Discrete Fourier transform giving incorrect results

I am trying to do discrete Fourier transforms in C.

Initially just the brute-force method. First I had the program open a data file (of amplitudes) and put the data into an array (just one, since I'm limiting myself to real-valued input).

But the transform looked wrong, so instead I tried to generate a simple wavefunction and check whether it transforms properly.

Here's my code, stripped of the bells and whistles:

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define M_PI 3.14159265358979323846

//the test wavefunction
double theoretical(double t)
{
    double a = sin(M_PI * t) + 2 * sin(2 * M_PI * t) + 4 * sin(4 * M_PI * t); 
    return a;
}
//-------------------------------------------------------------------------
void dftreal(double inreal[], double outreal[], double outimag[], int linecount) 
{
    int n, k;
    for (k = 0; k < linecount; k++)
    {
        double sumreal = 0;
        double sumimag = 0;

        for (n = 0; n < linecount; n++) 
        {
            double angle = 2 * M_PI * n * ( k / (double) linecount);
            sumreal +=  inreal[n] * cos(angle);
            sumimag +=  inreal[n] * sin(angle);
        }
        outreal[k] = sumreal;
        outimag[k] = sumimag;
    }
}
//=========================================================================
int main(void)
{
     int linecount = 44100;
     //creates all necessary arrays
     double inreal[linecount], outreal[linecount], outimag[linecount], p[linecount]; 

     FILE *fout = fopen("Output.txt", "w");

     for (int i = 0 ; i < linecount ; ++i)
     {
         inreal[i] = theoretical( i / (double) linecount);
     }

     //actually computes the transform
     dftreal(inreal, outreal, outimag, linecount); 

     for (int i = 0 ; i < linecount ; ++i)
     {
          p[i] = 2*(outreal[i] * outreal[i] + outimag[i] * outimag[i]);
          fprintf(fout, "%f %f \n", (i / (double) linecount), p[i]);
     }
     fclose(fout);
     printf("\nEnd of program");
     getchar();
     return 0;
}

The program compiles, completes, but instead of several sharp peaks on a power(frequency) plot, I get this: .

A single frequency or different frequencies give the exact same inverted-bathtub-curve.

I checked several sources about the DFT and I still don't know what is going wrong, there do not seem to be any glaring errors with the function:

dftreal

itself. I'd like to ask for help on what could be causing the issue. I'm using the MinGW compiler on Windows 7. Thanks!