12a
0999
(K12a
0999
)
A knot diagram
1
Linearized knot diagam
4 6 12 9 2 10 11 1 5 7 3 8
Solving Sequence
6,10
7 11
3,8
12 2 5 9 4 1
c
6
c
10
c
7
c
11
c
2
c
5
c
9
c
4
c
1
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h826872493u
24
+ 41514578887u
23
+ ··· + 26691174904b + 267919895192,
75775316763u
24
− 724263180731u
23
+ ··· + 53382349808a − 515069062880,
u
25
− 11u
24
+ ··· − 80u + 16i
I
u
2
= h−10u
35
− 12u
34
+ ··· + 8b + 68, −68u
35
a + 508u
35
+ ··· − 1145a + 7276, u
36
+ 4u
35
+ ··· + 16u + 1i
I
u
3
= h−7u
10
+ 4u
9
+ 36u
8
− 34u
7
− 43u
6
+ 60u
5
+ 10u
4
− 31u
3
− 19u
2
+ 11b + 16u + 17,
− 8u
10
+ 25u
9
+ 38u
8
− 163u
7
+ 31u
6
+ 298u
5
− 262u
4
− 136u
3
+ 269u
2
+ 11a − 32u − 78,
u
11
− 2u
10
− 5u
9
+ 14u
8
+ u
7
− 27u
6
+ 18u
5
+ 15u
4
− 20u
3
− u
2
+ 6u + 1i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 109 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
=
h8.27×10
8
u
24
+4 .15×10
10
u
23
+· · ·+2. 67×10
10
b+2.68×10
11
, 7.58×10
10
u
24
−
7.24 × 10
11
u
23
+ · · · + 5.34 × 10
10
a − 5.15 × 10
11
, u
25
− 11u
24
+ · · · − 80u + 16i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
−1.41948u
24
+ 13.5675u
23
+ ··· − 51.2819u + 9.64868
−0.0309792u
24
− 1.55537u
23
+ ··· + 37.1258u − 10.0378
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
0.167582u
24
− 3.50276u
23
+ ··· + 58.5852u − 16.0667
3.79748u
24
− 34.4987u
23
+ ··· + 133.770u − 29.2311
a
2
=
−1.45046u
24
+ 12.0121u
23
+ ··· − 14.1561u − 0.389094
−0.0309792u
24
− 1.55537u
23
+ ··· + 37.1258u − 10.0378
a
5
=
3.96506u
24
− 38.0015u
23
+ ··· + 190.355u − 44.2978
3.79748u
24
− 34.4987u
23
+ ··· + 132.770u − 29.2311
a
9
=
−1.73754u
24
+ 15.9703u
23
+ ··· − 68.0866u + 14.9573
0.976986u
24
− 8.80582u
23
+ ··· + 24.7513u − 4.30668
a
4
=
6.50025u
24
− 60.8358u
23
+ ··· + 275.705u − 62.6895
−2.16560u
24
+ 22.8582u
23
+ ··· − 153.338u + 36.8239
a
1
=
−4.43829u
24
+ 41.9516u
23
+ ··· − 195.816u + 43.9195
−1.35725u
24
+ 12.5528u
23
+ ··· − 50.4134u + 10.8323
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
145412112683
3336396863
u
24
−
1365948008373
3336396863
u
23
+ ··· +
6268794612260
3336396863
u −
1430304974606
3336396863
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 22u
24
+ ··· + 5120u + 512
c
2
, c
3
, c
5
c
11
u
25
− u
24
+ ··· − 4u + 1
c
4
, c
8
, c
9
c
12
u
25
− 11u
23
+ ··· + u − 1
c
6
, c
7
, c
10
u
25
− 11u
24
+ ··· − 80u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 2y
24
+ ··· + 76808192y −262144
c
2
, c
3
, c
5
c
11
y
25
− 15y
24
+ ··· + 50y −1
c
4
, c
8
, c
9
c
12
y
25
− 22y
24
+ ··· + 21y −1
c
6
, c
7
, c
10
y
25
− 23y
24
+ ··· − 1408y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00934
a = −0.805015
b = 1.63266
−7.20191 30.6470
u = 0.012976 + 1.033860I
a = 0.633148 − 0.106162I
b = 0.791764 + 0.522766I
3.03037 − 1.54703I 6.68506 + 3.68219I
u = 0.012976 − 1.033860I
a = 0.633148 + 0.106162I
b = 0.791764 − 0.522766I
3.03037 + 1.54703I 6.68506 − 3.68219I
u = −0.881775 + 0.323566I
a = −0.378664 + 0.249573I
b = 0.365509 − 0.726585I
6.42854 − 2.68579I 9.83614 + 1.93428I
u = −0.881775 − 0.323566I
a = −0.378664 − 0.249573I
b = 0.365509 + 0.726585I
6.42854 + 2.68579I 9.83614 − 1.93428I
u = −0.477303 + 0.717814I
a = 0.009597 − 0.906421I
b = 1.269930 + 0.185562I
−7.01624 − 2.33284I −5.90770 + 2.60194I
u = −0.477303 − 0.717814I
a = 0.009597 + 0.906421I
b = 1.269930 − 0.185562I
−7.01624 + 2.33284I −5.90770 − 2.60194I
u = −0.482722 + 1.037880I
a = −0.369971 + 0.530061I
b = −1.214990 − 0.563112I
1.10842 − 12.71280I 2.59152 + 8.71606I
u = −0.482722 − 1.037880I
a = −0.369971 − 0.530061I
b = −1.214990 + 0.563112I
1.10842 + 12.71280I 2.59152 − 8.71606I
u = 1.329560 + 0.203875I
a = 0.28740 − 1.62065I
b = −0.662175 + 0.545556I
2.65006 + 2.55544I 3.11128 − 1.65198I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.329560 − 0.203875I
a = 0.28740 + 1.62065I
b = −0.662175 − 0.545556I
2.65006 − 2.55544I 3.11128 + 1.65198I
u = −0.98981 + 1.06101I
a = 0.181907 + 0.253452I
b = −0.954754 + 0.361220I
2.30832 + 5.78881I 2.00000 − 7.25000I
u = −0.98981 − 1.06101I
a = 0.181907 − 0.253452I
b = −0.954754 − 0.361220I
2.30832 − 5.78881I 2.00000 + 7.25000I
u = 0.516035
a = 0.631196
b = 0.157637
0.767709 13.0610
u = 1.49267 + 0.27371I
a = −0.65793 + 1.31350I
b = 1.148310 − 0.509995I
−0.65901 + 5.99024I 0. − 4.38665I
u = 1.49267 − 0.27371I
a = −0.65793 − 1.31350I
b = 1.148310 + 0.509995I
−0.65901 − 5.99024I 0. + 4.38665I
u = 1.47479 + 0.50270I
a = 0.123556 + 1.187480I
b = 1.108500 − 0.652505I
7.77371 + 7.32084I 7.72526 − 5.56309I
u = 1.47479 − 0.50270I
a = 0.123556 − 1.187480I
b = 1.108500 + 0.652505I
7.77371 − 7.32084I 7.72526 + 5.56309I
u = 1.58061 + 0.03704I
a = −0.272956 − 1.225950I
b = 0.151992 + 1.145230I
14.6920 + 3.8040I 11.54426 − 2.08774I
u = 1.58061 − 0.03704I
a = −0.272956 + 1.225950I
b = 0.151992 − 1.145230I
14.6920 − 3.8040I 11.54426 + 2.08774I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54138 + 0.37767I
a = 0.30399 − 1.46629I
b = −1.36369 + 0.77531I
7.5940 + 17.7952I 5.80164 − 8.80793I
u = 1.54138 − 0.37767I
a = 0.30399 + 1.46629I
b = −1.36369 − 0.77531I
7.5940 − 17.7952I 5.80164 + 8.80793I
u = 0.123896 + 0.326612I
a = −1.67598 + 1.41797I
b = −0.709073 − 0.106576I
−1.292320 − 0.176707I −7.01154 + 0.09257I
u = 0.123896 − 0.326612I
a = −1.67598 − 1.41797I
b = −0.709073 + 0.106576I
−1.292320 + 0.176707I −7.01154 − 0.09257I
u = 2.04475
a = 0.305643
b = −0.652933
13.8003 0
7
II. I
u
2
= h−10u
35
− 12u
34
+ · · · + 8b + 68, −68u
35
a + 508u
35
+ · · · − 1145a +
7276, u
36
+ 4u
35
+ · · · + 16u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
a
5
4
u
35
+
3
2
u
34
+ ··· +
57
8
u −
17
2
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
−
5
4
u
35
a − 2u
35
+ ··· +
17
2
a −
439
8
27
8
u
35
+
59
8
u
34
+ ··· +
123
4
u −
53
8
a
2
=
5
4
u
35
+
3
2
u
34
+ ··· + a −
17
2
5
4
u
35
+
3
2
u
34
+ ··· +
57
8
u −
17
2
a
5
=
2.37500au
35
+ 6.62500au
34
+ ··· + 3.12500a − 23.5000
47
8
u
35
a − 2u
35
+ ··· +
35
8
a −
635
8
a
9
=
1
2
u
35
a −
41
8
u
35
+ ··· +
37
4
a −
385
8
−
9
4
u
35
a +
63
8
u
35
+ ··· −
5
2
a + 84
a
4
=
−2u
35
a +
67
2
u
35
+ ··· −
627
8
a +
1065
2
27
8
u
35
a + u
35
+ ··· +
11
4
a −
15
4
a
1
=
−2u
35
a + u
35
+ ··· +
61
8
a −
495
8
−
31
8
u
35
a + 3u
35
+ ··· −
23
8
a −
55
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 148u
35
+
1111
2
u
34
+ ··· + 1907u +
3931
2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
36
+ 11u
35
+ ··· + 12u + 1)
2
c
2
, c
3
, c
5
c
11
u
72
+ 5u
71
+ ··· + 44u + 31
c
4
, c
8
, c
9
c
12
u
72
+ 15u
71
+ ··· + 1022u + 149
c
6
, c
7
, c
10
(u
36
+ 4u
35
+ ··· + 16u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
36
+ 9y
35
+ ··· − 78y + 1)
2
c
2
, c
3
, c
5
c
11
y
72
− 109y
71
+ ··· − 5904y + 961
c
4
, c
8
, c
9
c
12
y
72
− 125y
71
+ ··· + 239896y + 22201
c
6
, c
7
, c
10
(y
36
− 36y
35
+ ··· − 228y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801734 + 0.696202I
a = 0.525131 − 0.532417I
b = −1.060570 − 0.298701I
−2.58334 − 1.89748I −1.79078 + 1.73365I
u = 0.801734 + 0.696202I
a = −0.146921 + 0.381228I
b = 1.240490 + 0.042488I
−2.58334 − 1.89748I −1.79078 + 1.73365I
u = 0.801734 − 0.696202I
a = 0.525131 + 0.532417I
b = −1.060570 + 0.298701I
−2.58334 + 1.89748I −1.79078 − 1.73365I
u = 0.801734 − 0.696202I
a = −0.146921 − 0.381228I
b = 1.240490 − 0.042488I
−2.58334 + 1.89748I −1.79078 − 1.73365I
u = 0.406976 + 0.842772I
a = 0.364285 + 0.941569I
b = 1.216290 − 0.277018I
−3.72449 + 7.15532I −1.32336 − 7.08750I
u = 0.406976 + 0.842772I
a = −0.346677 − 0.608804I
b = −1.251710 + 0.596442I
−3.72449 + 7.15532I −1.32336 − 7.08750I
u = 0.406976 − 0.842772I
a = 0.364285 − 0.941569I
b = 1.216290 + 0.277018I
−3.72449 − 7.15532I −1.32336 + 7.08750I
u = 0.406976 − 0.842772I
a = −0.346677 + 0.608804I
b = −1.251710 − 0.596442I
−3.72449 − 7.15532I −1.32336 + 7.08750I
u = −0.392598 + 1.003430I
a = −0.903413 − 0.103360I
b = −0.821320 − 0.340230I
2.79209 + 2.82464I 5.35953 − 2.15606I
u = −0.392598 + 1.003430I
a = 0.442073 − 0.041027I
b = 0.867684 − 0.552611I
2.79209 + 2.82464I 5.35953 − 2.15606I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392598 − 1.003430I
a = −0.903413 + 0.103360I
b = −0.821320 + 0.340230I
2.79209 − 2.82464I 5.35953 + 2.15606I
u = −0.392598 − 1.003430I
a = 0.442073 + 0.041027I
b = 0.867684 + 0.552611I
2.79209 − 2.82464I 5.35953 + 2.15606I
u = 1.245720 + 0.066167I
a = 0.18634 − 1.49060I
b = 0.326160 + 0.291125I
2.11796 + 2.01943I 0
u = 1.245720 + 0.066167I
a = 0.60423 − 1.62536I
b = −0.872185 + 0.570997I
2.11796 + 2.01943I 0
u = 1.245720 − 0.066167I
a = 0.18634 + 1.49060I
b = 0.326160 − 0.291125I
2.11796 − 2.01943I 0
u = 1.245720 − 0.066167I
a = 0.60423 + 1.62536I
b = −0.872185 − 0.570997I
2.11796 − 2.01943I 0
u = −1.237270 + 0.197913I
a = −0.45596 + 1.50174I
b = 0.255758 − 0.212067I
5.29216 − 7.38796I 0
u = −1.237270 + 0.197913I
a = 0.03864 − 1.81341I
b = 1.097400 + 0.775615I
5.29216 − 7.38796I 0
u = −1.237270 − 0.197913I
a = −0.45596 − 1.50174I
b = 0.255758 + 0.212067I
5.29216 + 7.38796I 0
u = −1.237270 − 0.197913I
a = 0.03864 + 1.81341I
b = 1.097400 − 0.775615I
5.29216 + 7.38796I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544706 + 0.473507I
a = −0.802270 − 0.233838I
b = −0.011900 + 0.907114I
4.45076 − 7.51019I 6.15354 + 7.01976I
u = −0.544706 + 0.473507I
a = 1.38473 − 1.19024I
b = 1.061310 + 0.548084I
4.45076 − 7.51019I 6.15354 + 7.01976I
u = −0.544706 − 0.473507I
a = −0.802270 + 0.233838I
b = −0.011900 − 0.907114I
4.45076 + 7.51019I 6.15354 − 7.01976I
u = −0.544706 − 0.473507I
a = 1.38473 + 1.19024I
b = 1.061310 − 0.548084I
4.45076 + 7.51019I 6.15354 − 7.01976I
u = 0.242081 + 0.642003I
a = −0.121015 − 0.723872I
b = −0.191735 + 0.659845I
0.52756 + 3.89617I 2.77520 − 6.34158I
u = 0.242081 + 0.642003I
a = 1.236690 + 0.347854I
b = 0.980806 − 0.514343I
0.52756 + 3.89617I 2.77520 − 6.34158I
u = 0.242081 − 0.642003I
a = −0.121015 + 0.723872I
b = −0.191735 − 0.659845I
0.52756 − 3.89617I 2.77520 + 6.34158I
u = 0.242081 − 0.642003I
a = 1.236690 − 0.347854I
b = 0.980806 + 0.514343I
0.52756 − 3.89617I 2.77520 + 6.34158I
u = −1.346270 + 0.118214I
a = −0.057599 + 1.129430I
b = −1.206250 − 0.403477I
3.10296 − 1.88811I 0
u = −1.346270 + 0.118214I
a = 0.807053 − 1.151850I
b = −1.140800 + 0.801114I
3.10296 − 1.88811I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.346270 − 0.118214I
a = −0.057599 − 1.129430I
b = −1.206250 + 0.403477I
3.10296 + 1.88811I 0
u = −1.346270 − 0.118214I
a = 0.807053 + 1.151850I
b = −1.140800 − 0.801114I
3.10296 + 1.88811I 0
u = 1.360600 + 0.024824I
a = −0.59798 − 2.02753I
b = −1.092470 + 0.227442I
4.48945 + 0.44139I 0
u = 1.360600 + 0.024824I
a = −1.56290 − 2.59175I
b = 1.95395 + 2.12838I
4.48945 + 0.44139I 0
u = 1.360600 − 0.024824I
a = −0.59798 + 2.02753I
b = −1.092470 − 0.227442I
4.48945 − 0.44139I 0
u = 1.360600 − 0.024824I
a = −1.56290 + 2.59175I
b = 1.95395 − 2.12838I
4.48945 − 0.44139I 0
u = 0.479497 + 0.411115I
a = 1.278950 + 0.303011I
b = −0.113905 − 0.253707I
1.58087 − 0.53277I 7.83505 − 0.25698I
u = 0.479497 + 0.411115I
a = 0.090316 + 0.483528I
b = 0.673813 + 0.606032I
1.58087 − 0.53277I 7.83505 − 0.25698I
u = 0.479497 − 0.411115I
a = 1.278950 − 0.303011I
b = −0.113905 + 0.253707I
1.58087 + 0.53277I 7.83505 + 0.25698I
u = 0.479497 − 0.411115I
a = 0.090316 − 0.483528I
b = 0.673813 − 0.606032I
1.58087 + 0.53277I 7.83505 + 0.25698I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.361950 + 0.320932I
a = −0.260335 + 1.373070I
b = −0.304737 − 0.598586I
5.50387 − 7.35891I 0
u = −1.361950 + 0.320932I
a = 0.02776 − 1.48728I
b = 1.165430 + 0.676249I
5.50387 − 7.35891I 0
u = −1.361950 − 0.320932I
a = −0.260335 − 1.373070I
b = −0.304737 + 0.598586I
5.50387 + 7.35891I 0
u = −1.361950 − 0.320932I
a = 0.02776 + 1.48728I
b = 1.165430 − 0.676249I
5.50387 + 7.35891I 0
u = −0.592608
a = −0.675564
b = −1.30375
0.850544 11.0660
u = −0.592608
a = 2.60037
b = −0.512864
0.850544 11.0660
u = −1.45678 + 0.15564I
a = −0.379396 + 0.929302I
b = 0.398711 − 0.870251I
7.76795 − 1.60452I 0
u = −1.45678 + 0.15564I
a = 0.074350 − 0.851116I
b = 0.638031 + 0.406509I
7.76795 − 1.60452I 0
u = −1.45678 − 0.15564I
a = −0.379396 − 0.929302I
b = 0.398711 + 0.870251I
7.76795 + 1.60452I 0
u = −1.45678 − 0.15564I
a = 0.074350 + 0.851116I
b = 0.638031 − 0.406509I
7.76795 + 1.60452I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50323 + 0.07660I
a = 1.32499 + 0.82787I
b = −0.737498 − 0.096809I
5.69053 − 0.15999I 0
u = −1.50323 + 0.07660I
a = −1.56911 − 1.05381I
b = 1.72400 + 0.87076I
5.69053 − 0.15999I 0
u = −1.50323 − 0.07660I
a = 1.32499 − 0.82787I
b = −0.737498 + 0.096809I
5.69053 + 0.15999I 0
u = −1.50323 − 0.07660I
a = −1.56911 + 1.05381I
b = 1.72400 − 0.87076I
5.69053 + 0.15999I 0
u = 1.49462 + 0.19720I
a = −0.16111 + 1.41989I
b = 1.33487 − 0.64551I
11.0335 + 10.1489I 0
u = 1.49462 + 0.19720I
a = 0.30102 + 1.55009I
b = −0.26778 − 1.48948I
11.0335 + 10.1489I 0
u = 1.49462 − 0.19720I
a = −0.16111 − 1.41989I
b = 1.33487 + 0.64551I
11.0335 − 10.1489I 0
u = 1.49462 − 0.19720I
a = 0.30102 − 1.55009I
b = −0.26778 + 1.48948I
11.0335 − 10.1489I 0
u = −1.48828 + 0.31375I
a = −0.45103 − 1.50201I
b = 1.161310 + 0.493885I
2.38283 − 11.34240I 0
u = −1.48828 + 0.31375I
a = 0.46240 + 1.61868I
b = −1.34786 − 0.90026I
2.38283 − 11.34240I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48828 − 0.31375I
a = −0.45103 + 1.50201I
b = 1.161310 − 0.493885I
2.38283 + 11.34240I 0
u = −1.48828 − 0.31375I
a = 0.46240 − 1.61868I
b = −1.34786 + 0.90026I
2.38283 + 11.34240I 0
u = 0.062588 + 0.462865I
a = −0.745882 + 1.101450I
b = −0.761483 − 0.431993I
−1.322960 − 0.095597I −5.44765 − 0.30752I
u = 0.062588 + 0.462865I
a = −1.69151 + 1.21537I
b = −0.841856 + 0.077327I
−1.322960 − 0.095597I −5.44765 − 0.30752I
u = 0.062588 − 0.462865I
a = −0.745882 − 1.101450I
b = −0.761483 + 0.431993I
−1.322960 + 0.095597I −5.44765 + 0.30752I
u = 0.062588 − 0.462865I
a = −1.69151 − 1.21537I
b = −0.841856 − 0.077327I
−1.322960 + 0.095597I −5.44765 + 0.30752I
u = 1.56665 + 0.25660I
a = 0.231175 − 0.827713I
b = −1.36349 + 0.49044I
9.69181 + 1.76230I 0
u = 1.56665 + 0.25660I
a = −0.223081 − 0.793724I
b = 0.469240 + 0.837793I
9.69181 + 1.76230I 0
u = 1.56665 − 0.25660I
a = 0.231175 + 0.827713I
b = −1.36349 − 0.49044I
9.69181 − 1.76230I 0
u = 1.56665 − 0.25660I
a = −0.223081 + 0.793724I
b = 0.469240 − 0.837793I
9.69181 − 1.76230I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0661431
a = 6.64617
b = −8.53647
−0.00224370 1841.00
u = −0.0661431
a = 128.621
b = −1.00230
−0.00224370 1841.00
18
III. I
u
3
= h−7u
10
+ 4u
9
+ · · · + 11b + 17, −8u
10
+ 25u
9
+ · · · + 11a −
78, u
11
− 2u
10
+ · · · + 6u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
3
=
0.727273u
10
− 2.27273u
9
+ ··· + 2.90909u + 7.09091
0.636364u
10
− 0.363636u
9
+ ··· − 1.45455u − 1.54545
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
0.272727u
10
− 2.72727u
9
+ ··· + 11.0909u + 9.90909
0.363636u
10
+ 0.363636u
9
+ ··· − 3.54545u − 2.45455
a
2
=
1.36364u
10
− 2.63636u
9
+ ··· + 1.45455u + 5.54545
0.636364u
10
− 0.363636u
9
+ ··· − 1.45455u − 1.54545
a
5
=
0.636364u
10
− 2.36364u
9
+ ··· + 5.54545u + 8.45455
0.363636u
10
+ 0.363636u
9
+ ··· − 4.54545u − 2.45455
a
9
=
2.09091u
10
− 3.90909u
9
+ ··· + 2.36364u + 9.63636
−u
10
+ u
9
+ 5u
8
− 8u
7
− 4u
6
+ 16u
5
− 7u
4
− 10u
3
+ 9u
2
+ 2u − 2
a
4
=
−0.363636u
10
+ 1.63636u
9
+ ··· − 6.45455u − 4.54545
−0.636364u
10
+ 0.363636u
9
+ ··· + 3.45455u + 1.54545
a
1
=
u
10
− 3u
9
− 4u
8
+ 19u
7
− 7u
6
− 31u
5
+ 34u
4
+ 8u
3
− 30u
2
+ 7u + 8
0.636364u
10
+ 0.636364u
9
+ ··· − 4.45455u − 2.54545
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
74
11
u
10
+
113
11
u
9
+
357
11
u
8
−
746
11
u
7
−
134
11
u
6
+
1178
11
u
5
−
724
11
u
4
−
422
11
u
3
+
456
11
u
2
+
144
11
u +
10
11
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 6u
10
+ ··· − 11u + 1
c
2
, c
11
u
11
− 5u
9
− u
8
+ 9u
7
+ 3u
6
− 10u
5
− 3u
4
+ 7u
3
+ 3u
2
− 2u − 1
c
3
, c
5
u
11
− 5u
9
+ u
8
+ 9u
7
− 3u
6
− 10u
5
+ 3u
4
+ 7u
3
− 3u
2
− 2u + 1
c
4
, c
8
u
11
− u
10
+ ··· − 5u + 1
c
6
, c
7
u
11
− 2u
10
+ ··· + 6u + 1
c
9
, c
12
u
11
+ u
10
+ ··· − 5u − 1
c
10
u
11
+ 2u
10
+ ··· + 6u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 2y
10
+ ··· + 21y −1
c
2
, c
3
, c
5
c
11
y
11
− 10y
10
+ ··· + 10y −1
c
4
, c
8
, c
9
c
12
y
11
− 13y
10
+ ··· + 45y −1
c
6
, c
7
, c
10
y
11
− 14y
10
+ ··· + 38y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.947758
a = −0.866165
b = 1.59894
−7.33878 −27.9880
u = 0.697676 + 0.834481I
a = 0.549586 + 0.594984I
b = 0.694924 + 0.358502I
3.09180 − 4.84097I 5.24884 + 3.87488I
u = 0.697676 − 0.834481I
a = 0.549586 − 0.594984I
b = 0.694924 − 0.358502I
3.09180 + 4.84097I 5.24884 − 3.87488I
u = 1.284570 + 0.369820I
a = 0.40416 + 1.72162I
b = 0.906586 − 0.628396I
5.41429 + 9.15643I 5.68722 − 10.47253I
u = 1.284570 − 0.369820I
a = 0.40416 − 1.72162I
b = 0.906586 + 0.628396I
5.41429 − 9.15643I 5.68722 + 10.47253I
u = −1.35854
a = 0.543106
b = −1.74021
4.07888 9.27100
u = 1.48788 + 0.09186I
a = 0.855967 − 1.087180I
b = −0.811433 + 0.624669I
6.02864 + 0.67022I 7.62823 − 2.72103I
u = 1.48788 − 0.09186I
a = 0.855967 + 1.087180I
b = −0.811433 − 0.624669I
6.02864 − 0.67022I 7.62823 + 2.72103I
u = −0.449664
a = 1.10365
b = −0.719426
−0.265950 2.42860
u = −0.183780
a = 5.68622
b = −1.23706
−0.0829640 0.0440200
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −2.00050
a = −0.0862312
b = 0.517601
14.0178 25.1160
23
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
−1
0
a
7
=
1
0
a
11
=
−1
0
a
3
=
0
−1
a
8
=
1
0
a
12
=
−1
−1
a
2
=
−1
−1
a
5
=
0
−1
a
9
=
−1
−1
a
4
=
1
0
a
1
=
−2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
11
, c
12
u − 1
c
3
, c
4
, c
5
c
8
u + 1
c
6
, c
7
, c
10
u
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
c
9
, c
11
, c
12
y −1
c
6
, c
7
, c
10
y
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
0 0
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
11
− 6u
10
+ ··· − 11u + 1)(u
25
− 22u
24
+ ··· + 5120u + 512)
· (u
36
+ 11u
35
+ ··· + 12u + 1)
2
c
2
, c
11
(u − 1)(u
11
− 5u
9
+ ··· − 2u − 1)
· (u
25
− u
24
+ ··· − 4u + 1)(u
72
+ 5u
71
+ ··· + 44u + 31)
c
3
, c
5
(u + 1)(u
11
− 5u
9
+ ··· − 2u + 1)
· (u
25
− u
24
+ ··· − 4u + 1)(u
72
+ 5u
71
+ ··· + 44u + 31)
c
4
, c
8
(u + 1)(u
11
− u
10
+ ··· − 5u + 1)(u
25
− 11u
23
+ ··· + u − 1)
· (u
72
+ 15u
71
+ ··· + 1022u + 149)
c
6
, c
7
u(u
11
− 2u
10
+ ··· + 6u + 1)(u
25
− 11u
24
+ ··· − 80u + 16)
· (u
36
+ 4u
35
+ ··· + 16u + 1)
2
c
9
, c
12
(u − 1)(u
11
+ u
10
+ ··· − 5u − 1)(u
25
− 11u
23
+ ··· + u − 1)
· (u
72
+ 15u
71
+ ··· + 1022u + 149)
c
10
u(u
11
+ 2u
10
+ ··· + 6u − 1)(u
25
− 11u
24
+ ··· − 80u + 16)
· (u
36
+ 4u
35
+ ··· + 16u + 1)
2
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
11
− 2y
10
+ ··· + 21y −1)
· (y
25
− 2y
24
+ ··· + 76808192y −262144)
· (y
36
+ 9y
35
+ ··· − 78y + 1)
2
c
2
, c
3
, c
5
c
11
(y −1)(y
11
− 10y
10
+ ··· + 10y −1)(y
25
− 15y
24
+ ··· + 50y −1)
· (y
72
− 109y
71
+ ··· − 5904y + 961)
c
4
, c
8
, c
9
c
12
(y −1)(y
11
− 13y
10
+ ··· + 45y −1)(y
25
− 22y
24
+ ··· + 21y −1)
· (y
72
− 125y
71
+ ··· + 239896y + 22201)
c
6
, c
7
, c
10
y(y
11
− 14y
10
+ ··· + 38y −1)(y
25
− 23y
24
+ ··· − 1408y −256)
· (y
36
− 36y
35
+ ··· − 228y + 1)
2
29
