12a
0229
(K12a
0229
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 10 4 12 5 8
Solving Sequence
4,10
9 5
1,8
7 3 2 6 12 11
c
9
c
4
c
8
c
7
c
3
c
1
c
6
c
12
c
10
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
45
− u
44
+ ··· + 64b − 1, −u
45
− u
44
+ ··· + 64a − 65, u
46
+ 9u
44
+ ··· + 7u
2
+ 1i
I
u
2
= h5.89603 × 10
55
u
65
+ 1.20824 × 10
54
u
64
+ ··· + 8.65172 × 10
55
b − 2.59504 × 10
56
,
− 3.37617 × 10
56
u
65
+ 7.20416 × 10
53
u
64
+ ··· + 1.47079 × 10
57
a + 7.90685 × 10
57
,
u
66
+ u
65
+ ··· − 10u + 17i
I
u
3
= hb − a − 1, a
6
+ a
5
u + a
4
+ 2a
3
u + au − 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 124 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−u
45
−u
44
+· · ·+64b−1, −u
45
−u
44
+· · ·+64a−65, u
46
+9u
44
+· · ·+7u
2
+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
0.0156250u
45
+ 0.0156250u
44
+ ··· + 0.0156250u + 1.01563
0.0156250u
45
+ 0.0156250u
44
+ ··· + 0.0156250u + 0.0156250
a
8
=
u
2
+ 1
u
2
a
7
=
−
9
32
u
45
−
7
32
u
44
+ ··· −
5
16
u +
3
4
−0.265625u
45
− 0.203125u
44
+ ··· − 0.296875u − 0.234375
a
3
=
0.546875u
45
− 2.51563u
44
+ ··· + 3.04688u − 4.82813
3
16
u
45
−
29
16
u
44
+ ··· +
19
8
u −
15
4
a
2
=
3.37500u
45
+ 2.65625u
44
+ ··· + 3.84375u + 8.18750
0.609375u
45
+ 2.07813u
44
+ ··· − 1.32813u + 5.20313
a
6
=
0.0156250u
45
− 0.0156250u
44
+ ··· + 2.01563u − 0.0156250
u
5
+ u
3
+ u
a
12
=
0.0156250u
45
+ 0.0156250u
44
+ ··· + 0.0156250u + 1.01563
−u
2
a
11
=
0.0156250u
45
+ 0.0156250u
44
+ ··· + 0.0156250u + 1.01563
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
105
8
u
45
−
21
16
u
44
+ ··· −
565
16
u −
113
8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 21u
45
+ ··· + 11u + 4
c
2
, c
6
u
46
− 3u
45
+ ··· − 9u + 2
c
3
u
46
+ 3u
45
+ ··· + 107u + 10
c
4
, c
5
, c
9
c
11
u
46
+ 9u
44
+ ··· + 7u
2
+ 1
c
7
, c
12
u
46
− 15u
45
+ ··· − 1507u + 86
c
8
, c
10
u
46
+ 18u
45
+ ··· + 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 9y
45
+ ··· + 223y + 16
c
2
, c
6
y
46
+ 21y
45
+ ··· + 11y + 4
c
3
y
46
− 3y
45
+ ··· + 1291y + 100
c
4
, c
5
, c
9
c
11
y
46
+ 18y
45
+ ··· + 14y + 1
c
7
, c
12
y
46
+ 33y
45
+ ··· + 3995y + 7396
c
8
, c
10
y
46
+ 34y
45
+ ··· + 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453798 + 0.886038I
a = −0.518488 − 0.986312I
b = −0.628069 − 0.859043I
−0.222379 + 1.215080I 1.36610 − 3.95525I
u = 0.453798 − 0.886038I
a = −0.518488 + 0.986312I
b = −0.628069 + 0.859043I
−0.222379 − 1.215080I 1.36610 + 3.95525I
u = −0.414852 + 0.902837I
a = −0.580217 + 1.132110I
b = −0.789537 + 0.917855I
−2.46322 + 3.60580I −2.18163 + 0.39698I
u = −0.414852 − 0.902837I
a = −0.580217 − 1.132110I
b = −0.789537 − 0.917855I
−2.46322 − 3.60580I −2.18163 − 0.39698I
u = 0.790815 + 0.593419I
a = −0.943712 + 1.023240I
b = −1.41071 − 0.42824I
2.22826 + 0.91205I 0.81467 − 2.41303I
u = 0.790815 − 0.593419I
a = −0.943712 − 1.023240I
b = −1.41071 + 0.42824I
2.22826 − 0.91205I 0.81467 + 2.41303I
u = 0.870127 + 0.560804I
a = −1.09824 + 1.81645I
b = −1.78431 − 0.02343I
5.68391 − 6.06712I 4.11286 + 2.85082I
u = 0.870127 − 0.560804I
a = −1.09824 − 1.81645I
b = −1.78431 + 0.02343I
5.68391 + 6.06712I 4.11286 − 2.85082I
u = −0.862114 + 0.584878I
a = −1.27282 − 1.61053I
b = −1.81791 + 0.20704I
7.53593 + 0.80904I 6.84506 + 1.79517I
u = −0.862114 − 0.584878I
a = −1.27282 + 1.61053I
b = −1.81791 − 0.20704I
7.53593 − 0.80904I 6.84506 − 1.79517I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.465756 + 0.955541I
a = −0.695688 + 0.882644I
b = −0.691882 + 0.533495I
−4.46301 − 3.83863I −5.71058 + 5.98205I
u = −0.465756 − 0.955541I
a = −0.695688 − 0.882644I
b = −0.691882 − 0.533495I
−4.46301 + 3.83863I −5.71058 − 5.98205I
u = −0.849958 + 0.645895I
a = −1.68005 − 1.09469I
b = −1.87294 + 0.67358I
7.74972 − 2.19444I 6.89266 + 2.45609I
u = −0.849958 − 0.645895I
a = −1.68005 + 1.09469I
b = −1.87294 − 0.67358I
7.74972 + 2.19444I 6.89266 − 2.45609I
u = 0.603424 + 0.895317I
a = −0.644386 − 0.881769I
b = −0.230788 − 1.016890I
1.23442 + 2.67713I 3.36922 − 2.59442I
u = 0.603424 − 0.895317I
a = −0.644386 + 0.881769I
b = −0.230788 + 1.016890I
1.23442 − 2.67713I 3.36922 + 2.59442I
u = 0.846880 + 0.673209I
a = −1.84146 + 0.85145I
b = −1.87497 − 0.89084I
6.08105 + 7.44745I 4.24669 − 7.37032I
u = 0.846880 − 0.673209I
a = −1.84146 − 0.85145I
b = −1.87497 + 0.89084I
6.08105 − 7.44745I 4.24669 + 7.37032I
u = −0.633634 + 0.963666I
a = −0.504280 + 1.072500I
b = 0.236366 + 1.006160I
0.71327 − 7.27313I 2.09224 + 8.76278I
u = −0.633634 − 0.963666I
a = −0.504280 − 1.072500I
b = 0.236366 − 1.006160I
0.71327 + 7.27313I 2.09224 − 8.76278I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.519262 + 1.061720I
a = −0.467890 − 0.377697I
b = −0.130004 + 0.410940I
−5.69377 + 3.58916I −6.74131 − 3.56160I
u = 0.519262 − 1.061720I
a = −0.467890 + 0.377697I
b = −0.130004 − 0.410940I
−5.69377 − 3.58916I −6.74131 + 3.56160I
u = −0.561338 + 1.069590I
a = −0.163899 + 0.477751I
b = 0.419844 − 0.312209I
−2.24882 − 7.06051I 0. + 6.94740I
u = −0.561338 − 1.069590I
a = −0.163899 − 0.477751I
b = 0.419844 + 0.312209I
−2.24882 + 7.06051I 0. − 6.94740I
u = 0.551052 + 1.101990I
a = −0.071980 − 0.190461I
b = 0.484358 + 0.807212I
−5.06717 + 11.24460I 0. − 10.47535I
u = 0.551052 − 1.101990I
a = −0.071980 + 0.190461I
b = 0.484358 − 0.807212I
−5.06717 − 11.24460I 0. + 10.47535I
u = −0.191800 + 0.663575I
a = 1.140210 + 0.799016I
b = 0.445705 + 0.848122I
−1.86300 − 6.50120I 0.01710 + 9.47650I
u = −0.191800 − 0.663575I
a = 1.140210 − 0.799016I
b = 0.445705 − 0.848122I
−1.86300 + 6.50120I 0.01710 − 9.47650I
u = −0.680385 + 1.122500I
a = 0.95163 + 1.31919I
b = 2.44651 + 0.41165I
3.16830 − 4.20595I 0
u = −0.680385 − 1.122500I
a = 0.95163 − 1.31919I
b = 2.44651 − 0.41165I
3.16830 + 4.20595I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637968 + 1.149790I
a = 1.075670 + 0.581931I
b = 2.30570 − 0.63580I
−1.36397 − 10.15130I 0
u = −0.637968 − 1.149790I
a = 1.075670 − 0.581931I
b = 2.30570 + 0.63580I
−1.36397 + 10.15130I 0
u = 0.672717 + 1.137900I
a = 1.13922 − 1.13976I
b = 2.61594 − 0.09172I
4.56281 + 9.42738I 0
u = 0.672717 − 1.137900I
a = 1.13922 + 1.13976I
b = 2.61594 + 0.09172I
4.56281 − 9.42738I 0
u = 0.657560 + 1.164620I
a = 1.43825 − 0.73998I
b = 2.85437 + 0.55872I
3.79893 + 12.38610I 0
u = 0.657560 − 1.164620I
a = 1.43825 + 0.73998I
b = 2.85437 − 0.55872I
3.79893 − 12.38610I 0
u = −0.653156 + 1.173940I
a = 1.54351 + 0.59524I
b = 2.94137 − 0.78964I
1.7441 − 17.6502I 0
u = −0.653156 − 1.173940I
a = 1.54351 − 0.59524I
b = 2.94137 + 0.78964I
1.7441 + 17.6502I 0
u = 0.227292 + 0.602534I
a = 0.946702 − 0.561087I
b = 0.236149 − 0.664410I
0.22874 + 1.90065I 3.25027 − 5.49087I
u = 0.227292 − 0.602534I
a = 0.946702 + 0.561087I
b = 0.236149 + 0.664410I
0.22874 − 1.90065I 3.25027 + 5.49087I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.095271 + 0.604484I
a = 1.38074 + 0.34813I
b = 0.623368 + 0.381223I
−3.48156 + 0.53333I −3.69135 + 1.16262I
u = −0.095271 − 0.604484I
a = 1.38074 − 0.34813I
b = 0.623368 − 0.381223I
−3.48156 − 0.53333I −3.69135 − 1.16262I
u = −0.549285 + 0.166329I
a = 1.121100 − 0.280064I
b = −0.194659 + 0.002810I
−0.57507 + 2.91660I 3.28484 − 3.07117I
u = −0.549285 − 0.166329I
a = 1.121100 + 0.280064I
b = −0.194659 − 0.002810I
−0.57507 − 2.91660I 3.28484 + 3.07117I
u = 0.402590 + 0.375609I
a = 0.746074 + 0.056866I
b = −0.183897 − 0.258268I
0.806831 + 0.956158I 5.88567 − 4.97178I
u = 0.402590 − 0.375609I
a = 0.746074 − 0.056866I
b = −0.183897 + 0.258268I
0.806831 − 0.956158I 5.88567 + 4.97178I
9
II. I
u
2
= h5.90 × 10
55
u
65
+ 1.21 × 10
54
u
64
+ · · · + 8.65 × 10
55
b − 2.60 ×
10
56
, −3.38 × 10
56
u
65
+ 7.20 × 10
53
u
64
+ · · · + 1.47 × 10
57
a + 7.91 ×
10
57
, u
66
+ u
65
+ · · · − 10u + 17i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
0.229548u
65
− 0.000489815u
64
+ ··· + 10.6902u − 5.37591
−0.681487u
65
− 0.0139654u
64
+ ··· − 17.8484u + 2.99945
a
8
=
u
2
+ 1
u
2
a
7
=
0.314447u
65
+ 0.631441u
64
+ ··· − 5.78592u + 10.7227
0.753344u
65
+ 1.32603u
64
+ ··· − 3.20704u + 11.8842
a
3
=
0.528089u
65
+ 0.521914u
64
+ ··· + 1.80947u + 6.24768
0.603420u
65
+ 0.952700u
64
+ ··· − 12.3700u + 15.2400
a
2
=
−0.668363u
65
− 0.869270u
64
+ ··· + 8.28192u − 15.7703
−0.807681u
65
− 1.24173u
64
+ ··· + 24.5036u − 19.7593
a
6
=
−0.721121u
65
− 0.184983u
64
+ ··· − 7.75991u + 0.596452
−0.897559u
65
− 1.04291u
64
+ ··· + 0.734986u − 15.4876
a
12
=
0.444584u
65
− 0.258086u
64
+ ··· + 20.5688u − 7.68902
0.0696875u
65
+ 0.849632u
64
+ ··· − 14.5846u + 12.9454
a
11
=
0.514272u
65
+ 0.591546u
64
+ ··· + 5.98415u + 4.25636
−0.396763u
65
+ 0.578071u
64
+ ··· − 22.5545u + 11.6317
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.06404u
65
+ 2.51384u
64
+ ··· + 43.1861u + 13.7906
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
33
+ 15u
32
+ ··· + u − 1)
2
c
2
, c
6
(u
33
+ u
32
+ ··· − u − 1)
2
c
3
(u
33
− u
32
+ ··· + u − 1)
2
c
4
, c
5
, c
9
c
11
u
66
+ u
65
+ ··· − 10u + 17
c
7
, c
12
(u
33
+ 5u
32
+ ··· − 31u − 3)
2
c
8
, c
10
u
66
+ 35u
65
+ ··· + 3300u + 289
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
33
+ 7y
32
+ ··· + 17y −1)
2
c
2
, c
6
(y
33
+ 15y
32
+ ··· + y −1)
2
c
3
(y
33
− y
32
+ ··· + 33y −1)
2
c
4
, c
5
, c
9
c
11
y
66
+ 35y
65
+ ··· + 3300y + 289
c
7
, c
12
(y
33
+ 27y
32
+ ··· + y −9)
2
c
8
, c
10
y
66
− 9y
65
+ ··· + 2025988y + 83521
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637997 + 0.746933I
a = 0.707376 + 0.907548I
b = −0.195908 + 0.640657I
1.67010 + 2.19825I 4.55384 − 3.61625I
u = 0.637997 − 0.746933I
a = 0.707376 − 0.907548I
b = −0.195908 − 0.640657I
1.67010 − 2.19825I 4.55384 + 3.61625I
u = 0.933581 + 0.405295I
a = 1.34875 − 1.61985I
b = 1.53578 + 0.13197I
6.10656 − 6.56751I 5.02440 + 3.41838I
u = 0.933581 − 0.405295I
a = 1.34875 + 1.61985I
b = 1.53578 − 0.13197I
6.10656 + 6.56751I 5.02440 − 3.41838I
u = −0.941437 + 0.387951I
a = 1.19662 + 1.81135I
b = 1.51420 − 0.00571I
4.13478 + 11.82880I 0. − 7.75337I
u = −0.941437 − 0.387951I
a = 1.19662 − 1.81135I
b = 1.51420 + 0.00571I
4.13478 − 11.82880I 0. + 7.75337I
u = 0.463996 + 0.911170I
a = 0.349493 + 0.244956I
b = −0.181570 − 0.482458I
−0.32048 + 2.39560I 0
u = 0.463996 − 0.911170I
a = 0.349493 − 0.244956I
b = −0.181570 + 0.482458I
−0.32048 − 2.39560I 0
u = 0.917264 + 0.455623I
a = 1.73989 − 1.11188I
b = 1.56702 + 0.48201I
6.63262 − 3.59396I 5.77642 + 0.I
u = 0.917264 − 0.455623I
a = 1.73989 + 1.11188I
b = 1.56702 − 0.48201I
6.63262 + 3.59396I 5.77642 + 0.I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.909922 + 0.481616I
a = 1.89942 + 0.84673I
b = 1.55154 − 0.66283I
5.11137 − 1.63491I 0
u = −0.909922 − 0.481616I
a = 1.89942 − 0.84673I
b = 1.55154 + 0.66283I
5.11137 + 1.63491I 0
u = −0.884648 + 0.397496I
a = 1.00792 + 1.16230I
b = 1.265670 − 0.236812I
0.90165 + 4.53523I −1.07914 − 3.09222I
u = −0.884648 − 0.397496I
a = 1.00792 − 1.16230I
b = 1.265670 + 0.236812I
0.90165 − 4.53523I −1.07914 + 3.09222I
u = −0.300390 + 0.920675I
a = 0.743283 − 0.035202I
b = 0.475253 + 0.493432I
−3.68002 + 0.57246I −4.31906 − 0.48605I
u = −0.300390 − 0.920675I
a = 0.743283 + 0.035202I
b = 0.475253 − 0.493432I
−3.68002 − 0.57246I −4.31906 + 0.48605I
u = −0.426964 + 0.941414I
a = 0.850654 + 0.582037I
b = 2.00701 − 1.44410I
−4.72027 − 1.50384I −5.59059 + 0.I
u = −0.426964 − 0.941414I
a = 0.850654 − 0.582037I
b = 2.00701 + 1.44410I
−4.72027 + 1.50384I −5.59059 + 0.I
u = 0.504477 + 0.902534I
a = 1.30481 − 1.05656I
b = 2.74183 + 1.39613I
0.09121 + 3.30675I 0
u = 0.504477 − 0.902534I
a = 1.30481 + 1.05656I
b = 2.74183 − 1.39613I
0.09121 − 3.30675I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.483934 + 0.821622I
a = 0.81128 − 1.51124I
b = 2.66915 + 0.72971I
0.382723 + 0.728314I 2.50985 − 3.12560I
u = 0.483934 − 0.821622I
a = 0.81128 + 1.51124I
b = 2.66915 − 0.72971I
0.382723 − 0.728314I 2.50985 + 3.12560I
u = −0.517251 + 0.927982I
a = 1.50014 + 0.89217I
b = 2.79665 − 1.66595I
−1.82082 − 8.41845I 0
u = −0.517251 − 0.927982I
a = 1.50014 − 0.89217I
b = 2.79665 + 1.66595I
−1.82082 + 8.41845I 0
u = −0.674112 + 0.632990I
a = 0.998351 − 0.705267I
b = 0.294000 − 0.777216I
1.67010 + 2.19825I 4.55384 − 3.61625I
u = −0.674112 − 0.632990I
a = 0.998351 + 0.705267I
b = 0.294000 + 0.777216I
1.67010 − 2.19825I 4.55384 + 3.61625I
u = −0.484653 + 0.774891I
a = 0.57010 + 1.76198I
b = 2.65809 − 0.41908I
−1.29130 + 4.30723I −0.15179 − 2.03529I
u = −0.484653 − 0.774891I
a = 0.57010 − 1.76198I
b = 2.65809 + 0.41908I
−1.29130 − 4.30723I −0.15179 + 2.03529I
u = −0.449397 + 1.001370I
a = 0.226897 + 0.101974I
b = −0.143046 + 1.013760I
−2.78381 − 6.56196I 0
u = −0.449397 − 1.001370I
a = 0.226897 − 0.101974I
b = −0.143046 − 1.013760I
−2.78381 + 6.56196I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.257434 + 1.094910I
a = 0.0251847 + 0.1071140I
b = 0.452509 − 0.902222I
−4.29591 0
u = −0.257434 − 1.094910I
a = 0.0251847 − 0.1071140I
b = 0.452509 + 0.902222I
−4.29591 0
u = 0.343777 + 1.105690I
a = 0.187558 + 0.200394I
b = 0.43156 + 1.64957I
−6.89729 + 3.47782I 0
u = 0.343777 − 1.105690I
a = 0.187558 − 0.200394I
b = 0.43156 − 1.64957I
−6.89729 − 3.47782I 0
u = −0.030805 + 1.168110I
a = 0.484368 + 0.318616I
b = 0.900369 + 0.205762I
−3.83648 + 1.45331I 0
u = −0.030805 − 1.168110I
a = 0.484368 − 0.318616I
b = 0.900369 − 0.205762I
−3.83648 − 1.45331I 0
u = 0.288407 + 1.172200I
a = −0.253326 + 0.071690I
b = −0.267177 + 1.092650I
−6.89729 − 3.47782I 0
u = 0.288407 − 1.172200I
a = −0.253326 − 0.071690I
b = −0.267177 − 1.092650I
−6.89729 + 3.47782I 0
u = 0.656637 + 1.031850I
a = −1.027100 + 0.658267I
b = −2.09488 − 0.71512I
0.90165 + 4.53523I 0
u = 0.656637 − 1.031850I
a = −1.027100 − 0.658267I
b = −2.09488 + 0.71512I
0.90165 − 4.53523I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.721713 + 0.991329I
a = −0.93016 + 1.47763I
b = −2.38581 + 0.26537I
5.11137 − 1.63491I 0
u = 0.721713 − 0.991329I
a = −0.93016 − 1.47763I
b = −2.38581 − 0.26537I
5.11137 + 1.63491I 0
u = −0.711282 + 1.012820I
a = −1.12655 − 1.28477I
b = −2.51046 + 0.04517I
6.63262 − 3.59396I 0
u = −0.711282 − 1.012820I
a = −1.12655 + 1.28477I
b = −2.51046 − 0.04517I
6.63262 + 3.59396I 0
u = −0.186059 + 0.718013I
a = −0.594692 + 0.693227I
b = 1.60792 − 0.14369I
−3.83648 − 1.45331I −1.02647 + 4.36257I
u = −0.186059 − 0.718013I
a = −0.594692 − 0.693227I
b = 1.60792 + 0.14369I
−3.83648 + 1.45331I −1.02647 − 4.36257I
u = −0.692455 + 1.054890I
a = −1.47281 − 0.84922I
b = −2.70026 + 0.70137I
6.10656 − 6.56751I 0
u = −0.692455 − 1.054890I
a = −1.47281 + 0.84922I
b = −2.70026 − 0.70137I
6.10656 + 6.56751I 0
u = −0.169724 + 1.257390I
a = −0.335329 + 0.769886I
b = −0.376907 + 0.480621I
−4.72027 + 1.50384I 0
u = −0.169724 − 1.257390I
a = −0.335329 − 0.769886I
b = −0.376907 − 0.480621I
−4.72027 − 1.50384I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687356 + 1.070450I
a = −1.59784 + 0.68287I
b = −2.76982 − 0.94884I
4.13478 + 11.82880I 0
u = 0.687356 − 1.070450I
a = −1.59784 − 0.68287I
b = −2.76982 + 0.94884I
4.13478 − 11.82880I 0
u = −0.614981 + 0.372347I
a = 0.383921 − 0.470183I
b = 0.654601 − 0.381474I
−0.32048 + 2.39560I 1.63078 − 3.31266I
u = −0.614981 − 0.372347I
a = 0.383921 + 0.470183I
b = 0.654601 + 0.381474I
−0.32048 − 2.39560I 1.63078 + 3.31266I
u = 0.663400 + 0.268651I
a = −0.169166 + 0.341915I
b = 0.662261 + 0.326054I
−2.78381 − 6.56196I −2.35976 + 7.19745I
u = 0.663400 − 0.268651I
a = −0.169166 − 0.341915I
b = 0.662261 − 0.326054I
−2.78381 + 6.56196I −2.35976 − 7.19745I
u = −0.068285 + 1.294260I
a = 0.384319 + 1.248130I
b = 0.583820 + 1.282150I
−1.29130 − 4.30723I 0
u = −0.068285 − 1.294260I
a = 0.384319 − 1.248130I
b = 0.583820 − 1.282150I
−1.29130 + 4.30723I 0
u = 0.095054 + 1.295640I
a = 0.141767 − 1.250960I
b = 0.254151 − 1.257110I
0.382723 − 0.728314I 0
u = 0.095054 − 1.295640I
a = 0.141767 + 1.250960I
b = 0.254151 + 1.257110I
0.382723 + 0.728314I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145273 + 1.310310I
a = −0.351267 − 1.269050I
b = −0.449389 − 1.233690I
0.09121 − 3.30675I 0
u = 0.145273 − 1.310310I
a = −0.351267 + 1.269050I
b = −0.449389 + 1.233690I
0.09121 + 3.30675I 0
u = −0.162182 + 1.319490I
a = −0.547615 + 1.282830I
b = −0.73741 + 1.24360I
−1.82082 + 8.41845I 0
u = −0.162182 − 1.319490I
a = −0.547615 − 1.282830I
b = −0.73741 − 1.24360I
−1.82082 − 8.41845I 0
u = 0.439112 + 0.257588I
a = 0.36727 + 1.36706I
b = 0.689236 + 0.303024I
−3.68002 + 0.57246I −4.31906 − 0.48605I
u = 0.439112 − 0.257588I
a = 0.36727 − 1.36706I
b = 0.689236 − 0.303024I
−3.68002 − 0.57246I −4.31906 + 0.48605I
19
III. I
u
3
= hb − a − 1, a
6
+ a
5
u + a
4
+ 2a
3
u + au − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−1
a
5
=
u
0
a
1
=
a
a + 1
a
8
=
0
−1
a
7
=
−a
2
−a
2
− a − 1
a
3
=
a
4
u
a
4
u + a
3
u + a
2
u + u
a
2
=
a
5
+ a
4
u + 2a
3
+ a
2
u + a + u
a
5
u + a
4
u + 2a
3
u + a
2
u + au + u
a
6
=
−au
−u
a
12
=
a
1
a
11
=
a + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
4
− 4a
2
− 4au − 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
, c
7
c
12
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
3
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
, c
5
, c
9
c
11
(u
2
+ 1)
6
c
8
, c
10
(u − 1)
12
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
6
, c
7
c
12
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
3
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
, c
5
, c
9
c
11
(y + 1)
12
c
8
, c
10
(y −1)
12
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.295542 + 1.002190I
b = 1.29554 + 1.00219I
−1.39926 − 0.92430I −2.28328 + 0.79423I
u = 1.000000I
a = −0.295542 + 1.002190I
b = 0.704458 + 1.002190I
−1.39926 + 0.92430I −2.28328 − 0.79423I
u = 1.000000I
a = −0.664531 − 0.428243I
b = 0.335469 − 0.428243I
−5.18047 − 0.92430I −9.71672 + 0.79423I
u = 1.000000I
a = 0.664531 − 0.428243I
b = 1.66453 − 0.42824I
−5.18047 + 0.92430I −9.71672 − 0.79423I
u = 1.000000I
a = 0.558752 − 1.073950I
b = 1.55875 − 1.07395I
−3.28987 + 5.69302I −6.00000 − 5.51057I
u = 1.000000I
a = −0.558752 − 1.073950I
b = 0.441248 − 1.073950I
−3.28987 − 5.69302I −6.00000 + 5.51057I
u = − 1.000000I
a = −0.295542 − 1.002190I
b = 0.704458 − 1.002190I
−1.39926 + 0.92430I −2.28328 − 0.79423I
u = − 1.000000I
a = 0.295542 − 1.002190I
b = 1.29554 − 1.00219I
−1.39926 − 0.92430I −2.28328 + 0.79423I
u = − 1.000000I
a = 0.664531 + 0.428243I
b = 1.66453 + 0.42824I
−5.18047 + 0.92430I −9.71672 − 0.79423I
u = − 1.000000I
a = −0.664531 + 0.428243I
b = 0.335469 + 0.428243I
−5.18047 − 0.92430I −9.71672 + 0.79423I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 0.558752 + 1.073950I
b = 1.55875 + 1.07395I
−3.28987 − 5.69302I −6.00000 + 5.51057I
u = − 1.000000I
a = −0.558752 + 1.073950I
b = 0.441248 + 1.073950I
−3.28987 + 5.69302I −6.00000 − 5.51057I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
33
+ 15u
32
+ ··· + u − 1)
2
· (u
46
+ 21u
45
+ ··· + 11u + 4)
c
2
, c
6
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
33
+ u
32
+ ··· − u − 1)
2
· (u
46
− 3u
45
+ ··· − 9u + 2)
c
3
(u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
33
− u
32
+ ··· + u − 1)
2
· (u
46
+ 3u
45
+ ··· + 107u + 10)
c
4
, c
5
, c
9
c
11
((u
2
+ 1)
6
)(u
46
+ 9u
44
+ ··· + 7u
2
+ 1)(u
66
+ u
65
+ ··· − 10u + 17)
c
7
, c
12
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
33
+ 5u
32
+ ··· − 31u − 3)
2
· (u
46
− 15u
45
+ ··· − 1507u + 86)
c
8
, c
10
((u − 1)
12
)(u
46
+ 18u
45
+ ··· + 14u + 1)
· (u
66
+ 35u
65
+ ··· + 3300u + 289)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
33
+ 7y
32
+ ··· + 17y −1)
2
· (y
46
+ 9y
45
+ ··· + 223y + 16)
c
2
, c
6
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
33
+ 15y
32
+ ··· + y −1)
2
· (y
46
+ 21y
45
+ ··· + 11y + 4)
c
3
((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
33
− y
32
+ ··· + 33y −1)
2
· (y
46
− 3y
45
+ ··· + 1291y + 100)
c
4
, c
5
, c
9
c
11
((y + 1)
12
)(y
46
+ 18y
45
+ ··· + 14y + 1)
· (y
66
+ 35y
65
+ ··· + 3300y + 289)
c
7
, c
12
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
33
+ 27y
32
+ ··· + y −9)
2
· (y
46
+ 33y
45
+ ··· + 3995y + 7396)
c
8
, c
10
((y −1)
12
)(y
46
+ 34y
45
+ ··· + 10y + 1)
· (y
66
− 9y
65
+ ··· + 2025988y + 83521)
26
