#include <cstdlib>
#include <iostream>
#include <NTL/ZZ.h>
#include <NTL/RR.h>
#include <fstream>
NTL_CLIENT
using namespace std;

RR sinh(RR x)
{
   return (exp(x)-exp(-x))/to_RR(2);
}

RR cosh(RR x)
{
   return (exp(x)+exp(-x))/to_RR(2);
}

int Int(RR x)
{
    return to_long(RoundToZZ(x));
}


int main(int argc, char *argv[])
{
    double n =1000000;
    int bin_digits= (int) (50+3.1416*sqrt(2*n/3)/log(2));
    RR::SetPrecision(bin_digits);
 
    
    RR _PI = ComputePi_RR();
    
    
    RR a, b, c, x, d,h,k,r;
    for (k = 1; k*k <= n; ++k) {
        a = sqrt(k)*pow(to_RR(n)-to_RR(1)/to_RR(24),to_RR(-3/2.));
        b= sqrt(to_RR(2)/to_RR(3)*_PI*_PI/k/k*(to_RR(n)-to_RR(1)/to_RR(24))    );
        b = b * cosh(b) - sinh(b);
        for (c = 0, h = 1; h <= k; ++h)
            if (GCD(Int(h), Int(k))==1) {
                for (d = 0, r = 1; r <= k-1; ++r)
                    d += r/k*(h*r/k - floor(h*r/k) - 1/2.);
                c += cos(_PI*(d - to_RR(2.*h*n/k)));
            }
        x += a * b * c;
        cout << k << endl;
    }
    cout << round(x/_PI/sqrt(to_RR(8))) << endl;
    
   ofstream out("result1e6.txt");
   out << round(x/_PI/sqrt(to_RR(8))) << endl;
   
    
    system("PAUSE");
    return EXIT_SUCCESS;
}