12a
0287
(K12a
0287
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 11 2 12 10 4 1 7 5
Solving Sequence
4,9
5
1,10
11 6 8 3 2 12 7
c
4
c
9
c
10
c
5
c
8
c
3
c
2
c
12
c
7
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.28450 × 10
165
u
139
+ 9.50032 × 10
165
u
138
+ ··· + 4.17997 × 10
165
b + 1.34496 × 10
167
,
− 3.45422 × 10
167
u
139
+ 5.01824 × 10
166
u
138
+ ··· + 9.19593 × 10
166
a + 3.61218 × 10
168
,
u
140
+ u
139
+ ··· + 14u + 11i
I
u
2
= hu
27
+ 11u
25
+ ··· + b + 10u, 5u
27
+ 37u
25
+ ··· + a + 13u, u
28
+ 7u
26
+ ··· + 5u
2
+ 1i
I
u
3
= hu
2
+ b, u
2
+ a − 1, u
9
+ u
7
+ u
5
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 177 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−5.28 × 10
165
u
139
+ 9.50 × 10
165
u
138
+ · · · + 4.18 × 10
165
b + 1.34 ×
10
167
, −3.45 × 10
167
u
139
+ 5.02 × 10
166
u
138
+ · · · + 9.20 × 10
166
a + 3.61 ×
10
168
, u
140
+ u
139
+ · · · + 14u + 11i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
1
=
3.75625u
139
− 0.545703u
138
+ ··· + 18.3027u − 39.2802
1.26424u
139
− 2.27282u
138
+ ··· − 5.05567u − 32.1762
a
10
=
u
u
a
11
=
−4.21132u
139
− 1.90514u
138
+ ··· − 28.7256u + 13.4197
−0.337816u
139
+ 0.850006u
138
+ ··· − 35.4920u + 9.27420
a
6
=
3.41851u
139
− 0.916546u
138
+ ··· + 18.8635u − 50.7061
−0.955936u
139
− 2.22549u
138
+ ··· + 14.6427u − 34.2575
a
8
=
u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
2
=
3.41935u
139
− 0.0188456u
138
+ ··· + 15.9636u − 43.2660
−0.152810u
139
− 3.05181u
138
+ ··· − 13.3247u − 36.1705
a
12
=
2.90592u
139
− 1.04471u
138
+ ··· + 4.44981u − 54.4255
0.423969u
139
− 2.13116u
138
+ ··· − 9.49081u − 28.3117
a
7
=
−4.11706u
139
− 1.14081u
138
+ ··· − 23.6884u + 35.9336
−2.17162u
139
− 2.14855u
138
+ ··· − 46.4276u + 7.90784
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.40385u
139
+ 2.28727u
138
+ ··· − 1.07060u − 7.80379
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 58u
139
+ ··· + 876101u + 17161
c
2
, c
6
u
140
− 2u
139
+ ··· + 17u + 131
c
3
u
140
− u
139
+ ··· − 24244188u + 5702444
c
4
, c
9
u
140
+ u
139
+ ··· + 14u + 11
c
5
u
140
+ u
139
+ ··· − 143354u + 167897
c
7
, c
11
u
140
+ 10u
139
+ ··· + 49344u + 2992
c
8
u
140
+ 71u
139
+ ··· + 1322u + 121
c
10
u
140
− 23u
139
+ ··· + 640u + 89
c
12
u
140
− u
139
+ ··· + 26u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ 62y
139
+ ··· − 8770457803y + 294499921
c
2
, c
6
y
140
+ 58y
139
+ ··· + 876101y + 17161
c
3
y
140
− 57y
139
+ ··· − 327195805998920y + 32517867573136
c
4
, c
9
y
140
+ 71y
139
+ ··· + 1322y + 121
c
5
y
140
− 39y
139
+ ··· − 427794952430y + 28189402609
c
7
, c
11
y
140
− 102y
139
+ ··· − 552000640y + 8952064
c
8
y
140
+ 7y
139
+ ··· + 781458y + 14641
c
10
y
140
− 13y
139
+ ··· − 780196y + 7921
c
12
y
140
− 13y
139
+ ··· + 104y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.911969 + 0.414142I
a = −0.295171 + 0.791970I
b = 0.539256 + 0.590000I
1.31840 − 4.43564I 0
u = 0.911969 − 0.414142I
a = −0.295171 − 0.791970I
b = 0.539256 − 0.590000I
1.31840 + 4.43564I 0
u = −0.724107 + 0.706862I
a = 1.57131 − 0.24069I
b = 1.33717 + 0.90378I
7.44163 − 5.54565I 0
u = −0.724107 − 0.706862I
a = 1.57131 + 0.24069I
b = 1.33717 − 0.90378I
7.44163 + 5.54565I 0
u = 0.573448 + 0.872478I
a = −1.38716 + 0.30535I
b = −1.41475 + 1.27921I
0.98342 + 4.84804I 0
u = 0.573448 − 0.872478I
a = −1.38716 − 0.30535I
b = −1.41475 − 1.27921I
0.98342 − 4.84804I 0
u = −0.249323 + 0.915343I
a = 0.113498 + 0.814881I
b = −0.415139 − 0.488688I
−3.96870 − 1.13105I 0
u = −0.249323 − 0.915343I
a = 0.113498 − 0.814881I
b = −0.415139 + 0.488688I
−3.96870 + 1.13105I 0
u = −0.371737 + 0.986379I
a = 1.31279 + 1.63815I
b = −0.17991 + 2.38626I
1.05783 + 3.25130I 0
u = −0.371737 − 0.986379I
a = 1.31279 − 1.63815I
b = −0.17991 − 2.38626I
1.05783 − 3.25130I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503794 + 0.799252I
a = −0.859487 + 0.896640I
b = −0.12251 + 1.61088I
1.76715 + 2.73079I 0
u = 0.503794 − 0.799252I
a = −0.859487 − 0.896640I
b = −0.12251 − 1.61088I
1.76715 − 2.73079I 0
u = 0.319065 + 0.887593I
a = −1.53683 + 0.81693I
b = −1.94899 + 1.51337I
1.17088 + 5.15716I 0
u = 0.319065 − 0.887593I
a = −1.53683 − 0.81693I
b = −1.94899 − 1.51337I
1.17088 − 5.15716I 0
u = 0.760627 + 0.745237I
a = −1.45122 − 0.27255I
b = −1.30533 + 0.94896I
5.97477 + 11.24740I 0
u = 0.760627 − 0.745237I
a = −1.45122 + 0.27255I
b = −1.30533 − 0.94896I
5.97477 − 11.24740I 0
u = 0.386677 + 0.999740I
a = −1.44116 + 1.04277I
b = −0.41987 + 2.11426I
1.72635 + 2.31795I 0
u = 0.386677 − 0.999740I
a = −1.44116 − 1.04277I
b = −0.41987 − 2.11426I
1.72635 − 2.31795I 0
u = −0.529092 + 0.760841I
a = −2.18860 + 0.27623I
b = −1.37970 − 1.09749I
1.35663 − 6.65828I 0
u = −0.529092 − 0.760841I
a = −2.18860 − 0.27623I
b = −1.37970 + 1.09749I
1.35663 + 6.65828I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882048 + 0.278481I
a = 0.009019 + 0.462736I
b = 0.146813 + 0.345498I
0.167945 − 0.191438I 0
u = 0.882048 − 0.278481I
a = 0.009019 − 0.462736I
b = 0.146813 − 0.345498I
0.167945 + 0.191438I 0
u = −0.911020 + 0.149587I
a = −0.404056 + 0.037828I
b = 0.174739 + 0.028208I
−0.81281 + 3.32987I 0
u = −0.911020 − 0.149587I
a = −0.404056 − 0.037828I
b = 0.174739 − 0.028208I
−0.81281 − 3.32987I 0
u = −0.432089 + 0.996285I
a = −2.34096 − 0.75184I
b = −1.41076 − 1.40605I
0.95739 − 6.37467I 0
u = −0.432089 − 0.996285I
a = −2.34096 + 0.75184I
b = −1.41076 + 1.40605I
0.95739 + 6.37467I 0
u = −0.855066 + 0.311267I
a = −1.47002 − 0.74678I
b = 0.17531 − 1.42918I
3.4637 + 14.2963I 0
u = −0.855066 − 0.311267I
a = −1.47002 + 0.74678I
b = 0.17531 + 1.42918I
3.4637 − 14.2963I 0
u = 0.383480 + 1.044560I
a = 1.29468 − 2.09361I
b = 1.40886 − 2.17172I
0.19673 − 2.64784I 0
u = 0.383480 − 1.044560I
a = 1.29468 + 2.09361I
b = 1.40886 + 2.17172I
0.19673 + 2.64784I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.822294 + 0.316409I
a = 1.46564 − 0.72560I
b = −0.05027 − 1.48893I
5.30338 − 8.23856I 0
u = 0.822294 − 0.316409I
a = 1.46564 + 0.72560I
b = −0.05027 + 1.48893I
5.30338 + 8.23856I 0
u = −0.407338 + 1.046110I
a = 1.37012 + 0.73523I
b = 1.93075 + 1.96344I
1.91948 − 1.55357I 0
u = −0.407338 − 1.046110I
a = 1.37012 − 0.73523I
b = 1.93075 − 1.96344I
1.91948 + 1.55357I 0
u = −0.277132 + 1.091270I
a = 0.210019 + 0.713495I
b = −0.425588 + 0.144621I
−3.56177 − 0.25782I 0
u = −0.277132 − 1.091270I
a = 0.210019 − 0.713495I
b = −0.425588 − 0.144621I
−3.56177 + 0.25782I 0
u = 0.557324 + 0.670520I
a = 1.90723 + 0.19763I
b = 1.009950 − 0.920696I
2.19061 + 1.51698I 0
u = 0.557324 − 0.670520I
a = 1.90723 − 0.19763I
b = 1.009950 + 0.920696I
2.19061 − 1.51698I 0
u = −0.588752 + 0.639692I
a = 0.879389 + 0.930406I
b = −0.13286 + 1.46117I
1.77091 + 2.37270I 0
u = −0.588752 − 0.639692I
a = 0.879389 − 0.930406I
b = −0.13286 − 1.46117I
1.77091 − 2.37270I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685835 + 0.900388I
a = −0.399211 − 1.303950I
b = 0.45329 − 1.43925I
6.88187 + 0.21608I 0
u = −0.685835 − 0.900388I
a = −0.399211 + 1.303950I
b = 0.45329 + 1.43925I
6.88187 − 0.21608I 0
u = −0.497345 + 1.026600I
a = −0.05339 − 2.30110I
b = 0.14269 − 2.52943I
4.21178 − 2.96840I 0
u = −0.497345 − 1.026600I
a = −0.05339 + 2.30110I
b = 0.14269 + 2.52943I
4.21178 + 2.96840I 0
u = 0.742425 + 0.885018I
a = 0.371900 − 1.170730I
b = −0.575239 − 1.275530I
5.58093 − 5.64547I 0
u = 0.742425 − 0.885018I
a = 0.371900 + 1.170730I
b = −0.575239 + 1.275530I
5.58093 + 5.64547I 0
u = −0.288711 + 1.120020I
a = 0.055580 + 0.507806I
b = −0.830418 − 0.229523I
−3.58932 + 0.00780I 0
u = −0.288711 − 1.120020I
a = 0.055580 − 0.507806I
b = −0.830418 + 0.229523I
−3.58932 − 0.00780I 0
u = 0.535179 + 1.051400I
a = −1.26686 + 0.76744I
b = −1.33178 + 2.30530I
2.70191 + 0.79233I 0
u = 0.535179 − 1.051400I
a = −1.26686 − 0.76744I
b = −1.33178 − 2.30530I
2.70191 − 0.79233I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085516 + 1.180600I
a = −0.123421 + 0.432627I
b = −0.128542 − 0.518350I
−4.53995 − 1.81669I 0
u = 0.085516 − 1.180600I
a = −0.123421 − 0.432627I
b = −0.128542 + 0.518350I
−4.53995 + 1.81669I 0
u = −0.798315 + 0.158064I
a = −0.741241 + 0.157814I
b = −0.0818703 − 0.0112551I
−0.86862 + 3.34041I 0
u = −0.798315 − 0.158064I
a = −0.741241 − 0.157814I
b = −0.0818703 + 0.0112551I
−0.86862 − 3.34041I 0
u = 0.510897 + 1.071460I
a = 0.14755 − 1.82024I
b = −1.51281 − 1.36578I
2.69466 + 4.26697I 0
u = 0.510897 − 1.071460I
a = 0.14755 + 1.82024I
b = −1.51281 + 1.36578I
2.69466 − 4.26697I 0
u = −0.504019 + 1.077930I
a = 1.31667 + 0.76730I
b = 1.59642 + 2.35524I
2.66785 − 5.26634I 0
u = −0.504019 − 1.077930I
a = 1.31667 − 0.76730I
b = 1.59642 − 2.35524I
2.66785 + 5.26634I 0
u = −0.777543 + 0.223808I
a = −1.45938 − 0.71051I
b = −0.260728 − 1.189920I
−1.90870 + 5.88396I 4.00000 − 6.87965I
u = −0.777543 − 0.223808I
a = −1.45938 + 0.71051I
b = −0.260728 + 1.189920I
−1.90870 − 5.88396I 4.00000 + 6.87965I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.379907 + 1.133040I
a = −0.392306 + 0.125578I
b = 0.359716 − 0.772154I
−7.48220 + 2.14063I 0
u = 0.379907 − 1.133040I
a = −0.392306 − 0.125578I
b = 0.359716 + 0.772154I
−7.48220 − 2.14063I 0
u = 0.764176 + 0.247294I
a = −1.78922 + 0.32789I
b = 0.212648 + 1.258030I
−0.93479 − 7.87402I 4.00000 + 7.57769I
u = 0.764176 − 0.247294I
a = −1.78922 − 0.32789I
b = 0.212648 − 1.258030I
−0.93479 + 7.87402I 4.00000 − 7.57769I
u = −0.530941 + 1.073870I
a = −0.59649 − 1.90781I
b = 1.22556 − 1.92500I
2.35475 − 9.76727I 0
u = −0.530941 − 1.073870I
a = −0.59649 + 1.90781I
b = 1.22556 + 1.92500I
2.35475 + 9.76727I 0
u = 0.511201 + 1.085870I
a = −0.81134 − 1.71392I
b = −0.84329 − 2.20566I
1.15469 + 9.56512I 0
u = 0.511201 − 1.085870I
a = −0.81134 + 1.71392I
b = −0.84329 + 2.20566I
1.15469 − 9.56512I 0
u = −0.715536 + 0.348808I
a = 0.947491 + 0.152160I
b = 0.076459 + 1.040320I
0.59136 + 2.31044I 4.00000 − 5.49298I
u = −0.715536 − 0.348808I
a = 0.947491 − 0.152160I
b = 0.076459 − 1.040320I
0.59136 − 2.31044I 4.00000 + 5.49298I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.300124 + 1.170360I
a = 0.060639 + 0.271340I
b = 1.053180 − 0.615704I
−5.22041 − 4.56927I 0
u = 0.300124 − 1.170360I
a = 0.060639 − 0.271340I
b = 1.053180 + 0.615704I
−5.22041 + 4.56927I 0
u = 0.222165 + 1.188980I
a = 0.569913 − 0.345685I
b = −0.323401 + 0.381331I
0.41796 − 5.15841I 0
u = 0.222165 − 1.188980I
a = 0.569913 + 0.345685I
b = −0.323401 − 0.381331I
0.41796 + 5.15841I 0
u = 0.503060 + 1.102730I
a = −0.705803 + 0.647032I
b = −0.59454 + 1.28486I
−1.09806 + 3.76347I 0
u = 0.503060 − 1.102730I
a = −0.705803 − 0.647032I
b = −0.59454 − 1.28486I
−1.09806 − 3.76347I 0
u = 0.525428 + 1.094590I
a = −2.09927 + 1.37574I
b = −1.36521 + 1.80930I
2.95162 + 7.00188I 0
u = 0.525428 − 1.094590I
a = −2.09927 − 1.37574I
b = −1.36521 − 1.80930I
2.95162 − 7.00188I 0
u = 0.390175 + 1.152860I
a = −0.237640 − 0.174763I
b = −0.434998 + 0.526964I
−1.73181 + 3.89697I 0
u = 0.390175 − 1.152860I
a = −0.237640 + 0.174763I
b = −0.434998 − 0.526964I
−1.73181 − 3.89697I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.725049 + 0.286531I
a = 1.59501 + 0.27107I
b = −0.073027 + 1.258600I
0.56147 + 2.93715I 6.93912 − 3.36871I
u = −0.725049 − 0.286531I
a = 1.59501 − 0.27107I
b = −0.073027 − 1.258600I
0.56147 − 2.93715I 6.93912 + 3.36871I
u = 0.256246 + 1.194190I
a = −0.403224 + 0.526139I
b = −0.428589 + 0.014810I
−4.69523 + 3.15950I 0
u = 0.256246 − 1.194190I
a = −0.403224 − 0.526139I
b = −0.428589 − 0.014810I
−4.69523 − 3.15950I 0
u = −0.309365 + 1.185560I
a = −0.860502 + 0.079393I
b = −0.199008 + 0.683391I
−6.20028 + 2.41913I 0
u = −0.309365 − 1.185560I
a = −0.860502 − 0.079393I
b = −0.199008 − 0.683391I
−6.20028 − 2.41913I 0
u = 0.493769 + 1.131300I
a = 1.84984 − 1.07514I
b = 1.68788 − 2.15259I
−6.69268 + 5.68760I 0
u = 0.493769 − 1.131300I
a = 1.84984 + 1.07514I
b = 1.68788 + 2.15259I
−6.69268 − 5.68760I 0
u = −0.412124 + 1.164170I
a = 0.658848 + 0.730608I
b = 0.647271 + 0.996129I
−4.64683 − 0.60445I 0
u = −0.412124 − 1.164170I
a = 0.658848 − 0.730608I
b = 0.647271 − 0.996129I
−4.64683 + 0.60445I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.268998 + 0.715960I
a = −1.06054 − 2.24870I
b = −0.680161 − 1.093680I
3.35259 − 1.39528I 1.67927 + 4.08016I
u = −0.268998 − 0.715960I
a = −1.06054 + 2.24870I
b = −0.680161 + 1.093680I
3.35259 + 1.39528I 1.67927 − 4.08016I
u = −0.309936 + 0.693725I
a = −1.48957 + 1.16494I
b = −1.51730 + 0.18423I
−2.72477 − 1.41570I −0.24846 + 4.76390I
u = −0.309936 − 0.693725I
a = −1.48957 − 1.16494I
b = −1.51730 − 0.18423I
−2.72477 + 1.41570I −0.24846 − 4.76390I
u = −0.556829 + 1.112940I
a = −1.33823 − 0.91168I
b = −0.68459 − 1.72487I
−1.64506 − 7.18301I 0
u = −0.556829 − 1.112940I
a = −1.33823 + 0.91168I
b = −0.68459 + 1.72487I
−1.64506 + 7.18301I 0
u = −0.217648 + 1.225930I
a = −0.420472 − 0.246603I
b = 0.455392 + 0.573187I
−1.61265 + 11.02410I 0
u = −0.217648 − 1.225930I
a = −0.420472 + 0.246603I
b = 0.455392 − 0.573187I
−1.61265 − 11.02410I 0
u = 0.607376 + 0.445106I
a = 2.40457 − 0.89073I
b = 0.100803 − 0.915692I
4.46559 + 3.74657I 10.94549 − 5.79337I
u = 0.607376 − 0.445106I
a = 2.40457 + 0.89073I
b = 0.100803 + 0.915692I
4.46559 − 3.74657I 10.94549 + 5.79337I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542497 + 1.128160I
a = −1.71190 − 1.08526I
b = −1.18635 − 2.35380I
−1.87982 − 7.74973I 0
u = −0.542497 − 1.128160I
a = −1.71190 + 1.08526I
b = −1.18635 + 2.35380I
−1.87982 + 7.74973I 0
u = −0.271336 + 1.223150I
a = 0.158492 + 0.175972I
b = 0.197295 + 0.823123I
−5.55443 − 0.46075I 0
u = −0.271336 − 1.223150I
a = 0.158492 − 0.175972I
b = 0.197295 − 0.823123I
−5.55443 + 0.46075I 0
u = −0.536975 + 0.504589I
a = 2.29279 − 0.29116I
b = 1.80332 + 0.27481I
5.74913 − 1.25065I 17.0911 + 2.4895I
u = −0.536975 − 0.504589I
a = 2.29279 + 0.29116I
b = 1.80332 − 0.27481I
5.74913 + 1.25065I 17.0911 − 2.4895I
u = −0.616872 + 0.399769I
a = 1.11263 − 1.45968I
b = 1.08954 + 1.16118I
4.31207 + 5.22253I 11.41114 − 7.60039I
u = −0.616872 − 0.399769I
a = 1.11263 + 1.45968I
b = 1.08954 − 1.16118I
4.31207 − 5.22253I 11.41114 + 7.60039I
u = 0.542135 + 1.149850I
a = 1.78469 − 1.12003I
b = 1.39724 − 2.59801I
−3.56785 + 12.76600I 0
u = 0.542135 − 1.149850I
a = 1.78469 + 1.12003I
b = 1.39724 + 2.59801I
−3.56785 − 12.76600I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.537064 + 1.158640I
a = 1.63348 + 1.41062I
b = 1.40218 + 2.24229I
−4.64179 − 10.77630I 0
u = −0.537064 − 1.158640I
a = 1.63348 − 1.41062I
b = 1.40218 − 2.24229I
−4.64179 + 10.77630I 0
u = −0.629792 + 1.120880I
a = −1.384600 − 0.218094I
b = −1.35353 − 1.13882I
−0.38936 − 5.55432I 0
u = −0.629792 − 1.120880I
a = −1.384600 + 0.218094I
b = −1.35353 + 1.13882I
−0.38936 + 5.55432I 0
u = 0.628629 + 0.334137I
a = 1.22200 − 0.78546I
b = 0.49265 − 1.81699I
5.13183 − 2.46029I 14.5121 + 3.1935I
u = 0.628629 − 0.334137I
a = 1.22200 + 0.78546I
b = 0.49265 + 1.81699I
5.13183 + 2.46029I 14.5121 − 3.1935I
u = 0.579520 + 1.151040I
a = −1.84127 + 1.20626I
b = −1.42150 + 2.37650I
2.81809 + 13.44720I 0
u = 0.579520 − 1.151040I
a = −1.84127 − 1.20626I
b = −1.42150 − 2.37650I
2.81809 − 13.44720I 0
u = −0.539679 + 1.174260I
a = 0.519756 + 0.565749I
b = 0.568295 + 1.209960I
−3.78985 − 8.29502I 0
u = −0.539679 − 1.174260I
a = 0.519756 − 0.565749I
b = 0.568295 − 1.209960I
−3.78985 + 8.29502I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588027 + 1.163950I
a = 1.82276 + 1.12851I
b = 1.50080 + 2.40647I
0.9078 − 19.6213I 0
u = −0.588027 − 1.163950I
a = 1.82276 − 1.12851I
b = 1.50080 − 2.40647I
0.9078 + 19.6213I 0
u = 0.557247 + 1.181640I
a = 0.792973 − 0.315005I
b = 0.704654 − 0.506911I
−2.62882 + 5.45005I 0
u = 0.557247 − 1.181640I
a = 0.792973 + 0.315005I
b = 0.704654 + 0.506911I
−2.62882 − 5.45005I 0
u = −0.435170 + 1.232080I
a = −0.1230310 − 0.0430721I
b = −0.042932 + 0.484585I
−4.41309 − 8.15300I 0
u = −0.435170 − 1.232080I
a = −0.1230310 + 0.0430721I
b = −0.042932 − 0.484585I
−4.41309 + 8.15300I 0
u = 0.567332 + 0.394477I
a = 1.019630 + 0.074384I
b = 0.363102 − 0.269838I
1.049830 + 0.546340I 8.89907 − 4.13660I
u = 0.567332 − 0.394477I
a = 1.019630 − 0.074384I
b = 0.363102 + 0.269838I
1.049830 − 0.546340I 8.89907 + 4.13660I
u = 0.631252 + 1.156750I
a = 1.223300 − 0.130066I
b = 1.36556 − 0.88130I
−0.97757 + 10.10480I 0
u = 0.631252 − 1.156750I
a = 1.223300 + 0.130066I
b = 1.36556 + 0.88130I
−0.97757 − 10.10480I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524327 + 0.417163I
a = −0.767776 − 0.494553I
b = −0.45482 − 1.90743I
3.51278 − 4.24004I 10.95131 + 5.69177I
u = −0.524327 − 0.417163I
a = −0.767776 + 0.494553I
b = −0.45482 + 1.90743I
3.51278 + 4.24004I 10.95131 − 5.69177I
u = 0.550711 + 0.376242I
a = −0.60192 − 1.85435I
b = −1.25214 + 0.79998I
4.68590 + 0.06128I 11.69405 + 1.52199I
u = 0.550711 − 0.376242I
a = −0.60192 + 1.85435I
b = −1.25214 − 0.79998I
4.68590 − 0.06128I 11.69405 − 1.52199I
u = 0.644120 + 0.158741I
a = −1.73023 + 0.65345I
b = 0.062149 + 1.058440I
−3.99564 − 1.31752I −0.467328 + 0.682592I
u = 0.644120 − 0.158741I
a = −1.73023 − 0.65345I
b = 0.062149 − 1.058440I
−3.99564 + 1.31752I −0.467328 − 0.682592I
u = 0.566261 + 0.341356I
a = −2.17889 − 0.76525I
b = −1.276800 − 0.452358I
3.27891 − 5.20337I 9.05791 + 8.92202I
u = 0.566261 − 0.341356I
a = −2.17889 + 0.76525I
b = −1.276800 + 0.452358I
3.27891 + 5.20337I 9.05791 − 8.92202I
u = −0.529988 + 0.369897I
a = −2.77730 − 1.24477I
b = −0.121672 − 0.729596I
4.70950 + 1.00343I 11.45787 − 2.33178I
u = −0.529988 − 0.369897I
a = −2.77730 + 1.24477I
b = −0.121672 + 0.729596I
4.70950 − 1.00343I 11.45787 + 2.33178I
18
II. I
u
2
=
hu
27
+11u
25
+· · ·+b+10u, 5u
27
+37u
25
+· · ·+a+13u, u
28
+7u
26
+· · ·+5u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
1
=
−5u
27
− 37u
25
+ ··· − 54u
3
− 13u
−u
27
− 11u
25
+ ··· − 36u
3
− 10u
a
10
=
u
u
a
11
=
4u
27
+ 5u
26
+ ··· + u + 3
2u
27
+ 3u
26
+ ··· + 5u + 5
a
6
=
6u
27
− u
26
+ ··· + 5u − 7
4u
27
+ u
26
+ ··· + 6u − 4
a
8
=
u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
2
=
−2u
27
− 16u
25
+ ··· − 24u
3
− 6u
u
27
+ 3u
25
+ ··· − 19u
3
− 6u
a
12
=
−2u
27
− 17u
25
+ ··· − 30u
3
− 8u
−4u
25
− 25u
23
+ ··· − 26u
3
− 7u
a
7
=
7u
27
+ 44u
25
+ ··· + 8u + 1
7u
27
− u
26
+ ··· − u
2
+ 12u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
27
− 8u
26
+ 56u
25
− 48u
24
+ 199u
23
− 160u
22
+ 448u
21
−
345u
20
+ 699u
19
− 548u
18
+ 809u
17
− 678u
16
+ 768u
15
− 716u
14
+ 718u
13
− 661u
12
+
695u
11
− 535u
10
+ 617u
9
− 351u
8
+ 417u
7
− 196u
6
+ 218u
5
− 92u
4
+ 77u
3
− 40u
2
+ 21u
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
28
− 13u
27
+ ··· − 13u + 1
c
2
u
28
− u
27
+ ··· − u + 1
c
3
u
28
− 5u
26
+ ··· − 3u + 2
c
4
u
28
+ 7u
26
+ ··· + 5u
2
+ 1
c
5
u
28
+ 2u
26
+ ··· − u
2
+ 1
c
6
u
28
+ u
27
+ ··· + u + 1
c
7
u
28
− 2u
27
+ ··· − 9u + 2
c
8
u
28
− 14u
27
+ ··· − 10u + 1
c
9
u
28
+ 7u
26
+ ··· + 5u
2
+ 1
c
10
u
28
+ 2u
27
+ ··· − 4u + 1
c
11
u
28
+ 2u
27
+ ··· + 9u + 2
c
12
u
28
− u
26
+ ··· + 2u
2
+ 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 17y
27
+ ··· + 9y + 1
c
2
, c
6
y
28
+ 13y
27
+ ··· + 13y + 1
c
3
y
28
− 10y
27
+ ··· + 19y + 4
c
4
, c
9
y
28
+ 14y
27
+ ··· + 10y + 1
c
5
y
28
+ 4y
27
+ ··· − 2y + 1
c
7
, c
11
y
28
− 30y
27
+ ··· − 81y + 4
c
8
y
28
+ 2y
27
+ ··· + 14y + 1
c
10
y
28
− 6y
27
+ ··· − 4y + 1
c
12
y
28
− 2y
27
+ ··· + 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246356 + 0.992130I
a = −0.197522 + 0.969064I
b = −0.746827 − 0.175524I
−4.52501 − 0.87421I −8.56542 + 0.29180I
u = −0.246356 − 0.992130I
a = −0.197522 − 0.969064I
b = −0.746827 + 0.175524I
−4.52501 + 0.87421I −8.56542 − 0.29180I
u = −0.864207 + 0.425314I
a = 0.428824 + 0.413511I
b = −0.309350 + 0.656983I
0.445438 + 0.785261I 1.99103 − 6.10447I
u = −0.864207 − 0.425314I
a = 0.428824 − 0.413511I
b = −0.309350 − 0.656983I
0.445438 − 0.785261I 1.99103 + 6.10447I
u = 0.923717 + 0.264773I
a = −0.523436 + 0.318504I
b = 0.078087 + 0.440572I
−0.61804 − 3.74943I 4.42797 + 12.08009I
u = 0.923717 − 0.264773I
a = −0.523436 − 0.318504I
b = 0.078087 − 0.440572I
−0.61804 + 3.74943I 4.42797 − 12.08009I
u = −0.416986 + 1.029260I
a = 2.06937 + 1.93429I
b = 1.21889 + 2.46136I
0.90891 + 1.92617I 5.46647 + 0.15507I
u = −0.416986 − 1.029260I
a = 2.06937 − 1.93429I
b = 1.21889 − 2.46136I
0.90891 − 1.92617I 5.46647 − 0.15507I
u = 0.456663 + 1.018340I
a = −1.84400 + 1.16970I
b = −1.64937 + 2.49156I
2.67136 + 3.59920I 7.09940 − 4.36419I
u = 0.456663 − 1.018340I
a = −1.84400 − 1.16970I
b = −1.64937 − 2.49156I
2.67136 − 3.59920I 7.09940 + 4.36419I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489765 + 1.030170I
a = −0.416119 + 0.278603I
b = −1.18589 + 1.19313I
2.92343 + 2.60230I 7.01890 − 2.95448I
u = 0.489765 − 1.030170I
a = −0.416119 − 0.278603I
b = −1.18589 − 1.19313I
2.92343 − 2.60230I 7.01890 + 2.95448I
u = −0.520699 + 1.058000I
a = −1.106450 − 0.151704I
b = −0.212517 − 0.139801I
1.69646 − 8.40594I 5.71938 + 7.38263I
u = −0.520699 − 1.058000I
a = −1.106450 + 0.151704I
b = −0.212517 + 0.139801I
1.69646 + 8.40594I 5.71938 − 7.38263I
u = 0.224911 + 1.184700I
a = −0.324907 + 0.067025I
b = −0.100430 − 0.614349I
−5.74281 − 0.38088I −3.97959 + 2.61173I
u = 0.224911 − 1.184700I
a = −0.324907 − 0.067025I
b = −0.100430 + 0.614349I
−5.74281 + 0.38088I −3.97959 − 2.61173I
u = −0.576647 + 0.515336I
a = −0.063705 − 0.170290I
b = −0.344606 + 0.835452I
3.39068 + 3.99126I 8.30649 − 2.20399I
u = −0.576647 − 0.515336I
a = −0.063705 + 0.170290I
b = −0.344606 − 0.835452I
3.39068 − 3.99126I 8.30649 + 2.20399I
u = 0.474600 + 0.580912I
a = 0.76177 − 1.35268I
b = 0.186589 − 0.083242I
4.37871 + 1.42891I 9.98847 − 4.18139I
u = 0.474600 − 0.580912I
a = 0.76177 + 1.35268I
b = 0.186589 + 0.083242I
4.37871 − 1.42891I 9.98847 + 4.18139I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380766 + 0.639682I
a = 2.05634 − 2.13605I
b = 0.49813 − 1.64440I
3.99424 + 0.03631I 9.17658 − 1.11949I
u = 0.380766 − 0.639682I
a = 2.05634 + 2.13605I
b = 0.49813 + 1.64440I
3.99424 − 0.03631I 9.17658 + 1.11949I
u = −0.285807 + 0.668453I
a = −2.47761 − 1.71909I
b = −1.27808 − 2.22443I
2.30039 − 5.11093I 8.86572 + 7.29347I
u = −0.285807 − 0.668453I
a = −2.47761 + 1.71909I
b = −1.27808 + 2.22443I
2.30039 + 5.11093I 8.86572 − 7.29347I
u = −0.597515 + 1.126700I
a = −1.151500 − 0.460817I
b = −0.82283 − 1.25243I
−1.74073 − 6.17220I 0.98791 + 5.18891I
u = −0.597515 − 1.126700I
a = −1.151500 + 0.460817I
b = −0.82283 + 1.25243I
−1.74073 + 6.17220I 0.98791 − 5.18891I
u = 0.557794 + 1.188720I
a = 0.788938 − 0.752916I
b = 0.66820 − 1.34798I
−3.50329 + 9.08102I 2.99669 − 10.86058I
u = 0.557794 − 1.188720I
a = 0.788938 + 0.752916I
b = 0.66820 + 1.34798I
−3.50329 − 9.08102I 2.99669 + 10.86058I
26
III. I
u
3
= hu
2
+ b, u
2
+ a − 1, u
9
+ u
7
+ u
5
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
10
=
u
u
a
11
=
u
3
u
3
+ u
a
6
=
−u
8
− u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
8
=
u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
2
=
−u
6
− u
4
− 2u
2
+ u + 1
u
8
− 2u
2
+ u
a
12
=
u
4
− u
2
+ 1
−u
6
− u
2
a
7
=
−u
4
+ u
3
+ u
2
− 1
u
6
+ u
3
+ u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 15u
5
+ 18u
4
+ 14u
3
+ 8u
2
+ u − 1
c
2
, c
6
, c
8
u
9
+ 2u
8
+ 3u
7
+ 2u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ u − 1
c
3
u
9
+ u
7
− 3u
6
+ 3u
5
− 2u
4
+ 2u
3
+ 5u
2
− 3u − 5
c
4
, c
9
, c
10
u
9
+ u
7
+ u
5
+ u − 1
c
5
u
9
+ 3u
7
− 4u
6
− 3u
5
− 4u
4
+ 6u
3
+ 2u
2
+ u − 3
c
7
, c
11
(u − 1)
9
c
12
u
9
− 2u
8
+ 7u
7
− 10u
6
+ 15u
5
− 18u
4
+ 14u
3
− 8u
2
+ u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
9
+ 10y
8
+ 39y
7
+ 66y
6
+ 31y
5
− 46y
4
− 42y
3
+ 17y −1
c
2
, c
6
, c
8
y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 18y
4
+ 14y
3
+ 8y
2
+ y −1
c
3
y
9
+ 2y
8
+ 7y
7
+ y
6
− 5y
5
+ 32y
4
− 24y
3
− 57y
2
+ 59y −25
c
4
, c
9
, c
10
y
9
+ 2y
8
+ 3y
7
+ 2y
6
+ 3y
5
+ 2y
4
+ 2y
3
+ y −1
c
5
y
9
+ 6y
8
+ 3y
7
− 22y
6
+ 15y
5
− 30y
4
+ 22y
3
− 16y
2
+ 13y −9
c
7
, c
11
(y −1)
9
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871677 + 0.460936I
a = 0.452641 + 0.803575I
b = −0.547359 + 0.803575I
1.64493 6.00000
u = −0.871677 − 0.460936I
a = 0.452641 − 0.803575I
b = −0.547359 − 0.803575I
1.64493 6.00000
u = 0.678786 + 0.656288I
a = 0.969964 − 0.890958I
b = −0.030036 − 0.890958I
1.64493 6.00000
u = 0.678786 − 0.656288I
a = 0.969964 + 0.890958I
b = −0.030036 + 0.890958I
1.64493 6.00000
u = 0.345109 + 1.036330I
a = 1.95487 − 0.71529I
b = 0.954870 − 0.715290I
1.64493 6.00000
u = 0.345109 − 1.036330I
a = 1.95487 + 0.71529I
b = 0.954870 + 0.715290I
1.64493 6.00000
u = −0.503510 + 1.059650I
a = 1.86934 + 1.06709I
b = 0.869337 + 1.067090I
1.64493 6.00000
u = −0.503510 − 1.059650I
a = 1.86934 − 1.06709I
b = 0.869337 − 1.067090I
1.64493 6.00000
u = 0.702584
a = 0.506375
b = −0.493625
1.64493 6.00000
30
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 15u
5
+ 18u
4
+ 14u
3
+ 8u
2
+ u − 1)
· (u
28
− 13u
27
+ ··· − 13u + 1)(u
140
+ 58u
139
+ ··· + 876101u + 17161)
c
2
(u
9
+ 2u
8
+ ··· + u − 1)(u
28
− u
27
+ ··· − u + 1)
· (u
140
− 2u
139
+ ··· + 17u + 131)
c
3
(u
9
+ u
7
− 3u
6
+ 3u
5
− 2u
4
+ 2u
3
+ 5u
2
− 3u − 5)
· (u
28
− 5u
26
+ ··· − 3u + 2)(u
140
− u
139
+ ··· − 2.42442 × 10
7
u + 5702444)
c
4
(u
9
+ u
7
+ u
5
+ u − 1)(u
28
+ 7u
26
+ ··· + 5u
2
+ 1)
· (u
140
+ u
139
+ ··· + 14u + 11)
c
5
(u
9
+ 3u
7
− 4u
6
− 3u
5
− 4u
4
+ 6u
3
+ 2u
2
+ u − 3)
· (u
28
+ 2u
26
+ ··· − u
2
+ 1)(u
140
+ u
139
+ ··· − 143354u + 167897)
c
6
(u
9
+ 2u
8
+ ··· + u − 1)(u
28
+ u
27
+ ··· + u + 1)
· (u
140
− 2u
139
+ ··· + 17u + 131)
c
7
((u − 1)
9
)(u
28
− 2u
27
+ ··· − 9u + 2)
· (u
140
+ 10u
139
+ ··· + 49344u + 2992)
c
8
(u
9
+ 2u
8
+ 3u
7
+ 2u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ u − 1)
· (u
28
− 14u
27
+ ··· − 10u + 1)(u
140
+ 71u
139
+ ··· + 1322u + 121)
c
9
(u
9
+ u
7
+ u
5
+ u − 1)(u
28
+ 7u
26
+ ··· + 5u
2
+ 1)
· (u
140
+ u
139
+ ··· + 14u + 11)
c
10
(u
9
+ u
7
+ u
5
+ u − 1)(u
28
+ 2u
27
+ ··· − 4u + 1)
· (u
140
− 23u
139
+ ··· + 640u + 89)
c
11
((u − 1)
9
)(u
28
+ 2u
27
+ ··· + 9u + 2)
· (u
140
+ 10u
139
+ ··· + 49344u + 2992)
c
12
(u
9
− 2u
8
+ 7u
7
− 10u
6
+ 15u
5
− 18u
4
+ 14u
3
− 8u
2
+ u + 1)
· (u
28
− u
26
+ ··· + 2u
2
+ 1)(u
140
− u
139
+ ··· + 26u + 1)
31
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
+ 10y
8
+ 39y
7
+ 66y
6
+ 31y
5
− 46y
4
− 42y
3
+ 17y −1)
· (y
28
+ 17y
27
+ ··· + 9y + 1)
· (y
140
+ 62y
139
+ ··· − 8770457803y + 294499921)
c
2
, c
6
(y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 18y
4
+ 14y
3
+ 8y
2
+ y −1)
· (y
28
+ 13y
27
+ ··· + 13y + 1)(y
140
+ 58y
139
+ ··· + 876101y + 17161)
c
3
(y
9
+ 2y
8
+ 7y
7
+ y
6
− 5y
5
+ 32y
4
− 24y
3
− 57y
2
+ 59y −25)
· (y
28
− 10y
27
+ ··· + 19y + 4)
· (y
140
− 57y
139
+ ··· − 327195805998920y + 32517867573136)
c
4
, c
9
(y
9
+ 2y
8
+ 3y
7
+ 2y
6
+ 3y
5
+ 2y
4
+ 2y
3
+ y −1)
· (y
28
+ 14y
27
+ ··· + 10y + 1)(y
140
+ 71y
139
+ ··· + 1322y + 121)
c
5
(y
9
+ 6y
8
+ 3y
7
− 22y
6
+ 15y
5
− 30y
4
+ 22y
3
− 16y
2
+ 13y −9)
· (y
28
+ 4y
27
+ ··· − 2y + 1)
· (y
140
− 39y
139
+ ··· − 427794952430y + 28189402609)
c
7
, c
11
((y −1)
9
)(y
28
− 30y
27
+ ··· − 81y + 4)
· (y
140
− 102y
139
+ ··· − 552000640y + 8952064)
c
8
(y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 18y
4
+ 14y
3
+ 8y
2
+ y −1)
· (y
28
+ 2y
27
+ ··· + 14y + 1)(y
140
+ 7y
139
+ ··· + 781458y + 14641)
c
10
(y
9
+ 2y
8
+ 3y
7
+ 2y
6
+ 3y
5
+ 2y
4
+ 2y
3
+ y −1)
· (y
28
− 6y
27
+ ··· − 4y + 1)(y
140
− 13y
139
+ ··· − 780196y + 7921)
c
12
(y
9
+ 10y
8
+ 39y
7
+ 66y
6
+ 31y
5
− 46y
4
− 42y
3
+ 17y −1)
· (y
28
− 2y
27
+ ··· + 4y + 1)(y
140
− 13y
139
+ ··· + 104y + 1)
32
