  Using extensive computer simulations, the behavior of the structural modes
--- more precisely, the eigenmodes of a phantom Rouse polymer --- are
characterized for a polymer in the three-dimensional repton model, and are used
to study the polymer's dynamics at time scales well before the tube renewal.
Although these modes are not the eigenmodes for a polymer in the repton model,
we show that numerically the modes maintain a high degree of statistical
independence. The correlations in the mode amplitudes decay exponentially with
$(p/N)^2A(t)$, in which $p$ is the mode number, $N$ is the polymer length and
$A(t)$ is a single function shared by all modes. In time, the quantity $A(t)$
causes an exponential decay for the mode amplitude correlation functions for
times $<1$; a stretched exponential with an exponent 1/2 between times 1 and
$\tau_R\sim N^2$, the time-scale for diffusion of tagged reptons along the
contour of the polymer; and again an exponential decay for times $t>\tau_R$.
Having assumed statistical independence and the validity of a single function
$A(t)$ for all modes, we compute the temporal behavior of three structural
quantities: the vectorial distance between the positions of the middle monomer
and the center-of-mass, the end-to-end vector, and the vector connecting two
nearby reptons around the middle of the polymer. Furthermore, we study the
mean-squared displacement of the center-of-mass and the middle repton, and
their relation with the temporal behavior of the modes.
