#index_first index_last length frequency knotoid_type polynomial 0 231 232 0.9 k0.1 + 1 0 230 231 0.85 k0.1 + 1 0 229 230 0.8 k0.1 + 1 0 228 229 1 k0.1 + 1 0 227 228 0.95 k0.1 + 1 0 226 227 0.95 k0.1 + 1 0 225 226 0.95 k0.1 + 1 0 224 225 0.7 k0.1 + 1 0 223 224 0.8 k0.1 + 1 0 222 223 0.75 k0.1 + 1 0 221 222 0.75 k0.1 + 1 0 220 221 0.45 k0.1 + 1 0 219 220 0.8 k0.1 + 1 0 218 219 0.75 k0.1 + 1 0 217 218 0.9 k0.1 + 1 0 216 217 0.55 k0.1 + 1 0 215 216 0.8 k0.1 + 1 0 214 215 0.8 k0.1 + 1 0 213 214 0.65 k0.1 + 1 0 212 213 0.65 k0.1 + 1 0 211 212 0.9 k0.1 + 1 0 210 211 0.9 k0.1 + 1 0 209 210 0.75 k0.1 + 1 0 208 209 0.8 k0.1 + 1 0 207 208 0.7 k0.1 + 1 0 206 207 0.5 k0.1 + 1 0 205 206 0.6 k0.1 + 1 0 204 205 0.6 k0.1 + 1 0 203 204 0.4 k0.1 + 1 0 202 203 0.45 k0.1 + 1 0 201 202 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 202 202 0.3 k0.1 + 1 1 201 201 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 202 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 203 203 0.4 k0.1 + 1 2 203 202 0.35 k0.1 + 1 2 202 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 203 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 204 203 0.4 k0.1 + 1 3 204 202 0.35 k0.1 + 1 3 203 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 204 201 0.5 k0.1 + 1 4 203 200 0.45 k0.1 + 1 3 203 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 202 199 0.3 k0.1 + 1 3 202 200 0.45 k0.1 + 1 3 203 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 202 201 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 201 199 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 202 199 0.3 k0.1 + 1 4 201 198 0.35 k0.1 + 1 3 201 199 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 200 197 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 201 197 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 202 199 0.3 k0.1 + 1 5 202 198 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 203 200 0.45 k0.1 + 1 5 203 199 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 204 201 0.5 k0.1 + 1 5 204 200 0.4 k0.1 + 1 5 203 199 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 204 199 0.55 k0.1 + 1 6 203 198 0.6 k0.1 + 1 5 203 199 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 202 197 0.4 k0.1 + 1 5 202 198 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 201 196 0.4 k0.1 + 1 5 201 197 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 200 195 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 7 201 195 0.3 k1.1 - A^(-4) - A^(-2)*v 6 202 197 0.4 k0.1 + 1 7 202 196 0.2 k0.1 + 1 7 201 195 0.3 k1.1 - A^(-4) - A^(-2)*v 8 202 195 0.35 k0.1 + 1 8 201 194 0.25 k1.1 - A^(-4) - A^(-2)*v 9 202 194 0.2 k1.1 - A^(-4) - A^(-2)*v 8 203 196 0.6 k0.1 + 1 9 203 195 0.35 k0.1 + 1 9 202 194 0.2 k1.1 - A^(-4) - A^(-2)*v 10 203 194 0.4 k0.1 + 1 10 202 193 0.35 k0.1 + 1 9 202 194 0.2 k1.1 - A^(-4) - A^(-2)*v 10 201 192 0.35 k1.1 - A^(-4) - A^(-2)*v 11 202 192 0.35 k0.1 + 1 11 201 191 0.25 k1.1 - A^(-4) - A^(-2)*v 12 202 191 0.25 k0.1 + 1 12 201 190 0.15 k0.1 + 1 11 201 191 0.25 k1.1 - A^(-4) - A^(-2)*v 12 200 189 0.25 k1.1 - A^(-4) - A^(-2)*v 13 201 189 0.3 k1.1 - A^(-4) - A^(-2)*v 12 202 191 0.25 k0.1 + 1 13 202 190 0.6 k0.1 + 1 13 201 189 0.3 k1.1 - A^(-4) - A^(-2)*v 14 202 189 0.25 k0.1 + 1 14 201 188 0.2 k1.1 - A^(-4) - A^(-2)*v 15 202 188 0.4 k0.1 + 1 15 201 187 0.2 k1.1 - A^(-4) - A^(-2)*v 16 202 187 0.55 k0.1 + 1 16 201 186 0.4 k1.1 - A^(-4) - A^(-2)*v 17 202 186 0.5 k0.1 + 1 17 201 185 0.4 k0.1 + 1 16 201 186 0.4 k1.1 - A^(-4) - A^(-2)*v 17 200 184 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 18 201 184 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 17 202 186 0.5 k0.1 + 1 18 202 185 0.35 k0.1 + 1 18 201 184 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 19 202 184 0.4 k0.1 + 1 19 201 183 0.5 k0.1 + 1 18 201 184 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 19 200 182 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 20 201 182 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 19 202 184 0.4 k0.1 + 1 20 202 183 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 19 203 185 0.4 k0.1 + 1 20 203 184 0.55 k0.1 + 1 20 202 183 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 21 203 183 0.4 k0.1 + 1 21 202 182 0.4 k0.1 + 1 20 202 183 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 21 201 181 0.35 k0.1 + 1 20 201 182 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 21 200 180 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 201 180 0.35 k0.1 + 1 22 200 179 0.25 k0.1 + 1 21 200 180 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 199 178 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 23 200 178 0.35 k0.1 + 1 23 199 177 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 24 200 177 0.35 k1.1 - A^(-4) - A^(-2)*v 23 201 179 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 200 179 0.25 k0.1 + 1 22 201 180 0.35 k0.1 + 1 23 201 179 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 202 181 0.35 k0.1 + 1 23 202 180 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 203 182 0.45 k0.1 + 1 23 203 181 0.45 k0.1 + 1 23 202 180 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 24 203 180 0.6 k0.1 + 1 24 202 179 0.45 k0.1 + 1 23 202 180 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 24 201 178 0.3 k0.1 + 1 23 201 179 0.2 k2.1 - A^(-10) + A^(-6) + A^(-4) 24 200 177 0.35 k1.1 - A^(-4) - A^(-2)*v 25 201 177 0.35 k0.1 + 1 25 200 176 0.25 k1.1 - A^(-4) - A^(-2)*v 26 201 176 0.6 k0.1 + 1 26 200 175 0.25 k0.1 + 1 25 200 176 0.25 k1.1 - A^(-4) - A^(-2)*v 26 199 174 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 27 200 174 0.4 k0.1 + 1 27 199 173 0.35 k1.1 - A^(-4) - A^(-2)*v 28 200 173 0.25 k0.1 + 1 28 199 172 0.45 k0.1 + 1 27 199 173 0.35 k1.1 - A^(-4) - A^(-2)*v 28 198 171 0.45 k1.1 - A^(-4) - A^(-2)*v 29 199 171 0.55 k0.1 + 1 29 198 170 0.55 k0.1 + 1 28 198 171 0.45 k1.1 - A^(-4) - A^(-2)*v 29 197 169 0.4 k0.1 + 1 28 197 170 0.5 k1.1 - A^(-4) - A^(-2)*v 29 196 168 0.6 k0.1 + 1 28 196 169 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 195 167 0.5 k0.1 + 1 28 195 168 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 194 166 0.5 k0.1 + 1 28 194 167 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 193 165 0.55 k0.1 + 1 28 193 166 0.6 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 192 164 0.45 k0.1 + 1 28 192 165 0.7 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 191 163 0.5 k0.1 + 1 28 191 164 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 29 190 162 0.5 k0.1 + 1 28 190 163 0.4 k0.1 + 1 28 191 164 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 27 190 164 0.3 k2.1 - A^(-10) + A^(-6) + A^(-4) 28 189 162 0.4 k1.1 - A^(-4) - A^(-2)*v 29 190 162 0.5 k0.1 + 1 29 189 161 0.5 k0.1 + 1 28 189 162 0.4 k1.1 - A^(-4) - A^(-2)*v 29 188 160 0.6 k0.1 + 1 28 188 161 0.4 k0.1 + 1 28 189 162 0.4 k1.1 - A^(-4) - A^(-2)*v 27 188 162 0.4 k1.1 - A^(-4) - A^(-2)*v 28 187 160 0.35 k0.1 + 1 27 187 161 0.4 k0.1 + 1 27 188 162 0.4 k1.1 - A^(-4) - A^(-2)*v 26 187 162 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 27 186 160 0.4 k1.1 - A^(-4) - A^(-2)*v 28 187 160 0.35 k0.1 + 1 28 186 159 0.45 k1.1 - A^(-4) - A^(-2)*v 29 187 159 0.65 k0.1 + 1 29 186 158 0.75 k0.1 + 1 28 186 159 0.45 k1.1 - A^(-4) - A^(-2)*v 29 185 157 0.55 k0.1 + 1 28 185 158 0.45 k0.1 + 1 28 186 159 0.45 k1.1 - A^(-4) - A^(-2)*v 27 185 159 0.55 k0.1 + 1 27 186 160 0.4 k1.1 - A^(-4) - A^(-2)*v 26 185 160 0.3 k0.1 + 1 26 186 161 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 25 185 161 0.4 k0.1 + 1 25 186 162 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 24 185 162 0.45 k0.1 + 1 24 186 163 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 23 185 163 0.55 k0.1 + 1 23 186 164 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 22 185 164 0.45 k0.1 + 1 22 186 165 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 21 185 165 0.5 k0.1 + 1 21 186 166 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 20 185 166 0.4 k0.1 + 1 20 186 167 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 19 185 167 0.5 k0.1 + 1 19 186 168 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 18 185 168 0.35 k0.1 + 1 18 186 169 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 17 185 169 0.4 k0.1 + 1 17 186 170 0.35 k0.1 + 1 18 186 169 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 17 187 171 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 16 186 171 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 17 185 169 0.4 k0.1 + 1 16 185 170 0.55 k0.1 + 1 16 186 171 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 15 185 171 0.35 k1.1 - A^(-4) - A^(-2)*v 16 184 169 0.45 k0.1 + 1 15 184 170 0.3 k0.1 + 1 15 185 171 0.35 k1.1 - A^(-4) - A^(-2)*v 14 184 171 0.5 k0.1 + 1 14 185 172 0.35 k0.1 + 1 15 185 171 0.35 k1.1 - A^(-4) - A^(-2)*v 14 186 173 0.35 k0.1 + 1 15 186 172 0.35 k0.1 + 1 15 185 171 0.35 k1.1 - A^(-4) - A^(-2)*v 16 186 171 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 15 187 173 0.35 k2.1 - A^(-10) + A^(-6) + A^(-4) 14 186 173 0.35 k0.1 + 1 14 187 174 0.4 k1.1 - A^(-4) - A^(-2)*v 13 186 174 0.35 k1.1 - A^(-4) - A^(-2)*v 14 185 172 0.35 k0.1 + 1 13 185 173 0.25 k1.1 - A^(-4) - A^(-2)*v 14 184 171 0.5 k0.1 + 1 13 184 172 0.55 k0.1 + 1 13 185 173 0.25 k1.1 - A^(-4) - A^(-2)*v 12 184 173 0.4 k0.1 + 1 12 185 174 0.45 k1.1 - A^(-4) - A^(-2)*v 11 184 174 0.35 k1.1 - A^(-4) - A^(-2)*v 12 183 172 0.5 k0.1 + 1 11 183 173 0.4 k0.1 + 1 11 184 174 0.35 k1.1 - A^(-4) - A^(-2)*v 10 183 174 0.5 k0.1 + 1 10 184 175 0.5 k0.1 + 1 11 184 174 0.35 k1.1 - A^(-4) - A^(-2)*v 10 185 176 0.6 k0.1 + 1 11 185 175 0.35 k1.1 - A^(-4) - A^(-2)*v 10 186 177 0.35 k0.1 + 1 11 186 176 0.45 k1.1 - A^(-4) - A^(-2)*v 10 187 178 0.35 k0.1 + 1 11 187 177 0.5 k1.1 - A^(-4) - A^(-2)*v 10 188 179 0.45 k1.1 - A^(-4) - A^(-2)*v 9 187 179 0.4 k0.1 + 1 9 188 180 0.4 k1.1 - A^(-4) - A^(-2)*v 8 187 180 0.3 k1.1 - A^(-4) - A^(-2)*v 9 186 178 0.35 k0.1 + 1 8 186 179 0.35 k1.1 - A^(-4) - A^(-2)*v 9 185 177 0.3 k0.1 + 1 8 185 178 0.4 k0.1 + 1 8 186 179 0.35 k1.1 - A^(-4) - A^(-2)*v 7 185 179 0.3 k0.1 + 1 7 186 180 0.25 k1.1 - A^(-4) - A^(-2)*v 6 185 180 0.45 k0.1 + 1 6 186 181 0.5 k0.1 + 1 7 186 180 0.25 k1.1 - A^(-4) - A^(-2)*v 6 187 182 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 5 186 182 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 6 185 180 0.45 k0.1 + 1 5 185 181 0.35 k0.1 + 1 5 186 182 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 185 182 0.35 k0.1 + 1 4 186 183 0.3 k0.1 + 1 5 186 182 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 187 184 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 186 184 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 185 182 0.35 k0.1 + 1 3 185 183 0.3 k0.1 + 1 3 186 184 0.25 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 185 184 0.35 k0.1 + 1 2 186 185 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 185 185 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 184 183 0.55 k0.1 + 1 1 184 184 0.3 k0.1 + 1 1 185 185 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 184 185 0.6 k0.1 + 1 0 185 186 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 183 184 0.45 k0.1 + 1 0 182 183 0.6 k0.1 + 1 0 181 182 0.7 k0.1 + 1 0 180 181 0.65 k0.1 + 1 0 179 180 0.75 k0.1 + 1 0 178 179 0.8 k0.1 + 1 0 177 178 0.9 k0.1 + 1 0 176 177 0.75 k0.1 + 1 0 175 176 0.5 k0.1 + 1 0 174 175 0.55 k0.1 + 1 0 173 174 0.85 k0.1 + 1 0 172 173 0.55 k0.1 + 1 0 171 172 0.75 k0.1 + 1 0 170 171 0.6 k0.1 + 1 0 169 170 0.85 k0.1 + 1 0 168 169 0.75 k0.1 + 1 0 167 168 0.55 k0.1 + 1 0 166 167 0.5 k0.1 + 1 0 165 166 0.65 k0.1 + 1 0 164 165 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 165 165 0.6 k0.1 + 1 1 164 164 0.45 k0.1 + 1 0 164 165 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 163 163 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 164 163 0.5 k0.1 + 1 2 163 162 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 3 164 162 0.5 k0.1 + 1 3 163 161 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 164 161 0.4 k0.1 + 1 4 163 160 0.5 k0.1 + 1 3 163 161 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 162 159 0.6 k0.1 + 1 3 162 160 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 4 161 158 0.6 k0.1 + 1 3 161 159 0.6 k0.1 + 1 3 162 160 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 161 160 0.6 k0.1 + 1 2 162 161 0.6 k0.1 + 1 3 162 160 0.45 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 163 162 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 162 162 0.7 k0.1 + 1 1 163 163 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 162 163 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 161 161 0.45 k0.1 + 1 0 161 162 0.6 k0.1 + 1 0 162 163 0.55 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 160 161 0.55 k0.1 + 1 0 159 160 0.5 k0.1 + 1 0 158 159 0.45 k0.1 + 1 0 157 158 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 158 158 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 159 160 0.5 k0.1 + 1 1 159 159 0.5 k0.1 + 1 1 158 158 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 159 158 0.65 k0.1 + 1 2 158 157 0.5 k0.1 + 1 1 158 158 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 2 157 156 0.6 k0.1 + 1 1 157 157 0.7 k0.1 + 1 1 158 158 0.4 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 157 158 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 1 156 156 0.6 k0.1 + 1 0 156 157 0.8 k0.1 + 1 0 157 158 0.5 k2.1 - A^(-10) + A^(-6) + A^(-4) 0 155 156 0.7 k0.1 + 1 0 154 155 0.9 k0.1 + 1 0 153 154 1 k0.1 + 1 0 152 153 0.9 k0.1 + 1 0 151 152 0.95 k0.1 + 1 0 150 151 0.95 k0.1 + 1 0 149 150 1 k0.1 + 1 0 148 149 0.95 k0.1 + 1 0 147 148 0.9 k0.1 + 1 0 146 147 0.9 k0.1 + 1 0 145 146 0.95 k0.1 + 1 0 144 145 1 k0.1 + 1 0 143 144 0.95 k0.1 + 1 0 142 143 0.95 k0.1 + 1 0 141 142 0.95 k0.1 + 1 0 140 141 0.95 k0.1 + 1 0 139 140 0.9 k0.1 + 1 0 138 139 0.9 k0.1 + 1 0 137 138 0.95 k0.1 + 1 0 136 137 0.85 k0.1 + 1 0 135 136 0.95 k0.1 + 1 0 134 135 1 k0.1 + 1 0 133 134 1 k0.1 + 1 0 132 133 1 k0.1 + 1 0 131 132 0.9 k0.1 + 1 0 130 131 0.95 k0.1 + 1 0 129 130 0.9 k0.1 + 1 0 128 129 1 k0.1 + 1 0 127 128 0.95 k0.1 + 1 0 126 127 0.95 k0.1 + 1 0 125 126 0.95 k0.1 + 1 0 124 125 1 k0.1 + 1 0 123 124 0.9 k0.1 + 1 0 122 123 0.95 k0.1 + 1 0 121 122 1 k0.1 + 1 0 120 121 1 k0.1 + 1 0 119 120 0.95 k0.1 + 1 0 118 119 1 k0.1 + 1 0 117 118 0.95 k0.1 + 1 0 116 117 0.85 k0.1 + 1 0 115 116 0.95 k0.1 + 1 0 114 115 0.9 k0.1 + 1 0 113 114 1 k0.1 + 1 0 112 113 0.95 k0.1 + 1 0 111 112 0.95 k0.1 + 1 0 110 111 0.95 k0.1 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