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The 360th nome is an Egyptian nome in Antarctica. Magicians are sent here for punishment. (Another such nome is the 300th nome in North Korea.)
It seems that Sarah Jacobi and a few other evil magicians were banished to the 360th nome for misusing their magic. Some magicians from here seem to be terrified of penguins, likely either due to being attacked by them, or because penguins remind them of Antarctica.