12n
0543
(K12n
0543
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 10 4 12 6 8 3 9
Solving Sequence
8,10 4,11
3 12 7 6 2 1 5 9
c
10
c
3
c
11
c
7
c
6
c
2
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7700u
17
+ 5343u
16
+ ··· + 94946b − 375396,
− 208501u
17
− 1574159u
16
+ ··· + 189892a − 47374, u
18
+ 9u
17
+ ··· − 32u − 8i
I
u
2
= h2u
15
− 8u
14
+ ··· + 4b − 3, −3u
15
a − u
15
+ ··· + 4a − 5,
u
16
− 5u
15
+ 13u
14
− 20u
13
+ 20u
12
− 13u
11
+ 7u
10
− 4u
9
+ 5u
8
− 6u
7
+ 7u
6
+ u
5
+ u
3
+ 2u
2
− 2u + 1i
I
u
3
= hu
5
− u
4
+ 4u
2
+ b − 3u + 1, u
6
+ 4u
3
+ u
2
+ a + u, u
7
− 2u
6
+ 2u
5
+ 3u
4
− 7u
3
+ 7u
2
− 4u + 1i
I
u
4
= hu
2
+ b − 1, −u
2
+ a + u, u
4
− u
2
+ 1i
I
u
5
= hu
2
+ b − 2u, −u
3
+ 3u
2
+ a − 2u − 1, u
4
− 4u
3
+ 5u
2
− 2u + 1i
I
u
6
= h−u
3
+ b + 1, u
2
+ a, u
4
− u
2
+ 1i
* 6 irreducible components of dim
C
= 0, with total 69 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−7700u
17
+ 5343u
16
+ · · · + 94946b − 375396, −2.09 × 10
5
u
17
−
1.57 × 10
6
u
16
+ · · · + 1.90 × 10
5
a − 4.74 × 10
4
, u
18
+ 9u
17
+ · · · − 32u − 8i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
1.09800u
17
+ 8.28976u
16
+ ··· − 15.7165u + 0.249479
0.0810987u
17
− 0.0562741u
16
+ ··· + 6.78168u + 3.95378
a
11
=
1
−u
2
a
3
=
−0.494223u
17
− 4.52911u
16
+ ··· + 19.6689u + 9.03346
0.806058u
17
+ 7.39600u
16
+ ··· − 28.8365u − 8.13519
a
12
=
−1.22543u
17
− 10.2441u
16
+ ··· + 36.7104u + 11.2034
−0.156958u
17
− 1.34093u
16
+ ··· + 11.8068u + 6.16152
a
7
=
1.55492u
17
+ 13.6648u
16
+ ··· − 63.8250u − 22.6427
0.784725u
17
+ 6.89000u
16
+ ··· − 28.0103u − 9.80343
a
6
=
0.770190u
17
+ 6.77476u
16
+ ··· − 35.8147u − 12.8393
0.784725u
17
+ 6.89000u
16
+ ··· − 28.0103u − 9.80343
a
2
=
0.290215u
17
+ 2.16110u
16
+ ··· + 2.43279u + 1.45741
−0.157274u
17
− 1.91408u
16
+ ··· + 16.4252u + 6.18248
a
1
=
2.34412u
17
+ 18.5078u
16
+ ··· − 50.0957u − 13.4097
−1.64756u
17
− 13.1645u
16
+ ··· + 21.7849u + 2.78798
a
5
=
2.10179u
17
+ 17.6337u
16
+ ··· − 59.4695u − 17.2935
−0.157274u
17
− 1.91408u
16
+ ··· + 16.4252u + 6.18248
a
9
=
0.321980u
17
+ 2.64919u
16
+ ··· − 15.1353u − 5.98303
−0.248631u
17
− 1.59965u
16
+ ··· + 4.32034u + 2.57584
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
296580
47473
u
17
−
2538267
47473
u
16
+ ··· +
10665772
47473
u +
3817158
47473
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 13u
17
+ ··· + 12928u + 256
c
2
, c
5
u
18
+ 11u
17
+ ··· − 32u + 16
c
3
, c
4
, c
7
c
11
u
18
+ u
17
+ ··· − 6u + 1
c
6
, c
8
, c
9
c
12
u
18
+ u
17
+ ··· − 3u − 1
c
10
u
18
+ 9u
17
+ ··· − 32u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 25y
17
+ ··· − 151904256y + 65536
c
2
, c
5
y
18
− 13y
17
+ ··· − 12928y + 256
c
3
, c
4
, c
7
c
11
y
18
+ 17y
17
+ ··· − 14y + 1
c
6
, c
8
, c
9
c
12
y
18
+ 3y
17
+ ··· − y + 1
c
10
y
18
− 5y
17
+ ··· − 416y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620829 + 0.451049I
a = −1.057030 − 0.908608I
b = −0.364836 − 0.513954I
−4.27022 − 1.76048I 4.57169 + 3.79716I
u = −0.620829 − 0.451049I
a = −1.057030 + 0.908608I
b = −0.364836 + 0.513954I
−4.27022 + 1.76048I 4.57169 − 3.79716I
u = 0.299337 + 0.584940I
a = −1.029310 − 0.829653I
b = −0.727675 + 1.001360I
−1.45016 + 2.06579I −1.19192 − 3.00311I
u = 0.299337 − 0.584940I
a = −1.029310 + 0.829653I
b = −0.727675 − 1.001360I
−1.45016 − 2.06579I −1.19192 + 3.00311I
u = −0.550550 + 0.319324I
a = 1.76918 − 0.57363I
b = 0.636691 − 0.143319I
0.60964 − 2.63332I 1.40533 + 10.85901I
u = −0.550550 − 0.319324I
a = 1.76918 + 0.57363I
b = 0.636691 + 0.143319I
0.60964 + 2.63332I 1.40533 − 10.85901I
u = 1.39562 + 0.46679I
a = 0.039259 + 0.359476I
b = 0.513460 − 1.193020I
1.25038 + 1.91482I 14.6915 − 3.0336I
u = 1.39562 − 0.46679I
a = 0.039259 − 0.359476I
b = 0.513460 + 1.193020I
1.25038 − 1.91482I 14.6915 + 3.0336I
u = −1.50565
a = 0.258519
b = −0.196820
7.31535 30.1030
u = 0.460925
a = −0.513715
b = 0.345924
0.812221 12.1610
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.99486 + 1.19077I
a = −0.774071 + 0.517855I
b = −1.71185 − 0.17534I
−7.59215 − 0.44788I 1.54300 − 0.72825I
u = −0.99486 − 1.19077I
a = −0.774071 − 0.517855I
b = −1.71185 + 0.17534I
−7.59215 + 0.44788I 1.54300 + 0.72825I
u = −1.13905 + 1.08250I
a = 0.869148 − 0.562899I
b = 1.65960 + 0.63204I
−7.10236 − 7.75507I 1.99474 + 5.37139I
u = −1.13905 − 1.08250I
a = 0.869148 + 0.562899I
b = 1.65960 − 0.63204I
−7.10236 + 7.75507I 1.99474 − 5.37139I
u = −1.13411 + 1.20889I
a = −0.943992 + 0.426963I
b = −1.89059 − 0.88824I
−14.6094 − 14.6374I 2.41427 + 6.49796I
u = −1.13411 − 1.20889I
a = −0.943992 − 0.426963I
b = −1.89059 + 0.88824I
−14.6094 + 14.6374I 2.41427 − 6.49796I
u = −1.23320 + 1.28187I
a = 0.504423 − 0.599474I
b = 1.81064 + 0.13552I
−14.4902 + 5.6411I 1.43945 − 2.69512I
u = −1.23320 − 1.28187I
a = 0.504423 + 0.599474I
b = 1.81064 − 0.13552I
−14.4902 − 5.6411I 1.43945 + 2.69512I
6
II. I
u
2
=
h2u
15
−8u
14
+· · ·+4b −3, −3u
15
a−u
15
+· · ·+4a −5, u
16
−5u
15
+· · ·−2u +1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
a
−
1
2
u
15
+ 2u
14
+ ··· −
1
2
u +
3
4
a
11
=
1
−u
2
a
3
=
1
2
u
15
− 2u
14
+ ··· + a −
3
4
−
1
2
u
15
+
9
4
u
14
+ ··· − u +
5
4
a
12
=
−
1
2
u
15
a −
7
4
u
15
+ ··· +
1
2
a + 2
1
4
u
15
a +
3
4
u
15
+ ··· −
1
2
a − 1
a
7
=
−
1
2
u
15
a − u
15
+ ··· +
3
4
a +
1
4
−
1
4
u
14
a −
3
4
u
15
+ ··· −
1
2
a +
1
4
a
6
=
−
1
2
u
15
a −
1
4
u
15
+ ··· +
5
4
a −
3
2
u
−
1
4
u
14
a −
3
4
u
15
+ ··· −
1
2
a +
1
4
a
2
=
−
1
4
u
15
a + u
15
+ ··· +
3
4
a − 1
1
4
u
14
a −
3
4
u
15
+ ··· +
1
4
a +
5
4
a
1
=
−
1
2
u
15
a +
5
4
u
15
+ ··· +
1
2
a −
3
2
1
2
u
14
a − u
15
+ ··· +
1
2
a +
3
2
a
5
=
−
3
4
u
15
a −
1
2
u
15
+ ··· +
7
4
a +
3
4
−
1
4
u
14
a −
1
4
u
15
+ ··· −
1
4
a +
1
2
a
9
=
−
1
4
u
15
a − u
15
+ ··· + a +
1
2
−
1
4
u
12
a −
1
4
u
12
+ ··· −
1
4
a −
1
4
(ii) Obstruction class = −1
(iii) Cusp Shap es = −2u
15
+ 10u
14
− 24u
13
+ 30u
12
− 14u
11
− 14u
10
+ 26u
9
− 18u
8
+
4u
7
+ 4u
6
− 4u
5
− 14u
4
+ 14u
3
− 6u + 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 22u
15
+ ··· − 46u + 1)
2
c
2
, c
5
(u
16
− 4u
15
+ ··· − 2u + 1)
2
c
3
, c
4
, c
7
c
11
u
32
+ 3u
31
+ ··· + 310u + 25
c
6
, c
8
, c
9
c
12
u
32
− u
31
+ ··· − 160u + 31
c
10
(u
16
− 5u
15
+ ··· − 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 50y
15
+ ··· − 1390y + 1)
2
c
2
, c
5
(y
16
− 22y
15
+ ··· + 46y + 1)
2
c
3
, c
4
, c
7
c
11
y
32
+ 33y
31
+ ··· − 34950y + 625
c
6
, c
8
, c
9
c
12
y
32
+ y
31
+ ··· + 7570y + 961
c
10
(y
16
+ y
15
+ ··· + 8y
2
+ 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.078548 + 0.995560I
a = 1.54698 − 0.54298I
b = 1.44017 − 0.27086I
−9.80009 + 4.24253I −0.116479 − 1.317997I
u = −0.078548 + 0.995560I
a = −0.035239 − 0.166444I
b = −0.42773 − 1.75221I
−9.80009 + 4.24253I −0.116479 − 1.317997I
u = −0.078548 − 0.995560I
a = 1.54698 + 0.54298I
b = 1.44017 + 0.27086I
−9.80009 − 4.24253I −0.116479 + 1.317997I
u = −0.078548 − 0.995560I
a = −0.035239 + 0.166444I
b = −0.42773 + 1.75221I
−9.80009 − 4.24253I −0.116479 + 1.317997I
u = −0.618832 + 0.582672I
a = −1.45203 + 0.63357I
b = −2.01398 − 0.36399I
−7.78284 − 7.28600I 5.19770 + 8.47550I
u = −0.618832 + 0.582672I
a = −1.96094 − 0.69795I
b = 0.059119 − 0.145681I
−7.78284 − 7.28600I 5.19770 + 8.47550I
u = −0.618832 − 0.582672I
a = −1.45203 − 0.63357I
b = −2.01398 + 0.36399I
−7.78284 + 7.28600I 5.19770 − 8.47550I
u = −0.618832 − 0.582672I
a = −1.96094 + 0.69795I
b = 0.059119 + 0.145681I
−7.78284 + 7.28600I 5.19770 − 8.47550I
u = 0.200052 + 0.779501I
a = −0.253970 − 0.886241I
b = −0.295454 + 0.605750I
−1.79763 + 1.95154I 0.19509 − 4.92419I
u = 0.200052 + 0.779501I
a = −1.277830 − 0.167455I
b = −1.41755 + 0.67875I
−1.79763 + 1.95154I 0.19509 − 4.92419I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200052 − 0.779501I
a = −0.253970 + 0.886241I
b = −0.295454 − 0.605750I
−1.79763 − 1.95154I 0.19509 + 4.92419I
u = 0.200052 − 0.779501I
a = −1.277830 + 0.167455I
b = −1.41755 − 0.67875I
−1.79763 − 1.95154I 0.19509 + 4.92419I
u = −0.707768 + 0.273164I
a = 0.773361 − 0.731696I
b = 0.540678 − 1.129560I
1.12133 − 2.90012I 15.0799 + 9.1644I
u = −0.707768 + 0.273164I
a = 1.54847 − 1.86155I
b = 0.407161 + 0.663234I
1.12133 − 2.90012I 15.0799 + 9.1644I
u = −0.707768 − 0.273164I
a = 0.773361 + 0.731696I
b = 0.540678 + 1.129560I
1.12133 + 2.90012I 15.0799 − 9.1644I
u = −0.707768 − 0.273164I
a = 1.54847 + 1.86155I
b = 0.407161 − 0.663234I
1.12133 + 2.90012I 15.0799 − 9.1644I
u = 0.450330 + 0.346781I
a = 0.81562 + 1.35279I
b = 1.246660 + 0.174676I
0.284266 + 0.252535I 7.69503 − 0.47605I
u = 0.450330 + 0.346781I
a = −1.82349 + 0.20268I
b = 0.315640 − 0.339236I
0.284266 + 0.252535I 7.69503 − 0.47605I
u = 0.450330 − 0.346781I
a = 0.81562 − 1.35279I
b = 1.246660 − 0.174676I
0.284266 − 0.252535I 7.69503 + 0.47605I
u = 0.450330 − 0.346781I
a = −1.82349 − 0.20268I
b = 0.315640 + 0.339236I
0.284266 − 0.252535I 7.69503 + 0.47605I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33361 + 0.53567I
a = −0.290025 − 0.940647I
b = −0.793311 + 0.827022I
−2.00097 + 1.60825I 1.16219 − 1.27845I
u = 1.33361 + 0.53567I
a = 0.180629 + 0.670081I
b = 0.570864 + 0.152271I
−2.00097 + 1.60825I 1.16219 − 1.27845I
u = 1.33361 − 0.53567I
a = −0.290025 + 0.940647I
b = −0.793311 − 0.827022I
−2.00097 − 1.60825I 1.16219 + 1.27845I
u = 1.33361 − 0.53567I
a = 0.180629 − 0.670081I
b = 0.570864 − 0.152271I
−2.00097 − 1.60825I 1.16219 + 1.27845I
u = 1.06623 + 1.07345I
a = −0.678241 − 0.653893I
b = −1.89910 − 0.26915I
−14.8835 + 3.9428I 1.33663 − 2.55221I
u = 1.06623 + 1.07345I
a = 1.032010 + 0.660075I
b = 1.54815 − 0.92691I
−14.8835 + 3.9428I 1.33663 − 2.55221I
u = 1.06623 − 1.07345I
a = −0.678241 + 0.653893I
b = −1.89910 + 0.26915I
−14.8835 − 3.9428I 1.33663 + 2.55221I
u = 1.06623 − 1.07345I
a = 1.032010 − 0.660075I
b = 1.54815 + 0.92691I
−14.8835 − 3.9428I 1.33663 + 2.55221I
u = 0.85493 + 1.30642I
a = −0.924256 − 0.154538I
b = −1.64201 + 0.68143I
−4.61900 + 6.08853I 1.44994 − 2.95702I
u = 0.85493 + 1.30642I
a = 0.798966 + 0.220587I
b = 1.86069 − 0.22989I
−4.61900 + 6.08853I 1.44994 − 2.95702I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.85493 − 1.30642I
a = −0.924256 + 0.154538I
b = −1.64201 − 0.68143I
−4.61900 − 6.08853I 1.44994 + 2.95702I
u = 0.85493 − 1.30642I
a = 0.798966 − 0.220587I
b = 1.86069 + 0.22989I
−4.61900 − 6.08853I 1.44994 + 2.95702I
13
III. I
u
3
= hu
5
− u
4
+ 4u
2
+ b − 3u + 1, u
6
+ 4u
3
+ u
2
+ a + u, u
7
− 2u
6
+
2u
5
+ 3u
4
− 7u
3
+ 7u
2
− 4u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
−u
6
− 4u
3
− u
2
− u
−u
5
+ u
4
− 4u
2
+ 3u − 1
a
11
=
1
−u
2
a
3
=
u
6
− 2u
5
+ u
4
+ 4u
3
− 7u
2
+ 3u − 1
−u
6
+ u
5
− u
4
− 4u
3
+ 3u
2
− 3u + 1
a
12
=
−3u
6
+ 5u
5
− 4u
4
− 11u
3
+ 18u
2
− 14u + 5
−2u
6
+ 3u
5
− 3u
4
− 7u
3
+ 10u
2
− 10u + 4
a
7
=
−5u
6
+ 8u
5
− 7u
4
− 18u
3
+ 28u
2
− 25u + 9
−u
6
+ 2u
5
− 2u
4
− 3u
3
+ 7u
2
− 7u + 3
a
6
=
−4u
6
+ 6u
5
− 5u
4
− 15u
3
+ 21u
2
− 18u + 6
−u
6
+ 2u
5
− 2u
4
− 3u
3
+ 7u
2
− 7u + 3
a
2
=
u
6
− u
4
+ 5u
3
+ u
2
− 3u + 2
u
6
− u
5
+ 4u
3
− 3u
2
a
1
=
−4u
6
+ 7u
5
− 5u
4
− 15u
3
+ 25u
2
− 16u + 5
−2u
6
+ 4u
5
− 4u
4
− 7u
3
+ 15u
2
− 14u + 5
a
5
=
−7u
6
+ 9u
5
− 6u
4
− 27u
3
+ 30u
2
− 21u + 8
−u
6
+ u
5
− 4u
3
+ 3u
2
a
9
=
−2u
6
+ 2u
5
− u
4
− 8u
3
+ 6u
2
− 3u + 1
−2u
6
+ 3u
5
− 2u
4
− 8u
3
+ 11u
2
− 7u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
6
− 6u
5
+ 3u
4
+ 33u
3
− 21u
2
+ 14u + 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− 6u
6
+ 11u
5
− 9u
4
+ 17u
3
− 21u
2
+ 7u − 1
c
2
u
7
+ 2u
6
− u
5
− u
4
+ 3u
3
− u
2
− 3u − 1
c
3
, c
7
u
7
− u
6
+ 3u
5
− 2u
4
+ 6u
3
− 5u
2
+ 6u − 1
c
4
, c
11
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 6u
3
+ 5u
2
+ 6u + 1
c
5
u
7
− 2u
6
− u
5
+ u
4
+ 3u
3
+ u
2
− 3u + 1
c
6
, c
8
u
7
− 3u
6
+ 4u
5
− 3u
4
+ u − 1
c
9
, c
12
u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u + 1
c
10
u
7
− 2u
6
+ 2u
5
+ 3u
4
− 7u
3
+ 7u
2
− 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
− 14y
6
+ 47y
5
+ 55y
4
+ 53y
3
− 221y
2
+ 7y −1
c
2
, c
5
y
7
− 6y
6
+ 11y
5
− 9y
4
+ 17y
3
− 21y
2
+ 7y −1
c
3
, c
4
, c
7
c
11
y
7
+ 5y
6
+ 17y
5
+ 34y
4
+ 50y
3
+ 43y
2
+ 26y −1
c
6
, c
8
, c
9
c
12
y
7
− y
6
− 2y
5
− 7y
4
+ 2y
3
− 6y
2
+ y −1
c
10
y
7
+ 2y
5
− 17y
4
− 5y
3
+ y
2
+ 2y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.275997 + 0.735389I
a = 1.76625 − 0.41875I
b = 1.44608 + 0.27177I
−8.98016 + 6.30105I −0.02240 − 4.97171I
u = 0.275997 − 0.735389I
a = 1.76625 + 0.41875I
b = 1.44608 − 0.27177I
−8.98016 − 6.30105I −0.02240 + 4.97171I
u = 0.596254 + 0.178118I
a = −1.53109 − 1.18504I
b = −0.457796 − 0.270377I
0.78802 + 2.21063I 7.70396 + 4.43025I
u = 0.596254 − 0.178118I
a = −1.53109 + 1.18504I
b = −0.457796 + 0.270377I
0.78802 − 2.21063I 7.70396 − 4.43025I
u = −1.55196
a = 0.122596
b = −0.485549
7.12086 −11.4550
u = 0.90373 + 1.37120I
a = −0.796458 − 0.161416I
b = −1.74551 + 0.56429I
−3.59296 + 6.79923I 8.04613 − 7.57361I
u = 0.90373 − 1.37120I
a = −0.796458 + 0.161416I
b = −1.74551 − 0.56429I
−3.59296 − 6.79923I 8.04613 + 7.57361I
17
IV. I
u
4
= hu
2
+ b − 1, −u
2
+ a + u, u
4
− u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
u
2
− u
−u
2
+ 1
a
11
=
1
−u
2
a
3
=
u
3
+ u
2
− u
−u
3
− u
2
+ u + 1
a
12
=
u
3
− u
2
− u + 1
u
a
7
=
−2u
3
+ 2u
2
+ u − 2
1
a
6
=
−2u
3
+ 2u
2
+ u − 3
1
a
2
=
−2u
3
+ 3u
2
− 1
−u
2
+ 1
a
1
=
−3u
3
+ 3u
2
− 2
u
3
+ 1
a
5
=
−u
3
+ 3u − 3
−u
3
+ 1
a
9
=
−2u
3
+ 2u
2
+ u − 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
, c
10
u
4
− u
2
+ 1
c
3
, c
11
(u
2
+ 1)
2
c
4
u
4
+ 2u
3
+ 5u
2
+ 4u + 1
c
6
(u + 1)
4
c
7
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
8
u
4
− 4u
3
+ 5u
2
− 2u + 1
c
9
(u − 1)
4
c
12
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
5
, c
10
(y
2
− y + 1)
2
c
3
, c
11
(y + 1)
4
c
4
, c
7
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
6
, c
9
(y −1)
4
c
8
, c
12
y
4
− 6y
3
+ 11y
2
+ 6y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.366025 + 0.366025I
b = 0.500000 − 0.866025I
2.02988I 6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.366025 − 0.366025I
b = 0.500000 + 0.866025I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 1.36603 − 1.36603I
b = 0.500000 + 0.866025I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 1.36603 + 1.36603I
b = 0.500000 − 0.866025I
2.02988I 6.00000 − 3.46410I
21
V. I
u
5
= hu
2
+ b − 2u, −u
3
+ 3u
2
+ a − 2u − 1, u
4
− 4u
3
+ 5u
2
− 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
u
3
− 3u
2
+ 2u + 1
−u
2
+ 2u
a
11
=
1
−u
2
a
3
=
−u + 2
2u
3
− 5u
2
+ 3u − 1
a
12
=
−u
3
+ 4u
2
− 5u + 2
−u + 1
a
7
=
−u
3
+ 4u
2
− 5u + 2
1
a
6
=
−u
3
+ 4u
2
− 5u + 1
1
a
2
=
u
3
− 4u
2
+ 4u
u
3
− 2u
2
+ u − 1
a
1
=
0
−u
a
5
=
0
−u
3
+ 2u
2
− u + 1
a
9
=
−u
3
+ 4u
2
− 5u + 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8u + 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
u
4
− u
2
+ 1
c
3
, c
4
, c
7
c
11
(u
2
+ 1)
2
c
6
, c
8
(u + 1)
4
c
9
, c
12
(u − 1)
4
c
10
u
4
− 4u
3
+ 5u
2
− 2u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
5
(y
2
− y + 1)
2
c
3
, c
4
, c
7
c
11
(y + 1)
4
c
6
, c
8
, c
9
c
12
(y −1)
4
c
10
y
4
− 6y
3
+ 11y
2
+ 6y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.133975 + 0.500000I
a = 1.86603 + 0.50000I
b = 0.500000 + 0.866025I
− 2.02988I 6.00000 + 3.46410I
u = 0.133975 − 0.500000I
a = 1.86603 − 0.50000I
b = 0.500000 − 0.866025I
2.02988I 6.00000 − 3.46410I
u = 1.86603 + 0.50000I
a = 0.133975 + 0.500000I
b = 0.500000 − 0.866025I
2.02988I 6.00000 − 3.46410I
u = 1.86603 − 0.50000I
a = 0.133975 − 0.500000I
b = 0.500000 + 0.866025I
− 2.02988I 6.00000 + 3.46410I
25
VI. I
u
6
= h−u
3
+ b + 1, u
2
+ a, u
4
− u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
4
=
−u
2
u
3
− 1
a
11
=
1
−u
2
a
3
=
−u
3
2u
3
− u
2
− u
a
12
=
−u
3
+ u
2u
3
− u
2
− 3u + 2
a
7
=
−u
3
+ u
−u
3
+ u − 1
a
6
=
1
−u
3
+ u − 1
a
2
=
−u
u
3
− 1
a
1
=
0
−u
a
5
=
0
u
2
− 1
a
9
=
−u
3
+ u
2u
3
− u
2
− 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
, c
10
u
4
− u
2
+ 1
c
3
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
4
, c
7
(u
2
+ 1)
2
c
6
u
4
− 4u
3
+ 5u
2
− 2u + 1
c
8
(u + 1)
4
c
9
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
c
11
u
4
+ 2u
3
+ 5u
2
+ 4u + 1
c
12
(u − 1)
4
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
5
, c
10
(y
2
− y + 1)
2
c
3
, c
11
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
4
, c
7
(y + 1)
4
c
6
, c
9
y
4
− 6y
3
+ 11y
2
+ 6y + 1
c
8
, c
12
(y −1)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.500000 − 0.866025I
b = −1.00000 + 1.00000I
2.02988I 6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.500000 + 0.866025I
b = −1.00000 − 1.00000I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = −0.500000 + 0.866025I
b = −1.00000 + 1.00000I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = −0.500000 − 0.866025I
b = −1.00000 − 1.00000I
2.02988I 6.00000 − 3.46410I
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
(u
7
− 6u
6
+ 11u
5
− 9u
4
+ 17u
3
− 21u
2
+ 7u − 1)
· ((u
16
+ 22u
15
+ ··· − 46u + 1)
2
)(u
18
+ 13u
17
+ ··· + 12928u + 256)
c
2
(u
4
− u
2
+ 1)
3
(u
7
+ 2u
6
− u
5
− u
4
+ 3u
3
− u
2
− 3u − 1)
· ((u
16
− 4u
15
+ ··· − 2u + 1)
2
)(u
18
+ 11u
17
+ ··· − 32u + 16)
c
3
, c
7
(u
2
+ 1)
4
(u
4
− 2u
3
+ 5u
2
− 4u + 1)
· (u
7
− u
6
+ ··· + 6u − 1)(u
18
+ u
17
+ ··· − 6u + 1)
· (u
32
+ 3u
31
+ ··· + 310u + 25)
c
4
, c
11
(u
2
+ 1)
4
(u
4
+ 2u
3
+ 5u
2
+ 4u + 1)
· (u
7
+ u
6
+ ··· + 6u + 1)(u
18
+ u
17
+ ··· − 6u + 1)
· (u
32
+ 3u
31
+ ··· + 310u + 25)
c
5
(u
4
− u
2
+ 1)
3
(u
7
− 2u
6
− u
5
+ u
4
+ 3u
3
+ u
2
− 3u + 1)
· ((u
16
− 4u
15
+ ··· − 2u + 1)
2
)(u
18
+ 11u
17
+ ··· − 32u + 16)
c
6
, c
8
(u + 1)
8
(u
4
− 4u
3
+ 5u
2
− 2u + 1)(u
7
− 3u
6
+ 4u
5
− 3u
4
+ u − 1)
· (u
18
+ u
17
+ ··· − 3u − 1)(u
32
− u
31
+ ··· − 160u + 31)
c
9
, c
12
(u − 1)
8
(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)(u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u + 1)
· (u
18
+ u
17
+ ··· − 3u − 1)(u
32
− u
31
+ ··· − 160u + 31)
c
10
(u
4
− u
2
+ 1)
2
(u
4
− 4u
3
+ 5u
2
− 2u + 1)
· (u
7
− 2u
6
+ 2u
5
+ 3u
4
− 7u
3
+ 7u
2
− 4u + 1)
· ((u
16
− 5u
15
+ ··· − 2u + 1)
2
)(u
18
+ 9u
17
+ ··· − 32u − 8)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
6
(y
7
− 14y
6
+ 47y
5
+ 55y
4
+ 53y
3
− 221y
2
+ 7y −1)
· (y
16
− 50y
15
+ ··· − 1390y + 1)
2
· (y
18
− 25y
17
+ ··· − 151904256y + 65536)
c
2
, c
5
(y
2
− y + 1)
6
(y
7
− 6y
6
+ 11y
5
− 9y
4
+ 17y
3
− 21y
2
+ 7y −1)
· ((y
16
− 22y
15
+ ··· + 46y + 1)
2
)(y
18
− 13y
17
+ ··· − 12928y + 256)
c
3
, c
4
, c
7
c
11
(y + 1)
8
(y
4
+ 6y
3
+ 11y
2
− 6y + 1)
· (y
7
+ 5y
6
+ 17y
5
+ 34y
4
+ 50y
3
+ 43y
2
+ 26y −1)
· (y
18
+ 17y
17
+ ··· − 14y + 1)(y
32
+ 33y
31
+ ··· − 34950y + 625)
c
6
, c
8
, c
9
c
12
(y −1)
8
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
· (y
7
− y
6
+ ··· + y −1)(y
18
+ 3y
17
+ ··· − y + 1)
· (y
32
+ y
31
+ ··· + 7570y + 961)
c
10
(y
2
− y + 1)
4
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
· (y
7
+ 2y
5
+ ··· + 2y −1)(y
16
+ y
15
+ ··· + 8y
2
+ 1)
2
· (y
18
− 5y
17
+ ··· − 416y + 64)
31
