code: def backlunds(ctx, t):
      r"""
      Computes the function
      `S(t) = \operatorname{arg} \zeta(\frac{1}{2} + it) / \pi`.
  
      See Titchmarsh Section 9.3 for details of the definition.
  
      **Examples**
  
          >>> from mpmath import *
          >>> mp.dps = 15; mp.pretty = True
          >>> backlunds(217.3)
          0.16302205431184
  
      Generally, the value is a small number. At Gram points it is an integer,
      frequently equal to 0::
  
          >>> chop(backlunds(grampoint(200)))
          0.0
          >>> backlunds(extraprec(10)(grampoint)(211))
          1.0
          >>> backlunds(extraprec(10)(grampoint)(232))
          -1.0
  
      The number of zeros of the Riemann zeta function up to height `t`
      satisfies `N(t) = \theta(t)/\pi + 1 + S(t)` (see :func:nzeros` and
      :func:`siegeltheta`)::
  
          >>> t = 1234.55
          >>> nzeros(t)
          842
          >>> siegeltheta(t)/pi+1+backlunds(t)
          842.0
  
      """
      return ctx.nzeros(t) - 1 - ctx.siegeltheta(t) / ctx.pi
  
file_path: catboost/contrib/python/mpmath/py3/mpmath/functions/zetazeros.py
imports: from .functions import defun, defun_wrapped
label_desc: Use image node_id 15 for calling a global function with example usage: backlunds(ctx, t) and returns: unknown