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dCdS2=beta*(-8*mu*sqrt(-E/rho^(4/3))*(-mu*sqrt(-E/rho^(4/3))*(-8*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E))/E + 81*pi*rho^2*exp(9*pi*rho^2/(4*mu^2*E))/(mu^2*E^2))/(sqrt(pi)*rho^(1/3)) + mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)*E) + (mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)) + 47.8562539744489*erf(3*sqrt(pi)*rho^(1/3)/(2*mu*sqrt(-E/rho^(4/3)))))/E - 143.568761923347*rho^(1/3)*exp(9*pi*rho^2/(4*mu^2*E))/(mu*sqrt(-E/rho^(4/3))*E))*dEdS^2/(sqrt(pi)*rho^(1/3)) + mu*sqrt(-E/rho^(4/3))*(4*mu*sqrt(-E/rho^(4/3))*(-8*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E))/E + 81*pi*rho^2*exp(9*pi*rho^2/(4*mu^2*E))/(mu^2*E^2))*dEdS^2/(sqrt(pi)*rho^(1/3)*E) - 4*mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)*d2EdS2/(sqrt(pi)*rho^(1/3)*E) + 2*mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)*dEdS^2/(sqrt(pi)*rho^(1/3)*E^2) - mu*sqrt(-E/rho^(4/3))*(32*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*d2EdS2/(pi*rho^2) - 72*exp(9*pi*rho^2/(4*mu^2*E))*d2EdS2/E - 324*pi*rho^2*exp(9*pi*rho^2/(4*mu^2*E))*d2EdS2/(mu^2*E^2) + 810*pi*rho^2*exp(9*pi*rho^2/(4*mu^2*E))*dEdS^2/(mu^2*E^3) + 729*pi^2*rho^4*exp(9*pi*rho^2/(4*mu^2*E))*dEdS^2/(mu^4*E^4))/(sqrt(pi)*rho^(1/3)) - 4*(mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)) + 47.8562539744489*erf(3*sqrt(pi)*rho^(1/3)/(2*mu*sqrt(-E/rho^(4/3)))))*d2EdS2/E + 2*(mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)) + 47.8562539744489*erf(3*sqrt(pi)*rho^(1/3)/(2*mu*sqrt(-E/rho^(4/3)))))*dEdS^2/E^2 + 4*(mu*sqrt(-E/rho^(4/3))*(-8*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E))/E + 81*pi*rho^2*exp(9*pi*rho^2/(4*mu^2*E))/(mu^2*E^2))/(sqrt(pi)*rho^(1/3)) - mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)*E) + 143.568761923347*rho^(1/3)*exp(9*pi*rho^2/(4*mu^2*E))/(mu*sqrt(-E/rho^(4/3))*E))*dEdS^2/E + 574.275047693387*rho^(1/3)*exp(9*pi*rho^2/(4*mu^2*E))*d2EdS2/(mu*sqrt(-E/rho^(4/3))*E) - 861.412571540081*rho^(1/3)*exp(9*pi*rho^2/(4*mu^2*E))*dEdS^2/(mu*sqrt(-E/rho^(4/3))*E^2) - 1292.11885731012*pi*rho^(7/3)*exp(9*pi*rho^2/(4*mu^2*E))*dEdS^2/(mu^3*sqrt(-E/rho^(4/3))*E^3))*E/(sqrt(pi)*rho^(1/3)) - (8*mu*sqrt(-E/rho^(4/3))*(mu*sqrt(-E/rho^(4/3))*(4*mu^2*(exp(9*pi*rho^2/(4*mu^2*E)) - 1)*E/(pi*rho^2) + 18*exp(9*pi*rho^2/(4*mu^2*E)) - 27)/(sqrt(pi)*rho^(1/3)) + 47.8562539744489*erf(3*sqrt(pi)*rho^(1/3)/(2*mu*sqrt(-E/rho^(4/3)))))/(sqrt(pi)*rho^(1/3)) - 243)*d2EdS2)/243
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