Laminated lattices Λ₂₅

J. H. Conway and N. J. A. Sloane, Laminated lattices, Ann. of Math. (2) 116 (1982), 593–620, doi:10.2307/2007025.

There are 23 different laminated lattices in 25 dimensions. Gram matrices for these lattices are given below as comma-separated values. See the table of densities for how these packings compare with other dimensions.

25 × 25 Gram matrix #1 (root system A₁²⁴)

8,4,-4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,0,4,2,2,-4,-4,4
4,8,-4,4,4,4,4,4,4,4,4,4,2,4,2,2,4,2,2,2,2,-2,-2,-4,4
-4,-4,8,0,0,-4,-4,-4,0,-4,-4,-4,-2,-2,-4,0,-2,0,-2,-2,-4,2,4,2,0
4,4,0,8,4,4,0,0,4,4,0,0,2,2,0,4,2,4,2,2,2,2,-2,-4,4
4,4,0,4,8,4,0,0,4,2,2,2,4,4,-2,4,4,4,-2,4,2,2,0,-4,4
4,4,-4,4,4,8,0,0,2,4,2,2,4,4,2,4,4,4,2,4,4,2,-2,-2,2
4,4,-4,0,0,0,8,4,2,2,4,4,2,0,2,-2,0,0,0,0,0,-2,-2,-2,2
4,4,-4,0,0,0,4,8,2,2,4,4,0,2,2,-2,0,-2,2,2,0,-2,-2,-2,2
4,4,0,4,4,2,2,2,8,4,0,0,4,4,-2,4,4,4,-2,4,2,2,-2,-4,4
4,4,-4,4,2,4,2,2,4,8,0,0,4,4,2,4,4,4,2,4,4,2,-4,-4,2
4,4,-4,0,2,2,4,4,0,0,8,4,2,0,2,-2,2,-2,0,0,0,-2,0,-2,2
4,4,-4,0,2,2,4,4,0,0,4,8,0,2,2,-2,0,0,0,0,0,-2,-2,0,2
4,2,-2,2,4,4,2,0,4,4,2,0,8,4,-2,4,4,4,-2,4,4,4,0,-4,2
2,4,-2,2,4,4,0,2,4,4,0,2,4,8,-2,4,4,4,0,4,4,2,0,-2,2
2,2,-4,0,-2,2,2,2,-2,2,2,2,-2,-2,8,0,0,-2,4,0,0,-2,-4,0,0
2,2,0,4,4,4,-2,-2,4,4,-2,-2,4,4,0,8,4,4,0,4,4,4,-2,-4,2
2,4,-2,2,4,4,0,0,4,4,2,0,4,4,0,4,8,4,-2,4,4,2,0,-4,2
2,2,0,4,4,4,0,-2,4,4,-2,0,4,4,-2,4,4,8,-2,4,4,4,0,-2,2
0,2,-2,2,-2,2,0,2,-2,2,0,0,-2,0,4,0,-2,-2,8,0,0,-2,-2,0,0
4,2,-2,2,4,4,0,2,4,4,0,0,4,4,0,4,4,4,0,8,4,4,-2,-4,2
2,2,-4,2,2,4,0,0,2,4,0,0,4,4,0,4,4,4,0,4,8,2,-2,-4,0
2,-2,2,2,2,2,-2,-2,2,2,-2,-2,4,2,-2,4,2,4,-2,4,2,8,0,-2,1
-4,-2,4,-2,0,-2,-2,-2,-2,-4,0,-2,0,0,-4,-2,0,0,-2,-2,-2,0,8,2,-1
-4,-4,2,-4,-4,-2,-2,-2,-4,-4,-2,0,-4,-2,0,-4,-4,-2,0,-4,-4,-2,2,8,-3
4,4,0,4,4,2,2,2,4,2,2,2,2,2,0,2,2,2,0,2,0,1,-1,-3,8

25 × 25 Gram matrix #2 (root system A₂¹²)

12,6,-6,6,6,6,6,6,6,6,6,6,6,3,3,3,3,3,0,6,3,3,-6,-6,6
6,12,-6,6,6,6,6,6,6,6,6,6,3,6,3,3,6,3,3,3,3,-3,-3,-6,6
-6,-6,12,0,0,-6,-6,-6,0,-6,-6,-6,-3,-3,-6,0,-3,0,-3,-3,-6,3,6,3,-2
6,6,0,12,6,6,0,0,6,6,0,0,3,3,0,6,3,6,3,3,3,3,-3,-6,6
6,6,0,6,12,6,0,0,6,3,3,3,6,6,-3,6,6,6,-3,6,3,3,0,-6,6
6,6,-6,6,6,12,0,0,3,6,3,3,6,6,3,6,6,6,3,6,6,3,-3,-3,5
6,6,-6,0,0,0,12,6,3,3,6,6,3,0,3,-3,0,0,0,0,0,-3,-3,-3,3
6,6,-6,0,0,0,6,12,3,3,6,6,0,3,3,-3,0,-3,3,3,0,-3,-3,-3,2
6,6,0,6,6,3,3,3,12,6,0,0,6,6,-3,6,6,6,-3,6,3,3,-3,-6,6
6,6,-6,6,3,6,3,3,6,12,0,0,6,6,3,6,6,6,3,6,6,3,-6,-6,5
6,6,-6,0,3,3,6,6,0,0,12,6,3,0,3,-3,3,-3,0,0,0,-3,0,-3,3
6,6,-6,0,3,3,6,6,0,0,6,12,0,3,3,-3,0,0,0,0,0,-3,-3,0,2
6,3,-3,3,6,6,3,0,6,6,3,0,12,6,-3,6,6,6,-3,6,6,6,0,-6,5
3,6,-3,3,6,6,0,3,6,6,0,3,6,12,-3,6,6,6,0,6,6,3,0,-3,4
3,3,-6,0,-3,3,3,3,-3,3,3,3,-3,-3,12,0,0,-3,6,0,0,-3,-6,0,0
3,3,0,6,6,6,-3,-3,6,6,-3,-3,6,6,0,12,6,6,0,6,6,6,-3,-6,4
3,6,-3,3,6,6,0,0,6,6,3,0,6,6,0,6,12,6,-3,6,6,3,0,-6,5
3,3,0,6,6,6,0,-3,6,6,-3,0,6,6,-3,6,6,12,-3,6,6,6,0,-3,5
0,3,-3,3,-3,3,0,3,-3,3,0,0,-3,0,6,0,-3,-3,12,0,0,-3,-3,0,0
6,3,-3,3,6,6,0,3,6,6,0,0,6,6,0,6,6,6,0,12,6,6,-3,-6,5
3,3,-6,3,3,6,0,0,3,6,0,0,6,6,0,6,6,6,0,6,12,3,-3,-6,3
3,-3,3,3,3,3,-3,-3,3,3,-3,-3,6,3,-3,6,3,6,-3,6,3,12,0,-3,3
-6,-3,6,-3,0,-3,-3,-3,-3,-6,0,-3,0,0,-6,-3,0,0,-3,-3,-3,0,12,3,-2
-6,-6,3,-6,-6,-3,-3,-3,-6,-6,-3,0,-6,-3,0,-6,-6,-3,0,-6,-6,-3,3,12,-6
6,6,-2,6,6,5,3,2,6,5,3,2,5,4,0,4,5,5,0,5,3,3,-2,-6,12

25 × 25 Gram matrix #3 (root system A₃⁸)

16,8,-8,8,8,8,8,8,8,8,8,8,8,4,4,4,4,4,0,8,4,4,-8,-8,0
8,16,-8,8,8,8,8,8,8,8,8,8,4,8,4,4,8,4,4,4,4,-4,-4,-8,0
-8,-8,16,0,0,-8,-8,-8,0,-8,-8,-8,-4,-4,-8,0,-4,0,-4,-4,-8,4,8,4,-4
8,8,0,16,8,8,0,0,8,8,0,0,4,4,0,8,4,8,4,4,4,4,-4,-8,0
8,8,0,8,16,8,0,0,8,4,4,4,8,8,-4,8,8,8,-4,8,4,4,0,-8,0
8,8,-8,8,8,16,0,0,4,8,4,4,8,8,4,8,8,8,4,8,8,4,-4,-4,6
8,8,-8,0,0,0,16,8,4,4,8,8,4,0,4,-4,0,0,0,0,0,-4,-4,-4,-2
8,8,-8,0,0,0,8,16,4,4,8,8,0,4,4,-4,0,-4,4,4,0,-4,-4,-4,-2
8,8,0,8,8,4,4,4,16,8,0,0,8,8,-4,8,8,8,-4,8,4,4,-4,-8,2
8,8,-8,8,4,8,4,4,8,16,0,0,8,8,4,8,8,8,4,8,8,4,-8,-8,4
8,8,-8,0,4,4,8,8,0,0,16,8,4,0,4,-4,4,-4,0,0,0,-4,0,-4,-2
8,8,-8,0,4,4,8,8,0,0,8,16,0,4,4,-4,0,0,0,0,0,-4,-4,0,-2
8,4,-4,4,8,8,4,0,8,8,4,0,16,8,-4,8,8,8,-4,8,8,8,0,-8,4
4,8,-4,4,8,8,0,4,8,8,0,4,8,16,-4,8,8,8,0,8,8,4,0,-4,4
4,4,-8,0,-4,4,4,4,-4,4,4,4,-4,-4,16,0,0,-4,8,0,0,-4,-8,0,0
4,4,0,8,8,8,-4,-4,8,8,-4,-4,8,8,0,16,8,8,0,8,8,8,-4,-8,4
4,8,-4,4,8,8,0,0,8,8,4,0,8,8,0,8,16,8,-4,8,8,4,0,-8,6
4,4,0,8,8,8,0,-4,8,8,-4,0,8,8,-4,8,8,16,-4,8,8,8,0,-4,6
0,4,-4,4,-4,4,0,4,-4,4,0,0,-4,0,8,0,-4,-4,16,0,0,-4,-4,0,0
8,4,-4,4,8,8,0,4,8,8,0,0,8,8,0,8,8,8,0,16,8,8,-4,-8,6
4,4,-8,4,4,8,0,0,4,8,0,0,8,8,0,8,8,8,0,8,16,4,-4,-8,8
4,-4,4,4,4,4,-4,-4,4,4,-4,-4,8,4,-4,8,4,8,-4,8,4,16,0,-4,3
-8,-4,8,-4,0,-4,-4,-4,-4,-8,0,-4,0,0,-8,-4,0,0,-4,-4,-4,0,16,4,-1
-8,-8,4,-8,-8,-4,-4,-4,-8,-8,-4,0,-8,-4,0,-8,-8,-4,0,-8,-8,-4,4,16,-1
0,0,-4,0,0,6,-2,-2,2,4,-2,-2,4,4,0,4,6,6,0,6,8,3,-1,-1,16

25 × 25 Gram matrix #4 (root system A₄⁶)

20,10,-10,10,10,10,10,10,10,10,10,10,10,5,5,5,5,5,0,10,5,5,-10,-10,1
10,20,-10,10,10,10,10,10,10,10,10,10,5,10,5,5,10,5,5,5,5,-5,-5,-10,-1
-10,-10,20,0,0,-10,-10,-10,0,-10,-10,-10,-5,-5,-10,0,-5,0,-5,-5,-10,5,10,5,4
10,10,0,20,10,10,0,0,10,10,0,0,5,5,0,10,5,10,5,5,5,5,-5,-10,-1
10,10,0,10,20,10,0,0,10,5,5,5,10,10,-5,10,10,10,-5,10,5,5,0,-10,-1
10,10,-10,10,10,20,0,0,5,10,5,5,10,10,5,10,10,10,5,10,10,5,-5,-5,-1
10,10,-10,0,0,0,20,10,5,5,10,10,5,0,5,-5,0,0,0,0,0,-5,-5,-5,1
10,10,-10,0,0,0,10,20,5,5,10,10,0,5,5,-5,0,-5,5,5,0,-5,-5,-5,1
10,10,0,10,10,5,5,5,20,10,0,0,10,10,-5,10,10,10,-5,10,5,5,-5,-10,-2
10,10,-10,10,5,10,5,5,10,20,0,0,10,10,5,10,10,10,5,10,10,5,-10,-10,-1
10,10,-10,0,5,5,10,10,0,0,20,10,5,0,5,-5,5,-5,0,0,0,-5,0,-5,0
10,10,-10,0,5,5,10,10,0,0,10,20,0,5,5,-5,0,0,0,0,0,-5,-5,0,2
10,5,-5,5,10,10,5,0,10,10,5,0,20,10,-5,10,10,10,-5,10,10,10,0,-10,-2
5,10,-5,5,10,10,0,5,10,10,0,5,10,20,-5,10,10,10,0,10,10,5,0,-5,-2
5,5,-10,0,-5,5,5,5,-5,5,5,5,-5,-5,20,0,0,-5,10,0,0,-5,-10,0,3
5,5,0,10,10,10,-5,-5,10,10,-5,-5,10,10,0,20,10,10,0,10,10,10,-5,-10,-2
5,10,-5,5,10,10,0,0,10,10,5,0,10,10,0,10,20,10,-5,10,10,5,0,-10,-3
5,5,0,10,10,10,0,-5,10,10,-5,0,10,10,-5,10,10,20,-5,10,10,10,0,-5,-2
0,5,-5,5,-5,5,0,5,-5,5,0,0,-5,0,10,0,-5,-5,20,0,0,-5,-5,0,2
10,5,-5,5,10,10,0,5,10,10,0,0,10,10,0,10,10,10,0,20,10,10,-5,-10,-1
5,5,-10,5,5,10,0,0,5,10,0,0,10,10,0,10,10,10,0,10,20,5,-5,-10,-10
5,-5,5,5,5,5,-5,-5,5,5,-5,-5,10,5,-5,10,5,10,-5,10,5,20,0,-5,4
-10,-5,10,-5,0,-5,-5,-5,-5,-10,0,-5,0,0,-10,-5,0,0,-5,-5,-5,0,20,5,1
-10,-10,5,-10,-10,-5,-5,-5,-10,-10,-5,0,-10,-5,0,-10,-10,-5,0,-10,-10,-5,5,20,4
1,-1,4,-1,-1,-1,1,1,-2,-1,0,2,-2,-2,3,-2,-3,-2,2,-1,-10,4,1,4,20

25 × 25 Gram matrix #5 (root system A₁₂²)

52,26,-26,26,26,26,26,26,26,26,26,26,26,13,13,13,13,13,0,26,13,13,-26,-26,-18
26,52,-26,26,26,26,26,26,26,26,26,26,13,26,13,13,26,13,13,13,13,-13,-13,-26,-19
-26,-26,52,0,0,-26,-26,-26,0,-26,-26,-26,-13,-13,-26,0,-13,0,-13,-13,-26,13,26,13,11
26,26,0,52,26,26,0,0,26,26,0,0,13,13,0,26,13,26,13,13,13,13,-13,-26,-18
26,26,0,26,52,26,0,0,26,13,13,13,26,26,-13,26,26,26,-13,26,13,13,0,-26,-18
26,26,-26,26,26,52,0,0,13,26,13,13,26,26,13,26,26,26,13,26,26,13,-13,-13,-26
26,26,-26,0,0,0,52,26,13,13,26,26,13,0,13,-13,0,0,0,0,0,-13,-13,-13,-4
26,26,-26,0,0,0,26,52,13,13,26,26,0,13,13,-13,0,-13,13,13,0,-13,-13,-13,-4
26,26,0,26,26,13,13,13,52,26,0,0,26,26,-13,26,26,26,-13,26,13,13,-13,-26,-26
26,26,-26,26,13,26,13,13,26,52,0,0,26,26,13,26,26,26,13,26,26,13,-26,-26,-26
26,26,-26,0,13,13,26,26,0,0,52,26,13,0,13,-13,13,-13,0,0,0,-13,0,-13,-2
26,26,-26,0,13,13,26,26,0,0,26,52,0,13,13,-13,0,0,0,0,0,-13,-13,0,-1
26,13,-13,13,26,26,13,0,26,26,13,0,52,26,-13,26,26,26,-13,26,26,26,0,-26,-26
13,26,-13,13,26,26,0,13,26,26,0,13,26,52,-13,26,26,26,0,26,26,13,0,-13,-26
13,13,-26,0,-13,13,13,13,-13,13,13,13,-13,-13,52,0,0,-13,26,0,0,-13,-26,0,1
13,13,0,26,26,26,-13,-13,26,26,-13,-13,26,26,0,52,26,26,0,26,26,26,-13,-26,-26
13,26,-13,13,26,26,0,0,26,26,13,0,26,26,0,26,52,26,-13,26,26,13,0,-26,-25
13,13,0,26,26,26,0,-13,26,26,-13,0,26,26,-13,26,26,52,-13,26,26,26,0,-13,-23
0,13,-13,13,-13,13,0,13,-13,13,0,0,-13,0,26,0,-13,-13,52,0,0,-13,-13,0,1
26,13,-13,13,26,26,0,13,26,26,0,0,26,26,0,26,26,26,0,52,26,26,-13,-26,-24
13,13,-26,13,13,26,0,0,13,26,0,0,26,26,0,26,26,26,0,26,52,13,-13,-26,-21
13,-13,13,13,13,13,-13,-13,13,13,-13,-13,26,13,-13,26,13,26,-13,26,13,52,0,-13,-20
-26,-13,26,-13,0,-13,-13,-13,-13,-26,0,-13,0,0,-26,-13,0,0,-13,-13,-13,0,52,13,11
-26,-26,13,-26,-26,-13,-13,-13,-26,-26,-13,0,-26,-13,0,-26,-26,-13,0,-26,-26,-13,13,52,19
-18,-19,11,-18,-18,-26,-4,-4,-26,-26,-2,-1,-26,-26,1,-26,-25,-23,1,-24,-21,-20,11,19,52

25 × 25 Gram matrix #6 (root system A₆⁴)

28,14,-14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,0,14,7,7,-14,-14,11
14,28,-14,14,14,14,14,14,14,14,14,14,7,14,7,7,14,7,7,7,7,-7,-7,-14,11
-14,-14,28,0,0,-14,-14,-14,0,-14,-14,-14,-7,-7,-14,0,-7,0,-7,-7,-14,7,14,7,-1
14,14,0,28,14,14,0,0,14,14,0,0,7,7,0,14,7,14,7,7,7,7,-7,-14,11
14,14,0,14,28,14,0,0,14,7,7,7,14,14,-7,14,14,14,-7,14,7,7,0,-14,11
14,14,-14,14,14,28,0,0,7,14,7,7,14,14,7,14,14,14,7,14,14,7,-7,-7,7
14,14,-14,0,0,0,28,14,7,7,14,14,7,0,7,-7,0,0,0,0,0,-7,-7,-7,5
14,14,-14,0,0,0,14,28,7,7,14,14,0,7,7,-7,0,-7,7,7,0,-7,-7,-7,5
14,14,0,14,14,7,7,7,28,14,0,0,14,14,-7,14,14,14,-7,14,7,7,-7,-14,7
14,14,-14,14,7,14,7,7,14,28,0,0,14,14,7,14,14,14,7,14,14,7,-14,-14,8
14,14,-14,0,7,7,14,14,0,0,28,14,7,0,7,-7,7,-7,0,0,0,-7,0,-7,6
14,14,-14,0,7,7,14,14,0,0,14,28,0,7,7,-7,0,0,0,0,0,-7,-7,0,6
14,7,-7,7,14,14,7,0,14,14,7,0,28,14,-7,14,14,14,-7,14,14,14,0,-14,8
7,14,-7,7,14,14,0,7,14,14,0,7,14,28,-7,14,14,14,0,14,14,7,0,-7,8
7,7,-14,0,-7,7,7,7,-7,7,7,7,-7,-7,28,0,0,-7,14,0,0,-7,-14,0,1
7,7,0,14,14,14,-7,-7,14,14,-7,-7,14,14,0,28,14,14,0,14,14,14,-7,-14,8
7,14,-7,7,14,14,0,0,14,14,7,0,14,14,0,14,28,14,-7,14,14,7,0,-14,8
7,7,0,14,14,14,0,-7,14,14,-7,0,14,14,-7,14,14,28,-7,14,14,14,0,-7,8
0,7,-7,7,-7,7,0,7,-7,7,0,0,-7,0,14,0,-7,-7,28,0,0,-7,-7,0,2
14,7,-7,7,14,14,0,7,14,14,0,0,14,14,0,14,14,14,0,28,14,14,-7,-14,8
7,7,-14,7,7,14,0,0,7,14,0,0,14,14,0,14,14,14,0,14,28,7,-7,-14,3
7,-7,7,7,7,7,-7,-7,7,7,-7,-7,14,7,-7,14,7,14,-7,14,7,28,0,-7,10
-14,-7,14,-7,0,-7,-7,-7,-7,-14,0,-7,0,0,-14,-7,0,0,-7,-7,-7,0,28,7,-1
-14,-14,7,-14,-14,-7,-7,-7,-14,-14,-7,0,-14,-7,0,-14,-14,-7,0,-14,-14,-7,7,28,-11
11,11,-1,11,11,7,5,5,7,8,6,6,8,8,1,8,8,8,2,8,3,10,-1,-11,28

25 × 25 Gram matrix #7 (root system A₇²D₅²)

32,16,-16,16,16,16,16,16,16,16,16,16,16,8,8,8,8,8,0,16,8,8,-16,-16,-11
16,32,-16,16,16,16,16,16,16,16,16,16,8,16,8,8,16,8,8,8,8,-8,-8,-16,-11
-16,-16,32,0,0,-16,-16,-16,0,-16,-16,-16,-8,-8,-16,0,-8,0,-8,-8,-16,8,16,8,6
16,16,0,32,16,16,0,0,16,16,0,0,8,8,0,16,8,16,8,8,8,8,-8,-16,-11
16,16,0,16,32,16,0,0,16,8,8,8,16,16,-8,16,16,16,-8,16,8,8,0,-16,-11
16,16,-16,16,16,32,0,0,8,16,8,8,16,16,8,16,16,16,8,16,16,8,-8,-8,-16
16,16,-16,0,0,0,32,16,8,8,16,16,8,0,8,-8,0,0,0,0,0,-8,-8,-8,-2
16,16,-16,0,0,0,16,32,8,8,16,16,0,8,8,-8,0,-8,8,8,0,-8,-8,-8,-2
16,16,0,16,16,8,8,8,32,16,0,0,16,16,-8,16,16,16,-8,16,8,8,-8,-16,-16
16,16,-16,16,8,16,8,8,16,32,0,0,16,16,8,16,16,16,8,16,16,8,-16,-16,-15
16,16,-16,0,8,8,16,16,0,0,32,16,8,0,8,-8,8,-8,0,0,0,-8,0,-8,0
16,16,-16,0,8,8,16,16,0,0,16,32,0,8,8,-8,0,0,0,0,0,-8,-8,0,-1
16,8,-8,8,16,16,8,0,16,16,8,0,32,16,-8,16,16,16,-8,16,16,16,0,-16,-15
8,16,-8,8,16,16,0,8,16,16,0,8,16,32,-8,16,16,16,0,16,16,8,0,-8,-16
8,8,-16,0,-8,8,8,8,-8,8,8,8,-8,-8,32,0,0,-8,16,0,0,-8,-16,0,1
8,8,0,16,16,16,-8,-8,16,16,-8,-8,16,16,0,32,16,16,0,16,16,16,-8,-16,-16
8,16,-8,8,16,16,0,0,16,16,8,0,16,16,0,16,32,16,-8,16,16,8,0,-16,-14
8,8,0,16,16,16,0,-8,16,16,-8,0,16,16,-8,16,16,32,-8,16,16,16,0,-8,-15
0,8,-8,8,-8,8,0,8,-8,8,0,0,-8,0,16,0,-8,-8,32,0,0,-8,-8,0,1
16,8,-8,8,16,16,0,8,16,16,0,0,16,16,0,16,16,16,0,32,16,16,-8,-16,-15
8,8,-16,8,8,16,0,0,8,16,0,0,16,16,0,16,16,16,0,16,32,8,-8,-16,-12
8,-8,8,8,8,8,-8,-8,8,8,-8,-8,16,8,-8,16,8,16,-8,16,8,32,0,-8,-13
-16,-8,16,-8,0,-8,-8,-8,-8,-16,0,-8,0,0,-16,-8,0,0,-8,-8,-8,0,32,8,7
-16,-16,8,-16,-16,-8,-8,-8,-16,-16,-8,0,-16,-8,0,-16,-16,-8,0,-16,-16,-8,8,32,10
-11,-11,6,-11,-11,-16,-2,-2,-16,-15,0,-1,-15,-16,1,-16,-14,-15,1,-15,-12,-13,7,10,32

25 × 25 Gram matrix #8 (root system A₈³)

36,18,-18,18,18,18,18,18,18,18,18,18,18,9,9,9,9,9,0,18,9,9,-18,-18,-13
18,36,-18,18,18,18,18,18,18,18,18,18,9,18,9,9,18,9,9,9,9,-9,-9,-18,-13
-18,-18,36,0,0,-18,-18,-18,0,-18,-18,-18,-9,-9,-18,0,-9,0,-9,-9,-18,9,18,9,8
18,18,0,36,18,18,0,0,18,18,0,0,9,9,0,18,9,18,9,9,9,9,-9,-18,-13
18,18,0,18,36,18,0,0,18,9,9,9,18,18,-9,18,18,18,-9,18,9,9,0,-18,-12
18,18,-18,18,18,36,0,0,9,18,9,9,18,18,9,18,18,18,9,18,18,9,-9,-9,-18
18,18,-18,0,0,0,36,18,9,9,18,18,9,0,9,-9,0,0,0,0,0,-9,-9,-9,-3
18,18,-18,0,0,0,18,36,9,9,18,18,0,9,9,-9,0,-9,9,9,0,-9,-9,-9,-3
18,18,0,18,18,9,9,9,36,18,0,0,18,18,-9,18,18,18,-9,18,9,9,-9,-18,-18
18,18,-18,18,9,18,9,9,18,36,0,0,18,18,9,18,18,18,9,18,18,9,-18,-18,-18
18,18,-18,0,9,9,18,18,0,0,36,18,9,0,9,-9,9,-9,0,0,0,-9,0,-9,-1
18,18,-18,0,9,9,18,18,0,0,18,36,0,9,9,-9,0,0,0,0,0,-9,-9,0,-1
18,9,-9,9,18,18,9,0,18,18,9,0,36,18,-9,18,18,18,-9,18,18,18,0,-18,-18
9,18,-9,9,18,18,0,9,18,18,0,9,18,36,-9,18,18,18,0,18,18,9,0,-9,-18
9,9,-18,0,-9,9,9,9,-9,9,9,9,-9,-9,36,0,0,-9,18,0,0,-9,-18,0,1
9,9,0,18,18,18,-9,-9,18,18,-9,-9,18,18,0,36,18,18,0,18,18,18,-9,-18,-18
9,18,-9,9,18,18,0,0,18,18,9,0,18,18,0,18,36,18,-9,18,18,9,0,-18,-16
9,9,0,18,18,18,0,-9,18,18,-9,0,18,18,-9,18,18,36,-9,18,18,18,0,-9,-16
0,9,-9,9,-9,9,0,9,-9,9,0,0,-9,0,18,0,-9,-9,36,0,0,-9,-9,0,0
18,9,-9,9,18,18,0,9,18,18,0,0,18,18,0,18,18,18,0,36,18,18,-9,-18,-16
9,9,-18,9,9,18,0,0,9,18,0,0,18,18,0,18,18,18,0,18,36,9,-9,-18,-15
9,-9,9,9,9,9,-9,-9,9,9,-9,-9,18,9,-9,18,9,18,-9,18,9,36,0,-9,-14
-18,-9,18,-9,0,-9,-9,-9,-9,-18,0,-9,0,0,-18,-9,0,0,-9,-9,-9,0,36,9,8
-18,-18,9,-18,-18,-9,-9,-9,-18,-18,-9,0,-18,-9,0,-18,-18,-9,0,-18,-18,-9,9,36,13
-13,-13,8,-13,-12,-18,-3,-3,-18,-18,-1,-1,-18,-18,1,-18,-16,-16,0,-16,-15,-14,8,13,36

25 × 25 Gram matrix #9 (root system A₉²D₆)

40,20,-20,20,20,20,20,20,20,20,20,20,20,10,10,10,10,10,0,20,10,10,-20,-20,-14
20,40,-20,20,20,20,20,20,20,20,20,20,10,20,10,10,20,10,10,10,10,-10,-10,-20,-14
-20,-20,40,0,0,-20,-20,-20,0,-20,-20,-20,-10,-10,-20,0,-10,0,-10,-10,-20,10,20,10,8
20,20,0,40,20,20,0,0,20,20,0,0,10,10,0,20,10,20,10,10,10,10,-10,-20,-14
20,20,0,20,40,20,0,0,20,10,10,10,20,20,-10,20,20,20,-10,20,10,10,0,-20,-14
20,20,-20,20,20,40,0,0,10,20,10,10,20,20,10,20,20,20,10,20,20,10,-10,-10,-20
20,20,-20,0,0,0,40,20,10,10,20,20,10,0,10,-10,0,0,0,0,0,-10,-10,-10,-3
20,20,-20,0,0,0,20,40,10,10,20,20,0,10,10,-10,0,-10,10,10,0,-10,-10,-10,-3
20,20,0,20,20,10,10,10,40,20,0,0,20,20,-10,20,20,20,-10,20,10,10,-10,-20,-20
20,20,-20,20,10,20,10,10,20,40,0,0,20,20,10,20,20,20,10,20,20,10,-20,-20,-20
20,20,-20,0,10,10,20,20,0,0,40,20,10,0,10,-10,10,-10,0,0,0,-10,0,-10,0
20,20,-20,0,10,10,20,20,0,0,20,40,0,10,10,-10,0,0,0,0,0,-10,-10,0,-1
20,10,-10,10,20,20,10,0,20,20,10,0,40,20,-10,20,20,20,-10,20,20,20,0,-20,-20
10,20,-10,10,20,20,0,10,20,20,0,10,20,40,-10,20,20,20,0,20,20,10,0,-10,-20
10,10,-20,0,-10,10,10,10,-10,10,10,10,-10,-10,40,0,0,-10,20,0,0,-10,-20,0,1
10,10,0,20,20,20,-10,-10,20,20,-10,-10,20,20,0,40,20,20,0,20,20,20,-10,-20,-20
10,20,-10,10,20,20,0,0,20,20,10,0,20,20,0,20,40,20,-10,20,20,10,0,-20,-18
10,10,0,20,20,20,0,-10,20,20,-10,0,20,20,-10,20,20,40,-10,20,20,20,0,-10,-19
0,10,-10,10,-10,10,0,10,-10,10,0,0,-10,0,20,0,-10,-10,40,0,0,-10,-10,0,1
20,10,-10,10,20,20,0,10,20,20,0,0,20,20,0,20,20,20,0,40,20,20,-10,-20,-19
10,10,-20,10,10,20,0,0,10,20,0,0,20,20,0,20,20,20,0,20,40,10,-10,-20,-16
10,-10,10,10,10,10,-10,-10,10,10,-10,-10,20,10,-10,20,10,20,-10,20,10,40,0,-10,-16
-20,-10,20,-10,0,-10,-10,-10,-10,-20,0,-10,0,0,-20,-10,0,0,-10,-10,-10,0,40,10,8
-20,-20,10,-20,-20,-10,-10,-10,-20,-20,-10,0,-20,-10,0,-20,-20,-10,0,-20,-20,-10,10,40,14
-14,-14,8,-14,-14,-20,-3,-3,-20,-20,0,-1,-20,-20,1,-20,-18,-19,1,-19,-16,-16,8,14,40

25 × 25 Gram matrix #10 (root system A₁₁D₇E₆)

48,24,-24,24,24,24,24,24,24,24,24,24,24,12,12,12,12,12,0,24,12,12,-24,-24,-17
24,48,-24,24,24,24,24,24,24,24,24,24,12,24,12,12,24,12,12,12,12,-12,-12,-24,-17
-24,-24,48,0,0,-24,-24,-24,0,-24,-24,-24,-12,-12,-24,0,-12,0,-12,-12,-24,12,24,12,10
24,24,0,48,24,24,0,0,24,24,0,0,12,12,0,24,12,24,12,12,12,12,-12,-24,-17
24,24,0,24,48,24,0,0,24,12,12,12,24,24,-12,24,24,24,-12,24,12,12,0,-24,-16
24,24,-24,24,24,48,0,0,12,24,12,12,24,24,12,24,24,24,12,24,24,12,-12,-12,-24
24,24,-24,0,0,0,48,24,12,12,24,24,12,0,12,-12,0,0,0,0,0,-12,-12,-12,-4
24,24,-24,0,0,0,24,48,12,12,24,24,0,12,12,-12,0,-12,12,12,0,-12,-12,-12,-4
24,24,0,24,24,12,12,12,48,24,0,0,24,24,-12,24,24,24,-12,24,12,12,-12,-24,-24
24,24,-24,24,12,24,12,12,24,48,0,0,24,24,12,24,24,24,12,24,24,12,-24,-24,-24
24,24,-24,0,12,12,24,24,0,0,48,24,12,0,12,-12,12,-12,0,0,0,-12,0,-12,-1
24,24,-24,0,12,12,24,24,0,0,24,48,0,12,12,-12,0,0,0,0,0,-12,-12,0,-1
24,12,-12,12,24,24,12,0,24,24,12,0,48,24,-12,24,24,24,-12,24,24,24,0,-24,-24
12,24,-12,12,24,24,0,12,24,24,0,12,24,48,-12,24,24,24,0,24,24,12,0,-12,-24
12,12,-24,0,-12,12,12,12,-12,12,12,12,-12,-12,48,0,0,-12,24,0,0,-12,-24,0,1
12,12,0,24,24,24,-12,-12,24,24,-12,-12,24,24,0,48,24,24,0,24,24,24,-12,-24,-24
12,24,-12,12,24,24,0,0,24,24,12,0,24,24,0,24,48,24,-12,24,24,12,0,-24,-22
12,12,0,24,24,24,0,-12,24,24,-12,0,24,24,-12,24,24,48,-12,24,24,24,0,-12,-22
0,12,-12,12,-12,12,0,12,-12,12,0,0,-12,0,24,0,-12,-12,48,0,0,-12,-12,0,1
24,12,-12,12,24,24,0,12,24,24,0,0,24,24,0,24,24,24,0,48,24,24,-12,-24,-22
12,12,-24,12,12,24,0,0,12,24,0,0,24,24,0,24,24,24,0,24,48,12,-12,-24,-19
12,-12,12,12,12,12,-12,-12,12,12,-12,-12,24,12,-12,24,12,24,-12,24,12,48,0,-12,-19
-24,-12,24,-12,0,-12,-12,-12,-12,-24,0,-12,0,0,-24,-12,0,0,-12,-12,-12,0,48,12,10
-24,-24,12,-24,-24,-12,-12,-12,-24,-24,-12,0,-24,-12,0,-24,-24,-12,0,-24,-24,-12,12,48,17
-17,-17,10,-17,-16,-24,-4,-4,-24,-24,-1,-1,-24,-24,1,-24,-22,-22,1,-22,-19,-19,10,17,48

25 × 25 Gram matrix #11 (root system A₁₅D₉)

64,32,-32,32,32,32,32,32,32,32,32,32,32,16,16,16,16,16,0,32,16,16,-32,-32,-23
32,64,-32,32,32,32,32,32,32,32,32,32,16,32,16,16,32,16,16,16,16,-16,-16,-32,-23
-32,-32,64,0,0,-32,-32,-32,0,-32,-32,-32,-16,-16,-32,0,-16,0,-16,-16,-32,16,32,16,14
32,32,0,64,32,32,0,0,32,32,0,0,16,16,0,32,16,32,16,16,16,16,-16,-32,-22
32,32,0,32,64,32,0,0,32,16,16,16,32,32,-16,32,32,32,-16,32,16,16,0,-32,-22
32,32,-32,32,32,64,0,0,16,32,16,16,32,32,16,32,32,32,16,32,32,16,-16,-16,-32
32,32,-32,0,0,0,64,32,16,16,32,32,16,0,16,-16,0,0,0,0,0,-16,-16,-16,-5
32,32,-32,0,0,0,32,64,16,16,32,32,0,16,16,-16,0,-16,16,16,0,-16,-16,-16,-6
32,32,0,32,32,16,16,16,64,32,0,0,32,32,-16,32,32,32,-16,32,16,16,-16,-32,-32
32,32,-32,32,16,32,16,16,32,64,0,0,32,32,16,32,32,32,16,32,32,16,-32,-32,-32
32,32,-32,0,16,16,32,32,0,0,64,32,16,0,16,-16,16,-16,0,0,0,-16,0,-16,-2
32,32,-32,0,16,16,32,32,0,0,32,64,0,16,16,-16,0,0,0,0,0,-16,-16,0,-2
32,16,-16,16,32,32,16,0,32,32,16,0,64,32,-16,32,32,32,-16,32,32,32,0,-32,-31
16,32,-16,16,32,32,0,16,32,32,0,16,32,64,-16,32,32,32,0,32,32,16,0,-16,-32
16,16,-32,0,-16,16,16,16,-16,16,16,16,-16,-16,64,0,0,-16,32,0,0,-16,-32,0,0
16,16,0,32,32,32,-16,-16,32,32,-16,-16,32,32,0,64,32,32,0,32,32,32,-16,-32,-32
16,32,-16,16,32,32,0,0,32,32,16,0,32,32,0,32,64,32,-16,32,32,16,0,-32,-30
16,16,0,32,32,32,0,-16,32,32,-16,0,32,32,-16,32,32,64,-16,32,32,32,0,-16,-29
0,16,-16,16,-16,16,0,16,-16,16,0,0,-16,0,32,0,-16,-16,64,0,0,-16,-16,0,2
32,16,-16,16,32,32,0,16,32,32,0,0,32,32,0,32,32,32,0,64,32,32,-16,-32,-30
16,16,-32,16,16,32,0,0,16,32,0,0,32,32,0,32,32,32,0,32,64,16,-16,-32,-26
16,-16,16,16,16,16,-16,-16,16,16,-16,-16,32,16,-16,32,16,32,-16,32,16,64,0,-16,-25
-32,-16,32,-16,0,-16,-16,-16,-16,-32,0,-16,0,0,-32,-16,0,0,-16,-16,-16,0,64,16,14
-32,-32,16,-32,-32,-16,-16,-16,-32,-32,-16,0,-32,-16,0,-32,-32,-16,0,-32,-32,-16,16,64,23
-23,-23,14,-22,-22,-32,-5,-6,-32,-32,-2,-2,-31,-32,0,-32,-30,-29,2,-30,-26,-25,14,23,64

25 × 25 Gram matrix #12 (root system A₁₇E₇)

72,36,-36,36,36,36,36,36,36,36,36,36,36,18,18,18,18,18,0,36,18,18,-36,-36,-26
36,72,-36,36,36,36,36,36,36,36,36,36,18,36,18,18,36,18,18,18,18,-18,-18,-36,-25
-36,-36,72,0,0,-36,-36,-36,0,-36,-36,-36,-18,-18,-36,0,-18,0,-18,-18,-36,18,36,18,15
36,36,0,72,36,36,0,0,36,36,0,0,18,18,0,36,18,36,18,18,18,18,-18,-36,-25
36,36,0,36,72,36,0,0,36,18,18,18,36,36,-18,36,36,36,-18,36,18,18,0,-36,-25
36,36,-36,36,36,72,0,0,18,36,18,18,36,36,18,36,36,36,18,36,36,18,-18,-18,-36
36,36,-36,0,0,0,72,36,18,18,36,36,18,0,18,-18,0,0,0,0,0,-18,-18,-18,-5
36,36,-36,0,0,0,36,72,18,18,36,36,0,18,18,-18,0,-18,18,18,0,-18,-18,-18,-6
36,36,0,36,36,18,18,18,72,36,0,0,36,36,-18,36,36,36,-18,36,18,18,-18,-36,-36
36,36,-36,36,18,36,18,18,36,72,0,0,36,36,18,36,36,36,18,36,36,18,-36,-36,-36
36,36,-36,0,18,18,36,36,0,0,72,36,18,0,18,-18,18,-18,0,0,0,-18,0,-18,-2
36,36,-36,0,18,18,36,36,0,0,36,72,0,18,18,-18,0,0,0,0,0,-18,-18,0,-1
36,18,-18,18,36,36,18,0,36,36,18,0,72,36,-18,36,36,36,-18,36,36,36,0,-36,-36
18,36,-18,18,36,36,0,18,36,36,0,18,36,72,-18,36,36,36,0,36,36,18,0,-18,-36
18,18,-36,0,-18,18,18,18,-18,18,18,18,-18,-18,72,0,0,-18,36,0,0,-18,-36,0,1
18,18,0,36,36,36,-18,-18,36,36,-18,-18,36,36,0,72,36,36,0,36,36,36,-18,-36,-36
18,36,-18,18,36,36,0,0,36,36,18,0,36,36,0,36,72,36,-18,36,36,18,0,-36,-34
18,18,0,36,36,36,0,-18,36,36,-18,0,36,36,-18,36,36,72,-18,36,36,36,0,-18,-32
0,18,-18,18,-18,18,0,18,-18,18,0,0,-18,0,36,0,-18,-18,72,0,0,-18,-18,0,2
36,18,-18,18,36,36,0,18,36,36,0,0,36,36,0,36,36,36,0,72,36,36,-18,-36,-34
18,18,-36,18,18,36,0,0,18,36,0,0,36,36,0,36,36,36,0,36,72,18,-18,-36,-29
18,-18,18,18,18,18,-18,-18,18,18,-18,-18,36,18,-18,36,18,36,-18,36,18,72,0,-18,-29
-36,-18,36,-18,0,-18,-18,-18,-18,-36,0,-18,0,0,-36,-18,0,0,-18,-18,-18,0,72,18,15
-36,-36,18,-36,-36,-18,-18,-18,-36,-36,-18,0,-36,-18,0,-36,-36,-18,0,-36,-36,-18,18,72,26
-26,-25,15,-25,-25,-36,-5,-6,-36,-36,-2,-1,-36,-36,1,-36,-34,-32,2,-34,-29,-29,15,26,72

25 × 25 Gram matrix #13 (root system D₄⁶)

24,12,-12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,6,0,12,6,6,-12,-12,-12
12,24,-12,12,12,12,12,12,12,12,12,12,6,12,6,6,12,6,6,6,6,-6,-6,-12,0
-12,-12,24,0,0,-12,-12,-12,0,-12,-12,-12,-6,-6,-12,0,-6,0,-6,-6,-12,6,12,6,10
12,12,0,24,12,12,0,0,12,12,0,0,6,6,0,12,6,12,6,6,6,6,-6,-12,0
12,12,0,12,24,12,0,0,12,6,6,6,12,12,-6,12,12,12,-6,12,6,6,0,-12,-2
12,12,-12,12,12,24,0,0,6,12,6,6,12,12,6,12,12,12,6,12,12,6,-6,-6,-6
12,12,-12,0,0,0,24,12,6,6,12,12,6,0,6,-6,0,0,0,0,0,-6,-6,-6,-6
12,12,-12,0,0,0,12,24,6,6,12,12,0,6,6,-6,0,-6,6,6,0,-6,-6,-6,-4
12,12,0,12,12,6,6,6,24,12,0,0,12,12,-6,12,12,12,-6,12,6,6,-6,-12,-2
12,12,-12,12,6,12,6,6,12,24,0,0,12,12,6,12,12,12,6,12,12,6,-12,-12,-7
12,12,-12,0,6,6,12,12,0,0,24,12,6,0,6,-6,6,-6,0,0,0,-6,0,-6,-5
12,12,-12,0,6,6,12,12,0,0,12,24,0,6,6,-6,0,0,0,0,0,-6,-6,0,-5
12,6,-6,6,12,12,6,0,12,12,6,0,24,12,-6,12,12,12,-6,12,12,12,0,-12,-9
6,12,-6,6,12,12,0,6,12,12,0,6,12,24,-6,12,12,12,0,12,12,6,0,-6,-2
6,6,-12,0,-6,6,6,6,-6,6,6,6,-6,-6,24,0,0,-6,12,0,0,-6,-12,0,-4
6,6,0,12,12,12,-6,-6,12,12,-6,-6,12,12,0,24,12,12,0,12,12,12,-6,-12,-3
6,12,-6,6,12,12,0,0,12,12,6,0,12,12,0,12,24,12,-6,12,12,6,0,-12,-3
6,6,0,12,12,12,0,-6,12,12,-6,0,12,12,-6,12,12,24,-6,12,12,12,0,-6,-3
0,6,-6,6,-6,6,0,6,-6,6,0,0,-6,0,12,0,-6,-6,24,0,0,-6,-6,0,3
12,6,-6,6,12,12,0,6,12,12,0,0,12,12,0,12,12,12,0,24,12,12,-6,-12,-8
6,6,-12,6,6,12,0,0,6,12,0,0,12,12,0,12,12,12,0,12,24,6,-6,-12,-7
6,-6,6,6,6,6,-6,-6,6,6,-6,-6,12,6,-6,12,6,12,-6,12,6,24,0,-6,-8
-12,-6,12,-6,0,-6,-6,-6,-6,-12,0,-6,0,0,-12,-6,0,0,-6,-6,-6,0,24,6,8
-12,-12,6,-12,-12,-6,-6,-6,-12,-12,-6,0,-12,-6,0,-12,-12,-6,0,-12,-12,-6,6,24,5
-12,0,10,0,-2,-6,-6,-4,-2,-7,-5,-5,-9,-2,-4,-3,-3,-3,3,-8,-7,-8,8,5,24

25 × 25 Gram matrix #14 (root system A₅⁴D₄)

24,12,-12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,6,0,12,6,6,-12,-12,-11
12,24,-12,12,12,12,12,12,12,12,12,12,6,12,6,6,12,6,6,6,6,-6,-6,-12,1
-12,-12,24,0,0,-12,-12,-12,0,-12,-12,-12,-6,-6,-12,0,-6,0,-6,-6,-12,6,12,6,9
12,12,0,24,12,12,0,0,12,12,0,0,6,6,0,12,6,12,6,6,6,6,-6,-12,1
12,12,0,12,24,12,0,0,12,6,6,6,12,12,-6,12,12,12,-6,12,6,6,0,-12,-2
12,12,-12,12,12,24,0,0,6,12,6,6,12,12,6,12,12,12,6,12,12,6,-6,-6,-7
12,12,-12,0,0,0,24,12,6,6,12,12,6,0,6,-6,0,0,0,0,0,-6,-6,-6,-4
12,12,-12,0,0,0,12,24,6,6,12,12,0,6,6,-6,0,-6,6,6,0,-6,-6,-6,-4
12,12,0,12,12,6,6,6,24,12,0,0,12,12,-6,12,12,12,-6,12,6,6,-6,-12,-1
12,12,-12,12,6,12,6,6,12,24,0,0,12,12,6,12,12,12,6,12,12,6,-12,-12,-6
12,12,-12,0,6,6,12,12,0,0,24,12,6,0,6,-6,6,-6,0,0,0,-6,0,-6,-4
12,12,-12,0,6,6,12,12,0,0,12,24,0,6,6,-6,0,0,0,0,0,-6,-6,0,-5
12,6,-6,6,12,12,6,0,12,12,6,0,24,12,-6,12,12,12,-6,12,12,12,0,-12,-9
6,12,-6,6,12,12,0,6,12,12,0,6,12,24,-6,12,12,12,0,12,12,6,0,-6,-3
6,6,-12,0,-6,6,6,6,-6,6,6,6,-6,-6,24,0,0,-6,12,0,0,-6,-12,0,-4
6,6,0,12,12,12,-6,-6,12,12,-6,-6,12,12,0,24,12,12,0,12,12,12,-6,-12,-3
6,12,-6,6,12,12,0,0,12,12,6,0,12,12,0,12,24,12,-6,12,12,6,0,-12,-3
6,6,0,12,12,12,0,-6,12,12,-6,0,12,12,-6,12,12,24,-6,12,12,12,0,-6,-3
0,6,-6,6,-6,6,0,6,-6,6,0,0,-6,0,12,0,-6,-6,24,0,0,-6,-6,0,2
12,6,-6,6,12,12,0,6,12,12,0,0,12,12,0,12,12,12,0,24,12,12,-6,-12,-9
6,6,-12,6,6,12,0,0,6,12,0,0,12,12,0,12,12,12,0,12,24,6,-6,-12,-7
6,-6,6,6,6,6,-6,-6,6,6,-6,-6,12,6,-6,12,6,12,-6,12,6,24,0,-6,-9
-12,-6,12,-6,0,-6,-6,-6,-6,-12,0,-6,0,0,-12,-6,0,0,-6,-6,-6,0,24,6,6
-12,-12,6,-12,-12,-6,-6,-6,-12,-12,-6,0,-12,-6,0,-12,-12,-6,0,-12,-12,-6,6,24,4
-11,1,9,1,-2,-7,-4,-4,-1,-6,-4,-5,-9,-3,-4,-3,-3,-3,2,-9,-7,-9,6,4,24

25 × 25 Gram matrix #15 (root system D₆⁴)

40,20,-20,20,20,20,20,20,20,20,20,20,20,10,10,10,10,10,0,20,10,10,-20,-20,-20
20,40,-20,20,20,20,20,20,20,20,20,20,10,20,10,10,20,10,10,10,10,-10,-10,-20,0
-20,-20,40,0,0,-20,-20,-20,0,-20,-20,-20,-10,-10,-20,0,-10,0,-10,-10,-20,10,20,10,16
20,20,0,40,20,20,0,0,20,20,0,0,10,10,0,20,10,20,10,10,10,10,-10,-20,0
20,20,0,20,40,20,0,0,20,10,10,10,20,20,-10,20,20,20,-10,20,10,10,0,-20,-4
20,20,-20,20,20,40,0,0,10,20,10,10,20,20,10,20,20,20,10,20,20,10,-10,-10,-12
20,20,-20,0,0,0,40,20,10,10,20,20,10,0,10,-10,0,0,0,0,0,-10,-10,-10,-8
20,20,-20,0,0,0,20,40,10,10,20,20,0,10,10,-10,0,-10,10,10,0,-10,-10,-10,-8
20,20,0,20,20,10,10,10,40,20,0,0,20,20,-10,20,20,20,-10,20,10,10,-10,-20,-4
20,20,-20,20,10,20,10,10,20,40,0,0,20,20,10,20,20,20,10,20,20,10,-20,-20,-12
20,20,-20,0,10,10,20,20,0,0,40,20,10,0,10,-10,10,-10,0,0,0,-10,0,-10,-8
20,20,-20,0,10,10,20,20,0,0,20,40,0,10,10,-10,0,0,0,0,0,-10,-10,0,-8
20,10,-10,10,20,20,10,0,20,20,10,0,40,20,-10,20,20,20,-10,20,20,20,0,-20,-16
10,20,-10,10,20,20,0,10,20,20,0,10,20,40,-10,20,20,20,0,20,20,10,0,-10,-6
10,10,-20,0,-10,10,10,10,-10,10,10,10,-10,-10,40,0,0,-10,20,0,0,-10,-20,0,-6
10,10,0,20,20,20,-10,-10,20,20,-10,-10,20,20,0,40,20,20,0,20,20,20,-10,-20,-6
10,20,-10,10,20,20,0,0,20,20,10,0,20,20,0,20,40,20,-10,20,20,10,0,-20,-6
10,10,0,20,20,20,0,-10,20,20,-10,0,20,20,-10,20,20,40,-10,20,20,20,0,-10,-5
0,10,-10,10,-10,10,0,10,-10,10,0,0,-10,0,20,0,-10,-10,40,0,0,-10,-10,0,3
20,10,-10,10,20,20,0,10,20,20,0,0,20,20,0,20,20,20,0,40,20,20,-10,-20,-15
10,10,-20,10,10,20,0,0,10,20,0,0,20,20,0,20,20,20,0,20,40,10,-10,-20,-12
10,-10,10,10,10,10,-10,-10,10,10,-10,-10,20,10,-10,20,10,20,-10,20,10,40,0,-10,-14
-20,-10,20,-10,0,-10,-10,-10,-10,-20,0,-10,0,0,-20,-10,0,0,-10,-10,-10,0,40,10,11
-20,-20,10,-20,-20,-10,-10,-10,-20,-20,-10,0,-20,-10,0,-20,-20,-10,0,-20,-20,-10,10,40,8
-20,0,16,0,-4,-12,-8,-8,-4,-12,-8,-8,-16,-6,-6,-6,-6,-5,3,-15,-12,-14,11,8,40

25 × 25 Gram matrix #16 (root system D₈³)

56,28,-28,28,28,28,28,28,28,28,28,28,28,14,14,14,14,14,0,28,14,14,-28,-28,-28
28,56,-28,28,28,28,28,28,28,28,28,28,14,28,14,14,28,14,14,14,14,-14,-14,-28,0
-28,-28,56,0,0,-28,-28,-28,0,-28,-28,-28,-14,-14,-28,0,-14,0,-14,-14,-28,14,28,14,22
28,28,0,56,28,28,0,0,28,28,0,0,14,14,0,28,14,28,14,14,14,14,-14,-28,0
28,28,0,28,56,28,0,0,28,14,14,14,28,28,-14,28,28,28,-14,28,14,14,0,-28,-4
28,28,-28,28,28,56,0,0,14,28,14,14,28,28,14,28,28,28,14,28,28,14,-14,-14,-14
28,28,-28,0,0,0,56,28,14,14,28,28,14,0,14,-14,0,0,0,0,0,-14,-14,-14,-14
28,28,-28,0,0,0,28,56,14,14,28,28,0,14,14,-14,0,-14,14,14,0,-14,-14,-14,-14
28,28,0,28,28,14,14,14,56,28,0,0,28,28,-14,28,28,28,-14,28,14,14,-14,-28,-6
28,28,-28,28,14,28,14,14,28,56,0,0,28,28,14,28,28,28,14,28,28,14,-28,-28,-17
28,28,-28,0,14,14,28,28,0,0,56,28,14,0,14,-14,14,-14,0,0,0,-14,0,-14,-11
28,28,-28,0,14,14,28,28,0,0,28,56,0,14,14,-14,0,0,0,0,0,-14,-14,0,-11
28,14,-14,14,28,28,14,0,28,28,14,0,56,28,-14,28,28,28,-14,28,28,28,0,-28,-22
14,28,-14,14,28,28,0,14,28,28,0,14,28,56,-14,28,28,28,0,28,28,14,0,-14,-8
14,14,-28,0,-14,14,14,14,-14,14,14,14,-14,-14,56,0,0,-14,28,0,0,-14,-28,0,-7
14,14,0,28,28,28,-14,-14,28,28,-14,-14,28,28,0,56,28,28,0,28,28,28,-14,-28,-6
14,28,-14,14,28,28,0,0,28,28,14,0,28,28,0,28,56,28,-14,28,28,14,0,-28,-6
14,14,0,28,28,28,0,-14,28,28,-14,0,28,28,-14,28,28,56,-14,28,28,28,0,-14,-7
0,14,-14,14,-14,14,0,14,-14,14,0,0,-14,0,28,0,-14,-14,56,0,0,-14,-14,0,4
28,14,-14,14,28,28,0,14,28,28,0,0,28,28,0,28,28,28,0,56,28,28,-14,-28,-21
14,14,-28,14,14,28,0,0,14,28,0,0,28,28,0,28,28,28,0,28,56,14,-14,-28,-16
14,-14,14,14,14,14,-14,-14,14,14,-14,-14,28,14,-14,28,14,28,-14,28,14,56,0,-14,-20
-28,-14,28,-14,0,-14,-14,-14,-14,-28,0,-14,0,0,-28,-14,0,0,-14,-14,-14,0,56,14,15
-28,-28,14,-28,-28,-14,-14,-14,-28,-28,-14,0,-28,-14,0,-28,-28,-14,0,-28,-28,-14,14,56,12
-28,0,22,0,-4,-14,-14,-14,-6,-17,-11,-11,-22,-8,-7,-6,-6,-7,4,-21,-16,-20,15,12,56

25 × 25 Gram matrix #17 (root system D₁₀E₇²)

72,36,-36,36,36,36,36,36,36,36,36,36,36,18,18,18,18,18,0,36,18,18,-36,-36,-36
36,72,-36,36,36,36,36,36,36,36,36,36,18,36,18,18,36,18,18,18,18,-18,-18,-36,0
-36,-36,72,0,0,-36,-36,-36,0,-36,-36,-36,-18,-18,-36,0,-18,0,-18,-18,-36,18,36,18,28
36,36,0,72,36,36,0,0,36,36,0,0,18,18,0,36,18,36,18,18,18,18,-18,-36,0
36,36,0,36,72,36,0,0,36,18,18,18,36,36,-18,36,36,36,-18,36,18,18,0,-36,-6
36,36,-36,36,36,72,0,0,18,36,18,18,36,36,18,36,36,36,18,36,36,18,-18,-18,-18
36,36,-36,0,0,0,72,36,18,18,36,36,18,0,18,-18,0,0,0,0,0,-18,-18,-18,-16
36,36,-36,0,0,0,36,72,18,18,36,36,0,18,18,-18,0,-18,18,18,0,-18,-18,-18,-18
36,36,0,36,36,18,18,18,72,36,0,0,36,36,-18,36,36,36,-18,36,18,18,-18,-36,-8
36,36,-36,36,18,36,18,18,36,72,0,0,36,36,18,36,36,36,18,36,36,18,-36,-36,-22
36,36,-36,0,18,18,36,36,0,0,72,36,18,0,18,-18,18,-18,0,0,0,-18,0,-18,-14
36,36,-36,0,18,18,36,36,0,0,36,72,0,18,18,-18,0,0,0,0,0,-18,-18,0,-14
36,18,-18,18,36,36,18,0,36,36,18,0,72,36,-18,36,36,36,-18,36,36,36,0,-36,-28
18,36,-18,18,36,36,0,18,36,36,0,18,36,72,-18,36,36,36,0,36,36,18,0,-18,-11
18,18,-36,0,-18,18,18,18,-18,18,18,18,-18,-18,72,0,0,-18,36,0,0,-18,-36,0,-9
18,18,0,36,36,36,-18,-18,36,36,-18,-18,36,36,0,72,36,36,0,36,36,36,-18,-36,-9
18,36,-18,18,36,36,0,0,36,36,18,0,36,36,0,36,72,36,-18,36,36,18,0,-36,-9
18,18,0,36,36,36,0,-18,36,36,-18,0,36,36,-18,36,36,72,-18,36,36,36,0,-18,-8
0,18,-18,18,-18,18,0,18,-18,18,0,0,-18,0,36,0,-18,-18,72,0,0,-18,-18,0,5
36,18,-18,18,36,36,0,18,36,36,0,0,36,36,0,36,36,36,0,72,36,36,-18,-36,-27
18,18,-36,18,18,36,0,0,18,36,0,0,36,36,0,36,36,36,0,36,72,18,-18,-36,-21
18,-18,18,18,18,18,-18,-18,18,18,-18,-18,36,18,-18,36,18,36,-18,36,18,72,0,-18,-26
-36,-18,36,-18,0,-18,-18,-18,-18,-36,0,-18,0,0,-36,-18,0,0,-18,-18,-18,0,72,18,20
-36,-36,18,-36,-36,-18,-18,-18,-36,-36,-18,0,-36,-18,0,-36,-36,-18,0,-36,-36,-18,18,72,16
-36,0,28,0,-6,-18,-16,-18,-8,-22,-14,-14,-28,-11,-9,-9,-9,-8,5,-27,-21,-26,20,16,72

25 × 25 Gram matrix #18 (root system D₁₂²)

88,44,-44,44,44,44,44,44,44,44,44,44,44,22,22,22,22,22,0,44,22,22,-44,-44,-44
44,88,-44,44,44,44,44,44,44,44,44,44,22,44,22,22,44,22,22,22,22,-22,-22,-44,0
-44,-44,88,0,0,-44,-44,-44,0,-44,-44,-44,-22,-22,-44,0,-22,0,-22,-22,-44,22,44,22,34
44,44,0,88,44,44,0,0,44,44,0,0,22,22,0,44,22,44,22,22,22,22,-22,-44,0
44,44,0,44,88,44,0,0,44,22,22,22,44,44,-22,44,44,44,-22,44,22,22,0,-44,-8
44,44,-44,44,44,88,0,0,22,44,22,22,44,44,22,44,44,44,22,44,44,22,-22,-22,-22
44,44,-44,0,0,0,88,44,22,22,44,44,22,0,22,-22,0,0,0,0,0,-22,-22,-22,-20
44,44,-44,0,0,0,44,88,22,22,44,44,0,22,22,-22,0,-22,22,22,0,-22,-22,-22,-22
44,44,0,44,44,22,22,22,88,44,0,0,44,44,-22,44,44,44,-22,44,22,22,-22,-44,-10
44,44,-44,44,22,44,22,22,44,88,0,0,44,44,22,44,44,44,22,44,44,22,-44,-44,-27
44,44,-44,0,22,22,44,44,0,0,88,44,22,0,22,-22,22,-22,0,0,0,-22,0,-22,-17
44,44,-44,0,22,22,44,44,0,0,44,88,0,22,22,-22,0,0,0,0,0,-22,-22,0,-17
44,22,-22,22,44,44,22,0,44,44,22,0,88,44,-22,44,44,44,-22,44,44,44,0,-44,-35
22,44,-22,22,44,44,0,22,44,44,0,22,44,88,-22,44,44,44,0,44,44,22,0,-22,-14
22,22,-44,0,-22,22,22,22,-22,22,22,22,-22,-22,88,0,0,-22,44,0,0,-22,-44,0,-10
22,22,0,44,44,44,-22,-22,44,44,-22,-22,44,44,0,88,44,44,0,44,44,44,-22,-44,-11
22,44,-22,22,44,44,0,0,44,44,22,0,44,44,0,44,88,44,-22,44,44,22,0,-44,-10
22,22,0,44,44,44,0,-22,44,44,-22,0,44,44,-22,44,44,88,-22,44,44,44,0,-22,-10
0,22,-22,22,-22,22,0,22,-22,22,0,0,-22,0,44,0,-22,-22,88,0,0,-22,-22,0,7
44,22,-22,22,44,44,0,22,44,44,0,0,44,44,0,44,44,44,0,88,44,44,-22,-44,-33
22,22,-44,22,22,44,0,0,22,44,0,0,44,44,0,44,44,44,0,44,88,22,-22,-44,-25
22,-22,22,22,22,22,-22,-22,22,22,-22,-22,44,22,-22,44,22,44,-22,44,22,88,0,-22,-32
-44,-22,44,-22,0,-22,-22,-22,-22,-44,0,-22,0,0,-44,-22,0,0,-22,-22,-22,0,88,22,24
-44,-44,22,-44,-44,-22,-22,-22,-44,-44,-22,0,-44,-22,0,-44,-44,-22,0,-44,-44,-22,22,88,20
-44,0,34,0,-8,-22,-20,-22,-10,-27,-17,-17,-35,-14,-10,-11,-10,-10,7,-33,-25,-32,24,20,88

25 × 25 Gram matrix #19 (root system D₁₆E₈)

120,60,-60,60,60,60,60,60,60,60,60,60,60,30,30,30,30,30,0,60,30,30,-60,-60,-60
60,120,-60,60,60,60,60,60,60,60,60,60,30,60,30,30,60,30,30,30,30,-30,-30,-60,0
-60,-60,120,0,0,-60,-60,-60,0,-60,-60,-60,-30,-30,-60,0,-30,0,-30,-30,-60,30,60,30,46
60,60,0,120,60,60,0,0,60,60,0,0,30,30,0,60,30,60,30,30,30,30,-30,-60,0
60,60,0,60,120,60,0,0,60,30,30,30,60,60,-30,60,60,60,-30,60,30,30,0,-60,-10
60,60,-60,60,60,120,0,0,30,60,30,30,60,60,30,60,60,60,30,60,60,30,-30,-30,-30
60,60,-60,0,0,0,120,60,30,30,60,60,30,0,30,-30,0,0,0,0,0,-30,-30,-30,-28
60,60,-60,0,0,0,60,120,30,30,60,60,0,30,30,-30,0,-30,30,30,0,-30,-30,-30,-30
60,60,0,60,60,30,30,30,120,60,0,0,60,60,-30,60,60,60,-30,60,30,30,-30,-60,-12
60,60,-60,60,30,60,30,30,60,120,0,0,60,60,30,60,60,60,30,60,60,30,-60,-60,-36
60,60,-60,0,30,30,60,60,0,0,120,60,30,0,30,-30,30,-30,0,0,0,-30,0,-30,-24
60,60,-60,0,30,30,60,60,0,0,60,120,0,30,30,-30,0,0,0,0,0,-30,-30,0,-24
60,30,-30,30,60,60,30,0,60,60,30,0,120,60,-30,60,60,60,-30,60,60,60,0,-60,-47
30,60,-30,30,60,60,0,30,60,60,0,30,60,120,-30,60,60,60,0,60,60,30,0,-30,-18
30,30,-60,0,-30,30,30,30,-30,30,30,30,-30,-30,120,0,0,-30,60,0,0,-30,-60,0,-15
30,30,0,60,60,60,-30,-30,60,60,-30,-30,60,60,0,120,60,60,0,60,60,60,-30,-60,-14
30,60,-30,30,60,60,0,0,60,60,30,0,60,60,0,60,120,60,-30,60,60,30,0,-60,-13
30,30,0,60,60,60,0,-30,60,60,-30,0,60,60,-30,60,60,120,-30,60,60,60,0,-30,-13
0,30,-30,30,-30,30,0,30,-30,30,0,0,-30,0,60,0,-30,-30,120,0,0,-30,-30,0,8
60,30,-30,30,60,60,0,30,60,60,0,0,60,60,0,60,60,60,0,120,60,60,-30,-60,-44
30,30,-60,30,30,60,0,0,30,60,0,0,60,60,0,60,60,60,0,60,120,30,-30,-60,-33
30,-30,30,30,30,30,-30,-30,30,30,-30,-30,60,30,-30,60,30,60,-30,60,30,120,0,-30,-44
-60,-30,60,-30,0,-30,-30,-30,-30,-60,0,-30,0,0,-60,-30,0,0,-30,-30,-30,0,120,30,32
-60,-60,30,-60,-60,-30,-30,-30,-60,-60,-30,0,-60,-30,0,-60,-60,-30,0,-60,-60,-30,30,120,26
-60,0,46,0,-10,-30,-28,-30,-12,-36,-24,-24,-47,-18,-15,-14,-13,-13,8,-44,-33,-44,32,26,120

25 × 25 Gram matrix #20 (root system D₂₄)

184,92,-92,92,92,92,92,92,92,92,92,92,92,46,46,46,46,46,0,92,46,46,-92,-92,-92
92,184,-92,92,92,92,92,92,92,92,92,92,46,92,46,46,92,46,46,46,46,-46,-46,-92,0
-92,-92,184,0,0,-92,-92,-92,0,-92,-92,-92,-46,-46,-92,0,-46,0,-46,-46,-92,46,92,46,70
92,92,0,184,92,92,0,0,92,92,0,0,46,46,0,92,46,92,46,46,46,46,-46,-92,0
92,92,0,92,184,92,0,0,92,46,46,46,92,92,-46,92,92,92,-46,92,46,46,0,-92,-16
92,92,-92,92,92,184,0,0,46,92,46,46,92,92,46,92,92,92,46,92,92,46,-46,-46,-46
92,92,-92,0,0,0,184,92,46,46,92,92,46,0,46,-46,0,0,0,0,0,-46,-46,-46,-42
92,92,-92,0,0,0,92,184,46,46,92,92,0,46,46,-46,0,-46,46,46,0,-46,-46,-46,-46
92,92,0,92,92,46,46,46,184,92,0,0,92,92,-46,92,92,92,-46,92,46,46,-46,-92,-20
92,92,-92,92,46,92,46,46,92,184,0,0,92,92,46,92,92,92,46,92,92,46,-92,-92,-56
92,92,-92,0,46,46,92,92,0,0,184,92,46,0,46,-46,46,-46,0,0,0,-46,0,-46,-36
92,92,-92,0,46,46,92,92,0,0,92,184,0,46,46,-46,0,0,0,0,0,-46,-46,0,-36
92,46,-46,46,92,92,46,0,92,92,46,0,184,92,-46,92,92,92,-46,92,92,92,0,-92,-73
46,92,-46,46,92,92,0,46,92,92,0,46,92,184,-46,92,92,92,0,92,92,46,0,-46,-29
46,46,-92,0,-46,46,46,46,-46,46,46,46,-46,-46,184,0,0,-46,92,0,0,-46,-92,0,-22
46,46,0,92,92,92,-46,-46,92,92,-46,-46,92,92,0,184,92,92,0,92,92,92,-46,-92,-23
46,92,-46,46,92,92,0,0,92,92,46,0,92,92,0,92,184,92,-46,92,92,46,0,-92,-21
46,46,0,92,92,92,0,-46,92,92,-46,0,92,92,-46,92,92,184,-46,92,92,92,0,-46,-21
0,46,-46,46,-46,46,0,46,-46,46,0,0,-46,0,92,0,-46,-46,184,0,0,-46,-46,0,14
92,46,-46,46,92,92,0,46,92,92,0,0,92,92,0,92,92,92,0,184,92,92,-46,-92,-68
46,46,-92,46,46,92,0,0,46,92,0,0,92,92,0,92,92,92,0,92,184,46,-46,-92,-51
46,-46,46,46,46,46,-46,-46,46,46,-46,-46,92,46,-46,92,46,92,-46,92,46,184,0,-46,-68
-92,-46,92,-46,0,-46,-46,-46,-46,-92,0,-46,0,0,-92,-46,0,0,-46,-46,-46,0,184,46,49
-92,-92,46,-92,-92,-46,-46,-46,-92,-92,-46,0,-92,-46,0,-92,-92,-46,0,-92,-92,-46,46,184,40
-92,0,70,0,-16,-46,-42,-46,-20,-56,-36,-36,-73,-29,-22,-23,-21,-21,14,-68,-51,-68,49,40,184

25 × 25 Gram matrix #21 (root system E₈³)

120,60,-60,60,60,60,60,60,60,60,60,60,60,30,30,30,30,30,0,60,30,30,-60,-60,-44
60,120,-60,60,60,60,60,60,60,60,60,60,30,60,30,30,60,30,30,30,30,-30,-30,-60,-41
-60,-60,120,0,0,-60,-60,-60,0,-60,-60,-60,-30,-30,-60,0,-30,0,-30,-30,-60,30,60,30,25
60,60,0,120,60,60,0,0,60,60,0,0,30,30,0,60,30,60,30,30,30,30,-30,-60,-44
60,60,0,60,120,60,0,0,60,30,30,30,60,60,-30,60,60,60,-30,60,30,30,0,-60,-39
60,60,-60,60,60,120,0,0,30,60,30,30,60,60,30,60,60,60,30,60,60,30,-30,-30,-60
60,60,-60,0,0,0,120,60,30,30,60,60,30,0,30,-30,0,0,0,0,0,-30,-30,-30,-8
60,60,-60,0,0,0,60,120,30,30,60,60,0,30,30,-30,0,-30,30,30,0,-30,-30,-30,-8
60,60,0,60,60,30,30,30,120,60,0,0,60,60,-30,60,60,60,-30,60,30,30,-30,-60,-60
60,60,-60,60,30,60,30,30,60,120,0,0,60,60,30,60,60,60,30,60,60,30,-60,-60,-60
60,60,-60,0,30,30,60,60,0,0,120,60,30,0,30,-30,30,-30,0,0,0,-30,0,-30,-2
60,60,-60,0,30,30,60,60,0,0,60,120,0,30,30,-30,0,0,0,0,0,-30,-30,0,-2
60,30,-30,30,60,60,30,0,60,60,30,0,120,60,-30,60,60,60,-30,60,60,60,0,-60,-60
30,60,-30,30,60,60,0,30,60,60,0,30,60,120,-30,60,60,60,0,60,60,30,0,-30,-57
30,30,-60,0,-30,30,30,30,-30,30,30,30,-30,-30,120,0,0,-30,60,0,0,-30,-60,0,2
30,30,0,60,60,60,-30,-30,60,60,-30,-30,60,60,0,120,60,60,0,60,60,60,-30,-60,-60
30,60,-30,30,60,60,0,0,60,60,30,0,60,60,0,60,120,60,-30,60,60,30,0,-60,-54
30,30,0,60,60,60,0,-30,60,60,-30,0,60,60,-30,60,60,120,-30,60,60,60,0,-30,-54
0,30,-30,30,-30,30,0,30,-30,30,0,0,-30,0,60,0,-30,-30,120,0,0,-30,-30,0,2
60,30,-30,30,60,60,0,30,60,60,0,0,60,60,0,60,60,60,0,120,60,60,-30,-60,-54
30,30,-60,30,30,60,0,0,30,60,0,0,60,60,0,60,60,60,0,60,120,30,-30,-60,-48
30,-30,30,30,30,30,-30,-30,30,30,-30,-30,60,30,-30,60,30,60,-30,60,30,120,0,-30,-49
-60,-30,60,-30,0,-30,-30,-30,-30,-60,0,-30,0,0,-60,-30,0,0,-30,-30,-30,0,120,30,26
-60,-60,30,-60,-60,-30,-30,-30,-60,-60,-30,0,-60,-30,0,-60,-60,-30,0,-60,-60,-30,30,120,43
-44,-41,25,-44,-39,-60,-8,-8,-60,-60,-2,-2,-60,-57,2,-60,-54,-54,2,-54,-48,-49,26,43,120

25 × 25 Gram matrix #22 (root system E₆⁴)

48,24,-24,24,24,24,24,24,24,24,24,24,24,12,12,12,12,12,0,24,12,12,-24,-24,19
24,48,-24,24,24,24,24,24,24,24,24,24,12,24,12,12,24,12,12,12,12,-12,-12,-24,19
-24,-24,48,0,0,-24,-24,-24,0,-24,-24,-24,-12,-12,-24,0,-12,0,-12,-12,-24,12,24,12,-2
24,24,0,48,24,24,0,0,24,24,0,0,12,12,0,24,12,24,12,12,12,12,-12,-24,19
24,24,0,24,48,24,0,0,24,12,12,12,24,24,-12,24,24,24,-12,24,12,12,0,-24,21
24,24,-24,24,24,48,0,0,12,24,12,12,24,24,12,24,24,24,12,24,24,12,-12,-12,12
24,24,-24,0,0,0,48,24,12,12,24,24,12,0,12,-12,0,0,0,0,0,-12,-12,-12,8
24,24,-24,0,0,0,24,48,12,12,24,24,0,12,12,-12,0,-12,12,12,0,-12,-12,-12,8
24,24,0,24,24,12,12,12,48,24,0,0,24,24,-12,24,24,24,-12,24,12,12,-12,-24,12
24,24,-24,24,12,24,12,12,24,48,0,0,24,24,12,24,24,24,12,24,24,12,-24,-24,15
24,24,-24,0,12,12,24,24,0,0,48,24,12,0,12,-12,12,-12,0,0,0,-12,0,-12,10
24,24,-24,0,12,12,24,24,0,0,24,48,0,12,12,-12,0,0,0,0,0,-12,-12,0,10
24,12,-12,12,24,24,12,0,24,24,12,0,48,24,-12,24,24,24,-12,24,24,24,0,-24,14
12,24,-12,12,24,24,0,12,24,24,0,12,24,48,-12,24,24,24,0,24,24,12,0,-12,14
12,12,-24,0,-12,12,12,12,-12,12,12,12,-12,-12,48,0,0,-12,24,0,0,-12,-24,0,2
12,12,0,24,24,24,-12,-12,24,24,-12,-12,24,24,0,48,24,24,0,24,24,24,-12,-24,14
12,24,-12,12,24,24,0,0,24,24,12,0,24,24,0,24,48,24,-12,24,24,12,0,-24,14
12,12,0,24,24,24,0,-12,24,24,-12,0,24,24,-12,24,24,48,-12,24,24,24,0,-12,14
0,12,-12,12,-12,12,0,12,-12,12,0,0,-12,0,24,0,-12,-12,48,0,0,-12,-12,0,2
24,12,-12,12,24,24,0,12,24,24,0,0,24,24,0,24,24,24,0,48,24,24,-12,-24,14
12,12,-24,12,12,24,0,0,12,24,0,0,24,24,0,24,24,24,0,24,48,12,-12,-24,6
12,-12,12,12,12,12,-12,-12,12,12,-12,-12,24,12,-12,24,12,24,-12,24,12,48,0,-12,17
-24,-12,24,-12,0,-12,-12,-12,-12,-24,0,-12,0,0,-24,-12,0,0,-12,-12,-12,0,48,12,-3
-24,-24,12,-24,-24,-12,-12,-12,-24,-24,-12,0,-24,-12,0,-24,-24,-12,0,-24,-24,-12,12,48,-20
19,19,-2,19,21,12,8,8,12,15,10,10,14,14,2,14,14,14,2,14,6,17,-3,-20,48

25 × 25 Gram matrix #23 (root system A₂₄)

100,50,-50,50,50,50,50,50,50,50,50,50,50,25,25,25,25,25,0,50,25,25,-50,-50,-36
50,100,-50,50,50,50,50,50,50,50,50,50,25,50,25,25,50,25,25,25,25,-25,-25,-50,-35
-50,-50,100,0,0,-50,-50,-50,0,-50,-50,-50,-25,-25,-50,0,-25,0,-25,-25,-50,25,50,25,21
50,50,0,100,50,50,0,0,50,50,0,0,25,25,0,50,25,50,25,25,25,25,-25,-50,-35
50,50,0,50,100,50,0,0,50,25,25,25,50,50,-25,50,50,50,-25,50,25,25,0,-50,-34
50,50,-50,50,50,100,0,0,25,50,25,25,50,50,25,50,50,50,25,50,50,25,-25,-25,-50
50,50,-50,0,0,0,100,50,25,25,50,50,25,0,25,-25,0,0,0,0,0,-25,-25,-25,-8
50,50,-50,0,0,0,50,100,25,25,50,50,0,25,25,-25,0,-25,25,25,0,-25,-25,-25,-8
50,50,0,50,50,25,25,25,100,50,0,0,50,50,-25,50,50,50,-25,50,25,25,-25,-50,-50
50,50,-50,50,25,50,25,25,50,100,0,0,50,50,25,50,50,50,25,50,50,25,-50,-50,-50
50,50,-50,0,25,25,50,50,0,0,100,50,25,0,25,-25,25,-25,0,0,0,-25,0,-25,-2
50,50,-50,0,25,25,50,50,0,0,50,100,0,25,25,-25,0,0,0,0,0,-25,-25,0,-2
50,25,-25,25,50,50,25,0,50,50,25,0,100,50,-25,50,50,50,-25,50,50,50,0,-50,-50
25,50,-25,25,50,50,0,25,50,50,0,25,50,100,-25,50,50,50,0,50,50,25,0,-25,-50
25,25,-50,0,-25,25,25,25,-25,25,25,25,-25,-25,100,0,0,-25,50,0,0,-25,-50,0,2
25,25,0,50,50,50,-25,-25,50,50,-25,-25,50,50,0,100,50,50,0,50,50,50,-25,-50,-50
25,50,-25,25,50,50,0,0,50,50,25,0,50,50,0,50,100,50,-25,50,50,25,0,-50,-46
25,25,0,50,50,50,0,-25,50,50,-25,0,50,50,-25,50,50,100,-25,50,50,50,0,-25,-44
0,25,-25,25,-25,25,0,25,-25,25,0,0,-25,0,50,0,-25,-25,100,0,0,-25,-25,0,1
50,25,-25,25,50,50,0,25,50,50,0,0,50,50,0,50,50,50,0,100,50,50,-25,-50,-47
25,25,-50,25,25,50,0,0,25,50,0,0,50,50,0,50,50,50,0,50,100,25,-25,-50,-40
25,-25,25,25,25,25,-25,-25,25,25,-25,-25,50,25,-25,50,25,50,-25,50,25,100,0,-25,-40
-50,-25,50,-25,0,-25,-25,-25,-25,-50,0,-25,0,0,-50,-25,0,0,-25,-25,-25,0,100,25,22
-50,-50,25,-50,-50,-25,-25,-25,-50,-50,-25,0,-50,-25,0,-50,-50,-25,0,-50,-50,-25,25,100,36
-36,-35,21,-35,-34,-50,-8,-8,-50,-50,-2,-2,-50,-50,2,-50,-46,-44,1,-47,-40,-40,22,36,100