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 (1.80000,3.78000) {$J_3$};
3 \draw[fill=black!0,draw=black!40,line width=.35pt] (0.60000,2.50000) rectangle ++(0.80000,0.80000);
4 \node[] at (1.00000,2.90000) {$0$};
5 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.40000,2.50000) rectangle ++(0.80000,0.80000);
6 \node[] at (1.80000,2.90000) {$0$};
7 \draw[fill=black!12,draw=black!40,line width=.35pt] (2.20000,2.50000) rectangle ++(0.80000,0.80000);
8 \node[] at (2.60000,2.90000) {$-1$};
9 \draw[fill=black!12,draw=black!40,line width=.35pt] (0.60000,1.70000) rectangle ++(0.80000,0.80000);
10 \node[] at (1.00000,2.10000) {$1$};
11 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.40000,1.70000) rectangle ++(0.80000,0.80000);
12 \node[] at (1.80000,2.10000) {$0$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.20000,1.70000) rectangle ++(0.80000,0.80000);
14 \node[] at (2.60000,2.10000) {$0$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt] (0.60000,0.90000) rectangle ++(0.80000,0.80000);
16 \node[] at (1.00000,1.30000) {$0$};
17 \draw[fill=black!12,draw=black!40,line width=.35pt] (1.40000,0.90000) rectangle ++(0.80000,0.80000);
18 \node[] at (1.80000,1.30000) {$1$};
19 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.20000,0.90000) rectangle ++(0.80000,0.80000);
20 \node[] at (2.60000,1.30000) {$0$};
21 \node[] at (6.67500,3.78000) {$e^{zJ_3}$};
22 \draw[fill=black!12,draw=black!40,line width=.35pt] (5.10000,2.25000) rectangle ++(1.05000,1.05000);
23 \node[] at (5.62500,2.77500) {$D_{0}$};
24 \draw[fill=black!12,draw=black!40,line width=.35pt] (6.15000,2.25000) rectangle ++(1.05000,1.05000);
25 \node[] at (6.67500,2.77500) {$- D_{2}$};
26 \draw[fill=black!12,draw=black!40,line width=.35pt] (7.20000,2.25000) rectangle ++(1.05000,1.05000);
27 \node[] at (7.72500,2.77500) {$- D_{1}$};
28 \draw[fill=black!12,draw=black!40,line width=.35pt] (5.10000,1.20000) rectangle ++(1.05000,1.05000);
29 \node[] at (5.62500,1.72500) {$D_{1}$};
30 \draw[fill=black!12,draw=black!40,line width=.35pt] (6.15000,1.20000) rectangle ++(1.05000,1.05000);
31 \node[] at (6.67500,1.72500) {$D_{0}$};
32 \draw[fill=black!12,draw=black!40,line width=.35pt] (7.20000,1.20000) rectangle ++(1.05000,1.05000);
33 \node[] at (7.72500,1.72500) {$- D_{2}$};
34 \draw[fill=black!12,draw=black!40,line width=.35pt] (5.10000,0.15000) rectangle ++(1.05000,1.05000);
35 \node[] at (5.62500,0.67500) {$D_{2}$};
36 \draw[fill=black!12,draw=black!40,line width=.35pt] (6.15000,0.15000) rectangle ++(1.05000,1.05000);
37 \node[] at (6.67500,0.67500) {$D_{1}$};
38 \draw[fill=black!12,draw=black!40,line width=.35pt] (7.20000,0.15000) rectangle ++(1.05000,1.05000);
39 \node[] at (7.72500,0.67500) {$D_{0}$};
40 \node[] at (10.80000,2.90000) {$J_3^3=-I$};
41 \node[] at (10.80000,1.70000) {$\mathbf D_3(0)=e_0$};
42 \node[] at (10.80000,0.60000) {$\det e^{zJ_3}=1$};
43 \node[] at (6.10000,-0.80000) {$D_0\mapsto-D_2,\qquad D_1\mapsto D_0,\qquad D_2\mapsto D_1$};
44 \end{tikzpicture}

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