Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[anchor=west] at (0.45000,3.65000) {$m=0$};
3 \node[] at (3.75000,3.65000) {$1.84981279919014347629$};
4 \node[] at (8.30000,3.65000) {$+3.60134\times10^{-2}$};
5 \node[] at (11.50000,3.65000) {$-5.243\times10^{-2}$};
6 \node[anchor=west] at (0.45000,2.70000) {$m=1$};
7 \node[] at (3.75000,2.70000) {$5.44123335502366335540$};
8 \node[] at (8.30000,2.70000) {$-1.64738\times10^{-4}$};
9 \node[] at (11.50000,2.70000) {$+2.471\times10^{-4}$};
10 \node[anchor=west] at (0.45000,1.75000) {$m=2$};
11 \node[] at (3.75000,1.75000) {$9.06899753487157765805$};
12 \node[] at (8.30000,1.75000) {$+7.13700\times10^{-7}$};
13 \node[] at (11.50000,1.75000) {$-1.071\times10^{-6}$};
14 \node[anchor=west] at (0.45000,0.80000) {$m=3$};
15 \node[] at (3.75000,0.80000) {$12.69659554654675729440$};
16 \node[] at (8.30000,0.80000) {$-3.09277\times10^{-9}$};
17 \node[] at (11.50000,0.80000) {$+4.639\times10^{-9}$};
18 \node[font=\sffamily\footnotesize] at (3.75000,4.50000) {certified lower endpoint};
19 \node[font=\sffamily\footnotesize] at (8.30000,4.50000) {$\tau_m-t_m$};
20 \node[font=\sffamily\footnotesize] at (11.50000,4.50000) {$\delta_m/\delta_m^{(1)}-1$};
21 \draw[black!50] (0.20000,4.10000) -- (12.90000,4.10000);
22 \node[] at (6.50000,-0.10000) {Each upper endpoint is the displayed lower endpoint plus $10^{-20}$.};
23 \node[font=\sffamily\footnotesize] at (6.50000,-0.70000) {Root intervals: exact rational certificates. Displacement columns: numerical diagnostics.};
24 \end{tikzpicture}

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