12n
0846
(K12n
0846
)
A knot diagram
1
Linearized knot diagam
4 10 11 10 1 12 3 4 1 8 7 6
Solving Sequence
7,11 4,12
3 8 6 1 5 10 2 9
c
11
c
3
c
7
c
6
c
12
c
5
c
10
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
21
+ 43u
20
+ ··· + 8b + 200, −15u
21
+ 129u
20
+ ··· + 16a + 272, u
22
− 9u
21
+ ··· − 176u + 16i
I
u
2
= hu
3
a − u
3
+ 3au − 2u
2
+ 2b + a − 3u − 5, 3u
3
a + 2u
2
a + u
3
+ a
2
+ 8au − 2u
2
+ 3a + 2u − 2,
u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
3
= hu
10
+ 7u
8
+ 17u
6
− u
5
+ 17u
4
− 2u
3
+ 7u
2
+ b + u + 1,
− u
13
− 10u
11
− 2u
10
− 37u
9
− 13u
8
− 61u
7
− 29u
6
− 39u
5
− 30u
4
− u
3
− 19u
2
+ 2a + 2u − 1,
u
14
+ 10u
12
+ 39u
10
− u
9
+ 75u
8
− 5u
7
+ 75u
6
− 6u
5
+ 39u
4
+ u
3
+ 10u
2
+ u + 2i
I
u
4
= h64742a
5
u
3
+ 484970a
4
u
3
+ ··· − 385898a − 56434, 3a
5
u
3
− 2a
4
u
3
+ ··· + 8a − 9,
u
4
+ u
3
+ 3u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 68 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−5u
21
+ 43u
20
+ · · · + 8b + 200, −15u
21
+ 129u
20
+ · · · + 16a +
272, u
22
− 9u
21
+ · · · − 176u + 16i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
4
=
15
16
u
21
−
129
16
u
20
+ ··· +
359
2
u − 17
5
8
u
21
−
43
8
u
20
+ ··· + 233u − 25
a
12
=
1
u
2
a
3
=
25
16
u
21
−
215
16
u
20
+ ··· +
825
2
u − 42
5
8
u
21
−
43
8
u
20
+ ··· + 233u − 25
a
8
=
−1.37500u
21
+ 11.2500u
20
+ ··· − 398.750u + 45.5000
−
9
8
u
21
+
73
8
u
20
+ ··· −
391
2
u + 22
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
10
=
0.812500u
21
− 6.81250u
20
+ ··· + 76.7500u − 6.50000
−
1
2
u
21
+
15
4
u
20
+ ··· −
81
2
u + 5
a
2
=
u
21
−
67
8
u
20
+ ··· +
837
4
u −
41
2
5
8
u
21
−
45
8
u
20
+ ··· +
477
2
u − 26
a
9
=
0.812500u
21
− 7.06250u
20
+ ··· + 255.250u − 27.5000
−
1
2
u
21
+
19
4
u
20
+ ··· −
273
2
u + 13
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1
2
u
21
−
9
2
u
20
+
53
2
u
19
− 114u
18
+ 395u
17
− 1141u
16
+
5639
2
u
15
−
12093
2
u
14
+ 11359u
13
−
37595
2
u
12
+
54937
2
u
11
−
70905
2
u
10
+
80651
2
u
9
− 40255u
8
+ 35027u
7
−
26326u
6
+ 16866u
5
−
18113
2
u
4
+ 3971u
3
− 1368u
2
+ 346u − 54
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 19u
21
+ ··· − 640u + 256
c
2
, c
8
u
22
+ u
21
+ ··· − 2u + 2
c
3
, c
7
u
22
+ 3u
20
+ ··· − u
2
+ 1
c
4
, c
9
u
22
+ 14u
20
+ ··· + u + 1
c
5
, c
6
, c
11
c
12
u
22
+ 9u
21
+ ··· + 176u + 16
c
10
u
22
+ 15u
21
+ ··· + 160u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 17y
21
+ ··· + 483328y + 65536
c
2
, c
8
y
22
+ 3y
21
+ ··· + 32y + 4
c
3
, c
7
y
22
+ 6y
21
+ ··· − 2y + 1
c
4
, c
9
y
22
+ 28y
21
+ ··· + 11y + 1
c
5
, c
6
, c
11
c
12
y
22
+ 25y
21
+ ··· − 384y + 256
c
10
y
22
+ 7y
21
+ ··· + 2432y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.287964 + 0.924780I
a = −0.34728 + 1.43125I
b = −0.805889 − 0.918892I
2.14244 − 3.29575I −1.06475 + 2.74337I
u = 0.287964 − 0.924780I
a = −0.34728 − 1.43125I
b = −0.805889 + 0.918892I
2.14244 + 3.29575I −1.06475 − 2.74337I
u = 0.927630 + 0.184659I
a = 0.129761 + 0.188778I
b = −0.777225 + 0.767673I
−6.83184 + 5.48292I −4.03618 − 4.85229I
u = 0.927630 − 0.184659I
a = 0.129761 − 0.188778I
b = −0.777225 − 0.767673I
−6.83184 − 5.48292I −4.03618 + 4.85229I
u = 0.842891 + 0.639931I
a = 0.429405 − 0.313332I
b = 0.187769 + 0.832828I
−2.36000 − 2.86683I 3.02711 + 5.17659I
u = 0.842891 − 0.639931I
a = 0.429405 + 0.313332I
b = 0.187769 − 0.832828I
−2.36000 + 2.86683I 3.02711 − 5.17659I
u = 0.702570 + 0.819082I
a = 0.363866 − 1.106770I
b = 0.97246 + 1.06574I
−4.90801 − 10.80840I −1.85897 + 7.63550I
u = 0.702570 − 0.819082I
a = 0.363866 + 1.106770I
b = 0.97246 − 1.06574I
−4.90801 + 10.80840I −1.85897 − 7.63550I
u = 0.117025 + 0.707443I
a = 0.327460 + 0.729010I
b = −0.504470 − 0.045202I
0.65660 − 1.39506I 0.82058 + 5.90353I
u = 0.117025 − 0.707443I
a = 0.327460 − 0.729010I
b = −0.504470 + 0.045202I
0.65660 + 1.39506I 0.82058 − 5.90353I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59656 + 1.29686I
a = −0.600773 + 0.160192I
b = 0.356754 − 0.547531I
−2.42718 + 0.16938I 2.49026 − 5.93197I
u = 0.59656 − 1.29686I
a = −0.600773 − 0.160192I
b = 0.356754 + 0.547531I
−2.42718 − 0.16938I 2.49026 + 5.93197I
u = 0.454810 + 0.112434I
a = 0.910049 + 0.178219I
b = 0.626422 + 0.465538I
−1.041380 − 0.734179I −6.66165 + 2.13353I
u = 0.454810 − 0.112434I
a = 0.910049 − 0.178219I
b = 0.626422 − 0.465538I
−1.041380 + 0.734179I −6.66165 − 2.13353I
u = 0.25923 + 1.61438I
a = −0.255394 + 1.262780I
b = −0.450728 − 1.096960I
5.16479 − 6.92628I 2.76500 + 4.70851I
u = 0.25923 − 1.61438I
a = −0.255394 − 1.262780I
b = −0.450728 + 1.096960I
5.16479 + 6.92628I 2.76500 − 4.70851I
u = 0.22193 + 1.65185I
a = 0.18340 + 1.86093I
b = −1.06261 − 1.33577I
3.3965 − 14.3712I 0.70200 + 6.98452I
u = 0.22193 − 1.65185I
a = 0.18340 − 1.86093I
b = −1.06261 + 1.33577I
3.3965 + 14.3712I 0.70200 − 6.98452I
u = 0.07299 + 1.69387I
a = −0.25150 − 1.73742I
b = 0.97828 + 1.19120I
11.37540 − 4.70341I −1.53492 − 1.20569I
u = 0.07299 − 1.69387I
a = −0.25150 + 1.73742I
b = 0.97828 − 1.19120I
11.37540 + 4.70341I −1.53492 + 1.20569I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01640 + 1.72547I
a = −0.138986 − 0.857092I
b = 0.479233 + 0.582586I
9.63715 − 1.43342I 1.85153 + 4.64223I
u = 0.01640 − 1.72547I
a = −0.138986 + 0.857092I
b = 0.479233 − 0.582586I
9.63715 + 1.43342I 1.85153 − 4.64223I
7
II. I
u
2
= hu
3
a − u
3
+ 3au − 2u
2
+ 2b + a − 3u − 5, 3u
3
a + u
3
+ · · · + 3a −
2, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
4
=
a
−
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
a +
5
2
a
12
=
1
u
2
a
3
=
−
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a +
5
2
−
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
a +
5
2
a
8
=
−
1
2
u
3
a −
3
2
u
3
+ ··· −
5
2
a −
5
2
u
3
+ u
2
+ 2u + 1
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
5
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
a
10
=
−
3
2
u
3
a −
1
2
u
3
+ ··· −
3
2
a +
3
2
u
a
2
=
u
2
a + u
2
+ 2a + 1
−
3
2
u
3
a −
1
2
u
3
+ ··· −
3
2
a +
7
2
a
9
=
−
1
2
u
3
a −
3
2
u
3
+ ··· −
3
2
a −
3
2
1
2
u
3
a +
3
2
u
3
+ ··· +
3
2
a +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
− 8u
2
− 24u − 14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ u
2
− 2u + 1)
2
c
2
, c
8
u
8
+ 2u
7
+ 3u
6
− 4u
5
− 3u
4
− 12u
3
+ 18u
2
− 14u + 41
c
3
, c
7
u
8
+ 2u
7
+ 3u
6
+ 5u
5
+ 15u
4
+ 12u
3
+ u
2
− 11u + 4
c
4
, c
9
u
8
− 2u
7
+ 5u
6
− 13u
5
+ 15u
4
− 26u
3
+ 29u
2
− 15u + 22
c
5
, c
6
, c
11
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
10
(u
4
− u
3
+ u
2
+ 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
2
c
2
, c
8
y
8
+ 2y
7
+ 19y
6
+ 50y
5
+ 159y
4
− 118y
3
− 258y
2
+ 1280y + 1681
c
3
, c
7
y
8
+ 2y
7
+ 19y
6
+ 19y
5
+ 163y
4
+ 20y
3
+ 385y
2
− 113y + 16
c
4
, c
9
y
8
+ 6y
7
+ 3y
6
− 65y
5
− 177y
4
+ 24y
3
+ 721y
2
+ 1051y + 484
c
5
, c
6
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.771008 − 0.709655I
b = 1.37255 + 1.06120I
−5.35681 + 2.83021I −5.65348 − 9.81749I
u = −0.395123 + 0.506844I
a = 0.40506 − 2.86559I
b = −0.415863 + 0.165981I
−5.35681 + 2.83021I −5.65348 − 9.81749I
u = −0.395123 − 0.506844I
a = −0.771008 + 0.709655I
b = 1.37255 − 1.06120I
−5.35681 − 2.83021I −5.65348 + 9.81749I
u = −0.395123 − 0.506844I
a = 0.40506 + 2.86559I
b = −0.415863 − 0.165981I
−5.35681 − 2.83021I −5.65348 + 9.81749I
u = −0.10488 + 1.55249I
a = 0.13089 + 1.50540I
b = 0.955379 − 0.991300I
8.64668 + 6.32793I 1.65348 − 5.12960I
u = −0.10488 + 1.55249I
a = 0.23506 − 2.20215I
b = −0.91206 + 1.63250I
8.64668 + 6.32793I 1.65348 − 5.12960I
u = −0.10488 − 1.55249I
a = 0.13089 − 1.50540I
b = 0.955379 + 0.991300I
8.64668 − 6.32793I 1.65348 + 5.12960I
u = −0.10488 − 1.55249I
a = 0.23506 + 2.20215I
b = −0.91206 − 1.63250I
8.64668 − 6.32793I 1.65348 + 5.12960I
11
III.
I
u
3
= hu
10
+7u
8
+· · ·+b+1, −u
13
−10u
11
+· · ·+2a−1, u
14
+10u
12
+· · ·+u+2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
4
=
1
2
u
13
+ 5u
11
+ ··· − u +
1
2
−u
10
− 7u
8
− 17u
6
+ u
5
− 17u
4
+ 2u
3
− 7u
2
− u − 1
a
12
=
1
u
2
a
3
=
1
2
u
13
+ 5u
11
+ ··· − 2u −
1
2
−u
10
− 7u
8
− 17u
6
+ u
5
− 17u
4
+ 2u
3
− 7u
2
− u − 1
a
8
=
−
1
2
u
13
− u
12
+ ··· − 3u −
7
2
−u
13
− 9u
11
+ ··· − 2u + 1
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
10
=
1
2
u
13
− u
12
+ ··· − u −
1
2
−u
13
− 9u
11
− 31u
9
+ u
8
− 50u
7
+ 5u
6
− 36u
5
+ 7u
4
− 8u
3
+ 2u
2
+ 1
a
2
=
−
1
2
u
13
− 5u
11
+ ··· − 8u +
3
2
u
9
+ 6u
7
+ 12u
5
+ 9u
3
+ u
2
+ 2u + 1
a
9
=
1
2
u
13
+ 4u
11
+ ··· − 2u +
1
2
−u
13
− u
12
+ ··· − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
13
+ 2u
12
+ 8u
11
+ 16u
10
+ 23u
9
+ 45u
8
+ 23u
7
+ 50u
6
−9u
5
+ 14u
4
−24u
3
−4u
2
−4u
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 10u
13
+ ··· + 16u + 1
c
2
, c
8
u
14
− u
13
+ ··· − 11u + 12
c
3
, c
7
u
14
+ 2u
12
+ ··· − 2u + 1
c
4
, c
9
u
14
+ 5u
12
+ ··· + u + 1
c
5
, c
6
u
14
+ 10u
12
+ ··· − u + 2
c
10
u
14
− 4u
13
+ ··· + 5u
2
+ 1
c
11
, c
12
u
14
+ 10u
12
+ ··· + u + 2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 10y
13
+ ··· − 116y + 1
c
2
, c
8
y
14
+ 5y
13
+ ··· − 169y + 144
c
3
, c
7
y
14
+ 4y
13
+ ··· − 2y + 1
c
4
, c
9
y
14
+ 10y
13
+ ··· − 9y + 1
c
5
, c
6
, c
11
c
12
y
14
+ 20y
13
+ ··· + 39y + 4
c
10
y
14
+ 6y
13
+ ··· + 10y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.216588 + 0.766661I
a = −0.79945 + 1.58663I
b = −0.734213 − 1.062220I
3.12382 − 4.21919I 5.40196 + 5.63555I
u = 0.216588 − 0.766661I
a = −0.79945 − 1.58663I
b = −0.734213 + 1.062220I
3.12382 + 4.21919I 5.40196 − 5.63555I
u = −0.378992 + 1.158350I
a = 0.707988 + 0.209626I
b = −0.481839 + 0.132352I
−2.78436 + 0.58627I −2.37749 − 2.49068I
u = −0.378992 − 1.158350I
a = 0.707988 − 0.209626I
b = −0.481839 − 0.132352I
−2.78436 − 0.58627I −2.37749 + 2.49068I
u = 0.370851 + 0.545702I
a = −1.071550 − 0.239968I
b = 0.288392 − 0.820734I
2.25383 + 2.26223I 8.00771 − 5.34861I
u = 0.370851 − 0.545702I
a = −1.071550 + 0.239968I
b = 0.288392 + 0.820734I
2.25383 − 2.26223I 8.00771 + 5.34861I
u = −0.304789 + 0.397142I
a = −0.53814 − 2.60756I
b = 0.717374 + 0.663663I
−5.08623 + 1.96121I −1.63137 − 0.59067I
u = −0.304789 − 0.397142I
a = −0.53814 + 2.60756I
b = 0.717374 − 0.663663I
−5.08623 − 1.96121I −1.63137 + 0.59067I
u = −0.08871 + 1.55131I
a = 0.42730 + 1.64814I
b = −1.009610 − 0.964029I
1.73020 + 3.34530I −1.14043 − 1.01217I
u = −0.08871 − 1.55131I
a = 0.42730 − 1.64814I
b = −1.009610 + 0.964029I
1.73020 − 3.34530I −1.14043 + 1.01217I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05772 + 1.67208I
a = −0.19555 − 1.81258I
b = 0.96827 + 1.26017I
11.81410 − 5.26341I 5.92578 + 7.14568I
u = 0.05772 − 1.67208I
a = −0.19555 + 1.81258I
b = 0.96827 − 1.26017I
11.81410 + 5.26341I 5.92578 − 7.14568I
u = 0.12734 + 1.69142I
a = 0.219396 − 0.895572I
b = 0.251625 + 0.782266I
10.33280 + 0.06735I 7.31384 − 0.14644I
u = 0.12734 − 1.69142I
a = 0.219396 + 0.895572I
b = 0.251625 − 0.782266I
10.33280 − 0.06735I 7.31384 + 0.14644I
16
IV. I
u
4
= h6.47 × 10
4
a
5
u
3
+ 4.85 × 10
5
a
4
u
3
+ · · · − 3.86 × 10
5
a − 5.64 ×
10
4
, 3a
5
u
3
− 2a
4
u
3
+ · · · + 8a − 9, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
4
=
a
−0.0689494a
5
u
3
− 0.516487a
4
u
3
+ ··· + 0.410977a + 0.0601015
a
12
=
1
u
2
a
3
=
−0.0689494a
5
u
3
− 0.516487a
4
u
3
+ ··· + 1.41098a + 0.0601015
−0.0689494a
5
u
3
− 0.516487a
4
u
3
+ ··· + 0.410977a + 0.0601015
a
8
=
0.140805a
5
u
3
− 0.346580a
4
u
3
+ ··· − 0.706629a − 1.69831
0.160361a
5
u
3
+ 0.183546a
4
u
3
+ ··· − 0.869155a − 1.38070
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
5
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
a
10
=
−0.000760401a
5
u
3
− 0.631549a
4
u
3
+ ··· − 1.72584a + 1.80502
−0.122303a
5
u
3
− 0.0408039a
4
u
3
+ ··· + 0.836778a − 0.878400
a
2
=
−0.0571962a
5
u
3
+ 0.310935a
4
u
3
+ ··· + 1.43692a − 0.163214
0.0409488a
5
u
3
− 0.886450a
4
u
3
+ ··· − 0.599105a − 0.139767
a
9
=
−0.177120a
5
u
3
+ 0.152318a
4
u
3
+ ··· + 1.00470a + 1.79206
0.101777a
5
u
3
− 0.569117a
4
u
3
+ ··· − 1.15970a − 1.37536
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
71470
469489
a
5
u
3
−
268064
469489
a
4
u
3
+ ··· +
60802
469489
a −
452394
469489
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ u
2
− 2u + 1)
6
c
2
, c
8
u
24
− 3u
23
+ ··· + 8u + 8
c
3
, c
7
u
24
− 5u
23
+ ··· − 4u + 8
c
4
, c
9
u
24
+ u
23
+ ··· − 32u + 8
c
5
, c
6
, c
11
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
6
c
10
(u
4
− u
3
+ u
2
+ 1)
6
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
c
2
, c
8
y
24
+ 9y
23
+ ··· + 1696y + 64
c
3
, c
7
y
24
+ 5y
23
+ ··· + 1136y + 64
c
4
, c
9
y
24
+ 21y
23
+ ··· + 3808y + 64
c
5
, c
6
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.637870 + 0.739647I
b = 0.115226 + 0.635056I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.395123 + 0.506844I
a = 1.159350 + 0.059125I
b = −0.490251 − 0.808077I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.395123 + 0.506844I
a = 1.27325 − 0.74075I
b = 0.957415 + 0.141715I
−5.35681 −5.65348 + 0.I
u = −0.395123 + 0.506844I
a = 0.86187 + 1.25769I
b = 0.76295 − 1.20476I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = −0.395123 + 0.506844I
a = −1.53954 − 0.58632I
b = −0.668828 + 0.802618I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = −0.395123 + 0.506844I
a = −0.16426 − 2.67779I
b = −0.57777 + 1.36729I
−5.35681 −5.65348 + 0.I
u = −0.395123 − 0.506844I
a = −0.637870 − 0.739647I
b = 0.115226 − 0.635056I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.395123 − 0.506844I
a = 1.159350 − 0.059125I
b = −0.490251 + 0.808077I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.395123 − 0.506844I
a = 1.27325 + 0.74075I
b = 0.957415 − 0.141715I
−5.35681 −5.65348 + 0.I
u = −0.395123 − 0.506844I
a = 0.86187 − 1.25769I
b = 0.76295 + 1.20476I
1.64493 − 4.57907I −2.00000 + 7.47354I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = −1.53954 + 0.58632I
b = −0.668828 − 0.802618I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = −0.395123 − 0.506844I
a = −0.16426 + 2.67779I
b = −0.57777 − 1.36729I
−5.35681 −5.65348 + 0.I
u = −0.10488 + 1.55249I
a = −0.076529 + 0.814337I
b = 0.668148 − 0.834125I
8.64668 1.65348 + 0.I
u = −0.10488 + 1.55249I
a = −0.53246 − 1.31285I
b = −0.031326 + 0.920559I
8.64668 1.65348 + 0.I
u = −0.10488 + 1.55249I
a = 0.083538 + 0.334406I
b = −1.249390 − 0.253465I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.10488 + 1.55249I
a = −0.55405 + 1.75382I
b = 0.023049 − 0.425939I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = −0.10488 + 1.55249I
a = 1.73172 + 0.96731I
b = −2.00583 − 0.96364I
1.64493 + 4.57907I −2.00000 − 7.47354I
u = −0.10488 + 1.55249I
a = −0.10502 + 2.63055I
b = −0.00339 − 1.81847I
1.64493 + 1.74886I −2.00000 + 2.34394I
u = −0.10488 − 1.55249I
a = −0.076529 − 0.814337I
b = 0.668148 + 0.834125I
8.64668 1.65348 + 0.I
u = −0.10488 − 1.55249I
a = −0.53246 + 1.31285I
b = −0.031326 − 0.920559I
8.64668 1.65348 + 0.I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = 0.083538 − 0.334406I
b = −1.249390 + 0.253465I
1.64493 − 1.74886I −2.00000 − 2.34394I
u = −0.10488 − 1.55249I
a = −0.55405 − 1.75382I
b = 0.023049 + 0.425939I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = −0.10488 − 1.55249I
a = 1.73172 − 0.96731I
b = −2.00583 + 0.96364I
1.64493 − 4.57907I −2.00000 + 7.47354I
u = −0.10488 − 1.55249I
a = −0.10502 − 2.63055I
b = −0.00339 + 1.81847I
1.64493 − 1.74886I −2.00000 − 2.34394I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
4
+ 3u
3
+ u
2
− 2u + 1)
8
)(u
14
− 10u
13
+ ··· + 16u + 1)
· (u
22
− 19u
21
+ ··· − 640u + 256)
c
2
, c
8
(u
8
+ 2u
7
+ 3u
6
− 4u
5
− 3u
4
− 12u
3
+ 18u
2
− 14u + 41)
· (u
14
− u
13
+ ··· − 11u + 12)(u
22
+ u
21
+ ··· − 2u + 2)
· (u
24
− 3u
23
+ ··· + 8u + 8)
c
3
, c
7
(u
8
+ 2u
7
+ 3u
6
+ 5u
5
+ 15u
4
+ 12u
3
+ u
2
− 11u + 4)
· (u
14
+ 2u
12
+ ··· − 2u + 1)(u
22
+ 3u
20
+ ··· − u
2
+ 1)
· (u
24
− 5u
23
+ ··· − 4u + 8)
c
4
, c
9
(u
8
− 2u
7
+ 5u
6
− 13u
5
+ 15u
4
− 26u
3
+ 29u
2
− 15u + 22)
· (u
14
+ 5u
12
+ ··· + u + 1)(u
22
+ 14u
20
+ ··· + u + 1)
· (u
24
+ u
23
+ ··· − 32u + 8)
c
5
, c
6
((u
4
− u
3
+ 3u
2
− 2u + 1)
8
)(u
14
+ 10u
12
+ ··· − u + 2)
· (u
22
+ 9u
21
+ ··· + 176u + 16)
c
10
((u
4
− u
3
+ u
2
+ 1)
8
)(u
14
− 4u
13
+ ··· + 5u
2
+ 1)
· (u
22
+ 15u
21
+ ··· + 160u + 16)
c
11
, c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
8
)(u
14
+ 10u
12
+ ··· + u + 2)
· (u
22
+ 9u
21
+ ··· + 176u + 16)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
8
)(y
14
− 10y
13
+ ··· − 116y + 1)
· (y
22
− 17y
21
+ ··· + 483328y + 65536)
c
2
, c
8
(y
8
+ 2y
7
+ 19y
6
+ 50y
5
+ 159y
4
− 118y
3
− 258y
2
+ 1280y + 1681)
· (y
14
+ 5y
13
+ ··· − 169y + 144)(y
22
+ 3y
21
+ ··· + 32y + 4)
· (y
24
+ 9y
23
+ ··· + 1696y + 64)
c
3
, c
7
(y
8
+ 2y
7
+ 19y
6
+ 19y
5
+ 163y
4
+ 20y
3
+ 385y
2
− 113y + 16)
· (y
14
+ 4y
13
+ ··· − 2y + 1)(y
22
+ 6y
21
+ ··· − 2y + 1)
· (y
24
+ 5y
23
+ ··· + 1136y + 64)
c
4
, c
9
(y
8
+ 6y
7
+ 3y
6
− 65y
5
− 177y
4
+ 24y
3
+ 721y
2
+ 1051y + 484)
· (y
14
+ 10y
13
+ ··· − 9y + 1)(y
22
+ 28y
21
+ ··· + 11y + 1)
· (y
24
+ 21y
23
+ ··· + 3808y + 64)
c
5
, c
6
, c
11
c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
)(y
14
+ 20y
13
+ ··· + 39y + 4)
· (y
22
+ 25y
21
+ ··· − 384y + 256)
c
10
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
)(y
14
+ 6y
13
+ ··· + 10y + 1)
· (y
22
+ 7y
21
+ ··· + 2432y + 256)
24
