ODE solver giving wrong results

Seems strange, when I simply copy and paste your code, i get

julia> sol = solve(prob, Vern7(), dt = 0.1, adaptive = false, reltol=1e-8);

julia> sol(1)
2-element Vector{ComplexF64}:
 3.125989776501887 + 0.000000000000000im
 5.058513100378909 + 0.000000000000000im

julia> 

which corresponds well enough to your analytical solution

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