11n
119
(K11n
119
)
A knot diagram
1
Linearized knot diagam
5 1 11 8 2 11 3 6 7 3 9
Solving Sequence
1,5
2 3
6,9
8 4 7 11 10
c
1
c
2
c
5
c
8
c
4
c
7
c
11
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
21
− 8u
20
+ ··· + b + 1, −25u
21
+ 124u
20
+ ··· + 2a + 34, u
22
− 6u
21
+ ··· − 10u + 2i
I
u
2
= hu
9
− 3u
7
− u
6
+ 5u
5
+ 3u
4
− 5u
3
− 5u
2
+ b + u + 3,
− u
9
− 3u
8
+ 4u
7
+ 5u
6
− 5u
5
− 12u
4
+ 4u
3
+ 8u
2
+ 2a + 3u − 6,
u
10
+ u
9
− 2u
8
− 3u
7
+ 3u
6
+ 6u
5
− 6u
3
− 3u
2
+ 2u + 2i
I
u
3
= hu
10
+ u
9
− u
8
− 2u
7
+ u
5
+ u
4
− u
2
a − au − u
2
+ b − u − 1, u
10
a − u
10
+ ··· + a + 1,
u
11
+ u
10
− 2u
9
− 3u
8
+ 2u
7
+ 4u
6
− 3u
4
− u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 54 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h2u
21
− 8u
20
+ · · · + b + 1, −25u
21
+ 124u
20
+ · · · + 2a + 34, u
22
−
6u
21
+ · · · − 10u + 2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
25
2
u
21
− 62u
20
+ ··· + 82u − 17
−2u
21
+ 8u
20
+ ··· − 3u − 1
a
8
=
17
2
u
21
− 44u
20
+ ··· + 61u − 13
−6u
21
+ 29u
20
+ ··· − 34u + 7
a
4
=
−
1
2
u
21
+ 5u
20
+ ··· − 18u + 5
u
21
− 6u
20
+ ··· + 13u − 3
a
7
=
21
2
u
21
− 54u
20
+ ··· + 76u − 16
−5u
21
+ 23u
20
+ ··· − 20u + 3
a
11
=
−
5
2
u
21
+ 12u
20
+ ··· − 18u + 5
−u
21
+ 5u
20
+ ··· − 4u + 1
a
10
=
−
9
2
u
21
+ 22u
20
+ ··· − 33u + 8
−2u
21
+ 11u
20
+ ··· − 18u + 5
a
10
=
−
9
2
u
21
+ 22u
20
+ ··· − 33u + 8
−2u
21
+ 11u
20
+ ··· − 18u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 14u
21
− 71u
20
+ 112u
19
+ 92u
18
− 557u
17
+ 596u
16
+ 457u
15
−
1669u
14
+ 1075u
13
+ 1272u
12
−2511u
11
+ 829u
10
+ 1721u
9
−2088u
8
+ 347u
7
+ 1061u
6
−
920u
5
+ 128u
4
+ 294u
3
− 268u
2
+ 118u − 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
22
+ 6u
21
+ ··· + 10u + 2
c
2
u
22
+ 10u
21
+ ··· − 12u + 4
c
3
, c
7
, c
10
u
22
+ u
21
+ ··· − 2u + 1
c
4
u
22
− u
21
+ ··· − 2u + 7
c
6
u
22
+ 24u
21
+ ··· + 22528u + 2048
c
8
, c
11
u
22
+ 2u
21
+ ··· + 2u + 1
c
9
u
22
− 11u
21
+ ··· + 122u + 26
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
22
− 10y
21
+ ··· + 12y + 4
c
2
y
22
+ 10y
21
+ ··· − 304y + 16
c
3
, c
7
, c
10
y
22
+ 35y
21
+ ··· + 4y + 1
c
4
y
22
+ 11y
21
+ ··· + 276y + 49
c
6
y
22
− 4y
21
+ ··· + 6291456y + 4194304
c
8
, c
11
y
22
+ 6y
21
+ ··· + 10y + 1
c
9
y
22
− 19y
21
+ ··· − 13636y + 676
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415944 + 0.915063I
a = −1.072660 − 0.878457I
b = 1.02363 + 1.11399I
−5.47166 + 8.64336I 0.86416 − 4.17929I
u = 0.415944 − 0.915063I
a = −1.072660 + 0.878457I
b = 1.02363 − 1.11399I
−5.47166 − 8.64336I 0.86416 + 4.17929I
u = −0.905217 + 0.345552I
a = −0.583392 + 0.385060I
b = −0.562525 + 1.184670I
−1.27214 − 0.90119I 0.90722 − 4.11146I
u = −0.905217 − 0.345552I
a = −0.583392 − 0.385060I
b = −0.562525 − 1.184670I
−1.27214 + 0.90119I 0.90722 + 4.11146I
u = 0.938475 + 0.452741I
a = −1.211750 − 0.402886I
b = 0.478302 − 0.375259I
−1.47927 − 1.70785I −2.03135 + 1.38197I
u = 0.938475 − 0.452741I
a = −1.211750 + 0.402886I
b = 0.478302 + 0.375259I
−1.47927 + 1.70785I −2.03135 − 1.38197I
u = −0.961052 + 0.415714I
a = 0.289661 − 0.427398I
b = −0.023327 − 1.083510I
−1.68977 + 3.84529I 0.76962 − 7.11396I
u = −0.961052 − 0.415714I
a = 0.289661 + 0.427398I
b = −0.023327 + 1.083510I
−1.68977 − 3.84529I 0.76962 + 7.11396I
u = 1.006010 + 0.554191I
a = 2.06591 + 0.80886I
b = −1.075660 + 0.915138I
0.29997 − 6.36774I −0.69331 + 5.66304I
u = 1.006010 − 0.554191I
a = 2.06591 − 0.80886I
b = −1.075660 − 0.915138I
0.29997 + 6.36774I −0.69331 − 5.66304I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.574081 + 0.572331I
a = 1.42670 + 1.36654I
b = −0.932058 − 0.660781I
1.59219 + 1.82500I 1.63588 − 1.17331I
u = 0.574081 − 0.572331I
a = 1.42670 − 1.36654I
b = −0.932058 + 0.660781I
1.59219 − 1.82500I 1.63588 + 1.17331I
u = 0.699271 + 0.989399I
a = −0.599352 + 0.221705I
b = 0.625328 − 0.499987I
−3.87629 − 3.75640I 1.54792 + 9.99919I
u = 0.699271 − 0.989399I
a = −0.599352 − 0.221705I
b = 0.625328 + 0.499987I
−3.87629 + 3.75640I 1.54792 − 9.99919I
u = −1.286580 + 0.073564I
a = 0.264997 − 0.359215I
b = 0.683728 − 1.124470I
−11.60060 − 5.70915I −5.06976 + 3.70908I
u = −1.286580 − 0.073564I
a = 0.264997 + 0.359215I
b = 0.683728 + 1.124470I
−11.60060 + 5.70915I −5.06976 − 3.70908I
u = 1.149220 + 0.647666I
a = −1.73202 − 0.77137I
b = 1.07821 − 1.26524I
−7.7036 − 14.3682I −1.51520 + 7.73205I
u = 1.149220 − 0.647666I
a = −1.73202 + 0.77137I
b = 1.07821 + 1.26524I
−7.7036 + 14.3682I −1.51520 − 7.73205I
u = 1.26179 + 0.79306I
a = 0.366388 − 0.137263I
b = 0.056443 + 0.483696I
−5.45392 − 3.28389I −19.7402 + 5.4613I
u = 1.26179 − 0.79306I
a = 0.366388 + 0.137263I
b = 0.056443 − 0.483696I
−5.45392 + 3.28389I −19.7402 − 5.4613I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108057 + 0.452974I
a = −0.214492 − 1.173680I
b = −0.352068 + 0.430105I
0.466609 − 1.223850I 4.32498 + 5.87640I
u = 0.108057 − 0.452974I
a = −0.214492 + 1.173680I
b = −0.352068 − 0.430105I
0.466609 + 1.223850I 4.32498 − 5.87640I
7
II.
I
u
2
= hu
9
− 3u
7
+ · · · + b + 3, −u
9
− 3u
8
+ · · · + 2a − 6, u
10
+ u
9
+ · · · + 2u + 2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
1
2
u
9
+
3
2
u
8
+ ··· −
3
2
u + 3
−u
9
+ 3u
7
+ u
6
− 5u
5
− 3u
4
+ 5u
3
+ 5u
2
− u − 3
a
8
=
−
1
2
u
9
+
1
2
u
8
+ ··· −
1
2
u + 1
u
7
− u
5
+ 2u
3
+ u
2
− 1
a
4
=
−
7
2
u
9
−
1
2
u
8
+ ··· −
3
2
u − 7
u
9
− 2u
7
− u
6
+ 4u
5
+ 2u
4
− 2u
3
− 3u
2
+ u + 1
a
7
=
−
1
2
u
9
+
1
2
u
8
+ ··· −
3
2
u + 2
−u
9
+ 3u
7
+ u
6
− 5u
5
− 3u
4
+ 4u
3
+ 5u
2
− 3
a
11
=
1
2
u
9
−
1
2
u
8
+ ··· +
3
2
u − 1
u
9
+ u
8
− 2u
7
− 2u
6
+ 3u
5
+ 4u
4
− 3u
2
− 2u + 1
a
10
=
1
2
u
9
−
1
2
u
8
+ ··· +
5
2
u − 2
2u
9
+ u
8
− 4u
7
− 3u
6
+ 7u
5
+ 7u
4
− 2u
3
− 7u
2
− 2u + 3
a
10
=
1
2
u
9
−
1
2
u
8
+ ··· +
5
2
u − 2
2u
9
+ u
8
− 4u
7
− 3u
6
+ 7u
5
+ 7u
4
− 2u
3
− 7u
2
− 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
9
− 4u
8
+ 12u
7
+ 8u
6
− 22u
5
− 18u
4
+ 9u
3
+ 16u
2
− 2u − 4
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
− 2u
8
− 3u
7
+ 3u
6
+ 6u
5
− 6u
3
− 3u
2
+ 2u + 2
c
2
u
10
+ 5u
9
+ ··· + 16u + 4
c
3
, c
7
u
10
+ u
9
+ 5u
8
+ 3u
7
+ 2u
6
− 2u
5
− 11u
4
− 5u
3
+ 4u
2
+ 3u + 1
c
4
u
10
− u
9
+ 5u
8
− u
7
+ 2u
6
+ 4u
5
+ 5u
4
− u
3
+ 4u
2
+ u + 1
c
5
u
10
− u
9
− 2u
8
+ 3u
7
+ 3u
6
− 6u
5
+ 6u
3
− 3u
2
− 2u + 2
c
6
u
10
+ u
9
− u
8
− 3u
7
+ 6u
6
− u
5
− 5u
4
+ 5u
3
− 2u + 1
c
8
, c
11
u
10
− 2u
9
+ 5u
7
− 5u
6
− u
5
+ 6u
4
− 3u
3
− u
2
+ u + 1
c
9
u
10
+ 8u
9
+ ··· + 6u + 2
c
10
u
10
− u
9
+ 5u
8
− 3u
7
+ 2u
6
+ 2u
5
− 11u
4
+ 5u
3
+ 4u
2
− 3u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
− 5y
9
+ ··· − 16y + 4
c
2
y
10
+ 7y
9
+ ··· + 8y + 16
c
3
, c
7
, c
10
y
10
+ 9y
9
+ 23y
8
− 7y
7
− 76y
6
+ 18y
5
+ 109y
4
− 97y
3
+ 24y
2
− y + 1
c
4
y
10
+ 9y
9
+ ··· + 7y + 1
c
6
y
10
− 3y
9
+ ··· − 4y + 1
c
8
, c
11
y
10
− 4y
9
+ ··· − 3y + 1
c
9
y
10
− 10y
9
+ ··· + 40y + 4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549591 + 0.807648I
a = −1.022010 + 0.680670I
b = 0.974163 − 0.530625I
3.57479 − 2.04304I 8.10074 + 2.61766I
u = −0.549591 − 0.807648I
a = −1.022010 − 0.680670I
b = 0.974163 + 0.530625I
3.57479 + 2.04304I 8.10074 − 2.61766I
u = −0.894446 + 0.383624I
a = 2.23680 − 2.15542I
b = −1.192680 − 0.156235I
−7.31599 + 1.59319I 1.11325 − 4.59194I
u = −0.894446 − 0.383624I
a = 2.23680 + 2.15542I
b = −1.192680 + 0.156235I
−7.31599 − 1.59319I 1.11325 + 4.59194I
u = 0.901394 + 0.162248I
a = 0.435559 + 0.459277I
b = 0.526185 + 0.973137I
−1.44150 + 1.63856I −1.63913 − 5.81422I
u = 0.901394 − 0.162248I
a = 0.435559 − 0.459277I
b = 0.526185 − 0.973137I
−1.44150 − 1.63856I −1.63913 + 5.81422I
u = −1.058430 + 0.638913I
a = −1.47976 + 0.79682I
b = 1.081130 + 0.779940I
2.02348 + 7.46141I 4.83399 − 7.19259I
u = −1.058430 − 0.638913I
a = −1.47976 − 0.79682I
b = 1.081130 − 0.779940I
2.02348 − 7.46141I 4.83399 + 7.19259I
u = 1.101080 + 0.716410I
a = −0.170585 + 0.035619I
b = −0.388800 − 0.327209I
−5.06545 − 3.26803I 2.59117 + 3.48613I
u = 1.101080 − 0.716410I
a = −0.170585 − 0.035619I
b = −0.388800 + 0.327209I
−5.06545 + 3.26803I 2.59117 − 3.48613I
11
III.
I
u
3
= hu
10
+ u
9
+ · · · + b − 1, u
10
a − u
10
+ · · · + a + 1, u
11
+ u
10
+ · · · + u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
a
−u
10
− u
9
+ u
8
+ 2u
7
− u
5
− u
4
+ u
2
a + au + u
2
+ u + 1
a
8
=
u
10
+ u
9
− 2u
8
− 3u
7
+ u
6
+ 3u
5
− u
3
a − u
2
a − 2u
3
− u
2
+ a + u
−2u
10
− 2u
9
+ ··· + u + 1
a
4
=
3u
10
− u
9
+ ··· + a − 1
−2u
10
a − 2u
9
a + ··· + 4u − 1
a
7
=
u
9
a + u
10
+ ··· + a − 1
−u
9
a − 2u
10
+ ··· + u + 1
a
11
=
u
9
a + u
10
+ ··· + a − 1
−u
9
a − 2u
10
+ ··· + au + 1
a
10
=
2u
9
a + u
10
+ ··· + a − 2
−2u
9
a − 2u
10
+ ··· + au + 1
a
10
=
2u
9
a + u
10
+ ··· + a − 2
−2u
9
a − 2u
10
+ ··· + au + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
10
− 12u
8
− 4u
7
+ 16u
6
+ 8u
5
− 8u
4
− 8u
3
+ 4u − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
2
c
2
(u
11
+ 5u
10
+ ··· + 2u + 1)
2
c
3
, c
7
, c
10
u
22
+ u
21
+ ··· − 18u + 59
c
4
u
22
− u
21
+ ··· + 1546u + 409
c
6
(u − 1)
22
c
8
, c
11
u
22
+ 9u
21
+ ··· + 56u + 7
c
9
(u
11
+ 9u
10
+ ··· + 10u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
11
− 5y
10
+ ··· + 2y −1)
2
c
2
(y
11
+ 3y
10
+ ··· − 10y −1)
2
c
3
, c
7
, c
10
y
22
+ 27y
21
+ ··· + 23040y + 3481
c
4
y
22
+ 15y
21
+ ··· + 1253256y + 167281
c
6
(y −1)
22
c
8
, c
11
y
22
− 5y
21
+ ··· + 504y + 49
c
9
(y
11
− 21y
10
+ ··· + 66y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959860 + 0.351396I
a = −1.82613 + 2.04832I
b = 2.03404 + 0.57190I
−8.21600 + 1.27541I −9.47945 − 0.80097I
u = −0.959860 + 0.351396I
a = 2.70937 − 1.39830I
b = 0.185361 − 0.335527I
−8.21600 + 1.27541I −9.47945 − 0.80097I
u = −0.959860 − 0.351396I
a = −1.82613 − 2.04832I
b = 2.03404 − 0.57190I
−8.21600 − 1.27541I −9.47945 + 0.80097I
u = −0.959860 − 0.351396I
a = 2.70937 + 1.39830I
b = 0.185361 + 0.335527I
−8.21600 − 1.27541I −9.47945 + 0.80097I
u = −0.488025 + 0.800566I
a = −0.986224 + 0.386436I
b = 0.522658 − 0.388649I
2.45893 − 1.64593I 0.049877 + 0.244807I
u = −0.488025 + 0.800566I
a = 0.816032 − 0.717910I
b = −1.061550 + 0.629616I
2.45893 − 1.64593I 0.049877 + 0.244807I
u = −0.488025 − 0.800566I
a = −0.986224 − 0.386436I
b = 0.522658 + 0.388649I
2.45893 + 1.64593I 0.049877 − 0.244807I
u = −0.488025 − 0.800566I
a = 0.816032 + 0.717910I
b = −1.061550 − 0.629616I
2.45893 + 1.64593I 0.049877 − 0.244807I
u = 1.11640
a = −0.497001 + 0.359330I
b = −0.064584 + 0.849005I
−3.19716 −5.81430
u = 1.11640
a = −0.497001 − 0.359330I
b = −0.064584 − 0.849005I
−3.19716 −5.81430
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031510 + 0.521913I
a = 0.42458 − 1.36387I
b = 1.53814 + 1.53725I
−6.95642 − 4.75030I −5.35891 + 6.77690I
u = 1.031510 + 0.521913I
a = −0.63779 − 1.77107I
b = 0.252273 − 0.903481I
−6.95642 − 4.75030I −5.35891 + 6.77690I
u = 1.031510 − 0.521913I
a = 0.42458 + 1.36387I
b = 1.53814 − 1.53725I
−6.95642 + 4.75030I −5.35891 − 6.77690I
u = 1.031510 − 0.521913I
a = −0.63779 + 1.77107I
b = 0.252273 + 0.903481I
−6.95642 + 4.75030I −5.35891 − 6.77690I
u = −1.081080 + 0.631709I
a = −1.37876 + 0.50428I
b = 0.630247 + 0.593092I
0.68511 + 7.02220I −2.49946 − 4.88619I
u = −1.081080 + 0.631709I
a = 1.36761 − 0.75322I
b = −1.14816 − 1.03156I
0.68511 + 7.02220I −2.49946 − 4.88619I
u = −1.081080 − 0.631709I
a = −1.37876 − 0.50428I
b = 0.630247 − 0.593092I
0.68511 − 7.02220I −2.49946 + 4.88619I
u = −1.081080 − 0.631709I
a = 1.36761 + 0.75322I
b = −1.14816 + 1.03156I
0.68511 − 7.02220I −2.49946 + 4.88619I
u = 0.439259 + 0.522038I
a = −0.618011 + 1.074030I
b = 0.527375 + 0.930749I
−5.28977 + 0.45477I −0.80492 − 1.36957I
u = 0.439259 + 0.522038I
a = −2.37368 − 0.13772I
b = 1.08420 − 1.22681I
−5.28977 + 0.45477I −0.80492 − 1.36957I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.439259 − 0.522038I
a = −0.618011 − 1.074030I
b = 0.527375 − 0.930749I
−5.28977 − 0.45477I −0.80492 + 1.36957I
u = 0.439259 − 0.522038I
a = −2.37368 + 0.13772I
b = 1.08420 + 1.22681I
−5.28977 − 0.45477I −0.80492 + 1.36957I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ u
9
− 2u
8
− 3u
7
+ 3u
6
+ 6u
5
− 6u
3
− 3u
2
+ 2u + 2)
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
2
· (u
22
+ 6u
21
+ ··· + 10u + 2)
c
2
(u
10
+ 5u
9
+ ··· + 16u + 4)(u
11
+ 5u
10
+ ··· + 2u + 1)
2
· (u
22
+ 10u
21
+ ··· − 12u + 4)
c
3
, c
7
(u
10
+ u
9
+ 5u
8
+ 3u
7
+ 2u
6
− 2u
5
− 11u
4
− 5u
3
+ 4u
2
+ 3u + 1)
· (u
22
+ u
21
+ ··· − 18u + 59)(u
22
+ u
21
+ ··· − 2u + 1)
c
4
(u
10
− u
9
+ 5u
8
− u
7
+ 2u
6
+ 4u
5
+ 5u
4
− u
3
+ 4u
2
+ u + 1)
· (u
22
− u
21
+ ··· − 2u + 7)(u
22
− u
21
+ ··· + 1546u + 409)
c
5
(u
10
− u
9
− 2u
8
+ 3u
7
+ 3u
6
− 6u
5
+ 6u
3
− 3u
2
− 2u + 2)
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
2
· (u
22
+ 6u
21
+ ··· + 10u + 2)
c
6
(u − 1)
22
(u
10
+ u
9
− u
8
− 3u
7
+ 6u
6
− u
5
− 5u
4
+ 5u
3
− 2u + 1)
· (u
22
+ 24u
21
+ ··· + 22528u + 2048)
c
8
, c
11
(u
10
− 2u
9
+ 5u
7
− 5u
6
− u
5
+ 6u
4
− 3u
3
− u
2
+ u + 1)
· (u
22
+ 2u
21
+ ··· + 2u + 1)(u
22
+ 9u
21
+ ··· + 56u + 7)
c
9
(u
10
+ 8u
9
+ ··· + 6u + 2)(u
11
+ 9u
10
+ ··· + 10u − 1)
2
· (u
22
− 11u
21
+ ··· + 122u + 26)
c
10
(u
10
− u
9
+ 5u
8
− 3u
7
+ 2u
6
+ 2u
5
− 11u
4
+ 5u
3
+ 4u
2
− 3u + 1)
· (u
22
+ u
21
+ ··· − 18u + 59)(u
22
+ u
21
+ ··· − 2u + 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
− 5y
9
+ ··· − 16y + 4)(y
11
− 5y
10
+ ··· + 2y −1)
2
· (y
22
− 10y
21
+ ··· + 12y + 4)
c
2
(y
10
+ 7y
9
+ ··· + 8y + 16)(y
11
+ 3y
10
+ ··· − 10y −1)
2
· (y
22
+ 10y
21
+ ··· − 304y + 16)
c
3
, c
7
, c
10
(y
10
+ 9y
9
+ 23y
8
− 7y
7
− 76y
6
+ 18y
5
+ 109y
4
− 97y
3
+ 24y
2
− y + 1)
· (y
22
+ 27y
21
+ ··· + 23040y + 3481)(y
22
+ 35y
21
+ ··· + 4y + 1)
c
4
(y
10
+ 9y
9
+ ··· + 7y + 1)(y
22
+ 11y
21
+ ··· + 276y + 49)
· (y
22
+ 15y
21
+ ··· + 1253256y + 167281)
c
6
((y −1)
22
)(y
10
− 3y
9
+ ··· − 4y + 1)
· (y
22
− 4y
21
+ ··· + 6291456y + 4194304)
c
8
, c
11
(y
10
− 4y
9
+ ··· − 3y + 1)(y
22
− 5y
21
+ ··· + 504y + 49)
· (y
22
+ 6y
21
+ ··· + 10y + 1)
c
9
(y
10
− 10y
9
+ ··· + 40y + 4)(y
11
− 21y
10
+ ··· + 66y −1)
2
· (y
22
− 19y
21
+ ··· − 13636y + 676)
19
