import sympy as sp

# Define the symbolic variables
m1, m2, m3, m4, m5, m6, m7, m8 = sp.symbols('m1 m2 m3 m4 m5 m6 m7 m8')
p1, p2 = sp.symbols('p1 p2')
alpha, xi1, xi2, N0, S0_star = sp.symbols('alpha xi1 xi2 N0 S0_star')
eta1, eta2 = sp.symbols('eta1 eta2')
omega1, omega2, omega3, omega4, omega5 = sp.symbols('omega1 omega2 omega3 omega4 omega5')
q, h, gamma1, gamma2, gamma3 = sp.symbols('q h gamma1 gamma2 gamma3')

# Construct the Jacobian matrix
J = sp.Matrix([
    [-m1, 0, p1, -alpha*xi1/(N0)*S0_star, -alpha*xi2/(N0)*S0_star, 0, p2, 0],
    [0, -m2, 0, alpha*xi1/(N0)*S0_star, 0, alpha*xi2/(N0)*S0_star, 0, 0],
    [eta1, 0, -m3, 0, eta2, 0, 0, 0],
    [0, omega5, 0, -m4, omega1, 0, 0, 0],
    [0, q, 0, 0, -m5, 0, 0, 0],
    [0, omega3, 0, omega4, omega2, -m6, 0, 0],
    [0, 0, 0, 0, 0, h, -m7, 0],
    [0, 0, 0, gamma1, 0, gamma3, gamma2, -m8]
])

# Calculate the eigenvalues
eigenvalues = J.eigenvals()
eigenvalues