When convert context free grammar to push down automata are these steps correct?

Question

The CFG is as follows −

S->aSa

S->aSa

S->c

When convert context free grammar to push down automata are these steps correct?

The rules for the conversion are as follows −

S(q0, ɛ, ɛ)=(q0, ɛ)

S(q0, ɛ,S)=(q0,aSa)

S(q0, ɛ,S)=(q0,bsb)

(q0, ɛ,S)=(q0,c)

Now start pop to convert

S(q0,a,a)=(q1, ɛ)

S(q1,b,b)=(q2, ɛ)

S(q2,c,c)=(q3, ɛ)

Are these steps correct especially when convert context free grammar to push down automata?

These steps; Now start pop to convert

S(q0,a,a)=(q1, ɛ)

S(q1,b,b)=(q2, ɛ)

S(q2,c,c)=(q3, ɛ)

Is the transition table correct? [Transition table[1] [1]: https://i.stack.imgur.com/TkP9v.png