Reciprocal cycles

A unit fraction contains $1$ in the numerator. The decimal representation of the unit fractions with denominators $2$ to $10$ are given:

$$ \begin{aligned} 1/2 &= 0.5\ 1/3 &= 0.(3)\ 1/4 &= 0.25\ 1/5 &= 0.2\ 1/6 &= 0.1(6)\ 1/7 &= 0.(142857)\ 1/8 &= 0.125\ 1/9 &= 0.(1)\ 1/10 &= 0.1\ \end{aligned} $$

Where $0.1(6)$ means $0.166666...$, and has a $1$-digit recurring cycle. It can be seen that $1/7$ has a $6$-digit recurring cycle.

Find the value of $d \lt 1000$ for which $1/d$ contains the longest recurring cycle in its decimal fraction part.