Here, we investigate the maximim number of real zeroes of a univariate polynomial of the form: f(z)*g(z)^p*z^l - h(z), where f, g, h all have degree k. These come from the system consisting of the empty simplex and the segment 0101 0 0 ... 0 001p where (p,q)=1 0 0 ... 0 000q & p < q 0 -1 ... -k The transformation z |--> z + k(1-x-y) and l:=q-pk-k > 0, gives 0 0 ... 0 1 0 1 x = f(z) \ 0 0 ... 0 0 1 p y = g(z) > f(z)*g(z)^p*z^(l+k) - h(z) = 0 0 1 ... k 0 0 l xy^pz^lz^k = h(z) / These systems are most interesting when l > 1 ______________________________________________________________________________________ When p = 1, it is easy to see that the maximum number of real solutions is 3k + d, where d = 1 or 2, depending upon the parity of l. ______________________________________________________________________________________ k p l Frequencies # time Machine ______________________________________________________________________________________ 2 2 1 [ 129176, 477598, 338259, 54943, 24] 1M 107,298 Pearl 2 2 2 [ 67255, 340340, 324441, 236512, 31452, 0] 1M 142,504 Trillian 2 2 3 [ 358049, 1447356, 1054627, 139503, 465, 0] 3M 450,512 Bunny 2 2 4 [ 334379, 1708791, 1621299, 1205840, 129691, 0,0] 5M 882,593 Bunny 2 2 5 [ 736580, 2897090, 2111188, 252113, 3029, 0,0] 6M 1016,798 Virgo 2 2 6 [1057234, 5533584, 5218501, 3839169, 351505, 7,0,0] 8M 1789,997 Leo 2 2 7 [1281896, 4814836, 3505830, 388699, 8739, 0,0,0] 10M 1339,151 Lyra 2 2 8 [ 489467, 2631598, 2455507, 1780130, 143285, 13,0,0,0] 7.5M 1189,956 Pavo 2 2 9 [1068302, 3840345, 2789729, 292273, 9351, 0,0,0,0] 8M 1474,671 Lupine 2 2 10 [ 387139, 2131918, 1972028, 1407135, 101752, 28,0,0,0,0] 6M 1300,526 Tuscany 2 2 11 [ 414036, 1435307, 1042931, 103611, 4115, 0,0,0,0,0] 3M 955,768 Newton 2 3 -3 [ 70153, 257613, 669894, 2340] 1M 54,087 Schubert 2 3 -2 [ 70310, 266128, 663165, 397, 0] 1M 52,545 Schubert 2 3 -1 [ 139474, 612717, 1245989, 1820, 0] 2M 234,028 Trillian 2 3 0 [ 141391, 891319, 2220891, 743096, 3303, 0] 5M 544,822 Trillian 2 3 1 [ 431429, 3264965, 2299727, 3879, 0, 0] 6M 357,945 Pavo 2 3 2 [ 212122, 1338350, 3758537, 690976, 15, 0,0] 6M 423,548 BigSur 2 3 3 [ 371923, 2580900, 2046522, 655, 0, 0,0] 5M 404,630 Lyra 2 3 4 [ 175464, 981360, 3349495, 493657, 24, 0,0,0] 5M 464,366 Saratoga 2 3 5 [1176798, 7612810, 6202628, 7764, 0, 0,0,0] 15M 1614,569 Pisces 2 3 6 [ 174071, 949712, 3437431, 438756, 30, 0,0,0,0] 5M 620,669 Hazel 2 3 7 [1539644, 9169083, 7264438, 26834, 1, 0,0,0,0] 9M 2386,506 Blueridge 2 3 8 [ 172374, 949806, 3480747, 397027, 46, 0,0,0,0,0] 5M 821,749 Dorado 2 3 9 [ 894730, 5086961, 3994809, 23498, 2, 0,0,0,0,0] 10M 1861,131 Pegasus 2 3 10 [ 170778, 986562, 3486178, 355404, 78, 0,0,0,0,0,0] 5M 1171,331 Schur 2 3 11 [ 859145, 4603446, 3507337, 30071, 1, 0,0,0,0,0,0] 8M 1974,301 Ivory 2 4 -3 [ 192262, 722575, 740074, 345089, 0] 2M 253,540 Trillian 2 4 -2 [ 108092, 364056, 333575, 194277, 0,0] 1M 126,574 Zaphod 2 4 -1 [ 98106, 377071, 367961, 156862, 0,0] 1M 153,773 Zaphod 2 4 0 [ 167855, 695150, 838889, 576444, 221662,0,0] 2.5M 389,619 Pearl 2 4 1 [ 271410, 893439, 659035, 174714, 1402,0,0] 2M 354,246 Ethel 2 4 2 [ 404659, 2027038, 2051127, 1270552, 246624,0,0,0] 6M 544,798 Saratoga 2 4 3 [1042674, 3766771, 2686638, 503109, 808,0,0,0] 8M 826,041 Leo 2 4 4 [ 403591, 2013058, 1957564, 1411072, 214715,0,0,0,0] 6M 704,362 Hazel 2 4 5 [1179316, 4779148, 3491705, 549062, 769,0,0,0,0] 10M 133,5473 Amazon 2 4 6 [ 335850, 1669263, 1618969, 1216169, 159749,0,0,0,0,0] 5M 753,044 Isis 2 4 7 [ 572884, 2404970, 1770026, 251107, 1013,0,0,0,0,0] 5M 852,900 Stella 2 4 8 [ 133219, 667428, 649630, 491249, 58474,0,0,0,0,0,0] 2M 1014,758 rcf1422-2 2 4 9 [ 228564, 964634, 711597, 94415, 790,0,0,0,0,0,0] 2M 657,591 rcf1422-3 2 4 10 [ 132381, 670574, 651984, 491386, 53675,0,0,0,0,0,0,0] 2M 781,551 rcf1537-8 2 4 11 [ 254120, 965903, 693644, 84766, 1567,0,0,0,0,0,0,0] 2M 1032,485 rcf1537-3 2 5 -3 [277734, 981987, 2734908, 5371, 0,0] 4M 572,789 Pearl 2 5 -2 [208616, 745818, 2044317, 1249, 0,0,0] 3M 427,646 Ethel 2 5 -1 [139004, 534479, 1324119, 2398, 0,0,0] 2M 340,721 Ethel 2 5 0 [ 34855, 179849, 494995, 288454,1847,0,0,0] 1M 228,740 Zaphod 2 5 1 [211222, 1221458, 1555611, 11709, 0,0,0,0] 3M 312,372 Saratoga 2 5 2 [248706, 1608472, 4048953,1090845,3024,0,0,0,0] 7M 819,495 Hazel 2 5 3 [502014, 3675518, 2813393, 9075, 0,0,0,0,0] 7M 919,594 Serpens 2 5 4 [212654, 1340692, 3685121, 761491, 42,0,0,0,0,0] 6M 1407,388 Noether 2 5 5 [217971, 1534867, 1246335, 827, 0,0,0,0,0,0] 3M 801,373 Noether 2 5 6 [ 71586, 433114, 1276423, 218822, 55,0,0,0,0,0,0] 2M 741,669 rcf1422-2 2 5 7 [157290, 1024620, 816874, 1216, 0,0,0,0,0,0,0] 2M 450,719 rcf1422-3 2 5 8 [ 35796, 208023, 657524, 98627, 30,0,0,0,0,0,0,0] 1M 362,018 Schubert 2 5 9 [ 81914, 510368, 406682, 1036, 0,0,0,0,0,0,0,0] 1M 413,168 Schubert 2 5 10 [ 35451, 204526, 669481, 90513, 29,0,0,0,0,0,0,0,0] 1M 481,570 Schubert 2 5 11 [ 85012, 509661, 403708, 1619, 0,0,0,0,0,0,0,0,0] 1M 547,932 Schubert 2 6 -3 [294057, 1092914, 1105519, 507496, 14,0,0] 3M 511,544 rcf1422-2 2 6 -2 [220026, 734579, 665365, 380030, 0,0,0,0] 2M 277,068 rcf1537-3 2 6 -1 [298111, 1132364, 1101688, 467837, 0,0,0,0] 3M 635,028 rcf1422-2 2 6 0 [136654, 532478, 655652, 473576, 201640,0,0,0,0] 2M 486,927 rcf1422-2 2 6 1 [333184, 1217464, 1065973, 382180, 1199,0,0,0,0] 3M 385,432 Chaco 2 6 2 [203378, 899515, 1038492, 665987, 192628,0,0,0,0,0] 3M 448,905 Denali 2 6 3 [411953, 1361575, 984040, 239667, 2765,0,0,0,0,0] 3M 448,502 Fermat 2 6 4 [203568, 995503, 1025387, 650441, 125101,0,0,0,0,0,0] 3M 655,536 Harley 2 6 5 [268569, 936795, 663281, 130871, 484,0,0,0,0,0,0] 2M 736,303 ???? 2 6 6 [136970, 672042, 665280, 453457, 72251,0,0,0,0,0,0,0] 2M 825,799 Rota 2 6 7 [126065, 474762, 340561, 58459, 153,0,0,0,0,0,0,0] 1M 409,393 Schubert 2 6 8 [ 68058, 336180, 328911, 234273, 32578,0,0,0,0,0,0,0,0] 1M 459,516 Schubert 2 6 9 [122541, 478588, 345096, 53547, 228,0,0,0,0,0,0,0,0] 1M 516,366 Schubert 2 6 10 [ 67742, 336790, 328540, 237025, 29903,0,0,0,0,0,0,0,0,0] 1M 583,589 Schubert 2 6 11 [121611, 480554, 347351, 50120, 364,0,0,0,0,0,0,0,0,0] 1M 660,824 Schubert 3 2 -1 [122510, 298527, 338520, 177133, 60018, 3292] 1M 107,140 Noether 3 2 0 [ 3330, 396446, 780524, 593849, 216447, 9401, 3] 2M 295,833 Catnip 3 2 1 [233787, 561946, 665748, 375962, 158349, 4208, 0] 2M 534,956 Ethel 3 2 2 [ 6886, 963015, 1951000, 1525285, 535901, 15923, 10,0] 5M 965,163 Catnip 3 2 3 [586213, 1411169, 1679972, 930401, 383202, 9043, 0,0] 5M 875,037 Bigsur 3 2 4 [ 12111, 988259, 1957438, 1508415, 516644, 17079, 54,0,0] 5M 979,096 Condor 3 2 5 [589752, 1437699, 1690734, 914260, 359797, 7758, 0,0,0] 5M 1143,632 Bethel 3 2 6 [ 15528, 816153, 1568638, 1185183, 397753, 16645, 100,0,0,0] 4M 1060,203 Ivory 3 2 7 [474614, 1172689, 1358044, 718065, 271300, 5288, 0,0,0,0] 4M 752,174 Spin 3 2 8 [ 35989, 1099239, 1982991, 1413422, 444586, 23543, 230,0,0,0,0] 5M 1563,223 Chaco 3 2 9 [248037, 631809, 681767, 329115, 107486, 1786, 0,0,0,0,0] 2M 1148,395 rcf1422-4 3 2 10 [ 20691, 465696, 796098, 544003, 162948, 10463, 101,0,0,0,0,0] 2M 714,001 miln323 3 2 11 [249475, 642327, 680315, 323482, 102893, 1508, 0,0,0,0,0,0] 2M 824,152 miln323 3 3 -3 [ 37, 310985, 261939, 426902, 137, 0,0] 1M 210,583 Pearl 3 3 -2 [ 506, 634308, 608545, 755088, 1553, 0,0] 2M 514,787 Badger 3 3 -1 [ 197, 162737, 356318, 397326, 82714, 708,0,0] 1M 284,842 Pearl 3 3 0 [ 1275, 346257, 482046, 170123, 299, 0,0,0] 1M 324,162 Pearl 3 3 1 [ 926, 812231, 1817036, 2259665, 110134, 8,0,0,0] 5M 871,132 Pisces 3 3 2 [ 7102, 1692148, 2352940, 947749, 61, 0,0,0,0] 5M 990,660 Rushmore 3 3 3 [ 526, 802558, 1736938, 2390970, 69003, 5,0,0,0,0] 5M 901,375 Catalina 3 3 4 [10108, 1354766, 1866837, 768188, 101, 0,0,0,0,0] 4M 1023,590 Smoky 3 3 5 [ 663, 968061, 2100729, 2858847, 71698, 2,0,0,0,0,0] 6M 1734,159 Glax 3 3 6 [25906, 1727944, 2338155, 907649, 346, 0,0,0,0,0,0] 5M 1603,098 Bigsur 3 3 7 [ 2191, 863268, 1988987, 2088931, 56621, 2,0,0,0,0,0,0] 5M 1632,297 Pisces 3 3 8 [22523, 729099, 936191, 311864, 323, 0,0,0,0,0,0,0] 2M 619,384 miln323 3 3 9 [ 836, 342444, 783087, 848653, 24980, 0,0,0,0,0,0,0,0] 2M 1690,924 Noether 3 3 10 [12367, 358991, 467393, 161048, 201, 0,0,0,0,0,0,0,0] 1M 1010,320 Noether 3 3 11 [ 600, 173676, 400602, 411514, 13608, 0,0,0,0,0,0,0,0,0] 1M 1202,407 Noether 3 4 -3 [359653, 680031, 502792, 323921, 133603, 0, 0,0] 2M 393,746 Noether 3 4 -2 [ 491, 358515, 670390, 562269, 329675, 78660, 0,0,0] 2M 467,723 Noether 3 4 -1 [362411, 766160, 966328, 577448, 265266, 62387, 0,0,0] 3M 642,782 Praxis 3 4 0 [ 3995, 404173, 762377, 565386, 236528, 30114,427,0,0,0] 2M 434,159 Denali 3 4 1 [354749, 842746, 1003673, 563556, 222985, 12291, 0,0,0,0] 3M 995,725 Farallon 3 4 2 [ 10398, 1009333, 1967628, 1455959, 527013, 29654, 15,0,0,0,0] 5M 1235,271 Shiloh 3 4 3 [470616, 1118106, 1330838, 753358, 317411, 9671, 0,0,0,0,0] 4M 1182,011 Rugby 3 4 4 [ 7301, 979930, 1969580, 1495917, 526725, 20543, 4,0,0,0,0,0] 5M 1221,894 Biblios 3 4 5 [359737, 859561, 1012538, 546573, 215627, 5964, 0,0,0,0,0,0] 3M 1358,835 rcf1537-9 3 4 6 [ 5924, 604004, 1200283, 885372, 293920, 10480, 17,0,0,0,0,0,0] 3M 996,691 Phoebe 3 4 7 [118815, 283025, 337401, 184246, 74570, 1943, 0,0,0,0,0,0,0] 1M 802,724 Noether 3 4 8 [ 2460, 203580, 401128, 293412, 95828, 3582, 10,0,0,0,0,0,0,0] 1M 1179,868 Rota 3 5 -3 [ 265, 633926, 590122, 774082, 1605, 0,0,0,0,0] 2M 680,652 Rota 3 5 -2 [ 3500, 3210688, 3126163, 3643705, 15943, 1,0,0,0,0] 10M 3593,498 Praxis 3 5 -1 [ 497, 326141, 675506, 715437, 278759,3660,0,0,0,0,0] 2M 595,591 rcf1422-3 3 5 0 [ 2152, 989946, 1133535, 864393, 9973, 1,0,0,0,0,0] 3M 948,284 Lyra 3 5 1 [ 1045, 817523, 1829157, 2068535, 281917,1823,0,0,0,0,0,0] 5M 1747,253 Pavo 3 5 2 [ 9636, 2088462, 2814534, 1083859, 3506, 3,0,0,0,0,0,0] 6M 1574,847 Sequoia 3 5 3 [ 2457, 848343, 1949899, 2060879, 138384, 38,0,0,0,0,0,0,0] 5M 1676,450 Leo 3 5 4 [16983, 3446984, 4681528, 1854029, 475, 1,0,0,0,0,0,0,0] 10M 4304,278 Calypso 3 5 5 [ 692, 334549, 760094, 865954, 38698, 13,0,0,0,0,0,0,0,0] 2M 561,790 Spin 3 5 6 [ 3283, 353598, 468993, 174068, 57, 1,0,0,0,0,0,0,0,0] 1M 830,374 Noether 3 5 7 [ 300, 166602, 378275, 439732, 15088, 3,0,0,0,0,0,0,0,0,0] 1M 937,580 Noether 4 2 -3 [ 170496, 641122, 647748, 385559, 122930, 28434, 3711] 2M 344,751 rcf1537-8 4 2 -2 [ 129878, 484023, 646252, 469349, 223924, 41485, 5019, 70] 2M 472,105 rcf1537-3 4 2 -1 [ 212728, 727017, 654695, 327949, 71000, 6432, 179, 0] 2M 388,450 rcf1537-8.1 4 2 0 [ 129958, 478656, 636897, 473418, 230462, 45680, 4877, 52,0] 2M 606,928 Praxis.1 4 2 1 [1024697, 3604695, 3344064, 1638229, 364810, 22947, 558, 0,0] 10M 3204,217 Rota 4 2 2 [ 179224, 968224, 1252814, 1032081, 466811, 94145, 6674, 27,0,0] 4M 899,610 Saratoga 4 2 3 [ 293453, 1066534, 1020727, 500687, 113277, 5159, 161, 2,0,0] 3M 1102,166 Crux 4 2 4 [ 386012, 1432709, 1906253, 1433323, 690146, 142785, 8654,118,0,0,0] 6M 1363,165 Harley 4 2 5 [ 531373, 1797593, 1681355, 797746, 184754, 6930, 246, 3,0,0,0] 4M 3383,556 rcf1537-9 4 2 6* [ 55308, 208887, 277791, 204611, 95666, 19746, 983, 8,0,0,0,0] 2M ????? rcf1422-4 4 2 7 [ 205546, 711670, 678900, 325470, 75899, 2403, 110, 2,0,0,0,0] 2M 1683,033 Ananke 4 2 8 [ 63616, 244643, 323381, 236192, 108631, 22582, 951, 4,0,0,0,0,0] 1M 506,625 miln323 4 2 9 [ 114928, 360802, 332964, 153250, 36979, 1033, 44, 0,0,0,0,0,0] 1M 733,938 Mac 4 2 10 [ 62989, 251153, 328313, 232048, 103206, 21524, 765, 2,0,0,0,0,0,0] 1M 833,698 Mac 4 2 11 [ 118077, 360943, 331600, 151308, 37107, 921, 44, 0,0,0,0,0,0,0] 1M 952,272 Mac 4 3 -3 [281664, 1582622, 2643947, 1156437, 333769, 1560, 1,0,0] 6M 1853,885 Calypso 4 3 -2 [122429, 872669, 1976753, 1600977, 391747,34868,556,1,0,0] 5M 1805,163 Noether 4 3 -1 [138332, 651606, 926792, 264599, 18612, 59,0,0,0,0] 2M 839,855 Noether 4 3 0 [ 57087, 384129, 828618, 617110, 111282, 1774,0,0,0,0,0] 2M 735,607 rcf1537-8 4 3 1 [198285, 965282, 1399252, 409419, 27758, 4,0,0,0,0,0] 3M 1116,552 Dorado 4 3 2 [ 88058, 580611, 1235859, 913001, 180889, 1582,0,0,0,0,0,0] 3M 913,936 Isis 4 3 3 [270292, 1308102, 1850450, 540803, 30344, 9,0,0,0,0,0,0] 4M 1415,433 Saratoga 4 3 4 [117790, 791754, 1664048, 1187939, 237126, 1343,0,0,0,0,0,0,0] 4M 1850,551 Pegasus 4 3 5 [265421, 1302627, 1853599, 554834, 23511, 8,0,0,0,0,0,0,0] 4M 3036,829 Ananke 4 3 6 [ 28817, 192692, 412054, 301336, 64820, 281,0,0,0,0,0,0,0,0] 1M 358,322 miln323 4 3 7 [ 69012, 331721, 455855, 138231, 5170, 11,0,0,0,0,0,0,0,0] 1M 664,766 Mac 4 3 8 [ 29167, 198641, 416347, 293438, 62214, 193,0,0,0,0,0,0,0,0,0] 1M 1025,525 Schur 4 3 9 [ 70541, 334935, 451111, 138908, 4495, 10,0,0,0,0,0,0,0,0,0] 1M 817,328 Mac 4 4 -3 [152951, 605477, 642625, 405907, 147517, 38963, 6560, 0,0,0,0] 2M 1125,199 Schubert 4 4 -2 [113947, 421437, 594027, 492904, 272389, 81249,21473,2574,0,0,0,0] 2M 1375,589 Schubert 4 4 -1 [196295, 695397, 651517, 352600, 88994, 14260, 922, 15,0,0,0,0] 2M 1478,749 Schubert 4 4 0 [123624, 472802, 641033, 476939, 233017, 46578, 5923, 84,0,0,0,0,0] 2M 877,540 Schur 4 4 1 [208710, 717796, 654277, 334657, 75820, 8405, 335, 0,0,0,0,0,0] 2M 900,495 Praxis.2 4 4 2 [127497, 473960, 636745, 475835, 232888, 47024, 5993, 58,0,0,0,0,0,0] 2M 910,907 Harley 4 4 3 [101665, 358454, 331523, 166932, 37754, 3558, 114, 0,0,0,0,0,0,0] 1M 339,489 Harley 4 4 4 [127751, 474800, 636789, 476284, 231883, 47232, 5208, 53,0,0,0,0,0,0,0] 2M 1251,677 Fermat 4 4 5 [201573, 715225, 668851, 332823, 75513, 5867, 148, 0,0,0,0,0,0,0,0] 2M 1469,192 Fermat 4 4 6 [ 64034, 237298, 318836, 238496, 115350, 23754, 2209, 23,0,0,0,0,0,0,0,0] 1M 1061,374 Schur 4 4 7 [ 98519, 356563, 337651, 166479, 38272, 2444, 70, 2,0,0,0,0,0,0,0,0] 1M 2286,465 Schubert 5 2 -3 [105822, 235457, 311851, 206855, 104043, 31362, 4389, 220,1] 1M 335,933 Mac 5 2 -2 [ 2544, 327920, 683234, 569529, 296858, 101111, 18188, 613,3,0] 2M 1254,247 Rota 5 2 -1 [207812, 450778, 604720, 420453, 228180, 75300, 12520, 237,0,0] 2M 1294,261 Noether 5 2 0 [ 4564, 332051, 681863, 568982, 295763, 99246, 17330, 201,0,0,0] 2M 720,897 Schur 5 2 1 [318868, 703575, 918828, 619677, 321540, 101223, 16171, 118,0,0,0] 3M 1204,106 Stella 5 2 2 [ 8378, 491807, 1005055, 852872, 456748, 156648, 28305, 187,0,0,0,0] 3M 1345,612 Tuscany 5 2 3 [209570, 457982, 599878, 415995, 226438, 76396, 13702, 39,0,0,0,0] 2M 2608,314 Schur 5 2 4 [ 11972, 503095, 1004678, 845781, 450787, 155312, 28121, 254,0,0,0,0,0] 3M 2015,645 Pegasus 5 2 5 [215591, 483235, 615596, 405564, 205883, 63636, 10461, 34,0,0,0,0,0] 2M 873,988 Harley 5 2 6 [ 12249, 354791, 678418, 555115, 285396, 96523, 17225, 283,0,0,0,0,0,0] 2M 2686,860 Schur 5 2 7 [107095, 240350, 305098, 203649, 104371, 33695, 5736, 6,0,0,0,0,0,0] 1M 354,540 Miln323 5 2 8 [ 6492, 175969, 335045, 276521, 145436, 50832, 9459, 246,0,0,0,0,0,0,0] 1M 406,798 Miln323 5 3 -3 [ 181, 128320, 328423, 335118, 169531, 35829, 2541,57,0,0,0,0] 1M 516,843 Mac 5 3 -2 [ 2835, 281238, 401893, 242956, 67697, 3368, 13, 0,0,0,0,0] 1M 490,156 Schur 5 3 -1 [ 246, 133796, 344547, 343446, 155842, 22037, 86, 0,0,0,0,0,0] 1M 608,204 MAC 5 3 0 [13555, 1367650, 1970303, 1253482, 381797, 13211, 2, 0,0,0,0,0,0] 5M 6640,642 Praxis 5 3 1 [ 608, 395527, 1002663, 1013366, 498124, 89672, 40, 0,0,0,0,0,0,0] 3M 2052,742 Glax 5 3 2 [10861, 815701, 1168629, 761601, 239286, 3921, 1, 0,0,0,0,0,0,0] 3M 2248,828 Harley 5 3 3 [ 846, 399208, 1004529, 1003533, 496912, 94958, 14, 0,0,0,0,0,0,0,0] 3M 2827,752 Tuscany 5 3 4 [24977, 1117323, 1562633, 991385, 301051, 2629, 2, 0,0,0,0,0,0,0,0] 4M 4862,172 Amazon 5 3 5 [ 767, 269052, 674354, 663419, 327804, 64591, 13, 0,0,0,0,0,0,0,0,0] 2M 2408,127 Ananke 5 3 6 [16413, 563978, 775352, 492635, 150654, 968, 0, 0,0,0,0,0,0,0,0,0] 2M 3841,569 Schur 5 3 7 [ 500, 136143, 340007, 329482, 161631, 32231, 6, 0,0,0,0,0,0,0,0,0,0] 1M 3617,689 Noether 6 2 -3 [ 54893, 314421, 366385, 198731, 52269, 11574, 1627, 97, 3,0,0] 1M 187,152 Miln303 6 2 -2 [ 28747, 209506, 310267, 274921, 130813, 35351, 9251,1089, 55,0,0,0] 1M 610,057 MAC 6 2 -1 [ 48306, 313592, 374450, 200074, 51304, 10806, 1401, 64, 3,0,0,0] 1M 680,947 MAC 6 2 0 [ 28666, 207831, 307067, 279981, 131185, 35520, 8719, 985, 46,0,0,0,0] 1M 928,829 Schur 6 2 1 [117508, 647472, 738639, 381137, 94264, 18592, 2307, 77, 4,0,0,0,0] 2M 894,970 Harley 6 2 2 [ 28527, 208356, 307161, 281786, 130141, 34872, 8263, 857, 37,0,0,0,0,0] 1M 796,160 Calypso 6 2 3 [ 95557, 629886, 756021, 397357, 98707, 20048, 2331, 89, 4,0,0,0,0,0] 2M 1282,728 Spin 6 2 4 [ 56617, 418800, 617076, 564995, 256553, 68616,15744,1540, 59,0,0,0,0,0,0] 2M 1486,717 Spin 6 2 5 [ 98718, 631297, 756160, 394293, 97788, 19470, 2205, 67, 2,0,0,0,0,0,0] 2M 1576,712 Spin 6 2 6 [ 27425, 208376, 308049, 283724, 129464, 34395, 7797, 739, 31,0,0,0,0,0,0,0] 1M 626,804 miln303 6 2 7 [ 98085, 627024, 758488, 396394, 98305, 19537, 2113, 53, 0,1,0,0,0,0,0,0] 2M 1458,375 miln303 6 2 8 [ 27148, 209557, 309775, 283528, 127922, 33888, 7463, 689, 30,0,0,0,0,0,0,0,0] 1M 848,876 miln303 6 3 -3 [19678, 267496, 496571, 182025, 31313, 2855, 61,1,0,0,0,0,0,0] 1M 263,991 miln323 6 3 -2 [10023, 112771, 434203, 339575, 91857,11023, 545,3,0,0,0,0,0,0,0] 1M 289,134 miln323 6 3 -1 [19682, 269562, 495895, 181607, 30639, 2561, 54,0,0,0,0,0,0,0,0] 1M 386,914 miln303 6 3 0 [19916, 203398, 887246, 686605,180343,21448,1044,0,0,0,0,0,0,0,0,0] 2M 861,777 miln303 6 3 1 [40694, 535645, 991143, 366572, 61143, 4721, 82,0,0,0,0,0,0,0,0,0] 2M 3296,223 Fermat 6 3 2 [19955, 197497, 900511, 687564,174320,19274, 879,0,0,0,0,0,0,0,0,0,0] 2M 1961,403 Harley 6 3 3 [41043, 532048, 989722, 368871, 63514, 4766, 36,0,0,0,0,0,0,0,0,0,0] 2M 5604,414 Phoebe 6 3 4 [19695, 186843, 905515, 696337,172174,18619, 817,0,0,0,0,0,0,0,0,0,0,0] 2M 1379,707 miln303 6 3 5 [21022, 267515, 493070, 184089, 31850, 2437, 17,0,0,0,0,0,0,0,0,0,0,0] 1M 666,317 miln323 6 3 6 [ 9732, 92106, 455186, 349719, 84194, 8713, 350,0,0,0,0,0,0,0,0,0,0,0,0] 1M 759,597 miln323 6 3 7 [21819, 269695, 490478, 183456, 32092, 2452, 8,0,0,0,0,0,0,0,0,0,0,0,0] 1M 864,251 miln323 sum(data[i],i=1..nops(data))/1000;