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It turns out that the function arg behaves differently than abs: it is expecting a symbolic expression, not a function: arg(F(S)) is possible, not arg(F). On the contrary, for abs (and many other functions), booth are possible and lead to the same result:

sage: bool(abs(F)(S) == abs(F(S)))
True

So to solve your issue, it suffices to write

P2 = plot_semilogx(arg(F(S)), xmin=0.1, xmax=100.0, ymax=0, ymin=-90)

To keep consistent notations, you can rewrite P1 as well, although this is not necessary in that case:

P1 = plot_loglog(abs(F(S)), xmin=0.1, xmax=100.0, ymin=0.1)