(ctx, t)
return n+n1+1
r"""
    Computes the number of zeros of the Riemann zeta function in
    `(0,1) \times (0,t]`, usually denoted by `N(t)`.

    **Examples**

    The first zero has imaginary part between 14 and 15::

        >>> from sympy.mpmath import *
        >>> mp.dps = 15; mp.pretty = True
        >>> nzeros(14)
        0
        >>> nzeros(15)
        1
        >>> zetazero(1)
        (0.5 + 14.1347251417347j)

    Some closely spaced zeros::

        >>> nzeros(10**7)
        21136125
        >>> zetazero(21136125)
        (0.5 + 9999999.32718175j)
        >>> zetazero(21136126)
        (0.5 + 10000000.2400236j)
        >>> nzeros(545439823.215)
        1500000001
        >>> zetazero(1500000001)
        (0.5 + 545439823.201985j)
        >>> zetazero(1500000002)
        (0.5 + 545439823.325697j)

    This confirms the data given by J. van de Lune,
    H. J. J. te Riele and D. T. Winter in 1986.
r"""
    Computes the number of zeros of the Riemann zeta function in
    `(0,1) \times (0,t]`, usually denoted by `N(t)`.
r Computes the number of zeros of the Riemann zeta function in ( 0 1 ) \ times ( 0 t ] usually denoted by N ( t ) .
def nzeros(ctx, t):
    r"""
    Computes the number of zeros of the Riemann zeta function in
    `(0,1) \times (0,t]`, usually denoted by `N(t)`.

    **Examples**

    The first zero has imaginary part between 14 and 15::

        >>> from sympy.mpmath import *
        >>> mp.dps = 15; mp.pretty = True
        >>> nzeros(14)
        0
        >>> nzeros(15)
        1
        >>> zetazero(1)
        (0.5 + 14.1347251417347j)

    Some closely spaced zeros::

        >>> nzeros(10**7)
        21136125
        >>> zetazero(21136125)
        (0.5 + 9999999.32718175j)
        >>> zetazero(21136126)
        (0.5 + 10000000.2400236j)
        >>> nzeros(545439823.215)
        1500000001
        >>> zetazero(1500000001)
        (0.5 + 545439823.201985j)
        >>> zetazero(1500000002)
        (0.5 + 545439823.325697j)

    This confirms the data given by J. van de Lune,
    H. J. J. te Riele and D. T. Winter in 1986.
    """
    if t < 14.1347251417347:
        return 0
    x = gram_index(ctx, t)
    k = int(ctx.floor(x))
    wpinitial = ctx.prec
    wpz, fp_tolerance = comp_fp_tolerance(ctx, k)
    ctx.prec = wpz
    a = ctx.siegelz(t)
    if k == -1 and a < 0:
        return 0
    elif k == -1 and a > 0:
        return 1
    if k+2 < 400000000:
        Rblock = find_rosser_block_zero(ctx, k+2)
    else:
        Rblock = search_supergood_block(ctx, k+2, fp_tolerance)
    n1, n2 = Rblock[1]
    if n2-n1 == 1:
        b = Rblock[3][0]
        if a*b > 0:
            ctx.prec = wpinitial
            return k+1
        else:
            ctx.prec = wpinitial
            return k+2
    my_zero_number,block, T, V = Rblock
    zero_number_block = n2-n1
    T, V, separated = separate_zeros_in_block(ctx,\
                                              zero_number_block, T, V,\
                                              limitloop=ctx.inf,\
                                            fp_tolerance=fp_tolerance)
    n = count_to(ctx, t, T, V)
    ctx.prec = wpinitial
    return n+n1+1
def nzeros ( ctx , t ) : if t < 14.1347251417347 : return 0 x = gram_index ( ctx , t ) k = int ( ctx . floor ( x ) ) wpinitial = ctx . prec wpz , fp_tolerance = comp_fp_tolerance ( ctx , k ) ctx . prec = wpz a = ctx . siegelz ( t ) if k == - 1 and a < 0 : return 0 elif k == - 1 and a > 0 : return 1 if k + 2 < 400000000 : Rblock = find_rosser_block_zero ( ctx , k + 2 ) else : Rblock = search_supergood_block ( ctx , k + 2 , fp_tolerance ) n1 , n2 = Rblock [ 1 ] if n2 - n1 == 1 : b = Rblock [ 3 ] [ 0 ] if a * b > 0 : ctx . prec = wpinitial return k + 1 else : ctx . prec = wpinitial return k + 2 my_zero_number , block , T , V = Rblock zero_number_block = n2 - n1 T , V , separated = separate_zeros_in_block ( ctx , zero_number_block , T , V , limitloop = ctx . inf , fp_tolerance = fp_tolerance ) n = count_to ( ctx , t , T , V ) ctx . prec = wpinitial return n + n1 + 1