12a
1026
(K12a
1026
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 12 11 10 1 2 3 6 5
Solving Sequence
5,12
6
1,9
4 2 8 3 11 7 10
c
5
c
12
c
4
c
1
c
8
c
3
c
11
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
12
+ 17u
11
+ ··· + 10b − 42, 9u
12
− 46u
11
+ ··· + 40a + 196, u
13
− 6u
12
+ ··· + 52u − 8i
I
u
2
= hu
7
a − 2u
6
a + 8u
5
a − 10u
4
a + 19u
3
a − 12u
2
a + 15au + 5b − 4a, 4u
6
a + u
7
+ ··· + 20a − 6,
u
8
− 3u
7
+ 10u
6
− 18u
5
+ 29u
4
− 31u
3
+ 27u
2
− 14u + 4i
I
u
3
= h13u
4
a
3
− 3u
4
a
2
+ ··· + 69a − 1, −2u
4
a
3
− u
4
a + ··· + 6a + 2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
I
u
4
= h−1.98276 × 10
25
a
7
u
4
+ 9.89103 × 10
25
a
6
u
4
+ ··· − 5.40442 × 10
26
a + 1.69204 × 10
27
,
2a
7
u
4
+ 3a
6
u
4
+ ··· + 299a + 412, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
I
u
5
= hu
19
+ u
18
+ ··· + 2b + 7, 6u
19
+ 26u
18
+ ··· + 26a + 299,
u
20
+ 14u
18
+ 83u
16
+ 274u
14
+ 562u
12
+ 767u
10
+ 738u
8
+ 519u
6
+ 261u
4
+ 85u
2
+ 13i
I
u
6
= h−u
4
+ u
3
− 3u
2
+ b + 2u − 1, u
3
+ a + 2u, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
I
u
7
= hu
4
a + 2u
4
+ 4u
2
a + 3u
3
− au + 8u
2
+ 3b + a + 7u + 5,
2u
4
a + u
3
a + 6u
2
a − u
3
+ a
2
+ 2au − u
2
+ 2a − 3u + 1, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
I
u
8
= h2b − u + 1, 3a − 2u, u
2
+ 3i
I
u
9
= hb
2
− b + 1, a, u − 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 10 irreducible components of dim
C
= 0, with total 130 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
1
I. I
u
1
= h−3u
12
+ 17u
11
+ · · · + 10b − 42, 9u
12
− 46u
11
+ · · · + 40a +
196, u
13
− 6u
12
+ · · · + 52u − 8i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−0.225000u
12
+ 1.15000u
11
+ ··· + 20.4000u − 4.90000
3
10
u
12
−
17
10
u
11
+ ··· −
91
5
u +
21
5
a
4
=
−0.175000u
12
+ 0.700000u
11
+ ··· − 0.300000u + 0.300000
0.650000u
12
− 3.60000u
11
+ ··· − 35.6000u + 6.60000
a
2
=
0.325000u
12
− 1.55000u
11
+ ··· − 10.8000u + 2.30000
−
2
5
u
12
+
21
10
u
11
+ ··· +
43
5
u −
3
5
a
8
=
−0.325000u
12
+ 2.05000u
11
+ ··· + 31.8000u − 7.30000
1
5
u
12
−
4
5
u
11
+ ··· −
34
5
u +
9
5
a
3
=
0.325000u
12
− 2.05000u
11
+ ··· − 31.8000u + 7.30000
2
5
u
12
−
21
10
u
11
+ ··· −
73
5
u +
13
5
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−0.475000u
12
+ 2.40000u
11
+ ··· + 25.9000u − 5.90000
1
20
u
12
−
1
5
u
11
+ ··· −
51
5
u +
11
5
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7
10
u
12
−
24
5
u
11
+
199
10
u
10
− 62u
9
+
722
5
u
8
−
1386
5
u
7
+
2109
5
u
6
−
2659
5
u
5
+
5333
10
u
4
−
2156
5
u
3
+
1341
5
u
2
−
644
5
u +
194
5
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
13
− 11u
12
+ ··· + 107u + 7
c
2
, c
4
, c
8
c
10
u
13
+ u
12
+ 3u
11
+ u
10
+ 9u
9
+ 5u
8
+ 9u
7
+ u
6
+ 6u
5
− 2u
3
− u − 1
c
3
, c
9
u
13
− 2u
12
+ ··· + 7u − 24
c
5
, c
6
, c
11
c
12
u
13
− 6u
12
+ ··· + 52u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
13
+ 3y
12
+ ··· + 15999y −49
c
2
, c
4
, c
8
c
10
y
13
+ 5y
12
+ ··· + y −1
c
3
, c
9
y
13
− 18y
12
+ ··· + 4849y −576
c
5
, c
6
, c
11
c
12
y
13
+ 14y
12
+ ··· + 208y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925588 + 0.229213I
a = 0.251266 − 0.164394I
b = −0.719509 − 0.945453I
−2.64658 + 9.80964I 0.48730 − 9.61538I
u = 0.925588 − 0.229213I
a = 0.251266 + 0.164394I
b = −0.719509 + 0.945453I
−2.64658 − 9.80964I 0.48730 + 9.61538I
u = −0.012360 + 0.896275I
a = −0.353446 − 0.826500I
b = −0.562920 − 0.195545I
−1.71733 + 1.71633I 2.68735 − 4.73670I
u = −0.012360 − 0.896275I
a = −0.353446 + 0.826500I
b = −0.562920 + 0.195545I
−1.71733 − 1.71633I 2.68735 + 4.73670I
u = 0.548935 + 1.070790I
a = −0.33469 + 1.40815I
b = 0.89400 + 1.20313I
−6.6253 + 14.6812I −1.43670 − 9.72736I
u = 0.548935 − 1.070790I
a = −0.33469 − 1.40815I
b = 0.89400 − 1.20313I
−6.6253 − 14.6812I −1.43670 + 9.72736I
u = 0.959730 + 0.890724I
a = 0.549017 − 0.142828I
b = 0.361184 − 0.750707I
−4.30776 − 3.71769I −7.51801 + 8.71663I
u = 0.959730 − 0.890724I
a = 0.549017 + 0.142828I
b = 0.361184 + 0.750707I
−4.30776 + 3.71769I −7.51801 − 8.71663I
u = 0.418088
a = −0.957441
b = 0.687897
0.881810 11.5670
u = 0.15342 + 1.73647I
a = −0.13933 − 1.90579I
b = −0.99446 − 1.40865I
−16.4057 + 17.5804I −2.58727 − 8.30259I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15342 − 1.73647I
a = −0.13933 + 1.90579I
b = −0.99446 + 1.40865I
−16.4057 − 17.5804I −2.58727 + 8.30259I
u = 0.21564 + 1.85083I
a = −0.244097 + 0.817556I
b = 0.177755 + 0.770665I
−13.97390 + 1.53205I −8.41618 − 4.24758I
u = 0.21564 − 1.85083I
a = −0.244097 − 0.817556I
b = 0.177755 − 0.770665I
−13.97390 − 1.53205I −8.41618 + 4.24758I
6
II.
I
u
2
= hu
7
a−2u
6
a+· · ·+5b−4a, 4u
6
a+u
7
+· · ·+20a−6, u
8
−3u
7
+· · ·−14u+4i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
a
−
1
5
u
7
a +
2
5
u
6
a + ··· − 3au +
4
5
a
a
4
=
1
2
u
7
a −
3
2
u
6
a + ··· − 2a +
1
2
−
1
5
u
7
a −
1
2
u
7
+ ··· +
14
5
a + 2
a
2
=
−
1
5
u
7
a −
1
2
u
7
+ ··· +
9
5
a +
5
2
2
5
u
7
a +
1
2
u
7
+ ··· −
8
5
a − 2
a
8
=
1
5
u
7
a −
2
5
u
6
a + ··· + 2au +
1
5
a
−au
a
3
=
1
5
u
7
a −
2
5
u
6
a + ··· +
1
5
a +
1
2
−
1
5
u
7
a −
1
2
u
7
+ ··· +
4
5
a + 2
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−
7
10
u
7
a −
1
4
u
7
+ ··· +
14
5
a +
3
2
−
4
5
u
7
a +
8
5
u
6
a + ··· +
6
5
a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 15u
6
− 41u
5
+ 79u
4
− 104u
3
+ 107u
2
− 70u + 30
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
16
− 13u
15
+ ··· − 328u + 41
c
2
, c
4
, c
8
c
10
u
16
+ u
15
+ ··· − 2u + 1
c
3
, c
9
(u
8
− u
6
− u
3
+ 2u
2
− u + 1)
2
c
5
, c
6
, c
11
c
12
(u
8
− 3u
7
+ 10u
6
− 18u
5
+ 29u
4
− 31u
3
+ 27u
2
− 14u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
16
+ y
15
+ ··· + 2788y + 1681
c
2
, c
4
, c
8
c
10
y
16
+ 7y
15
+ ··· − 6y + 1
c
3
, c
9
(y
8
− 2y
7
+ y
6
+ 4y
5
− 2y
4
− 3y
3
+ 2y
2
+ 3y + 1)
2
c
5
, c
6
, c
11
c
12
(y
8
+ 11y
7
+ 50y
6
+ 124y
5
+ 189y
4
+ 181y
3
+ 93y
2
+ 20y + 16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.673128 + 1.045810I
a = 0.301794 − 1.174260I
b = −0.803268 − 1.117440I
−6.47283 + 5.59386I −6.60310 − 4.62010I
u = 0.673128 + 1.045810I
a = −0.633138 + 0.444550I
b = −0.073509 + 0.875041I
−6.47283 + 5.59386I −6.60310 − 4.62010I
u = 0.673128 − 1.045810I
a = 0.301794 + 1.174260I
b = −0.803268 + 1.117440I
−6.47283 − 5.59386I −6.60310 + 4.62010I
u = 0.673128 − 1.045810I
a = −0.633138 − 0.444550I
b = −0.073509 − 0.875041I
−6.47283 − 5.59386I −6.60310 + 4.62010I
u = 0.504550 + 0.414188I
a = −0.841060 + 0.591436I
b = 0.745591 + 0.724115I
1.86670 + 1.71603I 7.94168 − 3.64767I
u = 0.504550 + 0.414188I
a = −0.275916 − 0.687804I
b = −0.631239 + 0.403393I
1.86670 + 1.71603I 7.94168 − 3.64767I
u = 0.504550 − 0.414188I
a = −0.841060 − 0.591436I
b = 0.745591 − 0.724115I
1.86670 − 1.71603I 7.94168 + 3.64767I
u = 0.504550 − 0.414188I
a = −0.275916 + 0.687804I
b = −0.631239 − 0.403393I
1.86670 − 1.71603I 7.94168 + 3.64767I
u = 0.143098 + 1.398100I
a = 0.462450 + 0.187513I
b = 0.412575 − 0.112689I
−3.91396 + 3.96633I 6.91340 + 0.89673I
u = 0.143098 + 1.398100I
a = 0.01496 − 1.62294I
b = −0.833636 − 1.113530I
−3.91396 + 3.96633I 6.91340 + 0.89673I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.143098 − 1.398100I
a = 0.462450 − 0.187513I
b = 0.412575 + 0.112689I
−3.91396 − 3.96633I 6.91340 − 0.89673I
u = 0.143098 − 1.398100I
a = 0.01496 + 1.62294I
b = −0.833636 + 1.113530I
−3.91396 − 3.96633I 6.91340 − 0.89673I
u = 0.17922 + 1.74365I
a = 0.360792 − 1.135170I
b = −0.251883 − 1.053690I
−16.1539 + 9.0459I −5.25198 − 5.62090I
u = 0.17922 + 1.74365I
a = 0.11012 + 1.80963I
b = 0.93537 + 1.35801I
−16.1539 + 9.0459I −5.25198 − 5.62090I
u = 0.17922 − 1.74365I
a = 0.360792 + 1.135170I
b = −0.251883 + 1.053690I
−16.1539 − 9.0459I −5.25198 + 5.62090I
u = 0.17922 − 1.74365I
a = 0.11012 − 1.80963I
b = 0.93537 − 1.35801I
−16.1539 − 9.0459I −5.25198 + 5.62090I
11
III. I
u
3
= h13u
4
a
3
− 3u
4
a
2
+ · · · + 69a − 1, −2u
4
a
3
− u
4
a + · · · + 6a +
2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
a
−1.44444a
3
u
4
+ 0.333333a
2
u
4
+ ··· − 7.66667a + 0.111111
a
4
=
2
9
u
4
a
3
+
2
3
u
4
a
2
+ ··· −
1
3
a −
2
9
−2.44444a
3
u
4
+ 2.66667a
2
u
4
+ ··· − 17.3333a − 5.55556
a
2
=
13
9
u
4
a
3
−
1
3
u
4
a
2
+ ··· +
20
3
a −
1
9
−1.22222a
3
u
4
+ 1.66667a
2
u
4
+ ··· − 10.3333a − 2.44444
a
8
=
−0.222222a
3
u
4
− 1.33333a
2
u
4
+ ··· + 3.66667a + 2.55556
−
5
3
u
4
a
3
− u
4
a
2
+ ··· − 5a +
8
3
a
3
=
2
9
u
4
a
3
+
4
3
u
4
a
2
+ ··· −
11
3
a −
23
9
−1.55556a
3
u
4
− 0.333333a
2
u
4
+ ··· − 5.33333a + 0.888889
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
5
9
u
4
a
3
+
2
3
u
4
a
2
+ ··· −
7
3
a −
14
9
−3u
4
a
3
− u
4
a
2
+ ··· − a
2
− 14a
(ii) Obstruction class = −1
(iii) Cusp Shapes =
40
3
u
4
a
3
+ 16a
3
u
3
−16u
4
a
2
+
136
3
a
3
u
2
+ 32u
4
a +
128
3
a
3
u −48a
2
u
2
+
48u
3
a +
92
3
u
4
+
64
3
a
3
+ 8a
2
u + 120u
2
a + 20u
3
−16a
2
+ 128au +
320
3
u
2
+ 88a +
148
3
u +
110
3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
+ u + 1)
10
c
2
, c
4
, c
8
c
10
u
20
− u
19
+ ··· + 6u + 1
c
3
, c
9
u
20
− 3u
19
+ ··· − 12u + 21
c
5
, c
6
, c
11
c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ y + 1)
10
c
2
, c
4
, c
8
c
10
y
20
+ 7y
19
+ ··· − 4y + 1
c
3
, c
9
y
20
+ 11y
19
+ ··· − 1908y + 441
c
5
, c
6
, c
11
c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = −0.904693 − 0.769663I
b = −0.632026 − 0.556108I
−1.81981 + 1.84580I 3.11432 − 2.70531I
u = −0.233677 + 0.885557I
a = −0.963301 − 0.933717I
b = 0.861170 − 0.585785I
−1.81981 − 6.27374I 3.11432 + 11.15109I
u = −0.233677 + 0.885557I
a = 0.158195 − 0.630606I
b = −0.252831 + 0.191559I
−1.81981 + 1.84580I 3.11432 − 2.70531I
u = −0.233677 + 0.885557I
a = 0.12388 + 2.28034I
b = −0.73445 + 1.53437I
−1.81981 − 6.27374I 3.11432 + 11.15109I
u = −0.233677 − 0.885557I
a = −0.904693 + 0.769663I
b = −0.632026 + 0.556108I
−1.81981 − 1.84580I 3.11432 + 2.70531I
u = −0.233677 − 0.885557I
a = −0.963301 + 0.933717I
b = 0.861170 + 0.585785I
−1.81981 + 6.27374I 3.11432 − 11.15109I
u = −0.233677 − 0.885557I
a = 0.158195 + 0.630606I
b = −0.252831 − 0.191559I
−1.81981 − 1.84580I 3.11432 + 2.70531I
u = −0.233677 − 0.885557I
a = 0.12388 − 2.28034I
b = −0.73445 − 1.53437I
−1.81981 + 6.27374I 3.11432 − 11.15109I
u = −0.416284
a = −0.354528 + 0.090103I
b = 0.805501 − 1.021500I
0.88218 − 4.05977I 11.60884 + 6.92820I
u = −0.416284
a = −0.354528 − 0.090103I
b = 0.805501 + 1.021500I
0.88218 + 4.05977I 11.60884 − 6.92820I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416284
a = 1.45208 + 1.99112I
b = −0.482901 − 0.462743I
0.88218 + 4.05977I 11.60884 − 6.92820I
u = −0.416284
a = 1.45208 − 1.99112I
b = −0.482901 + 0.462743I
0.88218 − 4.05977I 11.60884 + 6.92820I
u = −0.05818 + 1.69128I
a = 0.073865 + 1.064830I
b = −1.074080 + 0.655525I
−10.95830 − 7.39151I 2.08126 + 9.29048I
u = −0.05818 + 1.69128I
a = 0.686831 − 0.325631I
b = 1.137160 − 0.408183I
−10.95830 + 0.72802I 2.08126 − 4.56592I
u = −0.05818 + 1.69128I
a = 0.37758 + 1.42971I
b = 0.113419 + 0.766429I
−10.95830 + 0.72802I 2.08126 − 4.56592I
u = −0.05818 + 1.69128I
a = 0.35009 − 2.53868I
b = 0.75904 − 1.91768I
−10.95830 − 7.39151I 2.08126 + 9.29048I
u = −0.05818 − 1.69128I
a = 0.073865 − 1.064830I
b = −1.074080 − 0.655525I
−10.95830 + 7.39151I 2.08126 − 9.29048I
u = −0.05818 − 1.69128I
a = 0.686831 + 0.325631I
b = 1.137160 + 0.408183I
−10.95830 − 0.72802I 2.08126 + 4.56592I
u = −0.05818 − 1.69128I
a = 0.37758 − 1.42971I
b = 0.113419 − 0.766429I
−10.95830 − 0.72802I 2.08126 + 4.56592I
u = −0.05818 − 1.69128I
a = 0.35009 + 2.53868I
b = 0.75904 + 1.91768I
−10.95830 + 7.39151I 2.08126 − 9.29048I
16
IV. I
u
4
= h−1.98 × 10
25
a
7
u
4
+ 9.89 × 10
25
a
6
u
4
+ · · · − 5.40 × 10
26
a + 1.69 ×
10
27
, 2a
7
u
4
+ 3a
6
u
4
+ · · · + 299a + 412, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
a
0.0231630a
7
u
4
− 0.115549a
6
u
4
+ ··· + 0.631354a − 1.97668
a
4
=
−0.0274758a
7
u
4
+ 0.111775a
6
u
4
+ ··· − 1.19459a + 5.60018
−0.0428376a
7
u
4
+ 0.165420a
6
u
4
+ ··· + 0.718981a + 9.06528
a
2
=
0.0396479a
7
u
4
+ 0.0263946a
6
u
4
+ ··· − 2.42546a − 5.34257
0.0754551a
7
u
4
− 0.0524429a
6
u
4
+ ··· + 1.43917a + 0.579745
a
8
=
−0.000834185a
7
u
4
− 0.110753a
6
u
4
+ ··· + 2.51506a − 1.28133
0.0223288a
7
u
4
− 0.226302a
6
u
4
+ ··· + 2.14641a − 3.25800
a
3
=
0.00657335a
7
u
4
− 0.0196410a
6
u
4
+ ··· − 3.57265a − 4.76746
0.0175399a
7
u
4
− 0.111532a
6
u
4
+ ··· + 1.18704a + 0.722514
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
0.105247a
7
u
4
+ 0.0542594a
6
u
4
+ ··· − 3.18898a − 6.29722
0.0451415a
7
u
4
+ 0.205954a
6
u
4
+ ··· − 1.91313a + 1.74778
(ii) Obstruction class = −1
(iii) Cusp Shapes =
9539523382442236510768
149311950360632514978053
a
7
u
4
−
164763234912438466289096
447935851081897544934159
a
6
u
4
+ ··· −
121369361505893912373208
149311950360632514978053
a −
9114397983880150556644478
447935851081897544934159
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
− 2u + 1)
10
c
2
, c
4
, c
8
c
10
u
40
+ u
39
+ ··· − 708u + 2217
c
3
, c
9
(u
20
+ u
19
+ ··· + 40u + 343)
2
c
5
, c
6
, c
11
c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
8
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
c
2
, c
4
, c
8
c
10
y
40
+ 13y
39
+ ··· + 124590744y + 4915089
c
3
, c
9
(y
20
− 25y
19
+ ··· − 1012764y + 117649)
2
c
5
, c
6
, c
11
c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
8
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = −0.784642 − 0.791408I
b = −0.009371 − 1.153560I
−5.10967 + 1.84580I −8.88568 − 2.70531I
u = −0.233677 + 0.885557I
a = −0.367052 − 1.285790I
b = −1.25398 − 1.03539I
−5.10967 + 1.84580I −8.88568 − 2.70531I
u = −0.233677 + 0.885557I
a = 1.35477 + 0.43992I
b = 0.139544 + 0.771173I
−5.10967 + 1.84580I −8.88568 − 2.70531I
u = −0.233677 + 0.885557I
a = 1.03773 + 1.17397I
b = 1.63591 + 1.17695I
−5.10967 − 6.27374I −8.8857 + 11.1511I
u = −0.233677 + 0.885557I
a = −0.43815 − 1.52704I
b = 0.99956 − 1.23269I
−5.10967 − 6.27374I −8.8857 + 11.1511I
u = −0.233677 + 0.885557I
a = 0.98322 + 1.91625I
b = −0.596618 + 1.204390I
−5.10967 − 6.27374I −8.8857 + 11.1511I
u = −0.233677 + 0.885557I
a = 0.72926 − 2.45624I
b = −0.014486 − 0.843941I
−5.10967 + 1.84580I −8.88568 − 2.70531I
u = −0.233677 + 0.885557I
a = −0.92923 + 2.58398I
b = −0.142425 + 0.529033I
−5.10967 − 6.27374I −8.8857 + 11.1511I
u = −0.233677 − 0.885557I
a = −0.784642 + 0.791408I
b = −0.009371 + 1.153560I
−5.10967 − 1.84580I −8.88568 + 2.70531I
u = −0.233677 − 0.885557I
a = −0.367052 + 1.285790I
b = −1.25398 + 1.03539I
−5.10967 − 1.84580I −8.88568 + 2.70531I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 − 0.885557I
a = 1.35477 − 0.43992I
b = 0.139544 − 0.771173I
−5.10967 − 1.84580I −8.88568 + 2.70531I
u = −0.233677 − 0.885557I
a = 1.03773 − 1.17397I
b = 1.63591 − 1.17695I
−5.10967 + 6.27374I −8.8857 − 11.1511I
u = −0.233677 − 0.885557I
a = −0.43815 + 1.52704I
b = 0.99956 + 1.23269I
−5.10967 + 6.27374I −8.8857 − 11.1511I
u = −0.233677 − 0.885557I
a = 0.98322 − 1.91625I
b = −0.596618 − 1.204390I
−5.10967 + 6.27374I −8.8857 − 11.1511I
u = −0.233677 − 0.885557I
a = 0.72926 + 2.45624I
b = −0.014486 + 0.843941I
−5.10967 − 1.84580I −8.88568 + 2.70531I
u = −0.233677 − 0.885557I
a = −0.92923 − 2.58398I
b = −0.142425 − 0.529033I
−5.10967 + 6.27374I −8.8857 − 11.1511I
u = −0.416284
a = −1.12225 + 1.12774I
b = 0.411711 − 1.062380I
−2.40769 − 4.05977I −0.39116 + 6.92820I
u = −0.416284
a = −1.12225 − 1.12774I
b = 0.411711 + 1.062380I
−2.40769 + 4.05977I −0.39116 − 6.92820I
u = −0.416284
a = 0.35045 + 1.64035I
b = −0.638561 − 0.911711I
−2.40769 + 4.05977I −0.39116 − 6.92820I
u = −0.416284
a = 0.35045 − 1.64035I
b = −0.638561 + 0.911711I
−2.40769 − 4.05977I −0.39116 + 6.92820I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416284
a = 0.82181 + 2.33488I
b = −0.750115 + 0.948474I
−2.40769 + 4.05977I −0.39116 − 6.92820I
u = −0.416284
a = 0.82181 − 2.33488I
b = −0.750115 − 0.948474I
−2.40769 − 4.05977I −0.39116 + 6.92820I
u = −0.416284
a = −1.14757 + 2.85557I
b = 0.654365 + 0.577136I
−2.40769 + 4.05977I −0.39116 − 6.92820I
u = −0.416284
a = −1.14757 − 2.85557I
b = 0.654365 − 0.577136I
−2.40769 − 4.05977I −0.39116 + 6.92820I
u = −0.05818 + 1.69128I
a = −0.575468 − 1.023550I
b = 0.243518 − 0.838061I
−14.2482 + 0.7280I −9.91874 − 4.56592I
u = −0.05818 + 1.69128I
a = 0.13851 + 1.50113I
b = −0.36137 + 1.37434I
−14.2482 + 0.7280I −9.91874 − 4.56592I
u = −0.05818 + 1.69128I
a = −0.52468 + 1.82556I
b = 0.344459 + 0.817677I
−14.2482 + 0.7280I −9.91874 − 4.56592I
u = −0.05818 + 1.69128I
a = −0.44379 + 1.84920I
b = −1.25771 + 1.45285I
−14.2482 − 7.3915I −9.91874 + 9.29048I
u = −0.05818 + 1.69128I
a = 0.71144 − 1.93489I
b = −0.103995 − 0.622502I
−14.2482 − 7.3915I −9.91874 + 9.29048I
u = −0.05818 + 1.69128I
a = −0.16586 − 2.06676I
b = 0.71770 − 1.35351I
−14.2482 − 7.3915I −9.91874 + 9.29048I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05818 + 1.69128I
a = 1.17815 + 1.74863I
b = 1.65404 + 1.52859I
−14.2482 + 0.7280I −9.91874 − 4.56592I
u = −0.05818 + 1.69128I
a = −1.80666 − 1.52955I
b = −2.17218 − 1.45548I
−14.2482 − 7.3915I −9.91874 + 9.29048I
u = −0.05818 − 1.69128I
a = −0.575468 + 1.023550I
b = 0.243518 + 0.838061I
−14.2482 − 0.7280I −9.91874 + 4.56592I
u = −0.05818 − 1.69128I
a = 0.13851 − 1.50113I
b = −0.36137 − 1.37434I
−14.2482 − 0.7280I −9.91874 + 4.56592I
u = −0.05818 − 1.69128I
a = −0.52468 − 1.82556I
b = 0.344459 − 0.817677I
−14.2482 − 0.7280I −9.91874 + 4.56592I
u = −0.05818 − 1.69128I
a = −0.44379 − 1.84920I
b = −1.25771 − 1.45285I
−14.2482 + 7.3915I −9.91874 − 9.29048I
u = −0.05818 − 1.69128I
a = 0.71144 + 1.93489I
b = −0.103995 + 0.622502I
−14.2482 + 7.3915I −9.91874 − 9.29048I
u = −0.05818 − 1.69128I
a = −0.16586 + 2.06676I
b = 0.71770 + 1.35351I
−14.2482 + 7.3915I −9.91874 − 9.29048I
u = −0.05818 − 1.69128I
a = 1.17815 − 1.74863I
b = 1.65404 − 1.52859I
−14.2482 − 0.7280I −9.91874 + 4.56592I
u = −0.05818 − 1.69128I
a = −1.80666 + 1.52955I
b = −2.17218 + 1.45548I
−14.2482 + 7.3915I −9.91874 − 9.29048I
23
V. I
u
5
= hu
19
+ u
18
+ · · · + 2b + 7, 6u
19
+ 26u
18
+ · · · + 26a + 299, u
20
+
14u
18
+ · · · + 85u
2
+ 13i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−
3
13
u
19
− u
18
+ ··· −
263
26
u −
23
2
−
1
2
u
19
−
1
2
u
18
+ ··· − 8u −
7
2
a
4
=
1.30769u
19
− 0.500000u
18
+ ··· + 16.6538u − 5.50000
1
2
u
19
− u
18
+ ··· + 4u −
21
2
a
2
=
19
26
u
19
−
1
2
u
18
+ ··· +
393
26
u − 2
−
3
2
u
18
+
1
2
u
17
+ ··· +
9
2
u − 16
a
8
=
−
19
26
u
19
−
1
2
u
18
+ ··· −
177
13
u − 5
−u
19
− 13u
17
+ ··· −
23
2
u + 3
a
3
=
19
26
u
19
−
1
2
u
18
+ ··· +
177
13
u − 5
−
1
2
u
19
−
1
2
u
18
+ ··· − 2u −
19
2
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−
4
13
u
19
− u
18
+ ··· −
93
13
u − 13
−
1
2
u
19
−
13
2
u
17
+ ··· −
19
2
u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 6u
18
+ 72u
16
+ 352u
14
+ 914u
12
+ 1408u
10
+ 1415u
8
+ 1015u
6
+ 512u
4
+ 158u
2
+ 15
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
20
− 8u
19
+ ··· + 2u + 1
c
2
, c
4
, c
8
c
10
u
20
− 2u
19
+ ··· − 4u + 1
c
3
, c
9
(u
10
− u
9
− 3u
8
+ 3u
7
+ 7u
6
− 4u
5
− 8u
4
− u
3
+ 5u
2
+ 3u − 1)
2
c
5
, c
6
, c
11
c
12
u
20
+ 14u
18
+ ··· + 85u
2
+ 13
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 14y
18
+ ··· − 16y + 1
c
2
, c
4
, c
8
c
10
y
20
+ 8y
19
+ ··· + 4y + 1
c
3
, c
9
(y
10
− 7y
9
+ ··· − 19y + 1)
2
c
5
, c
6
, c
11
c
12
(y
10
+ 14y
9
+ ··· + 85y + 13)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292954 + 0.839226I
a = −0.45802 + 1.38942I
b = −0.699531 + 0.471567I
−4.45321 + 5.61478I −0.94997 − 3.81742I
u = 0.292954 − 0.839226I
a = −0.45802 − 1.38942I
b = −0.699531 − 0.471567I
−4.45321 − 5.61478I −0.94997 + 3.81742I
u = −0.292954 + 0.839226I
a = −0.76762 − 1.54520I
b = 0.759941 − 1.172910I
−4.45321 − 5.61478I −0.94997 + 3.81742I
u = −0.292954 − 0.839226I
a = −0.76762 + 1.54520I
b = 0.759941 + 1.172910I
−4.45321 + 5.61478I −0.94997 − 3.81742I
u = −0.578949 + 0.658786I
a = −0.825562 + 0.060286I
b = −0.321887 − 0.870956I
−3.49395 + 2.59792I −3.58756 − 3.56344I
u = −0.578949 − 0.658786I
a = −0.825562 − 0.060286I
b = −0.321887 + 0.870956I
−3.49395 − 2.59792I −3.58756 + 3.56344I
u = 0.578949 + 0.658786I
a = 0.944411 − 0.622307I
b = 0.575029 − 0.074063I
−3.49395 − 2.59792I −3.58756 + 3.56344I
u = 0.578949 − 0.658786I
a = 0.944411 + 0.622307I
b = 0.575029 + 0.074063I
−3.49395 + 2.59792I −3.58756 − 3.56344I
u = 0.701594I
a = −1.19157 − 1.33290I
b = 0.233625 − 0.999908I
−4.42214 −6.61610
u = − 0.701594I
a = −1.19157 + 1.33290I
b = 0.233625 + 0.999908I
−4.42214 −6.61610
27
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.060025 + 1.313210I
a = 0.544429 + 0.310811I
b = 0.198498 + 0.446154I
−4.33175 + 4.31090I −5.13581 − 8.57420I
u = 0.060025 − 1.313210I
a = 0.544429 − 0.310811I
b = 0.198498 − 0.446154I
−4.33175 − 4.31090I −5.13581 + 8.57420I
u = −0.060025 + 1.313210I
a = −0.11611 − 1.73797I
b = 0.80084 − 1.17005I
−4.33175 − 4.31090I −5.13581 + 8.57420I
u = −0.060025 − 1.313210I
a = −0.11611 + 1.73797I
b = 0.80084 + 1.17005I
−4.33175 + 4.31090I −5.13581 − 8.57420I
u = −0.06323 + 1.68896I
a = −0.12947 + 1.91613I
b = −0.96456 + 1.37630I
−13.4730 + 6.8978I −0.54611 + 3.29895I
u = −0.06323 − 1.68896I
a = −0.12947 − 1.91613I
b = −0.96456 − 1.37630I
−13.4730 − 6.8978I −0.54611 − 3.29895I
u = 0.06323 + 1.68896I
a = 0.48519 − 1.38402I
b = 0.942552 − 0.808832I
−13.4730 − 6.8978I −0.54611 − 3.29895I
u = 0.06323 − 1.68896I
a = 0.48519 + 1.38402I
b = 0.942552 + 0.808832I
−13.4730 + 6.8978I −0.54611 + 3.29895I
u = 1.71295I
a = 0.014324 + 1.229180I
b = −0.524504 + 0.922982I
−13.1612 −2.94490
u = − 1.71295I
a = 0.014324 − 1.229180I
b = −0.524504 − 0.922982I
−13.1612 −2.94490
28
VI.
I
u
6
= h−u
4
+ u
3
− 3u
2
+ b + 2u − 1, u
3
+ a + 2u, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−u
3
− 2u
u
4
− u
3
+ 3u
2
− 2u + 1
a
4
=
u
u
a
2
=
u
u
a
8
=
−u
2
− 1
u
4
+ 2u
2
a
3
=
u
2
+ 1
u
2
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−u
2
− 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
− 4u
3
+ 16u
2
− 12u + 14
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
5
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
5
− u
4
+ u
2
+ u − 1
c
5
, c
6
, c
11
c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
5
c
2
, c
3
, c
4
c
8
, c
9
, c
10
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
c
5
, c
6
, c
11
c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233677 + 0.885557I
a = 0.069642 − 1.221720I
b = −0.758138 − 0.584034I
−1.81981 + 2.21397I 3.11432 − 4.22289I
u = 0.233677 − 0.885557I
a = 0.069642 + 1.221720I
b = −0.758138 + 0.584034I
−1.81981 − 2.21397I 3.11432 + 4.22289I
u = 0.416284
a = −0.904706
b = 0.645200
0.882183 11.6090
u = 0.05818 + 1.69128I
a = 0.38271 + 1.43804I
b = 0.935538 + 0.903908I
−10.95830 + 3.33174I 2.08126 − 2.36228I
u = 0.05818 − 1.69128I
a = 0.38271 − 1.43804I
b = 0.935538 − 0.903908I
−10.95830 − 3.33174I 2.08126 + 2.36228I
32
VII.
I
u
7
= hu
4
a+2u
4
+· · ·+a+5, 2u
4
a+u
3
a+· · ·+2a+1, u
5
+u
4
+4u
3
+3u
2
+3u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
a
−
1
3
u
4
a −
2
3
u
4
+ ··· −
1
3
a −
5
3
a
4
=
−
1
3
u
4
a +
4
3
u
4
+ ··· +
2
3
a +
7
3
−
1
3
u
4
a +
1
3
u
4
+ ··· +
2
3
a −
2
3
a
2
=
−
1
3
u
4
a +
4
3
u
4
+ ··· +
2
3
a +
7
3
−
1
3
u
4
a +
1
3
u
4
+ ··· +
2
3
a −
2
3
a
8
=
1
3
u
4
a −
1
3
u
4
+ ··· +
4
3
a −
1
3
−u
4
− 2u
3
+ au − 4u
2
− 4u − 2
a
3
=
1
3
u
4
a +
5
3
u
4
+ ··· +
4
3
a +
8
3
−
1
3
u
4
a +
1
3
u
4
+ ··· −
1
3
a −
2
3
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
1
3
u
4
a −
1
3
u
4
+ ··· +
4
3
a +
2
3
−2u
4
− 2u
3
+ au − 6u
2
− 4u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
+ 4u
3
+ 16u
2
+ 12u + 2
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u + 1)
10
c
2
, c
4
, c
8
c
10
u
10
+ u
9
+ 4u
8
+ 16u
6
+ 2u
5
+ 19u
4
+ 3u
3
+ 12u
2
+ 2u + 3
c
3
, c
9
(u
5
+ u
4
− u
2
+ u + 1)
2
c
5
, c
6
, c
11
c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)
10
c
2
, c
4
, c
8
c
10
y
10
+ 7y
9
+ ··· + 68y + 9
c
3
, c
9
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
2
c
5
, c
6
, c
11
c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = 0.128608 − 1.279670I
b = 0.92954 − 1.29747I
−5.10967 − 2.21397I −8.88568 + 4.22289I
u = −0.233677 + 0.885557I
a = 1.45731 + 1.33332I
b = −0.171405 + 0.713431I
−5.10967 − 2.21397I −8.88568 + 4.22289I
u = −0.233677 − 0.885557I
a = 0.128608 + 1.279670I
b = 0.92954 + 1.29747I
−5.10967 + 2.21397I −8.88568 − 4.22289I
u = −0.233677 − 0.885557I
a = 1.45731 − 1.33332I
b = −0.171405 − 0.713431I
−5.10967 + 2.21397I −8.88568 − 4.22289I
u = −0.416284
a = −1.09755 + 0.97112I
b = −0.322600 − 0.692564I
−2.40769 −0.391160
u = −0.416284
a = −1.09755 − 0.97112I
b = −0.322600 + 0.692564I
−2.40769 −0.391160
u = −0.05818 + 1.69128I
a = −0.68121 − 1.55202I
b = 0.363268 − 0.820011I
−14.2482 − 3.3317I −9.91874 + 2.36228I
u = −0.05818 + 1.69128I
a = −0.80715 + 1.92179I
b = −1.29881 + 1.72392I
−14.2482 − 3.3317I −9.91874 + 2.36228I
u = −0.05818 − 1.69128I
a = −0.68121 + 1.55202I
b = 0.363268 + 0.820011I
−14.2482 + 3.3317I −9.91874 − 2.36228I
u = −0.05818 − 1.69128I
a = −0.80715 − 1.92179I
b = −1.29881 − 1.72392I
−14.2482 + 3.3317I −9.91874 − 2.36228I
36
VIII. I
u
8
= h2b − u + 1, 3a − 2u, u
2
+ 3i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
3
a
1
=
u
u
a
9
=
2
3
u
1
2
u −
1
2
a
4
=
−
1
3
u
−
1
2
u −
1
2
a
2
=
5
6
u −
1
2
u − 1
a
8
=
1
6
u −
3
2
−2
a
3
=
−
1
6
u −
3
2
−
1
2
u −
5
2
a
11
=
−u
−2u
a
7
=
−2
−3
a
10
=
−
1
6
u +
1
2
−
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
− u + 1
c
2
, c
4
, c
8
c
10
u
2
+ u + 1
c
3
, c
9
(u + 1)
2
c
5
, c
6
, c
11
c
12
u
2
+ 3
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
2
+ y + 1
c
3
, c
9
(y −1)
2
c
5
, c
6
, c
11
c
12
(y + 3)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 1.154700I
b = −0.500000 + 0.866025I
−13.1595 −3.00000
u = − 1.73205I
a = − 1.154700I
b = −0.500000 − 0.866025I
−13.1595 −3.00000
40
IX. I
u
9
= hb
2
− b + 1, a, u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
1
a
6
=
1
−1
a
1
=
1
1
a
9
=
0
b
a
4
=
1
b − 1
a
2
=
b − 1
−2b + 2
a
8
=
−b
0
a
3
=
−b + 1
b − 1
a
11
=
−1
2
a
7
=
2
−3
a
10
=
b − 1
−b + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
− 3u + 3
c
2
, c
4
, c
8
c
10
u
2
− u + 1
c
3
, c
9
(u + 1)
2
c
5
, c
6
, c
11
c
12
(u − 1)
2
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
− 3y + 9
c
2
, c
4
, c
8
c
10
y
2
+ y + 1
c
3
, c
5
, c
6
c
9
, c
11
, c
12
(y −1)
2
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 0.500000 + 0.866025I
−3.28987 −3.00000
u = 1.00000
a = 0
b = 0.500000 − 0.866025I
−3.28987 −3.00000
44
X. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
−1
0
a
6
=
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
11
=
−1
0
a
7
=
1
0
a
10
=
−1
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
45
(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
46
(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
47
(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
48
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
5
(u + 1)
10
(u
2
− 3u + 3)(u
2
− u + 1)
2
(u
2
+ u + 1)
10
· ((u
4
+ u
3
− 2u + 1)
10
)(u
13
− 11u
12
+ ··· + 107u + 7)
· (u
16
− 13u
15
+ ··· − 328u + 41)(u
20
− 8u
19
+ ··· + 2u + 1)
c
2
, c
4
, c
8
c
10
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
5
− u
4
+ u
2
+ u − 1)
· (u
10
+ u
9
+ 4u
8
+ 16u
6
+ 2u
5
+ 19u
4
+ 3u
3
+ 12u
2
+ 2u + 3)
· (u
13
+ u
12
+ 3u
11
+ u
10
+ 9u
9
+ 5u
8
+ 9u
7
+ u
6
+ 6u
5
− 2u
3
− u − 1)
· (u
16
+ u
15
+ ··· − 2u + 1)(u
20
− 2u
19
+ ··· − 4u + 1)
· (u
20
− u
19
+ ··· + 6u + 1)(u
40
+ u
39
+ ··· − 708u + 2217)
c
3
, c
9
(u + 1)
4
(u
2
− u + 1)(u
5
− u
4
+ u
2
+ u − 1)(u
5
+ u
4
− u
2
+ u + 1)
2
· (u
8
− u
6
− u
3
+ 2u
2
− u + 1)
2
· (u
10
− u
9
− 3u
8
+ 3u
7
+ 7u
6
− 4u
5
− 8u
4
− u
3
+ 5u
2
+ 3u − 1)
2
· (u
13
− 2u
12
+ ··· + 7u − 24)(u
20
− 3u
19
+ ··· − 12u + 21)
· (u
20
+ u
19
+ ··· + 40u + 343)
2
c
5
, c
6
, c
11
c
12
u
2
(u − 1)
2
(u
2
+ 3)(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
14
· (u
8
− 3u
7
+ 10u
6
− 18u
5
+ 29u
4
− 31u
3
+ 27u
2
− 14u + 4)
2
· (u
13
− 6u
12
+ ··· + 52u − 8)(u
20
+ 14u
18
+ ··· + 85u
2
+ 13)
49
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
5
(y −1)
10
(y
2
− 3y + 9)(y
2
+ y + 1)
12
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
· (y
13
+ 3y
12
+ ··· + 15999y −49)(y
16
+ y
15
+ ··· + 2788y + 1681)
· (y
20
+ 14y
18
+ ··· − 16y + 1)
c
2
, c
4
, c
8
c
10
((y
2
+ y + 1)
3
)(y
5
− y
4
+ ··· + 3y −1)(y
10
+ 7y
9
+ ··· + 68y + 9)
· (y
13
+ 5y
12
+ ··· + y −1)(y
16
+ 7y
15
+ ··· − 6y + 1)
· (y
20
+ 7y
19
+ ··· − 4y + 1)(y
20
+ 8y
19
+ ··· + 4y + 1)
· (y
40
+ 13y
39
+ ··· + 124590744y + 4915089)
c
3
, c
9
(y −1)
4
(y
2
+ y + 1)(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
3
· (y
8
− 2y
7
+ y
6
+ 4y
5
− 2y
4
− 3y
3
+ 2y
2
+ 3y + 1)
2
· ((y
10
− 7y
9
+ ··· − 19y + 1)
2
)(y
13
− 18y
12
+ ··· + 4849y −576)
· (y
20
− 25y
19
+ ··· − 1012764y + 117649)
2
· (y
20
+ 11y
19
+ ··· − 1908y + 441)
c
5
, c
6
, c
11
c
12
y
2
(y −1)
2
(y + 3)
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
15
· (y
8
+ 11y
7
+ 50y
6
+ 124y
5
+ 189y
4
+ 181y
3
+ 93y
2
+ 20y + 16)
2
· ((y
10
+ 14y
9
+ ··· + 85y + 13)
2
)(y
13
+ 14y
12
+ ··· + 208y −64)
50
