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[] at (2.22500,4.10000) {$1$};
3 \node[] at (4.47500,4.10000) {$\xi$};
4 \node[] at (6.72500,4.10000) {$\xi^2$};
5 \node[anchor=east] at (0.85000,3.34000) {$1$};
6 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,2.93000) rectangle ++(2.25000,0.82000);
7 \node[] at (2.22500,3.34000) {$1$};
8 \draw[fill=black!0,draw=black!40,line width=.35pt] (3.35000,2.93000) rectangle ++(2.25000,0.82000);
9 \node[] at (4.47500,3.34000) {$\xi$};
10 \draw[fill=black!0,draw=black!40,line width=.35pt] (5.60000,2.93000) rectangle ++(2.25000,0.82000);
11 \node[] at (6.72500,3.34000) {$\xi^2$};
12 \node[anchor=east] at (0.85000,2.52000) {$\xi$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,2.11000) rectangle ++(2.25000,0.82000);
14 \node[] at (2.22500,2.52000) {$\xi$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt] (3.35000,2.11000) rectangle ++(2.25000,0.82000);
16 \node[] at (4.47500,2.52000) {$\xi^2$};
17 \draw[fill=black!20,draw=black!40,line width=.35pt] (5.60000,2.11000) rectangle ++(2.25000,0.82000);
18 \node[] at (6.72500,2.52000) {$-1$};
19 \node[anchor=east] at (0.85000,1.70000) {$\xi^2$};
20 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,1.29000) rectangle ++(2.25000,0.82000);
21 \node[] at (2.22500,1.70000) {$\xi^2$};
22 \draw[fill=black!20,draw=black!40,line width=.35pt] (3.35000,1.29000) rectangle ++(2.25000,0.82000);
23 \node[] at (4.47500,1.70000) {$-1$};
24 \draw[fill=black!20,draw=black!40,line width=.35pt] (5.60000,1.29000) rectangle ++(2.25000,0.82000);
25 \node[] at (6.72500,1.70000) {$-\xi$};
26 \node[] at (10.25000,3.20000) {$\xi^3=-1$};
27 \node[] at (10.25000,2.10000) {wrap once: change sign};
28 \node[] at (10.25000,1.00000) {$\xi^2\xi^2=-\xi$};
29 \node[font=\sffamily\footnotesize] at (6.30000,0.15000) {$D_{3,0}(z+w)=D_{3,0}(z)D_{3,0}(w)-D_{3,1}(z)D_{3,2}(w)-D_{3,2}(z)D_{3,1}(w)$};
30 \end{tikzpicture}

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