SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\SL2Invariant"];
<< SL2Invariant.m
SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\SL2Invariant\\k=2"];

OverbayP2Data=Get["C:\\drorbn\\AcademicPensieve\\People\\Overbay\\OverbayP2Data.m"];

$k=2; 
ℏ=γ=1;
$QZipFail=True;
tab=Table[
fname="Data/"<>(K/.{
Knot[n_,k_]:>ToString[n]<>"_"<>ToString[k],
Knot[n_,Alternating, k_]:>ToString[n]<>"a"<>ToString[k],
Knot[n_,NonAlternating, k_]:>ToString[n]<>"n"<>ToString[k]
})<>".m";
Get[fname],
{K,AllKnots[{3,12}]}
]

Length[tab]

Ks=First /@ tab

Knot[3,1]/.tab

ρ1[K_]:=ϵSeries@@(K/.tab)[[2,4,1;;2]];
ρ2[K_]:=ϵSeries@@(K/.tab)[[2,4,1;;3]]

{ρ1[Knot[3,1]],ρ2[Knot[3,1]]}

Union[ρ1/@Ks]//Length

Union[ρ2/@Ks]//Length

classes1=DeleteCases[GatherBy[Ks,ρ1], {_}]

Tally[Length/@classes1]

classes2=DeleteCases[GatherBy[Ks,ρ2], {_}]

Tally[Length/@classes2]

Complement[classes1,classes2]

Complement[classes2,classes1]

equiv={Knot[12,Alternating,427],Knot[12,Alternating,435],Knot[12,Alternating,990]};
Length@Union[ρ1/@equiv]
Length@Union[ρ2/@equiv]

equiv={Knot[10,106],Knot[12,NonAlternating,369]};
Length@Union[ρ1/@equiv]
Length@Union[ρ2/@equiv]

Total[First /@ ({Knot[10,106],Knot[12,NonAlternating,369]}/.tab)]

First /@ ({Knot[12,Alternating,427],Knot[12,Alternating,435],Knot[12,Alternating,990],Knot[10,106],Knot[12,NonAlternating,369]}/.tab)

Total[First /@ ({Knot[12,Alternating,427],Knot[12,Alternating,435],Knot[12,Alternating,990],Knot[10,106],Knot[12,NonAlternating,369]}/.tab)]

Total[First /@ ({Knot[12,NonAlternating,60],Knot[12,NonAlternating,61],Knot[12,NonAlternating,219]}/.tab)]