Dilation Factors

Evaluated to X(38847)

Last update: 2020-06-06

As stated in the preamble just before X(38497):

Suppose that P and U are distinct points in the plane of a triangle ABC. Let Γ(P,U)) denote the circle with center P and pass-through point U. Suppose that V is a point distinct from U, and let D(P,U,V) denote the dilation from P that maps Γ(P,U)) onto Γ(P,V)).

In the lists below, the dilation center, P, is the circumcenter, X(3). For many choices of V, the dilation factor for mapping a point U on the circumcircle to a point V is not a rational function. For example, if V = X(1), the dilation factor is

Sqrt[(a^3 - a^2*b - a*b^2 + b^3 - a^2*c + 3*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3)/(a*b*c)],

and if V = X(2), the dilation factor is

Sqrt[(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)/(9*a^2*b^2*c^2)].

The equation of a circle with dilation factor d is
a^2*y*z + b^2*z*x + c^2*x*y - (1 - d^2)*R^2*(x + y + z)^2 = 0.

In general, the dilation factor for mapping U on the circumcircle to a point V is |X(3)V|/R. The appearance of n in the following list means that this dilation factor, for V = X(n), is a rational function of a,b,c:

{8, 76, 156, 183, 220, 221, 246, 252, 277, 290, 339, 399, 847, 911, 944, 956, 1078, 1145, 1150, 1511, 1614, 1623, 1809, 1975, 2338, 2932, 2967, 2968, 2969, 2970, 2971, 2972, 2973, 2974, 2975, 3160, 3172, 3207, 3445, 3470, 3511, 3730, 4996, 5152, 5191, 5303, 5609, 5649, 5657, 5687, 5690, 5731, 5744, 5767, 5768, 5769, 5770, 5771, 5773, 5774, 5775, 5876, 5939, 5944, 5968, 5976, 5989, 6090, 6184, 6224, 6241, 6350, 6394, 6800, 7723, 7771, 7782, 7952, 7998, 7999, 8008, 8009, 8192, 8743, 8778, 8870, 9149, 9155, 9159, 9215, 9216, 9475, 9486, 9707, 9717, 9803, 9828, 9869, 9945, 9952, 10016, 10017, 10104, 10354, 10355, 10571, 10609, 10620, 11257, 11258, 11440, 11441, 11444, 11449, 11454, 11456, 11459, 11464, 11468, 11491, 11590, 11591, 11592, 12041, 12042, 12091, 12111, 12168, 12174, 12188, 12203, 12247, 12270, 12281, 12308, 12331, 12358, 12412, 12531, 12645, 12773, 12825, 13108, 13115, 13171, 13188, 13226, 13310, 13325, 13326, 13416, 13491, 13512, 14026, 14094, 14246, 14247, 14248, 14249, 14250, 14251, 14252, 14253, 14254, 14255, 14256, 14257, 14258, 14259, 14260, 14261, 14262, 14263, 14264, 14265, 14266, 14267, 14268, 14382, 14385, 14640, 14650, 14663, 14670, 14880, 14919, 15020, 15021, 15023, 15034, 15035, 15036, 15039, 15040, 15041, 15042, 15051, 15054, 15055, 15066, 15067, 15068, 15072, 15080, 15100, 15101, 15102, 15106, 15132, 15154, 15155, 15156, 15157, 15251, 15252, 15468, 15623, 15626, 15725, 16020, 16486, 17100, 17740, 17854, 18340, 18341, 18526, 18861, 19914, 20481, 20672, 20999, 21166, 21444, 21448, 21664, 21665, 21666, 21766, 22102, 22240, 22584, 22712, 23059, 23060, 23235, 23239, 23858, 24047, 24144, 24880, 24977, 25043, 26864, 26895, 26896, 28447, 28448, 30283, 30524, 30525, 31187, 31387, 31635, 31841, 32128, 32138, 32139, 32141, 32142, 32153, 32171, 32210, 32540, 32595, 32609, 32637, 33089, 33533, 33758, 33813, 33814, 33848, 33927, 33983, 33997, 34042, 34234, 34243, 34332, 34333, 34334, 34335, 34336, 34337, 34338, 34469, 34473, 34474, 34513, 34586, 34756, 34758, 34773, 34834, 34885, 35012, 35072, 35193, 35231, 35232, 35451, 35464, 35910, 36055, 36822, 36921, 36944, 38497, 38498, 38499, 38500, 38501, 38502, 38503, 38504, 38505, 38506, 38507, 38508, 38509, 38510, 38511, 38512, 38513, 38514, 38515, 38516, 38517, 38518, 38519, 38520, 38521, 38522, 38523, 38524, 38525, 38526, 38527, 38528, 38529, 38539, 38551, 38552, 38553, 38554, 38555, 38556, 38557, 38558, 38559, 38560, 38561, 38562, 38563, 38564, 38565, 38566, 38567, 38568, 38569, 38570, 38571, 38572, 38573, 38574, 38575, 38576, 38577, 38578, 38579, 38580, 38581, 38582, 38583, 38584, 38585, 38586, 38587, 38588, 38589, 38590, 38591, 38592, 38593, 38594, 38595, 38596, 38597, 38598, 38599, 38600, 38601, 38602, 38603, 38604, 38605, 38606, 38607, 38608, 38609, 38610, 38611, 38612, 38613, 38614, 38615, 38616, 38617, 38618, 38619, 38620, 38621, 38622, 38623, 38624, 38625, 38626, 38627, 38628, 38629, 38630, 38631, 38632, 38633, 38634, 38635, 38636, 38637, 38638, 38639, 38640, 38641, 38642, 38643, 38644, 38645, 38646, 38647, 38648, 38649, 38650, 38651, 38652, 38653, 38654, 38655, 38656, 38657, 38658, 38659, 38660, 38661, 38662, 38663, 38664, 38665, 38666, 38667, 38668, 38669, 38670, 38671, 38672, 38673, 38674, 38675, 38676, 38677, 38678, 38679, 38680, 38681, 38682, 38683, 38684, 38685, 38686, 38687, 38688, 38689, 38690, 38691, 38692, 38693, 38694, 38695, 38696, 38697, 38698, 38699, 38700, 38701, 38702, 38703, 38704, 38705, 38706, 38707, 38708, 38709, 38710, 38711, 38712, 38713, 38714, 38715, 38716, 38717, 38718, 38719, 38722}

The appearance of i₁, i₂, . . . i_k, under Index means that the k points all lie on the circle Γ(X(3),X(i₁)), and the appearance of f(a,b,c)/g(a,b,c) means that this is the dilation factor for the k points, where f and g are polynomials of the same degree of homogeneity in a,b,c.

Index	Dilation Factor
8, 944, 18340, 38497, 38498, 38499, 38500, 38501, 38502, 38503, 38504, 38505, 38506, 38507, 38508, 38509, 38510, 38511, 38512, 38513, 38514, 38515, 38516, 38517, 38518, 38519	(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)/(ab*c)
76, 11257, 13325, 13326, 38520, 38521, 38522, 38523, 38524, 38525, 38526, 38527, 38528, 38529	(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)/(a^2b^2 + a^2c^2 + b^2c^2)
156, 32138	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2))
183	(-2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^4 - 4a^2b^2 + b^4 - 4a^2c^2 - 4b^2c^2 + c^4)
220	(2(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + 2a^2bc + 2ab^2c - 2b^3c + 2a^2c^2 + 2abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4)
221	(2(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2))
246	(a^8 - 2a^6b^2 + 2a^4b^4 - 2a^2b^6 + b^8 - 2a^6c^2 + a^4b^2c^2 + a^2b^4c^2 - 2b^6c^2 + 2a^4c^4 + a^2b^2c^4 + 2b^4c^4 - 2a^2c^6 - 2b^2c^6 + c^8)/(a^6b^2 - 2a^4b^4 + a^2b^6 + a^6c^2 + b^6c^2 - 2a^4c^4 - 2b^4c^4 + a^2c^6 + b^2c^6)
252	(a^12 - 4a^10b^2 + 7a^8b^4 - 8a^6b^6 + 7a^4b^8 - 4a^2b^10 + b^12 - 4a^10c^2 + 8a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 8a^2b^8c^2 - 4b^10c^2 + 7a^8c^4 - 4a^6b^2c^4 + 3a^4b^4c^4 - 4a^2b^6c^4 + 7b^8c^4 - 8a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 8b^6c^6 + 7a^4c^8 + 8a^2b^2c^8 + 7b^4c^8 - 4a^2c^10 - 4b^2c^10 + c^12)/((a^3 - a^2b - ab^2 + b^3 + a^2c - abc + b^2c - ac^2 - bc^2 - c^3)(a^3 + a^2b - ab^2 - b^3 + a^2c + abc + b^2c - ac^2 + bc^2 - c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + abc - b^2c - ac^2 - bc^2 + c^3)(a^3 + a^2b - ab^2 - b^3 - a^2c - abc - b^2c - ac^2 + b*c^2 + c^3))
277	((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + a^2bc + ab^2c - 2b^3c + 2a^2c^2 + abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4))/(abc(3a^4 - 8a^3b + 10a^2b^2 - 8ab^3 + 3b^4 - 8a^3c + 4a^2bc + 4ab^2c - 8b^3c + 10a^2c^2 + 4abc^2 + 10b^2c^2 - 8ac^3 - 8bc^3 + 3*c^4))
290	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6b^2 - 2a^4b^4 + a^2b^6 + a^6c^2 - a^4b^2c^2 - a^2b^4c^2 + b^6c^2 - 2a^4c^4 - a^2b^2c^4 - 2b^4c^4 + a^2c^6 + b^2c^6))/(a^8b^4 - 2a^6b^6 + a^4b^8 + a^8b^2c^2 - a^6b^4c^2 - a^4b^6c^2 + a^2b^8c^2 + a^8c^4 - a^6b^2c^4 + 3a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + a^2b^2c^8 + b^4*c^8)
339	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 2a^6b^2c^2 + 2a^4b^4c^2 - 2a^2b^6c^2 + b^8c^2 - a^6c^4 + 2a^4b^2c^4 + 2a^2b^4c^4 - b^6c^4 - a^4c^6 - 2a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8)
399, 8008, 8009, 10620, 11258, 12188, 12331, 12773, 13115, 13188, 13310, 13512, 14663, 15154, 15155, 32595, 38572, 38573, 38574, 38575, 38576, 38577, 38578, 38579, 38580, 38581, 38582, 38583, 38584, 38585, 38586, 38587, 38588, 38589, 38590, 38591, 38592, 38593, 38594, 38595, 38596, 38597, 38598	2
847	(a^12 - 3a^10b^2 + 3a^8b^4 - 2a^6b^6 + 3a^4b^8 - 3a^2b^10 + b^12 - 3a^10c^2 + 7a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 7a^2b^8c^2 - 3b^10c^2 + 3a^8c^4 - 4a^6b^2c^4 + 6a^4b^4c^4 - 4a^2b^6c^4 + 3b^8c^4 - 2a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 2b^6c^6 + 3a^4c^8 + 7a^2b^2c^8 + 3b^4c^8 - 3a^2c^10 - 3b^2c^10 + c^12)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 - a^8b^2c^2 - a^2b^8c^2 + b^10c^2 - 4a^8c^4 + 4a^4b^4c^4 - 4b^8c^4 + 6a^6c^6 + 6b^6c^6 - 4a^4c^8 - a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2*c^10)
911	((a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4)(a^5 - a^4b - ab^4 + b^5 - a^4c + 2a^2b^2c - b^4c + 2a^2bc^2 + 2ab^2c^2 - ac^4 - bc^4 + c^5))/(a^9 - a^8b - 4a^6b^3 + 4a^5b^4 + 4a^4b^5 - 4a^3b^6 - ab^8 + b^9 - a^8c + a^7bc + 2a^6b^2c - a^5b^3c - 2a^4b^4c - a^3b^5c + 2a^2b^6c + ab^7c - b^8c + 2a^6bc^2 + 2a^5b^2c^2 - 4a^4b^3c^2 - 4a^3b^4c^2 + 2a^2b^5c^2 + 2ab^6c^2 - 4a^6c^3 - a^5bc^3 - 4a^4b^2c^3 + 18a^3b^3c^3 - 4a^2b^4c^3 - ab^5c^3 - 4b^6c^3 + 4a^5c^4 - 2a^4bc^4 - 4a^3b^2c^4 - 4a^2b^3c^4 - 2ab^4c^4 + 4b^5c^4 + 4a^4c^5 - a^3bc^5 + 2a^2b^2c^5 - ab^3c^5 + 4b^4c^5 - 4a^3c^6 + 2a^2bc^6 + 2ab^2c^6 - 4b^3c^6 + abc^7 - ac^8 - b*c^8 + c^9)
956	(-2(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - bc^2 + c^3)
1078	(-a^4 + a^2b^2 - b^4 + a^2c^2 + b^2c^2 - c^4)/(a^4 - 3a^2b^2 + b^4 - 3a^2c^2 - 3b^2*c^2 + c^4)
1145	(a^3 - a^2b - ab^2 + b^3 - a^2c + 4abc - b^2c - ac^2 - bc^2 + c^3)/(2abc)
1150	-(((a + b)(a + c)(b + c)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(a^3 - 2a^2b - 2ab^2 + b^3 - 2a^2c - 2b^2c - 2ac^2 - 2b*c^2 + c^3)))
1511, 12041, 12042, 14650, 33813, 33814, 35231, 35232, 38599, 38600, 38601, 38602, 38603, 38604, 38605, 38606, 38607, 38608, 38609, 38610, 38611, 38612, 38613, 38614, 38615, 38616, 38617, 38618, 38619, 38620, 38621, 38622, 38623, 38624, 38625	1/2
1614, 11440	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
1623	(3abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(2a^6 - 2a^5b - 2a^4b^2 + 4a^3b^3 - 2a^2b^4 - 2ab^5 + 2b^6 - 2a^5c + a^4bc + a^3b^2c + a^2b^3c + ab^4c - 2b^5c - 2a^4c^2 + a^3bc^2 - 3a^2b^2c^2 + ab^3c^2 - 2b^4c^2 + 4a^3c^3 + a^2bc^3 + ab^2c^3 + 4b^3c^3 - 2a^2c^4 + abc^4 - 2b^2c^4 - 2ac^5 - 2bc^5 + 2*c^6)
1809	-(((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^9 - 3a^8b + 8a^6b^3 - 6a^5b^4 - 6a^4b^5 + 8a^3b^6 - 3ab^8 + b^9 - 3a^8c + 11a^7bc - 12a^6b^2c - 11a^5b^3c + 30a^4b^4c - 11a^3b^5c - 12a^2b^6c + 11ab^7c - 3b^8c - 12a^6bc^2 + 36a^5b^2c^2 - 24a^4b^3c^2 - 24a^3b^4c^2 + 36a^2b^5c^2 - 12ab^6c^2 + 8a^6c^3 - 11a^5bc^3 - 24a^4b^2c^3 + 54a^3b^3c^3 - 24a^2b^4c^3 - 11ab^5c^3 + 8b^6c^3 - 6a^5c^4 + 30a^4bc^4 - 24a^3b^2c^4 - 24a^2b^3c^4 + 30ab^4c^4 - 6b^5c^4 - 6a^4c^5 - 11a^3bc^5 + 36a^2b^2c^5 - 11ab^3c^5 - 6b^4c^5 + 8a^3c^6 - 12a^2bc^6 - 12ab^2c^6 + 8b^3c^6 + 11abc^7 - 3ac^8 - 3bc^8 + c^9))
1975	(2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^4 + b^4 + c^4)
2338	((a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4)(3a^5 - a^4b - 2a^3b^2 - 2a^2b^3 - ab^4 + 3b^5 - a^4c + 2a^2b^2c - b^4c - 2a^3c^2 + 2a^2bc^2 + 2ab^2c^2 - 2b^3c^2 - 2a^2c^3 - 2b^2c^3 - ac^4 - bc^4 + 3c^5))/(a^9 - 2a^8b + 3a^7b^2 - 7a^6b^3 + 5a^5b^4 + 5a^4b^5 - 7a^3b^6 + 3a^2b^7 - 2ab^8 + b^9 - 2a^8c + 3a^7bc + 2a^6b^2c - 3a^5b^3c - 3a^3b^5c + 2a^2b^6c + 3ab^7c - 2b^8c + 3a^7c^2 + 2a^6bc^2 - 5a^4b^3c^2 - 5a^3b^4c^2 + 2ab^6c^2 + 3b^7c^2 - 7a^6c^3 - 3a^5bc^3 - 5a^4b^2c^3 + 30a^3b^3c^3 - 5a^2b^4c^3 - 3ab^5c^3 - 7b^6c^3 + 5a^5c^4 - 5a^3b^2c^4 - 5a^2b^3c^4 + 5b^5c^4 + 5a^4c^5 - 3a^3bc^5 - 3ab^3c^5 + 5b^4c^5 - 7a^3c^6 + 2a^2bc^6 + 2ab^2c^6 - 7b^3c^6 + 3a^2c^7 + 3abc^7 + 3b^2c^7 - 2ac^8 - 2b*c^8 + c^9)
2932	(2abc)/(a^3 - a^2b - ab^2 + b^3 - a^2c + 4abc - b^2c - ac^2 - bc^2 + c^3)
2967, 38551, 38552, 38553	(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10)/(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 2a^6b^2c^2 + 2a^4b^4c^2 - 2a^2b^6c^2 + b^8c^2 - a^6c^4 + 2a^4b^2c^4 + 2a^2b^4c^4 - b^6c^4 - a^4c^6 - 2a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8)
2968, 10017, 38554	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(2abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))
2969	(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + a^7bc + 2a^6b^2c - a^5b^3c - 2a^4b^4c - a^3b^5c + 2a^2b^6c + ab^7c - b^8c - 2a^7c^2 + 2a^6bc^2 + 2a^5b^2c^2 - 2a^4b^3c^2 - 2a^3b^4c^2 + 2a^2b^5c^2 + 2ab^6c^2 - 2b^7c^2 + 2a^6c^3 - a^5bc^3 - 2a^4b^2c^3 + 6a^3b^3c^3 - 2a^2b^4c^3 - ab^5c^3 + 2b^6c^3 - 2a^4bc^4 - 2a^3b^2c^4 - 2a^2b^3c^4 - 2ab^4c^4 - a^3bc^5 + 2a^2b^2c^5 - ab^3c^5 + 2a^3c^6 + 2a^2bc^6 + 2ab^2c^6 + 2b^3c^6 - 2a^2c^7 + abc^7 - 2b^2c^7 - ac^8 - bc^8 + c^9)/(2abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + a^4bc + ab^4c - b^5c - a^4c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 + abc^4 - b^2c^4 - ac^5 - b*c^5 + c^6))
2970	(a^12 - 3a^10b^2 + 3a^8b^4 - 2a^6b^6 + 3a^4b^8 - 3a^2b^10 + b^12 - 3a^10c^2 + 7a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 7a^2b^8c^2 - 3b^10c^2 + 3a^8c^4 - 4a^6b^2c^4 + 6a^4b^4c^4 - 4a^2b^6c^4 + 3b^8c^4 - 2a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 2b^6c^6 + 3a^4c^8 + 7a^2b^2c^8 + 3b^4c^8 - 3a^2c^10 - 3b^2c^10 + c^12)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 - a^6b^4c^2 - a^4b^6c^2 + b^10c^2 - 4a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - a^4b^2c^6 - a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 - 4b^4c^8 + a^2c^10 + b^2*c^10)
2971	(a^10 - 3a^8b^2 + 2a^6b^4 + 2a^4b^6 - 3a^2b^8 + b^10 - 3a^8c^2 + 9a^6b^2c^2 - 8a^4b^4c^2 + 9a^2b^6c^2 - 3b^8c^2 + 2a^6c^4 - 8a^4b^2c^4 - 8a^2b^4c^4 + 2b^6c^4 + 2a^4c^6 + 9a^2b^2c^6 + 2b^4c^6 - 3a^2c^8 - 3b^2c^8 + c^10)/(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 6a^6b^2c^2 + 6a^4b^4c^2 - 6a^2b^6c^2 + b^8c^2 - a^6c^4 + 6a^4b^2c^4 + 6a^2b^4c^4 - b^6c^4 - a^4c^6 - 6a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8)
2972	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 4a^8b^2c^2 - 5a^6b^4c^2 - 5a^4b^6c^2 + 4a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 5a^6b^2c^4 + 18a^4b^4c^4 - 5a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 5a^4b^2c^6 - 5a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 4a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10)
2973	(a^10 - a^9b - 2a^8b^2 + 2a^7b^3 + a^6b^4 - 2a^5b^5 + a^4b^6 + 2a^3b^7 - 2a^2b^8 - ab^9 + b^10 - a^9c + a^8bc + 2a^7b^2c - 2a^6b^3c - 2a^3b^6c + 2a^2b^7c + ab^8c - b^9c - 2a^8c^2 + 2a^7bc^2 + 2a^6b^2c^2 - 2a^5b^3c^2 - 2a^3b^5c^2 + 2a^2b^6c^2 + 2ab^7c^2 - 2b^8c^2 + 2a^7c^3 - 2a^6bc^3 - 2a^5b^2c^3 + 2a^4b^3c^3 + 2a^3b^4c^3 - 2a^2b^5c^3 - 2ab^6c^3 + 2b^7c^3 + a^6c^4 + 2a^3b^3c^4 + b^6c^4 - 2a^5c^5 - 2a^3b^2c^5 - 2a^2b^3c^5 - 2b^5c^5 + a^4c^6 - 2a^3bc^6 + 2a^2b^2c^6 - 2ab^3c^6 + b^4c^6 + 2a^3c^7 + 2a^2bc^7 + 2ab^2c^7 + 2b^3c^7 - 2a^2c^8 + abc^8 - 2b^2c^8 - ac^9 - bc^9 + c^10)/(a^8b^2 - 2a^7b^3 - a^6b^4 + 4a^5b^5 - a^4b^6 - 2a^3b^7 + a^2b^8 + a^8c^2 - 2a^4b^4c^2 + b^8c^2 - 2a^7c^3 + 2a^4b^3c^3 + 2a^3b^4c^3 - 2b^7c^3 - a^6c^4 - 2a^4b^2c^4 + 2a^3b^3c^4 - 2a^2b^4c^4 - b^6c^4 + 4a^5c^5 + 4b^5c^5 - a^4c^6 - b^4c^6 - 2a^3c^7 - 2b^3c^7 + a^2c^8 + b^2c^8)
2974	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 6a^6b^2c^2 + 6a^4b^4c^2 - 6a^2b^6c^2 + b^8c^2 - a^6c^4 + 6a^4b^2c^4 + 6a^2b^4c^4 - b^6c^4 - a^4c^6 - 6a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8)
2975, 11491, 38555, 38556, 38557, 38558, 38559, 38560, 38561, 38562, 38563, 38564, 38565, 38566, 38567, 38568, 38569, 38570, 38571	(-a^3 + a^2b + ab^2 - b^3 + a^2c - 3abc + b^2c + ac^2 + bc^2 - c^3)/(a^3 - a^2b - ab^2 + b^3 - a^2c + abc - b^2c - ac^2 - b*c^2 + c^3)
3160	(a^7 - a^6b - 3a^5b^2 + 3a^4b^3 + 3a^3b^4 - 3a^2b^5 - ab^6 + b^7 - a^6c + 7a^5bc - 3a^4b^2c - 6a^3b^3c - 3a^2b^4c + 7ab^5c - b^6c - 3a^5c^2 - 3a^4bc^2 + 6a^3b^2c^2 + 6a^2b^3c^2 - 3ab^4c^2 - 3b^5c^2 + 3a^4c^3 - 6a^3bc^3 + 6a^2b^2c^3 - 6ab^3c^3 + 3b^4c^3 + 3a^3c^4 - 3a^2bc^4 - 3ab^2c^4 + 3b^3c^4 - 3a^2c^5 + 7abc^5 - 3b^2c^5 - ac^6 - bc^6 + c^7)/(abc(5a^4 - 4a^3b - 2a^2b^2 - 4ab^3 + 5b^4 - 4a^3c + 4a^2bc + 4ab^2c - 4b^3c - 2a^2c^2 + 4abc^2 - 2b^2c^2 - 4ac^3 - 4bc^3 + 5c^4))
3172	(4(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10))/(3a^10 - a^8b^2 - 2a^6b^4 - 2a^4b^6 - a^2b^8 + 3b^10 - a^8c^2 + 2a^4b^4c^2 - b^8c^2 - 2a^6c^4 + 2a^4b^2c^4 + 2a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 2b^4c^6 - a^2c^8 - b^2c^8 + 3*c^10)
3207	(2(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(3a^4 - 2a^3b - 2a^2b^2 - 2ab^3 + 3b^4 - 2a^3c + 2a^2bc + 2ab^2c - 2b^3c - 2a^2c^2 + 2abc^2 - 2b^2c^2 - 2ac^3 - 2bc^3 + 3*c^4)
3445	(2(a^3 - 2a^2b - 2ab^2 + b^3 - 2a^2c + 9abc - 2b^2c - 2ac^2 - 2bc^2 + c^3))/(a^3 - 3a^2b - 3ab^2 + b^3 - 3a^2c + 16abc - 3b^2c - 3ac^2 - 3b*c^2 + c^3)
3470	(3(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2)/(a^12 - 9a^8b^4 + 16a^6b^6 - 9a^4b^8 + b^12 + 12a^8b^2c^2 - 12a^6b^4c^2 - 12a^4b^6c^2 + 12a^2b^8c^2 - 9a^8c^4 - 12a^6b^2c^4 + 39a^4b^4c^4 - 12a^2b^6c^4 - 9b^8c^4 + 16a^6c^6 - 12a^4b^2c^6 - 12a^2b^4c^6 + 16b^6c^6 - 9a^4c^8 + 12a^2b^2c^8 - 9b^4c^8 + c^12)
3511	(2a^2b^2c^2(a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8b^4 - 2a^6b^6 + a^4b^8 + a^8b^2c^2 - a^6b^4c^2 - a^4b^6c^2 + a^2b^8c^2 + a^8c^4 - a^6b^2c^4 + 3a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + a^2b^2c^8 + b^4*c^8)
3730	(-a^4 + a^3b + ab^3 - b^4 + a^3c - a^2bc - ab^2c + b^3c - abc^2 + ac^3 + bc^3 - c^4)/(a^3b - 2a^2b^2 + ab^3 + a^3c - a^2bc - ab^2c + b^3c - 2a^2c^2 - abc^2 - 2b^2c^2 + ac^3 + bc^3)
4996	-((abc)/(a^3 - a^2b - ab^2 + b^3 - a^2c + abc - b^2c - ac^2 - bc^2 + c^3))
5152	(a^2b^2 + a^2c^2 + b^2c^2)/(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)
5191	((a^2 + b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(2a^8 - 3a^6b^2 + 2a^4b^4 - 3a^2b^6 + 2b^8 - 3a^6c^2 + 2a^4b^2c^2 + 2a^2b^4c^2 - 3b^6c^2 + 2a^4c^4 + 2a^2b^2c^4 + 2b^4c^4 - 3a^2c^6 - 3b^2c^6 + 2c^8)
5303	(-a^3 + a^2b + ab^2 - b^3 + a^2c - 3abc + b^2c + ac^2 + bc^2 - c^3)/(3a^3 - 3a^2b - 3ab^2 + 3b^3 - 3a^2c + 5abc - 3b^2c - 3ac^2 - 3bc^2 + 3*c^3)
5609, 30524, 30525	3/2
5649	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)(a^8 - a^6b^2 - a^2b^6 + b^8 - a^6c^2 + a^4b^2c^2 + a^2b^4c^2 - b^6c^2 + a^2b^2c^4 - a^2c^6 - b^2c^6 + c^8))/(a^18 - 3a^16b^2 + 6a^14b^4 - 10a^12b^6 + 6a^10b^8 + 6a^8b^10 - 10a^6b^12 + 6a^4b^14 - 3a^2b^16 + b^18 - 3a^16c^2 + 3a^14b^2c^2 + 3a^2b^14c^2 - 3b^16c^2 + 6a^14c^4 + 3a^10b^4c^4 - 9a^8b^6c^4 - 9a^6b^8c^4 + 3a^4b^10c^4 + 6b^14c^4 - 10a^12c^6 - 9a^8b^4c^6 + 39a^6b^6c^6 - 9a^4b^8c^6 - 10b^12c^6 + 6a^10c^8 - 9a^6b^4c^8 - 9a^4b^6c^8 + 6b^10c^8 + 6a^8c^10 + 3a^4b^4c^10 + 6b^8c^10 - 10a^6c^12 - 10b^6c^12 + 6a^4c^14 + 3a^2b^2c^14 + 6b^4c^14 - 3a^2c^16 - 3b^2*c^16 + c^18)
5657, 5731	(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)/(3abc)
5687	(2(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^3 - a^2b - ab^2 + b^3 - a^2c + 4abc - b^2c - ac^2 - b*c^2 + c^3)
5690, 34773	(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)/(2abc)
5744	((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(5a^3 - 5a^2b - 5ab^2 + 5b^3 - 5a^2c + 6abc - 5b^2c - 5ac^2 - 5bc^2 + 5c^3))
5767	((a + b)(a + c)(b + c)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc*(a^3 + b^3 + c^3))
5768	-(((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 6abc - b^2c - ac^2 - b*c^2 + c^3)))
5769	-(((a + b)(a + c)(b + c)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - b*c^2 + c^3)))
5770	((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(3ab(a - b - c)(a + b - c)c*(a - b + c))
5771	((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(4abc(a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - b*c^2 + c^3))
5773	-(((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^4b - a^3b^2 - a^2b^3 + ab^4 + a^4c - 2a^2b^2c + b^4c - a^3c^2 - 2a^2bc^2 - 2ab^2c^2 - b^3c^2 - a^2c^3 - b^2c^3 + ac^4 + bc^4))/(abc(2a^5 - 3a^4b + a^3b^2 + a^2b^3 - 3ab^4 + 2b^5 - 3a^4c + 4a^3bc - 2a^2b^2c + 4ab^3c - 3b^4c + a^3c^2 - 2a^2bc^2 - 2ab^2c^2 + b^3c^2 + a^2c^3 + 4abc^3 + b^2c^3 - 3ac^4 - 3bc^4 + 2*c^5)))
5774	(-2(a^2b + ab^2 + a^2c + abc + b^2c + ac^2 + bc^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(a^3 - 3a^2b - 3ab^2 + b^3 - 3a^2c - 3b^2c - 3ac^2 - 3bc^2 + c^3))
5775	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(3a^3 - 3a^2b - 3ab^2 + 3b^3 - 3a^2c - 2abc - 3b^2c - 3ac^2 - 3bc^2 + 3c^3))/(abc(7a^3 - 7a^2b - 7ab^2 + 7b^3 - 7a^2c + 6abc - 7b^2c - 7ac^2 - 7bc^2 + 7*c^3))
5876, 13491	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2a^2b^2c^2)
5939	(-a^4 + 4a^2b^2 - b^4 + 4a^2c^2 + 4b^2c^2 - c^4)/(2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))
5944	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))
5968	(2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 4a^6b^2c^2 + 4a^4b^4c^2 - 4a^2b^6c^2 + b^8c^2 - a^6c^4 + 4a^4b^2c^4 + 4a^2b^4c^4 - b^6c^4 - a^4c^6 - 4a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2*c^8))
5976, 38641, 38642, 38643, 38644, 38645, 38646, 38647, 38648, 38649, 38650, 38651, 38652	(a^4 + b^4 + c^4)/(2(a^2b^2 + a^2c^2 + b^2c^2))
5989, 38653, 38654, 38655, 38656, 38657, 38658, 38659, 38660, 38661, 38662, 38663	(2(a^2b^2 + a^2c^2 + b^2c^2))/(a^4 + b^4 + c^4)
6090	(4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 6a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))
6184	((a^2 + b^2 + c^2)(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(2(a^4b^2 - 2a^3b^3 + a^2b^4 + a^4bc - a^3b^2c - a^2b^3c + ab^4c + a^4c^2 - a^3bc^2 + 3a^2b^2c^2 - ab^3c^2 + b^4c^2 - 2a^3c^3 - a^2bc^3 - ab^2c^3 - 2b^3c^3 + a^2c^4 + abc^4 + b^2*c^4))
6224, 12247	(-a^3 + a^2b + ab^2 - b^3 + a^2c - abc + b^2c + ac^2 + bc^2 - c^3)/(abc)
6241, 12111	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(a^2b^2*c^2)
6350	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(3a^6 - 4a^5b - 3a^4b^2 + 8a^3b^3 - 3a^2b^4 - 4ab^5 + 3b^6 - 4a^5c + 4a^4bc + 4ab^4c - 4b^5c - 3a^4c^2 + 6a^2b^2c^2 - 3b^4c^2 + 8a^3c^3 + 8b^3c^3 - 3a^2c^4 + 4abc^4 - 3b^2c^4 - 4ac^5 - 4bc^5 + 3c^6))
6394	-(((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^12 - 5a^10b^2 + 7a^8b^4 - 6a^6b^6 + 7a^4b^8 - 5a^2b^10 + b^12 - 5a^10c^2 + 7a^8b^2c^2 - 2a^6b^4c^2 - 2a^4b^6c^2 + 7a^2b^8c^2 - 5b^10c^2 + 7a^8c^4 - 2a^6b^2c^4 - 6a^4b^4c^4 - 2a^2b^6c^4 + 7b^8c^4 - 6a^6c^6 - 2a^4b^2c^6 - 2a^2b^4c^6 - 6b^6c^6 + 7a^4c^8 + 7a^2b^2c^8 + 7b^4c^8 - 5a^2c^10 - 5b^2*c^10 + c^12))
6800	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6))
7723, 12091	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))/(2a^2b^2*c^2)
7771	(-a^4 + a^2b^2 - b^4 + a^2c^2 + b^2c^2 - c^4)/(2a^4 - 5a^2b^2 + 2b^4 - 5a^2c^2 - 5b^2c^2 + 2c^4)
7782	(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)/(2a^4 - 3a^2b^2 + 2b^4 - 3a^2c^2 - 3b^2c^2 + 2c^4)
7952	(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + 5a^7bc - 2a^6b^2c - 5a^5b^3c + 6a^4b^4c - 5a^3b^5c - 2a^2b^6c + 5ab^7c - b^8c - 2a^7c^2 - 2a^6bc^2 + 10a^5b^2c^2 - 6a^4b^3c^2 - 6a^3b^4c^2 + 10a^2b^5c^2 - 2ab^6c^2 - 2b^7c^2 + 2a^6c^3 - 5a^5bc^3 - 6a^4b^2c^3 + 18a^3b^3c^3 - 6a^2b^4c^3 - 5ab^5c^3 + 2b^6c^3 + 6a^4bc^4 - 6a^3b^2c^4 - 6a^2b^3c^4 + 6ab^4c^4 - 5a^3bc^5 + 10a^2b^2c^5 - 5ab^3c^5 + 2a^3c^6 - 2a^2bc^6 - 2ab^2c^6 + 2b^3c^6 - 2a^2c^7 + 5abc^7 - 2b^2c^7 - ac^8 - bc^8 + c^9)/(abc(3a^6 - 2a^5b - 3a^4b^2 + 4a^3b^3 - 3a^2b^4 - 2ab^5 + 3b^6 - 2a^5c + 6a^4bc - 4a^3b^2c - 4a^2b^3c + 6ab^4c - 2b^5c - 3a^4c^2 - 4a^3bc^2 + 14a^2b^2c^2 - 4ab^3c^2 - 3b^4c^2 + 4a^3c^3 - 4a^2bc^3 - 4ab^2c^3 + 4b^3c^3 - 3a^2c^4 + 6abc^4 - 3b^2c^4 - 2ac^5 - 2bc^5 + 3c^6))
7998, 9159	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(9a^2b^2c^2)
7999	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(7a^2b^2c^2)
8192	(-4abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - 2a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)
8743	(2(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10))/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 2a^6b^2c^2 + 2a^4b^4c^2 - 2a^2b^6c^2 + b^8c^2 - 2a^6c^4 + 2a^4b^2c^4 + 2a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 2a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2*c^8 + c^10)
8778	(4(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10))/(5a^10 - 7a^8b^2 + 2a^6b^4 + 2a^4b^6 - 7a^2b^8 + 5b^10 - 7a^8c^2 + 8a^6b^2c^2 - 2a^4b^4c^2 + 8a^2b^6c^2 - 7b^8c^2 + 2a^6c^4 - 2a^4b^2c^4 - 2a^2b^4c^4 + 2b^6c^4 + 2a^4c^6 + 8a^2b^2c^6 + 2b^4c^6 - 7a^2c^8 - 7b^2c^8 + 5c^10)
8870	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^8b^4 - 2a^6b^6 + a^4b^8 + 3a^8b^2c^2 - a^6b^4c^2 - a^4b^6c^2 + 3a^2b^8c^2 + a^8c^4 - a^6b^2c^4 - 3a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + 3a^2b^2c^8 + b^4c^8))/(a^12b^4 - a^10b^6 - a^6b^10 + a^4b^12 + a^12b^2c^2 - a^10b^4c^2 - 2a^8b^6c^2 - 2a^6b^8c^2 - a^4b^10c^2 + a^2b^12c^2 + a^12c^4 - a^10b^2c^4 + 2a^8b^4c^4 + 3a^6b^6c^4 + 2a^4b^8c^4 - a^2b^10c^4 + b^12c^4 - a^10c^6 - 2a^8b^2c^6 + 3a^6b^4c^6 + 3a^4b^6c^6 - 2a^2b^8c^6 - b^10c^6 - 2a^6b^2c^8 + 2a^4b^4c^8 - 2a^2b^6c^8 - a^6c^10 - a^4b^2c^10 - a^2b^4c^10 - b^6c^10 + a^4c^12 + a^2b^2c^12 + b^4c^12)
9149	(6a^2b^2c^2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 4a^6b^2c^2 + 4a^4b^4c^2 - 4a^2b^6c^2 + b^8c^2 - a^6c^4 + 4a^4b^2c^4 + 4a^2b^4c^4 - b^6c^4 - a^4c^6 - 4a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2*c^8)
9155	((a^2 + b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3(a^6b^2 - 2a^4b^4 + a^2b^6 + a^6c^2 + b^6c^2 - 2a^4c^4 - 2b^4c^4 + a^2c^6 + b^2*c^6))
9215, 9216	-(((a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^12 - 4a^10b^2 + 17a^8b^4 - 28a^6b^6 + 17a^4b^8 - 4a^2b^10 + b^12 - 4a^10c^2 - 12a^8b^2c^2 + 14a^6b^4c^2 + 14a^4b^6c^2 - 12a^2b^8c^2 - 4b^10c^2 + 17a^8c^4 + 14a^6b^2c^4 - 45a^4b^4c^4 + 14a^2b^6c^4 + 17b^8c^4 - 28a^6c^6 + 14a^4b^2c^6 + 14a^2b^4c^6 - 28b^6c^6 + 17a^4c^8 - 12a^2b^2c^8 + 17b^4c^8 - 4a^2c^10 - 4b^2*c^10 + c^12))
9475	((a^2 + b^2 + c^2)(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10))/(3a^10b^2 - 4a^8b^4 + 2a^6b^6 - 4a^4b^8 + 3a^2b^10 + 3a^10c^2 - 4a^8b^2c^2 + a^6b^4c^2 + a^4b^6c^2 - 4a^2b^8c^2 + 3b^10c^2 - 4a^8c^4 + a^6b^2c^4 + 6a^4b^4c^4 + a^2b^6c^4 - 4b^8c^4 + 2a^6c^6 + a^4b^2c^6 + a^2b^4c^6 + 2b^6c^6 - 4a^4c^8 - 4a^2b^2c^8 - 4b^4c^8 + 3a^2c^10 + 3b^2*c^10)
9486	-(((a^2 + b^2 + c^2)(a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6))/(2a^8 - 7a^6b^2 + 18a^4b^4 - 7a^2b^6 + 2b^8 - 7a^6c^2 - 6a^4b^2c^2 - 6a^2b^4c^2 - 7b^6c^2 + 18a^4c^4 - 6a^2b^2c^4 + 18b^4c^4 - 7a^2c^6 - 7b^2c^6 + 2c^8))
9707	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3a^6 - 3a^4b^2 - 3a^2b^4 + 3b^6 - 3a^4c^2 + 4a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + 3c^6)
9717	(4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2)/(2a^12 - a^10b^2 - 14a^8b^4 + 26a^6b^6 - 14a^4b^8 - a^2b^10 + 2b^12 - a^10c^2 + 22a^8b^2c^2 - 21a^6b^4c^2 - 21a^4b^6c^2 + 22a^2b^8c^2 - b^10c^2 - 14a^8c^4 - 21a^6b^2c^4 + 66a^4b^4c^4 - 21a^2b^6c^4 - 14b^8c^4 + 26a^6c^6 - 21a^4b^2c^6 - 21a^2b^4c^6 + 26b^6c^6 - 14a^4c^8 + 22a^2b^2c^8 - 14b^4c^8 - a^2c^10 - b^2c^10 + 2*c^12)
9803	(-a^3 + a^2b + ab^2 - b^3 + a^2c + abc + b^2c + ac^2 + bc^2 - c^3)/(abc)
9828	(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 4a^6b^2c^2 + 4a^4b^4c^2 - 4a^2b^6c^2 + b^8c^2 - a^6c^4 + 4a^4b^2c^4 + 4a^2b^4c^4 - b^6c^4 - a^4c^6 - 4a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8)/(6a^2b^2c^2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2*c^2 + c^4))
9869	(2a^4b^2 + 2a^2b^4 + 2a^4c^2 - 3a^2b^2c^2 + 2b^4c^2 + 2a^2c^4 + 2b^2c^4)/(9a^2b^2c^2)
9945, 13226	(-a^3 + a^2b + ab^2 - b^3 + a^2c + 2abc + b^2c + ac^2 + bc^2 - c^3)/(4abc)
9952	(-3a^3 + 3a^2b + 3ab^2 - 3b^3 + 3a^2c - 2abc + 3b^2c + 3ac^2 + 3bc^2 - 3c^3)/(4ab*c)
10016	(2abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))
10104	(-a^4 + a^2b^2 - b^4 + a^2c^2 + b^2c^2 - c^4)/((a - b - c)(a + b - c)(a - b + c)(a + b + c))
10354	(7a^6 - 15a^4b^2 - 15a^2b^4 + 7b^6 - 15a^4c^2 + 42a^2b^2c^2 - 15b^4c^2 - 15a^2c^4 - 15b^2c^4 + 7c^6)/(2(a^6 + 3a^4b^2 + 3a^2b^4 + b^6 + 3a^4c^2 - 48a^2b^2c^2 + 3b^4c^2 + 3a^2c^4 + 3b^2c^4 + c^6))
10355	(2(a^6 + 3a^4b^2 + 3a^2b^4 + b^6 + 3a^4c^2 - 48a^2b^2c^2 + 3b^4c^2 + 3a^2c^4 + 3b^2c^4 + c^6))/(7a^6 - 15a^4b^2 - 15a^2b^4 + 7b^6 - 15a^4c^2 + 42a^2b^2c^2 - 15b^4c^2 - 15a^2c^4 - 15b^2c^4 + 7c^6)
10571	(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6)/(a^5b - 2a^3b^3 + ab^5 + a^5c - 3a^4bc + 2a^3b^2c + 2a^2b^3c - 3ab^4c + b^5c + 2a^3bc^2 - 4a^2b^2c^2 + 2ab^3c^2 - 2a^3c^3 + 2a^2bc^3 + 2ab^2c^3 - 2b^3c^3 - 3abc^4 + ac^5 + bc^5)
10609, 15725	(-a^3 + a^2b + ab^2 - b^3 + a^2c + b^2c + ac^2 + bc^2 - c^3)/(2ab*c)
11441	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 4a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
11444	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(5a^2b^2c^2)
11449, 11468	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2a^6 - 2a^4b^2 - 2a^2b^4 + 2b^6 - 2a^4c^2 + 5a^2b^2c^2 - 2b^4c^2 - 2a^2c^4 - 2b^2c^4 + 2*c^6)
11454, 11464	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2a^6 - 2a^4b^2 - 2a^2b^4 + 2b^6 - 2a^4c^2 + 3a^2b^2c^2 - 2b^4c^2 - 2a^2c^4 - 2b^2c^4 + 2*c^6)
11456	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)
11459, 15072	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(3a^2b^2c^2)
11590	((a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - bc^2 + c^3)^2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(4a^2b^2c^2(a^3 - a^2b - ab^2 + b^3 - a^2c - abc - b^2c - ac^2 - bc^2 + c^3)^2)
11591	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(4a^2b^2c^2)
11592	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(16a^2b^2c^2)
12168, 13171	(-4a^2b^2c^2)/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - 2a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)
12174	(-4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - 2a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
12203	(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)/(a^4 + a^2b^2 + b^4 + a^2c^2 + b^2c^2 + c^4)
12270, 12281	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(a^2b^2c^2)
12308	4
12358	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))/(4a^2b^2*c^2)
12412	(4a^2b^2c^2)/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2))
12531	(2a^3 - 2a^2b - 2ab^2 + 2b^3 - 2a^2c + 5abc - 2b^2c - 2ac^2 - 2bc^2 + 2c^3)/(abc)
12645, 18526	(2(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc)
12825, 17854	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 4a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2a^2b^2c^2)
13108	(2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^2b^2 + a^2c^2 + b^2*c^2)
13416	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))/(8a^2b^2*c^2)
14026	(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)^2/(ab(a + b - 2c)(2a - b - c)c(a - 2*b + c))
14094, 15054, 15156, 15157, 23235, 38664, 38665, 38666, 38667, 38668, 38669, 38670, 38671, 38672, 38673, 38674, 38675, 38676, 38677, 38678, 38679, 38680, 38681, 38682, 38683, 38684, 38685, 38686, 38687, 38688, 38689	3
14246	(3(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 8a^6b^2c^2 + 9a^4b^4c^2 - 8a^2b^6c^2 + b^8c^2 - 2a^6c^4 + 9a^4b^2c^4 + 9a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 8a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2c^8 + c^10)
14247	(a^10 - a^6b^4 - a^4b^6 + b^10 + a^4b^4c^2 - a^6c^4 + a^4b^2c^4 + a^2b^4c^4 - b^6c^4 - a^4c^6 - b^4c^6 + c^10)/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 2a^6b^2c^2 - 5a^4b^4c^2 - 2a^2b^6c^2 + b^8c^2 - 2a^6c^4 - 5a^4b^2c^4 - 5a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 2a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2c^8 + c^10)
14248	(4(a^10 - 3a^8b^2 + 2a^6b^4 + 2a^4b^6 - 3a^2b^8 + b^10 - 3a^8c^2 + 9a^6b^2c^2 - 8a^4b^4c^2 + 9a^2b^6c^2 - 3b^8c^2 + 2a^6c^4 - 8a^4b^2c^4 - 8a^2b^4c^4 + 2b^6c^4 + 2a^4c^6 + 9a^2b^2c^6 + 2b^4c^6 - 3a^2c^8 - 3b^2c^8 + c^10))/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 20a^6b^2c^2 + 22a^4b^4c^2 - 20a^2b^6c^2 + b^8c^2 - 2a^6c^4 + 22a^4b^2c^4 + 22a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 20a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2*c^8 + c^10)
14249	(a^12 - a^10b^2 - 5a^8b^4 + 10a^6b^6 - 5a^4b^8 - a^2b^10 + b^12 - a^10c^2 + 11a^8b^2c^2 - 10a^6b^4c^2 - 10a^4b^6c^2 + 11a^2b^8c^2 - b^10c^2 - 5a^8c^4 - 10a^6b^2c^4 + 30a^4b^4c^4 - 10a^2b^6c^4 - 5b^8c^4 + 10a^6c^6 - 10a^4b^2c^6 - 10a^2b^4c^6 + 10b^6c^6 - 5a^4c^8 + 11a^2b^2c^8 - 5b^4c^8 - a^2c^10 - b^2c^10 + c^12)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 5a^8b^2c^2 - 6a^6b^4c^2 - 6a^4b^6c^2 + 5a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 6a^6b^2c^4 + 20a^4b^4c^4 - 6a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 6a^4b^2c^6 - 6a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 5a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10)
14250	(-a^10 - 2a^8b^2 + 3a^6b^4 + 3a^4b^6 - 2a^2b^8 - b^10 - 2a^8c^2 - 4a^6b^2c^2 + 3a^4b^4c^2 - 4a^2b^6c^2 - 2b^8c^2 + 3a^6c^4 + 3a^4b^2c^4 + 3a^2b^4c^4 + 3b^6c^4 + 3a^4c^6 - 4a^2b^2c^6 + 3b^4c^6 - 2a^2c^8 - 2b^2c^8 - c^10)/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 20a^6b^2c^2 - 43a^4b^4c^2 - 20a^2b^6c^2 + b^8c^2 - 2a^6c^4 - 43a^4b^2c^4 - 43a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 20a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2c^8 + c^10)
14251	(a^2b^2c^2(a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)^2)/((a^2b^2 + a^2c^2 + b^2c^2)(a^8b^4 - 2a^6b^6 + a^4b^8 - a^6b^4c^2 - a^4b^6c^2 + a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + b^4c^8))
14252	((a^2 + b^2 + c^2)(2a^10b^4 - 2a^8b^6 - 2a^6b^8 + 2a^4b^10 + 5a^10b^2c^2 - 7a^8b^4c^2 + 4a^6b^6c^2 - 7a^4b^8c^2 + 5a^2b^10c^2 + 2a^10c^4 - 7a^8b^2c^4 + 5a^6b^4c^4 + 5a^4b^6c^4 - 7a^2b^8c^4 + 2b^10c^4 - 2a^8c^6 + 4a^6b^2c^6 + 5a^4b^4c^6 + 4a^2b^6c^6 - 2b^8c^6 - 2a^6c^8 - 7a^4b^2c^8 - 7a^2b^4c^8 - 2b^6c^8 + 2a^4c^10 + 5a^2b^2c^10 + 2b^4c^10))/((a^2b^2 + a^2c^2 + b^2c^2)(8a^8b^4 - 16a^6b^6 + 8a^4b^8 + 11a^8b^2c^2 - 11a^6b^4c^2 - 11a^4b^6c^2 + 11a^2b^8c^2 + 8a^8c^4 - 11a^6b^2c^4 + 6a^4b^4c^4 - 11a^2b^6c^4 + 8b^8c^4 - 16a^6c^6 - 11a^4b^2c^6 - 11a^2b^4c^6 - 16b^6c^6 + 8a^4c^8 + 11a^2b^2c^8 + 8b^4c^8))
14253	-(((a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^10 - 3a^8b^2 + 2a^6b^4 + 2a^4b^6 - 3a^2b^8 + b^10 - 3a^8c^2 + 9a^6b^2c^2 - 8a^4b^4c^2 + 9a^2b^6c^2 - 3b^8c^2 + 2a^6c^4 - 8a^4b^2c^4 - 8a^2b^4c^4 + 2b^6c^4 + 2a^4c^6 + 9a^2b^2c^6 + 2b^4c^6 - 3a^2c^8 - 3b^2c^8 + c^10))/(a^16 - 8a^14b^2 + 28a^12b^4 - 56a^10b^6 + 70a^8b^8 - 56a^6b^10 + 28a^4b^12 - 8a^2b^14 + b^16 - 8a^14c^2 + 28a^12b^2c^2 - 49a^10b^4c^2 + 25a^8b^6c^2 + 25a^6b^8c^2 - 49a^4b^10c^2 + 28a^2b^12c^2 - 8b^14c^2 + 28a^12c^4 - 49a^10b^2c^4 + 89a^8b^4c^4 - 68a^6b^6c^4 + 89a^4b^8c^4 - 49a^2b^10c^4 + 28b^12c^4 - 56a^10c^6 + 25a^8b^2c^6 - 68a^6b^4c^6 - 68a^4b^6c^6 + 25a^2b^8c^6 - 56b^10c^6 + 70a^8c^8 + 25a^6b^2c^8 + 89a^4b^4c^8 + 25a^2b^6c^8 + 70b^8c^8 - 56a^6c^10 - 49a^4b^2c^10 - 49a^2b^4c^10 - 56b^6c^10 + 28a^4c^12 + 28a^2b^2c^12 + 28b^4c^12 - 8a^2c^14 - 8b^2c^14 + c^16))
14254, 14670	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 2a^8b^2c^2 - 3a^6b^4c^2 - 3a^4b^6c^2 + 2a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 3a^6b^2c^4 + 12a^4b^4c^4 - 3a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 3a^4b^2c^6 - 3a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 2a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2*c^10)
14255	((a^4 - 4a^2b^2 + b^4 - 4a^2c^2 - 4b^2c^2 + c^4)(a^12 - 27a^8b^4 + 56a^6b^6 - 27a^4b^8 + b^12 + 48a^8b^2c^2 - 54a^6b^4c^2 - 54a^4b^6c^2 + 48a^2b^8c^2 - 27a^8c^4 - 54a^6b^2c^4 + 171a^4b^4c^4 - 54a^2b^6c^4 - 27b^8c^4 + 56a^6c^6 - 54a^4b^2c^6 - 54a^2b^4c^6 + 56b^6c^6 - 27a^4c^8 + 48a^2b^2c^8 - 27b^4c^8 + c^12))/(a^14b^2 - 12a^12b^4 + 51a^10b^6 - 88a^8b^8 + 51a^6b^10 - 12a^4b^12 + a^2b^14 + a^14c^2 + 4a^12b^2c^2 - 66a^10b^4c^2 + 113a^8b^6c^2 + 113a^6b^8c^2 - 66a^4b^10c^2 + 4a^2b^12c^2 + b^14c^2 - 12a^12c^4 - 66a^10b^2c^4 + 60a^8b^4c^4 - 150a^6b^6c^4 + 60a^4b^8c^4 - 66a^2b^10c^4 - 12b^12c^4 + 51a^10c^6 + 113a^8b^2c^6 - 150a^6b^4c^6 - 150a^4b^6c^6 + 113a^2b^8c^6 + 51b^10c^6 - 88a^8c^8 + 113a^6b^2c^8 + 60a^4b^4c^8 + 113a^2b^6c^8 - 88b^8c^8 + 51a^6c^10 - 66a^4b^2c^10 - 66a^2b^4c^10 + 51b^6c^10 - 12a^4c^12 + 4a^2b^2c^12 - 12b^4c^12 + a^2c^14 + b^2c^14)
14256	((a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^7 - a^6b - 3a^5b^2 + 3a^4b^3 + 3a^3b^4 - 3a^2b^5 - ab^6 + b^7 - a^6c + 7a^5bc - 3a^4b^2c - 6a^3b^3c - 3a^2b^4c + 7ab^5c - b^6c - 3a^5c^2 - 3a^4bc^2 + 6a^3b^2c^2 + 6a^2b^3c^2 - 3ab^4c^2 - 3b^5c^2 + 3a^4c^3 - 6a^3bc^3 + 6a^2b^2c^3 - 6ab^3c^3 + 3b^4c^3 + 3a^3c^4 - 3a^2bc^4 - 3ab^2c^4 + 3b^3c^4 - 3a^2c^5 + 7abc^5 - 3b^2c^5 - ac^6 - bc^6 + c^7))/(abc(a^7 - 5a^6b + 9a^5b^2 - 5a^4b^3 - 5a^3b^4 + 9a^2b^5 - 5ab^6 + b^7 - 5a^6c - 6a^5bc + 5a^4b^2c + 12a^3b^3c + 5a^2b^4c - 6ab^5c - 5b^6c + 9a^5c^2 + 5a^4bc^2 - 14a^3b^2c^2 - 14a^2b^3c^2 + 5ab^4c^2 + 9b^5c^2 - 5a^4c^3 + 12a^3bc^3 - 14a^2b^2c^3 + 12ab^3c^3 - 5b^4c^3 - 5a^3c^4 + 5a^2bc^4 + 5ab^2c^4 - 5b^3c^4 + 9a^2c^5 - 6abc^5 + 9b^2c^5 - 5ac^6 - 5b*c^6 + c^7))
14257	((a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - bc^2 + c^3)(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + 5a^7bc - 2a^6b^2c - 5a^5b^3c + 6a^4b^4c - 5a^3b^5c - 2a^2b^6c + 5ab^7c - b^8c - 2a^7c^2 - 2a^6bc^2 + 10a^5b^2c^2 - 6a^4b^3c^2 - 6a^3b^4c^2 + 10a^2b^5c^2 - 2ab^6c^2 - 2b^7c^2 + 2a^6c^3 - 5a^5bc^3 - 6a^4b^2c^3 + 18a^3b^3c^3 - 6a^2b^4c^3 - 5ab^5c^3 + 2b^6c^3 + 6a^4bc^4 - 6a^3b^2c^4 - 6a^2b^3c^4 + 6ab^4c^4 - 5a^3bc^5 + 10a^2b^2c^5 - 5ab^3c^5 + 2a^3c^6 - 2a^2bc^6 - 2ab^2c^6 + 2b^3c^6 - 2a^2c^7 + 5abc^7 - 2b^2c^7 - ac^8 - bc^8 + c^9))/(abc(a^9 - 3a^8b + 8a^6b^3 - 6a^5b^4 - 6a^4b^5 + 8a^3b^6 - 3ab^8 + b^9 - 3a^8c + 6a^7bc - 8a^6b^2c - 6a^5b^3c + 22a^4b^4c - 6a^3b^5c - 8a^2b^6c + 6ab^7c - 3b^8c - 8a^6bc^2 + 24a^5b^2c^2 - 16a^4b^3c^2 - 16a^3b^4c^2 + 24a^2b^5c^2 - 8ab^6c^2 + 8a^6c^3 - 6a^5bc^3 - 16a^4b^2c^3 + 28a^3b^3c^3 - 16a^2b^4c^3 - 6ab^5c^3 + 8b^6c^3 - 6a^5c^4 + 22a^4bc^4 - 16a^3b^2c^4 - 16a^2b^3c^4 + 22ab^4c^4 - 6b^5c^4 - 6a^4c^5 - 6a^3bc^5 + 24a^2b^2c^5 - 6ab^3c^5 - 6b^4c^5 + 8a^3c^6 - 8a^2bc^6 - 8ab^2c^6 + 8b^3c^6 + 6abc^7 - 3ac^8 - 3bc^8 + c^9))
14258	((a^3 + a^2b + ab^2 + b^3 + a^2c + 2abc + b^2c + ac^2 + bc^2 + c^3)(a^7 + a^6b - a^5b^2 - a^4b^3 - a^3b^4 - a^2b^5 + ab^6 + b^7 + a^6c + 3a^5bc - a^4b^2c - 2a^3b^3c - a^2b^4c + 3ab^5c + b^6c - a^5c^2 - a^4bc^2 + 2a^3b^2c^2 + 2a^2b^3c^2 - ab^4c^2 - b^5c^2 - a^4c^3 - 2a^3bc^3 + 2a^2b^2c^3 - 2ab^3c^3 - b^4c^3 - a^3c^4 - a^2bc^4 - ab^2c^4 - b^3c^4 - a^2c^5 + 3abc^5 - b^2c^5 + ac^6 + bc^6 + c^7))/(abc(a^7 + a^6b + 3a^5b^2 + 3a^4b^3 + 3a^3b^4 + 3a^2b^5 + ab^6 + b^7 + a^6c + 6a^5bc + 19a^4b^2c + 28a^3b^3c + 19a^2b^4c + 6ab^5c + b^6c + 3a^5c^2 + 19a^4bc^2 + 38a^3b^2c^2 + 38a^2b^3c^2 + 19ab^4c^2 + 3b^5c^2 + 3a^4c^3 + 28a^3bc^3 + 38a^2b^2c^3 + 28ab^3c^3 + 3b^4c^3 + 3a^3c^4 + 19a^2bc^4 + 19ab^2c^4 + 3b^3c^4 + 3a^2c^5 + 6abc^5 + 3b^2c^5 + ac^6 + b*c^6 + c^7))
14259	(-2(a^10 + 3a^8b^2 - 4a^6b^4 - 4a^4b^6 + 3a^2b^8 + b^10 + 3a^8c^2 + 9a^6b^2c^2 - 8a^4b^4c^2 + 9a^2b^6c^2 + 3b^8c^2 - 4a^6c^4 - 8a^4b^2c^4 - 8a^2b^4c^4 - 4b^6c^4 - 4a^4c^6 + 9a^2b^2c^6 - 4b^4c^6 + 3a^2c^8 + 3b^2c^8 + c^10))/(a^10 + a^8b^2 - 2a^6b^4 - 2a^4b^6 + a^2b^8 + b^10 + a^8c^2 - 38a^6b^2c^2 - 86a^4b^4c^2 - 38a^2b^6c^2 + b^8c^2 - 2a^6c^4 - 86a^4b^2c^4 - 86a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - 38a^2b^2c^6 - 2b^4c^6 + a^2c^8 + b^2*c^8 + c^10)
14260	(2(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)^2)/(a^5b - 2a^3b^3 + ab^5 + a^5c - 6a^4bc + 5a^3b^2c + 5a^2b^3c - 6ab^4c + b^5c + 5a^3bc^2 - 12a^2b^2c^2 + 5ab^3c^2 - 2a^3c^3 + 5a^2bc^3 + 5ab^2c^3 - 2b^3c^3 - 6abc^4 + ac^5 + bc^5)
14261	(3(a^3 - 2a^2b - 2ab^2 + b^3 - 2a^2c + 9abc - 2b^2c - 2ac^2 - 2bc^2 + c^3))/(a^2b + ab^2 + a^2c - 7abc + b^2c + ac^2 + b*c^2)
14262	(6(a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6))/(a^6 + 3a^4b^2 + 3a^2b^4 + b^6 + 3a^4c^2 - 48a^2b^2c^2 + 3b^4c^2 + 3a^2c^4 + 3b^2*c^4 + c^6)
14263	(-2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6))/(a^8b^2 + 3a^6b^4 + 3a^4b^6 + a^2b^8 + a^8c^2 - 20a^6b^2c^2 + 12a^4b^4c^2 - 20a^2b^6c^2 + b^8c^2 + 3a^6c^4 + 12a^4b^2c^4 + 12a^2b^4c^4 + 3b^6c^4 + 3a^4c^6 - 20a^2b^2c^6 + 3b^4c^6 + a^2c^8 + b^2c^8)
14264	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 2a^8b^2c^2 - 3a^6b^4c^2 - 3a^4b^6c^2 + 2a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 3a^6b^2c^4 + 12a^4b^4c^4 - 3a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 3a^4b^2c^6 - 3a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 2a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10)
14265	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6b^2 - 2a^4b^4 + a^2b^6 + a^6c^2 + b^6c^2 - 2a^4c^4 - 2b^4c^4 + a^2c^6 + b^2c^6))/(a^8b^4 - 2a^6b^6 + a^4b^8 - a^6b^4c^2 - a^4b^6c^2 + a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + b^4*c^8)
14266	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^5b - 2a^3b^3 + ab^5 + a^5c - 2a^4bc + a^3b^2c + a^2b^3c - 2ab^4c + b^5c + a^3bc^2 + ab^3c^2 - 2a^3c^3 + a^2bc^3 + ab^2c^3 - 2b^3c^3 - 2abc^4 + ac^5 + bc^5))/(abc(a^5b - 2a^3b^3 + ab^5 + a^5c - 6a^4bc + 5a^3b^2c + 5a^2b^3c - 6ab^4c + b^5c + 5a^3bc^2 - 12a^2b^2c^2 + 5ab^3c^2 - 2a^3c^3 + 5a^2bc^3 + 5ab^2c^3 - 2b^3c^3 - 6abc^4 + ac^5 + bc^5))
14267	-(((a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + a^2bc + ab^2c - 2b^3c + 2a^2c^2 + abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4)(a^4b - a^3b^2 - a^2b^3 + ab^4 + a^4c + b^4c - a^3c^2 - b^3c^2 - a^2c^3 - b^2c^3 + ac^4 + bc^4))/(abc(a^5b - 4a^4b^2 + 6a^3b^3 - 4a^2b^4 + ab^5 + a^5c - 2a^4bc + 3a^3b^2c + 3a^2b^3c - 2ab^4c + b^5c - 4a^4c^2 + 3a^3bc^2 - 12a^2b^2c^2 + 3ab^3c^2 - 4b^4c^2 + 6a^3c^3 + 3a^2bc^3 + 3ab^2c^3 + 6b^3c^3 - 4a^2c^4 - 2abc^4 - 4b^2c^4 + ac^5 + bc^5)))
14268	((a^3 - a^2b - ab^2 + b^3 - a^2c - 4abc - b^2c - ac^2 - bc^2 + c^3)(a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + a^2bc + ab^2c - 2b^3c + 2a^2c^2 + abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4))/(abc(a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4 - 4a^3c + 2a^2bc + 2ab^2c - 4b^3c + 6a^2c^2 + 2abc^2 + 6b^2c^2 - 4ac^3 - 4bc^3 + c^4))
14382	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^8b^4 - 2a^6b^6 + a^4b^8 + a^8b^2c^2 - a^6b^4c^2 - a^4b^6c^2 + a^2b^8c^2 + a^8c^4 - a^6b^2c^4 + 3a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + a^2b^2c^8 + b^4c^8))/(a^10b^6 - 2a^8b^8 + a^6b^10 + a^12b^2c^2 - a^8b^6c^2 - a^6b^8c^2 + a^2b^12c^2 - 6a^8b^4c^4 + 7a^6b^6c^4 - 6a^4b^8c^4 + a^10c^6 - a^8b^2c^6 + 7a^6b^4c^6 + 7a^4b^6c^6 - a^2b^8c^6 + b^10c^6 - 2a^8c^8 - a^6b^2c^8 - 6a^4b^4c^8 - a^2b^6c^8 - 2b^8c^8 + a^6c^10 + b^6c^10 + a^2b^2*c^12)
14385	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2/(a^12 - a^10b^2 - 5a^8b^4 + 10a^6b^6 - 5a^4b^8 - a^2b^10 + b^12 - a^10c^2 + 10a^8b^2c^2 - 9a^6b^4c^2 - 9a^4b^6c^2 + 10a^2b^8c^2 - b^10c^2 - 5a^8c^4 - 9a^6b^2c^4 + 27a^4b^4c^4 - 9a^2b^6c^4 - 5b^8c^4 + 10a^6c^6 - 9a^4b^2c^6 - 9a^2b^4c^6 + 10b^6c^6 - 5a^4c^8 + 10a^2b^2c^8 - 5b^4c^8 - a^2c^10 - b^2*c^10 + c^12)
14640	(a^12 - a^10b^2 - 5a^8b^4 + 10a^6b^6 - 5a^4b^8 - a^2b^10 + b^12 - a^10c^2 + 11a^8b^2c^2 - 10a^6b^4c^2 - 10a^4b^6c^2 + 11a^2b^8c^2 - b^10c^2 - 5a^8c^4 - 10a^6b^2c^4 + 30a^4b^4c^4 - 10a^2b^6c^4 - 5b^8c^4 + 10a^6c^6 - 10a^4b^2c^6 - 10a^2b^4c^6 + 10b^6c^6 - 5a^4c^8 + 11a^2b^2c^8 - 5b^4c^8 - a^2c^10 - b^2c^10 + c^12)/(12a^2b^2c^2(a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))
14880	(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2*c^2 + c^4)/(a^4 + b^4 + c^4)
14919	(3(a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^12 - 9a^8b^4 + 16a^6b^6 - 9a^4b^8 + b^12 + 15a^8b^2c^2 - 15a^6b^4c^2 - 15a^4b^6c^2 + 15a^2b^8c^2 - 9a^8c^4 - 15a^6b^2c^4 + 48a^4b^4c^4 - 15a^2b^6c^4 - 9b^8c^4 + 16a^6c^6 - 15a^4b^2c^6 - 15a^2b^4c^6 + 16b^6c^6 - 9a^4c^8 + 15a^2b^2c^8 - 9b^4*c^8 + c^12)
15020	3/7
15021, 15034	3/5
15023	3/19
15035, 15055, 21166, 23239, 34473, 34474, 38690, 38691, 38692, 38693, 38694, 38695, 38696, 38697, 38698, 38699, 38700, 38701, 38702, 38703, 38704, 38705, 38706, 38707, 38708, 38709, 38710, 38711, 38712, 38713, 38714, 38715, 38716, 38717, 38718, 38719	1/3
15036	1/7
15039	6/7
15040	2/5
15041, 28447, 28448, 32609	2/3
15042	2/13
15051	1/5
15066	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 12a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
15067	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(6a^2b^2c^2)
15068	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 6a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
15080	(-a^6 + a^4b^2 + a^2b^4 - b^6 + a^4c^2 - 3a^2b^2c^2 + b^4c^2 + a^2c^4 + b^2c^4 - c^6)/(2a^6 - 2a^4b^2 - 2a^2b^4 + 2b^6 - 2a^4c^2 - 3a^2b^2c^2 - 2b^4c^2 - 2a^2c^4 - 2b^2c^4 + 2*c^6)
15100, 15102	(-a^6 + a^4b^2 + a^2b^4 - b^6 + a^4c^2 + a^2b^2c^2 + b^4c^2 + a^2c^4 + b^2c^4 - c^6)/(a^2b^2c^2)
15101	(-a^6 + a^4b^2 + a^2b^4 - b^6 + a^4c^2 + a^2b^2c^2 + b^4c^2 + a^2c^4 + b^2c^4 - c^6)/(2a^2b^2*c^2)
15106	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 6a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)
15132	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))
15251	-((a + b + c)(a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + a^2bc + ab^2c - 2b^3c + 2a^2c^2 + abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4))/(4abc(a^2 - ab + b^2 - ac - bc + c^2))
15252	(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + 5a^7bc - 2a^6b^2c - 5a^5b^3c + 6a^4b^4c - 5a^3b^5c - 2a^2b^6c + 5ab^7c - b^8c - 2a^7c^2 - 2a^6bc^2 + 10a^5b^2c^2 - 6a^4b^3c^2 - 6a^3b^4c^2 + 10a^2b^5c^2 - 2ab^6c^2 - 2b^7c^2 + 2a^6c^3 - 5a^5bc^3 - 6a^4b^2c^3 + 18a^3b^3c^3 - 6a^2b^4c^3 - 5ab^5c^3 + 2b^6c^3 + 6a^4bc^4 - 6a^3b^2c^4 - 6a^2b^3c^4 + 6ab^4c^4 - 5a^3bc^5 + 10a^2b^2c^5 - 5ab^3c^5 + 2a^3c^6 - 2a^2bc^6 - 2ab^2c^6 + 2b^3c^6 - 2a^2c^7 + 5abc^7 - 2b^2c^7 - ac^8 - bc^8 + c^9)/(4abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))
15468	(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 2a^8b^2c^2 - 3a^6b^4c^2 - 3a^4b^6c^2 + 2a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 3a^6b^2c^4 + 12a^4b^4c^4 - 3a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 3a^4b^2c^6 - 3a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 2a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10)/(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2)
15623	(-2abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^5b - 2a^3b^3 + ab^5 + a^5c - 2a^4bc + a^3b^2c + a^2b^3c - 2ab^4c + b^5c + a^3bc^2 - 4a^2b^2c^2 + ab^3c^2 - 2a^3c^3 + a^2bc^3 + ab^2c^3 - 2b^3c^3 - 2abc^4 + ac^5 + b*c^5)
15626	(2abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^5b - 2a^3b^3 + ab^5 + a^5c - 2a^4bc + a^3b^2c + a^2b^3c - 2ab^4c + b^5c + a^3bc^2 + ab^3c^2 - 2a^3c^3 + a^2bc^3 + ab^2c^3 - 2b^3c^3 - 2abc^4 + ac^5 + bc^5)
16020	((a + b + c)(a^4 - 2a^3b + 2a^2b^2 - 2ab^3 + b^4 - 2a^3c + a^2bc + ab^2c - 2b^3c + 2a^2c^2 + abc^2 + 2b^2c^2 - 2ac^3 - 2bc^3 + c^4))/(abc(5a^2 - 6ab + 5b^2 - 6ac - 6bc + 5*c^2))
16486	(2(a^3 - 2a^2b - 2ab^2 + b^3 - 2a^2c + 9abc - 2b^2c - 2ac^2 - 2bc^2 + c^3))/(a^3 + a^2b + ab^2 + b^3 + a^2c - 12abc + b^2c + ac^2 + b*c^2 + c^3)
17100, 18861	(abc)/(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - b*c^2 + c^3)
17740	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^3 + a^2b + ab^2 + b^3 + a^2c + 2abc + b^2c + ac^2 + bc^2 + c^3))/(abc(3a^3 - a^2b - ab^2 + 3b^3 - a^2c + 6abc - b^2c - ac^2 - bc^2 + 3c^3))
18341	((a^2 - ab + b^2 - c^2)(a^2 - b^2 + bc - c^2)(a^2 - b^2 - ac + c^2))/(abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - b*c^2 + c^3))
19914	-(((a - b - c)(a + b - c)(a - b + c))/(abc))
20481	(2(a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6))/(a^6 + 3a^4b^2 + 3a^2b^4 + b^6 + 3a^4c^2 - 48a^2b^2c^2 + 3b^4c^2 + 3a^2c^4 + 3b^2*c^4 + c^6)
20672	(2(ab + ac + bc)(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(a^6 + a^5b - 3a^4b^2 + 2a^3b^3 - 3a^2b^4 + ab^5 + b^6 + a^5c - 3a^4bc + 2a^3b^2c + 2a^2b^3c - 3ab^4c + b^5c - 3a^4c^2 + 2a^3bc^2 + 2ab^3c^2 - 3b^4c^2 + 2a^3c^3 + 2a^2bc^3 + 2ab^2c^3 + 2b^3c^3 - 3a^2c^4 - 3abc^4 - 3b^2c^4 + ac^5 + bc^5 + c^6)
20999	(2abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + a^4bc + ab^4c - b^5c - a^4c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 + abc^4 - b^2c^4 - ac^5 - b*c^5 + c^6)
21444	(a^2b^2c^2(a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8b^4 - 2a^6b^6 + a^4b^8 - a^6b^4c^2 - a^4b^6c^2 + a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + b^4c^8)
21448	(4(a^6 - 3a^4b^2 - 3a^2b^4 + b^6 - 3a^4c^2 + 15a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + c^6))/(a^6 - 9a^4b^2 - 9a^2b^4 + b^6 - 9a^4c^2 + 78a^2b^2c^2 - 9b^4c^2 - 9a^2c^4 - 9b^2*c^4 + c^6)
21664	(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + 5a^7bc - 2a^6b^2c - 5a^5b^3c + 6a^4b^4c - 5a^3b^5c - 2a^2b^6c + 5ab^7c - b^8c - 2a^7c^2 - 2a^6bc^2 + 10a^5b^2c^2 - 6a^4b^3c^2 - 6a^3b^4c^2 + 10a^2b^5c^2 - 2ab^6c^2 - 2b^7c^2 + 2a^6c^3 - 5a^5bc^3 - 6a^4b^2c^3 + 18a^3b^3c^3 - 6a^2b^4c^3 - 5ab^5c^3 + 2b^6c^3 + 6a^4bc^4 - 6a^3b^2c^4 - 6a^2b^3c^4 + 6ab^4c^4 - 5a^3bc^5 + 10a^2b^2c^5 - 5ab^3c^5 + 2a^3c^6 - 2a^2bc^6 - 2ab^2c^6 + 2b^3c^6 - 2a^2c^7 + 5abc^7 - 2b^2c^7 - ac^8 - bc^8 + c^9)/(2abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))
21665	(a^10 - a^9b - 2a^7b^3 - a^6b^4 + 6a^5b^5 - a^4b^6 - 2a^3b^7 - ab^9 + b^10 - a^9c + a^8bc + 2a^7b^2c - 2a^6b^3c - 2a^3b^6c + 2a^2b^7c + ab^8c - b^9c + 2a^7bc^2 + 6a^6b^2c^2 - 6a^5b^3c^2 - 4a^4b^4c^2 - 6a^3b^5c^2 + 6a^2b^6c^2 + 2ab^7c^2 - 2a^7c^3 - 2a^6bc^3 - 6a^5b^2c^3 + 10a^4b^3c^3 + 10a^3b^4c^3 - 6a^2b^5c^3 - 2ab^6c^3 - 2b^7c^3 - a^6c^4 - 4a^4b^2c^4 + 10a^3b^3c^4 - 4a^2b^4c^4 - b^6c^4 + 6a^5c^5 - 6a^3b^2c^5 - 6a^2b^3c^5 + 6b^5c^5 - a^4c^6 - 2a^3bc^6 + 6a^2b^2c^6 - 2ab^3c^6 - b^4c^6 - 2a^3c^7 + 2a^2bc^7 + 2ab^2c^7 - 2b^3c^7 + abc^8 - ac^9 - bc^9 + c^10)/(a^8b^2 - 2a^7b^3 - a^6b^4 + 4a^5b^5 - a^4b^6 - 2a^3b^7 + a^2b^8 + a^8c^2 + 4a^6b^2c^2 - 4a^5b^3c^2 - 2a^4b^4c^2 - 4a^3b^5c^2 + 4a^2b^6c^2 + b^8c^2 - 2a^7c^3 - 4a^5b^2c^3 + 6a^4b^3c^3 + 6a^3b^4c^3 - 4a^2b^5c^3 - 2b^7c^3 - a^6c^4 - 2a^4b^2c^4 + 6a^3b^3c^4 - 2a^2b^4c^4 - b^6c^4 + 4a^5c^5 - 4a^3b^2c^5 - 4a^2b^3c^5 + 4b^5c^5 - a^4c^6 + 4a^2b^2c^6 - b^4c^6 - 2a^3c^7 - 2b^3c^7 + a^2c^8 + b^2c^8)
21666	(a^12 - a^11b - 3a^10b^2 + 3a^9b^3 + 3a^8b^4 - 2a^7b^5 - 2a^6b^6 - 2a^5b^7 + 3a^4b^8 + 3a^3b^9 - 3a^2b^10 - ab^11 + b^12 - a^11c + 3a^10bc + a^9b^2c - 7a^8b^3c + 4a^6b^5c + 4a^5b^6c - 7a^3b^8c + a^2b^9c + 3ab^10c - b^11c - 3a^10c^2 + a^9bc^2 + 8a^8b^2c^2 - 2a^7b^3c^2 - 5a^6b^4c^2 + 2a^5b^5c^2 - 5a^4b^6c^2 - 2a^3b^7c^2 + 8a^2b^8c^2 + ab^9c^2 - 3b^10c^2 + 3a^9c^3 - 7a^8bc^3 - 2a^7b^2c^3 + 10a^6b^3c^3 - 4a^5b^4c^3 - 4a^4b^5c^3 + 10a^3b^6c^3 - 2a^2b^7c^3 - 7ab^8c^3 + 3b^9c^3 + 3a^8c^4 - 5a^6b^2c^4 - 4a^5b^3c^4 + 12a^4b^4c^4 - 4a^3b^5c^4 - 5a^2b^6c^4 + 3b^8c^4 - 2a^7c^5 + 4a^6bc^5 + 2a^5b^2c^5 - 4a^4b^3c^5 - 4a^3b^4c^5 + 2a^2b^5c^5 + 4ab^6c^5 - 2b^7c^5 - 2a^6c^6 + 4a^5bc^6 - 5a^4b^2c^6 + 10a^3b^3c^6 - 5a^2b^4c^6 + 4ab^5c^6 - 2b^6c^6 - 2a^5c^7 - 2a^3b^2c^7 - 2a^2b^3c^7 - 2b^5c^7 + 3a^4c^8 - 7a^3bc^8 + 8a^2b^2c^8 - 7ab^3c^8 + 3b^4c^8 + 3a^3c^9 + a^2bc^9 + ab^2c^9 + 3b^3c^9 - 3a^2c^10 + 3abc^10 - 3b^2c^10 - ac^11 - bc^11 + c^12)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 - 2a^9b^2c + 2a^8b^3c + 6a^7b^4c - 6a^6b^5c - 6a^5b^6c + 6a^4b^7c + 2a^3b^8c - 2a^2b^9c + a^10c^2 - 2a^9bc^2 + 2a^8b^2c^2 - 2a^7b^3c^2 - 3a^6b^4c^2 + 8a^5b^5c^2 - 3a^4b^6c^2 - 2a^3b^7c^2 + 2a^2b^8c^2 - 2ab^9c^2 + b^10c^2 + 2a^8bc^3 - 2a^7b^2c^3 + 2a^6b^3c^3 - 2a^5b^4c^3 - 2a^4b^5c^3 + 2a^3b^6c^3 - 2a^2b^7c^3 + 2ab^8c^3 - 4a^8c^4 + 6a^7bc^4 - 3a^6b^2c^4 - 2a^5b^3c^4 + 6a^4b^4c^4 - 2a^3b^5c^4 - 3a^2b^6c^4 + 6ab^7c^4 - 4b^8c^4 - 6a^6bc^5 + 8a^5b^2c^5 - 2a^4b^3c^5 - 2a^3b^4c^5 + 8a^2b^5c^5 - 6ab^6c^5 + 6a^6c^6 - 6a^5bc^6 - 3a^4b^2c^6 + 2a^3b^3c^6 - 3a^2b^4c^6 - 6ab^5c^6 + 6b^6c^6 + 6a^4bc^7 - 2a^3b^2c^7 - 2a^2b^3c^7 + 6ab^4c^7 - 4a^4c^8 + 2a^3bc^8 + 2a^2b^2c^8 + 2ab^3c^8 - 4b^4c^8 - 2a^2bc^9 - 2ab^2c^9 + a^2c^10 + b^2*c^10)
21766	(-2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - 24a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)
22102	(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6)/(4abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - b*c^2 + c^3))
22240	(a^10 - a^8b^2 - a^2b^8 + b^10 - a^8c^2 + a^6b^2c^2 + a^2b^6c^2 - b^8c^2 + a^2b^2c^6 - a^2c^8 - b^2c^8 + c^10)/(2a^8b^2 - 2a^6b^4 - 2a^4b^6 + 2a^2b^8 + 2a^8c^2 - a^6b^2c^2 - 2a^4b^4c^2 - a^2b^6c^2 + 2b^8c^2 - 2a^6c^4 - 2a^4b^2c^4 - 2a^2b^4c^4 - 2b^6c^4 - 2a^4c^6 - a^2b^2c^6 - 2b^4c^6 + 2a^2c^8 + 2b^2*c^8)
22584	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))/(a^2b^2c^2)
22712	(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)/(3(a^2b^2 + a^2c^2 + b^2*c^2))
23059	((a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - bc^2 + c^3)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/((a^3 - a^2b - ab^2 + b^3 - a^2c - abc - b^2c - ac^2 - bc^2 + c^3)(a^6 - a^4b^2 - a^2b^4 + b^6 + a^4bc - a^3b^2c - a^2b^3c + ab^4c - a^4c^2 - a^3bc^2 + 2a^2b^2c^2 - ab^3c^2 - b^4c^2 - a^2bc^3 - ab^2c^3 - a^2c^4 + abc^4 - b^2c^4 + c^6))
23060	(-3(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6))
23858	(6abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 5a^4bc - 4a^3b^2c - 4a^2b^3c + 5ab^4c - b^5c - a^4c^2 - 4a^3bc^2 + 12a^2b^2c^2 - 4ab^3c^2 - b^4c^2 + 2a^3c^3 - 4a^2bc^3 - 4ab^2c^3 + 2b^3c^3 - a^2c^4 + 5abc^4 - b^2c^4 - ac^5 - b*c^5 + c^6)
24047	(-a^4 + a^3b + ab^3 - b^4 + a^3c - a^2bc - ab^2c + b^3c - abc^2 + ac^3 + bc^3 - c^4)/(a^4 + a^3b - 4a^2b^2 + ab^3 + b^4 + a^3c - a^2bc - ab^2c + b^3c - 4a^2c^2 - abc^2 - 4b^2c^2 + ac^3 + bc^3 + c^4)
24144	((a^3 - a^2b - ab^2 + b^3 + a^2c - abc + b^2c - ac^2 - bc^2 - c^3)(a^3 + a^2b - ab^2 - b^3 + a^2c + abc + b^2c - ac^2 + bc^2 - c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + abc - b^2c - ac^2 - bc^2 + c^3)(a^3 + a^2b - ab^2 - b^3 - a^2c - abc - b^2c - ac^2 + bc^2 + c^3))/(a^12 - 4a^10b^2 + 7a^8b^4 - 8a^6b^6 + 7a^4b^8 - 4a^2b^10 + b^12 - 4a^10c^2 + 8a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 8a^2b^8c^2 - 4b^10c^2 + 7a^8c^4 - 4a^6b^2c^4 + 3a^4b^4c^4 - 4a^2b^6c^4 + 7b^8c^4 - 8a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 8b^6c^6 + 7a^4c^8 + 8a^2b^2c^8 + 7b^4c^8 - 4a^2c^10 - 4b^2*c^10 + c^12)
24880	(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c - b^5c - a^4c^2 + 3a^2b^2c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 - b^2c^4 - ac^5 - bc^5 + c^6)/(abc(3a^3 - 2a^2b - 2ab^2 + 3b^3 - 2a^2c - abc - 2b^2c - 2ac^2 - 2bc^2 + 3*c^3))
24977	-(((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^12 - 4a^10b^2 + 7a^8b^4 - 8a^6b^6 + 7a^4b^8 - 4a^2b^10 + b^12 - 4a^10c^2 + 8a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 8a^2b^8c^2 - 4b^10c^2 + 7a^8c^4 - 4a^6b^2c^4 + 3a^4b^4c^4 - 4a^2b^6c^4 + 7b^8c^4 - 8a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 8b^6c^6 + 7a^4c^8 + 8a^2b^2c^8 + 7b^4c^8 - 4a^2c^10 - 4b^2c^10 + c^12))/((a^4 - 2a^2b^2 + b^4 - a^2c^2 - b^2c^2)(a^2b^2 - b^4 + a^2c^2 + 2b^2c^2 - c^4)(a^4 - a^2b^2 - 2a^2c^2 - b^2c^2 + c^4)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2*c^4 + c^6)))
25043	(-a^12 + 4a^10b^2 - 7a^8b^4 + 8a^6b^6 - 7a^4b^8 + 4a^2b^10 - b^12 + 4a^10c^2 - 8a^8b^2c^2 + 4a^6b^4c^2 + 4a^4b^6c^2 - 8a^2b^8c^2 + 4b^10c^2 - 7a^8c^4 + 4a^6b^2c^4 - 3a^4b^4c^4 + 4a^2b^6c^4 - 7b^8c^4 + 8a^6c^6 + 4a^4b^2c^6 + 4a^2b^4c^6 + 8b^6c^6 - 7a^4c^8 - 8a^2b^2c^8 - 7b^4c^8 + 4a^2c^10 + 4b^2c^10 - c^12)/((a^4 - 2a^2b^2 + b^4 - a^2c^2 - b^2c^2)(a^2b^2 - b^4 + a^2c^2 + 2b^2c^2 - c^4)(a^4 - a^2b^2 - 2a^2c^2 - b^2c^2 + c^4))
26864	(4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(5a^6 - 5a^4b^2 - 5a^2b^4 + 5b^6 - 5a^4c^2 + 6a^2b^2c^2 - 5b^4c^2 - 5a^2c^4 - 5b^2c^4 + 5c^6)
26895	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(4a^10b^2 - 16a^8b^4 + 24a^6b^6 - 16a^4b^8 + 4a^2b^10 + 4a^10c^2 - 11a^8b^2c^2 + 7a^6b^4c^2 + 7a^4b^6c^2 - 11a^2b^8c^2 + 4b^10c^2 - 16a^8c^4 + 7a^6b^2c^4 + 18a^4b^4c^4 + 7a^2b^6c^4 - 16b^8c^4 + 24a^6c^6 + 7a^4b^2c^6 + 7a^2b^4c^6 + 24b^6c^6 - 16a^4c^8 - 11a^2b^2c^8 - 16b^4c^8 + 4a^2c^10 + 4b^2c^10)
26896	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(4a^10b^2 - 16a^8b^4 + 24a^6b^6 - 16a^4b^8 + 4a^2b^10 + 4a^10c^2 - 13a^8b^2c^2 + 9a^6b^4c^2 + 9a^4b^6c^2 - 13a^2b^8c^2 + 4b^10c^2 - 16a^8c^4 + 9a^6b^2c^4 + 14a^4b^4c^4 + 9a^2b^6c^4 - 16b^8c^4 + 24a^6c^6 + 9a^4b^2c^6 + 9a^2b^4c^6 + 24b^6c^6 - 16a^4c^8 - 13a^2b^2c^8 - 16b^4c^8 + 4a^2c^10 + 4b^2c^10)
30283	(4(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^3 - a^2b - ab^2 + b^3 - a^2c + 6abc - b^2c - ac^2 - b*c^2 + c^3)
31187	(2(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c - b^5c - a^4c^2 + 3a^2b^2c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 - b^2c^4 - ac^5 - bc^5 + c^6))/(abc(7a^3 - 5a^2b - 5ab^2 + 7b^3 - 5a^2c - 5b^2c - 5ac^2 - 5bc^2 + 7c^3))
31387	(-a^9 + a^8b + 2a^7b^2 - 2a^6b^3 - 2a^3b^6 + 2a^2b^7 + ab^8 - b^9 + a^8c - a^7bc - 2a^6b^2c + a^5b^3c + 2a^4b^4c + a^3b^5c - 2a^2b^6c - ab^7c + b^8c + 2a^7c^2 - 2a^6bc^2 - 2a^5b^2c^2 + 2a^4b^3c^2 + 2a^3b^4c^2 - 2a^2b^5c^2 - 2ab^6c^2 + 2b^7c^2 - 2a^6c^3 + a^5bc^3 + 2a^4b^2c^3 - 6a^3b^3c^3 + 2a^2b^4c^3 + ab^5c^3 - 2b^6c^3 + 2a^4bc^4 + 2a^3b^2c^4 + 2a^2b^3c^4 + 2ab^4c^4 + a^3bc^5 - 2a^2b^2c^5 + ab^3c^5 - 2a^3c^6 - 2a^2bc^6 - 2ab^2c^6 - 2b^3c^6 + 2a^2c^7 - abc^7 + 2b^2c^7 + ac^8 + bc^8 - c^9)/(abc(a^6 - 2a^5b - a^4b^2 + 4a^3b^3 - a^2b^4 - 2ab^5 + b^6 - 2a^5c + 2a^4bc + 2ab^4c - 2b^5c - a^4c^2 - 2a^2b^2c^2 - b^4c^2 + 4a^3c^3 + 4b^3c^3 - a^2c^4 + 2abc^4 - b^2c^4 - 2ac^5 - 2bc^5 + c^6))
31635	-(((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^8 - 2a^6b^2 + 2a^4b^4 - 2a^2b^6 + b^8 - 2a^6c^2 + 2a^4b^2c^2 + 2a^2b^4c^2 - 2b^6c^2 + 2a^4c^4 + 2a^2b^2c^4 + 2b^4c^4 - 2a^2c^6 - 2b^2c^6 + c^8))/(a^12 - 5a^10b^2 + 9a^8b^4 - 10a^6b^6 + 9a^4b^8 - 5a^2b^10 + b^12 - 5a^10c^2 + 9a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 9a^2b^8c^2 - 5b^10c^2 + 9a^8c^4 - 4a^6b^2c^4 - 4a^2b^6c^4 + 9b^8c^4 - 10a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 10b^6c^6 + 9a^4c^8 + 9a^2b^2c^8 + 9b^4c^8 - 5a^2c^10 - 5b^2c^10 + c^12))
31841	(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6)/(2abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - b*c^2 + c^3))
32128	((a + b)(a - b - c)(a + b - c)(a + c)(a - b + c)(b + c)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(abc(a^5b - 2a^3b^3 + ab^5 + a^5c - 2a^4bc + a^3b^2c + a^2b^3c - 2ab^4c + b^5c + a^3bc^2 - 4a^2b^2c^2 + ab^3c^2 - 2a^3c^3 + a^2bc^3 + ab^2c^3 - 2b^3c^3 - 2abc^4 + ac^5 + bc^5))
32139	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))
32141, 32153	(-a^3 + a^2b + ab^2 - b^3 + a^2c - 3abc + b^2c + ac^2 + bc^2 - c^3)/((a - b - c)(a + b - c)*(a - b + c))
32142	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(8a^2b^2c^2)
32171, 32210	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(2(a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2))
32540	(2a^2b^2c^2(a^2 + b^2 + c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)^2)/((a^4 + b^4 + c^4)(a^8b^4 - 2a^6b^6 + a^4b^8 - a^6b^4c^2 - a^4b^6c^2 + a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 + b^8c^4 - 2a^6c^6 - a^4b^2c^6 - a^2b^4c^6 - 2b^6c^6 + a^4c^8 + b^4c^8))
32637	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2/(a^12 - 8a^10b^2 + 23a^8b^4 - 32a^6b^6 + 23a^4b^8 - 8a^2b^10 + b^12 - 8a^10c^2 + 24a^8b^2c^2 - 16a^6b^4c^2 - 16a^4b^6c^2 + 24a^2b^8c^2 - 8b^10c^2 + 23a^8c^4 - 16a^6b^2c^4 - 5a^4b^4c^4 - 16a^2b^6c^4 + 23b^8c^4 - 32a^6c^6 - 16a^4b^2c^6 - 16a^2b^4c^6 - 32b^6c^6 + 23a^4c^8 + 24a^2b^2c^8 + 23b^4c^8 - 8a^2c^10 - 8b^2c^10 + c^12)
33089	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^3 + a^2b + ab^2 + b^3 + a^2c + abc + b^2c + ac^2 + bc^2 + c^3))/(abc(2a^3 + 2b^3 + 3abc + 2*c^3))
33533	(-a^6 + a^4b^2 + a^2b^4 - b^6 + a^4c^2 - 3a^2b^2c^2 + b^4c^2 + a^2c^4 + b^2c^4 - c^6)/((a - b - c)(a + b - c)(a - b + c)(a + b + c)*(a^2 + b^2 + c^2))
33758	((a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^8b^4 - 2a^6b^6 + a^4b^8 + 2a^6b^4c^2 + 2a^4b^6c^2 + a^8c^4 + 2a^6b^2c^4 + 15a^4b^4c^4 + 2a^2b^6c^4 + b^8c^4 - 2a^6c^6 + 2a^4b^2c^6 + 2a^2b^4c^6 - 2b^6c^6 + a^4c^8 + b^4c^8))/(3a^10b^6 - 6a^8b^8 + 3a^6b^10 + a^12b^2c^2 + 2a^10b^4c^2 - 5a^8b^6c^2 - 5a^6b^8c^2 + 2a^4b^10c^2 + a^2b^12c^2 + 2a^10b^2c^4 - 10a^8b^4c^4 + 15a^6b^6c^4 - 10a^4b^8c^4 + 2a^2b^10c^4 + 3a^10c^6 - 5a^8b^2c^6 + 15a^6b^4c^6 + 15a^4b^6c^6 - 5a^2b^8c^6 + 3b^10c^6 - 6a^8c^8 - 5a^6b^2c^8 - 10a^4b^4c^8 - 5a^2b^6c^8 - 6b^8c^8 + 3a^6c^10 + 2a^4b^2c^10 + 2a^2b^4c^10 + 3b^6c^10 + a^2b^2*c^12)
33848	(-4abc(a^3 - a^2b - ab^2 + b^3 - a^2c - b^2c - ac^2 - bc^2 + c^3)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^8b - a^7b^2 - 3a^6b^3 + 3a^5b^4 + 3a^4b^5 - 3a^3b^6 - a^2b^7 + ab^8 + a^8c - 2a^7bc + 4a^6b^2c + 2a^5b^3c - 10a^4b^4c + 2a^3b^5c + 4a^2b^6c - 2ab^7c + b^8c - a^7c^2 + 4a^6bc^2 - 18a^5b^2c^2 + 15a^4b^3c^2 + 15a^3b^4c^2 - 18a^2b^5c^2 + 4ab^6c^2 - b^7c^2 - 3a^6c^3 + 2a^5bc^3 + 15a^4b^2c^3 - 36a^3b^3c^3 + 15a^2b^4c^3 + 2ab^5c^3 - 3b^6c^3 + 3a^5c^4 - 10a^4bc^4 + 15a^3b^2c^4 + 15a^2b^3c^4 - 10ab^4c^4 + 3b^5c^4 + 3a^4c^5 + 2a^3bc^5 - 18a^2b^2c^5 + 2ab^3c^5 + 3b^4c^5 - 3a^3c^6 + 4a^2bc^6 + 4ab^2c^6 - 3b^3c^6 - a^2c^7 - 2abc^7 - b^2c^7 + ac^8 + bc^8)
33927	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)^2)/(3(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 2a^8b^2c^2 - 3a^6b^4c^2 - 3a^4b^6c^2 + 2a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 3a^6b^2c^4 + 12a^4b^4c^4 - 3a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 3a^4b^2c^6 - 3a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 2a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2*c^10))
33983	(-2a^2b^2c^2(a^4 - 4a^2b^2 + b^4 - 4a^2c^2 - 4b^2c^2 + c^4)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^10b^4 - a^8b^6 - a^6b^8 + a^4b^10 + 3a^10b^2c^2 - 9a^8b^4c^2 + 8a^6b^6c^2 - 9a^4b^8c^2 + 3a^2b^10c^2 + a^10c^4 - 9a^8b^2c^4 + 7a^6b^4c^4 + 7a^4b^6c^4 - 9a^2b^8c^4 + b^10c^4 - a^8c^6 + 8a^6b^2c^6 + 7a^4b^4c^6 + 8a^2b^6c^6 - b^8c^6 - a^6c^8 - 9a^4b^2c^8 - 9a^2b^4c^8 - b^6c^8 + a^4c^10 + 3a^2b^2c^10 + b^4*c^10)
33997	(-6(a^2b^2 + a^2c^2 + b^2c^2))/(a^4 - 4a^2b^2 + b^4 - 4a^2c^2 - 4b^2c^2 + c^4)
34042	(2(a^3 - a^2b - ab^2 + b^3 - a^2c - 2abc - b^2c - ac^2 - bc^2 + c^3)(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))/(a^9 - a^8b - 2a^7b^2 + 2a^6b^3 + 2a^3b^6 - 2a^2b^7 - ab^8 + b^9 - a^8c + 2a^7bc - 8a^6b^2c - 2a^5b^3c + 18a^4b^4c - 2a^3b^5c - 8a^2b^6c + 2ab^7c - b^8c - 2a^7c^2 - 8a^6bc^2 + 28a^5b^2c^2 - 18a^4b^3c^2 - 18a^3b^4c^2 + 28a^2b^5c^2 - 8ab^6c^2 - 2b^7c^2 + 2a^6c^3 - 2a^5bc^3 - 18a^4b^2c^3 + 36a^3b^3c^3 - 18a^2b^4c^3 - 2ab^5c^3 + 2b^6c^3 + 18a^4bc^4 - 18a^3b^2c^4 - 18a^2b^3c^4 + 18ab^4c^4 - 2a^3bc^5 + 28a^2b^2c^5 - 2ab^3c^5 + 2a^3c^6 - 8a^2bc^6 - 8ab^2c^6 + 2b^3c^6 - 2a^2c^7 + 2abc^7 - 2b^2c^7 - ac^8 - b*c^8 + c^9)
34234	-(((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^5b - 2a^3b^3 + ab^5 + a^5c - a^4bc - ab^4c + b^5c - 2a^3c^3 - 2b^3c^3 - abc^4 + ac^5 + bc^5))/(abc(a^6 - 3a^5b - a^4b^2 + 6a^3b^3 - a^2b^4 - 3ab^5 + b^6 - 3a^5c + 11a^4bc - 8a^3b^2c - 8a^2b^3c + 11ab^4c - 3b^5c - a^4c^2 - 8a^3bc^2 + 18a^2b^2c^2 - 8ab^3c^2 - b^4c^2 + 6a^3c^3 - 8a^2bc^3 - 8ab^2c^3 + 6b^3c^3 - a^2c^4 + 11abc^4 - b^2c^4 - 3ac^5 - 3b*c^5 + c^6)))
34243	((a^3 - a^2b - ab^2 + b^3 - a^2c - abc - b^2c - ac^2 - bc^2 + c^3)(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c - b^5c - a^4c^2 + 3a^2b^2c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 - b^2c^4 - ac^5 - bc^5 + c^6))/(abc(a^6 - 2a^5b - a^4b^2 + 4a^3b^3 - a^2b^4 - 2ab^5 + b^6 - 2a^5c + a^3b^2c + a^2b^3c - 2b^5c - a^4c^2 + a^3bc^2 + 5a^2b^2c^2 + ab^3c^2 - b^4c^2 + 4a^3c^3 + a^2bc^3 + ab^2c^3 + 4b^3c^3 - a^2c^4 - b^2c^4 - 2ac^5 - 2bc^5 + c^6))
34332	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(2abc(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + a^4bc + ab^4c - b^5c - a^4c^2 - b^4c^2 + 2a^3c^3 + 2b^3c^3 - a^2c^4 + abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))
34333	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 - a^6b^4c^2 - a^4b^6c^2 + b^10c^2 - 4a^8c^4 - a^6b^2c^4 + 6a^4b^4c^4 - a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - a^4b^2c^6 - a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 - 4b^4c^8 + a^2c^10 + b^2*c^10)
34334	(a^12 - a^10b^2 - 5a^8b^4 + 10a^6b^6 - 5a^4b^8 - a^2b^10 + b^12 - a^10c^2 + 11a^8b^2c^2 - 10a^6b^4c^2 - 10a^4b^6c^2 + 11a^2b^8c^2 - b^10c^2 - 5a^8c^4 - 10a^6b^2c^4 + 30a^4b^4c^4 - 10a^2b^6c^4 - 5b^8c^4 + 10a^6c^6 - 10a^4b^2c^6 - 10a^2b^4c^6 + 10b^6c^6 - 5a^4c^8 + 11a^2b^2c^8 - 5b^4c^8 - a^2c^10 - b^2c^10 + c^12)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 + 4a^8b^2c^2 - 5a^6b^4c^2 - 5a^4b^6c^2 + 4a^2b^8c^2 + b^10c^2 - 4a^8c^4 - 5a^6b^2c^4 + 18a^4b^4c^4 - 5a^2b^6c^4 - 4b^8c^4 + 6a^6c^6 - 5a^4b^2c^6 - 5a^2b^4c^6 + 6b^6c^6 - 4a^4c^8 + 4a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10)
34335	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(a^8b^2 - 2a^7b^3 - a^6b^4 + 4a^5b^5 - a^4b^6 - 2a^3b^7 + a^2b^8 + a^8c^2 - 2a^4b^4c^2 + b^8c^2 - 2a^7c^3 + 2a^4b^3c^3 + 2a^3b^4c^3 - 2b^7c^3 - a^6c^4 - 2a^4b^2c^4 + 2a^3b^3c^4 - 2a^2b^4c^4 - b^6c^4 + 4a^5c^5 + 4b^5c^5 - a^4c^6 - b^4c^6 - 2a^3c^7 - 2b^3c^7 + a^2c^8 + b^2*c^8)
34336	(a^12 - 3a^10b^2 - a^8b^4 + 6a^6b^6 - a^4b^8 - 3a^2b^10 + b^12 - 3a^10c^2 + 11a^8b^2c^2 - 8a^6b^4c^2 - 8a^4b^6c^2 + 11a^2b^8c^2 - 3b^10c^2 - a^8c^4 - 8a^6b^2c^4 + 18a^4b^4c^4 - 8a^2b^6c^4 - b^8c^4 + 6a^6c^6 - 8a^4b^2c^6 - 8a^2b^4c^6 + 6b^6c^6 - a^4c^8 + 11a^2b^2c^8 - b^4c^8 - 3a^2c^10 - 3b^2c^10 + c^12)/(a^10b^2 - 2a^6b^6 + a^2b^10 + a^10c^2 - 12a^8b^2c^2 + 11a^6b^4c^2 + 11a^4b^6c^2 - 12a^2b^8c^2 + b^10c^2 + 11a^6b^2c^4 - 30a^4b^4c^4 + 11a^2b^6c^4 - 2a^6c^6 + 11a^4b^2c^6 + 11a^2b^4c^6 - 2b^6c^6 - 12a^2b^2c^8 + a^2c^10 + b^2c^10)
34337	(a^10 - 2a^9b + a^8b^2 - 2a^6b^4 + 4a^5b^5 - 2a^4b^6 + a^2b^8 - 2ab^9 + b^10 - 2a^9c + 3a^8bc - a^7b^2c + a^6b^3c - a^5b^4c - a^4b^5c + a^3b^6c - a^2b^7c + 3ab^8c - 2b^9c + a^8c^2 - a^7bc^2 + 2a^6b^2c^2 - 3a^5b^3c^2 + 2a^4b^4c^2 - 3a^3b^5c^2 + 2a^2b^6c^2 - ab^7c^2 + b^8c^2 + a^6bc^3 - 3a^5b^2c^3 + 2a^4b^3c^3 + 2a^3b^4c^3 - 3a^2b^5c^3 + ab^6c^3 - 2a^6c^4 - a^5bc^4 + 2a^4b^2c^4 + 2a^3b^3c^4 + 2a^2b^4c^4 - ab^5c^4 - 2b^6c^4 + 4a^5c^5 - a^4bc^5 - 3a^3b^2c^5 - 3a^2b^3c^5 - ab^4c^5 + 4b^5c^5 - 2a^4c^6 + a^3bc^6 + 2a^2b^2c^6 + ab^3c^6 - 2b^4c^6 - a^2bc^7 - ab^2c^7 + a^2c^8 + 3abc^8 + b^2c^8 - 2ac^9 - 2bc^9 + c^10)/(2abc(a^7 - 2a^6b + 2a^5b^2 - a^4b^3 - a^3b^4 + 2a^2b^5 - 2ab^6 + b^7 - 2a^6c + a^5bc + 2a^3b^3c + ab^5c - 2b^6c + 2a^5c^2 - 2a^3b^2c^2 - 2a^2b^3c^2 + 2b^5c^2 - a^4c^3 + 2a^3bc^3 - 2a^2b^2c^3 + 2ab^3c^3 - b^4c^3 - a^3c^4 - b^3c^4 + 2a^2c^5 + abc^5 + 2b^2c^5 - 2ac^6 - 2bc^6 + c^7))
34338	(a^18 - 5a^16b^2 + 10a^14b^4 - 10a^12b^6 + 4a^10b^8 + 4a^8b^10 - 10a^6b^12 + 10a^4b^14 - 5a^2b^16 + b^18 - 5a^16c^2 + 21a^14b^2c^2 - 34a^12b^4c^2 + 27a^10b^6c^2 - 18a^8b^8c^2 + 27a^6b^10c^2 - 34a^4b^12c^2 + 21a^2b^14c^2 - 5b^16c^2 + 10a^14c^4 - 34a^12b^2c^4 + 42a^10b^4c^4 - 18a^8b^6c^4 - 18a^6b^8c^4 + 42a^4b^10c^4 - 34a^2b^12c^4 + 10b^14c^4 - 10a^12c^6 + 27a^10b^2c^6 - 18a^8b^4c^6 + 18a^6b^6c^6 - 18a^4b^8c^6 + 27a^2b^10c^6 - 10b^12c^6 + 4a^10c^8 - 18a^8b^2c^8 - 18a^6b^4c^8 - 18a^4b^6c^8 - 18a^2b^8c^8 + 4b^10c^8 + 4a^8c^10 + 27a^6b^2c^10 + 42a^4b^4c^10 + 27a^2b^6c^10 + 4b^8c^10 - 10a^6c^12 - 34a^4b^2c^12 - 34a^2b^4c^12 - 10b^6c^12 + 10a^4c^14 + 21a^2b^2c^14 + 10b^4c^14 - 5a^2c^16 - 5b^2c^16 + c^18)/(a^16b^2 - 5a^14b^4 + 9a^12b^6 - 5a^10b^8 - 5a^8b^10 + 9a^6b^12 - 5a^4b^14 + a^2b^16 + a^16c^2 - 6a^14b^2c^2 + 16a^12b^4c^2 - 26a^10b^6c^2 + 30a^8b^8c^2 - 26a^6b^10c^2 + 16a^4b^12c^2 - 6a^2b^14c^2 + b^16c^2 - 5a^14c^4 + 16a^12b^2c^4 - 14a^10b^4c^4 + 3a^8b^6c^4 + 3a^6b^8c^4 - 14a^4b^10c^4 + 16a^2b^12c^4 - 5b^14c^4 + 9a^12c^6 - 26a^10b^2c^6 + 3a^8b^4c^6 + 12a^6b^6c^6 + 3a^4b^8c^6 - 26a^2b^10c^6 + 9b^12c^6 - 5a^10c^8 + 30a^8b^2c^8 + 3a^6b^4c^8 + 3a^4b^6c^8 + 30a^2b^8c^8 - 5b^10c^8 - 5a^8c^10 - 26a^6b^2c^10 - 14a^4b^4c^10 - 26a^2b^6c^10 - 5b^8c^10 + 9a^6c^12 + 16a^4b^2c^12 + 16a^2b^4c^12 + 9b^6c^12 - 5a^4c^14 - 6a^2b^2c^14 - 5b^4c^14 + a^2c^16 + b^2c^16)
34469	(4(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(3a^6 - 3a^4b^2 - 3a^2b^4 + 3b^6 - 3a^4c^2 + 10a^2b^2c^2 - 3b^4c^2 - 3a^2c^4 - 3b^2c^4 + 3c^6)
34513	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(3(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))
34586	(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6)/(a^5b - 2a^3b^3 + ab^5 + a^5c - 4a^4bc + 3a^3b^2c + 3a^2b^3c - 4ab^4c + b^5c + 3a^3bc^2 - 6a^2b^2c^2 + 3ab^3c^2 - 2a^3c^3 + 3a^2bc^3 + 3ab^2c^3 - 2b^3c^3 - 4abc^4 + ac^5 + bc^5)
34756	(2(a^18 - 5a^16b^2 + 10a^14b^4 - 10a^12b^6 + 4a^10b^8 + 4a^8b^10 - 10a^6b^12 + 10a^4b^14 - 5a^2b^16 + b^18 - 5a^16c^2 + 21a^14b^2c^2 - 34a^12b^4c^2 + 27a^10b^6c^2 - 18a^8b^8c^2 + 27a^6b^10c^2 - 34a^4b^12c^2 + 21a^2b^14c^2 - 5b^16c^2 + 10a^14c^4 - 34a^12b^2c^4 + 42a^10b^4c^4 - 18a^8b^6c^4 - 18a^6b^8c^4 + 42a^4b^10c^4 - 34a^2b^12c^4 + 10b^14c^4 - 10a^12c^6 + 27a^10b^2c^6 - 18a^8b^4c^6 + 18a^6b^6c^6 - 18a^4b^8c^6 + 27a^2b^10c^6 - 10b^12c^6 + 4a^10c^8 - 18a^8b^2c^8 - 18a^6b^4c^8 - 18a^4b^6c^8 - 18a^2b^8c^8 + 4b^10c^8 + 4a^8c^10 + 27a^6b^2c^10 + 42a^4b^4c^10 + 27a^2b^6c^10 + 4b^8c^10 - 10a^6c^12 - 34a^4b^2c^12 - 34a^2b^4c^12 - 10b^6c^12 + 10a^4c^14 + 21a^2b^2c^14 + 10b^4c^14 - 5a^2c^16 - 5b^2c^16 + c^18))/(a^18 - 3a^16b^2 + 8a^12b^6 - 6a^10b^8 - 6a^8b^10 + 8a^6b^12 - 3a^2b^16 + b^18 - 3a^16c^2 + 6a^14b^2c^2 + 8a^12b^4c^2 - 38a^10b^6c^2 + 54a^8b^8c^2 - 38a^6b^10c^2 + 8a^4b^12c^2 + 6a^2b^14c^2 - 3b^16c^2 + 8a^12b^2c^4 - 8a^10b^4c^4 - 8a^4b^10c^4 + 8a^2b^12c^4 + 8a^12c^6 - 38a^10b^2c^6 + 28a^6b^6c^6 - 38a^2b^10c^6 + 8b^12c^6 - 6a^10c^8 + 54a^8b^2c^8 + 54a^2b^8c^8 - 6b^10c^8 - 6a^8c^10 - 38a^6b^2c^10 - 8a^4b^4c^10 - 38a^2b^6c^10 - 6b^8c^10 + 8a^6c^12 + 8a^4b^2c^12 + 8a^2b^4c^12 + 8b^6c^12 + 6a^2b^2c^14 - 3a^2c^16 - 3b^2*c^16 + c^18)
34758	-((abc(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3))/(a^6 - 2a^5b - a^4b^2 + 4a^3b^3 - a^2b^4 - 2ab^5 + b^6 - 2a^5c + 8a^4bc - 6a^3b^2c - 6a^2b^3c + 8ab^4c - 2b^5c - a^4c^2 - 6a^3bc^2 + 13a^2b^2c^2 - 6ab^3c^2 - b^4c^2 + 4a^3c^3 - 6a^2bc^3 - 6ab^2c^3 + 4b^3c^3 - a^2c^4 + 8abc^4 - b^2c^4 - 2ac^5 - 2bc^5 + c^6))
34834	((a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6))/(2(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 + a^10c^2 - a^8b^2c^2 - a^2b^8c^2 + b^10c^2 - 4a^8c^4 + 3a^4b^4c^4 - 4b^8c^4 + 6a^6c^6 + 6b^6c^6 - 4a^4c^8 - a^2b^2c^8 - 4b^4c^8 + a^2c^10 + b^2c^10))
34885	-(((a^2b^2 + a^2c^2 + b^2c^2)(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4))/(a^8 - 2a^6b^2 + a^4b^4 - 2a^2b^6 + b^8 - 2a^6c^2 - 4a^4b^2c^2 - 4a^2b^4c^2 - 2b^6c^2 + a^4c^4 - 4a^2b^2c^4 + b^4c^4 - 2a^2c^6 - 2b^2*c^6 + c^8))
35012	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)^2)/(a^10b^2 - 4a^8b^4 + 6a^6b^6 - 4a^4b^8 + a^2b^10 - 4a^9b^2c + 4a^8b^3c + 12a^7b^4c - 12a^6b^5c - 12a^5b^6c + 12a^4b^7c + 4a^3b^8c - 4a^2b^9c + a^10c^2 - 4a^9bc^2 + 12a^8b^2c^2 - 16a^7b^3c^2 - 13a^6b^4c^2 + 40a^5b^5c^2 - 13a^4b^6c^2 - 16a^3b^7c^2 + 12a^2b^8c^2 - 4ab^9c^2 + b^10c^2 + 4a^8bc^3 - 16a^7b^2c^3 + 40a^6b^3c^3 - 28a^5b^4c^3 - 28a^4b^5c^3 + 40a^3b^6c^3 - 16a^2b^7c^3 + 4ab^8c^3 - 4a^8c^4 + 12a^7bc^4 - 13a^6b^2c^4 - 28a^5b^3c^4 + 66a^4b^4c^4 - 28a^3b^5c^4 - 13a^2b^6c^4 + 12ab^7c^4 - 4b^8c^4 - 12a^6bc^5 + 40a^5b^2c^5 - 28a^4b^3c^5 - 28a^3b^4c^5 + 40a^2b^5c^5 - 12ab^6c^5 + 6a^6c^6 - 12a^5bc^6 - 13a^4b^2c^6 + 40a^3b^3c^6 - 13a^2b^4c^6 - 12ab^5c^6 + 6b^6c^6 + 12a^4bc^7 - 16a^3b^2c^7 - 16a^2b^3c^7 + 12ab^4c^7 - 4a^4c^8 + 4a^3bc^8 + 12a^2b^2c^8 + 4ab^3c^8 - 4b^4c^8 - 4a^2bc^9 - 4ab^2c^9 + a^2c^10 + b^2c^10)
35072	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^4 - a^3b - ab^3 + b^4 - a^3c + a^2bc + ab^2c - b^3c + abc^2 - ac^3 - bc^3 + c^4))/(2(a^8b^2 - 2a^7b^3 - a^6b^4 + 4a^5b^5 - a^4b^6 - 2a^3b^7 + a^2b^8 - a^8bc + a^7b^2c + 3a^6b^3c - 3a^5b^4c - 3a^4b^5c + 3a^3b^6c + a^2b^7c - ab^8c + a^8c^2 + a^7bc^2 - 3a^6b^2c^2 - a^5b^3c^2 + 4a^4b^4c^2 - a^3b^5c^2 - 3a^2b^6c^2 + ab^7c^2 + b^8c^2 - 2a^7c^3 + 3a^6bc^3 - a^5b^2c^3 - a^2b^5c^3 + 3ab^6c^3 - 2b^7c^3 - a^6c^4 - 3a^5bc^4 + 4a^4b^2c^4 + 4a^2b^4c^4 - 3ab^5c^4 - b^6c^4 + 4a^5c^5 - 3a^4bc^5 - a^3b^2c^5 - a^2b^3c^5 - 3ab^4c^5 + 4b^5c^5 - a^4c^6 + 3a^3bc^6 - 3a^2b^2c^6 + 3ab^3c^6 - b^4c^6 - 2a^3c^7 + a^2bc^7 + ab^2c^7 - 2b^3c^7 + a^2c^8 - abc^8 + b^2c^8))
35193	(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)/(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + a^3b^2c + a^2b^3c - b^5c - a^4c^2 + a^3bc^2 + 5a^2b^2c^2 + ab^3c^2 - b^4c^2 + 2a^3c^3 + a^2bc^3 + ab^2c^3 + 2b^3c^3 - a^2c^4 - b^2c^4 - ac^5 - bc^5 + c^6)
35451	(2abc)/(a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)
35464	(2(a^2b^2 + a^2c^2 + b^2c^2))/(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2*c^2 + c^4)
35910	(2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)(a^8 - a^6b^2 - a^2b^6 + b^8 - a^6c^2 + a^4b^2c^2 + a^2b^4c^2 - b^6c^2 + a^2b^2c^4 - a^2c^6 - b^2c^6 + c^8))/(3(a^12b^2 - 3a^10b^4 + 2a^8b^6 + 2a^6b^8 - 3a^4b^10 + a^2b^12 + a^12c^2 + a^8b^4c^2 - 4a^6b^6c^2 + a^4b^8c^2 + b^12c^2 - 3a^10c^4 + a^8b^2c^4 + 2a^6b^4c^4 + 2a^4b^6c^4 + a^2b^8c^4 - 3b^10c^4 + 2a^8c^6 - 4a^6b^2c^6 + 2a^4b^4c^6 - 4a^2b^6c^6 + 2b^8c^6 + 2a^6c^8 + a^4b^2c^8 + a^2b^4c^8 + 2b^6c^8 - 3a^4c^10 - 3b^4c^10 + a^2c^12 + b^2c^12))
36055	((a^2 - b^2 - c^2)(a^2 + b^2 - c^2)(a^2 - b^2 + c^2)(a^6 - a^5b - a^4b^2 + 2a^3b^3 - a^2b^4 - ab^5 + b^6 - a^5c + 3a^4bc - 2a^3b^2c - 2a^2b^3c + 3ab^4c - b^5c - a^4c^2 - 2a^3bc^2 + 6a^2b^2c^2 - 2ab^3c^2 - b^4c^2 + 2a^3c^3 - 2a^2bc^3 - 2ab^2c^3 + 2b^3c^3 - a^2c^4 + 3abc^4 - b^2c^4 - ac^5 - bc^5 + c^6))/(a^12 - 2a^11b + 6a^9b^3 - 9a^8b^4 - 4a^7b^5 + 16a^6b^6 - 4a^5b^7 - 9a^4b^8 + 6a^3b^9 - 2ab^11 + b^12 - 2a^11c + 7a^10bc - 9a^9b^2c - 6a^8b^3c + 32a^7b^4c - 22a^6b^5c - 22a^5b^6c + 32a^4b^7c - 6a^3b^8c - 9a^2b^9c + 7ab^10c - 2b^11c - 9a^9bc^2 + 32a^8b^2c^2 - 28a^7b^3c^2 - 32a^6b^4c^2 + 74a^5b^5c^2 - 32a^4b^6c^2 - 28a^3b^7c^2 + 32a^2b^8c^2 - 9ab^9c^2 + 6a^9c^3 - 6a^8bc^3 - 28a^7b^2c^3 + 76a^6b^3c^3 - 48a^5b^4c^3 - 48a^4b^5c^3 + 76a^3b^6c^3 - 28a^2b^7c^3 - 6ab^8c^3 + 6b^9c^3 - 9a^8c^4 + 32a^7bc^4 - 32a^6b^2c^4 - 48a^5b^3c^4 + 114a^4b^4c^4 - 48a^3b^5c^4 - 32a^2b^6c^4 + 32ab^7c^4 - 9b^8c^4 - 4a^7c^5 - 22a^6bc^5 + 74a^5b^2c^5 - 48a^4b^3c^5 - 48a^3b^4c^5 + 74a^2b^5c^5 - 22ab^6c^5 - 4b^7c^5 + 16a^6c^6 - 22a^5bc^6 - 32a^4b^2c^6 + 76a^3b^3c^6 - 32a^2b^4c^6 - 22ab^5c^6 + 16b^6c^6 - 4a^5c^7 + 32a^4bc^7 - 28a^3b^2c^7 - 28a^2b^3c^7 + 32ab^4c^7 - 4b^5c^7 - 9a^4c^8 - 6a^3bc^8 + 32a^2b^2c^8 - 6ab^3c^8 - 9b^4c^8 + 6a^3c^9 - 9a^2bc^9 - 9ab^2c^9 + 6b^3c^9 + 7abc^10 - 2ac^11 - 2bc^11 + c^12)
36822	(2(a^4 - a^2b^2 + b^4 - a^2c^2 - b^2c^2 + c^4)(a^6b^2 - 2a^4b^4 + a^2b^6 + a^6c^2 + b^6c^2 - 2a^4c^4 - 2b^4c^4 + a^2c^6 + b^2c^6))/((a^2 + b^2 + c^2)(a^8b^2 - a^6b^4 - a^4b^6 + a^2b^8 + a^8c^2 - 4a^6b^2c^2 + 4a^4b^4c^2 - 4a^2b^6c^2 + b^8c^2 - a^6c^4 + 4a^4b^2c^4 + 4a^2b^4c^4 - b^6c^4 - a^4c^6 - 4a^2b^2c^6 - b^4c^6 + a^2c^8 + b^2c^8))
36921	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(2a^5b - 4a^3b^3 + 2ab^5 + 2a^5c - 5a^4bc + 3a^3b^2c + 3a^2b^3c - 5ab^4c + 2b^5c + 3a^3bc^2 - 6a^2b^2c^2 + 3ab^3c^2 - 4a^3c^3 + 3a^2bc^3 + 3ab^2c^3 - 4b^3c^3 - 5abc^4 + 2ac^5 + 2bc^5))/(abc(a + b + c)(a^5 - a^4b - ab^4 + b^5 - a^4c + a^3bc + ab^3c - b^4c + abc^3 - ac^4 - bc^4 + c^5))
36944	((a^3 - a^2b - ab^2 + b^3 - a^2c + 3abc - b^2c - ac^2 - bc^2 + c^3)(a^5b - 2a^3b^3 + ab^5 + a^5c - 4a^4bc + 3a^3b^2c + 3a^2b^3c - 4ab^4c + b^5c + 3a^3bc^2 - 6a^2b^2c^2 + 3ab^3c^2 - 2a^3c^3 + 3a^2bc^3 + 3ab^2c^3 - 2b^3c^3 - 4abc^4 + ac^5 + bc^5))/(abc(2a^6 - 3a^5b - 2a^4b^2 + 6a^3b^3 - 2a^2b^4 - 3ab^5 + 2b^6 - 3a^5c + 10a^4bc - 7a^3b^2c - 7a^2b^3c + 10ab^4c - 3b^5c - 2a^4c^2 - 7a^3bc^2 + 18a^2b^2c^2 - 7ab^3c^2 - 2b^4c^2 + 6a^3c^3 - 7a^2bc^3 - 7ab^2c^3 + 6b^3c^3 - 2a^2c^4 + 10abc^4 - 2b^2c^4 - 3ac^5 - 3bc^5 + 2c^6))
38539	(-2(a^6 - a^4b^2 - a^2b^4 + b^6 - a^4c^2 + 3a^2b^2c^2 - b^4c^2 - a^2c^4 - b^2c^4 + c^6)(a^12 - 4a^10b^2 + 7a^8b^4 - 8a^6b^6 + 7a^4b^8 - 4a^2b^10 + b^12 - 4a^10c^2 + 8a^8b^2c^2 - 4a^6b^4c^2 - 4a^4b^6c^2 + 8a^2b^8c^2 - 4b^10c^2 + 7a^8c^4 - 4a^6b^2c^4 + 3a^4b^4c^4 - 4a^2b^6c^4 + 7b^8c^4 - 8a^6c^6 - 4a^4b^2c^6 - 4a^2b^4c^6 - 8b^6c^6 + 7a^4c^8 + 8a^2b^2c^8 + 7b^4c^8 - 4a^2c^10 - 4b^2c^10 + c^12))/(a^18 - 3a^16b^2 + 8a^12b^6 - 6a^10b^8 - 6a^8b^10 + 8a^6b^12 - 3a^2b^16 + b^18 - 3a^16c^2 + 3a^14b^2c^2 + 14a^12b^4c^2 - 35a^10b^6c^2 + 42a^8b^8c^2 - 35a^6b^10c^2 + 14a^4b^12c^2 + 3a^2b^14c^2 - 3b^16c^2 + 14a^12b^2c^4 - 23a^10b^4c^4 + 9a^8b^6c^4 + 9a^6b^8c^4 - 23a^4b^10c^4 + 14a^2b^12c^4 + 8a^12c^6 - 35a^10b^2c^6 + 9a^8b^4c^6 + 9a^6b^6c^6 + 9a^4b^8c^6 - 35a^2b^10c^6 + 8b^12c^6 - 6a^10c^8 + 42a^8b^2c^8 + 9a^6b^4c^8 + 9a^4b^6c^8 + 42a^2b^8c^8 - 6b^10c^8 - 6a^8c^10 - 35a^6b^2c^10 - 23a^4b^4c^10 - 35a^2b^6c^10 - 6b^8c^10 + 8a^6c^12 + 14a^4b^2c^12 + 14a^2b^4c^12 + 8b^6c^12 + 3a^2b^2c^14 - 3a^2c^16 - 3b^2*c^16 + c^18)
38626, 38627, 38628, 38629, 38630, 38631, 38632	9/4
38633, 38634, 38635, 38636, 38637, 38638, 38639, 38640	4/9
38722	-((abc)/((a - b - c)(a + b - c)(a - b + c)))

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