Now without a calculator:

1991*1993*1995*1997*1999*2001*2003*2005*2007 (only care about last 3 digits)

same as

(2000-7)(2000+7)(2000-5)(2000+5)(2000-3)(2000+3)(2000-1)(2000+1)(2000-9) mod1000

= (1000-49)(1000-25)(1000-9)(1000-1)(1000-9) mod 1000

= (-49*-25*-9*-1*-9) Mod1000

= -(49*25*81) mod1000

= -(49*25*80+49*25) mod1000

= -(49*2000+49*25) mod1000

= -(49*25) mod1000

= -(40*25+9*25) mod1000

= -(9*25) mod 1000

= -225 mod 1000

= 1000-225 mod1000

= 775 mod 1000

7+7+5 = 19