12a
1025
(K12a
1025
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 11 12 10 1 2 3 6 5
Solving Sequence
5,11
6 12 7
1,9
4 2 8 3 10
c
5
c
11
c
6
c
12
c
4
c
1
c
8
c
3
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8u
18
− 37u
17
+ ··· + 2b + 46, 33u
18
+ 154u
17
+ ··· + 8a − 196, u
19
+ 6u
18
+ ··· + 4u − 8i
I
u
2
= h−3u
10
a − 7u
9
a + 3u
8
a + 8u
7
a − 13u
6
a − 6u
5
a + 8u
4
a − 18u
3
a − 6u
2
a + 9au + b − 8a,
− 4u
9
a − 7u
10
+ ··· + 4a − 18, u
11
+ 4u
10
+ 3u
9
− 4u
8
+ 9u
6
+ u
5
+ 2u
4
+ 12u
3
+ u
2
− 2u + 4i
I
u
3
= h19502u
7
a
3
− 21027u
7
a
2
+ ··· − 98205a + 12679, 2u
7
a
3
− 3u
7
a
2
+ ··· − 2a + 5,
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
4
= h−7.80310 × 10
46
a
7
u
7
+ 1.01169 × 10
47
a
6
u
7
+ ··· + 1.16866 × 10
48
a + 5.76531 × 10
47
,
− 2a
7
u
7
− 10u
7
a
6
+ ··· + 388a − 283, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
5
= h−3u
31
− 13u
30
+ ··· + 2b − 305, 631u
31
+ 546u
30
+ ··· + 78a + 12324, u
32
− 17u
30
+ ··· + 17u
2
− 39i
I
u
6
= h−u
7
+ 3u
5
− 2u
3
+ b − u, u
5
− 2u
3
+ a + u, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
7
= h−u
7
a + 2u
6
a − 2u
7
+ 2u
5
a + 2u
6
− 4u
4
a + 5u
5
− u
3
a − 4u
4
+ u
2
a − 3u
3
+ b + 2a − u + 3,
− 2u
7
a + 2u
6
a − u
7
+ 5u
5
a − 4u
4
a + 2u
5
− 4u
3
a + 3u
4
+ 2u
2
a + a
2
− au − 5u
2
+ 2a − 3u + 2,
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 195 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−8u
18
− 37u
17
+ · · · + 2b + 46, 33u
18
+ 154u
17
+ · · · + 8a −
196, u
19
+ 6u
18
+ · · · + 4u − 8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−
33
8
u
18
−
77
4
u
17
+ ··· − 31u +
49
2
4u
18
+
37
2
u
17
+ ··· + 29u − 23
a
4
=
−
13
8
u
18
− 8u
17
+ ··· −
23
2
u +
21
2
−
21
4
u
18
− 23u
17
+ ··· − 26u + 25
a
2
=
5
8
u
18
+
13
4
u
17
+ ··· + 5u −
7
2
−
7
2
u
18
−
35
2
u
17
+ ··· − 33u + 25
a
8
=
−
25
8
u
18
−
61
4
u
17
+ ··· − 27u +
41
2
−
1
2
u
18
− 3u
17
+ ··· − 6u + 5
a
3
=
−
23
8
u
18
−
53
4
u
17
+ ··· − 20u +
35
2
−
11
2
u
18
−
51
2
u
17
+ ··· − 41u + 33
a
10
=
−3.12500u
18
− 13.5000u
17
+ ··· − 15.5000u + 13.5000
7
4
u
18
+ 9u
17
+ ··· + 17u − 13
(ii) Obstruction class = −1
(iii) Cusp Shapes =
19
2
u
18
+ 36u
17
+
41
2
u
16
− 36u
15
+
97
2
u
14
+ 132u
13
−
91
2
u
12
−
24u
11
+ 186u
10
+ 31u
9
+
53
2
u
8
+ 182u
7
+
61
2
u
6
+ 65u
5
+
215
2
u
4
+ 16u
3
+ 63u
2
+ 4u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
19
− 17u
18
+ ··· + 287u + 73
c
2
, c
4
, c
8
c
10
u
19
+ u
18
+ ··· − u − 1
c
3
, c
9
u
19
− 2u
18
+ ··· − u + 8
c
5
, c
6
, c
11
u
19
+ 6u
18
+ ··· + 4u − 8
c
12
u
19
− 18u
18
+ ··· + 18468u − 2216
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
19
− 9y
18
+ ··· + 666077y −5329
c
2
, c
4
, c
8
c
10
y
19
− y
18
+ ··· + 13y −1
c
3
, c
9
y
19
− 18y
18
+ ··· + 1249y −64
c
5
, c
6
, c
11
y
19
− 14y
18
+ ··· + 208y −64
c
12
y
19
− 8y
18
+ ··· + 32723920y −4910656
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709745 + 0.730285I
a = −0.258506 − 0.953257I
b = −0.755251 − 0.717037I
−2.03197 + 8.96060I 2.84841 − 12.66101I
u = 0.709745 − 0.730285I
a = −0.258506 + 0.953257I
b = −0.755251 + 0.717037I
−2.03197 − 8.96060I 2.84841 + 12.66101I
u = 0.186145 + 0.879926I
a = 0.46153 + 2.33829I
b = 1.00566 + 1.25604I
−6.8086 + 15.8690I 0.12525 − 9.18098I
u = 0.186145 − 0.879926I
a = 0.46153 − 2.33829I
b = 1.00566 − 1.25604I
−6.8086 − 15.8690I 0.12525 + 9.18098I
u = 0.658306 + 0.912470I
a = 0.782879 − 0.112346I
b = 0.619935 − 0.425591I
−2.40898 − 3.25505I 6.9874 + 16.0679I
u = 0.658306 − 0.912470I
a = 0.782879 + 0.112346I
b = 0.619935 + 0.425591I
−2.40898 + 3.25505I 6.9874 − 16.0679I
u = 1.060720 + 0.501828I
a = −0.924368 + 0.574213I
b = −0.91352 + 1.17079I
−4.13541 − 10.97830I 2.41741 + 5.86474I
u = 1.060720 − 0.501828I
a = −0.924368 − 0.574213I
b = −0.91352 − 1.17079I
−4.13541 + 10.97830I 2.41741 − 5.86474I
u = −0.187090 + 0.762030I
a = −0.744207 − 0.660545I
b = −0.442488 − 0.196300I
−2.15136 + 1.44412I 5.18074 − 1.70147I
u = −0.187090 − 0.762030I
a = −0.744207 + 0.660545I
b = −0.442488 + 0.196300I
−2.15136 − 1.44412I 5.18074 + 1.70147I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.284930 + 0.407140I
a = −0.266492 − 0.998983I
b = 0.546134 − 0.399233I
1.40301 − 5.90085I 7.35606 + 8.38070I
u = −1.284930 − 0.407140I
a = −0.266492 + 0.998983I
b = 0.546134 + 0.399233I
1.40301 + 5.90085I 7.35606 − 8.38070I
u = −1.40516
a = 0.687894
b = −0.909327
6.64749 13.3450
u = −1.38924 + 0.37756I
a = 1.03923 + 1.64419I
b = −1.08787 + 1.28548I
−1.8311 − 20.3870I 4.18663 + 10.65697I
u = −1.38924 − 0.37756I
a = 1.03923 − 1.64419I
b = −1.08787 − 1.28548I
−1.8311 + 20.3870I 4.18663 − 10.65697I
u = −1.49857 + 0.13199I
a = −0.577538 − 0.299514I
b = 1.071510 − 0.799617I
5.36721 − 11.65510I 7.98385 + 9.40931I
u = −1.49857 − 0.13199I
a = −0.577538 + 0.299514I
b = 1.071510 + 0.799617I
5.36721 + 11.65510I 7.98385 − 9.40931I
u = 0.470871
a = −0.300004
b = 0.675904
0.843314 11.7740
u = −1.57590
a = 0.0870582
b = −0.854789
6.18911 18.7100
6
II. I
u
2
= h−3u
10
a − 7u
9
a + · · · + b − 8a, −4u
9
a − 7u
10
+ · · · + 4a − 18, u
11
+
4u
10
+ · · · − 2u + 4i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
a
3u
10
a + 7u
9
a + ··· − 9au + 8a
a
4
=
3
2
u
10
a − u
10
+ ··· + 4a −
3
2
−4u
10
a −
1
2
u
10
+ ··· − 10a +
1
2
u
a
2
=
−3u
10
a +
1
2
u
10
+ ··· − 7a +
5
2
5u
10
a +
1
2
u
10
+ ··· + 12a +
1
2
u
a
8
=
−3u
10
a − 7u
9
a + ··· + 8au − 7a
−5u
10
a − 12u
9
a + ··· + 13au − 12a
a
3
=
2u
10
a − u
10
+ ··· + 5a −
3
2
−
1
2
u
10
− u
9
+ ··· + au +
1
2
u
a
10
=
5
2
u
10
a −
1
4
u
10
+ ··· + 8a −
1
2
2u
10
a − u
10
+ ··· + 6a − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 16u
10
+ 39u
9
− 13u
8
− 44u
7
+ 75u
6
+ 39u
5
− 54u
4
+ 109u
3
+ 48u
2
− 64u + 58
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
22
− 24u
21
+ ··· − 19393u + 1763
c
2
, c
4
, c
8
c
10
u
22
+ 2u
19
+ ··· + 3u + 1
c
3
, c
9
(u
11
+ u
10
− u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
− 1)
2
c
5
, c
6
, c
11
(u
11
+ 4u
10
+ 3u
9
− 4u
8
+ 9u
6
+ u
5
+ 2u
4
+ 12u
3
+ u
2
− 2u + 4)
2
c
12
(u
11
− 12u
10
+ ··· + 670u − 124)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
22
− 14y
21
+ ··· + 4402211y + 3108169
c
2
, c
4
, c
8
c
10
y
22
+ 16y
20
+ ··· − 7y + 1
c
3
, c
9
(y
11
− y
10
+ 4y
8
− 2y
7
− 3y
6
+ 7y
5
− 5y
3
+ 3y
2
+ 2y − 1)
2
c
5
, c
6
, c
11
(y
11
− 10y
10
+ ··· − 4y − 16)
2
c
12
(y
11
− 2y
10
+ ··· + 19612y − 15376)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210854 + 0.924372I
a = −0.288859 + 1.113730I
b = 0.160583 + 0.786630I
−6.34106 + 7.03153I −4.95033 − 7.71063I
u = 0.210854 + 0.924372I
a = −0.51363 − 2.12870I
b = −0.97487 − 1.17661I
−6.34106 + 7.03153I −4.95033 − 7.71063I
u = 0.210854 − 0.924372I
a = −0.288859 − 1.113730I
b = 0.160583 − 0.786630I
−6.34106 − 7.03153I −4.95033 + 7.71063I
u = 0.210854 − 0.924372I
a = −0.51363 + 2.12870I
b = −0.97487 + 1.17661I
−6.34106 − 7.03153I −4.95033 + 7.71063I
u = 1.038000 + 0.605884I
a = 0.938719 − 0.487233I
b = 0.887750 − 1.011390I
−3.82481 − 1.73068I −5.80090 + 0.49536I
u = 1.038000 + 0.605884I
a = −0.139780 + 0.544571I
b = 0.085916 + 0.710196I
−3.82481 − 1.73068I −5.80090 + 0.49536I
u = 1.038000 − 0.605884I
a = 0.938719 + 0.487233I
b = 0.887750 + 1.011390I
−3.82481 + 1.73068I −5.80090 − 0.49536I
u = 1.038000 − 0.605884I
a = −0.139780 − 0.544571I
b = 0.085916 − 0.710196I
−3.82481 + 1.73068I −5.80090 − 0.49536I
u = 0.407098 + 0.511028I
a = −0.850397 − 0.404251I
b = −0.692471 + 0.395759I
2.05024 + 1.72126I 8.54110 − 3.80336I
u = 0.407098 + 0.511028I
a = −0.130348 + 1.238060I
b = 0.797814 + 0.689545I
2.05024 + 1.72126I 8.54110 − 3.80336I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407098 − 0.511028I
a = −0.850397 + 0.404251I
b = −0.692471 − 0.395759I
2.05024 − 1.72126I 8.54110 + 3.80336I
u = 0.407098 − 0.511028I
a = −0.130348 − 1.238060I
b = 0.797814 − 0.689545I
2.05024 − 1.72126I 8.54110 + 3.80336I
u = −1.40649 + 0.16331I
a = 1.009700 + 0.511325I
b = −1.063190 + 0.736394I
7.81324 − 4.10222I 12.81849 + 4.00795I
u = −1.40649 + 0.16331I
a = −0.229507 − 0.746116I
b = 0.874612 + 0.175339I
7.81324 − 4.10222I 12.81849 + 4.00795I
u = −1.40649 − 0.16331I
a = 1.009700 − 0.511325I
b = −1.063190 − 0.736394I
7.81324 + 4.10222I 12.81849 − 4.00795I
u = −1.40649 − 0.16331I
a = −0.229507 + 0.746116I
b = 0.874612 − 0.175339I
7.81324 + 4.10222I 12.81849 − 4.00795I
u = −1.40354 + 0.39691I
a = 0.697877 + 0.666519I
b = −0.333033 + 0.789828I
−1.24688 − 11.76520I 0.95863 + 10.20992I
u = −1.40354 + 0.39691I
a = −0.87761 − 1.60371I
b = 1.05438 − 1.23493I
−1.24688 − 11.76520I 0.95863 + 10.20992I
u = −1.40354 − 0.39691I
a = 0.697877 − 0.666519I
b = −0.333033 − 0.789828I
−1.24688 + 11.76520I 0.95863 − 10.20992I
u = −1.40354 − 0.39691I
a = −0.87761 + 1.60371I
b = 1.05438 + 1.23493I
−1.24688 + 11.76520I 0.95863 − 10.20992I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.69185
a = −0.187966
b = −1.29033
6.38838 69.8660
u = −1.69185
a = −0.0443785
b = −0.304645
6.38838 69.8660
12
III. I
u
3
= h19502u
7
a
3
− 21027u
7
a
2
+ · · · − 98205a + 12679, 2u
7
a
3
− 3u
7
a
2
+
· · · − 2a + 5, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
a
−0.661062a
3
u
7
+ 0.712755a
2
u
7
+ ··· + 3.32887a − 0.429782
a
4
=
−0.437646a
3
u
7
+ 0.959357a
2
u
7
+ ··· + 3.29813a − 1.00051
0.559574a
3
u
7
+ 1.72279a
2
u
7
+ ··· + 3.69147a − 2.66235
a
2
=
−0.661062a
3
u
7
+ 0.712755a
2
u
7
+ ··· + 2.32887a − 0.429782
0.0260669a
3
u
7
+ 0.450256a
2
u
7
+ ··· + 2.89658a − 0.561506
a
8
=
−0.0615233a
3
u
7
− 0.931358a
2
u
7
+ ··· − 0.0497949a + 0.655571
−0.894004a
3
u
7
+ 0.716450a
2
u
7
+ ··· + 3.75631a − 0.0660995
a
3
=
−0.634995a
3
u
7
+ 1.16301a
2
u
7
+ ··· + 5.22545a − 0.991288
0.197485a
3
u
7
− 0.484797a
2
u
7
+ ··· + 1.41934a − 0.269618
a
10
=
−0.467510a
3
u
7
− 0.618894a
2
u
7
+ ··· + 2.69489a + 1.85214
−0.830379a
3
u
7
+ 1.29009a
2
u
7
+ ··· + 4.67943a + 0.242161
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
49440
29501
u
7
a
3
−
149640
29501
u
7
a
2
+ ··· −
377448
29501
a +
369314
29501
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
+ u + 1)
16
c
2
, c
4
, c
8
c
10
u
32
− u
31
+ ··· + 2u + 1
c
3
, c
9
u
32
− 3u
31
+ ··· − 426u + 43
c
5
, c
6
, c
11
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
4
c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ y + 1)
16
c
2
, c
4
, c
8
c
10
y
32
+ 7y
31
+ ··· + 4y + 1
c
3
, c
9
y
32
+ 19y
31
+ ··· − 51272y + 1849
c
5
, c
6
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
4
c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.066150 − 0.632667I
b = 0.395082 + 0.646442I
1.04066 − 5.19100I 7.41522 + 7.43899I
u = −1.180120 + 0.268597I
a = 0.427622 − 0.205756I
b = −0.848982 − 0.718464I
1.04066 + 2.92853I 7.41522 − 6.41741I
u = −1.180120 + 0.268597I
a = −0.16498 − 1.56786I
b = 0.523132 − 0.775492I
1.04066 − 5.19100I 7.41522 + 7.43899I
u = −1.180120 + 0.268597I
a = 1.59366 + 1.10585I
b = 0.50164 + 1.57819I
1.04066 + 2.92853I 7.41522 − 6.41741I
u = −1.180120 − 0.268597I
a = −0.066150 + 0.632667I
b = 0.395082 − 0.646442I
1.04066 + 5.19100I 7.41522 − 7.43899I
u = −1.180120 − 0.268597I
a = 0.427622 + 0.205756I
b = −0.848982 + 0.718464I
1.04066 − 2.92853I 7.41522 + 6.41741I
u = −1.180120 − 0.268597I
a = −0.16498 + 1.56786I
b = 0.523132 + 0.775492I
1.04066 + 5.19100I 7.41522 − 7.43899I
u = −1.180120 − 0.268597I
a = 1.59366 − 1.10585I
b = 0.50164 − 1.57819I
1.04066 − 2.92853I 7.41522 + 6.41741I
u = −0.108090 + 0.747508I
a = −0.868562 − 0.327518I
b = −0.684993 − 0.017263I
−2.15941 + 1.48127I 4.27708 − 3.36025I
u = −0.108090 + 0.747508I
a = −0.026951 − 1.315960I
b = 0.938515 − 0.577223I
−2.15941 − 6.63826I 4.27708 + 10.49616I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 + 0.747508I
a = −0.678238 − 1.187640I
b = −0.319305 − 0.390448I
−2.15941 + 1.48127I 4.27708 − 3.36025I
u = −0.108090 + 0.747508I
a = −0.51181 + 3.41311I
b = −0.78945 + 1.65083I
−2.15941 − 6.63826I 4.27708 + 10.49616I
u = −0.108090 − 0.747508I
a = −0.868562 + 0.327518I
b = −0.684993 + 0.017263I
−2.15941 − 1.48127I 4.27708 + 3.36025I
u = −0.108090 − 0.747508I
a = −0.026951 + 1.315960I
b = 0.938515 + 0.577223I
−2.15941 + 6.63826I 4.27708 − 10.49616I
u = −0.108090 − 0.747508I
a = −0.678238 + 1.187640I
b = −0.319305 + 0.390448I
−2.15941 − 1.48127I 4.27708 + 3.36025I
u = −0.108090 − 0.747508I
a = −0.51181 − 3.41311I
b = −0.78945 − 1.65083I
−2.15941 + 6.63826I 4.27708 − 10.49616I
u = 1.37100
a = 0.729330 + 0.242760I
b = −1.22631 − 1.06765I
6.50273 + 4.05977I 13.8640 − 6.9282I
u = 1.37100
a = 0.729330 − 0.242760I
b = −1.22631 + 1.06765I
6.50273 − 4.05977I 13.8640 + 6.9282I
u = 1.37100
a = −1.10950 + 0.90124I
b = 0.677222 − 0.116600I
6.50273 − 4.05977I 13.8640 + 6.9282I
u = 1.37100
a = −1.10950 − 0.90124I
b = 0.677222 + 0.116600I
6.50273 + 4.05977I 13.8640 − 6.9282I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 + 0.318930I
a = 0.526075 − 0.967286I
b = −0.066786 − 0.430851I
2.37968 + 2.38377I 9.42845 + 1.63403I
u = 1.334530 + 0.318930I
a = 0.308397 + 0.685913I
b = 1.150340 − 0.134985I
2.37968 + 2.38377I 9.42845 + 1.63403I
u = 1.334530 + 0.318930I
a = 1.23271 − 1.03718I
b = −1.016490 − 0.493234I
2.37968 + 10.50330I 9.4284 − 12.2224I
u = 1.334530 + 0.318930I
a = −1.40627 + 1.90054I
b = 0.96474 + 1.71454I
2.37968 + 10.50330I 9.4284 − 12.2224I
u = 1.334530 − 0.318930I
a = 0.526075 + 0.967286I
b = −0.066786 + 0.430851I
2.37968 − 2.38377I 9.42845 − 1.63403I
u = 1.334530 − 0.318930I
a = 0.308397 − 0.685913I
b = 1.150340 + 0.134985I
2.37968 − 2.38377I 9.42845 − 1.63403I
u = 1.334530 − 0.318930I
a = 1.23271 + 1.03718I
b = −1.016490 + 0.493234I
2.37968 − 10.50330I 9.4284 + 12.2224I
u = 1.334530 − 0.318930I
a = −1.40627 − 1.90054I
b = 0.96474 − 1.71454I
2.37968 − 10.50330I 9.4284 + 12.2224I
u = −0.463640
a = 0.461453 + 0.953605I
b = 0.775560 + 1.017420I
0.84504 + 4.05977I 11.89446 − 6.92820I
u = −0.463640
a = 0.461453 − 0.953605I
b = 0.775560 − 1.017420I
0.84504 − 4.05977I 11.89446 + 6.92820I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.463640
a = 1.05322 + 1.66989I
b = −0.473908 − 0.494946I
0.84504 + 4.05977I 11.89446 − 6.92820I
u = −0.463640
a = 1.05322 − 1.66989I
b = −0.473908 + 0.494946I
0.84504 − 4.05977I 11.89446 + 6.92820I
19
IV. I
u
4
= h−7.80 × 10
46
a
7
u
7
+ 1.01 × 10
47
a
6
u
7
+ · · · + 1.17 × 10
48
a + 5.77 ×
10
47
, −2a
7
u
7
− 10u
7
a
6
+ · · · + 388a − 283, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
a
0.560431a
7
u
7
− 0.726615a
6
u
7
+ ··· − 8.39349a − 4.14074
a
4
=
−0.398353a
7
u
7
+ 0.437759a
6
u
7
+ ··· + 4.59100a + 3.94324
0.150019a
7
u
7
− 0.711664a
6
u
7
+ ··· − 7.88417a − 5.18997
a
2
=
−0.210776a
7
u
7
+ 0.0814284a
6
u
7
+ ··· + 9.65613a + 8.47478
0.0439712a
7
u
7
+ 0.297620a
6
u
7
+ ··· − 20.3953a − 6.11248
a
8
=
−0.0110440a
7
u
7
+ 0.00600824a
6
u
7
+ ··· + 7.53628a + 2.78572
0.701062a
7
u
7
− 0.836421a
6
u
7
+ ··· − 5.63674a − 3.07530
a
3
=
−0.167792a
7
u
7
+ 0.285874a
6
u
7
+ ··· + 1.56554a + 3.06816
0.0319172a
7
u
7
+ 0.306598a
6
u
7
+ ··· − 15.4302a − 5.98076
a
10
=
0.0717695a
7
u
7
− 0.420316a
6
u
7
+ ··· − 15.6597a − 9.66648
0.624793a
7
u
7
− 0.888235a
6
u
7
+ ··· + 10.4453a + 4.87187
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.878386a
7
u
7
− 1.54194a
6
u
7
+ ··· + 59.8466a + 21.7637
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
− 2u + 1)
16
c
2
, c
4
, c
8
c
10
u
64
+ u
63
+ ··· − 27708u + 17623
c
3
, c
9
(u
32
+ u
31
+ ··· + 2738u + 1369)
2
c
5
, c
6
, c
11
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
8
c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
8
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
− y
3
+ 6y
2
− 4y + 1)
16
c
2
, c
4
, c
8
c
10
y
64
+ 25y
63
+ ··· + 16352870252y + 310570129
c
3
, c
9
(y
32
− 33y
31
+ ··· − 29148748y + 1874161)
2
c
5
, c
6
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
8
c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
8
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.557498 − 0.750065I
b = 0.076022 − 1.368170I
−2.24921 − 5.19100I −4.58478 + 7.43899I
u = −1.180120 + 0.268597I
a = −0.375594 + 0.789251I
b = −0.106109 + 0.977961I
−2.24921 − 5.19100I −4.58478 + 7.43899I
u = −1.180120 + 0.268597I
a = −0.793981 − 0.339728I
b = −0.89684 − 1.40532I
−2.24921 + 2.92853I −4.58478 − 6.41741I
u = −1.180120 + 0.268597I
a = 0.468251 + 1.215000I
b = 0.525494 + 1.281730I
−2.24921 + 2.92853I −4.58478 − 6.41741I
u = −1.180120 + 0.268597I
a = −1.19699 − 2.19170I
b = 1.57698 − 0.84563I
−2.24921 − 5.19100I −4.58478 + 7.43899I
u = −1.180120 + 0.268597I
a = 0.81930 + 2.49677I
b = −1.86154 + 0.87114I
−2.24921 + 2.92853I −4.58478 − 6.41741I
u = −1.180120 + 0.268597I
a = 1.98998 + 1.92913I
b = 0.049106 + 0.370276I
−2.24921 + 2.92853I −4.58478 − 6.41741I
u = −1.180120 + 0.268597I
a = −2.14361 − 1.84821I
b = 0.066014 − 0.612653I
−2.24921 − 5.19100I −4.58478 + 7.43899I
u = −1.180120 − 0.268597I
a = −0.557498 + 0.750065I
b = 0.076022 + 1.368170I
−2.24921 + 5.19100I −4.58478 − 7.43899I
u = −1.180120 − 0.268597I
a = −0.375594 − 0.789251I
b = −0.106109 − 0.977961I
−2.24921 + 5.19100I −4.58478 − 7.43899I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 − 0.268597I
a = −0.793981 + 0.339728I
b = −0.89684 + 1.40532I
−2.24921 − 2.92853I −4.58478 + 6.41741I
u = −1.180120 − 0.268597I
a = 0.468251 − 1.215000I
b = 0.525494 − 1.281730I
−2.24921 − 2.92853I −4.58478 + 6.41741I
u = −1.180120 − 0.268597I
a = −1.19699 + 2.19170I
b = 1.57698 + 0.84563I
−2.24921 + 5.19100I −4.58478 − 7.43899I
u = −1.180120 − 0.268597I
a = 0.81930 − 2.49677I
b = −1.86154 − 0.87114I
−2.24921 − 2.92853I −4.58478 + 6.41741I
u = −1.180120 − 0.268597I
a = 1.98998 − 1.92913I
b = 0.049106 − 0.370276I
−2.24921 − 2.92853I −4.58478 + 6.41741I
u = −1.180120 − 0.268597I
a = −2.14361 + 1.84821I
b = 0.066014 + 0.612653I
−2.24921 + 5.19100I −4.58478 − 7.43899I
u = −0.108090 + 0.747508I
a = 1.04622 + 1.05153I
b = 0.010366 + 0.720950I
−5.44928 + 1.48127I −7.72292 − 3.36025I
u = −0.108090 + 0.747508I
a = −0.44885 − 1.74318I
b = 0.134832 − 1.154790I
−5.44928 + 1.48127I −7.72292 − 3.36025I
u = −0.108090 + 0.747508I
a = 0.58177 − 2.43120I
b = 1.10937 − 1.26574I
−5.44928 − 6.63826I −7.72292 + 10.49616I
u = −0.108090 + 0.747508I
a = −1.52809 − 2.24345I
b = −1.30778 − 1.23908I
−5.44928 + 1.48127I −7.72292 − 3.36025I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 + 0.747508I
a = 0.28742 + 2.71361I
b = −0.653169 + 1.231330I
−5.44928 − 6.63826I −7.72292 + 10.49616I
u = −0.108090 + 0.747508I
a = 0.46144 − 2.77434I
b = −0.139839 − 0.881992I
−5.44928 + 1.48127I −7.72292 − 3.36025I
u = −0.108090 + 0.747508I
a = −0.80607 + 2.71119I
b = −0.069757 + 0.589599I
−5.44928 − 6.63826I −7.72292 + 10.49616I
u = −0.108090 + 0.747508I
a = 2.49172 + 2.13386I
b = 1.77121 + 1.33383I
−5.44928 − 6.63826I −7.72292 + 10.49616I
u = −0.108090 − 0.747508I
a = 1.04622 − 1.05153I
b = 0.010366 − 0.720950I
−5.44928 − 1.48127I −7.72292 + 3.36025I
u = −0.108090 − 0.747508I
a = −0.44885 + 1.74318I
b = 0.134832 + 1.154790I
−5.44928 − 1.48127I −7.72292 + 3.36025I
u = −0.108090 − 0.747508I
a = 0.58177 + 2.43120I
b = 1.10937 + 1.26574I
−5.44928 + 6.63826I −7.72292 − 10.49616I
u = −0.108090 − 0.747508I
a = −1.52809 + 2.24345I
b = −1.30778 + 1.23908I
−5.44928 − 1.48127I −7.72292 + 3.36025I
u = −0.108090 − 0.747508I
a = 0.28742 − 2.71361I
b = −0.653169 − 1.231330I
−5.44928 + 6.63826I −7.72292 − 10.49616I
u = −0.108090 − 0.747508I
a = 0.46144 + 2.77434I
b = −0.139839 + 0.881992I
−5.44928 − 1.48127I −7.72292 + 3.36025I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 − 0.747508I
a = −0.80607 − 2.71119I
b = −0.069757 − 0.589599I
−5.44928 + 6.63826I −7.72292 − 10.49616I
u = −0.108090 − 0.747508I
a = 2.49172 − 2.13386I
b = 1.77121 − 1.33383I
−5.44928 + 6.63826I −7.72292 − 10.49616I
u = 1.37100
a = 0.854808 + 0.560981I
b = −0.553456 − 0.800848I
3.21286 + 4.05977I 1.86404 − 6.92820I
u = 1.37100
a = 0.854808 − 0.560981I
b = −0.553456 + 0.800848I
3.21286 − 4.05977I 1.86404 + 6.92820I
u = 1.37100
a = −0.587473 + 0.738539I
b = 0.939573 − 0.544398I
3.21286 − 4.05977I 1.86404 + 6.92820I
u = 1.37100
a = −0.587473 − 0.738539I
b = 0.939573 + 0.544398I
3.21286 + 4.05977I 1.86404 − 6.92820I
u = 1.37100
a = −0.461575 + 0.539242I
b = 0.61771 + 1.67070I
3.21286 − 4.05977I 1.86404 + 6.92820I
u = 1.37100
a = −0.461575 − 0.539242I
b = 0.61771 − 1.67070I
3.21286 + 4.05977I 1.86404 − 6.92820I
u = 1.37100
a = 0.574413 + 1.258640I
b = −0.454734 + 0.925998I
3.21286 − 4.05977I 1.86404 + 6.92820I
u = 1.37100
a = 0.574413 − 1.258640I
b = −0.454734 − 0.925998I
3.21286 + 4.05977I 1.86404 − 6.92820I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 + 0.318930I
a = −1.026690 + 0.231419I
b = 0.123131 + 0.528178I
−0.91019 + 2.38377I −2.57155 + 1.63403I
u = 1.334530 + 0.318930I
a = 1.044130 − 0.266668I
b = 1.14771 − 1.52608I
−0.91019 + 2.38377I −2.57155 + 1.63403I
u = 1.334530 + 0.318930I
a = 0.930223 − 0.590383I
b = −0.332844 − 0.999590I
−0.91019 + 2.38377I −2.57155 + 1.63403I
u = 1.334530 + 0.318930I
a = 0.233928 − 1.382460I
b = 0.249060 − 1.010950I
−0.91019 + 2.38377I −2.57155 + 1.63403I
u = 1.334530 + 0.318930I
a = −1.47286 − 0.39492I
b = −1.75709 + 1.62937I
−0.91019 + 10.50330I −2.57155 − 12.22237I
u = 1.334530 + 0.318930I
a = −0.00136 + 1.87131I
b = 0.054075 + 0.713119I
−0.91019 + 10.50330I −2.57155 − 12.22237I
u = 1.334530 + 0.318930I
a = 1.25518 − 1.52608I
b = −1.26284 − 1.19072I
−0.91019 + 10.50330I −2.57155 − 12.22237I
u = 1.334530 + 0.318930I
a = −1.62346 + 1.47579I
b = 0.74699 + 1.20121I
−0.91019 + 10.50330I −2.57155 − 12.22237I
u = 1.334530 − 0.318930I
a = −1.026690 − 0.231419I
b = 0.123131 − 0.528178I
−0.91019 − 2.38377I −2.57155 − 1.63403I
u = 1.334530 − 0.318930I
a = 1.044130 + 0.266668I
b = 1.14771 + 1.52608I
−0.91019 − 2.38377I −2.57155 − 1.63403I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 − 0.318930I
a = 0.930223 + 0.590383I
b = −0.332844 + 0.999590I
−0.91019 − 2.38377I −2.57155 − 1.63403I
u = 1.334530 − 0.318930I
a = 0.233928 + 1.382460I
b = 0.249060 + 1.010950I
−0.91019 − 2.38377I −2.57155 − 1.63403I
u = 1.334530 − 0.318930I
a = −1.47286 + 0.39492I
b = −1.75709 − 1.62937I
−0.91019 − 10.50330I −2.57155 + 12.22237I
u = 1.334530 − 0.318930I
a = −0.00136 − 1.87131I
b = 0.054075 − 0.713119I
−0.91019 − 10.50330I −2.57155 + 12.22237I
u = 1.334530 − 0.318930I
a = 1.25518 + 1.52608I
b = −1.26284 + 1.19072I
−0.91019 − 10.50330I −2.57155 + 12.22237I
u = 1.334530 − 0.318930I
a = −1.62346 − 1.47579I
b = 0.74699 − 1.20121I
−0.91019 − 10.50330I −2.57155 + 12.22237I
u = −0.463640
a = −0.288618 + 0.831332I
b = −0.621112 − 0.938012I
−2.44483 + 4.05977I −0.10554 − 6.92820I
u = −0.463640
a = −0.288618 − 0.831332I
b = −0.621112 + 0.938012I
−2.44483 − 4.05977I −0.10554 + 6.92820I
u = −0.463640
a = −0.776492 + 0.123909I
b = 0.408992 − 1.078900I
−2.44483 − 4.05977I −0.10554 + 6.92820I
u = −0.463640
a = −0.776492 − 0.123909I
b = 0.408992 + 1.078900I
−2.44483 + 4.05977I −0.10554 − 6.92820I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.463640
a = 0.11351 + 3.49812I
b = −0.759051 + 0.889385I
−2.44483 + 4.05977I −0.10554 − 6.92820I
u = −0.463640
a = 0.11351 − 3.49812I
b = −0.759051 − 0.889385I
−2.44483 − 4.05977I −0.10554 + 6.92820I
u = −0.463640
a = −0.56308 + 3.66494I
b = 0.669519 + 0.537158I
−2.44483 + 4.05977I −0.10554 − 6.92820I
u = −0.463640
a = −0.56308 − 3.66494I
b = 0.669519 − 0.537158I
−2.44483 − 4.05977I −0.10554 + 6.92820I
29
V. I
u
5
= h−3u
31
− 13u
30
+ · · · + 2b − 305, 631u
31
+ 546u
30
+ · · · + 78a +
12324, u
32
− 17u
30
+ · · · + 17u
2
− 39i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−
631
78
u
31
− 7u
30
+ ··· −
6085
39
u − 158
3
2
u
31
+
13
2
u
30
+ ··· +
127
2
u +
305
2
a
4
=
−
463
78
u
31
−
3
2
u
30
+ ··· −
5788
39
u − 68
−
3
2
u
31
+ 6u
30
+ ··· −
31
2
u +
239
2
a
2
=
−
383
78
u
31
− 3u
30
+ ··· −
3743
39
u −
75
2
−4u
31
+
23
2
u
30
+ ··· −
121
2
u +
475
2
a
8
=
−
475
78
u
31
− 4u
30
+ ··· −
8153
78
u −
121
2
−3u
31
+ 9u
30
+ ··· −
75
2
u +
383
2
a
3
=
−3.91026u
31
+ 1.50000u
30
+ ··· − 90.9744u + 63.5000
−7u
31
+
29
2
u
30
+ ··· − 158u +
631
2
a
10
=
−3.06410u
31
− 1.50000u
30
+ ··· − 55.5897u − 15.5000
−
3
2
u
31
+ 9u
30
+ ··· − 68u +
463
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −41u
30
+ 618u
28
− 4128u
26
+ 15994u
24
− 39319u
22
+ 62512u
20
− 61321u
18
+
29367u
16
+ 5630u
14
− 17324u
12
+ 10795u
10
− 1247u
8
− 4569u
6
+ 3660u
4
+ 92u
2
− 726
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
32
− 11u
31
+ ··· − u − 1
c
2
, c
4
, c
8
c
10
u
32
− u
31
+ ··· − 3u − 1
c
3
, c
9
(u
16
− 5u
14
+ ··· − u − 1)
2
c
5
, c
6
, c
11
u
32
− 17u
30
+ ··· + 17u
2
− 39
c
12
u
32
− 6u
30
+ ··· − 217u
2
− 39
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
32
− 23y
31
+ ··· − 19y + 1
c
2
, c
4
, c
8
c
10
y
32
+ 11y
31
+ ··· − 49y + 1
c
3
, c
9
(y
16
− 10y
15
+ ··· − 15y + 1)
2
c
5
, c
6
, c
11
(y
16
− 17y
15
+ ··· + 17y − 39)
2
c
12
(y
16
− 6y
15
+ ··· − 217y − 39)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629647 + 0.624776I
a = 1.087040 + 0.364560I
b = 0.446274 + 0.076076I
−2.92940 − 2.54300I −1.89886 + 3.79711I
u = 0.629647 − 0.624776I
a = 1.087040 − 0.364560I
b = 0.446274 − 0.076076I
−2.92940 + 2.54300I −1.89886 − 3.79711I
u = −0.629647 + 0.624776I
a = −0.876629 − 0.237763I
b = −0.568453 − 0.779279I
−2.92940 + 2.54300I −1.89886 − 3.79711I
u = −0.629647 − 0.624776I
a = −0.876629 + 0.237763I
b = −0.568453 + 0.779279I
−2.92940 − 2.54300I −1.89886 + 3.79711I
u = −1.155620 + 0.193870I
a = 0.026191 − 0.747935I
b = 0.231443 − 1.171860I
−1.25945 − 5.31731I 5.75169 + 8.91890I
u = −1.155620 − 0.193870I
a = 0.026191 + 0.747935I
b = 0.231443 + 1.171860I
−1.25945 + 5.31731I 5.75169 − 8.91890I
u = 1.155620 + 0.193870I
a = 0.89998 − 2.52353I
b = −0.866062 − 0.104892I
−1.25945 + 5.31731I 5.75169 − 8.91890I
u = 1.155620 − 0.193870I
a = 0.89998 + 2.52353I
b = −0.866062 + 0.104892I
−1.25945 − 5.31731I 5.75169 + 8.91890I
u = −1.186450 + 0.242984I
a = −0.578544 − 0.781239I
b = −0.66039 − 1.33386I
−1.64172 + 2.45344I 5.90890 + 1.74732I
u = −1.186450 − 0.242984I
a = −0.578544 + 0.781239I
b = −0.66039 + 1.33386I
−1.64172 − 2.45344I 5.90890 − 1.74732I
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.186450 + 0.242984I
a = −1.13678 + 2.20772I
b = 0.939979 + 0.399562I
−1.64172 − 2.45344I 5.90890 − 1.74732I
u = 1.186450 − 0.242984I
a = −1.13678 − 2.20772I
b = 0.939979 − 0.399562I
−1.64172 + 2.45344I 5.90890 + 1.74732I
u = 0.132917 + 0.749514I
a = −0.86511 + 1.69692I
b = −0.699135 + 0.630594I
−4.69890 + 6.03416I 0.76733 − 4.01841I
u = 0.132917 − 0.749514I
a = −0.86511 − 1.69692I
b = −0.699135 − 0.630594I
−4.69890 − 6.03416I 0.76733 + 4.01841I
u = −0.132917 + 0.749514I
a = 0.12614 − 2.42491I
b = 0.86022 − 1.20009I
−4.69890 − 6.03416I 0.76733 + 4.01841I
u = −0.132917 − 0.749514I
a = 0.12614 + 2.42491I
b = 0.86022 + 1.20009I
−4.69890 + 6.03416I 0.76733 − 4.01841I
u = −1.330500 + 0.012725I
a = 0.181503 + 0.796558I
b = 0.259461 + 1.177500I
4.40410 + 3.95061I 10.52838 − 5.72470I
u = −1.330500 − 0.012725I
a = 0.181503 − 0.796558I
b = 0.259461 − 1.177500I
4.40410 − 3.95061I 10.52838 + 5.72470I
u = 1.330500 + 0.012725I
a = −0.944495 + 0.876787I
b = 0.797351 − 0.622026I
4.40410 − 3.95061I 10.52838 + 5.72470I
u = 1.330500 − 0.012725I
a = −0.944495 − 0.876787I
b = 0.797351 + 0.622026I
4.40410 + 3.95061I 10.52838 − 5.72470I
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322590 + 0.271417I
a = 1.099260 − 0.461970I
b = −0.385356 − 0.772550I
−0.41737 + 3.31971I 2.07879 − 6.21557I
u = 1.322590 − 0.271417I
a = 1.099260 + 0.461970I
b = −0.385356 + 0.772550I
−0.41737 − 3.31971I 2.07879 + 6.21557I
u = −1.322590 + 0.271417I
a = −0.388950 − 0.825612I
b = −0.380975 − 1.234850I
−0.41737 − 3.31971I 2.07879 + 6.21557I
u = −1.322590 − 0.271417I
a = −0.388950 + 0.825612I
b = −0.380975 + 1.234850I
−0.41737 + 3.31971I 2.07879 − 6.21557I
u = 0.647214I
a = −0.56816 − 2.03623I
b = 0.305163 − 0.999497I
−4.63655 −4.61210
u = − 0.647214I
a = −0.56816 + 2.03623I
b = 0.305163 + 0.999497I
−4.63655 −4.61210
u = 1.341580 + 0.324582I
a = 1.33926 − 1.48068I
b = −0.99699 − 1.16492I
−0.06232 + 9.94150I 5.86760 − 6.47381I
u = 1.341580 − 0.324582I
a = 1.33926 + 1.48068I
b = −0.99699 + 1.16492I
−0.06232 − 9.94150I 5.86760 + 6.47381I
u = −1.341580 + 0.324582I
a = 0.541338 + 0.541357I
b = 0.622958 + 0.855164I
−0.06232 − 9.94150I 5.86760 + 6.47381I
u = −1.341580 − 0.324582I
a = 0.541338 − 0.541357I
b = 0.622958 − 0.855164I
−0.06232 + 9.94150I 5.86760 − 6.47381I
35
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70928
a = −0.118891
b = −0.151635
6.33211 −72.3960
u = 1.70928
a = 0.234821
b = 1.34066
6.33211 −72.3960
36
VI.
I
u
6
= h−u
7
+3u
5
−2u
3
+b−u, u
5
−2u
3
+a+u, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
−u
3
+ 2u
−u
3
+ u
a
2
=
−u
3
+ 2u
−u
3
+ u
a
8
=
u
2
− 1
−u
4
+ 2u
2
a
3
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
10
=
u
2
− 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 12u
4
+ 4u
3
+ 8u
2
− 8u + 14
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
8
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
5
, c
6
, c
11
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
12
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
8
c
2
, c
3
, c
4
c
8
, c
9
, c
10
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
5
, c
6
, c
11
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 0.462196 − 0.399257I
b = 0.570868 − 0.730671I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = 1.180120 − 0.268597I
a = 0.462196 + 0.399257I
b = 0.570868 + 0.730671I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.108090 + 0.747508I
a = −0.62965 − 1.71558I
b = −0.855237 − 0.665892I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.108090 − 0.747508I
a = −0.62965 + 1.71558I
b = −0.855237 + 0.665892I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = −1.37100
a = 1.06085
b = −1.09818
6.50273 13.8640
u = −1.334530 + 0.318930I
a = −0.72011 − 1.45930I
b = 1.031810 − 0.655470I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.334530 − 0.318930I
a = −0.72011 + 1.45930I
b = 1.031810 + 0.655470I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = 0.463640
a = −0.285734
b = 0.603304
0.845036 11.8940
40
VII. I
u
7
= h−u
7
a − 2u
7
+ · · · + 2a + 3, −2u
7
a − u
7
+ · · · + 2a + 2, u
8
− u
7
−
3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
a
u
7
a + 2u
7
+ ··· − 2a − 3
a
4
=
−u
7
a − 2u
7
+ ··· + 3a + 5
−u
7
a − u
7
+ ··· + a + 1
a
2
=
−u
7
a − 2u
7
+ ··· + 3a + 5
−u
7
a − u
7
+ ··· + a + 1
a
8
=
−u
7
a − u
7
+ ··· + 3a + 2
u
7
a + 2u
7
+ ··· − a − 2
a
3
=
−2u
7
a − 3u
7
+ ··· + 4a + 7
−au
a
10
=
−u
7
a − u
7
+ ··· + 3a + 3
u
7
a + 2u
7
+ ··· − a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 12u
4
− 4u
3
+ 8u
2
+ 8u + 2
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u + 1)
16
c
2
, c
4
, c
8
c
10
u
16
+ u
15
+ ··· − 6u − 1
c
3
, c
9
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
2
c
5
, c
6
, c
11
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
2
c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
2
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y − 1)
16
c
2
, c
4
, c
8
c
10
y
16
+ 7y
15
+ ··· − 28y + 1
c
3
, c
9
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
2
c
5
, c
6
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
2
c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −1.328740 − 0.071969I
b = −0.71876 − 1.56857I
−2.24921 − 1.13123I −4.58478 + 0.51079I
u = −1.180120 + 0.268597I
a = −0.46141 + 1.37240I
b = 0.147896 + 0.837895I
−2.24921 − 1.13123I −4.58478 + 0.51079I
u = −1.180120 − 0.268597I
a = −1.328740 + 0.071969I
b = −0.71876 + 1.56857I
−2.24921 + 1.13123I −4.58478 − 0.51079I
u = −1.180120 − 0.268597I
a = −0.46141 − 1.37240I
b = 0.147896 − 0.837895I
−2.24921 + 1.13123I −4.58478 − 0.51079I
u = −0.108090 + 0.747508I
a = 1.00762 + 1.81519I
b = −0.250978 + 0.716087I
−5.44928 − 2.57849I −7.72292 + 3.56796I
u = −0.108090 + 0.747508I
a = 1.07794 − 2.39718I
b = 1.10622 − 1.38198I
−5.44928 − 2.57849I −7.72292 + 3.56796I
u = −0.108090 − 0.747508I
a = 1.00762 − 1.81519I
b = −0.250978 − 0.716087I
−5.44928 + 2.57849I −7.72292 − 3.56796I
u = −0.108090 − 0.747508I
a = 1.07794 + 2.39718I
b = 1.10622 + 1.38198I
−5.44928 + 2.57849I −7.72292 − 3.56796I
u = 1.37100
a = 1.06835
b = −0.163298
3.21286 1.86400
u = 1.37100
a = −0.308001
b = 1.26148
3.21286 1.86400
44
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 + 0.318930I
a = 0.83920 − 1.57571I
b = −1.38108 − 1.30487I
−0.91019 + 6.44354I −2.57155 − 5.29417I
u = 1.334530 + 0.318930I
a = −1.50012 + 0.99373I
b = 0.349274 + 0.649404I
−0.91019 + 6.44354I −2.57155 − 5.29417I
u = 1.334530 − 0.318930I
a = 0.83920 + 1.57571I
b = −1.38108 + 1.30487I
−0.91019 − 6.44354I −2.57155 + 5.29417I
u = 1.334530 − 0.318930I
a = −1.50012 − 0.99373I
b = 0.349274 − 0.649404I
−0.91019 − 6.44354I −2.57155 + 5.29417I
u = −0.463640
a = −1.51467 + 0.34965I
b = −0.301652 − 0.738262I
−2.44483 −0.105540
u = −0.463640
a = −1.51467 − 0.34965I
b = −0.301652 + 0.738262I
−2.44483 −0.105540
45
VIII. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
−1
0
a
6
=
1
0
a
12
=
−1
0
a
7
=
1
0
a
1
=
−1
0
a
9
=
0
b
a
4
=
1
−b − 1
a
2
=
b
−b
a
8
=
−b
b
a
3
=
0
−b
a
10
=
−1
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
46
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
2
− u + 1
c
2
, c
4
, c
8
c
10
u
2
+ u + 1
c
5
, c
6
, c
11
c
12
u
2
47
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
y
2
+ y + 1
c
5
, c
6
, c
11
c
12
y
2
48
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
49
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
8
(u + 1)
16
(u
2
− u + 1)(u
2
+ u + 1)
16
(u
4
+ u
3
− 2u + 1)
16
· (u
19
− 17u
18
+ ··· + 287u + 73)(u
22
− 24u
21
+ ··· − 19393u + 1763)
· (u
32
− 11u
31
+ ··· − u − 1)
c
2
, c
4
, c
8
c
10
(u
2
+ u + 1)(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
16
+ u
15
+ ··· − 6u − 1)(u
19
+ u
18
+ ··· − u − 1)
· (u
22
+ 2u
19
+ ··· + 3u + 1)(u
32
− u
31
+ ··· + 2u + 1)
· (u
32
− u
31
+ ··· − 3u − 1)(u
64
+ u
63
+ ··· − 27708u + 17623)
c
3
, c
9
(u
2
− u + 1)(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
2
· ((u
11
+ u
10
+ ··· + u
2
− 1)
2
)(u
16
− 5u
14
+ ··· − u − 1)
2
· (u
19
− 2u
18
+ ··· − u + 8)(u
32
− 3u
31
+ ··· − 426u + 43)
· (u
32
+ u
31
+ ··· + 2738u + 1369)
2
c
5
, c
6
, c
11
u
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
14
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
11
+ 4u
10
+ 3u
9
− 4u
8
+ 9u
6
+ u
5
+ 2u
4
+ 12u
3
+ u
2
− 2u + 4)
2
· (u
19
+ 6u
18
+ ··· + 4u − 8)(u
32
− 17u
30
+ ··· + 17u
2
− 39)
c
12
u
2
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
14
· (u
11
− 12u
10
+ ··· + 670u − 124)
2
· (u
19
− 18u
18
+ ··· + 18468u − 2216)(u
32
− 6u
30
+ ··· − 217u
2
− 39)
50
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
8
(y − 1)
16
(y
2
+ y + 1)
17
(y
4
− y
3
+ 6y
2
− 4y + 1)
16
· (y
19
− 9y
18
+ ··· + 666077y − 5329)
· (y
22
− 14y
21
+ ··· + 4402211y + 3108169)
· (y
32
− 23y
31
+ ··· − 19y + 1)
c
2
, c
4
, c
8
c
10
(y
2
+ y + 1)(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
16
+ 7y
15
+ ··· − 28y + 1)(y
19
− y
18
+ ··· + 13y − 1)
· (y
22
+ 16y
20
+ ··· − 7y + 1)(y
32
+ 7y
31
+ ··· + 4y + 1)
· (y
32
+ 11y
31
+ ··· − 49y + 1)
· (y
64
+ 25y
63
+ ··· + 16352870252y + 310570129)
c
3
, c
9
(y
2
+ y + 1)(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
11
− y
10
+ 4y
8
− 2y
7
− 3y
6
+ 7y
5
− 5y
3
+ 3y
2
+ 2y − 1)
2
· ((y
16
− 10y
15
+ ··· − 15y + 1)
2
)(y
19
− 18y
18
+ ··· + 1249y − 64)
· (y
32
− 33y
31
+ ··· − 29148748y + 1874161)
2
· (y
32
+ 19y
31
+ ··· − 51272y + 1849)
c
5
, c
6
, c
11
y
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
15
· ((y
11
− 10y
10
+ ··· − 4y − 16)
2
)(y
16
− 17y
15
+ ··· + 17y − 39)
2
· (y
19
− 14y
18
+ ··· + 208y − 64)
c
12
y
2
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
15
· (y
11
− 2y
10
+ ··· + 19612y − 15376)
2
· (y
16
− 6y
15
+ ··· − 217y − 39)
2
· (y
19
− 8y
18
+ ··· + 32723920y − 4910656)
51
