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(1) Yep, it should return something symbolic, but unfortunately it doesn't right now. Some relevant tickets are #4102 and #7636 (see the referenced thread). I'll try to make it a priority to get that done for 4.6.2.

(2) I don't think anything's been done with that yet either. mpmath provides efficient numerical evaluation of the zeros (see here ). It should be easy to make a symbolic wrapper around that. I've made this #10636.