12a
0746
(K12a
0746
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 1 11 2 7 5 6 4 10
Solving Sequence
10,12 1,5
6 4 9 3 2 11 7 8
c
12
c
5
c
4
c
9
c
3
c
1
c
11
c
6
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1872295u
40
+ 66648388u
39
+ ··· + 16384b + 56849186816,
− 1204339u
40
− 38682066u
39
+ ··· + 32768a + 33461256192,
u
41
+ 36u
40
+ ··· + 753664u + 32768i
I
u
2
= h−1.34031 × 10
114
a
29
u
2
+ 8.19598 × 10
113
a
28
u
2
+ ··· − 1.54708 × 10
113
a + 1.81464 × 10
113
,
a
29
u
2
− 3a
28
u
2
+ ··· + 376065a − 197787, u
3
− u
2
+ 1i
I
u
3
= h3u
22
− 27u
21
+ ··· + b + 8, 10u
22
− 108u
21
+ ··· + a + 11, u
23
− 11u
22
+ ··· + 6u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 154 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
=
h1.87×10
6
u
40
+6.66×10
7
u
39
+· · ·+1.64×10
4
b+5.68×10
10
, −1.20×10
6
u
40
−
3.87×10
7
u
39
+· · ·+3.28×10
4
a+ 3.35×10
10
, u
41
+36u
40
+· · ·+753664u+32768i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
36.7535u
40
+ 1180.48u
39
+ ··· − 2.15671 × 10
7
u − 1.02116 × 10
6
−114.276u
40
− 4067.89u
39
+ ··· − 7.75799 × 10
7
u − 3469799
a
6
=
−105.890u
40
− 3697.76u
39
+ ··· − 5.02880 × 10
7
u − 2.22550 × 10
6
188.678u
40
+ 6690.58u
39
+ ··· + 1.11377 × 10
8
u + 4948929
a
4
=
151.029u
40
+ 5248.38u
39
+ ··· + 5.60128 × 10
7
u + 2.44864 × 10
6
−114.276u
40
− 4067.89u
39
+ ··· − 7.75799 × 10
7
u − 3469799
a
9
=
−0.996094u
40
− 34.8672u
39
+ ··· − 720833u − 32767.5
−
1
128
u
39
−
17
64
u
38
+ ··· −
5631
2
u − 128
a
3
=
−70.0146u
40
− 2541.25u
39
+ ··· − 6.41108 × 10
7
u − 2.91215 × 10
6
−162.712u
40
− 5404.01u
39
+ ··· + 4.14685 × 10
6
u + 284302
a
2
=
−3.80273u
40
− 133.703u
39
+ ··· + 1.67651 × 10
6
u + 92160.5
−7.14063u
40
− 242.551u
39
+ ··· − 524672.u − 18112
a
11
=
−
1
256
u
40
−
17
128
u
39
+ ··· − 64u +
1
2
1
128
u
40
+
35
128
u
39
+ ··· +
5889
2
u + 128
a
7
=
15.9481u
40
+ 686.796u
39
+ ··· + 4.13601 × 10
7
u + 1877871
187.066u
40
+ 6323.84u
39
+ ··· + 2.36552 × 10
7
u + 956542
a
8
=
−4.98438u
40
− 175.410u
39
+ ··· − 3.13728 × 10
6
u − 140671
−0.902344u
40
− 29.0820u
39
+ ··· − 594048u − 29568
(ii) Obstruction class = −1
(iii) Cusp Shapes =
338489
4096
u
40
+
6389611
2048
u
39
+ ··· + 101047790u + 4578666
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
41
+ 13u
40
+ ··· + 160u + 64
c
2
, c
7
u
41
+ 7u
40
+ ··· − 56u − 8
c
3
u
41
− 7u
40
+ ··· − 90808u − 82952
c
4
, c
6
, c
10
c
11
u
41
− u
40
+ ··· + u + 1
c
5
, c
9
u
41
− 3u
39
+ ··· + 11u
2
− 1
c
12
u
41
+ 36u
40
+ ··· + 753664u + 32768
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
41
+ 27y
40
+ ··· − 34304y −4096
c
2
, c
7
y
41
− 13y
40
+ ··· + 160y −64
c
3
y
41
− 9y
40
+ ··· + 128877877536y −6881034304
c
4
, c
6
, c
10
c
11
y
41
− 29y
40
+ ··· − 11y −1
c
5
, c
9
y
41
− 6y
40
+ ··· + 22y −1
c
12
y
41
− 12y
40
+ ··· + 4294967296y −1073741824
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.494014 + 0.701063I
a = 0.409463 + 1.060830I
b = 0.312502 + 0.783120I
−2.26568 + 4.00425I 0
u = −0.494014 − 0.701063I
a = 0.409463 − 1.060830I
b = 0.312502 − 0.783120I
−2.26568 − 4.00425I 0
u = −0.679352 + 0.497133I
a = 0.52438 + 1.38712I
b = −0.003532 + 0.738483I
−1.28548 − 7.83101I 0
u = −0.679352 − 0.497133I
a = 0.52438 − 1.38712I
b = −0.003532 − 0.738483I
−1.28548 + 7.83101I 0
u = −0.595725 + 0.586119I
a = 0.465409 + 1.248190I
b = 0.131910 + 0.781629I
−5.73006 − 1.89264I 0
u = −0.595725 − 0.586119I
a = 0.465409 − 1.248190I
b = 0.131910 − 0.781629I
−5.73006 + 1.89264I 0
u = −0.638217 + 0.462865I
a = −0.46096 − 1.41417I
b = −0.024247 − 0.688483I
−0.16397 − 2.42178I 0
u = −0.638217 − 0.462865I
a = −0.46096 + 1.41417I
b = −0.024247 + 0.688483I
−0.16397 + 2.42178I 0
u = −0.381047 + 0.557336I
a = −0.196071 − 1.164500I
b = −0.261553 − 0.610371I
−1.177580 − 0.730802I 0
u = −0.381047 − 0.557336I
a = −0.196071 + 1.164500I
b = −0.261553 + 0.610371I
−1.177580 + 0.730802I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220982 + 0.635974I
a = −0.066893 − 0.971313I
b = −0.383287 − 0.536330I
−1.196420 − 0.686597I 0
u = −0.220982 − 0.635974I
a = −0.066893 + 0.971313I
b = −0.383287 + 0.536330I
−1.196420 + 0.686597I 0
u = −0.535272 + 0.041843I
a = −0.03970 − 1.81222I
b = −0.004595 − 0.454090I
2.83170 − 2.66585I 0
u = −0.535272 − 0.041843I
a = −0.03970 + 1.81222I
b = −0.004595 + 0.454090I
2.83170 + 2.66585I 0
u = −0.03812 + 1.48635I
a = −0.193307 − 0.307958I
b = −0.856986 − 0.426230I
−1.58172 + 4.75393I 0
u = −0.03812 − 1.48635I
a = −0.193307 + 0.307958I
b = −0.856986 + 0.426230I
−1.58172 − 4.75393I 0
u = −1.29282 + 0.89016I
a = −0.120939 − 1.059210I
b = 1.44499 − 0.60902I
7.5896 − 18.8889I 0
u = −1.29282 − 0.89016I
a = −0.120939 + 1.059210I
b = 1.44499 + 0.60902I
7.5896 + 18.8889I 0
u = −1.31919 + 0.85653I
a = −0.190725 − 1.009320I
b = 1.35678 − 0.58313I
1.73884 − 12.70420I 0
u = −1.31919 − 0.85653I
a = −0.190725 + 1.009320I
b = 1.35678 + 0.58313I
1.73884 + 12.70420I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30409 + 0.89542I
a = 0.112178 + 1.034570I
b = −1.44431 + 0.58076I
8.6919 − 12.9687I 0
u = −1.30409 − 0.89542I
a = 0.112178 − 1.034570I
b = −1.44431 − 0.58076I
8.6919 + 12.9687I 0
u = −1.39385 + 0.82232I
a = −0.249205 − 0.882711I
b = 1.265940 − 0.478660I
3.40814 − 5.76593I 0
u = −1.39385 − 0.82232I
a = −0.249205 + 0.882711I
b = 1.265940 + 0.478660I
3.40814 + 5.76593I 0
u = −1.36265 + 0.87524I
a = 0.161547 + 0.929339I
b = −1.35943 + 0.49662I
6.04010 − 9.92499I 0
u = −1.36265 − 0.87524I
a = 0.161547 − 0.929339I
b = −1.35943 − 0.49662I
6.04010 + 9.92499I 0
u = 0.91303 + 1.42279I
a = −0.038442 + 0.198861I
b = 0.788921 + 0.209788I
1.61353 + 1.37467I 0
u = 0.91303 − 1.42279I
a = −0.038442 − 0.198861I
b = 0.788921 − 0.209788I
1.61353 − 1.37467I 0
u = −1.46025 + 0.98895I
a = 0.034082 + 0.742902I
b = −1.40055 + 0.29202I
11.9449 − 8.5283I 0
u = −1.46025 − 0.98895I
a = 0.034082 − 0.742902I
b = −1.40055 − 0.29202I
11.9449 + 8.5283I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74926 + 0.43149I
a = 0.535712 + 0.368017I
b = −0.999153 + 0.163720I
1.06152 − 7.56290I 0
u = −1.74926 − 0.43149I
a = 0.535712 − 0.368017I
b = −0.999153 − 0.163720I
1.06152 + 7.56290I 0
u = −1.50520 + 1.01021I
a = −0.033661 − 0.682040I
b = 1.376430 − 0.245763I
11.74060 − 2.35789I 0
u = −1.50520 − 1.01021I
a = −0.033661 + 0.682040I
b = 1.376430 + 0.245763I
11.74060 + 2.35789I 0
u = −1.85197
a = 0.605999
b = −0.956151
−2.89727 0
u = −0.51953 + 1.79430I
a = −0.311173 − 0.112547I
b = −1.071610 − 0.412248I
5.01069 + 10.47520I 0
u = −0.51953 − 1.79430I
a = −0.311173 + 0.112547I
b = −1.071610 + 0.412248I
5.01069 − 10.47520I 0
u = −0.48632 + 1.95335I
a = 0.259519 + 0.091738I
b = 1.059950 + 0.359083I
5.99467 + 4.35481I 0
u = −0.48632 − 1.95335I
a = 0.259519 − 0.091738I
b = 1.059950 − 0.359083I
5.99467 − 4.35481I 0
u = −2.01115 + 0.42725I
a = −0.404223 − 0.233635I
b = 1.049910 − 0.089496I
3.11118 − 2.16671I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.01115 − 0.42725I
a = −0.404223 + 0.233635I
b = 1.049910 + 0.089496I
3.11118 + 2.16671I 0
9
II. I
u
2
= h−1.34 × 10
114
a
29
u
2
+ 8.20 × 10
113
a
28
u
2
+ · · · − 1.55 × 10
113
a +
1.81 × 10
113
, a
29
u
2
− 3a
28
u
2
+ · · · + 376065a − 197787, u
3
− u
2
+ 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
a
23.4794a
29
u
2
− 14.3576a
28
u
2
+ ··· + 2.71016a − 3.17887
a
6
=
−23.4794a
29
u
2
+ 14.3576a
28
u
2
+ ··· − 1.71016a + 3.17887
−27.3348a
29
u
2
+ 27.3560a
28
u
2
+ ··· + 3.17365a − 5.12591
a
4
=
−23.4794a
29
u
2
+ 14.3576a
28
u
2
+ ··· − 1.71016a + 3.17887
23.4794a
29
u
2
− 14.3576a
28
u
2
+ ··· + 2.71016a − 3.17887
a
9
=
a
2
u
−3.17106a
29
u
2
− 0.698057a
28
u
2
+ ··· + 1.92192a + 1.25518
a
3
=
−31.9841a
29
u
2
+ 23.7739a
28
u
2
+ ··· − 2.37529a + 3.16621
−36.2658a
29
u
2
+ 53.0390a
28
u
2
+ ··· − 1.06179a − 3.97206
a
2
=
6.78809a
29
u
2
+ 9.35682a
28
u
2
+ ··· + 1.47987a + 0.523084
94.6666a
29
u
2
− 99.3068a
28
u
2
+ ··· + 1.75209a + 1.13744
a
11
=
16.4889a
29
u
2
− 11.1613a
28
u
2
+ ··· + 0.398085a − 0.546245
−25.9756a
29
u
2
+ 15.4354a
28
u
2
+ ··· + 0.595930a + 0.830310
a
7
=
−39.5709a
29
u
2
+ 24.8065a
28
u
2
+ ··· + 7.53533a − 1.91582
−22.4865a
29
u
2
+ 33.8142a
28
u
2
+ ··· − 14.1437a − 0.0624415
a
8
=
10.3333a
29
u
2
− 21.1205a
28
u
2
+ ··· + 6.37351a + 1.67760
−75.5055a
29
u
2
+ 80.2424a
28
u
2
+ ··· − 6.87074a − 2.17822
(ii) Obstruction class = −1
(iii) Cusp Shapes = 52.9371a
29
u
2
− 16.2200a
28
u
2
+ ··· − 9.05243a + 0.463477
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
6
c
2
, c
7
(u
15
− u
14
+ ··· + 2u − 1)
6
c
3
(u
15
+ u
14
+ ··· − 4u − 1)
6
c
4
, c
6
, c
10
c
11
u
90
+ u
89
+ ··· + 119082u − 20779
c
5
, c
9
u
90
+ 3u
89
+ ··· + 464u − 43
c
12
(u
3
− u
2
+ 1)
30
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
6
c
2
, c
7
(y
15
− 5y
14
+ ··· + 12y
3
− 1)
6
c
3
(y
15
− y
14
+ ··· + 16y −1)
6
c
4
, c
6
, c
10
c
11
y
90
− 69y
89
+ ··· − 21058454840y + 431766841
c
5
, c
9
y
90
+ 23y
89
+ ··· + 88800y + 1849
c
12
(y
3
− y
2
+ 2y −1)
30
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.198485 − 0.968997I
b = −0.694930 − 1.099660I
4.92757 − 1.26387I 3.53451 + 0.17150I
u = 0.877439 + 0.744862I
a = 0.371784 − 0.910068I
b = −0.912624 − 0.535628I
0.08992 + 4.90214I −3.33798 − 5.65067I
u = 0.877439 + 0.744862I
a = 0.159762 + 0.960463I
b = 0.595959 + 1.123610I
5.44406 + 4.33335I 4.64158 − 5.71992I
u = 0.877439 + 0.744862I
a = −0.838607 − 0.592740I
b = −0.355737 + 0.306163I
5.44406 + 1.32289I 4.64158 − 0.23897I
u = 0.877439 + 0.744862I
a = 0.909407 − 0.268588I
b = −0.365280 − 0.653329I
2.93698 − 6.38968I 0.34485 + 4.41190I
u = 0.877439 + 0.744862I
a = 0.132786 − 0.935412I
b = −0.022537 − 1.398180I
2.93698 + 12.04590I 0.34485 − 10.37079I
u = 0.877439 + 0.744862I
a = −0.100613 + 0.931593I
b = 0.072834 + 1.359600I
3.89372 + 6.34664I 2.20327 − 5.56972I
u = 0.877439 + 0.744862I
a = −0.281606 − 0.878991I
b = −0.862552 − 0.726604I
0.48639 + 2.82812I −2.07315 − 2.97945I
u = 0.877439 + 0.744862I
a = 0.858189 + 0.699478I
b = 0.467845 − 0.303279I
4.92757 + 6.92011I 3.53451 − 6.13039I
u = 0.877439 + 0.744862I
a = −0.860296 + 0.181110I
b = 0.318140 + 0.586816I
3.89372 − 0.69040I 2.20327 − 0.38918I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.371348 − 0.789042I
b = −1.183520 − 0.597870I
4.92757 + 6.92011I 3.53451 − 6.13039I
u = 0.877439 + 0.744862I
a = 0.572239 + 0.977295I
b = 0.746751 + 0.022825I
0.48639 + 2.82812I −2.00000 − 2.97945I
u = 0.877439 + 0.744862I
a = 0.137577 − 0.832217I
b = 0.089498 − 1.235180I
−2.29749 + 6.43153I −5.67348 − 7.45617I
u = 0.877439 + 0.744862I
a = 0.357793 + 0.741926I
b = 1.187160 + 0.517480I
5.44406 + 1.32289I 4.64158 − 0.23897I
u = 0.877439 + 0.744862I
a = −0.004665 + 0.807225I
b = 0.093049 + 1.047120I
1.55950 + 4.48897I 2.00066 − 6.94350I
u = 0.877439 + 0.744862I
a = 0.633092 − 0.463259I
b = −0.595731 − 0.536286I
−2.29749 − 0.77528I −5.67348 + 1.49727I
u = 0.877439 + 0.744862I
a = −0.236441 + 1.237330I
b = 1.087060 + 0.511062I
0.089924 + 0.754105I −3.33798 + 0.I
u = 0.877439 + 0.744862I
a = −0.045040 − 1.346060I
b = −1.144440 − 0.356431I
1.55950 + 4.48897I 0. − 6.94350I
u = 0.877439 + 0.744862I
a = 0.121715 − 0.636837I
b = 0.270487 − 0.931692I
0.089924 + 0.754105I −3.33798 − 0.30823I
u = 0.877439 + 0.744862I
a = 0.53100 + 1.33570I
b = 1.084130 + 0.016709I
4.92757 − 1.26387I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.45129 − 1.37089I
b = −1.119650 − 0.076995I
5.44406 + 4.33335I 0
u = 0.877439 + 0.744862I
a = −0.012024 + 0.552750I
b = 0.920975 + 0.296695I
1.55950 + 1.16728I 2.00066 + 0.98460I
u = 0.877439 + 0.744862I
a = −0.10536 + 1.49620I
b = 1.237800 + 0.443667I
−2.29749 + 6.43153I 0
u = 0.877439 + 0.744862I
a = −0.388709 − 0.214363I
b = −1.194610 + 0.112491I
2.93698 − 6.38968I 0.34485 + 4.41190I
u = 0.877439 + 0.744862I
a = 0.349082 + 0.272090I
b = 1.170340 − 0.032932I
3.89372 − 0.69040I 2.20327 − 0.38918I
u = 0.877439 + 0.744862I
a = −0.03053 − 1.60206I
b = −1.305370 − 0.357996I
3.89372 + 6.34664I 0
u = 0.877439 + 0.744862I
a = −0.354568 − 0.154720I
b = 0.296292 + 0.020701I
1.55950 + 1.16728I 2.00066 + 0.98460I
u = 0.877439 + 0.744862I
a = −0.098435 + 0.363229I
b = −0.508129 + 0.572146I
0.08992 + 4.90214I −3.33798 − 5.65067I
u = 0.877439 + 0.744862I
a = −0.01217 + 1.63528I
b = 1.326900 + 0.386050I
2.93698 + 12.04590I 0
u = 0.877439 + 0.744862I
a = −0.204433 − 0.044838I
b = −0.915203 + 0.211781I
−2.29749 − 0.77528I −5.67348 + 1.49727I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = −0.198485 + 0.968997I
b = −0.694930 + 1.099660I
4.92757 + 1.26387I 3.53451 − 0.17150I
u = 0.877439 − 0.744862I
a = 0.371784 + 0.910068I
b = −0.912624 + 0.535628I
0.08992 − 4.90214I −3.33798 + 5.65067I
u = 0.877439 − 0.744862I
a = 0.159762 − 0.960463I
b = 0.595959 − 1.123610I
5.44406 − 4.33335I 4.64158 + 5.71992I
u = 0.877439 − 0.744862I
a = −0.838607 + 0.592740I
b = −0.355737 − 0.306163I
5.44406 − 1.32289I 4.64158 + 0.23897I
u = 0.877439 − 0.744862I
a = 0.909407 + 0.268588I
b = −0.365280 + 0.653329I
2.93698 + 6.38968I 0.34485 − 4.41190I
u = 0.877439 − 0.744862I
a = 0.132786 + 0.935412I
b = −0.022537 + 1.398180I
2.93698 − 12.04590I 0.34485 + 10.37079I
u = 0.877439 − 0.744862I
a = −0.100613 − 0.931593I
b = 0.072834 − 1.359600I
3.89372 − 6.34664I 2.20327 + 5.56972I
u = 0.877439 − 0.744862I
a = −0.281606 + 0.878991I
b = −0.862552 + 0.726604I
0.48639 − 2.82812I −2.07315 + 2.97945I
u = 0.877439 − 0.744862I
a = 0.858189 − 0.699478I
b = 0.467845 + 0.303279I
4.92757 − 6.92011I 3.53451 + 6.13039I
u = 0.877439 − 0.744862I
a = −0.860296 − 0.181110I
b = 0.318140 − 0.586816I
3.89372 + 0.69040I 2.20327 + 0.38918I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = −0.371348 + 0.789042I
b = −1.183520 + 0.597870I
4.92757 − 6.92011I 3.53451 + 6.13039I
u = 0.877439 − 0.744862I
a = 0.572239 − 0.977295I
b = 0.746751 − 0.022825I
0.48639 − 2.82812I −2.00000 + 2.97945I
u = 0.877439 − 0.744862I
a = 0.137577 + 0.832217I
b = 0.089498 + 1.235180I
−2.29749 − 6.43153I −5.67348 + 7.45617I
u = 0.877439 − 0.744862I
a = 0.357793 − 0.741926I
b = 1.187160 − 0.517480I
5.44406 − 1.32289I 4.64158 + 0.23897I
u = 0.877439 − 0.744862I
a = −0.004665 − 0.807225I
b = 0.093049 − 1.047120I
1.55950 − 4.48897I 2.00066 + 6.94350I
u = 0.877439 − 0.744862I
a = 0.633092 + 0.463259I
b = −0.595731 + 0.536286I
−2.29749 + 0.77528I −5.67348 − 1.49727I
u = 0.877439 − 0.744862I
a = −0.236441 − 1.237330I
b = 1.087060 − 0.511062I
0.089924 − 0.754105I −3.33798 + 0.I
u = 0.877439 − 0.744862I
a = −0.045040 + 1.346060I
b = −1.144440 + 0.356431I
1.55950 − 4.48897I 0. + 6.94350I
u = 0.877439 − 0.744862I
a = 0.121715 + 0.636837I
b = 0.270487 + 0.931692I
0.089924 − 0.754105I −3.33798 + 0.30823I
u = 0.877439 − 0.744862I
a = 0.53100 − 1.33570I
b = 1.084130 − 0.016709I
4.92757 + 1.26387I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = −0.45129 + 1.37089I
b = −1.119650 + 0.076995I
5.44406 − 4.33335I 0
u = 0.877439 − 0.744862I
a = −0.012024 − 0.552750I
b = 0.920975 − 0.296695I
1.55950 − 1.16728I 2.00066 − 0.98460I
u = 0.877439 − 0.744862I
a = −0.10536 − 1.49620I
b = 1.237800 − 0.443667I
−2.29749 − 6.43153I 0
u = 0.877439 − 0.744862I
a = −0.388709 + 0.214363I
b = −1.194610 − 0.112491I
2.93698 + 6.38968I 0.34485 − 4.41190I
u = 0.877439 − 0.744862I
a = 0.349082 − 0.272090I
b = 1.170340 + 0.032932I
3.89372 + 0.69040I 2.20327 + 0.38918I
u = 0.877439 − 0.744862I
a = −0.03053 + 1.60206I
b = −1.305370 + 0.357996I
3.89372 − 6.34664I 0
u = 0.877439 − 0.744862I
a = −0.354568 + 0.154720I
b = 0.296292 − 0.020701I
1.55950 − 1.16728I 2.00066 − 0.98460I
u = 0.877439 − 0.744862I
a = −0.098435 − 0.363229I
b = −0.508129 − 0.572146I
0.08992 − 4.90214I −3.33798 + 5.65067I
u = 0.877439 − 0.744862I
a = −0.01217 − 1.63528I
b = 1.326900 − 0.386050I
2.93698 − 12.04590I 0
u = 0.877439 − 0.744862I
a = −0.204433 + 0.044838I
b = −0.915203 − 0.211781I
−2.29749 + 0.77528I −5.67348 − 1.49727I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −0.403780 + 1.129560I
b = 1.43132 + 0.52104I
5.69708 + 1.66084I 8.52993 − 3.96405I
u = −0.754878
a = −0.403780 − 1.129560I
b = 1.43132 − 0.52104I
5.69708 − 1.66084I 8.52993 + 3.96405I
u = −0.754878
a = −0.092959 + 1.224570I
b = 1.50634 + 0.79741I
8.03130 + 3.51852I 8.73253 − 2.59027I
u = −0.754878
a = −0.092959 − 1.224570I
b = 1.50634 − 0.79741I
8.03130 − 3.51852I 8.73253 + 2.59027I
u = −0.754878
a = 0.069471 + 1.279600I
b = −1.47299 + 0.85189I
7.07456 − 9.21780I 6.87411 + 7.39135I
u = −0.754878
a = 0.069471 − 1.279600I
b = −1.47299 − 0.85189I
7.07456 + 9.21780I 6.87411 − 7.39135I
u = −0.754878
a = −0.126876 + 0.612176I
b = 1.83118 + 0.39406I
9.58164 + 1.50523I 11.17084 − 2.74048I
u = −0.754878
a = −0.126876 − 0.612176I
b = 1.83118 − 0.39406I
9.58164 − 1.50523I 11.17084 + 2.74048I
u = −0.754878
a = 0.243400 + 1.354700I
b = −1.31484 + 0.72928I
1.84009 − 3.60340I 0. + 4.47672I
u = −0.754878
a = 0.243400 − 1.354700I
b = −1.31484 − 0.72928I
1.84009 + 3.60340I 0. − 4.47672I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 0.093933 + 0.494243I
b = −1.88877 + 0.32776I
9.06515 + 4.09199I 10.06378 − 3.15094I
u = −0.754878
a = 0.093933 − 0.494243I
b = −1.88877 − 0.32776I
9.06515 − 4.09199I 10.06378 + 3.15094I
u = −0.754878
a = 0.397055
b = −1.77764
4.62398 4.45610
u = −0.754878
a = 0.58388 + 1.51765I
b = −1.115040 + 0.460107I
4.22751 + 2.07402I 0
u = −0.754878
a = 0.58388 − 1.51765I
b = −1.115040 − 0.460107I
4.22751 − 2.07402I 0
u = −0.754878
a = −1.03635 + 1.75516I
b = 1.031310 + 0.145485I
4.22751 + 2.07402I 0
u = −0.754878
a = −1.03635 − 1.75516I
b = 1.031310 − 0.145485I
4.22751 − 2.07402I 0
u = −0.754878
a = −2.05514
b = 1.47083
4.62398 0
u = −0.754878
a = 1.59129 + 1.54290I
b = −1.211590 − 0.026531I
5.69708 + 1.66084I 0
u = −0.754878
a = 1.59129 − 1.54290I
b = −1.211590 + 0.026531I
5.69708 − 1.66084I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −1.55806 + 1.98871I
b = 1.071580 − 0.110620I
1.84009 − 3.60340I 0
u = −0.754878
a = −1.55806 − 1.98871I
b = 1.071580 + 0.110620I
1.84009 + 3.60340I 0
u = −0.754878
a = 2.33002 + 0.98414I
b = −1.42352 − 0.09868I
9.58164 + 1.50523I 0
u = −0.754878
a = 2.33002 − 0.98414I
b = −1.42352 + 0.09868I
9.58164 − 1.50523I 0
u = −0.754878
a = −2.43118 + 0.80728I
b = 1.45629 − 0.08693I
9.06515 + 4.09199I 0
u = −0.754878
a = −2.43118 − 0.80728I
b = 1.45629 + 0.08693I
9.06515 − 4.09199I 0
u = −0.754878
a = 1.92531 + 1.98075I
b = −1.167290 − 0.204310I
8.03130 + 3.51852I 0
u = −0.754878
a = 1.92531 − 1.98075I
b = −1.167290 + 0.204310I
8.03130 − 3.51852I 0
u = −0.754878
a = −1.89885 + 2.09446I
b = 1.134480 − 0.227567I
7.07456 − 9.21780I 0
u = −0.754878
a = −1.89885 − 2.09446I
b = 1.134480 + 0.227567I
7.07456 + 9.21780I 0
21
III. I
u
3
=
h3u
22
−27u
21
+· · ·+b+8, 10u
22
−108u
21
+· · ·+a+11, u
23
−11u
22
+· · ·+6u
2
−1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
−10u
22
+ 108u
21
+ ··· − 3u − 11
−3u
22
+ 27u
21
+ ··· − u − 8
a
6
=
−8u
22
+ 85u
21
+ ··· + 8u − 1
4u
22
− 43u
21
+ ··· − 3u − 7
a
4
=
−7u
22
+ 81u
21
+ ··· − 2u − 3
−3u
22
+ 27u
21
+ ··· − u − 8
a
9
=
u
20
− 10u
19
+ ··· + 2u − 6
−u
22
+ 11u
21
+ ··· + 8u
2
− 5u
a
3
=
−10u
22
+ 106u
21
+ ··· + 19u − 23
−9u
22
+ 89u
21
+ ··· − 10u + 1
a
2
=
5u
22
− 64u
21
+ ··· + 36u − 36
−13u
22
+ 141u
21
+ ··· − 25u + 9
a
11
=
u
22
− 12u
21
+ ··· + 14u − 6
−u
22
+ 11u
21
+ ··· − 6u + 1
a
7
=
−u
22
+ 3u
21
+ ··· − 15u + 8
−u
22
+ 15u
21
+ ··· − 25u
2
+ 6u
a
8
=
−15u
22
+ 167u
21
+ ··· − 42u + 18
4u
22
− 46u
21
+ ··· + 17u − 12
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
22
+ 81u
21
− 410u
20
+ 1170u
19
− 1958u
18
+ 1526u
17
+
1040u
16
− 4555u
15
+ 6002u
14
− 3400u
13
− 1645u
12
+ 5003u
11
− 4170u
10
+ 749u
9
+
1750u
8
− 1724u
7
+ 369u
6
+ 495u
5
− 422u
4
+ 37u
3
+ 87u
2
− 33u − 14
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 8u
22
+ ··· + 10u − 1
c
2
u
23
− 4u
21
+ ··· − 5u
2
+ 1
c
3
u
23
− 4u
21
+ ··· − 2u + 1
c
4
, c
10
u
23
+ u
22
+ ··· − u − 1
c
5
, c
9
u
23
+ 2u
21
+ ··· − 2u
3
+ 1
c
6
, c
11
u
23
− u
22
+ ··· − u + 1
c
7
u
23
− 4u
21
+ ··· + 5u
2
− 1
c
8
u
23
+ 8u
22
+ ··· + 10u + 1
c
12
u
23
− 11u
22
+ ··· + 6u
2
− 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
23
+ 16y
22
+ ··· + 6y −1
c
2
, c
7
y
23
− 8y
22
+ ··· + 10y −1
c
3
y
23
− 8y
22
+ ··· + 14y −1
c
4
, c
6
, c
10
c
11
y
23
− 23y
22
+ ··· + 19y −1
c
5
, c
9
y
23
+ 4y
22
+ ··· + 2y
2
− 1
c
12
y
23
− 11y
22
+ ··· + 12y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555835 + 0.810467I
a = 0.849298 + 0.647053I
b = 0.826105 + 0.507900I
−0.12521 + 4.12503I −4.08197 − 7.95735I
u = 0.555835 − 0.810467I
a = 0.849298 − 0.647053I
b = 0.826105 − 0.507900I
−0.12521 − 4.12503I −4.08197 + 7.95735I
u = 0.786171 + 0.561866I
a = −0.436369 − 1.285730I
b = −0.624578 − 0.481706I
3.19343 + 4.34636I 0.49903 − 6.72980I
u = 0.786171 − 0.561866I
a = −0.436369 + 1.285730I
b = −0.624578 + 0.481706I
3.19343 − 4.34636I 0.49903 + 6.72980I
u = 0.120384 + 1.045060I
a = −0.780496 + 0.140247I
b = −1.046350 − 0.451258I
6.20855 + 3.41376I 4.45181 − 1.64497I
u = 0.120384 − 1.045060I
a = −0.780496 − 0.140247I
b = −1.046350 + 0.451258I
6.20855 − 3.41376I 4.45181 + 1.64497I
u = 0.169009 + 0.901271I
a = 1.023990 − 0.096921I
b = 1.033420 + 0.518597I
5.34046 + 9.23426I 2.20279 − 7.27152I
u = 0.169009 − 0.901271I
a = 1.023990 + 0.096921I
b = 1.033420 − 0.518597I
5.34046 − 9.23426I 2.20279 + 7.27152I
u = 0.702175 + 0.572443I
a = 0.66719 + 1.28026I
b = 0.654499 + 0.532828I
2.76459 − 0.64228I −1.28641 − 1.06865I
u = 0.702175 − 0.572443I
a = 0.66719 − 1.28026I
b = 0.654499 − 0.532828I
2.76459 + 0.64228I −1.28641 + 1.06865I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.879890
a = 0.883672
b = −1.46168
5.65000 9.56220
u = 1.098620 + 0.729899I
a = −0.020822 − 0.768926I
b = −0.680777 − 0.308139I
1.84637 + 2.11057I 4.08819 − 2.37531I
u = 1.098620 − 0.729899I
a = −0.020822 + 0.768926I
b = −0.680777 + 0.308139I
1.84637 − 2.11057I 4.08819 + 2.37531I
u = −0.586856 + 0.194737I
a = 1.39378 + 0.83860I
b = −1.60010 − 0.15916I
8.74207 + 1.13330I 0.99092 + 1.78318I
u = −0.586856 − 0.194737I
a = 1.39378 − 0.83860I
b = −1.60010 + 0.15916I
8.74207 − 1.13330I 0.99092 − 1.78318I
u = −0.591496
a = −1.74248
b = 1.64031
4.02295 −11.4490
u = −0.550238 + 0.150886I
a = −1.67417 − 0.80866I
b = 1.64624 + 0.14078I
8.24346 − 4.36576I −1.19442 + 6.94819I
u = −0.550238 − 0.150886I
a = −1.67417 + 0.80866I
b = 1.64624 − 0.14078I
8.24346 + 4.36576I −1.19442 − 6.94819I
u = 1.42729 + 0.41125I
a = −0.497723 + 0.516534I
b = 0.613329 + 0.151958I
0.13693 + 6.97577I −4.04353 − 6.37741I
u = 1.42729 − 0.41125I
a = −0.497723 − 0.516534I
b = 0.613329 − 0.151958I
0.13693 − 6.97577I −4.04353 + 6.37741I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72002
a = −0.522429
b = 0.647002
−3.77845 −13.2960
u = 1.65329 + 0.81351I
a = 0.165937 − 0.354502I
b = −0.734604 − 0.163087I
1.82545 + 1.89698I 0. − 8.77753I
u = 1.65329 − 0.81351I
a = 0.165937 + 0.354502I
b = −0.734604 + 0.163087I
1.82545 − 1.89698I 0. + 8.77753I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
6
)(u
23
− 8u
22
+ ··· + 10u − 1)
· (u
41
+ 13u
40
+ ··· + 160u + 64)
c
2
((u
15
− u
14
+ ··· + 2u − 1)
6
)(u
23
− 4u
21
+ ··· − 5u
2
+ 1)
· (u
41
+ 7u
40
+ ··· − 56u − 8)
c
3
((u
15
+ u
14
+ ··· − 4u − 1)
6
)(u
23
− 4u
21
+ ··· − 2u + 1)
· (u
41
− 7u
40
+ ··· − 90808u − 82952)
c
4
, c
10
(u
23
+ u
22
+ ··· − u − 1)(u
41
− u
40
+ ··· + u + 1)
· (u
90
+ u
89
+ ··· + 119082u − 20779)
c
5
, c
9
(u
23
+ 2u
21
+ ··· − 2u
3
+ 1)(u
41
− 3u
39
+ ··· + 11u
2
− 1)
· (u
90
+ 3u
89
+ ··· + 464u − 43)
c
6
, c
11
(u
23
− u
22
+ ··· − u + 1)(u
41
− u
40
+ ··· + u + 1)
· (u
90
+ u
89
+ ··· + 119082u − 20779)
c
7
((u
15
− u
14
+ ··· + 2u − 1)
6
)(u
23
− 4u
21
+ ··· + 5u
2
− 1)
· (u
41
+ 7u
40
+ ··· − 56u − 8)
c
8
((u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
6
)(u
23
+ 8u
22
+ ··· + 10u + 1)
· (u
41
+ 13u
40
+ ··· + 160u + 64)
c
12
((u
3
− u
2
+ 1)
30
)(u
23
− 11u
22
+ ··· + 6u
2
− 1)
· (u
41
+ 36u
40
+ ··· + 753664u + 32768)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y
15
+ 11y
14
+ ··· − 84y
2
− 1)
6
)(y
23
+ 16y
22
+ ··· + 6y −1)
· (y
41
+ 27y
40
+ ··· − 34304y −4096)
c
2
, c
7
((y
15
− 5y
14
+ ··· + 12y
3
− 1)
6
)(y
23
− 8y
22
+ ··· + 10y −1)
· (y
41
− 13y
40
+ ··· + 160y −64)
c
3
((y
15
− y
14
+ ··· + 16y −1)
6
)(y
23
− 8y
22
+ ··· + 14y −1)
· (y
41
− 9y
40
+ ··· + 128877877536y −6881034304)
c
4
, c
6
, c
10
c
11
(y
23
− 23y
22
+ ··· + 19y −1)(y
41
− 29y
40
+ ··· − 11y −1)
· (y
90
− 69y
89
+ ··· − 21058454840y + 431766841)
c
5
, c
9
(y
23
+ 4y
22
+ ··· + 2y
2
− 1)(y
41
− 6y
40
+ ··· + 22y −1)
· (y
90
+ 23y
89
+ ··· + 88800y + 1849)
c
12
((y
3
− y
2
+ 2y −1)
30
)(y
23
− 11y
22
+ ··· + 12y −1)
· (y
41
− 12y
40
+ ··· + 4294967296y −1073741824)
29
