12n
0740
(K12n
0740
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 11 3 11 2 1 5 8 10
Solving Sequence
1,9 5,10
11 6 4 2 8 3 7 12
c
9
c
10
c
5
c
4
c
1
c
8
c
3
c
6
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.79550 × 10
17
u
29
+ 2.44036 × 10
18
u
28
+ ··· + 5.15180 × 10
17
b − 1.38475 × 10
18
,
− 2.66097 × 10
17
u
29
− 3.83157 × 10
18
u
28
+ ··· + 5.15180 × 10
17
a − 5.56966 × 10
18
,
u
30
+ 14u
29
+ ··· + 196u + 16i
I
u
2
= h−220u
11
a
3
− 53u
11
a
2
+ ··· − 345a + 469, −54u
11
a
3
+ 45u
11
a
2
+ ··· − 1650a − 74,
u
12
− 3u
11
+ 8u
10
− 13u
9
+ 19u
8
− 23u
7
+ 25u
6
− 25u
5
+ 20u
4
− 15u
3
+ 10u
2
− 5u + 3i
I
u
3
= h−62145u
17
+ 526568u
16
+ ··· + 56783b + 322467,
485418u
17
− 4751066u
16
+ ··· + 738179a − 8037342, u
18
− 9u
17
+ ··· − 45u + 13i
I
u
4
= h8a
3
u + 6a
3
− 7a
2
u + a
2
+ 35au + 50b + 45a − 23u − 61, a
4
+ a
3
u + a
3
− a
2
u + 4a
2
+ 5au − a − 6u − 5,
u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 104 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
= h1.80 × 10
17
u
29
+ 2.44 × 10
18
u
28
+ · · · + 5.15 × 10
17
b − 1.38 ×
10
18
, −2.66 × 10
17
u
29
− 3.83 × 10
18
u
28
+ · · · + 5.15 × 10
17
a − 5.57 ×
10
18
, u
30
+ 14u
29
+ · · · + 196u + 16i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.516513u
29
+ 7.43735u
28
+ ··· + 140.972u + 10.8111
−0.348519u
29
− 4.73692u
28
+ ··· + 19.4278u + 2.68790
a
10
=
1
u
2
a
11
=
0.296247u
29
+ 4.14543u
28
+ ··· + 32.3275u + 1.56658
−0.155522u
29
− 2.01976u
28
+ ··· + 24.7639u + 2.25160
a
6
=
0.267313u
29
+ 3.75667u
28
+ ··· + 107.255u + 8.33432
−0.130864u
29
− 1.73147u
28
+ ··· + 25.8846u + 3.13569
a
4
=
0.167994u
29
+ 2.70043u
28
+ ··· + 160.399u + 13.4990
−0.348519u
29
− 4.73692u
28
+ ··· + 19.4278u + 2.68790
a
2
=
0.271573u
29
+ 3.91281u
28
+ ··· + 127.444u + 8.93601
−0.110791u
29
− 1.30944u
28
+ ··· + 45.2923u + 4.34517
a
8
=
−0.776602u
29
− 10.6341u
28
+ ··· − 145.532u − 10.1408
0.00330517u
29
− 0.532040u
28
+ ··· − 115.013u − 10.6530
a
3
=
0.416283u
29
+ 5.42329u
28
+ ··· + 107.374u + 8.39097
0.228207u
29
+ 3.73456u
28
+ ··· + 129.856u + 11.6598
a
7
=
0.302005u
29
+ 3.74514u
28
+ ··· + 39.4511u + 1.58179
0.410407u
29
+ 6.01738u
28
+ ··· + 125.320u + 11.0560
a
12
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
4925743045415160
4441203039779213
u
29
−
63522435107648417
4441203039779213
u
28
+···+
783280962850760800
4441203039779213
u+
100283588087439718
4441203039779213
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
30
− u
29
+ ··· + u + 1
c
2
, c
6
u
30
− 13u
29
+ ··· − 46u + 4
c
3
u
30
− u
29
+ ··· − 58u + 23
c
5
, c
10
u
30
+ u
29
+ ··· − 8u
2
+ 1
c
7
, c
11
u
30
+ u
29
+ ··· + 13u + 2
c
8
u
30
− 23u
29
+ ··· − 25088u + 2048
c
9
, c
12
u
30
− 14u
29
+ ··· − 196u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
+ 9y
29
+ ··· + 27y + 1
c
2
, c
6
y
30
− 7y
29
+ ··· − 140y + 16
c
3
y
30
+ 3y
29
+ ··· + 5238y + 529
c
5
, c
10
y
30
− 29y
29
+ ··· − 16y + 1
c
7
, c
11
y
30
+ 31y
29
+ ··· + 195y + 4
c
8
y
30
+ 3y
29
+ ··· − 12845056y + 4194304
c
9
, c
12
y
30
+ 16y
29
+ ··· + 6864y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.008449 + 1.038050I
a = 0.19283 + 1.93584I
b = 0.875100 − 1.101510I
1.75922 + 2.08616I −0.70875 − 3.66623I
u = −0.008449 − 1.038050I
a = 0.19283 − 1.93584I
b = 0.875100 + 1.101510I
1.75922 − 2.08616I −0.70875 + 3.66623I
u = 0.100473 + 0.896678I
a = −0.809633 − 1.017280I
b = −0.085198 + 0.821995I
1.52091 − 2.28612I 0.91878 + 3.77911I
u = 0.100473 − 0.896678I
a = −0.809633 + 1.017280I
b = −0.085198 − 0.821995I
1.52091 + 2.28612I 0.91878 − 3.77911I
u = −0.521031 + 0.986835I
a = −0.45037 − 1.35721I
b = −0.84200 + 1.18633I
5.95512 + 6.91831I 3.78632 − 0.34811I
u = −0.521031 − 0.986835I
a = −0.45037 + 1.35721I
b = −0.84200 − 1.18633I
5.95512 − 6.91831I 3.78632 + 0.34811I
u = −0.178076 + 0.864147I
a = 0.58856 + 1.68337I
b = 0.774314 − 1.068170I
1.49951 + 2.61667I 1.71047 − 2.35153I
u = −0.178076 − 0.864147I
a = 0.58856 − 1.68337I
b = 0.774314 + 1.068170I
1.49951 − 2.61667I 1.71047 + 2.35153I
u = −0.083596 + 1.147820I
a = −0.23908 − 1.46108I
b = −0.639871 + 0.967627I
3.76134 − 0.67427I 6.55860 + 2.69018I
u = −0.083596 − 1.147820I
a = −0.23908 + 1.46108I
b = −0.639871 − 0.967627I
3.76134 + 0.67427I 6.55860 − 2.69018I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746615 + 0.920318I
a = 0.617510 + 0.248273I
b = −0.195032 − 0.802929I
5.30862 − 2.03318I 13.21436 + 4.72317I
u = −0.746615 − 0.920318I
a = 0.617510 − 0.248273I
b = −0.195032 + 0.802929I
5.30862 + 2.03318I 13.21436 − 4.72317I
u = 0.049970 + 0.694974I
a = 0.545450 − 1.292250I
b = −0.750678 + 0.197340I
2.97639 + 0.56649I 1.66356 + 2.53022I
u = 0.049970 − 0.694974I
a = 0.545450 + 1.292250I
b = −0.750678 − 0.197340I
2.97639 − 0.56649I 1.66356 − 2.53022I
u = −1.347510 + 0.262663I
a = 0.360072 + 0.067366I
b = −0.926246 − 0.689155I
−9.86335 − 10.01860I 0. + 6.83043I
u = −1.347510 − 0.262663I
a = 0.360072 − 0.067366I
b = −0.926246 + 0.689155I
−9.86335 + 10.01860I 0. − 6.83043I
u = −1.296810 + 0.492873I
a = −0.447016 − 0.001247I
b = 0.845978 + 0.667950I
−9.34766 − 1.90724I 0
u = −1.296810 − 0.492873I
a = −0.447016 + 0.001247I
b = 0.845978 − 0.667950I
−9.34766 + 1.90724I 0
u = −0.75549 + 1.23771I
a = −0.011672 + 1.404000I
b = 1.10163 − 1.17925I
−6.85242 + 8.97569I 0
u = −0.75549 − 1.23771I
a = −0.011672 − 1.404000I
b = 1.10163 + 1.17925I
−6.85242 − 8.97569I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.70214 + 1.34239I
a = 0.07842 − 1.49511I
b = −1.12757 + 1.20390I
−6.4102 + 17.0561I 0
u = −0.70214 − 1.34239I
a = 0.07842 + 1.49511I
b = −1.12757 − 1.20390I
−6.4102 − 17.0561I 0
u = −1.09815 + 1.16174I
a = −0.221067 − 0.658397I
b = −0.325690 + 0.894880I
−4.25072 + 0.10093I 0
u = −1.09815 − 1.16174I
a = −0.221067 + 0.658397I
b = −0.325690 − 0.894880I
−4.25072 − 0.10093I 0
u = −0.93186 + 1.30875I
a = 0.236542 + 0.853013I
b = 0.422858 − 0.999422I
−3.41653 + 8.45839I 0
u = −0.93186 − 1.30875I
a = 0.236542 − 0.853013I
b = 0.422858 + 0.999422I
−3.41653 − 8.45839I 0
u = −0.130584 + 0.190445I
a = −1.68626 + 1.76732I
b = 0.260420 + 0.577778I
0.175219 − 1.183220I 2.13993 + 5.80206I
u = −0.130584 − 0.190445I
a = −1.68626 − 1.76732I
b = 0.260420 − 0.577778I
0.175219 + 1.183220I 2.13993 − 5.80206I
u = 0.64988 + 1.72077I
a = −0.004280 + 0.359831I
b = 0.111989 − 0.254072I
−0.90966 − 3.07303I 0
u = 0.64988 − 1.72077I
a = −0.004280 − 0.359831I
b = 0.111989 + 0.254072I
−0.90966 + 3.07303I 0
7
II. I
u
2
= h−220u
11
a
3
− 53u
11
a
2
+ · · · − 345a + 469, −54u
11
a
3
+ 45u
11
a
2
+
· · · − 1650a − 74, u
12
− 3u
11
+ · · · − 5u + 3i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
a
1.29412a
3
u
11
+ 0.311765a
2
u
11
+ ··· + 2.02941a − 2.75882
a
10
=
1
u
2
a
11
=
0.111765a
3
u
11
+ 0.323529a
2
u
11
+ ··· + 1.84118a − 2.45098
−0.494118a
2
u
11
+ 0.0235294u
11
+ ··· + 1.51765a
2
+ 0.0705882
a
6
=
0.123529a
3
u
11
− 0.158824a
2
u
11
+ ··· − 5.01765a − 3.90588
−0.852941a
3
u
11
+ 1.74706a
2
u
11
+ ··· + 3.26471a − 3.03529
a
4
=
1.29412a
3
u
11
+ 0.311765a
2
u
11
+ ··· + 3.02941a − 2.75882
1.29412a
3
u
11
+ 0.311765a
2
u
11
+ ··· + 2.02941a − 2.75882
a
2
=
0.335294a
3
u
11
+ 0.476471a
2
u
11
+ ··· + 2.52353a + 9.71765
0.423529a
3
u
11
− 0.0470588a
2
u
11
+ ··· + 2.08235a + 1.43529
a
8
=
−0.200000a
3
u
11
+ 0.700000a
2
u
11
+ ··· − 0.900000a + 11.5667
0.423529a
3
u
11
− 0.0470588a
2
u
11
+ ··· + 2.08235a + 0.435294
a
3
=
1.35294a
3
u
11
+ 0.882353a
2
u
11
+ ··· − 9.76471a + 9.58824
0.358824a
3
u
11
+ 0.288235a
2
u
11
+ ··· + 2.80588a − 0.541176
a
7
=
1.15882a
3
u
11
− 0.370588a
2
u
11
+ ··· − 2.59412a − 14.4471
−0.447059a
3
u
11
+ 2.10588a
2
u
11
+ ··· − 8.36471a − 0.729412
a
12
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
144
85
u
11
a
3
+
16
85
u
11
a
2
+ ··· −
708
85
a −
318
85
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
48
− u
47
+ ··· − 14u + 1
c
2
, c
6
(u
12
+ 3u
11
+ ··· + 3u + 1)
4
c
3
u
48
− 3u
47
+ ··· + 4712118u + 1068997
c
5
, c
10
u
48
− u
47
+ ··· − 51466u + 6859
c
7
, c
11
u
48
− 3u
47
+ ··· + 4752u + 121
c
8
(u
2
+ u + 1)
24
c
9
, c
12
(u
12
+ 3u
11
+ ··· + 5u + 3)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
48
− 3y
47
+ ··· − 48y + 1
c
2
, c
6
(y
12
− y
11
+ ··· + 3y + 1)
4
c
3
y
48
+ 45y
47
+ ··· + 23945168738324y + 1142754586009
c
5
, c
10
y
48
− 51y
47
+ ··· − 1210663780y + 47045881
c
7
, c
11
y
48
+ 51y
47
+ ··· − 8371022y + 14641
c
8
(y
2
+ y + 1)
24
c
9
, c
12
(y
12
+ 7y
11
+ ··· + 35y + 9)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420764 + 0.913546I
a = 0.234639 − 0.310765I
b = 1.289820 + 0.174877I
−7.04292 + 3.63020I −1.77003 − 2.67858I
u = −0.420764 + 0.913546I
a = 1.25869 + 1.01337I
b = −1.65916 − 1.21045I
−7.04292 + 7.68996I −1.77003 − 9.60678I
u = −0.420764 + 0.913546I
a = 0.75156 − 2.28473I
b = −0.348546 + 0.282925I
−7.04292 + 7.68996I −1.77003 − 9.60678I
u = −0.420764 + 0.913546I
a = −0.13874 + 2.68737I
b = 0.51730 − 1.44984I
−7.04292 + 3.63020I −1.77003 − 2.67858I
u = −0.420764 − 0.913546I
a = 0.234639 + 0.310765I
b = 1.289820 − 0.174877I
−7.04292 − 3.63020I −1.77003 + 2.67858I
u = −0.420764 − 0.913546I
a = 1.25869 − 1.01337I
b = −1.65916 + 1.21045I
−7.04292 − 7.68996I −1.77003 + 9.60678I
u = −0.420764 − 0.913546I
a = 0.75156 + 2.28473I
b = −0.348546 − 0.282925I
−7.04292 − 7.68996I −1.77003 + 9.60678I
u = −0.420764 − 0.913546I
a = −0.13874 − 2.68737I
b = 0.51730 + 1.44984I
−7.04292 − 3.63020I −1.77003 + 2.67858I
u = 0.295106 + 0.923595I
a = −0.554428 − 1.151090I
b = −0.133109 − 0.080601I
2.77107 + 0.79988I 0.02056 + 1.79181I
u = 0.295106 + 0.923595I
a = 1.05566 − 1.10395I
b = −0.934687 + 0.998484I
2.77107 + 0.79988I 0.02056 + 1.79181I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295106 + 0.923595I
a = 1.42563 − 0.84907I
b = 0.710142 + 0.479994I
2.77107 − 3.25989I 0.02056 + 8.72001I
u = 0.295106 + 0.923595I
a = 0.27668 + 2.41066I
b = −0.97115 − 1.86367I
2.77107 − 3.25989I 0.02056 + 8.72001I
u = 0.295106 − 0.923595I
a = −0.554428 + 1.151090I
b = −0.133109 + 0.080601I
2.77107 − 0.79988I 0.02056 − 1.79181I
u = 0.295106 − 0.923595I
a = 1.05566 + 1.10395I
b = −0.934687 − 0.998484I
2.77107 − 0.79988I 0.02056 − 1.79181I
u = 0.295106 − 0.923595I
a = 1.42563 + 0.84907I
b = 0.710142 − 0.479994I
2.77107 + 3.25989I 0.02056 − 8.72001I
u = 0.295106 − 0.923595I
a = 0.27668 − 2.41066I
b = −0.97115 + 1.86367I
2.77107 + 3.25989I 0.02056 − 8.72001I
u = 1.002840 + 0.240514I
a = 0.122850 − 0.710506I
b = 0.853211 + 0.839616I
−3.60424 − 3.13751I −8.13937 + 9.38471I
u = 1.002840 + 0.240514I
a = −0.565247 + 0.035897I
b = 1.068890 − 0.471788I
−3.60424 + 0.92226I −8.13937 + 2.45650I
u = 1.002840 + 0.240514I
a = −0.291285 + 0.370590I
b = −0.609909 + 0.315996I
−3.60424 + 0.92226I −8.13937 + 2.45650I
u = 1.002840 + 0.240514I
a = −0.046613 − 0.234517I
b = −0.947781 − 0.364233I
−3.60424 − 3.13751I −8.13937 + 9.38471I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002840 − 0.240514I
a = 0.122850 + 0.710506I
b = 0.853211 − 0.839616I
−3.60424 + 3.13751I −8.13937 − 9.38471I
u = 1.002840 − 0.240514I
a = −0.565247 − 0.035897I
b = 1.068890 + 0.471788I
−3.60424 − 0.92226I −8.13937 − 2.45650I
u = 1.002840 − 0.240514I
a = −0.291285 − 0.370590I
b = −0.609909 − 0.315996I
−3.60424 − 0.92226I −8.13937 − 2.45650I
u = 1.002840 − 0.240514I
a = −0.046613 + 0.234517I
b = −0.947781 + 0.364233I
−3.60424 + 3.13751I −8.13937 − 9.38471I
u = −0.461620 + 0.763725I
a = −0.594654 + 0.611108I
b = −1.158800 − 0.235440I
−7.50607 − 4.01700I −3.05660 + 2.18818I
u = −0.461620 + 0.763725I
a = −0.975854 − 0.793065I
b = 1.49076 + 1.07883I
−7.50607 + 0.04277I −3.05660 − 4.74002I
u = −0.461620 + 0.763725I
a = −0.62642 + 2.31633I
b = 0.455936 − 0.261329I
−7.50607 + 0.04277I −3.05660 − 4.74002I
u = −0.461620 + 0.763725I
a = 0.07661 − 2.76035I
b = −0.52252 + 1.51257I
−7.50607 − 4.01700I −3.05660 + 2.18818I
u = −0.461620 − 0.763725I
a = −0.594654 − 0.611108I
b = −1.158800 + 0.235440I
−7.50607 + 4.01700I −3.05660 − 2.18818I
u = −0.461620 − 0.763725I
a = −0.975854 + 0.793065I
b = 1.49076 − 1.07883I
−7.50607 − 0.04277I −3.05660 + 4.74002I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461620 − 0.763725I
a = −0.62642 − 2.31633I
b = 0.455936 + 0.261329I
−7.50607 − 0.04277I −3.05660 + 4.74002I
u = −0.461620 − 0.763725I
a = 0.07661 + 2.76035I
b = −0.52252 − 1.51257I
−7.50607 + 4.01700I −3.05660 − 2.18818I
u = 0.644336 + 1.169420I
a = −0.224819 + 0.865040I
b = −1.015020 − 0.673671I
−0.87149 − 6.78221I −5.42450 + 9.11637I
u = 0.644336 + 1.169420I
a = −0.099676 + 0.869507I
b = −0.210230 − 0.380235I
−0.87149 − 2.72244I −5.42450 + 2.18817I
u = 0.644336 + 1.169420I
a = −0.446440 − 0.047632I
b = 0.771850 + 0.047155I
−0.87149 − 2.72244I −5.42450 + 2.18817I
u = 0.644336 + 1.169420I
a = −0.21389 − 1.74893I
b = 1.02266 + 1.32659I
−0.87149 − 6.78221I −5.42450 + 9.11637I
u = 0.644336 − 1.169420I
a = −0.224819 − 0.865040I
b = −1.015020 + 0.673671I
−0.87149 + 6.78221I −5.42450 − 9.11637I
u = 0.644336 − 1.169420I
a = −0.099676 − 0.869507I
b = −0.210230 + 0.380235I
−0.87149 + 2.72244I −5.42450 − 2.18817I
u = 0.644336 − 1.169420I
a = −0.446440 + 0.047632I
b = 0.771850 − 0.047155I
−0.87149 + 2.72244I −5.42450 − 2.18817I
u = 0.644336 − 1.169420I
a = −0.21389 + 1.74893I
b = 1.02266 − 1.32659I
−0.87149 + 6.78221I −5.42450 − 9.11637I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44010 + 1.37677I
a = −0.328049 − 0.901932I
b = 0.652553 + 0.752898I
1.44924 − 4.10454I 4.36993 + 6.79554I
u = 0.44010 + 1.37677I
a = −0.285622 + 0.652606I
b = −0.348000 − 0.381177I
1.44924 − 4.10454I 4.36993 + 6.79554I
u = 0.44010 + 1.37677I
a = 0.397056 + 1.324180I
b = −1.29046 − 1.01688I
1.44924 − 8.16430I 4.3699 + 13.7237I
u = 0.44010 + 1.37677I
a = 0.12570 − 1.73097I
b = 0.816263 + 1.094770I
1.44924 − 8.16430I 4.3699 + 13.7237I
u = 0.44010 − 1.37677I
a = −0.328049 + 0.901932I
b = 0.652553 − 0.752898I
1.44924 + 4.10454I 4.36993 − 6.79554I
u = 0.44010 − 1.37677I
a = −0.285622 − 0.652606I
b = −0.348000 + 0.381177I
1.44924 + 4.10454I 4.36993 − 6.79554I
u = 0.44010 − 1.37677I
a = 0.397056 − 1.324180I
b = −1.29046 + 1.01688I
1.44924 + 8.16430I 4.3699 − 13.7237I
u = 0.44010 − 1.37677I
a = 0.12570 + 1.73097I
b = 0.816263 − 1.094770I
1.44924 + 8.16430I 4.3699 − 13.7237I
15
III.
I
u
3
= h−6.21 × 10
4
u
17
+ 5.27 × 10
5
u
16
+ · · · + 5.68 × 10
4
b + 3.22 × 10
5
, 4.85 ×
10
5
u
17
−4.75×10
6
u
16
+· · ·+7.38×10
5
a−8.04×10
6
, u
18
−9u
17
+· · ·−45u+13i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−0.657588u
17
+ 6.43620u
16
+ ··· − 35.6158u + 10.8881
1.09443u
17
− 9.27334u
16
+ ··· + 24.8670u − 5.67894
a
10
=
1
u
2
a
11
=
−0.0419790u
17
+ 0.137352u
16
+ ··· − 1.46627u + 1.30610
0.0340947u
17
− 0.0322984u
16
+ ··· + 0.0538013u + 0.102495
a
6
=
−0.151814u
17
+ 1.64620u
16
+ ··· − 9.99282u + 4.35385
0.784108u
17
− 6.98660u
16
+ ··· + 33.5038u − 10.4362
a
4
=
0.436841u
17
− 2.83714u
16
+ ··· − 10.7488u + 5.20913
1.09443u
17
− 9.27334u
16
+ ··· + 24.8670u − 5.67894
a
2
=
−0.546859u
17
+ 4.48245u
16
+ ··· − 9.54762u + 0.989853
−0.439286u
17
+ 4.06903u
16
+ ··· − 22.6188u + 7.10917
a
8
=
−0.343180u
17
+ 2.13692u
16
+ ··· + 12.9823u − 4.25290
−0.836236u
17
+ 7.62276u
16
+ ··· − 33.3547u + 10.1721
a
3
=
−0.302452u
17
+ 2.82244u
16
+ ··· − 14.5097u + 3.03165
−0.213532u
17
+ 2.17852u
16
+ ··· − 16.4211u + 5.64940
a
7
=
−0.0660910u
17
+ 0.0173928u
16
+ ··· + 26.3408u − 7.19948
−0.387088u
17
+ 3.67661u
16
+ ··· − 15.0344u + 3.16692
a
12
=
u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
239665
56783
u
17
−
1891871
56783
u
16
+ ··· +
4159158
56783
u −
1061966
56783
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
18
− u
17
+ ··· + u + 1
c
2
u
18
− 8u
17
+ ··· − 7u + 1
c
3
u
18
− u
17
+ ··· − 14u + 11
c
5
u
18
+ u
17
+ ··· + 4u + 1
c
6
u
18
+ 8u
17
+ ··· + 7u + 1
c
7
u
18
+ u
17
+ ··· + 4u + 1
c
8
u
18
− 8u
17
+ ··· − u + 1
c
9
u
18
− 9u
17
+ ··· − 45u + 13
c
10
u
18
− u
17
+ ··· − 4u + 1
c
11
u
18
− u
17
+ ··· − 4u + 1
c
12
u
18
+ 9u
17
+ ··· + 45u + 13
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
18
− y
17
+ ··· + 9y + 1
c
2
, c
6
y
18
− 8y
17
+ ··· + 5y + 1
c
3
y
18
+ 5y
17
+ ··· + 68y + 121
c
5
, c
10
y
18
− 15y
17
+ ··· − 2y + 1
c
7
, c
11
y
18
+ 17y
17
+ ··· − 8y + 1
c
8
y
18
+ 2y
17
+ ··· − 9y + 1
c
9
, c
12
y
18
+ 11y
17
+ ··· + 1147y + 169
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298057 + 0.857334I
a = −0.204887 − 1.188570I
b = 0.917720 + 0.365951I
2.86873 − 1.41914I −0.00227 + 5.81292I
u = 0.298057 − 0.857334I
a = −0.204887 + 1.188570I
b = 0.917720 − 0.365951I
2.86873 + 1.41914I −0.00227 − 5.81292I
u = 1.104840 + 0.063258I
a = 0.0614125 + 0.0904156I
b = −0.872313 − 0.463543I
−3.53798 − 2.03888I −7.34728 + 3.69480I
u = 1.104840 − 0.063258I
a = 0.0614125 − 0.0904156I
b = −0.872313 + 0.463543I
−3.53798 + 2.03888I −7.34728 − 3.69480I
u = −0.324478 + 0.767766I
a = −0.43390 − 2.15456I
b = 0.894501 + 0.794834I
−6.94375 + 6.44664I −0.79828 − 2.66618I
u = −0.324478 − 0.767766I
a = −0.43390 + 2.15456I
b = 0.894501 − 0.794834I
−6.94375 − 6.44664I −0.79828 + 2.66618I
u = 0.572894 + 1.154750I
a = 0.264264 − 1.367920I
b = 0.85224 + 1.18381I
5.98080 − 7.72911I 4.36597 + 9.45283I
u = 0.572894 − 1.154750I
a = 0.264264 + 1.367920I
b = 0.85224 − 1.18381I
5.98080 + 7.72911I 4.36597 − 9.45283I
u = 0.697552 + 1.113470I
a = 0.012054 + 0.966995I
b = −0.818095 − 0.737226I
−0.54597 − 4.78777I −3.04717 + 6.54355I
u = 0.697552 − 1.113470I
a = 0.012054 − 0.966995I
b = −0.818095 + 0.737226I
−0.54597 + 4.78777I −3.04717 − 6.54355I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323243 + 0.538024I
a = 0.56440 + 2.43929I
b = −0.841574 − 0.708571I
−7.29059 − 1.21516I −1.54684 + 1.80912I
u = −0.323243 − 0.538024I
a = 0.56440 − 2.43929I
b = −0.841574 + 0.708571I
−7.29059 + 1.21516I −1.54684 − 1.80912I
u = 1.058500 + 0.915875I
a = −0.493256 + 0.216116I
b = 0.292506 − 0.767500I
4.44840 + 1.75312I 3.26197 − 3.17049I
u = 1.058500 − 0.915875I
a = −0.493256 − 0.216116I
b = 0.292506 + 0.767500I
4.44840 − 1.75312I 3.26197 + 3.17049I
u = 0.48893 + 1.35129I
a = 0.12976 + 1.48454I
b = −1.05912 − 1.03702I
0.89547 − 7.52978I −3.11582 + 5.02731I
u = 0.48893 − 1.35129I
a = 0.12976 − 1.48454I
b = −1.05912 + 1.03702I
0.89547 + 7.52978I −3.11582 − 5.02731I
u = 0.92695 + 1.78794I
a = 0.061691 − 0.348186I
b = 0.134133 + 0.374688I
−0.80993 − 3.27591I 12.7297 + 21.5391I
u = 0.92695 − 1.78794I
a = 0.061691 + 0.348186I
b = 0.134133 − 0.374688I
−0.80993 + 3.27591I 12.7297 − 21.5391I
20
IV. I
u
4
=
h8a
3
u−7a
2
u+· · ·+45a−61, a
4
+a
3
u+a
3
−a
2
u+4a
2
+5au−a−6u−5, u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
a
−0.160000a
3
u + 0.140000a
2
u + ··· − 0.900000a + 1.22000
a
10
=
1
−1
a
11
=
0.420000a
3
u − 0.180000a
2
u + ··· + 0.300000a + 1.36000
1
25
a
3
u −
4
25
a
2
u + ··· +
3
5
a −
42
25
a
6
=
1.18000a
3
u + 0.780000a
2
u + ··· − 1.30000a + 0.440000
−
1
10
a
3
u −
1
10
a
2
u + ··· +
1
2
a +
1
5
a
4
=
−0.160000a
3
u + 0.140000a
2
u + ··· + 0.100000a + 1.22000
−0.160000a
3
u + 0.140000a
2
u + ··· − 0.900000a + 1.22000
a
2
=
−0.220000a
3
u − 0.620000a
2
u + ··· + 0.700000a − 1.76000
−0.280000a
3
u + 0.120000a
2
u + ··· − 0.200000a − 0.240000
a
8
=
−0.480000a
3
u + 0.420000a
2
u + ··· − 0.700000a + 3.66000
7
25
a
3
u −
3
25
a
2
u + ··· +
1
5
a −
19
25
a
3
=
0.960000a
3
u + 0.160000a
2
u + ··· − 0.600000a − 1.32000
−0.380000a
3
u + 0.0200000a
2
u + ··· + 0.300000a − 0.0400000
a
7
=
0.220000a
3
u + 0.620000a
2
u + ··· − 0.700000a + 1.76000
7
25
a
3
u −
3
25
a
2
u + ··· +
1
5
a +
6
25
a
12
=
u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
28
25
a
3
u +
4
25
a
3
+
12
25
a
2
u −
16
25
a
2
−
12
5
au −
4
5
a +
168
25
u +
176
25
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 6u
4
+ 6u
2
+ 2u + 1
c
2
(u + 1)
8
c
3
u
8
+ 6u
7
+ 19u
6
+ 42u
5
+ 68u
4
+ 78u
3
+ 62u
2
+ 36u + 13
c
5
u
8
− 3u
6
+ 2u
5
+ 10u
4
+ 6u
3
− 2u
2
− 2u + 1
c
6
(u − 1)
8
c
7
, c
11
(u
4
− u
2
+ 1)
2
c
8
(u
2
+ u + 1)
4
c
9
, c
12
(u
2
+ 1)
4
c
10
u
8
− 3u
6
− 2u
5
+ 10u
4
− 6u
3
− 2u
2
+ 2u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
8
+ 6y
7
+ 29y
6
+ 68y
5
+ 90y
4
+ 74y
3
+ 48y
2
+ 8y + 1
c
2
, c
6
(y −1)
8
c
3
y
8
+ 2y
7
− 7y
6
+ 8y
5
+ 22y
4
− 182y
3
− 4y
2
+ 316y + 169
c
5
, c
10
y
8
− 6y
7
+ 29y
6
− 68y
5
+ 90y
4
− 74y
3
+ 48y
2
− 8y + 1
c
7
, c
11
(y
2
− y + 1)
4
c
8
(y
2
+ y + 1)
4
c
9
, c
12
(y + 1)
8
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.027380 + 0.057186I
b = 0.197915 − 0.359271I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.000000I
a = −0.66136 − 1.42321I
b = 0.302085 + 1.225300I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.000000I
a = −0.98594 − 1.88020I
b = −0.630141 + 0.750055I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = 1.000000I
a = −0.38009 + 2.24622I
b = 1.13014 − 1.61608I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = 1.027380 − 0.057186I
b = 0.197915 + 0.359271I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = −0.66136 + 1.42321I
b = 0.302085 − 1.225300I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = −0.98594 + 1.88020I
b = −0.630141 − 0.750055I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = − 1.000000I
a = −0.38009 − 2.24622I
b = 1.13014 + 1.61608I
3.28987 − 2.02988I 6.00000 + 3.46410I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
8
+ 2u
7
+ ··· + 2u + 1)(u
18
− u
17
+ ··· + u + 1)
· (u
30
− u
29
+ ··· + u + 1)(u
48
− u
47
+ ··· − 14u + 1)
c
2
((u + 1)
8
)(u
12
+ 3u
11
+ ··· + 3u + 1)
4
(u
18
− 8u
17
+ ··· − 7u + 1)
· (u
30
− 13u
29
+ ··· − 46u + 4)
c
3
(u
8
+ 6u
7
+ 19u
6
+ 42u
5
+ 68u
4
+ 78u
3
+ 62u
2
+ 36u + 13)
· (u
18
− u
17
+ ··· − 14u + 11)(u
30
− u
29
+ ··· − 58u + 23)
· (u
48
− 3u
47
+ ··· + 4712118u + 1068997)
c
5
(u
8
− 3u
6
+ ··· − 2u + 1)(u
18
+ u
17
+ ··· + 4u + 1)
· (u
30
+ u
29
+ ··· − 8u
2
+ 1)(u
48
− u
47
+ ··· − 51466u + 6859)
c
6
((u − 1)
8
)(u
12
+ 3u
11
+ ··· + 3u + 1)
4
(u
18
+ 8u
17
+ ··· + 7u + 1)
· (u
30
− 13u
29
+ ··· − 46u + 4)
c
7
((u
4
− u
2
+ 1)
2
)(u
18
+ u
17
+ ··· + 4u + 1)(u
30
+ u
29
+ ··· + 13u + 2)
· (u
48
− 3u
47
+ ··· + 4752u + 121)
c
8
((u
2
+ u + 1)
28
)(u
18
− 8u
17
+ ··· − u + 1)
· (u
30
− 23u
29
+ ··· − 25088u + 2048)
c
9
((u
2
+ 1)
4
)(u
12
+ 3u
11
+ ··· + 5u + 3)
4
(u
18
− 9u
17
+ ··· − 45u + 13)
· (u
30
− 14u
29
+ ··· − 196u + 16)
c
10
(u
8
− 3u
6
+ ··· + 2u + 1)(u
18
− u
17
+ ··· − 4u + 1)
· (u
30
+ u
29
+ ··· − 8u
2
+ 1)(u
48
− u
47
+ ··· − 51466u + 6859)
c
11
((u
4
− u
2
+ 1)
2
)(u
18
− u
17
+ ··· − 4u + 1)(u
30
+ u
29
+ ··· + 13u + 2)
· (u
48
− 3u
47
+ ··· + 4752u + 121)
c
12
((u
2
+ 1)
4
)(u
12
+ 3u
11
+ ··· + 5u + 3)
4
(u
18
+ 9u
17
+ ··· + 45u + 13)
· (u
30
− 14u
29
+ ··· − 196u + 16)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
8
+ 6y
7
+ 29y
6
+ 68y
5
+ 90y
4
+ 74y
3
+ 48y
2
+ 8y + 1)
· (y
18
− y
17
+ ··· + 9y + 1)(y
30
+ 9y
29
+ ··· + 27y + 1)
· (y
48
− 3y
47
+ ··· − 48y + 1)
c
2
, c
6
((y −1)
8
)(y
12
− y
11
+ ··· + 3y + 1)
4
(y
18
− 8y
17
+ ··· + 5y + 1)
· (y
30
− 7y
29
+ ··· − 140y + 16)
c
3
(y
8
+ 2y
7
− 7y
6
+ 8y
5
+ 22y
4
− 182y
3
− 4y
2
+ 316y + 169)
· (y
18
+ 5y
17
+ ··· + 68y + 121)(y
30
+ 3y
29
+ ··· + 5238y + 529)
· (y
48
+ 45y
47
+ ··· + 23945168738324y + 1142754586009)
c
5
, c
10
(y
8
− 6y
7
+ 29y
6
− 68y
5
+ 90y
4
− 74y
3
+ 48y
2
− 8y + 1)
· (y
18
− 15y
17
+ ··· − 2y + 1)(y
30
− 29y
29
+ ··· − 16y + 1)
· (y
48
− 51y
47
+ ··· − 1210663780y + 47045881)
c
7
, c
11
((y
2
− y + 1)
4
)(y
18
+ 17y
17
+ ··· − 8y + 1)
· (y
30
+ 31y
29
+ ··· + 195y + 4)
· (y
48
+ 51y
47
+ ··· − 8371022y + 14641)
c
8
((y
2
+ y + 1)
28
)(y
18
+ 2y
17
+ ··· − 9y + 1)
· (y
30
+ 3y
29
+ ··· − 12845056y + 4194304)
c
9
, c
12
((y + 1)
8
)(y
12
+ 7y
11
+ ··· + 35y + 9)
4
· (y
18
+ 11y
17
+ ··· + 1147y + 169)(y
30
+ 16y
29
+ ··· + 6864y + 256)
26
