11a
248
(K11a
248
)
A knot diagram
1
Linearized knot diagam
9 8 1 2 3 11 10 5 4 6 7
Solving Sequence
6,11
7
1,4
3 5 10 8 2 9
c
6
c
11
c
3
c
5
c
10
c
7
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−7806u
39
− 28939u
38
+ ··· + 1091b + 30599, 20501u
39
+ 69845u
38
+ ··· + 4364a − 128043,
u
40
+ 5u
39
+ ··· + 9u − 4i
I
u
2
= hu
26
a + u
26
+ ··· + b − u, −4u
26
a + 4u
26
+ ··· − a + 5, u
27
− 2u
26
+ ··· − 4u
2
− 1i
I
u
3
= h−u
11
+ 6u
9
+ u
8
− 12u
7
− 5u
6
+ 8u
5
+ 7u
4
+ 2u
3
− 2u
2
+ b − 3u,
u
12
− 6u
10
− u
9
+ 13u
8
+ 4u
7
− 11u
6
− 6u
5
+ u
4
+ 4u
3
+ 3u
2
+ a − 2u − 2,
u
13
− 2u
12
− 5u
11
+ 10u
10
+ 10u
9
− 17u
8
− 11u
7
+ 8u
6
+ 7u
5
+ 7u
4
− u
3
− 7u
2
− 1i
I
u
4
= hb + 1, a
2
− 3a + 3, u + 1i
* 4 irreducible components of dim
C
= 0, with total 109 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−7806u
39
− 28939u
38
+ · · · + 1091b + 30599, 20501u
39
+ 69845u
38
+
· · · + 4364a − 128043, u
40
+ 5u
39
+ · · · + 9u − 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−4.69775u
39
− 16.0048u
38
+ ··· − 70.7569u + 29.3407
7.15490u
39
+ 26.5252u
38
+ ··· + 78.3217u − 28.0467
a
3
=
12.9365u
39
+ 44.7789u
38
+ ··· + 77.7912u − 24.2945
−13.4088u
39
− 49.4097u
38
+ ··· − 90.1567u + 27.8689
a
5
=
−7.68492u
39
− 28.0323u
38
+ ··· − 26.6533u + 1.57356
11.5527u
39
+ 43.6728u
38
+ ··· + 54.5325u − 10.8295
a
10
=
−u
u
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
2
=
7.93103u
39
+ 26.6478u
38
+ ··· + 51.3183u − 18.2514
−11.2988u
39
− 41.7883u
38
+ ··· − 83.6975u + 27.0073
a
9
=
1.73854u
39
+ 0.0602658u
38
+ ··· + 26.7647u − 19.7436
−1.46379u
39
− 2.72044u
38
+ ··· − 15.8863u + 10.2997
a
9
=
1.73854u
39
+ 0.0602658u
38
+ ··· + 26.7647u − 19.7436
−1.46379u
39
− 2.72044u
38
+ ··· − 15.8863u + 10.2997
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10012
1091
u
39
−
44785
1091
u
38
+ ··· +
78319
1091
u −
64130
1091
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
40
− u
39
+ ··· + 2u − 1
c
2
, c
9
u
40
+ 2u
38
+ ··· − u − 1
c
3
, c
5
u
40
+ 6u
39
+ ··· − 23u + 1
c
4
u
40
+ 22u
39
+ ··· + 9u + 2
c
6
, c
10
, c
11
u
40
− 5u
39
+ ··· − 9u − 4
c
7
u
40
+ 15u
39
+ ··· + 89u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
40
+ 17y
39
+ ··· + 44y + 1
c
2
, c
9
y
40
+ 4y
39
+ ··· − 23y + 1
c
3
, c
5
y
40
− 24y
39
+ ··· − 199y + 1
c
4
y
40
+ 28y
38
+ ··· − 5y + 4
c
6
, c
10
, c
11
y
40
− 37y
39
+ ··· − 9y + 16
c
7
y
40
− y
39
+ ··· − 937y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833239 + 0.478940I
a = 1.36899 + 1.05581I
b = 0.113249 − 0.613771I
−0.67356 − 9.11808I 3.09330 + 5.04292I
u = 0.833239 − 0.478940I
a = 1.36899 − 1.05581I
b = 0.113249 + 0.613771I
−0.67356 + 9.11808I 3.09330 − 5.04292I
u = 0.944818 + 0.044872I
a = −1.88518 − 0.83264I
b = 1.092540 + 0.590515I
−1.64126 − 1.68382I −2.62360 + 4.24820I
u = 0.944818 − 0.044872I
a = −1.88518 + 0.83264I
b = 1.092540 − 0.590515I
−1.64126 + 1.68382I −2.62360 − 4.24820I
u = 1.045020 + 0.426092I
a = 1.40350 − 0.24037I
b = −0.777991 − 0.700678I
−1.51874 + 7.98713I 1.00079 − 8.43785I
u = 1.045020 − 0.426092I
a = 1.40350 + 0.24037I
b = −0.777991 + 0.700678I
−1.51874 − 7.98713I 1.00079 + 8.43785I
u = 0.127215 + 0.839082I
a = −0.212294 + 0.072049I
b = −0.507546 + 1.079890I
−4.35513 − 3.45950I −3.88332 + 4.09172I
u = 0.127215 − 0.839082I
a = −0.212294 − 0.072049I
b = −0.507546 − 1.079890I
−4.35513 + 3.45950I −3.88332 − 4.09172I
u = 0.277504 + 0.801125I
a = 0.171151 − 0.043121I
b = 0.77473 + 1.69376I
−2.45998 + 13.64270I 1.03420 − 9.07195I
u = 0.277504 − 0.801125I
a = 0.171151 + 0.043121I
b = 0.77473 − 1.69376I
−2.45998 − 13.64270I 1.03420 + 9.07195I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.777292
a = −0.568128
b = −0.113354
1.36099 8.46400
u = 0.225491 + 0.702834I
a = 0.212358 + 0.335622I
b = −0.39127 − 1.71232I
−3.63204 + 5.12135I −5.87713 − 8.64312I
u = 0.225491 − 0.702834I
a = 0.212358 − 0.335622I
b = −0.39127 + 1.71232I
−3.63204 − 5.12135I −5.87713 + 8.64312I
u = 0.290696 + 0.655817I
a = −0.279795 + 0.357972I
b = 0.417996 − 0.903025I
−3.25229 + 1.41438I −4.70580 − 2.22096I
u = 0.290696 − 0.655817I
a = −0.279795 − 0.357972I
b = 0.417996 + 0.903025I
−3.25229 − 1.41438I −4.70580 + 2.22096I
u = −1.283570 + 0.210194I
a = 0.89404 − 1.55425I
b = −0.229292 + 0.859047I
1.12425 − 2.76728I 0. + 3.97586I
u = −1.283570 − 0.210194I
a = 0.89404 + 1.55425I
b = −0.229292 − 0.859047I
1.12425 + 2.76728I 0. − 3.97586I
u = 1.317130 + 0.218392I
a = −2.22707 − 0.75204I
b = 2.17192 + 1.88185I
1.43716 + 2.94730I 0
u = 1.317130 − 0.218392I
a = −2.22707 + 0.75204I
b = 2.17192 − 1.88185I
1.43716 − 2.94730I 0
u = 0.646576 + 0.028959I
a = −1.71193 − 0.86713I
b = 0.662046 + 0.361055I
−1.67832 − 1.69625I −1.45396 + 4.31564I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.646576 − 0.028959I
a = −1.71193 + 0.86713I
b = 0.662046 − 0.361055I
−1.67832 + 1.69625I −1.45396 − 4.31564I
u = −1.307710 + 0.361702I
a = −0.730497 + 0.872523I
b = −0.038517 − 0.940647I
0.125718 − 0.859000I 0
u = −1.307710 − 0.361702I
a = −0.730497 − 0.872523I
b = −0.038517 + 0.940647I
0.125718 + 0.859000I 0
u = −1.374750 + 0.100729I
a = −0.937295 + 0.058184I
b = 0.401012 + 0.417839I
4.00380 + 0.89695I 0
u = −1.374750 − 0.100729I
a = −0.937295 − 0.058184I
b = 0.401012 − 0.417839I
4.00380 − 0.89695I 0
u = 1.395900 + 0.204775I
a = 1.022420 + 0.746778I
b = −0.98876 − 1.47035I
5.90256 + 4.07376I 0
u = 1.395900 − 0.204775I
a = 1.022420 − 0.746778I
b = −0.98876 + 1.47035I
5.90256 − 4.07376I 0
u = −1.38885 + 0.28086I
a = 2.23443 − 1.30007I
b = −1.61945 + 1.79021I
1.50108 − 8.69698I 0
u = −1.38885 − 0.28086I
a = 2.23443 + 1.30007I
b = −1.61945 − 1.79021I
1.50108 + 8.69698I 0
u = −0.024475 + 0.578228I
a = 1.202030 + 0.432697I
b = 0.84787 − 1.24338I
−2.81557 − 0.07740I −5.03252 − 0.22412I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024475 − 0.578228I
a = 1.202030 − 0.432697I
b = 0.84787 + 1.24338I
−2.81557 + 0.07740I −5.03252 + 0.22412I
u = −0.293128 + 0.498415I
a = −0.724756 + 0.441160I
b = −0.324784 + 0.529368I
0.54657 − 1.42879I 5.31935 + 4.51277I
u = −0.293128 − 0.498415I
a = −0.724756 − 0.441160I
b = −0.324784 − 0.529368I
0.54657 + 1.42879I 5.31935 − 4.51277I
u = −1.43383 + 0.26362I
a = 0.738341 − 1.202280I
b = −0.54490 + 1.45255I
2.31251 − 4.79347I 0
u = −1.43383 − 0.26362I
a = 0.738341 + 1.202280I
b = −0.54490 − 1.45255I
2.31251 + 4.79347I 0
u = −1.42214 + 0.32372I
a = −2.22593 + 1.15650I
b = 1.72849 − 2.18761I
2.9545 − 17.7145I 0
u = −1.42214 − 0.32372I
a = −2.22593 − 1.15650I
b = 1.72849 + 2.18761I
2.9545 + 17.7145I 0
u = −1.51106 + 0.03418I
a = −0.041421 + 0.318529I
b = 0.551162 − 0.994771I
7.13383 + 7.90887I 0
u = −1.51106 − 0.03418I
a = −0.041421 − 0.318529I
b = 0.551162 + 0.994771I
7.13383 − 7.90887I 0
u = 1.64915
a = 0.275951
b = −0.563647
9.99305 0
8
II. I
u
2
=
hu
26
a+u
26
+· · ·+b − u, −4u
26
a+4u
26
+· · ·−a + 5, u
27
−2u
26
+· · ·−4u
2
−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
a
−u
26
a − u
26
+ ··· + au + u
a
3
=
−u
26
a − 2u
26
+ ··· − u − 2
u
26
a − u
26
+ ··· + a + 2u
a
5
=
2u
26
a − 3u
26
+ ··· + a − 1
u
26
− 2u
25
+ ··· − a + 2
a
10
=
−u
u
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
2
=
−3u
26
+ 3u
25
+ ··· + a − 2
u
26
a − u
25
a + ··· + 3u + 1
a
9
=
u
26
a − 2u
26
+ ··· − 4u − 1
3u
26
− 2u
25
+ ··· − a + 2
a
9
=
u
26
a − 2u
26
+ ··· − 4u − 1
3u
26
− 2u
25
+ ··· − a + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
26
+ 3u
25
+ 11u
24
−26u
23
−56u
22
+ 83u
21
+ 159u
20
−80u
19
−
221u
18
− 163u
17
− 35u
16
+ 448u
15
+ 606u
14
− 142u
13
− 752u
12
− 576u
11
+ 66u
10
+
578u
9
+ 432u
8
+ 26u
7
− 126u
6
− 129u
5
− 81u
4
− 38u
3
− 27u
2
− 5u + 3
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
54
− 4u
53
+ ··· − u + 1
c
2
, c
9
u
54
− 2u
53
+ ··· − 109u + 37
c
3
, c
5
u
54
− 3u
53
+ ··· + 18u + 27
c
4
(u
27
− 13u
26
+ ··· − u + 2)
2
c
6
, c
10
, c
11
(u
27
+ 2u
26
+ ··· + 4u
2
+ 1)
2
c
7
(u
27
− 9u
26
+ ··· + 37u − 8)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
54
− 12y
53
+ ··· + 5y + 1
c
2
, c
9
y
54
+ 50y
52
+ ··· + 67373y + 1369
c
3
, c
5
y
54
+ 13y
53
+ ··· − 6318y + 729
c
4
(y
27
− 3y
26
+ ··· + 53y −4)
2
c
6
, c
10
, c
11
(y
27
− 24y
26
+ ··· − 8y −1)
2
c
7
(y
27
+ 5y
26
+ ··· − 375y −64)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895940 + 0.471258I
a = 0.342281 − 0.519659I
b = −0.095449 + 0.261445I
1.130920 + 0.684553I 13.8481 − 5.2893I
u = −0.895940 + 0.471258I
a = −1.183610 + 0.725180I
b = −0.274271 − 0.648456I
1.130920 + 0.684553I 13.8481 − 5.2893I
u = −0.895940 − 0.471258I
a = 0.342281 + 0.519659I
b = −0.095449 − 0.261445I
1.130920 − 0.684553I 13.8481 + 5.2893I
u = −0.895940 − 0.471258I
a = −1.183610 − 0.725180I
b = −0.274271 + 0.648456I
1.130920 − 0.684553I 13.8481 + 5.2893I
u = −1.100980 + 0.299749I
a = 0.95742 − 1.49151I
b = −0.305719 + 1.067790I
−0.896800 + 0.835412I −3.62755 − 4.72274I
u = −1.100980 + 0.299749I
a = −2.01018 − 0.00904I
b = 1.02376 − 1.27878I
−0.896800 + 0.835412I −3.62755 − 4.72274I
u = −1.100980 − 0.299749I
a = 0.95742 + 1.49151I
b = −0.305719 − 1.067790I
−0.896800 − 0.835412I −3.62755 + 4.72274I
u = −1.100980 − 0.299749I
a = −2.01018 + 0.00904I
b = 1.02376 + 1.27878I
−0.896800 − 0.835412I −3.62755 + 4.72274I
u = −0.258632 + 0.812574I
a = −0.204845 + 0.236106I
b = −0.67915 + 1.58038I
−0.86178 − 5.25397I 6.46955 + 10.01314I
u = −0.258632 + 0.812574I
a = −0.036879 + 0.212663I
b = 0.520153 − 0.752899I
−0.86178 − 5.25397I 6.46955 + 10.01314I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258632 − 0.812574I
a = −0.204845 − 0.236106I
b = −0.67915 − 1.58038I
−0.86178 + 5.25397I 6.46955 − 10.01314I
u = −0.258632 − 0.812574I
a = −0.036879 − 0.212663I
b = 0.520153 + 0.752899I
−0.86178 + 5.25397I 6.46955 − 10.01314I
u = −0.135996 + 0.743408I
a = 0.688838 + 0.344087I
b = 0.74927 + 1.65652I
−3.79952 − 4.67674I −5.91242 + 7.08419I
u = −0.135996 + 0.743408I
a = −0.008951 + 0.347544I
b = 0.87796 − 1.45827I
−3.79952 − 4.67674I −5.91242 + 7.08419I
u = −0.135996 − 0.743408I
a = 0.688838 − 0.344087I
b = 0.74927 − 1.65652I
−3.79952 + 4.67674I −5.91242 − 7.08419I
u = −0.135996 − 0.743408I
a = −0.008951 − 0.347544I
b = 0.87796 + 1.45827I
−3.79952 + 4.67674I −5.91242 − 7.08419I
u = 1.275050 + 0.128798I
a = 0.872080 − 0.946956I
b = −0.44926 + 1.70261I
3.61252 − 2.75180I 4.02480 + 5.63147I
u = 1.275050 + 0.128798I
a = −1.61610 − 2.37871I
b = 0.40151 + 2.10435I
3.61252 − 2.75180I 4.02480 + 5.63147I
u = 1.275050 − 0.128798I
a = 0.872080 + 0.946956I
b = −0.44926 − 1.70261I
3.61252 + 2.75180I 4.02480 − 5.63147I
u = 1.275050 − 0.128798I
a = −1.61610 + 2.37871I
b = 0.40151 − 2.10435I
3.61252 + 2.75180I 4.02480 − 5.63147I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426561 + 0.478609I
a = −0.264904 + 0.981766I
b = −0.637652 + 0.148109I
0.44505 − 1.73895I 7.45580 + 5.77840I
u = −0.426561 + 0.478609I
a = −1.227590 + 0.092870I
b = −0.262831 + 0.693605I
0.44505 − 1.73895I 7.45580 + 5.77840I
u = −0.426561 − 0.478609I
a = −0.264904 − 0.981766I
b = −0.637652 − 0.148109I
0.44505 + 1.73895I 7.45580 − 5.77840I
u = −0.426561 − 0.478609I
a = −1.227590 − 0.092870I
b = −0.262831 − 0.693605I
0.44505 + 1.73895I 7.45580 − 5.77840I
u = −1.361910 + 0.175704I
a = 0.121170 + 0.544702I
b = −0.840179 + 0.397373I
5.91990 + 0.72025I 11.02491 − 0.63973I
u = −1.361910 + 0.175704I
a = −2.78369 + 0.64886I
b = 2.75677 − 0.87534I
5.91990 + 0.72025I 11.02491 − 0.63973I
u = −1.361910 − 0.175704I
a = 0.121170 − 0.544702I
b = −0.840179 − 0.397373I
5.91990 − 0.72025I 11.02491 + 0.63973I
u = −1.361910 − 0.175704I
a = −2.78369 − 0.64886I
b = 2.75677 + 0.87534I
5.91990 − 0.72025I 11.02491 + 0.63973I
u = 1.346310 + 0.301034I
a = 0.93357 + 1.81656I
b = 0.46852 − 1.68017I
0.87383 + 8.44603I −0.29895 − 8.39876I
u = 1.346310 + 0.301034I
a = −2.51803 − 0.62945I
b = 2.12120 + 1.38215I
0.87383 + 8.44603I −0.29895 − 8.39876I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.346310 − 0.301034I
a = 0.93357 − 1.81656I
b = 0.46852 + 1.68017I
0.87383 − 8.44603I −0.29895 + 8.39876I
u = 1.346310 − 0.301034I
a = −2.51803 + 0.62945I
b = 2.12120 − 1.38215I
0.87383 − 8.44603I −0.29895 + 8.39876I
u = −1.361280 + 0.230867I
a = 0.76323 + 1.29097I
b = −0.68764 − 1.90684I
5.17654 − 7.89313I 8.62044 + 9.21586I
u = −1.361280 + 0.230867I
a = 2.95892 − 1.08916I
b = −2.13759 + 2.13430I
5.17654 − 7.89313I 8.62044 + 9.21586I
u = −1.361280 − 0.230867I
a = 0.76323 − 1.29097I
b = −0.68764 + 1.90684I
5.17654 + 7.89313I 8.62044 − 9.21586I
u = −1.361280 − 0.230867I
a = 2.95892 + 1.08916I
b = −2.13759 − 2.13430I
5.17654 + 7.89313I 8.62044 − 9.21586I
u = 1.392250 + 0.184425I
a = 0.689778 + 0.165914I
b = −0.713590 − 1.011530I
6.04501 + 4.08549I 10.80221 − 3.62417I
u = 1.392250 + 0.184425I
a = 1.47187 + 1.27394I
b = −1.51868 − 1.81027I
6.04501 + 4.08549I 10.80221 − 3.62417I
u = 1.392250 − 0.184425I
a = 0.689778 − 0.165914I
b = −0.713590 + 1.011530I
6.04501 − 4.08549I 10.80221 + 3.62417I
u = 1.392250 − 0.184425I
a = 1.47187 − 1.27394I
b = −1.51868 + 1.81027I
6.04501 − 4.08549I 10.80221 + 3.62417I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.162222 + 0.561060I
a = −0.051560 − 0.625386I
b = −0.96597 − 1.94808I
0.32804 + 4.95240I 2.66900 − 10.41191I
u = 0.162222 + 0.561060I
a = 1.86160 + 0.59224I
b = −0.603163 + 0.183472I
0.32804 + 4.95240I 2.66900 − 10.41191I
u = 0.162222 − 0.561060I
a = −0.051560 + 0.625386I
b = −0.96597 + 1.94808I
0.32804 − 4.95240I 2.66900 + 10.41191I
u = 0.162222 − 0.561060I
a = 1.86160 − 0.59224I
b = −0.603163 − 0.183472I
0.32804 − 4.95240I 2.66900 + 10.41191I
u = 1.41446 + 0.33004I
a = −1.46356 − 0.33947I
b = 1.30700 + 0.85510I
4.46105 + 9.38162I 9.06666 − 9.66600I
u = 1.41446 + 0.33004I
a = 1.96789 + 1.01697I
b = −1.41394 − 2.11422I
4.46105 + 9.38162I 9.06666 − 9.66600I
u = 1.41446 − 0.33004I
a = −1.46356 + 0.33947I
b = 1.30700 − 0.85510I
4.46105 − 9.38162I 9.06666 + 9.66600I
u = 1.41446 − 0.33004I
a = 1.96789 − 1.01697I
b = −1.41394 + 2.11422I
4.46105 − 9.38162I 9.06666 + 9.66600I
u = 1.48928
a = 0.414877 + 0.101829I
b = −0.663673 − 0.708724I
9.10414 14.2140
u = 1.48928
a = 0.414877 − 0.101829I
b = −0.663673 + 0.708724I
9.10414 14.2140
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206359 + 0.377187I
a = 0.000240 − 1.391780I
b = 0.959931 + 1.036890I
0.97705 − 2.90650I 6.25021 − 1.54831I
u = 0.206359 + 0.377187I
a = −2.67387 − 0.24264I
b = −0.437309 + 0.531753I
0.97705 − 2.90650I 6.25021 − 1.54831I
u = 0.206359 − 0.377187I
a = 0.000240 + 1.391780I
b = 0.959931 − 1.036890I
0.97705 + 2.90650I 6.25021 + 1.54831I
u = 0.206359 − 0.377187I
a = −2.67387 + 0.24264I
b = −0.437309 − 0.531753I
0.97705 + 2.90650I 6.25021 + 1.54831I
17
III.
I
u
3
= h−u
11
+6u
9
+· · ·+b−3u, u
12
−6u
10
+· · ·+a−2, u
13
−2u
12
+· · ·−7u
2
−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−u
12
+ 6u
10
+ ··· + 2u + 2
u
11
− 6u
9
− u
8
+ 12u
7
+ 5u
6
− 8u
5
− 7u
4
− 2u
3
+ 2u
2
+ 3u
a
3
=
−4u
12
+ 2u
11
+ ··· − 20u
3
− 21u
2
2u
12
− u
11
+ ··· + 4u + 2
a
5
=
−2u
12
+ 13u
10
+ ··· − 10u − 1
u
12
− u
11
− 6u
10
+ 4u
9
+ 13u
8
− 3u
7
− 10u
6
− 5u
5
− 3u
4
+ 6u
3
+ 6u
2
+ 2
a
10
=
−u
u
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
2
=
−2u
12
+ u
11
+ ··· + 3u + 1
u
12
− 6u
10
+ ··· + 4u + 1
a
9
=
−3u
12
+ 3u
11
+ ··· + u − 4
u
12
− u
11
− 6u
10
+ 4u
9
+ 14u
8
− 3u
7
− 14u
6
− 6u
5
+ 2u
4
+ 8u
3
+ 5u
2
− u
a
9
=
−3u
12
+ 3u
11
+ ··· + u − 4
u
12
− u
11
− 6u
10
+ 4u
9
+ 14u
8
− 3u
7
− 14u
6
− 6u
5
+ 2u
4
+ 8u
3
+ 5u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −12u
12
+3u
11
+69u
10
+4u
9
−142u
8
−61u
7
+92u
6
+111u
5
+61u
4
−41u
3
−73u
2
−22u−10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
13
+ u
12
+ ··· − 2u
2
+ 1
c
2
, c
9
u
13
− 2u
11
+ ··· + u + 1
c
3
, c
5
u
13
+ 4u
12
+ ··· + 7u + 1
c
4
u
13
− 9u
12
+ ··· + 22u − 3
c
6
u
13
− 2u
12
+ ··· − 7u
2
− 1
c
7
u
13
+ 6u
12
+ ··· + 8u + 3
c
10
, c
11
u
13
+ 2u
12
+ ··· + 7u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
13
− 7y
12
+ ··· + 4y −1
c
2
, c
9
y
13
− 4y
12
+ ··· + 7y −1
c
3
, c
5
y
13
+ 8y
12
+ ··· + 11y −1
c
4
y
13
+ 3y
12
+ ··· − 38y −9
c
6
, c
10
, c
11
y
13
− 14y
12
+ ··· − 14y −1
c
7
y
13
− 6y
12
+ ··· − 122y −9
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.009960 + 0.393104I
a = 0.925275 − 0.638185I
b = −0.104514 + 0.740294I
0.418219 + 0.647136I 0.16669 − 3.99472I
u = −1.009960 − 0.393104I
a = 0.925275 + 0.638185I
b = −0.104514 − 0.740294I
0.418219 − 0.647136I 0.16669 + 3.99472I
u = −0.167884 + 0.751728I
a = −0.226076 − 0.027387I
b = 0.47713 − 1.33789I
−2.18684 − 4.76062I 0.16967 + 6.96566I
u = −0.167884 − 0.751728I
a = −0.226076 + 0.027387I
b = 0.47713 + 1.33789I
−2.18684 + 4.76062I 0.16967 − 6.96566I
u = 1.341150 + 0.144131I
a = 1.56947 + 0.55075I
b = −0.882764 − 0.005150I
4.89774 − 1.83075I 8.30741 + 4.84620I
u = 1.341150 − 0.144131I
a = 1.56947 − 0.55075I
b = −0.882764 + 0.005150I
4.89774 + 1.83075I 8.30741 − 4.84620I
u = −1.374030 + 0.142033I
a = −0.56717 + 1.54087I
b = 0.23741 − 2.17678I
5.16744 − 5.48401I 6.26872 + 7.46655I
u = −1.374030 − 0.142033I
a = −0.56717 − 1.54087I
b = 0.23741 + 2.17678I
5.16744 + 5.48401I 6.26872 − 7.46655I
u = 1.365520 + 0.295205I
a = −2.00613 − 0.78110I
b = 1.34623 + 1.31239I
2.66514 + 8.52224I 6.00968 − 8.13315I
u = 1.365520 − 0.295205I
a = −2.00613 + 0.78110I
b = 1.34623 − 1.31239I
2.66514 − 8.52224I 6.00968 + 8.13315I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.015927 + 0.356982I
a = 2.40486 + 0.90799I
b = −0.330299 + 1.152730I
0.51888 + 3.68063I 0.09698 − 6.26701I
u = 0.015927 − 0.356982I
a = 2.40486 − 0.90799I
b = −0.330299 − 1.152730I
0.51888 − 3.68063I 0.09698 + 6.26701I
u = 1.65857
a = −0.200450
b = 0.513607
9.93750 −69.0380
22
IV. I
u
4
= hb + 1, a
2
− 3a + 3, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
7
=
1
−1
a
1
=
−1
0
a
4
=
a
−1
a
3
=
a − 1
−1
a
5
=
a
−1
a
10
=
1
−1
a
8
=
1
−1
a
2
=
2a − 3
−a + 1
a
9
=
−2a + 4
a − 2
a
9
=
−2a + 4
a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
9
u
2
− u + 1
c
3
, c
5
, c
6
(u + 1)
2
c
4
, c
7
u
2
c
10
, c
11
(u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
c
9
y
2
+ y + 1
c
3
, c
5
, c
6
c
10
, c
11
(y −1)
2
c
4
, c
7
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.50000 + 0.86603I
b = −1.00000
0 3.00000
u = −1.00000
a = 1.50000 − 0.86603I
b = −1.00000
0 3.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
2
− u + 1)(u
13
+ u
12
+ ··· − 2u
2
+ 1)(u
40
− u
39
+ ··· + 2u − 1)
· (u
54
− 4u
53
+ ··· − u + 1)
c
2
, c
9
(u
2
− u + 1)(u
13
− 2u
11
+ ··· + u + 1)(u
40
+ 2u
38
+ ··· − u − 1)
· (u
54
− 2u
53
+ ··· − 109u + 37)
c
3
, c
5
((u + 1)
2
)(u
13
+ 4u
12
+ ··· + 7u + 1)(u
40
+ 6u
39
+ ··· − 23u + 1)
· (u
54
− 3u
53
+ ··· + 18u + 27)
c
4
u
2
(u
13
− 9u
12
+ ··· + 22u − 3)(u
27
− 13u
26
+ ··· − u + 2)
2
· (u
40
+ 22u
39
+ ··· + 9u + 2)
c
6
((u + 1)
2
)(u
13
− 2u
12
+ ··· − 7u
2
− 1)(u
27
+ 2u
26
+ ··· + 4u
2
+ 1)
2
· (u
40
− 5u
39
+ ··· − 9u − 4)
c
7
u
2
(u
13
+ 6u
12
+ ··· + 8u + 3)(u
27
− 9u
26
+ ··· + 37u − 8)
2
· (u
40
+ 15u
39
+ ··· + 89u + 4)
c
10
, c
11
((u − 1)
2
)(u
13
+ 2u
12
+ ··· + 7u
2
+ 1)(u
27
+ 2u
26
+ ··· + 4u
2
+ 1)
2
· (u
40
− 5u
39
+ ··· − 9u − 4)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
+ y + 1)(y
13
− 7y
12
+ ··· + 4y −1)(y
40
+ 17y
39
+ ··· + 44y + 1)
· (y
54
− 12y
53
+ ··· + 5y + 1)
c
2
, c
9
(y
2
+ y + 1)(y
13
− 4y
12
+ ··· + 7y −1)(y
40
+ 4y
39
+ ··· − 23y + 1)
· (y
54
+ 50y
52
+ ··· + 67373y + 1369)
c
3
, c
5
((y −1)
2
)(y
13
+ 8y
12
+ ··· + 11y −1)(y
40
− 24y
39
+ ··· − 199y + 1)
· (y
54
+ 13y
53
+ ··· − 6318y + 729)
c
4
y
2
(y
13
+ 3y
12
+ ··· − 38y −9)(y
27
− 3y
26
+ ··· + 53y −4)
2
· (y
40
+ 28y
38
+ ··· − 5y + 4)
c
6
, c
10
, c
11
((y −1)
2
)(y
13
− 14y
12
+ ··· − 14y −1)(y
27
− 24y
26
+ ··· − 8y −1)
2
· (y
40
− 37y
39
+ ··· − 9y + 16)
c
7
y
2
(y
13
− 6y
12
+ ··· − 122y −9)(y
27
+ 5y
26
+ ··· − 375y −64)
2
· (y
40
− y
39
+ ··· − 937y + 16)
28
