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			The symptoms are: 1) car throws codes P0410 and P1411 as soon as the secondary air monitoring system kicks back in after a CEL reset, 2) engine hunts for idle between 600 and 1000 rpm after coming up to operating temperature, and 3) remote key operates unpredictably.
 all ties together as engine intake/exhaust/cat/O2 but the unpredictable remote key does not.
 
 but if you assume the electrical to be the root cause, remote key also ties in.
 I would check the battery.  volt meter in DC and AC.
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