Solutions of x/y+y/z+z/x=n

In case of -100 ≤ n ≤ -1 where 0 ≤ (x,y,z) ≤ 1000

n	x	y	z
-4	-1	2	4
-4	1	2	-4
-4	112	441	-324
-4	144	567	-196
-9	-1	3	9
-9	1	3	-9
-10	-4	112	49
-10	7	-196	16
-16	-1	4	16
-16	1	4	-16
-16	-20	325	338
-16	50	52	-845
-17	7	441	-81
-17	9	567	-49
-22	4	144	-81
-22	9	324	-16
-24	-2	28	49
-24	4	7	-98
-25	-1	5	25
-25	1	5	-25
-25	2	28	-49
-25	-4	7	98
-36	-1	6	36
-36	1	6	-36
-49	-1	7	49
-49	1	7	-49
-49	7	882	-324
-49	-7	931	361
-57	3	117	-169
-57	-9	13	507
-60	-12	171	722
-64	-1	8	64
-64	1	8	-64
-81	-1	9	81
-81	1	9	-81
-100	-1	10	100
-100	1	10	-100

Parametrized solution

-n^2 : (1, n, -n^2), (-1, n, n^2)

In case of 1 ≤ n ≤ 100 where 0 ≤ (x,y,z) ≤ 1000

n	x	y	z
3	1	1	1
5	1	2	4
6	2	12	9
6	3	18	4
9	12	63	98
9	18	28	147
14	28	637	338
15	3	-63	49
15	-7	147	9
19	5	225	81
19	9	405	25
40	2	-36	81
40	4	-9	162
41	2	36	81
41	4	9	162
41	4	-208	169
41	5	350	196
41	-13	676	16
41	14	980	25
66	3	126	196
66	9	14	588
87	5	-525	441