[Antreas P. Hatzipolakis]:
[Peter Moses]:
Hi Antreas,
X(12100) = X[2] + 3 X[3].
and
(3 t - 5) X[2] - 3 (t + 1) X[3].
For t = 2 (ie A'2, B'2, C'2 = the reflections of A1, B1, C1 in OA', OB', OC', resp.):
26 a^4-25 a^2 b^2-b^4-25 a^2 c^2+2 b^2 c^2-c^4::
Let ABC be a triangle and A'B'C' the cevian triangle of G.
Denote:
A1, B1, C1 = the midpoints of AA', BB', CC', resp.
A2, B2, C2 = orthogonal projections of A1, B1, C1 on OA', OB', OC', resp.
Oa, Ob, Oc = the circumcenters of AA1A2, BB1B2, CC1C2, resp.
The centroid of OaObOc lies on the Euler line of ABC.
GENERALIZATION
Denote:
A1, B1, C1 = the midpoints of AA', BB', CC', resp.
A2, B2, C2 = orthogonal projections of A1, B1, C1 on OA', OB', OC', resp.
Oa, Ob, Oc = the circumcenters of AA1A2, BB1B2, CC1C2, resp.
The centroid of OaObOc lies on the Euler line of ABC.
GENERALIZATION
Let ABC be a triangle and A'B'C' the cevian triangle of G.
Denote:
A1, B1, C1 = the midpoints of AA', BB', CC', resp.
A2, B2, C2 = orthogonal projections of A1, B1, C1 on OA', OB', OC', resp.
Denote:
A1, B1, C1 = the midpoints of AA', BB', CC', resp.
A2, B2, C2 = orthogonal projections of A1, B1, C1 on OA', OB', OC', resp.
A'2, B'2, C'2 points on A1A2, B1B2, C1C2, resp. such that
A1A'1/A1A2 = B1B'1 / B1B2 = C1C'1/C1C2 = t
Oa, Ob, Oc = the circumcenters of AA1A'2, BB1B'2, CC1C'2, resp.
The centroid of OaObOc lies on the Euler line of ABC.
(ie the locus of the centroid of OaObOc, as t varies, is the Euler line of ABC)
A1A'1/A1A2 = B1B'1 / B1B2 = C1C'1/C1C2 = t
Oa, Ob, Oc = the circumcenters of AA1A'2, BB1B'2, CC1C'2, resp.
The centroid of OaObOc lies on the Euler line of ABC.
(ie the locus of the centroid of OaObOc, as t varies, is the Euler line of ABC)
[Peter Moses]:
Hi Antreas,
X(12100) = X[2] + 3 X[3].
and
(3 t - 5) X[2] - 3 (t + 1) X[3].
For t = 2 (ie A'2, B'2, C'2 = the reflections of A1, B1, C1 in OA', OB', OC', resp.):
26 a^4-25 a^2 b^2-b^4-25 a^2 c^2+2 b^2 c^2-c^4::
on lines {{2,3},{541,13392},{3098,8584},{5306,8588},{5585,15048},{7280,15170},{8589,9300},{12007,14810},{12042,15300},{13339,13482}}.
midpoint of X(i) and X(j) for these {i,j}: {{2, 15690}, {5, 15691}, {20, 14893}, {140, 376}, {381, 12103}, {546, 15686}, {547, 550}, {548, 549}, {3534, 5066}, {3853, 15681}, {8703, 12100}}.
reflection of X(i) in X(j) for these {i,j}: {{547, 12108}, {3530, 14891}, {3628, 549}, {3850, 10124}, {3860, 2}, {3861, 547}, {5066, 11540}, {10109, 11812}, {10124, 3530}, {11737, 140}, {11812, 12100}, {12102, 11737}, {14891, 3}, {15687, 12811}}.
X[2] - 9 X[3], 13 X[2] - 9 X[5], 13 X[3] - X[5], 7 X[5] - 13 X[140], 7 X[2] - 9 X[140], 7 X[3] - X[140], 7 X[3] + X[376], 7 X[2] + 9 X[376], 7 X[5] + 13 X[376], 17 X[5] - 13 X[381], 17 X[2] - 9 X[381], 17 X[140] - 7 X[381], 17 X[3] - X[381], 17 X[376] + 7 X[381], 7 X[140] - X[382], 7 X[376] + X[382], 19 X[381] - 17 X[546], 19 X[5] - 13 X[546], 19 X[2] - 9 X[546], 19 X[140] - 7 X[546], 19 X[3] - X[546], 19 X[376] + 7 X[546], 11 X[546] - 19 X[547], 11 X[381] - 17 X[547], 11 X[5] - 13 X[547], 11 X[2] - 9 X[547], 11 X[140] - 7 X[547], 11 X[3] - X[547], 11 X[376] + 7 X[547], 5 X[376] - 7 X[548], 5 X[3] + X[548], X[4] + 5 X[548], 5 X[140] + 7 X[548], 5 X[2] + 9 X[548], 5 X[547] + 11 X[548], 5 X[5] + 13 X[548], 5 X[381] + 17 X[548], 5 X[546] + 19 X[548], 5 X[546] - 19 X[549], 5 X[381] - 17 X[549], 5 X[5] - 13 X[549], 5 X[547] - 11 X[549], 5 X[2] - 9 X[549], 5 X[140] - 7 X[549], X[4] - 5 X[549], 5 X[3] - X[549], 5 X[376] + 7 X[549], 11 X[376] - 7 X[550], 11 X[548] - 5 X[550], 11 X[3] + X[550], 11 X[549] + 5 X[550], 11 X[140] + 7 X[550], 11 X[2] + 9 X[550], 11 X[5] + 13 X[550], 11 X[381] + 17 X[550], 11 X[546] + 19 X[550], 11 X[140] - 5 X[3091], 7 X[547] - 5 X[3091], 11 X[376] + 5 X[3091], 7 X[550] + 5 X[3091], 19 X[3] + 5 X[3522], X[546] + 5 X[3522], 11 X[549] - 15 X[3524], 11 X[3] - 3 X[3524], X[547] - 3 X[3524], X[550] + 3 X[3524], 11 X[548] + 15 X[3524], 5 X[547] - 7 X[3526], 11 X[549] - 7 X[3526], 15 X[3524] - 7 X[3526], 11 X[548] + 7 X[3526], 5 X[550] + 7 X[3526], 17 X[3] + 7 X[3528], X[381] + 7 X[3528], 4 X[546] - 19 X[3530], 4 X[381] - 17 X[3530], 4 X[5] - 13 X[3530], 4 X[547] - 11 X[3530], 12 X[3524] - 11 X[3530], 4 X[2] - 9 X[3530], 4 X[140] - 7 X[3530], 4 X[549] - 5 X[3530], 4 X[3] - X[3530], 4 X[548] + 5 X[3530], 4 X[376] + 7 X[3530], 4 X[550] + 11 X[3530], 15 X[550] - 11 X[3534], 15 X[376] - 7 X[3534], 3 X[548] - X[3534], 15 X[3] + X[3534], 3 X[549] + X[3534], 5 X[2] + 3 X[3534], 15 X[3530] + 4 X[3534], 3 X[4] + 5 X[3534], 15 X[140] + 7 X[3534], 15 X[547] + 11 X[3534], 15 X[5] + 13 X[3534], 15 X[381] + 17 X[3534], 15 X[546] + 19 X[3534], 5 X[632] - X[3543], 10 X[546] - 19 X[3628], 10 X[381] - 17 X[3628], 10 X[5] - 13 X[3628], 10 X[547] - 11 X[3628], 14 X[3526] - 11 X[3628], 10 X[2] - 9 X[3628], 10 X[140] - 7 X[3628], 2 X[4] - 5 X[3628], 5 X[3530] - 2 X[3628], 10 X[3] - X[3628], 2 X[548] + X[3628], 2 X[3534] + 3 X[3628], 10 X[376] + 7 X[3628], 10 X[550] + 11 X[3628], 15 X[3091] - 7 X[3830], 11 X[2] - 3 X[3830], 3 X[547] - X[3830], 9 X[3524] - X[3830], 3 X[550] + X[3830], 11 X[3534] + 5 X[3830], 15 X[3091] - 11 X[3845], 7 X[3830] - 11 X[3845], 3 X[382] - 7 X[3845], 7 X[2] - 3 X[3845], 3 X[140] - X[3845], 3 X[376] + X[3845], 7 X[3534] + 5 X[3845], 16 X[546] - 19 X[3850], 16 X[381] - 17 X[3850], 16 X[5] - 13 X[3850], 16 X[547] - 11 X[3850], 16 X[2] - 9 X[3850], 16 X[140] - 7 X[3850], 16 X[549] - 5 X[3850], 8 X[3628] - 5 X[3850], 16 X[3] - X[3850], 4 X[3530] - X[3850], 16 X[548] + 5 X[3850], 16 X[376] + 7 X[3850], 16 X[550] + 11 X[3850], 16 X[3534] + 15 X[3850], 7 X[3523] - X[3853], 5 X[382] - 14 X[3856], 7 X[4] - 10 X[3856], 5 X[3845] - 6 X[3856], 7 X[3628] - 4 X[3856], 5 X[140] - 2 X[3856], 7 X[549] - 2 X[3856], 5 X[376] + 2 X[3856], 7 X[548] + 2 X[3856], 7 X[3534] + 6 X[3856], 5 X[20] + 7 X[3857], 11 X[3525] - 5 X[3859], 18 X[546] - 19 X[3860], 18 X[381] - 17 X[3860], 18 X[5] - 13 X[3860], 18 X[547] - 11 X[3860], 6 X[3830] - 11 X[3860], 9 X[3850] - 8 X[3860], 18 X[140] - 7 X[3860], 6 X[3845] - 7 X[3860], 18 X[549] - 5 X[3860], 9 X[3628] - 5 X[3860], 9 X[3530] - 2 X[3860], 18 X[3] - X[3860], 18 X[548] + 5 X[3860], 6 X[3534] + 5 X[3860], 18 X[376] + 7 X[3860], 18 X[550] + 11 X[3860], 11 X[3860] - 9 X[3861], 11 X[3850] - 8 X[3861], 10 X[3091] - 7 X[3861], 14 X[3526] - 5 X[3861], 11 X[3628] - 5 X[3861], 2 X[3830] - 3 X[3861], 11 X[3530] - 2 X[3861], 6 X[3524] - X[3861], 2 X[550] + X[3861], 19 X[549] - 15 X[5054], 19 X[3530] - 12 X[5054], 19 X[3524] - 11 X[5054], 19 X[3] - 3 X[5054], X[546] - 3 X[5054], 5 X[3522] + 3 X[5054], 19 X[548] + 15 X[5054], 7 X[4] - 15 X[5055], 5 X[3845] - 9 X[5055], 7 X[3628] - 6 X[5055], 5 X[140] - 3 X[5055], 7 X[549] - 3 X[5055], 2 X[3856] - 3 X[5055], 5 X[376] + 3 X[5055], 7 X[548] + 3 X[5055], 7 X[3534] + 9 X[5055], 17 X[376] - X[5059], 17 X[140] + X[5059], 7 X[381] + X[5059], 17 X[3845] + 3 X[5059], 17 X[382] + 7 X[5059], 15 X[546] - 19 X[5066], 15 X[381] - 17 X[5066], 15 X[3850] - 16 X[5066], 15 X[5] - 13 X[5066], 15 X[547] - 11 X[5066], 5 X[3830] - 11 X[5066], 15 X[140] - 7 X[5066], 5 X[3845] - 7 X[5066], 6 X[3856] - 7 X[5066], 9 X[5055] - 7 X[5066], 5 X[3860] - 6 X[5066], 3 X[4] - 5 X[5066], 15 X[3530] - 4 X[5066], 5 X[2] - 3 X[5066], 3 X[3628] - 2 X[5066], 15 X[3] - X[5066], 3 X[549] - X[5066], 3 X[548] + X[5066], 15 X[376] + 7 X[5066], 15 X[550] + 11 X[5066], 19 X[140] - 13 X[5067], 7 X[546] - 13 X[5067], 19 X[376] + 13 X[5067], 5 X[3853] - 11 X[5072], 5 X[3627] - 17 X[7486], 3 X[3098] + X[8584], 15 X[3522] - 19 X[8703], 3 X[550] - 11 X[8703], 3 X[376] - 7 X[8703], 3 X[548] - 5 X[8703], X[3534] - 5 X[8703], 3 X[3] + X[8703], X[2] + 3 X[8703], 3 X[3530] + 4 X[8703], 3 X[549] + 5 X[8703], X[5066] + 5 X[8703], X[3860] + 6 X[8703], 3 X[140] + 7 X[8703], X[3845] + 7 X[8703], 3 X[3628] + 10 X[8703], 3 X[547] + 11 X[8703], 9 X[3524] + 11 X[8703], X[3830] + 11 X[8703], 3 X[5] + 13 X[8703], 3 X[3850] + 16 X[8703], 3 X[381] + 17 X[8703], 3 X[546] + 19 X[8703], 9 X[5054] + 19 X[8703], 12 X[546] - 19 X[10109], 12 X[381] - 17 X[10109], 12 X[5] - 13 X[10109], 12 X[547] - 11 X[10109], 4 X[3830] - 11 X[10109], 6 X[3861] - 11 X[10109], 12 X[140] - 7 X[10109], 4 X[3845] - 7 X[10109], 12 X[549] - 5 X[10109], 6 X[3628] - 5 X[10109], 4 X[5066] - 5 X[10109], 3 X[3850] - 4 X[10109], 4 X[2] - 3 X[10109], 2 X[3860] - 3 X[10109], 12 X[3] - X[10109], 3 X[3530] - X[10109], 4 X[8703] + X[10109], 12 X[548] + 5 X[10109], 4 X[3534] + 5 X[10109], 12 X[376] + 7 X[10109], 12 X[550] + 11 X[10109], 8 X[546] - 19 X[10124], 8 X[381] - 17 X[10124], 8 X[5066] - 15 X[10124], 8 X[5] - 13 X[10124], 8 X[547] - 11 X[10124], 4 X[3861] - 11 X[10124], 8 X[2] - 9 X[10124], 4 X[3860] - 9 X[10124], 8 X[140] - 7 X[10124], 8 X[549] - 5 X[10124], 4 X[3628] - 5 X[10124], 2 X[10109] - 3 X[10124], 8 X[3] - X[10124], 8 X[8703] + 3 X[10124], 8 X[548] + 5 X[10124], 8 X[376] + 7 X[10124], 8 X[550] + 11 X[10124], 8 X[3534] + 15 X[10124], X[3627] - 13 X[10299], 5 X[381] - 13 X[10303], 17 X[549] - 13 X[10303], 17 X[548] + 13 X[10303], X[3534] - 9 X[10304], 5 X[8703] - 9 X[10304], X[548] - 3 X[10304], 5 X[3] + 3 X[10304], X[549] + 3 X[10304], X[3628] + 6 X[10304], X[5055] + 7 X[10304], X[5066] + 9 X[10304], 5 X[3524] + 11 X[10304], 5 X[3530] + 12 X[10304], X[4] + 15 X[10304], 5 X[5054] + 19 X[10304], 13 X[3534] - 5 X[11001], 13 X[8703] - X[11001], 3 X[5] + X[11001], 13 X[2] + 3 X[11001], 13 X[10109] + 4 X[11001], 13 X[5066] + 5 X[11001], 13 X[3860] + 6 X[11001], 13 X[3845] + 7 X[11001], 13 X[3830] + 11 X[11001], 7 X[3857] - 15 X[11539], X[20] + 3 X[11539], 15 X[10124] - 16 X[11540], 15 X[140] - 14 X[11540], 5 X[3845] - 14 X[11540], 9 X[5055] - 14 X[11540], 5 X[3860] - 12 X[11540], 3 X[4] - 10 X[11540], 15 X[3530] - 8 X[11540], 5 X[10109] - 8 X[11540], 3 X[3856] - 7 X[11540], 5 X[2] - 6 X[11540], 3 X[3628] - 4 X[11540], 15 X[3] - 2 X[11540], 3 X[549] - 2 X[11540], 3 X[548] + 2 X[11540], X[3534] + 2 X[11540], 5 X[8703] + 2 X[11540], 9 X[10304] + 2 X[11540], 15 X[376] + 14 X[11540], 7 X[3853] - X[11541], 14 X[546] - 19 X[11737], 14 X[381] - 17 X[11737], 14 X[5066] - 15 X[11737], 14 X[5] - 13 X[11737], 14 X[547] - 11 X[11737], 10 X[3091] - 11 X[11737], 7 X[3861] - 11 X[11737], 14 X[2] - 9 X[11737], 7 X[3860] - 9 X[11737], 7 X[3850] - 8 X[11737], 2 X[382] - 7 X[11737], 7 X[10109] - 6 X[11737], 14 X[549] - 5 X[11737], 7 X[3628] - 5 X[11737], 4 X[3856] - 5 X[11737], 6 X[5055] - 5 X[11737], 7 X[10124] - 4 X[11737], 2 X[3845] - 3 X[11737], 7 X[3530] - 2 X[11737], 14 X[3] - X[11737], 2 X[376] + X[11737], 14 X[8703] + 3 X[11737], 14 X[548] + 5 X[11737], 14 X[550] + 11 X[11737], 14 X[3534] + 15 X[11737], 2 X[5059] + 17 X[11737], 6 X[546] - 19 X[11812], 18 X[5054] - 19 X[11812], 6 X[381] - 17 X[11812], 6 X[5] - 13 X[11812], 6 X[547] - 11 X[11812], 18 X[3524] - 11 X[11812], 2 X[3830] - 11 X[11812], 3 X[3861] - 11 X[11812], 3 X[3850] - 8 X[11812], 6 X[140] - 7 X[11812], 2 X[3845] - 7 X[11812], 3 X[11737] - 7 X[11812], 6 X[549] - 5 X[11812], 3 X[3628] - 5 X[11812], 2 X[5066] - 5 X[11812], 4 X[11540] - 5 X[11812], 3 X[10124] - 4 X[11812], 2 X[2] - 3 X[11812], X[3860] - 3 X[11812], 3 X[3530] - 2 X[11812], 6 X[3] - X[11812], 2 X[8703] + X[11812], 6 X[548] + 5 X[11812], 2 X[3534] + 5 X[11812], 18 X[10304] + 5 X[11812], 6 X[376] + 7 X[11812], 6 X[550] + 11 X[11812], 2 X[11001] + 13 X[11812], 3 X[546] - 19 X[12100], 9 X[5054] - 19 X[12100], 3 X[381] - 17 X[12100], 3 X[3850] - 16 X[12100], 3 X[11737] - 14 X[12100], 3 X[5] - 13 X[12100], 3 X[547] - 11 X[12100], 9 X[3524] - 11 X[12100], X[3830] - 11 X[12100], 3 X[3628] - 10 X[12100], 3 X[10124] - 8 X[12100], 3 X[140] - 7 X[12100], X[3845] - 7 X[12100], X[3860] - 6 X[12100], 3 X[549] - 5 X[12100], X[5066] - 5 X[12100], 2 X[11540] - 5 X[12100], 3 X[3530] - 4 X[12100], X[10109] - 4 X[12100], X[2] - 3 X[12100], 3 X[3] - X[12100], 3 X[548] + 5 X[12100], X[3534] + 5 X[12100], 9 X[10304] + 5 X[12100], 3 X[376] + 7 X[12100], 3 X[550] + 11 X[12100], X[11001] + 13 X[12100], 15 X[3522] + 19 X[12100], 9 X[3830] - 11 X[12101], 9 X[3845] - 7 X[12101], 9 X[5066] - 5 X[12101], 18 X[11540] - 5 X[12101], 9 X[10109] - 4 X[12101], 3 X[3860] - 2 X[12101], 9 X[11812] - 2 X[12101], 9 X[12100] - X[12101], 9 X[8703] + X[12101], 9 X[3534] + 5 X[12101], 9 X[11001] + 13 X[12101], 14 X[3861] - 11 X[12102], 14 X[3860] - 9 X[12102], 4 X[382] - 7 X[12102], 14 X[3628] - 5 X[12102], 8 X[3856] - 5 X[12102], 12 X[5055] - 5 X[12102], 7 X[3850] - 4 X[12102], 4 X[3845] - 3 X[12102], 7 X[10109] - 3 X[12102], 14 X[11812] - 3 X[12102], 7 X[10124] - 2 X[12102], 4 X[140] - X[12102], 7 X[3530] - X[12102], 4 X[376] + X[12102], 4 X[5059] + 17 X[12102], 17 X[3534] - 15 X[12103], 17 X[550] - 11 X[12103], 17 X[376] - 7 X[12103], X[5059] - 7 X[12103], 17 X[548] - 5 X[12103], 17 X[8703] - 3 X[12103], 7 X[3528] - X[12103], 17 X[3] + X[12103], 17 X[12100] + 3 X[12103], 17 X[3530] + 4 X[12103], 17 X[549] + 5 X[12103], 13 X[10303] + 5 X[12103], 17 X[11812] + 6 X[12103], 17 X[140] + 7 X[12103], 17 X[10124] + 8 X[12103], 17 X[2] + 9 X[12103], 17 X[3628] + 10 X[12103], 17 X[547] + 11 X[12103], 17 X[10109] + 12 X[12103], 17 X[5] + 13 X[12103], 17 X[11737] + 14 X[12103], 17 X[5066] + 15 X[12103], 17 X[3850] + 16 X[12103], 17 X[3860] + 18 X[12103], 17 X[546] + 19 X[12103], 11 X[2] - 18 X[12108], 11 X[10124] - 16 X[12108], 11 X[11540] - 15 X[12108], 11 X[140] - 14 X[12108], 5 X[3091] - 14 X[12108], 11 X[11812] - 12 X[12108], 11 X[549] - 10 X[12108], 7 X[3526] - 10 X[12108], 11 X[3530] - 8 X[12108], X[3830] - 6 X[12108], 11 X[12100] - 6 X[12108], X[3861] - 4 X[12108], 11 X[3] - 2 X[12108], 3 X[3524] - 2 X[12108], X[550] + 2 X[12108], 11 X[8703] + 6 X[12108], 11 X[548] + 10 X[12108], 11 X[376] + 14 X[12108], 5 X[631] - 2 X[12811], 3 X[3839] - 5 X[12812], 11 X[3522] - 19 X[14093], 11 X[8703] - 15 X[14093], X[550] - 5 X[14093], 11 X[3] + 5 X[14093], X[547] + 5 X[14093], 3 X[3524] + 5 X[14093], 2 X[12108] + 5 X[14093], X[3091] + 7 X[14093], X[3861] + 10 X[14093], X[3830] + 15 X[14093], 11 X[12100] + 15 X[14093], X[12007] + 5 X[14810], 3 X[3545] - 7 X[14869], 4 X[4] - 15 X[14890], 5 X[3850] - 12 X[14890], 4 X[5066] - 9 X[14890], 5 X[10109] - 9 X[14890], 8 X[11540] - 9 X[14890], 10 X[11812] - 9 X[14890], 4 X[5055] - 7 X[14890], 5 X[10124] - 6 X[14890], 4 X[549] - 3 X[14890], 5 X[3530] - 3 X[14890], 2 X[3628] - 3 X[14890], 4 X[10304] + X[14890], 4 X[548] + 3 X[14890], 4 X[3534] + 9 X[14890], 2 X[546] - 19 X[14891], 6 X[5054] - 19 X[14891], 2 X[381] - 17 X[14891], 2 X[5066] - 15 X[14891], 4 X[11540] - 15 X[14891], X[12102] - 14 X[14891], 2 X[5] - 13 X[14891], 2 X[547] - 11 X[14891], 6 X[3524] - 11 X[14891], X[3861] - 11 X[14891], 4 X[12108] - 11 X[14891], 3 X[14890] - 10 X[14891], 2 X[2] - 9 X[14891], X[3860] - 9 X[14891], X[3850] - 8 X[14891], 2 X[140] - 7 X[14891], X[11737] - 7 X[14891], X[10109] - 6 X[14891], 2 X[549] - 5 X[14891], X[3628] - 5 X[14891], X[10124] - 4 X[14891], X[11812] - 3 X[14891], 2 X[12100] - 3 X[14891], 2 X[8703] + 3 X[14891], 2 X[548] + 5 X[14891], 6 X[10304] + 5 X[14891], 2 X[376] + 7 X[14891], 2 X[550] + 11 X[14891], 10 X[14093] + 11 X[14891], 2 X[3534] + 15 X[14891], 14 X[3528] + 17 X[14891], 2 X[12103] + 17 X[14891], 10 X[3522] + 19 X[14891], 5 X[632] - 3 X[14892], X[3543] - 3 X[14892], 7 X[3857] - 5 X[14893], 3 X[11539] - X[14893], 5 X[1657] + 19 X[15022], 3 X[12042] + X[15300], 15 X[382] - 7 X[15640], 15 X[12102] - 4 X[15640], 15 X[11737] - 2 X[15640], 15 X[140] - X[15640], 5 X[3845] - X[15640], 6 X[3856] - X[15640], 9 X[5055] - X[15640], 7 X[5066] - X[15640], 14 X[11540] - X[15640], 15 X[376] + X[15640], 7 X[3534] + X[15640], 15 X[5059] + 17 X[15640], 7 X[3523] + X[15681], 11 X[5072] + 5 X[15681], X[11541] + 7 X[15681], 19 X[3830] - 11 X[15682], 19 X[12101] - 9 X[15682], 19 X[3845] - 7 X[15682], 19 X[3860] - 6 X[15682], 19 X[5066] - 5 X[15682], 19 X[10109] - 4 X[15682], 19 X[2] - 3 X[15682], 19 X[11812] - 2 X[15682], 3 X[546] - X[15682], 9 X[5054] - X[15682], 19 X[12100] - X[15682], 15 X[3522] + X[15682], 19 X[8703] + X[15682], 19 X[3534] + 5 X[15682], 19 X[11001] + 13 X[15682], 11 X[3534] - 3 X[15683], 11 X[548] - X[15683], 5 X[550] - X[15683], 5 X[547] + X[15683], 11 X[549] + X[15683], 15 X[3524] + X[15683], 7 X[3526] + X[15683], 10 X[12108] + X[15683], 11 X[3628] + 2 X[15683], 5 X[3861] + 2 X[15683], 5 X[3830] + 3 X[15683], 11 X[5066] + 3 X[15683], 11 X[4] + 5 X[15683], 13 X[4] - 5 X[15684], 13 X[5066] - 3 X[15684], 13 X[3628] - 2 X[15684], 5 X[5] - X[15684], 13 X[549] - X[15684], 13 X[548] + X[15684], 13 X[3534] + 3 X[15684], 5 X[11001] + 3 X[15684], 13 X[15683] + 11 X[15684], 9 X[5059] - 17 X[15685], 9 X[376] - X[15685], 7 X[2] + X[15685], 9 X[140] + X[15685], 3 X[3845] + X[15685], 7 X[3860] + 2 X[15685], 9 X[11737] + 2 X[15685], 7 X[12101] + 3 X[15685], 9 X[12102] + 4 X[15685], 18 X[3856] + 5 X[15685], 3 X[15640] + 5 X[15685], 9 X[382] + 7 X[15685], 19 X[12103] - 17 X[15686], 19 X[3534] - 15 X[15686], 19 X[550] - 11 X[15686], 19 X[376] - 7 X[15686], 19 X[548] - 5 X[15686], 19 X[8703] - 3 X[15686], 5 X[3522] - X[15686], 19 X[3] + X[15686], 3 X[5054] + X[15686], 19 X[14891] + 2 X[15686], 19 X[12100] + 3 X[15686], X[15682] + 3 X[15686], 19 X[3530] + 4 X[15686], 19 X[549] + 5 X[15686], 19 X[11812] + 6 X[15686], 19 X[140] + 7 X[15686], 13 X[5067] + 7 X[15686], 19 X[10124] + 8 X[15686], 19 X[2] + 9 X[15686], 19 X[3628] + 10 X[15686], 19 X[547] + 11 X[15686], 19 X[10109] + 12 X[15686], 19 X[5] + 13 X[15686], 19 X[11737] + 14 X[15686], 19 X[5066] + 15 X[15686], 19 X[3850] + 16 X[15686], 19 X[381] + 17 X[15686], 19 X[3860] + 18 X[15686], 5 X[631] - X[15687], 13 X[548] - 15 X[15688], 13 X[8703] - 9 X[15688], X[11001] - 9 X[15688], 13 X[10304] - 5 X[15688], 13 X[3] + 3 X[15688], X[5] + 3 X[15688], 13 X[14891] + 6 X[15688], 13 X[12100] + 9 X[15688], 13 X[3524] + 11 X[15688], 13 X[3530] + 12 X[15688], 13 X[549] + 15 X[15688], X[15684] + 15 X[15688], 13 X[11812] + 18 X[15688], 13 X[5054] + 19 X[15688], 5 X[631] + 3 X[15689], 2 X[12811] + 3 X[15689], X[15687] + 3 X[15689], 9 X[15686] - 19 X[15690], 9 X[12103] - 17 X[15690], 3 X[11001] - 13 X[15690], 9 X[550] - 11 X[15690], 9 X[376] - 7 X[15690], X[15685] - 7 X[15690], 9 X[548] - 5 X[15690], 3 X[3534] - 5 X[15690], 3 X[8703] - X[15690], 9 X[3] + X[15690], 3 X[12100] + X[15690], X[3860] + 2 X[15690], 3 X[11812] + 2 X[15690], 9 X[14891] + 2 X[15690], X[12101] + 3 X[15690], 9 X[3530] + 4 X[15690], 3 X[10109] + 4 X[15690], 9 X[549] + 5 X[15690], 3 X[5066] + 5 X[15690], 6 X[11540] + 5 X[15690], 9 X[140] + 7 X[15690], 3 X[3845] + 7 X[15690], 9 X[10124] + 8 X[15690], 9 X[3628] + 10 X[15690], 9 X[547] + 11 X[15690], 3 X[3830] + 11 X[15690], 18 X[12108] + 11 X[15690], 9 X[5] + 13 X[15690], 9 X[11737] + 14 X[15690], 9 X[3850] + 16 X[15690], 9 X[381] + 17 X[15690], 9 X[546] + 19 X[15690], 3 X[15682] + 19 X[15690], 13 X[15686] - 19 X[15691], 13 X[12103] - 17 X[15691], 13 X[3534] - 15 X[15691], 13 X[550] - 11 X[15691], 13 X[15690] - 9 X[15691], 13 X[376] - 7 X[15691], 13 X[548] - 5 X[15691], 13 X[8703] - 3 X[15691], X[11001] - 3 X[15691], 3 X[15688] - X[15691], 13 X[3] + X[15691], 13 X[14891] + 2 X[15691], 13 X[12100] + 3 X[15691], 13 X[3530] + 4 X[15691], 13 X[549] + 5 X[15691], X[15684] + 5 X[15691], 13 X[11812] + 6 X[15691], 13 X[140] + 7 X[15691], 13 X[10124] + 8 X[15691], 13 X[2] + 9 X[15691], 13 X[3628] + 10 X[15691], 13 X[547] + 11 X[15691], 13 X[10109] + 12 X[15691], 13 X[11737] + 14 X[15691], 13 X[5066] + 15 X[15691], 13 X[3850] + 16 X[15691], 13 X[381] + 17 X[15691], 13 X[3860] + 18 X[15691], 13 X[546] + 19 X[15691], 13 X[12100] - 15 X[15692], 13 X[14891] - 10 X[15692], 13 X[3] - 5 X[15692], X[5] - 5 X[15692], 3 X[15688] + 5 X[15692], X[15691] + 5 X[15692], 13 X[14093] + 11 X[15692], 13 X[8703] + 15 X[15692], X[11001] + 15 X[15692], 13 X[3522] + 19 X[15692], 7 X[2] - 15 X[15693], 3 X[3091] - 11 X[15693], 3 X[11737] - 10 X[15693], 7 X[11812] - 10 X[15693], 3 X[140] - 5 X[15693], X[3845] - 5 X[15693], 7 X[12100] - 5 X[15693], 3 X[376] + 5 X[15693], 7 X[8703] + 5 X[15693], X[15685] + 15 X[15693], 7 X[15690] + 15 X[15693], X[3627] - 5 X[15694], 13 X[10299] - 5 X[15694], 9 X[8703] - 5 X[15695], 3 X[15690] - 5 X[15695], 3 X[2] + 5 X[15695], 9 X[12100] + 5 X[15695], X[12101] + 5 X[15695], 9 X[15693] + 7 X[15695], 3 X[3860] + 10 X[15695], 9 X[11812] + 10 X[15695], 3 X[3545] + 5 X[15696], 7 X[14869] + 5 X[15696], 17 X[15690] - 15 X[15697], 17 X[15695] - 9 X[15697], 17 X[8703] - 5 X[15697], 3 X[12103] - 5 X[15697], 3 X[381] + 5 X[15697], 17 X[12100] + 5 X[15697], 17 X[15693] + 7 X[15697], 17 X[11812] + 10 X[15697], 17 X[2] + 15 X[15697], 3 X[3628] - 14 X[15698], 5 X[11812] - 14 X[15698], 15 X[14891] - 14 X[15698], 3 X[3526] - 11 X[15698], 15 X[3] - 7 X[15698], 3 X[549] - 7 X[15698], X[5066] - 7 X[15698], 2 X[11540] - 7 X[15698], 5 X[12100] - 7 X[15698], 3 X[548] + 7 X[15698], X[3534] + 7 X[15698], 5 X[8703] + 7 X[15698], 9 X[10304] + 7 X[15698], 15 X[3528] + 17 X[15698], 11 X[5072] - 15 X[15699], 7 X[3523] - 3 X[15699], X[3853] - 3 X[15699], X[15681] + 3 X[15699], 3 X[11539] - 7 X[15700], X[14893] - 7 X[15700], X[3857] - 5 X[15700], X[20] + 7 X[15700], 13 X[11812] - 14 X[15701], 3 X[5] - 7 X[15701], 13 X[12100] - 7 X[15701], 15 X[15692] - 7 X[15701], 13 X[15698] - 5 X[15701], 13 X[8703] + 7 X[15701], X[11001] + 7 X[15701], 9 X[15688] + 7 X[15701], 3 X[15691] + 7 X[15701], X[1657] + 7 X[15702], X[3529] + 7 X[15703], 5 X[5059] - 17 X[15704], 7 X[15683] - 11 X[15704], 5 X[15685] - 9 X[15704], 7 X[3534] - 3 X[15704], 5 X[376] - X[15704], 7 X[548] - X[15704], 5 X[140] + X[15704], 7 X[549] + X[15704], 2 X[3856] + X[15704], 3 X[5055] + X[15704], 7 X[3628] + 2 X[15704], 5 X[11737] + 2 X[15704], 5 X[3845] + 3 X[15704], 7 X[5066] + 3 X[15704], 14 X[11540] + 3 X[15704], X[15640] + 3 X[15704], 5 X[12102] + 4 X[15704], 7 X[4] + 5 X[15704], 5 X[382] + 7 X[15704], 7 X[15684] + 13 X[15704], 17 X[14891] - 18 X[15705], 17 X[3] - 9 X[15705], X[381] - 9 X[15705], 7 X[3528] + 9 X[15705], X[12103] + 9 X[15705], 17 X[10304] + 15 X[15705], 5 X[3628] - 18 X[15706], 5 X[14890] - 12 X[15706], X[4] - 9 X[15706], 5 X[549] - 9 X[15706], 5 X[10304] + 3 X[15706], 5 X[548] + 9 X[15706], 5 X[632] - 9 X[15707], X[3543] - 9 X[15707], X[14892] - 3 X[15707], 7 X[11737] - 18 X[15708], 7 X[5055] - 15 X[15708], 7 X[140] - 9 X[15708], X[382] - 9 X[15708], 7 X[376] + 9 X[15708], 13 X[3628] - 18 X[15709], 13 X[14890] - 12 X[15709], 5 X[5] - 9 X[15709], 13 X[549] - 9 X[15709], X[15684] - 9 X[15709], 13 X[15706] - 5 X[15709], 13 X[10304] + 3 X[15709], 5 X[15688] + 3 X[15709], 13 X[548] + 9 X[15709], 5 X[15691] + 9 X[15709], X[14891] - 18 X[15710], X[15705] - 17 X[15710], X[3] - 9 X[15710], X[10304] + 15 X[15710], X[12101] - 15 X[15711], 9 X[15692] - 13 X[15711], X[3860] - 10 X[15711], 3 X[11812] - 10 X[15711], 9 X[14891] - 10 X[15711], 3 X[15693] - 7 X[15711], X[2] - 5 X[15711], 9 X[3] - 5 X[15711], 3 X[12100] - 5 X[15711], X[15695] + 3 X[15711], 3 X[8703] + 5 X[15711], X[15690] + 5 X[15711], 9 X[14093] + 11 X[15711], 3 X[15697] + 17 X[15711], 9 X[3522] + 19 X[15711], 17 X[12100] - 15 X[15712], 17 X[15692] - 13 X[15712], 17 X[14891] - 10 X[15712], 17 X[15711] - 9 X[15712], 17 X[3] - 5 X[15712], X[381] - 5 X[15712], 9 X[15705] - 5 X[15712], X[15697] + 3 X[15712], 7 X[3528] + 5 X[15712], X[12103] + 5 X[15712], 17 X[14093] + 11 X[15712], 17 X[8703] + 15 X[15712], 17 X[3522] + 19 X[15712], 11 X[2] - 15 X[15713], 3 X[3861] - 10 X[15713], 11 X[11812] - 10 X[15713], 3 X[3091] - 7 X[15713], 11 X[15693] - 7 X[15713], 3 X[547] - 5 X[15713], 9 X[3524] - 5 X[15713], X[3830] - 5 X[15713], 11 X[12100] - 5 X[15713], 6 X[12108] - 5 X[15713], 11 X[15711] - 3 X[15713], 3 X[14093] + X[15713], 3 X[550] + 5 X[15713], 11 X[8703] + 5 X[15713], 11 X[15695] + 9 X[15713], 11 X[15690] + 15 X[15713], 11 X[15697] + 17 X[15713], X[15712] - 17 X[15714], X[12100] - 15 X[15714], X[15692] - 13 X[15714], X[14891] - 10 X[15714], X[15711] - 9 X[15714], X[3] - 5 X[15714], 9 X[15710] - 5 X[15714], X[14093] + 11 X[15714], X[8703] + 15 X[15714], X[3522] + 19 X[15714], 19 X[3] - 11 X[15715], X[546] - 11 X[15715], 3 X[5054] - 11 X[15715], 5 X[3522] + 11 X[15715], X[15686] + 11 X[15715], 3 X[2] - 11 X[15716], 9 X[12100] - 11 X[15716], X[12101] - 11 X[15716], 15 X[15711] - 11 X[15716], 9 X[8703] + 11 X[15716], 3 X[15690] + 11 X[15716], 5 X[15695] + 11 X[15716], 5 X[140] - 11 X[15717], 7 X[549] - 11 X[15717], 2 X[3856] - 11 X[15717], 3 X[5055] - 11 X[15717], 5 X[376] + 11 X[15717], 7 X[548] + 11 X[15717], X[15704] + 11 X[15717], 3 X[3545] - 11 X[15718], 7 X[14869] - 11 X[15718], 5 X[15696] + 11 X[15718], 3 X[381] - 11 X[15719], 17 X[12100] - 11 X[15719], 15 X[15712] - 11 X[15719], 17 X[15716] - 9 X[15719], 17 X[8703] + 11 X[15719], 3 X[12103] + 11 X[15719], 5 X[15697] + 11 X[15719], 3 X[3839] - 11 X[15720], 5 X[12812] - 11 X[15720], 3 X[14269] - 11 X[15721], 9 X[2] - 17 X[15722], 3 X[12101] - 17 X[15722], 9 X[15690] + 17 X[15722], 15 X[15695] + 17 X[15722], 7 X[5] - 11 X[15723], 13 X[140] - 11 X[15723], 13 X[15717] - 5 X[15723], 13 X[376] + 11 X[15723], 7 X[15691] + 11 X[15723].
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3, 15711), (2, 376, 15685), (2, 3860, 10109), (2, 8703, 15690), (2, 15685, 3845), (2, 15711, 12100), (3, 381, 15705), (3, 3528, 15712), (3, 3534, 15698), (3, 5054, 15715), (3, 8703, 12100), (3, 10304, 549), (3, 14093, 3524), (3, 15688, 15692), (3, 15695, 15716), (3, 15710, 15714), (4, 15706, 549), (5, 549, 15709), (5, 15688, 15691), (20, 11539, 14893), (20, 15700, 11539), (140, 546, 5067), (140, 548, 15704), (140, 3856, 3628), (140, 12100, 15693), (140, 15704, 3856), (376, 3524, 3091), (376, 5055, 15704), (376, 15640, 3534), (376, 15692, 15723), (376, 15693, 3845), (376, 15708, 382), (376, 15717, 5055), (381, 15705, 15712), (547, 3524, 12108), (548, 5066, 3534), (548, 12100, 5066), (548, 14891, 14890), (548, 15698, 11540), (548, 15717, 3856), (549, 3534, 5066), (549, 3628, 14890), (549, 3857, 11539), (549, 5055, 140), (549, 5066, 11540), (549, 8703, 3534), (549, 10304, 548), (549, 11540, 11812), (549, 15683, 547), (549, 15698, 12100), (549, 15704, 5055), (550, 3524, 547), (550, 12108, 3861), (550, 15713, 3830), (631, 15689, 15687), (632, 3543, 14892), (3091, 3830, 3845), (3091, 15693, 15713), (3522, 5054, 15686), (3522, 15715, 5054), (3523, 15681, 15699), (3524, 3526, 549), (3524, 3830, 15713), (3524, 14093, 550), (3524, 15683, 3526), (3526, 3534, 3830), (3528, 15705, 381), (3528, 15712, 12103), (3528, 15719, 15697), (3530, 10109, 11812), (3530, 12102, 140), (3530, 14890, 549), (3534, 3830, 15683), (3534, 5055, 15640), (3534, 8703, 548), (3534, 10304, 8703), (3534, 12100, 11540), (3534, 15640, 15704), (3534, 15684, 11001), (3534, 15693, 5055), (3534, 15698, 549), (3543, 15707, 632), (3545, 15718, 14869), (3628, 5066, 10109), (3628, 11737, 5055), (3628, 11812, 11540), (3628, 14890, 10124), (3628, 15704, 12102), (3830, 12100, 12108), (3830, 15713, 547), (3845, 5055, 5066), (3845, 5066, 3856), (3845, 8703, 376), (3845, 15693, 140), (3845, 15704, 15640), (3856, 5055, 11737), (3860, 11812, 2), (3861, 14891, 3524), (5054, 15686, 546), (5055, 15640, 3845), (5055, 15717, 549), (5059, 15712, 140), (5059, 15717, 10303), (5066, 11540, 3628), (5066, 12100, 549), (8703, 14891, 10109), (8703, 15698, 5066), (8703, 15701, 15691), (8703, 15711, 2), (8703, 15713, 550), (8703, 15716, 12101), (8703, 15719, 12103), (10109, 11812, 10124), (10304, 15698, 3534), (10304, 15709, 15688), (10304, 15717, 376), (11001, 15692, 15701), (11001, 15701, 5), (11001, 15723, 3845), (11540, 11812, 14890), (11540, 15640, 11737), (11812, 12100, 3530), (11812, 14891, 12100), (12100, 15690, 2), (12108, 15713, 11812), (15640, 15698, 15693), (15681, 15699, 3853), (15683, 15713, 5066), (15684, 15692, 549), (15684, 15709, 5), (15685, 15693, 2), (15688, 15692, 5), (15688, 15701, 11001), (15693, 15723, 15701), (15695, 15716, 2), (15696, 15718, 3545), (15697, 15705, 15719), (15697, 15719, 381), (15704, 15717, 140).
Best regards,
Peter Moses.
midpoint of X(i) and X(j) for these {i,j}: {{2, 15690}, {5, 15691}, {20, 14893}, {140, 376}, {381, 12103}, {546, 15686}, {547, 550}, {548, 549}, {3534, 5066}, {3853, 15681}, {8703, 12100}}.
reflection of X(i) in X(j) for these {i,j}: {{547, 12108}, {3530, 14891}, {3628, 549}, {3850, 10124}, {3860, 2}, {3861, 547}, {5066, 11540}, {10109, 11812}, {10124, 3530}, {11737, 140}, {11812, 12100}, {12102, 11737}, {14891, 3}, {15687, 12811}}.
X[2] - 9 X[3], 13 X[2] - 9 X[5], 13 X[3] - X[5], 7 X[5] - 13 X[140], 7 X[2] - 9 X[140], 7 X[3] - X[140], 7 X[3] + X[376], 7 X[2] + 9 X[376], 7 X[5] + 13 X[376], 17 X[5] - 13 X[381], 17 X[2] - 9 X[381], 17 X[140] - 7 X[381], 17 X[3] - X[381], 17 X[376] + 7 X[381], 7 X[140] - X[382], 7 X[376] + X[382], 19 X[381] - 17 X[546], 19 X[5] - 13 X[546], 19 X[2] - 9 X[546], 19 X[140] - 7 X[546], 19 X[3] - X[546], 19 X[376] + 7 X[546], 11 X[546] - 19 X[547], 11 X[381] - 17 X[547], 11 X[5] - 13 X[547], 11 X[2] - 9 X[547], 11 X[140] - 7 X[547], 11 X[3] - X[547], 11 X[376] + 7 X[547], 5 X[376] - 7 X[548], 5 X[3] + X[548], X[4] + 5 X[548], 5 X[140] + 7 X[548], 5 X[2] + 9 X[548], 5 X[547] + 11 X[548], 5 X[5] + 13 X[548], 5 X[381] + 17 X[548], 5 X[546] + 19 X[548], 5 X[546] - 19 X[549], 5 X[381] - 17 X[549], 5 X[5] - 13 X[549], 5 X[547] - 11 X[549], 5 X[2] - 9 X[549], 5 X[140] - 7 X[549], X[4] - 5 X[549], 5 X[3] - X[549], 5 X[376] + 7 X[549], 11 X[376] - 7 X[550], 11 X[548] - 5 X[550], 11 X[3] + X[550], 11 X[549] + 5 X[550], 11 X[140] + 7 X[550], 11 X[2] + 9 X[550], 11 X[5] + 13 X[550], 11 X[381] + 17 X[550], 11 X[546] + 19 X[550], 11 X[140] - 5 X[3091], 7 X[547] - 5 X[3091], 11 X[376] + 5 X[3091], 7 X[550] + 5 X[3091], 19 X[3] + 5 X[3522], X[546] + 5 X[3522], 11 X[549] - 15 X[3524], 11 X[3] - 3 X[3524], X[547] - 3 X[3524], X[550] + 3 X[3524], 11 X[548] + 15 X[3524], 5 X[547] - 7 X[3526], 11 X[549] - 7 X[3526], 15 X[3524] - 7 X[3526], 11 X[548] + 7 X[3526], 5 X[550] + 7 X[3526], 17 X[3] + 7 X[3528], X[381] + 7 X[3528], 4 X[546] - 19 X[3530], 4 X[381] - 17 X[3530], 4 X[5] - 13 X[3530], 4 X[547] - 11 X[3530], 12 X[3524] - 11 X[3530], 4 X[2] - 9 X[3530], 4 X[140] - 7 X[3530], 4 X[549] - 5 X[3530], 4 X[3] - X[3530], 4 X[548] + 5 X[3530], 4 X[376] + 7 X[3530], 4 X[550] + 11 X[3530], 15 X[550] - 11 X[3534], 15 X[376] - 7 X[3534], 3 X[548] - X[3534], 15 X[3] + X[3534], 3 X[549] + X[3534], 5 X[2] + 3 X[3534], 15 X[3530] + 4 X[3534], 3 X[4] + 5 X[3534], 15 X[140] + 7 X[3534], 15 X[547] + 11 X[3534], 15 X[5] + 13 X[3534], 15 X[381] + 17 X[3534], 15 X[546] + 19 X[3534], 5 X[632] - X[3543], 10 X[546] - 19 X[3628], 10 X[381] - 17 X[3628], 10 X[5] - 13 X[3628], 10 X[547] - 11 X[3628], 14 X[3526] - 11 X[3628], 10 X[2] - 9 X[3628], 10 X[140] - 7 X[3628], 2 X[4] - 5 X[3628], 5 X[3530] - 2 X[3628], 10 X[3] - X[3628], 2 X[548] + X[3628], 2 X[3534] + 3 X[3628], 10 X[376] + 7 X[3628], 10 X[550] + 11 X[3628], 15 X[3091] - 7 X[3830], 11 X[2] - 3 X[3830], 3 X[547] - X[3830], 9 X[3524] - X[3830], 3 X[550] + X[3830], 11 X[3534] + 5 X[3830], 15 X[3091] - 11 X[3845], 7 X[3830] - 11 X[3845], 3 X[382] - 7 X[3845], 7 X[2] - 3 X[3845], 3 X[140] - X[3845], 3 X[376] + X[3845], 7 X[3534] + 5 X[3845], 16 X[546] - 19 X[3850], 16 X[381] - 17 X[3850], 16 X[5] - 13 X[3850], 16 X[547] - 11 X[3850], 16 X[2] - 9 X[3850], 16 X[140] - 7 X[3850], 16 X[549] - 5 X[3850], 8 X[3628] - 5 X[3850], 16 X[3] - X[3850], 4 X[3530] - X[3850], 16 X[548] + 5 X[3850], 16 X[376] + 7 X[3850], 16 X[550] + 11 X[3850], 16 X[3534] + 15 X[3850], 7 X[3523] - X[3853], 5 X[382] - 14 X[3856], 7 X[4] - 10 X[3856], 5 X[3845] - 6 X[3856], 7 X[3628] - 4 X[3856], 5 X[140] - 2 X[3856], 7 X[549] - 2 X[3856], 5 X[376] + 2 X[3856], 7 X[548] + 2 X[3856], 7 X[3534] + 6 X[3856], 5 X[20] + 7 X[3857], 11 X[3525] - 5 X[3859], 18 X[546] - 19 X[3860], 18 X[381] - 17 X[3860], 18 X[5] - 13 X[3860], 18 X[547] - 11 X[3860], 6 X[3830] - 11 X[3860], 9 X[3850] - 8 X[3860], 18 X[140] - 7 X[3860], 6 X[3845] - 7 X[3860], 18 X[549] - 5 X[3860], 9 X[3628] - 5 X[3860], 9 X[3530] - 2 X[3860], 18 X[3] - X[3860], 18 X[548] + 5 X[3860], 6 X[3534] + 5 X[3860], 18 X[376] + 7 X[3860], 18 X[550] + 11 X[3860], 11 X[3860] - 9 X[3861], 11 X[3850] - 8 X[3861], 10 X[3091] - 7 X[3861], 14 X[3526] - 5 X[3861], 11 X[3628] - 5 X[3861], 2 X[3830] - 3 X[3861], 11 X[3530] - 2 X[3861], 6 X[3524] - X[3861], 2 X[550] + X[3861], 19 X[549] - 15 X[5054], 19 X[3530] - 12 X[5054], 19 X[3524] - 11 X[5054], 19 X[3] - 3 X[5054], X[546] - 3 X[5054], 5 X[3522] + 3 X[5054], 19 X[548] + 15 X[5054], 7 X[4] - 15 X[5055], 5 X[3845] - 9 X[5055], 7 X[3628] - 6 X[5055], 5 X[140] - 3 X[5055], 7 X[549] - 3 X[5055], 2 X[3856] - 3 X[5055], 5 X[376] + 3 X[5055], 7 X[548] + 3 X[5055], 7 X[3534] + 9 X[5055], 17 X[376] - X[5059], 17 X[140] + X[5059], 7 X[381] + X[5059], 17 X[3845] + 3 X[5059], 17 X[382] + 7 X[5059], 15 X[546] - 19 X[5066], 15 X[381] - 17 X[5066], 15 X[3850] - 16 X[5066], 15 X[5] - 13 X[5066], 15 X[547] - 11 X[5066], 5 X[3830] - 11 X[5066], 15 X[140] - 7 X[5066], 5 X[3845] - 7 X[5066], 6 X[3856] - 7 X[5066], 9 X[5055] - 7 X[5066], 5 X[3860] - 6 X[5066], 3 X[4] - 5 X[5066], 15 X[3530] - 4 X[5066], 5 X[2] - 3 X[5066], 3 X[3628] - 2 X[5066], 15 X[3] - X[5066], 3 X[549] - X[5066], 3 X[548] + X[5066], 15 X[376] + 7 X[5066], 15 X[550] + 11 X[5066], 19 X[140] - 13 X[5067], 7 X[546] - 13 X[5067], 19 X[376] + 13 X[5067], 5 X[3853] - 11 X[5072], 5 X[3627] - 17 X[7486], 3 X[3098] + X[8584], 15 X[3522] - 19 X[8703], 3 X[550] - 11 X[8703], 3 X[376] - 7 X[8703], 3 X[548] - 5 X[8703], X[3534] - 5 X[8703], 3 X[3] + X[8703], X[2] + 3 X[8703], 3 X[3530] + 4 X[8703], 3 X[549] + 5 X[8703], X[5066] + 5 X[8703], X[3860] + 6 X[8703], 3 X[140] + 7 X[8703], X[3845] + 7 X[8703], 3 X[3628] + 10 X[8703], 3 X[547] + 11 X[8703], 9 X[3524] + 11 X[8703], X[3830] + 11 X[8703], 3 X[5] + 13 X[8703], 3 X[3850] + 16 X[8703], 3 X[381] + 17 X[8703], 3 X[546] + 19 X[8703], 9 X[5054] + 19 X[8703], 12 X[546] - 19 X[10109], 12 X[381] - 17 X[10109], 12 X[5] - 13 X[10109], 12 X[547] - 11 X[10109], 4 X[3830] - 11 X[10109], 6 X[3861] - 11 X[10109], 12 X[140] - 7 X[10109], 4 X[3845] - 7 X[10109], 12 X[549] - 5 X[10109], 6 X[3628] - 5 X[10109], 4 X[5066] - 5 X[10109], 3 X[3850] - 4 X[10109], 4 X[2] - 3 X[10109], 2 X[3860] - 3 X[10109], 12 X[3] - X[10109], 3 X[3530] - X[10109], 4 X[8703] + X[10109], 12 X[548] + 5 X[10109], 4 X[3534] + 5 X[10109], 12 X[376] + 7 X[10109], 12 X[550] + 11 X[10109], 8 X[546] - 19 X[10124], 8 X[381] - 17 X[10124], 8 X[5066] - 15 X[10124], 8 X[5] - 13 X[10124], 8 X[547] - 11 X[10124], 4 X[3861] - 11 X[10124], 8 X[2] - 9 X[10124], 4 X[3860] - 9 X[10124], 8 X[140] - 7 X[10124], 8 X[549] - 5 X[10124], 4 X[3628] - 5 X[10124], 2 X[10109] - 3 X[10124], 8 X[3] - X[10124], 8 X[8703] + 3 X[10124], 8 X[548] + 5 X[10124], 8 X[376] + 7 X[10124], 8 X[550] + 11 X[10124], 8 X[3534] + 15 X[10124], X[3627] - 13 X[10299], 5 X[381] - 13 X[10303], 17 X[549] - 13 X[10303], 17 X[548] + 13 X[10303], X[3534] - 9 X[10304], 5 X[8703] - 9 X[10304], X[548] - 3 X[10304], 5 X[3] + 3 X[10304], X[549] + 3 X[10304], X[3628] + 6 X[10304], X[5055] + 7 X[10304], X[5066] + 9 X[10304], 5 X[3524] + 11 X[10304], 5 X[3530] + 12 X[10304], X[4] + 15 X[10304], 5 X[5054] + 19 X[10304], 13 X[3534] - 5 X[11001], 13 X[8703] - X[11001], 3 X[5] + X[11001], 13 X[2] + 3 X[11001], 13 X[10109] + 4 X[11001], 13 X[5066] + 5 X[11001], 13 X[3860] + 6 X[11001], 13 X[3845] + 7 X[11001], 13 X[3830] + 11 X[11001], 7 X[3857] - 15 X[11539], X[20] + 3 X[11539], 15 X[10124] - 16 X[11540], 15 X[140] - 14 X[11540], 5 X[3845] - 14 X[11540], 9 X[5055] - 14 X[11540], 5 X[3860] - 12 X[11540], 3 X[4] - 10 X[11540], 15 X[3530] - 8 X[11540], 5 X[10109] - 8 X[11540], 3 X[3856] - 7 X[11540], 5 X[2] - 6 X[11540], 3 X[3628] - 4 X[11540], 15 X[3] - 2 X[11540], 3 X[549] - 2 X[11540], 3 X[548] + 2 X[11540], X[3534] + 2 X[11540], 5 X[8703] + 2 X[11540], 9 X[10304] + 2 X[11540], 15 X[376] + 14 X[11540], 7 X[3853] - X[11541], 14 X[546] - 19 X[11737], 14 X[381] - 17 X[11737], 14 X[5066] - 15 X[11737], 14 X[5] - 13 X[11737], 14 X[547] - 11 X[11737], 10 X[3091] - 11 X[11737], 7 X[3861] - 11 X[11737], 14 X[2] - 9 X[11737], 7 X[3860] - 9 X[11737], 7 X[3850] - 8 X[11737], 2 X[382] - 7 X[11737], 7 X[10109] - 6 X[11737], 14 X[549] - 5 X[11737], 7 X[3628] - 5 X[11737], 4 X[3856] - 5 X[11737], 6 X[5055] - 5 X[11737], 7 X[10124] - 4 X[11737], 2 X[3845] - 3 X[11737], 7 X[3530] - 2 X[11737], 14 X[3] - X[11737], 2 X[376] + X[11737], 14 X[8703] + 3 X[11737], 14 X[548] + 5 X[11737], 14 X[550] + 11 X[11737], 14 X[3534] + 15 X[11737], 2 X[5059] + 17 X[11737], 6 X[546] - 19 X[11812], 18 X[5054] - 19 X[11812], 6 X[381] - 17 X[11812], 6 X[5] - 13 X[11812], 6 X[547] - 11 X[11812], 18 X[3524] - 11 X[11812], 2 X[3830] - 11 X[11812], 3 X[3861] - 11 X[11812], 3 X[3850] - 8 X[11812], 6 X[140] - 7 X[11812], 2 X[3845] - 7 X[11812], 3 X[11737] - 7 X[11812], 6 X[549] - 5 X[11812], 3 X[3628] - 5 X[11812], 2 X[5066] - 5 X[11812], 4 X[11540] - 5 X[11812], 3 X[10124] - 4 X[11812], 2 X[2] - 3 X[11812], X[3860] - 3 X[11812], 3 X[3530] - 2 X[11812], 6 X[3] - X[11812], 2 X[8703] + X[11812], 6 X[548] + 5 X[11812], 2 X[3534] + 5 X[11812], 18 X[10304] + 5 X[11812], 6 X[376] + 7 X[11812], 6 X[550] + 11 X[11812], 2 X[11001] + 13 X[11812], 3 X[546] - 19 X[12100], 9 X[5054] - 19 X[12100], 3 X[381] - 17 X[12100], 3 X[3850] - 16 X[12100], 3 X[11737] - 14 X[12100], 3 X[5] - 13 X[12100], 3 X[547] - 11 X[12100], 9 X[3524] - 11 X[12100], X[3830] - 11 X[12100], 3 X[3628] - 10 X[12100], 3 X[10124] - 8 X[12100], 3 X[140] - 7 X[12100], X[3845] - 7 X[12100], X[3860] - 6 X[12100], 3 X[549] - 5 X[12100], X[5066] - 5 X[12100], 2 X[11540] - 5 X[12100], 3 X[3530] - 4 X[12100], X[10109] - 4 X[12100], X[2] - 3 X[12100], 3 X[3] - X[12100], 3 X[548] + 5 X[12100], X[3534] + 5 X[12100], 9 X[10304] + 5 X[12100], 3 X[376] + 7 X[12100], 3 X[550] + 11 X[12100], X[11001] + 13 X[12100], 15 X[3522] + 19 X[12100], 9 X[3830] - 11 X[12101], 9 X[3845] - 7 X[12101], 9 X[5066] - 5 X[12101], 18 X[11540] - 5 X[12101], 9 X[10109] - 4 X[12101], 3 X[3860] - 2 X[12101], 9 X[11812] - 2 X[12101], 9 X[12100] - X[12101], 9 X[8703] + X[12101], 9 X[3534] + 5 X[12101], 9 X[11001] + 13 X[12101], 14 X[3861] - 11 X[12102], 14 X[3860] - 9 X[12102], 4 X[382] - 7 X[12102], 14 X[3628] - 5 X[12102], 8 X[3856] - 5 X[12102], 12 X[5055] - 5 X[12102], 7 X[3850] - 4 X[12102], 4 X[3845] - 3 X[12102], 7 X[10109] - 3 X[12102], 14 X[11812] - 3 X[12102], 7 X[10124] - 2 X[12102], 4 X[140] - X[12102], 7 X[3530] - X[12102], 4 X[376] + X[12102], 4 X[5059] + 17 X[12102], 17 X[3534] - 15 X[12103], 17 X[550] - 11 X[12103], 17 X[376] - 7 X[12103], X[5059] - 7 X[12103], 17 X[548] - 5 X[12103], 17 X[8703] - 3 X[12103], 7 X[3528] - X[12103], 17 X[3] + X[12103], 17 X[12100] + 3 X[12103], 17 X[3530] + 4 X[12103], 17 X[549] + 5 X[12103], 13 X[10303] + 5 X[12103], 17 X[11812] + 6 X[12103], 17 X[140] + 7 X[12103], 17 X[10124] + 8 X[12103], 17 X[2] + 9 X[12103], 17 X[3628] + 10 X[12103], 17 X[547] + 11 X[12103], 17 X[10109] + 12 X[12103], 17 X[5] + 13 X[12103], 17 X[11737] + 14 X[12103], 17 X[5066] + 15 X[12103], 17 X[3850] + 16 X[12103], 17 X[3860] + 18 X[12103], 17 X[546] + 19 X[12103], 11 X[2] - 18 X[12108], 11 X[10124] - 16 X[12108], 11 X[11540] - 15 X[12108], 11 X[140] - 14 X[12108], 5 X[3091] - 14 X[12108], 11 X[11812] - 12 X[12108], 11 X[549] - 10 X[12108], 7 X[3526] - 10 X[12108], 11 X[3530] - 8 X[12108], X[3830] - 6 X[12108], 11 X[12100] - 6 X[12108], X[3861] - 4 X[12108], 11 X[3] - 2 X[12108], 3 X[3524] - 2 X[12108], X[550] + 2 X[12108], 11 X[8703] + 6 X[12108], 11 X[548] + 10 X[12108], 11 X[376] + 14 X[12108], 5 X[631] - 2 X[12811], 3 X[3839] - 5 X[12812], 11 X[3522] - 19 X[14093], 11 X[8703] - 15 X[14093], X[550] - 5 X[14093], 11 X[3] + 5 X[14093], X[547] + 5 X[14093], 3 X[3524] + 5 X[14093], 2 X[12108] + 5 X[14093], X[3091] + 7 X[14093], X[3861] + 10 X[14093], X[3830] + 15 X[14093], 11 X[12100] + 15 X[14093], X[12007] + 5 X[14810], 3 X[3545] - 7 X[14869], 4 X[4] - 15 X[14890], 5 X[3850] - 12 X[14890], 4 X[5066] - 9 X[14890], 5 X[10109] - 9 X[14890], 8 X[11540] - 9 X[14890], 10 X[11812] - 9 X[14890], 4 X[5055] - 7 X[14890], 5 X[10124] - 6 X[14890], 4 X[549] - 3 X[14890], 5 X[3530] - 3 X[14890], 2 X[3628] - 3 X[14890], 4 X[10304] + X[14890], 4 X[548] + 3 X[14890], 4 X[3534] + 9 X[14890], 2 X[546] - 19 X[14891], 6 X[5054] - 19 X[14891], 2 X[381] - 17 X[14891], 2 X[5066] - 15 X[14891], 4 X[11540] - 15 X[14891], X[12102] - 14 X[14891], 2 X[5] - 13 X[14891], 2 X[547] - 11 X[14891], 6 X[3524] - 11 X[14891], X[3861] - 11 X[14891], 4 X[12108] - 11 X[14891], 3 X[14890] - 10 X[14891], 2 X[2] - 9 X[14891], X[3860] - 9 X[14891], X[3850] - 8 X[14891], 2 X[140] - 7 X[14891], X[11737] - 7 X[14891], X[10109] - 6 X[14891], 2 X[549] - 5 X[14891], X[3628] - 5 X[14891], X[10124] - 4 X[14891], X[11812] - 3 X[14891], 2 X[12100] - 3 X[14891], 2 X[8703] + 3 X[14891], 2 X[548] + 5 X[14891], 6 X[10304] + 5 X[14891], 2 X[376] + 7 X[14891], 2 X[550] + 11 X[14891], 10 X[14093] + 11 X[14891], 2 X[3534] + 15 X[14891], 14 X[3528] + 17 X[14891], 2 X[12103] + 17 X[14891], 10 X[3522] + 19 X[14891], 5 X[632] - 3 X[14892], X[3543] - 3 X[14892], 7 X[3857] - 5 X[14893], 3 X[11539] - X[14893], 5 X[1657] + 19 X[15022], 3 X[12042] + X[15300], 15 X[382] - 7 X[15640], 15 X[12102] - 4 X[15640], 15 X[11737] - 2 X[15640], 15 X[140] - X[15640], 5 X[3845] - X[15640], 6 X[3856] - X[15640], 9 X[5055] - X[15640], 7 X[5066] - X[15640], 14 X[11540] - X[15640], 15 X[376] + X[15640], 7 X[3534] + X[15640], 15 X[5059] + 17 X[15640], 7 X[3523] + X[15681], 11 X[5072] + 5 X[15681], X[11541] + 7 X[15681], 19 X[3830] - 11 X[15682], 19 X[12101] - 9 X[15682], 19 X[3845] - 7 X[15682], 19 X[3860] - 6 X[15682], 19 X[5066] - 5 X[15682], 19 X[10109] - 4 X[15682], 19 X[2] - 3 X[15682], 19 X[11812] - 2 X[15682], 3 X[546] - X[15682], 9 X[5054] - X[15682], 19 X[12100] - X[15682], 15 X[3522] + X[15682], 19 X[8703] + X[15682], 19 X[3534] + 5 X[15682], 19 X[11001] + 13 X[15682], 11 X[3534] - 3 X[15683], 11 X[548] - X[15683], 5 X[550] - X[15683], 5 X[547] + X[15683], 11 X[549] + X[15683], 15 X[3524] + X[15683], 7 X[3526] + X[15683], 10 X[12108] + X[15683], 11 X[3628] + 2 X[15683], 5 X[3861] + 2 X[15683], 5 X[3830] + 3 X[15683], 11 X[5066] + 3 X[15683], 11 X[4] + 5 X[15683], 13 X[4] - 5 X[15684], 13 X[5066] - 3 X[15684], 13 X[3628] - 2 X[15684], 5 X[5] - X[15684], 13 X[549] - X[15684], 13 X[548] + X[15684], 13 X[3534] + 3 X[15684], 5 X[11001] + 3 X[15684], 13 X[15683] + 11 X[15684], 9 X[5059] - 17 X[15685], 9 X[376] - X[15685], 7 X[2] + X[15685], 9 X[140] + X[15685], 3 X[3845] + X[15685], 7 X[3860] + 2 X[15685], 9 X[11737] + 2 X[15685], 7 X[12101] + 3 X[15685], 9 X[12102] + 4 X[15685], 18 X[3856] + 5 X[15685], 3 X[15640] + 5 X[15685], 9 X[382] + 7 X[15685], 19 X[12103] - 17 X[15686], 19 X[3534] - 15 X[15686], 19 X[550] - 11 X[15686], 19 X[376] - 7 X[15686], 19 X[548] - 5 X[15686], 19 X[8703] - 3 X[15686], 5 X[3522] - X[15686], 19 X[3] + X[15686], 3 X[5054] + X[15686], 19 X[14891] + 2 X[15686], 19 X[12100] + 3 X[15686], X[15682] + 3 X[15686], 19 X[3530] + 4 X[15686], 19 X[549] + 5 X[15686], 19 X[11812] + 6 X[15686], 19 X[140] + 7 X[15686], 13 X[5067] + 7 X[15686], 19 X[10124] + 8 X[15686], 19 X[2] + 9 X[15686], 19 X[3628] + 10 X[15686], 19 X[547] + 11 X[15686], 19 X[10109] + 12 X[15686], 19 X[5] + 13 X[15686], 19 X[11737] + 14 X[15686], 19 X[5066] + 15 X[15686], 19 X[3850] + 16 X[15686], 19 X[381] + 17 X[15686], 19 X[3860] + 18 X[15686], 5 X[631] - X[15687], 13 X[548] - 15 X[15688], 13 X[8703] - 9 X[15688], X[11001] - 9 X[15688], 13 X[10304] - 5 X[15688], 13 X[3] + 3 X[15688], X[5] + 3 X[15688], 13 X[14891] + 6 X[15688], 13 X[12100] + 9 X[15688], 13 X[3524] + 11 X[15688], 13 X[3530] + 12 X[15688], 13 X[549] + 15 X[15688], X[15684] + 15 X[15688], 13 X[11812] + 18 X[15688], 13 X[5054] + 19 X[15688], 5 X[631] + 3 X[15689], 2 X[12811] + 3 X[15689], X[15687] + 3 X[15689], 9 X[15686] - 19 X[15690], 9 X[12103] - 17 X[15690], 3 X[11001] - 13 X[15690], 9 X[550] - 11 X[15690], 9 X[376] - 7 X[15690], X[15685] - 7 X[15690], 9 X[548] - 5 X[15690], 3 X[3534] - 5 X[15690], 3 X[8703] - X[15690], 9 X[3] + X[15690], 3 X[12100] + X[15690], X[3860] + 2 X[15690], 3 X[11812] + 2 X[15690], 9 X[14891] + 2 X[15690], X[12101] + 3 X[15690], 9 X[3530] + 4 X[15690], 3 X[10109] + 4 X[15690], 9 X[549] + 5 X[15690], 3 X[5066] + 5 X[15690], 6 X[11540] + 5 X[15690], 9 X[140] + 7 X[15690], 3 X[3845] + 7 X[15690], 9 X[10124] + 8 X[15690], 9 X[3628] + 10 X[15690], 9 X[547] + 11 X[15690], 3 X[3830] + 11 X[15690], 18 X[12108] + 11 X[15690], 9 X[5] + 13 X[15690], 9 X[11737] + 14 X[15690], 9 X[3850] + 16 X[15690], 9 X[381] + 17 X[15690], 9 X[546] + 19 X[15690], 3 X[15682] + 19 X[15690], 13 X[15686] - 19 X[15691], 13 X[12103] - 17 X[15691], 13 X[3534] - 15 X[15691], 13 X[550] - 11 X[15691], 13 X[15690] - 9 X[15691], 13 X[376] - 7 X[15691], 13 X[548] - 5 X[15691], 13 X[8703] - 3 X[15691], X[11001] - 3 X[15691], 3 X[15688] - X[15691], 13 X[3] + X[15691], 13 X[14891] + 2 X[15691], 13 X[12100] + 3 X[15691], 13 X[3530] + 4 X[15691], 13 X[549] + 5 X[15691], X[15684] + 5 X[15691], 13 X[11812] + 6 X[15691], 13 X[140] + 7 X[15691], 13 X[10124] + 8 X[15691], 13 X[2] + 9 X[15691], 13 X[3628] + 10 X[15691], 13 X[547] + 11 X[15691], 13 X[10109] + 12 X[15691], 13 X[11737] + 14 X[15691], 13 X[5066] + 15 X[15691], 13 X[3850] + 16 X[15691], 13 X[381] + 17 X[15691], 13 X[3860] + 18 X[15691], 13 X[546] + 19 X[15691], 13 X[12100] - 15 X[15692], 13 X[14891] - 10 X[15692], 13 X[3] - 5 X[15692], X[5] - 5 X[15692], 3 X[15688] + 5 X[15692], X[15691] + 5 X[15692], 13 X[14093] + 11 X[15692], 13 X[8703] + 15 X[15692], X[11001] + 15 X[15692], 13 X[3522] + 19 X[15692], 7 X[2] - 15 X[15693], 3 X[3091] - 11 X[15693], 3 X[11737] - 10 X[15693], 7 X[11812] - 10 X[15693], 3 X[140] - 5 X[15693], X[3845] - 5 X[15693], 7 X[12100] - 5 X[15693], 3 X[376] + 5 X[15693], 7 X[8703] + 5 X[15693], X[15685] + 15 X[15693], 7 X[15690] + 15 X[15693], X[3627] - 5 X[15694], 13 X[10299] - 5 X[15694], 9 X[8703] - 5 X[15695], 3 X[15690] - 5 X[15695], 3 X[2] + 5 X[15695], 9 X[12100] + 5 X[15695], X[12101] + 5 X[15695], 9 X[15693] + 7 X[15695], 3 X[3860] + 10 X[15695], 9 X[11812] + 10 X[15695], 3 X[3545] + 5 X[15696], 7 X[14869] + 5 X[15696], 17 X[15690] - 15 X[15697], 17 X[15695] - 9 X[15697], 17 X[8703] - 5 X[15697], 3 X[12103] - 5 X[15697], 3 X[381] + 5 X[15697], 17 X[12100] + 5 X[15697], 17 X[15693] + 7 X[15697], 17 X[11812] + 10 X[15697], 17 X[2] + 15 X[15697], 3 X[3628] - 14 X[15698], 5 X[11812] - 14 X[15698], 15 X[14891] - 14 X[15698], 3 X[3526] - 11 X[15698], 15 X[3] - 7 X[15698], 3 X[549] - 7 X[15698], X[5066] - 7 X[15698], 2 X[11540] - 7 X[15698], 5 X[12100] - 7 X[15698], 3 X[548] + 7 X[15698], X[3534] + 7 X[15698], 5 X[8703] + 7 X[15698], 9 X[10304] + 7 X[15698], 15 X[3528] + 17 X[15698], 11 X[5072] - 15 X[15699], 7 X[3523] - 3 X[15699], X[3853] - 3 X[15699], X[15681] + 3 X[15699], 3 X[11539] - 7 X[15700], X[14893] - 7 X[15700], X[3857] - 5 X[15700], X[20] + 7 X[15700], 13 X[11812] - 14 X[15701], 3 X[5] - 7 X[15701], 13 X[12100] - 7 X[15701], 15 X[15692] - 7 X[15701], 13 X[15698] - 5 X[15701], 13 X[8703] + 7 X[15701], X[11001] + 7 X[15701], 9 X[15688] + 7 X[15701], 3 X[15691] + 7 X[15701], X[1657] + 7 X[15702], X[3529] + 7 X[15703], 5 X[5059] - 17 X[15704], 7 X[15683] - 11 X[15704], 5 X[15685] - 9 X[15704], 7 X[3534] - 3 X[15704], 5 X[376] - X[15704], 7 X[548] - X[15704], 5 X[140] + X[15704], 7 X[549] + X[15704], 2 X[3856] + X[15704], 3 X[5055] + X[15704], 7 X[3628] + 2 X[15704], 5 X[11737] + 2 X[15704], 5 X[3845] + 3 X[15704], 7 X[5066] + 3 X[15704], 14 X[11540] + 3 X[15704], X[15640] + 3 X[15704], 5 X[12102] + 4 X[15704], 7 X[4] + 5 X[15704], 5 X[382] + 7 X[15704], 7 X[15684] + 13 X[15704], 17 X[14891] - 18 X[15705], 17 X[3] - 9 X[15705], X[381] - 9 X[15705], 7 X[3528] + 9 X[15705], X[12103] + 9 X[15705], 17 X[10304] + 15 X[15705], 5 X[3628] - 18 X[15706], 5 X[14890] - 12 X[15706], X[4] - 9 X[15706], 5 X[549] - 9 X[15706], 5 X[10304] + 3 X[15706], 5 X[548] + 9 X[15706], 5 X[632] - 9 X[15707], X[3543] - 9 X[15707], X[14892] - 3 X[15707], 7 X[11737] - 18 X[15708], 7 X[5055] - 15 X[15708], 7 X[140] - 9 X[15708], X[382] - 9 X[15708], 7 X[376] + 9 X[15708], 13 X[3628] - 18 X[15709], 13 X[14890] - 12 X[15709], 5 X[5] - 9 X[15709], 13 X[549] - 9 X[15709], X[15684] - 9 X[15709], 13 X[15706] - 5 X[15709], 13 X[10304] + 3 X[15709], 5 X[15688] + 3 X[15709], 13 X[548] + 9 X[15709], 5 X[15691] + 9 X[15709], X[14891] - 18 X[15710], X[15705] - 17 X[15710], X[3] - 9 X[15710], X[10304] + 15 X[15710], X[12101] - 15 X[15711], 9 X[15692] - 13 X[15711], X[3860] - 10 X[15711], 3 X[11812] - 10 X[15711], 9 X[14891] - 10 X[15711], 3 X[15693] - 7 X[15711], X[2] - 5 X[15711], 9 X[3] - 5 X[15711], 3 X[12100] - 5 X[15711], X[15695] + 3 X[15711], 3 X[8703] + 5 X[15711], X[15690] + 5 X[15711], 9 X[14093] + 11 X[15711], 3 X[15697] + 17 X[15711], 9 X[3522] + 19 X[15711], 17 X[12100] - 15 X[15712], 17 X[15692] - 13 X[15712], 17 X[14891] - 10 X[15712], 17 X[15711] - 9 X[15712], 17 X[3] - 5 X[15712], X[381] - 5 X[15712], 9 X[15705] - 5 X[15712], X[15697] + 3 X[15712], 7 X[3528] + 5 X[15712], X[12103] + 5 X[15712], 17 X[14093] + 11 X[15712], 17 X[8703] + 15 X[15712], 17 X[3522] + 19 X[15712], 11 X[2] - 15 X[15713], 3 X[3861] - 10 X[15713], 11 X[11812] - 10 X[15713], 3 X[3091] - 7 X[15713], 11 X[15693] - 7 X[15713], 3 X[547] - 5 X[15713], 9 X[3524] - 5 X[15713], X[3830] - 5 X[15713], 11 X[12100] - 5 X[15713], 6 X[12108] - 5 X[15713], 11 X[15711] - 3 X[15713], 3 X[14093] + X[15713], 3 X[550] + 5 X[15713], 11 X[8703] + 5 X[15713], 11 X[15695] + 9 X[15713], 11 X[15690] + 15 X[15713], 11 X[15697] + 17 X[15713], X[15712] - 17 X[15714], X[12100] - 15 X[15714], X[15692] - 13 X[15714], X[14891] - 10 X[15714], X[15711] - 9 X[15714], X[3] - 5 X[15714], 9 X[15710] - 5 X[15714], X[14093] + 11 X[15714], X[8703] + 15 X[15714], X[3522] + 19 X[15714], 19 X[3] - 11 X[15715], X[546] - 11 X[15715], 3 X[5054] - 11 X[15715], 5 X[3522] + 11 X[15715], X[15686] + 11 X[15715], 3 X[2] - 11 X[15716], 9 X[12100] - 11 X[15716], X[12101] - 11 X[15716], 15 X[15711] - 11 X[15716], 9 X[8703] + 11 X[15716], 3 X[15690] + 11 X[15716], 5 X[15695] + 11 X[15716], 5 X[140] - 11 X[15717], 7 X[549] - 11 X[15717], 2 X[3856] - 11 X[15717], 3 X[5055] - 11 X[15717], 5 X[376] + 11 X[15717], 7 X[548] + 11 X[15717], X[15704] + 11 X[15717], 3 X[3545] - 11 X[15718], 7 X[14869] - 11 X[15718], 5 X[15696] + 11 X[15718], 3 X[381] - 11 X[15719], 17 X[12100] - 11 X[15719], 15 X[15712] - 11 X[15719], 17 X[15716] - 9 X[15719], 17 X[8703] + 11 X[15719], 3 X[12103] + 11 X[15719], 5 X[15697] + 11 X[15719], 3 X[3839] - 11 X[15720], 5 X[12812] - 11 X[15720], 3 X[14269] - 11 X[15721], 9 X[2] - 17 X[15722], 3 X[12101] - 17 X[15722], 9 X[15690] + 17 X[15722], 15 X[15695] + 17 X[15722], 7 X[5] - 11 X[15723], 13 X[140] - 11 X[15723], 13 X[15717] - 5 X[15723], 13 X[376] + 11 X[15723], 7 X[15691] + 11 X[15723].
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3, 15711), (2, 376, 15685), (2, 3860, 10109), (2, 8703, 15690), (2, 15685, 3845), (2, 15711, 12100), (3, 381, 15705), (3, 3528, 15712), (3, 3534, 15698), (3, 5054, 15715), (3, 8703, 12100), (3, 10304, 549), (3, 14093, 3524), (3, 15688, 15692), (3, 15695, 15716), (3, 15710, 15714), (4, 15706, 549), (5, 549, 15709), (5, 15688, 15691), (20, 11539, 14893), (20, 15700, 11539), (140, 546, 5067), (140, 548, 15704), (140, 3856, 3628), (140, 12100, 15693), (140, 15704, 3856), (376, 3524, 3091), (376, 5055, 15704), (376, 15640, 3534), (376, 15692, 15723), (376, 15693, 3845), (376, 15708, 382), (376, 15717, 5055), (381, 15705, 15712), (547, 3524, 12108), (548, 5066, 3534), (548, 12100, 5066), (548, 14891, 14890), (548, 15698, 11540), (548, 15717, 3856), (549, 3534, 5066), (549, 3628, 14890), (549, 3857, 11539), (549, 5055, 140), (549, 5066, 11540), (549, 8703, 3534), (549, 10304, 548), (549, 11540, 11812), (549, 15683, 547), (549, 15698, 12100), (549, 15704, 5055), (550, 3524, 547), (550, 12108, 3861), (550, 15713, 3830), (631, 15689, 15687), (632, 3543, 14892), (3091, 3830, 3845), (3091, 15693, 15713), (3522, 5054, 15686), (3522, 15715, 5054), (3523, 15681, 15699), (3524, 3526, 549), (3524, 3830, 15713), (3524, 14093, 550), (3524, 15683, 3526), (3526, 3534, 3830), (3528, 15705, 381), (3528, 15712, 12103), (3528, 15719, 15697), (3530, 10109, 11812), (3530, 12102, 140), (3530, 14890, 549), (3534, 3830, 15683), (3534, 5055, 15640), (3534, 8703, 548), (3534, 10304, 8703), (3534, 12100, 11540), (3534, 15640, 15704), (3534, 15684, 11001), (3534, 15693, 5055), (3534, 15698, 549), (3543, 15707, 632), (3545, 15718, 14869), (3628, 5066, 10109), (3628, 11737, 5055), (3628, 11812, 11540), (3628, 14890, 10124), (3628, 15704, 12102), (3830, 12100, 12108), (3830, 15713, 547), (3845, 5055, 5066), (3845, 5066, 3856), (3845, 8703, 376), (3845, 15693, 140), (3845, 15704, 15640), (3856, 5055, 11737), (3860, 11812, 2), (3861, 14891, 3524), (5054, 15686, 546), (5055, 15640, 3845), (5055, 15717, 549), (5059, 15712, 140), (5059, 15717, 10303), (5066, 11540, 3628), (5066, 12100, 549), (8703, 14891, 10109), (8703, 15698, 5066), (8703, 15701, 15691), (8703, 15711, 2), (8703, 15713, 550), (8703, 15716, 12101), (8703, 15719, 12103), (10109, 11812, 10124), (10304, 15698, 3534), (10304, 15709, 15688), (10304, 15717, 376), (11001, 15692, 15701), (11001, 15701, 5), (11001, 15723, 3845), (11540, 11812, 14890), (11540, 15640, 11737), (11812, 12100, 3530), (11812, 14891, 12100), (12100, 15690, 2), (12108, 15713, 11812), (15640, 15698, 15693), (15681, 15699, 3853), (15683, 15713, 5066), (15684, 15692, 549), (15684, 15709, 5), (15685, 15693, 2), (15688, 15692, 5), (15688, 15701, 11001), (15693, 15723, 15701), (15695, 15716, 2), (15696, 15718, 3545), (15697, 15705, 15719), (15697, 15719, 381), (15704, 15717, 140).
Best regards,
Peter Moses.
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