total num of chars: 18 total num of families: 14 chars where some sequence of nonzero coeffs is not unimodal in abs value: none chars where some polynomial has both positive and negative coeffs: none chars where some polynomial has strictly negative coeffs: 1.4 = 73 in family 1.4 = 73 1.211 = 331111 in family 1.211 = 331111 11.3 = 5311(11) in family 1.31 = 5311 1.31 = 5311 in family 1.31 = 5311 | 0 rationally smooth elements where some sequence of nonzero coeffs is not unimodal in abs value. | 0 rationally smooth elements where some polynomial has both positive and negative coeffs. | 194 rationally smooth elements where some polynomial has strictly negative coeffs. 1.4 = 73 in family 1.4 = 73 #103 [ 2, 5, 4, 3, 1 ] #104 [ 2, 4, 3, 1, 5 ] #107 [ 5, 4, 3, 1, 2 ] #108 [ 4, 3, 1, 2, 5 ] #112 [ 2, 3, 1, 5, 4 ] #120 [ 3, 1, 2, 5, 4 ] #124 [ 2, 3, 1, 4, 5 ] #130 [ 3, 1, 2, 4, 5 ] #144 [ 1, 2, 5, 4, 3 ] #145 [ 1, 2, 4, 3, 5 ] #150 [ 1, 5, 4, 3, 2 ] #151 [ 1, 4, 3, 2, 5 ] #155 [ 1, 2, 3, 5, 4 ] #159 [ 1, 3, 2, 5, 4 ] #164 [ 1, 2, 3, 4, 5 ] #165 [ 1, 3, 2, 4, 5 ] #169 [ 2, 4, 5, 4, 3, 1 ] #173 [ 4, 5, 4, 3, 1, 2 ] #174 [ 2, 5, 4, 3, 1, 2 ] #175 [ 2, 4, 3, 1, 2, 5 ] #177 [ 2, 3, 5, 4, 3, 1 ] #181 [ 3, 5, 4, 3, 1, 2 ] #182 [ 2, 3, 1, 2, 5, 4 ] #184 [ 2, 3, 1, 4, 5, 4 ] #185 [ 2, 3, 4, 3, 1, 5 ] #189 [ 3, 4, 3, 1, 2, 5 ] #190 [ 3, 1, 2, 4, 5, 4 ] #191 [ 2, 3, 1, 2, 4, 5 ] #206 [ 1, 2, 5, 4, 3, 1 ] #207 [ 1, 2, 4, 3, 1, 5 ] #212 [ 1, 2, 4, 5, 4, 3 ] #213 [ 1, 5, 4, 3, 1, 2 ] #214 [ 1, 4, 3, 1, 2, 5 ] #215 [ 1, 2, 3, 1, 5, 4 ] #217 [ 1, 4, 5, 4, 3, 2 ] #218 [ 1, 2, 5, 4, 3, 2 ] #219 [ 1, 2, 4, 3, 2, 5 ] #221 [ 1, 2, 3, 5, 4, 3 ] #222 [ 1, 3, 1, 2, 5, 4 ] #224 [ 1, 2, 3, 1, 4, 5 ] #225 [ 1, 3, 5, 4, 3, 2 ] #226 [ 1, 2, 3, 2, 5, 4 ] #228 [ 1, 2, 3, 4, 5, 4 ] #229 [ 1, 2, 3, 4, 3, 5 ] #230 [ 1, 3, 1, 2, 4, 5 ] #233 [ 1, 3, 2, 4, 5, 4 ] #234 [ 1, 3, 4, 3, 2, 5 ] #235 [ 1, 2, 3, 2, 4, 5 ] #236 [ 2, 5, 4, 3, 1, 2, 3 ] #237 [ 2, 4, 3, 1, 2, 3, 5 ] #238 [ 2, 3, 1, 2, 3, 5, 4 ] #239 [ 2, 3, 1, 2, 3, 4, 5 ] #241 [ 3, 1, 5, 4, 3, 1, 2 ] #242 [ 2, 3, 1, 5, 4, 3, 1 ] #243 [ 2, 4, 5, 4, 3, 1, 2 ] #246 [ 2, 4, 3, 5, 4, 3, 1 ] #247 [ 3, 1, 4, 3, 1, 2, 5 ] #248 [ 2, 3, 1, 4, 3, 1, 5 ] #249 [ 4, 3, 5, 4, 3, 1, 2 ] #251 [ 2, 3, 4, 3, 1, 5, 4 ] #255 [ 3, 4, 3, 1, 2, 5, 4 ] #256 [ 2, 3, 1, 2, 4, 5, 4 ] #258 [ 3, 2, 5, 4, 3, 1, 2 ] #261 [ 2, 3, 2, 5, 4, 3, 1 ] #263 [ 3, 2, 4, 3, 1, 2, 5 ] #265 [ 2, 3, 2, 4, 3, 1, 5 ] #267 [ 1, 5, 4, 3, 1, 2, 3 ] #268 [ 1, 4, 3, 1, 2, 3, 5 ] #269 [ 1, 3, 1, 2, 3, 5, 4 ] #270 [ 1, 3, 1, 2, 3, 4, 5 ] #274 [ 1, 2, 4, 5, 4, 3, 1 ] #277 [ 1, 3, 1, 5, 4, 3, 2 ] #278 [ 1, 2, 3, 1, 5, 4, 3 ] #281 [ 1, 4, 5, 4, 3, 1, 2 ] #285 [ 1, 3, 1, 4, 3, 2, 5 ] #286 [ 1, 2, 3, 1, 4, 3, 5 ] #287 [ 1, 2, 4, 5, 4, 3, 2 ] #288 [ 1, 2, 4, 3, 5, 4, 3 ] #289 [ 1, 2, 3, 1, 4, 5, 4 ] #290 [ 1, 4, 3, 5, 4, 3, 2 ] #292 [ 1, 2, 3, 4, 3, 5, 4 ] #293 [ 1, 3, 1, 2, 4, 5, 4 ] #294 [ 1, 3, 2, 5, 4, 3, 2 ] #295 [ 1, 2, 3, 2, 5, 4, 3 ] #297 [ 1, 3, 4, 3, 2, 5, 4 ] #298 [ 1, 2, 3, 2, 4, 5, 4 ] #299 [ 1, 3, 2, 4, 3, 2, 5 ] #300 [ 1, 2, 3, 2, 4, 3, 5 ] #301 [ 2, 4, 5, 4, 3, 1, 2, 3 ] #302 [ 2, 3, 1, 2, 3, 4, 5, 4 ] #303 [ 4, 3, 1, 5, 4, 3, 1, 2 ] #304 [ 2, 4, 3, 1, 5, 4, 3, 1 ] #305 [ 2, 3, 1, 2, 3, 5, 4, 3 ] #306 [ 2, 3, 1, 2, 3, 4, 3, 5 ] #307 [ 3, 1, 5, 4, 3, 1, 2, 3 ] #311 [ 3, 1, 4, 3, 1, 2, 3, 5 ] #312 [ 2, 3, 4, 3, 5, 4, 3, 1 ] #313 [ 3, 2, 5, 4, 3, 1, 2, 3 ] #315 [ 2, 3, 1, 2, 5, 4, 3, 1 ] #316 [ 3, 4, 3, 5, 4, 3, 1, 2 ] #317 [ 4, 3, 2, 5, 4, 3, 1, 2 ] #320 [ 3, 2, 4, 3, 1, 2, 3, 5 ] #321 [ 2, 3, 1, 2, 4, 3, 1, 5 ] #326 [ 2, 3, 2, 4, 3, 1, 5, 4 ] #327 [ 1, 4, 5, 4, 3, 1, 2, 3 ] #328 [ 1, 3, 1, 2, 3, 4, 5, 4 ] #339 [ 1, 3, 1, 4, 3, 2, 5, 4 ] #340 [ 1, 2, 3, 1, 4, 3, 5, 4 ] #341 [ 1, 3, 1, 2, 3, 5, 4, 3 ] #342 [ 1, 3, 1, 2, 3, 4, 3, 5 ] #345 [ 1, 3, 1, 2, 5, 4, 3, 2 ] #348 [ 1, 3, 1, 2, 4, 3, 2, 5 ] #349 [ 1, 2, 3, 4, 3, 5, 4, 3 ] #350 [ 1, 4, 3, 2, 5, 4, 3, 2 ] #352 [ 1, 3, 4, 3, 5, 4, 3, 2 ] #354 [ 1, 2, 3, 2, 4, 3, 5, 4 ] #356 [ 4, 3, 1, 5, 4, 3, 1, 2, 3 ] #364 [ 2, 3, 1, 2, 3, 4, 3, 5, 4 ] #365 [ 4, 3, 2, 5, 4, 3, 1, 2, 3 ] #393 [ 1, 3, 1, 2, 3, 4, 3, 5, 4 ] 11.3 = 5311(11) in family 1.31 = 5311 #55 [ 2, 4, 3, 1 ] #59 [ 4, 3, 1, 2 ] #64 [ 2, 3, 1, 4 ] #72 [ 3, 1, 2, 4 ] #90 [ 1, 2, 4, 3 ] #94 [ 1, 4, 3, 2 ] #98 [ 1, 2, 3, 4 ] #99 [ 1, 3, 2, 4 ] #109 [ 2, 4, 3, 1, 2 ] #113 [ 2, 3, 4, 3, 1 ] #119 [ 3, 4, 3, 1, 2 ] #121 [ 2, 3, 1, 2, 4 ] #141 [ 1, 2, 4, 3, 1 ] #146 [ 1, 4, 3, 1, 2 ] #149 [ 1, 2, 3, 1, 4 ] #153 [ 1, 2, 4, 3, 2 ] #156 [ 1, 2, 3, 4, 3 ] #157 [ 1, 3, 1, 2, 4 ] #160 [ 1, 3, 4, 3, 2 ] #161 [ 1, 2, 3, 2, 4 ] #177 [ 2, 3, 5, 4, 3, 1 ] #181 [ 3, 5, 4, 3, 1, 2 ] #185 [ 2, 3, 4, 3, 1, 5 ] #189 [ 3, 4, 3, 1, 2, 5 ] #221 [ 1, 2, 3, 5, 4, 3 ] #225 [ 1, 3, 5, 4, 3, 2 ] #229 [ 1, 2, 3, 4, 3, 5 ] #234 [ 1, 3, 4, 3, 2, 5 ] 1.31 = 5311 in family 1.31 = 5311 #55 [ 2, 4, 3, 1 ] #59 [ 4, 3, 1, 2 ] #64 [ 2, 3, 1, 4 ] #72 [ 3, 1, 2, 4 ] #90 [ 1, 2, 4, 3 ] #94 [ 1, 4, 3, 2 ] #98 [ 1, 2, 3, 4 ] #99 [ 1, 3, 2, 4 ] #103 [ 2, 5, 4, 3, 1 ] #104 [ 2, 4, 3, 1, 5 ] #107 [ 5, 4, 3, 1, 2 ] #108 [ 4, 3, 1, 2, 5 ] #109 [ 2, 4, 3, 1, 2 ] #112 [ 2, 3, 1, 5, 4 ] #113 [ 2, 3, 4, 3, 1 ] #119 [ 3, 4, 3, 1, 2 ] #120 [ 3, 1, 2, 5, 4 ] #121 [ 2, 3, 1, 2, 4 ] #124 [ 2, 3, 1, 4, 5 ] #130 [ 3, 1, 2, 4, 5 ] #141 [ 1, 2, 4, 3, 1 ] #144 [ 1, 2, 5, 4, 3 ] #145 [ 1, 2, 4, 3, 5 ] #146 [ 1, 4, 3, 1, 2 ] #149 [ 1, 2, 3, 1, 4 ] #150 [ 1, 5, 4, 3, 2 ] #151 [ 1, 4, 3, 2, 5 ] #153 [ 1, 2, 4, 3, 2 ] #155 [ 1, 2, 3, 5, 4 ] #156 [ 1, 2, 3, 4, 3 ] #157 [ 1, 3, 1, 2, 4 ] #159 [ 1, 3, 2, 5, 4 ] #160 [ 1, 3, 4, 3, 2 ] #161 [ 1, 2, 3, 2, 4 ] #164 [ 1, 2, 3, 4, 5 ] #165 [ 1, 3, 2, 4, 5 ] #169 [ 2, 4, 5, 4, 3, 1 ] #173 [ 4, 5, 4, 3, 1, 2 ] #174 [ 2, 5, 4, 3, 1, 2 ] #175 [ 2, 4, 3, 1, 2, 5 ] #177 [ 2, 3, 5, 4, 3, 1 ] #181 [ 3, 5, 4, 3, 1, 2 ] #182 [ 2, 3, 1, 2, 5, 4 ] #184 [ 2, 3, 1, 4, 5, 4 ] #185 [ 2, 3, 4, 3, 1, 5 ] #189 [ 3, 4, 3, 1, 2, 5 ] #190 [ 3, 1, 2, 4, 5, 4 ] #191 [ 2, 3, 1, 2, 4, 5 ] #206 [ 1, 2, 5, 4, 3, 1 ] #207 [ 1, 2, 4, 3, 1, 5 ] #212 [ 1, 2, 4, 5, 4, 3 ] #213 [ 1, 5, 4, 3, 1, 2 ] #214 [ 1, 4, 3, 1, 2, 5 ] #215 [ 1, 2, 3, 1, 5, 4 ] #217 [ 1, 4, 5, 4, 3, 2 ] #218 [ 1, 2, 5, 4, 3, 2 ] #219 [ 1, 2, 4, 3, 2, 5 ] #221 [ 1, 2, 3, 5, 4, 3 ] #222 [ 1, 3, 1, 2, 5, 4 ] #224 [ 1, 2, 3, 1, 4, 5 ] #225 [ 1, 3, 5, 4, 3, 2 ] #226 [ 1, 2, 3, 2, 5, 4 ] #228 [ 1, 2, 3, 4, 5, 4 ] #229 [ 1, 2, 3, 4, 3, 5 ] #230 [ 1, 3, 1, 2, 4, 5 ] #233 [ 1, 3, 2, 4, 5, 4 ] #234 [ 1, 3, 4, 3, 2, 5 ] #235 [ 1, 2, 3, 2, 4, 5 ] #236 [ 2, 5, 4, 3, 1, 2, 3 ] #237 [ 2, 4, 3, 1, 2, 3, 5 ] #238 [ 2, 3, 1, 2, 3, 5, 4 ] #239 [ 2, 3, 1, 2, 3, 4, 5 ] #241 [ 3, 1, 5, 4, 3, 1, 2 ] #242 [ 2, 3, 1, 5, 4, 3, 1 ] #243 [ 2, 4, 5, 4, 3, 1, 2 ] #246 [ 2, 4, 3, 5, 4, 3, 1 ] #247 [ 3, 1, 4, 3, 1, 2, 5 ] #248 [ 2, 3, 1, 4, 3, 1, 5 ] #249 [ 4, 3, 5, 4, 3, 1, 2 ] #251 [ 2, 3, 4, 3, 1, 5, 4 ] #255 [ 3, 4, 3, 1, 2, 5, 4 ] #256 [ 2, 3, 1, 2, 4, 5, 4 ] #258 [ 3, 2, 5, 4, 3, 1, 2 ] #261 [ 2, 3, 2, 5, 4, 3, 1 ] #263 [ 3, 2, 4, 3, 1, 2, 5 ] #265 [ 2, 3, 2, 4, 3, 1, 5 ] #267 [ 1, 5, 4, 3, 1, 2, 3 ] #268 [ 1, 4, 3, 1, 2, 3, 5 ] #269 [ 1, 3, 1, 2, 3, 5, 4 ] #270 [ 1, 3, 1, 2, 3, 4, 5 ] #274 [ 1, 2, 4, 5, 4, 3, 1 ] #277 [ 1, 3, 1, 5, 4, 3, 2 ] #278 [ 1, 2, 3, 1, 5, 4, 3 ] #281 [ 1, 4, 5, 4, 3, 1, 2 ] #285 [ 1, 3, 1, 4, 3, 2, 5 ] #286 [ 1, 2, 3, 1, 4, 3, 5 ] #287 [ 1, 2, 4, 5, 4, 3, 2 ] #288 [ 1, 2, 4, 3, 5, 4, 3 ] #289 [ 1, 2, 3, 1, 4, 5, 4 ] #290 [ 1, 4, 3, 5, 4, 3, 2 ] #292 [ 1, 2, 3, 4, 3, 5, 4 ] #293 [ 1, 3, 1, 2, 4, 5, 4 ] #294 [ 1, 3, 2, 5, 4, 3, 2 ] #295 [ 1, 2, 3, 2, 5, 4, 3 ] #297 [ 1, 3, 4, 3, 2, 5, 4 ] #298 [ 1, 2, 3, 2, 4, 5, 4 ] #299 [ 1, 3, 2, 4, 3, 2, 5 ] #300 [ 1, 2, 3, 2, 4, 3, 5 ] #301 [ 2, 4, 5, 4, 3, 1, 2, 3 ] #302 [ 2, 3, 1, 2, 3, 4, 5, 4 ] #303 [ 4, 3, 1, 5, 4, 3, 1, 2 ] #304 [ 2, 4, 3, 1, 5, 4, 3, 1 ] #305 [ 2, 3, 1, 2, 3, 5, 4, 3 ] #306 [ 2, 3, 1, 2, 3, 4, 3, 5 ] #307 [ 3, 1, 5, 4, 3, 1, 2, 3 ] #311 [ 3, 1, 4, 3, 1, 2, 3, 5 ] #312 [ 2, 3, 4, 3, 5, 4, 3, 1 ] #313 [ 3, 2, 5, 4, 3, 1, 2, 3 ] #315 [ 2, 3, 1, 2, 5, 4, 3, 1 ] #316 [ 3, 4, 3, 5, 4, 3, 1, 2 ] #317 [ 4, 3, 2, 5, 4, 3, 1, 2 ] #320 [ 3, 2, 4, 3, 1, 2, 3, 5 ] #321 [ 2, 3, 1, 2, 4, 3, 1, 5 ] #326 [ 2, 3, 2, 4, 3, 1, 5, 4 ] #327 [ 1, 4, 5, 4, 3, 1, 2, 3 ] #328 [ 1, 3, 1, 2, 3, 4, 5, 4 ] #339 [ 1, 3, 1, 4, 3, 2, 5, 4 ] #340 [ 1, 2, 3, 1, 4, 3, 5, 4 ] #341 [ 1, 3, 1, 2, 3, 5, 4, 3 ] #342 [ 1, 3, 1, 2, 3, 4, 3, 5 ] #345 [ 1, 3, 1, 2, 5, 4, 3, 2 ] #348 [ 1, 3, 1, 2, 4, 3, 2, 5 ] #349 [ 1, 2, 3, 4, 3, 5, 4, 3 ] #350 [ 1, 4, 3, 2, 5, 4, 3, 2 ] #352 [ 1, 3, 4, 3, 5, 4, 3, 2 ] #354 [ 1, 2, 3, 2, 4, 3, 5, 4 ] #356 [ 4, 3, 1, 5, 4, 3, 1, 2, 3 ] #357 [ 3, 4, 3, 1, 5, 4, 3, 1, 2 ] #358 [ 2, 3, 4, 3, 1, 5, 4, 3, 1 ] #364 [ 2, 3, 1, 2, 3, 4, 3, 5, 4 ] #365 [ 4, 3, 2, 5, 4, 3, 1, 2, 3 ] #368 [ 2, 4, 3, 2, 5, 4, 3, 1, 2 ] #370 [ 3, 4, 3, 2, 5, 4, 3, 1, 2 ] #373 [ 2, 3, 2, 4, 3, 1, 2, 5, 4 ] #374 [ 2, 3, 2, 4, 3, 5, 4, 3, 1 ] #381 [ 1, 4, 3, 1, 5, 4, 3, 1, 2 ] #382 [ 1, 2, 4, 3, 1, 5, 4, 3, 1 ] #384 [ 1, 3, 1, 4, 3, 1, 2, 5, 4 ] #385 [ 1, 3, 1, 4, 3, 5, 4, 3, 2 ] #386 [ 1, 2, 3, 1, 4, 3, 5, 4, 3 ] #387 [ 1, 2, 3, 1, 4, 3, 1, 5, 4 ] #393 [ 1, 3, 1, 2, 3, 4, 3, 5, 4 ] #395 [ 1, 2, 4, 3, 2, 5, 4, 3, 2 ] #396 [ 1, 3, 4, 3, 2, 5, 4, 3, 2 ] #397 [ 1, 2, 3, 2, 4, 3, 5, 4, 3 ] #398 [ 1, 2, 3, 2, 4, 3, 2, 5, 4 ] #399 [ 3, 1, 4, 3, 1, 5, 4, 3, 1, 2 ] #400 [ 2, 3, 1, 4, 3, 1, 5, 4, 3, 1 ] #405 [ 2, 3, 1, 2, 3, 4, 3, 5, 4, 3 ] #406 [ 3, 4, 3, 1, 5, 4, 3, 1, 2, 3 ] #407 [ 2, 4, 3, 2, 5, 4, 3, 1, 2, 3 ] #408 [ 2, 3, 1, 2, 3, 4, 3, 1, 5, 4 ] #410 [ 3, 4, 3, 2, 5, 4, 3, 1, 2, 3 ] #411 [ 3, 2, 4, 3, 2, 5, 4, 3, 1, 2 ] #413 [ 2, 3, 2, 4, 3, 2, 5, 4, 3, 1 ] #414 [ 2, 3, 2, 4, 3, 1, 5, 4, 3, 1 ] #420 [ 1, 3, 1, 4, 3, 1, 5, 4, 3, 2 ] #421 [ 1, 3, 1, 4, 3, 2, 5, 4, 3, 2 ] #422 [ 1, 2, 3, 1, 4, 3, 1, 5, 4, 3 ] #423 [ 1, 4, 3, 1, 5, 4, 3, 1, 2, 3 ] #424 [ 1, 3, 1, 2, 3, 4, 3, 2, 5, 4 ] #428 [ 1, 3, 1, 2, 3, 4, 3, 5, 4, 3 ] #431 [ 1, 3, 2, 4, 3, 2, 5, 4, 3, 2 ] #432 [ 1, 2, 3, 2, 4, 3, 2, 5, 4, 3 ] #433 [ 3, 1, 4, 3, 1, 5, 4, 3, 1, 2, 3 ] #438 [ 2, 3, 1, 2, 3, 4, 3, 1, 5, 4, 3 ] #439 [ 2, 3, 1, 2, 4, 3, 1, 5, 4, 3, 1 ] #440 [ 3, 2, 4, 3, 2, 5, 4, 3, 1, 2, 3 ] #442 [ 2, 3, 2, 4, 3, 1, 2, 5, 4, 3, 1 ] #444 [ 1, 3, 1, 2, 3, 4, 3, 2, 5, 4, 3 ] #446 [ 1, 3, 1, 4, 3, 1, 2, 5, 4, 3, 2 ] #450 [ 1, 3, 1, 2, 4, 3, 2, 5, 4, 3, 2 ] #456 [ 3, 1, 4, 3, 1, 5, 4, 3, 1, 2, 3, 4 ] #457 [ 2, 3, 2, 4, 3, 1, 2, 3, 4, 5, 4, 3 ] #459 [ 3, 2, 4, 3, 2, 5, 4, 3, 1, 2, 3, 4 ] #460 [ 2, 3, 2, 4, 3, 1, 2, 3, 5, 4, 3, 1 ] #464 [ 1, 3, 1, 4, 3, 1, 2, 3, 4, 5, 4, 3 ] #468 [ 1, 3, 1, 4, 3, 1, 2, 3, 5, 4, 3, 2 ] 1.211 = 331111 in family 1.211 = 331111 #244 [ 2, 3, 1, 2, 3, 4, 3 ] #245 [ 3, 1, 4, 3, 1, 2, 3 ] #252 [ 3, 2, 4, 3, 1, 2, 3 ] #253 [ 2, 3, 1, 2, 4, 3, 1 ] #282 [ 1, 3, 1, 2, 3, 4, 3 ] #283 [ 1, 3, 1, 2, 4, 3, 2 ]