Let K be the Gaussian rational field and E an elliptic curve over K with j=1728. Let E(q) be the twist of E by q, where q is a product of distinct primary primes of degree two in K, i.e., the negation of rational primes congruent to 3 modulo 4. Let w(q) be the root number of the Hecke character attached to E(q). Let w_2(q) be the local root number of w(q) at the prime above 2. We will show that the limit of the average of a sequence w(q)/w_2(q) with |q|<X , as X tends to infinity is 0. This is a joint work with Taekyung Kim and Keunyoung Jeong.