A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern *A <\/em>of order n <\/em>is called spectrally arbitrary if the complex matrices in the ray pattern class of A<\/em> give rise to all possible n<\/em>th degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern.<\/em> We call that a spectrally arbitrary ray pattern A <\/em>of order n <\/em>is minimally spectrally arbitrary if any nonzero entry of A<\/em> is replaced, then A <\/em>is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.<\/p>\r\n","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 156, 2019"}*