total num of chars: 25 total num of families: 11 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: phi{4,1} = F4(a1) in family phi{4,1} = F4(a1) phi{9,2} = F4(a2) in family phi{9,2} = F4(a2) phi{9,6}' = F4(a3)(31) in family phi{12,4} = F4(a3) phi{12,4} = F4(a3) in family phi{12,4} = F4(a3) phi{16,5} = C3(a1) in family phi{12,4} = F4(a3) phi{9,6}'' = B2 in family phi{12,4} = F4(a3) phi{4,13} = ~A1 in family phi{4,13} = ~A1 | 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. | 98 rationally smooth elements where some polynomial has strictly negative coeffs. phi{4,1} = F4(a1) in family phi{4,1} = F4(a1) #31 [ 4, 3, 2, 1 ] #32 [ 3, 2, 1, 4 ] #35 [ 2, 1, 4, 3 ] #40 [ 2, 1, 3, 4 ] #47 [ 1, 4, 3, 2 ] #48 [ 1, 3, 2, 4 ] #50 [ 1, 2, 4, 3 ] #53 [ 1, 2, 3, 4 ] #54 [ 3, 4, 3, 2, 1 ] #55 [ 4, 3, 2, 1, 3 ] #60 [ 2, 4, 3, 2, 1 ] #61 [ 3, 2, 1, 3, 4 ] #62 [ 2, 1, 3, 4, 3 ] #65 [ 2, 3, 2, 1, 4 ] #66 [ 1, 4, 3, 2, 1 ] #67 [ 1, 3, 2, 1, 4 ] #68 [ 1, 3, 4, 3, 2 ] #69 [ 1, 2, 1, 4, 3 ] #71 [ 1, 4, 3, 2, 3 ] #72 [ 1, 2, 4, 3, 2 ] #74 [ 1, 2, 1, 3, 4 ] #75 [ 1, 2, 3, 4, 3 ] #76 [ 1, 3, 2, 3, 4 ] #77 [ 1, 2, 3, 2, 4 ] #78 [ 3, 4, 3, 2, 1, 3 ] #80 [ 2, 1, 4, 3, 2, 1 ] #82 [ 2, 4, 3, 2, 1, 3 ] #83 [ 3, 2, 1, 3, 4, 3 ] #85 [ 2, 1, 3, 2, 1, 4 ] #86 [ 2, 3, 2, 1, 3, 4 ] #88 [ 1, 3, 4, 3, 2, 1 ] #90 [ 1, 2, 1, 4, 3, 2 ] #91 [ 1, 3, 4, 3, 2, 3 ] #93 [ 1, 2, 4, 3, 2, 3 ] #94 [ 1, 2, 1, 3, 4, 3 ] #95 [ 1, 2, 1, 3, 2, 4 ] #96 [ 1, 3, 2, 3, 4, 3 ] #97 [ 1, 2, 3, 2, 3, 4 ] #99 [ 2, 4, 3, 2, 1, 3, 2 ] #100 [ 3, 2, 4, 3, 2, 1, 3 ] #101 [ 3, 4, 3, 2, 1, 3, 4 ] #102 [ 2, 3, 2, 1, 3, 2, 4 ] #103 [ 2, 3, 2, 1, 3, 4, 3 ] #107 [ 1, 2, 1, 4, 3, 2, 3 ] #108 [ 1, 2, 1, 3, 2, 3, 4 ] #109 [ 1, 2, 1, 4, 3, 2, 1 ] #110 [ 1, 3, 2, 4, 3, 2, 3 ] #111 [ 1, 3, 4, 3, 2, 3, 4 ] #112 [ 1, 2, 1, 3, 2, 1, 4 ] #113 [ 1, 2, 3, 2, 3, 4, 3 ] #115 [ 2, 4, 3, 2, 1, 3, 2, 3 ] #116 [ 2, 3, 2, 1, 3, 2, 3, 4 ] #117 [ 3, 2, 4, 3, 2, 1, 3, 2 ] #119 [ 2, 3, 2, 3, 4, 3, 2, 1 ] #120 [ 2, 3, 2, 4, 3, 2, 1, 3 ] #121 [ 1, 4, 3, 2, 1, 3, 2, 3 ] #122 [ 1, 3, 2, 1, 3, 2, 3, 4 ] #123 [ 1, 2, 1, 3, 2, 3, 4, 3 ] #124 [ 1, 2, 3, 2, 4, 3, 2, 3 ] #125 [ 1, 2, 3, 2, 3, 4, 3, 2 ] #126 [ 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #127 [ 2, 1, 3, 2, 1, 3, 2, 3, 4 ] #128 [ 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #129 [ 2, 3, 2, 1, 3, 2, 3, 4, 3 ] #131 [ 2, 3, 2, 3, 4, 3, 2, 1, 3 ] #132 [ 2, 3, 2, 1, 3, 4, 3, 2, 1 ] #133 [ 2, 3, 2, 4, 3, 2, 1, 3, 2 ] #135 [ 1, 3, 4, 3, 2, 1, 3, 2, 3 ] #136 [ 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #137 [ 1, 2, 1, 3, 2, 3, 4, 3, 2 ] #138 [ 1, 2, 1, 3, 2, 4, 3, 2, 3 ] #139 [ 1, 2, 3, 2, 3, 4, 3, 2, 3 ] #140 [ 3, 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #141 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #142 [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2 ] #144 [ 2, 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #147 [ 1, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #148 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] #150 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] #152 [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3 ] #153 [ 2, 3, 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #156 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #158 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #161 [ 2, 3, 2, 1, 3, 4, 3, 2, 1, 3, 2, 3 ] phi{9,2} = F4(a2) in family phi{9,2} = F4(a2) #82 [ 2, 4, 3, 2, 1, 3 ] #86 [ 2, 3, 2, 1, 3, 4 ] #93 [ 1, 2, 4, 3, 2, 3 ] #97 [ 1, 2, 3, 2, 3, 4 ] #99 [ 2, 4, 3, 2, 1, 3, 2 ] #100 [ 3, 2, 4, 3, 2, 1, 3 ] #102 [ 2, 3, 2, 1, 3, 2, 4 ] #103 [ 2, 3, 2, 1, 3, 4, 3 ] #107 [ 1, 2, 1, 4, 3, 2, 3 ] #108 [ 1, 2, 1, 3, 2, 3, 4 ] #110 [ 1, 3, 2, 4, 3, 2, 3 ] #113 [ 1, 2, 3, 2, 3, 4, 3 ] phi{9,6}' = F4(a3)(31) in family phi{12,4} = F4(a3) #82 [ 2, 4, 3, 2, 1, 3 ] #86 [ 2, 3, 2, 1, 3, 4 ] #93 [ 1, 2, 4, 3, 2, 3 ] #97 [ 1, 2, 3, 2, 3, 4 ] #99 [ 2, 4, 3, 2, 1, 3, 2 ] #100 [ 3, 2, 4, 3, 2, 1, 3 ] #102 [ 2, 3, 2, 1, 3, 2, 4 ] #103 [ 2, 3, 2, 1, 3, 4, 3 ] #107 [ 1, 2, 1, 4, 3, 2, 3 ] #108 [ 1, 2, 1, 3, 2, 3, 4 ] #110 [ 1, 3, 2, 4, 3, 2, 3 ] #113 [ 1, 2, 3, 2, 3, 4, 3 ] #115 [ 2, 4, 3, 2, 1, 3, 2, 3 ] #116 [ 2, 3, 2, 1, 3, 2, 3, 4 ] #117 [ 3, 2, 4, 3, 2, 1, 3, 2 ] #119 [ 2, 3, 2, 3, 4, 3, 2, 1 ] #120 [ 2, 3, 2, 4, 3, 2, 1, 3 ] #121 [ 1, 4, 3, 2, 1, 3, 2, 3 ] #122 [ 1, 3, 2, 1, 3, 2, 3, 4 ] #123 [ 1, 2, 1, 3, 2, 3, 4, 3 ] #124 [ 1, 2, 3, 2, 4, 3, 2, 3 ] #125 [ 1, 2, 3, 2, 3, 4, 3, 2 ] #128 [ 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #129 [ 2, 3, 2, 1, 3, 2, 3, 4, 3 ] #132 [ 2, 3, 2, 1, 3, 4, 3, 2, 1 ] #133 [ 2, 3, 2, 4, 3, 2, 1, 3, 2 ] #135 [ 1, 3, 4, 3, 2, 1, 3, 2, 3 ] #136 [ 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #137 [ 1, 2, 1, 3, 2, 3, 4, 3, 2 ] #138 [ 1, 2, 1, 3, 2, 4, 3, 2, 3 ] #144 [ 2, 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #148 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] phi{12,4} = F4(a3) in family phi{12,4} = F4(a3) #82 [ 2, 4, 3, 2, 1, 3 ] #86 [ 2, 3, 2, 1, 3, 4 ] #93 [ 1, 2, 4, 3, 2, 3 ] #97 [ 1, 2, 3, 2, 3, 4 ] #99 [ 2, 4, 3, 2, 1, 3, 2 ] #100 [ 3, 2, 4, 3, 2, 1, 3 ] #102 [ 2, 3, 2, 1, 3, 2, 4 ] #103 [ 2, 3, 2, 1, 3, 4, 3 ] #107 [ 1, 2, 1, 4, 3, 2, 3 ] #108 [ 1, 2, 1, 3, 2, 3, 4 ] #110 [ 1, 3, 2, 4, 3, 2, 3 ] #113 [ 1, 2, 3, 2, 3, 4, 3 ] #117 [ 3, 2, 4, 3, 2, 1, 3, 2 ] #123 [ 1, 2, 1, 3, 2, 3, 4, 3 ] phi{16,5} = C3(a1) in family phi{12,4} = F4(a3) #18 [ 4, 3, 2 ] #19 [ 3, 2, 4 ] #22 [ 2, 4, 3 ] #24 [ 2, 3, 4 ] #31 [ 4, 3, 2, 1 ] #32 [ 3, 2, 1, 4 ] #33 [ 3, 4, 3, 2 ] #35 [ 2, 1, 4, 3 ] #36 [ 4, 3, 2, 3 ] #38 [ 2, 4, 3, 2 ] #40 [ 2, 1, 3, 4 ] #41 [ 3, 2, 3, 4 ] #42 [ 2, 3, 4, 3 ] #43 [ 2, 3, 2, 4 ] #47 [ 1, 4, 3, 2 ] #48 [ 1, 3, 2, 4 ] #50 [ 1, 2, 4, 3 ] #53 [ 1, 2, 3, 4 ] #54 [ 3, 4, 3, 2, 1 ] #55 [ 4, 3, 2, 1, 3 ] #56 [ 3, 4, 3, 2, 3 ] #60 [ 2, 4, 3, 2, 1 ] #61 [ 3, 2, 1, 3, 4 ] #62 [ 2, 1, 3, 4, 3 ] #63 [ 3, 2, 3, 4, 3 ] #65 [ 2, 3, 2, 1, 4 ] #66 [ 1, 4, 3, 2, 1 ] #67 [ 1, 3, 2, 1, 4 ] #68 [ 1, 3, 4, 3, 2 ] #69 [ 1, 2, 1, 4, 3 ] #71 [ 1, 4, 3, 2, 3 ] #72 [ 1, 2, 4, 3, 2 ] #74 [ 1, 2, 1, 3, 4 ] #75 [ 1, 2, 3, 4, 3 ] #76 [ 1, 3, 2, 3, 4 ] #77 [ 1, 2, 3, 2, 4 ] #78 [ 3, 4, 3, 2, 1, 3 ] #80 [ 2, 1, 4, 3, 2, 1 ] #83 [ 3, 2, 1, 3, 4, 3 ] #84 [ 3, 4, 3, 2, 3, 4 ] #85 [ 2, 1, 3, 2, 1, 4 ] #88 [ 1, 3, 4, 3, 2, 1 ] #90 [ 1, 2, 1, 4, 3, 2 ] #91 [ 1, 3, 4, 3, 2, 3 ] #94 [ 1, 2, 1, 3, 4, 3 ] #95 [ 1, 2, 1, 3, 2, 4 ] #96 [ 1, 3, 2, 3, 4, 3 ] #101 [ 3, 4, 3, 2, 1, 3, 4 ] #109 [ 1, 2, 1, 4, 3, 2, 1 ] #111 [ 1, 3, 4, 3, 2, 3, 4 ] #112 [ 1, 2, 1, 3, 2, 1, 4 ] #115 [ 2, 4, 3, 2, 1, 3, 2, 3 ] #116 [ 2, 3, 2, 1, 3, 2, 3, 4 ] #117 [ 3, 2, 4, 3, 2, 1, 3, 2 ] #119 [ 2, 3, 2, 3, 4, 3, 2, 1 ] #120 [ 2, 3, 2, 4, 3, 2, 1, 3 ] #121 [ 1, 4, 3, 2, 1, 3, 2, 3 ] #122 [ 1, 3, 2, 1, 3, 2, 3, 4 ] #123 [ 1, 2, 1, 3, 2, 3, 4, 3 ] #124 [ 1, 2, 3, 2, 4, 3, 2, 3 ] #125 [ 1, 2, 3, 2, 3, 4, 3, 2 ] #126 [ 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #127 [ 2, 1, 3, 2, 1, 3, 2, 3, 4 ] #128 [ 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #129 [ 2, 3, 2, 1, 3, 2, 3, 4, 3 ] #131 [ 2, 3, 2, 3, 4, 3, 2, 1, 3 ] #132 [ 2, 3, 2, 1, 3, 4, 3, 2, 1 ] #133 [ 2, 3, 2, 4, 3, 2, 1, 3, 2 ] #135 [ 1, 3, 4, 3, 2, 1, 3, 2, 3 ] #136 [ 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #137 [ 1, 2, 1, 3, 2, 3, 4, 3, 2 ] #138 [ 1, 2, 1, 3, 2, 4, 3, 2, 3 ] #139 [ 1, 2, 3, 2, 3, 4, 3, 2, 3 ] #140 [ 3, 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #141 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #142 [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2 ] #144 [ 2, 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #147 [ 1, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #148 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] #150 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] #152 [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3 ] #153 [ 2, 3, 2, 1, 4, 3, 2, 1, 3, 2, 3 ] #156 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #158 [ 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 3 ] #161 [ 2, 3, 2, 1, 3, 4, 3, 2, 1, 3, 2, 3 ] phi{9,6}'' = B2 in family phi{12,4} = F4(a3) #117 [ 3, 2, 4, 3, 2, 1, 3, 2 ] #123 [ 1, 2, 1, 3, 2, 3, 4, 3 ] #128 [ 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #129 [ 2, 3, 2, 1, 3, 2, 3, 4, 3 ] #132 [ 2, 3, 2, 1, 3, 4, 3, 2, 1 ] #133 [ 2, 3, 2, 4, 3, 2, 1, 3, 2 ] #135 [ 1, 3, 4, 3, 2, 1, 3, 2, 3 ] #136 [ 1, 3, 2, 1, 3, 2, 3, 4, 3 ] #137 [ 1, 2, 1, 3, 2, 3, 4, 3, 2 ] #138 [ 1, 2, 1, 3, 2, 4, 3, 2, 3 ] #144 [ 2, 3, 2, 4, 3, 2, 1, 3, 2, 3 ] #148 [ 1, 3, 2, 1, 3, 2, 3, 4, 3, 2 ] phi{4,13} = ~A1 in family phi{4,13} = ~A1 #21 [ 3, 2, 3 ] #36 [ 4, 3, 2, 3 ] #41 [ 3, 2, 3, 4 ]