Here is your list with the actual numbers of troops contributed from each state:
Tennessee: 31,092
Kansas: 20,149
District of Columbia: 12,284
Delaware: 12,284
Dakota: 206
Colorado: 4,903
California: 15,725
Maryland: 46,638
Minnesota: 24,020
Nebraska: 3,157
Nevada: 1,080
New Hampshire: 33,937
New Mexico: 6,561
Oregon: 1,810
Rhode Island: 23,236
Vermont: 33,288
West Virginia: 32,068
Washington Territory: 964
Source: Dyer’s Compendium
Another factor that should be taken into account is the geographical size of the states compared to Tennessee (which could probably hold the District of Columbia, Delaware, Rhode Island and Vermont within its boundaries). Geographical size will also influence the size of the pool of available manpower within each state.
The following list shows the 1860 Census of Population data:
Tennessee 834,082
Kansas: 107,204
District of Columbia: 71,895
Delaware: 110,418
Dakota: 4,837
Colorado: 34,277
California: 379,994
Maryland: 599,860
Minnesota: 172,023
Nebraska: 28,826
Nevada: 6,857
New Hampshire: 326,073
New Mexico: 95,516
Oregon: 52,465
Rhode Island: 174,620
Vermont: 315,098
West Virginia: Not a state in 1860
Washington Territory: 11,594
Note: These are total population figures, not just adult males.
Source: U. S. Bureau of the Census, 1860 Decennial Census of Population