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We investigate the generalized Chevallier&#8722;Polarski&#8722;Linder (CPL) parametrization, which contains the pivoting redshift <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> as an extra free parameter, in order to examine whether the evolution of the dark energy equation of state can be better described by a different parametrization. We use various data combinations from cosmic microwave background (CMB), baryon acoustic oscillations (BAO), redshift space distortion (RSD), weak lensing (WL), joint light curve analysis (JLA), and cosmic chronometers (CC), and we include a Gaussian prior on the Hubble constant value, in order to extract the observational constraints on various quantities. For the case of free <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> we find that for all data combinations it always remains unconstrained, and there is a degeneracy with the value of the dark energy equation of state <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>w</mi> <mn>0</mn> <mi>p</mi> </msubsup> </semantics> </math> </inline-formula> at <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>. For the case where <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> is fixed to specific values, and for the full data combination, we find that with increasing <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> the mean value of <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>w</mi> <mn>0</mn> <mi>p</mi> </msubsup> </semantics> </math> </inline-formula> slowly moves into the phantom regime, however the cosmological constant is always allowed within 1<inline-formula> <math display="inline"> <semantics> <mi>&#963;</mi> </semantics> </math> </inline-formula> confidence-level. In fact, the significant effect is that with increasing <inline-formula> <math display="inline"> <semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>, the correlations between <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>w</mi> <mn>0</mn> <mi>p</mi> </msubsup> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>w</mi> <mi>a</mi> </msub> </semantics> </math> </inline-formula> (the free parameter of the dark energy equation of state quantifying its evolution with redshift), change from negative to positive, with the case <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics> </math> </inline-formula> corresponding to no correlation. The fact that the two parameters describing the dark energy equation of state are uncorrelated for <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics> </math> </inline-formula> justifies why a non-zero pivoting redshift needs to be taken into account.