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In this paper we obtain new $\zeta$-synergetic formula namely an exactsecondary complete hybrid formula. This one is generated by some set oftrigonometric and power functions together with the square of module of theRiemann's zeta-function on the critical line. By means of this new formula, wedefine a two-parametric continuum set of a three-parametric invariants.

Jacob's ladders and new synergetic formula generating infinite set of $\zeta$-cooperative three-parametric invariants