12a
0938
(K12a
0938
)
A knot diagram
1
Linearized knot diagam
4 6 9 1 2 10 11 12 3 8 7 5
Solving Sequence
5,12
1 4 2
6,7
11 8 9 3 10
c
12
c
4
c
1
c
5
c
11
c
7
c
8
c
3
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −u
12
− u
11
− 5u
10
− 4u
9
− 9u
8
− 6u
7
− 5u
6
− 3u
5
+ 3u
4
+ u
3
+ 3u
2
+ a + u,
u
15
+ u
14
+ 7u
13
+ 6u
12
+ 19u
11
+ 14u
10
+ 22u
9
+ 14u
8
+ 3u
7
+ 2u
6
− 14u
5
− 6u
4
− 6u
3
− 4u
2
+ 3u − 1i
I
u
2
= hu
59
+ 2u
58
+ ··· + 2b − 2, u
59
+ 3u
58
+ ··· + 2a − 4, u
60
+ 3u
59
+ ··· − 8u − 1i
I
u
3
= hb + u, a − u + 2, u
3
− u
2
+ 2u − 1i
I
u
4
= h−u
2
a − u
2
+ b − a − 1, u
2
a + a
2
+ u
2
+ 2a + 2, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 84 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, −u
12
− u
11
+ · · · + a + u, u
15
+ u
14
+ · · · + 3u − 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
u
12
+ u
11
+ 5u
10
+ 4u
9
+ 9u
8
+ 6u
7
+ 5u
6
+ 3u
5
− 3u
4
− u
3
− 3u
2
− u
u
a
11
=
−u
13
− u
12
+ ··· + u
2
+ 1
−u
2
a
8
=
u
14
+ u
13
+ ··· − 3u
2
− 2u
u
3
+ u
a
9
=
u
14
+ u
13
+ ··· − 3u
2
− 3u
u
3
+ u
a
3
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
10
=
−u
9
− u
8
− 4u
7
− 3u
6
− 5u
5
− 3u
4
− u
2
+ 3u
−u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
14
− 4u
13
− 26u
12
− 26u
11
− 68u
10
− 66u
9
− 78u
8
− 74u
7
−
16u
6
− 16u
5
+ 38u
4
+ 34u
3
+ 16u
2
+ 24u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
u
15
− u
14
+ ··· + 3u + 1
c
2
, c
5
, c
6
c
8
u
15
+ u
14
+ ··· + u + 1
c
3
, c
9
u
15
− 7u
14
+ ··· + 32u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
15
+ 13y
14
+ ··· + y −1
c
2
, c
5
, c
6
c
8
y
15
− 15y
14
+ ··· + y −1
c
3
, c
9
y
15
+ 7y
14
+ ··· − 320y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864712 + 0.110290I
a = −1.86907 − 0.45625I
b = −0.864712 + 0.110290I
−11.11480 + 6.35352I −15.5001 − 4.2472I
u = −0.864712 − 0.110290I
a = −1.86907 + 0.45625I
b = −0.864712 − 0.110290I
−11.11480 − 6.35352I −15.5001 + 4.2472I
u = 0.105102 + 1.139200I
a = −0.439069 + 0.083556I
b = 0.105102 + 1.139200I
4.69451 − 2.19799I −5.25826 + 3.25670I
u = 0.105102 − 1.139200I
a = −0.439069 − 0.083556I
b = 0.105102 − 1.139200I
4.69451 + 2.19799I −5.25826 − 3.25670I
u = 0.811305
a = 2.34658
b = 0.811305
−6.37976 −14.9760
u = −0.423940 + 1.181130I
a = −1.389210 + 0.220558I
b = −0.423940 + 1.181130I
−4.55475 + 2.89595I −9.71000 − 3.23135I
u = −0.423940 − 1.181130I
a = −1.389210 − 0.220558I
b = −0.423940 − 1.181130I
−4.55475 − 2.89595I −9.71000 + 3.23135I
u = 0.360108 + 1.291100I
a = 2.54683 + 0.20383I
b = 0.360108 + 1.291100I
1.68042 − 8.43141I −6.38008 + 6.14293I
u = 0.360108 − 1.291100I
a = 2.54683 − 0.20383I
b = 0.360108 − 1.291100I
1.68042 + 8.43141I −6.38008 − 6.14293I
u = 0.035636 + 1.359960I
a = −0.27580 − 2.64222I
b = 0.035636 + 1.359960I
9.79675 − 2.45365I 1.09794 + 3.27080I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.035636 − 1.359960I
a = −0.27580 + 2.64222I
b = 0.035636 − 1.359960I
9.79675 + 2.45365I 1.09794 − 3.27080I
u = −0.378630 + 1.355350I
a = −2.48655 − 0.69111I
b = −0.378630 + 1.355350I
−1.8779 + 15.2909I −7.04558 − 8.68185I
u = −0.378630 − 1.355350I
a = −2.48655 + 0.69111I
b = −0.378630 − 1.355350I
−1.8779 − 15.2909I −7.04558 + 8.68185I
u = 0.260784 + 0.226947I
a = −0.260409 − 0.646690I
b = 0.260784 + 0.226947I
−0.369166 − 0.786960I −8.71574 + 8.77230I
u = 0.260784 − 0.226947I
a = −0.260409 + 0.646690I
b = 0.260784 − 0.226947I
−0.369166 + 0.786960I −8.71574 − 8.77230I
6
II.
I
u
2
= hu
59
+2u
58
+· · ·+2b−2, u
59
+3u
58
+· · ·+2a−4, u
60
+3u
59
+· · ·−8u−1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−
1
2
u
59
−
3
2
u
58
+ ··· +
1
2
u + 2
−
1
2
u
59
− u
58
+ ··· + 6u + 1
a
11
=
4u
59
+
21
2
u
58
+ ··· −
67
2
u −
9
2
−u
59
− u
58
+ ··· − 13u −
5
2
a
8
=
−
5
2
u
59
− 8u
58
+ ··· + 57u + 14
−
3
2
u
59
− 4u
58
+ ··· + 20u +
9
2
a
9
=
−u
59
− 4u
58
+ ··· + 37u +
19
2
−
3
2
u
59
− 4u
58
+ ··· + 20u +
9
2
a
3
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
10
=
6u
59
+ 14u
58
+ ··· − 66u −
29
2
7
2
u
59
+ 9u
58
+ ··· − 33u −
13
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
21
2
u
59
− 17u
58
+ ··· − 3u −
19
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
u
60
− 3u
59
+ ··· + 8u − 1
c
2
, c
5
, c
6
c
8
u
60
+ 3u
59
+ ··· + 520u − 137
c
3
, c
9
(u
30
+ 3u
29
+ ··· − 12u − 8)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
60
+ 49y
59
+ ··· − 28y + 1
c
2
, c
5
, c
6
c
8
y
60
− 43y
59
+ ··· − 297252y + 18769
c
3
, c
9
(y
30
+ 21y
29
+ ··· − 208y + 64)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866352 + 0.087987I
a = −0.71052 − 1.48467I
b = −0.427481 − 1.154580I
−7.91257 + 1.72426I −12.74360 − 0.42116I
u = −0.866352 − 0.087987I
a = −0.71052 + 1.48467I
b = −0.427481 + 1.154580I
−7.91257 − 1.72426I −12.74360 + 0.42116I
u = −0.859274 + 0.126720I
a = −2.20772 + 0.88605I
b = −0.384752 + 1.346570I
−6.53967 + 10.84120I −11.31201 − 6.59674I
u = −0.859274 − 0.126720I
a = −2.20772 − 0.88605I
b = −0.384752 − 1.346570I
−6.53967 − 10.84120I −11.31201 + 6.59674I
u = 0.811961 + 0.030859I
a = 1.90730 + 1.95853I
b = 0.359515 + 1.269110I
−2.44025 − 4.21285I −10.79867 + 3.36820I
u = 0.811961 − 0.030859I
a = 1.90730 − 1.95853I
b = 0.359515 − 1.269110I
−2.44025 + 4.21285I −10.79867 − 3.36820I
u = −0.812151 + 0.025025I
a = 1.154180 − 0.235909I
b = 0.546996 − 0.494154I
−5.29824 + 1.96304I −14.0240 − 3.7195I
u = −0.812151 − 0.025025I
a = 1.154180 + 0.235909I
b = 0.546996 + 0.494154I
−5.29824 − 1.96304I −14.0240 + 3.7195I
u = −0.426044 + 1.131210I
a = −0.727875 − 0.277369I
b = −0.389512 − 1.332390I
−3.46235 − 6.23114I 0
u = −0.426044 − 1.131210I
a = −0.727875 + 0.277369I
b = −0.389512 + 1.332390I
−3.46235 + 6.23114I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770784 + 0.061460I
a = 1.079330 − 0.274511I
b = 0.14357 − 1.41247I
0.79615 + 4.22762I −10.05667 − 4.58015I
u = −0.770784 − 0.061460I
a = 1.079330 + 0.274511I
b = 0.14357 + 1.41247I
0.79615 − 4.22762I −10.05667 + 4.58015I
u = −0.427481 + 1.154580I
a = −1.142560 − 0.223262I
b = −0.866352 − 0.087987I
−7.91257 − 1.72426I 0
u = −0.427481 − 1.154580I
a = −1.142560 + 0.223262I
b = −0.866352 + 0.087987I
−7.91257 + 1.72426I 0
u = −0.027147 + 1.235000I
a = 0.583477 + 0.915228I
b = 0.668715 − 0.159496I
2.08860 + 0.78309I 0
u = −0.027147 − 1.235000I
a = 0.583477 − 0.915228I
b = 0.668715 + 0.159496I
2.08860 − 0.78309I 0
u = 0.522307 + 0.542494I
a = −1.97898 + 0.17315I
b = −0.361715 − 1.287380I
−1.20998 − 6.18837I −9.36869 + 6.76347I
u = 0.522307 − 0.542494I
a = −1.97898 − 0.17315I
b = −0.361715 + 1.287380I
−1.20998 + 6.18837I −9.36869 − 6.76347I
u = 0.546996 + 0.494154I
a = −1.138140 + 0.625120I
b = −0.812151 − 0.025025I
−5.29824 − 1.96304I −14.0240 + 3.7195I
u = 0.546996 − 0.494154I
a = −1.138140 − 0.625120I
b = −0.812151 + 0.025025I
−5.29824 + 1.96304I −14.0240 − 3.7195I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.579343 + 0.445290I
a = −0.104195 + 0.571803I
b = −0.357093 + 1.248530I
−1.51678 + 2.24498I −10.41829 + 0.03554I
u = 0.579343 − 0.445290I
a = −0.104195 − 0.571803I
b = −0.357093 − 1.248530I
−1.51678 − 2.24498I −10.41829 − 0.03554I
u = −0.312553 + 1.230880I
a = −0.243366 − 1.021580I
b = 0.17696 + 1.40609I
4.37363 − 0.32326I 0
u = −0.312553 − 1.230880I
a = −0.243366 + 1.021580I
b = 0.17696 − 1.40609I
4.37363 + 0.32326I 0
u = −0.058694 + 1.275980I
a = 2.05305 + 1.65274I
b = 0.273445 − 1.345740I
6.82843 + 4.21576I 0
u = −0.058694 − 1.275980I
a = 2.05305 − 1.65274I
b = 0.273445 + 1.345740I
6.82843 − 4.21576I 0
u = 0.358239 + 1.242060I
a = 0.325203 − 1.127520I
b = 0.358239 − 1.242060I
1.29928 0
u = 0.358239 − 1.242060I
a = 0.325203 + 1.127520I
b = 0.358239 + 1.242060I
1.29928 0
u = 0.088419 + 1.291380I
a = −0.283489 − 0.576292I
b = 0.071835 + 0.504277I
4.18867 − 2.01435I 0
u = 0.088419 − 1.291380I
a = −0.283489 + 0.576292I
b = 0.071835 − 0.504277I
4.18867 + 2.01435I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.357093 + 1.248530I
a = 0.277613 + 0.172882I
b = 0.579343 + 0.445290I
−1.51678 + 2.24498I 0
u = −0.357093 − 1.248530I
a = 0.277613 − 0.172882I
b = 0.579343 − 0.445290I
−1.51678 − 2.24498I 0
u = 0.243342 + 1.288680I
a = −0.821950 + 0.307839I
b = −0.276488 − 0.137898I
2.60325 − 3.14855I 0
u = 0.243342 − 1.288680I
a = −0.821950 − 0.307839I
b = −0.276488 + 0.137898I
2.60325 + 3.14855I 0
u = 0.668715 + 0.159496I
a = −1.85649 − 0.59763I
b = −0.027147 − 1.235000I
2.08860 − 0.78309I −8.05433 + 0.68374I
u = 0.668715 − 0.159496I
a = −1.85649 + 0.59763I
b = −0.027147 + 1.235000I
2.08860 + 0.78309I −8.05433 − 0.68374I
u = 0.359515 + 1.269110I
a = 1.51041 − 0.74478I
b = 0.811961 + 0.030859I
−2.44025 − 4.21285I 0
u = 0.359515 − 1.269110I
a = 1.51041 + 0.74478I
b = 0.811961 − 0.030859I
−2.44025 + 4.21285I 0
u = −0.361715 + 1.287380I
a = 0.935893 + 0.612906I
b = 0.522307 − 0.542494I
−1.20998 + 6.18837I 0
u = −0.361715 − 1.287380I
a = 0.935893 − 0.612906I
b = 0.522307 + 0.542494I
−1.20998 − 6.18837I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336582 + 1.312290I
a = 1.70878 + 1.42762I
b = 0.12149 − 1.42413I
5.10162 + 8.23172I 0
u = −0.336582 − 1.312290I
a = 1.70878 − 1.42762I
b = 0.12149 + 1.42413I
5.10162 − 8.23172I 0
u = 0.628824
a = −1.09503
b = −0.227844
−1.43510 −5.45290
u = 0.273445 + 1.345740I
a = −2.12347 + 1.22513I
b = −0.058694 − 1.275980I
6.82843 − 4.21576I 0
u = 0.273445 − 1.345740I
a = −2.12347 − 1.22513I
b = −0.058694 + 1.275980I
6.82843 + 4.21576I 0
u = −0.389512 + 1.332390I
a = 0.361503 − 0.573917I
b = −0.426044 − 1.131210I
−3.46235 + 6.23114I 0
u = −0.389512 − 1.332390I
a = 0.361503 + 0.573917I
b = −0.426044 + 1.131210I
−3.46235 − 6.23114I 0
u = −0.384752 + 1.346570I
a = −1.06494 − 1.02113I
b = −0.859274 + 0.126720I
−6.53967 + 10.84120I 0
u = −0.384752 − 1.346570I
a = −1.06494 + 1.02113I
b = −0.859274 − 0.126720I
−6.53967 − 10.84120I 0
u = 0.17696 + 1.40609I
a = 0.131316 − 0.931855I
b = −0.312553 + 1.230880I
4.37363 − 0.32326I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17696 − 1.40609I
a = 0.131316 + 0.931855I
b = −0.312553 − 1.230880I
4.37363 + 0.32326I 0
u = 0.14357 + 1.41247I
a = −0.252805 + 0.551347I
b = −0.770784 − 0.061460I
0.79615 − 4.22762I 0
u = 0.14357 − 1.41247I
a = −0.252805 − 0.551347I
b = −0.770784 + 0.061460I
0.79615 + 4.22762I 0
u = 0.12149 + 1.42413I
a = −1.37385 + 1.60217I
b = −0.336582 − 1.312290I
5.10162 − 8.23172I 0
u = 0.12149 − 1.42413I
a = −1.37385 − 1.60217I
b = −0.336582 + 1.312290I
5.10162 + 8.23172I 0
u = 0.071835 + 0.504277I
a = −0.61146 − 1.51320I
b = 0.088419 + 1.291380I
4.18867 − 2.01435I −2.24660 + 4.20023I
u = 0.071835 − 0.504277I
a = −0.61146 + 1.51320I
b = 0.088419 − 1.291380I
4.18867 + 2.01435I −2.24660 − 4.20023I
u = −0.276488 + 0.137898I
a = 3.15020 − 1.98893I
b = 0.243342 − 1.288680I
2.60325 + 3.14855I −0.03228 − 4.59727I
u = −0.276488 − 0.137898I
a = 3.15020 + 1.98893I
b = 0.243342 + 1.288680I
2.60325 − 3.14855I −0.03228 + 4.59727I
u = −0.227844
a = 3.02215
b = 0.628824
−1.43510 −5.45290
15
III. I
u
3
= hb + u, a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
2
− u + 1
a
2
=
u
2
+ 1
u
2
− u + 1
a
6
=
−1
0
a
7
=
u − 2
−u
a
11
=
u
2
− 2u + 1
−u
2
a
8
=
−u
2
− 1
−u
2
+ u − 1
a
9
=
−u
−u
2
+ u − 1
a
3
=
u
u
2
− u + 1
a
10
=
−u
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
u
3
− u
2
+ 2u − 1
c
2
, c
6
, c
8
u
3
+ u
2
− 1
c
3
, c
9
u
3
c
4
, c
10
, c
11
u
3
+ u
2
+ 2u + 1
c
5
u
3
− u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
, c
6
c
8
y
3
− y
2
+ 2y −1
c
3
, c
9
y
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.78492 + 1.30714I
b = −0.215080 − 1.307140I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = −1.78492 − 1.30714I
b = −0.215080 + 1.307140I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −1.43016
b = −0.569840
−2.22691 −18.0390
19
IV. I
u
4
= h−u
2
a − u
2
+ b − a − 1, u
2
a + a
2
+ u
2
+ 2a + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
2
− u + 1
a
2
=
u
2
+ 1
u
2
− u + 1
a
6
=
−1
0
a
7
=
a
u
2
a + u
2
+ a + 1
a
11
=
u
2
a − au + 2u
2
+ 2a − u + 4
au + u
2
+ 2
a
8
=
−u
2
a − a
−u
2
a + au − a
a
9
=
−au
−u
2
a + au − a
a
3
=
u
u
2
− u + 1
a
10
=
−au
−u
2
a + au − a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
a + 5au − 3u
2
− 3a + 3u − 12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
6
, c
8
(u
3
+ u
2
− 1)
2
c
3
, c
9
u
6
c
4
, c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
5
(u
3
− u
2
+ 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
5
, c
6
c
8
(y
3
− y
2
+ 2y − 1)
2
c
3
, c
9
y
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.162359 − 0.986732I
b = −0.215080 + 1.307140I
6.04826 −6 − 1.085931 + 0.10I
u = 0.215080 + 1.307140I
a = −0.500000 + 0.424452I
b = −0.569840
1.91067 − 2.82812I −9.95703 + 1.11003I
u = 0.215080 − 1.307140I
a = 0.162359 + 0.986732I
b = −0.215080 − 1.307140I
6.04826 −6 − 1.085931 + 0.10I
u = 0.215080 − 1.307140I
a = −0.500000 − 0.424452I
b = −0.569840
1.91067 + 2.82812I −9.95703 − 1.11003I
u = 0.569840
a = −1.16236 + 0.98673I
b = −0.215080 + 1.307140I
1.91067 + 2.82812I −9.95703 − 1.11003I
u = 0.569840
a = −1.16236 − 0.98673I
b = −0.215080 − 1.307140I
1.91067 − 2.82812I −9.95703 + 1.11003I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
15
− u
14
+ ··· + 3u + 1)(u
60
− 3u
59
+ ··· + 8u − 1)
c
2
, c
6
, c
8
((u
3
+ u
2
− 1)
3
)(u
15
+ u
14
+ ··· + u + 1)(u
60
+ 3u
59
+ ··· + 520u − 137)
c
3
, c
9
u
9
(u
15
− 7u
14
+ ··· + 32u − 8)(u
30
+ 3u
29
+ ··· − 12u − 8)
2
c
4
, c
10
, c
11
((u
3
+ u
2
+ 2u + 1)
3
)(u
15
− u
14
+ ··· + 3u + 1)(u
60
− 3u
59
+ ··· + 8u − 1)
c
5
((u
3
− u
2
+ 1)
3
)(u
15
+ u
14
+ ··· + u + 1)(u
60
+ 3u
59
+ ··· + 520u − 137)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
15
+ 13y
14
+ ··· + y − 1)
· (y
60
+ 49y
59
+ ··· − 28y + 1)
c
2
, c
5
, c
6
c
8
((y
3
− y
2
+ 2y − 1)
3
)(y
15
− 15y
14
+ ··· + y − 1)
· (y
60
− 43y
59
+ ··· − 297252y + 18769)
c
3
, c
9
y
9
(y
15
+ 7y
14
+ ··· − 320y − 64)(y
30
+ 21y
29
+ ··· − 208y + 64)
2
25
