Results of Numerical Methods
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 3.3#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell_{k}(z_{j}) = \Kroneckerdelta{k}{j}} | ell[k]*(z[j])= KroneckerDelta[k, j] |
Subscript[\[ScriptL], k]*(Subscript[z, j])= KroneckerDelta[k, j] |
Failure | Failure | Fail -1.414213562+2.585786436*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {ell[k] = 2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {ell[k] = 2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {ell[k] = -2^(1/2)-I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = 2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)-I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {ell[k] = -2^(1/2)+I*2^(1/2), z[j] = -2^(1/2)+I*2^(1/2), KroneckerDelta[k,j] = -2^(1/2)+I*2^(1/2)} |
Successful |
| 3.3.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{R_{n,t}} <= c_{n}h^{n+1}\abs{f^{(n+1)}(\xi)}} | abs(R[n , t])< = c[n]*(h)^(n + 1)* abs((f)^(n + 1)*(xi)) |
Abs[Subscript[R, n , t]]< = Subscript[c, n]*(h)^(n + 1)* Abs[(f)^(n + 1)*(\[Xi])] |
Failure | Failure | Skip | Skip |
| 3.4.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}} | (1)/(factorial(k))=(1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi) |
Divide[1,(k)!]=Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}] |
Failure | Failure | Skip | Error |
| 3.5.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-pt}\BesselJ{0}@{t}\diff{t} = \frac{1}{\sqrt{p^{2}+1}}} | int(exp(- p*t)*BesselJ(0, t), t = 0..infinity)=(1)/(sqrt((p)^(2)+ 1)) |
Integrate[Exp[- p*t]*BesselJ[0, t], {t, 0, Infinity}]=Divide[1,Sqrt[(p)^(2)+ 1]] |
Successful | Failure | - | Error |
| 3.5.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{g_{k}}{n}\left(1-\sum_{j=1}^{\floor{n/2}}\frac{b_{j}}{4j^{2}-1}\cos@{2jk\cpi/n}\right)} | w[k]=(g[k])/(n)*(1 - sum((b[j])/(4*(j)^(2)- 1)*cos(2*j*k*Pi/ n), j = 1..floor(n/ 2))) |
Subscript[w, k]=Divide[Subscript[g, k],n]*(1 - Sum[Divide[Subscript[b, j],4*(j)^(2)- 1]*Cos[2*j*k*Pi/ n], {j, 1, Floor[n/ 2]}]) |
Failure | Failure | Skip | Skip |
| 3.5#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n-1}}} | gamma[n]=(Pi)/((2)^(2*n - 1)) |
Subscript[\[Gamma], n]=Divide[Pi,(2)^(2*n - 1)] |
Failure | Failure | Fail -.156582765+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.021514480+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.316038792+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}-.156582765-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.021514480-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.316038792-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-2.985009889-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.806912644-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.512388332-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-2.985009889+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.806912644+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.512388332+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = \cos@{\frac{2k-1}{2n}\cpi}} | x[k]= cos((2*k - 1)/(2*n)*Pi) |
Subscript[x, k]= Cos[Divide[2*k - 1,2*n]*Pi] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.7071067809+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.5481881582+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.414213561+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}2.121320343+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.414213563+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}2.121320342+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}2.280238966+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}1.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.7071067809-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.5481881582-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.414213561-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}2.121320343-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.414213563-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}2.121320342-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}2.280238966-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.121320343-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.280238966-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.414213563-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-.7071067809-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.414213561-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-.7071067815-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-.5481881577-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.121320343+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.280238966+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.414213563+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-.7071067809+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.414213561+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-.7071067815+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-.5481881577+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{\cpi}{n}} | w[k]=(Pi)/(n) |
Subscript[w, k]=Divide[Pi,n] |
Failure | Failure | Fail -1.727379092+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), n = 1}-.156582765+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), n = 2}.367016011+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), n = 3}-1.727379092-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), n = 1}-.156582765-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), n = 2}.367016011-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), n = 3}-4.555806216-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), n = 1}-2.985009889-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), n = 2}-2.461411113-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), n = 3}-4.555806216+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), n = 1}-2.985009889+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), n = 2}-2.461411113+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), n = 3} |
Fail
Complex[-1.727379091216698, 1.4142135623730951] <- {Rule[n, 1], Rule[Subscript[w, k], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.1565827644218014, 1.4142135623730951] <- {Rule[n, 2], Rule[Subscript[w, k], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3670160111764975, 1.4142135623730951] <- {Rule[n, 3], Rule[Subscript[w, k], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.727379091216698, -1.4142135623730951] <- {Rule[n, 1], Rule[Subscript[w, k], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.1565827644218014, -1.4142135623730951] <- {Rule[n, 2], Rule[Subscript[w, k], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.3670160111764975, -1.4142135623730951] <- {Rule[n, 3], Rule[Subscript[w, k], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, -1.4142135623730951] <- {Rule[n, 1], Rule[Subscript[w, k], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.9850098891679915, -1.4142135623730951] <- {Rule[n, 2], Rule[Subscript[w, k], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4614111135696928, -1.4142135623730951] <- {Rule[n, 3], Rule[Subscript[w, k], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, 1.4142135623730951] <- {Rule[n, 1], Rule[Subscript[w, k], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.9850098891679915, 1.4142135623730951] <- {Rule[n, 2], Rule[Subscript[w, k], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4614111135696928, 1.4142135623730951] <- {Rule[n, 3], Rule[Subscript[w, k], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 3.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = \cos@{\frac{k}{n+1}\cpi}} | x[k]= cos((k)/(n + 1)*Pi) |
Subscript[x, k]= Cos[Divide[k,n + 1]*Pi] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.9142135618+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.7071067809+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}2.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.914213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.414213561+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}2.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}2.121320343+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}1.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.9142135618-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.7071067809-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}2.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.914213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.414213561-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}2.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}2.121320343-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-1.914213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.121320343-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-.9142135615-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.414213563-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-.7071067809-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-1.914213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.121320343+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-.9142135615+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.414213563+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-.7071067809+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{\cpi}{n+1}\sin^{2}@{\frac{k}{n+1}\cpi}} | w[k]=(Pi)/(n + 1)*(sin((k)/(n + 1)*Pi))^(2) |
Subscript[w, k]=Divide[Pi,n + 1]*(Sin[Divide[k,n + 1]*Pi])^(2) |
Failure | Failure | Fail -.156582765+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.6288153988+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}1.021514480+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.414213562+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.6288153991+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.6288153985+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}-.156582765+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.414213562+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.021514480+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}-.156582765-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.6288153988-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}1.021514480-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.414213562-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.6288153991-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.6288153985-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}-.156582765-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.414213562-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.021514480-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.985009889-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.199611725-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-1.806912644-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.414213562-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.199611725-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.199611726-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-2.985009889-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.414213562-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.806912644-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.985009889+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.199611725+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-1.806912644+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.414213562+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.199611725+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.199611726+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-2.985009889+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.414213562+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.806912644+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n+1}}} | gamma[n]=(Pi)/((2)^(2*n + 1)) |
Subscript[\[Gamma], n]=Divide[Pi,(2)^(2*n + 1)] |
Failure | Failure | Fail 1.021514480+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.316038792+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.389669869+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.021514480-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.316038792-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.389669869-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.806912644-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.512388332-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.438757255-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.806912644+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.512388332+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.438757255+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = +\cos@{\frac{2k}{2n+1}\cpi}} | x[k]= + cos((2*k)/(2*n + 1)*Pi) |
Subscript[x, k]= + Cos[Divide[2*k,2*n + 1]*Pi] |
Failure | Failure | Fail 1.914213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}1.105196568+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.7907237604+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.914213561+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}2.223230556+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.636734496+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}2.223230556+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}2.315182430+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}1.914213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}1.105196568-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.7907237604-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.914213561-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}2.223230556-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.636734496-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}2.223230556-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}2.315182430-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-.9142135623-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-1.723230556-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.037703364-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-.9142135631-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-.6051965675-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.191692628-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-2.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-.6051965680-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-.5132446937-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-.9142135623+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-1.723230556+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.037703364+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-.9142135631+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-.6051965675+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.191692628+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-2.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-.6051965680+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-.5132446937+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = -\cos@{\frac{2k}{2n+1}\cpi}} | x[k]= - cos((2*k)/(2*n + 1)*Pi) |
Subscript[x, k]= - Cos[Divide[2*k,2*n + 1]*Pi] |
Failure | Failure | Fail .9142135623+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}1.723230556+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}2.037703364+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.9142135631+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.6051965675+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.191692628+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}2.414213562+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}.6051965680+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.5132446937+1.414213562*I <- {x[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.9142135623-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}1.723230556-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}2.037703364-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.9142135631-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.6051965675-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.191692628-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}2.414213562-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}.6051965680-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.5132446937-1.414213562*I <- {x[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.914213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-1.105196568-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-.7907237604-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.914213561-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.223230556-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.636734496-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-.414213562-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-2.223230556-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-2.315182430-1.414213562*I <- {x[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-1.914213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-1.105196568+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-.7907237604+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.914213561+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.223230556+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.636734496+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-.414213562+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-2.223230556+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-2.315182430+1.414213562*I <- {x[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{4\cpi}{2n+1}\sin^{2}@{\frac{k}{2n+1}\cpi}} | w[k]=(4*Pi)/(2*n + 1)*(sin((k)/(2*n + 1)*Pi))^(2) |
Subscript[w, k]=Divide[4*Pi,2*n + 1]*(Sin[Divide[k,2*n + 1]*Pi])^(2) |
Failure | Failure | Fail -1.727379092+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.5458987077+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}1.076258798+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.727379090+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}-.859064240+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.316881337+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.414213562+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}-.859064238+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}-.292092105+1.414213562*I <- {w[k] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}-1.727379092-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.5458987077-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}1.076258798-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.727379090-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}-.859064240-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.316881337-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.414213562-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}-.859064238-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}-.292092105-1.414213562*I <- {w[k] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-4.555806216-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.282528416-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-1.752168326-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-4.555806214-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-3.687491364-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.511545787-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.414213562-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-3.687491362-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-3.120519229-1.414213562*I <- {w[k] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-4.555806216+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.282528416+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-1.752168326+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-4.555806214+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-3.687491364+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.511545787+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.414213562+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-3.687491362+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-3.120519229+1.414213562*I <- {w[k] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Successful |
| 3.5#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n}}} | gamma[n]=(Pi)/((2)^(2*n)) |
Subscript[\[Gamma], n]=Divide[Pi,(2)^(2*n)] |
Failure | Failure | Fail .6288153985+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.217864021+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.365126177+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}.6288153985-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.217864021-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.365126177-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-2.199611726-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.610563103-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.463300947-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-2.199611726+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.610563103+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.463300947+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.5#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \dfrac{\EulerGamma@{n+\alpha+1}\EulerGamma@{n+\beta+1}\EulerGamma@{n+\alpha+\beta+1}}{(2n+\alpha+\beta+1)(\EulerGamma@{2n+\alpha+\beta+1})^{2}}2^{2n+\alpha+\beta+1}n!} | gamma[n]=(GAMMA(n + alpha + 1)*GAMMA(n + beta + 1)*GAMMA(n + alpha + beta + 1))/((2*n + alpha + beta + 1)*(GAMMA(2*n + alpha + beta + 1))^(2))*(2)^(2*n + alpha + beta + 1)* factorial(n) |
Subscript[\[Gamma], n]=Divide[Gamma[n + \[Alpha]+ 1]*Gamma[n + \[Beta]+ 1]*Gamma[n + \[Alpha]+ \[Beta]+ 1],(2*n + \[Alpha]+ \[Beta]+ 1)*(Gamma[2*n + \[Alpha]+ \[Beta]+ 1])^(2)]*(2)^(2*n + \[Alpha]+ \[Beta]+ 1)* (n)! |
Failure | Failure | Fail 1.288578300+1.528723368*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.395381063+1.444046993*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.411166396+1.421669573*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.288578300-1.299703756*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.395381063-1.384380131*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.411166396-1.406757551*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.539848824-1.299703756*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.433046061-1.384380131*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.417260728-1.406757551*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.539848824+1.528723368*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.433046061+1.444046993*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.417260728+1.421669573*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.307324532+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.387709512+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.407572146+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.307324532-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.387709512-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.407572146-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.521102592-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.440717612-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.420854978-1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.521102592+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.440717612+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.420854978+1.414213562*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.694351284+1.120027150*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.410467245+1.261060460*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.395747012+1.375259486*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.694351284-1.708399974*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.410467245-1.567366664*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.395747012-1.453167638*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.134075840-1.708399974*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.417959879-1.567366664*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.432680112-1.453167638*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.134075840+1.120027150*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.417959879+1.261060460*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.432680112+1.375259486*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.687803394+2.017411429*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.485586870+1.582353268*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.431816615+1.457407834*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.687803394-.8110156946*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.485586870-1.246073856*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.431816615-1.371019290*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.140623730-.8110156946*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.342840254-1.246073856*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.396610509-1.371019290*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.140623730+2.017411429*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.342840254+1.582353268*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.396610509+1.457407834*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.307324532+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.387709512+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.407572146+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.307324532-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.387709512-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.407572146-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.521102592-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.440717612-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.420854978-1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.521102592+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.440717612+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.420854978+1.414213562*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.288578300+1.299703756*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.395381063+1.384380131*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.411166396+1.406757551*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.288578300-1.528723368*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.395381063-1.444046993*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.411166396-1.421669573*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.539848824-1.528723368*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.433046061-1.444046993*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.417260728-1.421669573*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.539848824+1.299703756*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.433046061+1.384380131*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.417260728+1.406757551*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.687803394+.8110156946*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.485586870+1.246073856*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.431816615+1.371019290*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.687803394-2.017411429*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.485586870-1.582353268*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.431816615-1.457407834*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.140623730-2.017411429*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.342840254-1.582353268*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.396610509-1.457407834*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.140623730+.8110156946*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.342840254+1.246073856*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.396610509+1.371019290*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.694351284+1.708399974*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.410467245+1.567366664*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.395747012+1.453167638*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.694351284-1.120027150*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.410467245-1.261060460*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.395747012-1.375259486*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.134075840-1.120027150*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.417959879-1.261060460*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.432680112-1.375259486*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.134075840+1.708399974*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.417959879+1.567366664*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.432680112+1.453167638*I <- {alpha = 2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.694351284+1.120027150*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.410467245+1.261060460*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.395747012+1.375259486*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.694351284-1.708399974*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.410467245-1.567366664*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.395747012-1.453167638*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.134075840-1.708399974*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.417959879-1.567366664*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.432680112-1.453167638*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.134075840+1.120027150*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.417959879+1.261060460*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.432680112+1.375259486*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.687803394+.8110156946*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.485586870+1.246073856*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.431816615+1.371019290*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.687803394-2.017411429*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.485586870-1.582353268*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.431816615-1.457407834*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.140623730-2.017411429*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.342840254-1.582353268*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.396610509-1.457407834*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.140623730+.8110156946*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.342840254+1.246073856*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.396610509+1.371019290*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.822713707+1.121988446*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.706838999+1.399437992*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.552635969+1.407451051*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.822713707-1.706438678*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.706838999-1.428989132*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.552635969-1.420976073*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.005713417-1.706438678*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.121588125-1.428989132*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.275791155-1.420976073*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.005713417+1.121988446*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.121588125+1.399437992*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.275791155+1.407451051*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.528876175+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}-2.067586110+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.059039933+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.528876175-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}-2.067586110-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.059039933-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.299550949-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-4.896013234-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.769387191-1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.299550949+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-4.896013234+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.769387191+1.414213562*I <- {alpha = -2^(1/2)-I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.687803394+2.017411429*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.485586870+1.582353268*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.431816615+1.457407834*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.687803394-.8110156946*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.485586870-1.246073856*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.431816615-1.371019290*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.140623730-.8110156946*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.342840254-1.246073856*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.396610509-1.371019290*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.140623730+2.017411429*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.342840254+1.582353268*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.396610509+1.457407834*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.694351284+1.708399974*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.410467245+1.567366664*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.395747012+1.453167638*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.694351284-1.120027150*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.410467245-1.261060460*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.395747012-1.375259486*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.134075840-1.120027150*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.417959879-1.261060460*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.432680112-1.375259486*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.134075840+1.708399974*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.417959879+1.567366664*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.432680112+1.453167638*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.528876175+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}-2.067586110+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.059039933+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.528876175-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}-2.067586110-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.059039933-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.299550949-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-4.896013234-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.769387191-1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.299550949+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-4.896013234+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.769387191+1.414213562*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.822713707+1.706438678*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}1.706838999+1.428989132*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}1.552635969+1.420976073*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.822713707-1.121988446*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}1.706838999-1.399437992*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}1.552635969-1.407451051*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.005713417-1.121988446*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-1.121588125-1.399437992*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-1.275791155-1.407451051*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.005713417+1.706438678*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-1.121588125+1.428989132*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-1.275791155+1.420976073*I <- {alpha = -2^(1/2)+I*2^(1/2), beta = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
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| 3.5#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = n!\,\EulerGamma@{n+\alpha+1}} | gamma[n]= factorial(n)*GAMMA(n + alpha + 1) |
Subscript[\[Gamma], n]= (n)!*Gamma[n + \[Alpha]+ 1] |
Failure | Failure | Fail 1.412834343-.765961897*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}7.571263072-13.47685670*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}146.1272685-169.6607305*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.412834343-3.594389021*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}7.571263072-16.30528382*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}146.1272685-172.4891577*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.415592781-3.594389021*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}4.742835948-16.30528382*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}143.2988413-172.4891577*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.415592781-.765961897*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}4.742835948-13.47685670*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}143.2988413-169.6607305*I <- {alpha = 2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.412834343+3.594389021*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}7.571263072+16.30528382*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}146.1272685+172.4891577*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.412834343+.765961897*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}7.571263072+13.47685670*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}146.1272685+169.6607305*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.415592781+.765961897*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}4.742835948+13.47685670*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}143.2988413+169.6607305*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.415592781+3.594389021*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}4.742835948+16.30528382*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}143.2988413+172.4891577*I <- {alpha = 2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.211930022+1.221345793*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}.6317112234+1.760399168*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}-.839690091+6.381019137*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.211930022-1.607081331*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}.6317112234-1.068027956*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}-.839690091+3.552592013*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.616497102-1.607081331*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-2.196715901-1.068027956*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-3.668117215+3.552592013*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.616497102+1.221345793*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-2.196715901+1.760399168*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-3.668117215+6.381019137*I <- {alpha = -2^(1/2)-I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3}1.211930022+1.607081331*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}.6317112234+1.068027956*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}-.839690091-3.552592013*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}1.211930022-1.221345793*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}.6317112234-1.760399168*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}-.839690091-6.381019137*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-1.616497102-1.221345793*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-2.196715901-1.760399168*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-3.668117215-6.381019137*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-1.616497102+1.607081331*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-2.196715901+1.068027956*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-3.668117215-3.552592013*I <- {alpha = -2^(1/2)+I*2^(1/2), gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.5#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \sqrt{\cpi}\,\frac{n!}{2^{n}}} | gamma[n]=sqrt(Pi)*(factorial(n))/((2)^(n)) |
Subscript[\[Gamma], n]=Sqrt[Pi]*Divide[(n)!,(2)^(n)] |
Failure | Failure | Fail .5279866365+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 1}.5279866365+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 2}.84873174e-1+1.414213562*I <- {gamma[n] = 2^(1/2)+I*2^(1/2), n = 3}.5279866365-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 1}.5279866365-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 2}.84873174e-1-1.414213562*I <- {gamma[n] = 2^(1/2)-I*2^(1/2), n = 3}-2.300440488-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 1}-2.300440488-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 2}-2.743553950-1.414213562*I <- {gamma[n] = -2^(1/2)-I*2^(1/2), n = 3}-2.300440488+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 1}-2.300440488+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 2}-2.743553950+1.414213562*I <- {gamma[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.5#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = \ln@{1/x}} | w*(x)= ln(1/ x) |
w*(x)= Log[1/ x] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {w = 2^(1/2)+I*2^(1/2), x = 1}3.521574305+2.828427124*I <- {w = 2^(1/2)+I*2^(1/2), x = 2}5.341252975+4.242640686*I <- {w = 2^(1/2)+I*2^(1/2), x = 3}1.414213562-1.414213562*I <- {w = 2^(1/2)-I*2^(1/2), x = 1}3.521574305-2.828427124*I <- {w = 2^(1/2)-I*2^(1/2), x = 2}5.341252975-4.242640686*I <- {w = 2^(1/2)-I*2^(1/2), x = 3}-1.414213562-1.414213562*I <- {w = -2^(1/2)-I*2^(1/2), x = 1}-2.135279943-2.828427124*I <- {w = -2^(1/2)-I*2^(1/2), x = 2}-3.144028397-4.242640686*I <- {w = -2^(1/2)-I*2^(1/2), x = 3}-1.414213562+1.414213562*I <- {w = -2^(1/2)+I*2^(1/2), x = 1}-2.135279943+2.828427124*I <- {w = -2^(1/2)+I*2^(1/2), x = 2}-3.144028397+4.242640686*I <- {w = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[3.5215743053061357, 2.8284271247461903] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[5.341252975787396, 4.242640687119286] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[3.5215743053061357, -2.8284271247461903] <- {Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[5.341252975787396, -4.242640687119286] <- {Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[-2.135279944186245, -2.8284271247461903] <- {Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-3.1440283984511757, -4.242640687119286] <- {Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[-2.135279944186245, 2.8284271247461903] <- {Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-3.1440283984511757, 4.242640687119286] <- {Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} |
| 3.5.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta}\zeta^{-s}p_{k}(1/\zeta)p_{\ell}(1/\zeta)\diff{\zeta} = 0} | int(exp(zeta)*(zeta)^(- s)* p[k]*(1/ zeta)* p[ell]*(1/ zeta), zeta = c - I*infinity..c + I*infinity)= 0 |
Integrate[Exp[\[zeta]]*(\[zeta])^(- s)* Subscript[p, k]*(1/ \[zeta])* Subscript[p, \[ScriptL]]*(1/ \[zeta]), {\[zeta], c - I*Infinity, c + I*Infinity}]= 0 |
Failure | Failure | Skip | Error |
| 3.5.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta-2\lambda\sqrt{\zeta}}\frac{\diff{\zeta}}{\zeta}} | erfc(lambda)=(1)/(2*Pi*I)*int(exp(zeta - 2*lambda*sqrt(zeta))*(1)/(zeta), zeta = c - I*infinity..c + I*infinity) |
Erfc[\[Lambda]]=Divide[1,2*Pi*I]*Integrate[Exp[\[zeta]- 2*\[Lambda]*Sqrt[\[zeta]]]*Divide[1,\[zeta]], {\[zeta], c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 3.5.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\lambda^{2}(t-2\sqrt{t})}\frac{\diff{t}}{t}} | erfc(lambda)=(1)/(2*Pi*I)*int(exp((lambda)^(2)*(t - 2*sqrt(t)))*(1)/(t), t = c - I*infinity..c + I*infinity) |
Erfc[\[Lambda]]=Divide[1,2*Pi*I]*Integrate[Exp[(\[Lambda])^(2)*(t - 2*Sqrt[t])]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 3.5.E45 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{e^{-\lambda^{2}}}{2\cpi}\int_{-\cpi}^{\cpi}e^{-\lambda^{2}\tan^{2}@{\frac{1}{2}\theta}}\diff{\theta}} | erfc(lambda)=(exp(- (lambda)^(2)))/(2*Pi)*int(exp(- (lambda)^(2)* (tan((1)/(2)*theta))^(2)), theta = - Pi..Pi) |
Erfc[\[Lambda]]=Divide[Exp[- (\[Lambda])^(2)],2*Pi]*Integrate[Exp[- (\[Lambda])^(2)* (Tan[Divide[1,2]*\[Theta]])^(2)], {\[Theta], - Pi, Pi}] |
Failure | Failure | Skip | Error |
| 3.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})} | w[n + 1]- 2*n*w[n]+ w[n - 1]= -(2/ Pi)*(1 -(- 1)^(n)) |
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1]= -(2/ Pi)*(1 -(- 1)^(n)) |
Failure | Failure | Fail 1.273239544+0.*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-2.828427124-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-4.383614704-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}1.273239544-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-2.828427124-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-4.383614704-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-1.555187580-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-5.656854248-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-7.212041828-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-1.555187580+0.*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-5.656854248-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-7.212041828-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}1.273239544-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-2.828427124-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-4.383614704-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}1.273239544-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-2.828427124-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-4.383614704-11.31370850*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-1.555187580-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-5.656854248-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-7.212041828-11.31370850*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-1.555187580-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-5.656854248-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-7.212041828-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}-1.555187580-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-5.656854248-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-7.212041828-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}-1.555187580-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-5.656854248-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-7.212041828-11.31370850*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-4.383614704-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-8.485281372-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-10.04046896-11.31370850*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-4.383614704-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-8.485281372-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-10.04046896-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}-1.555187580+0.*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-5.656854248-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-7.212041828-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}-1.555187580-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-5.656854248-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-7.212041828-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-4.383614704-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-8.485281372-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-10.04046896-8.485281372*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-4.383614704+0.*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-8.485281372-2.828427124*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-10.04046896-5.656854248*I <- {w[n] = 2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}1.273239544+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-2.828427124+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-4.383614704+11.31370850*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}1.273239544+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-2.828427124+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-4.383614704+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-1.555187580+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-5.656854248+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-7.212041828+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-1.555187580+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-5.656854248+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-7.212041828+11.31370850*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}1.273239544+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-2.828427124+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-4.383614704+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}1.273239544+0.*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-2.828427124+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-4.383614704+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-1.555187580+0.*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-5.656854248+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-7.212041828+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-1.555187580+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-5.656854248+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-7.212041828+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}-1.555187580+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-5.656854248+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-7.212041828+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}-1.555187580+0.*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-5.656854248+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-7.212041828+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-4.383614704+0.*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-8.485281372+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-10.04046896+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-4.383614704+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-8.485281372+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-10.04046896+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}-1.555187580+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}-5.656854248+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}-7.212041828+11.31370850*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}-1.555187580+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}-5.656854248+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}-7.212041828+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}-4.383614704+2.828427124*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}-8.485281372+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}-10.04046896+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}-4.383614704+5.656854248*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}-8.485281372+8.485281372*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}-10.04046896+11.31370850*I <- {w[n] = 2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}6.930093792+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}8.485281372+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}12.58694804+11.31370850*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}6.930093792+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}8.485281372+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}12.58694804+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}4.101666668+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}5.656854248+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}9.758520916+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}4.101666668+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}5.656854248+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}9.758520916+11.31370850*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}6.930093792+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}8.485281372+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}12.58694804+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}6.930093792+0.*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}8.485281372+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}12.58694804+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}4.101666668+0.*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}5.656854248+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}9.758520916+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}4.101666668+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}5.656854248+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}9.758520916+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}4.101666668+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}5.656854248+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}9.758520916+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}4.101666668+0.*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}5.656854248+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}9.758520916+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}1.273239544+0.*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}2.828427124+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}6.930093792+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}1.273239544+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}2.828427124+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}6.930093792+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}4.101666668+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}5.656854248+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}9.758520916+11.31370850*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}4.101666668+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}5.656854248+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}9.758520916+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}1.273239544+2.828427124*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}2.828427124+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}6.930093792+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}1.273239544+5.656854248*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}2.828427124+8.485281372*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}6.930093792+11.31370850*I <- {w[n] = -2^(1/2)-I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}6.930093792+0.*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}8.485281372-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}12.58694804-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}6.930093792-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}8.485281372-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}12.58694804-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}4.101666668-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}5.656854248-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}9.758520916-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}4.101666668+0.*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}5.656854248-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}9.758520916-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}6.930093792-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}8.485281372-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}12.58694804-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}6.930093792-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}8.485281372-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}12.58694804-11.31370850*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}4.101666668-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}5.656854248-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}9.758520916-11.31370850*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}4.101666668-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}5.656854248-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}9.758520916-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = 2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}4.101666668-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}5.656854248-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}9.758520916-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}4.101666668-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}5.656854248-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}9.758520916-11.31370850*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}1.273239544-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}2.828427124-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}6.930093792-11.31370850*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}1.273239544-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}2.828427124-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}6.930093792-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)-I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3}4.101666668+0.*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 1}5.656854248-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 2}9.758520916-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)+I*2^(1/2), n = 3}4.101666668-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 1}5.656854248-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 2}9.758520916-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = 2^(1/2)-I*2^(1/2), n = 3}1.273239544-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 1}2.828427124-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 2}6.930093792-8.485281372*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)-I*2^(1/2), n = 3}1.273239544+0.*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 1}2.828427124-2.828427124*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 2}6.930093792-5.656854248*I <- {w[n] = -2^(1/2)+I*2^(1/2), w[n-1] = -2^(1/2)+I*2^(1/2), w[n+1] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |
| 3.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}} | abs(z[n + 1]- zeta)< A*(abs(z[n]- zeta))^(p) |
Abs[Subscript[z, n + 1]- \[zeta]]< A*(Abs[Subscript[z, n]- \[zeta]])^(p) |
Failure | Failure | Skip | Error |
| 3.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}} | phi*(x)= x + x*(cot(x))^(2)- cot(x) |
\[Phi]*(x)= x + x*(Cot[x])^(2)- Cot[x] |
Failure | Failure | Fail .6440232505+1.414213562*I <- {phi = 2^(1/2)+I*2^(1/2), x = 1}-.481313046e-1+2.828427124*I <- {phi = 2^(1/2)+I*2^(1/2), x = 2}-153.4139169+4.242640686*I <- {phi = 2^(1/2)+I*2^(1/2), x = 3}.6440232505-1.414213562*I <- {phi = 2^(1/2)-I*2^(1/2), x = 1}-.481313046e-1-2.828427124*I <- {phi = 2^(1/2)-I*2^(1/2), x = 2}-153.4139169-4.242640686*I <- {phi = 2^(1/2)-I*2^(1/2), x = 3}-2.184403873-1.414213562*I <- {phi = -2^(1/2)-I*2^(1/2), x = 1}-5.704985552-2.828427124*I <- {phi = -2^(1/2)-I*2^(1/2), x = 2}-161.8991983-4.242640686*I <- {phi = -2^(1/2)-I*2^(1/2), x = 3}-2.184403873+1.414213562*I <- {phi = -2^(1/2)+I*2^(1/2), x = 1}-5.704985552+2.828427124*I <- {phi = -2^(1/2)+I*2^(1/2), x = 2}-161.8991983+4.242640686*I <- {phi = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[0.6440232508700339, 1.4142135623730951] <- {Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.04813130374017138, 2.8284271247461903] <- {Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-153.41391694554147, 4.242640687119286] <- {Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6440232508700339, -1.4142135623730951] <- {Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.04813130374017138, -2.8284271247461903] <- {Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-153.41391694554147, -4.242640687119286] <- {Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.184403873876156, -1.4142135623730951] <- {Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.704985553232552, -2.8284271247461903] <- {Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-161.89919831978006, -4.242640687119286] <- {Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.184403873876156, 1.4142135623730951] <- {Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.704985553232552, 2.8284271247461903] <- {Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-161.89919831978006, 4.242640687119286] <- {Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 3.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}} | diff(z, alpha)= -(diff(f, alpha))/(diff(f, z)) |
D[z, \[Alpha]]= -Divide[D[f, \[Alpha]],D[f, z]] |
Error | Failure | - | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 3.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{x}{a_{19}} = -\frac{20^{19}}{19!}} | diff(x, a[19])= -((20)^(19))/(factorial(19)) |
D[x, Subscript[a, 19]]= -Divide[(20)^(19),(19)!] |
Failure | Failure | - | Fail
4.309980412182177*^7 <- {} |
| 3.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{j,k,n} = \frac{\Pochhammersym{\beta+n+j}{k-1}}{\Pochhammersym{\beta+n+k}{k-1}}} | c[j , k , n]=(pochhammer(beta + n + j, k - 1))/(pochhammer(beta + n + k, k - 1)) |
Subscript[c, j , k , n]=Divide[Pochhammer[\[Beta]+ n + j, k - 1],Pochhammer[\[Beta]+ n + k, k - 1]] |
Failure | Failure | Fail .414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.4414781079+1.085101381*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.4516276191+1.143236990*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.4549477373+1.184751233*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}.8570095371+.9508656039*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}.8010420964+1.015789618*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.7580126529+1.064620824*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.4414781079-1.743325743*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.4516276191-1.685190134*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.4549477373-1.643675891*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}.8570095371-1.877561520*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}.8010420964-1.812637506*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.7580126529-1.763806300*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.386949016-1.743325743*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.376799505-1.685190134*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.373479387-1.643675891*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.971417587-1.877561520*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-2.027385028-1.812637506*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-2.070414471-1.763806300*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.386949016+1.085101381*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.376799505+1.143236990*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.373479387+1.184751233*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.971417587+.9508656039*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-2.027385028+1.015789618*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-2.070414471+1.064620824*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.6276520718+1.666209962*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.5793672000+1.632278667*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.5476645197+1.605271343*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}.9663885424+1.643106249*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}.8925940654+1.638133459*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.8347533131+1.629020817*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.6276520718-1.162217162*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.5793672000-1.196148457*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.5476645197-1.223155781*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}.9663885424-1.185320875*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}.8925940654-1.190293665*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.8347533131-1.199406307*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.200775052-1.162217162*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.249059924-1.196148457*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.280762604-1.223155781*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.862038582-1.185320875*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.935833059-1.190293665*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.993673811-1.199406307*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.200775052+1.666209962*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.249059924+1.632278667*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.280762604+1.605271343*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.862038582+1.643106249*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.935833059+1.638133459*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.993673811+1.629020817*I <- {beta = 2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.208760653+1.480035998*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.068408876+1.504539086*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.9681846297+1.512554560*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.365761498+1.438978420*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.303002493+1.461954053*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.239497495+1.478981212*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.208760653-1.348391126*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.068408876-1.323888038*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.9681846297-1.315872564*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.365761498-1.389448704*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.303002493-1.366473071*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.239497495-1.349445912*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.619666471-1.348391126*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.760018248-1.323888038*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.860242494-1.315872564*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.462665626-1.389448704*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.525424631-1.366473071*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.588929629-1.349445912*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.619666471+1.480035998*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.760018248+1.504539086*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.860242494+1.512554560*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.462665626+1.438978420*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.525424631+1.461954053*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.588929629+1.478981212*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.022586689+.8989274172*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.9406692954+1.015497410*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.8754678474+1.092034450*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.454501359+1.134354288*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.338758501+1.136173062*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.249113702+1.147535975*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.022586689-1.929499707*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.9406692954-1.812929714*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.8754678474-1.736392674*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.454501359-1.694072836*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.338758501-1.692254062*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.249113702-1.680891149*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.805840435-1.929499707*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.887757829-1.812929714*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.952959277-1.736392674*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.373925765-1.694072836*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.489668623-1.692254062*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.579313422-1.680891149*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.805840435+.8989274172*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.887757829+1.015497410*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.952959277+1.092034450*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.373925765+1.134354288*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.489668623+1.136173062*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.579313422+1.147535975*I <- {beta = 2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.6276520718+1.162217162*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.5793672000+1.196148457*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.5476645197+1.223155781*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}.9663885424+1.185320875*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}.8925940654+1.190293665*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.8347533131+1.199406307*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.6276520718-1.666209962*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.5793672000-1.632278667*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.5476645197-1.605271343*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}.9663885424-1.643106249*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}.8925940654-1.638133459*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.8347533131-1.629020817*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.200775052-1.666209962*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.249059924-1.632278667*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.280762604-1.605271343*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.862038582-1.643106249*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.935833059-1.638133459*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.993673811-1.629020817*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.200775052+1.162217162*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.249059924+1.196148457*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.280762604+1.223155781*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.862038582+1.185320875*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.935833059+1.190293665*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.993673811+1.199406307*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.4414781079+1.743325743*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.4516276191+1.685190134*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.4549477373+1.643675891*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}.8570095371+1.877561520*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}.8010420964+1.812637506*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.7580126529+1.763806300*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.4414781079-1.085101381*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.4516276191-1.143236990*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.4549477373-1.184751233*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}.8570095371-.9508656039*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}.8010420964-1.015789618*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.7580126529-1.064620824*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.386949016-1.085101381*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.376799505-1.143236990*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.373479387-1.184751233*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.971417587-.9508656039*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-2.027385028-1.015789618*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-2.070414471-1.064620824*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.386949016+1.743325743*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.376799505+1.685190134*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.373479387+1.643675891*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.971417587+1.877561520*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-2.027385028+1.812637506*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-2.070414471+1.763806300*I <- {beta = 2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.022586689+1.929499707*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.9406692954+1.812929714*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.8754678474+1.736392674*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.454501359+1.694072836*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.338758501+1.692254062*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.249113702+1.680891149*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.022586689-.8989274172*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.9406692954-1.015497410*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.8754678474-1.092034450*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.454501359-1.134354288*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.338758501-1.136173062*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.249113702-1.147535975*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.805840435-.8989274172*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.887757829-1.015497410*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.952959277-1.092034450*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.373925765-1.134354288*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.489668623-1.136173062*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.579313422-1.147535975*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.805840435+1.929499707*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.887757829+1.812929714*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.952959277+1.736392674*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.373925765+1.694072836*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.489668623+1.692254062*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.579313422+1.680891149*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.208760653+1.348391126*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.068408876+1.323888038*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.9681846297+1.315872564*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.365761498+1.389448704*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.303002493+1.366473071*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.239497495+1.349445912*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.208760653-1.480035998*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.068408876-1.504539086*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.9681846297-1.512554560*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.365761498-1.438978420*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.303002493-1.461954053*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.239497495-1.478981212*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.619666471-1.480035998*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.760018248-1.504539086*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.860242494-1.512554560*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.462665626-1.438978420*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.525424631-1.461954053*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.588929629-1.478981212*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.619666471+1.348391126*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.760018248+1.323888038*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.860242494+1.315872564*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.462665626+1.389448704*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.525424631+1.366473071*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.588929629+1.349445912*I <- {beta = 2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.062965440+1.100968446*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.8188417771+1.088593921*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.6901956924+1.128665076*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.301520357+1.278959578*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.160940783+1.211570289*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.043585169+1.188452138*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.062965440-1.727458678*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.8188417771-1.739833203*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.6901956924-1.699762048*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.301520357-1.549467546*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.160940783-1.616856835*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.043585169-1.639974986*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.765461684-1.727458678*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.009585347-1.739833203*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.138231432-1.699762048*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.526906767-1.549467546*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.667486341-1.616856835*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.784841955-1.639974986*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.765461684+1.100968446*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.009585347+1.088593921*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.138231432+1.128665076*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.526906767+1.278959578*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.667486341+1.211570289*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.784841955+1.188452138*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.176974456+2.094448161*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.358346064+1.930576773*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.4209779976+1.811275669*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.178459123+2.298092290*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.021003047+2.078730984*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.9181834183+1.950465404*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.176974456-.7339789634*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.358346064-.8978503507*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.4209779976-1.017151455*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.178459123-.5303348337*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.021003047-.7496961397*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.9181834183-.8779617197*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.651452668-.7339789634*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.470081060-.8978503507*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.407449126-1.017151455*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.649968001-.5303348337*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.807424077-.7496961397*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.910243706-.8779617197*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.651452668+2.094448161*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.470081060+1.930576773*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.407449126+1.811275669*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.649968001+2.298092290*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.807424077+2.078730984*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.910243706+1.950465404*I <- {beta = -2^(1/2)-I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.170454171+2.980439145*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.200328917+2.391072486*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.103588591+2.080493364*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}2.287834949+1.429364769*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.820657734+1.610780651*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.583618705+1.678273943*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.170454171+.152012021*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.200328917-.4373546378*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.103588591-.7479337601*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}2.287834949-1.399062355*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.820657734-1.217646473*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.583618705-1.150153181*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.657972953+.152012021*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.628098207-.4373546378*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.724838533-.7479337601*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-.5405921748-1.399062355*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.007769390-1.217646473*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.244808419-1.150153181*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.657972953+2.980439145*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.628098207+2.391072486*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.724838533+2.080493364*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-.5405921748+1.429364769*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.007769390+1.610780651*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.244808419+1.678273943*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}2.056445155+1.986959430*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.660824630+1.549089634*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.372806286+1.397882770*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.328864314+1.311777698*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.420213409+1.419014033*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.408005224+1.410431868*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}2.056445155-.8414676945*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.660824630-1.279337490*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.372806286-1.430544354*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.328864314-1.516649426*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.420213409-1.409413091*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.408005224-1.417995256*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-.7719819688-.8414676945*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.167602494-1.279337490*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.455620838-1.430544354*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.499562810-1.516649426*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.408213715-1.409413091*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.420421900-1.417995256*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-.7719819688+1.986959430*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.167602494+1.549089634*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.455620838+1.397882770*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.499562810+1.311777698*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.408213715+1.419014033*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.420421900+1.410431868*I <- {beta = -2^(1/2)-I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.176974456+.7339789634*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.358346064+.8978503507*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.4209779976+1.017151455*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.178459123+.5303348337*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.021003047+.7496961397*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.9181834183+.8779617197*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.176974456-2.094448161*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.358346064-1.930576773*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.4209779976-1.811275669*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.178459123-2.298092290*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.021003047-2.078730984*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.9181834183-1.950465404*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.651452668-2.094448161*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.470081060-1.930576773*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.407449126-1.811275669*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.649968001-2.298092290*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.807424077-2.078730984*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.910243706-1.950465404*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.651452668+.7339789634*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.470081060+.8978503507*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.407449126+1.017151455*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.649968001+.5303348337*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.807424077+.7496961397*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.910243706+.8779617197*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.062965440+1.727458678*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.8188417771+1.739833203*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.6901956924+1.699762048*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.301520357+1.549467546*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.160940783+1.616856835*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.043585169+1.639974986*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.062965440-1.100968446*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.8188417771-1.088593921*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.6901956924-1.128665076*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.301520357-1.278959578*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.160940783-1.211570289*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.043585169-1.188452138*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.765461684-1.100968446*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.009585347-1.088593921*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.138231432-1.128665076*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.526906767-1.278959578*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.667486341-1.211570289*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.784841955-1.188452138*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.765461684+1.727458678*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.009585347+1.739833203*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.138231432+1.699762048*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.526906767+1.549467546*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.667486341+1.616856835*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.784841955+1.639974986*I <- {beta = -2^(1/2)+I*2^(1/2), j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}2.056445155+.8414676945*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.660824630+1.279337490*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.372806286+1.430544354*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.328864314+1.516649426*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.420213409+1.409413091*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.408005224+1.417995256*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}2.056445155-1.986959430*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.660824630-1.549089634*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.372806286-1.397882770*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.328864314-1.311777698*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.420213409-1.419014033*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.408005224-1.410431868*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-.7719819688-1.986959430*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.167602494-1.549089634*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.455620838-1.397882770*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.499562810-1.311777698*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.408213715-1.419014033*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.420421900-1.410431868*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-.7719819688+.8414676945*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.167602494+1.279337490*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.455620838+1.430544354*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.499562810+1.516649426*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.408213715+1.409413091*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.420421900+1.417995256*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.170454171-.152012021*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.200328917+.4373546378*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.103588591+.7479337601*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}2.287834949+1.399062355*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.820657734+1.217646473*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.583618705+1.150153181*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.170454171-2.980439145*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.200328917-2.391072486*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.103588591-2.080493364*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}2.287834949-1.429364769*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.820657734-1.610780651*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.583618705-1.678273943*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.657972953-2.980439145*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.628098207-2.391072486*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.724838533-2.080493364*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-.5405921748-1.429364769*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.007769390-1.610780651*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.244808419-1.678273943*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.657972953-.152012021*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.628098207+.4373546378*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.724838533+.7479337601*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-.5405921748+1.399062355*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.007769390+1.217646473*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.244808419+1.150153181*I <- {beta = -2^(1/2)+I*2^(1/2), j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
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| 3.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{j,k,n} = \frac{\Pochhammersym{-\gamma-n-j}{k-1}}{\Pochhammersym{-\gamma-n-k}{k-1}}} | c[j , k , n]=(pochhammer(- gamma - n - j, k - 1))/(pochhammer(- gamma - n - k, k - 1)) |
Subscript[c, j , k , n]=Divide[Pochhammer[- \[Gamma]- n - j, k - 1],Pochhammer[- \[Gamma]- n - k, k - 1]] |
Failure | Failure | Fail .414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.5779684184+1.018874367*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.5421923338+1.105245476*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.5192456196+1.160643744*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.172531926+.9838385492*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.024835947+1.027375301*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.9256178569+1.067899574*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.5779684184-1.809552757*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.5421923338-1.723181648*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.5192456196-1.667783380*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.172531926-1.844588575*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.024835947-1.801051823*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.9256178569-1.760527550*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.250458706-1.809552757*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.286234790-1.723181648*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.309181504-1.667783380*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.655895198-1.844588575*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.803591177-1.801051823*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.902809267-1.760527550*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.250458706+1.018874367*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.286234790+1.105245476*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.309181504+1.160643744*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.655895198+.9838385492*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.803591177+1.027375301*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.902809267+1.067899574*I <- {j = 2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}.5779684184+1.809552757*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}.5421923338+1.723181648*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}.5192456196+1.667783380*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.172531926+1.844588575*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.024835947+1.801051823*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}.9256178569+1.760527550*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}.5779684184-1.018874367*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}.5421923338-1.105245476*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}.5192456196-1.160643744*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.172531926-.9838385492*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.024835947-1.027375301*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}.9256178569-1.067899574*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-2.250458706-1.018874367*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-2.286234790-1.105245476*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-2.309181504-1.160643744*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.655895198-.9838385492*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.803591177-1.027375301*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.902809267-1.067899574*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-2.250458706+1.809552757*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-2.286234790+1.723181648*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-2.309181504+1.667783380*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.655895198+1.844588575*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.803591177+1.801051823*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.902809267+1.760527550*I <- {j = 2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.368646809+1.809552757*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.160128505+1.723181648*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.026385256+1.667783380*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.544693175+1.355999798*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.485132544+1.487671898*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.400158487+1.542440204*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.368646809-1.018874367*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.160128505-1.105245476*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.026385256-1.160643744*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.544693175-1.472427326*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.485132544-1.340755226*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.400158487-1.285986920*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.459780315-1.018874367*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.668298619-1.105245476*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.802041868-1.160643744*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.283733949-1.472427326*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.343294580-1.340755226*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.428268637-1.285986920*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.459780315+1.809552757*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.668298619+1.723181648*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.802041868+1.667783380*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.283733949+1.355999798*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.343294580+1.487671898*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.428268637+1.542440204*I <- {j = -2^(1/2)-I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 1}.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 2}.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 1, n = 3}1.368646809+1.018874367*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 1}1.160128505+1.105245476*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 2}1.026385256+1.160643744*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 2, n = 3}1.544693175+1.472427326*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 1}1.485132544+1.340755226*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 2}1.400158487+1.285986920*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)+I*2^(1/2), k = 3, n = 3}.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 1}.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 2}.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 1, n = 3}1.368646809-1.809552757*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 1}1.160128505-1.723181648*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 2}1.026385256-1.667783380*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 2, n = 3}1.544693175-1.355999798*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 1}1.485132544-1.487671898*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 2}1.400158487-1.542440204*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = 2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 1}-2.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 2}-2.414213562-1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 1, n = 3}-1.459780315-1.809552757*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 1}-1.668298619-1.723181648*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 2}-1.802041868-1.667783380*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 2, n = 3}-1.283733949-1.355999798*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 1}-1.343294580-1.487671898*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 2}-1.428268637-1.542440204*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)-I*2^(1/2), k = 3, n = 3}-2.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 1}-2.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 2}-2.414213562+1.414213562*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 1, n = 3}-1.459780315+1.018874367*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 1}-1.668298619+1.105245476*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 2}-1.802041868+1.160643744*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 2, n = 3}-1.283733949+1.472427326*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 1}-1.343294580+1.340755226*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 2}-1.428268637+1.285986920*I <- {j = -2^(1/2)+I*2^(1/2), c[j,k,n] = -2^(1/2)+I*2^(1/2), k = 3, n = 3} |
Skip |
| 3.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n}@{x} = \cos@{n\acos@@{x}}} | ChebyshevT(n, x)= cos(n*arccos(x)) |
ChebyshevT[n, x]= Cos[n*ArcCos[x]] |
Failure | Successful | Skip | - |
| 3.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n+1}@{x}-2x\ChebyshevpolyT{n}@{x}+\ChebyshevpolyT{n-1}@{x} = 0} | ChebyshevT(n + 1, x)- 2*x*ChebyshevT(n, x)+ ChebyshevT(n - 1, x)= 0 |
ChebyshevT[n + 1, x]- 2*x*ChebyshevT[n, x]+ ChebyshevT[n - 1, x]= 0 |
Successful | Successful | - | - |
| 3.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-1}^{1}\frac{\ChebyshevpolyT{j}@{x}\ChebyshevpolyT{k}@{x}}{\sqrt{1-x^{2}}}\diff{x} = \begin{cases}\cpi,&j} | int((ChebyshevT(j, x)*ChebyshevT(k, x))/(sqrt(1 - (x)^(2))), x = - 1..1)= |
Integrate[Divide[ChebyshevT[j, x]*ChebyshevT[k, x],Sqrt[1 - (x)^(2)]], {x, - 1, 1}]= |
Error | Failure | - | Error |
| 3.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}\cpi,&j = k} | |
|
Error | Failure | - | Error |
| 3.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = 0,\\ \frac{1}{2}\cpi,&j} | k = 0 ,(1)/(2)*Pi , |
k = 0 ,Divide[1,2]*Pi , |
Error | Failure | - | Skip |
| 3.11.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}n,&j = k} | |
|
Error | Error | - | - |
| 3.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon_{n}(x) = d_{n+1}\ChebyshevpolyT{n+1}@{\frac{2x-a-b}{b-a}}} | epsilon[n]*(x)= d[n + 1]*ChebyshevT(n + 1, (2*x - a - b)/(b - a)) |
Subscript[\[Epsilon], n]*(x)= Subscript[d, n + 1]*ChebyshevT[n + 1, Divide[2*x - a - b,b - a]] |
Failure | Failure | Skip | Skip |
| 3.11.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{n-1}\phi_{k}(x_{j})\conj{\phi_{\ell}(x_{j})} = n\Kroneckerdelta{k}{\ell}} | sum(phi[k]*(x[j])* conjugate(phi[ell]*(x[j])), j = 0..n - 1)= n*KroneckerDelta[k, ell] |
Sum[Subscript[\[Phi], k]*(Subscript[x, j])* Conjugate[Subscript[\[Phi], \[ScriptL]]*(Subscript[x, j])], {j, 0, n - 1}]= n*KroneckerDelta[k, \[ScriptL]] |
Failure | Failure | Skip | Skip |
| 3.11.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{k} = \frac{1}{n}\sum_{j=0}^{n-1}f_{j}\conj{\phi_{k}(x_{j})}} | a[k]=(1)/(n)*sum(f[j]*conjugate(phi[k]*(x[j])), j = 0..n - 1) |
Subscript[a, k]=Divide[1,n]*Sum[Subscript[f, j]*Conjugate[Subscript[\[Phi], k]*(Subscript[x, j])], {j, 0, n - 1}] |
Failure | Failure | Skip | Skip |
| 3.11#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega_{n} = e^{2\cpi i/n}} | omega[n]= exp(2*Pi*I/ n) |
Subscript[\[Omega], n]= Exp[2*Pi*I/ n] |
Failure | Failure | Fail .414213562+1.414213561*I <- {omega[n] = 2^(1/2)+I*2^(1/2), n = 1}2.414213562+1.414213562*I <- {omega[n] = 2^(1/2)+I*2^(1/2), n = 2}1.914213562+.5481881580*I <- {omega[n] = 2^(1/2)+I*2^(1/2), n = 3}.414213562-1.414213563*I <- {omega[n] = 2^(1/2)-I*2^(1/2), n = 1}2.414213562-1.414213562*I <- {omega[n] = 2^(1/2)-I*2^(1/2), n = 2}1.914213562-2.280238966*I <- {omega[n] = 2^(1/2)-I*2^(1/2), n = 3}-2.414213562-1.414213563*I <- {omega[n] = -2^(1/2)-I*2^(1/2), n = 1}-.414213562-1.414213562*I <- {omega[n] = -2^(1/2)-I*2^(1/2), n = 2}-.9142135623-2.280238966*I <- {omega[n] = -2^(1/2)-I*2^(1/2), n = 3}-2.414213562+1.414213561*I <- {omega[n] = -2^(1/2)+I*2^(1/2), n = 1}-.414213562+1.414213562*I <- {omega[n] = -2^(1/2)+I*2^(1/2), n = 2}-.9142135623+.5481881580*I <- {omega[n] = -2^(1/2)+I*2^(1/2), n = 3} |
Successful |