Which has more Shannon entropy (H): a discrete Power-law distribution, or a discrete normal Gaussian distribution, and how to calculate? TY

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Which has more Shannon entropy (H): a discrete Power-law distribution, or a discrete normal Gaussian distribution, and how to calculate? TY
I've tried summing the individual probabilities $P(x_1), P(x_2), P(x_3)\ldots$then multiplying the sum by $\log_2$ of the sum.

However, the power-law shape doesn't seem to be relevant. Please, help me understand how to calculate these two distinct (discrete) distributions.

Thank you.