11a
352
(K11a
352
)
A knot diagram
1
Linearized knot diagam
7 6 1 11 10 9 4 3 2 5 8
Solving Sequence
4,11 5,8
1 3 9 7 10 6 2
c
4
c
11
c
3
c
8
c
7
c
10
c
5
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
9
+ 16u
8
− 53u
7
+ 124u
6
− 204u
5
+ 242u
4
− 203u
3
+ 82u
2
+ 16b + 2u − 12,
− 3u
9
+ 24u
8
− 101u
7
+ 292u
6
− 620u
5
+ 978u
4
− 1147u
3
+ 970u
2
+ 32a − 494u + 116,
u
10
− 6u
9
+ 23u
8
− 62u
7
+ 124u
6
− 190u
5
+ 221u
4
− 188u
3
+ 110u
2
− 40u + 8i
I
u
2
= hau + b, −3u
6
a + 2u
6
+ ··· − 12a + 17, u
7
− 4u
6
+ 11u
5
− 20u
4
+ 26u
3
− 23u
2
+ 14u − 4i
I
u
3
= h−1348740987753a
7
u
3
+ 686668738913a
6
u
3
+ ··· − 41120280504a + 141432788735,
− a
7
u
3
− 4a
6
u
3
+ ··· + 10a + 96, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
4
= h11a
3
u
3
+ 16u
3
a
2
+ ··· − 5a − 3,
a
3
u
3
− u
3
a
2
+ a
4
+ 2a
3
u − 2u
3
a − 2a
2
u − 3u
2
a − 2u
3
+ a
2
− 5au − 2u
2
− 6a − 5u − 4,
u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
5
= h−u
15
+ u
14
− 11u
13
+ 9u
12
− 46u
11
+ 30u
10
− 87u
9
+ 44u
8
− 63u
7
+ 24u
6
+ u
5
+ u
4
+ 3u
2
+ 2b − 9u + 3,
− 3u
15
− 5u
14
+ ··· + 10a − 45, u
16
+ 11u
14
+ 47u
12
+ 96u
10
+ 90u
8
+ 26u
6
− u
4
+ 8u
2
+ 5i
I
u
6
= h−u
3
− au − u
2
+ b − 2u − 1, −u
3
a − u
3
+ a
2
− 2au − 2u + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
7
= hu
3
− u
2
+ b + 2u − 1, −u
3
+ a − 2u, u
4
− u
3
+ 3u
2
− 2u + 1i
I
v
1
= ha, b − 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 101 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
9
+ 16u
8
+ · · · + 16b − 12, −3u
9
+ 24u
8
+ · · · + 32a + 116, u
10
−
6u
9
+ · · · − 40u + 8i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
3
32
u
9
−
3
4
u
8
+ ··· +
247
16
u −
29
8
3
16
u
9
− u
8
+ ··· −
1
8
u +
3
4
a
1
=
13
32
u
9
− 2u
8
+ ··· +
73
16
u +
1
8
−
7
16
u
9
+
5
2
u
8
+ ··· −
123
8
u +
13
4
a
3
=
3
32
u
9
−
3
4
u
8
+ ··· +
167
16
u −
13
8
5
16
u
9
− 2u
8
+ ··· +
105
8
u −
11
4
a
9
=
3
32
u
9
−
1
2
u
8
+ ··· +
55
16
u −
1
8
7
16
u
9
−
3
2
u
8
+ ··· −
5
8
u +
3
4
a
7
=
9
32
u
9
−
7
4
u
8
+ ··· +
245
16
u −
23
8
3
16
u
9
− u
8
+ ··· −
1
8
u +
3
4
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
5
32
u
9
−
3
4
u
8
+ ··· +
113
16
u −
11
8
−
3
16
u
9
+ u
8
+ ··· +
17
8
u −
3
4
a
2
=
5
32
u
9
−
3
4
u
8
+ ··· +
113
16
u −
11
8
−
3
16
u
9
+ u
8
+ ··· +
17
8
u −
3
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3
4
u
9
−3u
8
+
45
4
u
7
−24u
6
+ 43u
5
−
105
2
u
4
+
187
4
u
3
−
47
2
u
2
−
9
2
u + 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
8
u
10
+ u
9
+ 7u
8
+ 4u
7
+ 23u
6
+ 9u
5
+ 40u
4
+ 9u
3
+ 33u
2
+ 2u + 10
c
2
, c
7
, c
9
c
11
u
10
+ u
9
− u
8
− 2u
7
+ 5u
6
+ 3u
5
− 3u
3
− u + 1
c
3
, c
6
u
10
− 9u
9
+ ··· − 15u + 11
c
4
, c
5
, c
10
u
10
− 6u
9
+ ··· − 40u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
10
+ 13y
9
+ ··· + 656y + 100
c
2
, c
7
, c
9
c
11
y
10
− 3y
9
+ 15y
8
− 20y
7
+ 43y
6
− 17y
5
+ 12y
4
+ 7y
3
− 6y
2
− y + 1
c
3
, c
6
y
10
+ 3y
9
+ ··· + 1601y + 121
c
4
, c
5
, c
10
y
10
+ 10y
9
+ ··· + 160y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827139 + 0.827690I
a = 0.124534 − 1.186260I
b = −1.084860 + 0.878124I
−3.86930 + 13.03600I −4.42534 − 9.74427I
u = 0.827139 − 0.827690I
a = 0.124534 + 1.186260I
b = −1.084860 − 0.878124I
−3.86930 − 13.03600I −4.42534 + 9.74427I
u = 1.231820 + 0.302946I
a = −0.687720 − 0.315351I
b = 0.751611 + 0.596797I
−2.14694 − 6.57736I −5.40678 + 10.73292I
u = 1.231820 − 0.302946I
a = −0.687720 + 0.315351I
b = 0.751611 − 0.596797I
−2.14694 + 6.57736I −5.40678 − 10.73292I
u = 0.314386 + 0.484120I
a = 0.850851 + 0.785005I
b = 0.112541 − 0.658708I
0.232399 + 1.335330I 1.84390 − 5.86434I
u = 0.314386 − 0.484120I
a = 0.850851 − 0.785005I
b = 0.112541 + 0.658708I
0.232399 − 1.335330I 1.84390 + 5.86434I
u = 0.25828 + 1.65152I
a = 0.458885 + 0.901810I
b = 1.37084 − 0.99078I
−12.0871 + 17.1582I −6.40595 − 8.48495I
u = 0.25828 − 1.65152I
a = 0.458885 − 0.901810I
b = 1.37084 + 0.99078I
−12.0871 − 17.1582I −6.40595 + 8.48495I
u = 0.36838 + 1.94011I
a = 0.003450 − 0.334444I
b = −0.650130 + 0.116508I
−9.27048 + 0.95500I −15.6058 − 6.9472I
u = 0.36838 − 1.94011I
a = 0.003450 + 0.334444I
b = −0.650130 − 0.116508I
−9.27048 − 0.95500I −15.6058 + 6.9472I
5
II. I
u
2
= hau + b, −3u
6
a + 2u
6
+ · · · − 12a + 17, u
7
− 4u
6
+ · · · + 14u − 4i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
a
−au
a
1
=
−
1
2
u
6
a +
1
4
u
6
+ ··· − 3a + 2
−
1
2
u
6
+ u
5
+ ··· + 2a − 1
a
3
=
−
1
4
u
6
+
1
2
u
5
+ ··· − a − 1
−u
5
a +
3
2
u
6
+ ··· −
15
2
u + 3
a
9
=
1
2
u
6
a −
1
4
u
6
+ ··· + a −
3
2
−u
6
a + 3u
5
a + ··· − 2a − 1
a
7
=
−au + a
−au
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
1
4
u
6
−
1
2
u
5
+ ··· − a + 2
−
1
2
u
6
+ u
5
+ ··· +
5
2
u − 1
a
2
=
1
4
u
6
−
1
2
u
5
+ ··· − a + 2
−
1
2
u
6
+ u
5
+ ··· +
5
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5u
6
− 13u
5
+ 32u
4
− 44u
3
+ 46u
2
− 32u + 14
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
7
+ u
5
+ u
4
− u − 1)
2
c
2
, c
7
, c
9
c
11
u
14
+ u
13
+ ··· + u + 1
c
3
, c
6
u
14
− 13u
13
+ ··· − 329u + 47
c
4
, c
5
, c
10
(u
7
− 4u
6
+ 11u
5
− 20u
4
+ 26u
3
− 23u
2
+ 14u − 4)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
7
+ 2y
6
+ y
5
− 3y
4
− 2y
3
+ 2y
2
+ y −1)
2
c
2
, c
7
, c
9
c
11
y
14
− 5y
13
+ ··· + y + 1
c
3
, c
6
y
14
− 3y
13
+ ··· + 2397y + 2209
c
4
, c
5
, c
10
(y
7
+ 6y
6
+ 13y
5
+ 16y
4
+ 32y
3
+ 39y
2
+ 12y −16)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316075 + 1.084870I
a = 0.447890 + 1.041020I
b = 0.987810 − 0.814945I
−0.56973 + 3.46571I 1.80998 − 1.90405I
u = 0.316075 + 1.084870I
a = −0.468498 + 0.032326I
b = 0.183150 + 0.498043I
−0.56973 + 3.46571I 1.80998 − 1.90405I
u = 0.316075 − 1.084870I
a = 0.447890 − 1.041020I
b = 0.987810 + 0.814945I
−0.56973 − 3.46571I 1.80998 + 1.90405I
u = 0.316075 − 1.084870I
a = −0.468498 − 0.032326I
b = 0.183150 − 0.498043I
−0.56973 − 3.46571I 1.80998 + 1.90405I
u = 1.051270 + 0.735259I
a = −0.268053 + 0.911867I
b = 0.952255 − 0.761533I
−3.76584 + 3.52764I −10.39771 − 1.47160I
u = 1.051270 + 0.735259I
a = 0.591875 − 0.190941I
b = −0.762614 − 0.234450I
−3.76584 + 3.52764I −10.39771 − 1.47160I
u = 1.051270 − 0.735259I
a = −0.268053 − 0.911867I
b = 0.952255 + 0.761533I
−3.76584 − 3.52764I −10.39771 + 1.47160I
u = 1.051270 − 0.735259I
a = 0.591875 + 0.190941I
b = −0.762614 + 0.234450I
−3.76584 − 3.52764I −10.39771 + 1.47160I
u = 0.658991
a = 0.825920 + 1.123020I
b = −0.544274 − 0.740063I
2.67359 5.12550
u = 0.658991
a = 0.825920 − 1.123020I
b = −0.544274 + 0.740063I
2.67359 5.12550
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30316 + 1.67229I
a = −0.402520 − 0.858604I
b = −1.31381 + 0.93342I
−11.8056 + 8.5528I −9.47503 − 5.91683I
u = 0.30316 + 1.67229I
a = 0.023386 + 0.600716I
b = 0.997484 − 0.221219I
−11.8056 + 8.5528I −9.47503 − 5.91683I
u = 0.30316 − 1.67229I
a = −0.402520 + 0.858604I
b = −1.31381 − 0.93342I
−11.8056 − 8.5528I −9.47503 + 5.91683I
u = 0.30316 − 1.67229I
a = 0.023386 − 0.600716I
b = 0.997484 + 0.221219I
−11.8056 − 8.5528I −9.47503 + 5.91683I
10
III. I
u
3
= h−1.35 × 10
12
a
7
u
3
+ 6.87 × 10
11
a
6
u
3
+ · · · − 4.11 × 10
10
a + 1.41 ×
10
11
, −a
7
u
3
− 4a
6
u
3
+ · · · + 10a + 96, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
a
2.06795a
7
u
3
− 1.05283a
6
u
3
+ ··· + 0.0630474a − 0.216851
a
1
=
−a
2
u
0.566545a
7
u
3
− 0.144764a
6
u
3
+ ··· + 0.0887731a + 1.58851
a
3
=
0.0804851a
7
u
3
+ 0.514618a
6
u
3
+ ··· − 1.21468a + 1.08057
0.476938a
7
u
3
+ 1.22479a
6
u
3
+ ··· + 0.337460a + 1.73643
a
9
=
0.353631a
7
u
3
− 0.0766819a
6
u
3
+ ··· − 1.06770a − 1.03933
0.277128a
7
u
3
+ 0.0000142253a
6
u
3
+ ··· − 0.621680a + 0.912067
a
7
=
2.06795a
7
u
3
− 1.05283a
6
u
3
+ ··· + 1.06305a − 0.216851
2.06795a
7
u
3
− 1.05283a
6
u
3
+ ··· + 0.0630474a − 0.216851
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
2
=
1.50926a
7
u
3
+ 1.35905a
6
u
3
+ ··· − 0.618723a + 0.472347
2.16896a
7
u
3
+ 0.686316a
6
u
3
+ ··· + 0.397134a + 1.30453
a
2
=
1.50926a
7
u
3
+ 1.35905a
6
u
3
+ ··· − 0.618723a + 0.472347
2.16896a
7
u
3
+ 0.686316a
6
u
3
+ ··· + 0.397134a + 1.30453
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1367231366824
326106026089
a
7
u
3
−
1370870830584
326106026089
a
6
u
3
+ ··· −
3308821571992
326106026089
a −
4028263148378
326106026089
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
16
− u
15
+ ··· − 24u + 79)
2
c
2
, c
7
, c
9
c
11
u
32
− u
31
+ ··· + 400u + 361
c
3
, c
6
(u
4
+ u
3
− 2u + 1)
8
c
4
, c
5
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
8
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
16
+ 19y
15
+ ··· + 44612y + 6241)
2
c
2
, c
7
, c
9
c
11
y
32
− 11y
31
+ ··· − 2524550y + 130321
c
3
, c
6
(y
4
− y
3
+ 6y
2
− 4y + 1)
8
c
4
, c
5
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.112909 − 0.977468I
b = −1.11104 + 1.26776I
−3.07886 − 5.47487I −10.1733 + 11.8369I
u = −0.395123 + 0.506844I
a = −1.186440 − 0.577565I
b = 1.053440 − 0.202017I
−3.07886 + 2.64466I −10.17326 − 2.01946I
u = −0.395123 + 0.506844I
a = 0.57298 + 1.37827I
b = 0.830529 − 0.979145I
−3.07886 + 2.64466I −10.17326 − 2.01946I
u = −0.395123 + 0.506844I
a = 1.25572 + 1.09950I
b = −0.761526 + 0.373132I
−3.07886 + 2.64466I −10.17326 − 2.01946I
u = −0.395123 + 0.506844I
a = −0.40614 − 1.88973I
b = 1.073750 + 0.876252I
−3.07886 − 5.47487I −10.1733 + 11.8369I
u = −0.395123 + 0.506844I
a = 1.99615 + 0.08248I
b = 0.924966 + 0.254177I
−3.07886 + 2.64466I −10.17326 − 2.01946I
u = −0.395123 + 0.506844I
a = −0.04809 + 2.15599I
b = −1.118270 − 0.540827I
−3.07886 − 5.47487I −10.1733 + 11.8369I
u = −0.395123 + 0.506844I
a = −2.61870 − 0.15060I
b = −0.540037 − 0.328993I
−3.07886 − 5.47487I −10.1733 + 11.8369I
u = −0.395123 − 0.506844I
a = −0.112909 + 0.977468I
b = −1.11104 − 1.26776I
−3.07886 + 5.47487I −10.1733 − 11.8369I
u = −0.395123 − 0.506844I
a = −1.186440 + 0.577565I
b = 1.053440 + 0.202017I
−3.07886 − 2.64466I −10.17326 + 2.01946I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 − 0.506844I
a = 0.57298 − 1.37827I
b = 0.830529 + 0.979145I
−3.07886 − 2.64466I −10.17326 + 2.01946I
u = −0.395123 − 0.506844I
a = 1.25572 − 1.09950I
b = −0.761526 − 0.373132I
−3.07886 − 2.64466I −10.17326 + 2.01946I
u = −0.395123 − 0.506844I
a = −0.40614 + 1.88973I
b = 1.073750 − 0.876252I
−3.07886 + 5.47487I −10.1733 − 11.8369I
u = −0.395123 − 0.506844I
a = 1.99615 − 0.08248I
b = 0.924966 − 0.254177I
−3.07886 − 2.64466I −10.17326 + 2.01946I
u = −0.395123 − 0.506844I
a = −0.04809 − 2.15599I
b = −1.118270 + 0.540827I
−3.07886 + 5.47487I −10.1733 − 11.8369I
u = −0.395123 − 0.506844I
a = −2.61870 + 0.15060I
b = −0.540037 + 0.328993I
−3.07886 + 5.47487I −10.1733 − 11.8369I
u = −0.10488 + 1.55249I
a = −0.391799 + 0.880227I
b = −1.41214 − 1.21990I
−10.08060 − 7.22373I −13.8267 + 9.4930I
u = −0.10488 + 1.55249I
a = 0.140656 − 0.862399I
b = 0.811814 + 0.187323I
−10.08060 + 0.89580I −13.8267 − 4.3634I
u = −0.10488 + 1.55249I
a = 0.721035 − 0.958305I
b = 1.32546 + 0.70058I
−10.08060 − 7.22373I −13.8267 + 9.4930I
u = −0.10488 + 1.55249I
a = −1.074960 − 0.865228I
b = −0.825212 + 0.300777I
−10.08060 + 0.89580I −13.8267 − 4.3634I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = −0.228603 − 0.516097I
b = −1.45600 + 1.57813I
−10.08060 + 0.89580I −13.8267 − 4.3634I
u = −0.10488 + 1.55249I
a = −0.084947 + 0.528649I
b = −1.324120 − 0.308813I
−10.08060 + 0.89580I −13.8267 − 4.3634I
u = −0.10488 + 1.55249I
a = 0.069010 + 0.388237I
b = 1.41842 − 2.08296I
−10.08060 − 7.22373I −13.8267 + 9.4930I
u = −0.10488 + 1.55249I
a = 1.39703 + 0.81926I
b = 0.609972 − 0.066421I
−10.08060 − 7.22373I −13.8267 + 9.4930I
u = −0.10488 − 1.55249I
a = −0.391799 − 0.880227I
b = −1.41214 + 1.21990I
−10.08060 + 7.22373I −13.8267 − 9.4930I
u = −0.10488 − 1.55249I
a = 0.140656 + 0.862399I
b = 0.811814 − 0.187323I
−10.08060 − 0.89580I −13.8267 + 4.3634I
u = −0.10488 − 1.55249I
a = 0.721035 + 0.958305I
b = 1.32546 − 0.70058I
−10.08060 + 7.22373I −13.8267 − 9.4930I
u = −0.10488 − 1.55249I
a = −1.074960 + 0.865228I
b = −0.825212 − 0.300777I
−10.08060 − 0.89580I −13.8267 + 4.3634I
u = −0.10488 − 1.55249I
a = −0.228603 + 0.516097I
b = −1.45600 − 1.57813I
−10.08060 − 0.89580I −13.8267 + 4.3634I
u = −0.10488 − 1.55249I
a = −0.084947 − 0.528649I
b = −1.324120 + 0.308813I
−10.08060 − 0.89580I −13.8267 + 4.3634I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 − 1.55249I
a = 0.069010 − 0.388237I
b = 1.41842 + 2.08296I
−10.08060 + 7.22373I −13.8267 − 9.4930I
u = −0.10488 − 1.55249I
a = 1.39703 − 0.81926I
b = 0.609972 + 0.066421I
−10.08060 + 7.22373I −13.8267 − 9.4930I
17
IV. I
u
4
=
h11a
3
u
3
+16u
3
a
2
+· · ·−5a−3, a
3
u
3
−u
3
a
2
+· · ·−6a−4, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
a
−0.354839a
3
u
3
− 0.516129a
2
u
3
+ ··· + 0.161290a + 0.0967742
a
1
=
−a
2
u
−0.193548a
3
u
3
+ 0.354839a
2
u
3
+ ··· − 0.548387a − 0.129032
a
3
=
0.129032a
3
u
3
+ 0.0967742a
2
u
3
+ ··· − 0.967742a + 0.419355
−0.193548a
3
u
3
+ 0.354839a
2
u
3
+ ··· − 0.548387a + 0.870968
a
9
=
−0.612903a
3
u
3
− 0.709677a
2
u
3
+ ··· + 1.09677a + 0.258065
−0.967742a
3
u
3
− 1.22581a
2
u
3
+ ··· + 0.258065a + 1.35484
a
7
=
−0.354839a
3
u
3
− 0.516129a
2
u
3
+ ··· + 1.16129a + 0.0967742
−0.354839a
3
u
3
− 0.516129a
2
u
3
+ ··· + 0.161290a + 0.0967742
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
2
=
0.129032a
3
u
3
+ 0.0967742a
2
u
3
+ ··· − 0.967742a + 0.419355
−0.193548a
3
u
3
+ 0.354839a
2
u
3
+ ··· − 1.54839a + 0.870968
a
2
=
0.129032a
3
u
3
+ 0.0967742a
2
u
3
+ ··· − 0.967742a + 0.419355
−0.193548a
3
u
3
+ 0.354839a
2
u
3
+ ··· − 1.54839a + 0.870968
(ii) Obstruction class = −1
(iii) Cusp Shapes =
48
31
a
3
u
3
+
168
31
a
3
u
2
−
88
31
u
3
a
2
+
192
31
a
3
u +
64
31
a
2
u
2
+
32
31
u
3
a +
80
31
a
3
−
104
31
a
2
u +
112
31
u
2
a +
44
31
u
3
−
64
31
a
2
+
128
31
au +
92
31
u
2
+
136
31
a +
52
31
u +
94
31
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ 3u
15
+ ··· + 48u + 13
c
2
, c
7
, c
9
c
11
u
16
+ u
15
+ ··· − 6u + 1
c
3
, c
6
(u
2
+ u + 1)
8
c
4
, c
5
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
16
− 9y
15
+ ··· + 244y + 169
c
2
, c
7
, c
9
c
11
y
16
− 5y
15
+ ··· − 12y + 1
c
3
, c
6
(y
2
+ y + 1)
8
c
4
, c
5
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.403594 + 1.336030I
b = −1.31743 − 0.78795I
0.21101 − 5.47487I 1.82674 + 11.83695I
u = −0.395123 + 0.506844I
a = −0.473603 − 0.227839I
b = 0.750541 − 0.814864I
0.21101 + 2.64466I 1.82674 − 2.01946I
u = −0.395123 + 0.506844I
a = 1.71802 + 0.14148I
b = −0.302610 + 0.150019I
0.21101 + 2.64466I 1.82674 − 2.01946I
u = −0.395123 + 0.506844I
a = −0.29340 − 2.37055I
b = 0.517688 + 0.732455I
0.21101 − 5.47487I 1.82674 + 11.83695I
u = −0.395123 − 0.506844I
a = −0.403594 − 1.336030I
b = −1.31743 + 0.78795I
0.21101 + 5.47487I 1.82674 − 11.83695I
u = −0.395123 − 0.506844I
a = −0.473603 + 0.227839I
b = 0.750541 + 0.814864I
0.21101 − 2.64466I 1.82674 + 2.01946I
u = −0.395123 − 0.506844I
a = 1.71802 − 0.14148I
b = −0.302610 − 0.150019I
0.21101 − 2.64466I 1.82674 + 2.01946I
u = −0.395123 − 0.506844I
a = −0.29340 + 2.37055I
b = 0.517688 − 0.732455I
0.21101 + 5.47487I 1.82674 − 11.83695I
u = −0.10488 + 1.55249I
a = 0.640303 − 0.455342I
b = 1.85487 + 0.75978I
−6.79074 − 7.22373I −1.82674 + 9.49300I
u = −0.10488 + 1.55249I
a = −0.406825 + 1.222250I
b = −0.639763 − 1.041820I
−6.79074 − 7.22373I −1.82674 + 9.49300I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = −0.655651 + 0.264242I
b = −0.704770 + 0.147728I
−6.79074 + 0.89580I −1.82674 − 4.36340I
u = −0.10488 + 1.55249I
a = −0.125250 − 0.445499I
b = 0.341471 + 1.045610I
−6.79074 + 0.89580I −1.82674 − 4.36340I
u = −0.10488 − 1.55249I
a = 0.640303 + 0.455342I
b = 1.85487 − 0.75978I
−6.79074 + 7.22373I −1.82674 − 9.49300I
u = −0.10488 − 1.55249I
a = −0.406825 − 1.222250I
b = −0.639763 + 1.041820I
−6.79074 + 7.22373I −1.82674 − 9.49300I
u = −0.10488 − 1.55249I
a = −0.655651 − 0.264242I
b = −0.704770 − 0.147728I
−6.79074 − 0.89580I −1.82674 + 4.36340I
u = −0.10488 − 1.55249I
a = −0.125250 + 0.445499I
b = 0.341471 − 1.045610I
−6.79074 − 0.89580I −1.82674 + 4.36340I
22
V. I
u
5
=
h−u
15
+u
14
+· · ·+2b+3, −3u
15
−5u
14
+· · ·+10a−45, u
16
+11u
14
+· · ·+8u
2
+5i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
3
10
u
15
+
1
2
u
14
+ ··· +
9
10
u +
9
2
1
2
u
15
−
1
2
u
14
+ ··· +
9
2
u −
3
2
a
1
=
−0.800000u
15
− 8.30000u
13
+ ··· − 4.90000u − 1.50000
1
2
u
14
−
1
2
u
13
+ ··· −
1
2
u + 4
a
3
=
−
4
5
u
15
+
1
2
u
14
+ ··· −
59
10
u +
3
2
1
2
u
14
− u
13
+ ··· −
7
2
u + 4
a
9
=
3
10
u
15
+
33
10
u
13
+ ··· +
7
5
u +
5
2
1
2
u
15
− u
14
+ ··· + 5u − 4
a
7
=
4
5
u
15
+
83
10
u
13
+ ··· +
27
5
u + 3
1
2
u
15
−
1
2
u
14
+ ··· +
9
2
u −
3
2
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−0.300000u
15
− 3.80000u
13
+ ··· − 3.90000u + 0.500000
1
2
u
15
+
9
2
u
13
+ ··· +
3
2
u + 4
a
2
=
−0.300000u
15
− 3.80000u
13
+ ··· − 3.90000u + 0.500000
1
2
u
15
+
9
2
u
13
+ ··· +
3
2
u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
14
− 70u
12
− 261u
10
− 429u
8
− 256u
6
+ 13u
4
− 18u
2
− 47
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ 5u
14
+ 16u
12
+ 29u
10
+ 32u
8
+ 25u
6
+ 21u
4
+ 17u
2
+ 5
c
2
, c
9
u
16
+ 2u
15
+ ··· + 5u + 1
c
3
u
16
+ 6u
15
+ ··· − u + 1
c
4
, c
5
, c
10
u
16
+ 11u
14
+ 47u
12
+ 96u
10
+ 90u
8
+ 26u
6
− u
4
+ 8u
2
+ 5
c
6
u
16
− 6u
15
+ ··· + u + 1
c
7
, c
11
u
16
− 2u
15
+ ··· − 5u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
8
+ 5y
7
+ 16y
6
+ 29y
5
+ 32y
4
+ 25y
3
+ 21y
2
+ 17y + 5)
2
c
2
, c
7
, c
9
c
11
y
16
− 6y
15
+ ··· − 3y + 1
c
3
, c
6
y
16
+ 2y
15
+ ··· − 9y + 1
c
4
, c
5
, c
10
(y
8
+ 11y
7
+ 47y
6
+ 96y
5
+ 90y
4
+ 26y
3
− y
2
+ 8y + 5)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.061345 + 0.846216I
a = 0.269977 + 0.738240I
b = −0.608149 + 0.273746I
−1.34598 + 4.15746I −5.62925 − 7.50254I
u = 0.061345 − 0.846216I
a = 0.269977 − 0.738240I
b = −0.608149 − 0.273746I
−1.34598 − 4.15746I −5.62925 + 7.50254I
u = −0.061345 + 0.846216I
a = 0.74103 − 1.31833I
b = 1.070140 + 0.707942I
−1.34598 − 4.15746I −5.62925 + 7.50254I
u = −0.061345 − 0.846216I
a = 0.74103 + 1.31833I
b = 1.070140 − 0.707942I
−1.34598 + 4.15746I −5.62925 − 7.50254I
u = 0.628232 + 0.289290I
a = −0.634558 − 0.611524I
b = −0.221742 − 0.567751I
−2.66853 + 4.46324I −5.70149 − 4.65131I
u = 0.628232 − 0.289290I
a = −0.634558 + 0.611524I
b = −0.221742 + 0.567751I
−2.66853 − 4.46324I −5.70149 + 4.65131I
u = −0.628232 + 0.289290I
a = −0.91910 − 1.42941I
b = 0.990925 + 0.632113I
−2.66853 − 4.46324I −5.70149 + 4.65131I
u = −0.628232 − 0.289290I
a = −0.91910 + 1.42941I
b = 0.990925 − 0.632113I
−2.66853 + 4.46324I −5.70149 − 4.65131I
u = 1.54123I
a = −0.322714 + 0.635595I
b = −0.979599 − 0.497378I
−8.98222 −7.40510
u = − 1.54123I
a = −0.322714 − 0.635595I
b = −0.979599 + 0.497378I
−8.98222 −7.40510
26
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11611 + 1.54836I
a = 0.610395 − 0.450323I
b = 0.768136 + 0.892821I
−9.31190 + 6.71368I −4.58299 − 3.37058I
u = 0.11611 − 1.54836I
a = 0.610395 + 0.450323I
b = 0.768136 − 0.892821I
−9.31190 − 6.71368I −4.58299 + 3.37058I
u = −0.11611 + 1.54836I
a = −0.537297 + 0.905219I
b = −1.33922 − 0.93704I
−9.31190 − 6.71368I −4.58299 + 3.37058I
u = −0.11611 − 1.54836I
a = −0.537297 − 0.905219I
b = −1.33922 + 0.93704I
−9.31190 + 6.71368I −4.58299 − 3.37058I
u = 1.74759I
a = −0.207724 + 0.389388I
b = −0.680492 − 0.363016I
−8.77819 −7.76740
u = − 1.74759I
a = −0.207724 − 0.389388I
b = −0.680492 + 0.363016I
−8.77819 −7.76740
27
VI. I
u
6
=
h−u
3
−au−u
2
+b−2u−1, −u
3
a−u
3
+a
2
−2au−2u+1, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
a
u
3
+ au + u
2
+ 2u + 1
a
1
=
u
3
a + u
2
a + u
3
+ 2au + u
2
+ a + 3u + 1
−1
a
3
=
u
3
a + u
2
a + u
3
+ 2au + u
2
+ a + 3u + 2
−1
a
9
=
u
3
+ au + a + 2u
au
a
7
=
u
3
+ au + u
2
+ a + 2u + 1
u
3
+ au + u
2
+ 2u + 1
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
2
=
u
2
a + u
3
+ au + u
2
+ a + 2u + 1
u
2
a + au + a − u − 1
a
2
=
u
2
a + u
3
+ au + u
2
+ a + 2u + 1
u
2
a + au + a − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u
2
+ 12u − 6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
4
− u
3
+ u
2
+ 1)
2
c
2
, c
7
, c
9
c
11
u
8
− u
7
− 2u
6
+ 4u
5
+ 9u
4
− u
3
− 7u
2
− u + 2
c
3
, c
6
(u + 1)
8
c
4
, c
5
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
2
, c
7
, c
9
c
11
y
8
− 5y
7
+ 30y
6
− 68y
5
+ 119y
4
− 127y
3
+ 83y
2
− 29y + 4
c
3
, c
6
(y −1)
8
c
4
, c
5
, c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.570974 − 0.808855I
b = 0.987376 + 0.750545I
−3.07886 − 1.41510I −10.17326 + 4.90874I
u = −0.395123 + 0.506844I
a = 0.02355 + 1.92973I
b = −0.635568 − 0.030203I
−3.07886 − 1.41510I −10.17326 + 4.90874I
u = −0.395123 − 0.506844I
a = −0.570974 + 0.808855I
b = 0.987376 − 0.750545I
−3.07886 + 1.41510I −10.17326 − 4.90874I
u = −0.395123 − 0.506844I
a = 0.02355 − 1.92973I
b = −0.635568 + 0.030203I
−3.07886 + 1.41510I −10.17326 − 4.90874I
u = −0.10488 + 1.55249I
a = 0.729106 − 1.111840I
b = 0.797853 + 0.337246I
−10.08060 − 3.16396I −13.82674 + 2.56480I
u = −0.10488 + 1.55249I
a = −0.181683 + 0.526191I
b = −1.64966 − 1.24854I
−10.08060 − 3.16396I −13.82674 + 2.56480I
u = −0.10488 − 1.55249I
a = 0.729106 + 1.111840I
b = 0.797853 − 0.337246I
−10.08060 + 3.16396I −13.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = −0.181683 − 0.526191I
b = −1.64966 + 1.24854I
−10.08060 + 3.16396I −13.82674 − 2.56480I
31
VII. I
u
7
= hu
3
− u
2
+ b + 2u − 1, −u
3
+ a − 2u, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
u
3
+ 2u
−u
3
+ u
2
− 2u + 1
a
1
=
1
0
a
3
=
1
0
a
9
=
u
2
+ 1
−u
3
+ u
2
− 2u + 1
a
7
=
u
2
+ 1
−u
3
+ u
2
− 2u + 1
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
3
+ u
2
− 2u + 1
a
2
=
u
u
a
2
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 12u + 6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
9
, c
11
u
4
− u
3
+ u
2
+ 1
c
3
, c
6
u
4
c
4
, c
5
, c
10
u
4
− u
3
+ 3u
2
− 2u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
9
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
, c
6
y
4
c
4
, c
5
, c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.547424 + 1.120870I
b = 0.351808 − 0.720342I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = 0.547424 − 1.120870I
b = 0.351808 + 0.720342I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = −0.547424 − 0.585652I
b = −0.851808 + 0.911292I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = −0.547424 + 0.585652I
b = −0.851808 − 0.911292I
−6.79074 − 3.16396I −1.82674 + 2.56480I
35
VIII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
−1
0
a
5
=
1
0
a
8
=
0
1
a
1
=
−1
−1
a
3
=
0
−1
a
9
=
0
1
a
7
=
1
1
a
10
=
−1
0
a
6
=
1
0
a
2
=
−1
−1
a
2
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
10
u
c
2
, c
6
, c
9
u − 1
c
3
, c
7
, c
11
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
10
y
c
2
, c
3
, c
6
c
7
, c
9
, c
11
y −1
38
(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
39
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u(u
4
− u
3
+ u
2
+ 1)
3
(u
7
+ u
5
+ u
4
− u − 1)
2
· (u
10
+ u
9
+ 7u
8
+ 4u
7
+ 23u
6
+ 9u
5
+ 40u
4
+ 9u
3
+ 33u
2
+ 2u + 10)
· (u
16
+ 5u
14
+ 16u
12
+ 29u
10
+ 32u
8
+ 25u
6
+ 21u
4
+ 17u
2
+ 5)
· ((u
16
− u
15
+ ··· − 24u + 79)
2
)(u
16
+ 3u
15
+ ··· + 48u + 13)
c
2
, c
9
(u − 1)(u
4
− u
3
+ u
2
+ 1)(u
8
− u
7
+ ··· − u + 2)
· (u
10
+ u
9
+ ··· − u + 1)(u
14
+ u
13
+ ··· + u + 1)
· (u
16
+ u
15
+ ··· − 6u + 1)(u
16
+ 2u
15
+ ··· + 5u + 1)
· (u
32
− u
31
+ ··· + 400u + 361)
c
3
u
4
(u + 1)
9
(u
2
+ u + 1)
8
(u
4
+ u
3
− 2u + 1)
8
· (u
10
− 9u
9
+ ··· − 15u + 11)(u
14
− 13u
13
+ ··· − 329u + 47)
· (u
16
+ 6u
15
+ ··· − u + 1)
c
4
, c
5
, c
10
u(u
4
− u
3
+ 3u
2
− 2u + 1)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
14
· (u
7
− 4u
6
+ 11u
5
− 20u
4
+ 26u
3
− 23u
2
+ 14u − 4)
2
· (u
10
− 6u
9
+ ··· − 40u + 8)
· (u
16
+ 11u
14
+ 47u
12
+ 96u
10
+ 90u
8
+ 26u
6
− u
4
+ 8u
2
+ 5)
c
6
u
4
(u − 1)(u + 1)
8
(u
2
+ u + 1)
8
(u
4
+ u
3
− 2u + 1)
8
· (u
10
− 9u
9
+ ··· − 15u + 11)(u
14
− 13u
13
+ ··· − 329u + 47)
· (u
16
− 6u
15
+ ··· + u + 1)
c
7
, c
11
(u + 1)(u
4
− u
3
+ u
2
+ 1)(u
8
− u
7
+ ··· − u + 2)
· (u
10
+ u
9
+ ··· − u + 1)(u
14
+ u
13
+ ··· + u + 1)
· (u
16
− 2u
15
+ ··· − 5u + 1)(u
16
+ u
15
+ ··· − 6u + 1)
· (u
32
− u
31
+ ··· + 400u + 361)
40
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
(y
7
+ 2y
6
+ y
5
− 3y
4
− 2y
3
+ 2y
2
+ y −1)
2
· (y
8
+ 5y
7
+ 16y
6
+ 29y
5
+ 32y
4
+ 25y
3
+ 21y
2
+ 17y + 5)
2
· (y
10
+ 13y
9
+ ··· + 656y + 100)(y
16
− 9y
15
+ ··· + 244y + 169)
· (y
16
+ 19y
15
+ ··· + 44612y + 6241)
2
c
2
, c
7
, c
9
c
11
(y −1)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
· (y
8
− 5y
7
+ 30y
6
− 68y
5
+ 119y
4
− 127y
3
+ 83y
2
− 29y + 4)
· (y
10
− 3y
9
+ 15y
8
− 20y
7
+ 43y
6
− 17y
5
+ 12y
4
+ 7y
3
− 6y
2
− y + 1)
· (y
14
− 5y
13
+ ··· + y + 1)(y
16
− 6y
15
+ ··· − 3y + 1)
· (y
16
− 5y
15
+ ··· − 12y + 1)(y
32
− 11y
31
+ ··· − 2524550y + 130321)
c
3
, c
6
y
4
(y −1)
9
(y
2
+ y + 1)
8
(y
4
− y
3
+ 6y
2
− 4y + 1)
8
· (y
10
+ 3y
9
+ ··· + 1601y + 121)(y
14
− 3y
13
+ ··· + 2397y + 2209)
· (y
16
+ 2y
15
+ ··· − 9y + 1)
c
4
, c
5
, c
10
y(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
15
· (y
7
+ 6y
6
+ 13y
5
+ 16y
4
+ 32y
3
+ 39y
2
+ 12y −16)
2
· (y
8
+ 11y
7
+ 47y
6
+ 96y
5
+ 90y
4
+ 26y
3
− y
2
+ 8y + 5)
2
· (y
10
+ 10y
9
+ ··· + 160y + 64)
41
