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For the finite field $\mathbb{F}_7$, find an additive Fourier transform of nontrivial multiplicative characters.

If the field contains $q$ elements, there are $q-2$ nontrivial values.

Where do I even start?

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    Are you trying to define the Fourier transform for $\mathbb{F}_7$, or are you trying to trying to find the Fourier transform of a multiplicative character on $\mathbb{F}_7^*$? My guess is the latter based on the fact that there are $q-2$ nontrivial multiplicative characters on $\mathbb{F}_q$.2011-04-22
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    I would edit it if I could, but technically the term "multiplicative character on $\mathbb{F}_7^*$" is redundant. It should read either multiplicative character of $\mathbb{F}_7$ or character of $\mathbb{F}_7^*$.2011-04-22

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