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http://functions.wolfram.com/04.06.19.0006.01
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Sign[Mod[m, n]] == (Floor[((-Im[n]) Re[m] + Im[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Im[n] + Re[m] - Floor[(Im[m] Im[n] + Re[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Re[n] + I (Im[m] - Floor[(Im[m] Im[n] + Re[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Im[n] - Floor[((-Im[n]) Re[m] + Im[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Re[n]))/
Sqrt[(Im[m] - Floor[(Im[m] Im[n] + Re[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Im[n] - Floor[((-Im[n]) Re[m] + Im[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Re[n])^2 + (Floor[((-Im[n]) Re[m] + Im[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Im[n] + Re[m] - Floor[(Im[m] Im[n] + Re[m] Re[n])/(Im[n]^2 + Re[n]^2)]
Re[n])^2]
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n </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <msup> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> 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