The Lattice KAPPA13
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:16:51 CEST 2014
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
Haftungsausschluss/Disclaimer
Gabriele Nebe