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I'd like to add a \rule in front of each first row after each break to further separate it from the \hline. I can hardcode it in the very first row but the breaks are dynamic so that's not possible there.

The table is in a twocolumn environment.

I tried to add the rule to the end of \tablehead but this gives me a misplaced \noalign:

\tablehead{\rule{0pt}{13pt}Name~~~~~~~~~~~~~~~~~~~~~~~ & Value\\\hline\rule{0pt}{13pt}}

Here's a MWE:

%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 unicode

\documentclass[a4paper, 12pt]{article}

\usepackage{supertabular}
\usepackage{lipsum}

\setlength\columnsep{40pt}
\setlength\columnseprule{0.1mm}

\begin{document}

\twocolumn[
    \section{Section}
    {\lipsum*[2]}
    \bigskip
]

\tablefirsthead{\rule{0pt}{13pt}Name~~~~~~~~~~~~~~~~~~~~~~~ & Value\\\hline}
\tablehead{\rule{0pt}{13pt}Name~~~~~~~~~~~~~~~~~~~~~~~ & Value\\\hline}
\tablelasttail{\hline}

\begin{supertabular}{lr}
\rule{0pt}{13pt}First & 1\\ Second & 2\\ Third & 3\\ Forth & 4\\ Fifth & 5\\
Sixth & 6\\ Seventh & 7\\ Eighth & 8\\ Ninth & 9\\ Tenth & 10\\
Eleventh & 11\\ Twelfth & 12\\ Thirteenth & 13\\ Fourteenth & 14\\ Fifteenth & 15\\
Sixteenth & 16\\ Seventeenth & 17\\ Eighteenth & 18\\ Nineteenth & 19\\ Twentieth & 20\\
Twenty-first & 21\\ Twenty-second & 22\\ Twenty-third & 23\\ Twenty-fourth & 24\\ Twenty-fifth & 25\\
Twenty-sixth & 26\\ Twenty-seventh & 27\\ Twenty-eighth & 28\\ Twenty-ninth & 29\\ Thirtieth & 30\\
Thirty-first & 31\\ Thirty-second & 32\\ Thirty-third & 33\\ Thirty-fourth & 34\\ Thirty-fifth & 35\\
Thirty-sixth & 36\\ Thirty-seventh & 37\\ Thirty-eighth & 38\\ Thirty-ninth & 39\\ Fortieth & 40\\
Forty-first & 41\\ Forty-second & 42\\ Forty-third & 43\\ Forty-fourth & 44\\ Forty-fifth & 45\\
Forty-sixth & 46\\ Forty-seventh & 47\\ Forty-eighth & 48\\ Forty-ninth & 49\\ Fiftieth & 50\\
Fifty-first & 51\\ Fifty-second & 52\\ Fifty-third & 53\\ Fifty-fourth & 54\\ Fifty-fifth & 55\\
Fifty-sixth & 56\\ Fifty-seventh & 57\\ Fifty-eighth & 58\\ Fifty-ninth & 59\\ Sixtieth & 60\\
\end{supertabular}

\end{document}

The problem is visible on the Twenty-sixth and Fifty-second element here: enter image description here

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This can be done by replacing \rule{0pt}{13pt} on each first line with \noalign{\vskip 3pt} after the head definitions:

%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 unicode

\documentclass[a4paper, 12pt]{article}

\usepackage{supertabular}
\usepackage{lipsum}

\setlength\columnsep{40pt}
\setlength\columnseprule{0.1mm}

\begin{document}

\twocolumn[
    \section{Section}
    {\lipsum*[2]}
    \bigskip
]

\tablefirsthead{\rule{0pt}{13pt}Name~~~~~~~~~~~~~~~~~~~~~~~ & Value\\\hline\noalign{\vskip 3pt}}
\tablehead{\rule{0pt}{13pt}Name~~~~~~~~~~~~~~~~~~~~~~~ & Value\\\hline\noalign{\vskip 3pt}}
\tablelasttail{\hline}

\begin{supertabular}{lr}
First & 1\\ Second & 2\\ Third & 3\\ Forth & 4\\ Fifth & 5\\
Sixth & 6\\ Seventh & 7\\ Eighth & 8\\ Ninth & 9\\ Tenth & 10\\
Eleventh & 11\\ Twelfth & 12\\ Thirteenth & 13\\ Fourteenth & 14\\ Fifteenth & 15\\
Sixteenth & 16\\ Seventeenth & 17\\ Eighteenth & 18\\ Nineteenth & 19\\ Twentieth & 20\\
Twenty-first & 21\\ Twenty-second & 22\\ Twenty-third & 23\\ Twenty-fourth & 24\\ Twenty-fifth & 25\\
Twenty-sixth & 26\\ Twenty-seventh & 27\\ Twenty-eighth & 28\\ Twenty-ninth & 29\\ Thirtieth & 30\\
Thirty-first & 31\\ Thirty-second & 32\\ Thirty-third & 33\\ Thirty-fourth & 34\\ Thirty-fifth & 35\\
Thirty-sixth & 36\\ Thirty-seventh & 37\\ Thirty-eighth & 38\\ Thirty-ninth & 39\\ Fortieth & 40\\
Forty-first & 41\\ Forty-second & 42\\ Forty-third & 43\\ Forty-fourth & 44\\ Forty-fifth & 45\\
Forty-sixth & 46\\ Forty-seventh & 47\\ Forty-eighth & 48\\ Forty-ninth & 49\\ Fiftieth & 50\\
Fifty-first & 51\\ Fifty-second & 52\\ Fifty-third & 53\\ Fifty-fourth & 54\\ Fifty-fifth & 55\\
Fifty-sixth & 56\\ Fifty-seventh & 57\\ Fifty-eighth & 58\\ Fifty-ninth & 59\\ Sixtieth & 60\\
\end{supertabular}

\end{document}

enter image description here

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