solving something you can help or not

[fading pond]

\begin{align*}
t &= 14.135,
\frac{t}{2} &= 7.0675,
\log \pi &\approx 1.14473,
7.0675 \log \pi &\approx 8.086.
\end{align*}

[drowsy thicket]

altaccountinthespotline

[fading pond]

\begin{align*}
Z(14.135) &\approx 2 \sum_{n=1}^{1} \frac{\cos\left(\theta(t) - 14.135 \cdot \log n\right)}{\sqrt{n}},
&= 2 \cdot \frac{\cos(\theta(t) - 0)}{\sqrt{1}},
&= 2 \cdot \cos(\theta(t)).
\end{align*}

[drowsy thicket]

altaccountinthespotline

[fading pond]

\begin{align*}
Z(14.135) &\approx 2 \sum_{n=1}^{1} \frac{\cos(\theta(t) - 14.135 \cdot \log n)}{\sqrt{n}},
&= 2 \cdot \frac{\cos(\theta(t) - 0)}{1},
&= 2 \cdot \cos(\theta(t)).
\end{align*}

[drowsy thicket]

altaccountinthespotline

[fading pond]

hmm

\begin{align*}

&\ \text{Compute intermediate values:}
& \quad t = 14.135
& \quad \frac{t}{2} = 7.0675
& \quad \log \pi \approx 1.1447298858494
&\ \text{Evaluate } \theta(t):
& \quad \theta(t) = \arg \Gamma\left(\frac{1}{4} + i\frac{t}{2}\right) - \frac{t}{2} \log \pi
& \quad \theta(t) \approx 4.256 - 7.0675 \times 1.1447298858494
& \quad \theta(t) \approx 4.256 - 8.088
& \quad \theta(t) \approx -3.832
&\ \text{Calculate } N:
& \quad N = \left\lfloor \sqrt{\frac{14.135}{2\pi}} \right\rfloor
& \quad N = \left\lfloor \sqrt{\frac{14.135}{6.28318}} \right\rfloor
& \quad N = \left\lfloor \sqrt{2.25} \right\rfloor
& \quad N = 1
&\ \text{Evaluate } Z(t):
& \quad Z(14.135) \approx 2 \sum_{n=1}^{1} \frac{\cos(\theta(t) - 14.135 \cdot \log n)}{\sqrt{n}}
& \quad Z(14.135) = 2 \cdot \cos(\theta(t))
& \quad Z(14.135) \approx 2 \cdot \cos(-3.832)
&\ \text{Final computation:}
& \quad \cos(-3.832) \approx -0.75
& \quad Z(14.135) \approx 2 \times (-0.75) = -1.5
\end{align*}