SetDirectory["C:\\drorbn\\AcademicPensieve\\Classes\\23-FastComputations"];
Once[<< KnotTheory`]

PK=PD[
X[4,48,5,47],X[5,40,6,41],X[6,68,7,67],X[11,97,12,96],
X[12,62,13,61],X[13,26,14,27],X[14,82,15,81],X[20,105,21,106],
X[22,43,23,44],X[23,65,24,64],X[24,9,25,10],X[25,99,26,98],
X[29,18,30,19],X[30,90,31,89],X[31,2,32,3],X[32,76,33,75],
X[35,53,36,52],X[36,72,37,71],X[39,49,40,48],X[44,21,45,22],
X[45,87,46,86],X[50,38,51,37],X[51,70,52,71],X[54,34,55,33],
X[55,74,56,75],X[56,4,57,3],X[57,88,58,89],X[58,20,59,19],
X[62,97,63,98],X[63,11,64,10],X[68,49,69,50],X[69,39,70,38],
X[72,53,73,54],X[73,35,74,34],X[76,2,77,1],X[77,90,78,91],
X[78,18,79,17],X[82,99,83,100],X[83,9,84,8],X[84,65,85,66],
X[85,43,86,42],X[87,105,88,104],X[92,16,93,15],X[93,80,94,81],
X[94,28,95,27],X[95,60,96,61],X[100,8,101,7],X[101,66,102,67],
X[102,42,103,41],X[103,46,104,47],X[106,60,107,59],X[107,28,108,29],
X[108,80,109,79],X[109,16,110,17],X[110,92,1,91]
];

Crossings[PK]

Jones[PK][q]

Alexander[PK][t]

?Kh

Kh[PD@Knot[3,1]][q,t]

SetOptions[Kh,JavaOptions->"-Xmx1024m"];
kh=Kh[PK][q,t]

(1/q)+2 q+(q^3)+(1/((q^5) (t^3)))+(2/((q^3) (t^2)))+(1/(q (t^2)))+((2 q)/t)+2 q t+3 (q^3) t+(q^5) t+3 (q^3) (t^2)+3 (q^5) (t^2)+2 (q^7) (t^2)+3 (q^5) (t^3)+3 (q^7) (t^3)+(q^9) (t^3)+2 (q^5) (t^4)+3 (q^7) (t^4)+3 (q^9) (t^4)+3 (q^7) (t^5)+5 (q^9) (t^5)+3 (q^11) (t^5)+3 (q^9) (t^6)+5 (q^11) (t^6)+3 (q^13) (t^6)+(q^9) (t^7)+4 (q^11) (t^7)+4 (q^13) (t^7)+2 (q^15) (t^7)+2 (q^11) (t^8)+5 (q^13) (t^8)+4 (q^15) (t^8)+(q^17) (t^8)+4 (q^13) (t^9)+5 (q^15) (t^9)+4 (q^17) (t^9)+(q^13) (t^10)+3 (q^15) (t^10)+6 (q^17) (t^10)+3 (q^19) (t^10)+2 (q^15) (t^11)+4 (q^17) (t^11)+4 (q^19) (t^11)+2 (q^21) (t^11)+(q^15) (t^12)+2 (q^17) (t^12)+6 (q^19) (t^12)+3 (q^21) (t^12)+(q^23) (t^12)+(q^17) (t^13)+4 (q^19) (t^13)+4 (q^21) (t^13)+4 (q^23) (t^13)+(q^19) (t^14)+4 (q^21) (t^14)+4 (q^23) (t^14)+2 (q^25) (t^14)+(q^19) (t^15)+3 (q^21) (t^15)+3 (q^23) (t^15)+3 (q^25) (t^15)+(q^27) (t^15)+(q^21) (t^16)+4 (q^23) (t^16)+5 (q^25) (t^16)+2 (q^27) (t^16)+2 (q^23) (t^17)+3 (q^25) (t^17)+4 (q^27) (t^17)+2 (q^29) (t^17)+2 (q^25) (t^18)+4 (q^27) (t^18)+2 (q^29) (t^18)+(q^31) (t^18)+(q^25) (t^19)+2 (q^27) (t^19)+4 (q^29) (t^19)+2 (q^31) (t^19)+(q^27) (t^20)+4 (q^29) (t^20)+3 (q^31) (t^20)+2 (q^33) (t^20)+(q^29) (t^21)+2 (q^31) (t^21)+3 (q^33) (t^21)+(q^35) (t^21)+2 (q^31) (t^22)+2 (q^33) (t^22)+(q^35) (t^22)+(q^31) (t^23)+(q^33) (t^23)+3 (q^35) (t^23)+(q^37) (t^23)+(q^33) (t^24)+2 (q^35) (t^24)+(q^37) (t^24)+(q^39) (t^24)+(q^35) (t^25)+2 (q^37) (t^25)+(q^39) (t^25)+(q^35) (t^26)+(q^37) (t^26)+(q^39) (t^26)+(q^41) (t^26)+2 (q^39) (t^27)+(q^41) (t^27)+(q^39) (t^28)+(q^41) (t^28)+(q^43) (t^28)+(q^41) (t^29)+(q^43) (t^29)+(q^45) (t^29)+(q^45) (t^30)+(q^45) (t^31)+(q^49) (t^32)

(CoefficientList[(q^5) (t^3)kh,{q,t}]/.{0..}->Nothing/. 0->"")//Reverse//MatrixForm