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$Version (* "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)" *) Clear["Global`*"] Plot[{Re[DirichletL[5, 3, 1/2 + I t]], Im[DirichletL[5, 3, 1/2 + I t]]}, {t, 0, 20}, PlotLegends -> "Expressions"] Use FindRoot with starting values near the zero crossings from the Plot. Use Chop to remove the imaginary artifacts. Chop[...


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