We give algorithms for the evaluation of sparse polynomials of the form \[ P = p 0 + p 1 x + p 2 x 4 + ⋯ + p N − 1 x ( N − 1 ) 2 , P=p_0 + p_1 x + p_2 x^4 + \cdots + p_{N-1} x^{(N-1)^2}, \] for various choices of coefficients p i p_i . First, we take p i = p i p_i=p^i , for some fixed p p ; in this case, we address the question of fast evaluation at a given point in the base ring, and we obtain a cost quasi-linear in N \sqrt {N} . We present experimental results that show the good behavior of this algorithm in a floating-point context, for the computation of Jacobi theta functions. Next, we consider the case of arbitrary coefficients; for this problem, we study the question of multiple evaluation: we show that one can evaluate such a polynomial at N N values in the base ring in subquadratic time.