two pairs of complex roots having small real parts, and imaginary parts with 21 common digits
The set made up by 6 roots of modulus has two very close real roots
matching in their first 28 digits, and 2 very close complex pairs
whose real and imaginary parts match in their first 27 digits.
This means that in order to separate the former two real roots by using a floating point computation, at least 63 digits of working precision are needed, while for the latter two roots at least 35 digits are needed. A similar result holds for the complex roots.