p= 3 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=2 != 0 (closed formula confirmed for all c1); image has order 72 = 8p^2; kappa of the GOOD_ORBIT seeds of regfull: [1, 2] = all nonzero residues, once each
p= 7 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=2 != 0 (closed formula confirmed for all c1); image has order 392 = 8p^2; kappa of the GOOD_ORBIT seeds of regfull: [1, 2, 3, 4, 5, 6] = all nonzero residues, once each
p=11 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=10 != 0 (closed formula confirmed for all c1); image has order 968 = 8p^2; kappa of the GOOD_ORBIT seeds of regfull: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] = all nonzero residues, once each
p=19 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=18 != 0 (closed formula confirmed for all c1)
p=23 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=10 != 0 (closed formula confirmed for all c1)
p=31 (3 mod 4): no eigenvectors for elements of order 4; phi_p with c1=0 has kappa=13 != 0 (closed formula confirmed for all c1)
p= 5 (1 mod 4): elements of order 4 HAVE eigenvectors (Lemma A does not apply); number of GOOD orbits found by regfull: 0
p=13 (1 mod 4): elements of order 4 HAVE eigenvectors (Lemma A does not apply)
ALL CHECKS PASSED
