 1 2 0 -2 0 2 1 1 0 -1 0 0 2 -1 0 1 0 0 -1 -1 1 1 0 -1 -1 0 0 0 0 0 1 0
  -5 0 -6 -3 1 -2 0 -4 0 1 -1 3 -2 -2 -2 3 0 2 0 -1 -1 1 1 1 -2 0 0 0 -1 -1 1 0 0 -1 0 -1 1 1 0 0 1 0
  -1 4 1 2 0 1 -1 1 0 -3 0 -2 4 0 0 -1 -1 -3 -1 2 1 -2 -1 0 1 0 0 -1 2 1 -1 0 -1 1 1 0 -1 -1 0 0 -1 0
  1 -8 5 1 -2 -3 2 -1 0 3 -1 0 -4 3 2 -1 0 2 1 -2 -1 2 0 1 0 0 -1 1 -3 1 1 0 0 -2 -1 0 2 1 -1 0 0 0
  -2 -5 7 5 -2 -3 -1 2 0 -2 0 -3 2 3 3 -3 -2 -3 0 1 0 -1 -1 -1 2 1 -1 0 0 1 0 1 -1 -1 -1 1 0 0 -1 1 -1 -1
  -9 1 1 2 -2 -4 -3 -2 0 -2 -1 -1 1 0 0 -1 -2 -3 0 2 -1 -2 -1 1 0 0 0 -1 1 1 -1 1 -2 -1 1 0 0 1 -1 1 -1 -1
  0 -2 -3 -3 -1 -1 1 -2 1 3 0 2 -3 0 0 2 1 3 0 -3 0 3 1 -1 -1 0 0 1 -2 -2 2 0 1 -1 -1 0 1 1 0 0 1 1
  -4 -2 2 -1 -1 -3 0 0 0 0 0 -1 -1 1 1 -1 -1 0 0 0 -1 1 0 0 -1 1 0 1 -1 -1 0 0 0 -1 -1 0 0 1 0 0 0 -1
  42 42
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 5 3 -2 -1 0 -1 1 0 -1 -1 0 1 1 -1 0 -1 0 1 0 -1 -1 1 1 0 0 0 0 2 -1 0 -1 0 1 0 1 0 -1 0 -1 0
  1 -2 6 1 -2 -1 1 2 0 0 0 -3 0 3 2 -3 -1 -1 0 0 0 0 -1 -1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 -1 0
  3 1 -2 4 4 1 -2 0 0 -2 1 1 3 -2 0 2 1 -1 -1 2 1 -2 1 1 0 1 -1 -1 0 0 0 1 -1 -1 0 0 0 0 0 0 0 -1
  -2 0 -2 2 1 -1 -1 -3 0 0 -1 2 0 -1 -1 2 0 0 0 1 0 -1 0 2 0 0 -1 -1 0 1 0 0 -1 -1 1 -1 1 0 -1 0 0 0
  -1 -2 2 -1 -2 -1 1 -1 0 2 -1 0 -3 1 0 -1 0 1 1 -1 -1 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 -1 -1 2 2 -1 -1 0 -1 -1 0 0 1 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 0 0 1 0 0
  3 3 -6 -1 4 3 -1 1 0 -1 2 2 2 -3 -1 3 2 1 -1 0 1 0 2 -1 -1 1 0 1 0 -2 0 0 1 0 -1 0 -1 0 1 -1 1 -1
  2 -2 6 3 -1 -1 0 1 1 0 0 -2 0 1 2 -2 0 -1 0 1 0 -1 0 0 1 0 0 0 0 1 0 1 -1 0 0 1 0 0 0 0 -1 -1
  -1 -2 2 -1 -2 -1 1 -1 0 2 -1 0 -3 1 0 -1 0 1 1 -1 -1 1 0 1 0 -1 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0
  2 1 -4 -2 2 2 0 1 -1 0 1 1 0 -1 -1 1 1 1 0 -1 0 1 1 -1 0 0 0 0 0 -2 1 0 1 0 -1 0 0 0 1 0 1 0
  -3 2 -2 -1 -1 0 0 -3 1 1 -1 2 -1 -2 -1 2 1 1 0 0 0 -1 1 2 -1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 -1 0 -1
  -1 -1 3 4 0 -2 -1 -1 0 -1 -1 -1 1 0 1 -1 -1 -2 0 2 0 -2 0 1 1 0 -1 -1 0 1 0 1 -1 -1 0 0 0 0 0 1 -1 -1
  1 1 -4 -4 1 2 1 1 -1 1 1 1 -1 0 -1 1 1 2 0 -2 0 2 0 -1 -1 0 0 1 0 -2 0 -1 2 1 -1 0 0 0 1 -1 1 0
  -3 2 -2 -1 -1 0 0 -2 0 0 -1 1 0 -1 -1 1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 -1 -1 0 0 1 -1 0 0 0 0 0 0
  0 1 1 5 2 -1 -2 0 0 -3 0 -1 4 -1 1 0 -1 -3 -1 3 1 -3 0 0 1 1 -1 -1 1 1 0 1 -2 -1 0 1 -1 0 0 1 -1 -1
  0 0 1 -3 -1 0 1 3 0 0 1 -2 0 1 1 -2 -1 0 0 -1 0 2 0 -2 0 0 1 1 0 -1 1 0 1 1 -1 1 -1 0 1 0 0 0
  -3 -2 0 1 -1 -2 0 -4 0 2 -2 2 -3 0 -1 1 0 1 1 0 -1 0 0 3 -1 -1 -1 -1 -1 1 0 0 -1 -1 1 -1 2 1 -1 0 0 0
  -3 0 -3 -4 -2 0 1 -3 1 3 -1 3 -4 -1 -2 2 1 3 1 -2 -1 2 1 2 -2 -1 1 0 -1 0 0 -1 1 1 1 -1 1 0 0 -1 1 1
  4 1 0 0 2 2 0 3 0 -1 2 -1 2 0 1 0 1 0 -1 0 1 0 0 -2 0 1 0 1 0 -1 0 0 1 0 -1 1 -1 0 1 0 0 -1
  -3 1 -3 1 1 -1 -1 -3 0 0 -1 2 0 -2 -1 2 0 0 0 1 0 -1 1 2 -1 0 -1 -1 0 0 0 0 -1 -1 0 -1 0 0 0 0 1 -1
  0 0 0 0 0 0 0 -1 1 1 0 1 -1 -1 0 1 1 1 0 0 0 0 1 1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0
  42 42
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  5 1 1 0 1 3 2 2 -1 0 0 -1 1 1 0 -1 0 0 0 0 1 0 -1 0 1 -1 -1 0 1 0 0 -1 1 1 0 0 0 -1 1 0 0 0
  3 3 -4 -5 0 4 3 -2 0 4 -1 3 -4 -1 -3 2 2 4 1 -2 0 2 0 2 -1 -2 0 0 0 0 0 -2 2 2 1 -1 1 -1 1 -2 1 1
  -6 -2 -1 0 -1 -3 -1 -1 -1 0 -1 0 -1 0 0 -1 -2 -1 1 0 -1 0 0 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 0 0 1 0 0
  5 1 -1 2 2 2 1 -2 0 1 -1 2 0 -1 -1 2 1 1 0 1 1 -1 0 2 0 -1 -1 -1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 -1 3 4 0 -2 -1 -1 0 -1 -1 -1 1 0 1 -1 -1 -2 0 2 0 -2 0 1 1 0 -1 -1 1 1 0 1 -2 -1 0 0 0 0 0 1 -1 -1
  -6 -5 4 6 -1 -6 -3 -2 0 -2 -1 -1 1 1 2 -1 -2 -3 0 2 -1 -2 0 1 1 1 -1 -1 -1 2 0 2 -3 -3 0 0 1 1 -2 2 -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 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 0 0 0 0 0 0 0 0
  -1 -1 3 4 0 -2 -1 -1 0 -1 -1 -1 1 0 1 -1 -1 -2 0 2 0 -2 0 1 1 0 -1 -1 0 1 0 1 -1 -1 0 0 0 0 0 1 -1 -1
  -5 -1 -4 -4 -1 -1 0 0 -1 1 0 1 -2 0 -1 0 -1 1 1 -2 -1 2 0 -1 -1 -1 1 0 0 -1 1 0 1 1 0 0 0 0 0 0 1 1
  -3 2 -5 -8 -2 1 2 -2 1 3 0 2 -4 -1 -2 2 2 4 0 -4 -1 3 1 0 -2 0 2 2 -1 -2 0 -1 2 1 0 -1 0 0 1 -2 1 1
  4 1 -1 -1 1 2 2 0 0 0 0 0 1 0 0 1 1 1 -1 -1 1 0 0 -1 1 0 -1 1 0 -1 0 -1 1 0 -1 0 0 0 1 0 0 0
  -3 0 -3 1 1 -2 -2 -1 0 -1 0 1 1 -2 0 1 -1 -1 0 1 0 -1 1 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 1 0 1 0 0
  -3 -2 2 -1 -2 -1 1 0 -1 1 -1 -1 -2 2 0 -2 -1 0 1 -1 -1 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  -5 -4 1 2 -1 -4 -2 -1 0 -1 0 0 0 1 1 0 -1 -1 0 0 -1 0 0 0 0 1 0 0 -1 0 0 1 -1 -2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 2 2 -1 -3 1 2 -3 1 2 -2 0 -2 1 -1 0 1 1 0 -1 0 0 -1 2 0 -1 0 0 0 1 -1 -1 0 1 1 -1 1 -1 0 -1 0 1
  2 -3 4 4 2 -1 -1 3 -1 -2 1 -2 2 1 2 -2 -1 -2 0 2 0 -1 0 -1 1 1 -1 0 0 0 0 1 -1 -1 -1 1 0 0 0 1 0 -1
  42 42
  -1 0 -1 -2 1 1 0 1 0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 1 2 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 -1 2 1 -1 -1 0 0 0 -1 0 -1 1 1 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
  3 1 -1 1 1 1 1 -1 0 1 0 1 0 -1 -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
  -3 0 0 0 -2 -2 -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
  3 1 1 1 0 0 0 0 0 0 0 -1 1 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
  3 2 1 2 0 0 0 -1 0 0 0 -1 2 0 0 0 1 -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
  -1 1 -2 -1 0 0 0 -1 0 0 0 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
  4 1 -1 1 2 1 0 0 -1 0 0 0 1 -1 -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
  -4 -1 0 0 -2 -2 -1 -1 0 1 -1 0 0 0 0 0 -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
  5 2 1 2 1 1 1 -1 0 1 0 -1 1 0 -1 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
  3 2 0 1 0 0 0 -1 0 1 0 0 1 -1 -1 1 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
  1 0 0 2 0 0 0 -1 -1 1 0 0 1 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 1 -1 -1 0 -1 0 0 0 0 1 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 2 -1 -1 -1 0 -1 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 0 0 0 0
  -1 0 2 1 -2 -1 0 0 0 0 0 -1 1 1 1 -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
  1 -3 1 1 1 0 0 1 -1 0 1 0 0 1 1 0 -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
  1 0 1 1 -1 -1 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 1 1 1 0 1 0 -1 0 0 -1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -1 1 -1 -1 0 -2 1 1 0 1 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
  -1 0 2 1 -2 -2 0 -1 0 0 0 -1 1 1 0 -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
  3 0 -1 1 1 1 0 0 0 1 0 1 0 -1 0 1 1 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 2 0 1 -2 -1 0 -3 1 2 -1 1 0 -1 -1 1 1 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
  4 -2 1 2 1 1 1 0 -1 1 0 0 0 1 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
  4 -2 0 0 3 2 0 3 -1 -1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -4 2 0 0 -3 -2 0 -3 1 1 -1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 0 2 1 0 0 1 -1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 0 -2 -1 0 0 -1 1 -1 -1 0 0 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 -1 2 2 -2 -2 -1 -1 0 1 0 0 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -1 0 0 -2 -1 0 -1 1 2 -1 1 -1 0 1 0 -1 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
  5 0 1 3 2 0 -1 0 -1 0 1 -1 2 0 -1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  4 -2 1 2 1 1 1 0 -1 1 0 0 0 1 0 0 0 1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  1 0 2 0 0 1 1 1 0 -1 0 -1 0 1 0 -1 -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
  4 -2 0 0 3 2 0 3 -1 -1 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 0 0 0 0 0
  3 -1 0 0 1 2 0 2 0 1 1 1 -2 0 0 0 1 1 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 2 0 1 -2 -1 0 -3 1 2 -1 1 0 -1 -1 1 1 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
  -2 2 0 0 -2 -2 -1 -1 1 0 0 0 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 1 0 0 0 0
  0 0 1 1 -1 -1 0 0 -1 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 0 0 0
  -2 -1 2 2 -2 -2 -1 -1 0 1 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 1 0 0
  -2 -2 -2 -1 1 0 -1 2 -1 -1 1 1 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 1 0
  4 1 -1 0 1 1 1 0 0 0 0 0 0 0 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 1
  42 42
  4 2 0 1 1 1 0 -1 0 0 0 0 1 -1 -1 1 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 1 0 0 0 -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
  -2 0 1 0 -1 -1 0 0 0 0 0 -1 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 2 -1 0 0 0 0 -1 1 0 0 0 1 -1 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -3 0 -1 0 -1 0 1 -1 0 0 0 -1 1 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 0
  -1 -4 0 0 0 0 0 2 -1 0 1 1 -1 1 1 -1 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 0 -1 -1 0 1 0 1 0 0 1 -1 0 1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 2 0 0 -2 -1 0 -1 1 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 0
  0 -4 -1 -1 1 1 0 2 -1 0 1 2 -2 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
  -3 -2 1 0 -2 -1 0 0 0 1 0 1 -1 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 0
  -2 -3 1 -1 0 0 0 2 0 0 0 0 -2 1 1 -1 -1 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 1 0 0 0 -1 0 0 0 0 0 -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
  -1 -3 0 0 0 0 0 2 -1 0 1 1 -1 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 0
  1 -1 0 0 1 0 0 1 -1 0 0 -1 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
  1 -1 0 0 1 0 0 1 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
  -3 1 1 0 -2 -1 0 -1 1 0 -1 -1 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
  1 3 0 1 0 0 0 -1 1 0 0 -1 1 0 -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 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 -1 -1 1 0 0 2 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
  -5 -2 1 -2 -2 -1 0 1 1 0 -1 0 -2 1 2 -1 -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
  -3 -4 -1 -2 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 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
  -3 -2 0 -1 -1 -1 0 1 0 0 0 0 -1 1 1 -1 -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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 -4 0 -1 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 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
  -3 -2 1 -1 -1 -1 0 1 0 0 -1 -1 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 3 0 1 1 1 0 -1 1 0 0 0 1 -1 -1 1 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
  -3 -3 0 -1 -1 -1 0 1 -1 0 0 0 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 -2 0 -1 0 -1 0 1 0 0 0 0 0 0 1 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 2 0 1 0 1 0 -1 0 0 0 0 0 0 -1 0 0 -1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 1 0 -1 0 1 -1 0 0 -1 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  2 1 0 1 1 0 0 0 0 0 0 -1 1 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
  -2 -2 1 0 -1 -1 0 1 0 0 0 0 -1 1 1 -1 -1 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
  -3 -2 1 -1 -1 -1 0 1 0 0 -1 -1 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  2 3 0 0 1 1 0 -1 1 0 -1 -1 1 -1 -1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  3 3 0 1 1 1 0 -1 1 0 0 0 1 -1 -1 1 1 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  1 -1 0 0 1 1 0 1 -1 0 0 0 -1 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
  -2 -4 0 -1 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 1 1 -1 -1 0 0 0 0 0 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 1 1 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 1 0 0 0 0
  0 0 -1 -1 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 0 0 0 0 0 0 0 0 1 0 0 0
  0 -2 1 1 0 -1 0 1 -1 0 0 -1 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  4 0 -2 0 3 2 0 1 -1 0 1 1 0 -1 -1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  -3 0 -1 -2 -1 0 0 0 1 0 0 1 -1 0 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 1
  42 42
  -2 0 -2 -1 0 0 -1 0 0 0 0 1 0 -1 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
  1 -1 2 1 0 0 0 1 -1 0 0 -1 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0
  1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 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
  1 0 1 1 0 0 1 0 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 1 1 0 -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 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -1 -1 0 0 0 0 1 0 0 0 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
  -1 1 1 0 -2 -1 0 -1 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 1 1 1 1 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 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 0 0 0 0 0 0 0 0 0 0
  0 0 2 0 -1 -1 1 0 1 0 0 -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 0 0 0 0 0 0
  1 -1 1 0 0 0 0 1 -1 0 0 -1 0 1 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
  1 -1 2 2 0 0 0 0 -1 0 0 -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 -1 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
  1 -1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0
  4 -2 1 0 2 2 1 2 -1 0 0 0 -1 1 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
  1 0 2 1 0 0 1 0 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
  4 2 1 1 1 1 1 -1 0 0 0 -1 1 0 -1 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
  3 2 0 1 1 0 1 -1 0 0 0 -1 1 0 -1 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
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  4 -1 2 1 1 1 1 1 -1 0 0 -1 0 1 0 -1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 -1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 1 0 -1 -1 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 0 0 0 0 0 0 0 0
  2 0 3 1 0 0 1 0 0 0 0 -2 0 1 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
  -2 0 -3 -1 0 0 -1 0 0 0 0 2 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -3 3 1 0 0 1 2 -1 0 0 -1 -1 2 1 -2 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 0 1 1 0 0 1 -1 0 0 0 0 1 0 0 -1 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
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  4 -1 2 1 1 1 1 1 -1 0 0 -1 0 1 0 -1 0 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
  1 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 0 1 0 0 0 0 0 0 0 0
  1 0 -1 0 1 1 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 1 0 0 0 0 0 0 0
  0 -1 0 -1 0 0 0 1 0 0 0 0 -1 0 1 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
  2 0 2 1 0 0 1 0 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 1 0 0 0 0 0
  -1 1 0 0 -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 1 0 0 0 0
  3 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  2 -3 3 1 0 0 1 2 -1 0 0 -1 -1 2 1 -2 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  -1 0 -3 0 1 0 -1 0 -1 0 0 1 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
  1 3 -1 0 0 0 0 -2 1 0 0 0 1 -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
  
• REFERENCES
  Constructed as Q(F,1,3,10) for F = Gram matrix of lattice
  (C2 x PSU(3.5)).S3 of dimension 21 as described in
  C.Bachoc and G. Nebe, Extremal lattices of minimum 8 related to the Mathieu group M22,
  J. reine angew. Mathematik, 494 (1998), 155-171
  
• LAST_LINE
  

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