What are some T20-50 schools that value SAT/ACT much higher than GPA?

I will be applying to colleges in the fall as an engineering major with the following:
1480 SAT (790 M 690 CRW)
33 ACT
3.5 GPA
With the lackluster GPA being my greatest downfall, what are some T20-50 schools in which my test scores will be much more influential than my GPA during the admissions process. Thank you for any insight.

i don’t know of any that admit to valuing test scores more than GPA, but here are some that, it seems, might value test scores more than most schools (some higher than the top 20…):

Caltech
MIT
Vanderbilt
Washington U
Northeastern

I realize only one of those is outside the top 20.

One way to figure it out is to look at schools in, say, ranking blocks of 10 (1-10, 11-20, 21-30, etc.) and see if one has markedly higher average test scores than the rest, relative to rank and overall rep. That’s the school that probably values test scores more than the rest. (though there may be other explanations…). Though schools 40-50 do not have all the same applicants, it may be likely that the overall caliber of applicants is similar among those schools… so if one school is letting in more high-stat kids, it may mean they are somewhat less holistic than some peers.

Also check GPA – if a school has higher test scores and GPA vs. ranking peers, then maybe they’re just more fixated on stats altogether and not just test scores.

At the other end of the spectrum – schools that don’t seem to care as much about test scores as their peers – are schools like Stanford, Penn, Brown, Johns Hopkins, Emory, and Georgetown.