code: def buttap(N):
      """Return (z,p,k) for analog prototype of Nth-order Butterworth filter.
  
      The filter will have an angular (e.g., rad/s) cutoff frequency of 1.
  
      See Also
      --------
      butter : Filter design function using this prototype
      scipy.signal.buttap
  
      """
      if abs(int(N)) != N:
          raise ValueError("Filter order must be a nonnegative integer")
      z = cupy.array([])
      m = cupy.arange(-N + 1, N, 2)
      # Middle value is 0 to ensure an exactly real pole
      p = -cupy.exp(1j * pi * m / (2 * N))
      k = 1
      return z, p, k
  
imports: import warnings
  import math
  from math import pi, prod
  import cupy
  from cupyx.scipy.special import binom
  import cupyx.scipy.special
  from cupyx.scipy.signal import _optimize
  from cupyx.scipy.signal._polyutils import roots, poly
  from cupyx.scipy.signal._lti_conversion import abcd_normalize
label_desc: Use image node_id 29 for calling a global function with example usage: buttap(N) and returns: z,  p,  k