> 
[lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],

> 
[0,lambda3/4,0,0,0,0,0,0,0,0],

> 
[0,0,lambda3/4,0,0,0,0,0,0,0],

> 
[0,0,0,lambda3/4,0,0,0,0,0,0],

> 
[0,0,0,0,lambda3/4,0,0,0,0,0],

> 
[0,0,0,0,0,lambda3,0,0,0,0],

> 
[lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],

> 
[0,0,0,0,0,0,0,lambda2,0,0],

> 
[0,0,0,0,0,0,0,0,lambda2,0],

> 
[I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]

> 
ar:=simplify(radnormal~(Eigenvalues(M1))) assuming real:

> 
P:=1176*lambda4^672*lambda4^5*lambda3+27*lambda4^4*lambda3^2 114*lambda4^3*lambda3^3+135*lambda4^2*lambda3^4 +36*lambda3^5*lambda4+12*lambda3^6;


(1) 
> 
map(u>simplify(simplify(radnormal(combine(evalc(Im(u))))),size),ar^%T) assuming lambda2::real, lambda3::real, lambda4::real, P>=0;


(2) 
> 
new:=map(proc(u) if not has(u,I) then u; else simplify(simplify(radnormal(combine(evalc((u))))),size) assuming lambda3::real, lambda4::real, P>=0; end if; end proc, ar):


(3) 
> 
#plot3d(P,lambda3=0.1..0.1,lambda4=0.1..0.1,axes=box,view=0.001..0.001);

