Which quant prop shops/ hedge funds offer summer internships?

I'm a rising junior at a target for quant work, and I'm looking to apply to proprietary trading firms and quant hedge funds in Chicago and NYC. I have a list of some places I'm interested in (in no particular order):
1. Jane Street
2. Old Mission
3. Five Rings Capital
4. Two Sigma
5. Citadel
6. DE Shaw
7. DRW
8. Jump
9. Virtu
10. Teza
11. Tower
12. SIG
13. Spot
14. TransMarket
15. Optiver
16. First New York
17. CTC
18. Belvedere
19. Akuna
20. 3Red Partners
21. Wolverine
22. IMC
23. Hudson River

Among a few others.

I'm sure that only a minority of these companies offer summer internships. Is it worth it to send an email to HR even if no internships are being advertised? For example, in the case of Teza, which I understand is a very reputable company, there doesn't seem to be any mention of internships despite the fact that I know they've taken undergrads before.

Any recommendations?

 

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