unicode-math default math fonts

I just tried to use the default math font as given by unicode-math, but somehow the symbols for sum, prod and (some) greek letters are missing when using setmathfont{latinmodern-math.otf} (as is suggested by the unicode-math package). Without explicitly setting the font it works perfectly well.

The trouble is just that I need to set fonts for some explicit characters (to be able to display them) but the remaining characters should not change (since the defaults just work well).

PS: This is some kind of a followup from Switching from LaTeX to XeLaTeX – fontspec and unicode-math defaults

What fonts are used in addition to latinmodern-math.otf in the default settings of unicode-math?

EDIT: M(not)WE

documentclass[a4paper, 12pt]{scrartcl}

% ----- Packages -----
% XeTeX
usepackage{unicode-math-xetex}
usepackage{fontspec-xetex}[Ligatures=TeX]
usepackage{xunicode} % for the inputfile encoding and unicode macros

% ----- Settings -----
KOMAoptions{
        paper=a4,           % set papersize
        fontsize=12pt,      % set fontsize to 12pt
        parskip=half,       % half a line will seperate paragraphs
}

setmainfont{lmroman10-regular.otf}
setmathfont{latinmodern-math.otf}
setmathfont{STIX2Math.otf}[range="27D5]
% setmathfont{STIX2Math.otf}[range="27D6]
% setmathfont{STIX2Math.otf}[range="27D7]
% setmathfont{STIX2Math.otf}[range="2A1D]
% setmathfont{STIX2Math.otf}[range="2A1E] % bigtriangleleft -> antijoin
% setmathfont{STIX2Math.otf}[range="22C9] % ltimes -> leftsemijoin
% setmathfont{STIX2Math.otf}[range="22CA] % rtimes -> rightsemijoin

begin{document}
[
        prod_{k=1}^{n} c cdot a_k = c^n cdot sum_{k=1}^na_k % this is not right ;)
]

$alpha leftouterjoin beta$

end{document}

Produces this:

documentclass[a4paper, 12pt]{scrartcl}

% ----- Packages -----
% XeTeX
usepackage{unicode-math}


setmainfont{lmroman10-regular.otf}
setmathfont{latinmodern-math.otf}
setmathfont{STIX2Math.otf}[range="27D5]


begin{document}

[
        prod_{k=1}^{n} c cdot a_k = c^n cdot sum_{k=1}^na_k % this is not right ;)
]
$alpha leftouterjoin beta$
end{document}