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evil n.  and  square n.

First numbers that belong to both sets:

9, 36, 144, 169, 225, 441, 576, 676, 729, 900, 1369, 1764, 2025, 2209, 2304, 2704, 2809, 2916, 3249, 3600, 3721, 3969, 4761, 5329, 5476, 6561, 6889, 7056, 8100, 8649, 8836, 9216, 9801, 10816, 11025, 11236, 11449, 11664, 11881, 12321, 12996, 13225, 14161, 14400, 14884, 15129, 15876, 17689, 18769, 19044, 19881, 21316, 21904, 22801, 24025, 25281, 25921, 26244, 27225, 27556, 28224, 29241, 31329, 32400, 33489, 34596, 34969, 35344, 36481, 36864, 38025, 39204, 39601, 41209, 42025, 42849, 43264, 44100, 44521, 44944, 45369, 45796, 46656, 47524, 47961, 48841, 49284, 51984, 52900, 54289, 56169, 56644, 57600, 58081, 59536, 60025, 60516, 62001, 63504, 64009, 65025, 68121, 70225, 70756, 72361, 74529, 75076, 76176, 76729, 78961, 79524, 82369, 83521, 84681, 85264, 85849, 87025, 87616, 89401, 91204, 91809, 96100, 96721, 99225, 100489, 101124, 103041, 103684, 104976, 106929, 108900, 109561, 110224, 110889, 112896, 113569, 114921, 116964, 120409, 125316, 128881, 129600, 130321, 133225, 133956, 134689, 136161, 137641, 138384, 139876, 141376, 142129, 145161, 145924, 147456, 149769, 152100, 152881, 156816, 157609, 158404, 159201, 162409, 164836, 168100, 168921, 170569, 171396, 172225, 173056, 173889, 175561, 176400, 178084, 179776, 181476, 182329, 183184, 186624, 190096, 190969, 191844, 194481, 195364, 196249, 197136, 199809, 203401, 205209, 207025, 207936, 210681, 211600, 212521, 214369, 216225, 217156, 221841, 224676, 225625, 226576, 227529, 230400, 232324, 233289, 238144, 239121, 240100, 241081, 242064, 245025, 248004, 249001, 253009, 254016, 256036, 257049, 260100, 267289, 271441, 272484, 275625, 279841, 280900, 283024, 284089, 286225, 289444, 292681, 298116, 300304, 304704, 305809, 306916, 308025, 310249, 315844, 318096, 328329, 329476, 332929, 334084, 338724, 341056, 343396, 344569, 348100, 349281, 350464, 351649, 357604, 358801, 364816, 366025, 367236, 368449, 370881, 378225, 380689, 384400, 385641, 386884, 390625, 393129, 396900, 398161, 401956, 404496, 408321, 410881, 412164, 414736, 419904, 421201, 426409, 427716, 429025, 431649, 434281, 435600.

Some larger examples :