R6alphabeta[x_]=x^6+(-6s)x^5+a4 x^4+a3 x^3+a2 x^2+a1 x+a0;
a0=-1-a2-a4;
a1=-a3-L+6 s;
a2=3/256 (48-1792 s^2+4608 s^4+160 s \[Alpha]-2304 s^3 \[Alpha]+40 \[Alpha]^2-96 s^2 \[Alpha]^2+136 s \[Alpha]^3-9 \[Alpha]^4+160 s \[Beta]-2304 s^3 \[Beta]-80 \[Alpha] \[Beta]+1600 s^2 \[Alpha] \[Beta]-200 s \[Alpha]^2 \[Beta]-12 \[Alpha]^3 \[Beta]+40 \[Beta]^2-96 s^2 \[Beta]^2-200 s \[Alpha] \[Beta]^2+42 \[Alpha]^2 \[Beta]^2+136 s \[Beta]^3-12 \[Alpha] \[Beta]^3-9 \[Beta]^4);
a3=1/4 (32 s-144 s^3+36 s^2 \[Alpha]+6 s \[Alpha]^2-\[Alpha]^3+36 s^2 \[Beta]-20 s \[Alpha] \[Beta]+\[Alpha]^2 \[Beta]+6 s \[Beta]^2+\[Alpha] \[Beta]^2-\[Beta]^3);
a4=3/8 (-4+48 s^2-4 s \[Alpha]-\[Alpha]^2-4 s \[Beta]+2 \[Alpha] \[Beta]-\[Beta]^2);
L=1/640 (208 s+41472 s^5+480 s^2 \[Alpha]-34560 s^4 \[Alpha]+24 s \[Alpha]^2+4320 s^3 \[Alpha]^2-32 \[Alpha]^3+2520 s^2 \[Alpha]^3-615 s \[Alpha]^4+24 \[Alpha]^5+480 s^2 \[Beta]-34560 s^4 \[Beta]-304 s \[Alpha] \[Beta]+31680 s^3 \[Alpha] \[Beta]+32 \[Alpha]^2 \[Beta]-7320 s^2 \[Alpha]^2 \[Beta]-180 s \[Alpha]^3 \[Beta]+120 \[Alpha]^4 \[Beta]+24 s \[Beta]^2+4320 s^3 \[Beta]^2+32 \[Alpha] \[Beta]^2-7320 s^2 \[Alpha] \[Beta]^2+2358 s \[Alpha]^2 \[Beta]^2-144 \[Alpha]^3 \[Beta]^2-32 \[Beta]^3+2520 s^2 \[Beta]^3-180 s \[Alpha] \[Beta]^3-144 \[Alpha]^2 \[Beta]^3-615 s \[Beta]^4+120 \[Alpha] \[Beta]^4+24 \[Beta]^5);