Index of frequency larger than power spectrum length
Any Discrete-Time Fourier Transform (with constant sampling frequency) will only give information about the signal up to a frequency of

$$f = \frac{f_s}{2} = f_N$$

\$f_N\$ is called the Nyquist frequency. Frequencies in the signal higher than \$f_N\$ are subject to aliasing (related to the Nyquist-Shannon sampling theorem).

So if you want to find information about a certain frequency \$f_x\$, you will need at least a sampling frequency of \$f_s &gt; 2\cdot f_x\$ and extra to accommodate for an anti-alias filter.

Increasing the number of points will only increase the resolution, without changing the Nyquist frequency.