Note on Dirichlet's L-Functions

At Chowla's suggestion, I have studied in for the primitive real characters modulo p, where p is a prime less than 500. I find that

m = 1, when p =3, 7,11, 23, 31, 47, 59, 71, 79, 8 3; 103, 131, 151, 167, 191, 199; 239, 251, 263, 271; 311, 359, 383; 419, 431, 439, 479.

m = 3, when p = 53; 211; 347.

It has not been possible to determine m when

p = 43, 67; 163, 173, 197; 283, 293; 307, 317, 331, 379; 443, 4.1, 463, 487, 499.

For all other odd primes p < 500, m = 2.