The watt numbers for your amps are RMS right?
Your car has a/c, so your alternator is around 65-75 amps.
You can still install that system in your car. If you use it in a reasonable way you wont have any problems.
That means..
Dont run it too long at full intensity while the car is @ idle. Obviously your lights will flash, but more importantly, you'll be putting tremandeaous stress on the alternator (each time the lights dim). Which will lead to premature failure of the alt.
Even during daily driving, dont always run the system @ full intensity.. Because, even when rolling, your alternator wont put out enough to compensate the demande of your system @ full power. Basically, it wont be able to charge the battery.
But I'D say you can get it.. Use it wisely, when the alternator decides to go, then put a better one in.. Around 150 amps should do. Then you can go nuts 24/7!
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Hope this helps.