frequency analysis: number of fft coefficients effect the maximum value of the power spectrum?

Hi!

I wonder how to interpret the data after applying a Short Time FFT (fftw3 
for real data) on audio samples (sinus tone 1400Hz).

My goal is to visualize the Energy in the frequency bands.

First, I do a 512 point FFT on the whole audio file (frame shift without 
overlap) and the highest value after computing

[1] re*re + imag * imag

is about 9997 in a fft bin.

Second, I do a 1024 point FFT and now the highest value after computing [1] 
is '228802'.

Why there is such a difference?
I mean, my 16Bit audio file is a sinus tone at 1400Hz, normalized to 100%, 
means minimum sample value is -32768, maximum 32767.

I think, the highest value of energy does not depend on the fft size I use 
to find this value?
Frequency analysis in CoolEdit show that the highest peak (0dB) of my sinus 
tone is at 1400Hz. The more FFT coefficients I use, the more spiky it is. 
But there is still a maximum of 0dB every time. And this maximum could be 
found at 1400Hz.

So, do I have to apply a certain normalization after computing [1]?

I want to map the results of [1] to a color map for displaying the 
spectrogram. But how to map it proper when the highest value differs with 
the number of fft-coefficients.

Thanks in advance, Michael