The Lattice KAPPA13

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 Sat Jan 31 00:53:54 EST 1998

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
BASIS
TRIANGULAR_BASIS
GRAM
GROUP_GENERATORS
REFERENCES
LAST_LINE

• NAME
  KAPPA13
  
• DIMENSION
  13
  
• DET
  972
  
• MINIMAL_NORM
  4
  
• KISSING_NUMBER
  918
  
• HERMITE_NUMBER
  .235634843000E+01
  
• GROUP_ORDER
  622080
  
• BASIS
  13 24
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.300000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  
• TRIANGULAR_BASIS
  13 13
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  -.100000000000E+01 .173205080757E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 -.115470053838E+01 .163299316186E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .115470053838E+01 .816496580928E+00
  .141421356237E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .141421356237E+01 .141421356237E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .122474487139E+01
  .707106781187E+00 .707106781187E+00 .122474487139E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .141421356237E+01 -.362597321469E-15
  .141421356237E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .122474487139E+01
  .707106781187E+00 .000000000000E+00 .000000000000E+00
  .707106781187E+00 .122474487139E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .122474487139E+01
  -.314018491737E-15 .707106781187E+00 -.362597321469E-15
  .707106781187E+00 .181298660735E-15 .122474487139E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .612372435696E+00
  .353553390593E+00 .353553390593E+00 .612372435696E+00
  -.106066017178E+01 .612372435696E+00 .612372435696E+00
  .106066017178E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 -.577350269190E+00 .816496580928E+00
  .707106781187E+00 .707106781187E+00 .000000000000E+00
  .707106781187E+00 .000000000000E+00 .181298660735E-15
  .707106781187E+00 .100000000000E+01 .000000000000E+00
  .000000000000E+00
  -.500000000000E+00 .288675134595E+00 .816496580928E+00
  .707106781187E+00 .707106781187E+00 -.362597321469E-15
  .707106781187E+00 .000000000000E+00 .000000000000E+00
  .707106781187E+00 -.500000000000E+00 .866025403784E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .816496580928E+00
  .141421356237E+01 -.133226762955E-14 -.153837014911E-14
  .115470053838E+01
  
• GRAM
  13 13
  4 -2 0 0 0 0 0 0 0 0 0 -1 0
  -2 4 -2 2 0 0 0 0 0 0 -1 1 0
  0 -2 4 0 0 2 0 2 2 1 2 1 0
  0 2 0 4 2 2 0 2 1 1 1 2 0
  0 0 0 2 4 2 2 1 1 1 2 2 0
  0 0 2 2 2 4 1 2 2 2 2 2 0
  0 0 0 0 2 1 4 1 2 -1 2 2 0
  0 0 2 2 1 2 1 4 2 1 2 2 0
  0 0 2 1 1 2 2 2 4 1 2 2 1
  0 0 1 1 1 2 -1 1 1 4 1 1 2
  0 -1 2 1 2 2 2 2 2 1 4 2 1
  -1 1 1 2 2 2 2 2 2 1 2 4 1
  0 0 0 0 0 0 0 0 1 2 1 1 4
  
• GROUP_GENERATORS
  5
  13 13
  0 -1 -1 0 -1 0 0 0 0 0 0 1 0
  0 1 1 0 0 0 1 0 -1 1 0 -1 0
  0 -1 0 1 0 0 1 0 0 0 -1 0 0
  0 0 0 1 -1 0 2 0 -1 1 0 -1 0
  0 0 -1 0 0 0 0 0 0 0 1 0 0
  1 1 0 -1 1 0 0 0 0 0 0 0 0
  -1 -2 -1 2 -1 0 1 -1 0 1 0 0 0
  -1 -2 -1 2 -1 0 2 0 0 1 -1 -1 0
  0 -1 -1 0 0 1 0 0 0 0 0 0 0
  2 3 -1 -5 3 1 -4 2 1 -2 1 1 0
  0 -1 -1 1 0 0 0 0 0 0 0 0 0
  0 0 -1 0 0 1 0 0 0 0 0 0 0
  2 3 -1 -5 3 2 -5 2 1 -3 1 1 1
  13 13
  0 0 0 0 0 0 0 0 -1 0 0 1 0
  1 2 0 -3 2 0 -2 1 1 -1 1 0 0
  -1 -1 1 3 -2 0 3 -1 -1 1 -1 -1 0
  1 3 1 -3 2 0 -2 1 0 -1 1 0 0
  0 1 0 -1 0 0 -1 0 0 0 1 0 0
  0 1 0 -1 0 1 -1 0 0 -1 1 0 0
  0 0 -1 0 -1 0 0 0 0 0 1 0 0
  0 1 1 0 0 0 1 0 -1 0 0 -1 0
  -1 -1 1 3 -2 -1 3 -1 -1 1 0 -1 0
  -1 -1 1 2 -1 0 2 -1 -1 1 0 -1 0
  -1 -1 0 2 -2 0 2 0 -1 1 0 -1 0
  0 1 0 0 0 0 0 0 0 0 1 -1 0
  0 0 1 1 0 0 1 0 -1 0 0 -1 1
  13 13
  -1 -2 -1 2 -1 -1 1 0 0 1 0 0 0
  1 1 1 0 0 0 0 -1 0 0 0 0 0
  -1 -1 0 1 -1 0 1 0 0 0 0 0 0
  0 -1 0 2 -1 0 1 -1 0 0 0 0 0
  0 -1 -1 0 0 1 -1 0 0 -1 0 1 0
  -1 -2 0 2 -1 0 1 -1 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 -1 1 0
  0 -1 0 1 -1 0 1 0 0 0 0 0 0
  -1 -2 1 3 -2 -1 3 -1 -1 1 -1 0 0
  0 0 0 0 0 0 -1 0 0 -1 1 0 0
  -1 -2 0 2 -1 0 1 0 0 0 -1 0 0
  1 1 1 -1 1 0 -1 0 0 -1 0 1 0
  1 2 1 -2 2 0 -2 1 0 -2 0 0 1
  13 13
  1 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 -1 1 1 -1 0 0 -1 0 0 0
  0 0 0 0 -1 0 0 0 0 0 1 0 0
  0 0 -1 0 0 1 -1 0 0 -1 1 0 0
  -1 -2 -1 2 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 -1 0 0 -1 1 0 0
  -1 -2 0 2 -1 0 1 0 0 0 -1 0 0
  0 0 -1 -1 0 1 -1 1 0 -1 1 0 0
  0 0 1 1 -1 0 1 0 -1 0 0 0 0
  1 2 0 -2 1 0 -2 1 0 -1 1 0 0
  -1 -2 -1 2 -2 0 1 0 0 0 0 0 0
  -1 -1 0 2 -1 0 1 0 0 0 0 -1 0
  0 0 0 1 -1 -1 1 0 0 1 0 0 -1
  13 13
  1 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 -1 1 1 -1 0 0 -1 0 0 0
  0 0 0 0 -1 0 0 0 0 0 1 0 0
  0 0 -1 0 0 1 -1 0 0 -1 1 0 0
  0 0 -1 0 0 0 0 0 0 0 1 0 0
  0 0 -1 0 -1 1 0 0 0 0 1 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0
  0 0 -1 -1 0 1 -1 1 0 -1 1 0 0
  0 0 -1 -1 0 1 -1 0 1 -1 1 0 0
  0 0 -1 -1 0 1 -1 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 -1 -1 0 1 -1 0 0 -1 1 1 0
  0 0 0 -1 1 1 -1 0 0 -1 0 0 1
  
• REFERENCES
  SPLAG Chapter 6.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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