i had a 250 watt amp running w/ a AEM pulley, only time lights would dim would be at idle, the rest of the time it was good.
Just make sure you don't crank your 1000 watt system up for a long long time at idle, or else you might run the battery down ... that is all.
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2008 WRX Hatch with a couple mods
2010 Tundra DC 5.7L with more mods
2004 S2000 with even more mods
2002 RSX-S with the most mods