The Lattice L_56,2^(7)(M)
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 13:18:09 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
L_56,2^(7)(M)
-
DIMENSION
56
-
GRAM
56 0
28
-14 28
14 -14 28
14 -14 0 28
-8 14 -10 -6 28
8 6 2 -2 -8 28
2 6 -8 -4 14 -6 28
-8 10 -14 -2 -4 0 -6 28
13 1 -5 5 11 2 9 -2 36
-8 9 -10 1 1 0 5 0 -12 28
-1 -9 -1 8 -5 0 0 0 -14 0 28
-9 5 -2 -11 -7 2 2 2 -2 -2 -8 28
9 -10 1 8 -1 1 8 -10 0 -2 14 -6 28
9 -2 5 -2 -2 -1 -2 7 9 -4 -5 -6 -10 28
-12 11 -2 -17 -4 11 -4 2 -5 -2 -5 13 0 -12 34
5 6 -4 1 -2 1 0 6 11 0 -6 2 -8 14 -1 28
-12 -2 6 -6 -12 0 -18 4 -18 -4 2 7 -4 -8 14 -9 36
6 -8 10 -2 2 -10 2 -2 8 -10 -2 -4 -4 12 -6 4 -10 28
-9 3 0 -3 -3 0 -12 0 -14 11 4 -8 -2 -1 5 3 3 -4 32
-12 -2 6 -6 -12 0 -18 4 -17 5 -2 6 -12 2 6 -4 12 -2 12 36
3 -5 -1 1 -10 4 4 -3 4 1 -1 9 1 -1 3 3 -3 -4 -4 5 28
6 -1 1 -2 -4 1 10 3 3 -3 -2 3 1 4 1 2 -6 0 -4 -3 14 28
-9 8 -8 1 8 -10 -1 8 -4 7 -3 -3 -10 5 -6 8 1 -4 4 5 -4 -4 28
8 1 9 -2 -9 10 -1 1 0 -4 -1 7 4 2 8 0 1 0 -2 -3 3 8 -14 28
-1 -1 -9 0 9 -1 8 -1 3 -1 8 -7 14 -4 0 -7 -4 -4 -1 -8 0 1 4 -10 28
-9 8 -8 -10 8 1 -1 8 1 -3 0 -5 0 3 4 -4 1 -4 6 5 1 1 8 -4 14 28
10 -10 0 4 -12 12 -2 -1 4 -4 5 3 10 1 4 2 -2 -3 0 -6 9 1 -12 10 1 1 32
1 -3 9 -5 -9 0 -5 0 -14 1 -1 0 1 2 6 -1 14 -1 0 8 -3 -1 -1 3 -1 -1 3 28
-13 10 -17 4 14 -8 4 4 8 9 -2 -4 -5 -6 2 2 0 -8 4 -6 -1 -6 8 -9 1 -1 -4 -11 38
5 -5 -5 9 -4 8 -8 1 8 -3 0 -5 2 -2 -3 -1 -1 -1 2 0 3 -5 -8 -6 4 1 12 0 4 28
6 -7 3 3 -10 6 -4 1 -1 -6 6 -2 11 -7 4 -8 1 3 2 -1 -3 3 -15 8 1 -2 8 3 -9 11 34
-14 3 -10 -8 10 -6 2 0 4 -7 -3 6 -3 -4 10 -1 -1 3 0 3 -5 -2 -2 -6 1 4 -4 -6 9 -1 1 38
-1 -1 9 -9 -9 2 -7 2 -12 -1 -3 2 -3 -2 8 -7 12 1 6 8 -5 -3 -8 4 -6 -1 4 14 -9 2 11 -2 28
12 -13 -1 18 -11 6 -5 2 -3 2 11 -7 6 -2 -14 -3 -1 -5 -3 -5 3 -5 -3 -6 4 -6 14 -1 -2 13 6 -12 5 36
-10 9 -9 -4 -1 -2 3 6 1 7 -9 10 -6 -3 6 -1 -1 -4 0 11 8 9 1 2 -7 4 -5 -3 2 -3 2 4 0 -11 32
9 1 5 3 -1 12 -5 -4 -2 -3 0 -6 5 -5 2 1 3 -8 5 -6 -9 -5 -3 1 5 1 6 7 -5 8 4 -4 7 10 -16 32
9 -5 5 -2 5 -3 6 0 6 -9 3 -6 8 3 -6 -6 -6 7 -5 -12 -4 -1 -9 7 4 4 11 1 -2 4 5 -4 6 4 -9 4 36
10 1 10 3 2 1 0 -8 2 -2 -9 -2 4 -4 3 2 -6 2 -2 -1 -2 3 1 8 -4 -5 -5 3 -8 -7 3 -5 -1 -5 3 3 3 32
5 -4 11 3 -7 10 -12 -1 -12 -1 9 -11 0 -3 -2 -5 12 -2 7 2 -2 -3 -3 1 0 3 3 10 -11 6 1 -15 10 11 -9 14 7 0 40
-14 8 1 -8 6 -12 3 0 -6 6 0 3 -9 4 0 1 4 3 5 11 1 1 5 3 -9 2 -15 -2 8 -14 -9 6 -3 -19 12 -18 -5 -2 -7 38
3 8 3 1 10 3 -4 -2 10 1 -11 -6 -9 10 -8 7 -4 -3 3 0 -6 0 3 0 -4 2 -10 -6 8 0 -9 2 -4 -4 -3 7 -7 1 1 4 38
5 -13 11 6 -3 -8 -10 -8 5 -5 -4 -4 -3 5 -11 0 6 3 5 2 -6 -5 3 -4 -8 -7 -5 -6 3 -1 -1 -1 -3 -3 -8 0 -4 -1 -3 1 6 40
-14 11 -16 1 1 -6 5 14 -5 8 3 8 -7 -2 0 3 -3 -7 0 7 8 5 12 -3 -3 6 -6 -7 9 -5 -6 5 -5 -2 16 -15 -8 -6 -13 11 -8 -10 36
-12 10 -2 -10 12 -6 1 0 0 -4 -8 7 -6 -4 4 -4 0 4 0 6 -1 -5 1 0 0 8 -4 0 3 1 -5 9 1 -10 4 -3 4 2 -5 12 4 -12 3 32
0 10 -6 -2 11 1 13 2 11 1 0 2 0 5 -7 6 -11 1 -7 -14 3 7 4 5 0 5 2 -8 2 -4 -7 -10 -13 -5 1 -7 -1 -6 -2 5 6 -3 7 4 38
5 1 1 4 8 -8 7 -2 11 -2 -8 0 -7 10 -10 6 -7 5 -9 -8 -7 -1 3 2 -8 -7 -2 0 8 -4 -10 2 -4 -6 2 -3 4 1 -10 3 10 8 -2 0 3 32
-10 0 -6 -2 6 -7 6 -8 2 4 -1 10 2 -8 0 -6 4 -8 0 -3 4 -4 -2 -4 3 0 2 -5 14 2 -4 8 -3 -2 5 -8 0 -9 -7 8 4 4 4 4 2 7 32
9 -8 6 11 3 -11 6 -8 3 -4 2 -3 1 2 -19 1 -4 2 -9 -7 3 3 6 -5 -2 -9 -7 -4 0 -2 -3 -8 -7 7 -8 -2 4 5 -4 -1 3 9 2 -1 2 10 2 32
-10 8 3 -5 13 -7 1 -10 -5 2 -2 0 -8 -6 -3 -1 -1 2 7 1 -3 -5 7 -5 -6 -1 -15 -5 5 -8 -11 1 -5 -12 2 -3 -9 5 1 10 7 6 3 10 7 2 4 5 36
1 -3 8 -7 -3 -7 7 -3 -11 2 5 4 8 -3 -1 -7 4 -2 3 -4 -6 -2 1 6 0 -2 1 4 -5 -13 2 -11 8 -5 -7 5 12 0 -1 1 -10 10 -4 -6 0 2 3 4 4 42
12 -16 3 18 2 -4 1 -12 10 -3 4 -14 6 0 -13 -2 -3 -2 -4 -10 -1 -1 0 -7 5 -4 2 -4 6 3 -5 -2 -13 8 -5 2 0 3 2 -4 1 15 -10 -12 -2 7 4 6 0 -4 40
-9 14 -12 -1 8 0 2 4 3 8 -9 2 -4 -5 3 3 -5 -7 4 5 -4 -1 4 -1 -3 5 -6 1 7 4 4 8 -1 -10 18 -2 -7 7 -7 6 5 -5 12 8 1 2 3 -7 8 -7 -4 32
-8 2 1 1 7 -9 -1 -2 -8 3 7 -2 3 -3 0 -4 7 2 1 3 -9 -8 11 -3 5 2 -7 1 7 -5 -4 0 -1 -4 -4 -2 0 3 0 10 1 2 4 3 3 2 4 2 4 7 -4 0 32
-13 8 -8 -3 6 -10 -4 11 2 -4 1 4 -7 2 5 10 5 2 5 2 0 -3 16 -8 5 5 -10 -6 12 -5 -12 3 -6 -9 1 -7 -4 -5 -3 10 0 0 12 6 4 -3 1 -3 6 -2 -6 0 10 36
-7 -6 -8 6 2 -6 -7 -2 2 -3 8 -7 6 -3 -1 -3 9 -6 7 -2 -2 -5 -3 -2 5 6 2 -4 12 7 7 15 -4 1 1 -5 -2 -8 -3 5 3 8 1 -2 -6 2 14 -1 -2 -13 12 3 1 0 40
-8 -6 -6 2 8 -18 8 2 -4 -2 10 0 1 3 -11 -5 -6 9 -3 -2 -5 -1 5 -6 6 1 -7 -6 4 -6 -5 15 -8 -4 0 -14 4 -7 -11 10 -5 0 9 6 -3 8 9 7 5 2 3 -2 5 5 10 36
-
DIVISORS
29^28
-
MINIMAL_NORM
28
-
KISSING_NUMBER
107880
-
HERMITE_NUMBER
5.20
-
SUBGROUP_ORDER
2^6 * 3^2 * 5 * 7 * 29
-
SUBGROUP_NAME
SL_2(29) o SL_2(3).2
-
SUBGROUP_GENERATORS
3
56 56
-4 1 5 0 0 -1 2 3 -1 -1 -5 -1 2 1 1 0 -3 -3 0 0 1 -1 -2 -1 -2 0 1 -1 -1 0 1 -1 -2 1 -1 0 -1 -2 1 0 -1 -1 -1 -1 -1 0 -1 1 0 0 1 1 2 1 1 1
-8 0 3 2 -3 4 4 -1 -1 -2 -1 -5 -2 -3 -4 4 2 1 -1 0 0 -1 0 2 4 -1 0 0 0 1 -1 1 1 0 2 -1 1 2 -2 -1 1 1 0 0 1 0 0 -1 -1 1 -1 -1 -1 0 0 0
-9 -2 5 0 -1 3 3 4 1 -1 -4 -2 3 -1 -3 1 0 -1 1 0 2 -1 0 0 -1 -1 0 -2 -1 0 0 -1 1 -1 -2 1 0 0 -1 0 -1 -2 -1 -2 0 1 0 0 0 -1 1 1 1 0 0 1
5 1 -2 -2 2 -4 -2 -1 -2 0 -3 2 2 2 4 -1 -3 -2 -1 1 -2 1 -1 0 -2 1 1 0 0 0 2 -1 -3 2 -1 -1 -1 -3 3 1 0 0 1 0 -2 0 -1 1 1 0 1 0 1 1 0 0
3 -5 -1 -4 2 2 -5 2 2 4 5 1 1 -1 -1 0 2 3 0 -2 1 0 3 1 2 -1 -2 0 1 1 -1 2 3 -1 2 2 0 2 -1 1 0 0 1 1 2 1 1 1 0 0 0 0 -2 -1 -1 -1
-12 5 12 2 -3 -1 8 3 1 -3 -5 -6 -2 -2 -4 2 0 -5 1 0 2 -3 -3 1 2 -2 3 -1 -3 2 0 1 -3 1 0 -2 -1 0 -1 -2 0 -1 -1 -2 -1 0 -2 -1 -1 1 0 0 2 1 1 1
12 -2 -8 -3 2 -1 -5 -2 -1 2 4 4 0 1 3 -2 0 3 0 0 -1 1 1 -1 -1 1 -2 1 2 -1 0 0 1 0 1 1 0 0 1 1 0 1 1 2 1 0 1 1 0 0 0 0 -1 0 0 -1
-1 1 -3 6 1 1 2 -4 -5 -3 -3 1 -1 2 3 2 -2 0 -2 1 -2 1 -2 -1 0 2 0 1 1 -1 1 -2 -1 1 0 -2 1 -1 1 0 1 2 0 1 -1 -1 -1 -1 0 1 -1 -1 0 0 1 0
1 0 -2 -5 -5 -1 -5 -3 3 1 2 -1 1 -2 0 -1 -3 0 -1 -2 -2 2 3 2 -1 1 -2 2 1 1 -1 1 0 2 1 0 0 -1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 -1 0
-8 8 1 2 -9 1 5 -4 -1 -5 -6 -7 -1 -4 -3 2 -2 0 -2 3 -3 1 -1 2 2 -1 3 1 -1 0 -1 0 -2 2 0 -3 1 -1 0 -1 1 1 -1 -1 -1 -1 0 0 0 1 0 -1 1 2 1 1
19 -4 -1 -4 12 -7 -5 5 3 9 10 9 -2 5 6 -5 3 -1 2 -1 1 -1 -1 -2 -2 1 0 0 0 1 1 2 -1 -1 1 2 -3 1 2 0 -1 0 2 2 0 0 0 1 1 0 0 0 -1 0 0 -2
6 7 -2 0 -3 -5 0 -3 2 -1 3 2 -2 0 0 -3 0 -1 1 1 -1 1 0 -1 -2 1 1 1 0 -1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 1 0 0 0
21 -3 -7 -4 9 -6 -9 2 -1 6 6 10 1 7 8 -6 -1 0 1 -1 1 0 -1 -4 -4 2 -2 0 2 -2 2 0 0 -1 0 3 -2 -1 3 1 -2 0 1 2 1 0 1 2 1 -1 1 1 0 0 0 -1
-16 1 6 5 -5 5 5 0 -1 -3 -7 -5 2 -2 -2 4 -3 -1 -2 0 -1 1 -1 1 0 1 0 0 -1 1 -1 -1 0 2 -1 -2 1 -1 -1 0 0 0 -2 -1 -1 0 -1 0 0 1 0 0 1 1 1 1
1 -2 -10 2 -2 4 -1 -7 -3 -4 0 0 -1 0 -1 1 1 3 0 0 -1 1 1 0 0 1 -3 1 2 -2 0 -2 2 -1 0 0 2 1 -1 0 1 1 1 1 1 0 1 -2 -1 0 -1 -1 -1 -1 -1 0
-6 1 4 1 -3 0 2 -1 2 1 1 -4 -2 -1 0 2 -1 -2 -2 -1 -2 1 0 2 0 1 0 1 -1 2 -1 1 -1 2 2 -1 0 0 -1 -1 0 1 -1 1 -1 -1 0 0 0 1 -1 -1 0 1 0 0
4 1 -1 2 3 -2 0 1 0 0 2 4 -1 3 1 -3 2 0 2 0 2 -1 -1 -3 -1 0 1 -1 0 -2 1 -1 0 -2 -2 1 0 1 0 0 0 -1 0 -1 0 0 0 -1 0 -1 0 1 0 -1 0 0
-2 -7 -4 -2 0 5 -2 0 1 1 1 0 3 -1 -1 1 1 3 0 -1 0 1 3 1 -1 0 -3 0 1 0 -1 -1 3 -1 0 2 1 1 -1 1 0 0 1 1 1 1 1 0 0 -1 0 0 -1 -1 -1 0
-14 0 3 3 -5 6 4 -2 -1 -3 -6 -6 1 -3 -4 5 -1 0 -2 1 -2 1 0 3 2 0 0 0 0 1 -1 0 1 1 0 -2 1 0 -1 -1 0 0 -1 -1 0 0 0 0 0 1 0 -1 0 1 0 1
-19 1 6 5 -6 7 7 -1 0 -5 -6 -9 -1 -6 -7 6 1 0 -1 1 0 0 0 3 4 -2 1 0 -2 1 -2 0 1 0 0 -2 2 1 -3 -1 1 0 -1 -2 0 0 0 -2 -1 1 -1 -1 0 0 0 1
-3 1 3 0 -2 0 2 -1 1 -1 0 -4 -3 -3 -2 2 1 -1 0 0 0 0 0 2 2 -1 0 0 -1 1 -1 1 -1 1 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 -1 -1 1 -1 0 0 0 0 0
-2 -3 -7 5 0 5 0 -5 -7 -4 -6 1 2 2 3 3 -3 2 -2 1 -2 2 -1 -1 -1 2 -3 0 2 -2 1 -3 1 1 -1 -1 2 -2 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0
-8 -1 3 4 0 3 3 0 -2 -1 -2 -4 -1 -1 -1 4 1 0 -2 0 0 0 0 1 3 -1 1 -1 -1 1 0 0 1 0 1 -1 1 1 -1 0 1 1 0 0 0 0 0 -1 0 1 -1 -1 -1 0 0 0
-6 2 -3 3 -4 3 3 -4 -5 -6 -9 -1 3 0 0 2 -4 0 -1 2 -2 1 -2 0 -2 2 -1 0 1 -2 1 -3 -1 2 -2 -2 1 -3 1 0 0 0 -1 -1 -1 0 -1 0 0 0 1 0 2 1 1 1
15 -4 -5 -3 7 -2 -8 2 0 5 7 7 0 4 4 -4 1 2 1 -2 2 0 1 -3 -1 0 -2 0 2 -1 0 1 2 -2 1 3 -1 1 1 1 -1 0 1 2 2 0 1 1 0 0 0 1 -1 -1 0 -1
-9 -6 2 3 1 8 2 1 -3 -2 -3 -3 0 -2 -4 5 2 2 0 -1 2 -1 0 1 4 -1 -2 -1 1 0 -1 0 3 -1 1 0 1 2 -2 0 0 0 0 0 2 1 0 -1 -1 1 -1 0 -1 -1 0 0
3 6 3 1 2 -5 2 1 -1 -2 -4 2 0 2 2 -2 -2 -4 2 1 1 -1 -4 -2 -3 1 2 0 -1 -1 2 -1 -4 2 -2 -2 -2 -3 2 -1 -1 -1 -1 -1 -2 0 -2 0 0 0 1 1 3 1 1 1
-5 0 -2 6 1 4 4 0 -5 -5 -6 0 1 2 0 1 0 1 1 1 2 -1 -3 -3 -1 0 0 -1 0 -3 1 -3 0 -1 -2 0 1 0 0 0 0 0 -1 -1 0 0 0 -1 -1 0 0 1 1 0 1 1
16 1 -13 -7 -2 -5 -11 -8 2 3 7 4 0 0 4 -4 -2 3 -2 0 -5 4 4 2 -1 2 -2 3 3 0 0 1 0 2 1 0 0 -1 2 2 1 1 2 2 0 0 1 1 1 0 0 -1 -2 0 -2 -1
-2 3 5 -1 -1 -2 2 2 2 -1 -1 -2 -1 -1 -2 -1 1 -2 2 0 2 -2 -1 0 1 -2 2 0 -1 0 0 1 -2 0 0 0 -1 0 0 -1 0 -1 0 -1 0 0 -1 0 -1 0 0 1 1 0 0 1
10 1 -8 -2 -1 -3 0 -3 -1 -2 1 3 -1 2 3 -4 -1 0 2 1 -1 -1 0 -1 -2 0 0 2 1 -2 1 -1 -2 0 0 0 0 -1 2 0 1 1 1 1 0 -1 0 0 0 -1 0 0 1 0 0 0
10 -2 -16 -1 -2 1 -7 -8 -1 -1 3 6 2 2 3 -3 -2 4 0 0 -4 4 3 -1 -3 3 -4 3 3 -2 0 -2 2 0 -1 0 2 -1 1 2 1 1 1 2 0 0 1 0 1 -1 0 -1 -1 -1 -1 -1
-13 3 -1 7 -5 6 9 -3 -5 -10 -11 -4 1 -2 -4 4 -1 0 1 3 0 -1 -3 -1 0 0 1 0 0 -3 1 -4 -1 0 -3 -3 2 -1 0 -1 1 0 -1 -2 -1 0 -1 -2 -1 0 0 0 2 0 1 2
5 4 10 -2 7 -8 3 8 2 2 1 2 -2 2 2 -3 1 -5 3 0 4 -4 -3 -2 0 -3 5 -1 -3 1 2 1 -5 0 0 0 -3 -1 2 -1 0 -1 1 -1 -2 0 -2 0 0 0 1 1 2 0 1 0
-9 -3 -3 3 -3 7 3 -6 -5 -5 -6 -5 0 -4 -4 7 1 2 -2 1 -2 1 0 3 3 1 -2 0 1 0 0 -1 1 1 0 -3 2 0 -1 0 1 1 1 0 0 1 0 -2 -1 1 -1 -1 -1 0 -1 0
-4 -2 3 2 3 2 1 4 -3 -1 -4 0 2 3 1 1 -1 -1 0 0 3 -2 -2 -2 0 -1 0 -2 0 -1 1 -1 1 -1 0 2 0 0 0 0 -1 -1 -1 -1 1 0 0 1 0 0 1 1 1 0 1 1
12 0 5 -4 7 -4 -3 9 5 7 7 7 0 2 1 -6 2 0 4 -1 4 -2 -1 -4 -3 0 1 0 0 -1 0 2 0 -2 0 3 -3 1 0 -1 -2 -2 -1 0 1 0 0 2 0 -1 1 2 1 0 1 0
-4 -7 4 -2 4 4 0 5 -1 2 1 -3 0 -1 -2 3 3 1 0 -2 4 -3 1 1 3 -3 -1 -2 -1 1 0 1 2 -2 3 3 0 2 -2 0 0 0 1 0 2 1 1 0 -1 0 0 0 -1 -1 -1 0
-17 -2 15 2 1 4 7 8 2 0 -4 -6 0 -2 -5 4 2 -3 1 -1 4 -3 -2 1 3 -3 2 -3 -3 2 -1 1 0 -1 0 0 -1 2 -2 -2 -1 -2 -1 -2 0 1 -1 0 -1 1 0 1 1 0 1 1
-2 -6 -3 -3 -2 6 0 -1 2 1 2 -2 0 -5 -4 2 3 4 0 0 -2 1 3 3 2 0 -2 1 1 1 -2 1 2 0 1 0 1 2 -2 1 1 0 1 0 1 1 1 0 0 0 -1 -1 -2 0 -1 -1
-11 4 -1 0 -11 3 0 -5 -1 -5 -7 -5 4 -3 -2 2 -6 0 -3 1 -4 3 2 3 0 1 -1 1 1 0 -1 -1 0 3 -1 -2 2 -3 0 1 0 0 -2 -1 -1 0 0 1 1 0 1 0 1 1 0 1
-1 5 0 -1 -6 -4 -4 -2 4 2 0 1 2 1 2 -3 -5 -2 -2 0 -3 3 1 0 -3 2 1 1 0 0 0 0 0 1 -2 0 0 -2 1 1 -1 -1 -2 -1 -1 -1 0 2 2 -1 1 0 1 1 0 1
1 0 -5 3 0 1 3 -5 -4 -3 -2 0 -2 -1 0 3 1 1 -1 2 -3 1 -1 1 2 1 0 1 1 0 1 -1 -1 1 0 -3 1 0 1 0 2 2 2 1 -1 0 -1 -2 0 1 -1 -2 -1 0 0 -1
-1 -6 4 -2 6 4 1 6 0 1 1 0 1 -2 -4 2 6 2 3 -1 5 -3 1 0 3 -3 -1 -2 0 0 0 1 2 -2 1 2 0 2 -2 0 0 -1 1 -1 2 2 0 -1 -1 -1 0 1 -1 -2 -1 0
-4 5 2 0 -6 -1 2 -1 0 -2 -4 -2 2 -1 0 0 -3 -1 -1 1 -2 1 0 1 0 0 1 0 0 0 0 0 -1 2 -1 -2 0 -2 1 0 0 0 -1 0 -1 0 -1 1 1 0 1 0 1 1 1 0
-3 3 -6 3 -3 3 0 -6 -4 -5 -7 1 4 -1 -1 2 -3 2 -1 2 -3 3 -1 0 -3 4 -1 1 2 -2 1 -3 0 2 -3 -3 1 -3 1 1 0 0 -1 -1 -2 0 -1 0 0 0 1 0 1 1 0 1
16 6 -1 -9 0 -9 -8 0 9 6 11 7 -1 -1 -1 -8 1 0 3 -1 -1 2 3 0 -3 1 1 2 1 1 -1 3 -1 0 -1 0 -3 0 1 0 -1 -2 0 0 -1 0 0 1 0 -1 1 1 0 0 -1 -1
11 2 6 -4 5 -8 0 7 5 6 9 3 -4 1 2 -5 3 -2 3 -1 3 -3 0 -1 0 -2 3 0 -2 1 0 3 -2 -1 2 2 -2 1 0 -1 0 0 0 0 0 -1 0 1 0 -1 0 1 0 0 0 -1
-2 -6 7 -5 4 0 -3 5 4 7 6 -2 0 -2 -3 3 5 0 -1 -2 2 -1 3 4 4 -2 -1 -3 -1 4 -1 4 3 -1 2 2 -1 3 -2 0 -1 -1 1 0 2 2 1 0 0 0 0 0 -3 -1 -2 -1
15 4 -2 -3 3 -7 -6 2 3 6 7 7 0 3 4 -6 -1 0 0 1 0 1 0 -3 -4 2 1 0 1 -1 0 1 1 -1 -1 2 -2 0 1 0 -2 -1 -2 0 1 -1 1 2 1 -1 1 1 0 1 1 0
8 -3 1 -7 4 -4 -8 3 4 7 5 4 2 1 2 -3 0 0 0 -2 0 1 2 0 -1 0 0 -1 0 2 0 2 0 0 0 2 -2 0 1 2 -1 -2 1 0 0 1 0 2 1 0 1 1 -1 0 -1 -1
-6 -3 0 0 -1 4 2 -2 -3 -2 -3 -5 -1 -3 -3 5 2 1 -1 0 0 -1 0 3 4 -1 -1 0 0 1 0 1 0 1 2 -1 1 1 -1 0 1 1 1 0 1 1 0 -1 -1 1 -1 -1 -1 0 -1 0
6 0 -5 -2 1 0 -3 0 1 1 1 4 3 1 0 -3 1 2 1 1 0 1 1 -2 -2 0 0 0 1 -2 1 -1 1 -1 -2 1 0 0 1 1 0 -1 1 0 0 1 0 0 1 -1 1 0 0 0 0 0
5 -6 -6 1 3 2 -4 -2 -1 3 4 3 0 2 3 1 1 2 -2 -1 -2 2 2 0 0 2 -3 0 2 0 0 0 3 -1 1 1 1 1 0 1 0 1 1 2 1 0 1 0 1 0 -1 -1 -2 -1 -1 -1
9 -3 -8 -3 2 0 -5 -3 1 1 4 5 0 1 1 -3 1 3 2 -1 -1 1 2 0 -1 1 -2 2 2 -1 0 0 0 0 0 0 0 0 1 1 1 0 2 1 0 0 0 0 0 0 0 0 -1 -1 -1 -1
23 -5 -13 -5 8 -4 -11 -2 2 7 11 12 1 4 6 -6 1 4 1 -1 -2 3 3 -2 -4 3 -3 2 3 -1 0 0 2 -1 0 2 -1 0 2 2 0 1 2 3 0 0 1 1 1 -1 0 0 -2 -1 -1 -2
56 56
32 -4 -2 -10 14 -12 -10 7 9 15 23 12 -6 5 6 -11 7 1 4 -3 3 -2 3 -2 -2 -1 0 1 0 2 -1 5 0 -3 4 6 -4 4 0 0 -1 0 2 3 2 -1 2 1 0 -1 -1 1 -3 -1 -1 -3
-22 -2 -1 3 -10 9 7 -8 -4 -10 -12 -11 2 -7 -7 10 -1 0 -2 1 -3 1 1 6 4 0 -2 0 0 1 0 -2 0 3 -1 -5 3 -1 -1 0 2 1 1 -1 -1 2 -1 -3 -1 1 -1 -2 0 0 -2 1
20 12 0 -5 -2 -15 -4 0 9 7 12 7 -4 3 5 -11 -2 -4 1 1 -4 2 0 -2 -5 2 4 3 -1 1 -1 3 -4 1 0 0 -3 -1 2 -1 -1 0 -2 1 -2 -3 0 2 2 -1 0 0 1 2 1 -1
26 -6 -4 -7 15 -7 -9 8 4 10 15 14 -1 7 6 -10 4 2 5 -3 5 -2 2 -5 -4 -1 -1 0 1 -1 1 1 1 -4 1 6 -3 2 1 1 -1 -1 2 2 1 0 1 1 0 -2 1 2 -1 -2 0 -2
-7 -2 -3 6 0 5 3 -3 -8 -6 -10 -1 3 1 1 5 -2 0 -1 1 0 0 -3 -1 0 2 -2 -1 1 -2 2 -3 0 1 -2 -2 2 -2 1 1 0 1 0 -1 0 1 -1 -1 0 0 0 0 1 0 0 1
7 -2 4 -9 0 -5 -1 2 9 6 13 -2 -6 -5 -4 -2 6 0 2 -2 0 -2 5 5 4 -3 1 1 -1 5 -3 5 0 -1 4 1 -2 4 -2 -1 1 0 2 1 1 0 1 -1 -1 0 -2 -1 -3 -1 -2 -2
9 -8 -11 1 7 4 -5 -2 -6 0 -1 5 2 3 4 1 1 4 0 0 1 0 -1 -2 -1 2 -4 0 3 -3 2 -2 2 -1 0 2 1 0 1 2 0 1 2 1 2 1 1 0 0 0 0 0 -1 -1 -1 0
-22 -6 1 3 -5 13 6 -2 -5 -8 -10 -10 3 -6 -8 9 2 4 -1 0 2 -1 2 4 5 -3 -2 -2 0 0 -1 -2 3 0 0 -1 3 1 -3 0 2 0 1 -1 1 2 0 -2 -2 1 0 0 -1 -1 -1 1
11 -6 4 -5 11 -4 -4 6 3 8 10 3 -3 2 2 -2 6 0 2 -3 5 -3 1 0 1 -2 -1 -1 -1 2 0 3 0 -1 3 4 -2 3 -1 0 -1 0 2 1 2 1 1 -1 -1 0 -1 1 -2 -1 -1 -1
-6 -3 -5 1 -3 4 -1 -4 -3 -4 -5 -2 2 -1 -1 3 -2 1 -1 0 -1 1 1 1 1 0 -2 0 1 -1 1 -2 1 0 -1 -1 2 -1 0 1 1 0 1 0 0 1 0 -1 0 0 0 -1 0 -1 -1 0
6 -2 -5 2 4 2 -1 2 -4 -1 -1 5 2 3 2 -2 0 3 1 1 2 -1 -1 -4 -1 0 0 -1 2 -3 1 -2 2 -3 -1 2 0 0 1 1 0 0 0 0 1 0 0 1 0 -1 1 1 0 -1 1 0
-5 1 1 0 -3 2 2 -2 0 -2 -4 -4 0 -3 -2 3 -1 -1 -1 1 -2 1 -1 2 0 1 0 1 0 0 0 0 -1 2 0 -2 0 -1 0 -1 0 0 0 0 -1 0 0 0 0 1 0 -1 1 1 0 1
17 -4 -3 -2 10 -4 -5 5 0 6 8 8 -2 5 5 -5 3 1 2 -1 3 -2 -1 -4 -1 0 0 -1 1 -1 1 1 1 -3 1 4 -2 2 1 1 -1 0 1 1 2 0 1 1 0 -1 0 1 -1 -1 0 -1
-8 0 5 2 -1 2 4 1 -1 -1 -1 -6 -2 -2 -2 3 2 0 -1 0 2 -2 0 2 4 -3 1 -1 -2 1 -1 1 0 0 2 0 1 1 -2 -1 1 1 0 0 1 0 0 -1 -1 1 -1 0 -1 0 0 0
-17 5 4 0 -14 2 5 -6 3 -5 -5 -11 -1 -7 -6 5 -2 -2 -3 1 -5 2 2 6 3 0 1 1 -1 3 -2 1 -1 3 0 -4 1 0 -1 -1 1 0 -1 -1 -1 0 0 -1 0 1 -1 -2 0 1 -1 1
-8 -3 1 1 -1 3 3 -2 0 -1 -1 -5 -1 -2 -2 4 2 0 -1 0 0 0 1 3 2 -1 -1 0 -1 1 0 0 0 1 1 -1 1 1 -1 -1 1 1 1 1 0 1 0 -2 -1 1 -1 -1 -1 0 -1 0
-14 13 7 0 -15 -2 5 -3 5 -4 -5 -7 1 -5 -5 0 -5 -3 -2 2 -5 3 1 3 0 0 4 1 -2 2 -2 1 -2 3 -2 -4 0 -2 0 -1 0 -1 -3 -2 -3 -1 -1 1 1 0 1 -1 2 2 1 1
3 3 0 4 2 -1 1 0 -2 0 -1 2 0 3 2 -1 0 -1 0 1 1 0 -3 -3 -3 2 0 0 0 -2 1 -1 -1 0 -1 0 0 -1 0 -1 -1 0 -2 0 0 -1 0 0 0 0 0 1 1 1 1 1
-24 7 7 7 -12 3 9 -4 -3 -9 -13 -10 1 -3 -4 6 -5 -4 -3 2 -3 1 -2 2 3 -1 3 -1 -2 1 0 -2 -2 2 -2 -5 2 -2 0 -1 1 0 -2 -2 -2 0 -2 -1 0 1 0 -1 2 1 1 1
-11 7 7 0 -9 -2 2 0 3 -2 -4 -5 1 -2 -2 0 -5 -4 -2 0 -2 1 0 1 0 -1 3 0 -2 1 -1 0 -1 1 -1 -2 0 -2 0 -1 0 -1 -2 -1 -2 -1 -1 1 1 0 1 0 2 1 1 1
13 -5 -5 -8 4 -3 -9 1 4 6 10 3 -1 1 3 -4 1 2 0 -2 1 0 4 1 0 -2 -2 1 1 1 -1 2 2 -1 3 4 -1 2 0 1 0 0 2 2 2 0 2 1 0 0 0 0 -2 -1 -1 -1
9 -8 -12 -4 2 3 -7 -3 -2 1 4 3 1 1 3 -1 0 5 -1 -1 -1 1 3 1 0 0 -4 1 3 -1 -1 -1 3 -1 2 3 1 1 0 2 1 1 2 2 2 0 2 1 0 0 0 0 -2 -1 -1 -1
-12 1 1 3 -4 4 3 -2 -3 -5 -8 -4 3 -2 -2 4 -2 0 -1 1 0 1 0 1 1 -1 0 -1 -1 -1 1 -2 0 1 -2 -2 2 -2 0 0 1 0 0 -1 -1 1 -1 -1 0 0 1 0 1 0 0 1
11 2 -5 -6 -3 -4 -3 -3 5 2 8 1 -3 -2 0 -4 1 1 1 0 -3 1 3 2 0 0 0 3 1 1 -2 2 -1 1 2 0 -1 1 0 0 1 1 1 2 0 -1 1 0 0 0 -1 -1 -1 0 -1 -1
0 -5 2 1 6 2 0 4 -5 0 -2 0 0 1 1 2 2 1 0 -1 4 -3 -1 -1 3 -2 0 -3 0 0 1 0 1 -2 1 2 0 1 0 1 0 0 1 -1 2 1 0 0 -1 0 0 1 -1 -1 0 0
-18 2 8 2 -6 4 5 0 -2 -5 -8 -9 1 -5 -5 6 -1 -1 -2 0 1 -1 0 3 5 -3 2 -2 -2 2 -1 0 0 1 0 -2 1 0 -1 0 1 0 0 -2 0 1 -1 -1 -1 1 0 0 0 0 0 1
1 -2 10 -2 6 0 3 8 5 5 8 -2 -5 -3 -5 0 8 1 3 -1 5 -4 1 1 4 -4 2 -1 -2 3 -2 4 1 -3 3 2 -2 5 -3 -2 0 -1 1 0 2 0 1 -1 -2 1 -1 0 -2 -1 0 -1
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4 -5 17 -5 13 -3 1 15 7 10 11 2 -4 0 -4 -2 9 -2 5 -4 9 -6 0 -1 2 -4 2 -3 -3 4 -1 5 1 -4 3 4 -4 5 -3 -2 -2 -3 0 -1 2 1 0 0 -2 0 0 2 -1 -1 0 -1
7 -4 8 -3 10 -2 -1 9 6 8 10 5 -3 1 -2 -3 7 0 4 -3 5 -3 0 -2 0 -1 1 -1 -1 2 -1 3 1 -3 2 3 -3 4 -2 -1 -1 -2 0 0 1 0 0 0 -1 0 0 1 -1 -1 0 -1
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17 -6 -1 -4 12 -3 -3 8 3 7 12 8 -3 3 1 -6 7 3 5 -2 6 -4 2 -3 0 -3 0 -1 0 0 0 2 2 -5 2 5 -2 4 -1 0 0 -1 2 1 2 0 1 0 -1 -1 0 1 -2 -2 0 -2
-6 -7 1 -2 3 4 -2 2 -1 0 -3 -1 3 0 -1 3 0 0 0 -2 2 -1 0 1 1 -1 -2 -1 0 0 1 -1 1 0 0 1 0 0 0 1 0 -1 2 0 0 2 0 0 0 0 1 0 0 -1 -1 0
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12 -3 3 1 12 -3 -3 7 -1 7 6 6 -1 5 4 -2 4 0 1 -1 4 -2 -3 -4 -1 1 0 -2 0 0 1 2 1 -2 1 3 -2 2 0 0 -2 0 0 1 2 0 1 1 0 0 0 1 -1 0 0 -1
22 -4 -2 -6 9 -9 -7 4 8 11 16 10 -4 5 6 -8 3 -2 3 -3 0 0 1 -2 -4 2 -1 2 0 1 0 3 -1 -1 2 3 -3 2 1 0 -1 0 1 3 0 -1 1 1 1 -1 -1 0 -1 0 -1 -2
11 6 -2 -6 -2 -8 -3 -1 5 3 5 5 1 0 1 -6 -1 -1 1 1 -3 2 2 0 -3 1 2 1 0 2 0 1 -2 1 -2 -1 -2 -1 2 1 0 -1 0 0 -2 0 -1 1 1 -1 1 0 0 1 0 -1
-10 8 -2 3 -11 1 1 -4 -1 -6 -10 -2 6 1 1 -1 -8 -2 -2 2 -3 3 -1 -2 -3 1 1 1 0 -3 1 -3 -1 2 -4 -2 2 -4 2 1 0 0 -2 -1 -2 0 -1 1 2 -1 2 0 3 1 1 2
-2 6 -4 -1 -9 -4 3 -7 0 -5 -2 -4 -2 -2 1 -1 -4 -2 -1 1 -4 1 1 3 0 0 1 2 -1 1 -1 -1 -3 3 0 -3 1 -2 1 0 2 2 0 0 -2 -1 -1 -1 0 0 -1 -1 1 1 0 0
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-11 -9 -3 1 2 10 0 0 -5 -5 -7 -3 4 -2 -3 6 0 3 0 -1 3 -1 1 1 2 -2 -3 -1 1 -2 1 -3 3 -1 0 1 2 0 -1 1 1 0 2 0 1 2 0 -1 -1 0 1 0 0 -2 -1 1
-7 9 -1 3 -10 1 4 -5 -1 -7 -8 -3 2 -2 -2 0 -5 -2 0 2 -3 2 -2 -1 -3 2 1 2 0 -2 0 -2 -2 2 -3 -4 1 -3 1 -1 0 0 -2 -1 -2 -1 -1 0 0 0 1 0 3 2 1 2
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22 -2 -8 -3 10 -6 -10 1 1 7 9 12 1 7 8 -7 -1 1 1 -1 0 2 0 -4 -6 3 -2 1 2 -2 1 0 1 -1 0 3 -2 -1 2 1 -2 0 0 2 0 -1 1 2 1 -1 1 1 0 0 0 -1
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-8 9 2 7 -6 0 6 -4 -3 -5 -9 -4 0 -1 0 3 -3 -2 -2 4 -4 2 -4 0 0 2 3 0 -1 -1 1 -1 -3 3 -2 -4 1 -3 1 -1 0 1 -2 -1 -2 -1 -1 0 1 1 0 -1 2 2 1 1
17 -3 1 -3 10 -6 -5 8 3 9 11 9 -2 6 6 -7 2 1 2 -2 3 -2 0 -4 -1 -1 1 0 0 0 0 2 0 -3 2 5 -2 2 1 1 -1 0 1 1 1 -1 1 2 1 -1 0 1 -1 -1 1 -2
-5 -9 6 -2 7 4 2 6 1 2 0 0 0 -1 -3 3 4 -1 3 -3 4 -3 -1 0 1 -1 -1 -1 -1 1 1 0 0 -1 1 1 -1 2 -1 0 0 -1 2 0 0 2 -1 -1 -1 0 0 0 0 -1 -1 0
0 5 7 2 2 -3 2 5 2 1 0 2 0 1 0 -2 0 -3 2 0 3 -1 -2 -3 -2 0 2 -1 -2 -1 1 0 -1 -1 -2 0 -1 -1 0 -1 -1 -1 -2 -1 -1 0 -1 0 0 -1 1 1 2 0 1 1
-14 3 -3 6 -7 6 6 -5 -8 -10 -14 -6 4 -1 -1 5 -4 0 -2 3 -1 1 -2 0 0 0 0 -1 0 -3 2 -4 -1 2 -3 -3 3 -3 1 0 1 1 -1 -1 -1 1 -1 -1 0 0 1 0 2 1 1 2
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56 56
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5 -5 -8 0 2 2 -6 -2 -2 2 2 4 2 3 4 -1 -2 3 -2 -1 -1 2 2 -1 -1 1 -3 0 2 -1 0 -1 3 -1 0 2 1 0 1 2 0 1 1 2 1 0 1 1 1 0 0 0 -1 -1 0 -1
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-2 -6 -4 4 4 6 -1 0 -4 -1 -3 3 3 2 0 2 1 3 0 0 1 0 -1 -2 0 1 -2 -1 2 -2 1 -2 3 -2 -1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 -1 -1 0 0
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13 -2 0 -4 7 -5 -4 5 2 6 5 7 1 4 4 -5 1 -1 2 -1 2 -1 0 -3 -3 0 0 -1 0 0 2 1 -1 -1 -1 2 -2 0 2 1 -1 -1 1 1 0 1 0 1 1 -1 1 1 0 0 0 -1
0 0 -5 0 -2 0 -5 -6 -4 -1 -2 0 2 1 3 2 -4 1 -4 0 -3 3 1 1 0 2 -2 0 2 0 0 -1 1 2 0 -1 1 -2 1 1 0 1 0 1 0 0 0 0 0 1 0 0 -1 0 0 0
7 -3 -3 -5 2 -3 -6 -1 2 4 5 3 0 1 2 -2 -1 0 -1 -2 -1 1 2 1 -1 1 -1 1 1 1 0 1 0 0 1 1 -1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 -1 0 -1 -1
-3 -7 2 1 7 4 0 4 -1 2 1 1 0 1 -1 2 3 1 1 -2 4 -2 0 0 1 -1 -1 -1 0 0 1 0 2 -2 1 2 0 2 -1 0 0 0 1 0 1 1 0 0 -1 0 0 0 -1 -1 -1 0
4 -6 -6 3 6 4 -2 0 -6 0 -1 3 1 3 3 2 1 3 -1 0 1 0 -1 -2 0 1 -2 -1 2 -2 1 -2 2 -2 1 2 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 -1 -1 0 0
-1 0 0 -1 -1 0 0 0 1 0 0 -1 0 -1 -1 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 0 0 0
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0 -4 -9 2 -1 3 -1 -5 -7 -4 -6 0 2 2 4 2 -4 1 -3 1 -2 1 0 0 0 1 -2 0 2 -2 2 -3 0 1 0 0 2 -2 2 2 1 2 1 1 0 0 0 0 1 0 0 -1 0 0 0 0
1 -5 -2 1 6 2 -1 1 -4 -1 -3 2 2 2 2 2 0 0 0 0 1 -1 -1 -1 0 0 -1 -1 1 -1 2 -2 0 0 0 0 0 -1 1 1 0 0 1 0 0 1 -1 0 0 0 0 0 0 -1 0 0
-5 -3 2 2 2 4 3 2 -1 -2 -2 0 1 -1 -3 2 2 1 2 0 2 -1 0 0 0 0 -1 -1 0 0 0 -1 1 -1 -1 0 0 1 -1 0 0 -1 0 -1 0 1 0 -1 -1 0 0 0 0 -1 0 0
1 -3 -4 2 1 2 2 -1 -4 -2 -4 1 1 2 1 1 0 0 0 1 0 -1 -1 -1 -1 1 -1 -1 1 -2 2 -2 0 -1 -1 0 1 -1 1 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 0
1 1 0 1 1 -1 -1 0 -1 0 0 1 0 1 1 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 0 0
-5 3 -6 5 -5 4 2 -7 -8 -8 -10 -2 2 -1 0 3 -4 2 -2 2 -3 2 -2 0 0 2 0 1 2 -2 0 -3 -1 2 -1 -3 2 -3 1 1 1 1 -1 -1 -1 -1 -1 0 0 1 0 0 1 1 1 1
0 2 -6 1 -5 1 0 -7 -1 -3 -1 -2 -1 -2 0 1 -2 1 -2 1 -4 3 1 2 -1 2 -1 2 1 0 -1 -1 0 2 0 -2 1 -1 0 0 1 1 0 1 -1 -1 0 -1 0 1 -1 -1 0 1 0 0
5 2 8 -5 4 -5 0 6 7 5 8 1 -3 -1 -2 -3 4 -2 3 -1 3 -2 0 0 0 -2 2 0 -2 2 -1 3 -1 -1 1 1 -3 2 -1 -2 -1 -1 0 0 0 0 0 0 -1 0 0 1 0 0 0 0
3 -4 3 -1 6 -1 -2 5 0 3 3 3 0 2 2 -1 1 0 1 -2 2 -2 0 -1 1 -1 0 0 0 1 0 1 0 -1 2 2 -1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 -1 -1 0 -1
1 6 5 2 0 -4 3 2 3 1 2 1 -2 1 0 -3 1 -2 2 0 1 -1 -2 -2 -1 0 3 1 -2 0 0 1 -2 0 0 -1 -1 0 0 -2 0 0 -1 0 -1 -1 -1 0 0 0 0 0 1 1 1 0
4 2 -2 -1 -2 -2 -1 -1 -1 0 -1 0 1 1 3 -2 -2 0 -1 1 -2 1 0 -1 -1 0 1 0 0 0 0 0 -1 1 0 0 0 -1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0
6 1 3 -2 4 -4 -3 3 2 4 3 4 0 2 2 -3 0 -1 1 -1 1 0 -1 -2 -1 0 1 0 0 0 0 1 -1 0 0 1 -2 0 1 0 -1 -1 0 0 0 0 -1 1 0 0 0 1 0 0 1 0
-2 2 6 -3 -1 -3 -1 2 3 2 2 -3 -1 -1 1 0 -1 -2 -1 -1 0 0 1 2 2 -2 1 0 -2 3 -1 2 -1 2 2 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
-7 3 4 2 -4 0 4 0 -2 -3 -5 -5 0 -1 -1 2 -1 -2 -1 1 0 -1 -2 1 1 0 1 -1 -1 0 0 0 -1 1 0 -1 0 -1 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 1 1 0 1
-11 8 4 4 -8 -1 8 -2 -1 -6 -8 -6 0 -2 -1 2 -3 -4 -1 3 -2 0 -2 1 1 -1 3 0 -2 0 1 -1 -3 3 -2 -4 1 -2 1 -1 1 1 -1 -1 -2 0 -2 -1 1 0 0 -1 2 1 1 1
-6 -1 -3 2 -5 5 1 -3 -4 -4 -5 -4 2 -1 -1 3 -2 2 -2 1 -1 1 1 1 1 0 -2 -1 1 -1 -1 -1 2 0 0 0 2 -1 -1 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0 0
2 -4 -4 -1 2 3 1 0 -2 -2 -1 1 0 -1 -1 0 1 2 2 0 1 -1 0 0 -1 0 -1 1 1 -1 0 -1 0 -1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0
4 4 -1 2 2 -2 0 -1 0 0 1 4 0 2 1 -2 1 0 1 1 0 1 -1 -3 -2 1 1 0 0 -1 1 -1 -1 0 -2 -1 0 0 1 0 0 0 0 0 -1 0 -1 -1 0 0 0 0 0 0 1 0
-2 3 -4 3 -4 2 2 -4 -3 -4 -4 -1 0 0 0 1 -2 1 -1 2 -2 1 -2 -1 -1 2 0 1 1 -2 0 -2 0 1 -1 -1 1 -1 0 0 0 1 -1 0 0 -1 0 0 0 0 0 0 1 1 1 1
4 -10 -9 2 7 6 -6 -1 -8 0 -3 5 4 5 4 2 -1 4 -2 -1 1 1 -1 -3 -1 2 -4 -2 4 -3 1 -3 4 -2 0 3 1 0 1 2 -1 0 1 1 2 1 1 1 0 0 0 1 -1 -1 0 0
-1 2 8 0 2 -2 4 5 1 1 1 -3 -3 -1 -1 1 3 -2 1 0 2 -3 -2 0 3 -2 3 -1 -2 1 0 2 -2 0 2 0 -1 1 -1 -1 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0
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PROPERTIES
Modular=1
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REFERENCES
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
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NOTES
CycloQuaternionic lattice of type Delta2
The first two generators belong to the subgroup SL2(29) circ SL2(3)
which fixes a 2-dimensional space of forms.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe