The Lattice P42.1
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 13:24:42 CEST 2014
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe