12n
0202
(K12n
0202
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 12 3 11 6 1 7 9
Solving Sequence
3,7 8,11
9 12 1 6 10 5 2 4
c
7
c
8
c
11
c
12
c
6
c
9
c
5
c
2
c
4
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.05235 × 10
52
u
33
+ 1.15512 × 10
53
u
32
+ ··· + 2.31768 × 10
52
b + 6.87378 × 10
54
,
− 8.21759 × 10
53
u
33
− 4.54814 × 10
54
u
32
+ ··· + 1.85414 × 10
53
a − 2.27389 × 10
56
,
u
34
+ 6u
33
+ ··· + 1504u + 128i
I
u
2
= h−185u
10
a
3
+ 209u
10
a
2
+ ··· − 1226a + 794, 6u
10
a
3
+ 37u
10
a
2
+ ··· − 398a − 413,
u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2i
I
u
3
= h26139164u
15
+ 19494102u
14
+ ··· + 39284803b + 1531021,
221512445u
15
+ 269307859u
14
+ ··· + 39284803a + 24902091,
u
16
+ u
15
− u
14
− 2u
13
− 3u
12
− 4u
11
+ 10u
10
+ 19u
9
+ 3u
8
− 20u
7
− 20u
6
+ 7u
5
+ 11u
4
+ 7u
3
+ 7u
2
+ 1i
I
u
4
= h5698393a
11
+ 73535365b + ··· + 1014170313a − 203703816,
a
12
− 4a
11
+ 6a
10
− 11a
9
+ 32a
8
− 45a
7
+ 28a
6
− 51a
5
+ 143a
4
− 191a
3
+ 132a
2
− 40a + 7, u − 1i
I
v
1
= ha, −8v
2
+ b + 26v −7, 4v
3
− 14v
2
+ 7v −1i
I
v
2
= ha, b
4
− b
3
+ 2b
2
− 2b + 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 113 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
= h2.05 × 10
52
u
33
+ 1.16 × 10
53
u
32
+ · · · + 2.32 × 10
52
b + 6.87 ×
10
54
, −8.22 × 10
53
u
33
− 4.55 × 10
54
u
32
+ · · · + 1.85 × 10
53
a − 2.27 ×
10
56
, u
34
+ 6u
33
+ · · · + 1504u + 128i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
4.43202u
33
+ 24.5296u
32
+ ··· + 11740.1u + 1226.38
−0.885519u
33
− 4.98395u
32
+ ··· − 2726.35u − 296.581
a
9
=
3.82928u
33
+ 21.1964u
32
+ ··· + 10122.3u + 1055.68
1.77988u
33
+ 9.85723u
32
+ ··· + 4665.13u + 481.509
a
12
=
3.54650u
33
+ 19.5456u
32
+ ··· + 9013.77u + 929.804
−0.885519u
33
− 4.98395u
32
+ ··· − 2726.35u − 296.581
a
1
=
1.06307u
33
+ 5.93274u
32
+ ··· + 3043.91u + 325.793
−2.44641u
33
− 13.4720u
32
+ ··· − 6083.54u − 619.031
a
6
=
−0.691837u
33
− 3.82621u
32
+ ··· − 1770.73u − 179.020
−2.07724u
33
− 11.4986u
32
+ ··· − 5450.40u − 563.433
a
10
=
4.16237u
33
+ 23.1776u
32
+ ··· + 11626.0u + 1231.40
1.99898u
33
+ 11.2399u
32
+ ··· + 6044.47u + 650.417
a
5
=
3.32446u
33
+ 18.3671u
32
+ ··· + 8593.18u + 887.775
2.26139u
33
+ 12.4344u
32
+ ··· + 5549.28u + 561.982
a
2
=
1.06307u
33
+ 5.93274u
32
+ ··· + 3043.91u + 325.793
−2.26139u
33
− 12.4344u
32
+ ··· − 5549.28u − 561.982
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14.4745u
33
− 80.2243u
32
+ ··· − 38793.6u − 4044.27
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 19u
33
+ ··· + 32880u + 256
c
2
, c
4
u
34
− 5u
33
+ ··· + 204u − 16
c
3
, c
7
u
34
− 6u
33
+ ··· − 1504u + 128
c
5
, c
6
, c
9
c
11
u
34
+ 12u
32
+ ··· − u − 1
c
8
, c
10
u
34
− 8u
32
+ ··· + 11u + 1
c
12
u
34
− 29u
33
+ ··· − 229376u + 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 3y
33
+ ··· − 959098624y + 65536
c
2
, c
4
y
34
− 19y
33
+ ··· − 32880y + 256
c
3
, c
7
y
34
− 12y
33
+ ··· − 388096y + 16384
c
5
, c
6
, c
9
c
11
y
34
+ 24y
33
+ ··· − y + 1
c
8
, c
10
y
34
− 16y
33
+ ··· − 37y + 1
c
12
y
34
+ 15y
33
+ ··· − 536870912y + 268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.090643 + 0.777275I
a = 0.932410 + 0.812112I
b = −0.511224 + 0.237290I
0.71635 + 1.25840I 9.52850 + 1.65312I
u = −0.090643 − 0.777275I
a = 0.932410 − 0.812112I
b = −0.511224 − 0.237290I
0.71635 − 1.25840I 9.52850 − 1.65312I
u = 0.306658 + 0.718173I
a = 0.662294 − 0.462387I
b = 0.195615 − 0.391603I
−1.69600 − 0.85978I −1.64649 + 1.83237I
u = 0.306658 − 0.718173I
a = 0.662294 + 0.462387I
b = 0.195615 + 0.391603I
−1.69600 + 0.85978I −1.64649 − 1.83237I
u = 1.292730 + 0.093074I
a = −1.291070 + 0.061590I
b = 0.761362 − 0.484380I
5.59278 + 0.13916I 9.58742 + 2.45732I
u = 1.292730 − 0.093074I
a = −1.291070 − 0.061590I
b = 0.761362 + 0.484380I
5.59278 − 0.13916I 9.58742 − 2.45732I
u = −0.871052 + 0.990780I
a = −0.406604 − 0.666697I
b = −0.072976 − 0.925253I
−1.67974 + 1.56924I 0. − 1.70901I
u = −0.871052 − 0.990780I
a = −0.406604 + 0.666697I
b = −0.072976 + 0.925253I
−1.67974 − 1.56924I 0. + 1.70901I
u = −1.288240 + 0.420045I
a = −1.135880 − 0.354651I
b = 0.894899 + 0.322623I
4.57328 − 5.79683I 6.00000 + 4.29308I
u = −1.288240 − 0.420045I
a = −1.135880 + 0.354651I
b = 0.894899 − 0.322623I
4.57328 + 5.79683I 6.00000 − 4.29308I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.304100 + 0.388118I
a = 1.251970 − 0.492836I
b = −0.510913 + 1.267090I
−6.83462 − 7.06965I 0. + 6.15439I
u = −1.304100 − 0.388118I
a = 1.251970 + 0.492836I
b = −0.510913 − 1.267090I
−6.83462 + 7.06965I 0. − 6.15439I
u = −1.359360 + 0.205447I
a = 0.692011 + 0.175208I
b = −0.778312 − 0.579500I
3.00226 − 0.76687I 6.00000 + 0.I
u = −1.359360 − 0.205447I
a = 0.692011 − 0.175208I
b = −0.778312 + 0.579500I
3.00226 + 0.76687I 6.00000 + 0.I
u = 1.154680 + 0.767394I
a = −0.894645 + 0.517297I
b = 0.262146 + 0.969895I
2.68203 + 3.10270I 6.00000 + 0.I
u = 1.154680 − 0.767394I
a = −0.894645 − 0.517297I
b = 0.262146 − 0.969895I
2.68203 − 3.10270I 6.00000 + 0.I
u = −0.510540 + 1.313970I
a = −0.051694 + 0.350554I
b = 0.55842 + 1.32975I
−5.67028 + 10.25340I 0. − 7.14529I
u = −0.510540 − 1.313970I
a = −0.051694 − 0.350554I
b = 0.55842 − 1.32975I
−5.67028 − 10.25340I 0. + 7.14529I
u = 0.286604 + 1.384360I
a = −0.024163 − 0.361453I
b = 0.503949 − 1.158680I
−4.18172 − 4.31448I 0
u = 0.286604 − 1.384360I
a = −0.024163 + 0.361453I
b = 0.503949 + 1.158680I
−4.18172 + 4.31448I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20850 + 0.89083I
a = −0.923171 − 0.397480I
b = 0.237804 − 1.150510I
−0.57232 − 8.89823I 0
u = −1.20850 − 0.89083I
a = −0.923171 + 0.397480I
b = 0.237804 + 1.150510I
−0.57232 + 8.89823I 0
u = 1.52570 + 0.09137I
a = 0.736791 + 0.196904I
b = −0.716836 − 0.876660I
3.16512 + 5.42087I 0
u = 1.52570 − 0.09137I
a = 0.736791 − 0.196904I
b = −0.716836 + 0.876660I
3.16512 − 5.42087I 0
u = −0.463998
a = −5.35214
b = 0.401353
−0.541158 31.3900
u = −1.32019 + 0.79594I
a = 1.40106 + 0.21908I
b = −0.61404 + 1.47259I
−2.9964 − 17.7107I 0
u = −1.32019 − 0.79594I
a = 1.40106 − 0.21908I
b = −0.61404 − 1.47259I
−2.9964 + 17.7107I 0
u = −0.448045 + 0.057573I
a = −0.050536 + 0.333276I
b = 0.22589 + 1.49925I
−10.84120 + 5.04921I 15.4774 + 2.0506I
u = −0.448045 − 0.057573I
a = −0.050536 − 0.333276I
b = 0.22589 − 1.49925I
−10.84120 − 5.04921I 15.4774 − 2.0506I
u = 1.40945 + 0.64929I
a = 1.283140 − 0.005753I
b = −0.63967 − 1.38569I
−0.33266 + 11.43620I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40945 − 0.64929I
a = 1.283140 + 0.005753I
b = −0.63967 + 1.38569I
−0.33266 − 11.43620I 0
u = −0.19301 + 1.65922I
a = 0.049963 + 0.259298I
b = 0.220997 + 0.996367I
−12.14010 + 0.90472I 0
u = −0.19301 − 1.65922I
a = 0.049963 − 0.259298I
b = 0.220997 − 0.996367I
−12.14010 − 0.90472I 0
u = −0.300279
a = 1.01338
b = −0.435581
0.684542 14.6620
8
II. I
u
2
= h−185u
10
a
3
+ 209u
10
a
2
+ · · · − 1226a + 794, 6u
10
a
3
+ 37u
10
a
2
+
· · · − 398a − 413, u
11
+ 2u
10
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
a
0.690299a
3
u
10
− 0.779851a
2
u
10
+ ··· + 4.57463a − 2.96269
a
9
=
−0.470149a
3
u
10
+ 0.279851a
2
u
10
+ ··· − 3.03731a + 0.462687
0.0298507a
2
u
10
+ 0.485075u
10
+ ··· + 0.0746269a
2
+ 0.462687
a
12
=
0.690299a
3
u
10
− 0.779851a
2
u
10
+ ··· + 5.57463a − 2.96269
0.690299a
3
u
10
− 0.779851a
2
u
10
+ ··· + 4.57463a − 2.96269
a
1
=
1
2
u
10
+
3
4
u
9
+ ··· +
11
4
u
2
−
3
2
1
2
u
10
+
1
2
u
9
+ ··· +
7
4
u
2
−
1
2
a
6
=
−0.100746a
3
u
10
− 0.380597a
2
u
10
+ ··· + 0.313433a + 0.850746
−0.570896a
3
u
10
− 0.100746a
2
u
10
+ ··· − 2.72388a − 0.686567
a
10
=
0.0597015a
3
u
10
− 0.220149a
2
u
10
+ ··· + 1.42537a − 3.03731
0.559701a
3
u
10
− 0.970149a
2
u
10
+ ··· + 5.42537a − 4.03731
a
5
=
−
1
4
u
10
+
3
4
u
8
+ ··· −
1
2
u −
1
2
−
3
4
u
10
−
3
4
u
9
+ ··· −
1
2
u + 1
a
2
=
1
2
u
10
+
3
4
u
9
+ ··· +
11
4
u
2
−
3
2
3
4
u
10
+
3
4
u
9
+ ··· +
1
2
u − 1
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
83
67
u
10
a
3
−
126
67
u
10
a
2
+ ··· +
784
67
a −
144
67
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 4u
10
+ ··· + 11u + 1)
4
c
2
, c
4
(u
11
− 2u
10
+ 4u
8
− 2u
7
− 4u
6
+ 5u
5
+ 2u
4
− 5u
3
+ u
2
+ 3u − 1)
4
c
3
, c
7
(u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2)
4
c
5
, c
6
, c
9
c
11
u
44
− 2u
43
+ ··· + 2932u + 661
c
8
, c
10
u
44
+ 10u
43
+ ··· + 1758u + 421
c
12
(u
2
+ u + 1)
22
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ 8y
10
+ ··· + 67y −1)
4
c
2
, c
4
(y
11
− 4y
10
+ ··· + 11y −1)
4
c
3
, c
7
(y
11
− 6y
10
+ ··· + 8y −4)
4
c
5
, c
6
, c
9
c
11
y
44
+ 30y
43
+ ··· + 6318180y + 436921
c
8
, c
10
y
44
− 2y
43
+ ··· − 1105128y + 177241
c
12
(y
2
+ y + 1)
22
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.217339 + 1.116860I
a = −0.009955 + 0.594446I
b = 1.080720 + 0.060619I
−1.72919 − 4.44881I 2.92816 + 6.35357I
u = 0.217339 + 1.116860I
a = 0.443379 + 0.335985I
b = −0.301589 + 1.082120I
−1.72919 − 4.44881I 2.92816 + 6.35357I
u = 0.217339 + 1.116860I
a = 0.183122 − 0.512572I
b = 0.700289 − 0.364504I
−1.72919 − 0.38904I 2.92816 − 0.57463I
u = 0.217339 + 1.116860I
a = 0.405942 − 0.327999I
b = −0.100215 − 0.881617I
−1.72919 − 0.38904I 2.92816 − 0.57463I
u = 0.217339 − 1.116860I
a = −0.009955 − 0.594446I
b = 1.080720 − 0.060619I
−1.72919 + 4.44881I 2.92816 − 6.35357I
u = 0.217339 − 1.116860I
a = 0.443379 − 0.335985I
b = −0.301589 − 1.082120I
−1.72919 + 4.44881I 2.92816 − 6.35357I
u = 0.217339 − 1.116860I
a = 0.183122 + 0.512572I
b = 0.700289 + 0.364504I
−1.72919 + 0.38904I 2.92816 + 0.57463I
u = 0.217339 − 1.116860I
a = 0.405942 + 0.327999I
b = −0.100215 + 0.881617I
−1.72919 + 0.38904I 2.92816 + 0.57463I
u = −1.116820 + 0.404951I
a = 0.367564 + 1.052860I
b = −0.088366 + 1.407570I
−4.26357 − 6.72730I 0.91876 + 9.34733I
u = −1.116820 + 0.404951I
a = −1.61003 + 0.21622I
b = 0.97212 − 1.45656I
−4.26357 − 6.72730I 0.91876 + 9.34733I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.116820 + 0.404951I
a = −0.153427 + 0.275989I
b = −0.38639 − 1.80698I
−4.26357 − 2.66753I 0.91876 + 2.41912I
u = −1.116820 + 0.404951I
a = 1.87372 + 0.16548I
b = −0.097911 + 1.066130I
−4.26357 − 2.66753I 0.91876 + 2.41912I
u = −1.116820 − 0.404951I
a = 0.367564 − 1.052860I
b = −0.088366 − 1.407570I
−4.26357 + 6.72730I 0.91876 − 9.34733I
u = −1.116820 − 0.404951I
a = −1.61003 − 0.21622I
b = 0.97212 + 1.45656I
−4.26357 + 6.72730I 0.91876 − 9.34733I
u = −1.116820 − 0.404951I
a = −0.153427 − 0.275989I
b = −0.38639 + 1.80698I
−4.26357 + 2.66753I 0.91876 − 2.41912I
u = −1.116820 − 0.404951I
a = 1.87372 − 0.16548I
b = −0.097911 − 1.066130I
−4.26357 + 2.66753I 0.91876 − 2.41912I
u = −0.323694 + 0.583510I
a = −2.18729 + 0.34333I
b = −0.58191 − 1.32255I
−6.66575 + 2.77184I −5.53927 − 4.58319I
u = −0.323694 + 0.583510I
a = −0.81002 + 2.90630I
b = −0.184279 + 1.140270I
−6.66575 − 1.28793I −5.53927 + 2.34501I
u = −0.323694 + 0.583510I
a = −4.27663 − 3.61387I
b = 0.41189 − 1.47115I
−6.66575 − 1.28793I −5.53927 + 2.34501I
u = −0.323694 + 0.583510I
a = 4.11785 + 4.41562I
b = 0.181553 + 1.290880I
−6.66575 + 2.77184I −5.53927 − 4.58319I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323694 − 0.583510I
a = −2.18729 − 0.34333I
b = −0.58191 + 1.32255I
−6.66575 − 2.77184I −5.53927 + 4.58319I
u = −0.323694 − 0.583510I
a = −0.81002 − 2.90630I
b = −0.184279 − 1.140270I
−6.66575 + 1.28793I −5.53927 − 2.34501I
u = −0.323694 − 0.583510I
a = −4.27663 + 3.61387I
b = 0.41189 + 1.47115I
−6.66575 + 1.28793I −5.53927 − 2.34501I
u = −0.323694 − 0.583510I
a = 4.11785 − 4.41562I
b = 0.181553 − 1.290880I
−6.66575 − 2.77184I −5.53927 + 4.58319I
u = −1.38823 + 0.36743I
a = 1.002740 + 0.157516I
b = −0.899581 + 0.768683I
3.68097 − 0.55463I 6.19194 − 2.44750I
u = −1.38823 + 0.36743I
a = 1.150210 + 0.262394I
b = −1.349990 − 0.139533I
3.68097 − 4.61439I 6.19194 + 4.48070I
u = −1.38823 + 0.36743I
a = −1.318500 + 0.350190I
b = 0.442958 − 1.080190I
3.68097 − 4.61439I 6.19194 + 4.48070I
u = −1.38823 + 0.36743I
a = −0.388078 − 0.318066I
b = 0.296789 + 0.626688I
3.68097 − 0.55463I 6.19194 − 2.44750I
u = −1.38823 − 0.36743I
a = 1.002740 − 0.157516I
b = −0.899581 − 0.768683I
3.68097 + 0.55463I 6.19194 + 2.44750I
u = −1.38823 − 0.36743I
a = 1.150210 − 0.262394I
b = −1.349990 + 0.139533I
3.68097 + 4.61439I 6.19194 − 4.48070I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38823 − 0.36743I
a = −1.318500 − 0.350190I
b = 0.442958 + 1.080190I
3.68097 + 4.61439I 6.19194 − 4.48070I
u = −1.38823 − 0.36743I
a = −0.388078 + 0.318066I
b = 0.296789 − 0.626688I
3.68097 + 0.55463I 6.19194 + 2.44750I
u = 0.552641
a = 0.753677 + 0.114672I
b = −0.156468 + 1.382340I
−3.80862 − 2.02988I 7.42944 + 3.46410I
u = 0.552641
a = 0.753677 − 0.114672I
b = −0.156468 − 1.382340I
−3.80862 + 2.02988I 7.42944 − 3.46410I
u = 0.552641
a = 0.24741 + 1.61926I
b = 0.546490 − 0.706801I
−3.80862 − 2.02988I 7.42944 + 3.46410I
u = 0.552641
a = 0.24741 − 1.61926I
b = 0.546490 + 0.706801I
−3.80862 + 2.02988I 7.42944 − 3.46410I
u = 1.33508 + 0.61220I
a = 1.056630 − 0.199046I
b = −0.774609 − 1.057170I
1.83471 + 6.62127I 3.78570 − 2.11482I
u = 1.33508 + 0.61220I
a = 1.069070 − 0.482704I
b = −1.45883 − 0.04222I
1.83471 + 10.68100I 3.78570 − 9.04302I
u = 1.33508 + 0.61220I
a = −1.53253 − 0.02543I
b = 0.460172 + 1.181660I
1.83471 + 10.68100I 3.78570 − 9.04302I
u = 1.33508 + 0.61220I
a = −0.384837 + 0.051738I
b = 0.287156 − 0.377419I
1.83471 + 6.62127I 3.78570 − 2.11482I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33508 − 0.61220I
a = 1.056630 + 0.199046I
b = −0.774609 + 1.057170I
1.83471 − 6.62127I 3.78570 + 2.11482I
u = 1.33508 − 0.61220I
a = 1.069070 + 0.482704I
b = −1.45883 + 0.04222I
1.83471 − 10.68100I 3.78570 + 9.04302I
u = 1.33508 − 0.61220I
a = −1.53253 + 0.02543I
b = 0.460172 − 1.181660I
1.83471 − 10.68100I 3.78570 + 9.04302I
u = 1.33508 − 0.61220I
a = −0.384837 − 0.051738I
b = 0.287156 + 0.377419I
1.83471 − 6.62127I 3.78570 + 2.11482I
16
III.
I
u
3
= h2.61 × 10
7
u
15
+ 1.95 × 10
7
u
14
+ · · · + 3.93 × 10
7
b + 1.53 × 10
6
, 2.22 ×
10
8
u
15
+2.69×10
8
u
14
+· · · +3.93×10
7
a+2.49×10
7
, u
16
+u
15
+· · · +7u
2
+1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−5.63863u
15
− 6.85527u
14
+ ··· − 37.3060u − 0.633886
−0.665376u
15
− 0.496225u
14
+ ··· − 3.75673u − 0.0389723
a
9
=
4.79895u
15
+ 4.13796u
14
+ ··· + 13.0962u − 10.2774
0.824960u
15
+ 0.614372u
14
+ ··· + 2.39162u − 0.704160
a
12
=
−6.30401u
15
− 7.35149u
14
+ ··· − 41.0628u − 0.672858
−0.665376u
15
− 0.496225u
14
+ ··· − 3.75673u − 0.0389723
a
1
=
−0.839243u
15
− 0.933409u
14
+ ··· − 5.49869u − 0.251285
−0.0768567u
15
− 0.0612071u
14
+ ··· − 0.173867u − 0.263317
a
6
=
0.471243u
15
− 2.73305u
14
+ ··· − 23.9979u − 20.9855
−0.0384779u
15
− 0.360948u
14
+ ··· − 1.88190u − 2.17767
a
10
=
−6.46359u
15
− 7.46964u
14
+ ··· − 39.6977u + 1.07027
−0.665376u
15
− 0.496225u
14
+ ··· − 3.75673u − 0.0389723
a
5
=
0.698532u
15
+ 0.903889u
14
+ ··· + 6.16407u + 0.0821341
−0.140712u
15
− 0.0295202u
14
+ ··· + 0.665376u − 0.169151
a
2
=
−0.839243u
15
− 0.933409u
14
+ ··· − 5.49869u − 0.251285
−0.140712u
15
− 0.0295202u
14
+ ··· + 0.665376u − 0.169151
a
4
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
48637972
39284803
u
15
−
69376959
39284803
u
14
+ ··· −
938513428
39284803
u −
748031538
39284803
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 11u
15
+ ··· − 14u + 1
c
2
u
16
+ 5u
15
+ ··· − 2u + 1
c
3
u
16
− u
15
+ ··· + 7u
2
+ 1
c
4
u
16
− 5u
15
+ ··· + 2u + 1
c
5
, c
11
u
16
+ 8u
14
+ ··· + u + 1
c
6
, c
9
u
16
+ 8u
14
+ ··· − u + 1
c
7
u
16
+ u
15
+ ··· + 7u
2
+ 1
c
8
, c
10
u
16
+ 5u
13
+ ··· + u + 1
c
12
u
16
− u
15
+ ··· − 5u
3
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 7y
15
+ ··· + 10y + 1
c
2
, c
4
y
16
− 11y
15
+ ··· − 14y + 1
c
3
, c
7
y
16
− 3y
15
+ ··· + 14y + 1
c
5
, c
6
, c
9
c
11
y
16
+ 16y
15
+ ··· + 13y + 1
c
8
, c
10
y
16
+ 10y
14
+ ··· + 13y + 1
c
12
y
16
+ 13y
15
+ ··· + 10y
2
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.052370 + 0.093173I
a = 1.075460 + 0.282531I
b = −0.46470 − 1.41010I
−3.49545 + 0.50348I 2.71128 + 2.00573I
u = −1.052370 − 0.093173I
a = 1.075460 − 0.282531I
b = −0.46470 + 1.41010I
−3.49545 − 0.50348I 2.71128 − 2.00573I
u = −0.622840 + 0.925423I
a = 0.018270 − 0.618863I
b = −0.151940 − 0.386230I
−0.58808 + 1.31504I 8.80198 − 1.38883I
u = −0.622840 − 0.925423I
a = 0.018270 + 0.618863I
b = −0.151940 + 0.386230I
−0.58808 − 1.31504I 8.80198 + 1.38883I
u = 1.076510 + 0.354751I
a = 1.149490 − 0.358418I
b = −0.33038 − 1.49665I
−4.10605 + 5.12330I 1.79464 − 4.59761I
u = 1.076510 − 0.354751I
a = 1.149490 + 0.358418I
b = −0.33038 + 1.49665I
−4.10605 − 5.12330I 1.79464 + 4.59761I
u = 1.297280 + 0.478050I
a = −0.928035 + 0.220896I
b = 0.519486 + 0.406969I
4.10119 + 2.04067I 8.23547 − 2.43425I
u = 1.297280 − 0.478050I
a = −0.928035 − 0.220896I
b = 0.519486 − 0.406969I
4.10119 − 2.04067I 8.23547 + 2.43425I
u = −0.087688 + 0.579530I
a = −2.31031 − 0.56135I
b = −0.327826 − 1.216860I
−5.36775 + 1.79338I 0.34629 − 1.89080I
u = −0.087688 − 0.579530I
a = −2.31031 + 0.56135I
b = −0.327826 + 1.216860I
−5.36775 − 1.79338I 0.34629 + 1.89080I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34186 + 0.69442I
a = −0.913689 − 0.152365I
b = 0.598222 − 0.683791I
1.85151 − 8.07513I 3.94739 + 7.62669I
u = −1.34186 − 0.69442I
a = −0.913689 + 0.152365I
b = 0.598222 + 0.683791I
1.85151 + 8.07513I 3.94739 − 7.62669I
u = 0.12375 + 1.58034I
a = −0.122869 + 0.244108I
b = −0.182452 + 1.029730I
−12.26790 − 0.74180I −11.4456 − 12.3713I
u = 0.12375 − 1.58034I
a = −0.122869 − 0.244108I
b = −0.182452 − 1.029730I
−12.26790 + 0.74180I −11.4456 + 12.3713I
u = 0.107210 + 0.370526I
a = 6.5317 − 13.1777I
b = 0.339598 − 1.296230I
−6.44646 − 2.13169I −16.3914 − 13.4331I
u = 0.107210 − 0.370526I
a = 6.5317 + 13.1777I
b = 0.339598 + 1.296230I
−6.44646 + 2.13169I −16.3914 + 13.4331I
21
IV. I
u
4
= h7.35 × 10
7
b + 5.70 × 10
6
a
11
+ · · · + 1.01 × 10
9
a − 2.04 × 10
8
, a
12
−
4a
11
+ · · · − 40a + 7, u − 1i
(i) Arc colorings
a
3
=
0
1
a
7
=
1
0
a
8
=
1
−1
a
11
=
a
−0.0774919a
11
+ 0.375771a
10
+ ··· − 13.7916a + 2.77015
a
9
=
−0.0658035a
11
+ 0.170020a
10
+ ··· + 0.329527a + 0.457557
0.0326852a
11
− 0.0584284a
10
+ ··· − 0.529330a + 1.48093
a
12
=
−0.0774919a
11
+ 0.375771a
10
+ ··· − 12.7916a + 2.77015
−0.0774919a
11
+ 0.375771a
10
+ ··· − 13.7916a + 2.77015
a
1
=
−0.115004a
11
+ 0.357585a
10
+ ··· − 7.24169a + 1.58880
0.0276033a
11
+ 0.00213387a
10
+ ··· − 3.14469a + 1.32247
a
6
=
−0.0326852a
11
+ 0.0584284a
10
+ ··· + 0.529330a − 1.48093
−0.0984887a
11
+ 0.228448a
10
+ ··· + 0.858857a − 3.02337
a
10
=
−0.0192689a
11
+ 0.122254a
10
+ ··· − 6.49712a + 1.88818
−0.0977752a
11
+ 0.448397a
10
+ ··· − 18.3971a + 4.85808
a
5
=
−0.0276033a
11
− 0.00213387a
10
+ ··· + 3.14469a − 1.32247
0.0874004a
11
− 0.359719a
10
+ ··· + 10.3864a − 2.91127
a
2
=
−0.115004a
11
+ 0.357585a
10
+ ··· − 7.24169a + 1.58880
−0.0874004a
11
+ 0.359719a
10
+ ··· − 10.3864a + 2.91127
a
4
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
25416
329755
a
11
+
161256
329755
a
10
+ ··· −
8569836
329755
a +
3150062
329755
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 2u
2
+ u + 1)
4
c
2
, c
4
(u
3
− u + 1)
4
c
3
, c
7
(u + 1)
12
c
5
, c
6
, c
9
c
11
u
12
+ 6u
10
+ ··· − 10u + 7
c
8
, c
10
u
12
+ 4u
11
+ ··· − 4u + 1
c
12
(u
2
+ u + 1)
6
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 2y
2
− 3y − 1)
4
c
2
, c
4
(y
3
− 2y
2
+ y − 1)
4
c
3
, c
7
(y − 1)
12
c
5
, c
6
, c
9
c
11
y
12
+ 12y
11
+ ··· + 180y + 49
c
8
, c
10
y
12
+ 8y
11
+ ··· + 318y
2
+ 1
c
12
(y
2
+ y + 1)
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.645260 + 0.761399I
b = −0.18361 + 1.40431I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = 0.645260 − 0.761399I
b = −0.18361 − 1.40431I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 1.00000
a = −1.16974 + 0.94446I
b = 1.00173 − 1.11183I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = −1.16974 − 0.94446I
b = 1.00173 + 1.11183I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 1.00000
a = 1.58114 + 0.42523I
b = −0.842500 + 0.098298I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 1.00000
a = 1.58114 − 0.42523I
b = −0.842500 − 0.098298I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = 0.192943 + 0.264572I
b = −0.15305 − 1.67625I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 1.00000
a = 0.192943 − 0.264572I
b = −0.15305 + 1.67625I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = 1.54661 + 0.66329I
b = −0.002722 − 0.821490I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = 1.54661 − 0.66329I
b = −0.002722 + 0.821490I
−3.28987 + 2.02988I 4.00000 − 3.46410I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.79622 + 1.78475I
b = 0.180141 − 1.048940I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 1.00000
a = −0.79622 − 1.78475I
b = 0.180141 + 1.048940I
−3.28987 + 2.02988I 4.00000 − 3.46410I
26
V. I
v
1
= ha, −8v
2
+ b + 26v − 7, 4v
3
− 14v
2
+ 7v − 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
8v
2
− 26v + 7
a
9
=
1
−4v
2
+ 12v − 1
a
12
=
8v
2
− 26v + 7
8v
2
− 26v + 7
a
1
=
−1
−4v
2
+ 14v − 7
a
6
=
4v
2
− 12v + 2
4v
2
− 12v + 1
a
10
=
−8v
2
+ 26v − 7
−20v
2
+ 64v − 16
a
5
=
1
4v
2
− 14v + 7
a
2
=
v − 1
−4v
2
+ 14v − 7
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −45v
2
+ 150v − 53
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
10
u
3
+ 2u + 1
c
9
, c
11
u
3
+ 2u − 1
c
12
u
3
− 3u
2
+ 5u − 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
3
+ 4y
2
+ 4y − 1
c
12
y
3
+ y
2
+ 13y − 4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.283866 + 0.068399I
a = 0
b = 0.22670 − 1.46771I
−11.08570 − 5.13794I −13.8357 + 8.5124I
v = 0.283866 − 0.068399I
a = 0
b = 0.22670 + 1.46771I
−11.08570 + 5.13794I −13.8357 − 8.5124I
v = 2.93227
a = 0
b = −0.453398
−0.857735 −0.0786320
30
VI. I
v
2
= ha, b
4
− b
3
+ 2b
2
− 2b + 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
b
a
9
=
1
−b
2
a
12
=
b
b
a
1
=
b
3
+ 2b
1
a
6
=
b
2
+ 1
b
2
a
10
=
−2b
3
+ b
2
− 3b + 3
−b
3
− b + 1
a
5
=
−b
3
− 2b
−1
a
2
=
b
3
+ 2b − 1
1
a
4
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
3
− 4b
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
8
c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
9
, c
11
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
12
(u
2
+ u + 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
4
+ 3y
3
+ 2y
2
+ 1
c
12
(y
2
+ y + 1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 0.621744 + 0.440597I
−4.93480 + 2.02988I −2.00000 − 3.46410I
v = −1.00000
a = 0
b = 0.621744 − 0.440597I
−4.93480 − 2.02988I −2.00000 + 3.46410I
v = −1.00000
a = 0
b = −0.121744 + 1.306620I
−4.93480 − 2.02988I −2.00000 + 3.46410I
v = −1.00000
a = 0
b = −0.121744 − 1.306620I
−4.93480 + 2.02988I −2.00000 − 3.46410I
34
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
3
+ 2u
2
+ u + 1)
4
(u
11
+ 4u
10
+ ··· + 11u + 1)
4
· (u
16
− 11u
15
+ ··· − 14u + 1)(u
34
+ 19u
33
+ ··· + 32880u + 256)
c
2
(u − 1)
7
(u
3
− u + 1)
4
· (u
11
− 2u
10
+ 4u
8
− 2u
7
− 4u
6
+ 5u
5
+ 2u
4
− 5u
3
+ u
2
+ 3u − 1)
4
· (u
16
+ 5u
15
+ ··· − 2u + 1)(u
34
− 5u
33
+ ··· + 204u − 16)
c
3
u
7
(u + 1)
12
· (u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2)
4
· (u
16
− u
15
+ ··· + 7u
2
+ 1)(u
34
− 6u
33
+ ··· − 1504u + 128)
c
4
(u + 1)
7
(u
3
− u + 1)
4
· (u
11
− 2u
10
+ 4u
8
− 2u
7
− 4u
6
+ 5u
5
+ 2u
4
− 5u
3
+ u
2
+ 3u − 1)
4
· (u
16
− 5u
15
+ ··· + 2u + 1)(u
34
− 5u
33
+ ··· + 204u − 16)
c
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 6u
10
+ ··· − 10u + 7)
· (u
16
+ 8u
14
+ ··· + u + 1)(u
34
+ 12u
32
+ ··· − u − 1)
· (u
44
− 2u
43
+ ··· + 2932u + 661)
c
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 6u
10
+ ··· − 10u + 7)
· (u
16
+ 8u
14
+ ··· − u + 1)(u
34
+ 12u
32
+ ··· − u − 1)
· (u
44
− 2u
43
+ ··· + 2932u + 661)
c
7
u
7
(u + 1)
12
· (u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2)
4
· (u
16
+ u
15
+ ··· + 7u
2
+ 1)(u
34
− 6u
33
+ ··· − 1504u + 128)
c
8
, c
10
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
12
+ 4u
11
+ ··· − 4u + 1)
· (u
16
+ 5u
13
+ ··· + u + 1)(u
34
− 8u
32
+ ··· + 11u + 1)
· (u
44
+ 10u
43
+ ··· + 1758u + 421)
c
9
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
12
+ 6u
10
+ ··· − 10u + 7)
· (u
16
+ 8u
14
+ ··· − u + 1)(u
34
+ 12u
32
+ ··· − u − 1)
· (u
44
− 2u
43
+ ··· + 2932u + 661)
c
11
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
12
+ 6u
10
+ ··· − 10u + 7)
· (u
16
+ 8u
14
+ ··· + u + 1)(u
34
+ 12u
32
+ ··· − u − 1)
· (u
44
− 2u
43
+ ··· + 2932u + 661)
c
12
((u
2
+ u + 1)
30
)(u
3
− 3u
2
+ 5u − 2)(u
16
− u
15
+ ··· − 5u
3
+ 1)
· (u
34
− 29u
33
+ ··· − 229376u + 16384)
35
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
7
)(y
3
− 2y
2
− 3y − 1)
4
(y
11
+ 8y
10
+ ··· + 67y − 1)
4
· (y
16
− 7y
15
+ ··· + 10y + 1)(y
34
− 3y
33
+ ··· − 9.59099 × 10
8
y + 65536)
c
2
, c
4
((y − 1)
7
)(y
3
− 2y
2
+ y − 1)
4
(y
11
− 4y
10
+ ··· + 11y − 1)
4
· (y
16
− 11y
15
+ ··· − 14y + 1)(y
34
− 19y
33
+ ··· − 32880y + 256)
c
3
, c
7
y
7
(y − 1)
12
(y
11
− 6y
10
+ ··· + 8y − 4)
4
(y
16
− 3y
15
+ ··· + 14y + 1)
· (y
34
− 12y
33
+ ··· − 388096y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
+ 12y
11
+ ··· + 180y + 49)
· (y
16
+ 16y
15
+ ··· + 13y + 1)(y
34
+ 24y
33
+ ··· − y + 1)
· (y
44
+ 30y
43
+ ··· + 6318180y + 436921)
c
8
, c
10
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
12
+ 8y
11
+ ··· + 318y
2
+ 1)
· (y
16
+ 10y
14
+ ··· + 13y + 1)(y
34
− 16y
33
+ ··· − 37y + 1)
· (y
44
− 2y
43
+ ··· − 1105128y + 177241)
c
12
((y
2
+ y + 1)
30
)(y
3
+ y
2
+ 13y − 4)(y
16
+ 13y
15
+ ··· + 10y
2
+ 1)
· (y
34
+ 15y
33
+ ··· − 536870912y + 268435456)
36
