A chap seeking details for a matching inductor for his 5/8λ vertical on 20m reported “my AA54 RigExpert analyser gives the following reading (SWR 8,2). (R 81,5). (X -158) ” measured looking into a “length of rg58 about 15-20 cm” and asked “is the inductor coil going to be enough or will I need an L match to bring the real resistance to 50 ohms”.
Note that the measurements are of a particular implementation and should not be taken to imply generally to 5/8λ verticals, but the solution method can be applied more generally. Lets assume that the measurement is not affected by common mode current.
The answer to the last question first is that a series inductor will not bring the VSWR much below 3. It is a common belief that a 5/8λ vertical can be matched simply with a series inductor.
There are many ways to match the measured antenna, and there are articles on this site describing some of them, but a simple and effective method in this case is the single stub tuner.
Above is a graphical solution using Simsmith. The section of line nearest the measurement load is -ve length, it is to back out the effect of the line section into which measurements were made (antenna feed point is at the cursor, 139-j191Ω). The next line section is the series section, followed by the S/C stub. In this case the series section and stub use RG213 to reduce loss. Total matching system loss is a little under 0.3dB, and the stub can easily be weatherproofed with hot glue and heat shrink tube.
One could use RG58, an exercise for the reader is to assess the loss of that option.
Obviously the length of the measurement section plays into the solution, and using its length to the mm in the model gives a more accurate result.