This is the list of MLq(K)=3, with the first rig Alexander quandle that gives the value 3, excluding the knots without such Alexander quandles. Knot[ 32] = 8_18: Q[ 1] = C[ 3, 1] Knot[ 70] = 9_35: Q[ 1] = C[ 3, 1] Knot[ 72] = 9_37: Q[ 1] = C[ 3, 1] Knot[ 75] = 9_40: Q[ 2] = C[ 4, 1] Knot[ 76] = 9_41: Q[ 8] = C[ 7, 1] Knot[ 81] = 9_46: Q[ 1] = C[ 3, 1] Knot[ 82] = 9_47: Q[ 1] = C[ 3, 1] Knot[ 83] = 9_48: Q[ 1] = C[ 3, 1] Knot[ 84] = 9_49: Q[ 3] = C[ 5, 1] Knot[145] = 10_61: Q[ 2] = C[ 4, 1] Knot[147] = 10_63: Q[ 2] = C[ 4, 1] Knot[149] = 10_65: Q[ 2] = C[ 4, 1] Knot[158] = 10_74: Q[ 1] = C[ 3, 1] Knot[159] = 10_75: Q[ 1] = C[ 3, 1] Knot[182] = 10_98: Q[ 1] = C[ 3, 1] Knot[183] = 10_99: Q[ 1] = C[ 3, 1] Knot[187] = 10_103: Q[ 3] = C[ 5, 1] Knot[199] = 10_115: Q[ 2] = C[ 4, 1] Knot[206] = 10_122: Q[ 18] = C[ 9, 3] Knot[207] = 10_123: Q[ 22] = C[ 9, 7] Knot[224] = 10_140: Q[ 2] = C[ 4, 1] Knot[226] = 10_142: Q[ 2] = C[ 4, 1] Knot[228] = 10_144: Q[ 2] = C[ 4, 1] Knot[239] = 10_155: Q[ 3] = C[ 5, 1] Knot[241] = 10_157: Q[ 8] = C[ 7, 1] Knot[247] = 10_163: Q[ 2] = C[ 4, 1] Knot[336] = 11a_87: Q[ 2] = C[ 4, 1] Knot[346] = 11a_97: Q[ 2] = C[ 4, 1] Knot[356] = 11a_107: Q[ 2] = C[ 4, 1] Knot[372] = 11a_123: Q[ 1] = C[ 3, 1] Knot[381] = 11a_132: Q[ 2] = C[ 4, 1] Knot[382] = 11a_133: Q[ 2] = C[ 4, 1] Knot[384] = 11a_135: Q[ 1] = C[ 3, 1] Knot[392] = 11a_143: Q[ 2] = C[ 4, 1] Knot[404] = 11a_155: Q[ 1] = C[ 3, 1] Knot[406] = 11a_157: Q[ 2] = C[ 4, 1] Knot[414] = 11a_165: Q[ 2] = C[ 4, 1] Knot[422] = 11a_173: Q[ 1] = C[ 3, 1] Knot[430] = 11a_181: Q[ 1] = C[ 3, 1] Knot[445] = 11a_196: Q[ 8] = C[ 7, 1] Knot[488] = 11a_239: Q[ 18] = C[ 9, 3] Knot[498] = 11a_249: Q[ 1] = C[ 3, 1] Knot[526] = 11a_277: Q[ 1] = C[ 3, 1] Knot[540] = 11a_291: Q[ 1] = C[ 3, 1] Knot[542] = 11a_293: Q[ 1] = C[ 3, 1] Knot[546] = 11a_297: Q[ 2] = C[ 4, 1] Knot[563] = 11a_314: Q[ 1] = C[ 3, 1] Knot[566] = 11a_317: Q[ 3] = C[ 5, 1] Knot[570] = 11a_321: Q[ 25] = C[11, 1] Knot[571] = 11a_322: Q[ 2] = C[ 4, 1] Knot[578] = 11a_329: Q[ 2] = C[ 4, 1] Knot[581] = 11a_332: Q[ 1] = C[ 3, 1] Knot[589] = 11a_340: Q[ 2] = C[ 4, 1] Knot[596] = 11a_347: Q[ 2] = C[ 4, 1] Knot[601] = 11a_352: Q[ 1] = C[ 3, 1] Knot[603] = 11a_354: Q[ 2] = C[ 4, 1] Knot[615] = 11a_366: Q[ 1] = C[ 3, 1] Knot[665] = 11n_49: Q[ 2] = C[ 4, 1] Knot[699] = 11n_83: Q[ 2] = C[ 4, 1] Knot[706] = 11n_90: Q[ 2] = C[ 4, 1] Knot[707] = 11n_91: Q[ 2] = C[ 4, 1] Knot[742] = 11n_126: Q[ 1] = C[ 3, 1] Knot[749] = 11n_133: Q[ 3] = C[ 5, 1] Knot[764] = 11n_148: Q[ 3] = C[ 5, 1] Knot[773] = 11n_157: Q[ 18] = C[ 9, 3] Knot[778] = 11n_162: Q[ 2] = C[ 4, 1] Knot[780] = 11n_164: Q[ 1] = C[ 3, 1] Knot[781] = 11n_165: Q[ 2] = C[ 4, 1] Knot[783] = 11n_167: Q[ 1] = C[ 3, 1] Knot[791] = 11n_175: Q[ 2] = C[ 4, 1] Knot[799] = 11n_183: Q[ 2] = C[ 4, 1] Knot[801] = 11n_185: Q[ 18] = C[ 9, 3] Knot[901] = 12a_0100: Q[ 3] = C[ 5, 1] Knot[978] = 12a_0177: Q[ 1] = C[ 3, 1] Knot[1016] = 12a_0215: Q[ 18] = C[ 9, 3] Knot[1017] = 12a_0216: Q[ 18] = C[ 9, 3] Knot[1019] = 12a_0218: Q[ 2] = C[ 4, 1] Knot[1045] = 12a_0244: Q[ 1] = C[ 3, 1] Knot[1046] = 12a_0245: Q[ 1] = C[ 3, 1] Knot[1049] = 12a_0248: Q[ 2] = C[ 4, 1] Knot[1050] = 12a_0249: Q[ 2] = C[ 4, 1] Knot[1054] = 12a_0253: Q[ 2] = C[ 4, 1] Knot[1066] = 12a_0265: Q[ 1] = C[ 3, 1] Knot[1071] = 12a_0270: Q[ 1] = C[ 3, 1] Knot[1080] = 12a_0279: Q[ 2] = C[ 4, 1] Knot[1092] = 12a_0291: Q[ 2] = C[ 4, 1] Knot[1096] = 12a_0295: Q[ 1] = C[ 3, 1] Knot[1098] = 12a_0297: Q[ 1] = C[ 3, 1] Knot[1099] = 12a_0298: Q[ 1] = C[ 3, 1] Knot[1112] = 12a_0311: Q[ 1] = C[ 3, 1] Knot[1113] = 12a_0312: Q[ 2] = C[ 4, 1] Knot[1128] = 12a_0327: Q[ 3] = C[ 5, 1] Knot[1133] = 12a_0332: Q[ 1] = C[ 3, 1] Knot[1148] = 12a_0347: Q[ 2] = C[ 4, 1] Knot[1149] = 12a_0348: Q[ 2] = C[ 4, 1] Knot[1177] = 12a_0376: Q[ 2] = C[ 4, 1] Knot[1182] = 12a_0381: Q[ 18] = C[ 9, 3] Knot[1187] = 12a_0386: Q[ 1] = C[ 3, 1] Knot[1197] = 12a_0396: Q[ 1] = C[ 3, 1] Knot[1209] = 12a_0408: Q[ 18] = C[ 9, 3] Knot[1214] = 12a_0413: Q[ 1] = C[ 3, 1] Knot[1228] = 12a_0427: Q[ 1] = C[ 3, 1] Knot[1230] = 12a_0429: Q[ 2] = C[ 4, 1] Knot[1234] = 12a_0433: Q[ 1] = C[ 3, 1] Knot[1236] = 12a_0435: Q[ 1] = C[ 3, 1] Knot[1245] = 12a_0444: Q[ 2] = C[ 4, 1] Knot[1249] = 12a_0448: Q[ 2] = C[ 4, 1] Knot[1266] = 12a_0465: Q[ 2] = C[ 4, 1] Knot[1267] = 12a_0466: Q[ 2] = C[ 4, 1] Knot[1276] = 12a_0475: Q[ 2] = C[ 4, 1] Knot[1282] = 12a_0481: Q[ 2] = C[ 4, 1] Knot[1294] = 12a_0493: Q[ 1] = C[ 3, 1] Knot[1295] = 12a_0494: Q[ 2] = C[ 4, 1] Knot[1304] = 12a_0503: Q[ 1] = C[ 3, 1] Knot[1362] = 12a_0561: Q[ 3] = C[ 5, 1] Knot[1364] = 12a_0563: Q[ 1] = C[ 3, 1] Knot[1370] = 12a_0569: Q[ 1] = C[ 3, 1] Knot[1375] = 12a_0574: Q[ 1] = C[ 3, 1] Knot[1377] = 12a_0576: Q[ 1] = C[ 3, 1] Knot[1395] = 12a_0594: Q[ 1] = C[ 3, 1] Knot[1416] = 12a_0615: Q[ 1] = C[ 3, 1] Knot[1435] = 12a_0634: Q[ 1] = C[ 3, 1] Knot[1448] = 12a_0647: Q[ 1] = C[ 3, 1] Knot[1465] = 12a_0664: Q[ 54] = C[13,11] Knot[1480] = 12a_0679: Q[ 1] = C[ 3, 1] Knot[1484] = 12a_0683: Q[ 1] = C[ 3, 1] Knot[1502] = 12a_0701: Q[ 1] = C[ 3, 1] Knot[1504] = 12a_0703: Q[ 2] = C[ 4, 1] Knot[1513] = 12a_0712: Q[ 1] = C[ 3, 1] Knot[1526] = 12a_0725: Q[ 1] = C[ 3, 1] Knot[1543] = 12a_0742: Q[ 1] = C[ 3, 1] Knot[1570] = 12a_0769: Q[ 1] = C[ 3, 1] Knot[1581] = 12a_0780: Q[ 3] = C[ 5, 1] Knot[1588] = 12a_0787: Q[ 1] = C[ 3, 1] Knot[1607] = 12a_0806: Q[ 2] = C[ 4, 1] Knot[1609] = 12a_0808: Q[ 2] = C[ 4, 1] Knot[1611] = 12a_0810: Q[ 1] = C[ 3, 1] Knot[1669] = 12a_0868: Q[ 64] = C[16, 3] Knot[1674] = 12a_0873: Q[ 1] = C[ 3, 1] Knot[1687] = 12a_0886: Q[ 1] = C[ 3, 1] Knot[1696] = 12a_0895: Q[ 1] = C[ 3, 1] Knot[1705] = 12a_0904: Q[ 2] = C[ 4, 1] Knot[1706] = 12a_0905: Q[ 1] = C[ 3, 1] Knot[1707] = 12a_0906: Q[ 8] = C[ 7, 1] Knot[1708] = 12a_0907: Q[ 3] = C[ 5, 1] Knot[1722] = 12a_0921: Q[ 3] = C[ 5, 1] Knot[1742] = 12a_0941: Q[ 2] = C[ 4, 1] Knot[1750] = 12a_0949: Q[ 2] = C[ 4, 1] Knot[1761] = 12a_0960: Q[ 2] = C[ 4, 1] Knot[1771] = 12a_0970: Q[ 2] = C[ 4, 1] Knot[1774] = 12a_0973: Q[ 1] = C[ 3, 1] Knot[1776] = 12a_0975: Q[ 3] = C[ 5, 1] Knot[1788] = 12a_0987: Q[ 1] = C[ 3, 1] Knot[1791] = 12a_0990: Q[ 1] = C[ 3, 1] Knot[1820] = 12a_1019: Q[ 4] = C[ 5, 2] Knot[1823] = 12a_1022: Q[ 1] = C[ 3, 1] Knot[1827] = 12a_1026: Q[ 2] = C[ 4, 1] Knot[1854] = 12a_1053: Q[ 18] = C[ 9, 3] Knot[1880] = 12a_1079: Q[ 2] = C[ 4, 1] Knot[1893] = 12a_1092: Q[ 1] = C[ 3, 1] Knot[1894] = 12a_1093: Q[ 1] = C[ 3, 1] Knot[1898] = 12a_1097: Q[ 18] = C[ 9, 3] Knot[1903] = 12a_1102: Q[ 2] = C[ 4, 1] Knot[1906] = 12a_1105: Q[ 2] = C[ 4, 1] Knot[1924] = 12a_1123: Q[ 1] = C[ 3, 1] Knot[1925] = 12a_1124: Q[ 2] = C[ 4, 1] Knot[1943] = 12a_1142: Q[ 1] = C[ 3, 1] Knot[1953] = 12a_1152: Q[ 2] = C[ 4, 1] Knot[1965] = 12a_1164: Q[ 2] = C[ 4, 1] Knot[1968] = 12a_1167: Q[ 64] = C[16, 3] Knot[1982] = 12a_1181: Q[ 1] = C[ 3, 1] Knot[1984] = 12a_1183: Q[ 25] = C[11, 1] Knot[1995] = 12a_1194: Q[ 3] = C[ 5, 1] Knot[2003] = 12a_1202: Q[ 2] = C[ 4, 1] Knot[2006] = 12a_1205: Q[ 2] = C[ 4, 1] Knot[2007] = 12a_1206: Q[ 8] = C[ 7, 1] Knot[2026] = 12a_1225: Q[ 1] = C[ 3, 1] Knot[2030] = 12a_1229: Q[ 64] = C[16, 3] Knot[2052] = 12a_1251: Q[ 2] = C[ 4, 1] Knot[2061] = 12a_1260: Q[ 1] = C[ 3, 1] Knot[2070] = 12a_1269: Q[ 2] = C[ 4, 1] Knot[2081] = 12a_1280: Q[ 18] = C[ 9, 3] Knot[2084] = 12a_1283: Q[ 1] = C[ 3, 1] Knot[2087] = 12a_1286: Q[ 1] = C[ 3, 1] Knot[2089] = 12a_1288: Q[ 1] = C[ 3, 1] Knot[2233] = 12n_0144: Q[ 18] = C[ 9, 3] Knot[2234] = 12n_0145: Q[ 2] = C[ 4, 1] Knot[2236] = 12n_0147: Q[ 3] = C[ 5, 1] Knot[2346] = 12n_0257: Q[ 3] = C[ 5, 1] Knot[2357] = 12n_0268: Q[ 1] = C[ 3, 1] Knot[2358] = 12n_0269: Q[ 1] = C[ 3, 1] Knot[2359] = 12n_0270: Q[ 1] = C[ 3, 1] Knot[2362] = 12n_0273: Q[ 18] = C[ 9, 3] Knot[2363] = 12n_0274: Q[ 2] = C[ 4, 1] Knot[2365] = 12n_0276: Q[ 3] = C[ 5, 1] Knot[2383] = 12n_0294: Q[ 18] = C[ 9, 3] Knot[2386] = 12n_0297: Q[ 2] = C[ 4, 1] Knot[2421] = 12n_0332: Q[ 1] = C[ 3, 1] Knot[2422] = 12n_0333: Q[ 1] = C[ 3, 1] Knot[2423] = 12n_0334: Q[ 1] = C[ 3, 1] Knot[2444] = 12n_0355: Q[ 2] = C[ 4, 1] Knot[2445] = 12n_0356: Q[ 2] = C[ 4, 1] Knot[2446] = 12n_0357: Q[ 2] = C[ 4, 1] Knot[2468] = 12n_0379: Q[ 1] = C[ 3, 1] Knot[2469] = 12n_0380: Q[ 1] = C[ 3, 1] Knot[2475] = 12n_0386: Q[ 1] = C[ 3, 1] Knot[2476] = 12n_0387: Q[ 1] = C[ 3, 1] Knot[2477] = 12n_0388: Q[ 1] = C[ 3, 1] Knot[2478] = 12n_0389: Q[ 1] = C[ 3, 1] Knot[2482] = 12n_0393: Q[ 2] = C[ 4, 1] Knot[2483] = 12n_0394: Q[ 2] = C[ 4, 1] Knot[2486] = 12n_0397: Q[ 8] = C[ 7, 1] Knot[2491] = 12n_0402: Q[ 1] = C[ 3, 1] Knot[2492] = 12n_0403: Q[ 1] = C[ 3, 1] Knot[2503] = 12n_0414: Q[ 3] = C[ 5, 1] Knot[2509] = 12n_0420: Q[ 1] = C[ 3, 1] Knot[2525] = 12n_0436: Q[ 2] = C[ 4, 1] Knot[2529] = 12n_0440: Q[ 1] = C[ 3, 1] Knot[2531] = 12n_0442: Q[ 2] = C[ 4, 1] Knot[2549] = 12n_0460: Q[ 1] = C[ 3, 1] Knot[2551] = 12n_0462: Q[ 2] = C[ 4, 1] Knot[2569] = 12n_0480: Q[ 1] = C[ 3, 1] Knot[2583] = 12n_0494: Q[ 1] = C[ 3, 1] Knot[2584] = 12n_0495: Q[ 1] = C[ 3, 1] Knot[2585] = 12n_0496: Q[ 1] = C[ 3, 1] Knot[2587] = 12n_0498: Q[ 2] = C[ 4, 1] Knot[2594] = 12n_0505: Q[ 1] = C[ 3, 1] Knot[2597] = 12n_0508: Q[ 1] = C[ 3, 1] Knot[2598] = 12n_0509: Q[ 8] = C[ 7, 1] Knot[2599] = 12n_0510: Q[ 25] = C[11, 1] Knot[2607] = 12n_0518: Q[ 1] = C[ 3, 1] Knot[2615] = 12n_0526: Q[ 18] = C[ 9, 3] Knot[2622] = 12n_0533: Q[ 2] = C[ 4, 1] Knot[2635] = 12n_0546: Q[ 1] = C[ 3, 1] Knot[2638] = 12n_0549: Q[ 1] = C[ 3, 1] Knot[2654] = 12n_0565: Q[ 1] = C[ 3, 1] Knot[2656] = 12n_0567: Q[ 1] = C[ 3, 1] Knot[2659] = 12n_0570: Q[ 1] = C[ 3, 1] Knot[2660] = 12n_0571: Q[ 1] = C[ 3, 1] Knot[2663] = 12n_0574: Q[ 1] = C[ 3, 1] Knot[2670] = 12n_0581: Q[ 1] = C[ 3, 1] Knot[2671] = 12n_0582: Q[ 1] = C[ 3, 1] Knot[2672] = 12n_0583: Q[ 1] = C[ 3, 1] Knot[2681] = 12n_0592: Q[ 8] = C[ 7, 1] Knot[2687] = 12n_0598: Q[ 1] = C[ 3, 1] Knot[2689] = 12n_0600: Q[ 1] = C[ 3, 1] Knot[2690] = 12n_0601: Q[ 1] = C[ 3, 1] Knot[2691] = 12n_0602: Q[ 1] = C[ 3, 1] Knot[2693] = 12n_0604: Q[ 1] = C[ 3, 1] Knot[2694] = 12n_0605: Q[ 1] = C[ 3, 1] Knot[2700] = 12n_0611: Q[ 3] = C[ 5, 1] Knot[2706] = 12n_0617: Q[ 2] = C[ 4, 1] Knot[2711] = 12n_0622: Q[ 1] = C[ 3, 1] Knot[2715] = 12n_0626: Q[ 1] = C[ 3, 1] Knot[2719] = 12n_0630: Q[ 18] = C[ 9, 3] Knot[2725] = 12n_0636: Q[ 1] = C[ 3, 1] Knot[2726] = 12n_0637: Q[ 1] = C[ 3, 1] Knot[2732] = 12n_0643: Q[ 8] = C[ 7, 1] Knot[2740] = 12n_0651: Q[199] = C[25, 3] Knot[2741] = 12n_0652: Q[ 18] = C[ 9, 3] Knot[2743] = 12n_0654: Q[ 1] = C[ 3, 1] Knot[2749] = 12n_0660: Q[ 2] = C[ 4, 1] Knot[2755] = 12n_0666: Q[ 1] = C[ 3, 1] Knot[2758] = 12n_0669: Q[ 1] = C[ 3, 1] Knot[2790] = 12n_0701: Q[ 1] = C[ 3, 1] Knot[2795] = 12n_0706: Q[ 2] = C[ 4, 1] Knot[2803] = 12n_0714: Q[ 18] = C[ 9, 3] Knot[2806] = 12n_0717: Q[ 18] = C[ 9, 3] Knot[2826] = 12n_0737: Q[ 1] = C[ 3, 1] Knot[2831] = 12n_0742: Q[ 18] = C[ 9, 3] Knot[2834] = 12n_0745: Q[ 3] = C[ 5, 1] Knot[2835] = 12n_0746: Q[199] = C[25, 3] Knot[2841] = 12n_0752: Q[ 2] = C[ 4, 1] Knot[2845] = 12n_0756: Q[ 1] = C[ 3, 1] Knot[2846] = 12n_0757: Q[ 2] = C[ 4, 1] Knot[2849] = 12n_0760: Q[ 3] = C[ 5, 1] Knot[2853] = 12n_0764: Q[ 18] = C[ 9, 3] Knot[2868] = 12n_0779: Q[ 2] = C[ 4, 1] Knot[2870] = 12n_0781: Q[199] = C[25, 3] Knot[2887] = 12n_0798: Q[ 2] = C[ 4, 1] Knot[2895] = 12n_0806: Q[ 1] = C[ 3, 1] Knot[2902] = 12n_0813: Q[ 1] = C[ 3, 1] Knot[2906] = 12n_0817: Q[ 8] = C[ 7, 1] Knot[2926] = 12n_0837: Q[ 54] = C[13,11] Knot[2927] = 12n_0838: Q[ 2] = C[ 4, 1] Knot[2928] = 12n_0839: Q[ 25] = C[11, 1] Knot[2929] = 12n_0840: Q[ 2] = C[ 4, 1] Knot[2932] = 12n_0843: Q[ 8] = C[ 7, 1] Knot[2933] = 12n_0844: Q[ 3] = C[ 5, 1] Knot[2935] = 12n_0846: Q[ 1] = C[ 3, 1] Knot[2936] = 12n_0847: Q[ 2] = C[ 4, 1] Knot[2958] = 12n_0869: Q[ 1] = C[ 3, 1] Knot[2962] = 12n_0873: Q[ 2] = C[ 4, 1] Knot[2963] = 12n_0874: Q[ 2] = C[ 4, 1] Knot[2965] = 12n_0876: Q[ 1] = C[ 3, 1] Knot[2966] = 12n_0877: Q[ 2] = C[ 4, 1] Knot[2967] = 12n_0878: Q[ 2] = C[ 4, 1] Knot[2968] = 12n_0879: Q[ 64] = C[16, 3] Knot[2970] = 12n_0881: Q[ 2] = C[ 4, 1] Knot[2972] = 12n_0883: Q[ 1] = C[ 3, 1] Knot[2976] = 12n_0887: Q[ 3] = C[ 5, 1] Knot[2977] = 12n_0888: Q[ 1] = C[ 3, 1]