Is it true that 

$$|\zeta(\frac{1}{2}+it)|< \frac{1}{4}+t^2$$ for all $t\geq 0$, where $\zeta$ denotes the Riemann zeta function ?

It is known that the left hand-side is $O(t^{0.25})$, and on the the Lindelof Hypothesis, it is actually $O(t^\epsilon)$ for any positive $\epsilon$. But since these results are only valid for large $|t|$, thyey dont seem to answer my question.

**Note:** I have added abs value for The LHS of inequality because it is not clear if $\zeta(\frac{1}{2}+it)$ is always real number