A laptop is not going to be drawing anywhere close to 400 watts.  It's not
the maximum capacity of the inverter that matters, its how much power you
are pulling through it.

The laptop should have a label showing how much power it draws, for example,
4.5 amps at 19.5 volts.  Multiply amps times volts to get watts needed to
power the laptop.

Then, look at the fuse for the vehicle power socket and multiply the fuse
rating, i.e., 20 amps, times 12 volts to get how many watts the power socket
can supply.

If the socket can supply 240 watts and the laptop draws 100, then you're
fine.

You may want to check out I-go power supplies for laptops.  They are
available with multiple connections so the same power supply can draw from
120 volt or 12 volts.

 The alternator should be able to handle another 400 Watts during the
day with no problem, because your headlights are off.  You could end
up in a bit of a power deficit if you are in stop and go driving at
night, with the lights on and a lot of idling - the alternator doesn't
give full output unless the engine is above 1800 - 2200 RPM.

 Where your problem will hit first is at the cigarette lighter socket
- don't use it.  Lighter sockets are usually supplied with small wire
and fused rather small, around 10 to 15 amps (140W to 210W), and that
400-watt inverter can easily draw more than that at full load.  And
lighter sockets have a thermal fuse inside, if you draw full power for
too long you'll pop it.  And the thermal fuse is not serviceable, you
have to replace the whole socket.

 If you have an "Accessory Power" socket in your car, great - if not,
go get the kit at an auto parts store (socket, dashboard bracket,
heavy wire, fuseholder and fuse, crimp terminals) and install one.
They are usually designed for 25 amp (350W) or 30A (420W) loads, and
they are fused, but it's a regular fuse where you can get to it.

 Okay, you've installed an accessory power socket.  Now that you've
gone through all that - you still aren't using the right power supply
device.  ;-)

 You have a lot of inefficiency when you turn 13.8V DC into 120V AC
(one conversion loss) then the laptop power supply converts the 120V
AC to 14 to 18V DC (second conversion loss).  Each conversion can lose
10% to 40% of the incoming power to heat and/or transformer losses
when going to AC, so that second conversion really hurts...

 Go get a dedicated laptop converter from Targus, Kensington, Go
Power, or the like.  Make one conversion directly from the
alternator's 13.8V DC to the laptop's filtered 14~18V DC.

 You still need the Accessory Power socket, you'll just cut the load
on it by an amp or two.  And on a car, every single amp counts.

   --<< Bruce >>--