12a
0873
(K12a
0873
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 12 3 2 11 1 5 8 10
Solving Sequence
1,9 5,10
11 4 2 8 7 3 12 6
c
9
c
10
c
4
c
1
c
8
c
7
c
3
c
12
c
5
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h108691u
38
− 518522u
37
+ ··· + 524288b − 511627,
688007u
38
− 3615026u
37
+ ··· + 524288a − 2014079, u
39
− 5u
38
+ ··· − 6u − 1i
I
u
2
= h6.85428 × 10
68
u
61
+ 3.56097 × 10
69
u
60
+ ··· + 4.46626 × 10
69
b − 6.45538 × 10
69
,
− 3.56475 × 10
68
u
61
− 1.48838 × 10
68
u
60
+ ··· + 4.46626 × 10
69
a + 1.70079 × 10
70
,
u
62
+ 11u
61
+ ··· + 11u + 2i
I
u
3
= hb − a, 32a
5
− 16a
4
+ 16a
3
− 4a
2
+ 2a − 1, u − 1i
I
u
4
= hb − u − 1, a + 2u + 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 108 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
= h1.09 × 10
5
u
38
− 5.19 × 10
5
u
37
+ · · · + 5.24 × 10
5
b − 5.12 × 10
5
, 6.88 ×
10
5
u
38
−3.62×10
6
u
37
+· · · +5.24×10
5
a−2.01×10
6
, u
39
−5u
38
+· · · − 6u −1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−1.31227u
38
+ 6.89511u
37
+ ··· + 14.1550u + 3.84155
−0.207312u
38
+ 0.989002u
37
+ ··· + 2.65564u + 0.975851
a
10
=
1
u
2
a
11
=
−
1
8
u
37
+
5
8
u
36
+ ··· +
11
4
u +
1
8
u
a
4
=
−1.51958u
38
+ 7.88412u
37
+ ··· + 16.8107u + 4.81740
−0.207312u
38
+ 0.989002u
37
+ ··· + 2.65564u + 0.975851
a
2
=
0.124998u
38
− 0.624989u
37
+ ··· + 5.87501u − 0.999998
−9.53674 × 10
−7
u
38
+ 5.72205 × 10
−6
u
37
+ ··· + 2.00000u + 9.53674 × 10
−7
a
8
=
1
8
u
38
−
5
8
u
37
+ ··· −
1
8
u + 1
−u
2
a
7
=
0.125425u
38
− 0.627522u
37
+ ··· − 2.12725u + 0.999544
0.000203133u
38
− 0.00120354u
37
+ ··· − 0.00107670u − 0.000218391
a
3
=
−0.000410080u
38
+ 0.00242996u
37
+ ··· + 4.00217u + 0.000440598
−0.000540733u
38
+ 0.00319862u
37
+ ··· + 1.00289u + 0.000586510
a
12
=
u
u
3
+ u
a
6
=
−1.26471u
38
+ 6.61468u
37
+ ··· + 14.4231u + 4.04886
−0.315355u
38
+ 1.65487u
37
+ ··· + 2.71527u + 1.14050
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3999055
2097152
u
38
+
10274157
1048576
u
37
+ ··· +
37199499
2097152
u +
9939535
2097152
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
− 8u
38
+ ··· + 78583u − 7136
c
2
, c
3
, c
6
u
39
− 2u
38
+ ··· + 13u + 4
c
4
, c
5
32(32u
39
− 16u
38
+ ··· + 2u + 2)
c
7
u
39
− 5u
37
+ ··· + 3664u + 704
c
8
, c
9
, c
11
c
12
u
39
+ 5u
38
+ ··· − 6u + 1
c
10
u
39
+ 3u
38
+ ··· + 5632u + 2048
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 24y
38
+ ··· + 2799146385y −50922496
c
2
, c
3
, c
6
y
39
− 36y
38
+ ··· + 145y −16
c
4
, c
5
1024(1024y
39
+ 21248y
38
+ ··· − 20y −4)
c
7
y
39
− 10y
38
+ ··· + 9786624y −495616
c
8
, c
9
, c
11
c
12
y
39
+ 23y
38
+ ··· + 16y −1
c
10
y
39
+ 13y
38
+ ··· − 77332480y −4194304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.724185 + 0.655758I
a = 0.330095 + 0.170004I
b = 0.738223 − 0.031571I
2.17537 − 4.39053I −3.44910 + 4.97696I
u = 0.724185 − 0.655758I
a = 0.330095 − 0.170004I
b = 0.738223 + 0.031571I
2.17537 + 4.39053I −3.44910 − 4.97696I
u = 0.798846 + 0.475502I
a = −0.164314 − 0.150407I
b = −0.630420 + 0.127305I
−2.50450 − 1.68373I −12.13938 + 2.32742I
u = 0.798846 − 0.475502I
a = −0.164314 + 0.150407I
b = −0.630420 − 0.127305I
−2.50450 + 1.68373I −12.13938 − 2.32742I
u = 1.066700 + 0.355106I
a = 0.0961583 + 0.0078123I
b = 0.524239 − 0.376281I
0.475249 + 0.503953I −4.00000 − 8.90257I
u = 1.066700 − 0.355106I
a = 0.0961583 − 0.0078123I
b = 0.524239 + 0.376281I
0.475249 − 0.503953I −4.00000 + 8.90257I
u = −0.211517 + 1.137440I
a = 0.23998 − 2.28740I
b = −0.464258 + 0.732877I
5.31272 + 2.00033I 4.35226 − 5.73915I
u = −0.211517 − 1.137440I
a = 0.23998 + 2.28740I
b = −0.464258 − 0.732877I
5.31272 − 2.00033I 4.35226 + 5.73915I
u = −0.324360 + 1.156690I
a = 0.02796 + 2.07352I
b = 0.697354 − 0.867496I
2.21977 + 6.32089I 0. − 7.80217I
u = −0.324360 − 1.156690I
a = 0.02796 − 2.07352I
b = 0.697354 + 0.867496I
2.21977 − 6.32089I 0. + 7.80217I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.026900 + 1.214660I
a = 1.23416 − 1.59634I
b = 0.132335 + 0.743058I
7.44405 + 0.69867I 9.09911 + 0.I
u = 0.026900 − 1.214660I
a = 1.23416 + 1.59634I
b = 0.132335 − 0.743058I
7.44405 − 0.69867I 9.09911 + 0.I
u = 0.122259 + 1.210610I
a = −1.34335 + 1.13263I
b = −0.327572 − 0.697824I
6.47328 − 4.27244I 0
u = 0.122259 − 1.210610I
a = −1.34335 − 1.13263I
b = −0.327572 + 0.697824I
6.47328 + 4.27244I 0
u = 0.182168 + 1.256440I
a = 1.13163 − 0.93796I
b = 0.456095 + 0.759995I
12.6122 − 8.2561I 0
u = 0.182168 − 1.256440I
a = 1.13163 + 0.93796I
b = 0.456095 − 0.759995I
12.6122 + 8.2561I 0
u = −0.407095 + 1.204330I
a = −0.13247 − 1.90492I
b = −0.843449 + 1.039000I
6.42042 + 10.35860I 0
u = −0.407095 − 1.204330I
a = −0.13247 + 1.90492I
b = −0.843449 − 1.039000I
6.42042 − 10.35860I 0
u = 1.319840 + 0.082124I
a = −0.0186151 + 0.0626784I
b = −0.127627 + 0.707014I
−0.85359 + 1.74269I 0
u = 1.319840 − 0.082124I
a = −0.0186151 − 0.0626784I
b = −0.127627 − 0.707014I
−0.85359 − 1.74269I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036557 + 1.324810I
a = −0.73447 + 1.53147I
b = −0.062358 − 1.015090I
15.0323 + 3.2046I 0
u = −0.036557 − 1.324810I
a = −0.73447 − 1.53147I
b = −0.062358 + 1.015090I
15.0323 − 3.2046I 0
u = 0.594439
a = −0.228045
b = 0.452360
−0.941763 −9.94040
u = 1.41463 + 0.10708I
a = 0.0231744 − 0.0841694I
b = 0.166254 − 0.853051I
4.93767 + 4.69901I 0
u = 1.41463 − 0.10708I
a = 0.0231744 + 0.0841694I
b = 0.166254 + 0.853051I
4.93767 − 4.69901I 0
u = −0.47769 + 1.37991I
a = −0.14495 − 1.60254I
b = −0.85620 + 1.49381I
9.12652 + 9.53608I 0
u = −0.47769 − 1.37991I
a = −0.14495 + 1.60254I
b = −0.85620 − 1.49381I
9.12652 − 9.53608I 0
u = −0.52260 + 1.38710I
a = 0.20032 + 1.57749I
b = 0.95190 − 1.54963I
8.2828 + 13.9866I 0
u = −0.52260 − 1.38710I
a = 0.20032 − 1.57749I
b = 0.95190 + 1.54963I
8.2828 − 13.9866I 0
u = −0.43911 + 1.42736I
a = 0.08082 + 1.54888I
b = 0.72748 − 1.56656I
16.0878 + 7.0331I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.43911 − 1.42736I
a = 0.08082 − 1.54888I
b = 0.72748 + 1.56656I
16.0878 − 7.0331I 0
u = −0.54482 + 1.40917I
a = −0.21934 − 1.54269I
b = −0.98301 + 1.61986I
14.2175 + 17.6988I 0
u = −0.54482 − 1.40917I
a = −0.21934 + 1.54269I
b = −0.98301 − 1.61986I
14.2175 − 17.6988I 0
u = 0.015211 + 0.418244I
a = −0.00352 − 1.79696I
b = −0.539074 − 0.214516I
2.76604 + 0.58348I −0.871646 + 0.155316I
u = 0.015211 − 0.418244I
a = −0.00352 + 1.79696I
b = −0.539074 + 0.214516I
2.76604 − 0.58348I −0.871646 − 0.155316I
u = −0.310457 + 0.116493I
a = −0.01154 − 3.00812I
b = −0.275051 − 0.775463I
5.36389 − 4.18845I 5.68066 + 2.80926I
u = −0.310457 − 0.116493I
a = −0.01154 + 3.00812I
b = −0.275051 + 0.775463I
5.36389 + 4.18845I 5.68066 − 2.80926I
u = −0.193758 + 0.118859I
a = −0.22771 + 3.00764I
b = 0.238959 + 0.534501I
0.026832 − 1.339450I 0.33272 + 4.35005I
u = −0.193758 − 0.118859I
a = −0.22771 − 3.00764I
b = 0.238959 − 0.534501I
0.026832 + 1.339450I 0.33272 − 4.35005I
8
II. I
u
2
= h6.85 × 10
68
u
61
+ 3.56 × 10
69
u
60
+ · · · + 4.47 × 10
69
b − 6.46 ×
10
69
, −3.56 × 10
68
u
61
− 1.49 × 10
68
u
60
+ · · · + 4.47 × 10
69
a + 1.70 ×
10
70
, u
62
+ 11u
61
+ · · · + 11u + 2i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.0798151u
61
+ 0.0333250u
60
+ ··· − 20.7102u − 3.80808
−0.153468u
61
− 0.797304u
60
+ ··· + 10.2193u + 1.44537
a
10
=
1
u
2
a
11
=
1
2
u
61
+
11
2
u
60
+ ··· +
45
2
u +
11
2
0.573998u
61
+ 5.87664u
60
+ ··· + 1.67615u + 0.498297
a
4
=
−0.0736529u
61
− 0.763979u
60
+ ··· − 10.4908u − 2.36271
−0.153468u
61
− 0.797304u
60
+ ··· + 10.2193u + 1.44537
a
2
=
0.636727u
61
+ 7.29918u
60
+ ··· + 7.35507u + 2.59664
0.175214u
61
+ 2.55480u
60
+ ··· + 10.5476u + 2.81253
a
8
=
−0.249149u
61
− 2.16664u
60
+ ··· − 0.729108u − 0.0644857
−0.437334u
61
− 4.84227u
60
+ ··· − 5.81568u − 0.147996
a
7
=
−0.0660678u
61
− 0.546435u
60
+ ··· + 9.22039u + 2.55081
−0.00796357u
61
− 0.597986u
60
+ ··· − 8.29547u − 1.03845
a
3
=
0.127793u
61
+ 1.67388u
60
+ ··· − 0.711897u + 0.745056
−0.0486349u
61
+ 0.0587942u
60
+ ··· + 8.88154u + 1.74770
a
12
=
u
u
3
+ u
a
6
=
−0.118114u
61
− 1.24898u
60
+ ··· − 12.0046u − 2.25218
−0.157786u
61
− 1.09012u
60
+ ··· + 9.47656u + 1.21142
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.03298u
61
− 9.77347u
60
+ ··· − 1.48702u − 3.35758
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
31
− 5u
30
+ ··· + 40u − 7)
2
c
2
, c
3
, c
6
(u
31
− u
30
+ ··· + 2u − 1)
2
c
4
, c
5
u
62
+ u
61
+ ··· − 768736u + 1008568
c
7
(u
31
+ 3u
30
+ ··· − 13u + 16)
2
c
8
, c
9
, c
11
c
12
u
62
− 11u
61
+ ··· − 11u + 2
c
10
(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
31
+ 23y
30
+ ··· − 640y −49)
2
c
2
, c
3
, c
6
(y
31
− 29y
30
+ ··· − 4y −1)
2
c
4
, c
5
y
62
+ 35y
61
+ ··· + 17185261710176y + 1017209410624
c
7
(y
31
− 9y
30
+ ··· + 1481y −256)
2
c
8
, c
9
, c
11
c
12
y
62
+ 43y
61
+ ··· + 59y + 4
c
10
(y
31
+ 11y
30
+ ··· − 4y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.610259 + 0.825368I
a = −0.931690 − 0.150611I
b = 0.443710 + 0.094556I
8.51398 + 2.56488I 0
u = −0.610259 − 0.825368I
a = −0.931690 + 0.150611I
b = 0.443710 − 0.094556I
8.51398 − 2.56488I 0
u = 0.122937 + 1.022420I
a = −2.25050 + 1.94438I
b = 2.32560 − 2.56890I
6.04268 0
u = 0.122937 − 1.022420I
a = −2.25050 − 1.94438I
b = 2.32560 + 2.56890I
6.04268 0
u = −1.057470 + 0.122121I
a = 0.1061940 − 0.0014004I
b = −0.525447 + 0.977392I
4.43131 + 4.14236I 0
u = −1.057470 − 0.122121I
a = 0.1061940 + 0.0014004I
b = −0.525447 − 0.977392I
4.43131 − 4.14236I 0
u = 0.384544 + 1.032370I
a = −0.165227 + 1.398420I
b = −0.249020 − 0.556976I
−0.70604 − 2.71284I 0
u = 0.384544 − 1.032370I
a = −0.165227 − 1.398420I
b = −0.249020 + 0.556976I
−0.70604 + 2.71284I 0
u = 0.229731 + 0.865676I
a = 0.07431 − 1.55871I
b = −0.161828 + 0.324905I
2.78691 + 0.40298I 0
u = 0.229731 − 0.865676I
a = 0.07431 + 1.55871I
b = −0.161828 − 0.324905I
2.78691 − 0.40298I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107024 + 1.111770I
a = −0.146050 + 1.303810I
b = 1.24176 − 0.94499I
2.56011 + 2.73446I 0
u = −0.107024 − 1.111770I
a = −0.146050 − 1.303810I
b = 1.24176 + 0.94499I
2.56011 − 2.73446I 0
u = −0.032223 + 1.128520I
a = −0.31654 − 2.21125I
b = −0.08856 + 2.34874I
3.39700 − 1.02630I 0
u = −0.032223 − 1.128520I
a = −0.31654 + 2.21125I
b = −0.08856 − 2.34874I
3.39700 + 1.02630I 0
u = −0.006360 + 1.130480I
a = 0.11158 − 1.51204I
b = −0.79447 + 1.31914I
3.28194 − 0.92992I 0
u = −0.006360 − 1.130480I
a = 0.11158 + 1.51204I
b = −0.79447 − 1.31914I
3.28194 + 0.92992I 0
u = −1.133880 + 0.044405I
a = −0.0770874 − 0.0659382I
b = 0.568051 − 1.100450I
3.76549 + 8.17190I 0
u = −1.133880 − 0.044405I
a = −0.0770874 + 0.0659382I
b = 0.568051 + 1.100450I
3.76549 − 8.17190I 0
u = −1.117680 + 0.233912I
a = −0.188714 − 0.026500I
b = 0.372056 − 0.969425I
10.80180 + 1.64856I 0
u = −1.117680 − 0.233912I
a = −0.188714 + 0.026500I
b = 0.372056 + 0.969425I
10.80180 − 1.64856I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822502 + 0.158011I
a = −0.244805 − 0.001735I
b = −0.871196 − 0.852594I
3.16164 − 5.89464I −2.05487 + 6.44091I
u = −0.822502 − 0.158011I
a = −0.244805 + 0.001735I
b = −0.871196 + 0.852594I
3.16164 + 5.89464I −2.05487 − 6.44091I
u = −0.146870 + 1.159030I
a = 0.207882 − 1.224920I
b = −1.48581 + 0.95451I
8.28224 + 6.04082I 0
u = −0.146870 − 1.159030I
a = 0.207882 + 1.224920I
b = −1.48581 − 0.95451I
8.28224 − 6.04082I 0
u = −0.096782 + 0.805839I
a = 2.52966 + 0.03471I
b = −1.94413 + 0.07132I
3.39700 + 1.02630I −2.18992 − 6.41690I
u = −0.096782 − 0.805839I
a = 2.52966 − 0.03471I
b = −1.94413 − 0.07132I
3.39700 − 1.02630I −2.18992 + 6.41690I
u = −1.199600 + 0.041449I
a = 0.0927293 + 0.0998903I
b = −0.537596 + 1.177980I
9.6232 + 11.6029I 0
u = −1.199600 − 0.041449I
a = 0.0927293 − 0.0998903I
b = −0.537596 − 1.177980I
9.6232 − 11.6029I 0
u = −0.006726 + 1.201560I
a = −0.46955 + 1.49677I
b = 1.39820 − 1.70670I
9.18224 − 3.33239I 0
u = −0.006726 − 1.201560I
a = −0.46955 − 1.49677I
b = 1.39820 + 1.70670I
9.18224 + 3.33239I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490970 + 1.143700I
a = 0.194340 − 1.288080I
b = 0.527968 + 0.677538I
3.16164 − 5.89464I 0
u = 0.490970 − 1.143700I
a = 0.194340 + 1.288080I
b = 0.527968 − 0.677538I
3.16164 + 5.89464I 0
u = 0.291842 + 0.579770I
a = −2.62106 + 0.29524I
b = 1.25399 − 1.40768I
9.18224 + 3.33239I 1.23670 − 3.21859I
u = 0.291842 − 0.579770I
a = −2.62106 − 0.29524I
b = 1.25399 + 1.40768I
9.18224 − 3.33239I 1.23670 + 3.21859I
u = −0.616831 + 0.185116I
a = 0.587876 − 0.081679I
b = 0.894509 + 0.695294I
−0.70604 − 2.71284I −7.89942 + 3.44665I
u = −0.616831 − 0.185116I
a = 0.587876 + 0.081679I
b = 0.894509 − 0.695294I
−0.70604 + 2.71284I −7.89942 − 3.44665I
u = −0.088079 + 1.373410I
a = 0.396910 + 1.207870I
b = −0.14566 − 1.47450I
8.51398 − 2.56488I 0
u = −0.088079 − 1.373410I
a = 0.396910 − 1.207870I
b = −0.14566 + 1.47450I
8.51398 + 2.56488I 0
u = 0.45719 + 1.41480I
a = 0.091928 − 1.140510I
b = 0.668394 + 1.157090I
4.43131 − 4.14236I 0
u = 0.45719 − 1.41480I
a = 0.091928 + 1.140510I
b = 0.668394 − 1.157090I
4.43131 + 4.14236I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61476 + 1.38269I
a = 0.579567 + 0.665230I
b = 0.213331 − 0.930964I
8.18677 + 1.99617I 0
u = −0.61476 − 1.38269I
a = 0.579567 − 0.665230I
b = 0.213331 + 0.930964I
8.18677 − 1.99617I 0
u = 0.53999 + 1.42345I
a = −0.134520 + 1.116050I
b = −0.808721 − 1.119170I
3.76549 − 8.17190I 0
u = 0.53999 − 1.42345I
a = −0.134520 − 1.116050I
b = −0.808721 + 1.119170I
3.76549 + 8.17190I 0
u = 0.424736 + 0.216093I
a = 2.89315 + 0.96518I
b = −0.584354 + 1.253910I
8.28224 − 6.04082I 0.35365 + 3.16093I
u = 0.424736 − 0.216093I
a = 2.89315 − 0.96518I
b = −0.584354 − 1.253910I
8.28224 + 6.04082I 0.35365 − 3.16093I
u = −0.53947 + 1.44416I
a = −0.545874 − 0.733782I
b = −0.192340 + 1.092650I
8.18677 − 1.99617I 0
u = −0.53947 − 1.44416I
a = −0.545874 + 0.733782I
b = −0.192340 − 1.092650I
8.18677 + 1.99617I 0
u = 0.41718 + 1.50113I
a = −0.052109 + 1.099920I
b = −0.65795 − 1.31593I
10.80180 − 1.64856I 0
u = 0.41718 − 1.50113I
a = −0.052109 − 1.099920I
b = −0.65795 + 1.31593I
10.80180 + 1.64856I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.321647 + 0.288477I
a = −1.51095 − 0.48074I
b = −0.849824 − 0.519815I
2.78691 + 0.40298I −3.07070 − 0.52831I
u = −0.321647 − 0.288477I
a = −1.51095 + 0.48074I
b = −0.849824 + 0.519815I
2.78691 − 0.40298I −3.07070 + 0.52831I
u = −0.68722 + 1.41015I
a = −0.541909 − 0.623677I
b = −0.338522 + 0.882572I
14.2937 + 5.0494I 0
u = −0.68722 − 1.41015I
a = −0.541909 + 0.623677I
b = −0.338522 − 0.882572I
14.2937 − 5.0494I 0
u = 0.57393 + 1.46248I
a = 0.142172 − 1.088250I
b = 0.88882 + 1.16417I
9.6232 − 11.6029I 0
u = 0.57393 − 1.46248I
a = 0.142172 + 1.088250I
b = 0.88882 − 1.16417I
9.6232 + 11.6029I 0
u = −0.55005 + 1.51837I
a = 0.491032 + 0.730161I
b = 0.284759 − 1.169250I
14.2937 − 5.0494I 0
u = −0.55005 − 1.51837I
a = 0.491032 − 0.730161I
b = 0.284759 + 1.169250I
14.2937 + 5.0494I 0
u = 0.029418 + 0.359742I
a = 3.19180 − 1.28434I
b = −1.013250 + 0.844224I
3.28194 + 0.92992I −1.59628 − 3.68841I
u = 0.029418 − 0.359742I
a = 3.19180 + 1.28434I
b = −1.013250 − 0.844224I
3.28194 − 0.92992I −1.59628 + 3.68841I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292960 + 0.183199I
a = −3.74455 − 1.03027I
b = 0.667529 − 1.072660I
2.56011 − 2.73446I −3.76690 + 3.38925I
u = 0.292960 − 0.183199I
a = −3.74455 + 1.03027I
b = 0.667529 + 1.072660I
2.56011 + 2.73446I −3.76690 − 3.38925I
18
III. I
u
3
= hb − a, 32a
5
− 16a
4
+ 16a
3
− 4a
2
+ 2a − 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
5
=
a
a
a
10
=
1
1
a
11
=
1
1
a
4
=
2a
a
a
2
=
−4a
2
−2a
2
+ 1
a
8
=
0
−1
a
7
=
16a
4
8a
4
− 4a
2
− 1
a
3
=
16a
4
24a
4
+ 4a
2
+ 1
a
12
=
1
2
a
6
=
2a
3a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 64a
4
− 32a
3
+ 33a
2
− 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
3
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
4
32(32u
5
+ 16u
4
+ 16u
3
+ 4u
2
+ 2u + 1)
c
5
32(32u
5
− 16u
4
+ 16u
3
− 4u
2
+ 2u − 1)
c
6
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
7
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
8
, c
9
(u − 1)
5
c
10
u
5
c
11
, c
12
(u + 1)
5
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
, c
3
, c
6
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
5
1024(1024y
5
+ 768y
4
+ 256y
3
+ 16y
2
− 4y −1)
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
9
, c
11
c
12
(y −1)
5
c
10
y
5
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.227849 + 0.600076I
b = 0.227849 + 0.600076I
4.22763 − 4.40083I −3.37934 + 2.16111I
u = 1.00000
a = 0.227849 − 0.600076I
b = 0.227849 − 0.600076I
4.22763 + 4.40083I −3.37934 − 2.16111I
u = 1.00000
a = −0.169555 + 0.411188I
b = −0.169555 + 0.411188I
−1.31583 + 1.53058I −9.21097 − 1.00704I
u = 1.00000
a = −0.169555 − 0.411188I
b = −0.169555 − 0.411188I
−1.31583 − 1.53058I −9.21097 + 1.00704I
u = 1.00000
a = 0.383413
b = 0.383413
0.756147 2.43060
22
IV. I
u
4
= hb − u − 1, a + 2u + 1, u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−2u − 1
u + 1
a
10
=
1
−1
a
11
=
u − 1
−u
a
4
=
−u
u + 1
a
2
=
u
−1
a
8
=
−u
1
a
7
=
−u
1
a
3
=
0
u
a
12
=
u
0
a
6
=
−u
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u + 1)
2
c
4
u
2
+ 2u + 2
c
5
u
2
− 2u + 2
c
6
(u − 1)
2
c
7
u
2
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y −1)
2
c
4
, c
5
y
2
+ 4
c
7
y
2
c
8
, c
9
, c
10
c
11
, c
12
(y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000 − 2.00000I
b = 1.00000 + 1.00000I
4.93480 4.00000
u = − 1.000000I
a = −1.00000 + 2.00000I
b = 1.00000 − 1.00000I
4.93480 4.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
2
)(u
5
+ u
4
+ ··· + u + 1)(u
31
− 5u
30
+ ··· + 40u − 7)
2
· (u
39
− 8u
38
+ ··· + 78583u − 7136)
c
2
, c
3
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
31
− u
30
+ ··· + 2u − 1)
2
· (u
39
− 2u
38
+ ··· + 13u + 4)
c
4
1024(u
2
+ 2u + 2)(32u
5
+ 16u
4
+ 16u
3
+ 4u
2
+ 2u + 1)
· (32u
39
− 16u
38
+ ··· + 2u + 2)(u
62
+ u
61
+ ··· − 768736u + 1008568)
c
5
1024(u
2
− 2u + 2)(32u
5
− 16u
4
+ 16u
3
− 4u
2
+ 2u − 1)
· (32u
39
− 16u
38
+ ··· + 2u + 2)(u
62
+ u
61
+ ··· − 768736u + 1008568)
c
6
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
31
− u
30
+ ··· + 2u − 1)
2
· (u
39
− 2u
38
+ ··· + 13u + 4)
c
7
u
2
(u
5
− 3u
4
+ ··· − u + 1)(u
31
+ 3u
30
+ ··· − 13u + 16)
2
· (u
39
− 5u
37
+ ··· + 3664u + 704)
c
8
, c
9
((u − 1)
5
)(u
2
+ 1)(u
39
+ 5u
38
+ ··· − 6u + 1)(u
62
− 11u
61
+ ··· − 11u + 2)
c
10
u
5
(u
2
+ 1)(u
31
− u
30
+ ··· + 2u
2
+ 1)
2
(u
39
+ 3u
38
+ ··· + 5632u + 2048)
c
11
, c
12
((u + 1)
5
)(u
2
+ 1)(u
39
+ 5u
38
+ ··· − 6u + 1)(u
62
− 11u
61
+ ··· − 11u + 2)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
31
+ 23y
30
+ ··· − 640y −49)
2
· (y
39
+ 24y
38
+ ··· + 2799146385y −50922496)
c
2
, c
3
, c
6
((y −1)
2
)(y
5
− 5y
4
+ ··· − y −1)(y
31
− 29y
30
+ ··· − 4y −1)
2
· (y
39
− 36y
38
+ ··· + 145y −16)
c
4
, c
5
1048576(y
2
+ 4)(1024y
5
+ 768y
4
+ 256y
3
+ 16y
2
− 4y −1)
· (1024y
39
+ 21248y
38
+ ··· − 20y −4)
· (y
62
+ 35y
61
+ ··· + 17185261710176y + 1017209410624)
c
7
y
2
(y
5
− y
4
+ ··· + 3y −1)(y
31
− 9y
30
+ ··· + 1481y −256)
2
· (y
39
− 10y
38
+ ··· + 9786624y −495616)
c
8
, c
9
, c
11
c
12
((y −1)
5
)(y + 1)
2
(y
39
+ 23y
38
+ ··· + 16y −1)
· (y
62
+ 43y
61
+ ··· + 59y + 4)
c
10
y
5
(y + 1)
2
(y
31
+ 11y
30
+ ··· − 4y −1)
2
· (y
39
+ 13y
38
+ ··· − 77332480y −4194304)
28
