Knot[4, 1] -> {15.875, Subscript[\[DoubleStruckCapitalE], {} -> {0}][
   (-1 + 3*T - T^2)/T, 0, 0, 
   {1, (-1 + 9*T - 29*T^2 + 36*T^3 - 36*T^5 + 29*T^6 - 9*T^7 + T^8)/T^4 + 
     (a*(-2 + 18*T - 58*T^2 + 72*T^3 - 72*T^5 + 58*T^6 - 18*T^7 + 2*T^8))/
      T^4 + ((-2 + 16*T - 42*T^2 + 30*T^3 + 30*T^4 - 42*T^5 + 16*T^6 - 2*T^7)*
       x*y)/T^4, (1 - 15*T + 83*T^2 - 128*T^3 - 797*T^4 + 5357*T^5 - 
       15934*T^6 + 29161*T^7 - 35456*T^8 + 29161*T^9 - 15934*T^10 + 
       5357*T^11 - 797*T^12 - 128*T^13 + 83*T^14 - 15*T^15 + T^16)/(2*T^8) + 
     (a*(2 - 30*T + 162*T^2 - 192*T^3 - 2038*T^4 + 12474*T^5 - 36308*T^6 + 
        65874*T^7 - 79884*T^8 + 65874*T^9 - 36308*T^10 + 12474*T^11 - 
        2038*T^12 - 192*T^13 + 162*T^14 - 30*T^15 + 2*T^16))/T^8 + 
     (a^2*(2 - 30*T + 162*T^2 - 192*T^3 - 2038*T^4 + 12474*T^5 - 36308*T^6 + 
        65874*T^7 - 79884*T^8 + 65874*T^9 - 36308*T^10 + 12474*T^11 - 
        2038*T^12 - 192*T^13 + 162*T^14 - 30*T^15 + 2*T^16))/T^8 + 
     (a*(4 - 52*T + 192*T^2 + 508*T^3 - 7068*T^4 + 28800*T^5 - 65404*T^6 + 
        91684*T^7 - 79884*T^8 + 40064*T^9 - 7212*T^10 - 3852*T^11 + 
        2992*T^12 - 892*T^13 + 132*T^14 - 8*T^15)*x*y)/T^8 + 
     ((3 - 43*T + 228*T^2 - 393*T^3 - 1197*T^4 + 7806*T^5 - 18561*T^6 + 
        24331*T^7 - 18561*T^8 + 7806*T^9 - 1197*T^10 - 393*T^11 + 228*T^12 - 
        43*T^13 + 3*T^14)*x^2*y^2)/T^8}]}
