#index_first index_last length frequency knotoid_type polynomial 0 104 105 0.5 k0.1 + 1 0 103 104 0.55 k0.1 + 1 0 102 103 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 103 103 0.45 k1.1 - A^(-4) - A^(-2)*v 0 104 105 0.5 k0.1 + 1 1 104 104 0.5 k0.1 + 1 1 103 103 0.45 k1.1 - A^(-4) - A^(-2)*v 2 104 103 0.45 k0.1 + 1 2 103 102 0.4 k1.1 - A^(-4) - A^(-2)*v 3 104 102 0.45 k0.1 + 1 3 103 101 0.5 k1.1 - A^(-4) - A^(-2)*v 4 104 101 0.75 k0.1 + 1 4 103 100 0.7 k0.1 + 1 3 103 101 0.5 k1.1 - A^(-4) - A^(-2)*v 4 102 99 0.6 k1.1 - A^(-4) - A^(-2)*v 5 103 99 0.65 k0.1 + 1 5 102 98 0.55 k0.1 + 1 4 102 99 0.6 k1.1 - A^(-4) - A^(-2)*v 5 101 97 0.7 k0.1 + 1 4 101 98 0.45 k0.1 + 1 4 102 99 0.6 k1.1 - A^(-4) - A^(-2)*v 3 101 99 0.3 k1.1 - A^(-4) - A^(-2)*v 4 100 97 0.4 k1.1 - A^(-4) - A^(-2)*v 5 101 97 0.7 k0.1 + 1 5 100 96 0.5 k1.1 - A^(-4) - A^(-2)*v 6 101 96 0.4 k1.1 - A^(-4) - A^(-2)*v 5 102 98 0.55 k0.1 + 1 6 102 97 0.7 k0.1 + 1 6 101 96 0.4 k1.1 - A^(-4) - A^(-2)*v 7 102 96 0.5 k0.1 + 1 7 101 95 0.5 k0.1 + 1 6 101 96 0.4 k1.1 - A^(-4) - A^(-2)*v 7 100 94 0.45 k0.1 + 1 6 100 95 0.35 k0.1 + 1 6 101 96 0.4 k1.1 - A^(-4) - A^(-2)*v 5 100 96 0.5 k1.1 - A^(-4) - A^(-2)*v 6 99 94 0.45 k0.1 + 1 5 99 95 0.4 k1.1 - A^(-4) - A^(-2)*v 6 98 93 0.65 k0.1 + 1 5 98 94 0.35 k0.1 + 1 5 99 95 0.4 k1.1 - A^(-4) - A^(-2)*v 4 98 95 0.3 k0.1 + 1 4 99 96 0.5 k1.1 - A^(-4) - A^(-2)*v 3 98 96 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 97 94 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 98 94 0.35 k0.1 + 1 5 97 93 0.55 k0.1 + 1 4 97 94 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 96 92 0.65 k0.1 + 1 4 96 93 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 95 91 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 96 91 0.65 k0.1 + 1 6 95 90 0.6 k0.1 + 1 5 95 91 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 94 89 0.7 k0.1 + 1 5 94 90 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 93 88 0.45 k0.1 + 1 5 93 89 0.5 k0.1 + 1 5 94 90 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 93 90 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 92 88 0.4 k0.1 + 1 4 92 89 0.4 k0.1 + 1 4 93 90 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 92 90 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 91 88 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 92 88 0.4 k0.1 + 1 5 91 87 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 92 87 0.7 k0.1 + 1 6 91 86 0.55 k0.1 + 1 5 91 87 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 90 85 0.55 k0.1 + 1 5 90 86 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 89 84 0.7 k0.1 + 1 5 89 85 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 88 83 0.55 k0.1 + 1 5 88 84 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 87 82 0.55 k0.1 + 1 5 87 83 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 86 81 0.55 k0.1 + 1 5 86 82 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 85 80 0.45 k0.1 + 1 5 85 81 0.45 k0.1 + 1 5 86 82 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 85 82 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 84 80 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 85 80 0.45 k0.1 + 1 6 84 79 0.6 k0.1 + 1 5 84 80 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 83 78 0.45 k0.1 + 1 5 83 79 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 82 77 0.5 k0.1 + 1 5 82 78 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 81 76 0.55 k0.1 + 1 5 81 77 0.3 k1.1 - A^(-4) - A^(-2)*v 6 80 75 0.55 k0.1 + 1 5 80 76 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 79 74 0.35 k1.1 - A^(-4) - A^(-2)*v 7 80 74 0.65 k0.1 + 1 7 79 73 0.6 k0.1 + 1 6 79 74 0.35 k1.1 - A^(-4) - A^(-2)*v 7 78 72 0.6 k0.1 + 1 6 78 73 0.75 k0.1 + 1 6 79 74 0.35 k1.1 - A^(-4) - A^(-2)*v 5 78 74 0.4 k1.1 - A^(-4) - A^(-2)*v 6 77 72 0.6 k0.1 + 1 5 77 73 0.5 k0.1 + 1 5 78 74 0.4 k1.1 - A^(-4) - A^(-2)*v 4 77 74 0.4 k1.1 - A^(-4) - A^(-2)*v 5 76 72 0.55 k0.1 + 1 4 76 73 0.55 k0.1 + 1 4 77 74 0.4 k1.1 - A^(-4) - A^(-2)*v 3 76 74 0.65 k1.1 - A^(-4) - A^(-2)*v 4 75 72 0.55 k0.1 + 1 3 75 73 0.6 k0.1 + 1 3 76 74 0.65 k1.1 - A^(-4) - A^(-2)*v 2 75 74 0.35 k1.1 - A^(-4) - A^(-2)*v 3 74 72 0.6 k0.1 + 1 2 74 73 0.5 k0.1 + 1 2 75 74 0.35 k1.1 - A^(-4) - A^(-2)*v 1 74 74 0.5 k0.1 + 1 1 75 75 0.5 k0.1 + 1 2 75 74 0.35 k1.1 - A^(-4) - A^(-2)*v 1 76 76 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 75 76 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 74 74 0.5 k0.1 + 1 0 74 75 0.55 k0.1 + 1 0 75 76 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 73 74 0.4 k0.1 + 1 0 72 73 0.8 k0.1 + 1 0 71 72 0.75 k0.1 + 1 0 70 71 0.75 k0.1 + 1 0 69 70 0.65 k0.1 + 1 0 68 69 0.85 k0.1 + 1 0 67 68 0.8 k0.1 + 1 0 66 67 0.75 k0.1 + 1 0 65 66 0.95 k0.1 + 1 0 64 65 0.95 k0.1 + 1 0 63 64 1 k0.1 + 1 0 62 63 0.95 k0.1 + 1 0 61 62 0.95 k0.1 + 1 0 60 61 0.95 k0.1 + 1 0 59 60 1 k0.1 + 1 0 58 59 0.9 k0.1 + 1 0 57 58 0.95 k0.1 + 1 0 56 57 1 k0.1 + 1 0 55 56 0.9 k0.1 + 1 0 54 55 1 k0.1 + 1 0 53 54 1 k0.1 + 1 0 52 53 1 k0.1 + 1 0 51 52 0.95 k0.1 + 1 0 50 51 1 k0.1 + 1 0 49 50 1 k0.1 + 1 0 48 49 1 k0.1 + 1 0 47 48 1 k0.1 + 1 0 46 47 1 k0.1 + 1 0 45 46 1 k0.1 + 1 0 44 45 0.9 k0.1 + 1 0 43 44 0.9 k0.1 + 1 0 42 43 0.95 k0.1 + 1 0 41 42 1 k0.1 + 1 0 40 41 0.95 k0.1 + 1 0 39 40 1 k0.1 + 1 0 38 39 1 k0.1 + 1 0 37 38 0.9 k0.1 + 1 0 36 37 0.9 k0.1 + 1 0 35 36 1 k0.1 + 1 0 34 35 1 k0.1 + 1 0 33 34 1 k0.1 + 1 0 32 33 1 k0.1 + 1 0 31 32 1 k0.1 + 1 0 30 31 1 k0.1 + 1 0 29 30 1 k0.1 + 1 0 28 29 1 k0.1 + 1 0 27 28 1 k0.1 + 1 0 26 27 1 k0.1 + 1 0 25 26 1 k0.1 + 1 0 24 25 1 k0.1 + 1 0 23 24 1 k0.1 + 1 0 22 23 1 k0.1 + 1 0 21 22 1 k0.1 + 1 0 20 21 1 k0.1 + 1 0 19 20 1 k0.1 + 1 0 18 19 1 k0.1 + 1 0 17 18 1 k0.1 + 1 0 16 17 1 k0.1 + 1 0 15 16 1 k0.1 + 1 0 14 15 1 k0.1 + 1 0 13 14 1 k0.1 + 1 0 12 13 1 k0.1 + 1 0 11 12 1 k0.1 + 1 0 10 11 1 k0.1 + 1 0 9 10 1 k0.1 + 1 0 8 9 1 k0.1 + 1 0 7 8 1 k0.1 + 1 0 6 7 1 k0.1 + 1 0 5 6 1 k0.1 + 1 0 4 5 1 k0.1 + 1 0 3 4 1 k0.1 + 1 0 2 3 1 k0.1 + 1 0 1 2 1 k0.1 + 1 0 2 3 1 k0.1 + 1 1 2 2 1 k0.1 + 1 1 3 3 1 k0.1 + 1 2 3 2 1 k0.1 + 1 2 4 3 1 k0.1 + 1 3 4 2 1 k0.1 + 1 3 5 3 1 k0.1 + 1 4 5 2 1 k0.1 + 1 4 6 3 1 k0.1 + 1 5 6 2 1 k0.1 + 1 5 7 3 1 k0.1 + 1 6 7 2 1 k0.1 + 1 6 8 3 1 k0.1 + 1 7 8 2 1 k0.1 + 1 7 9 3 1 k0.1 + 1 8 9 2 1 k0.1 + 1 8 10 3 1 k0.1 + 1 9 10 2 1 k0.1 + 1 9 11 3 1 k0.1 + 1 10 11 2 1 k0.1 + 1 10 12 3 1 k0.1 + 1 11 12 2 1 k0.1 + 1 11 13 3 1 k0.1 + 1 12 13 2 1 k0.1 + 1 12 14 3 1 k0.1 + 1 13 14 2 1 k0.1 + 1 13 15 3 1 k0.1 + 1 14 15 2 1 k0.1 + 1 14 16 3 1 k0.1 + 1 15 16 2 1 k0.1 + 1 15 17 3 1 k0.1 + 1 16 17 2 1 k0.1 + 1 16 18 3 1 k0.1 + 1 17 18 2 1 k0.1 + 1 17 19 3 1 k0.1 + 1 18 19 2 1 k0.1 + 1 18 20 3 1 k0.1 + 1 19 20 2 1 k0.1 + 1 19 21 3 1 k0.1 + 1 20 21 2 1 k0.1 + 1 20 22 3 1 k0.1 + 1 21 22 2 1 k0.1 + 1 21 23 3 1 k0.1 + 1 22 23 2 1 k0.1 + 1 22 24 3 1 k0.1 + 1 23 24 2 1 k0.1 + 1 23 25 3 1 k0.1 + 1 24 25 2 1 k0.1 + 1 24 26 3 1 k0.1 + 1 25 26 2 1 k0.1 + 1 25 27 3 1 k0.1 + 1 26 27 2 1 k0.1 + 1 26 28 3 1 k0.1 + 1 27 28 2 1 k0.1 + 1 27 29 3 1 k0.1 + 1 28 29 2 1 k0.1 + 1 28 30 3 1 k0.1 + 1 29 30 2 1 k0.1 + 1 29 31 3 1 k0.1 + 1 30 31 2 1 k0.1 + 1 30 32 3 1 k0.1 + 1 31 32 2 1 k0.1 + 1 31 33 3 1 k0.1 + 1 32 33 2 1 k0.1 + 1 32 34 3 1 k0.1 + 1 33 34 2 1 k0.1 + 1 33 35 3 1 k0.1 + 1 34 35 2 1 k0.1 + 1 34 36 3 1 k0.1 + 1 35 36 2 1 k0.1 + 1 35 37 3 1 k0.1 + 1 36 37 2 1 k0.1 + 1 36 38 3 1 k0.1 + 1 37 38 2 1 k0.1 + 1 37 39 3 1 k0.1 + 1 38 39 2 1 k0.1 + 1 38 40 3 1 k0.1 + 1 39 40 2 1 k0.1 + 1 39 41 3 1 k0.1 + 1 40 41 2 1 k0.1 + 1 40 42 3 1 k0.1 + 1 41 42 2 1 k0.1 + 1 41 43 3 1 k0.1 + 1 42 43 2 1 k0.1 + 1 42 44 3 1 k0.1 + 1 43 44 2 1 k0.1 + 1 43 45 3 1 k0.1 + 1 44 45 2 1 k0.1 + 1 44 46 3 1 k0.1 + 1 45 46 2 1 k0.1 + 1 45 47 3 1 k0.1 + 1 46 47 2 1 k0.1 + 1 46 48 3 1 k0.1 + 1 47 48 2 1 k0.1 + 1 47 49 3 1 k0.1 + 1 48 49 2 1 k0.1 + 1 48 50 3 1 k0.1 + 1 49 50 2 1 k0.1 + 1 49 51 3 1 k0.1 + 1 50 51 2 1 k0.1 + 1 50 52 3 1 k0.1 + 1 51 52 2 1 k0.1 + 1 51 53 3 1 k0.1 + 1 52 53 2 1 k0.1 + 1 52 54 3 1 k0.1 + 1 53 54 2 1 k0.1 + 1 53 55 3 1 k0.1 + 1 54 55 2 1 k0.1 + 1 54 56 3 1 k0.1 + 1 55 56 2 1 k0.1 + 1 55 57 3 1 k0.1 + 1 56 57 2 1 k0.1 + 1 56 58 3 1 k0.1 + 1 57 58 2 1 k0.1 + 1 57 59 3 1 k0.1 + 1 58 59 2 1 k0.1 + 1 58 60 3 1 k0.1 + 1 59 60 2 1 k0.1 + 1 59 61 3 1 k0.1 + 1 60 61 2 1 k0.1 + 1 60 62 3 1 k0.1 + 1 61 62 2 1 k0.1 + 1 61 63 3 1 k0.1 + 1 62 63 2 1 k0.1 + 1 62 64 3 1 k0.1 + 1 63 64 2 1 k0.1 + 1 63 65 3 1 k0.1 + 1 64 65 2 1 k0.1 + 1 64 66 3 1 k0.1 + 1 65 66 2 1 k0.1 + 1 65 67 3 1 k0.1 + 1 66 67 2 1 k0.1 + 1 66 68 3 1 k0.1 + 1 67 68 2 1 k0.1 + 1 67 69 3 1 k0.1 + 1 68 69 2 1 k0.1 + 1 68 70 3 1 k0.1 + 1 69 70 2 1 k0.1 + 1 69 71 3 1 k0.1 + 1 70 71 2 1 k0.1 + 1 70 72 3 1 k0.1 + 1 71 72 2 1 k0.1 + 1 71 73 3 1 k0.1 + 1 72 73 2 1 k0.1 + 1 72 74 3 1 k0.1 + 1 73 74 2 1 k0.1 + 1 73 75 3 1 k0.1 + 1 74 75 2 1 k0.1 + 1 74 76 3 1 k0.1 + 1 75 76 2 1 k0.1 + 1 75 77 3 1 k0.1 + 1 76 77 2 1 k0.1 + 1 76 78 3 1 k0.1 + 1 77 78 2 1 k0.1 + 1 77 79 3 1 k0.1 + 1 78 79 2 1 k0.1 + 1 78 80 3 1 k0.1 + 1 79 80 2 1 k0.1 + 1 79 81 3 1 k0.1 + 1 80 81 2 1 k0.1 + 1 80 82 3 1 k0.1 + 1 81 82 2 1 k0.1 + 1 81 83 3 1 k0.1 + 1 82 83 2 1 k0.1 + 1 82 84 3 1 k0.1 + 1 83 84 2 1 k0.1 + 1 83 85 3 1 k0.1 + 1 84 85 2 1 k0.1 + 1 84 86 3 1 k0.1 + 1 85 86 2 1 k0.1 + 1 85 87 3 1 k0.1 + 1 86 87 2 1 k0.1 + 1 86 88 3 1 k0.1 + 1 87 88 2 1 k0.1 + 1 87 89 3 1 k0.1 + 1 88 89 2 1 k0.1 + 1 88 90 3 1 k0.1 + 1 89 90 2 1 k0.1 + 1 89 91 3 1 k0.1 + 1 90 91 2 1 k0.1 + 1 90 92 3 1 k0.1 + 1 91 92 2 1 k0.1 + 1 91 93 3 1 k0.1 + 1 92 93 2 1 k0.1 + 1 92 94 3 1 k0.1 + 1 93 94 2 1 k0.1 + 1 93 95 3 1 k0.1 + 1 94 95 2 1 k0.1 + 1 94 96 3 1 k0.1 + 1 95 96 2 1 k0.1 + 1 95 97 3 1 k0.1 + 1 96 97 2 1 k0.1 + 1 96 98 3 1 k0.1 + 1 97 98 2 1 k0.1 + 1 97 99 3 1 k0.1 + 1 98 99 2 1 k0.1 + 1 98 100 3 1 k0.1 + 1 99 100 2 1 k0.1 + 1 99 101 3 1 k0.1 + 1 100 101 2 1 k0.1 + 1 100 102 3 1 k0.1 + 1 101 102 2 1 k0.1 + 1 101 103 3 1 k0.1 + 1 102 103 2 1 k0.1 + 1 102 104 3 1 k0.1 + 1 103 104 2 1 k0.1 + 1