Flutter onset characteristic is an important consideration for transport aircraft design. Previous work with high fidelity aerostructural optimization has shown a tendency for optimization algorithms to produce unrealistically high aspect ratio designs, particularly when maximizing range or minimizing fuel burn, in an effort to maximize aerodynamic efficiency. In this work, we propose an efficient high fidelity flutter solution method. The flow and the structural dynamics have been modeled with time-spectral (TS) method. The TS method is designed to capture the dominant modes of periodic behaviors efficiently. We develop a coupled Newton-Krylov solver to solve this motion-fluid-structure coupled problem. In the literature, Newton-based TS flutter methods have been proposed in a segregated form. In the current work, the whole coupled system is directly solved. By doing so, one motion-fluid-structure solution is required instead of O(N CSD) × O(N iter) CFD solutions where N CSD is the structural degree-of-freedom for all time instances and N iter is the number of Newton steps. We demonstrate the method on the classic AGARD 445.6 case.