Fill points using interpolating closet two points

I have following USD LIBOR rates for key maturities and want to fill LIBOR rates for all dates from day 1 to 360 days by interpolating available rates. Appreciate very much for help.

USD Days (x) Rate (y)
*USD LIBOR - overnight 1 0.39340*%
*USD LIBOR - 1 week 7 0.42095*%
*USD LIBOR - 2 weeks 14 -
*USD LIBOR - 1 month 30 0.44930*%
*USD LIBOR - 2 months 60 0.52440*%
*USD LIBOR - 3 months 90 0.62360*%
*USD LIBOR - 4 months 120 -
*USD LIBOR - 5 months 150 -
*USD LIBOR - 6 months 180 0.89410*%
*USD LIBOR - 7 months 210 -
*USD LIBOR - 8 months 240 -
*USD LIBOR - 9 months 270 -
*USD LIBOR - 10 months 300 -
*USD LIBOR - 11 months 330 -
*USD LIBOR - 12 months 360 1.20520*%

New table should be as follows.
Days(x) Rate (y)
1 0.39340*%
2 ?
3 ?
. ?
. ?
. ?
360 1.20520*%

Formula should be worked for negative rates since LIBOR EUR is currently negative.