Notations
---------

Assume m is an odd integer >1. 

We denote by L_m the set of all (odd) unimodular integral lattices in the standard Euclidean space R^m.

For L in L_m, the even lattice L_even = { x in L, x.x = 0 mod 2} has determinant 4, and the kernel of L_even \otimes Z/4 is isomorphic to Z/4. By a "marking" of L we mean a generator of this kernel. 

We denote by L'_m the set of all pairs (L,k) where L is in L_m, and k is a marking of L.

Write m=2n+1 and choose w=[w_1, w_2, ..., w_n] a decreasing sequence of positive odd integers. Denote by U_w ``the'' irreducible representation of the compact group SO(m) whose highest weight is the nonincreasing sequence of integers (w_i-2n+2i-1)/2 for i=1,...,n. 

Both L_m and L'_m have a natural action of the orthogonal group O(m) of R^m. Define the following finite dimensional vector spaces

S_w(m) = { f : L_m -> U_w  |  f(gL)=gf(L) for all g in SO(m) and L in L_m}

S'_w(m) = { f : L'_m -> U_w  |  f(g(L,k)) = g f(L,k) for all g in SO(m) and (L,k) in L'_m } 

Tables
------

The following tables give, for all m <= 23 and w_1 <=21,

[w_1, w_2, ... , w_n ] :  a b 

with a = dim S_w(m) and b = dim S'_w(m)  -  dim S_w(m), whenever ab is nonzero. 

I have computed them using the algorithms of the paper "The characteristic masses of Niemeier lattices", to appear in Journal de theorie des nombres de Bordeaux. Tables for higher w_1 can be given on demand.
 

m = 3
-----

[1] : 1 0
[7] : 0 1
[9] : 1 0
[13] : 1 1
[15] : 0 1
[17] : 1 0
[19] : 1 1
[21] : 1 1


m = 5
-----

[3, 1] : 1 0
[11, 1] : 1 0
[11, 7] : 0 1
[11, 9] : 1 0
[13, 1] : 0 1
[15, 1] : 1 0
[15, 5] : 1 0
[15, 7] : 0 1
[15, 9] : 1 0
[15, 13] : 1 1
[17, 5] : 0 1
[17, 7] : 1 1
[17, 9] : 1 1
[17, 13] : 1 1
[17, 15] : 0 1
[19, 1] : 2 0
[19, 3] : 0 1
[19, 5] : 1 0
[19, 7] : 0 1
[19, 9] : 2 1
[19, 11] : 0 1
[19, 13] : 2 1
[19, 15] : 0 1
[19, 17] : 1 0
[21, 1] : 0 1
[21, 3] : 1 0
[21, 5] : 0 1
[21, 7] : 2 1
[21, 9] : 1 2
[21, 11] : 2 1
[21, 13] : 1 2
[21, 15] : 1 1
[21, 17] : 1 1
[21, 19] : 1 1


m = 7
-----

[5, 3, 1] : 1 0
[13, 3, 1] : 1 0
[13, 11, 1] : 1 0
[13, 11, 9] : 1 1
[15, 11, 5] : 0 1
[17, 3, 1] : 1 0
[17, 7, 1] : 1 0
[17, 9, 1] : 0 1
[17, 11, 1] : 1 0
[17, 11, 5] : 1 0
[17, 11, 7] : 0 1
[17, 11, 9] : 1 0
[17, 13, 1] : 0 1
[17, 15, 1] : 2 0
[17, 15, 5] : 1 0
[17, 15, 7] : 0 1
[17, 15, 9] : 1 0
[17, 15, 13] : 1 1
[19, 3, 1] : 0 1
[19, 9, 1] : 1 0
[19, 9, 7] : 0 1
[19, 11, 1] : 0 1
[19, 11, 3] : 1 0
[19, 11, 5] : 0 1
[19, 11, 7] : 1 1
[19, 11, 9] : 1 1
[19, 13, 3] : 0 1
[19, 13, 5] : 1 0
[19, 13, 7] : 1 1
[19, 15, 1] : 0 1
[19, 15, 3] : 1 0
[19, 15, 5] : 0 1
[19, 15, 7] : 2 1
[19, 15, 9] : 1 1
[19, 15, 11] : 1 0
[19, 15, 13] : 0 1
[19, 17, 3] : 1 0
[19, 17, 5] : 0 1
[19, 17, 7] : 1 2
[19, 17, 9] : 1 1
[19, 17, 11] : 1 0
[19, 17, 13] : 0 1
[19, 17, 15] : 1 1
[21, 3, 1] : 2 0
[21, 7, 1] : 1 0
[21, 7, 5] : 1 0
[21, 9, 1] : 0 1
[21, 9, 5] : 0 1
[21, 11, 1] : 3 0
[21, 11, 3] : 0 1
[21, 11, 5] : 2 1
[21, 11, 7] : 0 2
[21, 11, 9] : 3 1
[21, 13, 1] : 0 1
[21, 13, 3] : 1 0
[21, 13, 5] : 1 2
[21, 13, 7] : 1 1
[21, 13, 9] : 1 1
[21, 15, 1] : 3 0
[21, 15, 3] : 0 2
[21, 15, 5] : 4 1
[21, 15, 7] : 1 3
[21, 15, 9] : 4 2
[21, 15, 11] : 1 2
[21, 15, 13] : 3 1
[21, 17, 1] : 0 1
[21, 17, 3] : 1 1
[21, 17, 5] : 2 3
[21, 17, 7] : 2 2
[21, 17, 9] : 3 3
[21, 17, 11] : 1 2
[21, 17, 13] : 2 2
[21, 17, 15] : 0 1
[21, 19, 1] : 3 0
[21, 19, 3] : 0 1
[21, 19, 5] : 3 2
[21, 19, 7] : 0 2
[21, 19, 9] : 4 2
[21, 19, 11] : 1 2
[21, 19, 13] : 3 2
[21, 19, 15] : 0 1
[21, 19, 17] : 2 1


m = 9
-----

[7, 5, 3, 1] : 2 0
[9, 5, 3, 1] : 0 1
[11, 5, 3, 1] : 1 0
[13, 5, 3, 1] : 0 1
[15, 5, 3, 1] : 2 0
[15, 13, 3, 1] : 1 0
[15, 13, 11, 1] : 1 0
[15, 13, 11, 9] : 2 1
[17, 5, 3, 1] : 0 1
[17, 13, 11, 9] : 1 2
[17, 15, 11, 5] : 0 1
[19, 5, 3, 1] : 2 0
[19, 9, 3, 1] : 1 0
[19, 13, 3, 1] : 1 0
[19, 13, 7, 1] : 1 0
[19, 13, 11, 1] : 1 0
[19, 13, 11, 3] : 0 1
[19, 13, 11, 5] : 1 0
[19, 13, 11, 9] : 2 2
[19, 15, 7, 5] : 0 1
[19, 15, 11, 5] : 0 1
[19, 17, 3, 1] : 3 0
[19, 17, 5, 1] : 0 1
[19, 17, 7, 1] : 2 0
[19, 17, 7, 5] : 1 0
[19, 17, 9, 1] : 0 2
[19, 17, 11, 1] : 3 0
[19, 17, 11, 5] : 1 0
[19, 17, 11, 7] : 0 1
[19, 17, 11, 9] : 1 0
[19, 17, 13, 1] : 0 2
[19, 17, 15, 1] : 3 0
[19, 17, 15, 5] : 1 0
[19, 17, 15, 7] : 0 1
[19, 17, 15, 9] : 1 0
[19, 17, 15, 13] : 2 2
[21, 5, 3, 1] : 0 1
[21, 11, 3, 1] : 1 0
[21, 13, 5, 1] : 1 0
[21, 13, 7, 1] : 0 1
[21, 13, 9, 1] : 1 0
[21, 13, 11, 3] : 1 0
[21, 13, 11, 5] : 0 1
[21, 13, 11, 7] : 1 1
[21, 13, 11, 9] : 2 2
[21, 15, 7, 1] : 1 0
[21, 15, 9, 1] : 0 1
[21, 15, 9, 3] : 1 0
[21, 15, 9, 5] : 0 1
[21, 15, 11, 3] : 0 1
[21, 15, 11, 5] : 1 1
[21, 15, 11, 7] : 1 1
[21, 15, 11, 9] : 0 1
[21, 15, 13, 5] : 0 1
[21, 17, 3, 1] : 0 2
[21, 17, 5, 1] : 2 0
[21, 17, 7, 1] : 0 2
[21, 17, 9, 1] : 3 0
[21, 17, 9, 3] : 0 1
[21, 17, 9, 5] : 1 0
[21, 17, 9, 7] : 0 1
[21, 17, 11, 1] : 0 3
[21, 17, 11, 3] : 2 0
[21, 17, 11, 5] : 1 2
[21, 17, 11, 7] : 2 1
[21, 17, 11, 9] : 1 1
[21, 17, 13, 1] : 2 0
[21, 17, 13, 3] : 0 1
[21, 17, 13, 5] : 2 0
[21, 17, 13, 7] : 0 1
[21, 17, 13, 9] : 1 0
[21, 17, 15, 1] : 0 2
[21, 17, 15, 3] : 1 0
[21, 17, 15, 5] : 1 1
[21, 17, 15, 7] : 2 1
[21, 17, 15, 9] : 1 1
[21, 17, 15, 13] : 2 2
[21, 19, 5, 1] : 0 1
[21, 19, 5, 3] : 1 0
[21, 19, 9, 1] : 0 1
[21, 19, 9, 3] : 1 0
[21, 19, 9, 5] : 0 1
[21, 19, 9, 7] : 3 2
[21, 19, 11, 1] : 1 0
[21, 19, 11, 3] : 1 1
[21, 19, 11, 5] : 0 1
[21, 19, 11, 7] : 3 4
[21, 19, 11, 9] : 1 1
[21, 19, 13, 1] : 0 2
[21, 19, 13, 3] : 2 1
[21, 19, 13, 5] : 1 1
[21, 19, 13, 7] : 3 2
[21, 19, 13, 9] : 1 1
[21, 19, 13, 11] : 1 0
[21, 19, 15, 3] : 1 1
[21, 19, 15, 5] : 1 1
[21, 19, 15, 7] : 3 3
[21, 19, 15, 9] : 1 1
[21, 19, 15, 11] : 1 0
[21, 19, 15, 13] : 0 1
[21, 19, 17, 3] : 1 0
[21, 19, 17, 5] : 0 1
[21, 19, 17, 7] : 3 3
[21, 19, 17, 9] : 1 1
[21, 19, 17, 11] : 1 0
[21, 19, 17, 13] : 0 1
[21, 19, 17, 15] : 2 2

m = 11
------

[9, 7, 5, 3, 1] : 2 0
[13, 7, 5, 3, 1] : 1 0
[13, 11, 5, 3, 1] : 1 0
[13, 11, 9, 3, 1] : 1 0
[15, 7, 5, 3, 1] : 0 1
[15, 11, 5, 3, 1] : 0 1
[17, 7, 5, 3, 1] : 3 0
[17, 9, 5, 3, 1] : 0 1
[17, 11, 5, 3, 1] : 2 0
[17, 11, 7, 3, 1] : 0 1
[17, 11, 9, 3, 1] : 1 0
[17, 13, 5, 3, 1] : 0 1
[17, 15, 5, 3, 1] : 3 0
[17, 15, 7, 3, 1] : 0 1
[17, 15, 9, 3, 1] : 1 0
[17, 15, 13, 3, 1] : 2 0
[17, 15, 13, 11, 1] : 2 0
[17, 15, 13, 11, 7] : 0 1
[17, 15, 13, 11, 9] : 2 0
[19, 7, 5, 3, 1] : 0 1
[19, 9, 5, 3, 1] : 1 0
[19, 11, 5, 3, 1] : 0 2
[19, 11, 7, 3, 1] : 1 0
[19, 11, 9, 3, 1] : 0 1
[19, 13, 5, 3, 1] : 1 0
[19, 13, 7, 3, 1] : 0 1
[19, 15, 5, 3, 1] : 0 1
[19, 15, 7, 3, 1] : 1 0
[19, 15, 9, 3, 1] : 0 1
[19, 15, 13, 11, 3] : 1 0
[19, 15, 13, 11, 5] : 0 1
[19, 15, 13, 11, 7] : 1 1
[19, 15, 13, 11, 9] : 1 1
[19, 17, 13, 11, 3] : 1 0
[19, 17, 13, 11, 5] : 0 1
[19, 17, 13, 11, 7] : 1 1
[19, 17, 13, 11, 9] : 1 1
[19, 17, 15, 11, 1] : 1 0
[19, 17, 15, 11, 7] : 0 2
[19, 17, 15, 11, 9] : 1 0
[19, 17, 15, 13, 1] : 0 1
[21, 7, 5, 3, 1] : 4 0
[21, 9, 5, 3, 1] : 0 2
[21, 11, 5, 3, 1] : 5 0
[21, 11, 7, 3, 1] : 0 1
[21, 11, 9, 3, 1] : 2 0
[21, 13, 5, 3, 1] : 0 3
[21, 13, 7, 3, 1] : 1 0
[21, 13, 9, 3, 1] : 0 1
[21, 15, 5, 3, 1] : 5 0
[21, 15, 7, 3, 1] : 0 2
[21, 15, 9, 3, 1] : 3 0
[21, 15, 11, 3, 1] : 0 1
[21, 15, 13, 3, 1] : 2 0
[21, 15, 13, 7, 1] : 1 0
[21, 15, 13, 11, 1] : 2 0
[21, 15, 13, 11, 3] : 0 1
[21, 15, 13, 11, 5] : 3 1
[21, 15, 13, 11, 7] : 1 2
[21, 15, 13, 11, 9] : 4 2
[21, 17, 5, 3, 1] : 0 2
[21, 17, 7, 3, 1] : 1 0
[21, 17, 9, 3, 1] : 0 1
[21, 17, 13, 11, 3] : 1 1
[21, 17, 13, 11, 5] : 2 3
[21, 17, 13, 11, 7] : 2 2
[21, 17, 13, 11, 9] : 3 4
[21, 17, 15, 9, 3] : 0 1
[21, 17, 15, 11, 3] : 1 0
[21, 17, 15, 11, 5] : 0 2
[21, 17, 15, 11, 7] : 1 1
[21, 17, 15, 11, 9] : 1 1
[21, 19, 5, 3, 1] : 6 0
[21, 19, 7, 3, 1] : 0 1
[21, 19, 9, 3, 1] : 4 0
[21, 19, 9, 7, 1] : 2 0
[21, 19, 9, 7, 5] : 1 0
[21, 19, 11, 3, 1] : 0 2
[21, 19, 11, 7, 1] : 0 1
[21, 19, 13, 3, 1] : 5 0
[21, 19, 13, 5, 1] : 0 1
[21, 19, 13, 7, 1] : 3 0
[21, 19, 13, 7, 3] : 0 1
[21, 19, 13, 7, 5] : 2 1
[21, 19, 13, 9, 1] : 0 1
[21, 19, 13, 11, 1] : 5 0
[21, 19, 13, 11, 3] : 0 3
[21, 19, 13, 11, 5] : 4 1
[21, 19, 13, 11, 7] : 1 2
[21, 19, 13, 11, 9] : 5 3
[21, 19, 15, 3, 1] : 0 1
[21, 19, 15, 5, 1] : 1 0
[21, 19, 15, 7, 1] : 0 2
[21, 19, 15, 7, 3] : 1 0
[21, 19, 15, 7, 5] : 0 2
[21, 19, 15, 9, 1] : 1 0
[21, 19, 15, 9, 3] : 0 1
[21, 19, 15, 11, 1] : 0 1
[21, 19, 15, 11, 3] : 2 0
[21, 19, 15, 11, 5] : 0 3
[21, 19, 15, 11, 7] : 1 1
[21, 19, 15, 11, 9] : 1 1
[21, 19, 17, 3, 1] : 6 0
[21, 19, 17, 5, 1] : 0 2
[21, 19, 17, 7, 1] : 6 0
[21, 19, 17, 7, 3] : 0 1
[21, 19, 17, 7, 5] : 3 0
[21, 19, 17, 9, 1] : 0 4
[21, 19, 17, 9, 3] : 1 0
[21, 19, 17, 9, 5] : 0 1
[21, 19, 17, 11, 1] : 7 0
[21, 19, 17, 11, 3] : 0 2
[21, 19, 17, 11, 5] : 3 0
[21, 19, 17, 11, 7] : 0 3
[21, 19, 17, 11, 9] : 3 0
[21, 19, 17, 13, 1] : 0 3
[21, 19, 17, 13, 3] : 1 0
[21, 19, 17, 13, 5] : 0 1
[21, 19, 17, 15, 1] : 6 0
[21, 19, 17, 15, 3] : 0 1
[21, 19, 17, 15, 5] : 3 0
[21, 19, 17, 15, 7] : 0 3
[21, 19, 17, 15, 9] : 3 0
[21, 19, 17, 15, 13] : 3 2


m = 13
------

[11, 9, 7, 5, 3, 1] : 3 0
[13, 9, 7, 5, 3, 1] : 0 1
[15, 9, 7, 5, 3, 1] : 2 0
[15, 13, 7, 5, 3, 1] : 1 0
[15, 13, 11, 5, 3, 1] : 1 0
[15, 13, 11, 9, 3, 1] : 1 0
[15, 13, 11, 9, 7, 1] : 1 0
[17, 9, 7, 5, 3, 1] : 0 1
[19, 9, 7, 5, 3, 1] : 5 0
[19, 11, 7, 5, 3, 1] : 0 1
[19, 13, 7, 5, 3, 1] : 3 0
[19, 13, 11, 5, 3, 1] : 2 0
[19, 13, 11, 9, 3, 1] : 2 0
[19, 13, 11, 9, 7, 1] : 1 0
[19, 15, 7, 5, 3, 1] : 0 2
[19, 15, 11, 5, 3, 1] : 0 1
[19, 17, 7, 5, 3, 1] : 6 0
[19, 17, 9, 5, 3, 1] : 0 2
[19, 17, 11, 5, 3, 1] : 4 0
[19, 17, 11, 7, 3, 1] : 0 1
[19, 17, 11, 9, 3, 1] : 2 0
[19, 17, 11, 9, 7, 1] : 1 0
[19, 17, 13, 5, 3, 1] : 0 2
[19, 17, 15, 5, 3, 1] : 6 0
[19, 17, 15, 7, 3, 1] : 0 2
[19, 17, 15, 9, 3, 1] : 3 0
[19, 17, 15, 9, 7, 1] : 1 0
[19, 17, 15, 11, 3, 1] : 0 1
[19, 17, 15, 13, 3, 1] : 6 0
[19, 17, 15, 13, 5, 1] : 0 1
[19, 17, 15, 13, 7, 1] : 2 0
[19, 17, 15, 13, 9, 1] : 0 1
[19, 17, 15, 13, 11, 1] : 5 0
[19, 17, 15, 13, 11, 3] : 0 1
[19, 17, 15, 13, 11, 5] : 1 0
[19, 17, 15, 13, 11, 7] : 0 2
[19, 17, 15, 13, 11, 9] : 4 1
[21, 9, 7, 5, 3, 1] : 0 3
[21, 11, 7, 5, 3, 1] : 2 0
[21, 13, 7, 5, 3, 1] : 0 2
[21, 13, 9, 5, 3, 1] : 1 0
[21, 13, 11, 5, 3, 1] : 0 1
[21, 13, 11, 7, 3, 1] : 1 0
[21, 13, 11, 9, 3, 1] : 0 1
[21, 13, 11, 9, 5, 1] : 1 0
[21, 15, 7, 5, 3, 1] : 2 0
[21, 15, 9, 5, 3, 1] : 0 1
[21, 15, 11, 5, 3, 1] : 1 0
[21, 15, 11, 7, 3, 1] : 0 1
[21, 15, 11, 9, 3, 1] : 1 0
[21, 15, 13, 5, 3, 1] : 0 1
[21, 17, 7, 5, 3, 1] : 0 4
[21, 17, 9, 5, 3, 1] : 3 0
[21, 17, 9, 7, 3, 1] : 0 1
[21, 17, 11, 5, 3, 1] : 0 4
[21, 17, 11, 7, 3, 1] : 2 0
[21, 17, 11, 7, 5, 1] : 0 1
[21, 17, 11, 9, 3, 1] : 0 2
[21, 17, 11, 9, 5, 1] : 1 0
[21, 17, 13, 5, 3, 1] : 3 0
[21, 17, 13, 7, 3, 1] : 0 2
[21, 17, 13, 9, 3, 1] : 1 0
[21, 17, 15, 5, 3, 1] : 0 4
[21, 17, 15, 7, 3, 1] : 3 0
[21, 17, 15, 7, 5, 1] : 0 1
[21, 17, 15, 9, 3, 1] : 0 3
[21, 17, 15, 9, 5, 1] : 1 0
[21, 17, 15, 11, 3, 1] : 2 0
[21, 17, 15, 13, 3, 1] : 0 3
[21, 17, 15, 13, 5, 1] : 3 0
[21, 17, 15, 13, 7, 1] : 0 1
[21, 17, 15, 13, 9, 1] : 2 0
[21, 17, 15, 13, 9, 7] : 0 1
[21, 17, 15, 13, 11, 1] : 0 3
[21, 17, 15, 13, 11, 3] : 2 0
[21, 17, 15, 13, 11, 5] : 0 2
[21, 17, 15, 13, 11, 7] : 2 1
[21, 17, 15, 13, 11, 9] : 2 3
[21, 19, 9, 5, 3, 1] : 0 1
[21, 19, 9, 7, 3, 1] : 1 0
[21, 19, 11, 7, 3, 1] : 0 2
[21, 19, 11, 7, 5, 1] : 1 0
[21, 19, 11, 9, 5, 1] : 0 1
[21, 19, 13, 5, 3, 1] : 0 1
[21, 19, 13, 7, 3, 1] : 1 0
[21, 19, 13, 7, 5, 1] : 0 1
[21, 19, 13, 9, 3, 1] : 0 1
[21, 19, 15, 7, 3, 1] : 0 1
[21, 19, 15, 7, 5, 1] : 1 0
[21, 19, 15, 9, 5, 1] : 0 1
[21, 19, 15, 13, 5, 3] : 1 0
[21, 19, 15, 13, 9, 3] : 1 0
[21, 19, 15, 13, 9, 5] : 0 1
[21, 19, 15, 13, 9, 7] : 1 1
[21, 19, 15, 13, 11, 1] : 1 0
[21, 19, 15, 13, 11, 3] : 1 1
[21, 19, 15, 13, 11, 5] : 0 1
[21, 19, 15, 13, 11, 7] : 1 2
[21, 19, 15, 13, 11, 9] : 1 1
[21, 19, 17, 13, 5, 3] : 1 0
[21, 19, 17, 13, 9, 3] : 1 0
[21, 19, 17, 13, 9, 5] : 0 1
[21, 19, 17, 13, 9, 7] : 1 1
[21, 19, 17, 13, 11, 1] : 1 0
[21, 19, 17, 13, 11, 3] : 1 1
[21, 19, 17, 13, 11, 5] : 0 1
[21, 19, 17, 13, 11, 7] : 1 2
[21, 19, 17, 13, 11, 9] : 1 1
[21, 19, 17, 15, 5, 1] : 1 0
[21, 19, 17, 15, 9, 1] : 1 0
[21, 19, 17, 15, 9, 7] : 1 2
[21, 19, 17, 15, 11, 1] : 0 2
[21, 19, 17, 15, 11, 3] : 2 0
[21, 19, 17, 15, 11, 5] : 0 2
[21, 19, 17, 15, 11, 7] : 3 2
[21, 19, 17, 15, 11, 9] : 1 2
[21, 19, 17, 15, 13, 1] : 2 0
[21, 19, 17, 15, 13, 3] : 0 1
[21, 19, 17, 15, 13, 5] : 1 0
[21, 19, 17, 15, 13, 7] : 1 4
[21, 19, 17, 15, 13, 9] : 2 0


m = 15
------

[13, 11, 9, 7, 5, 3, 1] : 5 0
[17, 11, 9, 7, 5, 3, 1] : 3 0
[17, 13, 9, 7, 5, 3, 1] : 0 1
[17, 15, 9, 7, 5, 3, 1] : 3 0
[17, 15, 13, 7, 5, 3, 1] : 3 0
[17, 15, 13, 9, 5, 3, 1] : 0 1
[17, 15, 13, 11, 5, 3, 1] : 2 0
[17, 15, 13, 11, 9, 3, 1] : 2 0
[17, 15, 13, 11, 9, 5, 1] : 0 1
[17, 15, 13, 11, 9, 7, 1] : 2 0
[17, 15, 13, 11, 9, 7, 5] : 2 1
[19, 11, 9, 7, 5, 3, 1] : 0 3
[19, 15, 9, 7, 5, 3, 1] : 0 2
[19, 15, 11, 7, 5, 3, 1] : 1 0
[19, 15, 13, 7, 5, 3, 1] : 0 1
[19, 15, 13, 11, 5, 3, 1] : 0 1
[19, 15, 13, 11, 7, 3, 1] : 1 0
[19, 15, 13, 11, 9, 3, 1] : 0 1
[19, 15, 13, 11, 9, 7, 1] : 0 1
[19, 15, 13, 11, 9, 7, 3] : 1 0
[19, 15, 13, 11, 9, 7, 5] : 0 1
[21, 11, 9, 7, 5, 3, 1] : 9 0
[21, 13, 9, 7, 5, 3, 1] : 0 2
[21, 15, 9, 7, 5, 3, 1] : 8 0
[21, 15, 11, 7, 5, 3, 1] : 0 2
[21, 15, 13, 7, 5, 3, 1] : 6 0
[21, 15, 13, 9, 5, 3, 1] : 0 1
[21, 15, 13, 11, 5, 3, 1] : 5 0
[21, 15, 13, 11, 7, 3, 1] : 0 1
[21, 15, 13, 11, 9, 3, 1] : 4 0
[21, 15, 13, 11, 9, 5, 1] : 0 1
[21, 15, 13, 11, 9, 7, 1] : 4 0
[21, 15, 13, 11, 9, 7, 3] : 0 1
[21, 15, 13, 11, 9, 7, 5] : 3 1
[21, 17, 9, 7, 5, 3, 1] : 0 4
[21, 17, 13, 7, 5, 3, 1] : 0 2
[21, 17, 13, 9, 5, 3, 1] : 1 0
[21, 17, 13, 11, 5, 3, 1] : 0 1
[21, 17, 13, 11, 9, 3, 1] : 0 1
[21, 17, 13, 11, 9, 5, 1] : 1 0
[21, 17, 13, 11, 9, 7, 1] : 0 1
[21, 17, 13, 11, 9, 7, 5] : 1 1
[21, 19, 9, 7, 5, 3, 1] : 12 0
[21, 19, 11, 7, 5, 3, 1] : 0 4
[21, 19, 13, 7, 5, 3, 1] : 10 0
[21, 19, 13, 9, 5, 3, 1] : 0 2
[21, 19, 13, 11, 5, 3, 1] : 7 0
[21, 19, 13, 11, 7, 3, 1] : 0 1
[21, 19, 13, 11, 9, 3, 1] : 6 0
[21, 19, 13, 11, 9, 5, 1] : 0 1
[21, 19, 13, 11, 9, 7, 1] : 4 0
[21, 19, 13, 11, 9, 7, 3] : 0 1
[21, 19, 13, 11, 9, 7, 5] : 3 1
[21, 19, 15, 7, 5, 3, 1] : 0 4
[21, 19, 15, 11, 5, 3, 1] : 0 2
[21, 19, 15, 11, 7, 3, 1] : 1 0
[21, 19, 15, 11, 9, 3, 1] : 0 1
[21, 19, 15, 11, 9, 7, 1] : 0 1
[21, 19, 15, 11, 9, 7, 3] : 1 0
[21, 19, 15, 11, 9, 7, 5] : 0 1
[21, 19, 17, 7, 5, 3, 1] : 16 0
[21, 19, 17, 9, 5, 3, 1] : 0 6
[21, 19, 17, 11, 5, 3, 1] : 13 0
[21, 19, 17, 11, 7, 3, 1] : 0 3
[21, 19, 17, 11, 9, 3, 1] : 8 0
[21, 19, 17, 11, 9, 5, 1] : 0 1
[21, 19, 17, 11, 9, 7, 1] : 5 0
[21, 19, 17, 11, 9, 7, 3] : 0 1
[21, 19, 17, 11, 9, 7, 5] : 3 1
[21, 19, 17, 13, 5, 3, 1] : 0 7
[21, 19, 17, 13, 7, 3, 1] : 1 0
[21, 19, 17, 13, 9, 3, 1] : 0 3
[21, 19, 17, 13, 9, 5, 1] : 1 0
[21, 19, 17, 13, 9, 7, 1] : 0 1
[21, 19, 17, 13, 9, 7, 5] : 1 1
[21, 19, 17, 15, 5, 3, 1] : 19 0
[21, 19, 17, 15, 7, 3, 1] : 0 6
[21, 19, 17, 15, 9, 3, 1] : 12 0
[21, 19, 17, 15, 9, 5, 1] : 0 2
[21, 19, 17, 15, 9, 7, 1] : 6 0
[21, 19, 17, 15, 9, 7, 3] : 0 1
[21, 19, 17, 15, 9, 7, 5] : 4 1
[21, 19, 17, 15, 11, 3, 1] : 0 5
[21, 19, 17, 15, 11, 7, 1] : 0 2
[21, 19, 17, 15, 11, 7, 3] : 1 0
[21, 19, 17, 15, 11, 7, 5] : 0 1
[21, 19, 17, 15, 13, 3, 1] : 16 0
[21, 19, 17, 15, 13, 5, 1] : 0 4
[21, 19, 17, 15, 13, 7, 1] : 9 0
[21, 19, 17, 15, 13, 7, 3] : 0 2
[21, 19, 17, 15, 13, 7, 5] : 5 1
[21, 19, 17, 15, 13, 9, 1] : 0 4
[21, 19, 17, 15, 13, 9, 5] : 1 2
[21, 19, 17, 15, 13, 11, 1] : 15 0
[21, 19, 17, 15, 13, 11, 3] : 0 4
[21, 19, 17, 15, 13, 11, 5] : 8 3
[21, 19, 17, 15, 13, 11, 7] : 0 5
[21, 19, 17, 15, 13, 11, 9] : 13 5


m = 17
------

[15, 13, 11, 9, 7, 5, 3, 1] : 9 0
[17, 13, 11, 9, 7, 5, 3, 1] : 0 3
[19, 13, 11, 9, 7, 5, 3, 1] : 8 0
[19, 17, 11, 9, 7, 5, 3, 1] : 8 0
[19, 17, 13, 9, 7, 5, 3, 1] : 0 2
[19, 17, 15, 9, 7, 5, 3, 1] : 7 0
[19, 17, 15, 13, 7, 5, 3, 1] : 7 0
[19, 17, 15, 13, 9, 5, 3, 1] : 0 2
[19, 17, 15, 13, 11, 5, 3, 1] : 7 0
[19, 17, 15, 13, 11, 9, 3, 1] : 6 0
[19, 17, 15, 13, 11, 9, 5, 1] : 0 2
[19, 17, 15, 13, 11, 9, 7, 1] : 5 0
[19, 17, 15, 13, 11, 9, 7, 5] : 4 2
[21, 13, 11, 9, 7, 5, 3, 1] : 0 4
[21, 17, 11, 9, 7, 5, 3, 1] : 0 5
[21, 17, 13, 9, 7, 5, 3, 1] : 3 0
[21, 17, 15, 9, 7, 5, 3, 1] : 0 4
[21, 17, 15, 11, 7, 5, 3, 1] : 1 0
[21, 17, 15, 13, 7, 5, 3, 1] : 0 4
[21, 17, 15, 13, 9, 5, 3, 1] : 4 0
[21, 17, 15, 13, 11, 5, 3, 1] : 0 4
[21, 17, 15, 13, 11, 7, 3, 1] : 1 0
[21, 17, 15, 13, 11, 9, 3, 1] : 0 4
[21, 17, 15, 13, 11, 9, 5, 1] : 4 0
[21, 17, 15, 13, 11, 9, 7, 1] : 0 4
[21, 17, 15, 13, 11, 9, 7, 3] : 1 0
[21, 17, 15, 13, 11, 9, 7, 5] : 3 3
[21, 19, 13, 9, 7, 5, 3, 1] : 0 2
[21, 19, 13, 11, 7, 5, 3, 1] : 1 0
[21, 19, 15, 11, 9, 5, 3, 1] : 1 0
[21, 19, 15, 13, 9, 5, 3, 1] : 0 1
[21, 19, 15, 13, 9, 7, 3, 1] : 1 0
[21, 19, 15, 13, 11, 7, 5, 1] : 1 0
[21, 19, 15, 13, 11, 9, 5, 1] : 0 1
[21, 19, 15, 13, 11, 9, 5, 3] : 1 0
[21, 19, 15, 13, 11, 9, 7, 3] : 1 0
[21, 19, 15, 13, 11, 9, 7, 5] : 0 1
[21, 19, 17, 13, 9, 7, 5, 1] : 1 0
[21, 19, 17, 13, 11, 9, 5, 3] : 1 0


m = 19
------

[17, 15, 13, 11, 9, 7, 5, 3, 1] : 16 0
[19, 15, 13, 11, 9, 7, 5, 3, 1] : 0 4
[21, 15, 13, 11, 9, 7, 5, 3, 1] : 20 0
[21, 17, 13, 11, 9, 7, 5, 3, 1] : 0 5
[21, 19, 13, 11, 9, 7, 5, 3, 1] : 25 0
[21, 19, 15, 11, 9, 7, 5, 3, 1] : 0 4
[21, 19, 17, 11, 9, 7, 5, 3, 1] : 26 0
[21, 19, 17, 13, 9, 7, 5, 3, 1] : 0 6
[21, 19, 17, 15, 9, 7, 5, 3, 1] : 27 0
[21, 19, 17, 15, 11, 7, 5, 3, 1] : 0 4
[21, 19, 17, 15, 13, 7, 5, 3, 1] : 26 0
[21, 19, 17, 15, 13, 9, 5, 3, 1] : 0 6
[21, 19, 17, 15, 13, 11, 5, 3, 1] : 28 0
[21, 19, 17, 15, 13, 11, 7, 3, 1] : 0 6
[21, 19, 17, 15, 13, 11, 9, 3, 1] : 25 0
[21, 19, 17, 15, 13, 11, 9, 5, 1] : 0 5
[21, 19, 17, 15, 13, 11, 9, 7, 1] : 17 0
[21, 19, 17, 15, 13, 11, 9, 7, 3] : 0 2
[21, 19, 17, 15, 13, 11, 9, 7, 5] : 8 2


m = 21
------

[19, 17, 15, 13, 11, 9, 7, 5, 3, 1] : 40 0
[21, 17, 15, 13, 11, 9, 7, 5, 3, 1] : 0 21


m = 23
------

[21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1] : 117 1