11a
325
(K11a
325
)
A knot diagram
1
Linearized knot diagam
7 9 1 11 8 2 10 3 6 5 4
Solving Sequence
2,9 3,6
7 10 1 4 8 5 11
c
2
c
6
c
9
c
1
c
3
c
8
c
5
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −36589u
20
− 75173u
19
+ ··· + 133419a + 168070, u
21
+ 7u
19
+ ··· + 2u − 1i
I
u
2
= h−1.50267 × 10
47
u
35
+ 7.89794 × 10
47
u
34
+ ··· + 8.17083 × 10
48
b + 1.26464 × 10
50
,
1.51725 × 10
32
u
35
+ 1.19597 × 10
32
u
34
+ ··· + 1.00338 × 10
33
a − 5.77606 × 10
33
, u
36
+ u
35
+ ··· − 88u + 121i
I
u
3
= hb + u, −u
9
− u
8
− 5u
7
− 5u
6
− 11u
5
− 9u
4
− 11u
3
− 6u
2
+ a − 5u − 1,
u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 67 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
= hb − u, −3.66 × 10
4
u
20
− 7.52 × 10
4
u
19
+ · · · + 1.33 × 10
5
a + 1.68 ×
10
5
, u
21
+ 7u
19
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0.274241u
20
+ 0.563435u
19
+ ··· − 0.725182u − 1.25972
u
a
7
=
0.274241u
20
+ 0.563435u
19
+ ··· + 0.274818u − 1.25972
u
a
10
=
−0.364446u
20
− 0.326445u
19
+ ··· + 0.141996u + 0.459290
−0.171242u
20
− 0.393302u
19
+ ··· + 0.147370u + 0.563435
a
1
=
0.563435u
20
− 0.171242u
19
+ ··· − 1.80820u + 1.27424
u
2
a
4
=
−0.535284u
20
+ 0.170748u
19
+ ··· + 1.53655u + 0.520353
0.0475045u
20
+ 0.315750u
19
+ ··· + 0.00530659u − 0.199304
a
8
=
−u
u
3
+ u
a
5
=
0.644788u
20
+ 0.909233u
19
+ ··· − 0.487914u − 1.42985
−0.254102u
20
+ 0.0146306u
19
+ ··· + 1.08378u − 0.175665
a
11
=
−0.582496u
20
− 0.577624u
19
+ ··· − 0.376093u + 0.851783
−0.441159u
20
− 0.406276u
19
+ ··· + 0.464934u + 0.246457
a
11
=
−0.582496u
20
− 0.577624u
19
+ ··· − 0.376093u + 0.851783
−0.441159u
20
− 0.406276u
19
+ ··· + 0.464934u + 0.246457
(ii) Obstruction class = −1
(iii) Cusp Shapes =
129645
44473
u
20
+
33237
44473
u
19
+ ··· −
265846
44473
u +
357015
44473
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
21
+ 7u
19
+ ··· + 2u − 1
c
3
, c
4
, c
10
c
11
u
21
− 6u
20
+ ··· + 38u − 4
c
5
, c
7
u
21
− 6u
19
+ ··· − 7u − 1
c
9
u
21
− 18u
20
+ ··· + 4352u − 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
21
+ 14y
20
+ ··· + 12y
2
− 1
c
3
, c
4
, c
10
c
11
y
21
+ 24y
20
+ ··· + 108y −16
c
5
, c
7
y
21
− 12y
20
+ ··· + 27y −1
c
9
y
21
+ 2y
20
+ ··· + 65536y −262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.089530 + 0.984696I
a = −0.10595 + 1.89249I
b = −0.089530 + 0.984696I
−0.41138 − 2.40421I 1.72315 + 4.22426I
u = −0.089530 − 0.984696I
a = −0.10595 − 1.89249I
b = −0.089530 − 0.984696I
−0.41138 + 2.40421I 1.72315 − 4.22426I
u = −0.709348 + 0.727206I
a = 1.013410 − 0.479147I
b = −0.709348 + 0.727206I
8.83155 − 2.25669I 7.66847 + 3.47538I
u = −0.709348 − 0.727206I
a = 1.013410 + 0.479147I
b = −0.709348 − 0.727206I
8.83155 + 2.25669I 7.66847 − 3.47538I
u = 0.241671 + 1.064200I
a = 0.20712 + 1.60998I
b = 0.241671 + 1.064200I
6.84048 + 5.76907I 4.07518 − 4.56239I
u = 0.241671 − 1.064200I
a = 0.20712 − 1.60998I
b = 0.241671 − 1.064200I
6.84048 − 5.76907I 4.07518 + 4.56239I
u = 0.819786 + 0.389956I
a = −0.690629 + 0.984448I
b = 0.819786 + 0.389956I
10.89630 − 2.89300I 9.55027 + 0.75508I
u = 0.819786 − 0.389956I
a = −0.690629 − 0.984448I
b = 0.819786 − 0.389956I
10.89630 + 2.89300I 9.55027 − 0.75508I
u = 0.420437 + 1.104620I
a = −1.57981 − 0.05796I
b = 0.420437 + 1.104620I
−1.62807 + 2.56050I 4.45468 − 5.57761I
u = 0.420437 − 1.104620I
a = −1.57981 + 0.05796I
b = 0.420437 − 1.104620I
−1.62807 − 2.56050I 4.45468 + 5.57761I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628080 + 0.259561I
a = 0.99006 + 1.03585I
b = −0.628080 + 0.259561I
2.86823 + 1.78605I 10.67672 − 1.49019I
u = −0.628080 − 0.259561I
a = 0.99006 − 1.03585I
b = −0.628080 − 0.259561I
2.86823 − 1.78605I 10.67672 + 1.49019I
u = −0.476681 + 1.277180I
a = 1.297630 + 0.183037I
b = −0.476681 + 1.277180I
−5.88506 − 6.78578I −0.85150 + 5.15843I
u = −0.476681 − 1.277180I
a = 1.297630 − 0.183037I
b = −0.476681 − 1.277180I
−5.88506 + 6.78578I −0.85150 − 5.15843I
u = 0.274697 + 0.539680I
a = −0.715108 − 0.945305I
b = 0.274697 + 0.539680I
0.19501 + 1.45011I 2.94900 − 3.15728I
u = 0.274697 − 0.539680I
a = −0.715108 + 0.945305I
b = 0.274697 − 0.539680I
0.19501 − 1.45011I 2.94900 + 3.15728I
u = 0.55258 + 1.36736I
a = −1.134920 + 0.188406I
b = 0.55258 + 1.36736I
−4.07842 + 11.41590I 1.76912 − 8.47188I
u = 0.55258 − 1.36736I
a = −1.134920 − 0.188406I
b = 0.55258 − 1.36736I
−4.07842 − 11.41590I 1.76912 + 8.47188I
u = −0.62291 + 1.42854I
a = 1.038290 + 0.171241I
b = −0.62291 + 1.42854I
4.0861 − 14.4126I 4.28661 + 7.20471I
u = −0.62291 − 1.42854I
a = 1.038290 − 0.171241I
b = −0.62291 − 1.42854I
4.0861 + 14.4126I 4.28661 − 7.20471I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.434772
a = −1.64018
b = 0.434772
0.983801 10.3970
7
II. I
u
2
= h−1.50 × 10
47
u
35
+ 7.90 × 10
47
u
34
+ · · · + 8.17 × 10
48
b + 1.26 ×
10
50
, 1.52 × 10
32
u
35
+ 1.20 × 10
32
u
34
+ · · · + 1.00 × 10
33
a − 5.78 ×
10
33
, u
36
+ u
35
+ · · · − 88u + 121i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
−0.151215u
35
− 0.119194u
34
+ ··· − 29.7352u + 5.75661
0.0183906u
35
− 0.0966602u
34
+ ··· + 19.1446u − 15.4775
a
7
=
−0.132824u
35
− 0.215854u
34
+ ··· − 10.5906u − 9.72088
0.0183906u
35
− 0.0966602u
34
+ ··· + 19.1446u − 15.4775
a
10
=
−0.142950u
35
− 0.110929u
34
+ ··· − 23.0740u + 5.02934
−0.0996243u
35
− 0.0572367u
34
+ ··· − 8.34916u + 0.642617
a
1
=
0.235158u
35
+ 0.150714u
34
+ ··· + 43.1286u − 10.6737
0.240469u
35
+ 0.255649u
34
+ ··· + 27.1442u − 2.79189
a
4
=
−0.231245u
35
− 0.605373u
34
+ ··· + 13.5883u − 48.7866
−0.0590880u
35
− 0.422425u
34
+ ··· + 36.6423u − 48.0768
a
8
=
−u
u
3
+ u
a
5
=
−0.181447u
35
− 0.279824u
34
+ ··· − 22.4844u − 9.51522
0.0242422u
35
− 0.0920959u
34
+ ··· + 19.7108u − 15.9838
a
11
=
−0.342315u
35
− 0.0676417u
34
+ ··· − 73.5185u + 27.0801
−0.340322u
35
− 0.200761u
34
+ ··· − 48.3147u + 13.7797
a
11
=
−0.342315u
35
− 0.0676417u
34
+ ··· − 73.5185u + 27.0801
−0.340322u
35
− 0.200761u
34
+ ··· − 48.3147u + 13.7797
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0198670u
35
+ 0.230113u
34
+ ··· − 18.4708u + 28.1644
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
36
+ u
35
+ ··· − 88u + 121
c
3
, c
4
, c
10
c
11
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
4
c
5
, c
7
u
36
+ 9u
35
+ ··· − 8u + 1
c
9
(u
2
+ u + 1)
18
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
36
+ 27y
35
+ ··· + 187308y + 14641
c
3
, c
4
, c
10
c
11
(y
9
+ 11y
8
+ 48y
7
+ 105y
6
+ 121y
5
+ 73y
4
+ 20y
3
− 6y
2
− 3y −1)
4
c
5
, c
7
y
36
+ 3y
35
+ ··· − 44y + 1
c
9
(y
2
+ y + 1)
18
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.039626 + 0.981491I
a = 0.860387 − 0.544166I
b = −0.29688 − 1.73262I
2.12882 − 0.18400I 2.24115 − 0.41812I
u = −0.039626 − 0.981491I
a = 0.860387 + 0.544166I
b = −0.29688 + 1.73262I
2.12882 + 0.18400I 2.24115 + 0.41812I
u = 0.154191 + 1.093140I
a = 0.840038 − 0.338907I
b = −0.794470 + 0.015853I
−2.09801 + 2.02988I −0.33330 − 3.46410I
u = 0.154191 − 1.093140I
a = 0.840038 + 0.338907I
b = −0.794470 − 0.015853I
−2.09801 − 2.02988I −0.33330 + 3.46410I
u = −0.129901 + 1.110370I
a = −0.821381 − 0.354208I
b = 0.40998 − 1.53870I
−4.89942 − 0.92019I −1.44626 − 2.77537I
u = −0.129901 − 1.110370I
a = −0.821381 + 0.354208I
b = 0.40998 + 1.53870I
−4.89942 + 0.92019I −1.44626 + 2.77537I
u = 1.165700 + 0.010466I
a = 0.435562 + 0.739012I
b = −0.334918 − 1.124560I
0.22800 + 5.44061I 3.88238 − 7.86053I
u = 1.165700 − 0.010466I
a = 0.435562 − 0.739012I
b = −0.334918 + 1.124560I
0.22800 − 5.44061I 3.88238 + 7.86053I
u = −0.334918 + 1.124560I
a = −0.828987 − 0.197728I
b = 1.165700 − 0.010466I
0.22800 − 5.44061I 3.88238 + 7.86053I
u = −0.334918 − 1.124560I
a = −0.828987 + 0.197728I
b = 1.165700 + 0.010466I
0.22800 + 5.44061I 3.88238 − 7.86053I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.794470 + 0.015853I
a = −0.607357 − 1.102190I
b = 0.154191 + 1.093140I
−2.09801 + 2.02988I −0.33330 − 3.46410I
u = −0.794470 − 0.015853I
a = −0.607357 + 1.102190I
b = 0.154191 − 1.093140I
−2.09801 − 2.02988I −0.33330 + 3.46410I
u = −0.806995 + 0.905050I
a = 0.258644 − 0.783077I
b = 0.264260 + 0.503586I
8.52641 − 3.47060I 5.48937 − 0.49112I
u = −0.806995 − 0.905050I
a = 0.258644 + 0.783077I
b = 0.264260 − 0.503586I
8.52641 + 3.47060I 5.48937 + 0.49112I
u = 0.446862 + 1.134250I
a = 0.811273 − 0.121202I
b = −1.395410 + 0.040090I
8.52641 + 7.53037I 5.48937 − 6.43708I
u = 0.446862 − 1.134250I
a = 0.811273 + 0.121202I
b = −1.395410 − 0.040090I
8.52641 − 7.53037I 5.48937 + 6.43708I
u = 0.021359 + 0.770389I
a = −1.105300 − 0.679667I
b = 0.528085 + 0.506138I
0.227995 + 1.380850I 3.88238 − 0.93232I
u = 0.021359 − 0.770389I
a = −1.105300 + 0.679667I
b = 0.528085 − 0.506138I
0.227995 − 1.380850I 3.88238 + 0.93232I
u = 0.528085 + 0.506138I
a = −0.325738 − 1.327740I
b = 0.021359 + 0.770389I
0.227995 + 1.380850I 3.88238 − 0.93232I
u = 0.528085 − 0.506138I
a = −0.325738 + 1.327740I
b = 0.021359 − 0.770389I
0.227995 − 1.380850I 3.88238 + 0.93232I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.153431 + 1.311480I
a = 0.695425 − 0.299890I
b = −0.66442 − 1.33987I
−4.89942 + 3.13958I −1.44626 − 9.70357I
u = 0.153431 − 1.311480I
a = 0.695425 + 0.299890I
b = −0.66442 + 1.33987I
−4.89942 − 3.13958I −1.44626 + 9.70357I
u = −1.395410 + 0.040090I
a = −0.340206 − 0.630399I
b = 0.446862 + 1.134250I
8.52641 + 7.53037I 5.48937 − 6.43708I
u = −1.395410 − 0.040090I
a = −0.340206 + 0.630399I
b = 0.446862 − 1.134250I
8.52641 − 7.53037I 5.48937 + 6.43708I
u = −0.134013 + 1.399190I
a = −0.647238 − 0.295359I
b = 0.95276 − 1.31505I
2.12882 − 4.24376I 2.24115 + 6.51008I
u = −0.134013 − 1.399190I
a = −0.647238 + 0.295359I
b = 0.95276 + 1.31505I
2.12882 + 4.24376I 2.24115 − 6.51008I
u = 0.264260 + 0.503586I
a = 1.75693 − 0.07092I
b = −0.806995 + 0.905050I
8.52641 − 3.47060I 5.48937 − 0.49112I
u = 0.264260 − 0.503586I
a = 1.75693 + 0.07092I
b = −0.806995 − 0.905050I
8.52641 + 3.47060I 5.48937 + 0.49112I
u = −0.66442 + 1.33987I
a = −0.667309 − 0.042265I
b = 0.153431 − 1.311480I
−4.89942 − 3.13958I −1.44626 + 9.70357I
u = −0.66442 − 1.33987I
a = −0.667309 + 0.042265I
b = 0.153431 + 1.311480I
−4.89942 + 3.13958I −1.44626 − 9.70357I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.40998 + 1.53870I
a = 0.606362 − 0.163388I
b = −0.129901 − 1.110370I
−4.89942 + 0.92019I 0. + 2.77537I
u = 0.40998 − 1.53870I
a = 0.606362 + 0.163388I
b = −0.129901 + 1.110370I
−4.89942 − 0.92019I 0. − 2.77537I
u = 0.95276 + 1.31505I
a = 0.612508 + 0.063552I
b = −0.134013 − 1.399190I
2.12882 + 4.24376I 0. − 6.51008I
u = 0.95276 − 1.31505I
a = 0.612508 − 0.063552I
b = −0.134013 + 1.399190I
2.12882 − 4.24376I 0. + 6.51008I
u = −0.29688 + 1.73262I
a = −0.533617 − 0.197147I
b = −0.039626 − 0.981491I
2.12882 + 0.18400I 0
u = −0.29688 − 1.73262I
a = −0.533617 + 0.197147I
b = −0.039626 + 0.981491I
2.12882 − 0.18400I 0
14
III. I
u
3
= hb + u, −u
9
− u
8
+ · · · + a − 1, u
10
+ 5u
8
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
u
9
+ u
8
+ 5u
7
+ 5u
6
+ 11u
5
+ 9u
4
+ 11u
3
+ 6u
2
+ 5u + 1
−u
a
7
=
u
9
+ u
8
+ 5u
7
+ 5u
6
+ 11u
5
+ 9u
4
+ 11u
3
+ 6u
2
+ 4u + 1
−u
a
10
=
−u
8
− u
7
− 5u
6
− 5u
5
− 10u
4
− 9u
3
− 8u
2
− 5u − 2
u
8
+ 4u
6
+ u
5
+ 6u
4
+ 2u
3
+ 3u
2
+ 2u + 1
a
1
=
−u
9
− 4u
7
− u
6
− 6u
5
− 2u
4
− 3u
3
− u + 2
u
2
a
4
=
u
9
+ u
8
+ 5u
7
+ 6u
6
+ 10u
5
+ 12u
4
+ 8u
3
+ 9u
2
+ 2u + 2
−u
9
− 4u
7
− 6u
5
− 3u
3
− u
2
− u
a
8
=
−u
u
3
+ u
a
5
=
u
9
+ u
8
+ 5u
7
+ 5u
6
+ 11u
5
+ 9u
4
+ 12u
3
+ 6u
2
+ 6u + 1
−u
5
− 2u
3
− 2u
a
11
=
−u
9
− 6u
7
− u
6
− 13u
5
− 3u
4
− 12u
3
− 3u
2
− 3u
u
9
+ 4u
7
+ 7u
5
+ 5u
3
+ 2u
a
11
=
−u
9
− 6u
7
− u
6
− 13u
5
− 3u
4
− 12u
3
− 3u
2
− 3u
u
9
+ 4u
7
+ 7u
5
+ 5u
3
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
9
−3u
8
−23u
7
−19u
6
−43u
5
−38u
4
−34u
3
−27u
2
−12u + 3
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
10
+ 5u
8
− u
7
+ 10u
6
− 3u
5
+ 9u
4
− 3u
3
+ 4u
2
+ 1
c
2
, c
6
u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ 1
c
3
, c
4
u
10
+ u
9
+ 7u
8
+ 6u
7
+ 17u
6
+ 12u
5
+ 17u
4
+ 8u
3
+ 7u
2
+ 1
c
5
, c
7
u
10
+ 3u
7
+ 3u
6
+ 3u
4
+ 4u
3
+ u
2
+ u + 1
c
9
u
10
− u
9
+ u
8
− 4u
7
+ 3u
6
+ 3u
4
− 3u
3
+ 1
c
10
, c
11
u
10
− u
9
+ 7u
8
− 6u
7
+ 17u
6
− 12u
5
+ 17u
4
− 8u
3
+ 7u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
10
+ 10y
9
+ ··· + 8y + 1
c
3
, c
4
, c
10
c
11
y
10
+ 13y
9
+ ··· + 14y + 1
c
5
, c
7
y
10
+ 6y
8
− 3y
7
+ 11y
6
− 4y
5
+ 9y
4
− 4y
3
− y
2
+ y + 1
c
9
y
10
+ y
9
− y
8
− 4y
7
+ 9y
6
− 4y
5
+ 11y
4
− 3y
3
+ 6y
2
+ 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280592 + 1.135800I
a = 1.269010 − 0.099088I
b = −0.280592 − 1.135800I
−2.18773 + 1.37103I 1.096751 − 0.038075I
u = 0.280592 − 1.135800I
a = 1.269010 + 0.099088I
b = −0.280592 + 1.135800I
−2.18773 − 1.37103I 1.096751 + 0.038075I
u = −0.536137 + 0.558503I
a = 0.240076 + 1.102590I
b = 0.536137 − 0.558503I
8.73669 − 4.86888I 6.80228 + 5.06388I
u = −0.536137 − 0.558503I
a = 0.240076 − 1.102590I
b = 0.536137 + 0.558503I
8.73669 + 4.86888I 6.80228 − 5.06388I
u = −0.339392 + 1.319900I
a = −0.628272 − 0.235688I
b = 0.339392 − 1.319900I
−4.67120 − 2.22664I 2.12135 + 1.13341I
u = −0.339392 − 1.319900I
a = −0.628272 + 0.235688I
b = 0.339392 + 1.319900I
−4.67120 + 2.22664I 2.12135 − 1.13341I
u = 0.205182 + 0.502042I
a = −0.29922 + 2.23836I
b = −0.205182 − 0.502042I
0.90716 + 2.13686I 9.07211 − 6.04607I
u = 0.205182 − 0.502042I
a = −0.29922 − 2.23836I
b = −0.205182 + 0.502042I
0.90716 − 2.13686I 9.07211 + 6.04607I
u = 0.38975 + 1.44195I
a = 0.418413 − 0.189778I
b = −0.38975 − 1.44195I
2.14990 + 2.75317I 2.40750 − 1.04370I
u = 0.38975 − 1.44195I
a = 0.418413 + 0.189778I
b = −0.38975 + 1.44195I
2.14990 − 2.75317I 2.40750 + 1.04370I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
10
+ 5u
8
− u
7
+ 10u
6
− 3u
5
+ 9u
4
− 3u
3
+ 4u
2
+ 1)
· (u
21
+ 7u
19
+ ··· + 2u − 1)(u
36
+ u
35
+ ··· − 88u + 121)
c
2
, c
6
(u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ 1)
· (u
21
+ 7u
19
+ ··· + 2u − 1)(u
36
+ u
35
+ ··· − 88u + 121)
c
3
, c
4
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
4
· (u
10
+ u
9
+ 7u
8
+ 6u
7
+ 17u
6
+ 12u
5
+ 17u
4
+ 8u
3
+ 7u
2
+ 1)
· (u
21
− 6u
20
+ ··· + 38u − 4)
c
5
, c
7
(u
10
+ 3u
7
+ ··· + u + 1)(u
21
− 6u
19
+ ··· − 7u − 1)
· (u
36
+ 9u
35
+ ··· − 8u + 1)
c
9
(u
2
+ u + 1)
18
(u
10
− u
9
+ u
8
− 4u
7
+ 3u
6
+ 3u
4
− 3u
3
+ 1)
· (u
21
− 18u
20
+ ··· + 4352u − 512)
c
10
, c
11
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 11u
5
+ 7u
4
+ 6u
3
+ 2u
2
+ u + 1)
4
· (u
10
− u
9
+ 7u
8
− 6u
7
+ 17u
6
− 12u
5
+ 17u
4
− 8u
3
+ 7u
2
+ 1)
· (u
21
− 6u
20
+ ··· + 38u − 4)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
10
+ 10y
9
+ ··· + 8y + 1)(y
21
+ 14y
20
+ ··· + 12y
2
− 1)
· (y
36
+ 27y
35
+ ··· + 187308y + 14641)
c
3
, c
4
, c
10
c
11
(y
9
+ 11y
8
+ 48y
7
+ 105y
6
+ 121y
5
+ 73y
4
+ 20y
3
− 6y
2
− 3y −1)
4
· (y
10
+ 13y
9
+ ··· + 14y + 1)(y
21
+ 24y
20
+ ··· + 108y −16)
c
5
, c
7
(y
10
+ 6y
8
− 3y
7
+ 11y
6
− 4y
5
+ 9y
4
− 4y
3
− y
2
+ y + 1)
· (y
21
− 12y
20
+ ··· + 27y −1)(y
36
+ 3y
35
+ ··· − 44y + 1)
c
9
((y
2
+ y + 1)
18
)(y
10
+ y
9
+ ··· + 6y
2
+ 1)
· (y
21
+ 2y
20
+ ··· + 65536y −262144)
20
