code: def zeta_offline(ctx, s, k=0):
      """
      Computes zeta^(k)(s) off the line
      """
      wpinitial = ctx.prec
      sigma = ctx._re(s)
      t = ctx._im(s)
      # --- compute wptheta, wpR, wpbasic ---
      ctx.prec = 53
      #  X see II Section 3.21 (109) and (110)
      if sigma > 0:
          X = ctx.power(abs(s), 0.5)
      else:
          X = ctx.power(2 * ctx.pi, sigma - 1) * ctx.power(
              abs(1 - s), 0.5 - sigma
          )
      # M1  see II Section 3.21 (111) and (112)
      if sigma > 0:
          M1 = 2 * ctx.sqrt(t / (2 * ctx.pi))
      else:
          M1 = 4 * t * X
      # M2  see II Section 3.21 (111) and (112)
      if 1 - sigma > 0:
          M2 = 2 * ctx.sqrt(t / (2 * ctx.pi))
      else:
          M2 = (
              4
              * t
              * ctx.power(2 * ctx.pi, -sigma)
              * ctx.power(abs(s), sigma - 0.5)
          )
      # T  see II Section 3.21 (113)
      abst = abs(0.5 - s)
      T = 2 * abst * math.log(abst)
      # computing wpbasic, wptheta, wpR  see II Section 3.21
      wpbasic = max(6, 3 + ctx.mag(t))
      wpbasic2 = (
          2
          + ctx.mag(2.12 * M1 + 21.2 * M2 * X + 1.3 * M2 * X * T)
          + wpinitial
          + 1
      )
      wpbasic = max(wpbasic, wpbasic2)
      wptheta = max(4, 3 + ctx.mag(2.7 * M2 * X) + wpinitial + 1)
      wpR = 3 + ctx.mag(1.1 + 2 * X) + wpinitial + 1
      ctx.prec = wptheta
      theta = ctx.siegeltheta(t - ctx.j * (sigma - ctx.mpf("0.5")))
      s1 = s
      s2 = ctx.conj(1 - s1)
      ctx.prec = wpR
      xrz, yrz = Rzeta_simul(ctx, s, k)
      if k > 0:
          ps1 = (
              ctx.psi(0, s1 / 2) + ctx.psi(0, (1 - s1) / 2)
          ) / 4 - ctx.ln(ctx.pi) / 2
      if k > 1:
          ps2 = (
              ctx.j
              * (ctx.psi(1, s1 / 2) - ctx.psi(1, (1 - s1) / 2))
              / 8
          )
      if k > 2:
          ps3 = -(ctx.psi(2, s1 / 2) + ctx.psi(2, (1 - s1) / 2)) / 16
      if k > 3:
          ps4 = (
              -ctx.j
              * (ctx.psi(3, s1 / 2) - ctx.psi(3, (1 - s1) / 2))
              / 32
          )
      ctx.prec = wpbasic
      exptheta = ctx.expj(-2 * theta)
      if k == 0:
          zv = xrz[0] + exptheta * yrz[0]
      if k == 1:
          zv1 = -yrz[1] - 2 * yrz[0] * ps1
          zv = xrz[1] + exptheta * zv1
      if k == 2:
          zv1 = (
              4 * yrz[1] * ps1
              + 4 * yrz[0] * (ps1**2)
              + yrz[2]
              + 2j * yrz[0] * ps2
          )
          zv = xrz[2] + exptheta * zv1
      if k == 3:
          zv1 = (
              -12 * yrz[1] * ps1**2
              - 8 * yrz[0] * ps1**3
              - 6 * yrz[2] * ps1
              - 6j * yrz[1] * ps2
          )
          zv1 = (
              zv1 - 12j * yrz[0] * ps1 * ps2 - yrz[3] + 2 * yrz[0] * ps3
          )
          zv = xrz[3] + exptheta * zv1
      if k == 4:
          zv1 = (
              32 * yrz[1] * ps1**3
              + 16 * yrz[0] * ps1**4
              + 24 * yrz[2] * ps1**2
          )
          zv1 = (
              zv1
              + 48j * yrz[1] * ps1 * ps2
              + 48j * yrz[0] * (ps1**2) * ps2
          )
          zv1 = (
              zv1
              + 12j * yrz[2] * ps2
              - 12 * yrz[0] * ps2**2
              + 8 * yrz[3] * ps1
              - 8 * yrz[1] * ps3
          )
          zv1 = (
              zv1 - 16 * yrz[0] * ps1 * ps3 + yrz[4] - 2j * yrz[0] * ps4
          )
          zv = xrz[4] + exptheta * zv1
      ctx.prec = wpinitial
      return zv
  
file_path: catboost/contrib/python/mpmath/py3/mpmath/functions/rszeta.py
imports: import math
  from .functions import defun
label_desc: Use image node_id 9 for calling a global function with example usage: zeta_offline(ctx, s, k) and returns: zv