The Lattice N(A15_D9)
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwthaachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:21:03 CEST 2014
INDEX FILE 
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DETERMINANT
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GRAM
BASIS
ROOT_SYSTEM
NOTES
LAST_LINE

NAME
N(A15_D9)

DIMENSION
24

DETERMINANT
1

MINIMAL_NORM
2

KISSING_NUMBER
384

DENSITY
.596E07

HERMITE_NUMBER
2

GROUP_ORDER
2^31 * 3^10 * 5^4 * 7^3 * 11 * 13

GRAM
24 0
2
1 2
1 1 2
1 1 1 2
1 1 1 1 2
1 1 1 1 1 2
1 1 1 1 1 1 2
1 1 1 1 1 1 1 2
0 0 0 0 0 0 0 1 2
0 0 0 0 0 0 0 1 1 2
0 0 0 0 0 0 0 1 1 1 2
0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 1 2
0 0 0 0 0 0 0 0 0 0 0 1 1 2
0 0 0 0 0 0 0 0 0 0 0 1 0 0 2
0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 2
0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 2
0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 2
1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 4
1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 4
1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 3 4
1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 3 3 4
1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 2 2 2 4
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 2 1 1 1 2 4

BASIS
24 25
.100000000000E+01 .000000000000E+00 .000000000000E+00
.100000000000E+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 .100000000000E+01 .000000000000E+00
.100000000000E+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 .100000000000E+01
.100000000000E+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 .000000000000E+00
.100000000000E+01 .100000000000E+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
.100000000000E+01 .000000000000E+00 .100000000000E+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
.100000000000E+01 .000000000000E+00 .000000000000E+00
.100000000000E+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
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+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
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+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 .000000000000E+00
.100000000000E+01 .100000000000E+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
.100000000000E+01 .000000000000E+00 .100000000000E+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
.100000000000E+01 .000000000000E+00 .000000000000E+00
.100000000000E+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 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+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 .100000000000E+01 .000000000000E+00
.000000000000E+00 .100000000000E+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 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+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 .100000000000E+01
.100000000000E+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 .100000000000E+01
.000000000000E+00 .100000000000E+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 .100000000000E+01
.000000000000E+00 .000000000000E+00 .100000000000E+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 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .750000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .750000000000E+00
.750000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .750000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .750000000000E+00 .250000000000E+00
.750000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .750000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .750000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .750000000000E+00 .750000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.875000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.875000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.875000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.875000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00

ROOT_SYSTEM
A15 D9

NOTES
One of the 24 even unimodular lattices in dimension 24 (the Niemeier lattices)

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe