The Lattice D1(1+i)^8
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 13:11:36 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
KISSING_NUMBER
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
HERMITE_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
D1(1+i)^8
-
DIMENSION
32
-
KISSING_NUMBER
192
-
GRAM
32 32
4 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 1 0 2 1 1 1
2 4 2 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 0 1 0 2 1
2 2 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 2 0 1 1 1 2
0 0 0 4 0 0 0 0 0 0 0 0 2 0 1 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 -1
2 2 0 0 4 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 -1 0 0 1 0 1 0 0 0 1 1 1 0
0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 0 0 0 -1 0 1 1 1 1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 4 2 0 0 0 0 0 0 1 0 0 0 1 0 0 -1 1 -1 1 0 0 0 0 0 0 0
0 0 0 0 0 0 2 4 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 -1
0 0 0 0 0 0 0 0 4 0 0 1 0 0 0 0 1 1 -1 -1 0 1 0 -1 1 0 -1 0 1 0 0 0
0 0 0 0 0 0 0 0 0 4 0 -2 0 0 -2 0 -1 0 -1 0 0 -1 -1 -1 0 0 -1 -2 0 -1 -1 0
0 0 0 0 0 0 0 0 0 0 4 -2 0 2 -1 0 -2 -1 -1 -2 2 -1 -1 -2 -2 0 0 -2 -2 -2 -2 -2
0 1 1 0 1 0 0 0 1 -2 -2 6 0 -2 3 0 3 3 2 2 -2 3 3 3 3 -1 3 3 3 3 3 3
0 0 0 2 0 0 0 0 0 0 0 0 4 0 1 0 0 2 1 -1 0 0 0 0 0 0 0 1 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 2 -2 0 4 0 0 -1 0 -1 -1 2 0 0 -1 -1 0 0 -1 -2 -1 -2 -1
0 0 0 1 0 0 1 1 0 -2 -1 3 1 0 6 0 3 3 3 1 -1 3 3 2 2 -2 3 3 2 1 1 2
0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 4 0 1 0 1 0 1 1 2 0 0 0 1 0 -1 0 0
0 0 0 1 0 0 0 1 1 -1 -2 3 0 -1 3 0 6 2 1 2 -1 3 2 3 2 -1 2 3 2 3 2 2
-1 0 1 1 -1 0 0 0 1 0 -1 3 2 0 3 1 2 6 2 2 -1 2 3 2 2 -2 3 3 2 0 1 2
0 0 0 0 0 0 1 0 -1 -1 -1 2 1 -1 3 0 1 2 6 2 0 2 2 1 2 -1 2 2 3 1 2 2
0 -1 1 0 -1 -1 0 0 -1 0 -2 2 -1 -1 1 1 2 2 2 6 -1 2 1 3 2 -1 2 3 2 3 1 2
0 0 0 0 0 0 0 0 0 0 2 -2 0 2 -1 0 -1 -1 0 -1 4 -1 -1 -1 -1 0 -2 -1 -2 -1 0 -1
0 0 0 0 0 1 -1 0 1 -1 -1 3 0 0 3 1 3 2 2 2 -1 6 2 3 2 -1 3 2 3 2 1 2
0 1 1 0 1 1 1 0 0 -1 -1 3 0 0 3 1 2 3 2 1 -1 2 6 2 2 -2 3 2 2 2 1 2
0 0 0 0 0 1 -1 -1 -1 -1 -2 3 0 -1 2 2 3 2 1 3 -1 3 2 6 2 -1 2 3 2 2 2 3
1 0 1 0 1 1 1 -1 1 0 -2 3 0 -1 2 0 2 2 2 2 -1 2 2 2 6 -2 2 2 3 2 2 3
0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -2 0 -1 -2 -1 -1 0 -1 -2 -1 -2 4 -2 -2 -1 -1 -1 -1
1 1 2 0 0 0 0 0 -1 -1 0 3 0 0 3 0 2 3 2 2 -2 3 3 2 2 -2 6 2 3 2 1 2
0 0 0 2 0 -1 0 0 0 -2 -2 3 1 -1 3 1 3 3 2 3 -1 2 2 3 2 -2 2 6 2 2 2 2
2 1 1 0 1 0 0 0 1 0 -2 3 0 -2 2 0 2 2 3 2 -2 3 2 2 3 -1 3 2 6 2 2 2
1 0 1 0 1 -1 0 0 0 -1 -2 3 -1 -1 1 -1 3 0 1 3 -1 2 2 2 2 -1 2 2 2 6 2 2
1 2 1 0 1 0 0 0 0 -1 -2 3 0 -2 1 0 2 1 2 1 0 1 1 2 2 -1 1 2 2 2 6 2
1 1 2 -1 0 0 0 -1 0 0 -2 3 0 -1 2 0 2 2 2 2 -1 2 2 3 3 -1 2 2 2 2 2 6
-
DIVISORS (elementary divisors)
2^16
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
2.83
-
HERMITIAN_GROUP_ORDER
2^19 * 3^2
-
HERMITIAN_GROUP_GENERATORS
3
32 32
0 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 -2 3 -1 2 1 1 -1 3 2 -2 0 0 0 0 -2 0 -2 2 0 0 0 0 2 -2 0 2 2 -2 -2 0 -2
1 -1 2 -1 0 0 0 0 1 2 0 0 -1 0 0 -1 0 0 2 -2 -1 0 0 2 0 1 0 2 -2 0 0 -2
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
-3 5 -3 -2 -5 -1 0 -2 -20 -7 13 -2 -1 2 2 6 4 12 -10 -2 -5 4 -2 -12 6 2 -18 -2 14 8 2 4
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
-3 5 -3 -3 -6 -1 1 -3 -23 -7 14 0 0 3 2 7 6 12 -12 -2 -5 4 -2 -14 6 1 -20 -2 16 8 2 4
-1 -1 0 0 1 1 0 0 3 1 -3 2 2 1 0 0 0 -4 0 2 2 -2 0 0 -2 -1 4 0 0 -2 0 0
-1 3 -1 -3 -4 0 1 -3 -17 -4 11 0 -1 2 2 4 4 10 -8 -2 -5 4 -2 -10 4 1 -16 0 10 6 2 2
-1 4 -4 -1 -3 0 -2 1 -5 -2 5 -2 0 -1 2 2 0 4 -4 0 0 0 0 -4 4 3 -4 0 4 4 0 2
0 2 -3 1 -1 0 -1 1 -3 -3 2 -2 -1 -1 0 1 0 4 -2 0 0 0 0 -2 2 1 -2 -2 2 2 0 2
-3 5 1 -5 -8 -2 3 -6 -35 -9 21 0 -3 5 2 9 9 20 -14 -7 -11 9 -5 -18 8 0 -33 -1 21 12 3 3
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 2 -3 1 -1 -1 -1 1 -3 -3 2 -2 -1 -1 0 1 0 4 -2 0 0 0 0 -2 2 1 -2 -2 2 2 0 2
0 0 0 1 0 -1 0 1 1 -1 -1 0 0 0 -1 0 0 -1 1 0 0 0 0 1 0 -1 1 -1 -1 -1 0 0
-3 5 -1 -3 -6 -1 2 -5 -28 -8 17 0 -2 4 2 8 8 16 -12 -4 -8 6 -4 -16 6 0 -26 -2 18 10 2 4
-2 3 2 -4 -5 -1 3 -5 -25 -6 15 1 -2 4 1 6 7 14 -10 -5 -8 7 -4 -13 4 -1 -24 0 15 8 2 2
-3 10 -3 -6 -12 -3 2 -6 -46 -13 29 -2 -5 4 3 12 11 29 -19 -9 -13 11 -6 -24 13 2 -43 -2 27 18 3 5
0 -3 4 -1 2 1 3 -2 1 2 -1 2 0 1 -1 -2 1 -2 2 -1 -1 1 -1 2 -3 -2 0 2 -1 -2 0 -2
-2 5 0 -5 -8 -2 3 -6 -33 -8 20 1 -3 5 2 9 9 19 -13 -7 -10 8 -5 -17 7 0 -31 -1 20 12 2 3
3 -9 5 3 10 4 0 3 36 12 -22 2 3 -3 -2 -12 -8 -22 16 6 9 -8 4 20 -12 -2 32 4 -22 -14 -2 -6
-2 4 0 -3 -6 -2 3 -5 -30 -9 17 0 -3 4 1 8 8 18 -12 -6 -9 8 -5 -16 6 -1 -28 -2 18 10 2 4
-3 8 -3 -4 -10 -3 1 -4 -38 -11 24 -2 -4 4 2 10 9 23 -16 -7 -11 9 -4 -20 11 2 -35 -2 23 14 3 5
-1 0 4 -2 -2 -1 3 -4 -14 -3 8 1 -2 3 0 3 5 8 -4 -4 -6 5 -3 -6 1 -2 -15 0 8 4 1 0
-3 7 -2 -5 -9 -2 2 -5 -34 -9 22 -1 -2 4 3 9 8 20 -15 -6 -10 8 -4 -18 9 2 -32 -1 21 13 3 4
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
-4 12 -5 -5 -14 -5 2 -6 -55 -18 33 -3 -6 5 2 16 13 35 -23 -11 -15 13 -7 -29 16 2 -50 -5 33 21 3 8
-1 -1 5 -3 -1 0 4 -5 -12 -1 6 3 -1 4 0 2 5 5 -3 -3 -5 4 -3 -5 -1 -3 -13 1 7 2 1 -1
-2 3 1 -4 -5 -1 3 -5 -25 -6 15 1 -2 4 1 6 7 14 -10 -5 -8 7 -4 -13 5 0 -24 0 15 8 2 2
-2 3 0 -3 -6 -2 2 -4 -24 -6 14 1 -2 4 1 7 6 13 -10 -5 -7 6 -3 -13 5 0 -22 -1 15 8 2 3
-2 -1 4 -3 0 1 3 -4 -8 0 4 1 0 2 1 1 3 3 -3 -2 -3 3 -2 -4 -1 -1 -8 2 5 2 1 -1
2 -5 6 0 4 1 1 1 15 7 -8 1 0 -1 -1 -6 -3 -9 9 0 1 -2 1 11 -5 -1 11 4 -11 -6 -1 -5
32 32
-3 5 -3 -3 -6 -1 0 -3 -23 -7 14 0 0 3 2 7 6 12 -12 -2 -5 4 -2 -14 6 1 -20 -2 16 8 2 4
-3 5 -3 -3 -6 -1 1 -4 -23 -7 14 0 0 3 2 7 6 12 -12 -2 -5 4 -2 -14 6 1 -20 -2 16 8 2 4
-1 -1 0 0 1 1 0 -1 3 1 -3 2 2 1 0 0 0 -4 0 2 2 -2 0 0 -2 -1 4 0 0 -2 0 0
-4 12 -8 -4 -12 -3 -1 -3 -41 -14 26 -4 -3 2 4 13 8 26 -20 -6 -9 8 -4 -24 14 4 -36 -4 26 18 2 8
-2 6 -3 -3 -7 -2 0 -3 -26 -8 17 -2 -2 2 2 7 6 16 -12 -4 -7 6 -2 -14 8 2 -24 -2 16 10 2 4
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
-3 5 -3 -2 -5 -1 0 -2 -20 -7 13 -2 -1 2 2 6 4 12 -10 -2 -5 4 -2 -12 6 2 -18 -2 14 8 2 4
0 -2 3 -1 2 1 1 -1 3 2 -2 0 0 0 0 -2 0 -2 2 0 0 0 0 2 -2 0 2 2 -2 -2 0 -2
-2 6 -2 -4 -8 -2 2 -5 -33 -9 20 0 -3 3 2 9 8 20 -14 -6 -8 8 -4 -18 8 1 -30 -2 20 12 2 4
3 -9 5 3 10 4 0 3 36 12 -22 2 3 -3 -2 -12 -8 -22 16 6 9 -8 4 20 -12 -2 32 4 -22 -14 -2 -6
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 4 -2 -2 -5 -2 0 -2 -18 -6 11 -1 -1 1 1 6 4 11 -8 -3 -4 4 -2 -10 6 1 -16 -2 11 7 1 3
-1 4 -4 -1 -3 0 -2 1 -5 -2 5 -2 0 -1 2 2 0 4 -4 0 0 0 0 -4 4 3 -4 0 4 4 0 2
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
1 1 -3 2 0 -1 -3 4 10 1 -5 -2 1 -3 0 -1 -4 -5 3 2 4 -3 2 5 1 2 10 -1 -6 -2 -1 0
-2 3 1 -4 -4 0 3 -5 -23 -5 14 0 -2 3 2 5 6 14 -10 -4 -7 6 -4 -12 4 0 -22 0 14 8 2 2
-2 9 -4 -4 -11 -4 0 -3 -38 -12 24 -3 -4 2 2 11 8 25 -16 -8 -10 9 -4 -20 13 3 -35 -3 22 16 2 5
1 -1 -1 1 2 1 -1 2 12 3 -7 -1 1 -3 0 -3 -4 -6 4 2 5 -3 1 6 -2 1 12 1 -7 -3 -1 -1
2 -8 3 4 9 2 -1 4 35 10 -22 2 4 -3 -2 -9 -8 -23 14 7 10 -8 4 18 -10 -2 32 2 -20 -14 -2 -4
1 -7 5 2 7 2 1 1 20 6 -14 2 2 -1 -2 -6 -4 -13 9 3 5 -4 1 11 -8 -3 18 2 -12 -9 -1 -3
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
2 -3 2 1 2 0 0 1 10 4 -7 2 1 -1 -1 -3 -2 -7 5 1 3 -2 1 6 -3 -1 9 1 -7 -5 -1 -2
0 2 -2 -1 -3 -1 -1 0 -5 -1 4 -1 0 0 1 2 0 3 -3 -1 -1 1 0 -3 3 2 -4 0 3 3 1 1
-1 3 -1 -2 -4 -1 0 -1 -14 -4 9 -1 -1 1 1 4 3 9 -6 -3 -4 3 -2 -7 5 1 -13 -1 8 6 1 2
1 -2 0 2 2 0 -2 3 12 3 -7 0 1 -2 -1 -3 -4 -7 5 2 4 -3 2 7 -2 0 11 0 -7 -4 -1 -1
-3 5 -1 -3 -6 -1 2 -5 -28 -8 17 0 -2 4 2 8 8 16 -12 -4 -8 6 -4 -16 6 0 -26 -2 18 10 2 4
1 -1 -1 2 2 0 -2 3 14 3 -9 0 2 -2 -1 -3 -4 -9 5 3 5 -4 2 7 -2 0 14 0 -8 -5 -1 -1
-3 9 -5 -4 -10 -3 0 -3 -36 -12 22 -3 -3 2 3 11 7 23 -17 -6 -8 8 -4 -20 12 3 -32 -3 22 15 2 6
0 -3 2 0 2 1 0 0 7 3 -5 2 2 0 0 -2 -1 -7 2 2 3 -2 1 3 -3 -1 7 1 -3 -4 0 -1
-2 6 -3 -3 -8 -3 0 -3 -30 -10 18 -1 -2 3 1 9 7 18 -13 -5 -8 7 -3 -17 9 1 -27 -3 18 11 2 5
-3 7 -5 -3 -8 -3 0 -3 -31 -11 19 -2 -2 2 2 10 7 19 -15 -4 -7 6 -3 -18 10 2 -27 -4 20 12 2 6
1 -4 1 2 4 1 -1 2 18 5 -12 2 3 -1 -1 -4 -4 -12 7 4 6 -5 2 9 -5 -1 17 0 -10 -7 -1 -2
32 32
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 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 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 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 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 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 -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 0 0 0 0 0 0 0
0 0 0 0 0 0 0 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 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 0 0 0 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 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 0 0
1 -2 3 -1 1 1 1 -1 2 3 -1 2 0 1 0 -2 1 -2 2 0 -1 0 0 2 -2 -1 0 2 -2 -2 0 -2
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
-2 3 1 -4 -4 0 3 -5 -23 -5 14 0 -2 3 2 5 6 14 -9 -4 -7 6 -4 -12 4 0 -22 0 14 8 2 2
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 1 0 0 0 0 0 0 0 0 0 0 0
1 -2 3 -1 1 1 1 -1 2 3 -1 2 0 1 0 -2 0 -2 2 0 -1 1 0 2 -2 -1 0 2 -2 -2 0 -2
-2 3 1 -4 -4 0 3 -5 -23 -5 14 0 -2 3 2 5 6 14 -10 -4 -7 6 -3 -12 4 0 -22 0 14 8 2 2
1 0 -2 1 0 0 -2 2 6 2 -3 0 1 -1 0 -1 -2 -4 2 2 2 -2 2 3 0 1 6 0 -4 -2 0 0
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 1 0 0 0 0 0 0
1 -2 3 -1 1 1 1 -1 2 3 -1 2 0 1 0 -2 0 -2 2 0 -1 0 0 2 -2 -1 1 2 -2 -2 0 -2
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 0
-1 3 -1 -3 -4 0 1 -3 -17 -4 11 0 -1 2 2 4 4 10 -8 -2 -5 4 -2 -10 4 1 -16 0 11 6 2 2
1 -2 3 -1 1 1 1 -1 2 3 -1 2 0 1 0 -2 0 -2 2 0 -1 0 0 2 -2 -1 0 2 -2 -1 0 -2
2 -5 4 2 5 1 0 2 19 7 -12 2 1 -1 -2 -6 -4 -12 10 2 4 -4 2 12 -6 -2 16 2 -12 -8 -1 -4
0 0 0 0 0 0 0 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
-
HERMITIAN_STRUCTURE
4
32 32
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
32 32
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
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
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 -3 2 1 3 1 1 -1 6 2 -5 2 1 1 0 -1 0 -6 2 2 2 -2 0 2 -4 -2 6 0 -2 -4 0 0
-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 0 0 0 0 0
3 -11 8 2 11 4 1 2 39 15 -24 4 4 -2 -2 -12 -8 -26 18 6 9 -8 4 22 -14 -3 34 6 -24 -16 -2 -8
-3 5 -3 -3 -6 -1 1 -4 -23 -7 14 0 0 3 2 7 6 12 -12 -2 -5 4 -2 -14 6 1 -20 -2 16 8 2 4
-2 6 -3 -3 -7 -2 1 -3 -26 -8 17 -2 -2 2 2 7 6 16 -12 -4 -7 6 -2 -14 8 2 -24 -2 16 10 2 4
2 -4 0 3 6 2 -3 5 30 9 -17 0 3 -4 0 -8 -8 -18 12 6 9 -8 4 16 -6 1 28 2 -18 -10 -2 -4
-1 3 -1 -3 -4 0 1 -3 -17 -4 11 0 -1 2 2 4 4 10 -8 -2 -5 4 -2 -10 4 1 -16 0 10 6 2 2
2 -6 2 4 8 2 -2 5 33 9 -19 0 3 -4 -2 -9 -8 -20 14 6 8 -8 4 18 -8 -1 30 2 -20 -12 -2 -4
0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 -1 0
2 -8 3 5 9 2 -1 4 34 10 -22 2 3 -3 -2 -9 -8 -22 14 6 10 -8 4 18 -10 -2 32 2 -20 -14 -2 -4
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
2 -6 4 2 6 1 1 1 20 7 -14 2 1 -2 -2 -6 -4 -13 10 2 6 -4 2 12 -7 -2 19 2 -13 -9 -2 -4
0 -2 3 -1 1 0 1 -1 3 3 -2 2 1 1 0 -1 0 -4 2 0 0 0 0 2 -2 -1 2 2 -2 -2 0 -2
-1 1 1 -2 -1 0 2 -3 -10 -2 5 0 -1 1 1 2 3 6 -4 -2 -2 3 -2 -5 1 0 -9 0 6 3 0 1
0 2 -1 -1 -3 -1 0 -1 -9 -2 5 0 -1 0 1 3 2 5 -4 -2 -1 2 -1 -5 3 1 -7 0 5 3 0 1
-1 0 -1 0 0 0 0 0 0 0 -1 0 1 0 0 1 0 -1 -1 0 2 -1 0 -1 0 0 2 0 1 0 0 1
-5 13 -5 -8 -16 -4 3 -9 -65 -19 39 -2 -5 7 4 18 16 39 -28 -11 -17 15 -8 -36 17 2 -59 -4 40 24 4 9
2 -6 2 4 8 2 -2 5 33 9 -19 0 3 -3 -2 -9 -8 -20 14 6 8 -8 4 18 -8 -1 30 2 -20 -12 -2 -4
1 -4 5 -1 4 2 2 -1 10 6 -6 1 0 -1 0 -5 -2 -6 6 0 2 -1 0 7 -5 -1 8 4 -7 -4 -1 -4
0 0 1 -1 -1 -1 1 -2 -6 -1 3 0 -1 0 0 2 2 4 -2 -2 -1 2 -1 -3 1 0 -5 0 3 2 0 0
1 -2 4 -1 1 0 2 -2 -1 2 -1 2 -1 1 -1 -1 1 0 2 -2 -1 2 -1 1 -2 -2 -2 2 -1 -1 -1 -2
1 -5 4 -1 4 3 1 -1 13 7 -9 3 2 0 0 -5 -2 -10 6 2 4 -3 1 7 -6 -1 12 4 -8 -6 -1 -4
-3 7 -6 -1 -7 -2 -1 -1 -23 -9 15 -2 -1 2 2 8 4 14 -12 -2 -5 4 -2 -14 8 2 -20 -4 16 10 2 6
-1 3 1 -4 -5 -1 3 -5 -26 -6 15 0 -3 2 1 6 7 16 -10 -6 -7 7 -4 -13 5 0 -24 0 15 9 1 2
-3 7 -3 -3 -8 -3 1 -4 -32 -10 18 -1 -3 3 2 10 8 19 -14 -6 -7 7 -4 -18 9 1 -28 -3 20 12 1 5
-1 4 -2 -3 -5 -1 0 -2 -19 -4 12 -1 -2 1 2 5 4 12 -8 -4 -4 4 -2 -10 6 2 -17 0 11 8 1 2
-2 3 0 -3 -4 -1 3 -5 -24 -7 13 0 -2 3 1 6 7 15 -10 -4 -6 6 -4 -13 4 -1 -22 -2 15 8 1 3
1 -3 3 0 3 1 1 0 7 3 -5 1 0 0 -1 -3 -1 -4 4 0 2 -1 0 5 -3 -1 6 2 -5 -3 -1 -2
1 0 -1 0 0 0 0 0 1 0 -2 0 0 -1 0 0 -1 0 0 0 2 0 0 0 0 0 2 0 -1 0 -1 0
32 32
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 -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 -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
-3 5 -1 -4 -6 -1 2 -5 -28 -8 17 0 -1 4 2 8 8 16 -12 -4 -8 6 -4 -16 6 0 -26 -2 18 10 2 4
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
-3 9 -5 -3 -10 -4 0 -3 -36 -12 22 -2 -3 3 2 12 8 22 -16 -6 -9 8 -4 -20 12 2 -32 -4 22 14 2 6
-2 6 -3 -3 -7 -2 0 -2 -26 -8 17 -2 -2 2 2 7 6 16 -12 -4 -7 6 -2 -14 8 2 -24 -2 16 10 2 4
1 1 0 0 -1 -1 -1 1 -3 -1 3 -2 -2 -1 0 0 0 4 0 -2 -2 2 0 0 2 1 -4 0 0 2 0 0
4 -12 8 4 12 3 1 3 41 14 -26 4 3 -2 -4 -13 -8 -26 20 6 9 -8 4 24 -14 -4 36 4 -26 -18 -2 -8
0 -2 5 -2 1 1 3 -3 -4 1 2 2 -1 2 0 -1 2 2 0 -2 -3 2 -2 0 -2 -2 -6 2 2 0 0 -2
-2 6 -2 -4 -8 -2 2 -5 -33 -9 20 0 -3 3 2 9 8 20 -14 -6 -9 8 -4 -18 8 1 -30 -2 20 12 2 4
1 -3 -1 4 5 1 -3 5 26 6 -16 -1 3 -3 -1 -6 -7 -16 10 6 8 -7 4 13 -5 0 25 0 -15 -9 -1 -2
-1 -3 2 0 3 1 1 -1 6 2 -5 2 2 1 0 -1 0 -6 2 2 2 -2 0 2 -4 -2 6 0 -2 -4 0 0
-2 6 -2 -4 -8 -2 2 -5 -33 -9 20 0 -3 3 2 9 8 20 -14 -6 -8 8 -4 -18 8 1 -30 -2 20 12 2 4
-3 6 -4 -2 -6 -2 0 -3 -24 -9 14 -2 -1 2 2 8 6 14 -12 -2 -5 5 -2 -15 7 1 -21 -4 16 9 2 5
-3 11 -8 -2 -11 -5 -1 -2 -39 -15 24 -4 -4 2 2 13 8 26 -18 -6 -9 8 -4 -22 14 3 -34 -6 24 16 2 8
2 -4 0 4 6 1 -3 5 28 7 -17 0 3 -3 -2 -7 -7 -17 12 6 8 -7 4 15 -6 -1 26 0 -17 -10 -2 -3
-1 0 -1 1 1 0 0 0 2 -1 -3 0 1 0 0 0 0 -2 0 2 2 -1 0 0 -1 -1 3 -2 0 -2 0 1
0 1 -2 0 0 0 -2 2 5 1 -2 -2 1 -2 1 -1 -2 -3 1 2 2 -2 2 2 1 2 5 0 -3 -1 0 0
-1 4 -5 1 -2 -1 -3 3 -1 -3 2 -4 0 -2 1 1 -2 3 -2 1 1 -1 1 -1 4 3 0 -2 1 3 0 2
0 0 0 0 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
1 -3 0 3 4 0 -2 3 19 5 -12 0 2 -2 -1 -4 -5 -12 8 4 6 -5 3 10 -4 0 18 0 -11 -7 -1 -2
-3 8 -6 -2 -8 -2 -1 -2 -27 -10 16 -2 -1 2 2 9 6 16 -14 -2 -5 5 -2 -17 9 2 -23 -4 18 10 2 6
-2 5 -7 2 -3 -2 -4 3 -3 -5 2 -3 1 -1 1 4 -1 2 -4 2 2 -2 1 -4 5 2 0 -4 4 3 0 4
0 -6 4 2 7 2 0 2 25 8 -16 2 4 -1 -1 -7 -5 -18 10 6 7 -6 3 13 -8 -2 23 2 -14 -11 -1 -4
1 1 -1 0 -2 -1 -1 1 -2 0 2 0 -1 0 0 1 0 2 0 -2 -1 0 0 0 2 1 -2 0 0 2 0 0
-1 3 -3 0 -3 -1 -1 0 -7 -3 3 -1 0 0 1 3 1 4 -4 0 0 1 0 -5 3 1 -5 -2 5 3 0 2
0 -1 -3 3 4 1 -3 4 19 3 -11 -2 3 -3 0 -4 -5 -11 6 6 7 -6 3 8 -3 1 19 -1 -10 -6 -1 0
4 -11 6 5 12 3 -2 6 48 15 -30 2 4 -4 -3 -14 -11 -30 22 8 12 -11 6 27 -13 -2 43 4 -30 -19 -3 -8
2 -5 1 4 7 2 -3 6 33 9 -19 -1 3 -4 -2 -9 -9 -19 14 6 9 -8 5 18 -7 0 30 2 -20 -11 -2 -4
2 -6 2 4 8 2 -2 5 33 9 -20 -1 3 -4 -2 -9 -8 -20 14 6 9 -8 4 18 -8 -1 31 2 -20 -12 -2 -4
-1 0 -2 1 1 1 -2 2 10 2 -5 -1 2 -1 1 -2 -3 -7 2 4 4 -4 2 4 -1 1 10 0 -4 -3 0 0
32 32
-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 0 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
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
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-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 -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
-3 5 -3 -3 -6 -1 0 -3 -23 -7 14 0 0 3 2 7 6 12 -12 -2 -5 4 -2 -14 6 1 -20 -2 16 8 2 4
-2 6 -3 -3 -7 -2 0 -3 -26 -8 17 -2 -2 2 2 7 6 16 -12 -4 -7 6 -2 -14 8 2 -24 -2 16 10 2 4
3 -8 4 4 9 2 -1 4 35 11 -22 2 3 -3 -2 -10 -8 -22 16 6 9 -8 4 20 -10 -2 32 2 -22 -14 -2 -6
-2 3 1 -4 -4 0 3 -5 -23 -6 14 0 -2 3 2 5 6 14 -10 -4 -7 6 -4 -12 4 0 -22 0 14 8 2 2
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
1 -3 -1 4 5 1 -3 5 26 6 -16 -1 3 -4 -1 -6 -7 -16 10 6 9 -7 4 13 -5 0 25 0 -15 -9 -2 -2
-1 -3 2 1 3 1 1 -1 6 2 -5 2 1 1 0 -1 0 -6 2 2 2 -2 0 2 -4 -2 6 0 -2 -4 0 0
-2 6 -2 -4 -8 -2 2 -5 -33 -9 20 0 -3 3 2 9 8 20 -14 -6 -9 8 -4 -18 8 1 -30 -2 20 12 2 4
-1 2 -2 0 -2 -1 0 -1 -7 -3 3 0 0 0 0 3 2 3 -4 0 0 1 0 -5 2 0 -5 -2 5 2 0 2
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
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0 -2 0 1 3 1 -1 2 13 4 -8 0 2 -2 0 -3 -3 -9 4 3 5 -4 2 6 -3 0 13 1 -7 -5 -1 -1
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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
2 -6 4 2 7 2 0 2 26 9 -16 1 2 -3 -1 -8 -6 -16 12 4 7 -6 3 15 -8 -1 23 3 -16 -10 -2 -5
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0 0 -1 1 1 0 -1 1 6 1 -4 0 1 -1 0 -1 -2 -4 2 2 3 -2 1 2 -1 0 6 0 -3 -2 -1 0
1 -7 4 2 8 3 0 2 29 10 -19 3 4 -2 -1 -8 -6 -20 12 6 9 -7 3 15 -10 -2 27 3 -17 -12 -2 -5
-2 6 -4 -2 -7 -2 -1 -1 -22 -7 15 -2 -2 2 2 7 4 14 -10 -4 -6 4 -2 -12 8 2 -20 -2 14 10 2 4
0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0
0 0 -1 1 1 0 -1 1 6 1 -4 0 1 -1 0 -1 -1 -4 2 2 3 -2 1 2 -1 0 6 -1 -3 -2 -1 0
2 -6 4 2 7 2 -1 3 26 9 -16 1 2 -3 -1 -8 -6 -16 12 4 7 -6 3 15 -7 -1 23 3 -17 -10 -2 -5
0 -2 1 1 3 1 0 1 9 2 -6 0 1 -1 -1 -3 -2 -5 4 2 3 -2 1 5 -3 -1 8 0 -5 -4 -1 -1
2 -6 2 4 8 2 -2 5 33 9 -20 0 3 -4 -2 -9 -8 -20 14 6 10 -8 4 18 -8 -1 31 2 -20 -12 -3 -4
0 -2 -1 2 3 1 -1 2 14 3 -9 0 2 -2 0 -3 -4 -9 4 4 6 -4 2 6 -3 0 14 0 -7 -5 -1 -1
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PROPERTIES
Modular=1
UnimodularHermitian=1
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REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
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NOTES
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe