\newcommand{\HLcell}{\cellcolor{blue!25}}

\begin{center}
\begin{doublespace}
\noindent\(\begin{array}{l|llllll}
  & \text{aH} & \text{aL} & \text{bH} & \text{bL} & \text{qH} & \text{qL} \\
\hline
 \text{3+3 = 6 $\equiv $ 2 (mod 4)} & 1 & 1 & 1 & 1 & 1 & 0 \\
 \text{3+2 = 5 $\equiv $ 1 (mod 4)} & 1 & 1 & 1 & 0 & 0 & 1 \\
 \text{3+1 = 4 $\equiv $ 0 (mod 4)} & 1 & 1 & 0 & 1 & 0 & 0 \\
 \text{\HLcell{}3+0 = 3 $\equiv $ 3 (mod 4)} & \HLcell{}1 & \HLcell{}1 & \HLcell{}0 & \HLcell{}0 & \HLcell{}1 & \HLcell{}1 \\
 \text{2+3 = 5 $\equiv $ 1 (mod 4)} & 1 & 0 & 1 & 1 & 0 & 1 \\
 \text{2+2 = 4 $\equiv $ 0 (mod 4)} & 1 & 0 & 1 & 0 & 0 & 0 \\
 \text{\HLcell{}2+1 = 3 $\equiv $ 3 (mod 4)} & \HLcell{}1 & \HLcell{}0 & \HLcell{}0 & \HLcell{}1 & \HLcell{}1 & \HLcell{}1 \\
 \text{2+0 = 2 $\equiv $ 2 (mod 4)} & 1 & 0 & 0 & 0 & 1 & 0 \\
 \text{1+3 = 4 $\equiv $ 0 (mod 4)} & 0 & 1 & 1 & 1 & 0 & 0 \\
 \text{\HLcell{}1+2 = 3 $\equiv $ 3 (mod 4)} & \HLcell{}0 & \HLcell{}1 & \HLcell{}1 & \HLcell{}0 & \HLcell{}1 & \HLcell{}1 \\
 \text{1+1 = 2 $\equiv $ 2 (mod 4)} & 0 & 1 & 0 & 1 & 1 & 0 \\
 \text{1+0 = 1 $\equiv $ 1 (mod 4)} & 0 & 1 & 0 & 0 & 0 & 1 \\
 \text{\HLcell{}0+3 = 3 $\equiv $ 3 (mod 4)} & \HLcell{}0 & \HLcell{}0 & \HLcell{}1 & \HLcell{}1 & \HLcell{}1 & \HLcell{}1 \\
 \text{0+2 = 2 $\equiv $ 2 (mod 4)} & 0 & 0 & 1 & 0 & 1 & 0 \\
 \text{0+1 = 1 $\equiv $ 1 (mod 4)} & 0 & 0 & 0 & 1 & 0 & 1 \\
 \text{0+0 = 0 $\equiv $ 0 (mod 4)} & 0 & 0 & 0 & 0 & 0 & 0 \\
\end{array}\)
\end{doublespace}
\end{center}