QuantumGroupsPath = "~/Documents/Math/QuantumGroups/trunk/package/";
AppendTo[$Path, QuantumGroupsPath];
<<QuantumGroups`

qDimension[G2][Irrep[G2][{0,2}]]

a=(q^60)
z=σ1 (q^(-48))+σ2 (q^(-30))
dK=(((a+(a^(-1))))/z)-1
dD=(((a-(a^(-1))))/z)+1

Table[Simplify[(dD/.{σ1->1,σ2->1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dD/.{σ1->1,σ2->-1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dD/.{σ1->-1,σ2->1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dD/.{σ1->-1,σ2->-1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dK/.{σ1->1,σ2->1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dK/.{σ1->1,σ2->-1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dK/.{σ1->-1,σ2->1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]

Table[Simplify[(dK/.{σ1->-1,σ2->-1,q->Exp[2 Pi I (k/26)] })==(((q^2)+1+(q^(-2)))/.{q->Exp[((2 Pi I)/52)]})],{k,1,25}]