  We consider families of tridiagonal- matrices with diagonal $\beta_{k} = \mu
k$ and off-diagonal entries $\alpha_{k} = i\lambda k\sqrt{k+1}$; $1 \leq k \leq
n$, $n \in \mathbb{N}$ and $i^{2} = -1$ where $\mu \in \mathbb{C}$ and $\lambda
\in \mathbb{C}$.\\\quad In Gribov theory ([7], A reggeon diagram technique,
Soviet Phys. JETP 26 (1968), no. 2, 414-423), the parmeters $\mu$ and $\lambda$
are reals and they are important in the reggeon field theory. In this theory
$\mu$ is the intercept of Pomeron which describes the energy of dependence of
total hadronic cross sections in the currently available range of energies and
$\lambda$ is the triple coupling of Pomeron.
  The main motive of the paper is the localization of eigenvalues $z_{k,n}(\mu,
\lambda)$ of the above matrices which are the zeros of the polynomials
$P_{n+1}^{^{\mu,\lambda}}(z)$ satisfying a three-term recurrence :
  $\left\{\begin{array}[c]{l}P_{0}^{^{\mu,\lambda}}(z) = 0\\\quad\\
P_{1}^{^{\mu,\lambda}}(z) = 1\\\quad \\ \alpha_{n-1}P_{n-1}^{^{\mu,\lambda}}(z)
+ \beta_{n}P_{n}^{^{\mu,\lambda}}(z) + \alpha_{n}P_{n+1}^{^{\mu,\lambda}}(z) =
zP_{n}^{^{\mu,\lambda}}(z);\quad n\geq 1\\ \end{array} \right. $
  \quad
  \n If $\mu \in \mathbb{R}$ and $\lambda \in \mathbb{R}$ then the above
matrices are complex symmetric, in this case we show existence of
complex-valued function $\xi(z)$ of bounded variation on $\mathbb{R}$ such that
the polynomials $P_{n}^{^{\mu,\lambda}}(z)$ are orthogonal with this weight
$\xi(z)$.\\ }
