Some code is missing -- please provide the actual expressions for % and %% used in your code.

For example, following your post and using these commands:

ptsgnlst2Fouriermat[{0, 1, I^(2/3), 1 + I^(2/3), 2}, {1, -1, 1, -1}]

Block[{start = 0, end = 1, m = -3., 
  f = mat2series[t, %, 7, -3., 33, MachinePrecision][[1]]}, 
 ParametricPlot[ReIm[f + Sum[E^(2 \[Pi] (k + 1/m) I t) I*(start - Exp[-2*I*\[Pi]/m]*end)/2/\[Pi]/(k + 1/m), {k, -33, 33}]], {t, 0, m}, Axes -> False]]

produces this image:

(Close but not quite...)

Update

After reading the last commands of OP's post, this works nicely:

Block[{start = 0, end = 2, m = 6., n = 32},
 f = mat2series[t, ptsgnlst2Fouriermat[{0, 1, I^(2/3), 1 + I^(2/3), 2}, {1, -1, 1, -1}], 4, m, n, MachinePrecision][[1]];
 ParametricPlot[ReIm[f + Sum[E^(2 \[Pi] (k + 1/m) I t) I*(start - Exp[-2*I*\[Pi]/m]*end)/2/\[Pi]/(k + 1/m), {k, -n, n}]], {t, 0, 6}, Axes -> False]]