v=Simplify[Sum[ζ[i]nsn[[i]],{i,1,8}]];

t=Tensor20;

v2=Simplify[Table[Sum[t[[a,b,c]]v[[a]]v[[c]],{a,1,20},{b,1,20}],{c,1,20}]];

eqs=caps.v2;

Collect[eqs[[1]],_ζ1,Simplify]

Length[eqs]

(eqs==0)/.{d1->3.7,d2->4.2}

roots={};

Do[AppendTo[roots,FindRoot[Take[eqs,7]/.ζ[1]->1/.{d1->3.7,d2->4.2},Table[{ζ[i],RandomReal[]},{i,2,8}],WorkingPrecision->30]];,{200}]

Sort[roots[[All,1,2]]]

Outer[Max[Abs[Chop[#1-#2]]]&,roots[[All,All,2]],roots[[All,All,2]],1];

Position[%,0]

DeleteCases[%,{a_,a_}]

J/.%

Det[%]

J=Table[D[Take[eqs,7]/.ζ[1]->1/.{d1->3.7,d2->4.2},ζ[i]],{i,2,8}]

Table[Max[Abs[Drop[eqs,7]/.ζ[1]->1/.{d1->3.7,d2->4.2}/.roots[[k]]]],{k,1,Length[roots]}]

Min[%]

NSolve[(eqs==0)/.{d1->3.7,d2->42.},Table[ζ[i],{i,1,8}]]