Alternating Riemann zeta function truncated series expansion as characteristic polynomial of Hermiti

Clear[Z, n, k, x, x, solDet, solSeries];
nn = 2;
MatrixForm[
  ZaMainDiagonal =
   Table[Table[
     ToExpression[StringJoin["a", ToString[n], ToString[k]]]*
      If[n == k, 1, 0], {k, 1, nn}], {n, 1, nn}]];
MatrixForm[
  ZaLower =
   Table[Table[
     ToExpression[StringJoin["a", ToString[n], ToString[k]]]*
      If[n > k, 1, 0], {k, 1, nn}], {n, 1, nn}]];
MatrixForm[ZaUpper = Transpose[ZaLower]];
MatrixForm[
  ZbLower =
   Table[Table[
     ToExpression[StringJoin["b", ToString[n], ToString[k]]]*
      If[n > k, I, 0], {k, 1, nn}], {n, 1, nn}]];
MatrixForm[ZbUpper = Transpose[ZbLower]];
MatrixForm[
 Z = ZaLower + ZaUpper + ZbLower - ZbUpper + ZaMainDiagonal -
   IdentityMatrix[nn]*x]
solDet = x /. Solve[Det[Z] == 0, x]
solSeries =
 x /. Solve[
   Normal[Series[Sum[(-1)^(n + 1)/n^x, {n, 1, nn}], {x, 0, nn}]] == 0,
    x]
Solve[solDet[[1]] == solSeries[[1]] && solDet[[2]] == solSeries[[2]]]