"Very quadratic nonresidue numbers"

[sweety439]

Positive "very quadratic nonresidue numbers": Positive integers n which is quadratic nonresidue mod all odd primes <=sqrt(n) not dividing n:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 27, 30, 32, 33, 35, 38, 42, 45, 47, 48, 62, 63, 68, 75, 77, 80, 83, 87, 90, 98, 105, 108, 110, 117, 132, 138, 140, 143, 150, 153, 167, 182, 195, 215, 227, 252, 255, 318, 398, 437, 447, 483, 572, 635, 930, 1295, 1722}

Negative "very quadratic nonresidue numbers": Negative integers -n which is quadratic nonresidue mod all odd primes <=sqrt(n) not dividing n:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 33, 37, 40, 42, 43, 45, 48, 57, 58, 60, 63, 67, 70, 72, 78, 85, 88, 93, 100, 102, 105, 112, 120, 130, 133, 135, 147, 148, 163, 165, 168, 177, 190, 210, 232, 240, 247, 253, 267, 268, 273, 280, 312, 330, 333, 345, 357, 385, 408, 462, 520, 522, 652, 708, 760, 840, 928, 1320, 1365, 1467, 1848}

Prove or disprove that these two sequences are both complete.

[sweety439]

Note: For these values of n:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 18, 21, 24, 30, 45, 105}

The range of primes is empty, thus these (positive or negative) numbers n are trivially very quadratic nonresidue numbers.

[sweety439]

These are the smallest odd prime p such that Legendre symbol(n,p) = 1, I am shocked that these two sequences are currently not in OEIS, only two related sequences for "pseudosquares": A002189 and A045535 are currently in OEIS.

Records:

Positive n:

1,3
2,7
3,11
17,13
33,17
63,19
143,31
398,37
635,41
930,47
1295,61
101283,71
341502,73
730847,79
845382,83
3009173,101

Negative n:

1,5
3,7
7,11
15,17
37,19
58,31
163,41
462,43
3063,53
15855,59
30493,67
106177,73
656755,79
5013702,103