A normalised extension of the first Chebyshev function in the lower half complex plane.

In the lower half complex plane, Re(s) < 1, an extension of the first Chebyshev function is proposed for arbitrary s, involving summands of ln(p)/p^s, for the primes. A closed expression for the sum is conjectured along the real axis for Re(s) < 1. Across the lower half complex plane, the absolute value of the function exhibits 1/Imaginary(s) decay and (diminishing) sharp modulation features about the positions of the non-trivial Riemann Zeta zeroes are observed.