Surely there could be multiply charged ions due to the fact that it was Electrospray Ionisation? If so, the m/z could only be a fraction of the real Molecular Mass. (Not that i'm saying that this is the case here, it doesn't look like it to me, i'm still a little bemused as to how you get a mass of 360 and only 3 1H environments.)
No, electrospray is a soft ionisation technique and often the opposite is observed - only the molecular ion and no fragmentation.
If the molecular ion is 360 that should tell you that the molecule has either no nitrogen atoms, or an even number (otherwise the molecular weight would be an odd number). You also have a peak at 316 - a loss of 44 from the molecular ion - which could indicate loss of CO2. Decarboxylation like that often indicates a carboxylic acid - this fits with the carbonyl peak in the IR.
Now because you have only a few proton environments you may have a highly saturated system and probably a symmetrical system - e.g. a couple of magnetically equivalent ethyl ester functions. Even so, 360 is quite a high molecular weight so I'd be guessing you could have some heavy atom in there (iodine, 127 perhaps?). You need a bit more info on the compound yet - a carbon spectrum and maybe some chemical tests.
I know that electrospray is a soft ionisation technique, it can still produce multiple charges on one ion with multiple charge sites, that's what i was saying, not that it would cause fragmentation.
Iodine sounds like a good idea, you've got a loss of 127 from 332 to 205 and a peak around 500 cm
-1 in the IR.
Not sure about Carboxylic Acid, wouldn't you expect a peak at high shift in the
1H spectrum and the peak at ~1100 cm
-1 in the IR which could be C-O is too low for a carboxylic acid, more likely to be from a secondary or tertiary alcohol or be a C-N instead.
The IR also supports primary amides with the two peaks near ~3333cm
-1 for N-H stretching, the peak at ~1690cm
-1 for C=O stretch and the peak at ~1600 for N-H bending (although on second thoughts, maybe this is a little strong for a bend and i'm just getting hung up on an idea).