Hair Algae in cycling tank...

[dextersmom]

Hello, I'm brand new to the site, and brand new to aquariums. Had a 10 gallon when I was in middle school but that was easily 20 years ago. My issue is I'm a little more than a week into the initial fishless cycle, and my tank seems to have a huge issue with this hairy algae...see picture below.



Did a master test and on two occasions and the levels were as follows:

8/22
pH - 7.2
NH - 3ppm
NO2 - 1ppm
NO3 - 10ppm

8/26
pH - 6.6
NH - 0
NO2 - 1ppm
NO3 - 40ppm

I've read that high nitrate levels can contribute to algae growth is this true? any advice on what I should do at this point? I'm thinking I should just leave it for now until the cycling is complete, but I could use a bit of reassurance...Thanks in advance!

Kyle