Those that have most luck with modified sine inverters are those who don't know about the limitations. If you have faith most things work ( at least up to a point).
I don't have the courage to try anything I suspect may be a problem so I can only comment on what I see others get away with. TV and radio almost always work. Laptop and drill chargers are a gamble, the simplest chargers work, the complex ones often don't, they die or shut the inverter down. Probably the same with a modem, most will be ok, the odd one may not.
Power tools all work except those with variable speed, the thyristor controllers just can't handle it.
Fortunately most things are now cheap enough to take a risk, quite often even things that don't work survive but that is not always the case.
Wait to get other peoples opinion but I suspect a modem will be ok
Flux