[C++] Riemann zeta function (first real C++ program)

#include <iostream>
#include <math.h>
#include <bits/stdc++.h>

double reZeta (double s, double t = 0, int lim = 1000) {
    double re; int i;
    for (i = 1; i <= lim; i++) {
        re += pow(i,-s)*cos(t*log(i));
    }
    re += ((s-1)*cos(t*log(lim))+(-t)*sin(t*log(lim)))*pow(lim,1-s)/((1-s)*(1-s)+t*t);
    return re;
}

double imZeta (double s, double t = 0, int lim = 1000) {
    double im; int i;
    for (i = 1; i <= lim; i++) {
        im -= pow(i,-s)*sin(t*log(i));
    }
    im += ((-t)*cos(t*log(lim))-(s-1)*sin(t*log(lim)))*pow(lim,1-s)/((1-s)*(1-s)+t*t);
    return im;
}

int main () {
    double s; double t;
    std::cout << "ζ(z)" << std::endl;
    while (s != 1 or t != 0) {
        std::cout << "Input consecutively the real and imaginary parts" << std::endl;
        std::cin >> s >> t;
        if (s == 1 and t == 0) {
            break;
        }
        std::cout << "ζ(" << s << "+" << t << "i" << ") ≈ " << reZeta(s,t) << "+" << imZeta(s,t) << "i" << std::endl;
    }
    return 0;
}