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I hope you enjoy it around here
You can turn the modem off at the mains whenever you do not wish to use it and can unplug the jack from your PC's network card however there is no real point in disconnecting the leads.
When you switch the power back on the modem, wait for it to do its test before switching on your PC.
Once the RDY light and SYNC light are still, you can turn on your computer.
Some people turn the modem off every night, others leave it on. Its u to you really.