  In this paper, we give a direct quantitative estimate of $L^1$norms of
non-harmonic trigonometric polynomials over large enough intervals. This
extends the result by Konyagin and Mc Gehee, Pigno, Smith to the settingof
trigonometric polynomials with non-integer frequencies.The result is a
quantitative extension of a result by Nazarov and also covers a resultby Hudson
and Leckband when the length of the interval goes to infinity.
