  The Seebeck coefficient (thermopower) $S$ of the cuprate superconductor
La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured across its doping phase
diagram (from $p = 0.12$ to $p = 0.25$), at various temperatures down to $T
\simeq 2$ K, in the normal state accessed by suppressing superconductivity with
a magnetic field up to $H = 37.5$ T. The magnitude of $S/T$ in the $T=0$ limit
is found to suddenly increase, by a factor $\simeq 5$, when the doping is
reduced below $p^{\star} = 0.23$, the critical doping for the onset of the
pseudogap phase. This confirms that the pseudogap phase causes a large
reduction of the carrier density $n$, consistent with a drop from $n = 1 + p$
above $p^{\star}$ to $n = p$ below $p^{\star}$, as previously inferred from
measurements of the Hall coefficient, resistivity and thermal conductivity.
When the doping is reduced below $p = 0.19$, a qualitative change is observed
whereby $S/T$ decreases as $T \to 0$, eventually to reach negative values at
$T=0$. In prior work on other cuprates, negative values of $S/T$ at $T \to 0$
were shown to result from a reconstruction of the Fermi surface caused by
charge-density-wave (CDW) order. We therefore identify $p_{\rm CDW} \simeq
0.19$ as the critical doping beyond which there is no CDW-induced Fermi surface
reconstruction. The fact that $p_{\rm CDW}$ is well separated from $p^{\star}$
reveals that there is a doping range below $p^{\star}$ where the transport
signatures of the pseudogap phase are unaffected by CDW correlations, as
previously found in YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$.
