Align TikZ node inside equation environment

Align TikZ node inside equation environment

I am trying to insert a TikZ node into an equation but I have some problems:
the = sign is not vertically centred inside the circle
the circle is not vertically aligned with the formula. I want to abtain
the same alignment of the first equation but I failed also using the
baseline option
the equal sign must be at same distance from ) as in the first equation
SOLUTIONS
UNSOLVED
Solved in comments using baseline=-\the\dimexpr\fontdimen22\textfont2\relax
UNSOLVED



\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand{\mathnodebase}{%
\tikz[inner sep = 0pt,baseline]{\node[circle,draw=black] (1) {$=$};}}
\newcommand{\mathnode}{%
\tikz[inner sep = 0pt]{\node[circle,draw=black] (1) {$=$};}}
\begin{document}
\begin{equation}
\prod_{z^n=-1}(w_1(z)^n+1) =
\end{equation}
\begin{equation}
\prod_{z^n=-1}(w_1(z)^n+1) \mathnodebase
\end{equation}
\begin{equation}
\prod_{z^n=-1}(w_1(z)^n+1) \mathnode
\end{equation}
\end{document}