11a
197
(K11a
197
)
A knot diagram
1
Linearized knot diagam
6 1 11 7 10 2 4 3 5 9 8
Solving Sequence
8,11 1,4
3 9 2 7 5 6 10
c
11
c
3
c
8
c
2
c
7
c
4
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 1133732u
18
− 5530440u
17
+ ··· + 1639243a + 14603996, u
19
− 3u
17
+ ··· + 5u + 1i
I
u
2
= h4.04940 × 10
223
u
67
+ 3.30886 × 10
224
u
66
+ ··· + 4.64646 × 10
224
b − 5.28089 × 10
226
,
2.91872 × 10
228
u
67
+ 2.08756 × 10
229
u
66
+ ··· + 5.97071 × 10
227
a − 5.77931 × 10
230
,
u
68
+ 7u
67
+ ··· + 375u + 257i
I
u
3
= hb + u, u
7
+ u
6
− 2u
4
+ u
2
+ a + 2u − 1, u
8
− u
6
− u
5
+ 2u
4
− u + 1i
I
u
4
= h−3u
7
− 2u
6
+ 2u
5
− 4u
4
+ 3u
2
+ b − 7u + 4, −4u
7
− 3u
6
+ 2u
5
− 6u
4
− u
3
+ 3u
2
+ a − 9u + 5,
u
8
− u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 3u + 1i
* 4 irreducible components of dim
C
= 0, with total 103 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, 1.13 × 10
6
u
18
− 5.53 × 10
6
u
17
+ · · · + 1.64 × 10
6
a + 1.46 ×
10
7
, u
19
− 3u
17
+ · · · + 5u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
4
=
−0.691619u
18
+ 3.37378u
17
+ ··· − 28.3695u − 8.90899
u
a
3
=
−0.691619u
18
+ 3.37378u
17
+ ··· − 29.3695u − 8.90899
u
a
9
=
−4.15807u
18
− 6.66141u
17
+ ··· + 52.3548u + 8.42543
0.622113u
18
+ 1.86560u
17
+ ··· − 15.1773u − 3.37378
a
2
=
−0.0695059u
18
+ 5.23938u
17
+ ··· − 44.5467u − 12.2828
−0.756830u
18
− 1.16457u
17
+ ··· + 10.9501u + 1.86560
a
7
=
−2.91384u
18
− 2.93021u
17
+ ··· + 20.0003u + 1.67787
0.622113u
18
+ 1.86560u
17
+ ··· − 15.1773u − 3.37378
a
5
=
4.05196u
18
− 2.08218u
17
+ ··· + 21.9378u + 3.05750
−1.38107u
18
− 0.495631u
17
+ ··· + 2.38762u − 0.443568
a
6
=
4.07319u
18
+ 0.0169841u
17
+ ··· − 3.37920u − 2.08628
−1.50818u
18
+ 0.134717u
17
+ ··· − 1.03345u − 1.31373
a
10
=
1.53997u
18
− 5.15071u
17
+ ··· + 38.3233u + 9.86555
0.959164u
18
+ 1.36657u
17
+ ··· − 11.2769u − 2.27262
a
10
=
1.53997u
18
− 5.15071u
17
+ ··· + 38.3233u + 9.86555
0.959164u
18
+ 1.36657u
17
+ ··· − 11.2769u − 2.27262
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
18167001
1639243
u
18
−
11571693
1639243
u
17
+ ··· +
103230908
1639243
u −
4877099
1639243
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
19
− 4u
17
+ ··· − u + 1
c
2
, c
10
u
19
+ 8u
18
+ ··· + 5u + 1
c
3
, c
11
u
19
− 3u
17
+ ··· + 5u + 1
c
4
, c
7
u
19
− 12u
18
+ ··· − 224u + 32
c
8
u
19
− 18u
18
+ ··· − 1184u + 192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
19
− 8y
18
+ ··· + 5y −1
c
2
, c
10
y
19
+ 12y
18
+ ··· − 23y −1
c
3
, c
11
y
19
− 6y
18
+ ··· + 29y −1
c
4
, c
7
y
19
+ 12y
18
+ ··· + 1536y −1024
c
8
y
19
− 4y
18
+ ··· + 50176y −36864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.922328 + 0.410149I
a = −0.097023 + 0.610902I
b = 0.922328 + 0.410149I
1.76273 + 1.04354I 2.78842 − 1.15879I
u = 0.922328 − 0.410149I
a = −0.097023 − 0.610902I
b = 0.922328 − 0.410149I
1.76273 − 1.04354I 2.78842 + 1.15879I
u = −0.299279 + 0.864422I
a = 0.725338 + 0.593270I
b = −0.299279 + 0.864422I
−5.58807 + 2.35049I −13.53566 − 3.60952I
u = −0.299279 − 0.864422I
a = 0.725338 − 0.593270I
b = −0.299279 − 0.864422I
−5.58807 − 2.35049I −13.53566 + 3.60952I
u = 0.935316 + 0.630010I
a = −0.525722 + 0.984674I
b = 0.935316 + 0.630010I
2.13851 + 0.27818I −1.57258 + 0.84514I
u = 0.935316 − 0.630010I
a = −0.525722 − 0.984674I
b = 0.935316 − 0.630010I
2.13851 − 0.27818I −1.57258 − 0.84514I
u = 0.864210 + 0.035102I
a = −0.89308 + 1.80124I
b = 0.864210 + 0.035102I
4.69963 + 7.70569I 1.03497 − 7.90507I
u = 0.864210 − 0.035102I
a = −0.89308 − 1.80124I
b = 0.864210 − 0.035102I
4.69963 − 7.70569I 1.03497 + 7.90507I
u = −0.826242 + 0.780318I
a = 0.848642 + 0.882375I
b = −0.826242 + 0.780318I
0.40114 − 10.64020I −4.95980 + 10.11213I
u = −0.826242 − 0.780318I
a = 0.848642 − 0.882375I
b = −0.826242 − 0.780318I
0.40114 + 10.64020I −4.95980 − 10.11213I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819203 + 0.976775I
a = −0.346065 + 0.826042I
b = −0.819203 + 0.976775I
−3.89495 − 2.33301I −11.16071 + 2.50399I
u = −0.819203 − 0.976775I
a = −0.346065 − 0.826042I
b = −0.819203 − 0.976775I
−3.89495 + 2.33301I −11.16071 − 2.50399I
u = −0.650261 + 0.049079I
a = 0.38648 + 2.74023I
b = −0.650261 + 0.049079I
6.12689 + 2.86646I 4.56371 − 2.58319I
u = −0.650261 − 0.049079I
a = 0.38648 − 2.74023I
b = −0.650261 − 0.049079I
6.12689 − 2.86646I 4.56371 + 2.58319I
u = 1.27254 + 0.88593I
a = 0.346542 + 0.895806I
b = 1.27254 + 0.88593I
8.44383 + 4.90113I 0.70738 − 1.64116I
u = 1.27254 − 0.88593I
a = 0.346542 − 0.895806I
b = 1.27254 − 0.88593I
8.44383 − 4.90113I 0.70738 + 1.64116I
u = −1.29108 + 0.99217I
a = −0.262717 + 0.934110I
b = −1.29108 + 0.99217I
5.2789 − 17.4106I −3.33834 + 9.88959I
u = −1.29108 − 0.99217I
a = −0.262717 − 0.934110I
b = −1.29108 − 0.99217I
5.2789 + 17.4106I −3.33834 − 9.88959I
u = −0.216670
a = −2.36478
b = −0.216670
−0.903842 −11.0550
6
II. I
u
2
= h4.05 × 10
223
u
67
+ 3.31 × 10
224
u
66
+ · · · + 4.65 × 10
224
b − 5.28 ×
10
226
, 2.92 × 10
228
u
67
+ 2.09 × 10
229
u
66
+ · · · + 5.97 × 10
227
a − 5.78 ×
10
230
, u
68
+ 7u
67
+ · · · + 375u + 257i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
4
=
−4.88839u
67
− 34.9634u
66
+ ··· + 4825.34u + 967.944
−0.0871501u
67
− 0.712125u
66
+ ··· + 396.084u + 113.654
a
3
=
−4.80124u
67
− 34.2513u
66
+ ··· + 4429.26u + 854.290
−0.0871501u
67
− 0.712125u
66
+ ··· + 396.084u + 113.654
a
9
=
−7.99115u
67
− 60.4866u
66
+ ··· + 10430.3u + 3443.31
1.61940u
67
+ 12.4687u
66
+ ··· − 2290.63u − 756.650
a
2
=
−6.77651u
67
− 48.1052u
66
+ ··· + 6300.23u + 1133.09
0.666031u
67
+ 4.36174u
66
+ ··· − 121.691u + 106.711
a
7
=
−4.48948u
67
− 33.7015u
66
+ ··· + 5341.98u + 1665.92
1.88227u
67
+ 14.3164u
66
+ ··· − 2795.65u − 1020.74
a
5
=
1.28662u
67
+ 6.44767u
66
+ ··· − 34.9011u + 812.874
0.546402u
67
+ 5.09202u
66
+ ··· − 1326.15u − 757.561
a
6
=
−4.16324u
67
− 34.1080u
66
+ ··· + 8461.50u + 3399.72
0.717867u
67
+ 6.15447u
66
+ ··· − 1764.97u − 755.279
a
10
=
−5.80661u
67
− 43.0967u
66
+ ··· + 4592.48u + 1354.29
2.28558u
67
+ 17.7608u
66
+ ··· − 2796.80u − 1065.18
a
10
=
−5.80661u
67
− 43.0967u
66
+ ··· + 4592.48u + 1354.29
2.28558u
67
+ 17.7608u
66
+ ··· − 2796.80u − 1065.18
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.644686u
67
+ 6.72660u
66
+ ··· − 1138.68u − 1495.39
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
68
− u
67
+ ··· − 12u + 1
c
2
, c
10
u
68
+ 25u
67
+ ··· + 60u + 1
c
3
, c
11
u
68
+ 7u
67
+ ··· + 375u + 257
c
4
, c
7
(u
34
+ 5u
33
+ ··· + 34u + 5)
2
c
8
(u
34
+ 9u
33
+ ··· + 4u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
68
− 25y
67
+ ··· − 60y + 1
c
2
, c
10
y
68
+ 39y
67
+ ··· − 600y + 1
c
3
, c
11
y
68
− 15y
67
+ ··· − 2055275y + 66049
c
4
, c
7
(y
34
+ 29y
33
+ ··· − 606y + 25)
2
c
8
(y
34
− 7y
33
+ ··· − 22y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935366 + 0.409909I
a = 0.174120 − 0.076305I
b = 0.935366 − 0.409909I
2.60763 0
u = 0.935366 − 0.409909I
a = 0.174120 + 0.076305I
b = 0.935366 + 0.409909I
2.60763 0
u = −0.654321 + 0.803747I
a = −0.383222 − 0.470738I
b = −0.654321 − 0.803747I
0.823819 0
u = −0.654321 − 0.803747I
a = −0.383222 + 0.470738I
b = −0.654321 + 0.803747I
0.823819 0
u = 0.086992 + 0.928184I
a = −1.49441 − 0.34424I
b = −0.718586 − 0.099000I
4.05974 + 3.04464I −5.00000 − 5.02705I
u = 0.086992 − 0.928184I
a = −1.49441 + 0.34424I
b = −0.718586 + 0.099000I
4.05974 − 3.04464I −5.00000 + 5.02705I
u = 0.888058 + 0.145938I
a = −0.362458 + 1.265120I
b = 1.096870 + 0.603105I
1.66267 + 2.38839I −5.00000 − 3.92268I
u = 0.888058 − 0.145938I
a = −0.362458 − 1.265120I
b = 1.096870 − 0.603105I
1.66267 − 2.38839I −5.00000 + 3.92268I
u = −0.885212 + 0.660115I
a = −0.747811 − 0.890107I
b = 0.786877 − 0.792245I
1.50330 − 5.20280I 0
u = −0.885212 − 0.660115I
a = −0.747811 + 0.890107I
b = 0.786877 + 0.792245I
1.50330 + 5.20280I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645959 + 0.609538I
a = −0.819920 − 0.300054I
b = 0.237861 − 0.469376I
−1.64111 − 0.20863I −8.20722 + 0.I
u = −0.645959 − 0.609538I
a = −0.819920 + 0.300054I
b = 0.237861 + 0.469376I
−1.64111 + 0.20863I −8.20722 + 0.I
u = 0.786877 + 0.792245I
a = 0.601596 − 0.979699I
b = −0.885212 − 0.660115I
1.50330 + 5.20280I 0
u = 0.786877 − 0.792245I
a = 0.601596 + 0.979699I
b = −0.885212 + 0.660115I
1.50330 − 5.20280I 0
u = −1.027720 + 0.439350I
a = −0.144640 − 0.772915I
b = 0.720497 − 0.909017I
−0.25133 − 4.16817I 0
u = −1.027720 − 0.439350I
a = −0.144640 + 0.772915I
b = 0.720497 + 0.909017I
−0.25133 + 4.16817I 0
u = 0.695237 + 0.876261I
a = −0.463175 + 0.146177I
b = −1.029460 + 0.540394I
1.12918 + 5.12471I 0
u = 0.695237 − 0.876261I
a = −0.463175 − 0.146177I
b = −1.029460 − 0.540394I
1.12918 − 5.12471I 0
u = 0.720497 + 0.909017I
a = −0.232294 − 0.721216I
b = −1.027720 − 0.439350I
−0.25133 + 4.16817I 0
u = 0.720497 − 0.909017I
a = −0.232294 + 0.721216I
b = −1.027720 + 0.439350I
−0.25133 − 4.16817I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.029460 + 0.540394I
a = 0.221154 + 0.411620I
b = 0.695237 + 0.876261I
1.12918 + 5.12471I 0
u = −1.029460 − 0.540394I
a = 0.221154 − 0.411620I
b = 0.695237 − 0.876261I
1.12918 − 5.12471I 0
u = −0.829237 + 0.028303I
a = −0.69769 − 2.02660I
b = 0.597312 − 0.062789I
5.57461 − 2.65210I 3.99824 + 1.76358I
u = −0.829237 − 0.028303I
a = −0.69769 + 2.02660I
b = 0.597312 + 0.062789I
5.57461 + 2.65210I 3.99824 − 1.76358I
u = 0.750141 + 0.908115I
a = −0.606651 − 0.697727I
b = −1.56205 − 0.58113I
0.20559 + 3.65421I 0
u = 0.750141 − 0.908115I
a = −0.606651 + 0.697727I
b = −1.56205 + 0.58113I
0.20559 − 3.65421I 0
u = −0.765342 + 0.905693I
a = −0.601112 + 0.874358I
b = −1.57861 + 0.95684I
−0.84333 − 8.53070I 0
u = −0.765342 − 0.905693I
a = −0.601112 − 0.874358I
b = −1.57861 − 0.95684I
−0.84333 + 8.53070I 0
u = 0.735761 + 0.292287I
a = 0.66785 + 1.40228I
b = 1.73061 + 1.32358I
6.19582 − 1.01878I 4.58808 − 1.16723I
u = 0.735761 − 0.292287I
a = 0.66785 − 1.40228I
b = 1.73061 − 1.32358I
6.19582 + 1.01878I 4.58808 + 1.16723I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711895 + 0.258153I
a = 0.58405 − 1.65179I
b = 1.45720 − 1.66487I
6.41329 − 4.23932I 5.89514 + 7.96165I
u = −0.711895 − 0.258153I
a = 0.58405 + 1.65179I
b = 1.45720 + 1.66487I
6.41329 + 4.23932I 5.89514 − 7.96165I
u = 1.096870 + 0.603105I
a = 0.057508 + 0.944434I
b = 0.888058 + 0.145938I
1.66267 + 2.38839I 0
u = 1.096870 − 0.603105I
a = 0.057508 − 0.944434I
b = 0.888058 − 0.145938I
1.66267 − 2.38839I 0
u = −0.869088 + 0.901011I
a = 0.563739 + 0.260530I
b = −0.476889 + 0.496046I
−3.86295 − 4.69165I 0
u = −0.869088 − 0.901011I
a = 0.563739 − 0.260530I
b = −0.476889 − 0.496046I
−3.86295 + 4.69165I 0
u = −0.718586 + 0.099000I
a = 0.00780 − 1.97090I
b = 0.086992 − 0.928184I
4.05974 − 3.04464I −8.15642 + 5.02705I
u = −0.718586 − 0.099000I
a = 0.00780 + 1.97090I
b = 0.086992 + 0.928184I
4.05974 + 3.04464I −8.15642 − 5.02705I
u = −0.476889 + 0.496046I
a = 1.024820 + 0.475673I
b = −0.869088 + 0.901011I
−3.86295 − 4.69165I −11.49179 + 4.07331I
u = −0.476889 − 0.496046I
a = 1.024820 − 0.475673I
b = −0.869088 − 0.901011I
−3.86295 + 4.69165I −11.49179 − 4.07331I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636750 + 0.128166I
a = 0.04371 − 1.98902I
b = −0.66517 − 1.83516I
4.76682 − 3.09252I 3.99662 + 6.42171I
u = −0.636750 − 0.128166I
a = 0.04371 + 1.98902I
b = −0.66517 + 1.83516I
4.76682 + 3.09252I 3.99662 − 6.42171I
u = 0.614911 + 0.115807I
a = −0.08677 + 1.88600I
b = −1.27800 + 1.84734I
3.65105 + 8.06945I 2.24961 − 10.45643I
u = 0.614911 − 0.115807I
a = −0.08677 − 1.88600I
b = −1.27800 − 1.84734I
3.65105 − 8.06945I 2.24961 + 10.45643I
u = 0.609867 + 0.075529I
a = 0.41718 + 1.72597I
b = −1.219630 + 0.681568I
0.49208 + 2.14474I −4.47534 − 2.22851I
u = 0.609867 − 0.075529I
a = 0.41718 − 1.72597I
b = −1.219630 − 0.681568I
0.49208 − 2.14474I −4.47534 + 2.22851I
u = −1.219630 + 0.681568I
a = 0.301017 − 0.720678I
b = 0.609867 + 0.075529I
0.49208 + 2.14474I 0
u = −1.219630 − 0.681568I
a = 0.301017 + 0.720678I
b = 0.609867 − 0.075529I
0.49208 − 2.14474I 0
u = 0.597312 + 0.062789I
a = 0.76391 − 2.86073I
b = −0.829237 − 0.028303I
5.57461 + 2.65210I 3.99824 − 1.76358I
u = 0.597312 − 0.062789I
a = 0.76391 + 2.86073I
b = −0.829237 + 0.028303I
5.57461 − 2.65210I 3.99824 + 1.76358I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237861 + 0.469376I
a = 1.13072 − 0.94503I
b = −0.645959 − 0.609538I
−1.64111 + 0.20863I −8.20722 + 0.26692I
u = 0.237861 − 0.469376I
a = 1.13072 + 0.94503I
b = −0.645959 + 0.609538I
−1.64111 − 0.20863I −8.20722 − 0.26692I
u = −1.21547 + 0.86314I
a = 0.310422 − 0.988272I
b = 1.32582 − 1.03680I
7.06234 − 11.08520I 0
u = −1.21547 − 0.86314I
a = 0.310422 + 0.988272I
b = 1.32582 + 1.03680I
7.06234 + 11.08520I 0
u = −1.56205 + 0.58113I
a = 0.124351 − 0.641489I
b = 0.750141 − 0.908115I
0.20559 − 3.65421I 0
u = −1.56205 − 0.58113I
a = 0.124351 + 0.641489I
b = 0.750141 + 0.908115I
0.20559 + 3.65421I 0
u = 1.32582 + 1.03680I
a = −0.315066 − 0.861723I
b = −1.21547 − 0.86314I
7.06234 + 11.08520I 0
u = 1.32582 − 1.03680I
a = −0.315066 + 0.861723I
b = −1.21547 + 0.86314I
7.06234 − 11.08520I 0
u = −1.57861 + 0.95684I
a = −0.187050 + 0.655406I
b = −0.765342 + 0.905693I
−0.84333 − 8.53070I 0
u = −1.57861 − 0.95684I
a = −0.187050 − 0.655406I
b = −0.765342 − 0.905693I
−0.84333 + 8.53070I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.66517 + 1.83516I
a = −0.652341 + 0.112700I
b = −0.636750 − 0.128166I
4.76682 + 3.09252I 0
u = −0.66517 − 1.83516I
a = −0.652341 − 0.112700I
b = −0.636750 + 0.128166I
4.76682 − 3.09252I 0
u = 1.73061 + 1.32358I
a = 0.371829 + 0.424591I
b = 0.735761 + 0.292287I
6.19582 − 1.01878I 0
u = 1.73061 − 1.32358I
a = 0.371829 − 0.424591I
b = 0.735761 − 0.292287I
6.19582 + 1.01878I 0
u = 1.45720 + 1.66487I
a = −0.448039 − 0.398539I
b = −0.711895 − 0.258153I
6.41329 + 4.23932I 0
u = 1.45720 − 1.66487I
a = −0.448039 + 0.398539I
b = −0.711895 + 0.258153I
6.41329 − 4.23932I 0
u = −1.27800 + 1.84734I
a = 0.489733 − 0.191687I
b = 0.614911 + 0.115807I
3.65105 + 8.06945I 0
u = −1.27800 − 1.84734I
a = 0.489733 + 0.191687I
b = 0.614911 − 0.115807I
3.65105 − 8.06945I 0
16
III. I
u
3
= hb + u, u
7
+ u
6
− 2u
4
+ u
2
+ a + 2u − 1, u
8
− u
6
− u
5
+ 2u
4
− u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
4
=
−u
7
− u
6
+ 2u
4
− u
2
− 2u + 1
−u
a
3
=
−u
7
− u
6
+ 2u
4
− u
2
− u + 1
−u
a
9
=
−u
7
− u
6
+ u
4
u
7
− u
5
− u
4
+ u
3
+ u − 1
a
2
=
−2u
7
− u
6
+ u
5
+ 3u
4
− u
3
− u
2
− 2u + 2
−u
5
+ u
3
− 2u
a
7
=
u
7
− u
6
− 2u
5
− u
4
+ 3u
3
− 2
u
7
− u
5
− u
4
+ 2u
3
+ u − 1
a
5
=
u
7
+ u
6
− u
5
− 3u
4
+ 2u
2
+ u − 1
u
6
+ u
5
− u
4
− 2u
3
+ u
2
+ u
a
6
=
u
7
− 2u
5
− 2u
4
+ 2u
3
+ 2u
2
− 1
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ u
2
a
10
=
u + 1
u
7
− u
5
+ u
3
− u
2
+ 1
a
10
=
u + 1
u
7
− u
5
+ u
3
− u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ 3u
6
+ 6u
5
+ 2u
4
− 9u
3
− u
2
− u − 1
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
− 2u
6
+ 3u
4
+ u
3
− 2u
2
− u + 1
c
2
, c
10
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1
c
3
, c
11
u
8
− u
6
− u
5
+ 2u
4
− u + 1
c
4
u
8
− u
7
+ 4u
6
− 4u
5
+ 6u
4
− 5u
3
+ 5u
2
− 2u + 1
c
6
, c
9
u
8
− 2u
6
+ 3u
4
− u
3
− 2u
2
+ u + 1
c
7
u
8
+ u
7
+ 4u
6
+ 4u
5
+ 6u
4
+ 5u
3
+ 5u
2
+ 2u + 1
c
8
u
8
+ 3u
7
+ 3u
6
+ u
5
− u
4
− u
3
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
8
− 4y
7
+ 10y
6
− 16y
5
+ 19y
4
− 17y
3
+ 12y
2
− 5y + 1
c
2
, c
10
y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
− y + 1
c
3
, c
11
y
8
− 2y
7
+ 5y
6
− 5y
5
+ 6y
4
− 4y
3
+ 4y
2
− y + 1
c
4
, c
7
y
8
+ 7y
7
+ 20y
6
+ 32y
5
+ 34y
4
+ 27y
3
+ 17y
2
+ 6y + 1
c
8
y
8
− 3y
7
+ y
6
− y
5
+ 5y
4
+ 5y
3
− 2y
2
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968184 + 0.381145I
a = 0.382665 − 0.800987I
b = −0.968184 − 0.381145I
0.794315 + 0.862931I −6.95751 − 0.59355I
u = 0.968184 − 0.381145I
a = 0.382665 + 0.800987I
b = −0.968184 + 0.381145I
0.794315 − 0.862931I −6.95751 + 0.59355I
u = −0.534261 + 0.758391I
a = 1.207080 − 0.334530I
b = 0.534261 − 0.758391I
2.78226 + 7.31144I −4.74402 − 5.01155I
u = −0.534261 − 0.758391I
a = 1.207080 + 0.334530I
b = 0.534261 + 0.758391I
2.78226 − 7.31144I −4.74402 + 5.01155I
u = 0.585320 + 0.576383I
a = −1.24580 − 1.30467I
b = −0.585320 − 0.576383I
5.20723 + 3.67399I −1.42456 − 6.52580I
u = 0.585320 − 0.576383I
a = −1.24580 + 1.30467I
b = −0.585320 + 0.576383I
5.20723 − 3.67399I −1.42456 + 6.52580I
u = −1.019240 + 0.742714I
a = 0.156057 − 0.473494I
b = 1.019240 − 0.742714I
−2.20407 − 5.83988I −6.87391 + 7.08087I
u = −1.019240 − 0.742714I
a = 0.156057 + 0.473494I
b = 1.019240 + 0.742714I
−2.20407 + 5.83988I −6.87391 − 7.08087I
20
IV. I
u
4
= h−3u
7
− 2u
6
+ 2u
5
− 4u
4
+ 3u
2
+ b − 7u + 4, −4u
7
− 3u
6
+ · · · +
a + 5, u
8
− u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 3u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
4
=
4u
7
+ 3u
6
− 2u
5
+ 6u
4
+ u
3
− 3u
2
+ 9u − 5
3u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
2
+ 7u − 4
a
3
=
u
7
+ u
6
+ 2u
4
+ u
3
+ 2u − 1
3u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
2
+ 7u − 4
a
9
=
3u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
2
+ 7u − 4
u
7
+ u
6
+ 2u
4
− u
2
+ 3u − 2
a
2
=
5u
7
+ 4u
6
− 2u
5
+ 8u
4
+ u
3
− 4u
2
+ 11u − 6
u
7
+ u
6
+ u
4
− u
2
+ 2u − 1
a
7
=
5u
7
+ 3u
6
− 3u
5
+ 8u
4
− u
3
− 5u
2
+ 12u − 9
u
7
− u
5
+ 2u
4
− u
3
− u
2
+ 4u − 3
a
5
=
−u
6
− u
5
− 2u
3
− u
2
+ u − 2
u
7
− u
5
+ 2u
4
− u
3
− 2u
2
+ 3u − 2
a
6
=
−3u
7
− 2u
6
+ 2u
5
− 5u
4
− u
3
+ 3u
2
− 7u + 3
−u
3
+ u − 1
a
10
=
u + 1
u
4
− u
2
+ u
a
10
=
u + 1
u
4
− u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
7
− 6u
6
+ 10u
5
− 15u
4
+ u
3
+ 11u
2
− 25u + 11
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
− 2u
6
− u
5
+ 3u
4
+ u
3
− 2u
2
+ 1
c
2
, c
10
u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1
c
3
, c
11
u
8
− u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 3u + 1
c
4
(u
4
+ 2u
2
+ u + 1)
2
c
6
, c
9
u
8
− 2u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
+ 1
c
7
(u
4
+ 2u
2
− u + 1)
2
c
8
(u
4
− u
3
+ 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
8
− 4y
7
+ 10y
6
− 17y
5
+ 21y
4
− 17y
3
+ 10y
2
− 4y + 1
c
2
, c
10
y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1
c
3
, c
11
y
8
− 2y
7
− y
6
+ 4y
5
+ y
4
+ 3y
3
+ y
2
− 3y + 1
c
4
, c
7
(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
c
8
(y
4
− y
3
+ 2y
2
+ 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.655106 + 0.740977I
a = 0.243445 + 0.679234I
b = 1.38224 + 0.31096I
−1.13814 + 3.38562I −9.49848 − 3.42631I
u = 0.655106 − 0.740977I
a = 0.243445 − 0.679234I
b = 1.38224 − 0.31096I
−1.13814 − 3.38562I −9.49848 + 3.42631I
u = 0.065777 + 1.058430I
a = −1.258400 − 0.403038I
b = −0.661359 + 0.124331I
4.42801 + 2.37936I −2.50152 + 3.27706I
u = 0.065777 − 1.058430I
a = −1.258400 + 0.403038I
b = −0.661359 − 0.124331I
4.42801 − 2.37936I −2.50152 − 3.27706I
u = 0.661359 + 0.124331I
a = 0.87507 + 1.88950I
b = −0.065777 + 1.058430I
4.42801 − 2.37936I −2.50152 − 3.27706I
u = 0.661359 − 0.124331I
a = 0.87507 − 1.88950I
b = −0.065777 − 1.058430I
4.42801 + 2.37936I −2.50152 + 3.27706I
u = −1.38224 + 0.31096I
a = 0.139876 + 0.483891I
b = −0.655106 + 0.740977I
−1.13814 − 3.38562I −9.49848 + 3.42631I
u = −1.38224 − 0.31096I
a = 0.139876 − 0.483891I
b = −0.655106 − 0.740977I
−1.13814 + 3.38562I −9.49848 − 3.42631I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
8
− 2u
6
+ 3u
4
+ u
3
− 2u
2
− u + 1)(u
8
− 2u
6
− u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
· (u
19
− 4u
17
+ ··· − u + 1)(u
68
− u
67
+ ··· − 12u + 1)
c
2
, c
10
(u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1)
· (u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1)
· (u
19
+ 8u
18
+ ··· + 5u + 1)(u
68
+ 25u
67
+ ··· + 60u + 1)
c
3
, c
11
(u
8
− u
6
− u
5
+ 2u
4
− u + 1)(u
8
− u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 3u + 1)
· (u
19
− 3u
17
+ ··· + 5u + 1)(u
68
+ 7u
67
+ ··· + 375u + 257)
c
4
(u
4
+ 2u
2
+ u + 1)
2
(u
8
− u
7
+ 4u
6
− 4u
5
+ 6u
4
− 5u
3
+ 5u
2
− 2u + 1)
· (u
19
− 12u
18
+ ··· − 224u + 32)(u
34
+ 5u
33
+ ··· + 34u + 5)
2
c
6
, c
9
(u
8
− 2u
6
+ 3u
4
− u
3
− 2u
2
+ u + 1)(u
8
− 2u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
+ 1)
· (u
19
− 4u
17
+ ··· − u + 1)(u
68
− u
67
+ ··· − 12u + 1)
c
7
(u
4
+ 2u
2
− u + 1)
2
(u
8
+ u
7
+ 4u
6
+ 4u
5
+ 6u
4
+ 5u
3
+ 5u
2
+ 2u + 1)
· (u
19
− 12u
18
+ ··· − 224u + 32)(u
34
+ 5u
33
+ ··· + 34u + 5)
2
c
8
(u
4
− u
3
+ 1)
2
(u
8
+ 3u
7
+ 3u
6
+ u
5
− u
4
− u
3
+ 1)
· (u
19
− 18u
18
+ ··· − 1184u + 192)(u
34
+ 9u
33
+ ··· + 4u + 1)
2
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(y
8
− 4y
7
+ 10y
6
− 17y
5
+ 21y
4
− 17y
3
+ 10y
2
− 4y + 1)
· (y
8
− 4y
7
+ 10y
6
− 16y
5
+ 19y
4
− 17y
3
+ 12y
2
− 5y + 1)
· (y
19
− 8y
18
+ ··· + 5y −1)(y
68
− 25y
67
+ ··· − 60y + 1)
c
2
, c
10
(y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1)
· (y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
− y + 1)
· (y
19
+ 12y
18
+ ··· − 23y −1)(y
68
+ 39y
67
+ ··· − 600y + 1)
c
3
, c
11
(y
8
− 2y
7
− y
6
+ 4y
5
+ y
4
+ 3y
3
+ y
2
− 3y + 1)
· (y
8
− 2y
7
+ 5y
6
− 5y
5
+ 6y
4
− 4y
3
+ 4y
2
− y + 1)
· (y
19
− 6y
18
+ ··· + 29y −1)(y
68
− 15y
67
+ ··· − 2055275y + 66049)
c
4
, c
7
(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
· (y
8
+ 7y
7
+ 20y
6
+ 32y
5
+ 34y
4
+ 27y
3
+ 17y
2
+ 6y + 1)
· (y
19
+ 12y
18
+ ··· + 1536y −1024)(y
34
+ 29y
33
+ ··· − 606y + 25)
2
c
8
(y
4
− y
3
+ 2y
2
+ 1)
2
(y
8
− 3y
7
+ y
6
− y
5
+ 5y
4
+ 5y
3
− 2y
2
+ 1)
· (y
19
− 4y
18
+ ··· + 50176y −36864)(y
34
− 7y
33
+ ··· − 22y + 1)
2
26
