Also, your 480,000 (unemployment claims) is the advance figure for the seasonally adjusted intial claims for the week of Jan. 30. That means people were filing for unemployment during that week. That does not have everything to do with how many people are on unemployment insurance. More people could have been taken off unemployment than those who are now claiming for the first time.
Also, the insured unemployment rate is only a part of the total unemployment rate. This is because not everyone who is unemployed gets unemployment, or people who are unemployed may have already had their benefits expire.
Here is the official report of unemployment claims:
ETA Press Release: Unemployment Insurance Weekly Claims Report
"In the week ending Jan. 30, the advance figure for seasonally adjusted initial claims was 480,000, an increase of 8,000 from the previous week's revised figure of 472,000. The 4-week moving average was 468,750, an increase of 11,750 from the previous week's revised average of 457,000.
The advance seasonally adjusted insured unemployment rate was 3.5 percent for the week ending Jan. 23, unchanged from the prior week's unrevised rate of 3.5 percent.
The advance number for seasonally adjusted insured unemployment during the week ending Jan. 23 was 4,602,000, an increase of 2,000 from the preceding week's revised level of 4,600,000. The 4-week moving average was 4,617,500, a decrease of 51,250 from the preceding week's revised average of 4,668,750."
As you can see from this report, the initial claims went up, but the number on unemployment insurance remained relatively the same, or even decreased when compared using a 4 week average.