Ramachandra's lower-bound conjecture for Dirichlet polynomials

Let $N\geq 2$ be an integer and let $a_n$ be complex numbers for $2\leq n\leq N$. Ramachandra's conjecture. For each $\delta>0$, there exists an $H>0$ such that

$$\int_0^H \left|1+\sum_{n=2}^N a_n n^{it}\right|^2\,dt>\delta,$$

for all integers $N\geq 2$ and all complex numbers $a_n$. The conjecture asks for a uniform positive lower bound preventing these Dirichlet polynomials from approximating $-1$ too closely on every interval $[0,H]$; the supplied text gives no evidence of a resolution.