“…While the Fourier transforms of the densities of the orthogonal groups all equal δ 0 (y)+1/2 in (−1, 1), they are mutually distinguishable for larger support (and are distinguishable from the unitary and symplectic cases for any support). There is now an enormous body of work showing the 1-level densities of many families (such as Dirichlet L-functions, elliptic curves, cuspidal newforms, Maass forms, number field L-functions, and symmetric powers of GL 2 automorphic representations) agree with the scaling limits of a random matrix ensemble; see [AAILMZ,AM,DM1,FiMi,FI,Gao,GK,Gü,HM,HR,ILS,KS1,KS2,Mil,MilPe,OS1,OS2,RR,Ro,Rub1,Rub2,ShTe,Ya,Yo] for some examples, and [DM1,DM2,ShTe] for discussions on how to determine the underlying symmetry. For additional readings on connections between random matrix theory, nuclear physics and number theory see Con,CFKRS,FM,For,KeSn1,KeSn2,KeSn3,Meh] We concentrate on extending the results of Iwaniec, Luo, and Sarnak in [ILS].…”