Tikz-Matrix - Nodes zur Zeilennummerierung zu Zeilenmitte zentrieren

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\documentclass[varwidth, margin=5mm]{standalone}
\usepackage[ngerman]{babel}
\usepackage{amsmath, amssymb, relsize, tikz}
\usetikzlibrary{matrix, fit, positioning}
\begin{document}
\begin{tikzpicture}[
font=\footnotesize, 
]
% Matrix
\matrix (m) [
matrix of math nodes,
inner sep=0pt, 
column sep=0.5em, row sep=0pt,
nodes={
text height=\ht\strutbox, text depth=\dp\strutbox,
inner sep=0.0em,text width=1em,align=center},
]
{%
a_1 \\ a_2 \\ a_3 \\ \vdots \\ a_4 \\
};%
% Zeilennummerierung
\tikzset{ZeilenNummer/.style={
font=\tiny,
    text height=\ht\strutbox,text depth=\dp\strutbox,
    text width=1em,align=center
}}
\node[ZeilenNummer, left = 0.5em of m-1-1]{$(1)$};
\node[ZeilenNummer, left = 0.5em of m-2-1]{$(2)$};
\node[ZeilenNummer, left = 0.5em of m-3-1]{$(3)$};
\node[ZeilenNummer, left = 0.5em of m-4-1, red]{$\vdots$};
\node[ZeilenNummer, left = 0.5em of m-5-1]{$(3)$};
\end{tikzpicture}
\end{document}
 
 
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