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 (1.82500,4.48000) {$n!b_n(r)$ for $n=3$};
3 \draw[fill=black!12,draw=black!40,line width=.35pt] (0.40000,3.05000) rectangle ++(0.95000,0.95000);
4 \node[] at (0.87500,3.52500) {$\frac{r}{2}$};
5 \draw[fill=black!12,draw=black!40,line width=.35pt] (1.35000,3.05000) rectangle ++(0.95000,0.95000);
6 \node[] at (1.82500,3.52500) {$-1$};
7 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.30000,3.05000) rectangle ++(0.95000,0.95000);
8 \node[] at (2.77500,3.52500) {$0$};
9 \draw[fill=black!12,draw=black!40,line width=.35pt] (0.40000,2.10000) rectangle ++(0.95000,0.95000);
10 \node[] at (0.87500,2.57500) {$\frac{r}{6}$};
11 \draw[fill=black!12,draw=black!40,line width=.35pt] (1.35000,2.10000) rectangle ++(0.95000,0.95000);
12 \node[] at (1.82500,2.57500) {$\frac{r}{2}$};
13 \draw[fill=black!12,draw=black!40,line width=.35pt] (2.30000,2.10000) rectangle ++(0.95000,0.95000);
14 \node[] at (2.77500,2.57500) {$-2$};
15 \draw[fill=black!12,draw=black!40,line width=.35pt] (0.40000,1.15000) rectangle ++(0.95000,0.95000);
16 \node[] at (0.87500,1.62500) {$\frac{r}{15}$};
17 \draw[fill=black!12,draw=black!40,line width=.35pt] (1.35000,1.15000) rectangle ++(0.95000,0.95000);
18 \node[] at (1.82500,1.62500) {$\frac{r}{6}$};
19 \draw[fill=black!12,draw=black!40,line width=.35pt] (2.30000,1.15000) rectangle ++(0.95000,0.95000);
20 \node[] at (2.77500,1.62500) {$\frac{r}{2}$};
21 \node[] at (2.00000,0.25000) {$\det /6=P_{2,3}(r)/720$};
22 \draw[fill=black!16,draw=black!40,line width=.35pt] (5.40000,1.00000) rectangle ++(1.05000,2.44000);
23 \node[] at (5.92500,2.22000) {61};
24 \node[] at (5.92500,0.55000) {$q=0$};
25 \draw[fill=black!16,draw=black!40,line width=.35pt] (7.05000,1.00000) rectangle ++(1.05000,3.00000);
26 \node[] at (7.57500,2.50000) {75};
27 \node[] at (7.57500,0.55000) {$q=1$};
28 \draw[fill=black!16,draw=black!40,line width=.35pt] (8.70000,1.00000) rectangle ++(1.05000,3.00000);
29 \node[] at (9.22500,2.50000) {75};
30 \node[] at (9.22500,0.55000) {$q=2$};
31 \draw[fill=black!16,draw=black!40,line width=.35pt] (10.35000,1.00000) rectangle ++(1.05000,2.44000);
32 \node[] at (10.87500,2.22000) {61};
33 \node[] at (10.87500,0.55000) {$q=3$};
34 \node[] at (8.40000,4.60000) {$P_{2,3}(2)=61+75+75+61=272$};
35 \node[] at (8.40000,-0.15000) {block weights: $1,15,15,1$};
36 \end{tikzpicture}

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