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given the values for \$\beta=5\$, for the Bessel of the first order:

\$ J_{0}(5)=-0.26, J_{1}(5)=0.34, J_{2}(5)=0.49...\$

in order to plot the amplitude spectrum of the FM wave, do you treat the negative numbers as absolute? The \$ J_{0}(5)\$ amplitude should be \$ |J_{0}(5)|\$ ?

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If a frequency component has negative amplitude, it means 180 degrees phase shift for that component. If you only compare component strengths, it's ok to use absolute values.

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