Why would someone use an amplitude modulation ratio lower than one in a power inverter?
4160VRMS is big and I would have thought a transformer would have been used to step up the voltage from a lower voltage DC powered 3 ph inverter but, assuming this is not the case you have to ask if the voltage requirement is line-voltage or phase-voltage. The question is not clear on this so I'm going to play safe and assume it means line voltage.

This means the phase voltage will be \$\sqrt3\$ lower at 2402VRMS. At this stage I will point out that if the zero in the question making 416V into 4160V is wrong then it should be easy to figure out the answer.

2402V RMS is a p-p voltage of 6792 volts and this will need to be the DC supply to the semiconductors. Simple as that. If you need 5% variation then raise the dc voltage by 5%. If you want to accomodate volt drop in the transistors then add another couple of volts.

So, just to be clear, to attain the output asked in the question I reckon a DC supply voltage of over 7132 volts is required. I don't know how much the output transistors will drop when hard-conducting but asssuming it's an IGBT maybe also add 3 more volts to the DC supply rail to be surer. 7135 volts DC.