“…2 l S(Q, N l )E 3,l (τ ; f /2, 4N, χ) +(2N l ) −f /2 S(Q, 2N l )E 4,l (τ ; f /2, 4N, χ)if φ is the principal character mod 4, where E 1 (τ ; f /2, 4N, χ) and E r,l (τ ; f /2, 4N, χ) (r = 2, 3, 4) are defined in[4]. Then ϑ(τ, Q(X)) − E(τ, Q(X)) ∈ S f /2 ( Γ 0 (4N ), χ).…”