12a
0677
(K12a
0677
)
A knot diagram
1
Linearized knot diagam
3 7 11 10 9 2 6 12 5 1 8 4
Solving Sequence
4,10 1,5
11 3 2 9 6 12 8 7
c
4
c
10
c
3
c
1
c
9
c
5
c
12
c
8
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.64622 × 10
208
u
95
− 1.80313 × 10
208
u
94
+ ··· + 1.14976 × 10
209
b + 3.29451 × 10
209
,
− 1.64003 × 10
210
u
95
− 3.12587 × 10
210
u
94
+ ··· + 1.14976 × 10
209
a + 1.12635 × 10
211
,
u
96
+ 2u
95
+ ··· − 44u − 1i
I
u
2
= h−u
23
+ u
22
+ ··· + b + 1, u
23
− u
22
+ ··· + a − 2u, u
24
− u
23
+ ··· − 2u − 1i
I
u
3
= hb − u, a − u, u
15
+ 3u
13
+ u
10
− 5u
9
+ 2u
8
− u
6
+ 5u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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
= h−1.65 × 10
208
u
95
− 1.80 × 10
208
u
94
+ · · · + 1.15 × 10
209
b + 3.29 ×
10
209
, −1.64 × 10
210
u
95
− 3.13 × 10
210
u
94
+ · · · + 1.15 × 10
209
a + 1.13 ×
10
211
, u
96
+ 2u
95
+ · · · − 44u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
14.2640u
95
+ 27.1870u
94
+ ··· − 4367.63u − 97.9634
0.143179u
95
+ 0.156826u
94
+ ··· − 29.3497u − 2.86538
a
5
=
1
u
2
a
11
=
−20.9593u
95
− 40.0137u
94
+ ··· + 6954.20u + 166.245
−1.49859u
95
− 2.89068u
94
+ ··· + 755.253u + 25.2178
a
3
=
47.3979u
95
+ 92.0448u
94
+ ··· − 21779.0u − 745.556
−1.33998u
95
− 2.62161u
94
+ ··· + 518.832u + 13.9434
a
2
=
−35.1741u
95
− 67.7608u
94
+ ··· + 14192.6u + 430.358
−1.10655u
95
− 2.18893u
94
+ ··· + 557.402u + 19.3210
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
14.1209u
95
+ 27.0302u
94
+ ··· − 4338.28u − 95.0980
0.143179u
95
+ 0.156826u
94
+ ··· − 29.3497u − 2.86538
a
8
=
−15.0602u
95
− 28.4628u
94
+ ··· + 4595.10u + 87.8304
−2.43281u
95
− 4.66738u
94
+ ··· + 912.262u + 29.7776
a
7
=
−17.2106u
95
− 32.6434u
94
+ ··· + 5403.52u + 114.640
−2.47071u
95
− 4.78095u
94
+ ··· + 921.828u + 30.0823
(ii) Obstruction class = −1
(iii) Cusp Shapes = −21.7341u
95
− 41.6313u
94
+ ··· + 7622.14u + 212.868
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
96
+ 30u
95
+ ··· + 7436u + 784
c
2
, c
6
u
96
+ 4u
95
+ ··· − 18u + 28
c
3
u
96
− 4u
94
+ ··· + 4071u + 689
c
4
, c
5
, c
9
u
96
− 2u
95
+ ··· + 44u − 1
c
8
, c
11
u
96
+ 5u
95
+ ··· − 5u − 1
c
10
u
96
+ 5u
95
+ ··· − 81964u − 2147
c
12
u
96
+ 10u
95
+ ··· + 15u + 919
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
96
+ 78y
95
+ ··· − 16700912y + 614656
c
2
, c
6
y
96
− 30y
95
+ ··· − 7436y + 784
c
3
y
96
− 8y
95
+ ··· − 8914117y + 474721
c
4
, c
5
, c
9
y
96
+ 108y
95
+ ··· − 430y + 1
c
8
, c
11
y
96
− 43y
95
+ ··· + 43y + 1
c
10
y
96
− 31y
95
+ ··· − 3936130634y + 4609609
c
12
y
96
− 26y
95
+ ··· − 25910511y + 844561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642382 + 0.747532I
a = 0.795130 + 0.138344I
b = 0.472640 − 0.665485I
−3.94945 − 2.66517I 0
u = −0.642382 − 0.747532I
a = 0.795130 − 0.138344I
b = 0.472640 + 0.665485I
−3.94945 + 2.66517I 0
u = −0.163407 + 0.924545I
a = 0.261179 + 0.268168I
b = 0.234294 − 1.199490I
−3.14695 + 1.92811I 0
u = −0.163407 − 0.924545I
a = 0.261179 − 0.268168I
b = 0.234294 + 1.199490I
−3.14695 − 1.92811I 0
u = 0.903619 + 0.565295I
a = −0.535787 + 1.141530I
b = −0.914191 + 0.864733I
2.89024 − 7.03208I 0
u = 0.903619 − 0.565295I
a = −0.535787 − 1.141530I
b = −0.914191 − 0.864733I
2.89024 + 7.03208I 0
u = −0.929020 + 0.527048I
a = 0.562011 + 1.179470I
b = 0.945981 + 0.878213I
2.02889 + 13.17570I 0
u = −0.929020 − 0.527048I
a = 0.562011 − 1.179470I
b = 0.945981 − 0.878213I
2.02889 − 13.17570I 0
u = 0.181695 + 1.084970I
a = −0.042512 + 0.852733I
b = −0.201475 + 0.736437I
3.00310 − 2.55486I 0
u = 0.181695 − 1.084970I
a = −0.042512 − 0.852733I
b = −0.201475 − 0.736437I
3.00310 + 2.55486I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768749 + 0.447591I
a = 0.400217 + 1.252690I
b = 0.892619 + 0.991735I
−4.77135 + 7.54773I 0
u = −0.768749 − 0.447591I
a = 0.400217 − 1.252690I
b = 0.892619 − 0.991735I
−4.77135 − 7.54773I 0
u = 0.636851 + 0.564667I
a = −0.293208 + 1.133200I
b = −0.756081 + 1.003730I
−1.11717 − 4.17193I 0
u = 0.636851 − 0.564667I
a = −0.293208 − 1.133200I
b = −0.756081 − 1.003730I
−1.11717 + 4.17193I 0
u = 0.514896 + 0.637434I
a = 0.10064 − 1.85594I
b = 0.869676 − 0.599743I
4.69245 − 7.43562I 0
u = 0.514896 − 0.637434I
a = 0.10064 + 1.85594I
b = 0.869676 + 0.599743I
4.69245 + 7.43562I 0
u = 0.973976 + 0.737024I
a = −0.781407 + 0.114647I
b = −0.591432 − 0.340680I
3.19863 + 0.84469I 0
u = 0.973976 − 0.737024I
a = −0.781407 − 0.114647I
b = −0.591432 + 0.340680I
3.19863 − 0.84469I 0
u = −0.428543 + 0.647277I
a = −0.08274 − 1.90952I
b = −0.880064 − 0.552500I
5.20927 + 1.65149I 0
u = −0.428543 − 0.647277I
a = −0.08274 + 1.90952I
b = −0.880064 + 0.552500I
5.20927 − 1.65149I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944349 + 0.798718I
a = 0.799480 + 0.115897I
b = 0.647671 − 0.386867I
2.65249 − 6.96191I 0
u = −0.944349 − 0.798718I
a = 0.799480 − 0.115897I
b = 0.647671 + 0.386867I
2.65249 + 6.96191I 0
u = −0.236293 + 1.239330I
a = 0.494149 − 1.100050I
b = −1.130850 − 0.431679I
5.89832 + 1.51423I 0
u = −0.236293 − 1.239330I
a = 0.494149 + 1.100050I
b = −1.130850 + 0.431679I
5.89832 − 1.51423I 0
u = 0.107408 + 1.259190I
a = −0.736269 − 0.944443I
b = 1.255590 − 0.410171I
5.28379 − 6.49457I 0
u = 0.107408 − 1.259190I
a = −0.736269 + 0.944443I
b = 1.255590 + 0.410171I
5.28379 + 6.49457I 0
u = 0.628395 + 0.382312I
a = −1.013710 − 0.101449I
b = −0.138801 − 0.519383I
−1.62526 − 0.07913I 0
u = 0.628395 − 0.382312I
a = −1.013710 + 0.101449I
b = −0.138801 + 0.519383I
−1.62526 + 0.07913I 0
u = −0.189595 + 1.329350I
a = 1.48599 − 0.27269I
b = −0.416741 − 0.346248I
4.55048 + 8.93153I 0
u = −0.189595 − 1.329350I
a = 1.48599 + 0.27269I
b = −0.416741 + 0.346248I
4.55048 − 8.93153I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529746 + 0.385802I
a = 0.15766 − 1.68350I
b = 0.685056 − 0.550946I
−0.93963 − 3.29917I −6.00000 + 8.60879I
u = 0.529746 − 0.385802I
a = 0.15766 + 1.68350I
b = 0.685056 + 0.550946I
−0.93963 + 3.29917I −6.00000 − 8.60879I
u = 0.639018 + 0.144804I
a = −0.89248 − 1.72577I
b = 0.261326 − 0.732585I
0.619188 − 0.521192I −6.00000 + 2.76597I
u = 0.639018 − 0.144804I
a = −0.89248 + 1.72577I
b = 0.261326 + 0.732585I
0.619188 + 0.521192I −6.00000 − 2.76597I
u = −0.122241 + 1.347590I
a = 1.164870 + 0.360161I
b = −0.409019 − 0.129946I
−0.04172 + 3.60886I 0
u = −0.122241 − 1.347590I
a = 1.164870 − 0.360161I
b = −0.409019 + 0.129946I
−0.04172 − 3.60886I 0
u = −0.020712 + 1.359000I
a = 0.507621 + 0.819342I
b = −0.321798 + 0.162935I
2.89704 − 2.03726I 0
u = −0.020712 − 1.359000I
a = 0.507621 − 0.819342I
b = −0.321798 − 0.162935I
2.89704 + 2.03726I 0
u = −0.626881 + 0.093618I
a = 1.13491 − 1.94814I
b = −0.206534 − 0.782673I
0.12716 + 6.04936I −9.84333 − 7.90866I
u = −0.626881 − 0.093618I
a = 1.13491 + 1.94814I
b = −0.206534 + 0.782673I
0.12716 − 6.04936I −9.84333 + 7.90866I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203006 + 1.353870I
a = −1.241370 − 0.414215I
b = 0.509372 − 0.379609I
5.31675 − 3.50792I 0
u = 0.203006 − 1.353870I
a = −1.241370 + 0.414215I
b = 0.509372 + 0.379609I
5.31675 + 3.50792I 0
u = −0.476489 + 0.385546I
a = 0.114169 + 1.240060I
b = 0.81049 + 1.22686I
−4.45427 + 0.50532I −12.41474 − 5.66405I
u = −0.476489 − 0.385546I
a = 0.114169 − 1.240060I
b = 0.81049 − 1.22686I
−4.45427 − 0.50532I −12.41474 + 5.66405I
u = −0.017518 + 1.391350I
a = −0.402070 − 0.496558I
b = 1.89370 − 0.86583I
2.01697 + 0.39078I 0
u = −0.017518 − 1.391350I
a = −0.402070 + 0.496558I
b = 1.89370 + 0.86583I
2.01697 − 0.39078I 0
u = 0.605239
a = −0.0580286
b = 0.280335
−0.954720 −11.9410
u = −0.07333 + 1.42923I
a = 0.422648 − 0.817461I
b = −1.34991 − 0.87351I
6.99819 + 2.24677I 0
u = −0.07333 − 1.42923I
a = 0.422648 + 0.817461I
b = −1.34991 + 0.87351I
6.99819 − 2.24677I 0
u = 0.19362 + 1.42570I
a = −0.585335 − 0.964116I
b = 0.984848 − 0.756326I
4.85639 − 5.95300I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19362 − 1.42570I
a = −0.585335 + 0.964116I
b = 0.984848 + 0.756326I
4.85639 + 5.95300I 0
u = −0.36108 + 1.39647I
a = 0.122876 − 0.802100I
b = −1.139770 − 0.340743I
3.48788 + 4.66001I 0
u = −0.36108 − 1.39647I
a = 0.122876 + 0.802100I
b = −1.139770 + 0.340743I
3.48788 − 4.66001I 0
u = 0.07894 + 1.44216I
a = −0.486845 + 0.329254I
b = 0.597577 + 0.105019I
4.25653 − 2.34263I 0
u = 0.07894 − 1.44216I
a = −0.486845 − 0.329254I
b = 0.597577 − 0.105019I
4.25653 + 2.34263I 0
u = −0.08287 + 1.45274I
a = −0.032477 − 0.564797I
b = 1.52142 − 1.45896I
8.24791 + 7.87039I 0
u = −0.08287 − 1.45274I
a = −0.032477 + 0.564797I
b = 1.52142 + 1.45896I
8.24791 − 7.87039I 0
u = 0.05320 + 1.46336I
a = 0.102394 − 0.626085I
b = −1.53564 − 1.33318I
9.50325 − 1.59468I 0
u = 0.05320 − 1.46336I
a = 0.102394 + 0.626085I
b = −1.53564 + 1.33318I
9.50325 + 1.59468I 0
u = 0.22989 + 1.44877I
a = −0.411847 − 0.386300I
b = 0.905278 − 0.212128I
4.49854 − 3.18827I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22989 − 1.44877I
a = −0.411847 + 0.386300I
b = 0.905278 + 0.212128I
4.49854 + 3.18827I 0
u = −0.15821 + 1.50551I
a = −0.322940 + 0.524993I
b = 1.51290 + 1.44929I
1.86412 + 2.79438I 0
u = −0.15821 − 1.50551I
a = −0.322940 − 0.524993I
b = 1.51290 − 1.44929I
1.86412 − 2.79438I 0
u = −0.26974 + 1.50622I
a = −0.426211 + 0.822881I
b = 1.37603 + 1.14435I
1.59018 + 11.31720I 0
u = −0.26974 − 1.50622I
a = −0.426211 − 0.822881I
b = 1.37603 − 1.14435I
1.59018 − 11.31720I 0
u = −0.16267 + 1.52973I
a = 0.382263 − 1.108690I
b = −1.03432 − 1.06257I
12.30370 + 3.96400I 0
u = −0.16267 − 1.52973I
a = 0.382263 + 1.108690I
b = −1.03432 + 1.06257I
12.30370 − 3.96400I 0
u = 0.18492 + 1.52917I
a = −0.417567 − 1.145640I
b = 0.98384 − 1.05662I
11.7350 − 10.0840I 0
u = 0.18492 − 1.52917I
a = −0.417567 + 1.145640I
b = 0.98384 + 1.05662I
11.7350 + 10.0840I 0
u = −0.432055 + 0.119830I
a = 2.55471 − 1.22452I
b = −0.044675 − 0.746253I
−4.65347 + 1.58657I −18.0760 − 5.0651I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.432055 − 0.119830I
a = 2.55471 + 1.22452I
b = −0.044675 + 0.746253I
−4.65347 − 1.58657I −18.0760 + 5.0651I
u = 0.22002 + 1.54229I
a = 0.298221 + 0.715340I
b = −1.34974 + 1.24577I
5.82778 − 7.35075I 0
u = 0.22002 − 1.54229I
a = 0.298221 − 0.715340I
b = −1.34974 − 1.24577I
5.82778 + 7.35075I 0
u = −0.302154 + 0.310620I
a = −0.75478 − 1.86193I
b = −0.802818 − 0.371080I
1.39676 + 0.94200I 2.74708 − 1.79626I
u = −0.302154 − 0.310620I
a = −0.75478 + 1.86193I
b = −0.802818 + 0.371080I
1.39676 − 0.94200I 2.74708 + 1.79626I
u = −0.39405 + 1.52992I
a = −0.136506 − 0.583115I
b = −1.240480 − 0.206889I
8.78555 + 7.95703I 0
u = −0.39405 − 1.52992I
a = −0.136506 + 0.583115I
b = −1.240480 + 0.206889I
8.78555 − 7.95703I 0
u = −0.33049 + 1.54999I
a = −0.329380 + 1.000270I
b = 1.30921 + 1.13495I
8.7501 + 17.7563I 0
u = −0.33049 − 1.54999I
a = −0.329380 − 1.000270I
b = 1.30921 − 1.13495I
8.7501 − 17.7563I 0
u = 0.36490 + 1.54676I
a = 0.117742 − 0.505610I
b = 1.221630 − 0.164568I
9.04062 − 2.10865I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36490 − 1.54676I
a = 0.117742 + 0.505610I
b = 1.221630 + 0.164568I
9.04062 + 2.10865I 0
u = 0.31398 + 1.55993I
a = 0.300575 + 0.960470I
b = −1.31158 + 1.14390I
9.7899 − 11.4746I 0
u = 0.31398 − 1.55993I
a = 0.300575 − 0.960470I
b = −1.31158 − 1.14390I
9.7899 + 11.4746I 0
u = −0.08128 + 1.64860I
a = 0.028304 + 0.509904I
b = 0.822211 + 0.788008I
11.99200 − 3.14737I 0
u = −0.08128 − 1.64860I
a = 0.028304 − 0.509904I
b = 0.822211 − 0.788008I
11.99200 + 3.14737I 0
u = 0.10434 + 1.64928I
a = −0.003519 + 0.543798I
b = −0.773988 + 0.990417I
12.24620 − 3.34962I 0
u = 0.10434 − 1.64928I
a = −0.003519 − 0.543798I
b = −0.773988 − 0.990417I
12.24620 + 3.34962I 0
u = −0.221340 + 0.262334I
a = −0.24762 − 2.74062I
b = 1.136950 − 0.677233I
2.50372 + 6.70631I −3.73155 − 9.87202I
u = −0.221340 − 0.262334I
a = −0.24762 + 2.74062I
b = 1.136950 + 0.677233I
2.50372 − 6.70631I −3.73155 + 9.87202I
u = 0.124604 + 0.292582I
a = 0.05172 − 3.01208I
b = −1.093190 − 0.559521I
3.60147 − 0.87136I −0.00314 + 3.86305I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.124604 − 0.292582I
a = 0.05172 + 3.01208I
b = −1.093190 + 0.559521I
3.60147 + 0.87136I −0.00314 − 3.86305I
u = 0.06671 + 1.72517I
a = −0.001259 + 0.505447I
b = −0.189722 + 0.994971I
12.32950 − 3.40052I 0
u = 0.06671 − 1.72517I
a = −0.001259 − 0.505447I
b = −0.189722 − 0.994971I
12.32950 + 3.40052I 0
u = −0.103847
a = −4.37876
b = 1.68237
−2.69516 13.1080
u = −0.0689560 + 0.0164691I
a = 22.0368 + 2.7202I
b = 0.001158 − 0.786430I
−1.81294 − 2.56110I −15.8787 + 2.7284I
u = −0.0689560 − 0.0164691I
a = 22.0368 − 2.7202I
b = 0.001158 + 0.786430I
−1.81294 + 2.56110I −15.8787 − 2.7284I
14
II.
I
u
2
= h−u
23
+u
22
+· · · + b+ 1, u
23
−u
22
+· · · + a− 2u, u
24
−u
23
+· · · − 2u− 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
−u
23
+ u
22
+ ··· − 2u
3
+ 2u
u
23
− u
22
+ ··· − 4u − 1
a
5
=
1
u
2
a
11
=
5u
23
− 4u
22
+ ··· − 2u − 1
u
23
− u
22
+ ··· − 2u
2
+ u
a
3
=
−u
23
+ 13u
22
+ ··· − 24u − 11
u
22
− u
21
+ ··· − 2u
3
+ 3u
2
a
2
=
−u
23
+ 13u
22
+ ··· − 3u − 11
8u
23
− 7u
22
+ ··· − 17u − 1
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
−2u
23
+ 2u
22
+ ··· + 6u + 1
u
23
− u
22
+ ··· − 4u − 1
a
8
=
−6u
23
+ 6u
22
+ ··· + u − 1
−u
21
+ u
20
+ ··· + 5u + 1
a
7
=
−5u
23
+ 5u
22
+ ··· + 12u
2
+ 4u
4u
23
− 4u
22
+ ··· − u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21u
23
+ 35u
22
− 273u
21
+ 422u
20
− 1500u
19
+ 2156u
18
−
4556u
17
+ 6074u
16
− 8415u
15
+ 10261u
14
− 9932u
13
+ 10626u
12
− 7936u
11
+ 6806u
10
−
4685u
9
+ 2969u
8
− 2022u
7
+ 1091u
6
− 519u
5
+ 154u
4
− 150u
3
− 138u
2
− 41u − 41
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 10u
23
+ ··· − 16u + 1
c
2
u
24
− 5u
22
+ ··· − 8u
2
+ 1
c
3
u
24
− u
23
+ ··· − 3u − 1
c
4
, c
5
u
24
− u
23
+ ··· − 2u − 1
c
6
u
24
− 5u
22
+ ··· − 8u
2
+ 1
c
7
u
24
+ 10u
23
+ ··· + 16u + 1
c
8
u
24
+ 4u
23
+ ··· + 3u + 1
c
9
u
24
+ u
23
+ ··· + 2u − 1
c
10
u
24
− 8u
22
+ ··· + 10u + 1
c
11
u
24
− 4u
23
+ ··· − 3u + 1
c
12
u
24
− 3u
23
+ ··· − u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
24
+ 18y
23
+ ··· − 12y + 1
c
2
, c
6
y
24
− 10y
23
+ ··· − 16y + 1
c
3
y
24
− y
23
+ ··· − 3y + 1
c
4
, c
5
, c
9
y
24
+ 27y
23
+ ··· + 12y + 1
c
8
, c
11
y
24
− 24y
23
+ ··· − 23y + 1
c
10
y
24
− 16y
23
+ ··· − 28y + 1
c
12
y
24
− 3y
23
+ ··· − y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882514
a = 0.775023
b = 0.725355
−0.303774 4.40390
u = 0.650217 + 0.467956I
a = 1.005720 − 0.043140I
b = 0.670895 − 0.303787I
3.09737 − 0.28324I −3.73574 + 2.47523I
u = 0.650217 − 0.467956I
a = 1.005720 + 0.043140I
b = 0.670895 + 0.303787I
3.09737 + 0.28324I −3.73574 − 2.47523I
u = −0.005795 + 1.248900I
a = 0.14014 + 1.74940I
b = −0.055008 + 1.016190I
1.26651 − 2.51743I −9.47589 + 2.84740I
u = −0.005795 − 1.248900I
a = 0.14014 − 1.74940I
b = −0.055008 − 1.016190I
1.26651 + 2.51743I −9.47589 − 2.84740I
u = −0.528342 + 0.503976I
a = −1.143570 + 0.069532I
b = −0.648115 − 0.388354I
2.38294 − 5.57243I −5.11246 + 2.79559I
u = −0.528342 − 0.503976I
a = −1.143570 − 0.069532I
b = −0.648115 + 0.388354I
2.38294 + 5.57243I −5.11246 − 2.79559I
u = −0.017126 + 1.282440I
a = 0.267953 + 1.068660I
b = −0.248287 + 1.383220I
−0.89975 + 1.19390I −6.13028 − 5.25521I
u = −0.017126 − 1.282440I
a = 0.267953 − 1.068660I
b = −0.248287 − 1.383220I
−0.89975 − 1.19390I −6.13028 + 5.25521I
u = −0.197638 + 1.311080I
a = 0.912382 − 0.623699I
b = −1.057030 + 0.054669I
5.47759 + 8.15375I −1.09675 − 7.59058I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197638 − 1.311080I
a = 0.912382 + 0.623699I
b = −1.057030 − 0.054669I
5.47759 − 8.15375I −1.09675 + 7.59058I
u = 0.236962 + 1.317760I
a = −0.739794 − 0.815911I
b = 0.979034 − 0.089971I
6.29425 − 2.85089I 1.25649 + 2.53657I
u = 0.236962 − 1.317760I
a = −0.739794 + 0.815911I
b = 0.979034 + 0.089971I
6.29425 + 2.85089I 1.25649 − 2.53657I
u = −0.016155 + 0.581226I
a = −0.16092 + 2.19525I
b = −0.030724 − 0.684852I
−1.28254 + 2.59452I 0.56909 − 3.77369I
u = −0.016155 − 0.581226I
a = −0.16092 − 2.19525I
b = −0.030724 + 0.684852I
−1.28254 − 2.59452I 0.56909 + 3.77369I
u = −0.15446 + 1.43775I
a = 0.351453 − 0.358325I
b = −1.62345 − 0.67224I
2.16033 + 1.97133I −3.78347 − 0.31532I
u = −0.15446 − 1.43775I
a = 0.351453 + 0.358325I
b = −1.62345 + 0.67224I
2.16033 − 1.97133I −3.78347 + 0.31532I
u = 0.30125 + 1.42260I
a = −0.282666 − 0.725720I
b = 0.909722 − 0.446607I
4.59240 − 4.26250I −1.37425 + 5.16068I
u = 0.30125 − 1.42260I
a = −0.282666 + 0.725720I
b = 0.909722 + 0.446607I
4.59240 + 4.26250I −1.37425 − 5.16068I
u = −0.076290 + 0.473510I
a = −0.414901 + 1.324540I
b = −0.192580 − 0.897422I
−3.93023 − 0.90838I −11.11521 − 1.01848I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.076290 − 0.473510I
a = −0.414901 − 1.324540I
b = −0.192580 + 0.897422I
−3.93023 + 0.90838I −11.11521 + 1.01848I
u = −0.383950
a = −0.626250
b = −1.39165
−2.94621 −20.3440
u = 0.05810 + 1.76037I
a = −0.010170 − 0.442675I
b = 0.128696 − 1.064870I
12.07500 − 3.44844I −19.5316 + 5.2163I
u = 0.05810 − 1.76037I
a = −0.010170 + 0.442675I
b = 0.128696 + 1.064870I
12.07500 + 3.44844I −19.5316 − 5.2163I
20
III. I
u
3
= hb − u, a − u, u
15
+ 3u
13
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
u
u
a
5
=
1
u
2
a
11
=
u
3
u
3
+ u
a
3
=
u
6
+ u
4
+ 1
u
6
+ 2u
4
+ u
2
a
2
=
u
11
+ 2u
9
+ u
3
u
11
+ 3u
9
+ 2u
7
− u
5
− u
3
+ u
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
0
u
a
8
=
u
u
a
7
=
−u
7
− 2u
5
+ 2u
−u
9
− 3u
7
− u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
10
− 8u
8
+ 4u
6
− 4u
5
+ 8u
4
− 4u
3
− 4u
2
+ 4u − 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
+ u
2
+ 2u + 1)
5
c
2
, c
6
(u
3
− u
2
+ 1)
5
c
3
u
15
− 3u
13
+ ··· − 4u − 1
c
4
, c
5
, c
9
c
12
u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 5u
5
+ 2u
4
+ u
3
− u
2
− 2u − 1
c
8
, c
11
u
15
− 6u
14
+ ··· + 2u + 1
c
10
u
15
+ 6u
14
+ ··· + 2u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
+ 3y
2
+ 2y −1)
5
c
2
, c
6
(y
3
− y
2
+ 2y −1)
5
c
3
y
15
− 6y
14
+ ··· + 6y −1
c
4
, c
5
, c
9
c
12
y
15
+ 6y
14
+ ··· + 2y −1
c
8
, c
10
, c
11
y
15
− 18y
14
+ ··· + 2y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.973023 + 0.225695I
a = −0.973023 + 0.225695I
b = −0.973023 + 0.225695I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.973023 − 0.225695I
a = −0.973023 − 0.225695I
b = −0.973023 − 0.225695I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.935820 + 0.276972I
a = 0.935820 + 0.276972I
b = 0.935820 + 0.276972I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.935820 − 0.276972I
a = 0.935820 − 0.276972I
b = 0.935820 − 0.276972I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.212589 + 1.029940I
a = −0.212589 + 1.029940I
b = −0.212589 + 1.029940I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.212589 − 1.029940I
a = −0.212589 − 1.029940I
b = −0.212589 − 1.029940I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.929962
a = −0.929962
b = −0.929962
−1.11345 −9.01950
u = 0.266832 + 0.879121I
a = 0.266832 + 0.879121I
b = 0.266832 + 0.879121I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.266832 − 0.879121I
a = 0.266832 − 0.879121I
b = 0.266832 − 0.879121I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.075026 + 1.285100I
a = −0.075026 + 1.285100I
b = −0.075026 + 1.285100I
−1.11345 −9.01951 + 0.I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075026 − 1.285100I
a = −0.075026 − 1.285100I
b = −0.075026 − 1.285100I
−1.11345 −9.01951 + 0.I
u = 0.540007 + 0.279583I
a = 0.540007 + 0.279583I
b = 0.540007 + 0.279583I
−1.11345 −9.01951 + 0.I
u = 0.540007 − 0.279583I
a = 0.540007 − 0.279583I
b = 0.540007 − 0.279583I
−1.11345 −9.01951 + 0.I
u = −0.017040 + 1.406390I
a = −0.017040 + 1.406390I
b = −0.017040 + 1.406390I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.017040 − 1.406390I
a = −0.017040 − 1.406390I
b = −0.017040 − 1.406390I
3.02413 − 2.82812I −2.49024 + 2.97945I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
5
)(u
24
− 10u
23
+ ··· − 16u + 1)
· (u
96
+ 30u
95
+ ··· + 7436u + 784)
c
2
((u
3
− u
2
+ 1)
5
)(u
24
− 5u
22
+ ··· − 8u
2
+ 1)(u
96
+ 4u
95
+ ··· − 18u + 28)
c
3
(u
15
− 3u
13
+ ··· − 4u − 1)(u
24
− u
23
+ ··· − 3u − 1)
· (u
96
− 4u
94
+ ··· + 4071u + 689)
c
4
, c
5
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 5u
5
+ 2u
4
+ u
3
− u
2
− 2u − 1)
· (u
24
− u
23
+ ··· − 2u − 1)(u
96
− 2u
95
+ ··· + 44u − 1)
c
6
((u
3
− u
2
+ 1)
5
)(u
24
− 5u
22
+ ··· − 8u
2
+ 1)(u
96
+ 4u
95
+ ··· − 18u + 28)
c
7
((u
3
+ u
2
+ 2u + 1)
5
)(u
24
+ 10u
23
+ ··· + 16u + 1)
· (u
96
+ 30u
95
+ ··· + 7436u + 784)
c
8
(u
15
− 6u
14
+ ··· + 2u + 1)(u
24
+ 4u
23
+ ··· + 3u + 1)
· (u
96
+ 5u
95
+ ··· − 5u − 1)
c
9
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 5u
5
+ 2u
4
+ u
3
− u
2
− 2u − 1)
· (u
24
+ u
23
+ ··· + 2u − 1)(u
96
− 2u
95
+ ··· + 44u − 1)
c
10
(u
15
+ 6u
14
+ ··· + 2u − 1)(u
24
− 8u
22
+ ··· + 10u + 1)
· (u
96
+ 5u
95
+ ··· − 81964u − 2147)
c
11
(u
15
− 6u
14
+ ··· + 2u + 1)(u
24
− 4u
23
+ ··· − 3u + 1)
· (u
96
+ 5u
95
+ ··· − 5u − 1)
c
12
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 5u
5
+ 2u
4
+ u
3
− u
2
− 2u − 1)
· (u
24
− 3u
23
+ ··· − u − 1)(u
96
+ 10u
95
+ ··· + 15u + 919)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
3
+ 3y
2
+ 2y −1)
5
)(y
24
+ 18y
23
+ ··· − 12y + 1)
· (y
96
+ 78y
95
+ ··· − 16700912y + 614656)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
5
)(y
24
− 10y
23
+ ··· − 16y + 1)
· (y
96
− 30y
95
+ ··· − 7436y + 784)
c
3
(y
15
− 6y
14
+ ··· + 6y −1)(y
24
− y
23
+ ··· − 3y + 1)
· (y
96
− 8y
95
+ ··· − 8914117y + 474721)
c
4
, c
5
, c
9
(y
15
+ 6y
14
+ ··· + 2y −1)(y
24
+ 27y
23
+ ··· + 12y + 1)
· (y
96
+ 108y
95
+ ··· − 430y + 1)
c
8
, c
11
(y
15
− 18y
14
+ ··· + 2y −1)(y
24
− 24y
23
+ ··· − 23y + 1)
· (y
96
− 43y
95
+ ··· + 43y + 1)
c
10
(y
15
− 18y
14
+ ··· + 2y −1)(y
24
− 16y
23
+ ··· − 28y + 1)
· (y
96
− 31y
95
+ ··· − 3936130634y + 4609609)
c
12
(y
15
+ 6y
14
+ ··· + 2y −1)(y
24
− 3y
23
+ ··· − y + 1)
· (y
96
− 26y
95
+ ··· − 25910511y + 844561)
27
