No, this is not true; see Table 5 in http://arxiv.org/abs/1001.2962 and conclusions. In particular , it is written that the real part is negative for the first time around $t=682112.9$ ; and this the smallest value given there (and it was found via testing at steps of size $.1$ so perhaps no much smaller ones were missed).
You might also be interested in this question's answers for related information for the critical line $1/2 + it$
No, this is not true; see Table 5 in http://arxiv.org/abs/1001.2962 and conclusions. In particular, it is written that the real part is negative for the first time around $t=682112.9$ .
You might also be interested in this question's answers for related information for the critical line $1/2 + it$