Problem with the output of a function I program

(This is the function that I programmed)

Zm2[Z_, nk_] := (zm2 = 0;
For[i = 0, i < Length[Z], i++, zm2 += nk[[i]] *Z[[i]]* Z[[i]];];
Return[zm2];);

(These are the input data)

z = List[82, 57, 40, 22, 41, 8];
n = List[0.1973, 0.002, 0.1068, 0.0930, 0.002, 0.5989];

(Hear I evaluate the function in the input data)

Zm2[z, n]

(This is the result)

1552.4 + List^3

I need to remove the +List^3; the value 1552.4 is correct, but I can't use the function for further calculations with the +List^3.

PLEASE IF SOMEONE CAN HELPE ME WITH THAT, THIS IS FOR MY THESIS WORK.

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First problem, subscripts start with 1 in Mathematica, not 0 like in many other languages.

One alternative

z = List[82, 57, 40, 22, 41, 8];
n = List[0.1973, 0.002, 0.1068, 0.0930, 0.002, 0.5989];
Zm2[Z_, nk_] := Sum[nk[[i]]*Z[[i]]^2, {i, 1, Length[Z]}];
Zm2[z, n]

which gives 1590.73

Or perhaps just using

Total[n*z^2]

which gives the same result, but that uses different features of Mathematica