Editing Openai/68ec50da-cf00-8005-b5f6-b683506e5853 (section)

===== All numerical values used in the document were computed in Python and embedded directly into the LaTeX: =====
* 6π2=0.6079271018540267\frac{6}{\pi^2}=0.6079271018540267π26=0.6079271018540267
* δ5=254π2=0.6332573977646111\delta_5=\frac{25}{4\pi^2}=0.6332573977646111δ5=4π225=0.6332573977646111 and 1−δ5=0.36674260223538891-\delta_5=0.36674260223538891−δ5=0.3667426022353889
* δ5, 3∣b=0.7124145724851875\delta_{5,\,3\mid b}=0.7124145724851875δ5,3∣b=0.7124145724851875 (so 1−δ5, 3∣b=0.287585427514812531-\delta_{5,\,3\mid b}=0.287585427514812531−δ5,3∣b=0.28758542751481253)
* δ5, 3∤b=0.5936788104043229\delta_{5,\,3\nmid b}=0.5936788104043229δ5,3∤b=0.5936788104043229 (so 1−δ5, 3∤b=0.40632118959567711-\delta_{5,\,3\nmid b}=0.40632118959567711−δ5,3∤b=0.4063211895956771)
* Θ29(1)∈[0.00442735, 0.00442835]\Theta_{29}^{(1)}\in[0.00442735,\,0.00442835]Θ29(1)∈[0.00442735,0.00442835], Θ29(2)∈[0.00883767, 0.00883967]\Theta_{29}^{(2)}\in[0.00883767,\,0.00883967]Θ29(2)∈[0.00883767,0.00883967] (rigorous intervals)
* Complement density (1−225)(1−2169)(1−2289)=0.9028209905612089(1-\frac{2}{25})(1-\frac{2}{169})(1-\frac{2}{289})=0.9028209905612089(1−252)(1−1692)(1−2892)=0.9028209905612089
* 225=0.08\frac{2}{25}=0.08252=0.08, 2169≈0.01183432\frac{2}{169}\approx 0.011834321692≈0.01183432, 2289≈0.00692042\frac{2}{289}\approx 0.006920422892≈0.00692042

(The two square roots of −1-1−1 modulo 52,132,1725^2,13^2,17^252,132,172 are 7,187,187,18; 70,9970,9970,99; 38,25138,25138,251 respectively—verified computationally and used to define A5±,A13±,A17±A_5^\pm, A_{13}^\pm, A_{17}^\pmA5±,A13±,A17±.)