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\subsection{General complex Prony, $N$D}  Let's consider the following system:  $$  m_k = \sum_{j=1}^N a_j x_j^k, \quad k \in \{0, 1, \ldots, 2N-1\}.  $$  Introduce variables $\{u_j\}$:  $$  \begin{cases}  u_1 = x_1 + x_2 + \ldots + x_N, \\  u_2 = x_1x_2 + x_1x_3 + \ldots + x_{N-1}x_N, \\  \ldots \\  u_N = x_1x_2\ldots x_N.  \end{cases}  $$  From the Viet's theorem, we have:  \begin{equation}  \label{eq3}  m_{l} = m_{l-1}u_1 - m_{l-2}u_2 + \ldots + (-1)^{N-1}m_{l-N} u_N.  \end{equation}    Thus, $\{u_j\}$ are solution of the following system of equations:  $$  \begin{pmatrix}  m_{N-1} & -m_{N-2} & \ldots & (-1)^{N-1} m_0 \\  m_{N} & -m_{N-1} & \ldots & (-1)^{N-1} m_1 \\  \vdots & \vdots & \ddots & \vdots \\  m_{2N-2} & -m_{2N-3} & \ldots & (-1)^{N-1} m_{N-1}  \end{pmatrix}  \times  \begin{pmatrix}  u_1 \\ u_2 \\ \vdots \\ u_N  \end{pmatrix}  =  \begin{pmatrix}  m_N \\ m_{N+1} \\ \vdots \\ m_{2N-1} \\  \end{pmatrix}.  $$  We can find $\{x_j\}$ from the following equation:  $$  x^N - u_1 x^{N-1} + \ldots + (-1)^N u_N = 0.  $$  We can find $\{a_j\}$ as a solution of the following system:  $$  \begin{pmatrix}  1 & 1 & \ldots & 1 \\  x_1 & x_2 & \ldots & x_d \\  x_1^2 & x_2^2 & \ldots & x_N^2 \\  \vdots & \vdots & \ddots & \vdots \\  x_1^{N-1} & x_2^{N-1} & \ldots & x_N^{N-1} \\  \end{pmatrix}  \times  \begin{pmatrix}  a_1 \\ a_2 \\ a_3\\ \vdots \\ a_N  \end{pmatrix}  =  \begin{pmatrix}  m_0 \\ m_1 \\ m_2 \\ \vdots \\ m_{N-1}  \end{pmatrix}.  $$