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\begin{align*}
& 0.5^{-5}J_{-5}(2.0) = -0.225 \Rightarrow -0.160 \quad \textrm{(normalized to match fft)} \\
& 0.5^{-4}J_{-4}(2.0) = 0.544 \Rightarrow 0.385 \\
& 0.5^{-3}J_{-3}(2.0) = -1.031 \Rightarrow -0.730 \\
& 0.5^{-2}J_{-2}(2.0) = 1.411 \Rightarrow 1.0 \\
& 0.5^{-1}J_{-1}(2.0) = -1.153 \Rightarrow -0.817 \\
& 0.5^{0}J_{0}(2.0) = 0.224 \Rightarrow 0.159 \\
& 0.5^{1}J_{1}(2.0) = 0.288 \Rightarrow 0.204 \\
& 0.5^{2}J_{2}(2.0) = 0.088 \Rightarrow 0.062 \\
\end{a