Point-free function in Haskell

Question

How do one define this point-free?

let argmax m = (fst.(maximumBy (comparing snd)).(zip [0..])) m

which works as expected. The most logical seems to just drop the m like this:

let argmax = (fst.(maximumBy (comparing snd)).(zip [0..]))

Works to define in ghci, but calling it with argmax [1,3,4,5,6,1] gives me

<interactive>:103:9:
    No instance for (Num ())
      arising from the literal `1'
    Possible fix: add an instance declaration for (Num ())
    In the expression: 1
    In the first argument of `argmax', namely `[1, 3, 4, 5, ....]'
    In the expression: argmax [1, 3, 4, 5, ....]

I think it has to do with the types:

:t (fst.(maximumBy (comparing snd)).(zip [0..]))
:: (Enum c, Num c, Ord a) => [a] -> c

for the point version:

argmax :: (Enum c, Num c, Ord a) => [a] -> c

for the point-free version:

argmax :: [()] -> Integer

Is this a ghci spookiness or am I doing something wrong?