12a
0122
(K12a
0122
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 1 10 4 11 7 9 6
Solving Sequence
3,8 4,5,12
6 9 2 1 11 10 7
c
3
c
5
c
8
c
2
c
1
c
11
c
9
c
7
c
4
, c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.85904 × 10
163
u
70
− 4.35691 × 10
163
u
69
+ ··· + 1.78033 × 10
166
d + 6.66454 × 10
165
,
6.92432 × 10
163
u
70
+ 3.87141 × 10
164
u
69
+ ··· + 1.42427 × 10
167
c − 4.02166 × 10
167
,
− 3.44890 × 10
145
u
70
− 6.44692 × 10
145
u
69
+ ··· + 2.51636 × 10
148
b − 3.51686 × 10
147
,
2.31798 × 10
146
u
70
+ 5.72081 × 10
146
u
69
+ ··· + 1.00654 × 10
149
a − 4.30269 × 10
149
,
u
71
+ 2u
70
+ ··· − 1536u
2
+ 512i
I
u
2
= hd, c − 1, −a
2
u
2
+ b + 2a − 2, 2u
8
a
2
− 3u
8
a + ··· + 3a − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
v
1
= hc, d − 1, b, a − 1, v
2
− v + 1i
I
v
2
= ha, d + 1, c + a, b − 1, v
2
+ v + 1i
I
v
3
= ha, d, c − 1, b − 1, v − 1i
I
v
4
= ha, d
2
v
2
+ dv + 1, v
2
dc − v
2
d + cv + a − v, da − c + 1, c
2
v
2
+ cav − 2v
2
c + a
2
− av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 103 representations.
* 1 irreducible components of dim
C
= 1
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
=
h−2.86 × 10
163
u
70
− 4.36 × 10
163
u
69
+ · · · + 1.78 × 10
166
d + 6.66 × 10
165
, 6.92 ×
10
163
u
70
+3.87×10
164
u
69
+· · ·+1.42×10
167
c−4.02×10
167
, −3.45×10
145
u
70
−
6.45 × 10
145
u
69
+ · · · + 2.52 × 10
148
b − 3.52 × 10
147
, 2.32 × 10
146
u
70
+ 5.72 ×
10
146
u
69
+ · · · + 1.01 × 10
149
a − 4.30 × 10
149
, u
71
+ 2u
70
+ · · · − 1536u
2
+ 512i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
−0.00230291u
70
− 0.00568363u
69
+ ··· + 2.16416u + 4.27473
0.00137059u
70
+ 0.00256201u
69
+ ··· − 0.903349u + 0.139760
a
12
=
−0.000486167u
70
− 0.00271817u
69
+ ··· + 1.59401u + 2.82367
0.00160590u
70
+ 0.00244724u
69
+ ··· − 0.182976u − 0.374342
a
6
=
−0.00198935u
70
− 0.00509444u
69
+ ··· + 1.69724u + 3.40383
−0.000342331u
70
− 0.000350145u
69
+ ··· − 0.477053u − 0.323800
a
9
=
u
−u
3
+ u
a
2
=
−0.00230291u
70
− 0.00568363u
69
+ ··· + 2.16416u + 4.27473
0.000610137u
70
+ 0.000608739u
69
+ ··· − 0.275743u − 0.691592
a
1
=
−0.00169278u
70
− 0.00507489u
69
+ ··· + 1.88842u + 3.58313
0.000610137u
70
+ 0.000608739u
69
+ ··· − 0.275743u − 0.691592
a
11
=
0.000942281u
70
− 0.000435385u
69
+ ··· + 0.824718u + 2.36850
0.00186115u
70
+ 0.00285291u
69
+ ··· − 0.220899u − 1.12345
a
10
=
0.000964925u
70
+ 0.00251480u
69
+ ··· − 0.510969u − 0.979894
−0.00121332u
70
− 0.00285890u
69
+ ··· + 0.588206u + 1.41140
a
7
=
−0.00150252u
70
− 0.00389403u
69
+ ··· + 1.52807u + 2.30414
−0.00101635u
70
− 0.00117586u
69
+ ··· − 0.0659421u − 0.519527
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000644196u
70
− 0.0111115u
69
+ ··· + 0.863041u + 15.1191
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 30u
70
+ ··· + 4640u + 256
c
2
, c
4
u
71
− 8u
70
+ ··· + 56u − 16
c
3
, c
8
u
71
− 2u
70
+ ··· + 1536u
2
− 512
c
5
, c
6
, c
12
u
71
+ 8u
70
+ ··· + 56u − 16
c
7
, c
10
u
71
+ 2u
70
+ ··· − 5u
2
− 4
c
9
, c
11
u
71
+ 24u
70
+ ··· − 40u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 30y
70
+ ··· + 5022208y − 65536
c
2
, c
4
y
71
− 30y
70
+ ··· + 4640y − 256
c
3
, c
8
y
71
− 30y
70
+ ··· + 1572864y − 262144
c
5
, c
6
, c
12
y
71
− 70y
70
+ ··· − 1504y − 256
c
7
, c
10
y
71
+ 24y
70
+ ··· − 40y − 16
c
9
, c
11
y
71
+ 48y
70
+ ··· − 6880y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372595 + 0.922213I
a = 0.485748 − 0.116000I
b = 0.947611 + 0.465102I
c = −0.384570 − 0.910845I
d = −0.352109 − 0.909932I
−0.206074 − 1.106620I 1.82615 + 2.10157I
u = 0.372595 − 0.922213I
a = 0.485748 + 0.116000I
b = 0.947611 − 0.465102I
c = −0.384570 + 0.910845I
d = −0.352109 + 0.909932I
−0.206074 + 1.106620I 1.82615 − 2.10157I
u = −0.661751 + 0.731261I
a = 0.455879 + 0.075380I
b = 1.135190 − 0.353055I
c = −0.541629 + 0.798372I
d = −0.648241 + 1.044530I
−5.31233 + 1.23150I −6.16629 − 0.79467I
u = −0.661751 − 0.731261I
a = 0.455879 − 0.075380I
b = 1.135190 + 0.353055I
c = −0.541629 − 0.798372I
d = −0.648241 − 1.044530I
−5.31233 − 1.23150I −6.16629 + 0.79467I
u = −0.216094 + 0.961248I
a = 0.507916 + 0.138278I
b = 0.832973 − 0.499020I
c = 0.383038 − 1.211050I
d = 1.32096 − 2.52250I
2.60149 + 2.06138I 6.60052 − 3.22142I
u = −0.216094 − 0.961248I
a = 0.507916 − 0.138278I
b = 0.832973 + 0.499020I
c = 0.383038 + 1.211050I
d = 1.32096 + 2.52250I
2.60149 − 2.06138I 6.60052 + 3.22142I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510340 + 0.919175I
a = 0.466316 − 0.105830I
b = 1.039430 + 0.462844I
c = 0.06669 + 1.49411I
d = 0.71893 + 3.03674I
−1.22762 − 4.53498I −0.48837 + 4.83158I
u = 0.510340 − 0.919175I
a = 0.466316 + 0.105830I
b = 1.039430 − 0.462844I
c = 0.06669 − 1.49411I
d = 0.71893 − 3.03674I
−1.22762 + 4.53498I −0.48837 − 4.83158I
u = −0.843761 + 0.417994I
a = 0.442312 + 0.038598I
b = 1.243760 − 0.195802I
c = −0.734788 + 0.784462I
d = −1.01432 + 1.24587I
−1.74336 − 3.95563I 0.57229 + 6.63484I
u = −0.843761 − 0.417994I
a = 0.442312 − 0.038598I
b = 1.243760 + 0.195802I
c = −0.734788 − 0.784462I
d = −1.01432 − 1.24587I
−1.74336 + 3.95563I 0.57229 − 6.63484I
u = 0.980094 + 0.401535I
a = 0.12281 − 1.97463I
b = −0.968625 + 0.504474I
c = −1.197140 − 0.714849I
d = −0.337051 + 0.964290I
0.13020 + 4.00402I 4.41276 − 6.69495I
u = 0.980094 − 0.401535I
a = 0.12281 + 1.97463I
b = −0.968625 − 0.504474I
c = −1.197140 + 0.714849I
d = −0.337051 − 0.964290I
0.13020 − 4.00402I 4.41276 + 6.69495I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482781 + 0.984718I
a = 0.465372 + 0.116264I
b = 1.022580 − 0.505302I
c = −0.456078 + 0.912887I
d = −0.380030 + 1.013380I
−0.99233 + 6.45679I 0.34368 − 6.97496I
u = −0.482781 − 0.984718I
a = 0.465372 − 0.116264I
b = 1.022580 + 0.505302I
c = −0.456078 − 0.912887I
d = −0.380030 − 1.013380I
−0.99233 − 6.45679I 0.34368 + 6.97496I
u = −0.777198 + 0.427799I
a = 0.07067 + 2.71633I
b = −0.990428 − 0.367895I
c = −1.55052 + 1.42781I
d = −0.496780 − 0.852703I
−1.94652 + 0.34051I −0.37051 + 3.03065I
u = −0.777198 − 0.427799I
a = 0.07067 − 2.71633I
b = −0.990428 + 0.367895I
c = −1.55052 − 1.42781I
d = −0.496780 + 0.852703I
−1.94652 − 0.34051I −0.37051 − 3.03065I
u = −1.127060 + 0.152551I
a = 0.625091 − 1.046840I
b = −0.579522 + 0.704176I
c = −2.04566 + 1.44271I
d = 1.04128 − 1.78221I
4.50468 + 2.47836I 7.49354 − 3.38416I
u = −1.127060 − 0.152551I
a = 0.625091 + 1.046840I
b = −0.579522 − 0.704176I
c = −2.04566 − 1.44271I
d = 1.04128 + 1.78221I
4.50468 − 2.47836I 7.49354 + 3.38416I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982347 + 0.611518I
a = −0.39397 + 1.91571I
b = −1.102990 − 0.500818I
c = −1.67667 + 0.41013I
d = −0.438066 − 1.090250I
−4.29573 − 6.37313I −3.00781 + 7.19219I
u = −0.982347 − 0.611518I
a = −0.39397 − 1.91571I
b = −1.102990 + 0.500818I
c = −1.67667 − 0.41013I
d = −0.438066 + 1.090250I
−4.29573 + 6.37313I −3.00781 − 7.19219I
u = −1.173990 + 0.222972I
a = 0.579369 − 0.967956I
b = −0.544738 + 0.760609I
c = −0.311368 − 0.051508I
d = 0.148549 + 1.017150I
5.09577 − 1.83902I 8.24819 + 0.I
u = −1.173990 − 0.222972I
a = 0.579369 + 0.967956I
b = −0.544738 − 0.760609I
c = −0.311368 + 0.051508I
d = 0.148549 − 1.017150I
5.09577 + 1.83902I 8.24819 + 0.I
u = 1.203430 + 0.094057I
a = 0.526070 + 1.096070I
b = −0.644095 − 0.741530I
c = −0.422317 + 0.128209I
d = 0.061447 − 1.014150I
5.36659 − 3.89584I 8.41567 + 5.55146I
u = 1.203430 − 0.094057I
a = 0.526070 − 1.096070I
b = −0.644095 + 0.741530I
c = −0.422317 − 0.128209I
d = 0.061447 + 1.014150I
5.36659 + 3.89584I 8.41567 − 5.55146I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117530 + 0.478181I
a = 0.592431 − 0.750598I
b = −0.352089 + 0.820889I
c = −2.11325 + 0.00351I
d = 0.82348 − 1.49852I
3.15531 − 5.12152I 0
u = −1.117530 − 0.478181I
a = 0.592431 + 0.750598I
b = −0.352089 − 0.820889I
c = −2.11325 − 0.00351I
d = 0.82348 + 1.49852I
3.15531 + 5.12152I 0
u = 1.137650 + 0.460214I
a = −0.04379 − 1.65202I
b = −1.016040 + 0.604894I
c = 1.76875 + 1.86712I
d = 0.70340 − 2.59306I
3.19656 + 2.55854I 0
u = 1.137650 − 0.460214I
a = −0.04379 + 1.65202I
b = −1.016040 − 0.604894I
c = 1.76875 − 1.86712I
d = 0.70340 + 2.59306I
3.19656 − 2.55854I 0
u = 0.725491 + 0.260568I
a = 0.454620 − 0.024037I
b = 1.193510 + 0.115977I
c = −0.858903 − 0.665057I
d = −1.33178 − 1.09391I
−1.09934 − 1.05821I 3.09814 − 1.72718I
u = 0.725491 − 0.260568I
a = 0.454620 + 0.024037I
b = 1.193510 − 0.115977I
c = −0.858903 + 0.665057I
d = −1.33178 + 1.09391I
−1.09934 + 1.05821I 3.09814 + 1.72718I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.247645 + 1.226350I
a = 0.509066 + 0.265043I
b = 0.545453 − 0.804634I
c = 0.148746 − 0.746604I
d = 0.89036 − 1.73101I
6.94619 + 1.12108I 0
u = 0.247645 − 1.226350I
a = 0.509066 − 0.265043I
b = 0.545453 + 0.804634I
c = 0.148746 + 0.746604I
d = 0.89036 + 1.73101I
6.94619 − 1.12108I 0
u = −0.464983 + 0.581438I
a = 0.788881 − 0.333426I
b = 0.075493 + 0.454564I
c = 0.323459 + 0.239200I
d = 0.936440 + 0.862765I
1.011140 + 0.938516I 3.66296 + 0.79830I
u = −0.464983 − 0.581438I
a = 0.788881 + 0.333426I
b = 0.075493 − 0.454564I
c = 0.323459 − 0.239200I
d = 0.936440 − 0.862765I
1.011140 − 0.938516I 3.66296 − 0.79830I
u = −0.368570 + 1.210560I
a = 0.515481 − 0.295559I
b = 0.459973 + 0.837098I
c = 0.122518 + 0.676794I
d = 0.83963 + 1.62701I
6.42018 + 4.68044I 0
u = −0.368570 − 1.210560I
a = 0.515481 + 0.295559I
b = 0.459973 − 0.837098I
c = 0.122518 − 0.676794I
d = 0.83963 − 1.62701I
6.42018 − 4.68044I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.248660 + 0.306382I
a = 0.516438 + 0.892389I
b = −0.514200 − 0.839448I
c = −1.73216 − 0.62281I
d = 0.84440 + 1.69272I
7.51654 + 1.91781I 0
u = 1.248660 − 0.306382I
a = 0.516438 − 0.892389I
b = −0.514200 + 0.839448I
c = −1.73216 + 0.62281I
d = 0.84440 − 1.69272I
7.51654 − 1.91781I 0
u = −0.504947 + 1.215580I
a = 0.443142 + 0.140469I
b = 1.050580 − 0.650000I
c = −0.011223 − 1.220060I
d = 0.60444 − 2.51848I
5.42990 + 4.32973I 0
u = −0.504947 − 1.215580I
a = 0.443142 − 0.140469I
b = 1.050580 + 0.650000I
c = −0.011223 + 1.220060I
d = 0.60444 + 2.51848I
5.42990 − 4.32973I 0
u = 1.152900 + 0.667545I
a = −0.37747 − 1.57567I
b = −1.143790 + 0.600204I
c = 2.23046 + 0.59659I
d = 0.41994 − 2.63177I
0.80414 + 10.42400I 0
u = 1.152900 − 0.667545I
a = −0.37747 + 1.57567I
b = −1.143790 − 0.600204I
c = 2.23046 − 0.59659I
d = 0.41994 + 2.63177I
0.80414 − 10.42400I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185800 + 0.609579I
a = −0.27825 − 1.55393I
b = −1.111650 + 0.623537I
c = −1.371570 − 0.115410I
d = −0.331493 + 1.161530I
2.33908 + 6.73341I 0
u = 1.185800 − 0.609579I
a = −0.27825 + 1.55393I
b = −1.111650 − 0.623537I
c = −1.371570 + 0.115410I
d = −0.331493 − 1.161530I
2.33908 − 6.73341I 0
u = 0.593784 + 1.208600I
a = 0.435237 − 0.132054I
b = 1.103920 + 0.638344I
c = −0.064916 + 1.245600I
d = 0.50321 + 2.55667I
4.48821 − 10.17210I 0
u = 0.593784 − 1.208600I
a = 0.435237 + 0.132054I
b = 1.103920 − 0.638344I
c = −0.064916 − 1.245600I
d = 0.50321 − 2.55667I
4.48821 + 10.17210I 0
u = −1.233000 + 0.545251I
a = −0.17535 + 1.50144I
b = −1.076740 − 0.657064I
c = 1.59832 − 1.09061I
d = 0.55162 + 2.51495I
5.82408 − 7.48275I 0
u = −1.233000 − 0.545251I
a = −0.17535 − 1.50144I
b = −1.076740 + 0.657064I
c = 1.59832 + 1.09061I
d = 0.55162 − 2.51495I
5.82408 + 7.48275I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176438 + 0.617781I
a = 0.536936 − 0.059094I
b = 0.840129 + 0.202520I
c = 1.43629 + 1.69472I
d = 3.37169 + 3.42725I
0.42738 + 1.60074I 0.77404 − 2.18898I
u = 0.176438 − 0.617781I
a = 0.536936 + 0.059094I
b = 0.840129 − 0.202520I
c = 1.43629 − 1.69472I
d = 3.37169 − 3.42725I
0.42738 − 1.60074I 0.77404 + 2.18898I
u = −1.181300 + 0.680585I
a = −0.38029 + 1.52881I
b = −1.153230 − 0.615988I
c = −1.45518 + 0.03477I
d = −0.355666 − 1.191500I
1.22414 − 12.55690I 0
u = −1.181300 − 0.680585I
a = −0.38029 − 1.52881I
b = −1.153230 + 0.615988I
c = −1.45518 − 0.03477I
d = −0.355666 + 1.191500I
1.22414 + 12.55690I 0
u = −0.010891 + 0.626888I
a = 0.651032 − 0.036187I
b = 0.531292 + 0.085114I
c = 1.184550 − 0.522827I
d = 0.081339 − 0.143491I
0.65592 − 2.35939I 1.51759 + 4.85897I
u = −0.010891 − 0.626888I
a = 0.651032 + 0.036187I
b = 0.531292 − 0.085114I
c = 1.184550 + 0.522827I
d = 0.081339 + 0.143491I
0.65592 + 2.35939I 1.51759 − 4.85897I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617428 + 0.085193I
a = 2.98131 − 1.84944I
b = −0.757787 + 0.150255I
c = 1.27420 − 1.43204I
d = −0.305853 + 0.300706I
−0.93328 + 2.67780I 3.99337 − 7.95500I
u = 0.617428 − 0.085193I
a = 2.98131 + 1.84944I
b = −0.757787 − 0.150255I
c = 1.27420 + 1.43204I
d = −0.305853 − 0.300706I
−0.93328 − 2.67780I 3.99337 + 7.95500I
u = −0.591164
a = 1.74742
b = −0.427729
c = 0.644601
d = 0.251389
1.02886 10.5160
u = 0.282782 + 0.492299I
a = 0.508237 − 0.042524I
b = 0.953908 + 0.163482I
c = −0.332411 − 0.449116I
d = −0.705044 − 0.471800I
−1.67984 − 0.60130I −3.90300 + 0.33160I
u = 0.282782 − 0.492299I
a = 0.508237 + 0.042524I
b = 0.953908 − 0.163482I
c = −0.332411 + 0.449116I
d = −0.705044 + 0.471800I
−1.67984 + 0.60130I −3.90300 − 0.33160I
u = 1.33133 + 0.61244I
a = 0.451627 + 0.707103I
b = −0.358449 − 1.004460I
c = −1.50323 + 0.13255I
d = 0.65119 + 1.56469I
10.54930 + 5.35435I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33133 − 0.61244I
a = 0.451627 − 0.707103I
b = −0.358449 + 1.004460I
c = −1.50323 − 0.13255I
d = 0.65119 − 1.56469I
10.54930 − 5.35435I 0
u = −1.29995 + 0.68416I
a = 0.458847 − 0.670856I
b = −0.305396 + 1.015540I
c = −1.51100 − 0.26879I
d = 0.62788 − 1.52561I
9.4739 − 11.4004I 0
u = −1.29995 − 0.68416I
a = 0.458847 + 0.670856I
b = −0.305396 − 1.015540I
c = −1.51100 + 0.26879I
d = 0.62788 + 1.52561I
9.4739 + 11.4004I 0
u = −1.27239 + 0.75883I
a = −0.42552 + 1.37781I
b = −1.204630 − 0.662591I
c = 1.69978 − 0.12049I
d = 0.32788 + 2.50055I
7.95427 − 11.37060I 0
u = −1.27239 − 0.75883I
a = −0.42552 − 1.37781I
b = −1.204630 + 0.662591I
c = 1.69978 + 0.12049I
d = 0.32788 − 2.50055I
7.95427 + 11.37060I 0
u = 1.24401 + 0.80606I
a = −0.49137 − 1.37976I
b = −1.229060 + 0.643191I
c = 1.80328 − 0.06773I
d = 0.28176 − 2.52102I
6.6365 + 17.3722I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24401 − 0.80606I
a = −0.49137 + 1.37976I
b = −1.229060 − 0.643191I
c = 1.80328 + 0.06773I
d = 0.28176 + 2.52102I
6.6365 − 17.3722I 0
u = 1.51788 + 0.06429I
a = 0.205748 − 1.062330I
b = −0.824278 + 0.907296I
c = −0.424327 + 0.865938I
d = 0.67197 − 2.01899I
13.78050 + 0.08878I 0
u = 1.51788 − 0.06429I
a = 0.205748 + 1.062330I
b = −0.824278 − 0.907296I
c = −0.424327 − 0.865938I
d = 0.67197 + 2.01899I
13.78050 − 0.08878I 0
u = −1.51414 + 0.16464I
a = 0.145714 + 1.112210I
b = −0.884193 − 0.883937I
c = −0.163454 − 0.908611I
d = 0.64894 + 2.08801I
13.6007 − 6.3599I 0
u = −1.51414 − 0.16464I
a = 0.145714 − 1.112210I
b = −0.884193 + 0.883937I
c = −0.163454 + 0.908611I
d = 0.64894 − 2.08801I
13.6007 + 6.3599I 0
16
II.
I
u
2
= hd, c −1, −a
2
u
2
+b+2a−2, 2u
8
a
2
−3u
8
a+· · ·+3a−1, u
9
−u
8
+· · ·−u+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
a
a
2
u
2
− 2a + 2
a
12
=
1
0
a
6
=
a
2
u
2
− a + 2
a
2
u
2
− 2a + 2
a
9
=
u
−u
3
+ u
a
2
=
a
−a
2
u
2
− u
2
a + 2a − 2
a
1
=
−a
2
u
2
− u
2
a + 3a − 2
−a
2
u
2
− u
2
a + 2a − 2
a
11
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
u
7
− 2u
5
+ 2u
3
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
a
7
=
−u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
− 4u
4
− 8u
3
+ 4u
2
− 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + 5u + 1
c
2
, c
4
, c
5
c
6
, c
12
u
27
− 9u
25
+ ··· − u + 1
c
3
, c
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
7
, c
10
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
c
9
, c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· − 15y − 1
c
2
, c
4
, c
5
c
6
, c
12
y
27
− 18y
26
+ ··· + 5y − 1
c
3
, c
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
7
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
c
9
, c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0.780004 + 0.567068I
b = −0.161261 − 0.609769I
c = 1.00000
d = 0
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 + 0.510351I
a = 0.448284 − 0.048652I
b = 1.204760 + 0.239279I
c = 1.00000
d = 0
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 + 0.510351I
a = −0.31258 − 2.66243I
b = −1.043500 + 0.370490I
c = 1.00000
d = 0
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = 0.780004 − 0.567068I
b = −0.161261 + 0.609769I
c = 1.00000
d = 0
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = 0.448284 + 0.048652I
b = 1.204760 − 0.239279I
c = 1.00000
d = 0
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = −0.31258 + 2.66243I
b = −1.043500 − 0.370490I
c = 1.00000
d = 0
−1.78344 − 2.09337I −0.51499 + 4.16283I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825933
a = 0.445577
b = 1.24428
c = 1.00000
d = 0
1.19845 8.65230
u = −0.825933
a = 1.24313 + 1.32082I
b = −0.622141 − 0.401472I
c = 1.00000
d = 0
1.19845 8.65230
u = −0.825933
a = 1.24313 − 1.32082I
b = −0.622141 + 0.401472I
c = 1.00000
d = 0
1.19845 8.65230
u = −1.173910 + 0.391555I
a = 0.569278 − 0.822486I
b = −0.431041 + 0.822025I
c = 1.00000
d = 0
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −1.173910 + 0.391555I
a = 0.06212 + 1.57425I
b = −0.974973 − 0.634235I
c = 1.00000
d = 0
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −1.173910 + 0.391555I
a = 0.413109 + 0.032243I
b = 1.40601 − 0.18779I
c = 1.00000
d = 0
4.37135 − 1.33617I 7.28409 + 0.70175I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173910 − 0.391555I
a = 0.569278 + 0.822486I
b = −0.431041 − 0.822025I
c = 1.00000
d = 0
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −1.173910 − 0.391555I
a = 0.06212 − 1.57425I
b = −0.974973 + 0.634235I
c = 1.00000
d = 0
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −1.173910 − 0.391555I
a = 0.413109 − 0.032243I
b = 1.40601 + 0.18779I
c = 1.00000
d = 0
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.141484 + 0.739668I
a = 0.654691 + 0.167520I
b = 0.433577 − 0.366819I
c = 1.00000
d = 0
0.61694 − 2.45442I 2.32792 + 2.91298I
u = 0.141484 + 0.739668I
a = 0.548644 − 0.094284I
b = 0.770392 + 0.304242I
c = 1.00000
d = 0
0.61694 − 2.45442I 2.32792 + 2.91298I
u = 0.141484 + 0.739668I
a = −4.48093 − 1.37474I
b = −1.203970 + 0.062577I
c = 1.00000
d = 0
0.61694 − 2.45442I 2.32792 + 2.91298I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 − 0.739668I
a = 0.654691 − 0.167520I
b = 0.433577 + 0.366819I
c = 1.00000
d = 0
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.141484 − 0.739668I
a = 0.548644 + 0.094284I
b = 0.770392 − 0.304242I
c = 1.00000
d = 0
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.141484 − 0.739668I
a = −4.48093 + 1.37474I
b = −1.203970 − 0.062577I
c = 1.00000
d = 0
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 1.172470 + 0.500383I
a = 0.552608 + 0.748050I
b = −0.361113 − 0.864843I
c = 1.00000
d = 0
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 1.172470 + 0.500383I
a = 0.411628 − 0.041272I
b = 1.40520 + 0.24116I
c = 1.00000
d = 0
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 1.172470 + 0.500383I
a = −0.11277 − 1.59540I
b = −1.044080 + 0.623685I
c = 1.00000
d = 0
3.59813 + 7.08493I 5.57680 − 5.91335I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172470 − 0.500383I
a = 0.552608 − 0.748050I
b = −0.361113 + 0.864843I
c = 1.00000
d = 0
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 1.172470 − 0.500383I
a = 0.411628 + 0.041272I
b = 1.40520 − 0.24116I
c = 1.00000
d = 0
3.59813 − 7.08493I 5.57680 + 5.91335I
u = 1.172470 − 0.500383I
a = −0.11277 + 1.59540I
b = −1.044080 − 0.623685I
c = 1.00000
d = 0
3.59813 − 7.08493I 5.57680 + 5.91335I
24
III. I
v
1
= hc, d − 1, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
1
0
a
12
=
0
1
a
6
=
1
−1
a
9
=
v
0
a
2
=
1
0
a
1
=
1
0
a
11
=
v − 1
1
a
10
=
v − 1
v
a
7
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
6
(u − 1)
2
c
7
, c
11
u
2
+ u + 1
c
9
, c
10
u
2
− u + 1
c
12
(u + 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
6
, c
12
(y − 1)
2
c
7
, c
9
, c
10
c
11
y
2
+ y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = 1.00000
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 1.00000
1.64493 + 2.02988I 9.00000 − 3.46410I
28
IV. I
v
2
= ha, d + 1, c + a, b − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
12
=
0
−1
a
6
=
0
1
a
9
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v + 1
−1
a
10
=
v + 1
v
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 5
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
5
, c
6
c
8
, c
12
u
2
c
4
(u + 1)
2
c
7
, c
11
u
2
+ u + 1
c
9
, c
10
u
2
− u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
5
, c
6
c
8
, c
12
y
2
c
7
, c
9
, c
10
c
11
y
2
+ y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
−1.64493 − 2.02988I −3.00000 + 3.46410I
32
V. I
v
3
= ha, d, c − 1, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
1
0
a
4
=
1
0
a
5
=
0
1
a
12
=
1
0
a
6
=
1
1
a
9
=
1
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
1
0
a
10
=
1
0
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
7
, c
8
c
9
, c
10
, c
11
u
c
4
, c
5
, c
6
u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
12
y − 1
c
3
, c
7
, c
8
c
9
, c
10
, c
11
y
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 1.00000
d = 0
0 0
36
VI. I
v
4
= ha, d
2
v
2
+ dv + 1, v
2
dc − v
2
d + · · · + a − v, da − c + 1, c
2
v
2
−
2v
2
c + · · · + a
2
− av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
12
=
1
d
a
6
=
1
d + 1
a
9
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v
2
d + 1
d
a
10
=
−v
2
d + dv
d
2
v
a
7
=
1
d
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
3
v − 4dv − v
2
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
37
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
2.02988I 0.28251 − 3.79845I
38
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
27
+ 18u
26
+ ··· + 5u + 1)
· (u
71
+ 30u
70
+ ··· + 4640u + 256)
c
2
u
2
(u − 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
c
3
, c
8
u
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
71
− 2u
70
+ ··· + 1536u
2
− 512)
c
4
u
2
(u + 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
c
5
, c
6
u
2
(u − 1)
2
(u + 1)(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
c
7
u(u
2
+ u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
71
+ 2u
70
+ ··· − 5u
2
− 4)
c
9
u(u
2
− u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
71
+ 24u
70
+ ··· − 40u − 16)
c
10
u(u
2
− u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
71
+ 2u
70
+ ··· − 5u
2
− 4)
c
11
u(u
2
+ u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
71
+ 24u
70
+ ··· − 40u − 16)
c
12
u
2
(u − 1)(u + 1)
2
(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
39
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· − 15y − 1)
· (y
71
+ 30y
70
+ ··· + 5022208y − 65536)
c
2
, c
4
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 30y
70
+ ··· + 4640y − 256)
c
3
, c
8
y
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
71
− 30y
70
+ ··· + 1572864y − 262144)
c
5
, c
6
, c
12
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 70y
70
+ ··· − 1504y − 256)
c
7
, c
10
y(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
71
+ 24y
70
+ ··· − 40y − 16)
c
9
, c
11
y(y
2
+ y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
71
+ 48y
70
+ ··· − 6880y − 256)
40
