Did you look at a table of the Normal distribution?
Here's one online:
Public Domain Normal Distribution Table
If you look up 0.975 (so being outside of that, either above or below, is less than 0.05 or 5%) in the body of the table you will see that it corresponds to a z of 1.96.
For a (double ended) significance of 1% you would look up 0.995 in the body of the table and see what z that corresponds to. If find both 0.9949 and 0.9951 in the table with z values of 2.57 and 2.58 respectively. Since 0.995 is between those, I would say that corresponds to a z value of 2.575.