We consider the simultaneous solution of large linear systems of the form AX=B, where A is complex symmetric and B is a set of RHS vectors. We present a new CG-type iterative method, CCG, which is based on a

tridiagonalization of A by a unitary matrix. Moreover, we combine CCG and its minimum residual variant CSYM with the single-seed technique to solve linear systems with multiple right-hand sides; we solve the seed system using CCG or CSYM and approximate solutions to the non-seed systems are obtained by Galerkin projection. We demonstrate the effectiveness of the proposed method by solving an electromagnetic application.