Here are the eigenvalues for the constants: {mub, muf, g2, kappas, kappaa, beta, lambda1, lambda2, lambda3, lambda4, lambda5} = {0.1803, 0.362, 1, -0.323, 0.162, 0.688, -0.038, -0.09, 374, 0.158, 143} K = 5 and two links with masses, g^2, Kappa_S, and Kappa_A nonzero This takes about 30 minutes on bvds In[6]:= expr = N[generalMatrix[makeham, 5, 2, 0, 1, {0.1803, 0.362, 1, -0.323, 0.162, 0, 0, 0, 0, 0, 0}, none]]; In[7]:= Sort[Chop[Eigenvalues[expr]]] Out[7]= {0.31505, 0.327639, 0.327639, 0.340845, 1.46397, 1.46397, 1.46397, 1.46397, \ 1.46397, 1.46397, 1.46861, 1.46861, 1.47439, 1.49569, 1.49569, 1.52714, \ 1.64909, 1.67238, 1.67238, 1.69555, 1.79004, 1.79716, 1.79716, 1.80415, \ 2.26744, 2.26744, 2.26744, 2.26744, 2.26744, 2.26744, 2.27308, 2.27308, \ 2.27802, 2.29105, 2.29105, 2.31435, 2.68808, 2.69488, 2.69488, 2.69657, \ 2.70442, 2.7132, 2.7132, 2.7348, 2.78507, 2.78507, 2.78507, 2.78507, 2.78507, \ 2.78507, 2.79287, 2.79287, 2.79841, 2.81726, 2.81726, 2.83846, 2.83946, \ 2.83946, 2.83946, 2.83946, 2.83946, 2.83946, 2.83979, 2.83979, 2.84599, \ 2.8614, 2.8614, 2.88328, 3.01855, 3.01855, 3.01855, 3.01855, 3.01855, \ 3.01855, 3.01855, 3.01855, 3.01855, 3.01855, 3.01855, 3.01855, 3.01863, \ 3.01863, 3.01868, 3.01875, 3.05893, 3.05893, 3.05893, 3.05893, 3.05893, \ 3.05893, 3.05952, 3.05952, 3.05989, 3.05989, 3.05989, 3.05989, 3.05989, \ 3.05989, 3.05996, 3.05996, 3.09154, 3.09693, 3.09693, 3.10084, 3.12799, \ 3.12799, 3.1305, 3.1309, 3.23351, 3.23351, 3.23427, 3.23548, 3.26831, \ 3.26831, 3.26831, 3.26831, 3.26831, 3.26831, 3.27509, 3.27509, 3.27509, \ 3.27509, 3.27509, 3.27509, 3.27904, 3.27904, 3.28473, 3.28473, 3.29768, \ 3.30127, 3.30127, 3.30367, 3.30367, 3.30982, 3.31629, 3.32232, 3.49052, \ 3.49192, 3.49192, 3.49662, 3.51936, 3.51982, 3.51982, 3.52946, 3.55783, \ 3.55783, 3.55783, 3.55783, 3.55783, 3.55783, 3.55783, 3.55783, 3.55783, \ 3.55783, 3.55783, 3.55783, 3.56074, 3.56074, 3.56442, 3.56459, 3.58151, \ 3.58151, 3.58151, 3.58151, 3.58151, 3.58151, 3.58416, 3.58416, 3.59305, \ 3.59429, 3.59429, 3.59955, 3.60383, 3.60383, 3.60383, 3.60383, 3.60383, \ 3.60383, 3.60827, 3.60827, 3.61321, 3.63093, 3.63093, 3.64956, 3.69311, \ 3.69311, 3.69311, 3.69311, 3.69311, 3.69311, 3.71544, 3.71544, 3.72058, \ 3.72058, 3.72068, 3.72068, 3.72068, 3.72068, 3.72068, 3.72068, 3.72653, \ 3.72653, 3.72653, 3.72653, 3.72653, 3.72653, 3.72653, 3.72653, 3.72653, \ 3.72653, 3.72653, 3.72653, 3.73064, 3.73064, 3.73126, 3.73377, 3.74146, \ 3.74993, 3.74993, 3.75317, 3.75317, 3.75349, 3.77023, 3.77023, 3.77023, \ 3.77023, 3.77023, 3.77023, 3.77941, 3.78786, 3.78786, 3.78944, 3.80265, \ 3.80265, 3.80906, 3.80906, 3.80906, 3.80906, 3.80906, 3.80906, 3.8231, \ 3.83519, 3.83519, 3.84427, 3.84427, 3.84427, 3.84427, 3.84427, 3.84427, \ 3.84826, 3.86321, 3.86321, 3.87387, 3.87387, 3.88779, 3.89317, 3.9165, \ 3.93244, 3.93244, 3.94979, 3.96915, 3.97798, 3.97798, 3.99131, 4.18754, \ 4.18754, 4.18754, 4.18754, 4.18754, 4.18754, 4.21218, 4.21218, 4.21282, \ 4.21282, 4.21282, 4.21282, 4.21282, 4.21282, 4.21661, 4.21661, 4.23715, \ 4.23715, 4.24187, 4.24864, 4.24913, 4.24913, 4.25674, 4.27426, 4.31415, \ 4.31415, 4.31511, 4.31618, 4.44847, 4.44847, 4.44847, 4.44847, 4.44847, \ 4.44847, 4.46554, 4.46554, 4.46653, 4.46653, 4.48274, 4.48376, 4.58133, \ 4.58133, 4.58133, 4.58133, 4.58133, 4.58133, 4.58596, 4.58596, 4.59022, \ 4.59107, 4.59107, 4.60031, 4.68845, 4.68845, 4.68845, 4.68845, 4.68845, \ 4.68845, 4.68845, 4.68845, 4.68845, 4.68845, 4.68845, 4.68845, 4.68845, \ 4.68845, 4.68846, 4.68846, 4.70886, 4.70886, 4.70886, 4.70886, 4.70886, \ 4.70886, 4.71135, 4.71135, 4.71215, 4.71215, 4.71517, 4.71517, 4.71517, \ 4.71517, 4.71517, 4.71517, 4.72914, 4.73592, 4.73592, 4.74166, 4.74514, \ 4.75548, 4.75548, 4.78005, 4.7991, 4.7991, 4.7991, 4.7991, 4.7991, 4.7991, \ 4.80897, 4.80897, 4.81801, 4.83798, 4.83798, 4.84856, 4.85918, 4.85918, \ 4.865, 4.87705, 4.9242, 4.9242, 4.9242, 4.9242, 4.9242, 4.9242, 4.93015, \ 4.93015, 4.93015, 4.93015, 4.93015, 4.93015, 4.93015, 4.93015, 4.93015, \ 4.93015, 4.93015, 4.93015, 4.93155, 4.93155, 4.93327, 4.93338, 4.94267, \ 4.94267, 4.94894, 4.94894, 4.95652, 4.95652, 4.95652, 4.95652, 4.95652, \ 4.95652, 4.95745, 4.9591, 4.9591, 4.9591, 4.9591, 4.9591, 4.9591, 4.9622, \ 4.9622, 4.96433, 4.96433, 4.98086, 4.98479, 4.98479, 4.98484, 4.99168, \ 5.00657, 5.01508, 5.01508, 5.03701, 5.03701, 5.03701, 5.03701, 5.03701, \ 5.03701, 5.04821, 5.04821, 5.05924, 5.06529, 5.10303, 5.10303, 5.12235, \ 5.12274, 5.12274, 5.1232, 5.12713, 5.17981, 5.17981, 5.17981, 5.17981, \ 5.17981, 5.17981, 5.19859, 5.19859, 5.20141, 5.20141, 5.21731, 5.22213, \ 5.50642, 5.50642, 5.50642, 5.50642, 5.50642, 5.50642, 5.51229, 5.51229, \ 5.51791, 5.52147, 5.52147, 5.53595, 5.70136, 5.70245, 5.70245, 5.70432, \ 5.72661, 5.72661, 5.72661, 5.72661, 5.72661, 5.72661, 5.73325, 5.73325, \ 5.73887, 5.73887, 5.74025, 5.75363, 5.76293, 5.76293, 5.76293, 5.76293, \ 5.76293, 5.76293, 5.77077, 5.77077, 5.77742, 5.77872, 5.77872, 5.79217, \ 5.86441, 5.86441, 5.86441, 5.86441, 5.86441, 5.86441, 5.86441, 5.86441, \ 5.86441, 5.86441, 5.86441, 5.86441, 5.86447, 5.86447, 5.86453, 5.86453, \ 5.88186, 5.88186, 5.88186, 5.88186, 5.88186, 5.88186, 5.88386, 5.88386, \ 5.8848, 5.8848, 5.88645, 5.88645, 5.88645, 5.88645, 5.88645, 5.88645, \ 5.90075, 5.90569, 5.90569, 5.91025, 5.91084, 5.91084, 5.91084, 5.91084, \ 5.91084, 5.91084, 5.91084, 5.91084, 5.91084, 5.91084, 5.91084, 5.91084, \ 5.91856, 5.91856, 5.93639, 5.93639, 5.93639, 5.93639, 5.93639, 5.93639, \ 5.93651, 5.93791, 5.93791, 5.94014, 5.94255, 5.94255, 5.94255, 5.94255, \ 5.94255, 5.94255, 5.95218, 5.96436, 5.96436, 5.96648, 5.96648, 5.98261, \ 5.98261, 5.98261, 5.98261, 5.98261, 5.98261, 5.99906, 5.99906, 6.00905, \ 6.01074, 6.01074, 6.01707, 6.01877, 6.02169, 6.03978, 6.03978, 6.05708, \ 6.21899, 6.22055, 6.22055, 6.2231, 6.23962, 6.23962, 6.23962, 6.23962, \ 6.23962, 6.23962, 6.25097, 6.25097, 6.25173, 6.25173, 6.25173, 6.25173, \ 6.25173, 6.25173, 6.25173, 6.25173, 6.25173, 6.25173, 6.25173, 6.25173, \ 6.25636, 6.25636, 6.25967, 6.25967, 6.26385, 6.27058, 6.2711, 6.27693, \ 6.27906, 6.27906, 6.27906, 6.27906, 6.27906, 6.27906, 6.28142, 6.28142, \ 6.28216, 6.28216, 6.28216, 6.28216, 6.28216, 6.28216, 6.30636, 6.30636, \ 6.31544, 6.31544, 6.32348, 6.32554, 6.32554, 6.32554, 6.32554, 6.32554, \ 6.32554, 6.32922, 6.32922, 6.33071, 6.33373, 6.33971, 6.33971, 6.35197, \ 6.42184, 6.42684, 6.42684, 6.43354, 6.54569, 6.54569, 6.54569, 6.54569, \ 6.54569, 6.54569, 6.54741, 6.54741, 6.54926, 6.55986, 6.55986, 6.57297, \ 6.5801, 6.5801, 6.5801, 6.5801, 6.5801, 6.5801, 6.58562, 6.58562, 6.58775, \ 6.58775, 6.59196, 6.5953, 6.66971, 6.66971, 6.66971, 6.66971, 6.66971, \ 6.66971, 6.68082, 6.68082, 6.68101, 6.68101, 6.69098, 6.69149, 6.88731, \ 6.88859, 6.88859, 6.89031, 6.97594, 6.97594, 6.97594, 6.97594, 6.97594, \ 6.97594, 6.97594, 6.97594, 6.97594, 6.97594, 6.97594, 6.97594, 6.98293, \ 6.98293, 6.99952, 6.99952, 6.99952, 6.99952, 6.99952, 6.99952, 6.99957, \ 7.00239, 7.00239, 7.00334, 7.00539, 7.00539, 7.00539, 7.00539, 7.00539, \ 7.00539, 7.02771, 7.02771, 7.06348, 7.06348, 7.06758, 7.07345, 7.09281, \ 7.11726, 7.11726, 7.16183, 7.16183, 7.16183, 7.16183, 7.16183, 7.16183, \ 7.17327, 7.17327, 7.18471, 7.22551, 7.28257, 7.28257, 7.31987, 7.36643, \ 7.36764, 7.36764, 7.36907, 7.63868, 7.63868, 7.63868, 7.63868, 7.63868, \ 7.63868, 7.64725, 7.64725, 7.65471, 7.65471, 7.65498, 7.6702, 8.30562, \ 8.30562, 8.30562, 8.30562, 8.30562, 8.30562, 8.30562, 8.30562, 8.30562, \ 8.30562, 8.30562, 8.30562, 8.30812, 8.30812, 8.31389, 8.31437, 8.31607, \ 8.31607, 8.31607, 8.31607, 8.31607, 8.31607, 8.31608, 8.31608, 8.31608, \ 8.31608, 8.31608, 8.31608, 8.31609, 8.31609, 8.32626, 8.32626, 8.33174, \ 8.33174, 8.3349, 8.33697, 8.41267, 8.41267, 8.41267, 8.41267, 8.41267, \ 8.41267, 8.41736, 8.41736, 8.41799, 8.41799, 8.42204, 8.42367, 8.52254, \ 8.52254, 8.52254, 8.52254, 8.52254, 8.52254, 8.52339, 8.52339, 8.52416, \ 8.52703, 8.52703, 8.53109, 8.6489, 8.65054, 8.65054, 8.6522} These are the diagonal matrix elements In[8]:= diag = Table[expr[[i, i]], {i, Length[expr]}] Out[8]= {2.68513, 2.68513, 2.68513, 2.68513, 2.75033, 2.75033, 2.75033, 2.75033, \ 2.76299, 2.76299, 2.76299, 2.76299, 2.75033, 2.75033, 2.75033, 2.75033, \ 2.68513, 2.68513, 2.68513, 2.68513, 3.61215, 3.61215, 3.61215, 3.61215, \ 3.61215, 3.61215, 3.61215, 3.61215, 4.85295, 4.85295, 4.85295, 4.85295, \ 4.85295, 4.85295, 4.85295, 4.85295, 5.08335, 5.08335, 5.08335, 5.08335, \ 5.08335, 5.08335, 5.08335, 5.08335, 5.11149, 5.11149, 5.11149, 5.11149, \ 5.11149, 5.11149, 5.11149, 5.11149, 3.61215, 3.61215, 3.61215, 3.61215, \ 3.61215, 3.61215, 3.61215, 3.61215, 4.85295, 4.85295, 4.85295, 4.85295, \ 4.85295, 4.85295, 4.85295, 4.85295, 5.08335, 5.08335, 5.08335, 5.08335, \ 5.08335, 5.08335, 5.08335, 5.08335, 5.11149, 5.11149, 5.11149, 5.11149, \ 5.11149, 5.11149, 5.11149, 5.11149, 3.66361, 3.66361, 3.66361, 3.66361, \ 3.66361, 3.66361, 3.66361, 3.66361, 4.90187, 4.90187, 4.90187, 4.90187, \ 4.90187, 4.90187, 4.90187, 4.90187, 5.08335, 5.08335, 5.08335, 5.08335, \ 5.08335, 5.08335, 5.08335, 5.08335, 3.66361, 3.66361, 3.66361, 3.66361, \ 3.66361, 3.66361, 3.66361, 3.66361, 4.90187, 4.90187, 4.90187, 4.90187, \ 4.90187, 4.90187, 4.90187, 4.90187, 5.08335, 5.08335, 5.08335, 5.08335, \ 5.08335, 5.08335, 5.08335, 5.08335, 3.66361, 3.66361, 3.66361, 3.66361, \ 3.66361, 3.66361, 3.66361, 3.66361, 4.85295, 4.85295, 4.85295, 4.85295, \ 4.85295, 4.85295, 4.85295, 4.85295, 3.66361, 3.66361, 3.66361, 3.66361, \ 3.66361, 3.66361, 3.66361, 3.66361, 4.85295, 4.85295, 4.85295, 4.85295, \ 4.85295, 4.85295, 4.85295, 4.85295, 3.61215, 3.61215, 3.61215, 3.61215, \ 3.61215, 3.61215, 3.61215, 3.61215, 3.61215, 3.61215, 3.61215, 3.61215, \ 3.61215, 3.61215, 3.61215, 3.61215, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.55552, 5.55552, \ 5.55552, 5.55552, 5.56658, 5.56658, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.90843, 5.90843, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.55552, 5.55552, \ 5.56658, 5.56658, 5.55552, 5.55552, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.90843, 5.90843, 5.89186, 5.89186, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.56658, 5.56658, \ 5.55552, 5.55552, 5.55552, 5.55552, 5.89186, 5.89186, 5.90843, 5.90843, \ 5.89186, 5.89186, 5.89186, 5.89186, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.56658, 5.56658, 5.55552, 5.55552, \ 5.55552, 5.55552, 5.55552, 5.55552, 5.90843, 5.90843, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.89186, 5.89186, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.55473, 5.55473, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.55473, 5.55473, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.54368, 5.54368, 5.55473, 5.55473, \ 5.54368, 5.54368, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.55473, 5.55473, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.90843, 5.90843, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.90843, 5.90843, 5.89186, 5.89186, 5.89186, 5.89186, 5.90843, 5.90843, \ 5.89186, 5.89186, 5.89186, 5.89186, 5.90843, 5.90843, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.89186, 5.89186, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.55552, 5.55552, \ 5.55552, 5.55552, 5.56658, 5.56658, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.90843, 5.90843, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.55552, 5.55552, \ 5.56658, 5.56658, 5.55552, 5.55552, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.90843, 5.90843, 5.89186, 5.89186, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.55552, 5.55552, 5.56658, 5.56658, \ 5.55552, 5.55552, 5.55552, 5.55552, 5.89186, 5.89186, 5.90843, 5.90843, \ 5.89186, 5.89186, 5.89186, 5.89186, 4.28074, 4.28074, 4.28074, 4.28074, \ 4.28074, 4.28074, 4.28074, 4.28074, 5.56658, 5.56658, 5.55552, 5.55552, \ 5.55552, 5.55552, 5.55552, 5.55552, 5.90843, 5.90843, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.89186, 5.89186, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.55473, 5.55473, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.55473, 5.55473, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.54368, 5.54368, 5.55473, 5.55473, \ 5.54368, 5.54368, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.55473, 5.55473, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.54368, 5.54368, 6.90341, 6.90341, 6.90341, 6.90341, \ 6.90341, 6.90341, 6.90341, 6.90341, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.90843, 5.90843, 5.89186, 5.89186, 5.89186, 5.89186, \ 5.90843, 5.90843, 5.89186, 5.89186, 5.89186, 5.89186, 5.90843, 5.90843, \ 5.89186, 5.89186, 5.89186, 5.89186, 5.90843, 5.90843, 5.89186, 5.89186, \ 5.89186, 5.89186, 5.89186, 5.89186, 4.16997, 4.16997, 4.16997, 4.16997, \ 4.16997, 4.16997, 4.16997, 4.16997, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.55473, 5.55473, 4.16997, 4.16997, 4.16997, 4.16997, \ 4.16997, 4.16997, 4.16997, 4.16997, 5.54368, 5.54368, 5.54368, 5.54368, \ 5.55473, 5.55473, 5.54368, 5.54368, 4.16997, 4.16997, 4.16997, 4.16997, \ 4.16997, 4.16997, 4.16997, 4.16997, 5.54368, 5.54368, 5.55473, 5.55473, \ 5.54368, 5.54368, 5.54368, 5.54368, 4.16997, 4.16997, 4.16997, 4.16997, \ 4.16997, 4.16997, 4.16997, 4.16997, 5.55473, 5.55473, 5.54368, 5.54368, \ 5.54368, 5.54368, 5.54368, 5.54368, 5.55552, 5.55552, 5.55552, 5.55552, \ 5.55552, 5.55552, 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