12a
0491
(K12a
0491
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 7 2 5 11 1 4 8 10
Solving Sequence
3,6
2 7 1 5
8,10
9 12 4 11
c
2
c
6
c
1
c
5
c
7
c
9
c
12
c
3
c
11
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h36464738633053u
37
+ 59977391192807u
36
+ ··· + 92390064679586b + 268221858684342,
152917149567933u
37
+ 224240062977026u
36
+ ··· + 184780129359172a + 822275190521781,
u
38
+ 2u
37
+ ··· + 11u + 4i
I
u
2
= h−264u
28
a + 1341u
28
+ ··· − 954a + 889, −4u
28
a − 11u
28
+ ··· + 2a + 10, u
29
+ u
28
+ ··· + u − 1i
I
u
3
= hu
2
+ 2b, −u
2
+ 2a + 2u − 1, u
4
− u
3
+ u
2
+ 1i
I
u
4
= h2au + 3b + a − u + 1, a
2
+ 2a − 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 104 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
=
h3.65×10
13
u
37
+6.00×10
13
u
36
+· · ·+9.24×10
13
b+2.68×10
14
, 1.53×10
14
u
37
+
2.24 × 10
14
u
36
+ · · · + 1.85 × 10
14
a + 8.22 × 10
14
, u
38
+ 2u
37
+ · · · + 11u + 4i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
5
=
u
3
u
5
+ u
3
+ u
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
10
=
−0.827563u
37
− 1.21355u
36
+ ··· − 4.66685u − 4.45002
−0.394682u
37
− 0.649176u
36
+ ··· − 3.90259u − 2.90315
a
9
=
−0.593828u
37
− 0.803497u
36
+ ··· − 3.09638u − 2.63169
−0.431051u
37
− 0.749146u
36
+ ··· − 4.65100u − 2.78242
a
12
=
−0.478729u
37
− 0.704715u
36
+ ··· − 1.21047u − 1.62604
−0.261516u
37
− 0.420727u
36
+ ··· − 2.23130u − 2.01168
a
4
=
−0.0607175u
37
− 0.142568u
36
+ ··· − 0.459914u + 0.0392307
0.0514098u
37
+ 0.0422745u
36
+ ··· + 0.976418u + 0.348449
a
11
=
−0.657135u
37
− 0.934060u
36
+ ··· − 3.63692u − 3.16531
−0.491481u
37
− 0.777655u
36
+ ··· − 4.82548u − 3.91534
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
140731106135951
46195032339793
u
37
+
664007827422593
184780129359172
u
36
+ ··· +
520000519209215
46195032339793
u +
686592782892934
46195032339793
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
38
+ 10u
37
+ ··· + 31u + 16
c
2
, c
6
u
38
− 2u
37
+ ··· − 11u + 4
c
3
, c
4
16(16u
38
− 24u
37
+ ··· + 8u + 4)
c
8
, c
9
, c
11
c
12
u
38
− 4u
37
+ ··· + 26u
2
+ 1
c
10
u
38
+ 3u
37
+ ··· + 2944u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
38
+ 38y
37
+ ··· − 865y + 256
c
2
, c
6
y
38
+ 10y
37
+ ··· + 31y + 16
c
3
, c
4
256(256y
38
+ 1856y
37
+ ··· + 368y + 16)
c
8
, c
9
, c
11
c
12
y
38
+ 14y
37
+ ··· + 52y + 1
c
10
y
38
− 11y
37
+ ··· − 2867200y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.816967 + 0.516691I
a = 0.66711 + 1.54872I
b = 0.259357 + 0.951073I
−2.09912 − 5.36511I −0.24379 + 7.67654I
u = −0.816967 − 0.516691I
a = 0.66711 − 1.54872I
b = 0.259357 − 0.951073I
−2.09912 + 5.36511I −0.24379 − 7.67654I
u = 0.088344 + 1.071360I
a = −0.786792 + 0.722196I
b = −0.06504 − 1.79265I
−8.07886 − 6.38919I −7.94198 + 5.19165I
u = 0.088344 − 1.071360I
a = −0.786792 − 0.722196I
b = −0.06504 + 1.79265I
−8.07886 + 6.38919I −7.94198 − 5.19165I
u = −0.267518 + 1.051470I
a = −1.003380 − 0.653197I
b = −0.72082 + 1.68906I
−2.74814 − 4.44465I −2.46238 + 9.81067I
u = −0.267518 − 1.051470I
a = −1.003380 + 0.653197I
b = −0.72082 − 1.68906I
−2.74814 + 4.44465I −2.46238 − 9.81067I
u = −0.430113 + 1.014270I
a = 1.43565 + 0.14917I
b = 0.515460 − 1.274350I
−1.89132 − 2.01335I 2.64980 + 1.56754I
u = −0.430113 − 1.014270I
a = 1.43565 − 0.14917I
b = 0.515460 + 1.274350I
−1.89132 + 2.01335I 2.64980 − 1.56754I
u = 0.414376 + 1.035890I
a = 1.79208 − 0.57007I
b = 0.67343 + 2.00434I
−6.1118 + 12.9461I −4.95394 − 9.99096I
u = 0.414376 − 1.035890I
a = 1.79208 + 0.57007I
b = 0.67343 − 2.00434I
−6.1118 − 12.9461I −4.95394 + 9.99096I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347501 + 0.797377I
a = 1.034560 + 0.900604I
b = 0.050426 − 0.214066I
1.31226 + 1.74609I −8.3147 − 14.9516I
u = 0.347501 − 0.797377I
a = 1.034560 − 0.900604I
b = 0.050426 + 0.214066I
1.31226 − 1.74609I −8.3147 + 14.9516I
u = 0.876268 + 0.787294I
a = 1.44677 − 1.98187I
b = 1.53330 − 1.23829I
4.92901 − 3.34858I 2.00441 + 3.76085I
u = 0.876268 − 0.787294I
a = 1.44677 + 1.98187I
b = 1.53330 + 1.23829I
4.92901 + 3.34858I 2.00441 − 3.76085I
u = 0.766483 + 0.236896I
a = −0.17616 + 2.12144I
b = −0.52364 + 1.60414I
−3.49461 − 8.73893I −0.20669 + 6.08042I
u = 0.766483 − 0.236896I
a = −0.17616 − 2.12144I
b = −0.52364 − 1.60414I
−3.49461 + 8.73893I −0.20669 − 6.08042I
u = −0.619277 + 1.044970I
a = −1.89941 + 0.04498I
b = −0.825361 + 1.032990I
−3.75027 + 0.04407I −3.65209 − 4.05484I
u = −0.619277 − 1.044970I
a = −1.89941 − 0.04498I
b = −0.825361 − 1.032990I
−3.75027 − 0.04407I −3.65209 + 4.05484I
u = −0.854926 + 0.879047I
a = −0.550203 + 0.024165I
b = 0.236741 + 0.729329I
8.59748 − 1.92899I 2.35323 − 2.21681I
u = −0.854926 − 0.879047I
a = −0.550203 − 0.024165I
b = 0.236741 − 0.729329I
8.59748 + 1.92899I 2.35323 + 2.21681I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.912785 + 0.820153I
a = −0.94587 − 2.31254I
b = −1.27653 − 1.84714I
2.71412 + 11.17750I 0.33746 − 5.40278I
u = −0.912785 − 0.820153I
a = −0.94587 + 2.31254I
b = −1.27653 + 1.84714I
2.71412 − 11.17750I 0.33746 + 5.40278I
u = −0.833449 + 0.933812I
a = −0.199843 − 0.181143I
b = −0.117944 + 0.737215I
8.42458 − 4.34753I 1.37292 + 7.42145I
u = −0.833449 − 0.933812I
a = −0.199843 + 0.181143I
b = −0.117944 − 0.737215I
8.42458 + 4.34753I 1.37292 − 7.42145I
u = 0.797919 + 0.999570I
a = −2.81176 + 0.15661I
b = −1.61632 − 1.43028I
4.26696 + 9.56924I 0.36726 − 8.73949I
u = 0.797919 − 0.999570I
a = −2.81176 − 0.15661I
b = −1.61632 + 1.43028I
4.26696 − 9.56924I 0.36726 + 8.73949I
u = 0.885259 + 0.924982I
a = −0.402714 + 0.630130I
b = −0.426798 + 0.629711I
7.35435 + 1.80474I 1.40236 + 2.23426I
u = 0.885259 − 0.924982I
a = −0.402714 − 0.630130I
b = −0.426798 − 0.629711I
7.35435 − 1.80474I 1.40236 − 2.23426I
u = −0.349555 + 0.626590I
a = 0.198914 − 0.644452I
b = −0.336980 − 0.349923I
−0.163419 − 1.129300I −2.57883 + 5.23119I
u = −0.349555 − 0.626590I
a = 0.198914 + 0.644452I
b = −0.336980 + 0.349923I
−0.163419 + 1.129300I −2.57883 − 5.23119I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890869 + 0.923910I
a = 1.069640 + 0.049549I
b = 0.354749 + 0.558656I
7.36330 + 4.74827I 1.63906 − 7.30375I
u = 0.890869 − 0.923910I
a = 1.069640 − 0.049549I
b = 0.354749 − 0.558656I
7.36330 − 4.74827I 1.63906 + 7.30375I
u = −0.831961 + 0.999886I
a = 3.00130 − 0.50242I
b = 1.30372 − 1.97922I
2.1422 − 17.6191I −0.56156 + 9.93310I
u = −0.831961 − 0.999886I
a = 3.00130 + 0.50242I
b = 1.30372 + 1.97922I
2.1422 + 17.6191I −0.56156 − 9.93310I
u = 0.416803 + 0.548680I
a = −0.185246 + 1.297020I
b = 0.360369 − 0.039227I
2.08077 + 1.28136I 8.26270 + 1.93719I
u = 0.416803 − 0.548680I
a = −0.185246 − 1.297020I
b = 0.360369 + 0.039227I
2.08077 − 1.28136I 8.26270 − 1.93719I
u = −0.567270 + 0.025000I
a = 0.44037 − 1.76748I
b = 0.371874 − 0.911456I
0.53666 − 1.46350I 5.15173 + 4.88406I
u = −0.567270 − 0.025000I
a = 0.44037 + 1.76748I
b = 0.371874 + 0.911456I
0.53666 + 1.46350I 5.15173 − 4.88406I
8
II. I
u
2
= h−264u
28
a + 1341u
28
+ · · · − 954a + 889, −4u
28
a − 11u
28
+ · · · +
2a + 10, u
29
+ u
28
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
5
=
u
3
u
5
+ u
3
+ u
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
10
=
a
0.228968au
28
− 1.16305u
28
+ ··· + 0.827407a − 0.771032
a
9
=
−0.111015au
28
+ 0.654814u
28
+ ··· + 0.326106a + 0.888985
0.402428au
28
− 1.49870u
28
+ ··· + 0.817866a − 0.597572
a
12
=
0.990460au
28
+ 1.17346u
28
+ ··· + 0.715525a − 3.00954
−0.508239au
28
− 1.48656u
28
+ ··· + 0.117953a − 1.50824
a
4
=
0.175195au
28
− 0.549003u
28
+ ··· + 1.86036a + 11.1752
1.55594au
28
+ 4.61925u
28
+ ··· − 0.695577a + 0.555941
a
11
=
0.990460au
28
+ 1.17346u
28
+ ··· + 0.715525a − 4.00954
−0.172593au
28
− 1.77103u
28
+ ··· − 0.0555074a − 2.17259
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
− 12u
26
+ 4u
25
− 48u
24
+ 12u
23
− 100u
22
+ 44u
21
−
208u
20
+ 92u
19
− 312u
18
+ 172u
17
− 424u
16
+ 252u
15
− 456u
14
+ 296u
13
− 432u
12
+
288u
11
−328u
10
+ 216u
9
−216u
8
+ 128u
7
−120u
6
+ 56u
5
−48u
4
+ 32u
3
−16u
2
+ 12u −6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u
29
+ 7u
28
+ ··· − u − 1)
2
c
2
, c
6
(u
29
− u
28
+ ··· + u + 1)
2
c
3
, c
4
u
58
+ 3u
57
+ ··· − 2526u + 541
c
8
, c
9
, c
11
c
12
u
58
+ 9u
57
+ ··· + 4u + 1
c
10
(u
29
− u
28
+ ··· + 3u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
29
+ 31y
28
+ ··· + 15y −1)
2
c
2
, c
6
(y
29
+ 7y
28
+ ··· − y −1)
2
c
3
, c
4
y
58
− 21y
57
+ ··· − 31273168y + 292681
c
8
, c
9
, c
11
c
12
y
58
+ 35y
57
+ ··· + 128y + 1
c
10
(y
29
− 9y
28
+ ··· − y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438147 + 0.901074I
a = 0.866777 + 0.306748I
b = 0.656173 − 0.646431I
−1.65464 − 2.09123I −0.28547 + 3.54352I
u = −0.438147 + 0.901074I
a = 1.84101 + 0.17982I
b = 0.137940 − 1.357250I
−1.65464 − 2.09123I −0.28547 + 3.54352I
u = −0.438147 − 0.901074I
a = 0.866777 − 0.306748I
b = 0.656173 + 0.646431I
−1.65464 + 2.09123I −0.28547 − 3.54352I
u = −0.438147 − 0.901074I
a = 1.84101 − 0.17982I
b = 0.137940 + 1.357250I
−1.65464 + 2.09123I −0.28547 − 3.54352I
u = 0.409980 + 0.948974I
a = −0.583985 − 0.702562I
b = 0.145390 + 0.076058I
−2.40330 + 7.55674I −2.27529 − 8.69605I
u = 0.409980 + 0.948974I
a = −1.79153 + 0.98779I
b = −0.53216 − 1.57404I
−2.40330 + 7.55674I −2.27529 − 8.69605I
u = 0.409980 − 0.948974I
a = −0.583985 + 0.702562I
b = 0.145390 − 0.076058I
−2.40330 − 7.55674I −2.27529 + 8.69605I
u = 0.409980 − 0.948974I
a = −1.79153 − 0.98779I
b = −0.53216 + 1.57404I
−2.40330 − 7.55674I −2.27529 + 8.69605I
u = 0.273126 + 0.909412I
a = 1.11650 − 1.20654I
b = −0.23945 + 1.49698I
−7.10499 + 2.50065I −9.49416 − 5.21299I
u = 0.273126 + 0.909412I
a = −1.81954 + 1.31388I
b = −0.578605 − 0.951313I
−7.10499 + 2.50065I −9.49416 − 5.21299I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.273126 − 0.909412I
a = 1.11650 + 1.20654I
b = −0.23945 − 1.49698I
−7.10499 − 2.50065I −9.49416 + 5.21299I
u = 0.273126 − 0.909412I
a = −1.81954 − 1.31388I
b = −0.578605 + 0.951313I
−7.10499 − 2.50065I −9.49416 + 5.21299I
u = 0.064282 + 0.911143I
a = −0.791876 − 0.089875I
b = 0.146627 + 0.566746I
−4.28946 − 2.39368I −6.11411 + 2.65936I
u = 0.064282 + 0.911143I
a = 0.79891 − 1.62494I
b = −0.167307 + 1.268310I
−4.28946 − 2.39368I −6.11411 + 2.65936I
u = 0.064282 − 0.911143I
a = −0.791876 + 0.089875I
b = 0.146627 − 0.566746I
−4.28946 + 2.39368I −6.11411 − 2.65936I
u = 0.064282 − 0.911143I
a = 0.79891 + 1.62494I
b = −0.167307 − 1.268310I
−4.28946 + 2.39368I −6.11411 − 2.65936I
u = −0.815394 + 0.851135I
a = 0.251672 − 1.225170I
b = −0.21594 − 1.64229I
−0.467923 + 0.042330I −2.03677 − 1.08568I
u = −0.815394 + 0.851135I
a = 1.94470 + 0.77465I
b = 0.879934 − 0.022790I
−0.467923 + 0.042330I −2.03677 − 1.08568I
u = −0.815394 − 0.851135I
a = 0.251672 + 1.225170I
b = −0.21594 + 1.64229I
−0.467923 − 0.042330I −2.03677 + 1.08568I
u = −0.815394 − 0.851135I
a = 1.94470 − 0.77465I
b = 0.879934 + 0.022790I
−0.467923 − 0.042330I −2.03677 + 1.08568I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886761 + 0.845005I
a = 0.106105 − 0.124341I
b = −0.449081 − 0.545099I
5.93451 + 4.97924I 2.81712 − 2.83205I
u = −0.886761 + 0.845005I
a = 0.81426 + 1.80965I
b = 1.02756 + 1.59116I
5.93451 + 4.97924I 2.81712 − 2.83205I
u = −0.886761 − 0.845005I
a = 0.106105 + 0.124341I
b = −0.449081 + 0.545099I
5.93451 − 4.97924I 2.81712 + 2.83205I
u = −0.886761 − 0.845005I
a = 0.81426 − 1.80965I
b = 1.02756 − 1.59116I
5.93451 − 4.97924I 2.81712 + 2.83205I
u = 0.829632 + 0.902432I
a = 1.44505 − 4.20042I
b = 2.65889 − 2.68627I
2.66705 + 3.09358I 3.95361 − 2.70964I
u = 0.829632 + 0.902432I
a = −5.01880 − 0.63860I
b = −2.63453 − 2.74484I
2.66705 + 3.09358I 3.95361 − 2.70964I
u = 0.829632 − 0.902432I
a = 1.44505 + 4.20042I
b = 2.65889 + 2.68627I
2.66705 − 3.09358I 3.95361 + 2.70964I
u = 0.829632 − 0.902432I
a = −5.01880 + 0.63860I
b = −2.63453 + 2.74484I
2.66705 − 3.09358I 3.95361 + 2.70964I
u = −0.796082 + 0.934420I
a = 1.88242 − 0.84301I
b = 0.15088 − 1.74671I
−0.72258 − 6.08103I −2.75508 + 6.19570I
u = −0.796082 + 0.934420I
a = −2.06357 − 0.52441I
b = −1.027530 + 0.185341I
−0.72258 − 6.08103I −2.75508 + 6.19570I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796082 − 0.934420I
a = 1.88242 + 0.84301I
b = 0.15088 + 1.74671I
−0.72258 + 6.08103I −2.75508 − 6.19570I
u = −0.796082 − 0.934420I
a = −2.06357 + 0.52441I
b = −1.027530 − 0.185341I
−0.72258 + 6.08103I −2.75508 − 6.19570I
u = 0.883056 + 0.860857I
a = −0.415604 + 0.501030I
b = −0.167930 + 0.016154I
6.67034 + 1.00685I 4.05949 − 2.19242I
u = 0.883056 + 0.860857I
a = −0.87318 + 1.88119I
b = −1.18293 + 1.38438I
6.67034 + 1.00685I 4.05949 − 2.19242I
u = 0.883056 − 0.860857I
a = −0.415604 − 0.501030I
b = −0.167930 − 0.016154I
6.67034 − 1.00685I 4.05949 + 2.19242I
u = 0.883056 − 0.860857I
a = −0.87318 − 1.88119I
b = −1.18293 − 1.38438I
6.67034 − 1.00685I 4.05949 + 2.19242I
u = −0.273342 + 0.693824I
a = −3.32819 + 2.07273I
b = 1.62368 + 3.27488I
−3.62270 − 1.16630I −0.21359 + 5.75923I
u = −0.273342 + 0.693824I
a = −2.49708 − 5.76954I
b = −3.05089 + 1.78246I
−3.62270 − 1.16630I −0.21359 + 5.75923I
u = −0.273342 − 0.693824I
a = −3.32819 − 2.07273I
b = 1.62368 − 3.27488I
−3.62270 + 1.16630I −0.21359 − 5.75923I
u = −0.273342 − 0.693824I
a = −2.49708 + 5.76954I
b = −3.05089 − 1.78246I
−3.62270 + 1.16630I −0.21359 − 5.75923I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.610942 + 0.390932I
a = 0.147063 − 1.231320I
b = 0.165975 − 0.936149I
−0.05631 − 1.79478I 3.97960 + 2.96423I
u = −0.610942 + 0.390932I
a = −0.322053 − 1.323370I
b = −0.678870 − 0.634625I
−0.05631 − 1.79478I 3.97960 + 2.96423I
u = −0.610942 − 0.390932I
a = 0.147063 + 1.231320I
b = 0.165975 + 0.936149I
−0.05631 + 1.79478I 3.97960 − 2.96423I
u = −0.610942 − 0.390932I
a = −0.322053 + 1.323370I
b = −0.678870 + 0.634625I
−0.05631 + 1.79478I 3.97960 − 2.96423I
u = 0.840392 + 0.961339I
a = 0.496454 + 0.102211I
b = 0.314511 − 0.035083I
6.35169 + 5.37662I 3.47961 − 2.73445I
u = 0.840392 + 0.961339I
a = 2.52374 + 0.40857I
b = 1.13451 + 1.54944I
6.35169 + 5.37662I 3.47961 − 2.73445I
u = 0.840392 − 0.961339I
a = 0.496454 − 0.102211I
b = 0.314511 + 0.035083I
6.35169 − 5.37662I 3.47961 + 2.73445I
u = 0.840392 − 0.961339I
a = 2.52374 − 0.40857I
b = 1.13451 − 1.54944I
6.35169 − 5.37662I 3.47961 + 2.73445I
u = −0.833145 + 0.972573I
a = 0.422071 + 0.340573I
b = 0.341866 − 0.590665I
5.53074 − 11.34930I 2.00299 + 7.67243I
u = −0.833145 + 0.972573I
a = −2.64455 + 0.38053I
b = −1.00673 + 1.69571I
5.53074 − 11.34930I 2.00299 + 7.67243I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833145 − 0.972573I
a = 0.422071 − 0.340573I
b = 0.341866 + 0.590665I
5.53074 + 11.34930I 2.00299 − 7.67243I
u = −0.833145 − 0.972573I
a = −2.64455 − 0.38053I
b = −1.00673 − 1.69571I
5.53074 + 11.34930I 2.00299 − 7.67243I
u = 0.627727 + 0.308177I
a = 0.116909 − 0.679446I
b = −0.457619 − 0.120076I
−0.39198 − 3.74340I 3.21764 + 3.16701I
u = 0.627727 + 0.308177I
a = 0.38122 − 1.46585I
b = 0.541718 − 1.267480I
−0.39198 − 3.74340I 3.21764 + 3.16701I
u = 0.627727 − 0.308177I
a = 0.116909 + 0.679446I
b = −0.457619 + 0.120076I
−0.39198 + 3.74340I 3.21764 − 3.16701I
u = 0.627727 − 0.308177I
a = 0.38122 + 1.46585I
b = 0.541718 + 1.267480I
−0.39198 + 3.74340I 3.21764 − 3.16701I
u = 0.451236
a = 1.49511 + 0.78863I
b = −0.036079 + 1.103390I
−4.65622 −2.67120
u = 0.451236
a = 1.49511 − 0.78863I
b = −0.036079 − 1.103390I
−4.65622 −2.67120
17
III. I
u
3
= hu
2
+ 2b, −u
2
+ 2a + 2u − 1, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
5
=
u
3
u
3
− u
2
− 1
a
8
=
−u
2
− 1
−u
2
a
10
=
1
2
u
2
− u +
1
2
−
1
2
u
2
a
9
=
−
1
2
u
2
− u −
1
2
−
3
2
u
2
a
12
=
3
2
u
2
− u +
3
2
1
2
u
2
a
4
=
1
4
u
3
+
1
4
1
4
u
3
−
1
4
u
2
−
1
4
a
11
=
1
2
u
2
− u +
1
2
−
1
2
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
15
4
u
3
+
15
4
u
2
− 4u +
7
4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
16(16u
4
+ 8u
3
+ 12u
2
+ 4u + 1)
c
4
16(16u
4
− 8u
3
+ 12u
2
− 4u + 1)
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
9
(u + 1)
4
c
10
u
4
c
11
, c
12
(u − 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
, c
4
256(256y
4
+ 320y
3
+ 112y
2
+ 8y + 1)
c
8
, c
9
, c
11
c
12
(y −1)
4
c
10
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = 0.654246 − 0.973764I
b = 0.197562 + 0.253422I
1.43393 − 1.41510I −0.21489 − 4.38336I
u = −0.351808 − 0.720342I
a = 0.654246 + 0.973764I
b = 0.197562 − 0.253422I
1.43393 + 1.41510I −0.21489 + 4.38336I
u = 0.851808 + 0.911292I
a = −0.404246 − 0.135046I
b = 0.052438 − 0.776246I
8.43568 + 3.16396I 3.58989 − 2.42402I
u = 0.851808 − 0.911292I
a = −0.404246 + 0.135046I
b = 0.052438 + 0.776246I
8.43568 − 3.16396I 3.58989 + 2.42402I
21
IV. I
u
4
= h2au + 3b + a − u + 1, a
2
+ 2a − 2, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
1
=
−u
−u − 1
a
5
=
1
0
a
8
=
−1
u + 1
a
10
=
a
−
2
3
au −
1
3
a +
1
3
u −
1
3
a
9
=
−
1
3
au +
1
3
a −
1
3
u −
2
3
−
1
3
au −
2
3
a +
2
3
u −
2
3
a
12
=
−
2
3
au −
1
3
a +
1
3
u +
2
3
−
1
3
au −
2
3
a −
4
3
u −
2
3
a
4
=
−au − a + 1
2
3
au −
2
3
a +
2
3
u −
2
3
a
11
=
u + 1
−
2
3
au −
1
3
a −
5
3
u −
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
, c
7
(u
2
+ u + 1)
2
c
3
u
4
− 2u
3
+ 2u
2
− 4u + 4
c
4
u
4
+ 2u
3
+ 2u
2
+ 4u + 4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
2
c
10
u
4
− u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
(y
2
+ y + 1)
2
c
3
, c
4
y
4
− 4y
2
+ 16
c
8
, c
9
, c
11
c
12
(y + 1)
4
c
10
(y
2
− y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.732051
b = −0.500000 − 0.133975I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −2.73205
b = −0.50000 + 1.86603I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.732051
b = −0.500000 + 0.133975I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −2.73205
b = −0.50000 − 1.86603I
−3.28987 + 2.02988I −6.00000 − 3.46410I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
− u + 1)
2
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
29
+ 7u
28
+ ··· − u − 1)
2
· (u
38
+ 10u
37
+ ··· + 31u + 16)
c
2
((u
2
+ u + 1)
2
)(u
4
− u
3
+ u
2
+ 1)(u
29
− u
28
+ ··· + u + 1)
2
· (u
38
− 2u
37
+ ··· − 11u + 4)
c
3
256(u
4
− 2u
3
+ 2u
2
− 4u + 4)(16u
4
+ 8u
3
+ 12u
2
+ 4u + 1)
· (16u
38
− 24u
37
+ ··· + 8u + 4)(u
58
+ 3u
57
+ ··· − 2526u + 541)
c
4
256(u
4
+ 2u
3
+ 2u
2
+ 4u + 4)(16u
4
− 8u
3
+ 12u
2
− 4u + 1)
· (16u
38
− 24u
37
+ ··· + 8u + 4)(u
58
+ 3u
57
+ ··· − 2526u + 541)
c
6
((u
2
− u + 1)
2
)(u
4
+ u
3
+ u
2
+ 1)(u
29
− u
28
+ ··· + u + 1)
2
· (u
38
− 2u
37
+ ··· − 11u + 4)
c
7
((u
2
+ u + 1)
2
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
29
+ 7u
28
+ ··· − u − 1)
2
· (u
38
+ 10u
37
+ ··· + 31u + 16)
c
8
, c
9
((u + 1)
4
)(u
2
+ 1)
2
(u
38
− 4u
37
+ ··· + 26u
2
+ 1)
· (u
58
+ 9u
57
+ ··· + 4u + 1)
c
10
u
4
(u
4
− u
2
+ 1)(u
29
− u
28
+ ··· + 3u − 1)
2
· (u
38
+ 3u
37
+ ··· + 2944u + 512)
c
11
, c
12
((u − 1)
4
)(u
2
+ 1)
2
(u
38
− 4u
37
+ ··· + 26u
2
+ 1)
· (u
58
+ 9u
57
+ ··· + 4u + 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
2
+ y + 1)
2
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
29
+ 31y
28
+ ··· + 15y −1)
2
· (y
38
+ 38y
37
+ ··· − 865y + 256)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
29
+ 7y
28
+ ··· − y −1)
2
· (y
38
+ 10y
37
+ ··· + 31y + 16)
c
3
, c
4
65536(y
4
− 4y
2
+ 16)(256y
4
+ 320y
3
+ 112y
2
+ 8y + 1)
· (256y
38
+ 1856y
37
+ ··· + 368y + 16)
· (y
58
− 21y
57
+ ··· − 31273168y + 292681)
c
8
, c
9
, c
11
c
12
((y −1)
4
)(y + 1)
4
(y
38
+ 14y
37
+ ··· + 52y + 1)
· (y
58
+ 35y
57
+ ··· + 128y + 1)
c
10
y
4
(y
2
− y + 1)
2
(y
29
− 9y
28
+ ··· − y −1)
2
· (y
38
− 11y
37
+ ··· − 2867200y + 262144)
27
