The Warlock's Will

Question

Your master, the great Warlock William the Wide, has recently passed away. In his will, he left you a crystal box with a grid of squares and names on top and a note:

The note reads:

You are certainly a gifted student, but are you my most gifted? This box lists some of the most talented students of mine over the past few millennia, but it's also missing several. Can you find what the others are supposed to be? This box, which contains all of my greatest magical artifacts, will only open if you fill in the rest of the names. If you do open the box, its contents are yours!

Best of luck,
William the Wide

Can you figure out what the missing names are?

Mathjax Version
$$\begin{array}{|c|c|c|c|c|} \hline Anicetus & & Chambliss & Louis\ I & \\ \hline & & Blefary & Frederick\ I & Jefferson \\ \hline Clement\ I & Eadwig & & & \\ \hline Stephen\ I & & Kuenn & & \\ \hline & Henry\ II & & Lambert\ I & Buchanan \\ \hline \end{array} $$

Markdown Table Version (suitable for copy-paste)

Anicetus		Chambliss	Louis I
		Blefary	Frederick I	Jefferson
Clement I	Eadwig
Stephen I		Kuenn
	Henry II		Lambert I	Buchanan

Answer 1

Each column of the grid ...

... hold a certain category of mostly historical persons: The names in the last column are obviously those of U.S. presidents. In the first column are early popes. The second column has kings of England. Gareth has found that the persons in the forth column hold Holy Roman Emperors. The people in the middle column are winners of the Major League Baseball Rookie of the Year Award. (Don't look like that – I was surprised, too.)

But what are the missing names? Note that ...

... the popes, English kings and U.S. presidents are fronm a relatively early era. If you follow the links above, you will note that they all lead to lists on Wikipedia. The presidents and the popes are even helpfully numbered.

Clement I was the fourth pope, Anicetus was the 11th and Stephen I was the 23rd. Likewise Jefferson was the 3rd president and Buchanan was the 15th president of the United states. Numbering the other categories, too, and putting those numbers in the grid, we get:

             11   .  25   2   .
              .   .  19  21   3
              4   6   .   .   .
             23   .   7   .   .
              .  24   .   8  15

This looks like ...

... a 5×5 magic square. When hunting for a solver, I came across this site, which has the square we ant upside down somewhere in the middle of the page:

             11  18  25   2   9
             10  12  19  21   3
              4   6  13  20  22
             23   5   7  14  16
             17  24   1   8  15

The warlock's best students were:

    Pope          Edgar the     Chris         Louis I       William H.
    Anicetus      Ætheling      Chambliss     the Pious     Harrison

    Pope          Edmund        Curt          Frederick I   Thomas
    Pius I        Ironside      Blefary       Barbarossa    Jefferson

    Pope          Eadwig        Bob           Lothair II    Grover
    Clement I                   Allison                     Cleveland

    Pope          Edmund I      Harvey        Otto III      Abraham
    Stephen I                   Kuenn                       Lincoln

    Pope          Henry II      Jackie        Lambert I     James
    Urban I                     Robinson                    Buchanan