12a
0742
(K12a
0742
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 10 11 2 7 1 6 4 5
Solving Sequence
2,7
8 3 9 4
1,11
6 10 5 12
c
7
c
2
c
8
c
3
c
1
c
6
c
10
c
5
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
32
− u
31
+ ··· + b − 1, −u
33
+ 5u
32
+ ··· + 2a − 8, u
34
− 3u
33
+ ··· + 8u − 2i
I
u
2
= h−2u
4
a − u
3
a + 3u
4
+ u
3
− u
2
+ 2b − 3a + 6, −2u
4
a − u
3
a + 3u
4
+ 3u
3
+ a
2
+ au − 2u
2
− 3a + u + 4,
u
5
+ u
4
+ 2u + 1i
I
u
3
= hb − 1, u
3
+ 2u
2
+ 2a − u, u
4
− u
2
+ 2i
I
u
4
= h−3u
15
a − 4u
14
a + ··· − 6a + 4, u
15
a − u
15
+ ··· + a
2
− a,
u
16
+ u
15
− 2u
14
− 3u
13
+ 4u
12
+ 7u
11
− 3u
10
− 10u
9
+ 9u
7
+ 3u
6
− 5u
5
− 4u
4
+ 2u
2
+ 2u + 1i
I
u
5
= hb + 1, a + u − 1, u
4
+ 1i
I
u
6
= hb, a + 1, u − 1i
I
u
7
= hb − 1, a − 1, u − 1i
I
u
8
= hb − 1, a, u − 1i
I
u
9
= hb − 1, a − 2, u + 1i
I
v
1
= ha, b + 1, v + 1i
* 10 irreducible components of dim
C
= 0, with total 89 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
= hu
32
−u
31
+· · ·+b−1, −u
33
+5u
32
+· · ·+2a−8, u
34
−3u
33
+· · ·+8u−2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
1
2
u
33
−
5
2
u
32
+ ··· − 9u + 4
−u
32
+ u
31
+ ··· − 4u + 1
a
6
=
3
2
u
33
−
7
2
u
32
+ ··· − 8u + 3
−u
33
+ 2u
32
+ ··· + 4u − 1
a
10
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 4u
6
− 3u
4
+ 2u
2
a
5
=
7
2
u
33
−
17
2
u
32
+ ··· − 20u + 6
−3u
33
+ 6u
32
+ ··· + 12u − 3
a
12
=
1
2
u
33
−
3
2
u
32
+ ··· − 5u + 2
−u
32
+ u
31
+ ··· − 3u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
33
+ 18u
32
+ 24u
31
− 98u
30
− 34u
29
+ 324u
28
− 48u
27
−
778u
26
+ 404u
25
+ 1380u
24
− 1192u
23
− 1882u
22
+ 2412u
21
+ 1850u
20
− 3712u
19
−
984u
18
+ 4390u
17
− 460u
16
− 3998u
15
+ 1854u
14
+ 2552u
13
− 2452u
12
− 726u
11
+
1942u
10
− 470u
9
− 954u
8
+ 796u
7
+ 110u
6
− 512u
5
+ 270u
4
+ 50u
3
− 132u
2
+ 74u − 20
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
34
+ 11u
33
+ ··· − 16u + 4
c
2
, c
7
u
34
+ 3u
33
+ ··· − 8u − 2
c
3
u
34
− 3u
33
+ ··· + 848u − 296
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
34
− u
33
+ ··· + u + 1
c
9
u
34
+ 21u
33
+ ··· − 40228u − 4366
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
34
+ 25y
33
+ ··· − 288y + 16
c
2
, c
7
y
34
− 11y
33
+ ··· + 16y + 4
c
3
y
34
+ y
33
+ ··· + 674464y + 87616
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
34
− 43y
33
+ ··· − 9y + 1
c
9
y
34
+ 13y
33
+ ··· + 56365904y + 19061956
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988927 + 0.109578I
a = −0.431526 + 1.228470I
b = 0.276236 + 0.567180I
−3.24927 + 2.65062I −6.82528 − 6.63039I
u = −0.988927 − 0.109578I
a = −0.431526 − 1.228470I
b = 0.276236 − 0.567180I
−3.24927 − 2.65062I −6.82528 + 6.63039I
u = −0.739127 + 0.741106I
a = 0.930370 + 0.017261I
b = −0.485252 − 0.215051I
3.09736 + 0.68740I 3.83595 − 3.91295I
u = −0.739127 − 0.741106I
a = 0.930370 − 0.017261I
b = −0.485252 + 0.215051I
3.09736 − 0.68740I 3.83595 + 3.91295I
u = 0.718436 + 0.774498I
a = 0.812978 + 0.075813I
b = −0.412168 − 0.529259I
2.64462 + 2.18332I 2.21430 − 4.77335I
u = 0.718436 − 0.774498I
a = 0.812978 − 0.075813I
b = −0.412168 + 0.529259I
2.64462 − 2.18332I 2.21430 + 4.77335I
u = 0.939426
a = 0.0259566
b = 0.428300
−1.90429 −3.14100
u = 0.891331 + 0.603370I
a = 0.422005 + 0.483472I
b = 0.066256 + 0.592921I
−0.69654 − 2.34709I −4.49475 + 2.27928I
u = 0.891331 − 0.603370I
a = 0.422005 − 0.483472I
b = 0.066256 − 0.592921I
−0.69654 + 2.34709I −4.49475 − 2.27928I
u = 1.005180 + 0.389797I
a = −0.154937 + 0.640657I
b = −1.52677 − 0.22591I
9.88665 + 2.86032I 4.26747 + 0.39615I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005180 − 0.389797I
a = −0.154937 − 0.640657I
b = −1.52677 + 0.22591I
9.88665 − 2.86032I 4.26747 − 0.39615I
u = −1.076760 + 0.192034I
a = −0.23388 − 1.88626I
b = −1.52621 − 0.30047I
8.67508 + 9.43470I 2.55855 − 6.18677I
u = −1.076760 − 0.192034I
a = −0.23388 + 1.88626I
b = −1.52621 + 0.30047I
8.67508 − 9.43470I 2.55855 + 6.18677I
u = −1.10214
a = 1.33391
b = 1.42323
3.37001 2.15130
u = 0.701066 + 0.850551I
a = −2.07986 + 0.41696I
b = 1.56353 + 0.32987I
15.6899 + 9.3353I 8.75460 − 3.54458I
u = 0.701066 − 0.850551I
a = −2.07986 − 0.41696I
b = 1.56353 − 0.32987I
15.6899 − 9.3353I 8.75460 + 3.54458I
u = 0.506457 + 0.733877I
a = 1.048590 + 0.101195I
b = −1.46790 − 0.05121I
8.81248 + 1.35417I 8.27726 − 0.26965I
u = 0.506457 − 0.733877I
a = 1.048590 − 0.101195I
b = −1.46790 + 0.05121I
8.81248 − 1.35417I 8.27726 + 0.26965I
u = −0.804999 + 0.836403I
a = −2.48607 + 0.64116I
b = 1.62501 + 0.21278I
17.5746 + 4.9413I 9.92383 − 3.25429I
u = −0.804999 − 0.836403I
a = −2.48607 − 0.64116I
b = 1.62501 − 0.21278I
17.5746 − 4.9413I 9.92383 + 3.25429I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966971 + 0.696899I
a = −0.486334 + 0.622660I
b = 0.511243 − 0.168909I
2.40071 + 4.80114I 1.91928 − 2.14166I
u = −0.966971 − 0.696899I
a = −0.486334 − 0.622660I
b = 0.511243 + 0.168909I
2.40071 − 4.80114I 1.91928 + 2.14166I
u = 1.032170 + 0.632265I
a = −0.17093 − 1.70332I
b = 1.43085 − 0.07072I
7.31130 − 6.52330I 5.94001 + 5.49172I
u = 1.032170 − 0.632265I
a = −0.17093 + 1.70332I
b = 1.43085 + 0.07072I
7.31130 + 6.52330I 5.94001 − 5.49172I
u = 0.986491 + 0.714526I
a = −1.35111 − 0.66802I
b = 0.407979 − 0.571160I
1.83243 − 7.82430I 0.40818 + 9.67142I
u = 0.986491 − 0.714526I
a = −1.35111 + 0.66802I
b = 0.407979 + 0.571160I
1.83243 + 7.82430I 0.40818 − 9.67142I
u = −0.957491 + 0.784549I
a = 1.91646 − 1.35507I
b = −1.62922 + 0.19094I
17.1033 + 1.1035I 9.17994 − 1.90960I
u = −0.957491 − 0.784549I
a = 1.91646 + 1.35507I
b = −1.62922 − 0.19094I
17.1033 − 1.1035I 9.17994 + 1.90960I
u = 1.022640 + 0.743834I
a = 1.85346 + 2.37415I
b = −1.55431 + 0.34115I
14.7022 − 15.2836I 7.11885 + 8.33563I
u = 1.022640 − 0.743834I
a = 1.85346 − 2.37415I
b = −1.55431 − 0.34115I
14.7022 + 15.2836I 7.11885 − 8.33563I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122815 + 0.705145I
a = −2.12345 − 0.61721I
b = 1.55687 − 0.26874I
12.6181 − 6.5965I 9.17145 + 3.77893I
u = 0.122815 − 0.705145I
a = −2.12345 + 0.61721I
b = 1.55687 + 0.26874I
12.6181 + 6.5965I 9.17145 − 3.77893I
u = 0.129052 + 0.423858I
a = 0.854310 + 0.046698I
b = −0.261902 + 0.382447I
0.121984 − 0.976428I 2.24524 + 6.97728I
u = 0.129052 − 0.423858I
a = 0.854310 − 0.046698I
b = −0.261902 − 0.382447I
0.121984 + 0.976428I 2.24524 − 6.97728I
8
II. I
u
2
= h−2u
4
a − u
3
a + 3u
4
+ u
3
− u
2
+ 2b − 3a + 6, −2u
4
a + 3u
4
+ · · · −
3a + 4, u
5
+ u
4
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
4
+ u
2
+ u + 1
−u
2
a
1
=
u
3
−u
4
− u
3
− u − 1
a
11
=
a
u
4
a −
3
2
u
4
+ ··· +
3
2
a − 3
a
6
=
3
2
u
4
a − u
4
+ ··· + 3a − 3
−
1
2
u
4
a + u
4
+ ··· − a +
5
2
a
10
=
u
4
− u
2
+ 2u + 2
u
3
− u
a
5
=
2u
4
a − 2u
4
+ ··· + 4a −
11
2
−
1
2
u
4
a +
1
2
u
4
+ ··· −
1
2
a +
3
2
a
12
=
u
4
a −
1
2
u
4
+ ··· +
5
2
a − 2
1
2
u
4
a − u
4
+ ··· + a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
+ 4u
2
− 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
c
2
, c
7
(u
5
− u
4
+ 2u − 1)
2
c
3
(u
5
+ 4u
4
+ 9u
3
+ 9u
2
+ 4u − 4)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 3u
5
− 3u
4
− u
3
+ 9u
2
− 2u − 5
c
9
(u
5
− u
4
+ 4u
3
− 2u
2
+ 4u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
9
(y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y −1)
2
c
2
, c
7
(y
5
− y
4
+ 4y
3
− 2y
2
+ 4y −1)
2
c
3
(y
5
+ 2y
4
+ 17y
3
+ 23y
2
+ 88y −16)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
10
− 9y
9
+ ··· − 94y + 25
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.760506 + 0.815892I
a = 0.989553 − 0.173629I
b = −0.733353 + 0.825839I
9.59182 − 1.13825I 8.09602 + 2.34058I
u = 0.760506 + 0.815892I
a = −2.89378 − 0.20313I
b = 1.49386 − 0.00995I
9.59182 − 1.13825I 8.09602 + 2.34058I
u = 0.760506 − 0.815892I
a = 0.989553 + 0.173629I
b = −0.733353 − 0.825839I
9.59182 + 1.13825I 8.09602 − 2.34058I
u = 0.760506 − 0.815892I
a = −2.89378 + 0.20313I
b = 1.49386 + 0.00995I
9.59182 + 1.13825I 8.09602 − 2.34058I
u = −1.001870 + 0.741764I
a = −1.58501 + 0.67934I
b = 0.487815 + 0.934585I
8.07331 + 10.61130I 5.23519 − 7.85454I
u = −1.001870 + 0.741764I
a = 2.22820 − 2.29189I
b = −1.48968 − 0.19282I
8.07331 + 10.61130I 5.23519 − 7.85454I
u = −1.001870 − 0.741764I
a = −1.58501 − 0.67934I
b = 0.487815 − 0.934585I
8.07331 − 10.61130I 5.23519 + 7.85454I
u = −1.001870 − 0.741764I
a = 2.22820 + 2.29189I
b = −1.48968 + 0.19282I
8.07331 − 10.61130I 5.23519 + 7.85454I
u = −0.517281
a = 1.16595
b = −1.15268
2.50323 −0.662420
u = −0.517281
a = 2.35611
b = 0.635404
2.50323 −0.662420
12
III. I
u
3
= hb − 1, u
3
+ 2u
2
+ 2a − u, u
4
− u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
−u
3
u
a
1
=
u
3
−u
a
11
=
−
1
2
u
3
− u
2
+
1
2
u
1
a
6
=
−
1
2
u
3
− u
2
+
1
2
u + 1
1
a
10
=
−1
0
a
5
=
−
1
2
u
3
− u
2
+
1
2
u
1
a
12
=
1
2
u
3
− u
2
+
1
2
u
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 2)
2
c
2
, c
3
, c
7
c
9
u
4
− u
2
+ 2
c
4
, c
10
(u + 1)
4
c
5
, c
6
, c
11
c
12
(u − 1)
4
c
8
(u
2
+ u + 2)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
+ 3y + 4)
2
c
2
, c
3
, c
7
c
9
(y
2
− y + 2)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y −1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = 0.19178 − 1.80095I
b = 1.00000
4.11234 − 5.33349I 6.00000 + 5.29150I
u = 0.978318 − 0.676097I
a = 0.19178 + 1.80095I
b = 1.00000
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −0.978318 + 0.676097I
a = −1.19178 + 0.84480I
b = 1.00000
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −0.978318 − 0.676097I
a = −1.19178 − 0.84480I
b = 1.00000
4.11234 − 5.33349I 6.00000 + 5.29150I
16
IV. I
u
4
=
h−3u
15
a−4u
14
a+· · ·−6a+4, u
15
a−u
15
+· · ·+a
2
−a, u
16
+u
15
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
a
3u
15
a + 4u
14
a + ··· + 6a − 4
a
6
=
3u
14
a + 3u
15
+ ··· + 3a + u
−5u
15
a + 3u
15
+ ··· − 7a + 7
a
10
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 4u
6
− 3u
4
+ 2u
2
a
5
=
5u
15
a + 6u
14
a + ··· + 10a − 7
−5u
15
a + 6u
15
+ ··· − 4a + 8
a
12
=
3u
15
a + u
15
+ ··· + 7a − 1
−3u
15
a + 5u
15
+ ··· − a + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
12
−8u
10
+ 16u
8
+ 4u
7
−16u
6
−8u
5
+ 12u
4
+ 8u
3
−4u
2
−4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
c
2
, c
7
(u
16
− u
15
+ ··· − 2u + 1)
2
c
3
(u
8
− 2u
7
+ 3u
6
+ u
4
+ 2u
2
− 2u + 1)
4
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
32
− u
31
+ ··· + 6u + 3
c
9
(u
16
− 5u
15
+ ··· − 4u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
9
(y
16
+ 11y
15
+ ··· − 8y + 1)
2
c
2
, c
7
(y
16
− 5y
15
+ ··· − 4y
2
+ 1)
2
c
3
(y
8
+ 2y
7
+ 11y
6
+ 10y
5
+ 7y
4
+ 10y
3
+ 6y
2
+ 1)
4
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
32
− 27y
31
+ ··· + 102y + 9
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017320 + 0.191091I
a = −0.34975 − 1.64157I
b = 0.458488 − 0.829230I
2.20856 − 5.29622I −0.10789 + 6.28296I
u = 1.017320 + 0.191091I
a = 0.23817 + 1.83664I
b = −1.41899 + 0.17495I
2.20856 − 5.29622I −0.10789 + 6.28296I
u = 1.017320 − 0.191091I
a = −0.34975 + 1.64157I
b = 0.458488 + 0.829230I
2.20856 + 5.29622I −0.10789 − 6.28296I
u = 1.017320 − 0.191091I
a = 0.23817 − 1.83664I
b = −1.41899 − 0.17495I
2.20856 + 5.29622I −0.10789 − 6.28296I
u = −0.908738 + 0.252477I
a = 1.024170 − 0.602730I
b = 0.650125 − 0.629128I
2.96149 + 0.25270I 1.61015 − 0.96511I
u = −0.908738 + 0.252477I
a = 0.672335 − 1.024320I
b = −1.358490 + 0.017727I
2.96149 + 0.25270I 1.61015 − 0.96511I
u = −0.908738 − 0.252477I
a = 1.024170 + 0.602730I
b = 0.650125 + 0.629128I
2.96149 − 0.25270I 1.61015 + 0.96511I
u = −0.908738 − 0.252477I
a = 0.672335 + 1.024320I
b = −1.358490 − 0.017727I
2.96149 − 0.25270I 1.61015 + 0.96511I
u = −0.708362 + 0.611401I
a = 0.955612 − 0.379206I
b = 0.244922 − 0.372311I
2.96149 − 0.25270I 1.61015 + 0.96511I
u = −0.708362 + 0.611401I
a = 0.938047 + 0.006205I
b = −1.153660 + 0.119834I
2.96149 − 0.25270I 1.61015 + 0.96511I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708362 − 0.611401I
a = 0.955612 + 0.379206I
b = 0.244922 + 0.372311I
2.96149 + 0.25270I 1.61015 − 0.96511I
u = −0.708362 − 0.611401I
a = 0.938047 − 0.006205I
b = −1.153660 − 0.119834I
2.96149 + 0.25270I 1.61015 − 0.96511I
u = −0.724199 + 0.826388I
a = 0.657035 − 0.259025I
b = −0.514081 + 0.923230I
8.92422 − 4.73566I 6.88636 + 2.91588I
u = −0.724199 + 0.826388I
a = −2.59244 − 0.38162I
b = 1.49162 − 0.17329I
8.92422 − 4.73566I 6.88636 + 2.91588I
u = −0.724199 − 0.826388I
a = 0.657035 + 0.259025I
b = −0.514081 − 0.923230I
8.92422 + 4.73566I 6.88636 − 2.91588I
u = −0.724199 − 0.826388I
a = −2.59244 + 0.38162I
b = 1.49162 + 0.17329I
8.92422 + 4.73566I 6.88636 − 2.91588I
u = 0.866890 + 0.696274I
a = 1.54948 − 0.22013I
b = −1.165260 − 0.286760I
5.64493 − 2.67607I 7.61139 + 3.32415I
u = 0.866890 + 0.696274I
a = −1.67678 − 2.03785I
b = 1.105310 − 0.336093I
5.64493 − 2.67607I 7.61139 + 3.32415I
u = 0.866890 − 0.696274I
a = 1.54948 + 0.22013I
b = −1.165260 + 0.286760I
5.64493 + 2.67607I 7.61139 − 3.32415I
u = 0.866890 − 0.696274I
a = −1.67678 + 2.03785I
b = 1.105310 + 0.336093I
5.64493 + 2.67607I 7.61139 − 3.32415I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960503 + 0.654282I
a = −0.422425 − 0.451767I
b = −0.055277 − 0.354087I
2.20856 + 5.29622I −0.10789 − 6.28296I
u = −0.960503 + 0.654282I
a = −0.64027 + 1.59232I
b = 1.072600 + 0.162995I
2.20856 + 5.29622I −0.10789 − 6.28296I
u = −0.960503 − 0.654282I
a = −0.422425 + 0.451767I
b = −0.055277 + 0.354087I
2.20856 − 5.29622I −0.10789 + 6.28296I
u = −0.960503 − 0.654282I
a = −0.64027 − 1.59232I
b = 1.072600 − 0.162995I
2.20856 − 5.29622I −0.10789 + 6.28296I
u = 0.977539 + 0.749941I
a = 0.252677 − 0.865283I
b = 0.767790 + 0.810448I
8.92422 − 4.73566I 6.88636 + 2.91588I
u = 0.977539 + 0.749941I
a = 2.43403 + 1.75259I
b = −1.49199 + 0.01594I
8.92422 − 4.73566I 6.88636 + 2.91588I
u = 0.977539 − 0.749941I
a = 0.252677 + 0.865283I
b = 0.767790 − 0.810448I
8.92422 + 4.73566I 6.88636 − 2.91588I
u = 0.977539 − 0.749941I
a = 2.43403 − 1.75259I
b = −1.49199 − 0.01594I
8.92422 + 4.73566I 6.88636 − 2.91588I
u = −0.059947 + 0.622852I
a = 0.761202 + 0.086440I
b = −0.568590 − 0.799912I
5.64493 + 2.67607I 7.61139 − 3.32415I
u = −0.059947 + 0.622852I
a = −2.80109 + 0.48436I
b = 1.43548 + 0.10364I
5.64493 + 2.67607I 7.61139 − 3.32415I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059947 − 0.622852I
a = 0.761202 − 0.086440I
b = −0.568590 + 0.799912I
5.64493 − 2.67607I 7.61139 + 3.32415I
u = −0.059947 − 0.622852I
a = −2.80109 − 0.48436I
b = 1.43548 − 0.10364I
5.64493 − 2.67607I 7.61139 + 3.32415I
23
V. I
u
5
= hb + 1, a + u − 1, u
4
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
3
−u
3
a
1
=
u
3
−u
3
a
11
=
−u + 1
−1
a
6
=
u
1
a
10
=
1
0
a
5
=
u − 1
1
a
12
=
u
3
− u + 1
−u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
2
+ 1)
2
c
2
, c
3
, c
7
c
9
u
4
+ 1
c
4
, c
10
(u − 1)
4
c
5
, c
6
, c
11
c
12
(u + 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y + 1)
4
c
2
, c
3
, c
7
c
9
(y
2
+ 1)
2
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y −1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 0.292893 − 0.707107I
b = −1.00000
4.93480 8.00000
u = 0.707107 − 0.707107I
a = 0.292893 + 0.707107I
b = −1.00000
4.93480 8.00000
u = −0.707107 + 0.707107I
a = 1.70711 − 0.70711I
b = −1.00000
4.93480 8.00000
u = −0.707107 − 0.707107I
a = 1.70711 + 0.70711I
b = −1.00000
4.93480 8.00000
27
VI. I
u
6
= hb, a + 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
7
=
1
0
a
8
=
1
1
a
3
=
−1
0
a
9
=
0
1
a
4
=
−1
−1
a
1
=
1
1
a
11
=
−1
0
a
6
=
1
0
a
10
=
−1
0
a
5
=
1
0
a
12
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
11
, c
12
u + 1
c
5
, c
6
, c
10
u
c
9
u − 1
29
(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
11
, c
12
y −1
c
5
, c
6
, c
10
y
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−1.64493 −6.00000
31
VII. I
u
7
= hb − 1, a − 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
7
=
1
0
a
8
=
1
1
a
3
=
−1
0
a
9
=
0
1
a
4
=
−1
−1
a
1
=
1
1
a
11
=
1
1
a
6
=
2
1
a
10
=
−1
0
a
5
=
1
1
a
12
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
10
u + 1
c
4
, c
11
, c
12
u
c
9
u − 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
9
, c
10
y −1
c
4
, c
11
, c
12
y
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
−1.64493 −6.00000
35
VIII. I
u
8
= hb − 1, a, u − 1i
(i) Arc colorings
a
2
=
0
1
a
7
=
1
0
a
8
=
1
1
a
3
=
−1
0
a
9
=
0
1
a
4
=
−1
−1
a
1
=
1
1
a
11
=
0
1
a
6
=
1
1
a
10
=
−1
0
a
5
=
0
1
a
12
=
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u − 1
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
0 0
39
IX. I
u
9
= hb − 1, a − 2, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
7
=
1
0
a
8
=
1
1
a
3
=
1
0
a
9
=
0
1
a
4
=
1
1
a
1
=
−1
−1
a
11
=
2
1
a
6
=
3
1
a
10
=
−1
0
a
5
=
2
1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
9
c
11
, c
12
u − 1
c
4
, c
7
, c
8
c
10
u + 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000
b = 1.00000
0 0
43
X. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
3
=
−1
0
a
9
=
1
0
a
4
=
−1
0
a
1
=
−1
0
a
11
=
0
−1
a
6
=
1
1
a
10
=
1
0
a
5
=
0
1
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
c
4
, c
10
u − 1
c
5
, c
6
, c
11
c
12
u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y −1
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
3.28987 12.0000
47
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u + 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
· ((u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
)(u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
· (u
34
+ 11u
33
+ ··· − 16u + 4)
c
2
, c
7
u(u − 1)(u + 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)(u
5
− u
4
+ 2u − 1)
2
· ((u
16
− u
15
+ ··· − 2u + 1)
2
)(u
34
+ 3u
33
+ ··· − 8u − 2)
c
3
u(u − 1)(u + 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)(u
5
+ 4u
4
+ ··· + 4u − 4)
2
· ((u
8
− 2u
7
+ 3u
6
+ u
4
+ 2u
2
− 2u + 1)
4
)(u
34
− 3u
33
+ ··· + 848u − 296)
c
4
, c
10
u(u − 1)
5
(u + 1)
7
· (u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 3u
5
− 3u
4
− u
3
+ 9u
2
− 2u − 5)
· (u
32
− u
31
+ ··· + 6u + 3)(u
34
− u
33
+ ··· + u + 1)
c
5
, c
6
, c
11
c
12
u(u − 1)
6
(u + 1)
6
· (u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 3u
5
− 3u
4
− u
3
+ 9u
2
− 2u − 5)
· (u
32
− u
31
+ ··· + 6u + 3)(u
34
− u
33
+ ··· + u + 1)
c
8
u(u + 1)
4
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
· ((u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
)(u
34
+ 11u
33
+ ··· − 16u + 4)
c
9
u(u − 1)
3
(u + 1)(u
4
+ 1)(u
4
− u
2
+ 2)(u
5
− u
4
+ ··· + 4u − 1)
2
· ((u
16
− 5u
15
+ ··· − 4u
2
+ 1)
2
)(u
34
+ 21u
33
+ ··· − 40228u − 4366)
48
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y(y −1)
4
(y + 1)
4
(y
2
+ 3y + 4)
2
· ((y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y −1)
2
)(y
16
+ 11y
15
+ ··· − 8y + 1)
2
· (y
34
+ 25y
33
+ ··· − 288y + 16)
c
2
, c
7
y(y −1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
5
− y
4
+ 4y
3
− 2y
2
+ 4y −1)
2
· ((y
16
− 5y
15
+ ··· − 4y
2
+ 1)
2
)(y
34
− 11y
33
+ ··· + 16y + 4)
c
3
y(y −1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
5
+ 2y
4
+ 17y
3
+ 23y
2
+ 88y −16)
2
· (y
8
+ 2y
7
+ 11y
6
+ 10y
5
+ 7y
4
+ 10y
3
+ 6y
2
+ 1)
4
· (y
34
+ y
33
+ ··· + 674464y + 87616)
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y(y −1)
12
(y
10
− 9y
9
+ ··· − 94y + 25)(y
32
− 27y
31
+ ··· + 102y + 9)
· (y
34
− 43y
33
+ ··· − 9y + 1)
c
9
y(y −1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· ((y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y −1)
2
)(y
16
+ 11y
15
+ ··· − 8y + 1)
2
· (y
34
+ 13y
33
+ ··· + 56365904y + 19061956)
49
