As explained in https://tex.stackexchange.com/a/229705/, the four hexadecimal digits specify the mathematical type of the symbol, the math font family and the slot in the font.
There is no “list of mathchars”. The LaTeX kernel sets up font families 0, 1, 2 and 3, which are mandatory in order that math can be typeset. However, font packages can change the assignments, adding new families or symbols, or even changing slots.
For instance, the LaTeX kernel defines
In both cases,
symbols refers to math family 2, and the result is that
\parallel in the LaTeX kernel is essentially equivalent to
\mathchar"326B, but with
fourier it becomes
stmaryrd package provides additional symbols, for instance
and we can't even translate this directly into
\mathchar syntax, because what font family number is assigned to
stmry is not known in advance, depending on several different factors. This will be equivalent to
<stmry> is some integer from 4 to 15 (translated into a hexadecimal digit).