12n
0843
(K12n
0843
)
A knot diagram
1
Linearized knot diagam
4 12 11 1 8 4 3 5 12 8 7 9
Solving Sequence
3,11 4,7
8 12 2 1 6 5 10 9
c
3
c
7
c
11
c
2
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, a − 1, u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 3u
2
+ 2u + 1i
I
u
2
= h6910924u
19
+ 111764718u
18
+ ··· + 18467014b + 50164092,
− 12541023u
19
− 199375543u
18
+ ··· + 36934028a − 54583614, u
20
+ 17u
19
+ ··· − 58u
2
+ 8i
I
u
3
= hb − u, 201231u
19
− 801753u
18
+ ··· + 26914a − 196045, u
20
− 4u
19
+ ··· − 4u + 1i
I
u
4
= h3171u
19
− 102100u
18
+ ··· + 26914b − 201231, a − 1, u
20
− 4u
19
+ ··· − 4u + 1i
I
u
5
= hb + u, a + 1, u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
4
− 2u
3
+ 1i
I
u
6
= h−47u
11
− 28u
10
+ ··· + 592b − 663, 663u
11
a + 949u
11
+ ··· − 913a − 2279,
u
12
− 3u
11
+ 4u
10
+ 3u
9
− 9u
8
+ 5u
7
+ 15u
6
− 23u
5
+ 20u
4
− 9u
3
+ 4u
2
− u + 1i
I
u
7
= hb + u, 2u
7
− 6u
6
+ 7u
5
− 2u
4
− 4u
2
+ a + 5u − 3, u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
8
= h−u
6
+ 2u
5
− 2u
4
− u
2
+ b + u − 2, a + 1, u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
9
= h−u
7
− 4u
6
− 7u
5
− 5u
4
+ u
2
+ b − u, −u
6
− 4u
5
− 7u
4
− 5u
3
+ a + u − 1,
u
8
+ 5u
7
+ 12u
6
+ 16u
5
+ 13u
4
+ 7u
3
+ 4u
2
+ 2u + 1i
I
u
10
= h−u
4
+ 2u
3
− 2u
2
+ b + 2u − 2, u
4
− 2u
3
+ u
2
+ a + 1, u
6
− 3u
5
+ 4u
4
− 4u
3
+ 4u
2
− 2u + 1i
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).
1
I
u
11
= hu
5
− 2u
4
+ u
3
+ b + u, 2u
5
− 6u
4
+ 7u
3
− 6u
2
+ a + 6u − 2, u
6
− 3u
5
+ 4u
4
− 4u
3
+ 4u
2
− 2u + 1i
I
u
12
= hb − u, a − 1, u
3
+ u
2
+ u − 1i
* 12 irreducible components of dim
C
= 0, with total 137 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hb − u, a − 1, u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
1
u
a
8
=
u + 1
u
a
12
=
u
u
2
+ u
a
2
=
−u
3
− u
2
+ 1
−u
4
− 2u
3
− u
2
a
1
=
−u
5
− 2u
4
− 3u
3
− u
2
+ 1
−u
3
+ u + 1
a
6
=
u
2
+ u + 1
−u
4
− u
3
+ u
a
5
=
u
4
+ 2u
3
+ 4u
2
+ 3u + 2
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1
a
10
=
u
3
+ 2u
2
+ u
u
3
+ u
2
+ u
a
9
=
u
5
+ 3u
4
+ 5u
3
+ 5u
2
+ 3u + 1
u
5
+ 2u
4
+ 4u
3
+ 3u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
5
+ 9u
4
+ 12u
3
+ 3u
2
+ 3u + 3
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
u
6
− 2u
5
+ 5u
4
− 4u
3
+ 5u
2
− u + 1
c
2
, c
6
, c
10
u
6
− 4u
5
+ 9u
4
− 11u
3
+ 10u
2
− 5u + 1
c
3
, c
7
, c
11
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 3u
2
− 2u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
y
6
+ 6y
5
+ 19y
4
+ 32y
3
+ 27y
2
+ 9y + 1
c
2
, c
6
, c
10
y
6
+ 2y
5
+ 13y
4
+ 21y
3
+ 8y
2
− 5y + 1
c
3
, c
7
, c
11
y
6
+ y
5
+ 7y
4
+ 4y
3
+ 3y
2
+ 2y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662897 + 0.491150I
a = 1.00000
b = −0.662897 + 0.491150I
0.95398 − 1.33057I 1.54996 + 3.49130I
u = −0.662897 − 0.491150I
a = 1.00000
b = −0.662897 − 0.491150I
0.95398 + 1.33057I 1.54996 − 3.49130I
u = 0.233407 + 0.727795I
a = 1.00000
b = 0.233407 + 0.727795I
5.70894 + 1.27621I −0.24770 − 2.88719I
u = 0.233407 − 0.727795I
a = 1.00000
b = 0.233407 − 0.727795I
5.70894 − 1.27621I −0.24770 + 2.88719I
u = −1.07051 + 1.17004I
a = 1.00000
b = −1.07051 + 1.17004I
1.5618 − 18.5814I −2.80226 + 9.65875I
u = −1.07051 − 1.17004I
a = 1.00000
b = −1.07051 − 1.17004I
1.5618 + 18.5814I −2.80226 − 9.65875I
6
II.
I
u
2
= h6.91 × 10
6
u
19
+ 1.12 × 10
8
u
18
+ · · · + 1.85 × 10
7
b + 5.02 × 10
7
, −1.25 ×
10
7
u
19
−1.99×10
8
u
18
+· · ·+3.69×10
7
a−5.46×10
7
, u
20
+17u
19
+· · ·−58u
2
+8i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
0.339552u
19
+ 5.39815u
18
+ ··· + 7.20308u + 1.47787
−0.374231u
19
− 6.05213u
18
+ ··· + 1.47787u − 2.71642
a
8
=
−0.0346787u
19
− 0.653974u
18
+ ··· + 8.68095u − 1.23855
−0.374231u
19
− 6.05213u
18
+ ··· + 1.47787u − 2.71642
a
12
=
0.692665u
19
+ 11.3252u
18
+ ··· − 16.9750u + 4.33805
−0.450082u
19
− 7.21967u
18
+ ··· + 5.33805u − 5.54132
a
2
=
−0.0222967u
19
− 0.221327u
18
+ ··· − 4.64076u − 3.18001
−0.274012u
19
− 4.37474u
18
+ ··· + 1.36131u − 3.42229
a
1
=
−0.601980u
19
− 9.66925u
18
+ ··· − 3.10107u − 7.86403
−0.161223u
19
− 2.34621u
18
+ ··· − 3.27616u − 0.168684
a
6
=
0.275116u
19
+ 4.43129u
18
+ ··· + 5.96453u + 1.75530
−0.359034u
19
− 5.59838u
18
+ ··· + 0.962383u − 1.68803
a
5
=
0.721282u
19
+ 11.6179u
18
+ ··· + 1.13408u + 1.99349
−1.07481u
19
− 17.4491u
18
+ ··· + 10.4961u − 10.9836
a
10
=
0.224229u
19
+ 3.63613u
18
+ ··· − 13.8402u − 3.14393
−0.0183541u
19
− 0.469426u
18
+ ··· − 0.203268u − 1.94066
a
9
=
1.19321u
19
+ 19.7559u
18
+ ··· − 15.6737u + 8.67976
0.0354594u
19
+ 0.212840u
18
+ ··· + 6.93641u − 5.05504
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
26183957
18467014
u
19
−
212046660
9233507
u
18
+ ··· +
52565092
9233507
u −
114548582
9233507
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
c
12
u
20
+ 4u
19
+ ··· + 6u + 1
c
2
u
20
− 21u
19
+ ··· − 5888u + 512
c
3
u
20
− 17u
19
+ ··· − 58u
2
+ 8
c
5
, c
8
u
20
− 10u
19
+ ··· − 432u + 64
c
6
, c
10
u
20
+ 4u
19
+ ··· + 9u + 1
c
7
, c
11
u
20
+ 4u
19
+ ··· + 4u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
12
y
20
+ 14y
19
+ ··· + 18y + 1
c
2
y
20
− y
19
+ ··· + 8454144y + 262144
c
3
y
20
− 3y
19
+ ··· − 928y + 64
c
5
, c
8
y
20
+ 6y
19
+ ··· − 256y + 4096
c
6
, c
10
y
20
− 8y
19
+ ··· − 29y + 1
c
7
, c
11
y
20
+ 4y
19
+ ··· + 10y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.591919 + 0.779585I
a = 1.47738 + 0.32947I
b = −1.13134 + 0.95673I
5.94853 − 3.83843I −3.28174 + 4.00815I
u = −0.591919 − 0.779585I
a = 1.47738 − 0.32947I
b = −1.13134 − 0.95673I
5.94853 + 3.83843I −3.28174 − 4.00815I
u = −0.824428 + 0.175693I
a = −1.38094 + 0.73565I
b = 1.009240 − 0.849113I
7.45841 − 1.00347I 0.36457 − 2.52329I
u = −0.824428 − 0.175693I
a = −1.38094 − 0.73565I
b = 1.009240 + 0.849113I
7.45841 + 1.00347I 0.36457 + 2.52329I
u = 0.193762 + 0.533092I
a = −0.90006 − 1.24975I
b = 0.491834 − 0.721967I
−1.94038 + 0.72654I −7.43882 + 4.55749I
u = 0.193762 − 0.533092I
a = −0.90006 + 1.24975I
b = 0.491834 + 0.721967I
−1.94038 − 0.72654I −7.43882 − 4.55749I
u = −0.86298 + 1.15143I
a = −1.069020 − 0.121423I
b = 1.06235 − 1.12612I
−2.00404 − 10.90100I −3.44699 + 8.30760I
u = −0.86298 − 1.15143I
a = −1.069020 + 0.121423I
b = 1.06235 + 1.12612I
−2.00404 + 10.90100I −3.44699 − 8.30760I
u = −1.01532 + 1.20528I
a = −0.852629 + 0.003707I
b = 0.861225 − 1.031420I
−3.04305 − 6.67086I −5.21791 + 2.63870I
u = −1.01532 − 1.20528I
a = −0.852629 − 0.003707I
b = 0.861225 + 1.031420I
−3.04305 + 6.67086I −5.21791 − 2.63870I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51357 + 0.59051I
a = 0.228246 + 0.440024I
b = −0.605304 − 0.531225I
−0.09983 + 3.38858I −2.41701 − 8.48871I
u = −1.51357 − 0.59051I
a = 0.228246 − 0.440024I
b = −0.605304 + 0.531225I
−0.09983 − 3.38858I −2.41701 + 8.48871I
u = 0.198279 + 0.120648I
a = 1.30829 + 4.75906I
b = −0.314766 + 1.101470I
3.52200 − 3.40437I −3.46913 + 3.36431I
u = 0.198279 − 0.120648I
a = 1.30829 − 4.75906I
b = −0.314766 − 1.101470I
3.52200 + 3.40437I −3.46913 − 3.36431I
u = −1.53446 + 1.05621I
a = 0.254710 − 0.346615I
b = −0.024746 + 0.800894I
0.49272 − 7.72234I −10.36662 + 6.86541I
u = −1.53446 − 1.05621I
a = 0.254710 + 0.346615I
b = −0.024746 − 0.800894I
0.49272 + 7.72234I −10.36662 − 6.86541I
u = −1.01845 + 1.57478I
a = −0.288306 + 0.080384I
b = 0.167038 − 0.535886I
−2.57404 − 2.62147I −15.2857 + 10.0855I
u = −1.01845 − 1.57478I
a = −0.288306 − 0.080384I
b = 0.167038 + 0.535886I
−2.57404 + 2.62147I −15.2857 − 10.0855I
u = −1.53091 + 1.32244I
a = −0.027667 − 0.334313I
b = 0.484465 + 0.475215I
2.10928 + 9.64745I −6.0000 − 14.3164I
u = −1.53091 − 1.32244I
a = −0.027667 + 0.334313I
b = 0.484465 − 0.475215I
2.10928 − 9.64745I −6.0000 + 14.3164I
11
III. I
u
3
= hb − u, 2.01 × 10
5
u
19
− 8.02 × 10
5
u
18
+ · · · + 2.69 × 10
4
a − 1.96 ×
10
5
, u
20
− 4u
19
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−7.47682u
19
+ 29.7894u
18
+ ··· − 36.6305u + 7.28413
u
a
8
=
−7.47682u
19
+ 29.7894u
18
+ ··· − 35.6305u + 7.28413
u
a
12
=
17.3713u
19
− 71.0832u
18
+ ··· + 123.789u − 31.5849
3.32229u
19
− 11.0375u
18
+ ··· + 8.00554u + 0.117820
a
2
=
1.59423u
19
− 2.41343u
18
+ ··· − 10.6391u − 1.01835
−1.44965u
19
+ 5.33845u
18
+ ··· − 2.84978u + 0.253994
a
1
=
2.19796u
19
− 6.68247u
18
+ ··· + 0.770751u − 4.72784
0.505759u
19
− 2.02586u
18
+ ··· + 5.17032u − 1.60010
a
6
=
−4.15453u
19
+ 18.7520u
18
+ ··· − 28.6249u + 7.40195
−0.502415u
19
+ 2.36568u
18
+ ··· − 4.68433u + 2.25165
a
5
=
6.35220u
19
− 16.2202u
18
+ ··· − 3.98086u + 4.50119
−0.391989u
19
+ 3.27629u
18
+ ··· − 8.30244u + 3.34528
a
10
=
24.0158u
19
− 93.1582u
18
+ ··· + 137.800u − 31.3493
3.32229u
19
− 11.0375u
18
+ ··· + 8.00554u + 0.117820
a
9
=
−0.498439u
19
− 6.37475u
18
+ ··· + 38.7268u − 18.0626
3.19473u
19
− 11.9776u
18
+ ··· + 16.8010u − 4.49101
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
182014
13457
u
19
+
673876
13457
u
18
+ ··· −
1440624
13457
u +
66848
13457
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 10u
19
+ ··· − 432u + 64
c
2
, c
6
u
20
+ 4u
19
+ ··· + 9u + 1
c
3
, c
7
u
20
+ 4u
19
+ ··· + 4u + 1
c
5
, c
8
, c
9
c
12
u
20
+ 4u
19
+ ··· + 6u + 1
c
10
u
20
− 21u
19
+ ··· − 5888u + 512
c
11
u
20
− 17u
19
+ ··· − 58u
2
+ 8
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
+ 6y
19
+ ··· − 256y + 4096
c
2
, c
6
y
20
− 8y
19
+ ··· − 29y + 1
c
3
, c
7
y
20
+ 4y
19
+ ··· + 10y + 1
c
5
, c
8
, c
9
c
12
y
20
+ 14y
19
+ ··· + 18y + 1
c
10
y
20
− y
19
+ ··· + 8454144y + 262144
c
11
y
20
− 3y
19
+ ··· − 928y + 64
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.491834 + 0.721967I
a = −0.379455 − 0.526881I
b = 0.491834 + 0.721967I
−1.94038 − 0.72654I −7.43882 − 4.55749I
u = 0.491834 − 0.721967I
a = −0.379455 + 0.526881I
b = 0.491834 − 0.721967I
−1.94038 + 0.72654I −7.43882 + 4.55749I
u = −0.314766 + 1.101470I
a = 0.053706 − 0.195362I
b = −0.314766 + 1.101470I
3.52200 − 3.40437I −3.46913 + 3.36431I
u = −0.314766 − 1.101470I
a = 0.053706 + 0.195362I
b = −0.314766 − 1.101470I
3.52200 + 3.40437I −3.46913 − 3.36431I
u = −0.605304 + 0.531225I
a = 0.92890 + 1.79077I
b = −0.605304 + 0.531225I
−0.09983 − 3.38858I −2.41701 + 8.48871I
u = −0.605304 − 0.531225I
a = 0.92890 − 1.79077I
b = −0.605304 − 0.531225I
−0.09983 + 3.38858I −2.41701 − 8.48871I
u = −0.024746 + 0.800894I
a = 1.37667 + 1.87340I
b = −0.024746 + 0.800894I
0.49272 − 7.72234I −10.36662 + 6.86541I
u = −0.024746 − 0.800894I
a = 1.37667 − 1.87340I
b = −0.024746 − 0.800894I
0.49272 + 7.72234I −10.36662 − 6.86541I
u = 1.009240 + 0.849113I
a = −0.564068 + 0.300488I
b = 1.009240 + 0.849113I
7.45841 + 1.00347I 0.36457 + 2.52329I
u = 1.009240 − 0.849113I
a = −0.564068 − 0.300488I
b = 1.009240 − 0.849113I
7.45841 − 1.00347I 0.36457 − 2.52329I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484465 + 0.475215I
a = −0.24586 + 2.97086I
b = 0.484465 + 0.475215I
2.10928 + 9.64745I −3.9407 − 14.3164I
u = 0.484465 − 0.475215I
a = −0.24586 − 2.97086I
b = 0.484465 − 0.475215I
2.10928 − 9.64745I −3.9407 + 14.3164I
u = 0.861225 + 1.031420I
a = −1.172820 + 0.005099I
b = 0.861225 + 1.031420I
−3.04305 + 6.67086I −5.21791 − 2.63870I
u = 0.861225 − 1.031420I
a = −1.172820 − 0.005099I
b = 0.861225 − 1.031420I
−3.04305 − 6.67086I −5.21791 + 2.63870I
u = 0.167038 + 0.535886I
a = −3.21835 + 0.89733I
b = 0.167038 + 0.535886I
−2.57404 + 2.62147I −15.2857 − 10.0855I
u = 0.167038 − 0.535886I
a = −3.21835 − 0.89733I
b = 0.167038 − 0.535886I
−2.57404 − 2.62147I −15.2857 + 10.0855I
u = −1.13134 + 0.95673I
a = 0.644805 − 0.143797I
b = −1.13134 + 0.95673I
5.94853 − 3.83843I −3.28174 + 4.00815I
u = −1.13134 − 0.95673I
a = 0.644805 + 0.143797I
b = −1.13134 − 0.95673I
5.94853 + 3.83843I −3.28174 − 4.00815I
u = 1.06235 + 1.12612I
a = −0.923523 − 0.104897I
b = 1.06235 + 1.12612I
−2.00404 + 10.90100I −3.44699 − 8.30760I
u = 1.06235 − 1.12612I
a = −0.923523 + 0.104897I
b = 1.06235 − 1.12612I
−2.00404 − 10.90100I −3.44699 + 8.30760I
16
IV. I
u
4
=
h3171u
19
− 102100u
18
+ · · · + 26914b − 201231, a − 1, u
20
− 4u
19
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
1
−0.117820u
19
+ 3.79356u
18
+ ··· − 22.6231u + 7.47682
a
8
=
−0.117820u
19
+ 3.79356u
18
+ ··· − 22.6231u + 8.47682
−0.117820u
19
+ 3.79356u
18
+ ··· − 22.6231u + 7.47682
a
12
=
u
3.32229u
19
− 11.0375u
18
+ ··· + 8.00554u + 0.117820
a
2
=
−2.25165u
19
+ 8.50420u
18
+ ··· − 13.4070u + 4.32229
−1.44965u
19
+ 5.33845u
18
+ ··· − 2.84978u + 0.253994
a
1
=
−3.34528u
19
+ 12.9892u
18
+ ··· − 16.0148u + 5.07870
−2.80196u
19
+ 9.51397u
18
+ ··· − 4.38512u + 0.364420
a
6
=
−0.117820u
19
+ 3.79356u
18
+ ··· − 22.6231u + 8.47682
−2.36947u
19
+ 12.2978u
18
+ ··· − 36.0301u + 10.7991
a
5
=
4.49101u
19
− 14.7693u
18
+ ··· + 12.3599u − 1.16307
3.33299u
19
− 10.7501u
18
+ ··· + 1.56071u + 0.402802
a
10
=
0.253994u
19
+ 0.433678u
18
+ ··· − 8.75284u + 1.83380
−3.06829u
19
+ 11.4712u
18
+ ··· − 15.7584u + 1.71598
a
9
=
−1.60010u
19
+ 5.89463u
18
+ ··· − 10.0474u + 1.23007
−3.43063u
19
+ 12.6272u
18
+ ··· − 15.7517u + 3.37174
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
182014
13457
u
19
+
673876
13457
u
18
+ ··· −
1440624
13457
u +
66848
13457
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
20
+ 4u
19
+ ··· + 6u + 1
c
2
, c
10
u
20
+ 4u
19
+ ··· + 9u + 1
c
3
, c
11
u
20
+ 4u
19
+ ··· + 4u + 1
c
6
u
20
− 21u
19
+ ··· − 5888u + 512
c
7
u
20
− 17u
19
+ ··· − 58u
2
+ 8
c
9
, c
12
u
20
− 10u
19
+ ··· − 432u + 64
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
20
+ 14y
19
+ ··· + 18y + 1
c
2
, c
10
y
20
− 8y
19
+ ··· − 29y + 1
c
3
, c
11
y
20
+ 4y
19
+ ··· + 10y + 1
c
6
y
20
− y
19
+ ··· + 8454144y + 262144
c
7
y
20
− 3y
19
+ ··· − 928y + 64
c
9
, c
12
y
20
+ 6y
19
+ ··· − 256y + 4096
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.491834 + 0.721967I
a = 1.00000
b = 0.193762 − 0.533092I
−1.94038 − 0.72654I −7.43882 − 4.55749I
u = 0.491834 − 0.721967I
a = 1.00000
b = 0.193762 + 0.533092I
−1.94038 + 0.72654I −7.43882 + 4.55749I
u = −0.314766 + 1.101470I
a = 1.00000
b = 0.198279 + 0.120648I
3.52200 − 3.40437I −3.46913 + 3.36431I
u = −0.314766 − 1.101470I
a = 1.00000
b = 0.198279 − 0.120648I
3.52200 + 3.40437I −3.46913 − 3.36431I
u = −0.605304 + 0.531225I
a = 1.00000
b = −1.51357 − 0.59051I
−0.09983 − 3.38858I −2.41701 + 8.48871I
u = −0.605304 − 0.531225I
a = 1.00000
b = −1.51357 + 0.59051I
−0.09983 + 3.38858I −2.41701 − 8.48871I
u = −0.024746 + 0.800894I
a = 1.00000
b = −1.53446 + 1.05621I
0.49272 − 7.72234I −10.36662 + 6.86541I
u = −0.024746 − 0.800894I
a = 1.00000
b = −1.53446 − 1.05621I
0.49272 + 7.72234I −10.36662 − 6.86541I
u = 1.009240 + 0.849113I
a = 1.00000
b = −0.824428 − 0.175693I
7.45841 + 1.00347I 0.36457 + 2.52329I
u = 1.009240 − 0.849113I
a = 1.00000
b = −0.824428 + 0.175693I
7.45841 − 1.00347I 0.36457 − 2.52329I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484465 + 0.475215I
a = 1.00000
b = −1.53091 + 1.32244I
2.10928 + 9.64745I −3.9407 − 14.3164I
u = 0.484465 − 0.475215I
a = 1.00000
b = −1.53091 − 1.32244I
2.10928 − 9.64745I −3.9407 + 14.3164I
u = 0.861225 + 1.031420I
a = 1.00000
b = −1.01532 − 1.20528I
−3.04305 + 6.67086I −5.21791 − 2.63870I
u = 0.861225 − 1.031420I
a = 1.00000
b = −1.01532 + 1.20528I
−3.04305 − 6.67086I −5.21791 + 2.63870I
u = 0.167038 + 0.535886I
a = 1.00000
b = −1.01845 − 1.57478I
−2.57404 + 2.62147I −15.2857 − 10.0855I
u = 0.167038 − 0.535886I
a = 1.00000
b = −1.01845 + 1.57478I
−2.57404 − 2.62147I −15.2857 + 10.0855I
u = −1.13134 + 0.95673I
a = 1.00000
b = −0.591919 + 0.779585I
5.94853 − 3.83843I −3.28174 + 4.00815I
u = −1.13134 − 0.95673I
a = 1.00000
b = −0.591919 − 0.779585I
5.94853 + 3.83843I −3.28174 − 4.00815I
u = 1.06235 + 1.12612I
a = 1.00000
b = −0.86298 − 1.15143I
−2.00404 + 10.90100I −3.44699 − 8.30760I
u = 1.06235 − 1.12612I
a = 1.00000
b = −0.86298 + 1.15143I
−2.00404 − 10.90100I −3.44699 + 8.30760I
21
V. I
u
5
= hb + u, a + 1, u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
4
− 2u
3
+ 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−1
−u
a
8
=
−u − 1
−u
a
12
=
u
u
2
+ u
a
2
=
−u
3
− u
2
+ 1
−u
4
− 2u
3
− u
2
a
1
=
−u
5
− 2u
4
− 3u
3
− u
2
+ 1
u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− u
2
a
6
=
−u
2
− u − 1
u
4
+ u
3
− u
a
5
=
u
6
+ 3u
5
+ 4u
4
+ 2u
3
− u
2
− u − 1
u
6
+ 2u
5
+ 3u
4
+ u
3
− u
a
10
=
u
3
+ 2u
2
+ u
u
3
+ u
2
+ u
a
9
=
−u
6
− 2u
5
− 2u
4
+ u
3
+ 2u
2
+ u
−u
7
− 3u
6
− 4u
5
− 2u
4
+ u
3
+ u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
7
+ 3u
6
− 3u
4
+ 9u
3
+ 9u
2
− 9
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
8
− 2u
7
+ 4u
6
− 2u
5
+ 3u
3
− 2u
2
− u + 1
c
2
, c
6
, c
10
u
8
+ 2u
7
+ u
6
− 3u
5
− 2u
4
+ u
3
+ 5u
2
+ 4u + 2
c
3
, c
7
, c
11
u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
4
− 2u
3
+ 1
c
4
, c
8
, c
12
u
8
+ 2u
7
+ 4u
6
+ 2u
5
− 3u
3
− 2u
2
+ u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
y
8
+ 4y
7
+ 8y
6
+ 4y
5
− 6y
4
− 5y
3
+ 10y
2
− 5y + 1
c
2
, c
6
, c
10
y
8
− 2y
7
+ 9y
6
− 7y
5
+ 8y
4
+ 7y
3
+ 9y
2
+ 4y + 4
c
3
, c
7
, c
11
y
8
− y
7
+ 6y
6
− 5y
5
+ 10y
4
+ 4y
3
− 4y
2
+ 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103931 + 0.718671I
a = −1.00000
b = 0.103931 − 0.718671I
−2.30991 + 1.50082I −12.82887 − 5.43370I
u = −0.103931 − 0.718671I
a = −1.00000
b = 0.103931 + 0.718671I
−2.30991 − 1.50082I −12.82887 + 5.43370I
u = 0.694301 + 0.211526I
a = −1.00000
b = −0.694301 − 0.211526I
1.98217 − 8.48228I −3.44672 + 5.24976I
u = 0.694301 − 0.211526I
a = −1.00000
b = −0.694301 + 0.211526I
1.98217 + 8.48228I −3.44672 − 5.24976I
u = −1.122430 + 0.641983I
a = −1.00000
b = 1.122430 − 0.641983I
9.81320 − 5.60717I 4.40282 + 4.85815I
u = −1.122430 − 0.641983I
a = −1.00000
b = 1.122430 + 0.641983I
9.81320 + 5.60717I 4.40282 − 4.85815I
u = −0.96794 + 1.10283I
a = −1.00000
b = 0.96794 − 1.10283I
−2.90573 − 8.64274I −4.62723 + 6.48607I
u = −0.96794 − 1.10283I
a = −1.00000
b = 0.96794 + 1.10283I
−2.90573 + 8.64274I −4.62723 − 6.48607I
25
VI. I
u
6
= h−47u
11
− 28u
10
+ · · · + 592b − 663, 663u
11
a + 949u
11
+ · · · −
913a − 2279, u
12
− 3u
11
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
a
0.0793919u
11
+ 0.0472973u
10
+ ··· + 0.422297u + 1.11993
a
8
=
0.0793919u
11
+ 0.0472973u
10
+ ··· + a + 1.11993
0.0793919u
11
+ 0.0472973u
10
+ ··· + 0.422297u + 1.11993
a
12
=
0.0793919au
11
− 0.322635u
11
+ ··· + 1.11993a + 1.60304
0.346284u
11
− 1.40541u
10
+ ··· − 0.280405u − 0.322635
a
2
=
−0.596284au
11
− 0.346284u
11
+ ··· − 0.427365a + 1.07264
−
3
4
u
11
+
7
4
u
10
+ ··· +
9
4
u
2
+
1
4
u
a
1
=
−0.395270au
11
− 0.145270u
11
+ ··· − 0.543919a − 0.0439189
0.217905au
11
− 0.532095u
11
+ ··· − 0.0591216a − 0.0591216
a
6
=
0.0793919u
11
+ 0.0472973u
10
+ ··· + a + 1.11993
−0.351351u
11
+ 1.21622u
10
+ ··· + 0.216216u + 1.40541
a
5
=
−0.520270au
11
+ 0.712838u
11
+ ··· + 0.831081a + 0.0236486
−0.118243au
11
+ 0.282095u
11
+ ··· − 0.402027a + 0.309122
a
10
=
−0.351351au
11
− 0.00506757u
11
+ ··· + 1.40541a + 2.08277
−0.430743au
11
− 0.0287162u
11
+ ··· + 0.285473a + 0.802365
a
9
=
0.280405au
11
− 0.518581u
11
+ ··· + 0.753378a + 0.886824
−0.712838au
11
+ 0.172297u
11
+ ··· + 0.976351a + 0.685811
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
489
74
u
11
+
566
37
u
10
−
448
37
u
9
−
2875
74
u
8
+
1670
37
u
7
+
943
74
u
6
−
4507
37
u
5
+
5645
74
u
4
−
1385
74
u
3
−
1039
37
u
2
+
233
37
u −
597
74
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
(u
12
+ 3u
11
+ ··· + 9u + 7)
2
c
2
, c
6
, c
10
(u
12
+ 2u
11
+ 2u
10
− 4u
9
− u
8
+ 4u
6
+ 24u
5
+ 6u
4
− 10u
3
+ 6u
2
+ 6u + 1)
2
c
3
, c
7
, c
11
(u
12
+ 3u
11
+ ··· + u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
(y
12
+ 7y
11
+ ··· + 227y + 49)
2
c
2
, c
6
, c
10
(y
12
+ 18y
10
+ ··· − 24y + 1)
2
c
3
, c
7
, c
11
(y
12
− y
11
+ ··· + 7y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.660686 + 0.508519I
a = 1.63037 + 0.35251I
b = −1.33481 − 0.55559I
6.76819 + 5.97824I 2.38371 − 7.63117I
u = 0.660686 + 0.508519I
a = −1.67518 + 0.44843I
b = 0.897901 + 1.061970I
6.76819 + 5.97824I 2.38371 − 7.63117I
u = 0.660686 − 0.508519I
a = 1.63037 − 0.35251I
b = −1.33481 + 0.55559I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = 0.660686 − 0.508519I
a = −1.67518 − 0.44843I
b = 0.897901 − 1.061970I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = 0.247330 + 0.683605I
a = −0.601210 + 0.100710I
b = 1.24643 − 1.36934I
−1.83339 + 2.29825I −8.3837 − 11.7360I
u = 0.247330 + 0.683605I
a = −1.18793 − 2.25312I
b = −0.217544 − 0.386081I
−1.83339 + 2.29825I −8.3837 − 11.7360I
u = 0.247330 − 0.683605I
a = −0.601210 − 0.100710I
b = 1.24643 + 1.36934I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = 0.247330 − 0.683605I
a = −1.18793 + 2.25312I
b = −0.217544 + 0.386081I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = 0.897901 + 1.061970I
a = −0.924786 + 0.475002I
b = 0.660686 + 0.508519I
6.76819 + 5.97824I 2.38371 − 7.63117I
u = 0.897901 + 1.061970I
a = 0.585965 − 0.126695I
b = −1.33481 − 0.55559I
6.76819 + 5.97824I 2.38371 − 7.63117I
29
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897901 − 1.061970I
a = −0.924786 − 0.475002I
b = 0.660686 − 0.508519I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = 0.897901 − 1.061970I
a = 0.585965 + 0.126695I
b = −1.33481 + 0.55559I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = −1.33481 + 0.55559I
a = −0.855605 + 0.439468I
b = 0.660686 − 0.508519I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = −1.33481 + 0.55559I
a = −0.557033 + 0.149112I
b = 0.897901 − 1.061970I
6.76819 − 5.97824I 2.38371 + 7.63117I
u = −1.33481 − 0.55559I
a = −0.855605 − 0.439468I
b = 0.660686 + 0.508519I
6.76819 + 5.97824I 2.38371 − 7.63117I
u = −1.33481 − 0.55559I
a = −0.557033 − 0.149112I
b = 0.897901 + 1.061970I
6.76819 + 5.97824I 2.38371 − 7.63117I
u = −0.217544 + 0.386081I
a = −1.61791 + 0.27102I
b = 1.24643 + 1.36934I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = −0.217544 + 0.386081I
a = 1.31133 − 3.96730I
b = 0.247330 − 0.683605I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = −0.217544 − 0.386081I
a = −1.61791 − 0.27102I
b = 1.24643 − 1.36934I
−1.83339 + 2.29825I −8.3837 − 11.7360I
u = −0.217544 − 0.386081I
a = 1.31133 + 3.96730I
b = 0.247330 + 0.683605I
−1.83339 + 2.29825I −8.3837 − 11.7360I
30
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24643 + 1.36934I
a = −0.183104 − 0.347289I
b = −0.217544 + 0.386081I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = 1.24643 + 1.36934I
a = 0.075109 + 0.227234I
b = 0.247330 − 0.683605I
−1.83339 − 2.29825I −8.3837 + 11.7360I
u = 1.24643 − 1.36934I
a = −0.183104 + 0.347289I
b = −0.217544 − 0.386081I
−1.83339 + 2.29825I −8.3837 − 11.7360I
u = 1.24643 − 1.36934I
a = 0.075109 − 0.227234I
b = 0.247330 + 0.683605I
−1.83339 + 2.29825I −8.3837 − 11.7360I
31
VII.
I
u
7
= hb + u, 2u
7
− 6u
6
+ 7u
5
− 2u
4
− 4u
2
+ a + 5u − 3, u
8
− 3u
7
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−2u
7
+ 6u
6
− 7u
5
+ 2u
4
+ 4u
2
− 5u + 3
−u
a
8
=
−2u
7
+ 6u
6
− 7u
5
+ 2u
4
+ 4u
2
− 6u + 3
−u
a
12
=
−2u
7
+ 7u
6
− 8u
5
+ 2u
4
+ u
3
+ 6u
2
− 6u + 3
−u
7
+ 2u
6
− 2u
5
− u
3
+ u
2
− u
a
2
=
2u
7
− 4u
6
+ 3u
5
+ 2u
3
− 3u
2
+ u − 1
−u
7
+ 3u
6
− 3u
5
+ u
4
+ 2u
2
− u + 1
a
1
=
2u
7
− 5u
6
+ 4u
5
+ u
3
− 4u
2
+ 2u − 2
u
7
− u
6
+ u
4
+ u
3
+ u
a
6
=
−u
7
+ 4u
6
− 5u
5
+ 2u
4
+ u
3
+ 3u
2
− 4u + 3
−u
7
+ 2u
6
− 2u
5
+ u
2
− 2u + 1
a
5
=
u
6
− u
5
+ u
4
+ u
3
+ u
2
+ 2
−2u
7
+ 3u
6
− 2u
5
− u
4
− u
3
+ u
2
− 2u + 1
a
10
=
−4u
7
+ 11u
6
− 12u
5
+ 2u
4
+ 8u
2
− 10u + 3
−u
7
+ 2u
6
− 2u
5
+ u
2
− u
a
9
=
u
7
− 2u
5
+ 2u
4
+ 3u
3
− 2u
−2u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 4u
2
− 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15u
7
+ 37u
6
− 35u
5
+ 2u
4
− 7u
3
+ 29u
2
− 29u + 7
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 4u
7
+ 10u
6
− 18u
5
+ 20u
4
− 15u
3
+ 8u
2
− 2u + 1
c
2
, c
6
u
8
− 2u
6
+ u
5
+ u
4
− 4u
3
+ 3u + 1
c
3
, c
7
u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1
c
4
u
8
+ 4u
7
+ 10u
6
+ 18u
5
+ 20u
4
+ 15u
3
+ 8u
2
+ 2u + 1
c
5
, c
9
u
8
− u
7
+ 3u
6
− 4u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
c
8
, c
12
u
8
+ u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1
c
10
u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 10u
4
+ 3u
3
− u
2
+ u + 1
c
11
u
8
+ 5u
7
+ 12u
6
+ 16u
5
+ 13u
4
+ 7u
3
+ 4u
2
+ 2u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
8
+ 4y
7
− 4y
6
− 28y
5
+ 6y
4
+ 43y
3
+ 44y
2
+ 12y + 1
c
2
, c
6
y
8
− 4y
7
+ 6y
6
− 5y
5
+ 11y
4
− 26y
3
+ 26y
2
− 9y + 1
c
3
, c
7
y
8
− y
7
+ 6y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 3y
2
+ 2y + 1
c
5
, c
8
, c
9
c
12
y
8
+ 5y
7
+ 9y
6
+ 6y
5
− 2y
3
+ y
2
+ 2y + 1
c
10
y
8
+ 4y
6
+ 34y
5
+ 18y
4
− 33y
3
+ 15y
2
− 3y + 1
c
11
y
8
− y
7
+ 10y
6
− 6y
5
+ 23y
4
+ 15y
3
+ 14y
2
+ 4y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883954 + 0.567268I
a = 1.52507 + 0.35374I
b = −0.883954 − 0.567268I
7.95377 + 2.68532I 3.33468 − 4.18449I
u = 0.883954 − 0.567268I
a = 1.52507 − 0.35374I
b = −0.883954 + 0.567268I
7.95377 − 2.68532I 3.33468 + 4.18449I
u = −0.704204 + 0.626099I
a = −0.144311 + 0.603307I
b = 0.704204 − 0.626099I
−1.49979 + 1.51030I −2.66904 − 3.09158I
u = −0.704204 − 0.626099I
a = −0.144311 − 0.603307I
b = 0.704204 + 0.626099I
−1.49979 − 1.51030I −2.66904 + 3.09158I
u = 0.228862 + 0.666962I
a = −0.38534 − 1.93462I
b = −0.228862 − 0.666962I
−2.24789 + 1.12072I −12.14274 − 5.83810I
u = 0.228862 − 0.666962I
a = −0.38534 + 1.93462I
b = −0.228862 + 0.666962I
−2.24789 − 1.12072I −12.14274 + 5.83810I
u = 1.09139 + 0.92852I
a = 0.504583 + 0.133700I
b = −1.09139 − 0.92852I
5.66352 + 5.68496I −6.02290 − 6.27011I
u = 1.09139 − 0.92852I
a = 0.504583 − 0.133700I
b = −1.09139 + 0.92852I
5.66352 − 5.68496I −6.02290 + 6.27011I
35
VIII. I
u
8
= h−u
6
+ 2u
5
− 2u
4
− u
2
+ b + u − 2, a + 1, u
8
− 3u
7
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−1
u
6
− 2u
5
+ 2u
4
+ u
2
− u + 2
a
8
=
u
6
− 2u
5
+ 2u
4
+ u
2
− u + 1
u
6
− 2u
5
+ 2u
4
+ u
2
− u + 2
a
12
=
u
−u
7
+ 2u
6
− 2u
5
− u
3
+ u
2
− u
a
2
=
u
7
− 2u
6
+ 2u
5
+ u
3
− 2u
2
+ 2u
−u
7
+ 3u
6
− 3u
5
+ u
4
+ 2u
2
− u + 1
a
1
=
u
7
− u
6
+ u
5
+ 2u
3
− u
2
+ 2u
−3u
7
+ 7u
6
− 6u
5
+ u
4
− 2u
3
+ 5u
2
− 3u + 2
a
6
=
u
6
− 2u
5
+ 2u
4
− u + 1
−u
7
+ 3u
6
− 4u
5
+ 3u
4
− u
3
+ 2u
2
− 3u + 3
a
5
=
2u
7
− 4u
6
+ 3u
5
+ u
4
+ u
3
− 3u
2
+ 2u − 1
u
7
− u
6
+ 2u
4
+ u
3
+ 1
a
10
=
u
7
− 2u
6
+ u
5
+ u
4
− 2u
2
+ u − 1
2u
7
− 4u
6
+ 3u
5
+ u
4
+ u
3
− 3u
2
+ 3u − 1
a
9
=
−u
6
+ u
5
− u
3
− u
2
− 1
3u
7
− 7u
6
+ 6u
5
+ 2u
3
− 5u
2
+ 4u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15u
7
+ 37u
6
− 35u
5
+ 2u
4
− 7u
3
+ 29u
2
− 29u + 7
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
− u
7
+ 3u
6
− 4u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
c
2
, c
10
u
8
− 2u
6
+ u
5
+ u
4
− 4u
3
+ 3u + 1
c
3
, c
11
u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1
c
4
, c
8
u
8
+ u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1
c
6
u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 10u
4
+ 3u
3
− u
2
+ u + 1
c
7
u
8
+ 5u
7
+ 12u
6
+ 16u
5
+ 13u
4
+ 7u
3
+ 4u
2
+ 2u + 1
c
9
u
8
− 4u
7
+ 10u
6
− 18u
5
+ 20u
4
− 15u
3
+ 8u
2
− 2u + 1
c
12
u
8
+ 4u
7
+ 10u
6
+ 18u
5
+ 20u
4
+ 15u
3
+ 8u
2
+ 2u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
8
+ 5y
7
+ 9y
6
+ 6y
5
− 2y
3
+ y
2
+ 2y + 1
c
2
, c
10
y
8
− 4y
7
+ 6y
6
− 5y
5
+ 11y
4
− 26y
3
+ 26y
2
− 9y + 1
c
3
, c
11
y
8
− y
7
+ 6y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 3y
2
+ 2y + 1
c
6
y
8
+ 4y
6
+ 34y
5
+ 18y
4
− 33y
3
+ 15y
2
− 3y + 1
c
7
y
8
− y
7
+ 10y
6
− 6y
5
+ 23y
4
+ 15y
3
+ 14y
2
+ 4y + 1
c
9
, c
12
y
8
+ 4y
7
− 4y
6
− 28y
5
+ 6y
4
+ 43y
3
+ 44y
2
+ 12y + 1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883954 + 0.567268I
a = −1.00000
b = 1.14742 + 1.17781I
7.95377 + 2.68532I 3.33468 − 4.18449I
u = 0.883954 − 0.567268I
a = −1.00000
b = 1.14742 − 1.17781I
7.95377 − 2.68532I 3.33468 + 4.18449I
u = −0.704204 + 0.626099I
a = −1.00000
b = −0.276106 − 0.515204I
−1.49979 + 1.51030I −2.66904 − 3.09158I
u = −0.704204 − 0.626099I
a = −1.00000
b = −0.276106 + 0.515204I
−1.49979 − 1.51030I −2.66904 + 3.09158I
u = 0.228862 + 0.666962I
a = −1.00000
b = 1.202130 − 0.699769I
−2.24789 + 1.12072I −12.14274 − 5.83810I
u = 0.228862 − 0.666962I
a = −1.00000
b = 1.202130 + 0.699769I
−2.24789 − 1.12072I −12.14274 + 5.83810I
u = 1.09139 + 0.92852I
a = −1.00000
b = 0.426552 + 0.614435I
5.66352 + 5.68496I −6.02290 − 6.27011I
u = 1.09139 − 0.92852I
a = −1.00000
b = 0.426552 − 0.614435I
5.66352 − 5.68496I −6.02290 + 6.27011I
39
IX. I
u
9
= h−u
7
− 4u
6
− 7u
5
− 5u
4
+ u
2
+ b − u, −u
6
− 4u
5
− 7u
4
− 5u
3
+ a +
u − 1, u
8
+ 5u
7
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
u
6
+ 4u
5
+ 7u
4
+ 5u
3
− u + 1
u
7
+ 4u
6
+ 7u
5
+ 5u
4
− u
2
+ u
a
8
=
u
7
+ 5u
6
+ 11u
5
+ 12u
4
+ 5u
3
− u
2
+ 1
u
7
+ 4u
6
+ 7u
5
+ 5u
4
− u
2
+ u
a
12
=
2u
7
+ 8u
6
+ 15u
5
+ 13u
4
+ 5u
3
+ u
2
+ 2u − 1
−2u
7
− 9u
6
− 19u
5
− 21u
4
− 13u
3
− 6u
2
− 4u − 2
a
2
=
−2u
7
− 11u
6
− 27u
5
− 35u
4
− 24u
3
− 9u
2
− 6u − 3
−2u
7
− 8u
6
− 14u
5
− 11u
4
− 3u
3
− 2u
2
− 2u
a
1
=
−2u
7
− 10u
6
− 23u
5
− 28u
4
− 18u
3
− 6u
2
− 4u − 2
−u
7
− 3u
6
− 4u
5
− u
4
+ 2u
3
+ u
2
+ 1
a
6
=
−u
4
− 3u
3
− 4u
2
− 2u
−u
5
− 4u
4
− 6u
3
− 4u
2
− u − 1
a
5
=
−2u
7
− 8u
6
− 14u
5
− 10u
4
− u
3
+ u
2
− 2u + 1
u
7
+ 6u
6
+ 15u
5
+ 19u
4
+ 12u
3
+ 4u
2
+ 3u + 2
a
10
=
−u
7
− 5u
6
− 12u
5
− 16u
4
− 13u
3
− 8u
2
− 6u − 3
−u
7
− 4u
6
− 8u
5
− 8u
4
− 5u
3
− 3u
2
− 2u
a
9
=
−2u
7
− 11u
6
− 28u
5
− 39u
4
− 31u
3
− 16u
2
− 10u − 6
−u
7
− 4u
6
− 8u
5
− 7u
4
− 3u
3
− u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
7
+ 23u
6
+ 50u
5
+ 54u
4
+ 23u
3
+ 5u
2
+ 8u
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
8
− u
7
+ 3u
6
− 4u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
c
2
u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 10u
4
+ 3u
3
− u
2
+ u + 1
c
3
u
8
+ 5u
7
+ 12u
6
+ 16u
5
+ 13u
4
+ 7u
3
+ 4u
2
+ 2u + 1
c
4
, c
12
u
8
+ u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1
c
5
u
8
− 4u
7
+ 10u
6
− 18u
5
+ 20u
4
− 15u
3
+ 8u
2
− 2u + 1
c
6
, c
10
u
8
− 2u
6
+ u
5
+ u
4
− 4u
3
+ 3u + 1
c
7
, c
11
u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1
c
8
u
8
+ 4u
7
+ 10u
6
+ 18u
5
+ 20u
4
+ 15u
3
+ 8u
2
+ 2u + 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
12
y
8
+ 5y
7
+ 9y
6
+ 6y
5
− 2y
3
+ y
2
+ 2y + 1
c
2
y
8
+ 4y
6
+ 34y
5
+ 18y
4
− 33y
3
+ 15y
2
− 3y + 1
c
3
y
8
− y
7
+ 10y
6
− 6y
5
+ 23y
4
+ 15y
3
+ 14y
2
+ 4y + 1
c
5
, c
8
y
8
+ 4y
7
− 4y
6
− 28y
5
+ 6y
4
+ 43y
3
+ 44y
2
+ 12y + 1
c
6
, c
10
y
8
− 4y
7
+ 6y
6
− 5y
5
+ 11y
4
− 26y
3
+ 26y
2
− 9y + 1
c
7
, c
11
y
8
− y
7
+ 6y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 3y
2
+ 2y + 1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426552 + 0.614435I
a = 1.85182 + 0.49068I
b = −1.09139 + 0.92852I
5.66352 − 5.68496I −6.02290 + 6.27011I
u = −0.426552 − 0.614435I
a = 1.85182 − 0.49068I
b = −1.09139 − 0.92852I
5.66352 + 5.68496I −6.02290 − 6.27011I
u = −1.202130 + 0.699769I
a = −0.099027 + 0.497173I
b = −0.228862 − 0.666962I
−2.24789 + 1.12072I −12.14274 − 5.83810I
u = −1.202130 − 0.699769I
a = −0.099027 − 0.497173I
b = −0.228862 + 0.666962I
−2.24789 − 1.12072I −12.14274 + 5.83810I
u = 0.276106 + 0.515204I
a = −0.37502 − 1.56783I
b = 0.704204 − 0.626099I
−1.49979 + 1.51030I −2.66904 − 3.09158I
u = 0.276106 − 0.515204I
a = −0.37502 + 1.56783I
b = 0.704204 + 0.626099I
−1.49979 − 1.51030I −2.66904 + 3.09158I
u = −1.14742 + 1.17781I
a = 0.622232 + 0.144327I
b = −0.883954 + 0.567268I
7.95377 − 2.68532I 3.33468 + 4.18449I
u = −1.14742 − 1.17781I
a = 0.622232 − 0.144327I
b = −0.883954 − 0.567268I
7.95377 + 2.68532I 3.33468 − 4.18449I
43
X. I
u
10
= h−u
4
+ 2u
3
− 2u
2
+ b + 2u − 2, u
4
− 2u
3
+ u
2
+ a + 1, u
6
− 3u
5
+
4u
4
− 4u
3
+ 4u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−u
4
+ 2u
3
− u
2
− 1
u
4
− 2u
3
+ 2u
2
− 2u + 2
a
8
=
u
2
− 2u + 1
u
4
− 2u
3
+ 2u
2
− 2u + 2
a
12
=
2u
5
− 6u
4
+ 7u
3
− 5u
2
+ 4u − 1
−u
5
+ 2u
4
− u
3
+ u
2
− u
a
2
=
u
−u
3
− u
a
1
=
0
−u
a
6
=
−u
5
+ 3u
4
− 4u
3
+ 4u
2
− 4u + 2
−u
5
+ 4u
4
− 6u
3
+ 5u
2
− 5u + 3
a
5
=
1
0
a
10
=
u
5
− 4u
4
+ 6u
3
− 4u
2
+ u
1
a
9
=
−u
4
+ 2u
3
− u
2
− 1
u
4
− 2u
3
+ 2u
2
− 2u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 2u + 1
c
2
, c
6
, c
10
u
6
+ 4u
5
+ 5u
4
+ 2u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y
6
− y
5
+ 6y
3
+ 8y
2
+ 4y + 1
c
2
, c
6
, c
10
y
6
− 6y
5
+ 25y
4
− 14y
3
+ 10y
2
− 4y + 1
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198713 + 0.922132I
a = 0.28582 − 1.57759I
b = 0.300767 − 0.633156I
−1.64493 −6.00000
u = −0.198713 − 0.922132I
a = 0.28582 + 1.57759I
b = 0.300767 + 0.633156I
−1.64493 −6.00000
u = 0.300767 + 0.633156I
a = −1.309910 − 0.308397I
b = 1.39795 − 0.57705I
−1.64493 −6.00000
u = 0.300767 − 0.633156I
a = −1.309910 + 0.308397I
b = 1.39795 + 0.57705I
−1.64493 −6.00000
u = 1.39795 + 0.57705I
a = 0.024087 − 0.462862I
b = −0.198713 + 0.922132I
−1.64493 −6.00000
u = 1.39795 − 0.57705I
a = 0.024087 + 0.462862I
b = −0.198713 − 0.922132I
−1.64493 −6.00000
47
XI. I
u
11
= hu
5
− 2u
4
+ u
3
+ b + u, 2u
5
− 6u
4
+ 7u
3
− 6u
2
+ a + 6u − 2, u
6
−
3u
5
+ 4u
4
− 4u
3
+ 4u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−2u
5
+ 6u
4
− 7u
3
+ 6u
2
− 6u + 2
−u
5
+ 2u
4
− u
3
− u
a
8
=
−3u
5
+ 8u
4
− 8u
3
+ 6u
2
− 7u + 2
−u
5
+ 2u
4
− u
3
− u
a
12
=
−3u
5
+ 8u
4
− 8u
3
+ 6u
2
− 7u + 1
−u
5
+ 2u
4
− u
3
+ u
2
− u
a
2
=
−2u
5
+ 6u
4
− 7u
3
+ 6u
2
− 6u + 4
−u
3
− u
a
1
=
−u
5
+ 4u
4
− 6u
3
+ 6u
2
− 5u + 4
−2u
3
+ 2u
2
− 2u + 1
a
6
=
−2u
5
+ 6u
4
− 6u
3
+ 4u
2
− 5u + 2
−2u
5
+ 4u
4
− 2u
3
− u
a
5
=
2u
5
− 4u
4
+ 3u
3
− 3u
2
+ 4u + 1
−u
5
+ 2u
4
− u
3
− u
2
+ u
a
10
=
−6u
5
+ 15u
4
− 14u
3
+ 11u
2
− 13u + 1
−2u
5
+ 5u
4
− 5u
3
+ 4u
2
− 3u
a
9
=
−5u
5
+ 11u
4
− 8u
3
+ 6u
2
− 8u − 2
−u
5
+ 2u
4
− 2u
3
+ u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 2u + 1
c
2
, c
6
, c
10
u
6
+ 4u
5
+ 5u
4
+ 2u + 1
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y
6
− y
5
+ 6y
3
+ 8y
2
+ 4y + 1
c
2
, c
6
, c
10
y
6
− 6y
5
+ 25y
4
− 14y
3
+ 10y
2
− 4y + 1
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198713 + 0.922132I
a = −0.723320 − 0.170295I
b = 1.39795 + 0.57705I
−1.64493 −6.00000
u = −0.198713 − 0.922132I
a = −0.723320 + 0.170295I
b = 1.39795 − 0.57705I
−1.64493 −6.00000
u = 0.300767 + 0.633156I
a = 0.11213 − 2.15464I
b = −0.198713 − 0.922132I
−1.64493 −6.00000
u = 0.300767 − 0.633156I
a = 0.11213 + 2.15464I
b = −0.198713 + 0.922132I
−1.64493 −6.00000
u = 1.39795 + 0.57705I
a = 0.111193 + 0.613734I
b = 0.300767 − 0.633156I
−1.64493 −6.00000
u = 1.39795 − 0.57705I
a = 0.111193 − 0.613734I
b = 0.300767 + 0.633156I
−1.64493 −6.00000
51
XII. I
u
12
= hb − u, a − 1, u
3
+ u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
1
u
a
8
=
u + 1
u
a
12
=
u
u
2
+ u
a
2
=
u
u
2
− 1
a
1
=
0
−u
a
6
=
u
2
+ u + 1
u
2
a
5
=
1
0
a
10
=
u
2
+ 1
1
a
9
=
1
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
52
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
u
3
− u
2
+ u + 1
c
2
, c
6
, c
10
u
3
− 2u
2
+ 2
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y
3
+ y
2
+ 3y −1
c
2
, c
6
, c
10
y
3
− 4y
2
+ 8y −4
54
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771845 + 1.115140I
a = 1.00000
b = −0.771845 + 1.115140I
−1.64493 −6.00000
u = −0.771845 − 1.115140I
a = 1.00000
b = −0.771845 − 1.115140I
−1.64493 −6.00000
u = 0.543689
a = 1.00000
b = 0.543689
−1.64493 −6.00000
55
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
(u
3
− u
2
+ u + 1)(u
6
− 2u
5
+ 5u
4
− 4u
3
+ 5u
2
− u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 2u + 1)
2
· (u
8
− 4u
7
+ 10u
6
− 18u
5
+ 20u
4
− 15u
3
+ 8u
2
− 2u + 1)
· (u
8
− 2u
7
+ 4u
6
− 2u
5
+ 3u
3
− 2u
2
− u + 1)
· (u
8
− u
7
+ 3u
6
− 4u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1)
2
· ((u
12
+ 3u
11
+ ··· + 9u + 7)
2
)(u
20
− 10u
19
+ ··· − 432u + 64)
· (u
20
+ 4u
19
+ ··· + 6u + 1)
2
c
2
, c
6
, c
10
(u
3
− 2u
2
+ 2)(u
6
− 4u
5
+ 9u
4
− 11u
3
+ 10u
2
− 5u + 1)
· (u
6
+ 4u
5
+ 5u
4
+ 2u + 1)
2
(u
8
− 2u
6
+ u
5
+ u
4
− 4u
3
+ 3u + 1)
2
· (u
8
+ 2u
7
+ u
6
− 3u
5
− 2u
4
+ u
3
+ 5u
2
+ 4u + 2)
· (u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 10u
4
+ 3u
3
− u
2
+ u + 1)
· (u
12
+ 2u
11
+ 2u
10
− 4u
9
− u
8
+ 4u
6
+ 24u
5
+ 6u
4
− 10u
3
+ 6u
2
+ 6u + 1)
2
· (u
20
− 21u
19
+ ··· − 5888u + 512)(u
20
+ 4u
19
+ ··· + 9u + 1)
2
c
3
, c
7
, c
11
(u
3
− u
2
+ u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 3u
2
− 2u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 2u + 1)
2
· (u
8
− 3u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
4
− 2u
3
+ 1)
· (u
8
+ 5u
7
+ 12u
6
+ 16u
5
+ 13u
4
+ 7u
3
+ 4u
2
+ 2u + 1)
· ((u
12
+ 3u
11
+ ··· + u + 1)
2
)(u
20
− 17u
19
+ ··· − 58u
2
+ 8)
· (u
20
+ 4u
19
+ ··· + 4u + 1)
2
c
4
, c
8
, c
12
(u
3
− u
2
+ u + 1)(u
6
− 2u
5
+ 5u
4
− 4u
3
+ 5u
2
− u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 2u + 1)
2
· (u
8
+ u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
2
· (u
8
+ 2u
7
+ 4u
6
+ 2u
5
− 3u
3
− 2u
2
+ u + 1)
· (u
8
+ 4u
7
+ 10u
6
+ 18u
5
+ 20u
4
+ 15u
3
+ 8u
2
+ 2u + 1)
· ((u
12
+ 3u
11
+ ··· + 9u + 7)
2
)(u
20
− 10u
19
+ ··· − 432u + 64)
· (u
20
+ 4u
19
+ ··· + 6u + 1)
2
56
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
(y
3
+ y
2
+ 3y −1)(y
6
− y
5
+ 6y
3
+ 8y
2
+ 4y + 1)
2
· (y
6
+ 6y
5
+ 19y
4
+ 32y
3
+ 27y
2
+ 9y + 1)
· (y
8
+ 4y
7
− 4y
6
− 28y
5
+ 6y
4
+ 43y
3
+ 44y
2
+ 12y + 1)
· (y
8
+ 4y
7
+ 8y
6
+ 4y
5
− 6y
4
− 5y
3
+ 10y
2
− 5y + 1)
· (y
8
+ 5y
7
+ 9y
6
+ 6y
5
− 2y
3
+ y
2
+ 2y + 1)
2
· ((y
12
+ 7y
11
+ ··· + 227y + 49)
2
)(y
20
+ 6y
19
+ ··· − 256y + 4096)
· (y
20
+ 14y
19
+ ··· + 18y + 1)
2
c
2
, c
6
, c
10
(y
3
− 4y
2
+ 8y −4)(y
6
− 6y
5
+ 25y
4
− 14y
3
+ 10y
2
− 4y + 1)
2
· (y
6
+ 2y
5
+ 13y
4
+ 21y
3
+ 8y
2
− 5y + 1)
· (y
8
+ 4y
6
+ 34y
5
+ 18y
4
− 33y
3
+ 15y
2
− 3y + 1)
· (y
8
− 4y
7
+ 6y
6
− 5y
5
+ 11y
4
− 26y
3
+ 26y
2
− 9y + 1)
2
· (y
8
− 2y
7
+ 9y
6
− 7y
5
+ 8y
4
+ 7y
3
+ 9y
2
+ 4y + 4)
· ((y
12
+ 18y
10
+ ··· − 24y + 1)
2
)(y
20
− 8y
19
+ ··· − 29y + 1)
2
· (y
20
− y
19
+ ··· + 8454144y + 262144)
c
3
, c
7
, c
11
(y
3
+ y
2
+ 3y −1)(y
6
− y
5
+ 6y
3
+ 8y
2
+ 4y + 1)
2
· (y
6
+ y
5
+ 7y
4
+ 4y
3
+ 3y
2
+ 2y + 1)
· (y
8
− y
7
+ 6y
6
− 5y
5
+ 10y
4
+ 4y
3
− 4y
2
+ 1)
· (y
8
− y
7
+ 6y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 3y
2
+ 2y + 1)
2
· (y
8
− y
7
+ 10y
6
− 6y
5
+ 23y
4
+ 15y
3
+ 14y
2
+ 4y + 1)
· ((y
12
− y
11
+ ··· + 7y + 1)
2
)(y
20
− 3y
19
+ ··· − 928y + 64)
· (y
20
+ 4y
19
+ ··· + 10y + 1)
2
57
