11a
158
(K11a
158
)
A knot diagram
1
Linearized knot diagam
5 1 10 8 2 11 4 6 3 7 9
Solving Sequence
2,6
5 1
3,9
10 8 4 7 11
c
5
c
1
c
2
c
9
c
8
c
4
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h23u
27
+ 131u
26
+ ··· + 4b + 148, 273u
27
+ 2147u
26
+ ··· + 8a − 1460, u
28
+ 9u
27
+ ··· − 52u − 8i
I
u
2
= h5.27001 × 10
16
a
5
u
7
− 2.11866 × 10
16
a
4
u
7
+ ··· − 8.58870 × 10
16
a + 2.09109 × 10
17
,
u
7
a
5
− 7u
7
a
4
+ ··· − 92a − 320, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= h−2u
16
+ 4u
15
+ ··· + b + 3, −4u
16
+ 7u
15
+ ··· + a + 11, u
17
− 2u
16
+ ··· − 4u + 1i
* 3 irreducible components of dim
C
= 0, with total 93 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
= h23u
27
+ 131u
26
+ · · · + 4b + 148, 273u
27
+ 2147u
26
+ · · · + 8a −
1460, u
28
+ 9u
27
+ · · · − 52u − 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
−34.1250u
27
− 268.375u
26
+ ··· + 1118.25u + 182.500
−
23
4
u
27
−
131
4
u
26
+ ··· − 150u − 37
a
10
=
−7.12500u
27
− 50.3750u
26
+ ··· + 178.250u + 30.5000
21
4
u
27
+
173
4
u
26
+ ··· − 236u − 43
a
8
=
−28.3750u
27
− 235.625u
26
+ ··· + 1268.25u + 219.500
−
23
4
u
27
−
131
4
u
26
+ ··· − 150u − 37
a
4
=
35
8
u
27
+
305
8
u
26
+ ··· −
923
4
u − 40
9
4
u
27
+
55
4
u
26
+ ··· +
75
2
u + 9
a
7
=
−
127
8
u
27
−
1007
8
u
26
+ ··· +
1119
2
u + 92
2u
27
+
31
2
u
26
+ ··· −
161
2
u − 15
a
11
=
−
77
8
u
27
−
671
8
u
26
+ ··· +
2185
4
u + 95
−
37
4
u
27
−
299
4
u
26
+ ··· +
681
2
u + 55
a
11
=
−
77
8
u
27
−
671
8
u
26
+ ··· +
2185
4
u + 95
−
37
4
u
27
−
299
4
u
26
+ ··· +
681
2
u + 55
(ii) Obstruction class = −1
(iii) Cusp Shapes = 72u
27
+ 580u
26
+ 1879u
25
+ 2101u
24
− 4589u
23
− 20304u
22
−
26684u
21
+ 10295u
20
+ 87084u
19
+ 117201u
18
+ 4207u
17
− 196492u
16
− 261463u
15
−
51078u
14
+ 257673u
13
+ 330937u
12
+ 85897u
11
− 201772u
10
− 247215u
9
− 76609u
8
+
80609u
7
+ 98024u
6
+ 35254u
5
− 10933u
4
− 17557u
3
− 8954u
2
− 2662u − 434
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
28
+ 9u
27
+ ··· − 52u − 8
c
2
u
28
+ 13u
27
+ ··· − 304u + 64
c
3
, c
4
, c
7
c
9
u
28
− u
27
+ ··· − 3u + 1
c
6
, c
10
u
28
+ 18u
27
+ ··· − 3328u − 256
c
8
, c
11
u
28
+ 2u
27
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
28
− 13y
27
+ ··· + 304y + 64
c
2
y
28
+ 7y
27
+ ··· − 204032y + 4096
c
3
, c
4
, c
7
c
9
y
28
− 27y
27
+ ··· − 3y + 1
c
6
, c
10
y
28
+ 14y
27
+ ··· − 303104y
2
+ 65536
c
8
, c
11
y
28
− 12y
27
+ ··· − 66y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993549 + 0.292986I
a = −0.209833 − 0.434545I
b = 0.017296 + 1.007040I
−2.36961 − 3.39893I −1.55352 + 8.34822I
u = 0.993549 − 0.292986I
a = −0.209833 + 0.434545I
b = 0.017296 − 1.007040I
−2.36961 + 3.39893I −1.55352 − 8.34822I
u = −0.745676 + 0.599578I
a = −1.08882 + 1.35793I
b = −0.997965 + 0.424920I
1.93199 − 0.88418I 2.93120 + 0.94418I
u = −0.745676 − 0.599578I
a = −1.08882 − 1.35793I
b = −0.997965 − 0.424920I
1.93199 + 0.88418I 2.93120 − 0.94418I
u = −0.910751 + 0.513446I
a = 1.303570 − 0.508382I
b = 0.664049 + 0.374496I
−1.19975 + 1.98781I −3.01378 − 1.84233I
u = −0.910751 − 0.513446I
a = 1.303570 + 0.508382I
b = 0.664049 − 0.374496I
−1.19975 − 1.98781I −3.01378 + 1.84233I
u = −0.924272 + 0.615006I
a = −1.94919 + 0.56217I
b = −1.167050 − 0.765226I
1.38789 + 5.70099I 1.78458 − 5.41589I
u = −0.924272 − 0.615006I
a = −1.94919 − 0.56217I
b = −1.167050 + 0.765226I
1.38789 − 5.70099I 1.78458 + 5.41589I
u = −0.582336 + 0.951705I
a = 1.14682 − 0.86852I
b = 1.45377 − 0.81817I
13.5292 − 10.0747I 8.45933 + 4.17008I
u = −0.582336 − 0.951705I
a = 1.14682 + 0.86852I
b = 1.45377 + 0.81817I
13.5292 + 10.0747I 8.45933 − 4.17008I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443366 + 1.056140I
a = 0.787450 + 0.068648I
b = 1.080890 − 0.000686I
12.38150 + 4.38665I 10.97973 − 3.34546I
u = −0.443366 − 1.056140I
a = 0.787450 − 0.068648I
b = 1.080890 + 0.000686I
12.38150 − 4.38665I 10.97973 + 3.34546I
u = 0.807574 + 0.208228I
a = 0.576875 + 0.559894I
b = −0.512192 − 1.107170I
−1.14045 + 1.47239I 6.24854 + 6.39498I
u = 0.807574 − 0.208228I
a = 0.576875 − 0.559894I
b = −0.512192 + 1.107170I
−1.14045 − 1.47239I 6.24854 − 6.39498I
u = −0.593204 + 1.035470I
a = −0.760509 + 0.545380I
b = −1.104210 + 0.569568I
7.89930 − 3.44261I 8.17074 + 2.94837I
u = −0.593204 − 1.035470I
a = −0.760509 − 0.545380I
b = −1.104210 − 0.569568I
7.89930 + 3.44261I 8.17074 − 2.94837I
u = −1.31909
a = 0.297585
b = −0.125254
−3.01060 −14.4720
u = −1.106870 + 0.732140I
a = 1.60551 − 0.89150I
b = 1.46289 + 1.05428I
11.9038 + 16.2350I 6.36027 − 8.32086I
u = −1.106870 − 0.732140I
a = 1.60551 + 0.89150I
b = 1.46289 − 1.05428I
11.9038 − 16.2350I 6.36027 + 8.32086I
u = 1.320980 + 0.142620I
a = −0.245968 + 0.237735I
b = 0.872613 − 0.596296I
5.89990 − 8.09391I 4.42894 + 6.82969I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.320980 − 0.142620I
a = −0.245968 − 0.237735I
b = 0.872613 + 0.596296I
5.89990 + 8.09391I 4.42894 − 6.82969I
u = −1.124600 + 0.770804I
a = −1.196350 + 0.572951I
b = −1.094850 − 0.891823I
6.23596 + 9.95004I 5.25531 − 7.03832I
u = −1.124600 − 0.770804I
a = −1.196350 − 0.572951I
b = −1.094850 + 0.891823I
6.23596 − 9.95004I 5.25531 + 7.03832I
u = −1.22157 + 0.75184I
a = 0.498779 − 0.680355I
b = 0.885139 + 0.340742I
10.00870 + 2.13523I 9.70507 + 0.I
u = −1.22157 − 0.75184I
a = 0.498779 + 0.680355I
b = 0.885139 − 0.340742I
10.00870 − 2.13523I 9.70507 + 0.I
u = 1.55763
a = 0.154610
b = −0.615944
−0.410918 16.4090
u = −0.088743 + 0.380871I
a = 0.555578 − 1.006500I
b = −0.189785 − 0.401445I
0.217297 + 1.036000I 3.27495 − 6.74585I
u = −0.088743 − 0.380871I
a = 0.555578 + 1.006500I
b = −0.189785 + 0.401445I
0.217297 − 1.036000I 3.27495 + 6.74585I
7
II. I
u
2
= h5.27 × 10
16
a
5
u
7
− 2.12 × 10
16
a
4
u
7
+ · · · − 8.59 × 10
16
a + 2.09 ×
10
17
, u
7
a
5
− 7u
7
a
4
+ · · · − 92a − 320, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
a
−0.382668a
5
u
7
+ 0.153841a
4
u
7
+ ··· + 0.623646a − 1.51839
a
10
=
−0.638309a
5
u
7
+ 0.178480a
4
u
7
+ ··· + 0.861026a + 0.0250433
0.274885a
5
u
7
+ 0.113800a
4
u
7
+ ··· + 0.225598a − 1.44869
a
8
=
0.382668a
5
u
7
− 0.153841a
4
u
7
+ ··· + 0.376354a + 1.51839
−0.382668a
5
u
7
+ 0.153841a
4
u
7
+ ··· + 0.623646a − 1.51839
a
4
=
−0.941009a
5
u
7
− 0.361240a
4
u
7
+ ··· + 0.0598849a + 1.73126
0.895289a
5
u
7
+ 0.368189a
4
u
7
+ ··· + 0.398274a + 2.83473
a
7
=
−0.830940a
5
u
7
− 0.669583a
4
u
7
+ ··· − 0.192170a + 8.12188
0.629283a
5
u
7
+ 0.240763a
4
u
7
+ ··· − 0.268495a − 0.378118
a
11
=
−0.517443a
5
u
7
− 0.185517a
4
u
7
+ ··· − 0.234948a + 3.55145
0.904169a
5
u
7
+ 0.354563a
4
u
7
+ ··· − 0.0428966a − 0.826810
a
11
=
−0.517443a
5
u
7
− 0.185517a
4
u
7
+ ··· − 0.234948a + 3.55145
0.904169a
5
u
7
+ 0.354563a
4
u
7
+ ··· − 0.0428966a − 0.826810
(ii) Obstruction class = −1
(iii) Cusp Shapes =
151426107279833992
137717486950419293
u
7
a
5
+
62688797470204452
137717486950419293
u
7
a
4
+ ··· +
124275431271284696
137717486950419293
a −
1073475726019287126
137717486950419293
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
6
c
2
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
6
c
3
, c
4
, c
7
c
9
u
48
− u
47
+ ··· + 348u − 701
c
6
, c
10
(u
3
− u
2
+ 2u − 1)
16
c
8
, c
11
u
48
+ 9u
47
+ ··· + 1494u + 1151
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
6
c
2
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
6
c
3
, c
4
, c
7
c
9
y
48
− 45y
47
+ ··· + 8666632y + 491401
c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)
16
c
8
, c
11
y
48
− 17y
47
+ ··· − 69505684y + 1324801
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.990670 − 0.401955I
b = 1.053470 + 0.110154I
6.91828 − 1.69689I 8.09453 + 2.46866I
u = 0.570868 + 0.730671I
a = −0.914373 − 0.642003I
b = −1.163590 − 0.530931I
2.78069 + 1.13123I 1.56526 − 0.51079I
u = 0.570868 + 0.730671I
a = 1.276700 + 0.398261I
b = 0.650677 + 0.052375I
2.78069 + 1.13123I 1.56526 − 0.51079I
u = 0.570868 + 0.730671I
a = −1.65233 + 0.32775I
b = −0.929486 + 0.952208I
6.91828 − 1.69689I 8.09453 + 2.46866I
u = 0.570868 + 0.730671I
a = −1.66990 − 0.72433I
b = −0.804262 − 0.625053I
6.91828 + 3.95936I 8.09453 − 3.49024I
u = 0.570868 + 0.730671I
a = 1.48925 + 1.36516I
b = 1.87266 + 0.67520I
6.91828 + 3.95936I 8.09453 − 3.49024I
u = 0.570868 − 0.730671I
a = 0.990670 + 0.401955I
b = 1.053470 − 0.110154I
6.91828 + 1.69689I 8.09453 − 2.46866I
u = 0.570868 − 0.730671I
a = −0.914373 + 0.642003I
b = −1.163590 + 0.530931I
2.78069 − 1.13123I 1.56526 + 0.51079I
u = 0.570868 − 0.730671I
a = 1.276700 − 0.398261I
b = 0.650677 − 0.052375I
2.78069 − 1.13123I 1.56526 + 0.51079I
u = 0.570868 − 0.730671I
a = −1.65233 − 0.32775I
b = −0.929486 − 0.952208I
6.91828 + 1.69689I 8.09453 − 2.46866I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 − 0.730671I
a = −1.66990 + 0.72433I
b = −0.804262 + 0.625053I
6.91828 − 3.95936I 8.09453 + 3.49024I
u = 0.570868 − 0.730671I
a = 1.48925 − 1.36516I
b = 1.87266 − 0.67520I
6.91828 − 3.95936I 8.09453 + 3.49024I
u = −0.855237 + 0.665892I
a = −0.600223 + 0.587228I
b = −1.14799 + 0.96444I
5.98076 + 2.57849I 4.70341 − 3.56796I
u = −0.855237 + 0.665892I
a = 1.53059 + 0.50816I
b = 0.916060 − 0.214976I
10.11830 − 0.24963I 11.23268 − 0.58851I
u = −0.855237 + 0.665892I
a = −1.50463 + 0.95331I
b = −0.774749 − 1.086430I
5.98076 + 2.57849I 4.70341 − 3.56796I
u = −0.855237 + 0.665892I
a = −0.12321 − 1.87124I
b = 1.73522 − 2.00771I
10.11830 + 5.40662I 11.23268 − 6.54740I
u = −0.855237 + 0.665892I
a = 1.04971 − 1.99633I
b = 0.620056 + 0.252279I
10.11830 + 5.40662I 11.23268 − 6.54740I
u = −0.855237 + 0.665892I
a = 2.43610 − 0.22189I
b = 1.19848 + 2.25399I
10.11830 − 0.24963I 11.23268 − 0.58851I
u = −0.855237 − 0.665892I
a = −0.600223 − 0.587228I
b = −1.14799 − 0.96444I
5.98076 − 2.57849I 4.70341 + 3.56796I
u = −0.855237 − 0.665892I
a = 1.53059 − 0.50816I
b = 0.916060 + 0.214976I
10.11830 + 0.24963I 11.23268 + 0.58851I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 − 0.665892I
a = −1.50463 − 0.95331I
b = −0.774749 + 1.086430I
5.98076 − 2.57849I 4.70341 + 3.56796I
u = −0.855237 − 0.665892I
a = −0.12321 + 1.87124I
b = 1.73522 + 2.00771I
10.11830 − 5.40662I 11.23268 + 6.54740I
u = −0.855237 − 0.665892I
a = 1.04971 + 1.99633I
b = 0.620056 − 0.252279I
10.11830 − 5.40662I 11.23268 + 6.54740I
u = −0.855237 − 0.665892I
a = 2.43610 + 0.22189I
b = 1.19848 − 2.25399I
10.11830 + 0.24963I 11.23268 + 0.58851I
u = −1.09818
a = −0.841554 + 0.067108I
b = 0.863475 + 0.758464I
1.45620 + 2.82812I 1.64572 − 2.97945I
u = −1.09818
a = −0.841554 − 0.067108I
b = 0.863475 − 0.758464I
1.45620 − 2.82812I 1.64572 + 2.97945I
u = −1.09818
a = −0.137898 + 0.764353I
b = −0.757872 − 0.848111I
1.45620 + 2.82812I 1.64572 − 2.97945I
u = −1.09818
a = −0.137898 − 0.764353I
b = −0.757872 + 0.848111I
1.45620 − 2.82812I 1.64572 + 2.97945I
u = −1.09818
a = 0.421321 + 0.253638I
b = −0.045426 − 0.584427I
−2.68138 −4.88355 + 0.I
u = −1.09818
a = 0.421321 − 0.253638I
b = −0.045426 + 0.584427I
−2.68138 −4.88355 + 0.I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 + 0.655470I
a = −0.196743 − 1.047410I
b = −1.107250 − 0.667224I
5.57925 − 3.61542I 6.08131 + 2.31472I
u = 1.031810 + 0.655470I
a = 0.573708 + 1.184710I
b = 0.754638 − 0.318605I
5.57925 − 3.61542I 6.08131 + 2.31472I
u = 1.031810 + 0.655470I
a = 1.220390 + 0.580900I
b = 0.873736 − 0.299034I
1.44167 − 6.44354I −0.44796 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.35060 − 0.80955I
b = −1.11587 + 0.94162I
1.44167 − 6.44354I −0.44796 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.93940 − 0.78420I
b = −0.981258 + 0.682787I
5.57925 − 9.27166I 6.08131 + 8.27362I
u = 1.031810 + 0.655470I
a = 1.86513 + 1.17845I
b = 1.89676 − 1.19078I
5.57925 − 9.27166I 6.08131 + 8.27362I
u = 1.031810 − 0.655470I
a = −0.196743 + 1.047410I
b = −1.107250 + 0.667224I
5.57925 + 3.61542I 6.08131 − 2.31472I
u = 1.031810 − 0.655470I
a = 0.573708 − 1.184710I
b = 0.754638 + 0.318605I
5.57925 + 3.61542I 6.08131 − 2.31472I
u = 1.031810 − 0.655470I
a = 1.220390 − 0.580900I
b = 0.873736 + 0.299034I
1.44167 + 6.44354I −0.44796 − 5.29417I
u = 1.031810 − 0.655470I
a = −1.35060 + 0.80955I
b = −1.11587 − 0.94162I
1.44167 + 6.44354I −0.44796 − 5.29417I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 − 0.655470I
a = −1.93940 + 0.78420I
b = −0.981258 − 0.682787I
5.57925 + 9.27166I 6.08131 − 8.27362I
u = 1.031810 − 0.655470I
a = 1.86513 − 1.17845I
b = 1.89676 + 1.19078I
5.57925 + 9.27166I 6.08131 − 8.27362I
u = 0.603304
a = −1.46576
b = −1.19124
2.97631 −2.91400
u = 0.603304
a = 1.78561 + 1.58163I
b = 1.40424 − 0.45076I
7.11390 + 2.82812I 3.61529 − 2.97945I
u = 0.603304
a = 1.78561 − 1.58163I
b = 1.40424 + 0.45076I
7.11390 − 2.82812I 3.61529 + 2.97945I
u = 0.603304
a = 2.85883
b = −0.156244
2.97631 −2.91400
u = 0.603304
a = −3.40485 + 0.20705I
b = 0.162019 + 0.878843I
7.11390 − 2.82812I 3.61529 + 2.97945I
u = 0.603304
a = −3.40485 − 0.20705I
b = 0.162019 − 0.878843I
7.11390 + 2.82812I 3.61529 − 2.97945I
15
III. I
u
3
=
h−2u
16
+4u
15
+· · ·+b+3, −4u
16
+7u
15
+· · ·+a+11, u
17
−2u
16
+· · ·−4u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
4u
16
− 7u
15
+ ··· + 18u − 11
2u
16
− 4u
15
+ ··· + 5u − 3
a
10
=
3u
16
− 6u
15
+ ··· + 14u − 10
2u
16
− 3u
15
+ ··· + 4u − 2
a
8
=
2u
16
− 3u
15
+ ··· + 13u − 8
2u
16
− 4u
15
+ ··· + 5u − 3
a
4
=
−3u
16
+ 3u
15
+ ··· − 4u + 6
u
16
− 2u
15
+ ··· + 6u − 1
a
7
=
3u
15
− 4u
14
+ ··· + u + 4
u
14
− 2u
13
+ ··· − 5u + 2
a
11
=
−3u
16
+ 4u
15
+ ··· − 8u − 1
−u
16
+ 6u
14
+ ··· − 7u + 1
a
11
=
−3u
16
+ 4u
15
+ ··· − 8u − 1
−u
16
+ 6u
14
+ ··· − 7u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
16
−5u
15
+ 5u
14
+ 10u
13
−22u
12
−5u
11
+ 41u
10
−8u
9
−60u
8
+
43u
7
+ 36u
6
− 40u
5
− 19u
4
+ 38u
3
− 3u
2
− 13u + 15
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 2u
16
+ ··· − 4u − 1
c
2
u
17
+ 10u
16
+ ··· + 16u + 1
c
3
, c
7
u
17
+ u
16
+ ··· − u − 1
c
4
, c
9
u
17
− u
16
+ ··· − u + 1
c
5
u
17
− 2u
16
+ ··· − 4u + 1
c
6
u
17
+ u
16
+ ··· − 3u
2
− 1
c
8
, c
11
u
17
− 2u
16
+ ··· + 6u − 1
c
10
u
17
− u
16
+ ··· + 3u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
17
− 10y
16
+ ··· + 16y −1
c
2
y
17
+ 2y
16
+ ··· + 84y −1
c
3
, c
4
, c
7
c
9
y
17
− 19y
16
+ ··· − 15y −1
c
6
, c
10
y
17
+ 11y
16
+ ··· − 6y −1
c
8
, c
11
y
17
− 4y
16
+ ··· + 20y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629702 + 0.775693I
a = −1.25479 − 0.72695I
b = −1.193870 − 0.354429I
4.15597 + 1.39250I 9.19957 − 1.48197I
u = 0.629702 − 0.775693I
a = −1.25479 + 0.72695I
b = −1.193870 + 0.354429I
4.15597 − 1.39250I 9.19957 + 1.48197I
u = −0.767528 + 0.633722I
a = −0.701511 + 0.032570I
b = 0.617635 − 1.158100I
8.95462 + 4.19752I 7.32669 − 3.30513I
u = −0.767528 − 0.633722I
a = −0.701511 − 0.032570I
b = 0.617635 + 1.158100I
8.95462 − 4.19752I 7.32669 + 3.30513I
u = −0.878628 + 0.059193I
a = 0.358916 − 0.547631I
b = −0.501796 + 0.960589I
−1.39291 − 1.89045I −2.83864 + 7.38305I
u = −0.878628 − 0.059193I
a = 0.358916 + 0.547631I
b = −0.501796 − 0.960589I
−1.39291 + 1.89045I −2.83864 − 7.38305I
u = 0.696362 + 0.452869I
a = 2.86004 − 0.26335I
b = 1.144470 − 0.618358I
8.03048 + 1.78919I 8.52582 + 1.37229I
u = 0.696362 − 0.452869I
a = 2.86004 + 0.26335I
b = 1.144470 + 0.618358I
8.03048 − 1.78919I 8.52582 − 1.37229I
u = −0.957492 + 0.679960I
a = 0.301934 − 0.283727I
b = 0.136055 + 0.999061I
8.34209 + 0.91407I 6.60931 − 1.66194I
u = −0.957492 − 0.679960I
a = 0.301934 + 0.283727I
b = 0.136055 − 0.999061I
8.34209 − 0.91407I 6.60931 + 1.66194I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.076890 + 0.501752I
a = 0.10184 + 1.47628I
b = 0.871848 + 0.190457I
6.67124 − 5.72894I 6.82775 + 5.57933I
u = 1.076890 − 0.501752I
a = 0.10184 − 1.47628I
b = 0.871848 − 0.190457I
6.67124 + 5.72894I 6.82775 − 5.57933I
u = 1.011850 + 0.683838I
a = −1.52981 − 0.82939I
b = −1.27766 + 0.69304I
3.02844 − 6.91224I 6.62356 + 6.67706I
u = 1.011850 − 0.683838I
a = −1.52981 + 0.82939I
b = −1.27766 − 0.69304I
3.02844 + 6.91224I 6.62356 − 6.67706I
u = −1.38732
a = 0.141915
b = −0.470019
−2.77503 19.9250
u = 1.43895
a = 0.437990
b = −0.276644
−0.814223 −3.92340
u = 0.326049
a = −3.85316
b = −0.846698
3.67637 11.4500
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
8
− u
7
+ ··· + 2u − 1)
6
)(u
17
+ 2u
16
+ ··· − 4u − 1)
· (u
28
+ 9u
27
+ ··· − 52u − 8)
c
2
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
6
· (u
17
+ 10u
16
+ ··· + 16u + 1)(u
28
+ 13u
27
+ ··· − 304u + 64)
c
3
, c
7
(u
17
+ u
16
+ ··· − u − 1)(u
28
− u
27
+ ··· − 3u + 1)
· (u
48
− u
47
+ ··· + 348u − 701)
c
4
, c
9
(u
17
− u
16
+ ··· − u + 1)(u
28
− u
27
+ ··· − 3u + 1)
· (u
48
− u
47
+ ··· + 348u − 701)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
6
)(u
17
− 2u
16
+ ··· − 4u + 1)
· (u
28
+ 9u
27
+ ··· − 52u − 8)
c
6
((u
3
− u
2
+ 2u − 1)
16
)(u
17
+ u
16
+ ··· − 3u
2
− 1)
· (u
28
+ 18u
27
+ ··· − 3328u − 256)
c
8
, c
11
(u
17
− 2u
16
+ ··· + 6u − 1)(u
28
+ 2u
27
+ ··· − 8u + 1)
· (u
48
+ 9u
47
+ ··· + 1494u + 1151)
c
10
((u
3
− u
2
+ 2u − 1)
16
)(u
17
− u
16
+ ··· + 3u
2
+ 1)
· (u
28
+ 18u
27
+ ··· − 3328u − 256)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
6
· (y
17
− 10y
16
+ ··· + 16y −1)(y
28
− 13y
27
+ ··· + 304y + 64)
c
2
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
6
· (y
17
+ 2y
16
+ ··· + 84y −1)(y
28
+ 7y
27
+ ··· − 204032y + 4096)
c
3
, c
4
, c
7
c
9
(y
17
− 19y
16
+ ··· − 15y −1)(y
28
− 27y
27
+ ··· − 3y + 1)
· (y
48
− 45y
47
+ ··· + 8666632y + 491401)
c
6
, c
10
((y
3
+ 3y
2
+ 2y −1)
16
)(y
17
+ 11y
16
+ ··· − 6y −1)
· (y
28
+ 14y
27
+ ··· − 303104y
2
+ 65536)
c
8
, c
11
(y
17
− 4y
16
+ ··· + 20y −1)(y
28
− 12y
27
+ ··· − 66y + 1)
· (y
48
− 17y
47
+ ··· − 69505684y + 1324801)
22
