Phylogenetic tree 5-0-1

Evolutionary model

Jukes Cantor model with root distribution $\pi = \left(\frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \right)$.
The transition matrix associated with edge $i$ is of the form $$M_j = \begin{pmatrix} a_i & b_i & b_i & b_i\\ b_i & a_i & b_i & b_i\\ b_i & b_i & a_i & b_i\\ b_i & b_i & b_i & a_i \end{pmatrix}$$ and the Fourier parameters are $\left(x^{(i)}_1, x^{(i)}_i, x^{(i)}_i, x^{(i)}_i\right)$ for all edges $i$.

Summary

Dimension: 7
Degree: 315
Probability coordinates: 51
Fourier coordinates: 31
dim of Singular locus: -
deg of Singular locus: -
MLdeg: -
EDdeg: 3819

Probability parametrization

$\begin{align} p_{\texttt{ACGAC}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_6b_2b_3b_5 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5a_6b_1b_3b_4 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCCG}} &= \frac{1}{2}(a_1a_3a_4b_2b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_4a_6b_1b_5 + a_2a_5b_1b_3b_4b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_4b_1b_2b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCGT}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_2a_3a_6b_1b_4b_5 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCAG}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_6b_2b_3b_5 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_6b_1b_4b_5 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGTA}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5a_6b_2b_3b_4 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGTC}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5a_6b_1b_3b_4 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACAGG}} &= \frac{1}{2}(a_1a_3a_6b_2b_4b_5 + a_1a_4a_5b_2b_3b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_5b_1b_3b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + a_4a_5a_6b_1b_2b_3 + a_4a_5b_1b_2b_3b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AAACG}} &= \frac{1}{2}(a_1a_2a_3a_6b_4b_5 + a_1a_2a_4b_3b_5b_6 + a_1a_2a_5b_3b_4b_6 + a_1a_2b_3b_4b_5b_6 + 3a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGGG}} &= \frac{1}{2}(a_1a_3a_4a_5b_2b_6 + a_1a_6b_2b_3b_4b_5 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4a_5b_1b_6 + a_2a_6b_1b_3b_4b_5 + 2a_2b_1b_3b_4b_5b_6 + a_3a_4a_5a_6b_1b_2 + a_3a_4a_5b_1b_2b_6 + a_6b_1b_2b_3b_4b_5 + 5b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACGA}} &= \frac{1}{2}(a_1a_2a_3b_4b_5b_6 + a_1a_2a_4b_3b_5b_6 + a_1a_2a_5a_6b_3b_4 + a_1a_2b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + 2a_4b_1b_2b_3b_5b_6 + 3a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACGC}} &= \frac{1}{2}(a_1a_2a_3a_5b_4b_6 + a_1a_2a_4b_3b_5b_6 + a_1a_2a_6b_3b_4b_5 + a_1a_2b_3b_4b_5b_6 + a_3a_5a_6b_1b_2b_4 + 2a_3a_5b_1b_2b_4b_6 + a_4a_6b_1b_2b_3b_5 + 2a_4b_1b_2b_3b_5b_6 + a_6b_1b_2b_3b_4b_5 + 5b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACACG}} &= \frac{1}{2}(a_1a_3a_6b_2b_4b_5 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_6b_1b_3b_5 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACAGT}} &= \frac{1}{2}(a_1a_3a_6b_2b_4b_5 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACAAG}} &= \frac{1}{2}(a_1a_3a_4a_6b_2b_5 + a_1a_5b_2b_3b_4b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4b_1b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + 2a_3a_4b_1b_2b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCGA}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5a_6b_2b_3b_4 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_6b_1b_4b_5 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGCG}} &= \frac{1}{2}(a_1a_3a_5b_2b_4b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_5b_1b_4b_6 + a_2a_4a_6b_1b_3b_5 + 2a_2b_1b_3b_4b_5b_6 + a_3a_5a_6b_1b_2b_4 + a_3a_5b_1b_2b_4b_6 + 2a_4b_1b_2b_3b_5b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGGT}} &= \frac{1}{2}(a_1a_3a_4b_2b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_4b_1b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_4a_6b_1b_2b_5 + a_3a_4b_1b_2b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACCA}} &= \frac{1}{2}(a_1a_2a_3a_4b_5b_6 + a_1a_2a_5a_6b_3b_4 + 2a_1a_2b_3b_4b_5b_6 + a_3a_4a_6b_1b_2b_5 + 2a_3a_4b_1b_2b_5b_6 + 3a_5b_1b_2b_3b_4b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCGC}} &= \frac{1}{2}(a_1a_3a_5b_2b_4b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_5a_6b_1b_4 + a_2a_4b_1b_3b_5b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_5b_1b_2b_4b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACAA}} &= \frac{1}{2}(a_1a_2a_3b_4b_5b_6 + a_1a_2a_4a_5a_6b_3 + 2a_1a_2b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + 3a_4a_5b_1b_2b_3b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGAG}} &= \frac{1}{2}(a_1a_3a_5b_2b_4b_6 + a_1a_4a_6b_2b_3b_5 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_5b_1b_4b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_5a_6b_1b_2b_4 + a_3a_5b_1b_2b_4b_6 + 2a_4b_1b_2b_3b_5b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACCC}} &= \frac{1}{2}(a_1a_2a_3a_4a_5b_6 + a_1a_2a_6b_3b_4b_5 + 2a_1a_2b_3b_4b_5b_6 + a_3a_4a_5a_6b_1b_2 + 2a_3a_4a_5b_1b_2b_6 + 2a_6b_1b_2b_3b_4b_5 + 7b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{AACAC}} &= \frac{1}{2}(a_1a_2a_3a_5b_4b_6 + a_1a_2a_4a_6b_3b_5 + 2a_1a_2b_3b_4b_5b_6 + a_3a_5a_6b_1b_2b_4 + 2a_3a_5b_1b_2b_4b_6 + 3a_4b_1b_2b_3b_5b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCCA}} &= \frac{1}{2}(a_1a_3a_4b_2b_5b_6 + a_1a_5a_6b_2b_3b_4 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4a_6b_1b_5 + a_2a_5b_1b_3b_4b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_4b_1b_2b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGTG}} &= \frac{1}{2}(a_1a_3a_5b_2b_4b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_5b_1b_4b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_5a_6b_1b_2b_4 + a_3a_5b_1b_2b_4b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCAA}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_5a_6b_2b_3 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_6b_1b_4b_5 + a_2a_4a_5b_1b_3b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + 2a_4a_5b_1b_2b_3b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGCT}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_6b_1b_3b_5 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGAT}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_6b_2b_3b_5 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + a_5b_1b_2b_3b_4b_6 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCCC}} &= \frac{1}{2}(a_1a_3a_4a_5b_2b_6 + a_1a_6b_2b_3b_4b_5 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4a_5a_6b_1 + 3a_2b_1b_3b_4b_5b_6 + 2a_3a_4a_5b_1b_2b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACCAC}} &= \frac{1}{2}(a_1a_3a_5b_2b_4b_6 + a_1a_4a_6b_2b_3b_5 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_5a_6b_1b_4 + a_2a_4b_1b_3b_5b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_5b_1b_2b_4b_6 + 2a_4b_1b_2b_3b_5b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) \\[0.5em] p_{\texttt{ACGTT}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_5b_2b_3b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_5b_1b_3b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + a_4a_5a_6b_1b_2b_3 + a_4a_5b_1b_2b_3b_6 + 4b_1b_2b_3b_4b_5b_6) p_{\texttt{ACAGA}} &= \frac{1}{2}(a_1a_3a_5a_6b_2b_4 + a_1a_4b_2b_3b_5b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_5b_1b_4b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + 2a_3a_5b_1b_2b_4b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{AAACA}} &= \frac{1}{2}(a_1a_2a_3a_5a_6b_4 + a_1a_2a_4b_3b_5b_6 + 2a_1a_2b_3b_4b_5b_6 + 3a_3a_5b_1b_2b_4b_6 + a_4a_6b_1b_2b_3b_5 + 2a_4b_1b_2b_3b_5b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) p_{\texttt{ACAGC}} &= \frac{1}{2}(a_1a_3a_6b_2b_4b_5 + a_1a_4b_2b_3b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4b_1b_3b_5b_6 + a_2a_5a_6b_1b_3b_4 + a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) p_{\texttt{AACGG}} &= \frac{1}{2}(a_1a_2a_3b_4b_5b_6 + a_1a_2a_4a_5b_3b_6 + a_1a_2a_6b_3b_4b_5 + a_1a_2b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + a_4a_5a_6b_1b_2b_3 + 2a_4a_5b_1b_2b_3b_6 + a_6b_1b_2b_3b_4b_5 + 5b_1b_2b_3b_4b_5b_6) p_{\texttt{ACGGA}} &= \frac{1}{2}(a_1a_3a_4b_2b_5b_6 + a_1a_5a_6b_2b_3b_4 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4b_1b_5b_6 + a_2a_5b_1b_3b_4b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_4a_6b_1b_2b_5 + a_3a_4b_1b_2b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{AAAAA}} &= \frac{1}{2}(a_1a_2a_3a_4a_5a_6 + 3a_1a_2b_3b_4b_5b_6 + 3a_3a_4a_5b_1b_2b_6 + 3a_6b_1b_2b_3b_4b_5 + 6b_1b_2b_3b_4b_5b_6) p_{\texttt{AAACC}} &= \frac{1}{2}(a_1a_2a_3a_6b_4b_5 + a_1a_2a_4a_5b_3b_6 + 2a_1a_2b_3b_4b_5b_6 + 3a_3b_1b_2b_4b_5b_6 + a_4a_5a_6b_1b_2b_3 + 2a_4a_5b_1b_2b_3b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) p_{\texttt{ACGGC}} &= \frac{1}{2}(a_1a_3a_4b_2b_5b_6 + a_1a_5b_2b_3b_4b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_4b_1b_5b_6 + a_2a_5a_6b_1b_3b_4 + 2a_2b_1b_3b_4b_5b_6 + a_3a_4a_6b_1b_2b_5 + a_3a_4b_1b_2b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{AAAAC}} &= \frac{1}{2}(a_1a_2a_3a_4a_6b_5 + a_1a_2a_5b_3b_4b_6 + 2a_1a_2b_3b_4b_5b_6 + 3a_3a_4b_1b_2b_5b_6 + a_5a_6b_1b_2b_3b_4 + 2a_5b_1b_2b_3b_4b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) p_{\texttt{ACACA}} &= \frac{1}{2}(a_1a_3a_5a_6b_2b_4 + a_1a_4b_2b_3b_5b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_5b_1b_4b_6 + a_2a_4a_6b_1b_3b_5 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_5b_1b_2b_4b_6 + 2a_4b_1b_2b_3b_5b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) p_{\texttt{ACCGG}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_5b_2b_3b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3a_6b_1b_4b_5 + a_2a_4a_5b_1b_3b_6 + 2a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + a_4a_5a_6b_1b_2b_3 + a_4a_5b_1b_2b_3b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{ACAAA}} &= \frac{1}{2}(a_1a_3a_4a_5a_6b_2 + 3a_1b_2b_3b_4b_5b_6 + a_2a_3a_4a_5b_1b_6 + a_2a_6b_1b_3b_4b_5 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_4a_5b_1b_2b_6 + 2a_6b_1b_2b_3b_4b_5 + 4b_1b_2b_3b_4b_5b_6) p_{\texttt{ACACC}} &= \frac{1}{2}(a_1a_3a_6b_2b_4b_5 + a_1a_4a_5b_2b_3b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_5a_6b_1b_3 + 2a_2b_1b_3b_4b_5b_6 + 2a_3b_1b_2b_4b_5b_6 + 2a_4a_5b_1b_2b_3b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) p_{\texttt{ACGCA}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4b_2b_3b_5b_6 + a_1a_5a_6b_2b_3b_4 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_6b_1b_3b_5 + a_2a_5b_1b_3b_4b_6 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4b_1b_2b_3b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + b_1b_2b_3b_4b_5b_6) p_{\texttt{AACCG}} &= \frac{1}{2}(a_1a_2a_3a_4b_5b_6 + a_1a_2a_5b_3b_4b_6 + a_1a_2a_6b_3b_4b_5 + a_1a_2b_3b_4b_5b_6 + a_3a_4a_6b_1b_2b_5 + 2a_3a_4b_1b_2b_5b_6 + a_5a_6b_1b_2b_3b_4 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 5b_1b_2b_3b_4b_5b_6) p_{\texttt{AACGT}} &= \frac{1}{2}(a_1a_2a_3b_4b_5b_6 + a_1a_2a_4b_3b_5b_6 + a_1a_2a_5b_3b_4b_6 + a_1a_2a_6b_3b_4b_5 + a_3a_6b_1b_2b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + a_4a_6b_1b_2b_3b_5 + 2a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + 2a_5b_1b_2b_3b_4b_6 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{ACGAA}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_5a_6b_2b_3 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_5b_1b_3b_6 + a_2a_6b_1b_3b_4b_5 + a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4a_5b_1b_2b_3b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) p_{\texttt{AACAG}} &= \frac{1}{2}(a_1a_2a_3b_4b_5b_6 + a_1a_2a_4a_6b_3b_5 + a_1a_2a_5b_3b_4b_6 + a_1a_2b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + 2a_3b_1b_2b_4b_5b_6 + 3a_4b_1b_2b_3b_5b_6 + a_5a_6b_1b_2b_3b_4 + 2a_5b_1b_2b_3b_4b_6 + a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) p_{\texttt{ACAAC}} &= \frac{1}{2}(a_1a_3a_4a_6b_2b_5 + a_1a_5b_2b_3b_4b_6 + 2a_1b_2b_3b_4b_5b_6 + a_2a_3a_4b_1b_5b_6 + a_2a_5a_6b_1b_3b_4 + 2a_2b_1b_3b_4b_5b_6 + 2a_3a_4b_1b_2b_5b_6 + 2a_5b_1b_2b_3b_4b_6 + 2a_6b_1b_2b_3b_4b_5 + 2b_1b_2b_3b_4b_5b_6) p_{\texttt{ACGCC}} &= \frac{1}{2}(a_1a_3b_2b_4b_5b_6 + a_1a_4a_5b_2b_3b_6 + a_1a_6b_2b_3b_4b_5 + a_1b_2b_3b_4b_5b_6 + a_2a_3b_1b_4b_5b_6 + a_2a_4a_5a_6b_1b_3 + 2a_2b_1b_3b_4b_5b_6 + a_3a_6b_1b_2b_4b_5 + a_3b_1b_2b_4b_5b_6 + 2a_4a_5b_1b_2b_3b_6 + a_6b_1b_2b_3b_4b_5 + 3b_1b_2b_3b_4b_5b_6) \end{align}$

Fourier parametrization

$\begin{align} q_{\texttt{AACAC}} &= x^{(1)}_{1}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{1} \\[0.5em] q_{\texttt{CGCCT}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACGTA}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CAAGT}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACCAA}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CAACA}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACCCC}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACGAT}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CAAAC}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{1}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CGTAA}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CCAAA}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{1}x^{(5)}_{1}x^{(6)}_{1} \\[0.5em] q_{\texttt{CGACG}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CCACC}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{1} \\[0.5em] q_{\texttt{CGCGA}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CACAA}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CAGTA}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{CACCC}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CAGAT}} &= x^{(1)}_{2}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{AAAAA}} &= x^{(1)}_{1}x^{(2)}_{1}x^{(3)}_{1}x^{(4)}_{1}x^{(5)}_{1}x^{(6)}_{1} \\[0.5em] q_{\texttt{AAACC}} &= x^{(1)}_{1}x^{(2)}_{1}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{1} \\[0.5em] q_{\texttt{CCCGT}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{1} \\[0.5em] q_{\texttt{CCCCA}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{1} \\[0.5em] q_{\texttt{CGATA}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACACA}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{2} \\[0.5em] q_{\texttt{ACAGT}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CGCAG}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CGAAT}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{CCCAC}} &= x^{(1)}_{2}x^{(2)}_{2}x^{(3)}_{2}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{1} \\[0.5em] q_{\texttt{ACAAC}} &= x^{(1)}_{1}x^{(2)}_{2}x^{(3)}_{1}x^{(4)}_{1}x^{(5)}_{2}x^{(6)}_{2} \\[0.5em] q_{\texttt{AACCA}} &= x^{(1)}_{1}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{1}x^{(6)}_{1} \\[0.5em] q_{\texttt{AACGT}} &= x^{(1)}_{1}x^{(2)}_{1}x^{(3)}_{2}x^{(4)}_{2}x^{(5)}_{2}x^{(6)}_{1} \end{align}$

Equivalent classes of probability parametrization

$\begin{align} \text{Class } &p_{\texttt{AAAAA}}:\ p_{\texttt{AAAAA}},\ p_{\texttt{CCCCC}},\ p_{\texttt{GGGGG}},\ p_{\texttt{TTTTT}} \\[0.5em] \text{Class } &p_{\texttt{AAAAC}}:\ p_{\texttt{AAAAC}},\ p_{\texttt{AAAAG}},\ p_{\texttt{AAAAT}},\ p_{\texttt{CCCCA}},\ p_{\texttt{CCCCG}},\ p_{\texttt{CCCCT}},\ p_{\texttt{GGGGA}},\ p_{\texttt{GGGGC}},\ p_{\texttt{GGGGT}},\ p_{\texttt{TTTTA}},\ p_{\texttt{TTTTC}},\ p_{\texttt{TTTTG}} \\[0.5em] \text{Class } &p_{\texttt{AAACA}}:\ p_{\texttt{AAACA}},\ p_{\texttt{AAAGA}},\ p_{\texttt{AAATA}},\ p_{\texttt{CCCAC}},\ p_{\texttt{CCCGC}},\ p_{\texttt{CCCTC}},\ p_{\texttt{GGGAG}},\ p_{\texttt{GGGCG}},\ p_{\texttt{GGGTG}},\ p_{\texttt{TTTAT}},\ p_{\texttt{TTTCT}},\ p_{\texttt{TTTGT}} \\[0.5em] \text{Class } &p_{\texttt{AAACC}}:\ p_{\texttt{AAACC}},\ p_{\texttt{AAAGG}},\ p_{\texttt{AAATT}},\ p_{\texttt{CCCAA}},\ p_{\texttt{CCCGG}},\ p_{\texttt{CCCTT}},\ p_{\texttt{GGGAA}},\ p_{\texttt{GGGCC}},\ p_{\texttt{GGGTT}},\ p_{\texttt{TTTAA}},\ p_{\texttt{TTTCC}},\ p_{\texttt{TTTGG}} \\[0.5em] \text{Class } &p_{\texttt{AAACG}}:\ p_{\texttt{AAACG}},\ p_{\texttt{AAACT}},\ p_{\texttt{AAAGC}},\ p_{\texttt{AAAGT}},\ p_{\texttt{AAATC}},\ p_{\texttt{AAATG}},\ p_{\texttt{CCCAG}},\ p_{\texttt{CCCAT}},\ p_{\texttt{CCCGA}},\ p_{\texttt{CCCGT}},\ p_{\texttt{CCCTA}},\ p_{\texttt{CCCTG}},\ p_{\texttt{GGGAC}},\ p_{\texttt{GGGAT}},\ p_{\texttt{GGGCA}},\ p_{\texttt{GGGCT}},\ p_{\texttt{GGGTA}},\ p_{\texttt{GGGTC}},\ p_{\texttt{TTTAC}},\ p_{\texttt{TTTAG}},\ p_{\texttt{TTTCA}},\ p_{\texttt{TTTCG}},\ p_{\texttt{TTTGA}},\ p_{\texttt{TTTGC}} \\[0.5em] \text{Class } &p_{\texttt{AACAA}}:\ p_{\texttt{AACAA}},\ p_{\texttt{AAGAA}},\ p_{\texttt{AATAA}},\ p_{\texttt{CCACC}},\ p_{\texttt{CCGCC}},\ p_{\texttt{CCTCC}},\ p_{\texttt{GGAGG}},\ p_{\texttt{GGCGG}},\ p_{\texttt{GGTGG}},\ p_{\texttt{TTATT}},\ p_{\texttt{TTCTT}},\ p_{\texttt{TTGTT}} \\[0.5em] \text{Class } &p_{\texttt{AACAC}}:\ p_{\texttt{AACAC}},\ p_{\texttt{AAGAG}},\ p_{\texttt{AATAT}},\ p_{\texttt{CCACA}},\ p_{\texttt{CCGCG}},\ p_{\texttt{CCTCT}},\ p_{\texttt{GGAGA}},\ p_{\texttt{GGCGC}},\ p_{\texttt{GGTGT}},\ p_{\texttt{TTATA}},\ p_{\texttt{TTCTC}},\ p_{\texttt{TTGTG}} \\[0.5em] \text{Class } &p_{\texttt{AACAG}}:\ p_{\texttt{AACAG}},\ p_{\texttt{AACAT}},\ p_{\texttt{AAGAC}},\ p_{\texttt{AAGAT}},\ p_{\texttt{AATAC}},\ p_{\texttt{AATAG}},\ p_{\texttt{CCACG}},\ p_{\texttt{CCACT}},\ p_{\texttt{CCGCA}},\ p_{\texttt{CCGCT}},\ p_{\texttt{CCTCA}},\ p_{\texttt{CCTCG}},\ p_{\texttt{GGAGC}},\ p_{\texttt{GGAGT}},\ p_{\texttt{GGCGA}},\ p_{\texttt{GGCGT}},\ p_{\texttt{GGTGA}},\ p_{\texttt{GGTGC}},\ p_{\texttt{TTATC}},\ p_{\texttt{TTATG}},\ p_{\texttt{TTCTA}},\ p_{\texttt{TTCTG}},\ p_{\texttt{TTGTA}},\ p_{\texttt{TTGTC}} \\[0.5em] \text{Class } &p_{\texttt{AACCA}}:\ p_{\texttt{AACCA}},\ p_{\texttt{AAGGA}},\ p_{\texttt{AATTA}},\ p_{\texttt{CCAAC}},\ p_{\texttt{CCGGC}},\ p_{\texttt{CCTTC}},\ p_{\texttt{GGAAG}},\ p_{\texttt{GGCCG}},\ p_{\texttt{GGTTG}},\ p_{\texttt{TTAAT}},\ p_{\texttt{TTCCT}},\ p_{\texttt{TTGGT}} \\[0.5em] \text{Class } &p_{\texttt{AACCC}}:\ p_{\texttt{AACCC}},\ p_{\texttt{AAGGG}},\ p_{\texttt{AATTT}},\ p_{\texttt{CCAAA}},\ p_{\texttt{CCGGG}},\ p_{\texttt{CCTTT}},\ p_{\texttt{GGAAA}},\ p_{\texttt{GGCCC}},\ p_{\texttt{GGTTT}},\ p_{\texttt{TTAAA}},\ p_{\texttt{TTCCC}},\ p_{\texttt{TTGGG}} \\[0.5em] \text{Class } &p_{\texttt{AACCG}}:\ p_{\texttt{AACCG}},\ p_{\texttt{AACCT}},\ p_{\texttt{AAGGC}},\ p_{\texttt{AAGGT}},\ p_{\texttt{AATTC}},\ p_{\texttt{AATTG}},\ p_{\texttt{CCAAG}},\ p_{\texttt{CCAAT}},\ p_{\texttt{CCGGA}},\ p_{\texttt{CCGGT}},\ p_{\texttt{CCTTA}},\ p_{\texttt{CCTTG}},\ p_{\texttt{GGAAC}},\ p_{\texttt{GGAAT}},\ p_{\texttt{GGCCA}},\ p_{\texttt{GGCCT}},\ p_{\texttt{GGTTA}},\ p_{\texttt{GGTTC}},\ p_{\texttt{TTAAC}},\ p_{\texttt{TTAAG}},\ p_{\texttt{TTCCA}},\ p_{\texttt{TTCCG}},\ p_{\texttt{TTGGA}},\ p_{\texttt{TTGGC}} \\[0.5em] \text{Class } &p_{\texttt{AACGA}}:\ p_{\texttt{AACGA}},\ p_{\texttt{AACTA}},\ p_{\texttt{AAGCA}},\ p_{\texttt{AAGTA}},\ p_{\texttt{AATCA}},\ p_{\texttt{AATGA}},\ p_{\texttt{CCAGC}},\ p_{\texttt{CCATC}},\ p_{\texttt{CCGAC}},\ p_{\texttt{CCGTC}},\ p_{\texttt{CCTAC}},\ p_{\texttt{CCTGC}},\ p_{\texttt{GGACG}},\ p_{\texttt{GGATG}},\ p_{\texttt{GGCAG}},\ p_{\texttt{GGCTG}},\ p_{\texttt{GGTAG}},\ p_{\texttt{GGTCG}},\ p_{\texttt{TTACT}},\ p_{\texttt{TTAGT}},\ p_{\texttt{TTCAT}},\ p_{\texttt{TTCGT}},\ p_{\texttt{TTGAT}},\ p_{\texttt{TTGCT}} \\[0.5em] \text{Class } &p_{\texttt{AACGC}}:\ p_{\texttt{AACGC}},\ p_{\texttt{AACTC}},\ p_{\texttt{AAGCG}},\ p_{\texttt{AAGTG}},\ p_{\texttt{AATCT}},\ p_{\texttt{AATGT}},\ p_{\texttt{CCAGA}},\ p_{\texttt{CCATA}},\ p_{\texttt{CCGAG}},\ p_{\texttt{CCGTG}},\ p_{\texttt{CCTAT}},\ p_{\texttt{CCTGT}},\ p_{\texttt{GGACA}},\ p_{\texttt{GGATA}},\ p_{\texttt{GGCAC}},\ p_{\texttt{GGCTC}},\ p_{\texttt{GGTAT}},\ p_{\texttt{GGTCT}},\ p_{\texttt{TTACA}},\ p_{\texttt{TTAGA}},\ p_{\texttt{TTCAC}},\ p_{\texttt{TTCGC}},\ p_{\texttt{TTGAG}},\ p_{\texttt{TTGCG}} \\[0.5em] \text{Class } &p_{\texttt{AACGG}}:\ p_{\texttt{AACGG}},\ p_{\texttt{AACTT}},\ p_{\texttt{AAGCC}},\ p_{\texttt{AAGTT}},\ p_{\texttt{AATCC}},\ p_{\texttt{AATGG}},\ p_{\texttt{CCAGG}},\ p_{\texttt{CCATT}},\ p_{\texttt{CCGAA}},\ p_{\texttt{CCGTT}},\ p_{\texttt{CCTAA}},\ p_{\texttt{CCTGG}},\ p_{\texttt{GGACC}},\ p_{\texttt{GGATT}},\ p_{\texttt{GGCAA}},\ p_{\texttt{GGCTT}},\ p_{\texttt{GGTAA}},\ p_{\texttt{GGTCC}},\ p_{\texttt{TTACC}},\ p_{\texttt{TTAGG}},\ p_{\texttt{TTCAA}},\ p_{\texttt{TTCGG}},\ p_{\texttt{TTGAA}},\ p_{\texttt{TTGCC}} \\[0.5em] \text{Class } &p_{\texttt{AACGT}}:\ p_{\texttt{AACGT}},\ p_{\texttt{AACTG}},\ p_{\texttt{AAGCT}},\ p_{\texttt{AAGTC}},\ p_{\texttt{AATCG}},\ p_{\texttt{AATGC}},\ p_{\texttt{CCAGT}},\ p_{\texttt{CCATG}},\ p_{\texttt{CCGAT}},\ p_{\texttt{CCGTA}},\ p_{\texttt{CCTAG}},\ p_{\texttt{CCTGA}},\ p_{\texttt{GGACT}},\ p_{\texttt{GGATC}},\ p_{\texttt{GGCAT}},\ p_{\texttt{GGCTA}},\ p_{\texttt{GGTAC}},\ p_{\texttt{GGTCA}},\ p_{\texttt{TTACG}},\ p_{\texttt{TTAGC}},\ p_{\texttt{TTCAG}},\ p_{\texttt{TTCGA}},\ p_{\texttt{TTGAC}},\ p_{\texttt{TTGCA}} \\[0.5em] \text{Class } &p_{\texttt{ACAAA}}:\ p_{\texttt{ACAAA}},\ p_{\texttt{AGAAA}},\ p_{\texttt{ATAAA}},\ p_{\texttt{CACCC}},\ p_{\texttt{CGCCC}},\ p_{\texttt{CTCCC}},\ p_{\texttt{GAGGG}},\ p_{\texttt{GCGGG}},\ p_{\texttt{GTGGG}},\ p_{\texttt{TATTT}},\ p_{\texttt{TCTTT}},\ p_{\texttt{TGTTT}} \\[0.5em] \text{Class } &p_{\texttt{ACAAC}}:\ p_{\texttt{ACAAC}},\ p_{\texttt{AGAAG}},\ p_{\texttt{ATAAT}},\ p_{\texttt{CACCA}},\ p_{\texttt{CGCCG}},\ p_{\texttt{CTCCT}},\ p_{\texttt{GAGGA}},\ p_{\texttt{GCGGC}},\ p_{\texttt{GTGGT}},\ p_{\texttt{TATTA}},\ p_{\texttt{TCTTC}},\ p_{\texttt{TGTTG}} \\[0.5em] \text{Class } &p_{\texttt{ACAAG}}:\ p_{\texttt{ACAAG}},\ p_{\texttt{ACAAT}},\ p_{\texttt{AGAAC}},\ p_{\texttt{AGAAT}},\ p_{\texttt{ATAAC}},\ p_{\texttt{ATAAG}},\ p_{\texttt{CACCG}},\ p_{\texttt{CACCT}},\ p_{\texttt{CGCCA}},\ p_{\texttt{CGCCT}},\ p_{\texttt{CTCCA}},\ p_{\texttt{CTCCG}},\ p_{\texttt{GAGGC}},\ p_{\texttt{GAGGT}},\ p_{\texttt{GCGGA}},\ p_{\texttt{GCGGT}},\ p_{\texttt{GTGGA}},\ p_{\texttt{GTGGC}},\ p_{\texttt{TATTC}},\ p_{\texttt{TATTG}},\ p_{\texttt{TCTTA}},\ p_{\texttt{TCTTG}},\ p_{\texttt{TGTTA}},\ p_{\texttt{TGTTC}} \\[0.5em] \text{Class } &p_{\texttt{ACACA}}:\ p_{\texttt{ACACA}},\ p_{\texttt{AGAGA}},\ p_{\texttt{ATATA}},\ p_{\texttt{CACAC}},\ p_{\texttt{CGCGC}},\ p_{\texttt{CTCTC}},\ p_{\texttt{GAGAG}},\ p_{\texttt{GCGCG}},\ p_{\texttt{GTGTG}},\ p_{\texttt{TATAT}},\ p_{\texttt{TCTCT}},\ p_{\texttt{TGTGT}} \\[0.5em] \text{Class } &p_{\texttt{ACACC}}:\ p_{\texttt{ACACC}},\ p_{\texttt{AGAGG}},\ p_{\texttt{ATATT}},\ p_{\texttt{CACAA}},\ p_{\texttt{CGCGG}},\ p_{\texttt{CTCTT}},\ p_{\texttt{GAGAA}},\ p_{\texttt{GCGCC}},\ p_{\texttt{GTGTT}},\ p_{\texttt{TATAA}},\ p_{\texttt{TCTCC}},\ p_{\texttt{TGTGG}} \\[0.5em] \text{Class } &p_{\texttt{ACACG}}:\ p_{\texttt{ACACG}},\ p_{\texttt{ACACT}},\ p_{\texttt{AGAGC}},\ p_{\texttt{AGAGT}},\ p_{\texttt{ATATC}},\ p_{\texttt{ATATG}},\ p_{\texttt{CACAG}},\ p_{\texttt{CACAT}},\ p_{\texttt{CGCGA}},\ p_{\texttt{CGCGT}},\ p_{\texttt{CTCTA}},\ p_{\texttt{CTCTG}},\ p_{\texttt{GAGAC}},\ p_{\texttt{GAGAT}},\ p_{\texttt{GCGCA}},\ p_{\texttt{GCGCT}},\ p_{\texttt{GTGTA}},\ p_{\texttt{GTGTC}},\ p_{\texttt{TATAC}},\ p_{\texttt{TATAG}},\ p_{\texttt{TCTCA}},\ p_{\texttt{TCTCG}},\ p_{\texttt{TGTGA}},\ p_{\texttt{TGTGC}} \\[0.5em] \text{Class } &p_{\texttt{ACAGA}}:\ p_{\texttt{ACAGA}},\ p_{\texttt{ACATA}},\ p_{\texttt{AGACA}},\ p_{\texttt{AGATA}},\ p_{\texttt{ATACA}},\ p_{\texttt{ATAGA}},\ p_{\texttt{CACGC}},\ p_{\texttt{CACTC}},\ p_{\texttt{CGCAC}},\ p_{\texttt{CGCTC}},\ p_{\texttt{CTCAC}},\ p_{\texttt{CTCGC}},\ p_{\texttt{GAGCG}},\ p_{\texttt{GAGTG}},\ p_{\texttt{GCGAG}},\ p_{\texttt{GCGTG}},\ p_{\texttt{GTGAG}},\ p_{\texttt{GTGCG}},\ p_{\texttt{TATCT}},\ p_{\texttt{TATGT}},\ p_{\texttt{TCTAT}},\ p_{\texttt{TCTGT}},\ p_{\texttt{TGTAT}},\ p_{\texttt{TGTCT}} \\[0.5em] \text{Class } &p_{\texttt{ACAGC}}:\ p_{\texttt{ACAGC}},\ p_{\texttt{ACATC}},\ p_{\texttt{AGACG}},\ p_{\texttt{AGATG}},\ p_{\texttt{ATACT}},\ p_{\texttt{ATAGT}},\ p_{\texttt{CACGA}},\ p_{\texttt{CACTA}},\ p_{\texttt{CGCAG}},\ p_{\texttt{CGCTG}},\ p_{\texttt{CTCAT}},\ p_{\texttt{CTCGT}},\ p_{\texttt{GAGCA}},\ p_{\texttt{GAGTA}},\ p_{\texttt{GCGAC}},\ p_{\texttt{GCGTC}},\ p_{\texttt{GTGAT}},\ p_{\texttt{GTGCT}},\ p_{\texttt{TATCA}},\ p_{\texttt{TATGA}},\ p_{\texttt{TCTAC}},\ p_{\texttt{TCTGC}},\ p_{\texttt{TGTAG}},\ p_{\texttt{TGTCG}} \\[0.5em] \text{Class } &p_{\texttt{ACAGG}}:\ p_{\texttt{ACAGG}},\ p_{\texttt{ACATT}},\ p_{\texttt{AGACC}},\ p_{\texttt{AGATT}},\ p_{\texttt{ATACC}},\ p_{\texttt{ATAGG}},\ p_{\texttt{CACGG}},\ p_{\texttt{CACTT}},\ p_{\texttt{CGCAA}},\ p_{\texttt{CGCTT}},\ p_{\texttt{CTCAA}},\ p_{\texttt{CTCGG}},\ p_{\texttt{GAGCC}},\ p_{\texttt{GAGTT}},\ p_{\texttt{GCGAA}},\ p_{\texttt{GCGTT}},\ p_{\texttt{GTGAA}},\ p_{\texttt{GTGCC}},\ p_{\texttt{TATCC}},\ p_{\texttt{TATGG}},\ p_{\texttt{TCTAA}},\ p_{\texttt{TCTGG}},\ p_{\texttt{TGTAA}},\ p_{\texttt{TGTCC}} \\[0.5em] \text{Class } &p_{\texttt{ACAGT}}:\ p_{\texttt{ACAGT}},\ p_{\texttt{ACATG}},\ p_{\texttt{AGACT}},\ p_{\texttt{AGATC}},\ p_{\texttt{ATACG}},\ p_{\texttt{ATAGC}},\ p_{\texttt{CACGT}},\ p_{\texttt{CACTG}},\ p_{\texttt{CGCAT}},\ p_{\texttt{CGCTA}},\ p_{\texttt{CTCAG}},\ p_{\texttt{CTCGA}},\ p_{\texttt{GAGCT}},\ p_{\texttt{GAGTC}},\ p_{\texttt{GCGAT}},\ p_{\texttt{GCGTA}},\ p_{\texttt{GTGAC}},\ p_{\texttt{GTGCA}},\ p_{\texttt{TATCG}},\ p_{\texttt{TATGC}},\ p_{\texttt{TCTAG}},\ p_{\texttt{TCTGA}},\ p_{\texttt{TGTAC}},\ p_{\texttt{TGTCA}} \\[0.5em] \text{Class } &p_{\texttt{ACCAA}}:\ p_{\texttt{ACCAA}},\ p_{\texttt{AGGAA}},\ p_{\texttt{ATTAA}},\ p_{\texttt{CAACC}},\ p_{\texttt{CGGCC}},\ p_{\texttt{CTTCC}},\ p_{\texttt{GAAGG}},\ p_{\texttt{GCCGG}},\ p_{\texttt{GTTGG}},\ p_{\texttt{TAATT}},\ p_{\texttt{TCCTT}},\ p_{\texttt{TGGTT}} \\[0.5em] \text{Class } &p_{\texttt{ACCAC}}:\ p_{\texttt{ACCAC}},\ p_{\texttt{AGGAG}},\ p_{\texttt{ATTAT}},\ p_{\texttt{CAACA}},\ p_{\texttt{CGGCG}},\ p_{\texttt{CTTCT}},\ p_{\texttt{GAAGA}},\ p_{\texttt{GCCGC}},\ p_{\texttt{GTTGT}},\ p_{\texttt{TAATA}},\ p_{\texttt{TCCTC}},\ p_{\texttt{TGGTG}} \\[0.5em] \text{Class } &p_{\texttt{ACCAG}}:\ p_{\texttt{ACCAG}},\ p_{\texttt{ACCAT}},\ p_{\texttt{AGGAC}},\ p_{\texttt{AGGAT}},\ p_{\texttt{ATTAC}},\ p_{\texttt{ATTAG}},\ p_{\texttt{CAACG}},\ p_{\texttt{CAACT}},\ p_{\texttt{CGGCA}},\ p_{\texttt{CGGCT}},\ p_{\texttt{CTTCA}},\ p_{\texttt{CTTCG}},\ p_{\texttt{GAAGC}},\ p_{\texttt{GAAGT}},\ p_{\texttt{GCCGA}},\ p_{\texttt{GCCGT}},\ p_{\texttt{GTTGA}},\ p_{\texttt{GTTGC}},\ p_{\texttt{TAATC}},\ p_{\texttt{TAATG}},\ p_{\texttt{TCCTA}},\ p_{\texttt{TCCTG}},\ p_{\texttt{TGGTA}},\ p_{\texttt{TGGTC}} \\[0.5em] \text{Class } &p_{\texttt{ACCCA}}:\ p_{\texttt{ACCCA}},\ p_{\texttt{AGGGA}},\ p_{\texttt{ATTTA}},\ p_{\texttt{CAAAC}},\ p_{\texttt{CGGGC}},\ p_{\texttt{CTTTC}},\ p_{\texttt{GAAAG}},\ p_{\texttt{GCCCG}},\ p_{\texttt{GTTTG}},\ p_{\texttt{TAAAT}},\ p_{\texttt{TCCCT}},\ p_{\texttt{TGGGT}} \\[0.5em] \text{Class } &p_{\texttt{ACCCC}}:\ p_{\texttt{ACCCC}},\ p_{\texttt{AGGGG}},\ p_{\texttt{ATTTT}},\ p_{\texttt{CAAAA}},\ p_{\texttt{CGGGG}},\ p_{\texttt{CTTTT}},\ p_{\texttt{GAAAA}},\ p_{\texttt{GCCCC}},\ p_{\texttt{GTTTT}},\ p_{\texttt{TAAAA}},\ p_{\texttt{TCCCC}},\ p_{\texttt{TGGGG}} \\[0.5em] \text{Class } &p_{\texttt{ACCCG}}:\ p_{\texttt{ACCCG}},\ p_{\texttt{ACCCT}},\ p_{\texttt{AGGGC}},\ p_{\texttt{AGGGT}},\ p_{\texttt{ATTTC}},\ p_{\texttt{ATTTG}},\ p_{\texttt{CAAAG}},\ p_{\texttt{CAAAT}},\ p_{\texttt{CGGGA}},\ p_{\texttt{CGGGT}},\ p_{\texttt{CTTTA}},\ p_{\texttt{CTTTG}},\ p_{\texttt{GAAAC}},\ p_{\texttt{GAAAT}},\ p_{\texttt{GCCCA}},\ p_{\texttt{GCCCT}},\ p_{\texttt{GTTTA}},\ p_{\texttt{GTTTC}},\ p_{\texttt{TAAAC}},\ p_{\texttt{TAAAG}},\ p_{\texttt{TCCCA}},\ p_{\texttt{TCCCG}},\ p_{\texttt{TGGGA}},\ p_{\texttt{TGGGC}} \\[0.5em] \text{Class } &p_{\texttt{ACCGA}}:\ p_{\texttt{ACCGA}},\ p_{\texttt{ACCTA}},\ p_{\texttt{AGGCA}},\ p_{\texttt{AGGTA}},\ p_{\texttt{ATTCA}},\ p_{\texttt{ATTGA}},\ p_{\texttt{CAAGC}},\ p_{\texttt{CAATC}},\ p_{\texttt{CGGAC}},\ p_{\texttt{CGGTC}},\ p_{\texttt{CTTAC}},\ p_{\texttt{CTTGC}},\ p_{\texttt{GAACG}},\ p_{\texttt{GAATG}},\ p_{\texttt{GCCAG}},\ p_{\texttt{GCCTG}},\ p_{\texttt{GTTAG}},\ p_{\texttt{GTTCG}},\ p_{\texttt{TAACT}},\ p_{\texttt{TAAGT}},\ p_{\texttt{TCCAT}},\ p_{\texttt{TCCGT}},\ p_{\texttt{TGGAT}},\ p_{\texttt{TGGCT}} \\[0.5em] \text{Class } &p_{\texttt{ACCGC}}:\ p_{\texttt{ACCGC}},\ p_{\texttt{ACCTC}},\ p_{\texttt{AGGCG}},\ p_{\texttt{AGGTG}},\ p_{\texttt{ATTCT}},\ p_{\texttt{ATTGT}},\ p_{\texttt{CAAGA}},\ p_{\texttt{CAATA}},\ p_{\texttt{CGGAG}},\ p_{\texttt{CGGTG}},\ p_{\texttt{CTTAT}},\ p_{\texttt{CTTGT}},\ p_{\texttt{GAACA}},\ p_{\texttt{GAATA}},\ p_{\texttt{GCCAC}},\ p_{\texttt{GCCTC}},\ p_{\texttt{GTTAT}},\ p_{\texttt{GTTCT}},\ p_{\texttt{TAACA}},\ p_{\texttt{TAAGA}},\ p_{\texttt{TCCAC}},\ p_{\texttt{TCCGC}},\ p_{\texttt{TGGAG}},\ p_{\texttt{TGGCG}} \\[0.5em] \text{Class } &p_{\texttt{ACCGG}}:\ p_{\texttt{ACCGG}},\ p_{\texttt{ACCTT}},\ p_{\texttt{AGGCC}},\ p_{\texttt{AGGTT}},\ p_{\texttt{ATTCC}},\ p_{\texttt{ATTGG}},\ p_{\texttt{CAAGG}},\ p_{\texttt{CAATT}},\ p_{\texttt{CGGAA}},\ p_{\texttt{CGGTT}},\ p_{\texttt{CTTAA}},\ p_{\texttt{CTTGG}},\ p_{\texttt{GAACC}},\ p_{\texttt{GAATT}},\ p_{\texttt{GCCAA}},\ p_{\texttt{GCCTT}},\ p_{\texttt{GTTAA}},\ p_{\texttt{GTTCC}},\ p_{\texttt{TAACC}},\ p_{\texttt{TAAGG}},\ p_{\texttt{TCCAA}},\ p_{\texttt{TCCGG}},\ p_{\texttt{TGGAA}},\ p_{\texttt{TGGCC}} \\[0.5em] \text{Class } &p_{\texttt{ACCGT}}:\ p_{\texttt{ACCGT}},\ p_{\texttt{ACCTG}},\ p_{\texttt{AGGCT}},\ p_{\texttt{AGGTC}},\ p_{\texttt{ATTCG}},\ p_{\texttt{ATTGC}},\ p_{\texttt{CAAGT}},\ p_{\texttt{CAATG}},\ p_{\texttt{CGGAT}},\ p_{\texttt{CGGTA}},\ p_{\texttt{CTTAG}},\ p_{\texttt{CTTGA}},\ p_{\texttt{GAACT}},\ p_{\texttt{GAATC}},\ p_{\texttt{GCCAT}},\ p_{\texttt{GCCTA}},\ p_{\texttt{GTTAC}},\ p_{\texttt{GTTCA}},\ p_{\texttt{TAACG}},\ p_{\texttt{TAAGC}},\ p_{\texttt{TCCAG}},\ p_{\texttt{TCCGA}},\ p_{\texttt{TGGAC}},\ p_{\texttt{TGGCA}} \\[0.5em] \text{Class } &p_{\texttt{ACGAA}}:\ p_{\texttt{ACGAA}},\ p_{\texttt{ACTAA}},\ p_{\texttt{AGCAA}},\ p_{\texttt{AGTAA}},\ p_{\texttt{ATCAA}},\ p_{\texttt{ATGAA}},\ p_{\texttt{CAGCC}},\ p_{\texttt{CATCC}},\ p_{\texttt{CGACC}},\ p_{\texttt{CGTCC}},\ p_{\texttt{CTACC}},\ p_{\texttt{CTGCC}},\ p_{\texttt{GACGG}},\ p_{\texttt{GATGG}},\ p_{\texttt{GCAGG}},\ p_{\texttt{GCTGG}},\ p_{\texttt{GTAGG}},\ p_{\texttt{GTCGG}},\ p_{\texttt{TACTT}},\ p_{\texttt{TAGTT}},\ p_{\texttt{TCATT}},\ p_{\texttt{TCGTT}},\ p_{\texttt{TGATT}},\ p_{\texttt{TGCTT}} \\[0.5em] \text{Class } &p_{\texttt{ACGAC}}:\ p_{\texttt{ACGAC}},\ p_{\texttt{ACTAC}},\ p_{\texttt{AGCAG}},\ p_{\texttt{AGTAG}},\ p_{\texttt{ATCAT}},\ p_{\texttt{ATGAT}},\ p_{\texttt{CAGCA}},\ p_{\texttt{CATCA}},\ p_{\texttt{CGACG}},\ p_{\texttt{CGTCG}},\ p_{\texttt{CTACT}},\ p_{\texttt{CTGCT}},\ p_{\texttt{GACGA}},\ p_{\texttt{GATGA}},\ p_{\texttt{GCAGC}},\ p_{\texttt{GCTGC}},\ p_{\texttt{GTAGT}},\ p_{\texttt{GTCGT}},\ p_{\texttt{TACTA}},\ p_{\texttt{TAGTA}},\ p_{\texttt{TCATC}},\ p_{\texttt{TCGTC}},\ p_{\texttt{TGATG}},\ p_{\texttt{TGCTG}} \\[0.5em] \text{Class } &p_{\texttt{ACGAG}}:\ p_{\texttt{ACGAG}},\ p_{\texttt{ACTAT}},\ p_{\texttt{AGCAC}},\ p_{\texttt{AGTAT}},\ p_{\texttt{ATCAC}},\ p_{\texttt{ATGAG}},\ p_{\texttt{CAGCG}},\ p_{\texttt{CATCT}},\ p_{\texttt{CGACA}},\ p_{\texttt{CGTCT}},\ p_{\texttt{CTACA}},\ p_{\texttt{CTGCG}},\ p_{\texttt{GACGC}},\ p_{\texttt{GATGT}},\ p_{\texttt{GCAGA}},\ p_{\texttt{GCTGT}},\ p_{\texttt{GTAGA}},\ p_{\texttt{GTCGC}},\ p_{\texttt{TACTC}},\ p_{\texttt{TAGTG}},\ p_{\texttt{TCATA}},\ p_{\texttt{TCGTG}},\ p_{\texttt{TGATA}},\ p_{\texttt{TGCTC}} \\[0.5em] \text{Class } &p_{\texttt{ACGAT}}:\ p_{\texttt{ACGAT}},\ p_{\texttt{ACTAG}},\ p_{\texttt{AGCAT}},\ p_{\texttt{AGTAC}},\ p_{\texttt{ATCAG}},\ p_{\texttt{ATGAC}},\ p_{\texttt{CAGCT}},\ p_{\texttt{CATCG}},\ p_{\texttt{CGACT}},\ p_{\texttt{CGTCA}},\ p_{\texttt{CTACG}},\ p_{\texttt{CTGCA}},\ p_{\texttt{GACGT}},\ p_{\texttt{GATGC}},\ p_{\texttt{GCAGT}},\ p_{\texttt{GCTGA}},\ p_{\texttt{GTAGC}},\ p_{\texttt{GTCGA}},\ p_{\texttt{TACTG}},\ p_{\texttt{TAGTC}},\ p_{\texttt{TCATG}},\ p_{\texttt{TCGTA}},\ p_{\texttt{TGATC}},\ p_{\texttt{TGCTA}} \\[0.5em] \text{Class } &p_{\texttt{ACGCA}}:\ p_{\texttt{ACGCA}},\ p_{\texttt{ACTCA}},\ p_{\texttt{AGCGA}},\ p_{\texttt{AGTGA}},\ p_{\texttt{ATCTA}},\ p_{\texttt{ATGTA}},\ p_{\texttt{CAGAC}},\ p_{\texttt{CATAC}},\ p_{\texttt{CGAGC}},\ p_{\texttt{CGTGC}},\ p_{\texttt{CTATC}},\ p_{\texttt{CTGTC}},\ p_{\texttt{GACAG}},\ p_{\texttt{GATAG}},\ p_{\texttt{GCACG}},\ p_{\texttt{GCTCG}},\ p_{\texttt{GTATG}},\ p_{\texttt{GTCTG}},\ p_{\texttt{TACAT}},\ p_{\texttt{TAGAT}},\ p_{\texttt{TCACT}},\ p_{\texttt{TCGCT}},\ p_{\texttt{TGAGT}},\ p_{\texttt{TGCGT}} \\[0.5em] \text{Class } &p_{\texttt{ACGCC}}:\ p_{\texttt{ACGCC}},\ p_{\texttt{ACTCC}},\ p_{\texttt{AGCGG}},\ p_{\texttt{AGTGG}},\ p_{\texttt{ATCTT}},\ p_{\texttt{ATGTT}},\ p_{\texttt{CAGAA}},\ p_{\texttt{CATAA}},\ p_{\texttt{CGAGG}},\ p_{\texttt{CGTGG}},\ p_{\texttt{CTATT}},\ p_{\texttt{CTGTT}},\ p_{\texttt{GACAA}},\ p_{\texttt{GATAA}},\ p_{\texttt{GCACC}},\ p_{\texttt{GCTCC}},\ p_{\texttt{GTATT}},\ p_{\texttt{GTCTT}},\ p_{\texttt{TACAA}},\ p_{\texttt{TAGAA}},\ p_{\texttt{TCACC}},\ p_{\texttt{TCGCC}},\ p_{\texttt{TGAGG}},\ p_{\texttt{TGCGG}} \\[0.5em] \text{Class } &p_{\texttt{ACGCG}}:\ p_{\texttt{ACGCG}},\ p_{\texttt{ACTCT}},\ p_{\texttt{AGCGC}},\ p_{\texttt{AGTGT}},\ p_{\texttt{ATCTC}},\ p_{\texttt{ATGTG}},\ p_{\texttt{CAGAG}},\ p_{\texttt{CATAT}},\ p_{\texttt{CGAGA}},\ p_{\texttt{CGTGT}},\ p_{\texttt{CTATA}},\ p_{\texttt{CTGTG}},\ p_{\texttt{GACAC}},\ p_{\texttt{GATAT}},\ p_{\texttt{GCACA}},\ p_{\texttt{GCTCT}},\ p_{\texttt{GTATA}},\ p_{\texttt{GTCTC}},\ p_{\texttt{TACAC}},\ p_{\texttt{TAGAG}},\ p_{\texttt{TCACA}},\ p_{\texttt{TCGCG}},\ p_{\texttt{TGAGA}},\ p_{\texttt{TGCGC}} \\[0.5em] \text{Class } &p_{\texttt{ACGCT}}:\ p_{\texttt{ACGCT}},\ p_{\texttt{ACTCG}},\ p_{\texttt{AGCGT}},\ p_{\texttt{AGTGC}},\ p_{\texttt{ATCTG}},\ p_{\texttt{ATGTC}},\ p_{\texttt{CAGAT}},\ p_{\texttt{CATAG}},\ p_{\texttt{CGAGT}},\ p_{\texttt{CGTGA}},\ p_{\texttt{CTATG}},\ p_{\texttt{CTGTA}},\ p_{\texttt{GACAT}},\ p_{\texttt{GATAC}},\ p_{\texttt{GCACT}},\ p_{\texttt{GCTCA}},\ p_{\texttt{GTATC}},\ p_{\texttt{GTCTA}},\ p_{\texttt{TACAG}},\ p_{\texttt{TAGAC}},\ p_{\texttt{TCACG}},\ p_{\texttt{TCGCA}},\ p_{\texttt{TGAGC}},\ p_{\texttt{TGCGA}} \\[0.5em] \text{Class } &p_{\texttt{ACGGA}}:\ p_{\texttt{ACGGA}},\ p_{\texttt{ACTTA}},\ p_{\texttt{AGCCA}},\ p_{\texttt{AGTTA}},\ p_{\texttt{ATCCA}},\ p_{\texttt{ATGGA}},\ p_{\texttt{CAGGC}},\ p_{\texttt{CATTC}},\ p_{\texttt{CGAAC}},\ p_{\texttt{CGTTC}},\ p_{\texttt{CTAAC}},\ p_{\texttt{CTGGC}},\ p_{\texttt{GACCG}},\ p_{\texttt{GATTG}},\ p_{\texttt{GCAAG}},\ p_{\texttt{GCTTG}},\ p_{\texttt{GTAAG}},\ p_{\texttt{GTCCG}},\ p_{\texttt{TACCT}},\ p_{\texttt{TAGGT}},\ p_{\texttt{TCAAT}},\ p_{\texttt{TCGGT}},\ p_{\texttt{TGAAT}},\ p_{\texttt{TGCCT}} \\[0.5em] \text{Class } &p_{\texttt{ACGGC}}:\ p_{\texttt{ACGGC}},\ p_{\texttt{ACTTC}},\ p_{\texttt{AGCCG}},\ p_{\texttt{AGTTG}},\ p_{\texttt{ATCCT}},\ p_{\texttt{ATGGT}},\ p_{\texttt{CAGGA}},\ p_{\texttt{CATTA}},\ p_{\texttt{CGAAG}},\ p_{\texttt{CGTTG}},\ p_{\texttt{CTAAT}},\ p_{\texttt{CTGGT}},\ p_{\texttt{GACCA}},\ p_{\texttt{GATTA}},\ p_{\texttt{GCAAC}},\ p_{\texttt{GCTTC}},\ p_{\texttt{GTAAT}},\ p_{\texttt{GTCCT}},\ p_{\texttt{TACCA}},\ p_{\texttt{TAGGA}},\ p_{\texttt{TCAAC}},\ p_{\texttt{TCGGC}},\ p_{\texttt{TGAAG}},\ p_{\texttt{TGCCG}} \\[0.5em] \text{Class } &p_{\texttt{ACGGG}}:\ p_{\texttt{ACGGG}},\ p_{\texttt{ACTTT}},\ p_{\texttt{AGCCC}},\ p_{\texttt{AGTTT}},\ p_{\texttt{ATCCC}},\ p_{\texttt{ATGGG}},\ p_{\texttt{CAGGG}},\ p_{\texttt{CATTT}},\ p_{\texttt{CGAAA}},\ p_{\texttt{CGTTT}},\ p_{\texttt{CTAAA}},\ p_{\texttt{CTGGG}},\ p_{\texttt{GACCC}},\ p_{\texttt{GATTT}},\ p_{\texttt{GCAAA}},\ p_{\texttt{GCTTT}},\ p_{\texttt{GTAAA}},\ p_{\texttt{GTCCC}},\ p_{\texttt{TACCC}},\ p_{\texttt{TAGGG}},\ p_{\texttt{TCAAA}},\ p_{\texttt{TCGGG}},\ p_{\texttt{TGAAA}},\ p_{\texttt{TGCCC}} \\[0.5em] \text{Class } &p_{\texttt{ACGGT}}:\ p_{\texttt{ACGGT}},\ p_{\texttt{ACTTG}},\ p_{\texttt{AGCCT}},\ p_{\texttt{AGTTC}},\ p_{\texttt{ATCCG}},\ p_{\texttt{ATGGC}},\ p_{\texttt{CAGGT}},\ p_{\texttt{CATTG}},\ p_{\texttt{CGAAT}},\ p_{\texttt{CGTTA}},\ p_{\texttt{CTAAG}},\ p_{\texttt{CTGGA}},\ p_{\texttt{GACCT}},\ p_{\texttt{GATTC}},\ p_{\texttt{GCAAT}},\ p_{\texttt{GCTTA}},\ p_{\texttt{GTAAC}},\ p_{\texttt{GTCCA}},\ p_{\texttt{TACCG}},\ p_{\texttt{TAGGC}},\ p_{\texttt{TCAAG}},\ p_{\texttt{TCGGA}},\ p_{\texttt{TGAAC}},\ p_{\texttt{TGCCA}} \\[0.5em] \text{Class } &p_{\texttt{ACGTA}}:\ p_{\texttt{ACGTA}},\ p_{\texttt{ACTGA}},\ p_{\texttt{AGCTA}},\ p_{\texttt{AGTCA}},\ p_{\texttt{ATCGA}},\ p_{\texttt{ATGCA}},\ p_{\texttt{CAGTC}},\ p_{\texttt{CATGC}},\ p_{\texttt{CGATC}},\ p_{\texttt{CGTAC}},\ p_{\texttt{CTAGC}},\ p_{\texttt{CTGAC}},\ p_{\texttt{GACTG}},\ p_{\texttt{GATCG}},\ p_{\texttt{GCATG}},\ p_{\texttt{GCTAG}},\ p_{\texttt{GTACG}},\ p_{\texttt{GTCAG}},\ p_{\texttt{TACGT}},\ p_{\texttt{TAGCT}},\ p_{\texttt{TCAGT}},\ p_{\texttt{TCGAT}},\ p_{\texttt{TGACT}},\ p_{\texttt{TGCAT}} \\[0.5em] \text{Class } &p_{\texttt{ACGTC}}:\ p_{\texttt{ACGTC}},\ p_{\texttt{ACTGC}},\ p_{\texttt{AGCTG}},\ p_{\texttt{AGTCG}},\ p_{\texttt{ATCGT}},\ p_{\texttt{ATGCT}},\ p_{\texttt{CAGTA}},\ p_{\texttt{CATGA}},\ p_{\texttt{CGATG}},\ p_{\texttt{CGTAG}},\ p_{\texttt{CTAGT}},\ p_{\texttt{CTGAT}},\ p_{\texttt{GACTA}},\ p_{\texttt{GATCA}},\ p_{\texttt{GCATC}},\ p_{\texttt{GCTAC}},\ p_{\texttt{GTACT}},\ p_{\texttt{GTCAT}},\ p_{\texttt{TACGA}},\ p_{\texttt{TAGCA}},\ p_{\texttt{TCAGC}},\ p_{\texttt{TCGAC}},\ p_{\texttt{TGACG}},\ p_{\texttt{TGCAG}} \\[0.5em] \text{Class } &p_{\texttt{ACGTG}}:\ p_{\texttt{ACGTG}},\ p_{\texttt{ACTGT}},\ p_{\texttt{AGCTC}},\ p_{\texttt{AGTCT}},\ p_{\texttt{ATCGC}},\ p_{\texttt{ATGCG}},\ p_{\texttt{CAGTG}},\ p_{\texttt{CATGT}},\ p_{\texttt{CGATA}},\ p_{\texttt{CGTAT}},\ p_{\texttt{CTAGA}},\ p_{\texttt{CTGAG}},\ p_{\texttt{GACTC}},\ p_{\texttt{GATCT}},\ p_{\texttt{GCATA}},\ p_{\texttt{GCTAT}},\ p_{\texttt{GTACA}},\ p_{\texttt{GTCAC}},\ p_{\texttt{TACGC}},\ p_{\texttt{TAGCG}},\ p_{\texttt{TCAGA}},\ p_{\texttt{TCGAG}},\ p_{\texttt{TGACA}},\ p_{\texttt{TGCAC}} \\[0.5em] \text{Class } &p_{\texttt{ACGTT}}:\ p_{\texttt{ACGTT}},\ p_{\texttt{ACTGG}},\ p_{\texttt{AGCTT}},\ p_{\texttt{AGTCC}},\ p_{\texttt{ATCGG}},\ p_{\texttt{ATGCC}},\ p_{\texttt{CAGTT}},\ p_{\texttt{CATGG}},\ p_{\texttt{CGATT}},\ p_{\texttt{CGTAA}},\ p_{\texttt{CTAGG}},\ p_{\texttt{CTGAA}},\ p_{\texttt{GACTT}},\ p_{\texttt{GATCC}},\ p_{\texttt{GCATT}},\ p_{\texttt{GCTAA}},\ p_{\texttt{GTACC}},\ p_{\texttt{GTCAA}},\ p_{\texttt{TACGG}},\ p_{\texttt{TAGCC}},\ p_{\texttt{TCAGG}},\ p_{\texttt{TCGAA}},\ p_{\texttt{TGACC}},\ p_{\texttt{TGCAA}} \end{align}$

Equivalent classes of Fourier parametrization

$\begin{align} \text{Class } &0:\ q_{\texttt{CAAAA}}, q_{\texttt{GAAAA}}, q_{\texttt{TAAAA}}, q_{\texttt{ACAAA}}, q_{\texttt{GCAAA}}, q_{\texttt{TCAAA}}, q_{\texttt{AGAAA}}, q_{\texttt{CGAAA}}, q_{\texttt{TGAAA}}, q_{\texttt{ATAAA}}, q_{\texttt{CTAAA}}, q_{\texttt{GTAAA}}, q_{\texttt{AACAA}}, q_{\texttt{GACAA}}, q_{\texttt{TACAA}}, q_{\texttt{CCCAA}}, q_{\texttt{GCCAA}}, q_{\texttt{TCCAA}}, q_{\texttt{AGCAA}}, q_{\texttt{CGCAA}}, q_{\texttt{GGCAA}}, q_{\texttt{ATCAA}}, q_{\texttt{CTCAA}}, q_{\texttt{TTCAA}}, q_{\texttt{AAGAA}}, q_{\texttt{CAGAA}}, q_{\texttt{TAGAA}}, q_{\texttt{ACGAA}}, q_{\texttt{CCGAA}}, q_{\texttt{GCGAA}}, q_{\texttt{CGGAA}}, q_{\texttt{GGGAA}}, q_{\texttt{TGGAA}}, q_{\texttt{ATGAA}}, q_{\texttt{GTGAA}}, q_{\texttt{TTGAA}}, q_{\texttt{AATAA}}, q_{\texttt{CATAA}}, q_{\texttt{GATAA}}, q_{\texttt{ACTAA}}, q_{\texttt{CCTAA}}, q_{\texttt{TCTAA}}, q_{\texttt{AGTAA}}, q_{\texttt{GGTAA}}, q_{\texttt{TGTAA}}, q_{\texttt{CTTAA}}, q_{\texttt{GTTAA}}, q_{\texttt{TTTAA}}, q_{\texttt{AAACA}}, q_{\texttt{GAACA}}, q_{\texttt{TAACA}}, q_{\texttt{CCACA}}, q_{\texttt{GCACA}}, q_{\texttt{TCACA}}, q_{\texttt{AGACA}}, q_{\texttt{CGACA}}, q_{\texttt{GGACA}}, q_{\texttt{ATACA}}, q_{\texttt{CTACA}}, q_{\texttt{TTACA}}, q_{\texttt{CACCA}}, q_{\texttt{GACCA}}, q_{\texttt{TACCA}}, q_{\texttt{ACCCA}}, q_{\texttt{GCCCA}}, q_{\texttt{TCCCA}}, q_{\texttt{AGCCA}}, q_{\texttt{CGCCA}}, q_{\texttt{TGCCA}}, q_{\texttt{ATCCA}}, q_{\texttt{CTCCA}}, q_{\texttt{GTCCA}}, q_{\texttt{AAGCA}}, q_{\texttt{CAGCA}}, q_{\texttt{GAGCA}}, q_{\texttt{ACGCA}}, q_{\texttt{CCGCA}}, q_{\texttt{TCGCA}}, q_{\texttt{AGGCA}}, q_{\texttt{GGGCA}}, q_{\texttt{TGGCA}}, q_{\texttt{CTGCA}}, q_{\texttt{GTGCA}}, q_{\texttt{TTGCA}}, q_{\texttt{AATCA}}, q_{\texttt{CATCA}}, q_{\texttt{TATCA}}, q_{\texttt{ACTCA}}, q_{\texttt{CCTCA}}, q_{\texttt{GCTCA}}, q_{\texttt{CGTCA}}, q_{\texttt{GGTCA}}, q_{\texttt{TGTCA}}, q_{\texttt{ATTCA}}, q_{\texttt{GTTCA}}, q_{\texttt{TTTCA}}, q_{\texttt{AAAGA}}, q_{\texttt{CAAGA}}, q_{\texttt{TAAGA}}, q_{\texttt{ACAGA}}, q_{\texttt{CCAGA}}, q_{\texttt{GCAGA}}, q_{\texttt{CGAGA}}, q_{\texttt{GGAGA}}, q_{\texttt{TGAGA}}, q_{\texttt{ATAGA}}, q_{\texttt{GTAGA}}, q_{\texttt{TTAGA}}, q_{\texttt{AACGA}}, q_{\texttt{CACGA}}, q_{\texttt{GACGA}}, q_{\texttt{ACCGA}}, q_{\texttt{CCCGA}}, q_{\texttt{TCCGA}}, q_{\texttt{AGCGA}}, q_{\texttt{GGCGA}}, q_{\texttt{TGCGA}}, q_{\texttt{CTCGA}}, q_{\texttt{GTCGA}}, q_{\texttt{TTCGA}}, q_{\texttt{CAGGA}}, q_{\texttt{GAGGA}}, q_{\texttt{TAGGA}}, q_{\texttt{ACGGA}}, q_{\texttt{GCGGA}}, q_{\texttt{TCGGA}}, q_{\texttt{AGGGA}}, q_{\texttt{CGGGA}}, q_{\texttt{TGGGA}}, q_{\texttt{ATGGA}}, q_{\texttt{CTGGA}}, q_{\texttt{GTGGA}}, q_{\texttt{AATGA}}, q_{\texttt{GATGA}}, q_{\texttt{TATGA}}, q_{\texttt{CCTGA}}, q_{\texttt{GCTGA}}, q_{\texttt{TCTGA}}, q_{\texttt{AGTGA}}, q_{\texttt{CGTGA}}, q_{\texttt{GGTGA}}, q_{\texttt{ATTGA}}, q_{\texttt{CTTGA}}, q_{\texttt{TTTGA}}, q_{\texttt{AAATA}}, q_{\texttt{CAATA}}, q_{\texttt{GAATA}}, q_{\texttt{ACATA}}, q_{\texttt{CCATA}}, q_{\texttt{TCATA}}, q_{\texttt{AGATA}}, q_{\texttt{GGATA}}, q_{\texttt{TGATA}}, q_{\texttt{CTATA}}, q_{\texttt{GTATA}}, q_{\texttt{TTATA}}, q_{\texttt{AACTA}}, q_{\texttt{CACTA}}, q_{\texttt{TACTA}}, q_{\texttt{ACCTA}}, q_{\texttt{CCCTA}}, q_{\texttt{GCCTA}}, q_{\texttt{CGCTA}}, q_{\texttt{GGCTA}}, q_{\texttt{TGCTA}}, q_{\texttt{ATCTA}}, q_{\texttt{GTCTA}}, q_{\texttt{TTCTA}}, q_{\texttt{AAGTA}}, q_{\texttt{GAGTA}}, q_{\texttt{TAGTA}}, q_{\texttt{CCGTA}}, q_{\texttt{GCGTA}}, q_{\texttt{TCGTA}}, q_{\texttt{AGGTA}}, q_{\texttt{CGGTA}}, q_{\texttt{GGGTA}}, q_{\texttt{ATGTA}}, q_{\texttt{CTGTA}}, q_{\texttt{TTGTA}}, q_{\texttt{CATTA}}, q_{\texttt{GATTA}}, q_{\texttt{TATTA}}, q_{\texttt{ACTTA}}, q_{\texttt{GCTTA}}, q_{\texttt{TCTTA}}, q_{\texttt{AGTTA}}, q_{\texttt{CGTTA}}, q_{\texttt{TGTTA}}, q_{\texttt{ATTTA}}, q_{\texttt{CTTTA}}, q_{\texttt{GTTTA}}, q_{\texttt{AAAAC}}, q_{\texttt{GAAAC}}, q_{\texttt{TAAAC}}, q_{\texttt{CCAAC}}, q_{\texttt{GCAAC}}, q_{\texttt{TCAAC}}, q_{\texttt{AGAAC}}, q_{\texttt{CGAAC}}, q_{\texttt{GGAAC}}, q_{\texttt{ATAAC}}, q_{\texttt{CTAAC}}, q_{\texttt{TTAAC}}, q_{\texttt{CACAC}}, q_{\texttt{GACAC}}, q_{\texttt{TACAC}}, q_{\texttt{ACCAC}}, q_{\texttt{GCCAC}}, q_{\texttt{TCCAC}}, q_{\texttt{AGCAC}}, q_{\texttt{CGCAC}}, q_{\texttt{TGCAC}}, q_{\texttt{ATCAC}}, q_{\texttt{CTCAC}}, q_{\texttt{GTCAC}}, q_{\texttt{AAGAC}}, q_{\texttt{CAGAC}}, q_{\texttt{GAGAC}}, q_{\texttt{ACGAC}}, q_{\texttt{CCGAC}}, q_{\texttt{TCGAC}}, q_{\texttt{AGGAC}}, q_{\texttt{GGGAC}}, q_{\texttt{TGGAC}}, q_{\texttt{CTGAC}}, q_{\texttt{GTGAC}}, q_{\texttt{TTGAC}}, q_{\texttt{AATAC}}, q_{\texttt{CATAC}}, q_{\texttt{TATAC}}, q_{\texttt{ACTAC}}, q_{\texttt{CCTAC}}, q_{\texttt{GCTAC}}, q_{\texttt{CGTAC}}, q_{\texttt{GGTAC}}, q_{\texttt{TGTAC}}, q_{\texttt{ATTAC}}, q_{\texttt{GTTAC}}, q_{\texttt{TTTAC}}, q_{\texttt{CAACC}}, q_{\texttt{GAACC}}, q_{\texttt{TAACC}}, q_{\texttt{ACACC}}, q_{\texttt{GCACC}}, q_{\texttt{TCACC}}, q_{\texttt{AGACC}}, q_{\texttt{CGACC}}, q_{\texttt{TGACC}}, q_{\texttt{ATACC}}, q_{\texttt{CTACC}}, q_{\texttt{GTACC}}, q_{\texttt{AACCC}}, q_{\texttt{GACCC}}, q_{\texttt{TACCC}}, q_{\texttt{CCCCC}}, q_{\texttt{GCCCC}}, q_{\texttt{TCCCC}}, q_{\texttt{AGCCC}}, q_{\texttt{CGCCC}}, q_{\texttt{GGCCC}}, q_{\texttt{ATCCC}}, q_{\texttt{CTCCC}}, q_{\texttt{TTCCC}}, q_{\texttt{AAGCC}}, q_{\texttt{CAGCC}}, q_{\texttt{TAGCC}}, q_{\texttt{ACGCC}}, q_{\texttt{CCGCC}}, q_{\texttt{GCGCC}}, q_{\texttt{CGGCC}}, q_{\texttt{GGGCC}}, q_{\texttt{TGGCC}}, q_{\texttt{ATGCC}}, q_{\texttt{GTGCC}}, q_{\texttt{TTGCC}}, q_{\texttt{AATCC}}, q_{\texttt{CATCC}}, q_{\texttt{GATCC}}, q_{\texttt{ACTCC}}, q_{\texttt{CCTCC}}, q_{\texttt{TCTCC}}, q_{\texttt{AGTCC}}, q_{\texttt{GGTCC}}, q_{\texttt{TGTCC}}, q_{\texttt{CTTCC}}, q_{\texttt{GTTCC}}, q_{\texttt{TTTCC}}, q_{\texttt{AAAGC}}, q_{\texttt{CAAGC}}, q_{\texttt{GAAGC}}, q_{\texttt{ACAGC}}, q_{\texttt{CCAGC}}, q_{\texttt{TCAGC}}, q_{\texttt{AGAGC}}, q_{\texttt{GGAGC}}, q_{\texttt{TGAGC}}, q_{\texttt{CTAGC}}, q_{\texttt{GTAGC}}, q_{\texttt{TTAGC}}, q_{\texttt{AACGC}}, q_{\texttt{CACGC}}, q_{\texttt{TACGC}}, q_{\texttt{ACCGC}}, q_{\texttt{CCCGC}}, q_{\texttt{GCCGC}}, q_{\texttt{CGCGC}}, q_{\texttt{GGCGC}}, q_{\texttt{TGCGC}}, q_{\texttt{ATCGC}}, q_{\texttt{GTCGC}}, q_{\texttt{TTCGC}}, q_{\texttt{AAGGC}}, q_{\texttt{GAGGC}}, q_{\texttt{TAGGC}}, q_{\texttt{CCGGC}}, q_{\texttt{GCGGC}}, q_{\texttt{TCGGC}}, q_{\texttt{AGGGC}}, q_{\texttt{CGGGC}}, q_{\texttt{GGGGC}}, q_{\texttt{ATGGC}}, q_{\texttt{CTGGC}}, q_{\texttt{TTGGC}}, q_{\texttt{CATGC}}, q_{\texttt{GATGC}}, q_{\texttt{TATGC}}, q_{\texttt{ACTGC}}, q_{\texttt{GCTGC}}, q_{\texttt{TCTGC}}, q_{\texttt{AGTGC}}, q_{\texttt{CGTGC}}, q_{\texttt{TGTGC}}, q_{\texttt{ATTGC}}, q_{\texttt{CTTGC}}, q_{\texttt{GTTGC}}, q_{\texttt{AAATC}}, q_{\texttt{CAATC}}, q_{\texttt{TAATC}}, q_{\texttt{ACATC}}, q_{\texttt{CCATC}}, q_{\texttt{GCATC}}, q_{\texttt{CGATC}}, q_{\texttt{GGATC}}, q_{\texttt{TGATC}}, q_{\texttt{ATATC}}, q_{\texttt{GTATC}}, q_{\texttt{TTATC}}, q_{\texttt{AACTC}}, q_{\texttt{CACTC}}, q_{\texttt{GACTC}}, q_{\texttt{ACCTC}}, q_{\texttt{CCCTC}}, q_{\texttt{TCCTC}}, q_{\texttt{AGCTC}}, q_{\texttt{GGCTC}}, q_{\texttt{TGCTC}}, q_{\texttt{CTCTC}}, q_{\texttt{GTCTC}}, q_{\texttt{TTCTC}}, q_{\texttt{CAGTC}}, q_{\texttt{GAGTC}}, q_{\texttt{TAGTC}}, q_{\texttt{ACGTC}}, q_{\texttt{GCGTC}}, q_{\texttt{TCGTC}}, q_{\texttt{AGGTC}}, q_{\texttt{CGGTC}}, q_{\texttt{TGGTC}}, q_{\texttt{ATGTC}}, q_{\texttt{CTGTC}}, q_{\texttt{GTGTC}}, q_{\texttt{AATTC}}, q_{\texttt{GATTC}}, q_{\texttt{TATTC}}, q_{\texttt{CCTTC}}, q_{\texttt{GCTTC}}, q_{\texttt{TCTTC}}, q_{\texttt{AGTTC}}, q_{\texttt{CGTTC}}, q_{\texttt{GGTTC}}, q_{\texttt{ATTTC}}, q_{\texttt{CTTTC}}, q_{\texttt{TTTTC}}, q_{\texttt{AAAAG}}, q_{\texttt{CAAAG}}, q_{\texttt{TAAAG}}, q_{\texttt{ACAAG}}, q_{\texttt{CCAAG}}, q_{\texttt{GCAAG}}, q_{\texttt{CGAAG}}, q_{\texttt{GGAAG}}, q_{\texttt{TGAAG}}, q_{\texttt{ATAAG}}, q_{\texttt{GTAAG}}, q_{\texttt{TTAAG}}, q_{\texttt{AACAG}}, q_{\texttt{CACAG}}, q_{\texttt{GACAG}}, q_{\texttt{ACCAG}}, q_{\texttt{CCCAG}}, q_{\texttt{TCCAG}}, q_{\texttt{AGCAG}}, q_{\texttt{GGCAG}}, q_{\texttt{TGCAG}}, q_{\texttt{CTCAG}}, q_{\texttt{GTCAG}}, q_{\texttt{TTCAG}}, q_{\texttt{CAGAG}}, q_{\texttt{GAGAG}}, q_{\texttt{TAGAG}}, q_{\texttt{ACGAG}}, q_{\texttt{GCGAG}}, q_{\texttt{TCGAG}}, q_{\texttt{AGGAG}}, q_{\texttt{CGGAG}}, q_{\texttt{TGGAG}}, q_{\texttt{ATGAG}}, q_{\texttt{CTGAG}}, q_{\texttt{GTGAG}}, q_{\texttt{AATAG}}, q_{\texttt{GATAG}}, q_{\texttt{TATAG}}, q_{\texttt{CCTAG}}, q_{\texttt{GCTAG}}, q_{\texttt{TCTAG}}, q_{\texttt{AGTAG}}, q_{\texttt{CGTAG}}, q_{\texttt{GGTAG}}, q_{\texttt{ATTAG}}, q_{\texttt{CTTAG}}, q_{\texttt{TTTAG}}, q_{\texttt{AAACG}}, q_{\texttt{CAACG}}, q_{\texttt{GAACG}}, q_{\texttt{ACACG}}, q_{\texttt{CCACG}}, q_{\texttt{TCACG}}, q_{\texttt{AGACG}}, q_{\texttt{GGACG}}, q_{\texttt{TGACG}}, q_{\texttt{CTACG}}, q_{\texttt{GTACG}}, q_{\texttt{TTACG}}, q_{\texttt{AACCG}}, q_{\texttt{CACCG}}, q_{\texttt{TACCG}}, q_{\texttt{ACCCG}}, q_{\texttt{CCCCG}}, q_{\texttt{GCCCG}}, q_{\texttt{CGCCG}}, q_{\texttt{GGCCG}}, q_{\texttt{TGCCG}}, q_{\texttt{ATCCG}}, q_{\texttt{GTCCG}}, q_{\texttt{TTCCG}}, q_{\texttt{AAGCG}}, q_{\texttt{GAGCG}}, q_{\texttt{TAGCG}}, q_{\texttt{CCGCG}}, q_{\texttt{GCGCG}}, q_{\texttt{TCGCG}}, q_{\texttt{AGGCG}}, q_{\texttt{CGGCG}}, q_{\texttt{GGGCG}}, q_{\texttt{ATGCG}}, q_{\texttt{CTGCG}}, q_{\texttt{TTGCG}}, q_{\texttt{CATCG}}, q_{\texttt{GATCG}}, q_{\texttt{TATCG}}, q_{\texttt{ACTCG}}, q_{\texttt{GCTCG}}, q_{\texttt{TCTCG}}, q_{\texttt{AGTCG}}, q_{\texttt{CGTCG}}, q_{\texttt{TGTCG}}, q_{\texttt{ATTCG}}, q_{\texttt{CTTCG}}, q_{\texttt{GTTCG}}, q_{\texttt{CAAGG}}, q_{\texttt{GAAGG}}, q_{\texttt{TAAGG}}, q_{\texttt{ACAGG}}, q_{\texttt{GCAGG}}, q_{\texttt{TCAGG}}, q_{\texttt{AGAGG}}, q_{\texttt{CGAGG}}, q_{\texttt{TGAGG}}, q_{\texttt{ATAGG}}, q_{\texttt{CTAGG}}, q_{\texttt{GTAGG}}, q_{\texttt{AACGG}}, q_{\texttt{GACGG}}, q_{\texttt{TACGG}}, q_{\texttt{CCCGG}}, q_{\texttt{GCCGG}}, q_{\texttt{TCCGG}}, q_{\texttt{AGCGG}}, q_{\texttt{CGCGG}}, q_{\texttt{GGCGG}}, q_{\texttt{ATCGG}}, q_{\texttt{CTCGG}}, q_{\texttt{TTCGG}}, q_{\texttt{AAGGG}}, q_{\texttt{CAGGG}}, q_{\texttt{TAGGG}}, q_{\texttt{ACGGG}}, q_{\texttt{CCGGG}}, q_{\texttt{GCGGG}}, q_{\texttt{CGGGG}}, q_{\texttt{GGGGG}}, q_{\texttt{TGGGG}}, q_{\texttt{ATGGG}}, q_{\texttt{GTGGG}}, q_{\texttt{TTGGG}}, q_{\texttt{AATGG}}, q_{\texttt{CATGG}}, q_{\texttt{GATGG}}, q_{\texttt{ACTGG}}, q_{\texttt{CCTGG}}, q_{\texttt{TCTGG}}, q_{\texttt{AGTGG}}, q_{\texttt{GGTGG}}, q_{\texttt{TGTGG}}, q_{\texttt{CTTGG}}, q_{\texttt{GTTGG}}, q_{\texttt{TTTGG}}, q_{\texttt{AAATG}}, q_{\texttt{GAATG}}, q_{\texttt{TAATG}}, q_{\texttt{CCATG}}, q_{\texttt{GCATG}}, q_{\texttt{TCATG}}, q_{\texttt{AGATG}}, q_{\texttt{CGATG}}, q_{\texttt{GGATG}}, q_{\texttt{ATATG}}, q_{\texttt{CTATG}}, q_{\texttt{TTATG}}, q_{\texttt{CACTG}}, q_{\texttt{GACTG}}, q_{\texttt{TACTG}}, q_{\texttt{ACCTG}}, q_{\texttt{GCCTG}}, q_{\texttt{TCCTG}}, q_{\texttt{AGCTG}}, q_{\texttt{CGCTG}}, q_{\texttt{TGCTG}}, q_{\texttt{ATCTG}}, q_{\texttt{CTCTG}}, q_{\texttt{GTCTG}}, q_{\texttt{AAGTG}}, q_{\texttt{CAGTG}}, q_{\texttt{GAGTG}}, q_{\texttt{ACGTG}}, q_{\texttt{CCGTG}}, q_{\texttt{TCGTG}}, q_{\texttt{AGGTG}}, q_{\texttt{GGGTG}}, q_{\texttt{TGGTG}}, q_{\texttt{CTGTG}}, q_{\texttt{GTGTG}}, q_{\texttt{TTGTG}}, q_{\texttt{AATTG}}, q_{\texttt{CATTG}}, q_{\texttt{TATTG}}, q_{\texttt{ACTTG}}, q_{\texttt{CCTTG}}, q_{\texttt{GCTTG}}, q_{\texttt{CGTTG}}, q_{\texttt{GGTTG}}, q_{\texttt{TGTTG}}, q_{\texttt{ATTTG}}, q_{\texttt{GTTTG}}, q_{\texttt{TTTTG}}, q_{\texttt{AAAAT}}, q_{\texttt{CAAAT}}, q_{\texttt{GAAAT}}, q_{\texttt{ACAAT}}, q_{\texttt{CCAAT}}, q_{\texttt{TCAAT}}, q_{\texttt{AGAAT}}, q_{\texttt{GGAAT}}, q_{\texttt{TGAAT}}, q_{\texttt{CTAAT}}, q_{\texttt{GTAAT}}, q_{\texttt{TTAAT}}, q_{\texttt{AACAT}}, q_{\texttt{CACAT}}, q_{\texttt{TACAT}}, q_{\texttt{ACCAT}}, q_{\texttt{CCCAT}}, q_{\texttt{GCCAT}}, q_{\texttt{CGCAT}}, q_{\texttt{GGCAT}}, q_{\texttt{TGCAT}}, q_{\texttt{ATCAT}}, q_{\texttt{GTCAT}}, q_{\texttt{TTCAT}}, q_{\texttt{AAGAT}}, q_{\texttt{GAGAT}}, q_{\texttt{TAGAT}}, q_{\texttt{CCGAT}}, q_{\texttt{GCGAT}}, q_{\texttt{TCGAT}}, q_{\texttt{AGGAT}}, q_{\texttt{CGGAT}}, q_{\texttt{GGGAT}}, q_{\texttt{ATGAT}}, q_{\texttt{CTGAT}}, q_{\texttt{TTGAT}}, q_{\texttt{CATAT}}, q_{\texttt{GATAT}}, q_{\texttt{TATAT}}, q_{\texttt{ACTAT}}, q_{\texttt{GCTAT}}, q_{\texttt{TCTAT}}, q_{\texttt{AGTAT}}, q_{\texttt{CGTAT}}, q_{\texttt{TGTAT}}, q_{\texttt{ATTAT}}, q_{\texttt{CTTAT}}, q_{\texttt{GTTAT}}, q_{\texttt{AAACT}}, q_{\texttt{CAACT}}, q_{\texttt{TAACT}}, q_{\texttt{ACACT}}, q_{\texttt{CCACT}}, q_{\texttt{GCACT}}, q_{\texttt{CGACT}}, q_{\texttt{GGACT}}, q_{\texttt{TGACT}}, q_{\texttt{ATACT}}, q_{\texttt{GTACT}}, q_{\texttt{TTACT}}, q_{\texttt{AACCT}}, q_{\texttt{CACCT}}, q_{\texttt{GACCT}}, q_{\texttt{ACCCT}}, q_{\texttt{CCCCT}}, q_{\texttt{TCCCT}}, q_{\texttt{AGCCT}}, q_{\texttt{GGCCT}}, q_{\texttt{TGCCT}}, q_{\texttt{CTCCT}}, q_{\texttt{GTCCT}}, q_{\texttt{TTCCT}}, q_{\texttt{CAGCT}}, q_{\texttt{GAGCT}}, q_{\texttt{TAGCT}}, q_{\texttt{ACGCT}}, q_{\texttt{GCGCT}}, q_{\texttt{TCGCT}}, q_{\texttt{AGGCT}}, q_{\texttt{CGGCT}}, q_{\texttt{TGGCT}}, q_{\texttt{ATGCT}}, q_{\texttt{CTGCT}}, q_{\texttt{GTGCT}}, q_{\texttt{AATCT}}, q_{\texttt{GATCT}}, q_{\texttt{TATCT}}, q_{\texttt{CCTCT}}, q_{\texttt{GCTCT}}, q_{\texttt{TCTCT}}, q_{\texttt{AGTCT}}, q_{\texttt{CGTCT}}, q_{\texttt{GGTCT}}, q_{\texttt{ATTCT}}, q_{\texttt{CTTCT}}, q_{\texttt{TTTCT}}, q_{\texttt{AAAGT}}, q_{\texttt{GAAGT}}, q_{\texttt{TAAGT}}, q_{\texttt{CCAGT}}, q_{\texttt{GCAGT}}, q_{\texttt{TCAGT}}, q_{\texttt{AGAGT}}, q_{\texttt{CGAGT}}, q_{\texttt{GGAGT}}, q_{\texttt{ATAGT}}, q_{\texttt{CTAGT}}, q_{\texttt{TTAGT}}, q_{\texttt{CACGT}}, q_{\texttt{GACGT}}, q_{\texttt{TACGT}}, q_{\texttt{ACCGT}}, q_{\texttt{GCCGT}}, q_{\texttt{TCCGT}}, q_{\texttt{AGCGT}}, q_{\texttt{CGCGT}}, q_{\texttt{TGCGT}}, q_{\texttt{ATCGT}}, q_{\texttt{CTCGT}}, q_{\texttt{GTCGT}}, q_{\texttt{AAGGT}}, q_{\texttt{CAGGT}}, q_{\texttt{GAGGT}}, q_{\texttt{ACGGT}}, q_{\texttt{CCGGT}}, q_{\texttt{TCGGT}}, q_{\texttt{AGGGT}}, q_{\texttt{GGGGT}}, q_{\texttt{TGGGT}}, q_{\texttt{CTGGT}}, q_{\texttt{GTGGT}}, q_{\texttt{TTGGT}}, q_{\texttt{AATGT}}, q_{\texttt{CATGT}}, q_{\texttt{TATGT}}, q_{\texttt{ACTGT}}, q_{\texttt{CCTGT}}, q_{\texttt{GCTGT}}, q_{\texttt{CGTGT}}, q_{\texttt{GGTGT}}, q_{\texttt{TGTGT}}, q_{\texttt{ATTGT}}, q_{\texttt{GTTGT}}, q_{\texttt{TTTGT}}, q_{\texttt{CAATT}}, q_{\texttt{GAATT}}, q_{\texttt{TAATT}}, q_{\texttt{ACATT}}, q_{\texttt{GCATT}}, q_{\texttt{TCATT}}, q_{\texttt{AGATT}}, q_{\texttt{CGATT}}, q_{\texttt{TGATT}}, q_{\texttt{ATATT}}, q_{\texttt{CTATT}}, q_{\texttt{GTATT}}, q_{\texttt{AACTT}}, q_{\texttt{GACTT}}, q_{\texttt{TACTT}}, q_{\texttt{CCCTT}}, q_{\texttt{GCCTT}}, q_{\texttt{TCCTT}}, q_{\texttt{AGCTT}}, q_{\texttt{CGCTT}}, q_{\texttt{GGCTT}}, q_{\texttt{ATCTT}}, q_{\texttt{CTCTT}}, q_{\texttt{TTCTT}}, q_{\texttt{AAGTT}}, q_{\texttt{CAGTT}}, q_{\texttt{TAGTT}}, q_{\texttt{ACGTT}}, q_{\texttt{CCGTT}}, q_{\texttt{GCGTT}}, q_{\texttt{CGGTT}}, q_{\texttt{GGGTT}}, q_{\texttt{TGGTT}}, q_{\texttt{ATGTT}}, q_{\texttt{GTGTT}}, q_{\texttt{TTGTT}}, q_{\texttt{AATTT}}, q_{\texttt{CATTT}}, q_{\texttt{GATTT}}, q_{\texttt{ACTTT}}, q_{\texttt{CCTTT}}, q_{\texttt{TCTTT}}, q_{\texttt{AGTTT}}, q_{\texttt{GGTTT}}, q_{\texttt{TGTTT}}, q_{\texttt{CTTTT}}, q_{\texttt{GTTTT}}, q_{\texttt{TTTTT}} \\[0.5em] \text{Class } &q_{\texttt{AAAAA}}:\ q_{\texttt{AAAAA}} \\[0.5em] \text{Class } &q_{\texttt{AAACC}}:\ q_{\texttt{AAACC}},\ q_{\texttt{AAAGG}},\ q_{\texttt{AAATT}} \\[0.5em] \text{Class } &q_{\texttt{AACAC}}:\ q_{\texttt{AACAC}},\ q_{\texttt{AAGAG}},\ q_{\texttt{AATAT}} \\[0.5em] \text{Class } &q_{\texttt{AACCA}}:\ q_{\texttt{AACCA}},\ q_{\texttt{AAGGA}},\ q_{\texttt{AATTA}} \\[0.5em] \text{Class } &q_{\texttt{AACGT}}:\ q_{\texttt{AACGT}},\ q_{\texttt{AACTG}},\ q_{\texttt{AAGCT}},\ q_{\texttt{AAGTC}},\ q_{\texttt{AATCG}},\ q_{\texttt{AATGC}} \\[0.5em] \text{Class } &q_{\texttt{ACAAC}}:\ q_{\texttt{ACAAC}},\ q_{\texttt{AGAAG}},\ q_{\texttt{ATAAT}} \\[0.5em] \text{Class } &q_{\texttt{ACACA}}:\ q_{\texttt{ACACA}},\ q_{\texttt{AGAGA}},\ q_{\texttt{ATATA}} \\[0.5em] \text{Class } &q_{\texttt{ACAGT}}:\ q_{\texttt{ACAGT}},\ q_{\texttt{ACATG}},\ q_{\texttt{AGACT}},\ q_{\texttt{AGATC}},\ q_{\texttt{ATACG}},\ q_{\texttt{ATAGC}} \\[0.5em] \text{Class } &q_{\texttt{ACCAA}}:\ q_{\texttt{ACCAA}},\ q_{\texttt{AGGAA}},\ q_{\texttt{ATTAA}} \\[0.5em] \text{Class } &q_{\texttt{ACCCC}}:\ q_{\texttt{ACCCC}},\ q_{\texttt{ACCGG}},\ q_{\texttt{ACCTT}},\ q_{\texttt{ACGCG}},\ q_{\texttt{ACGGC}},\ q_{\texttt{ACTCT}},\ q_{\texttt{ACTTC}},\ q_{\texttt{AGCCG}},\ q_{\texttt{AGCGC}},\ q_{\texttt{AGGCC}},\ q_{\texttt{AGGGG}},\ q_{\texttt{AGGTT}},\ q_{\texttt{AGTGT}},\ q_{\texttt{AGTTG}},\ q_{\texttt{ATCCT}},\ q_{\texttt{ATCTC}},\ q_{\texttt{ATGGT}},\ q_{\texttt{ATGTG}},\ q_{\texttt{ATTCC}},\ q_{\texttt{ATTGG}},\ q_{\texttt{ATTTT}} \\[0.5em] \text{Class } &q_{\texttt{ACGAT}}:\ q_{\texttt{ACGAT}},\ q_{\texttt{ACTAG}},\ q_{\texttt{AGCAT}},\ q_{\texttt{AGTAC}},\ q_{\texttt{ATCAG}},\ q_{\texttt{ATGAC}} \\[0.5em] \text{Class } &q_{\texttt{ACGTA}}:\ q_{\texttt{ACGTA}},\ q_{\texttt{ACTGA}},\ q_{\texttt{AGCTA}},\ q_{\texttt{AGTCA}},\ q_{\texttt{ATCGA}},\ q_{\texttt{ATGCA}} \\[0.5em] \text{Class } &q_{\texttt{CAAAC}}:\ q_{\texttt{CAAAC}},\ q_{\texttt{GAAAG}},\ q_{\texttt{TAAAT}} \\[0.5em] \text{Class } &q_{\texttt{CAACA}}:\ q_{\texttt{CAACA}},\ q_{\texttt{GAAGA}},\ q_{\texttt{TAATA}} \\[0.5em] \text{Class } &q_{\texttt{CAAGT}}:\ q_{\texttt{CAAGT}},\ q_{\texttt{CAATG}},\ q_{\texttt{GAACT}},\ q_{\texttt{GAATC}},\ q_{\texttt{TAACG}},\ q_{\texttt{TAAGC}} \\[0.5em] \text{Class } &q_{\texttt{CACAA}}:\ q_{\texttt{CACAA}},\ q_{\texttt{GAGAA}},\ q_{\texttt{TATAA}} \\[0.5em] \text{Class } &q_{\texttt{CACCC}}:\ q_{\texttt{CACCC}},\ q_{\texttt{CACGG}},\ q_{\texttt{CACTT}},\ q_{\texttt{CAGCG}},\ q_{\texttt{CAGGC}},\ q_{\texttt{CATCT}},\ q_{\texttt{CATTC}},\ q_{\texttt{GACCG}},\ q_{\texttt{GACGC}},\ q_{\texttt{GAGCC}},\ q_{\texttt{GAGGG}},\ q_{\texttt{GAGTT}},\ q_{\texttt{GATGT}},\ q_{\texttt{GATTG}},\ q_{\texttt{TACCT}},\ q_{\texttt{TACTC}},\ q_{\texttt{TAGGT}},\ q_{\texttt{TAGTG}},\ q_{\texttt{TATCC}},\ q_{\texttt{TATGG}},\ q_{\texttt{TATTT}} \\[0.5em] \text{Class } &q_{\texttt{CAGAT}}:\ q_{\texttt{CAGAT}},\ q_{\texttt{CATAG}},\ q_{\texttt{GACAT}},\ q_{\texttt{GATAC}},\ q_{\texttt{TACAG}},\ q_{\texttt{TAGAC}} \\[0.5em] \text{Class } &q_{\texttt{CAGTA}}:\ q_{\texttt{CAGTA}},\ q_{\texttt{CATGA}},\ q_{\texttt{GACTA}},\ q_{\texttt{GATCA}},\ q_{\texttt{TACGA}},\ q_{\texttt{TAGCA}} \\[0.5em] \text{Class } &q_{\texttt{CCAAA}}:\ q_{\texttt{CCAAA}},\ q_{\texttt{GGAAA}},\ q_{\texttt{TTAAA}} \\[0.5em] \text{Class } &q_{\texttt{CCACC}}:\ q_{\texttt{CCACC}},\ q_{\texttt{CCAGG}},\ q_{\texttt{CCATT}},\ q_{\texttt{GGACC}},\ q_{\texttt{GGAGG}},\ q_{\texttt{GGATT}},\ q_{\texttt{TTACC}},\ q_{\texttt{TTAGG}},\ q_{\texttt{TTATT}} \\[0.5em] \text{Class } &q_{\texttt{CCCAC}}:\ q_{\texttt{CCCAC}},\ q_{\texttt{CCGAG}},\ q_{\texttt{CCTAT}},\ q_{\texttt{GGCAC}},\ q_{\texttt{GGGAG}},\ q_{\texttt{GGTAT}},\ q_{\texttt{TTCAC}},\ q_{\texttt{TTGAG}},\ q_{\texttt{TTTAT}} \\[0.5em] \text{Class } &q_{\texttt{CCCCA}}:\ q_{\texttt{CCCCA}},\ q_{\texttt{CCGGA}},\ q_{\texttt{CCTTA}},\ q_{\texttt{GGCCA}},\ q_{\texttt{GGGGA}},\ q_{\texttt{GGTTA}},\ q_{\texttt{TTCCA}},\ q_{\texttt{TTGGA}},\ q_{\texttt{TTTTA}} \\[0.5em] \text{Class } &q_{\texttt{CCCGT}}:\ q_{\texttt{CCCGT}},\ q_{\texttt{CCCTG}},\ q_{\texttt{CCGCT}},\ q_{\texttt{CCGTC}},\ q_{\texttt{CCTCG}},\ q_{\texttt{CCTGC}},\ q_{\texttt{GGCGT}},\ q_{\texttt{GGCTG}},\ q_{\texttt{GGGCT}},\ q_{\texttt{GGGTC}},\ q_{\texttt{GGTCG}},\ q_{\texttt{GGTGC}},\ q_{\texttt{TTCGT}},\ q_{\texttt{TTCTG}},\ q_{\texttt{TTGCT}},\ q_{\texttt{TTGTC}},\ q_{\texttt{TTTCG}},\ q_{\texttt{TTTGC}} \\[0.5em] \text{Class } &q_{\texttt{CGAAT}}:\ q_{\texttt{CGAAT}},\ q_{\texttt{CTAAG}},\ q_{\texttt{GCAAT}},\ q_{\texttt{GTAAC}},\ q_{\texttt{TCAAG}},\ q_{\texttt{TGAAC}} \\[0.5em] \text{Class } &q_{\texttt{CGACG}}:\ q_{\texttt{CGACG}},\ q_{\texttt{CGAGC}},\ q_{\texttt{CTACT}},\ q_{\texttt{CTATC}},\ q_{\texttt{GCACG}},\ q_{\texttt{GCAGC}},\ q_{\texttt{GTAGT}},\ q_{\texttt{GTATG}},\ q_{\texttt{TCACT}},\ q_{\texttt{TCATC}},\ q_{\texttt{TGAGT}},\ q_{\texttt{TGATG}} \\[0.5em] \text{Class } &q_{\texttt{CGATA}}:\ q_{\texttt{CGATA}},\ q_{\texttt{CTAGA}},\ q_{\texttt{GCATA}},\ q_{\texttt{GTACA}},\ q_{\texttt{TCAGA}},\ q_{\texttt{TGACA}} \\[0.5em] \text{Class } &q_{\texttt{CGCAG}}:\ q_{\texttt{CGCAG}},\ q_{\texttt{CGGAC}},\ q_{\texttt{CTCAT}},\ q_{\texttt{CTTAC}},\ q_{\texttt{GCCAG}},\ q_{\texttt{GCGAC}},\ q_{\texttt{GTGAT}},\ q_{\texttt{GTTAG}},\ q_{\texttt{TCCAT}},\ q_{\texttt{TCTAC}},\ q_{\texttt{TGGAT}},\ q_{\texttt{TGTAG}} \\[0.5em] \text{Class } &q_{\texttt{CGCCT}}:\ q_{\texttt{CGCCT}},\ q_{\texttt{CGCTC}},\ q_{\texttt{CGGGT}},\ q_{\texttt{CGGTG}},\ q_{\texttt{CGTCC}},\ q_{\texttt{CGTGG}},\ q_{\texttt{CGTTT}},\ q_{\texttt{CTCCG}},\ q_{\texttt{CTCGC}},\ q_{\texttt{CTGCC}},\ q_{\texttt{CTGGG}},\ q_{\texttt{CTGTT}},\ q_{\texttt{CTTGT}},\ q_{\texttt{CTTTG}},\ q_{\texttt{GCCCT}},\ q_{\texttt{GCCTC}},\ q_{\texttt{GCGGT}},\ q_{\texttt{GCGTG}},\ q_{\texttt{GCTCC}},\ q_{\texttt{GCTGG}},\ q_{\texttt{GCTTT}},\ q_{\texttt{GTCCC}},\ q_{\texttt{GTCGG}},\ q_{\texttt{GTCTT}},\ q_{\texttt{GTGCG}},\ q_{\texttt{GTGGC}},\ q_{\texttt{GTTCT}},\ q_{\texttt{GTTTC}},\ q_{\texttt{TCCCG}},\ q_{\texttt{TCCGC}},\ q_{\texttt{TCGCC}},\ q_{\texttt{TCGGG}},\ q_{\texttt{TCGTT}},\ q_{\texttt{TCTGT}},\ q_{\texttt{TCTTG}},\ q_{\texttt{TGCCC}},\ q_{\texttt{TGCGG}},\ q_{\texttt{TGCTT}},\ q_{\texttt{TGGCG}},\ q_{\texttt{TGGGC}},\ q_{\texttt{TGTCT}},\ q_{\texttt{TGTTC}} \\[0.5em] \text{Class } &q_{\texttt{CGCGA}}:\ q_{\texttt{CGCGA}},\ q_{\texttt{CGGCA}},\ q_{\texttt{CTCTA}},\ q_{\texttt{CTTCA}},\ q_{\texttt{GCCGA}},\ q_{\texttt{GCGCA}},\ q_{\texttt{GTGTA}},\ q_{\texttt{GTTGA}},\ q_{\texttt{TCCTA}},\ q_{\texttt{TCTCA}},\ q_{\texttt{TGGTA}},\ q_{\texttt{TGTGA}} \\[0.5em] \text{Class } &q_{\texttt{CGTAA}}:\ q_{\texttt{CGTAA}},\ q_{\texttt{CTGAA}},\ q_{\texttt{GCTAA}},\ q_{\texttt{GTCAA}},\ q_{\texttt{TCGAA}},\ q_{\texttt{TGCAA}} \end{align}$

Invariants in Fourier coordinates

Ideal generated by $$-$$

Gröbner basis of ideal of invariants

Gröbner basis with $0$ elements

Additional information

The cardinality of the smallest set of generators that define the ideal of phylogenetic invariants: -
The largest degree of a generator in the degree reverse lexicographic reduced Gröbner basis: -
The largest degree of an element in a minimal generating set for the ideal of phylogenetic invariants: -
The cardinality of the degree reverse lexicographic reduced Gröbner basis of the ideal of phylogenetic invariants: -

Specialized Fourier transform

$\frac{1}{63} \begin{pmatrix} 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63\\ 63 & -21 & -21 & 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & 63 & -21 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & 63\\ 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21\\ 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & 63 & -21 & 21 & -21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & -21 & 21 & -21 & 63 & -21 & 21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & 21 & -21 & -21 & 21 & -21 & -21 & 63 & -21 & 21 & 21 & -21 & -21\\ 63 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21\\ 63 & 63 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & -21 & 21 & -21 & 63 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & 63 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & 63 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & 21 & -21\\ 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & 15 & 3 & -21 & 15 & 3 & 15 & -21 & 3 & 3 & 3 & 3 & -9 & -21 & 15 & 3 & 15 & -21 & 3 & 3 & 3 & 3 & -9 & 15 & -21 & 3 & -21 & 63 & -21 & 3 & -21 & 15 & 3 & 3 & 3 & 3 & -9 & 3 & -21 & 15 & 3 & 3 & 15 & -21 & 3 & -9 & 3 & 3 & 3\\ 63 & -21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21\\ 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21\\ 63 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21\\ 63 & 63 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & 21 & -21\\ 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & 15 & 3 & -21 & 15 & 3 & 15 & -21 & 3 & 3 & 3 & 3 & -9 & 63 & -21 & -21 & -21 & 15 & 3 & -21 & 3 & 15 & 3 & -21 & 15 & 3 & 15 & -21 & 3 & 3 & 3 & 3 & -9 & -21 & 3 & 15 & 3 & 3 & 3 & 3 & -9 & 15 & 3 & -21 & 3 & 3 & -9 & 3 & 3\\ 63 & -21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21\\ 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21\\ 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21\\ 63 & -21 & -21 & 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & -21 & 7 & -21 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & -21 & 7 & -21 & 7 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & 7 & -21\\ 63 & -21 & 63 & -21 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & 7 & 7 & -21 & 7 & 7 & -21 & 7 & 7 & 7 & 7 & -21 & 7 & 7 & -21 & 7 & 7 & -21 & 7 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & -21 & 7 & 7 & 7 & -21 & 7\\ 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & -21 & -21 & -21 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & -21 & -21 & -21 & -21 & 7 & 7 & 7 & 7\\ 63 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & 63 & -21 & 21 & -21 & -21 & 21 & -21 & 7 & 7 & 7 & 7 & -7 & 7 & -7 & 7 & -7 & 7 & 7 & -7 & 7 & -21 & 7 & -7 & 7 & 7 & -7 & 7 & -7 & 7 & -7 & -7 & 7 & 7 & -7 & 7 & 7 & -21 & 7 & -7 & -7 & 7 & 7\\ 63 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & 63 & -21 & -21 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21 & -21 & -21 & 21 & 21\\ 63 & -21 & -21 & -21 & 21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & 21 & -21 & 21 & -21 & 21 & 0 & 21 & -21 & 0 & 0 & 0 & 21 & -21 & -21 & 21 & 0 & 21 & -21 & 0 & 0 & 0 & 21 & -21 & -21 & 21 & 0 & 0 & 21 & -21 & 0 & 0 & 0 & 0 & 21 & -21 & 0 & 0 & -21 & 21\\ 63 & 63 & -21 & -21 & -21 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21\\ 63 & -21 & 63 & -21 & -21 & -21 & -21 & 21 & -21 & -21 & 21 & -21 & -21 & 21 & 21 & -21 & 21 & 0 & -21 & 21 & 0 & -21 & 21 & 0 & 0 & 21 & -21 & 0 & 21 & -21 & 0 & 21 & -21 & 0 & 0 & 0 & 0 & 21 & -21 & 0 & 0 & 21 & -21 & 0 & 0 & 21 & -21 & 0 & 0 & 21 & -21\\ 63 & -21 & -21 & 15 & 3 & -21 & 15 & 3 & 15 & -21 & 3 & 3 & 3 & 3 & -9 & -21 & 3 & 9 & 3 & 3 & -3 & 9 & -3 & -9 & 3 & 3 & 3 & -3 & 3 & -21 & 9 & -3 & 9 & -9 & 3 & 9 & -3 & -9 & 3 & -3 & 9 & -9 & 3 & -9 & -9 & 21 & -3 & 3 & 3 & -3 & -3\\ 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & 21 & 21 & 21 & 0 & 0 & 0 & 0 & 21 & 21 & 21 & -21 & -21 & -21 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 21 & 21 & 21 & 21 & -21 & -21 & -21 & -21\\ 63 & 63 & 63 & 63 & 63 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & -21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 & 21 \end{pmatrix} ] $

Inverse specialized Fourier transform

$\frac{1}{256} \begin{pmatrix} 1 & 3 & 3 & 3 & 6 & 3 & 3 & 6 & 3 & 21 & 6 & 6 & 3 & 3 & 6 & 3 & 21 & 6 & 6 & 3 & 9 & 9 & 9 & 18 & 6 & 12 & 6 & 12 & 42 & 12 & 6\\ 3 & -3 & -3 & 9 & -6 & -3 & 9 & -6 & 9 & -21 & -6 & 18 & -3 & 9 & -6 & 9 & -21 & -6 & 18 & 9 & -9 & -9 & 27 & -18 & -6 & -12 & 18 & -12 & -42 & 36 & 18\\ 3 & -3 & 9 & -3 & -6 & 9 & -3 & -6 & 9 & -21 & 18 & -6 & 9 & -3 & -6 & 9 & -21 & 18 & -6 & 9 & -9 & 27 & -9 & -18 & 18 & -12 & -6 & 36 & -42 & -12 & 18\\ 3 & 9 & -3 & -3 & -6 & -3 & -3 & -6 & 9 & 15 & -6 & -6 & -3 & -3 & -6 & 9 & 15 & -6 & -6 & 9 & 27 & -9 & -9 & -18 & -6 & -12 & -6 & -12 & 30 & -12 & 18\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & 18 & -18 & -18 & -18 & 36 & -12 & 24 & -12 & -24 & 12 & -24 & 36\\ 3 & 9 & -3 & -3 & -6 & 9 & 9 & 18 & -3 & -21 & -6 & -6 & 9 & 9 & 18 & -3 & -21 & -6 & -6 & 9 & 27 & -9 & -9 & -18 & 18 & 36 & 18 & -12 & -42 & -12 & -6\\ 3 & -3 & 9 & -3 & -6 & -3 & 9 & -6 & -3 & 15 & -6 & -6 & -3 & 9 & -6 & -3 & 15 & -6 & -6 & 9 & -9 & 27 & -9 & -18 & -6 & -12 & 18 & -12 & 30 & -12 & -6\\ 6 & -6 & -6 & -6 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & 18 & -18 & -18 & -18 & 36 & -12 & -24 & 36 & 24 & 12 & -24 & -12\\ 3 & -3 & -3 & 9 & -6 & 9 & -3 & -6 & -3 & 15 & -6 & -6 & 9 & -3 & -6 & -3 & 15 & -6 & -6 & 9 & -9 & -9 & 27 & -18 & 18 & -12 & -6 & -12 & 30 & -12 & -6\\ 3 & 9 & 9 & 9 & 18 & -3 & -3 & -6 & -3 & -21 & -6 & -6 & -3 & -3 & -6 & -3 & -21 & -6 & -6 & 9 & 27 & 27 & 27 & 54 & -6 & -12 & -6 & -12 & -42 & -12 & -6\\ 6 & -6 & -6 & 18 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & 18 & -18 & -18 & 54 & -36 & -12 & 24 & -12 & 24 & 12 & -24 & -12\\ 6 & -6 & -6 & -6 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & 18 & -18 & -18 & -18 & 36 & 36 & -24 & -12 & -24 & 12 & 24 & -12\\ 6 & -6 & 18 & -6 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & 18 & -18 & 54 & -18 & -36 & -12 & 24 & -12 & -24 & 12 & 24 & -12\\ 6 & 18 & -6 & -6 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & 18 & 54 & -18 & -18 & -36 & -12 & -24 & -12 & 24 & 12 & 24 & -12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & 18 & -18 & -18 & -18 & 36 & -12 & 24 & -12 & 24 & -36 & 24 & -12\\ 3 & 9 & 9 & 9 & 18 & -3 & -3 & -6 & -3 & -21 & -6 & -6 & 9 & 9 & 18 & 9 & 63 & 18 & 18 & -3 & -9 & -9 & -9 & -18 & -6 & -12 & -6 & -12 & -42 & -12 & -6\\ 3 & -3 & -3 & 9 & -6 & 9 & -3 & -6 & -3 & 15 & -6 & -6 & -3 & 9 & -6 & 9 & -21 & -6 & 18 & -3 & 3 & 3 & -9 & 6 & -6 & 12 & -6 & 12 & 6 & -12 & -6\\ 6 & -6 & -6 & 18 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & 18 & -12 & 18 & -42 & -12 & 36 & -6 & 6 & 6 & -18 & 12 & 12 & 0 & -12 & 0 & 36 & -24 & -12\\ 3 & -3 & 9 & -3 & -6 & -3 & 9 & -6 & -3 & 15 & -6 & -6 & 9 & -3 & -6 & 9 & -21 & 18 & -6 & -3 & 3 & -9 & 3 & 6 & -6 & 12 & -6 & -12 & 6 & 12 & -6\\ 3 & 9 & -3 & -3 & -6 & 9 & 9 & 18 & -3 & -21 & -6 & -6 & -3 & -3 & -6 & 9 & 15 & -6 & -6 & -3 & -9 & 3 & 3 & 6 & -6 & -12 & -6 & 12 & 6 & 12 & -6\\ 6 & -6 & -6 & -6 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & 6 & 6 & 6 & -12 & 12 & 0 & -12 & 0 & -12 & 24 & -12\\ 6 & -6 & 18 & -6 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & 18 & -6 & -12 & 18 & -42 & 36 & -12 & -6 & 6 & -18 & 6 & 12 & -12 & 0 & 12 & -24 & 36 & 0 & -12\\ 6 & -6 & -6 & -6 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & 6 & 6 & 6 & -12 & -12 & 0 & 12 & 24 & -12 & 0 & -12\\ 6 & 18 & -6 & -6 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -6 & -12 & 18 & 30 & -12 & -12 & -6 & -18 & 6 & 6 & 12 & 12 & 24 & 12 & 0 & -36 & 0 & -12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & 6 & 6 & 6 & -12 & 12 & -24 & 12 & 0 & 12 & 0 & -12\\ 3 & 9 & -3 & -3 & -6 & -3 & -3 & -6 & 9 & 15 & -6 & -6 & 9 & 9 & 18 & -3 & -21 & -6 & -6 & -3 & -9 & 3 & 3 & 6 & -6 & -12 & -6 & 12 & 6 & 12 & -6\\ 3 & -3 & 9 & -3 & -6 & 9 & -3 & -6 & 9 & -21 & 18 & -6 & -3 & 9 & -6 & -3 & 15 & -6 & -6 & -3 & 3 & -9 & 3 & 6 & -6 & 12 & -6 & -12 & 6 & 12 & -6\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & 6 & -12 & 12 & 0 & -12 & 0 & -12 & 24 & -12\\ 3 & -3 & -3 & 9 & -6 & -3 & 9 & -6 & 9 & -21 & -6 & 18 & 9 & -3 & -6 & -3 & 15 & -6 & -6 & -3 & 3 & 3 & -9 & 6 & -6 & 12 & -6 & 12 & 6 & -12 & -6\\ 3 & 9 & 9 & 9 & 18 & 9 & 9 & 18 & 9 & 63 & 18 & 18 & -3 & -3 & -6 & -3 & -21 & -6 & -6 & -3 & -9 & -9 & -9 & -18 & -6 & -12 & -6 & -12 & -42 & -12 & -6\\ 6 & -6 & -6 & 18 & -12 & -6 & 18 & -12 & 18 & -42 & -12 & 36 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & -18 & 12 & 12 & 0 & -12 & 0 & 36 & -24 & -12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & 6 & 6 & 6 & -12 & -12 & 0 & 12 & 24 & -12 & 0 & -12\\ 6 & -6 & 18 & -6 & -12 & 18 & -6 & -12 & 18 & -42 & 36 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & 6 & -18 & 6 & 12 & -12 & 0 & 12 & -24 & 36 & 0 & -12\\ 6 & 18 & -6 & -6 & -12 & -6 & -6 & -12 & 18 & 30 & -12 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -18 & 6 & 6 & 12 & 12 & 24 & 12 & 0 & -36 & 0 & -12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & 18 & 6 & -12 & -12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & 6 & 6 & 6 & -12 & 12 & -24 & 12 & 0 & 12 & 0 & -12\\ 6 & 18 & -6 & -6 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & 18 & 18 & 36 & -6 & -42 & -12 & -12 & -6 & -18 & 6 & 6 & 12 & -12 & -24 & -12 & 0 & 36 & 0 & 12\\ 6 & -6 & -6 & -6 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & 6 & -12 & -12 & 24 & -12 & 0 & -12 & 0 & 12\\ 6 & -6 & 18 & -6 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & 18 & -12 & -6 & 30 & -12 & -12 & -6 & 6 & -18 & 6 & 12 & 12 & 0 & -12 & 24 & -36 & 0 & 12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & 6 & -12 & 12 & 0 & -12 & -24 & 12 & 0 & 12\\ 6 & -6 & -6 & -6 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & 6 & 6 & 6 & -12 & -12 & 24 & -12 & 0 & -12 & 0 & 12\\ 6 & 18 & -6 & -6 & -12 & 18 & 18 & 36 & -6 & -42 & -12 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -18 & 6 & 6 & 12 & -12 & -24 & -12 & 0 & 36 & 0 & 12\\ 6 & -6 & 18 & -6 & -12 & -6 & 18 & -12 & -6 & 30 & -12 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & 6 & -18 & 6 & 12 & 12 & 0 & -12 & 24 & -36 & 0 & 12\\ 6 & -6 & -6 & -6 & 12 & -6 & 18 & -12 & -6 & 6 & 12 & -12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & 6 & 6 & 6 & -12 & 12 & 0 & -12 & -24 & 12 & 0 & 12\\ 6 & -6 & -6 & 18 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & 18 & -6 & -12 & -6 & 30 & -12 & -12 & -6 & 6 & 6 & -18 & 12 & -12 & 0 & 12 & 0 & -36 & 24 & 12\\ 6 & -6 & -6 & 18 & -12 & 18 & -6 & -12 & -6 & 30 & -12 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & -18 & 12 & -12 & 0 & 12 & 0 & -36 & 24 & 12\\ 6 & 18 & 18 & 18 & 36 & -6 & -6 & -12 & -6 & -42 & -12 & -12 & -6 & -6 & -12 & -6 & -42 & -12 & -12 & -6 & -18 & -18 & -18 & -36 & 12 & 24 & 12 & 24 & 84 & 24 & 12\\ 6 & -6 & -6 & 18 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & -6 & 12 & -6 & 6 & 12 & -12 & -6 & 6 & 6 & -18 & 12 & 12 & -24 & 12 & -24 & -12 & 24 & 12\\ 6 & -6 & -6 & -6 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & 6 & 6 & 6 & -12 & -12 & 0 & 12 & 0 & 12 & -24 & 12\\ 6 & -6 & -6 & -6 & 12 & 18 & -6 & -12 & -6 & 6 & -12 & 12 & -6 & -6 & 12 & -6 & -18 & 12 & 12 & -6 & 6 & 6 & 6 & -12 & -12 & 0 & 12 & 0 & 12 & -24 & 12\\ 6 & -6 & 18 & -6 & -12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & -6 & 12 & -6 & 6 & -12 & 12 & -6 & 6 & -18 & 6 & 12 & 12 & -24 & 12 & 24 & -12 & -24 & 12\\ 6 & 18 & -6 & -6 & -12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -6 & -12 & -6 & 6 & 12 & 12 & -6 & -18 & 6 & 6 & 12 & 12 & 24 & 12 & -24 & -12 & -24 & 12 \end{pmatrix} $