11a
239
(K11a
239
)
A knot diagram
1
Linearized knot diagam
7 1 6 8 9 10 2 11 3 4 5
Solving Sequence
1,7
2 3
5,8
4 11 9 10 6
c
1
c
2
c
7
c
4
c
11
c
8
c
10
c
6
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
16
− 18u
15
+ ··· + 4b + 36, −11u
16
+ 64u
15
+ ··· + 8a − 132, u
17
− 6u
16
+ ··· + 28u − 8i
I
u
2
= h−u
2
a + au + b,
4u
5
a − 9u
6
− 4u
4
a + 19u
5
− 4u
3
a − 7u
4
+ 8u
2
a − 30u
3
+ 8a
2
− 12au + 53u
2
+ 12a − 61u + 22,
u
7
− 3u
6
+ 3u
5
+ 2u
4
− 9u
3
+ 13u
2
− 10u + 4i
I
u
3
= h−2.57269 × 10
30
a
7
u
5
+ 1.10741 × 10
30
a
6
u
5
+ ··· − 6.76928 × 10
31
a − 1.39005 × 10
31
,
a
7
u
5
− 3a
6
u
5
+ ··· − 8a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
4
= h29259u
5
a
3
+ 22409u
5
a
2
+ ··· + 58215a + 25537, −u
5
a
3
+ u
5
a + ··· + a
4
+ 2a,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
5
= h5u
21
− u
20
+ ··· + 2b − 5, 22u
21
− 27u
20
+ ··· + 6a + 3,
u
22
− 8u
20
+ 29u
18
− 65u
16
+ 96u
14
− 95u
12
+ 59u
10
− 20u
8
+ 5u
6
− 8u
4
+ 8u
2
− 3i
I
u
6
= h−u
5
− u
4
− u
2
a − au + u
2
+ b + u + 1, u
5
a + 2u
4
a − u
4
− 2u
2
a − u
3
+ a
2
− au − u
2
+ 2u,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
7
= h−u
5
+ u
3
+ b − u, u
5
− 2u
3
+ a + u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 145 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
= h3u
16
− 18u
15
+ · · · + 4b + 36, −11u
16
+ 64u
15
+ · · · + 8a −
132, u
17
− 6u
16
+ · · · + 28u − 8i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
11
8
u
16
− 8u
15
+ ··· −
89
2
u +
33
2
−
3
4
u
16
+
9
2
u
15
+ ··· + 26u − 9
a
8
=
−u
−u
3
+ u
a
4
=
11
8
u
16
−
15
2
u
15
+ ··· −
65
2
u +
21
2
−
3
4
u
16
+ 2u
15
+ ··· − 5u
2
+ 1
a
11
=
−
7
8
u
16
+
21
4
u
15
+ ··· + 19u −
13
2
2u
16
−
19
2
u
15
+ ··· − 24u + 7
a
9
=
1
8
u
16
−
3
2
u
15
+ ··· −
19
2
u +
7
2
−
3
4
u
16
+ 5u
15
+ ··· + 28u − 11
a
10
=
−
9
8
u
16
+ 6u
15
+ ··· +
45
2
u −
11
2
−
1
4
u
16
+ 2u
15
+ ··· + 22u − 11
a
6
=
−
7
8
u
16
+
13
4
u
15
+ ··· + 2u −
1
2
2u
15
−
15
2
u
14
+ ··· + 18u − 7
a
6
=
−
7
8
u
16
+
13
4
u
15
+ ··· + 2u −
1
2
2u
15
−
15
2
u
14
+ ··· + 18u − 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
29
2
u
16
+ 72u
15
−
209
2
u
14
−120u
13
+
1253
2
u
12
−780u
11
−
287
2
u
10
+
1656u
9
−
4241
2
u
8
+ 703u
7
+
2779
2
u
6
− 2264u
5
+
3031
2
u
4
− 319u
3
− 255u
2
+ 226u − 62
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
7
u
17
− 6u
16
+ ··· + 28u − 8
c
2
u
17
+ 10u
16
+ ··· + 208u + 64
c
3
, c
8
u
17
− 13u
16
+ ··· + 259u − 47
c
4
, c
6
, c
9
c
11
u
17
− u
16
+ ··· + u − 1
c
5
, c
10
u
17
+ 2u
16
+ ··· − u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
17
− 10y
16
+ ··· + 208y −64
c
2
y
17
− 6y
16
+ ··· + 47360y −4096
c
3
, c
8
y
17
− 13y
16
+ ··· − 7555y −2209
c
4
, c
6
, c
9
c
11
y
17
− 5y
16
+ ··· + 21y −1
c
5
, c
10
y
17
− 12y
16
+ ··· + 177y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334231 + 0.945289I
a = 1.186990 + 0.667740I
b = −1.11552 − 1.11726I
−1.10093 + 13.85920I −2.71296 − 7.57439I
u = 0.334231 − 0.945289I
a = 1.186990 − 0.667740I
b = −1.11552 + 1.11726I
−1.10093 − 13.85920I −2.71296 + 7.57439I
u = 0.788176 + 0.924452I
a = −0.655874 − 0.649894I
b = 1.016290 + 0.314455I
2.41973 + 2.94950I 2.91048 − 5.30771I
u = 0.788176 − 0.924452I
a = −0.655874 + 0.649894I
b = 1.016290 − 0.314455I
2.41973 − 2.94950I 2.91048 + 5.30771I
u = 0.857122 + 0.870195I
a = 1.129770 + 0.148811I
b = −1.086350 + 0.571276I
2.21297 − 9.35015I −0.11785 + 9.82632I
u = 0.857122 − 0.870195I
a = 1.129770 − 0.148811I
b = −1.086350 − 0.571276I
2.21297 + 9.35015I −0.11785 − 9.82632I
u = 0.337237 + 0.670381I
a = −1.111840 + 0.085153I
b = 0.766763 + 0.185332I
1.74054 + 0.98669I 3.14210 − 1.82725I
u = 0.337237 − 0.670381I
a = −1.111840 − 0.085153I
b = 0.766763 − 0.185332I
1.74054 − 0.98669I 3.14210 + 1.82725I
u = 1.164700 + 0.502631I
a = 0.659288 + 0.927604I
b = −0.659915 + 0.384127I
−0.77068 − 5.56913I −2.33811 + 7.26294I
u = 1.164700 − 0.502631I
a = 0.659288 − 0.927604I
b = −0.659915 − 0.384127I
−0.77068 + 5.56913I −2.33811 − 7.26294I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.187760 + 0.627012I
a = −1.63439 − 0.99047I
b = 1.13230 − 1.24110I
−3.7013 − 19.5737I −5.36728 + 10.75666I
u = 1.187760 − 0.627012I
a = −1.63439 + 0.99047I
b = 1.13230 + 1.24110I
−3.7013 + 19.5737I −5.36728 − 10.75666I
u = −1.340970 + 0.177838I
a = 0.340570 − 0.263792I
b = 0.885606 − 1.042740I
−6.89672 − 10.17430I −7.93890 + 7.26215I
u = −1.340970 − 0.177838I
a = 0.340570 + 0.263792I
b = 0.885606 + 1.042740I
−6.89672 + 10.17430I −7.93890 − 7.26215I
u = 1.46179
a = 0.501964
b = 0.338845
−7.70589 −19.1410
u = −0.515829
a = −0.663529
b = −0.518819
−1.37384 −7.65930
u = −1.60248
a = −0.167458
b = −0.698369
−6.69142 13.6450
6
II. I
u
2
= h−u
2
a + au + b, 4u
5
a − 9u
6
+ · · · + 12a + 22, u
7
− 3u
6
+ 3u
5
+
2u
4
− 9u
3
+ 13u
2
− 10u + 4i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
a
u
2
a − au
a
8
=
−u
−u
3
+ u
a
4
=
u
3
a − u
2
a + a
u
5
a − u
4
a − u
3
a + 2u
2
a − au
a
11
=
−
1
2
u
6
a −
1
2
u
6
+ ··· + 2a +
3
2
u
6
a +
1
2
u
6
+ ··· − 2a +
3
2
u
a
9
=
u
6
−
3
2
u
5
+ ··· + a −
1
2
−
1
2
u
6
+
1
2
u
5
+ ··· + au −
1
2
u
a
10
=
−
1
2
u
6
+ u
5
+ ··· + a +
3
2
1
2
u
6
−
1
2
u
5
+ ··· + au +
3
2
u
a
6
=
1
2
u
6
a −
1
4
u
6
+ ··· −
13
4
u +
3
2
−u
5
a + u
6
+ ··· − 2a − 3
a
6
=
1
2
u
6
a −
1
4
u
6
+ ··· −
13
4
u +
3
2
−u
5
a + u
6
+ ··· − 2a − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7u
6
− 10u
5
− u
4
+ 26u
3
− 27u
2
+ 16u + 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
7
− 3u
6
+ 3u
5
+ 2u
4
− 9u
3
+ 13u
2
− 10u + 4)
2
c
2
(u
7
+ 3u
6
+ 3u
5
− 7u
3
+ 5u
2
− 4u + 16)
2
c
3
, c
8
u
14
− 15u
13
+ ··· − 1309u + 187
c
4
, c
6
, c
9
c
11
u
14
+ u
13
+ ··· + 4u + 1
c
5
, c
10
(u
7
− u
6
+ u
5
− u
4
+ u
3
+ u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
7
− 3y
6
+ 3y
5
− 7y
3
− 5y
2
− 4y −16)
2
c
2
(y
7
− 3y
6
− 5y
5
− 80y
4
− 71y
3
+ 31y
2
− 144y −256)
2
c
3
, c
8
y
14
− 3y
13
+ ··· − 5797y + 34969
c
4
, c
6
, c
9
c
11
y
14
− 3y
13
+ ··· − 2y + 1
c
5
, c
10
(y
7
+ y
6
+ y
5
+ 3y
4
+ y
3
+ y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.814935 + 0.691474I
a = 0.818477 + 1.080010I
b = −0.985169 − 0.322797I
4.60437 − 2.63118I 2.98391 + 3.36378I
u = 0.814935 + 0.691474I
a = −1.56532 − 0.18032I
b = 1.063050 − 0.568346I
4.60437 − 2.63118I 2.98391 + 3.36378I
u = 0.814935 − 0.691474I
a = 0.818477 − 1.080010I
b = −0.985169 + 0.322797I
4.60437 + 2.63118I 2.98391 − 3.36378I
u = 0.814935 − 0.691474I
a = −1.56532 + 0.18032I
b = 1.063050 + 0.568346I
4.60437 + 2.63118I 2.98391 − 3.36378I
u = 0.244291 + 1.049540I
a = −1.068000 − 0.437680I
b = 1.13868 + 1.13618I
0.04250 + 5.03576I −2.7810 − 16.4347I
u = 0.244291 + 1.049540I
a = 0.330014 + 0.179733I
b = −0.327975 − 0.408300I
0.04250 + 5.03576I −2.7810 − 16.4347I
u = 0.244291 − 1.049540I
a = −1.068000 + 0.437680I
b = 1.13868 − 1.13618I
0.04250 − 5.03576I −2.7810 + 16.4347I
u = 0.244291 − 1.049540I
a = 0.330014 − 0.179733I
b = −0.327975 + 0.408300I
0.04250 − 5.03576I −2.7810 + 16.4347I
u = 1.229510 + 0.632474I
a = −0.783908 − 0.339718I
b = 0.405865 − 0.683351I
−2.94764 − 10.98550I −7.63392 + 11.66372I
u = 1.229510 + 0.632474I
a = 1.43734 + 1.01814I
b = −1.10890 + 1.20639I
−2.94764 − 10.98550I −7.63392 + 11.66372I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.229510 − 0.632474I
a = −0.783908 + 0.339718I
b = 0.405865 + 0.683351I
−2.94764 + 10.98550I −7.63392 − 11.66372I
u = 1.229510 − 0.632474I
a = 1.43734 − 1.01814I
b = −1.10890 − 1.20639I
−2.94764 + 10.98550I −7.63392 − 11.66372I
u = −1.57747
a = −0.168609 + 0.061232I
b = −0.685543 + 0.248960I
−6.68831 6.86200
u = −1.57747
a = −0.168609 − 0.061232I
b = −0.685543 − 0.248960I
−6.68831 6.86200
11
III. I
u
3
= h−2.57 × 10
30
a
7
u
5
+ 1.11 × 10
30
a
6
u
5
+ · · · − 6.77 × 10
31
a − 1.39 ×
10
31
, a
7
u
5
− 3a
6
u
5
+ · · · − 8a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
a
0.0725908a
7
u
5
− 0.0312466a
6
u
5
+ ··· + 1.91001a + 0.392216
a
8
=
−u
−u
3
+ u
a
4
=
−0.0137916a
7
u
5
+ 0.00218527a
6
u
5
+ ··· + 0.411608a + 0.495146
0.151420a
7
u
5
− 0.00837117a
6
u
5
+ ··· + 2.66136a + 0.605770
a
11
=
0.00470703a
7
u
5
− 0.00280449a
6
u
5
+ ··· + 0.181900a + 0.413915
−0.103428a
7
u
5
+ 0.0229172a
6
u
5
+ ··· + 1.71283a − 1.57617
a
9
=
0.142900a
7
u
5
− 0.162959a
6
u
5
+ ··· − 0.921925a + 1.11192
−0.0326497a
7
u
5
− 0.0359075a
6
u
5
+ ··· + 3.38577a − 1.09902
a
10
=
0.138594a
7
u
5
− 0.138648a
6
u
5
+ ··· − 1.12523a + 1.42701
−0.00903181a
7
u
5
− 0.0141319a
6
u
5
+ ··· + 3.74823a − 0.965404
a
6
=
0.0782518a
7
u
5
− 0.0823113a
6
u
5
+ ··· + 0.426516a − 1.12444
0.0398061a
7
u
5
+ 0.0659338a
6
u
5
+ ··· − 2.81464a + 1.61215
a
6
=
0.0782518a
7
u
5
− 0.0823113a
6
u
5
+ ··· + 0.426516a − 1.12444
0.0398061a
7
u
5
+ 0.0659338a
6
u
5
+ ··· − 2.81464a + 1.61215
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4371177550733369341379808
37338217638487684273785061
a
7
u
5
−
8613150463936407409230296
37338217638487684273785061
a
6
u
5
+
··· −
483487231400196111720296296
37338217638487684273785061
a −
520800134167026485786802942
37338217638487684273785061
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
c
3
, c
8
(u
4
+ u
3
− 2u + 1)
12
c
4
, c
6
, c
9
c
11
u
48
− u
47
+ ··· + 258u + 67
c
5
, c
10
(u
24
− u
23
+ ··· − 148u + 43)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
c
3
, c
8
(y
4
− y
3
+ 6y
2
− 4y + 1)
12
c
4
, c
6
, c
9
c
11
y
48
+ 21y
47
+ ··· + 251016y + 4489
c
5
, c
10
(y
24
− 21y
23
+ ··· − 20872y + 1849)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.457748 − 0.979472I
b = −0.468678 − 1.255150I
−5.18047 + 3.13546I −15.7167 − 6.1340I
u = 1.002190 + 0.295542I
a = 0.673790 + 0.414822I
b = −0.203937 + 1.370430I
−5.18047 − 4.98407I −15.7167 + 7.7224I
u = 1.002190 + 0.295542I
a = 0.368896 − 0.698369I
b = 0.199323 − 1.036770I
−5.18047 − 4.98407I −15.7167 + 7.7224I
u = 1.002190 + 0.295542I
a = 0.600740 − 0.091577I
b = 0.77443 + 1.38879I
−5.18047 + 3.13546I −15.7167 − 6.1340I
u = 1.002190 + 0.295542I
a = 2.07317 + 2.02956I
b = −1.54509 + 0.60670I
−5.18047 − 4.98407I −15.7167 + 7.7224I
u = 1.002190 + 0.295542I
a = −1.79302 − 2.40528I
b = 1.74582 − 0.65394I
−5.18047 + 3.13546I −15.7167 − 6.1340I
u = 1.002190 + 0.295542I
a = −2.51170 − 1.86755I
b = −0.110952 − 0.260042I
−5.18047 + 3.13546I −15.7167 − 6.1340I
u = 1.002190 + 0.295542I
a = 2.73201 + 1.67151I
b = 0.037319 + 0.504525I
−5.18047 − 4.98407I −15.7167 + 7.7224I
u = 1.002190 − 0.295542I
a = −0.457748 + 0.979472I
b = −0.468678 + 1.255150I
−5.18047 − 3.13546I −15.7167 + 6.1340I
u = 1.002190 − 0.295542I
a = 0.673790 − 0.414822I
b = −0.203937 − 1.370430I
−5.18047 + 4.98407I −15.7167 − 7.7224I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 − 0.295542I
a = 0.368896 + 0.698369I
b = 0.199323 + 1.036770I
−5.18047 + 4.98407I −15.7167 − 7.7224I
u = 1.002190 − 0.295542I
a = 0.600740 + 0.091577I
b = 0.77443 − 1.38879I
−5.18047 − 3.13546I −15.7167 + 6.1340I
u = 1.002190 − 0.295542I
a = 2.07317 − 2.02956I
b = −1.54509 − 0.60670I
−5.18047 + 4.98407I −15.7167 − 7.7224I
u = 1.002190 − 0.295542I
a = −1.79302 + 2.40528I
b = 1.74582 + 0.65394I
−5.18047 − 3.13546I −15.7167 + 6.1340I
u = 1.002190 − 0.295542I
a = −2.51170 + 1.86755I
b = −0.110952 + 0.260042I
−5.18047 − 3.13546I −15.7167 + 6.1340I
u = 1.002190 − 0.295542I
a = 2.73201 − 1.67151I
b = 0.037319 − 0.504525I
−5.18047 + 4.98407I −15.7167 − 7.7224I
u = −0.428243 + 0.664531I
a = −0.541502 − 0.997202I
b = 0.213230 + 0.751517I
−1.39926 + 3.13546I −8.28328 − 6.13398I
u = −0.428243 + 0.664531I
a = 0.241612 + 0.808856I
b = −0.496583 − 0.413571I
−1.39926 + 3.13546I −8.28328 − 6.13398I
u = −0.428243 + 0.664531I
a = −0.078871 − 1.180870I
b = 0.301803 − 0.762568I
−1.39926 − 4.98407I −8.28328 + 7.72243I
u = −0.428243 + 0.664531I
a = −0.300534 + 0.237449I
b = −0.146082 + 1.344830I
−1.39926 + 3.13546I −8.28328 − 6.13398I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = −1.55909 + 0.46475I
b = 0.696177 + 1.068770I
−1.39926 + 3.13546I −8.28328 − 6.13398I
u = −0.428243 + 0.664531I
a = −1.38135 + 1.00825I
b = 0.644388 − 1.011590I
−1.39926 − 4.98407I −8.28328 + 7.72243I
u = −0.428243 + 0.664531I
a = 1.83610 + 0.25167I
b = −1.14936 − 1.56331I
−1.39926 − 4.98407I −8.28328 + 7.72243I
u = −0.428243 + 0.664531I
a = 1.43866 − 1.35771I
b = −1.065770 + 0.881470I
−1.39926 − 4.98407I −8.28328 + 7.72243I
u = −0.428243 − 0.664531I
a = −0.541502 + 0.997202I
b = 0.213230 − 0.751517I
−1.39926 − 3.13546I −8.28328 + 6.13398I
u = −0.428243 − 0.664531I
a = 0.241612 − 0.808856I
b = −0.496583 + 0.413571I
−1.39926 − 3.13546I −8.28328 + 6.13398I
u = −0.428243 − 0.664531I
a = −0.078871 + 1.180870I
b = 0.301803 + 0.762568I
−1.39926 + 4.98407I −8.28328 − 7.72243I
u = −0.428243 − 0.664531I
a = −0.300534 − 0.237449I
b = −0.146082 − 1.344830I
−1.39926 − 3.13546I −8.28328 + 6.13398I
u = −0.428243 − 0.664531I
a = −1.55909 − 0.46475I
b = 0.696177 − 1.068770I
−1.39926 − 3.13546I −8.28328 + 6.13398I
u = −0.428243 − 0.664531I
a = −1.38135 − 1.00825I
b = 0.644388 + 1.011590I
−1.39926 + 4.98407I −8.28328 − 7.72243I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = 1.83610 − 0.25167I
b = −1.14936 + 1.56331I
−1.39926 + 4.98407I −8.28328 − 7.72243I
u = −0.428243 − 0.664531I
a = 1.43866 + 1.35771I
b = −1.065770 − 0.881470I
−1.39926 + 4.98407I −8.28328 − 7.72243I
u = −1.073950 + 0.558752I
a = −0.918192 + 0.038272I
b = 0.295211 + 0.810996I
−3.28987 + 1.63325I −12.00000 + 1.41763I
u = −1.073950 + 0.558752I
a = −0.408987 + 0.794851I
b = −0.234870 + 1.115430I
−3.28987 + 1.63325I −12.00000 + 1.41763I
u = −1.073950 + 0.558752I
a = 0.871839 + 0.152692I
b = −0.048095 − 0.363748I
−3.28987 + 1.63325I −12.00000 + 1.41763I
u = −1.073950 + 0.558752I
a = −0.602261 − 0.354328I
b = −0.92695 + 1.50690I
−3.28987 + 1.63325I −12.00000 + 1.41763I
u = −1.073950 + 0.558752I
a = 0.75465 + 1.25519I
b = 1.59249 − 1.70119I
−3.28987 + 9.75279I −12.0000 − 12.4388I
u = −1.073950 + 0.558752I
a = 0.30374 − 1.56582I
b = −0.111915 − 0.755296I
−3.28987 + 9.75279I −12.0000 − 12.4388I
u = −1.073950 + 0.558752I
a = −1.95539 + 0.89217I
b = 1.26240 + 1.08359I
−3.28987 + 9.75279I −12.0000 − 12.4388I
u = −1.073950 + 0.558752I
a = 2.11344 − 0.77539I
b = −0.754320 − 1.137930I
−3.28987 + 9.75279I −12.0000 − 12.4388I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = −0.918192 − 0.038272I
b = 0.295211 − 0.810996I
−3.28987 − 1.63325I −12.00000 − 1.41763I
u = −1.073950 − 0.558752I
a = −0.408987 − 0.794851I
b = −0.234870 − 1.115430I
−3.28987 − 1.63325I −12.00000 − 1.41763I
u = −1.073950 − 0.558752I
a = 0.871839 − 0.152692I
b = −0.048095 + 0.363748I
−3.28987 − 1.63325I −12.00000 − 1.41763I
u = −1.073950 − 0.558752I
a = −0.602261 + 0.354328I
b = −0.92695 − 1.50690I
−3.28987 − 1.63325I −12.00000 − 1.41763I
u = −1.073950 − 0.558752I
a = 0.75465 − 1.25519I
b = 1.59249 + 1.70119I
−3.28987 − 9.75279I −12.0000 + 12.4388I
u = −1.073950 − 0.558752I
a = 0.30374 + 1.56582I
b = −0.111915 + 0.755296I
−3.28987 − 9.75279I −12.0000 + 12.4388I
u = −1.073950 − 0.558752I
a = −1.95539 − 0.89217I
b = 1.26240 − 1.08359I
−3.28987 − 9.75279I −12.0000 + 12.4388I
u = −1.073950 − 0.558752I
a = 2.11344 + 0.77539I
b = −0.754320 + 1.137930I
−3.28987 − 9.75279I −12.0000 + 12.4388I
19
IV. I
u
4
= h29259u
5
a
3
+ 22409u
5
a
2
+ · · · + 58215a + 25537, −u
5
a
3
+ u
5
a +
· · · + a
4
+ 2a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
a
−0.333957a
3
u
5
− 0.255773a
2
u
5
+ ··· − 0.664456a − 0.291475
a
8
=
−u
−u
3
+ u
a
4
=
0.258375a
3
u
5
+ 0.626642a
2
u
5
+ ··· + 0.968806a + 0.435118
−0.424663a
3
u
5
− 0.139146a
2
u
5
+ ··· − 1.60531a − 0.730839
a
11
=
0.103489a
3
u
5
− 0.0715305a
2
u
5
+ ··· + 0.944346a + 1.67934
−0.00241973a
3
u
5
− 0.0406789a
2
u
5
+ ··· − 0.479233a − 0.813281
a
9
=
0.409540a
3
u
5
− 0.115097a
2
u
5
+ ··· + 0.360106a + 0.147832
−0.0755824a
3
u
5
+ 0.370870a
2
u
5
+ ··· − 0.695650a + 0.143643
a
10
=
0.333957a
3
u
5
+ 0.255773a
2
u
5
+ ··· − 0.335544a + 0.291475
−0.333957a
3
u
5
− 0.255773a
2
u
5
+ ··· − 0.664456a − 0.291475
a
6
=
0.142741a
3
u
5
+ 0.305331a
2
u
5
+ ··· − 0.0788582a + 1.27780
−0.326595a
3
u
5
− 0.207481a
2
u
5
+ ··· − 0.635659a − 1.67560
a
6
=
0.142741a
3
u
5
+ 0.305331a
2
u
5
+ ··· − 0.0788582a + 1.27780
−0.326595a
3
u
5
− 0.207481a
2
u
5
+ ··· − 0.635659a − 1.67560
(ii) Obstruction class = −1
(iii) Cusp Shapes =
84848
87613
u
5
a
3
+
222968
87613
u
5
a
2
+ ··· +
15672
87613
a +
372470
87613
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
4
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
c
3
, c
8
(u
2
+ u + 1)
12
c
4
, c
6
, c
9
c
11
u
24
+ u
23
+ ··· + 4u + 1
c
5
, c
10
u
24
+ 3u
23
+ ··· + 114u + 31
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
c
3
, c
8
(y
2
+ y + 1)
12
c
4
, c
6
, c
9
c
11
y
24
+ 3y
23
+ ··· − 8y + 1
c
5
, c
10
y
24
+ 15y
23
+ ··· + 25444y + 961
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.337338 + 0.829459I
b = −0.199854 − 0.781144I
−1.89061 − 4.98407I −3.71672 + 7.72243I
u = 1.002190 + 0.295542I
a = −0.781973 + 0.104129I
b = 0.776686 + 0.745871I
−1.89061 + 3.13546I −3.71672 − 6.13398I
u = 1.002190 + 0.295542I
a = 0.48786 + 1.59395I
b = −0.589768 + 0.819748I
−1.89061 − 4.98407I −3.71672 + 7.72243I
u = 1.002190 + 0.295542I
a = −1.72936 − 0.60119I
b = −0.41531 − 1.44901I
−1.89061 + 3.13546I −3.71672 − 6.13398I
u = 1.002190 − 0.295542I
a = 0.337338 − 0.829459I
b = −0.199854 + 0.781144I
−1.89061 + 4.98407I −3.71672 − 7.72243I
u = 1.002190 − 0.295542I
a = −0.781973 − 0.104129I
b = 0.776686 − 0.745871I
−1.89061 − 3.13546I −3.71672 + 6.13398I
u = 1.002190 − 0.295542I
a = 0.48786 − 1.59395I
b = −0.589768 − 0.819748I
−1.89061 + 4.98407I −3.71672 − 7.72243I
u = 1.002190 − 0.295542I
a = −1.72936 + 0.60119I
b = −0.41531 + 1.44901I
−1.89061 − 3.13546I −3.71672 + 6.13398I
u = −0.428243 + 0.664531I
a = 0.755292 + 1.009740I
b = −0.371900 − 0.003878I
1.89061 + 3.13546I 3.71672 − 6.13398I
u = −0.428243 + 0.664531I
a = −1.245150 − 0.328581I
b = 1.128940 + 0.724032I
1.89061 + 3.13546I 3.71672 − 6.13398I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = −1.09300 + 1.05874I
b = 1.06242 − 1.34996I
1.89061 − 4.98407I 3.71672 + 7.72243I
u = −0.428243 + 0.664531I
a = 1.92783 − 0.97509I
b = −0.817270 + 0.334261I
1.89061 − 4.98407I 3.71672 + 7.72243I
u = −0.428243 − 0.664531I
a = 0.755292 − 1.009740I
b = −0.371900 + 0.003878I
1.89061 − 3.13546I 3.71672 + 6.13398I
u = −0.428243 − 0.664531I
a = −1.245150 + 0.328581I
b = 1.128940 − 0.724032I
1.89061 − 3.13546I 3.71672 + 6.13398I
u = −0.428243 − 0.664531I
a = −1.09300 − 1.05874I
b = 1.06242 + 1.34996I
1.89061 + 4.98407I 3.71672 − 7.72243I
u = −0.428243 − 0.664531I
a = 1.92783 + 0.97509I
b = −0.817270 − 0.334261I
1.89061 + 4.98407I 3.71672 − 7.72243I
u = −1.073950 + 0.558752I
a = 0.124813 − 1.010030I
b = −1.214610 + 0.323938I
1.63325I 0. + 1.41763I
u = −1.073950 + 0.558752I
a = −0.583237 + 0.928763I
b = 0.193738 + 0.326753I
1.63325I 0. + 1.41763I
u = −1.073950 + 0.558752I
a = −1.77856 + 0.70986I
b = 0.991934 + 0.425381I
9.75279I 0. − 12.43877I
u = −1.073950 + 0.558752I
a = 2.07814 − 1.06623I
b = −1.04502 − 1.63482I
9.75279I 0. − 12.43877I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.124813 + 1.010030I
b = −1.214610 − 0.323938I
− 1.63325I 0. − 1.41763I
u = −1.073950 − 0.558752I
a = −0.583237 − 0.928763I
b = 0.193738 − 0.326753I
− 1.63325I 0. − 1.41763I
u = −1.073950 − 0.558752I
a = −1.77856 − 0.70986I
b = 0.991934 − 0.425381I
− 9.75279I 0. + 12.43877I
u = −1.073950 − 0.558752I
a = 2.07814 + 1.06623I
b = −1.04502 + 1.63482I
− 9.75279I 0. + 12.43877I
25
V. I
u
5
=
h5u
21
−u
20
+· · ·+2b−5, 22u
21
−27u
20
+· · ·+6a+3, u
22
−8u
20
+· · ·+8u
2
−3i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−
11
3
u
21
+
9
2
u
20
+ ··· +
19
6
u −
1
2
−
5
2
u
21
+
1
2
u
20
+ ··· −
23
2
u +
5
2
a
8
=
−u
−u
3
+ u
a
4
=
−
25
6
u
21
+ 5u
20
+ ··· +
2
3
u + 7
−2u
21
−
3
2
u
20
+ ··· −
21
2
u −
7
2
a
11
=
−
5
3
u
21
+ 3u
20
+ ··· −
41
6
u +
17
2
3u
21
+ 2u
20
+ ··· +
5
2
u + 4
a
9
=
7
6
u
21
− 2u
20
+ ··· +
4
3
u −
21
2
5u
21
+ 7u
20
+ ··· + 7u +
25
2
a
10
=
−
5
6
u
21
−
5
2
u
20
+ ··· −
8
3
u −
23
2
9
2
u
21
+ 7u
20
+ ··· −
1
2
u + 11
a
6
=
−
4
3
u
21
+ 3u
20
+ ··· −
2
3
u +
5
2
3u
21
− 22u
19
+ ··· +
17
2
u + 5
a
6
=
−
4
3
u
21
+ 3u
20
+ ··· −
2
3
u +
5
2
3u
21
− 22u
19
+ ··· +
17
2
u + 5
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −21u
20
+149u
18
−468u
16
+901u
14
−1086u
12
+816u
10
−304u
8
+31u
6
−53u
4
+110u
2
−51
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
22
− 8u
20
+ ··· + 8u
2
− 3
c
2
(u
11
+ 8u
10
+ ··· + 8u + 3)
2
c
3
, c
8
u
22
− 8u
21
+ ··· − u − 1
c
4
, c
6
, c
9
c
11
u
22
− 2u
21
+ ··· − 4u − 1
c
5
, c
10
(u
11
+ u
10
− 3u
9
− 4u
8
+ 4u
7
+ 5u
6
− 5u
5
− 4u
4
+ 8u
3
+ 2u
2
− u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
11
− 8y
10
+ ··· + 8y −3)
2
c
2
(y
11
− 6y
10
+ ··· + 16y −9)
2
c
3
, c
8
y
22
− 16y
21
+ ··· − 11y + 1
c
4
, c
6
, c
9
c
11
y
22
+ 8y
21
+ ··· − 28y + 1
c
5
, c
10
(y
11
− 7y
10
+ ··· − 3y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960008 + 0.311265I
a = 2.13610 − 2.32098I
b = −0.953626 − 0.297733I
−4.63619 − 2.72788I −3.55265 − 2.90330I
u = −0.960008 − 0.311265I
a = 2.13610 + 2.32098I
b = −0.953626 + 0.297733I
−4.63619 + 2.72788I −3.55265 + 2.90330I
u = 0.960008 + 0.311265I
a = 0.557092 + 0.459872I
b = 0.57629 + 1.32709I
−4.63619 + 2.72788I −3.55265 + 2.90330I
u = 0.960008 − 0.311265I
a = 0.557092 − 0.459872I
b = 0.57629 − 1.32709I
−4.63619 − 2.72788I −3.55265 − 2.90330I
u = −0.917066 + 0.263679I
a = −2.01041 + 2.78490I
b = 0.905203 + 0.036742I
−4.39205 + 5.08643I −2.94559 − 9.60994I
u = −0.917066 − 0.263679I
a = −2.01041 − 2.78490I
b = 0.905203 − 0.036742I
−4.39205 − 5.08643I −2.94559 + 9.60994I
u = 0.917066 + 0.263679I
a = 0.123926 + 0.668097I
b = −0.290016 + 1.220730I
−4.39205 − 5.08643I −2.94559 + 9.60994I
u = 0.917066 − 0.263679I
a = 0.123926 − 0.668097I
b = −0.290016 − 1.220730I
−4.39205 + 5.08643I −2.94559 − 9.60994I
u = 0.958173 + 0.586442I
a = 0.520358 + 0.305725I
b = 0.274503 + 1.358430I
−3.10505 − 2.43732I −10.07137 + 9.32376I
u = 0.958173 − 0.586442I
a = 0.520358 − 0.305725I
b = 0.274503 − 1.358430I
−3.10505 + 2.43732I −10.07137 − 9.32376I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958173 + 0.586442I
a = −1.026600 − 0.216633I
b = 0.277789 + 0.634862I
−3.10505 + 2.43732I −10.07137 − 9.32376I
u = −0.958173 − 0.586442I
a = −1.026600 + 0.216633I
b = 0.277789 − 0.634862I
−3.10505 − 2.43732I −10.07137 + 9.32376I
u = −1.091460 + 0.565363I
a = −1.90932 + 0.88290I
b = 1.01015 + 1.08285I
−2.38202 + 9.18219I −3.93831 − 7.03572I
u = −1.091460 − 0.565363I
a = −1.90932 − 0.88290I
b = 1.01015 − 1.08285I
−2.38202 − 9.18219I −3.93831 + 7.03572I
u = 1.091460 + 0.565363I
a = −0.359824 − 0.126466I
b = −0.478799 − 0.895773I
−2.38202 − 9.18219I −3.93831 + 7.03572I
u = 1.091460 − 0.565363I
a = −0.359824 + 0.126466I
b = −0.478799 + 0.895773I
−2.38202 + 9.18219I −3.93831 − 7.03572I
u = 0.261071 + 0.718323I
a = −0.628641 + 0.084315I
b = 0.025215 − 0.703097I
−0.17337 + 4.31510I −2.70293 − 4.01489I
u = 0.261071 − 0.718323I
a = −0.628641 − 0.084315I
b = 0.025215 + 0.703097I
−0.17337 − 4.31510I −2.70293 + 4.01489I
u = −0.261071 + 0.718323I
a = 1.53803 − 0.65442I
b = −0.865680 + 0.991862I
−0.17337 − 4.31510I −2.70293 + 4.01489I
u = −0.261071 − 0.718323I
a = 1.53803 + 0.65442I
b = −0.865680 − 0.991862I
−0.17337 + 4.31510I −2.70293 − 4.01489I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67677
a = 0.269386
b = 1.20909
−6.81120 −59.5780
u = −1.67677
a = −0.150821
b = −0.171150
−6.81120 −59.5780
31
VI. I
u
6
= h−u
5
− u
4
− u
2
a − au + u
2
+ b + u + 1, u
5
a + 2u
4
a + · · · + a
2
+
2u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
a
u
5
+ u
4
+ u
2
a + au − u
2
− u − 1
a
8
=
−u
−u
3
+ u
a
4
=
−u
5
− u
3
a − u
4
− u
2
a + u
3
+ 2u
2
+ a + u
−u
5
a − u
4
a + 2u
5
+ u
3
a + 2u
4
+ 2u
2
a + au − 2u
2
− u − 1
a
11
=
−u
4
a + u
5
− u
3
a + 3u
4
+ u
2
a + u
3
+ 2au − 2u
2
+ a − u
u
4
a + u
3
a + u
3
− au − u
2
− 2u − 1
a
9
=
−u
4
a + u
5
− u
3
a + 3u
4
+ u
2
a + u
3
+ 2au − 2u
2
+ a − 2u
u
4
a + u
3
a − au − u
2
− u − 1
a
10
=
u
5
+ 2u
4
+ au − 2u
2
+ a − u
−au
a
6
=
−u
5
− u
3
a − u
4
− u
2
a + u
3
+ u
2
+ a + u + 1
−u
5
a − u
4
a + 2u
5
+ u
3
a + 2u
4
+ 2u
2
a + au − u
2
− u − 1
a
6
=
−u
5
− u
3
a − u
4
− u
2
a + u
3
+ u
2
+ a + u + 1
−u
5
a − u
4
a + 2u
5
+ u
3
a + 2u
4
+ 2u
2
a + au − u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
− 4u
2
− 4u − 10
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
3
, c
8
(u + 1)
12
c
4
, c
6
, c
9
c
11
u
12
− u
11
+ 2u
10
+ 2u
9
+ 3u
8
+ 3u
7
+ 17u
6
+ 9u
5
+ 19u
4
+ 5u
3
+ 6u
2
+ 1
c
5
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
3
, c
8
(y −1)
12
c
4
, c
6
, c
9
c
11
y
12
+ 3y
11
+ ··· + 12y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 1.207500 − 0.512559I
b = 0.51345 + 1.52069I
−5.18047 − 0.92430I −15.7167 + 0.7942I
u = 1.002190 + 0.295542I
a = 0.47863 − 1.41379I
b = −0.085204 − 0.856161I
−5.18047 − 0.92430I −15.7167 + 0.7942I
u = 1.002190 − 0.295542I
a = 1.207500 + 0.512559I
b = 0.51345 − 1.52069I
−5.18047 + 0.92430I −15.7167 − 0.7942I
u = 1.002190 − 0.295542I
a = 0.47863 + 1.41379I
b = −0.085204 + 0.856161I
−5.18047 + 0.92430I −15.7167 − 0.7942I
u = −0.428243 + 0.664531I
a = −1.241310 + 0.272628I
b = 0.170133 − 0.403810I
−1.39926 − 0.92430I −8.28328 + 0.79423I
u = −0.428243 + 0.664531I
a = 0.896343 − 1.037440I
b = −1.172330 + 0.699352I
−1.39926 − 0.92430I −8.28328 + 0.79423I
u = −0.428243 − 0.664531I
a = −1.241310 − 0.272628I
b = 0.170133 + 0.403810I
−1.39926 + 0.92430I −8.28328 − 0.79423I
u = −0.428243 − 0.664531I
a = 0.896343 + 1.037440I
b = −1.172330 − 0.699352I
−1.39926 + 0.92430I −8.28328 − 0.79423I
u = −1.073950 + 0.558752I
a = 1.69281 − 0.56928I
b = −0.344080 − 0.571978I
−3.28987 + 5.69302I −12.00000 − 5.51057I
u = −1.073950 + 0.558752I
a = −1.53397 + 1.00692I
b = 1.41803 + 1.13073I
−3.28987 + 5.69302I −12.00000 − 5.51057I
35
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 1.69281 + 0.56928I
b = −0.344080 + 0.571978I
−3.28987 − 5.69302I −12.00000 + 5.51057I
u = −1.073950 − 0.558752I
a = −1.53397 − 1.00692I
b = 1.41803 − 1.13073I
−3.28987 − 5.69302I −12.00000 + 5.51057I
36
VII. I
u
7
= h−u
5
+ u
3
+ b − u, u
5
− 2u
3
+ a + u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
8
=
−u
−u
3
+ u
a
4
=
u
2
− 1
−u
2
a
11
=
−u
−u
3
+ u
a
9
=
−u
−u
3
+ u
a
10
=
u
4
− u
2
+ 1
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
6
=
u
2
− 1
−u
2
a
6
=
u
2
− 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
− 4u
2
+ 4u + 2
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
2
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
8
u
6
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
3
, c
8
y
6
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.315740 + 0.200172I
b = −0.428243 + 0.664531I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 − 0.295542I
a = −0.315740 − 0.200172I
b = −0.428243 − 0.664531I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.428243 + 0.664531I
a = −1.49099 − 0.22339I
b = 1.002190 + 0.295542I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 − 0.664531I
a = −1.49099 + 0.22339I
b = 1.002190 − 0.295542I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.073950 + 0.558752I
a = 1.30674 + 1.20014I
b = −1.073950 + 0.558752I
− 5.69302I 0. + 5.51057I
u = 1.073950 − 0.558752I
a = 1.30674 − 1.20014I
b = −1.073950 − 0.558752I
5.69302I 0. − 5.51057I
40
VIII. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
−1
0
a
2
=
1
0
a
3
=
1
0
a
5
=
0
b
a
8
=
−1
0
a
4
=
−b
b
a
11
=
1
−b − 1
a
9
=
b
−b
a
10
=
0
−b
a
6
=
−1
b + 1
a
6
=
−1
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
c
3
, c
5
, c
8
c
10
u
2
− u + 1
c
4
, c
6
, c
9
c
11
u
2
+ u + 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
44
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
14
· (u
7
− 3u
6
+ 3u
5
+ 2u
4
− 9u
3
+ 13u
2
− 10u + 4)
2
· (u
17
− 6u
16
+ ··· + 28u − 8)(u
22
− 8u
20
+ ··· + 8u
2
− 3)
c
2
u
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
15
· ((u
7
+ 3u
6
+ ··· − 4u + 16)
2
)(u
11
+ 8u
10
+ ··· + 8u + 3)
2
· (u
17
+ 10u
16
+ ··· + 208u + 64)
c
3
, c
8
u
6
(u + 1)
12
(u
2
− u + 1)(u
2
+ u + 1)
12
(u
4
+ u
3
− 2u + 1)
12
· (u
14
− 15u
13
+ ··· − 1309u + 187)(u
17
− 13u
16
+ ··· + 259u − 47)
· (u
22
− 8u
21
+ ··· − u − 1)
c
4
, c
6
, c
9
c
11
(u
2
+ u + 1)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
· (u
12
− u
11
+ 2u
10
+ 2u
9
+ 3u
8
+ 3u
7
+ 17u
6
+ 9u
5
+ 19u
4
+ 5u
3
+ 6u
2
+ 1)
· (u
14
+ u
13
+ ··· + 4u + 1)(u
17
− u
16
+ ··· + u − 1)
· (u
22
− 2u
21
+ ··· − 4u − 1)(u
24
+ u
23
+ ··· + 4u + 1)
· (u
48
− u
47
+ ··· + 258u + 67)
c
5
, c
10
(u
2
− u + 1)(u
6
− u
5
+ ··· − u + 1)
2
(u
6
+ u
5
+ ··· + u + 1)
· (u
7
− u
6
+ u
5
− u
4
+ u
3
+ u − 1)
2
· (u
11
+ u
10
− 3u
9
− 4u
8
+ 4u
7
+ 5u
6
− 5u
5
− 4u
4
+ 8u
3
+ 2u
2
− u + 1)
2
· (u
17
+ 2u
16
+ ··· − u + 4)(u
24
− u
23
+ ··· − 148u + 43)
2
· (u
24
+ 3u
23
+ ··· + 114u + 31)
45
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
15
· ((y
7
− 3y
6
+ ··· − 4y − 16)
2
)(y
11
− 8y
10
+ ··· + 8y − 3)
2
· (y
17
− 10y
16
+ ··· + 208y − 64)
c
2
y
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
15
· (y
7
− 3y
6
− 5y
5
− 80y
4
− 71y
3
+ 31y
2
− 144y − 256)
2
· ((y
11
− 6y
10
+ ··· + 16y − 9)
2
)(y
17
− 6y
16
+ ··· + 47360y − 4096)
c
3
, c
8
y
6
(y − 1)
12
(y
2
+ y + 1)
13
(y
4
− y
3
+ 6y
2
− 4y + 1)
12
· (y
14
− 3y
13
+ ··· − 5797y + 34969)
· (y
17
− 13y
16
+ ··· − 7555y − 2209)(y
22
− 16y
21
+ ··· − 11y + 1)
c
4
, c
6
, c
9
c
11
(y
2
+ y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
12
+ 3y
11
+ ··· + 12y + 1)(y
14
− 3y
13
+ ··· − 2y + 1)
· (y
17
− 5y
16
+ ··· + 21y − 1)(y
22
+ 8y
21
+ ··· − 28y + 1)
· (y
24
+ 3y
23
+ ··· − 8y + 1)(y
48
+ 21y
47
+ ··· + 251016y + 4489)
c
5
, c
10
(y
2
+ y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· ((y
7
+ y
6
+ y
5
+ 3y
4
+ y
3
+ y − 1)
2
)(y
11
− 7y
10
+ ··· − 3y − 1)
2
· (y
17
− 12y
16
+ ··· + 177y − 16)
· (y
24
− 21y
23
+ ··· − 20872y + 1849)
2
· (y
24
+ 15y
23
+ ··· + 25444y + 961)
46
