Continued Fraction Expansion of Fourth Power of Pi

Theorem
The continued fraction expansion of the $4$th power of $\pi$ begins:
 * $\pi^4 \approx 97 + \cfrac 1 {2 + \cfrac 1 {2 + \cfrac 1 {3 + \cfrac 1 {1 + \cfrac 1 {16 \, 539} } } } }$

The continued fraction expansion shown above evaluates to $\dfrac {2143} {22}$ or $\paren {97 \cdotp 4 \dot 0 \dot 9}$ which is $\approx 1.2 \times 10^{-7}$ lower than the exact value.