  We consider the third order differential equation derived from the deformed
Seiberg-Witten differential for pure ${\cal N}=2$ SYM with gauge group $SU(3)$
in Nekrasov-Shatashvili limit of $\Omega$-background. We show that this is the
same differential equation that emerges in the context of Ordinary Differential
Equation/Integrable Models (ODI/IM) correspondence for $2d$ $A_2$ Toda CFT with
central charge $c=98$. We derive the corresponding $QQ$ and related $TQ$
functional relations and establish the asymptotic behaviour of $Q$ and $T$
functions at small instanton parameter $q \rightarrow 0$. Moreover, numerical
integration of the Floquet monodromy matrix of the differential equation leads
to evaluation of the $A$-cycles $a_{1,2,3}$ at any point of the moduli space of
vacua parametrised by the vector multiplet scalar VEVs $\langle
\textbf{tr}\,\phi^2\rangle$ and $\langle \textbf{tr}\,\phi^3\rangle$ even for
large values of $q$ which are well beyond the reach of instanton calculus. The
numerical results at small $q$ are in excellent agreement with instanton
calculation. We conjecture a very simple relation between Baxter's $T$-function
and $A$-cycle periods $a_{1,2,3}$, which is an extension of Alexei
Zamolodchikov's conjecture about Mathieu equation.
