#index_first index_last length frequency knotoid_type polynomial 0 241 242 0.9 k0.1 + 1 0 240 241 0.75 k0.1 + 1 0 239 240 0.8 k0.1 + 1 0 238 239 0.9 k0.1 + 1 0 237 238 1 k0.1 + 1 0 236 237 0.75 k0.1 + 1 0 235 236 0.8 k0.1 + 1 0 234 235 0.95 k0.1 + 1 0 233 234 0.85 k0.1 + 1 0 232 233 0.7 k0.1 + 1 0 231 232 0.75 k0.1 + 1 0 230 231 0.8 k0.1 + 1 0 229 230 0.85 k0.1 + 1 0 228 229 0.85 k0.1 + 1 0 227 228 0.75 k0.1 + 1 0 226 227 0.75 k0.1 + 1 0 225 226 0.8 k0.1 + 1 0 224 225 0.8 k0.1 + 1 0 223 224 0.7 k0.1 + 1 0 222 223 0.75 k0.1 + 1 0 221 222 0.75 k0.1 + 1 0 220 221 0.65 k0.1 + 1 0 219 220 0.65 k0.1 + 1 0 218 219 0.8 k0.1 + 1 0 217 218 0.75 k0.1 + 1 0 216 217 0.65 k0.1 + 1 0 215 216 0.8 k0.1 + 1 0 214 215 0.85 k0.1 + 1 0 213 214 0.45 k0.1 + 1 0 212 213 0.6 k0.1 + 1 0 211 212 0.7 k0.1 + 1 0 210 211 0.65 k0.1 + 1 0 209 210 0.6 k0.1 + 1 0 208 209 0.7 k0.1 + 1 0 207 208 0.65 k0.1 + 1 0 206 207 0.5 k0.1 + 1 0 205 206 0.5 k0.1 + 1 0 204 205 0.65 k0.1 + 1 0 203 204 0.5 k0.1 + 1 0 202 203 0.75 k0.1 + 1 0 201 202 0.5 k0.1 + 1 0 200 201 0.75 k0.1 + 1 0 199 200 0.65 k0.1 + 1 0 198 199 0.65 k0.1 + 1 0 197 198 0.75 k0.1 + 1 0 196 197 0.7 k0.1 + 1 0 195 196 0.85 k0.1 + 1 0 194 195 0.9 k0.1 + 1 0 193 194 0.9 k0.1 + 1 0 192 193 0.55 k0.1 + 1 0 191 192 0.65 k0.1 + 1 0 190 191 0.5 k0.1 + 1 0 189 190 0.65 k0.1 + 1 0 188 189 0.75 k0.1 + 1 0 187 188 0.9 k0.1 + 1 0 186 187 0.8 k0.1 + 1 0 185 186 0.75 k0.1 + 1 0 184 185 0.65 k0.1 + 1 0 183 184 0.8 k0.1 + 1 0 182 183 0.85 k0.1 + 1 0 181 182 0.85 k0.1 + 1 0 180 181 0.75 k0.1 + 1 0 179 180 0.7 k0.1 + 1 0 178 179 0.9 k0.1 + 1 0 177 178 0.9 k0.1 + 1 0 176 177 0.95 k0.1 + 1 0 175 176 0.85 k0.1 + 1 0 174 175 0.8 k0.1 + 1 0 173 174 0.75 k0.1 + 1 0 172 173 0.8 k0.1 + 1 0 171 172 0.85 k0.1 + 1 0 170 171 0.75 k0.1 + 1 0 169 170 0.9 k0.1 + 1 0 168 169 0.75 k0.1 + 1 0 167 168 0.8 k0.1 + 1 0 166 167 0.95 k0.1 + 1 0 165 166 0.8 k0.1 + 1 0 164 165 0.9 k0.1 + 1 0 163 164 0.8 k0.1 + 1 0 162 163 1 k0.1 + 1 0 161 162 0.9 k0.1 + 1 0 160 161 0.9 k0.1 + 1 0 159 160 0.95 k0.1 + 1 0 158 159 0.95 k0.1 + 1 0 157 158 0.75 k0.1 + 1 0 156 157 0.8 k0.1 + 1 0 155 156 0.85 k0.1 + 1 0 154 155 0.6 k0.1 + 1 0 153 154 0.8 k0.1 + 1 0 152 153 0.8 k0.1 + 1 0 151 152 0.85 k0.1 + 1 0 150 151 0.85 k0.1 + 1 0 149 150 0.7 k0.1 + 1 0 148 149 0.85 k0.1 + 1 0 147 148 0.75 k0.1 + 1 0 146 147 0.8 k0.1 + 1 0 145 146 0.7 k0.1 + 1 0 144 145 0.9 k0.1 + 1 0 143 144 0.9 k0.1 + 1 0 142 143 0.9 k0.1 + 1 0 141 142 0.7 k0.1 + 1 0 140 141 0.8 k0.1 + 1 0 139 140 0.75 k0.1 + 1 0 138 139 0.95 k0.1 + 1 0 137 138 1 k0.1 + 1 0 136 137 0.9 k0.1 + 1 0 135 136 0.65 k0.1 + 1 0 134 135 0.75 k0.1 + 1 0 133 134 0.6 k0.1 + 1 0 132 133 0.75 k0.1 + 1 0 131 132 0.65 k0.1 + 1 0 130 131 0.55 k0.1 + 1 0 129 130 0.9 k0.1 + 1 0 128 129 0.95 k0.1 + 1 0 127 128 0.95 k0.1 + 1 0 126 127 0.9 k0.1 + 1 0 125 126 0.9 k0.1 + 1 0 124 125 0.85 k0.1 + 1 0 123 124 0.8 k0.1 + 1 0 122 123 0.9 k0.1 + 1 0 121 122 0.9 k0.1 + 1 0 120 121 0.65 k0.1 + 1 0 119 120 0.8 k0.1 + 1 0 118 119 0.8 k0.1 + 1 0 117 118 0.85 k0.1 + 1 0 116 117 0.7 k0.1 + 1 0 115 116 0.8 k0.1 + 1 0 114 115 0.75 k0.1 + 1 0 113 114 0.85 k0.1 + 1 0 112 113 0.85 k0.1 + 1 0 111 112 0.85 k0.1 + 1 0 110 111 0.9 k0.1 + 1 0 109 110 0.7 k0.1 + 1 0 108 109 0.5 k0.1 + 1 0 107 108 0.65 k0.1 + 1 0 106 107 0.6 k0.1 + 1 0 105 106 0.55 k0.1 + 1 0 104 105 0.6 k0.1 + 1 0 103 104 0.8 k0.1 + 1 0 102 103 0.85 k0.1 + 1 0 101 102 1 k0.1 + 1 0 100 101 0.9 k0.1 + 1 0 99 100 0.85 k0.1 + 1 0 98 99 0.95 k0.1 + 1 0 97 98 1 k0.1 + 1 0 96 97 0.95 k0.1 + 1 0 95 96 0.9 k0.1 + 1 0 94 95 0.9 k0.1 + 1 0 93 94 0.9 k0.1 + 1 0 92 93 0.9 k0.1 + 1 0 91 92 0.8 k0.1 + 1 0 90 91 0.9 k0.1 + 1 0 89 90 0.8 k0.1 + 1 0 88 89 1 k0.1 + 1 0 87 88 0.85 k0.1 + 1 0 86 87 0.65 k0.1 + 1 0 85 86 0.8 k0.1 + 1 0 84 85 0.75 k0.1 + 1 0 83 84 0.75 k0.1 + 1 0 82 83 0.6 k0.1 + 1 0 81 82 0.85 k0.1 + 1 0 80 81 0.7 k0.1 + 1 0 79 80 0.7 k0.1 + 1 0 78 79 0.55 k0.1 + 1 0 77 78 0.55 k0.1 + 1 0 76 77 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 77 77 0.55 k0.1 + 1 1 76 76 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 77 76 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 78 78 0.6 k0.1 + 1 2 78 77 0.55 k0.1 + 1 2 77 76 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 78 76 0.55 k0.1 + 1 3 77 75 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 78 75 0.55 k0.1 + 1 4 77 74 0.55 k0.1 + 1 3 77 75 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 76 73 0.65 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 77 73 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 78 75 0.55 k0.1 + 1 5 78 74 0.6 k0.1 + 1 5 77 73 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 78 73 0.55 k0.1 + 1 6 77 72 0.45 k0.1 + 1 5 77 73 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 76 71 0.5 k0.1 + 1 5 76 72 0.55 k0.1 + 1 5 77 73 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 76 73 0.65 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 75 71 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 76 71 0.5 k0.1 + 1 6 75 70 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 76 70 0.45 k0.1 + 1 7 75 69 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 8 76 69 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 77 71 0.5 k0.1 + 1 8 77 70 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 78 72 0.5 k0.1 + 1 8 78 71 0.45 k0.1 + 1 8 77 70 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 9 78 70 0.6 k0.1 + 1 9 77 69 0.45 k0.1 + 1 8 77 70 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 9 76 68 0.4 k1.1 - A^(-4) - A^(-2)*v 10 77 68 0.5 k0.1 + 1 10 76 67 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 11 77 67 0.6 k1.1 - A^(-4) - A^(-2)*v 10 78 69 0.55 k1.1 - A^(-4) - A^(-2)*v 9 77 69 0.45 k0.1 + 1 9 78 70 0.6 k0.1 + 1 10 78 69 0.55 k1.1 - A^(-4) - A^(-2)*v 9 79 71 0.65 k0.1 + 1 10 79 70 0.65 k0.1 + 1 10 78 69 0.55 k1.1 - A^(-4) - A^(-2)*v 11 79 69 0.8 k0.1 + 1 11 78 68 0.7 k0.1 + 1 10 78 69 0.55 k1.1 - A^(-4) - A^(-2)*v 11 77 67 0.6 k1.1 - A^(-4) - A^(-2)*v 12 78 67 0.75 k0.1 + 1 12 77 66 0.55 k0.1 + 1 11 77 67 0.6 k1.1 - A^(-4) - A^(-2)*v 12 76 65 0.7 k1.1 - A^(-4) - A^(-2)*v 13 77 65 0.5 k0.1 + 1 13 76 64 0.5 k1.1 - A^(-4) - A^(-2)*v 14 77 64 0.6 k0.1 + 1 14 76 63 0.5 k1.1 - A^(-4) - A^(-2)*v 15 77 63 0.8 k0.1 + 1 15 76 62 0.7 k0.1 + 1 14 76 63 0.5 k1.1 - A^(-4) - A^(-2)*v 15 75 61 0.75 k0.1 + 1 14 75 62 0.45 k1.1 - A^(-4) - A^(-2)*v 15 74 60 0.6 k0.1 + 1 14 74 61 0.75 k1.1 - A^(-4) - A^(-2)*v 15 73 59 0.5 k0.1 + 1 14 73 60 0.55 k0.1 + 1 14 74 61 0.75 k1.1 - A^(-4) - A^(-2)*v 13 73 61 0.45 k1.1 - A^(-4) - A^(-2)*v 14 72 59 0.8 k0.1 + 1 13 72 60 0.55 k0.1 + 1 13 73 61 0.45 k1.1 - A^(-4) - A^(-2)*v 12 72 61 0.7 k1.1 - A^(-4) - A^(-2)*v 13 71 59 0.55 k1.1 - A^(-4) - A^(-2)*v 14 72 59 0.8 k0.1 + 1 14 71 58 0.75 k0.1 + 1 13 71 59 0.55 k1.1 - A^(-4) - A^(-2)*v 14 70 57 0.6 k1.1 - A^(-4) - A^(-2)*v 15 71 57 0.7 k0.1 + 1 15 70 56 0.6 k0.1 + 1 14 70 57 0.6 k1.1 - A^(-4) - A^(-2)*v 15 69 55 0.7 k0.1 + 1 14 69 56 0.75 k0.1 + 1 14 70 57 0.6 k1.1 - A^(-4) - A^(-2)*v 13 69 57 0.65 k0.1 + 1 13 70 58 0.55 k1.1 - A^(-4) - A^(-2)*v 12 69 58 0.45 k0.1 + 1 12 70 59 0.85 k1.1 - A^(-4) - A^(-2)*v 11 69 59 0.55 k0.1 + 1 11 70 60 0.5 k1.1 - A^(-4) - A^(-2)*v 10 69 60 0.4 k0.1 + 1 10 70 61 0.35 k1.1 - A^(-4) - A^(-2)*v 9 69 61 0.5 k0.1 + 1 9 70 62 0.4 k1.1 - A^(-4) - A^(-2)*v 8 69 62 0.55 k0.1 + 1 8 70 63 0.4 k0.1 + 1 9 70 62 0.4 k1.1 - A^(-4) - A^(-2)*v 8 71 64 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 70 64 0.4 k0.1 + 1 7 71 65 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 70 65 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 69 63 0.45 k0.1 + 1 6 69 64 0.5 k0.1 + 1 6 70 65 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 69 65 0.6 k0.1 + 1 5 70 66 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 69 66 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 68 64 0.55 k0.1 + 1 4 68 65 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 67 63 0.55 k0.1 + 1 4 67 64 0.75 k0.1 + 1 4 68 65 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 67 65 0.75 k0.1 + 1 3 68 66 0.55 k0.1 + 1 4 68 65 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 69 67 0.55 k0.1 + 1 4 69 66 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 70 68 0.9 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 69 68 0.5 k0.1 + 1 2 70 69 0.7 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 69 69 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 68 67 0.6 k0.1 + 1 1 68 68 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 67 66 0.65 k0.1 + 1 1 67 67 0.7 k0.1 + 1 1 68 68 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 67 68 0.7 k0.1 + 1 0 68 69 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 66 67 0.7 k0.1 + 1 0 65 66 0.95 k0.1 + 1 0 64 65 0.8 k0.1 + 1 0 63 64 0.75 k0.1 + 1 0 62 63 0.95 k0.1 + 1 0 61 62 0.8 k0.1 + 1 0 60 61 0.9 k0.1 + 1 0 59 60 0.9 k0.1 + 1 0 58 59 1 k0.1 + 1 0 57 58 0.95 k0.1 + 1 0 56 57 0.95 k0.1 + 1 0 55 56 0.8 k0.1 + 1 0 54 55 0.7 k0.1 + 1 0 53 54 0.8 k0.1 + 1 0 52 53 0.95 k0.1 + 1 0 51 52 0.75 k0.1 + 1 0 50 51 0.65 k0.1 + 1 0 49 50 0.7 k0.1 + 1 0 48 49 0.8 k0.1 + 1 0 47 48 0.7 k0.1 + 1 0 46 47 0.7 k0.1 + 1 0 45 46 0.75 k0.1 + 1 0 44 45 1 k0.1 + 1 0 43 44 0.95 k0.1 + 1 0 42 43 0.95 k0.1 + 1 0 41 42 1 k0.1 + 1 0 40 41 1 k0.1 + 1 0 39 40 1 k0.1 + 1 0 38 39 0.95 k0.1 + 1 0 37 38 0.95 k0.1 + 1 0 36 37 1 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 0.95 k0.1 + 1 0 29 30 1 k0.1 + 1 0 28 29 0.95 k0.1 + 1 0 27 28 0.95 k0.1 + 1 0 26 27 1 k0.1 + 1 0 25 26 0.95 k0.1 + 1 0 24 25 1 k0.1 + 1 0 23 24 1 k0.1 + 1 0 22 23 1 k0.1 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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 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