total num of chars: 20
total num of families: 10

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:
    1.111 = 221111               in family 1.111 = 221111              
    3.1 = 62                     in family 3.1 = 62                    
    11.11 = 2222                 in family 11.11 = 2222                
    2.11 = 4211                  in family 2.11 = 4211                 

| 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.
| 70 rationally smooth elements where some polynomial has strictly negative coeffs.
    3.1 = 62                     in family 3.1 = 62                    
      #34 [ 4, 3, 2, 1 ]
      #36 [ 3, 2, 1, 4 ]
      #39 [ 2, 1, 4, 3 ]
      #42 [ 2, 1, 3, 4 ]
      #46 [ 1, 4, 3, 2 ]
      #48 [ 1, 3, 2, 4 ]
      #50 [ 1, 2, 4, 3 ]
      #52 [ 1, 2, 3, 4 ]
      #53 [ 4, 3, 2, 1, 2 ]
      #54 [ 3, 2, 1, 2, 4 ]
      #55 [ 2, 1, 2, 4, 3 ]
      #56 [ 2, 1, 2, 3, 4 ]
      #57 [ 3, 4, 3, 2, 1 ]
      #60 [ 2, 4, 3, 2, 1 ]
      #63 [ 2, 3, 2, 1, 4 ]
      #64 [ 2, 1, 3, 4, 3 ]
      #68 [ 1, 4, 3, 2, 1 ]
      #69 [ 1, 3, 4, 3, 2 ]
      #70 [ 1, 3, 2, 1, 4 ]
      #71 [ 1, 2, 1, 4, 3 ]
      #72 [ 1, 2, 4, 3, 2 ]
      #73 [ 1, 2, 1, 3, 4 ]
      #74 [ 1, 2, 3, 4, 3 ]
      #75 [ 1, 2, 3, 2, 4 ]
      #76 [ 3, 4, 3, 2, 1, 2 ]
      #77 [ 2, 1, 2, 3, 4, 3 ]
      #79 [ 2, 1, 2, 4, 3, 2 ]
      #80 [ 2, 1, 2, 3, 2, 4 ]
      #81 [ 3, 2, 4, 3, 2, 1 ]
      #82 [ 2, 4, 3, 2, 1, 2 ]
      #85 [ 2, 3, 2, 1, 4, 3 ]
      #86 [ 2, 3, 2, 1, 2, 4 ]
      #91 [ 1, 3, 4, 3, 2, 1 ]
      #93 [ 1, 3, 2, 4, 3, 2 ]
      #94 [ 1, 2, 1, 3, 4, 3 ]
      #95 [ 1, 2, 3, 2, 4, 3 ]
      #96 [ 2, 4, 3, 2, 1, 2, 3 ]
      #97 [ 2, 3, 2, 1, 2, 3, 4 ]
      #98 [ 3, 2, 4, 3, 2, 1, 2 ]
      #100 [ 2, 1, 2, 3, 2, 4, 3 ]
      #101 [ 2, 3, 2, 4, 3, 2, 1 ]
      #109 [ 1, 2, 3, 2, 4, 3, 2 ]
      #110 [ 3, 2, 4, 3, 2, 1, 2, 3 ]
      #111 [ 3, 2, 1, 4, 3, 2, 1, 2 ]
      #112 [ 2, 3, 2, 1, 2, 3, 4, 3 ]
      #113 [ 2, 1, 2, 3, 2, 4, 3, 2 ]
      #114 [ 2, 3, 2, 4, 3, 2, 1, 2 ]
      #119 [ 1, 2, 1, 2, 3, 2, 4, 3 ]
      #121 [ 2, 3, 2, 1, 2, 3, 4, 3, 2 ]
      #122 [ 2, 3, 2, 1, 4, 3, 2, 1, 2 ]
      #123 [ 2, 3, 2, 4, 3, 2, 1, 2, 3 ]
      #127 [ 1, 3, 2, 1, 4, 3, 2, 1, 2 ]
      #128 [ 1, 2, 1, 2, 3, 2, 1, 4, 3 ]
      #129 [ 1, 2, 1, 2, 3, 2, 4, 3, 2 ]
      #130 [ 2, 3, 2, 4, 3, 2, 1, 2, 3, 4 ]
    2.11 = 4211                  in family 2.11 = 4211                 
      #18 [ 3, 2, 1 ]
      #23 [ 2, 1, 3 ]
      #29 [ 1, 3, 2 ]
      #30 [ 1, 2, 3 ]
      #31 [ 3, 2, 1, 2 ]
      #33 [ 2, 1, 2, 3 ]
      #38 [ 2, 3, 2, 1 ]
      #47 [ 1, 3, 2, 1 ]
      #49 [ 1, 2, 1, 3 ]
      #51 [ 1, 2, 3, 2 ]
      #53 [ 4, 3, 2, 1, 2 ]
      #54 [ 3, 2, 1, 2, 4 ]
      #55 [ 2, 1, 2, 4, 3 ]
      #56 [ 2, 1, 2, 3, 4 ]
      #58 [ 2, 1, 2, 3, 2 ]
      #60 [ 2, 4, 3, 2, 1 ]
      #61 [ 2, 3, 2, 1, 2 ]
      #63 [ 2, 3, 2, 1, 4 ]
      #72 [ 1, 2, 4, 3, 2 ]
      #75 [ 1, 2, 3, 2, 4 ]
      #76 [ 3, 4, 3, 2, 1, 2 ]
      #77 [ 2, 1, 2, 3, 4, 3 ]
      #78 [ 2, 3, 2, 1, 2, 3 ]
      #79 [ 2, 1, 2, 4, 3, 2 ]
      #80 [ 2, 1, 2, 3, 2, 4 ]
      #82 [ 2, 4, 3, 2, 1, 2 ]
      #86 [ 2, 3, 2, 1, 2, 4 ]
      #96 [ 2, 4, 3, 2, 1, 2, 3 ]
      #97 [ 2, 3, 2, 1, 2, 3, 4 ]
      #98 [ 3, 2, 4, 3, 2, 1, 2 ]
      #100 [ 2, 1, 2, 3, 2, 4, 3 ]
      #110 [ 3, 2, 4, 3, 2, 1, 2, 3 ]
      #112 [ 2, 3, 2, 1, 2, 3, 4, 3 ]
    11.11 = 2222                 in family 11.11 = 2222                
      #32 [ 2, 1, 2, 4 ]
      #53 [ 4, 3, 2, 1, 2 ]
      #54 [ 3, 2, 1, 2, 4 ]
      #55 [ 2, 1, 2, 4, 3 ]
      #56 [ 2, 1, 2, 3, 4 ]
    1.111 = 221111               in family 1.111 = 221111              
      #16 [ 2, 1, 2 ]
      #31 [ 3, 2, 1, 2 ]
      #33 [ 2, 1, 2, 3 ]