12n
0279
(K12n
0279
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 10 2 5 6 12 8 7 9
Solving Sequence
5,11 4,8
7 12 3 10 6 2 1 9
c
4
c
7
c
11
c
3
c
10
c
5
c
2
c
1
c
9
c
6
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h27831408u
16
+ 38249416u
15
+ ··· + 40002991b + 40510496,
− 24958754u
16
− 42710149u
15
+ ··· + 40002991a − 62762092, u
17
+ u
16
+ ··· + u − 1i
I
u
2
= hb + u + 1, u
2
+ a − 1, u
3
+ u
2
+ 1i
I
u
3
= h−u
3
+ b − u, a + u + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
4
= h−u
3
+ b − 2u − 1, a, u
4
− u
3
+ 3u
2
− u + 1i
I
u
5
= h−au + 3b + a + 3u, a
2
+ au − a − 3, u
2
+ u + 1i
I
u
6
= h−2.19461 × 10
15
u
13
− 2.90056 × 10
15
u
12
+ ··· + 6.79307 × 10
17
b − 2.81232 × 10
17
,
− 3.53923 × 10
17
u
13
− 5.35522 × 10
17
u
12
+ ··· + 7.20066 × 10
19
a − 1.96602 × 10
20
,
u
14
+ u
13
+ ··· − 98u + 53i
I
u
7
= hb − 1, a, u
2
+ u + 1i
I
u
8
= hb − u, a, u
2
+ u + 1i
* 8 irreducible components of dim
C
= 0, with total 50 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
= h2.78 × 10
7
u
16
+ 3.82 × 10
7
u
15
+ · · · + 4.00 × 10
7
b + 4.05 × 10
7
, −2.50 ×
10
7
u
16
− 4.27 × 10
7
u
15
+ · · · + 4.00 × 10
7
a − 6.28 × 10
7
, u
17
+ u
16
+ · · · + u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
0.623922u
16
+ 1.06767u
15
+ ··· − 4.19761u + 1.56893
−0.695733u
16
− 0.956164u
15
+ ··· + 4.01744u − 1.01269
a
7
=
−0.0718110u
16
+ 0.111510u
15
+ ··· − 0.180171u + 0.556248
−0.695733u
16
− 0.956164u
15
+ ··· + 4.01744u − 1.01269
a
12
=
0.463872u
16
+ 0.672655u
15
+ ··· + 0.262187u − 0.138788
−0.152299u
16
− 0.109999u
15
+ ··· + 0.667583u − 0.892029
a
3
=
0.683246u
16
+ 1.06132u
15
+ ··· − 4.69765u + 1.76057
−0.917110u
16
− 0.866468u
15
+ ··· + 2.11890u − 0.443964
a
10
=
0.664842u
16
+ 0.607334u
15
+ ··· + 0.648473u + 2.52008
−0.0486712u
16
+ 0.175319u
15
+ ··· + 0.946131u − 1.76684
a
6
=
−1.82038u
16
− 2.59604u
15
+ ··· + 4.42105u + 1.28803
0.390419u
16
+ 0.580544u
15
+ ··· + 0.744719u + 0.433797
a
2
=
0.842480u
16
+ 0.955949u
15
+ ··· + 0.0116457u + 2.65839
−0.369554u
16
+ 0.163720u
15
+ ··· − 0.697278u − 1.38144
a
1
=
−0.295603u
16
− 0.654268u
15
+ ··· + 1.33796u + 0.594847
0.323305u
16
+ 0.418596u
15
+ ··· − 2.19115u + 0.801058
a
9
=
0.456059u
16
+ 0.624327u
15
+ ··· + 1.25113u + 2.05621
−0.0909712u
16
+ 0.0800344u
15
+ ··· + 1.68586u − 1.61454
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
217036647
40002991
u
16
−
332499894
40002991
u
15
+ ··· +
1336970457
40002991
u +
36116891
40002991
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 8u
16
+ ··· − 2u − 1
c
2
, c
5
, c
6
u
17
+ 4u
15
+ ··· + 2u + 1
c
3
u
17
+ 3u
16
+ ··· + 96u + 29
c
4
, c
9
, c
12
u
17
− u
16
+ ··· + u + 1
c
7
u
17
− 2u
16
+ ··· + 4u − 1
c
8
u
17
+ 4u
16
+ ··· + 358u − 23
c
10
u
17
− 2u
16
+ ··· − 8u + 4
c
11
u
17
− u
16
+ ··· + 192u + 79
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 36y
16
+ ··· + 70y −1
c
2
, c
5
, c
6
y
17
+ 8y
16
+ ··· − 2y −1
c
3
y
17
+ 31y
16
+ ··· − 13636y −841
c
4
, c
9
, c
12
y
17
+ 21y
16
+ ··· − 21y −1
c
7
y
17
+ 18y
15
+ ··· − 10y −1
c
8
y
17
− 36y
16
+ ··· + 196750y −529
c
10
y
17
+ 8y
16
+ ··· + 96y −16
c
11
y
17
− 33y
16
+ ··· − 62044y −6241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.057958 + 1.037160I
a = −1.281730 − 0.156187I
b = −0.146308 − 0.285619I
0.90500 − 3.77030I 1.82474 + 3.48475I
u = −0.057958 − 1.037160I
a = −1.281730 + 0.156187I
b = −0.146308 + 0.285619I
0.90500 + 3.77030I 1.82474 − 3.48475I
u = 0.245125 + 1.028970I
a = −1.09741 + 0.90076I
b = 0.457121 + 1.056880I
4.13880 − 5.40035I 4.91651 + 8.34008I
u = 0.245125 − 1.028970I
a = −1.09741 − 0.90076I
b = 0.457121 − 1.056880I
4.13880 + 5.40035I 4.91651 − 8.34008I
u = −0.397934 + 0.813970I
a = −0.976997 − 0.362526I
b = 1.21505 − 1.10098I
−0.17756 + 4.89986I −2.88050 − 11.83276I
u = −0.397934 − 0.813970I
a = −0.976997 + 0.362526I
b = 1.21505 + 1.10098I
−0.17756 − 4.89986I −2.88050 + 11.83276I
u = 0.355960 + 0.790874I
a = −0.144449 + 0.440961I
b = 0.821906 + 0.423349I
−0.33729 − 2.00763I −4.27790 + 4.10487I
u = 0.355960 − 0.790874I
a = −0.144449 − 0.440961I
b = 0.821906 − 0.423349I
−0.33729 + 2.00763I −4.27790 − 4.10487I
u = 1.21780
a = 1.23271
b = −0.577819
−2.39027 −14.2090
u = 0.299458 + 0.466008I
a = 2.32811 + 0.28399I
b = −1.079530 − 0.618458I
−3.08489 − 6.04547I −8.76917 + 6.36123I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.299458 − 0.466008I
a = 2.32811 − 0.28399I
b = −1.079530 + 0.618458I
−3.08489 + 6.04547I −8.76917 − 6.36123I
u = −0.108066 + 0.363788I
a = 0.949976 − 0.957388I
b = 0.119264 + 0.837933I
0.52238 − 1.49726I 2.87825 + 5.01467I
u = −0.108066 − 0.363788I
a = 0.949976 + 0.957388I
b = 0.119264 − 0.837933I
0.52238 + 1.49726I 2.87825 − 5.01467I
u = −0.71553 + 2.03646I
a = 0.617685 + 0.005897I
b = −1.02465 − 1.09864I
17.8274 + 5.4627I −0.12519 − 2.24848I
u = −0.71553 − 2.03646I
a = 0.617685 − 0.005897I
b = −1.02465 + 1.09864I
17.8274 − 5.4627I −0.12519 + 2.24848I
u = −0.72995 + 2.19477I
a = 0.988459 + 0.323341I
b = −1.07394 + 1.02493I
17.5899 + 13.2299I −0.46218 − 5.67701I
u = −0.72995 − 2.19477I
a = 0.988459 − 0.323341I
b = −1.07394 − 1.02493I
17.5899 − 13.2299I −0.46218 + 5.67701I
6
II. I
u
2
= hb + u + 1, u
2
+ a − 1, u
3
+ u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−u
2
+ 1
−u − 1
a
7
=
−u
2
− u
−u − 1
a
12
=
−u
2
− u
−1
a
3
=
−u
2
− u + 1
−u
2
− u − 1
a
10
=
2u + 1
−u
2
− u
a
6
=
u
2
+ u − 1
u + 1
a
2
=
u + 2
−2u
2
− 2u
a
1
=
u
2
+ u
−u
2
a
9
=
2u + 2
−u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
2
+ 7u + 3
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
3
− 2u
2
+ u + 1
c
2
, c
5
u
3
+ u + 1
c
3
, c
11
(u + 1)
3
c
4
, c
12
u
3
+ u
2
+ 1
c
6
, c
8
u
3
+ u − 1
c
9
u
3
− u
2
− 1
c
10
u
3
+ 3u
2
+ 4u + 3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
3
− 2y
2
+ 5y −1
c
2
, c
5
, c
6
c
8
y
3
+ 2y
2
+ y −1
c
3
, c
11
(y −1)
3
c
4
, c
9
, c
12
y
3
− y
2
− 2y −1
c
10
y
3
− y
2
− 2y −9
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232786 + 0.792552I
a = 1.57395 − 0.36899I
b = −1.23279 − 0.79255I
−2.26573 − 6.33267I 0.03790 + 8.49978I
u = 0.232786 − 0.792552I
a = 1.57395 + 0.36899I
b = −1.23279 + 0.79255I
−2.26573 + 6.33267I 0.03790 − 8.49978I
u = −1.46557
a = −1.14790
b = 0.465571
−2.04827 9.92420
10
III. I
u
3
= h−u
3
+ b − u, a + u + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−u − 1
u
3
+ u
a
7
=
u
3
− 1
u
3
+ u
a
12
=
3u
2
− 4u + 3
−u + 1
a
3
=
−2u
3
+ 3u
2
− u + 1
−u
3
+ u
2
− 2u + 1
a
10
=
u
3
+ 2u
2
+ u
−u
3
+ u
2
− 2u + 2
a
6
=
−u
2
− 2u
2u
3
− u
2
+ 3u − 2
a
2
=
−2u
3
+ 2u
2
− 2u + 3
−u
3
− 2u
a
1
=
−3u
3
+ 7u
2
− 8u + 5
−2u
a
9
=
−u
3
+ 5u
2
− 4u + 2
−u
3
+ u
2
− 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
+ 5u − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 2u
2
− 3u + 1
c
2
, c
5
u
4
− 2u
3
+ 2u
2
− u + 1
c
3
u
4
− u
3
+ 9u
2
− u + 1
c
4
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
c
6
u
4
+ 2u
3
+ 2u
2
+ u + 1
c
7
(u
2
+ u + 1)
2
c
8
u
4
− 3u
3
+ 8u
2
− 12u + 7
c
9
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
10
u
4
+ 2u
3
− u + 7
c
11
u
4
+ 4u
3
− u
2
− 10u + 7
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
+ 4y
3
+ 6y
2
− 5y + 1
c
2
, c
5
, c
6
y
4
+ 2y
2
+ 3y + 1
c
3
y
4
+ 17y
3
+ 81y
2
+ 17y + 1
c
4
, c
9
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
7
(y
2
+ y + 1)
2
c
8
y
4
+ 7y
3
+ 6y
2
− 32y + 49
c
10
y
4
− 4y
3
+ 18y
2
− y + 49
c
11
y
4
− 18y
3
+ 95y
2
− 114y + 49
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −1.62174 − 0.44060I
b = 0.500000 + 0.866025I
3.28987 − 4.05977I 1.50000 + 4.33013I
u = 0.621744 − 0.440597I
a = −1.62174 + 0.44060I
b = 0.500000 − 0.866025I
3.28987 + 4.05977I 1.50000 − 4.33013I
u = −0.121744 + 1.306620I
a = −0.87826 − 1.30662I
b = 0.500000 − 0.866025I
3.28987 + 4.05977I 1.50000 − 4.33013I
u = −0.121744 − 1.306620I
a = −0.87826 + 1.30662I
b = 0.500000 + 0.866025I
3.28987 − 4.05977I 1.50000 + 4.33013I
14
IV. I
u
4
= h−u
3
+ b − 2u − 1, a, u
4
− u
3
+ 3u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
0
u
3
+ 2u + 1
a
7
=
u
3
+ 2u + 1
u
3
+ 2u + 1
a
12
=
−u
2
+ u − 2
−u
2
+ 2u − 2
a
3
=
−u
3
+ u
2
− 3u + 2
−u
3
− 3u + 1
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
−u + 1
−2u + 1
a
1
=
−u
3
− 2u − 1
−u
3
− 2u − 1
a
9
=
u
3
+ 2u + 1
u
3
+ u
2
+ 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
− u
2
+ 5u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
11
(u
2
− u + 1)
2
c
2
, c
12
(u
2
+ u + 1)
2
c
4
, c
5
u
4
− u
3
+ 3u
2
− u + 1
c
7
, c
8
u
4
+ u
3
− 2u + 1
c
10
u
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
9
, c
11
c
12
(y
2
+ y + 1)
2
c
4
, c
5
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
7
, c
8
y
4
− y
3
+ 6y
2
− 4y + 1
c
10
y
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148403 + 0.632502I
a = 0
b = 1.12196 + 1.05376I
− 4.05977I 0.24584 + 1.91854I
u = 0.148403 − 0.632502I
a = 0
b = 1.12196 − 1.05376I
4.05977I 0.24584 − 1.91854I
u = 0.35160 + 1.49853I
a = 0
b = −0.621964 + 0.187730I
4.05977I −7.74584 − 7.60774I
u = 0.35160 − 1.49853I
a = 0
b = −0.621964 − 0.187730I
− 4.05977I −7.74584 + 7.60774I
18
V. I
u
5
= h−au + 3b + a + 3u, a
2
+ au − a − 3, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u + 1
a
8
=
a
1
3
au −
1
3
a − u
a
7
=
1
3
au +
2
3
a − u
1
3
au −
1
3
a − u
a
12
=
5
3
au +
1
3
a
−
1
3
au −
2
3
a + 1
a
3
=
2
3
au +
4
3
a + u + 3
−
1
3
au −
2
3
a + u + 1
a
10
=
2au + a + 3u
−u − 1
a
6
=
au − a − 2
−u
a
2
=
−
5
3
au −
4
3
a − 2u
u + 1
a
1
=
−
4
3
au −
14
3
a − 3u − 5
−
1
3
au +
1
3
a + 1
a
9
=
7
3
au −
1
3
a + 2u − 3
−2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2au − 3a − 5u − 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 5u
3
+ 9u
2
− 5u + 1
c
2
, c
12
u
4
− u
3
+ 3u
2
− u + 1
c
3
u
4
+ 4u
3
+ 6u
2
+ u + 1
c
4
, c
5
(u
2
+ u + 1)
2
c
6
, c
9
u
4
+ u
3
+ 3u
2
+ u + 1
c
7
u
4
+ u
3
− 2u + 1
c
8
u
4
+ 4u
3
+ 6u
2
+ 7u + 7
c
10
u
4
+ 6u
2
+ 9u + 9
c
11
u
4
+ u
3
+ 3u
2
+ 7u + 7
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 7y
3
+ 33y
2
− 7y + 1
c
2
, c
6
, c
9
c
12
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
3
y
4
− 4y
3
+ 30y
2
+ 11y + 1
c
4
, c
5
(y
2
+ y + 1)
2
c
7
y
4
− y
3
+ 6y
2
− 4y + 1
c
8
y
4
− 4y
3
− 6y
2
+ 35y + 49
c
10
y
4
+ 12y
3
+ 54y
2
+ 27y + 81
c
11
y
4
+ 5y
3
+ 9y
2
− 7y + 49
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.095530 − 0.257041I
b = 1.12196 − 1.05376I
4.05977I 0.24584 − 1.91854I
u = −0.500000 + 0.866025I
a = 2.59553 − 0.60898I
b = −0.621964 + 0.187730I
4.05977I −7.74584 − 7.60774I
u = −0.500000 − 0.866025I
a = −1.095530 + 0.257041I
b = 1.12196 + 1.05376I
− 4.05977I 0.24584 + 1.91854I
u = −0.500000 − 0.866025I
a = 2.59553 + 0.60898I
b = −0.621964 − 0.187730I
− 4.05977I −7.74584 + 7.60774I
22
VI. I
u
6
= h−2.19 × 10
15
u
13
− 2.90 × 10
15
u
12
+ · · · + 6.79 × 10
17
b − 2.81 ×
10
17
, −3.54 × 10
17
u
13
− 5.36 × 10
17
u
12
+ · · · + 7.20 × 10
19
a − 1.97 ×
10
20
, u
14
+ u
13
+ · · · − 98u + 53i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
0.00491515u
13
+ 0.00743713u
12
+ ··· − 1.48607u + 2.73033
0.00323066u
13
+ 0.00426988u
12
+ ··· + 2.16045u + 0.413997
a
7
=
0.00814581u
13
+ 0.0117070u
12
+ ··· + 0.674379u + 3.14433
0.00323066u
13
+ 0.00426988u
12
+ ··· + 2.16045u + 0.413997
a
12
=
0.0123724u
13
+ 0.00795343u
12
+ ··· + 13.9704u − 1.71865
0.00300637u
13
+ 0.00251071u
12
+ ··· + 3.63641u − 0.788348
a
3
=
−0.0104555u
13
− 0.0107429u
12
+ ··· − 7.46839u + 0.477030
−0.00265698u
13
− 0.00317978u
12
+ ··· − 2.34330u + 0.220186
a
10
=
0.00740443u
13
+ 0.00396765u
12
+ ··· + 8.94568u − 0.309042
0.00196165u
13
+ 0.00147507u
12
+ ··· + 3.38830u − 0.621258
a
6
=
0.00576580u
13
+ 0.00758083u
12
+ ··· + 0.830146u + 2.59522
0.00344632u
13
+ 0.00301915u
12
+ ··· + 2.30371u + 0.222657
a
2
=
−0.00273723u
13
− 0.000789063u
12
+ ··· − 3.15318u + 1.21964
−0.00164957u
13
− 0.00328941u
12
+ ··· − 0.583214u + 0.127768
a
1
=
−0.00210562u
13
− 0.00837365u
12
+ ··· − 4.25378u + 1.54174
0.00386701u
13
+ 0.00234040u
12
+ ··· − 0.635377u + 0.240016
a
9
=
0.00720203u
13
+ 0.00980153u
12
+ ··· + 2.73758u + 2.32633
0.00313757u
13
+ 0.000888876u
12
+ ··· + 3.09172u + 0.122919
(ii) Obstruction class = −1
(iii) Cusp Shapes =
40856511771921327
1358614961701335812
u
13
+
59994346491964077
1358614961701335812
u
12
+ ··· +
13415037849513161527
679307480850667906
u −
6319351487276365787
1358614961701335812
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 8u
13
+ ··· − 25u + 1
c
2
, c
5
, c
6
u
14
− 4u
12
+ ··· + 9u + 1
c
3
u
14
+ 42u
12
+ ··· + 78137u + 7937
c
4
, c
9
, c
12
u
14
− u
13
+ ··· + 98u + 53
c
7
(u
7
+ u
6
− u
4
+ 2u
3
+ 2u
2
− 1)
2
c
8
u
14
− 16u
12
+ ··· − 13u − 1
c
10
u
14
− 2u
13
+ ··· − 160u + 64
c
11
u
14
− 19u
12
+ ··· − 10u + 173
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 32y
13
+ ··· − 313y + 1
c
2
, c
5
, c
6
y
14
− 8y
13
+ ··· − 25y + 1
c
3
y
14
+ 84y
13
+ ··· − 978977713y + 62995969
c
4
, c
9
, c
12
y
14
+ 31y
13
+ ··· + 83040y + 2809
c
7
(y
7
− y
6
+ 6y
5
− 5y
4
+ 10y
3
− 6y
2
+ 4y −1)
2
c
8
y
14
− 32y
13
+ ··· − 235y + 1
c
10
y
14
+ 24y
13
+ ··· + 21504y + 4096
c
11
y
14
− 38y
13
+ ··· + 34846y + 29929
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502626 + 0.663141I
a = −0.514604 + 0.044435I
b = 0.676751 + 0.491075I
−0.37711 − 1.83261I −2.26809 + 4.51372I
u = 0.502626 − 0.663141I
a = −0.514604 − 0.044435I
b = 0.676751 − 0.491075I
−0.37711 + 1.83261I −2.26809 − 4.51372I
u = 1.19118
a = 1.38337
b = −0.577619
−2.39017 −14.4470
u = 1.26649
a = 1.09551
b = −0.577619
−2.39017 −14.4470
u = −0.008952 + 0.262276I
a = 2.85503 − 0.49795I
b = 0.676751 + 0.491075I
−0.37711 − 1.83261I −2.26809 + 4.51372I
u = −0.008952 − 0.262276I
a = 2.85503 + 0.49795I
b = 0.676751 − 0.491075I
−0.37711 + 1.83261I −2.26809 − 4.51372I
u = −0.74076 + 1.86468I
a = 1.085270 − 0.357270I
b = −0.850452 − 0.793787I
6.35486 − 2.92126I 1.82532 + 2.85511I
u = −0.74076 − 1.86468I
a = 1.085270 + 0.357270I
b = −0.850452 + 0.793787I
6.35486 + 2.92126I 1.82532 − 2.85511I
u = −1.28802 + 1.77121I
a = 0.796866 + 0.008028I
b = −0.850452 + 0.793787I
6.35486 + 2.92126I 1.82532 − 2.85511I
u = −1.28802 − 1.77121I
a = 0.796866 − 0.008028I
b = −0.850452 − 0.793787I
6.35486 − 2.92126I 1.82532 + 2.85511I
26
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16280 + 2.37083I
a = −1.063400 + 0.533787I
b = 0.962510 + 0.950397I
18.2464 − 3.4867I 0.16603 + 2.41435I
u = −0.16280 − 2.37083I
a = −1.063400 − 0.533787I
b = 0.962510 − 0.950397I
18.2464 + 3.4867I 0.16603 − 2.41435I
u = −0.03091 + 2.59918I
a = −0.549536 + 0.031095I
b = 0.962510 − 0.950397I
18.2464 + 3.4867I 0.16603 − 2.41435I
u = −0.03091 − 2.59918I
a = −0.549536 − 0.031095I
b = 0.962510 + 0.950397I
18.2464 − 3.4867I 0.16603 + 2.41435I
27
VII. I
u
7
= hb − 1, a, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u + 1
a
8
=
0
1
a
7
=
1
1
a
12
=
u
2u
a
3
=
u + 1
2u + 1
a
10
=
0
u
a
6
=
1
u + 1
a
2
=
0
u + 1
a
1
=
−1
−1
a
9
=
1
u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
11
u
2
− u + 1
c
2
, c
4
, c
5
c
12
u
2
+ u + 1
c
7
, c
8
(u + 1)
2
c
10
u
2
29
(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
9
, c
11
, c
12
y
2
+ y + 1
c
7
, c
8
(y −1)
2
c
10
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 1.00000
0 −3.00000
u = −0.500000 − 0.866025I
a = 0
b = 1.00000
0 −3.00000
31
VIII. I
u
8
= hb − u, a, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u + 1
a
8
=
0
u
a
7
=
u
u
a
12
=
1
u + 1
a
3
=
2
u + 2
a
10
=
0
u
a
6
=
1
u + 1
a
2
=
u + 2
u + 1
a
1
=
−u
−u
a
9
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
, c
9
c
11
u
2
− u + 1
c
2
, c
4
, c
5
c
12
u
2
+ u + 1
c
10
u
2
33
(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
11
, c
12
y
2
+ y + 1
c
10
y
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
0 0
u = −0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
0 0
35
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
(u
3
− 2u
2
+ u + 1)(u
4
+ 2u
2
− 3u + 1)
· (u
4
− 5u
3
+ 9u
2
− 5u + 1)(u
14
− 8u
13
+ ··· − 25u + 1)
· (u
17
+ 8u
16
+ ··· − 2u − 1)
c
2
, c
5
((u
2
+ u + 1)
4
)(u
3
+ u + 1)(u
4
− 2u
3
+ ··· − u + 1)(u
4
− u
3
+ ··· − u + 1)
· (u
14
− 4u
12
+ ··· + 9u + 1)(u
17
+ 4u
15
+ ··· + 2u + 1)
c
3
((u + 1)
3
)(u
2
− u + 1)
4
(u
4
− u
3
+ ··· − u + 1)(u
4
+ 4u
3
+ ··· + u + 1)
· (u
14
+ 42u
12
+ ··· + 78137u + 7937)(u
17
+ 3u
16
+ ··· + 96u + 29)
c
4
, c
12
((u
2
+ u + 1)
4
)(u
3
+ u
2
+ 1)(u
4
− u
3
+ ··· − 2u + 1)(u
4
− u
3
+ ··· − u + 1)
· (u
14
− u
13
+ ··· + 98u + 53)(u
17
− u
16
+ ··· + u + 1)
c
6
((u
2
− u + 1)
4
)(u
3
+ u − 1)(u
4
+ u
3
+ ··· + u + 1)(u
4
+ 2u
3
+ ··· + u + 1)
· (u
14
− 4u
12
+ ··· + 9u + 1)(u
17
+ 4u
15
+ ··· + 2u + 1)
c
7
((u + 1)
2
)(u
2
− u + 1)(u
2
+ u + 1)
2
(u
3
− 2u
2
+ u + 1)(u
4
+ u
3
− 2u + 1)
2
· ((u
7
+ u
6
− u
4
+ 2u
3
+ 2u
2
− 1)
2
)(u
17
− 2u
16
+ ··· + 4u − 1)
c
8
(u + 1)
2
(u
2
− u + 1)(u
3
+ u − 1)(u
4
− 3u
3
+ 8u
2
− 12u + 7)
· (u
4
+ u
3
− 2u + 1)(u
4
+ 4u
3
+ ··· + 7u + 7)(u
14
− 16u
12
+ ··· − 13u − 1)
· (u
17
+ 4u
16
+ ··· + 358u − 23)
c
9
((u
2
− u + 1)
4
)(u
3
− u
2
− 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
4
+ u
3
+ ··· + u + 1)
· (u
14
− u
13
+ ··· + 98u + 53)(u
17
− u
16
+ ··· + u + 1)
c
10
u
8
(u
3
+ 3u
2
+ 4u + 3)(u
4
+ 6u
2
+ 9u + 9)(u
4
+ 2u
3
− u + 7)
· (u
14
− 2u
13
+ ··· − 160u + 64)(u
17
− 2u
16
+ ··· − 8u + 4)
c
11
((u + 1)
3
)(u
2
− u + 1)
4
(u
4
+ u
3
+ ··· + 7u + 7)(u
4
+ 4u
3
+ ··· − 10u + 7)
· (u
14
− 19u
12
+ ··· − 10u + 173)(u
17
− u
16
+ ··· + 192u + 79)
36
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
(y
3
− 2y
2
+ 5y −1)(y
4
− 7y
3
+ 33y
2
− 7y + 1)
· (y
4
+ 4y
3
+ 6y
2
− 5y + 1)(y
14
+ 32y
13
+ ··· − 313y + 1)
· (y
17
+ 36y
16
+ ··· + 70y −1)
c
2
, c
5
, c
6
(y
2
+ y + 1)
4
(y
3
+ 2y
2
+ y −1)(y
4
+ 2y
2
+ 3y + 1)
· (y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
14
− 8y
13
+ ··· − 25y + 1)
· (y
17
+ 8y
16
+ ··· − 2y −1)
c
3
(y −1)
3
(y
2
+ y + 1)
4
(y
4
− 4y
3
+ 30y
2
+ 11y + 1)
· (y
4
+ 17y
3
+ 81y
2
+ 17y + 1)
· (y
14
+ 84y
13
+ ··· − 978977713y + 62995969)
· (y
17
+ 31y
16
+ ··· − 13636y −841)
c
4
, c
9
, c
12
(y
2
+ y + 1)
4
(y
3
− y
2
− 2y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
14
+ 31y
13
+ ··· + 83040y + 2809)
· (y
17
+ 21y
16
+ ··· − 21y −1)
c
7
(y −1)
2
(y
2
+ y + 1)
3
(y
3
− 2y
2
+ 5y −1)(y
4
− y
3
+ 6y
2
− 4y + 1)
2
· (y
7
− y
6
+ 6y
5
− 5y
4
+ 10y
3
− 6y
2
+ 4y −1)
2
· (y
17
+ 18y
15
+ ··· − 10y −1)
c
8
((y −1)
2
)(y
2
+ y + 1)(y
3
+ 2y
2
+ y −1)(y
4
− 4y
3
+ ··· + 35y + 49)
· (y
4
− y
3
+ 6y
2
− 4y + 1)(y
4
+ 7y
3
+ 6y
2
− 32y + 49)
· (y
14
− 32y
13
+ ··· − 235y + 1)(y
17
− 36y
16
+ ··· + 196750y −529)
c
10
y
8
(y
3
− y
2
− 2y −9)(y
4
− 4y
3
+ 18y
2
− y + 49)
· (y
4
+ 12y
3
+ 54y
2
+ 27y + 81)(y
14
+ 24y
13
+ ··· + 21504y + 4096)
· (y
17
+ 8y
16
+ ··· + 96y −16)
c
11
(y −1)
3
(y
2
+ y + 1)
4
(y
4
− 18y
3
+ 95y
2
− 114y + 49)
· (y
4
+ 5y
3
+ 9y
2
− 7y + 49)(y
14
− 38y
13
+ ··· + 34846y + 29929)
· (y
17
− 33y
16
+ ··· − 62044y −6241)
37
