12a
0708
(K12a
0708
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 9 11 1 2 5 7 4 10
Solving Sequence
4,11
12
5,7
6 3 10 1 8 2 9
c
11
c
4
c
6
c
3
c
10
c
12
c
7
c
2
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.09180 × 10
106
u
45
+ 2.54989 × 10
106
u
44
+ ··· + 1.47540 × 10
109
b − 9.66672 × 10
108
,
− 3.14133 × 10
108
u
45
+ 6.29434 × 10
108
u
44
+ ··· + 5.90159 × 10
110
a − 2.38197 × 10
111
,
u
46
− 2u
45
+ ··· + 841u − 160i
I
u
2
= hu
31
− u
30
+ ··· + a + 2, 2u
31
a + 4u
31
+ ··· + 6a + 4, u
32
− u
31
+ ··· + 2u − 1i
I
u
3
= hb + 1, 16a
4
+ 32a
3
+ 16a
2
+ 1, u + 1i
I
u
4
= h2u
2
a − au + 3u
2
+ b + 2a − u + 5, 70u
2
a + 25a
2
− 40au + 91u
2
+ 130a − 42u + 169, u
3
− u
2
+ 2u − 1i
I
u
5
= hb − 1, 8a
3
− 12a
2
+ 6a − 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 123 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.09 × 10
106
u
45
+ 2.55 × 10
106
u
44
+ · · · + 1.48 × 10
109
b − 9.67 ×
10
108
, −3.14 × 10
108
u
45
+ 6.29 × 10
108
u
44
+ · · · + 5.90 × 10
110
a − 2.38 ×
10
111
, u
46
− 2u
45
+ · · · + 841u − 160i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
0.00532285u
45
− 0.0106655u
44
+ ··· − 6.13310u + 4.03615
0.000740005u
45
− 0.00172827u
44
+ ··· + 1.78965u + 0.655195
a
6
=
0.00458285u
45
− 0.00893723u
44
+ ··· − 7.92275u + 3.38096
0.000740005u
45
− 0.00172827u
44
+ ··· + 1.78965u + 0.655195
a
3
=
0.00266979u
45
− 0.00467810u
44
+ ··· − 7.89898u + 1.66017
0.000649223u
45
− 0.00112824u
44
+ ··· + 0.509083u + 0.599334
a
10
=
0.00386651u
45
− 0.00706006u
44
+ ··· − 7.67006u + 4.50026
0.000120669u
45
− 0.000217602u
44
+ ··· − 0.420533u + 0.840929
a
1
=
0.00308435u
45
− 0.00557645u
44
+ ··· − 6.66439u + 3.23217
0.000567357u
45
− 0.00102442u
44
+ ··· − 0.589724u + 0.521928
a
8
=
0.000163084u
45
− 0.000998201u
44
+ ··· + 4.27507u + 0.948641
−0.000225587u
45
− 0.000445073u
44
+ ··· + 3.77056u − 0.0255609
a
2
=
0.00488531u
45
− 0.00821426u
44
+ ··· − 15.9169u + 3.03609
0.00128027u
45
− 0.00211403u
44
+ ··· − 2.99501u + 1.51400
a
9
=
0.00411477u
45
− 0.00750092u
44
+ ··· − 7.70291u + 4.38186
0.000191354u
45
− 0.000279609u
44
+ ··· − 0.394775u + 0.968236
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00201846u
45
− 0.00557907u
44
+ ··· − 13.0415u + 5.45038
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 23u
45
+ ··· + 112u + 64
c
2
, c
8
u
46
+ 3u
45
+ ··· + 28u + 8
c
3
, c
12
128(128u
46
− 576u
45
+ ··· − 9u + 1)
c
4
, c
11
u
46
+ 2u
45
+ ··· − 841u − 160
c
5
, c
6
, c
9
c
10
u
46
+ u
45
+ ··· − 14u − 1
c
7
u
46
− 3u
45
+ ··· − 24020u + 12872
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 3y
45
+ ··· − 45312y + 4096
c
2
, c
8
y
46
+ 23y
45
+ ··· + 112y + 64
c
3
, c
12
16384(16384y
46
− 569344y
45
+ ··· − 97y + 1)
c
4
, c
11
y
46
− 28y
45
+ ··· − 649361y + 25600
c
5
, c
6
, c
9
c
10
y
46
+ 31y
45
+ ··· + 78y + 1
c
7
y
46
− 17y
45
+ ··· + 1347455088y + 165688384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966769 + 0.336158I
a = 0.487792 + 0.360103I
b = 0.823732 + 0.567954I
−1.06197 + 2.22747I −2.33539 − 2.53265I
u = 0.966769 − 0.336158I
a = 0.487792 − 0.360103I
b = 0.823732 − 0.567954I
−1.06197 − 2.22747I −2.33539 + 2.53265I
u = −1.022710 + 0.054575I
a = 1.065410 − 0.295918I
b = 0.0351231 − 0.1143600I
−4.15103 + 3.62905I −9.89130 − 4.16048I
u = −1.022710 − 0.054575I
a = 1.065410 + 0.295918I
b = 0.0351231 + 0.1143600I
−4.15103 − 3.62905I −9.89130 + 4.16048I
u = 0.300795 + 1.016240I
a = 0.098981 + 0.607252I
b = 0.114437 + 0.723964I
0.64788 − 2.52803I 4.19226 + 0.68863I
u = 0.300795 − 1.016240I
a = 0.098981 − 0.607252I
b = 0.114437 − 0.723964I
0.64788 + 2.52803I 4.19226 − 0.68863I
u = 0.920916
a = −0.662681
b = 0.145994
−1.48897 −6.56270
u = −1.089920 + 0.144544I
a = −0.610206 + 0.169024I
b = −1.154580 + 0.317622I
−0.053677 + 0.799227I −3.87957 − 8.61272I
u = −1.089920 − 0.144544I
a = −0.610206 − 0.169024I
b = −1.154580 − 0.317622I
−0.053677 − 0.799227I −3.87957 + 8.61272I
u = 0.830377 + 0.297025I
a = −0.408161 − 0.736370I
b = 0.270178 − 0.394032I
−1.84309 − 0.93078I −5.79685 + 4.30580I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830377 − 0.297025I
a = −0.408161 + 0.736370I
b = 0.270178 + 0.394032I
−1.84309 + 0.93078I −5.79685 − 4.30580I
u = −1.20992
a = −0.752195
b = −1.48735
−1.03932 −8.02530
u = 0.467930 + 0.629000I
a = −0.488824 − 1.031510I
b = 0.576714 − 0.673740I
0.40716 − 5.93075I 1.20971 + 10.32229I
u = 0.467930 − 0.629000I
a = −0.488824 + 1.031510I
b = 0.576714 + 0.673740I
0.40716 + 5.93075I 1.20971 − 10.32229I
u = 1.256000 + 0.034981I
a = 0.807767 + 0.042667I
b = 1.61598 + 0.10458I
−4.20433 − 4.10865I −10.31107 + 4.30154I
u = 1.256000 − 0.034981I
a = 0.807767 − 0.042667I
b = 1.61598 − 0.10458I
−4.20433 + 4.10865I −10.31107 − 4.30154I
u = −0.196424 + 1.258430I
a = 0.327145 − 0.489998I
b = −0.372089 − 1.349360I
−9.1285 + 12.2286I −6.60036 − 8.01621I
u = −0.196424 − 1.258430I
a = 0.327145 + 0.489998I
b = −0.372089 + 1.349360I
−9.1285 − 12.2286I −6.60036 + 8.01621I
u = 0.226130 + 1.306880I
a = −0.283030 − 0.536087I
b = 0.311390 − 1.307260I
−6.02382 − 6.82285I −4.45743 + 5.16086I
u = 0.226130 − 1.306880I
a = −0.283030 + 0.536087I
b = 0.311390 + 1.307260I
−6.02382 + 6.82285I −4.45743 − 5.16086I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.152157 + 1.357930I
a = 0.196395 − 0.491844I
b = −0.222197 − 1.374140I
−10.97740 + 2.63730I −9.44645 − 2.07014I
u = −0.152157 − 1.357930I
a = 0.196395 + 0.491844I
b = −0.222197 + 1.374140I
−10.97740 − 2.63730I −9.44645 + 2.07014I
u = −0.415745 + 0.454460I
a = 0.339820 − 1.213850I
b = −0.630617 − 0.516212I
1.71362 + 1.56853I 5.64296 − 4.27493I
u = −0.415745 − 0.454460I
a = 0.339820 + 1.213850I
b = −0.630617 + 0.516212I
1.71362 − 1.56853I 5.64296 + 4.27493I
u = 1.47895 + 0.51753I
a = 0.69888 + 1.63660I
b = −0.55966 + 1.47409I
−14.4351 − 18.4106I 0
u = 1.47895 − 0.51753I
a = 0.69888 − 1.63660I
b = −0.55966 − 1.47409I
−14.4351 + 18.4106I 0
u = −1.49451 + 0.51469I
a = −0.66292 + 1.61664I
b = 0.51926 + 1.45348I
−11.4919 + 13.1095I 0
u = −1.49451 − 0.51469I
a = −0.66292 − 1.61664I
b = 0.51926 − 1.45348I
−11.4919 − 13.1095I 0
u = 1.50459 + 0.53805I
a = 0.67757 + 1.55296I
b = −0.46575 + 1.50413I
−16.3159 − 9.1985I 0
u = 1.50459 − 0.53805I
a = 0.67757 − 1.55296I
b = −0.46575 − 1.50413I
−16.3159 + 9.1985I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.319923 + 0.205407I
a = −0.49892 − 1.47670I
b = −0.684519 − 0.269684I
1.299950 + 0.545169I 7.33327 − 2.66356I
u = −0.319923 − 0.205407I
a = −0.49892 + 1.47670I
b = −0.684519 + 0.269684I
1.299950 − 0.545169I 7.33327 + 2.66356I
u = −1.58193 + 0.48587I
a = −0.47480 + 1.54895I
b = 0.375465 + 1.314860I
−7.50745 + 10.56620I 0
u = −1.58193 − 0.48587I
a = −0.47480 − 1.54895I
b = 0.375465 − 1.314860I
−7.50745 − 10.56620I 0
u = −1.58450 + 0.64719I
a = −0.554722 + 1.269070I
b = 0.10580 + 1.45206I
−15.5466 + 4.8809I 0
u = −1.58450 − 0.64719I
a = −0.554722 − 1.269070I
b = 0.10580 − 1.45206I
−15.5466 − 4.8809I 0
u = 0.10957 + 1.71612I
a = −0.044906 − 0.687293I
b = 0.041280 − 1.188470I
−1.28695 − 3.16258I 0
u = 0.10957 − 1.71612I
a = −0.044906 + 0.687293I
b = 0.041280 + 1.188470I
−1.28695 + 3.16258I 0
u = 1.64163 + 0.51374I
a = 0.42138 + 1.45572I
b = −0.280308 + 1.292080I
−7.10146 − 4.90994I 0
u = 1.64163 − 0.51374I
a = 0.42138 − 1.45572I
b = −0.280308 − 1.292080I
−7.10146 + 4.90994I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56809 + 0.75350I
a = −0.505362 + 1.120240I
b = −0.063645 + 1.376890I
−13.07240 − 4.75404I 0
u = −1.56809 − 0.75350I
a = −0.505362 − 1.120240I
b = −0.063645 − 1.376890I
−13.07240 + 4.75404I 0
u = 1.62673 + 0.71859I
a = 0.469280 + 1.190400I
b = −0.021734 + 1.350920I
−10.16390 − 0.95021I 0
u = 1.62673 − 0.71859I
a = 0.469280 − 1.190400I
b = −0.021734 − 1.350920I
−10.16390 + 0.95021I 0
u = 0.160935 + 0.124811I
a = 2.02700 − 2.96588I
b = 0.836429 − 0.145266I
−0.85613 + 3.53276I 2.89113 − 3.11148I
u = 0.160935 − 0.124811I
a = 2.02700 + 2.96588I
b = 0.836429 + 0.145266I
−0.85613 − 3.53276I 2.89113 + 3.11148I
9
II.
I
u
2
= hu
31
−u
30
+· · ·+a+2, 2u
31
a+4u
31
+· · ·+6a+4, u
32
−u
31
+· · ·+2u−1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
a
−u
31
+ u
30
+ ··· − a − 2
a
6
=
u
31
− u
30
+ ··· + 2a + 2
−u
31
+ u
30
+ ··· − a − 2
a
3
=
−2u
31
a − u
31
+ ··· − 4a − 12
u
31
+ u
30
+ ··· + a + 4
a
10
=
u
31
a + 4u
31
+ ··· + 2a + 6
−u
5
a − u
6
+ 2u
3
a + 2u
4
− au − 2
a
1
=
−u
31
a − 6u
31
+ ··· − 4a − 6
2u
31
− 2u
30
+ ··· + 2u + 4
a
8
=
−2u
31
a + u
31
+ ··· + 8u − 8
−u
31
+ 3u
30
+ ··· − a + 2u
a
2
=
−u
31
a + u
30
a + ··· − 2a − 11
u
23
a + u
24
+ ··· + 4au + 5
a
9
=
u
31
a + 4u
31
+ ··· + 2a + 5
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
29
− 48u
27
− 4u
26
+ 252u
25
+ 44u
24
− 740u
23
− 208u
22
+ 1264u
21
+ 536u
20
−
1080u
19
− 768u
18
− 64u
17
+ 480u
16
+ 1008u
15
+ 176u
14
− 612u
13
− 436u
12
− 320u
11
+
120u
10
+ 424u
9
+ 128u
8
+ 4u
7
− 60u
6
− 108u
5
− 12u
4
+ 4u
3
+ 4u
2
+ 12u − 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
32
+ 17u
31
+ ··· − 8u
2
+ 1)
2
c
2
, c
8
(u
32
− u
31
+ ··· + 2u − 1)
2
c
3
, c
12
u
64
+ 9u
63
+ ··· − 753639276u + 67447447
c
4
, c
11
(u
32
+ u
31
+ ··· − 2u − 1)
2
c
5
, c
6
, c
9
c
10
u
64
− 3u
63
+ ··· − 588u + 173
c
7
(u
32
+ u
31
+ ··· − 14u − 5)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
32
− 3y
31
+ ··· − 16y + 1)
2
c
2
, c
8
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
c
3
, c
12
y
64
− 41y
63
+ ··· − 61152709244965460y + 4549158106817809
c
4
, c
11
(y
32
− 27y
31
+ ··· + 16y
2
+ 1)
2
c
5
, c
6
, c
9
c
10
y
64
+ 47y
63
+ ··· + 352484y + 29929
c
7
(y
32
− 23y
31
+ ··· − 296y + 25)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.029010 + 0.281289I
a = −0.51554 − 1.89839I
b = −0.184298 + 0.584080I
−7.18816 − 3.89503I −5.35061 + 2.90091I
u = −1.029010 + 0.281289I
a = 2.50665 − 1.47322I
b = 0.000618 − 1.174080I
−7.18816 − 3.89503I −5.35061 + 2.90091I
u = −1.029010 − 0.281289I
a = −0.51554 + 1.89839I
b = −0.184298 − 0.584080I
−7.18816 + 3.89503I −5.35061 − 2.90091I
u = −1.029010 − 0.281289I
a = 2.50665 + 1.47322I
b = 0.000618 + 1.174080I
−7.18816 + 3.89503I −5.35061 − 2.90091I
u = 1.134230 + 0.236397I
a = 0.980915 − 0.877845I
b = −0.148002 + 0.499701I
−4.61920 − 0.52783I −1.59448 + 0.64788I
u = 1.134230 + 0.236397I
a = −1.52583 − 2.25642I
b = 0.013222 − 1.162460I
−4.61920 − 0.52783I −1.59448 + 0.64788I
u = 1.134230 − 0.236397I
a = 0.980915 + 0.877845I
b = −0.148002 − 0.499701I
−4.61920 + 0.52783I −1.59448 − 0.64788I
u = 1.134230 − 0.236397I
a = −1.52583 + 2.25642I
b = 0.013222 + 1.162460I
−4.61920 + 0.52783I −1.59448 − 0.64788I
u = −0.166316 + 0.775774I
a = 0.808888 + 0.712460I
b = −0.825267 − 0.097868I
−4.56459 + 7.88151I −2.19556 − 6.68910I
u = −0.166316 + 0.775774I
a = −0.0657221 − 0.0170222I
b = 0.363273 + 1.276150I
−4.56459 + 7.88151I −2.19556 − 6.68910I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.166316 − 0.775774I
a = 0.808888 − 0.712460I
b = −0.825267 + 0.097868I
−4.56459 − 7.88151I −2.19556 + 6.68910I
u = −0.166316 − 0.775774I
a = −0.0657221 + 0.0170222I
b = 0.363273 − 1.276150I
−4.56459 − 7.88151I −2.19556 + 6.68910I
u = −0.729645 + 0.240963I
a = 1.45927 − 2.11943I
b = −0.276623 + 1.009120I
−7.57192 + 3.88889I −6.89128 − 4.90467I
u = −0.729645 + 0.240963I
a = 3.23608 + 0.77843I
b = −0.191669 − 1.139020I
−7.57192 + 3.88889I −6.89128 − 4.90467I
u = −0.729645 − 0.240963I
a = 1.45927 + 2.11943I
b = −0.276623 − 1.009120I
−7.57192 − 3.88889I −6.89128 + 4.90467I
u = −0.729645 − 0.240963I
a = 3.23608 − 0.77843I
b = −0.191669 + 1.139020I
−7.57192 − 3.88889I −6.89128 + 4.90467I
u = 0.028912 + 0.764004I
a = −0.299643 + 0.562116I
b = 0.400000 + 0.404029I
0.72469 − 2.24194I 3.34310 + 3.79727I
u = 0.028912 + 0.764004I
a = 0.162226 + 0.322313I
b = −0.320483 + 0.804010I
0.72469 − 2.24194I 3.34310 + 3.79727I
u = 0.028912 − 0.764004I
a = −0.299643 − 0.562116I
b = 0.400000 − 0.404029I
0.72469 + 2.24194I 3.34310 − 3.79727I
u = 0.028912 − 0.764004I
a = 0.162226 − 0.322313I
b = −0.320483 − 0.804010I
0.72469 + 2.24194I 3.34310 − 3.79727I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140851 + 0.748200I
a = −0.709175 + 0.790182I
b = 0.682560 − 0.075530I
−1.72365 − 3.15266I 1.32272 + 3.41480I
u = 0.140851 + 0.748200I
a = 0.0333149 + 0.0647892I
b = −0.307956 + 1.198040I
−1.72365 − 3.15266I 1.32272 + 3.41480I
u = 0.140851 − 0.748200I
a = −0.709175 − 0.790182I
b = 0.682560 + 0.075530I
−1.72365 + 3.15266I 1.32272 − 3.41480I
u = 0.140851 − 0.748200I
a = 0.0333149 − 0.0647892I
b = −0.307956 − 1.198040I
−1.72365 + 3.15266I 1.32272 − 3.41480I
u = −0.191682 + 0.700576I
a = 0.880290 + 0.968655I
b = −0.656498 − 0.316929I
−5.63421 − 0.39737I −3.83598 − 0.58140I
u = −0.191682 + 0.700576I
a = 0.1209190 + 0.0078234I
b = 0.189622 + 1.284130I
−5.63421 − 0.39737I −3.83598 − 0.58140I
u = −0.191682 − 0.700576I
a = 0.880290 − 0.968655I
b = −0.656498 + 0.316929I
−5.63421 + 0.39737I −3.83598 + 0.58140I
u = −0.191682 − 0.700576I
a = 0.1209190 − 0.0078234I
b = 0.189622 − 1.284130I
−5.63421 + 0.39737I −3.83598 + 0.58140I
u = 1.237710 + 0.313650I
a = −0.051272 − 0.281362I
b = −0.562964 + 0.030592I
−2.99336 − 1.65231I −0.593029 + 0.153087I
u = 1.237710 + 0.313650I
a = −0.73176 − 1.73401I
b = 0.269869 − 1.127560I
−2.99336 − 1.65231I −0.593029 + 0.153087I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.237710 − 0.313650I
a = −0.051272 + 0.281362I
b = −0.562964 − 0.030592I
−2.99336 + 1.65231I −0.593029 − 0.153087I
u = 1.237710 − 0.313650I
a = −0.73176 + 1.73401I
b = 0.269869 + 1.127560I
−2.99336 + 1.65231I −0.593029 − 0.153087I
u = −1.288430 + 0.161328I
a = −0.570936 + 0.715075I
b = 0.699448 + 0.786398I
−8.29586 + 2.81562I −9.51638 − 3.82546I
u = −1.288430 + 0.161328I
a = 0.31199 − 2.19283I
b = 0.05037 − 1.42430I
−8.29586 + 2.81562I −9.51638 − 3.82546I
u = −1.288430 − 0.161328I
a = −0.570936 − 0.715075I
b = 0.699448 − 0.786398I
−8.29586 − 2.81562I −9.51638 + 3.82546I
u = −1.288430 − 0.161328I
a = 0.31199 + 2.19283I
b = 0.05037 + 1.42430I
−8.29586 − 2.81562I −9.51638 + 3.82546I
u = −1.281200 + 0.325415I
a = 0.226257 − 0.016136I
b = 0.840939 − 0.011072I
−3.35102 + 6.17510I −1.73067 − 6.90538I
u = −1.281200 + 0.325415I
a = 0.57150 − 1.75742I
b = −0.426115 − 1.231530I
−3.35102 + 6.17510I −1.73067 − 6.90538I
u = −1.281200 − 0.325415I
a = 0.226257 + 0.016136I
b = 0.840939 + 0.011072I
−3.35102 − 6.17510I −1.73067 + 6.90538I
u = −1.281200 − 0.325415I
a = 0.57150 + 1.75742I
b = −0.426115 + 1.231530I
−3.35102 − 6.17510I −1.73067 + 6.90538I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.350330 + 0.317347I
a = 0.318468 + 0.345827I
b = 1.228340 + 0.141912I
−6.42571 + 7.01747I −3.66223 − 4.88322I
u = −1.350330 + 0.317347I
a = 0.44971 − 1.81002I
b = −0.52447 − 1.52854I
−6.42571 + 7.01747I −3.66223 − 4.88322I
u = −1.350330 − 0.317347I
a = 0.318468 − 0.345827I
b = 1.228340 − 0.141912I
−6.42571 − 7.01747I −3.66223 + 4.88322I
u = −1.350330 − 0.317347I
a = 0.44971 + 1.81002I
b = −0.52447 + 1.52854I
−6.42571 − 7.01747I −3.66223 + 4.88322I
u = −1.39424
a = −0.06274 + 1.60634I
b = 0.65801 + 1.51623I
−10.6095 −7.48250
u = −1.39424
a = −0.06274 − 1.60634I
b = 0.65801 − 1.51623I
−10.6095 −7.48250
u = 1.364340 + 0.293820I
a = −0.254483 + 0.452864I
b = −1.260800 + 0.297832I
−10.54050 − 3.23058I −8.64791 + 1.85611I
u = 1.364340 + 0.293820I
a = −0.43118 − 1.83794I
b = 0.43888 − 1.61941I
−10.54050 − 3.23058I −8.64791 + 1.85611I
u = 1.364340 − 0.293820I
a = −0.254483 − 0.452864I
b = −1.260800 − 0.297832I
−10.54050 + 3.23058I −8.64791 − 1.85611I
u = 1.364340 − 0.293820I
a = −0.43118 + 1.83794I
b = 0.43888 + 1.61941I
−10.54050 + 3.23058I −8.64791 − 1.85611I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599844
a = −2.90400 + 1.64616I
b = 0.192006 − 1.053850I
−4.51808 −4.26170
u = 0.599844
a = −2.90400 − 1.64616I
b = 0.192006 + 1.053850I
−4.51808 −4.26170
u = 1.364190 + 0.328069I
a = −0.387418 + 0.382336I
b = −1.327060 + 0.107914I
−9.3963 − 11.8758I −6.77954 + 7.99531I
u = 1.364190 + 0.328069I
a = −0.43191 − 1.80017I
b = 0.59297 − 1.57615I
−9.3963 − 11.8758I −6.77954 + 7.99531I
u = 1.364190 − 0.328069I
a = −0.387418 − 0.382336I
b = −1.327060 − 0.107914I
−9.3963 + 11.8758I −6.77954 − 7.99531I
u = 1.364190 − 0.328069I
a = −0.43191 + 1.80017I
b = 0.59297 + 1.57615I
−9.3963 + 11.8758I −6.77954 − 7.99531I
u = 1.41547 + 0.02215I
a = 0.01718 + 1.51055I
b = −0.78380 + 1.52731I
−14.1165 − 4.3986I −10.80847 + 3.53545I
u = 1.41547 + 0.02215I
a = −0.03120 − 1.64235I
b = −0.63462 − 1.63829I
−14.1165 − 4.3986I −10.80847 + 3.53545I
u = 1.41547 − 0.02215I
a = 0.01718 − 1.51055I
b = −0.78380 − 1.52731I
−14.1165 + 4.3986I −10.80847 − 3.53545I
u = 1.41547 − 0.02215I
a = −0.03120 + 1.64235I
b = −0.63462 + 1.63829I
−14.1165 + 4.3986I −10.80847 − 3.53545I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248101 + 0.323031I
a = −1.59617 + 0.51525I
b = 0.086437 + 1.153950I
−3.79093 − 1.03498I −3.18759 + 6.41402I
u = 0.248101 + 0.323031I
a = −2.01466 + 2.37922I
b = 0.224060 − 0.856864I
−3.79093 − 1.03498I −3.18759 + 6.41402I
u = 0.248101 − 0.323031I
a = −1.59617 − 0.51525I
b = 0.086437 − 1.153950I
−3.79093 + 1.03498I −3.18759 − 6.41402I
u = 0.248101 − 0.323031I
a = −2.01466 − 2.37922I
b = 0.224060 + 0.856864I
−3.79093 + 1.03498I −3.18759 − 6.41402I
19
III. I
u
3
= hb + 1, 16a
4
+ 32a
3
+ 16a
2
+ 1, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
5
=
1
0
a
7
=
a
−1
a
6
=
a + 1
−1
a
3
=
−a
2
− 2a − 1
a
a
10
=
−a + 1
1
a
1
=
−a
2
+ a + 1
a + 1
a
8
=
−2a
3
+ a
2
+ 4a + 1
2a
2
+ 3a
a
2
=
−4a
3
− 10a
2
− 5a +
1
4
4a
3
+ 4a
2
+ 2a + 1
a
9
=
−a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16a
2
+ 16a − 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
8
u
4
+ 2u
2
+ 2
c
3
16(16u
4
− 32u
3
+ 16u
2
+ 1)
c
4
, c
5
, c
6
(u − 1)
4
c
7
u
4
− 2u
2
+ 2
c
9
, c
10
, c
11
(u + 1)
4
c
12
16(16u
4
+ 32u
3
+ 16u
2
+ 1)
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
8
(y
2
+ 2y + 2)
2
c
3
, c
12
256(256y
4
− 512y
3
+ 288y
2
+ 32y + 1)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
4
c
7
(y
2
− 2y + 2)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.049340 + 0.227545I
b = −1.00000
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = −1.00000
a = −1.049340 − 0.227545I
b = −1.00000
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = −1.00000
a = 0.049342 + 0.227545I
b = −1.00000
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = −1.00000
a = 0.049342 − 0.227545I
b = −1.00000
−2.46740 + 3.66386I −4.00000 − 4.00000I
23
IV. I
u
4
=
h2u
2
a−au+3u
2
+b+2a−u+5, 70u
2
a+91u
2
+· · ·+130a+169, u
3
−u
2
+2u−1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
2
+ 3u − 1
a
7
=
a
−2u
2
a + au − 3u
2
− 2a + u − 5
a
6
=
2u
2
a − au + 3u
2
+ 3a − u + 5
−2u
2
a + au − 3u
2
− 2a + u − 5
a
3
=
−5.20000au
2
− 11.5600u
2
+ ··· − 8.80000a − 20.0400
2u
2
a − au +
24
5
u
2
+ 3a −
3
5
u +
41
5
a
10
=
3u
2
a − au +
41
5
u
2
+ 5a −
17
5
u +
74
5
−1
a
1
=
−5.80000au
2
− 15.0400u
2
+ ··· − 10.2000a − 25.3600
u
2
a − au +
21
5
u
2
+ 2a −
7
5
u +
29
5
a
8
=
u
2
a −
49
25
u
2
+
38
25
u −
91
25
−4u
2
a − 4u
2
− 2a − 7
a
2
=
−8.60000au
2
− 21.8800u
2
+ ··· − 15.4000a − 36.9200
2u
2
a − 2au +
42
5
u
2
+ 4a −
14
5
u +
53
5
a
9
=
2u
2
a + au +
31
5
u
2
+ 3a −
12
5
u +
59
5
2u
2
a − 5au + 2u
2
+ 3a − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 12
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
u
6
+ u
4
+ 2u
2
+ 1
c
3
25(25u
6
− 110u
5
+ 187u
4
− 124u
3
+ 12u
2
+ 10u + 1)
c
4
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
6
, c
9
c
10
(u
2
+ 1)
3
c
7
u
6
+ 5u
4
+ 10u
2
+ 1
c
12
25(25u
6
+ 110u
5
+ 187u
4
+ 124u
3
+ 12u
2
− 10u + 1)
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
8
(y
3
+ y
2
+ 2y + 1)
2
c
3
, c
12
625(625y
6
− 2750y
5
+ 8289y
4
− 8638y
3
+ 2998y
2
− 76y + 1)
c
5
, c
6
, c
9
c
10
(y + 1)
6
c
7
(y
3
+ 5y
2
+ 10y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.024694 + 0.898953I
b = 1.000000I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.176573 − 0.381910I
b = − 1.000000I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.024694 − 0.898953I
b = − 1.000000I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.176573 + 0.381910I
b = 1.000000I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 0.569840
a = −2.59873 + 0.48086I
b = − 1.000000I
−4.40332 −11.0200
u = 0.569840
a = −2.59873 − 0.48086I
b = 1.000000I
−4.40332 −11.0200
27
V. I
u
5
= hb − 1, 8a
3
− 12a
2
+ 6a − 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
11
=
1
0
a
12
=
1
1
a
5
=
−1
0
a
7
=
a
1
a
6
=
a − 1
1
a
3
=
a
2
− 2a + 1
a
a
10
=
a + 1
1
a
1
=
−a
2
− a + 1
−a + 1
a
8
=
−4a
2
+
11
2
a −
5
4
−2a
2
+ 3a
a
2
=
−2a
2
+
3
4
−2a
2
+ a +
1
2
a
9
=
a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 34a
2
− 34a +
17
2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
3
c
3
512(2u − 1)
3
c
4
, c
5
, c
6
(u + 1)
3
c
9
, c
10
, c
11
(u − 1)
3
c
12
512(2u + 1)
3
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
3
c
3
, c
12
262144(4y −1)
3
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
3
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000
b = 1.00000
0 0
u = 1.00000
a = 0.500000
b = 1.00000
0 0
u = 1.00000
a = 0.500000
b = 1.00000
0 0
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
2
− 2u + 2)
2
(u
3
− u
2
+ 2u − 1)
2
(u
32
+ 17u
31
+ ··· − 8u
2
+ 1)
2
· (u
46
+ 23u
45
+ ··· + 112u + 64)
c
2
, c
8
u
3
(u
4
+ 2u
2
+ 2)(u
6
+ u
4
+ 2u
2
+ 1)(u
32
− u
31
+ ··· + 2u − 1)
2
· (u
46
+ 3u
45
+ ··· + 28u + 8)
c
3
26214400(2u − 1)
3
(16u
4
− 32u
3
+ 16u
2
+ 1)
· (25u
6
− 110u
5
+ 187u
4
− 124u
3
+ 12u
2
+ 10u + 1)
· (128u
46
− 576u
45
+ ··· − 9u + 1)
· (u
64
+ 9u
63
+ ··· − 753639276u + 67447447)
c
4
((u − 1)
4
)(u + 1)
3
(u
3
+ u
2
+ 2u + 1)
2
(u
32
+ u
31
+ ··· − 2u − 1)
2
· (u
46
+ 2u
45
+ ··· − 841u − 160)
c
5
, c
6
((u − 1)
4
)(u + 1)
3
(u
2
+ 1)
3
(u
46
+ u
45
+ ··· − 14u − 1)
· (u
64
− 3u
63
+ ··· − 588u + 173)
c
7
u
3
(u
4
− 2u
2
+ 2)(u
6
+ 5u
4
+ 10u
2
+ 1)(u
32
+ u
31
+ ··· − 14u − 5)
2
· (u
46
− 3u
45
+ ··· − 24020u + 12872)
c
9
, c
10
((u − 1)
3
)(u + 1)
4
(u
2
+ 1)
3
(u
46
+ u
45
+ ··· − 14u − 1)
· (u
64
− 3u
63
+ ··· − 588u + 173)
c
11
((u − 1)
3
)(u + 1)
4
(u
3
− u
2
+ 2u − 1)
2
(u
32
+ u
31
+ ··· − 2u − 1)
2
· (u
46
+ 2u
45
+ ··· − 841u − 160)
c
12
26214400(2u + 1)
3
(16u
4
+ 32u
3
+ 16u
2
+ 1)
· (25u
6
+ 110u
5
+ 187u
4
+ 124u
3
+ 12u
2
− 10u + 1)
· (128u
46
− 576u
45
+ ··· − 9u + 1)
· (u
64
+ 9u
63
+ ··· − 753639276u + 67447447)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
2
+ 4)
2
(y
3
+ 3y
2
+ 2y −1)
2
(y
32
− 3y
31
+ ··· − 16y + 1)
2
· (y
46
+ 3y
45
+ ··· − 45312y + 4096)
c
2
, c
8
y
3
(y
2
+ 2y + 2)
2
(y
3
+ y
2
+ 2y + 1)
2
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
· (y
46
+ 23y
45
+ ··· + 112y + 64)
c
3
, c
12
687194767360000(4y −1)
3
(256y
4
− 512y
3
+ 288y
2
+ 32y + 1)
· (625y
6
− 2750y
5
+ 8289y
4
− 8638y
3
+ 2998y
2
− 76y + 1)
· (16384y
46
− 569344y
45
+ ··· − 97y + 1)
· (y
64
− 41y
63
+ ··· − 61152709244965460y + 4549158106817809)
c
4
, c
11
((y −1)
7
)(y
3
+ 3y
2
+ 2y −1)
2
(y
32
− 27y
31
+ ··· + 16y
2
+ 1)
2
· (y
46
− 28y
45
+ ··· − 649361y + 25600)
c
5
, c
6
, c
9
c
10
((y −1)
7
)(y + 1)
6
(y
46
+ 31y
45
+ ··· + 78y + 1)
· (y
64
+ 47y
63
+ ··· + 352484y + 29929)
c
7
y
3
(y
2
− 2y + 2)
2
(y
3
+ 5y
2
+ 10y + 1)
2
· (y
32
− 23y
31
+ ··· − 296y + 25)
2
· (y
46
− 17y
45
+ ··· + 1347455088y + 165688384)
33
