12a
0244
(K12a
0244
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 1 11 4 12 8 5 9
Solving Sequence
4,10 5,8
9 11 12 1 7 3 6 2
c
4
c
8
c
10
c
11
c
12
c
7
c
3
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.70055 × 10
176
u
48
+ 7.34394 × 10
176
u
47
+ ··· + 3.67864 × 10
181
b + 1.37942 × 10
180
,
1.66691 × 10
178
u
48
− 4.46314 × 10
178
u
47
+ ··· + 7.35728 × 10
181
a − 1.26886 × 10
182
,
u
49
− 3u
48
+ ··· + 22528u − 8192i
I
u
2
= hu
39
+ u
38
+ ··· + b + a, −u
38
− u
37
+ ··· + a
2
− 2u, u
40
+ u
39
+ ··· + 2u
3
+ 1i
I
u
3
= hb + u − 1, a + 1, u
2
+ 1i
I
v
1
= ha, v
5
− 2v
4
+ 16v
2
+ 64b − 16v −32, v
6
− 2v
5
+ 16v
3
− 16v
2
− 32v + 64i
* 4 irreducible components of dim
C
= 0, with total 137 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−2.70 × 10
176
u
48
+ 7.34 × 10
176
u
47
+ · · · + 3.68 × 10
181
b + 1.38 ×
10
180
, 1.67 × 10
178
u
48
− 4.46 × 10
178
u
47
+ · · · + 7.36 × 10
181
a − 1.27 ×
10
182
, u
49
− 3u
48
+ · · · + 22528u − 8192i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
8
=
−0.000226567u
48
+ 0.000606629u
47
+ ··· + 1.52293u + 1.72464
7.34115 × 10
−6
u
48
− 0.0000199637u
47
+ ··· + 0.829123u − 0.0374982
a
9
=
−0.000219225u
48
+ 0.000586666u
47
+ ··· + 2.35206u + 1.68714
7.34115 × 10
−6
u
48
− 0.0000199637u
47
+ ··· + 0.829123u − 0.0374982
a
11
=
0.000219225u
48
− 0.000586666u
47
+ ··· − 2.35206u − 1.68714
0.0000401811u
48
− 0.000116259u
47
+ ··· + 0.632956u − 0.619217
a
12
=
0.000226567u
48
− 0.000606629u
47
+ ··· − 1.52293u − 1.72464
0.0000425308u
48
− 0.000121702u
47
+ ··· + 0.619218u − 0.636090
a
1
=
0.000485973u
48
− 0.00130955u
47
+ ··· − 4.24203u − 4.03099
0.0000827120u
48
− 0.000237961u
47
+ ··· + 0.252174u − 1.25531
a
7
=
−0.000485973u
48
+ 0.00130955u
47
+ ··· + 4.24203u + 4.03099
8.34395 × 10
−6
u
48
− 0.0000219487u
47
+ ··· + 0.890893u − 0.0398997
a
3
=
−0.000168254u
48
+ 0.000608654u
47
+ ··· + 21.4016u − 4.40654
−0.0000103751u
48
+ 0.0000252373u
47
+ ··· − 0.598442u + 0.217313
a
6
=
−0.000521632u
48
+ 0.00132466u
47
+ ··· + 4.22379u + 4.65438
0.0000432685u
48
− 0.000176386u
47
+ ··· − 1.49474u + 0.280657
a
2
=
0.000322947u
48
− 0.000185023u
47
+ ··· + 22.4579u − 14.2537
−4.94378 × 10
−7
u
48
+ 0.000105337u
47
+ ··· + 5.55953u − 3.65339
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000380518u
48
+ 0.00154592u
47
+ ··· + 10.5498u − 9.69012
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 24u
48
+ ··· + 209u + 16
c
2
, c
5
u
49
+ 2u
48
+ ··· + 5u − 4
c
3
u
49
+ 2u
48
+ ··· + 11533u − 1348
c
4
u
49
− 3u
48
+ ··· + 22528u − 8192
c
6
u
49
+ 5u
47
+ ··· + 3280u − 704
c
7
, c
9
, c
10
c
12
u
49
− 6u
48
+ ··· − 3u − 1
c
8
, c
11
64(64u
49
+ 32u
48
+ ··· + 2u − 2)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
+ 4y
48
+ ··· + 19265y −256
c
2
, c
5
y
49
− 24y
48
+ ··· + 209y −16
c
3
y
49
− 16y
48
+ ··· − 79033007y −1817104
c
4
y
49
+ 15y
48
+ ··· − 1312817152y −67108864
c
6
y
49
+ 10y
48
+ ··· + 2659584y −495616
c
7
, c
9
, c
10
c
12
y
49
+ 20y
48
+ ··· − 3y −1
c
8
, c
11
4096(4096y
49
+ 13312y
48
+ ··· + 92y −4)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.368475 + 0.893141I
a = −0.437549 − 0.399190I
b = 0.737723 + 0.241805I
1.92348 + 0.00460I 8.35725 + 2.45568I
u = 0.368475 − 0.893141I
a = −0.437549 + 0.399190I
b = 0.737723 − 0.241805I
1.92348 − 0.00460I 8.35725 − 2.45568I
u = 0.842817 + 0.242258I
a = −0.530033 + 0.832526I
b = 0.663612 + 0.011137I
0.962056 + 0.593478I 9.83701 − 0.71197I
u = 0.842817 − 0.242258I
a = −0.530033 − 0.832526I
b = 0.663612 − 0.011137I
0.962056 − 0.593478I 9.83701 + 0.71197I
u = 0.559841 + 0.536004I
a = −0.53197 + 1.42690I
b = 0.699672 + 0.362657I
2.41634 − 4.82675I 8.03609 + 0.84928I
u = 0.559841 − 0.536004I
a = −0.53197 − 1.42690I
b = 0.699672 − 0.362657I
2.41634 + 4.82675I 8.03609 − 0.84928I
u = −0.229788 + 0.731298I
a = 0.411254 − 0.473412I
b = −0.708646 + 0.424150I
0.29548 − 4.94189I 3.78549 + 3.03515I
u = −0.229788 − 0.731298I
a = 0.411254 + 0.473412I
b = −0.708646 − 0.424150I
0.29548 + 4.94189I 3.78549 − 3.03515I
u = −1.234010 + 0.152432I
a = 0.272970 + 0.661526I
b = −0.665993 − 0.160510I
1.28810 + 3.67507I 9.11198 − 8.01331I
u = −1.234010 − 0.152432I
a = 0.272970 − 0.661526I
b = −0.665993 + 0.160510I
1.28810 − 3.67507I 9.11198 + 8.01331I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466677 + 0.528402I
a = 0.59247 + 1.57999I
b = −0.604388 + 0.427330I
3.99412 + 0.17438I 10.39352 + 6.49892I
u = −0.466677 − 0.528402I
a = 0.59247 − 1.57999I
b = −0.604388 − 0.427330I
3.99412 − 0.17438I 10.39352 − 6.49892I
u = 0.282727 + 0.643800I
a = −0.36034 + 1.88017I
b = 0.450725 + 0.695185I
1.35942 + 6.44982I 1.02359 − 10.63060I
u = 0.282727 − 0.643800I
a = −0.36034 − 1.88017I
b = 0.450725 − 0.695185I
1.35942 − 6.44982I 1.02359 + 10.63060I
u = −0.315447 + 0.593282I
a = 0.46079 + 1.85815I
b = −0.467003 + 0.604505I
3.45035 − 1.63795I 5.33084 + 7.67119I
u = −0.315447 − 0.593282I
a = 0.46079 − 1.85815I
b = −0.467003 − 0.604505I
3.45035 + 1.63795I 5.33084 − 7.67119I
u = 0.158584 + 0.553955I
a = −0.35372 + 2.17336I
b = 0.231235 + 0.617765I
−0.566080 − 0.618769I −6.81815 − 5.24173I
u = 0.158584 − 0.553955I
a = −0.35372 − 2.17336I
b = 0.231235 − 0.617765I
−0.566080 + 0.618769I −6.81815 + 5.24173I
u = 0.09699 + 1.43219I
a = −0.534665 − 0.241451I
b = 0.882372 − 0.109511I
1.58820 − 2.84063I 8.54119 + 5.77994I
u = 0.09699 − 1.43219I
a = −0.534665 + 0.241451I
b = 0.882372 + 0.109511I
1.58820 + 2.84063I 8.54119 − 5.77994I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547826
a = −0.866970
b = 0.455204
0.796835 12.7290
u = 0.12397 + 1.48331I
a = 0.592077 − 0.186758I
b = −0.959246 − 0.254074I
−0.13274 + 8.15426I 0. − 10.76131I
u = 0.12397 − 1.48331I
a = 0.592077 + 0.186758I
b = −0.959246 + 0.254074I
−0.13274 − 8.15426I 0. + 10.76131I
u = −0.121555 + 0.434531I
a = 0.161534 − 0.434467I
b = −0.242298 + 0.488090I
−1.65447 + 1.14516I −1.78214 − 1.36399I
u = −0.121555 − 0.434531I
a = 0.161534 + 0.434467I
b = −0.242298 − 0.488090I
−1.65447 − 1.14516I −1.78214 + 1.36399I
u = −0.87541 + 1.33937I
a = −0.847085 + 0.136222I
b = 1.14989 − 1.27447I
−2.00616 − 11.44390I 0
u = −0.87541 − 1.33937I
a = −0.847085 − 0.136222I
b = 1.14989 + 1.27447I
−2.00616 + 11.44390I 0
u = 0.83857 + 1.36720I
a = 0.822217 + 0.111733I
b = −1.12745 − 1.17302I
−2.80653 + 6.29571I 0
u = 0.83857 − 1.36720I
a = 0.822217 − 0.111733I
b = −1.12745 + 1.17302I
−2.80653 − 6.29571I 0
u = −0.93367 + 1.31311I
a = −0.874203 + 0.181115I
b = 1.14130 − 1.43722I
−3.7042 − 14.1241I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.93367 − 1.31311I
a = −0.874203 − 0.181115I
b = 1.14130 + 1.43722I
−3.7042 + 14.1241I 0
u = 0.94786 + 1.30304I
a = 0.884231 + 0.192561I
b = −1.14645 − 1.48582I
−6.0599 + 19.3328I 0
u = 0.94786 − 1.30304I
a = 0.884231 − 0.192561I
b = −1.14645 + 1.48582I
−6.0599 − 19.3328I 0
u = 0.95012 + 1.34531I
a = 0.847783 + 0.197155I
b = −1.04401 − 1.42940I
−8.6305 + 11.2680I 0
u = 0.95012 − 1.34531I
a = 0.847783 − 0.197155I
b = −1.04401 + 1.42940I
−8.6305 − 11.2680I 0
u = −1.72761 + 0.48817I
a = 0.023488 + 0.597292I
b = −0.625176 − 0.374928I
−1.19477 + 5.51666I 0
u = −1.72761 − 0.48817I
a = 0.023488 − 0.597292I
b = −0.625176 + 0.374928I
−1.19477 − 5.51666I 0
u = −0.99063 + 1.51104I
a = −0.718316 + 0.217666I
b = 0.71001 − 1.23551I
−11.0575 − 10.1048I 0
u = −0.99063 − 1.51104I
a = −0.718316 − 0.217666I
b = 0.71001 + 1.23551I
−11.0575 + 10.1048I 0
u = 1.71747 + 0.63604I
a = 0.030820 + 0.615704I
b = 0.642764 − 0.440374I
−3.80716 − 10.65800I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.71747 − 0.63604I
a = 0.030820 − 0.615704I
b = 0.642764 + 0.440374I
−3.80716 + 10.65800I 0
u = 0.93386 + 1.57716I
a = 0.683898 + 0.174596I
b = −0.715567 − 1.087200I
−7.28990 + 6.05374I 0
u = 0.93386 − 1.57716I
a = 0.683898 − 0.174596I
b = −0.715567 + 1.087200I
−7.28990 − 6.05374I 0
u = −1.00509 + 1.64625I
a = −0.636396 + 0.204182I
b = 0.573726 − 1.063490I
−10.59990 − 1.53094I 0
u = −1.00509 − 1.64625I
a = −0.636396 − 0.204182I
b = 0.573726 + 1.063490I
−10.59990 + 1.53094I 0
u = 2.08301 + 0.44387I
a = −0.006089 + 0.490124I
b = 0.503747 − 0.371081I
−5.90814 − 2.11885I 0
u = 2.08301 − 0.44387I
a = −0.006089 − 0.490124I
b = 0.503747 + 0.371081I
−5.90814 + 2.11885I 0
u = −0.77831 + 2.00547I
a = 0.355315 − 0.191289I
b = −0.558149 − 0.094316I
−4.07344 + 0.80035I 0
u = −0.77831 − 2.00547I
a = 0.355315 + 0.191289I
b = −0.558149 + 0.094316I
−4.07344 − 0.80035I 0
9
II.
I
u
2
= hu
39
+u
38
+· · ·+b+a, −u
38
−u
37
+· · ·+a
2
−2u, u
40
+u
39
+· · ·+2u
3
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
8
=
a
−u
39
− u
38
+ ··· − 2u
2
− a
a
9
=
−u
39
− u
38
+ ··· − u
2
a − 2u
2
−u
39
− u
38
+ ··· − 2u
2
− a
a
11
=
u
39
+ u
38
+ ··· − u
2
a + 2u
2
−u
39
− u
38
+ ··· + a + 2u
a
12
=
a + u
−u
39
− u
38
+ ··· + a + u
a
1
=
−u
5
− u
−u
5
− u
3
− u
a
7
=
u
5
+ u
−u
7
− u
5
− 2u
3
− u
a
3
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
6
=
u
17
+ 2u
15
+ 5u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
u
17
+ 3u
15
+ 7u
13
+ 10u
11
+ 11u
9
+ 8u
7
+ 4u
5
− u
a
2
=
u
31
+ 4u
29
+ ··· − 8u
5
− 2u
3
−u
33
− 5u
31
+ ··· + 2u
5
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
39
+ 24u
37
−4u
36
+ 100u
35
−24u
34
+ 296u
33
−96u
32
+ 708u
31
−276u
30
+ 1396u
29
−
632u
28
+ 2340u
27
− 1196u
26
+ 3376u
25
− 1908u
24
+ 4220u
23
− 2612u
22
+ 4592u
21
−
3072u
20
+ 4332u
19
− 3112u
18
+ 3520u
17
− 2692u
16
+ 2428u
15
− 1956u
14
+ 1372u
13
−
1160u
12
+ 604u
11
− 524u
10
+ 168u
9
− 152u
8
− 8u
6
− 28u
5
+ 16u
4
− 16u
3
+ 4u
2
+ 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
40
+ 19u
39
+ ··· + 2u
2
+ 1)
2
c
2
, c
5
(u
40
+ u
39
+ ··· + 2u + 1)
2
c
3
(u
40
− u
39
+ ··· + 70u + 25)
2
c
4
(u
40
+ u
39
+ ··· + 2u
3
+ 1)
2
c
6
(u
40
+ 3u
39
+ ··· + 61u + 16)
2
c
7
, c
9
, c
10
c
12
u
80
+ 13u
79
+ ··· − 5u + 2
c
8
, c
11
u
80
− u
79
+ ··· − 801912u + 50408
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
40
+ 5y
39
+ ··· + 4y + 1)
2
c
2
, c
5
(y
40
− 19y
39
+ ··· + 2y
2
+ 1)
2
c
3
(y
40
− 11y
39
+ ··· − 11300y + 625)
2
c
4
(y
40
+ 13y
39
+ ··· − 2y
2
+ 1)
2
c
6
(y
40
+ 9y
39
+ ··· + 4695y + 256)
2
c
7
, c
9
, c
10
c
12
y
80
+ 51y
79
+ ··· − 165y + 4
c
8
, c
11
y
80
+ 35y
79
+ ··· + 31771018144y + 2540966464
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750165 + 0.681685I
a = 0.593182 − 0.803436I
b = −0.559757 + 0.825418I
−3.67391 + 0.06553I 2.34805 + 0.65182I
u = −0.750165 + 0.681685I
a = 0.156983 + 0.121751I
b = −1.027030 − 0.636612I
−3.67391 + 0.06553I 2.34805 + 0.65182I
u = −0.750165 − 0.681685I
a = 0.593182 + 0.803436I
b = −0.559757 − 0.825418I
−3.67391 − 0.06553I 2.34805 − 0.65182I
u = −0.750165 − 0.681685I
a = 0.156983 − 0.121751I
b = −1.027030 + 0.636612I
−3.67391 − 0.06553I 2.34805 − 0.65182I
u = −0.135322 + 1.008900I
a = −1.228870 − 0.485355I
b = 0.002457 − 1.309000I
−5.33497 − 2.81020I 1.28879 + 3.60415I
u = −0.135322 + 1.008900I
a = 1.36420 − 0.52355I
b = 0.011780 − 0.600939I
−5.33497 − 2.81020I 1.28879 + 3.60415I
u = −0.135322 − 1.008900I
a = −1.228870 + 0.485355I
b = 0.002457 + 1.309000I
−5.33497 + 2.81020I 1.28879 − 3.60415I
u = −0.135322 − 1.008900I
a = 1.36420 + 0.52355I
b = 0.011780 + 0.600939I
−5.33497 + 2.81020I 1.28879 − 3.60415I
u = 0.072343 + 1.034030I
a = 1.275190 − 0.510382I
b = 0.072553 − 1.185810I
−9.36972 − 0.03674I −5.04849 − 0.16943I
u = 0.072343 + 1.034030I
a = −1.34753 − 0.52364I
b = −0.097218 − 0.794282I
−9.36972 − 0.03674I −5.04849 − 0.16943I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072343 − 1.034030I
a = 1.275190 + 0.510382I
b = 0.072553 + 1.185810I
−9.36972 + 0.03674I −5.04849 + 0.16943I
u = 0.072343 − 1.034030I
a = −1.34753 + 0.52364I
b = −0.097218 + 0.794282I
−9.36972 + 0.03674I −5.04849 + 0.16943I
u = 0.494587 + 0.916866I
a = 0.730044 − 0.412475I
b = −0.213277 − 1.340310I
−5.75447 − 1.67611I −0.019667 + 0.725806I
u = 0.494587 + 0.916866I
a = −1.224630 − 0.504391I
b = 0.492998 + 0.469591I
−5.75447 − 1.67611I −0.019667 + 0.725806I
u = 0.494587 − 0.916866I
a = 0.730044 + 0.412475I
b = −0.213277 + 1.340310I
−5.75447 + 1.67611I −0.019667 − 0.725806I
u = 0.494587 − 0.916866I
a = −1.224630 + 0.504391I
b = 0.492998 − 0.469591I
−5.75447 + 1.67611I −0.019667 − 0.725806I
u = 0.141807 + 1.046970I
a = 1.221630 − 0.517444I
b = 0.066268 − 1.340020I
−7.69560 + 7.54884I −1.84455 − 7.16323I
u = 0.141807 + 1.046970I
a = −1.36344 − 0.52952I
b = −0.133850 − 0.573342I
−7.69560 + 7.54884I −1.84455 − 7.16323I
u = 0.141807 − 1.046970I
a = 1.221630 + 0.517444I
b = 0.066268 + 1.340020I
−7.69560 − 7.54884I −1.84455 + 7.16323I
u = 0.141807 − 1.046970I
a = −1.36344 + 0.52952I
b = −0.133850 + 0.573342I
−7.69560 − 7.54884I −1.84455 + 7.16323I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.591229 + 0.886634I
a = 1.111810 − 0.459595I
b = −0.665188 + 0.643870I
−3.10117 − 2.31784I 4.10490 + 3.06865I
u = −0.591229 + 0.886634I
a = −0.520585 − 0.427039I
b = 0.220427 − 1.085890I
−3.10117 − 2.31784I 4.10490 + 3.06865I
u = −0.591229 − 0.886634I
a = 1.111810 + 0.459595I
b = −0.665188 − 0.643870I
−3.10117 + 2.31784I 4.10490 − 3.06865I
u = −0.591229 − 0.886634I
a = −0.520585 + 0.427039I
b = 0.220427 + 1.085890I
−3.10117 + 2.31784I 4.10490 − 3.06865I
u = −0.813779 + 0.691568I
a = 0.426879 − 0.874755I
b = −0.234341 + 0.909793I
−1.24510 + 7.46361I 5.61835 − 4.86663I
u = −0.813779 + 0.691568I
a = 0.386900 + 0.183187I
b = −1.37779 − 0.38778I
−1.24510 + 7.46361I 5.61835 − 4.86663I
u = −0.813779 − 0.691568I
a = 0.426879 + 0.874755I
b = −0.234341 − 0.909793I
−1.24510 − 7.46361I 5.61835 + 4.86663I
u = −0.813779 − 0.691568I
a = 0.386900 − 0.183187I
b = −1.37779 + 0.38778I
−1.24510 − 7.46361I 5.61835 + 4.86663I
u = 0.800451 + 0.709449I
a = −0.417698 − 0.811169I
b = 0.253470 + 0.776905I
0.91595 − 2.43691I 8.87403 + 0.79132I
u = 0.800451 + 0.709449I
a = −0.382753 + 0.101721I
b = 1.250550 − 0.301108I
0.91595 − 2.43691I 8.87403 + 0.79132I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800451 − 0.709449I
a = −0.417698 + 0.811169I
b = 0.253470 − 0.776905I
0.91595 + 2.43691I 8.87403 − 0.79132I
u = 0.800451 − 0.709449I
a = −0.382753 − 0.101721I
b = 1.250550 + 0.301108I
0.91595 + 2.43691I 8.87403 − 0.79132I
u = 0.784697 + 0.767022I
a = −0.245575 − 0.630555I
b = 0.144977 + 0.306438I
1.89343 − 0.15085I 10.02823 + 0.49618I
u = 0.784697 + 0.767022I
a = −0.539122 − 0.136467I
b = 1.041340 + 0.152160I
1.89343 − 0.15085I 10.02823 + 0.49618I
u = 0.784697 − 0.767022I
a = −0.245575 + 0.630555I
b = 0.144977 − 0.306438I
1.89343 + 0.15085I 10.02823 − 0.49618I
u = 0.784697 − 0.767022I
a = −0.539122 + 0.136467I
b = 1.041340 − 0.152160I
1.89343 + 0.15085I 10.02823 − 0.49618I
u = −0.780403 + 0.800609I
a = 0.697495 − 0.176644I
b = −1.078800 + 0.402101I
0.65358 − 4.71182I 7.76114 + 5.41408I
u = −0.780403 + 0.800609I
a = 0.082908 − 0.623965I
b = 0.0751238 + 0.0671472I
0.65358 − 4.71182I 7.76114 + 5.41408I
u = −0.780403 − 0.800609I
a = 0.697495 + 0.176644I
b = −1.078800 − 0.402101I
0.65358 + 4.71182I 7.76114 − 5.41408I
u = −0.780403 − 0.800609I
a = 0.082908 + 0.623965I
b = 0.0751238 − 0.0671472I
0.65358 + 4.71182I 7.76114 − 5.41408I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591289 + 0.962091I
a = 0.595213 − 0.567307I
b = −0.434157 − 1.191100I
−6.36686 + 5.78108I −0.88901 − 6.61715I
u = 0.591289 + 0.962091I
a = −1.186500 − 0.394784I
b = 0.517584 + 0.762892I
−6.36686 + 5.78108I −0.88901 − 6.61715I
u = 0.591289 − 0.962091I
a = 0.595213 + 0.567307I
b = −0.434157 + 1.191100I
−6.36686 − 5.78108I −0.88901 + 6.61715I
u = 0.591289 − 0.962091I
a = −1.186500 + 0.394784I
b = 0.517584 − 0.762892I
−6.36686 − 5.78108I −0.88901 + 6.61715I
u = −0.175614 + 0.839189I
a = −1.241180 − 0.297538I
b = 0.25416 − 1.41029I
−4.04306 − 1.72242I 2.69743 + 5.15094I
u = −0.175614 + 0.839189I
a = 1.41679 − 0.54165I
b = −0.541981 − 0.547133I
−4.04306 − 1.72242I 2.69743 + 5.15094I
u = −0.175614 − 0.839189I
a = −1.241180 + 0.297538I
b = 0.25416 + 1.41029I
−4.04306 + 1.72242I 2.69743 − 5.15094I
u = −0.175614 − 0.839189I
a = 1.41679 + 0.54165I
b = −0.541981 + 0.547133I
−4.04306 + 1.72242I 2.69743 − 5.15094I
u = −0.741020 + 0.934800I
a = 1.056660 − 0.208822I
b = −0.944973 + 0.947973I
0.239370 − 1.028260I 7.02738 + 0.15735I
u = −0.741020 + 0.934800I
a = −0.315635 − 0.725977I
b = 0.698154 − 0.604000I
0.239370 − 1.028260I 7.02738 + 0.15735I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741020 − 0.934800I
a = 1.056660 + 0.208822I
b = −0.944973 − 0.947973I
0.239370 + 1.028260I 7.02738 − 0.15735I
u = −0.741020 − 0.934800I
a = −0.315635 + 0.725977I
b = 0.698154 + 0.604000I
0.239370 + 1.028260I 7.02738 − 0.15735I
u = 0.733685 + 0.961157I
a = −1.103390 − 0.210369I
b = 0.883099 + 1.028080I
1.29840 + 5.88166I 8.65065 − 6.09482I
u = 0.733685 + 0.961157I
a = 0.369704 − 0.750788I
b = −0.784267 − 0.717456I
1.29840 + 5.88166I 8.65065 − 6.09482I
u = 0.733685 − 0.961157I
a = −1.103390 + 0.210369I
b = 0.883099 − 1.028080I
1.29840 − 5.88166I 8.65065 + 6.09482I
u = 0.733685 − 0.961157I
a = 0.369704 + 0.750788I
b = −0.784267 + 0.717456I
1.29840 − 5.88166I 8.65065 + 6.09482I
u = −0.694921 + 0.997432I
a = −0.476422 − 0.744456I
b = 0.794289 − 0.972074I
−4.61773 − 5.57768I 0.56138 + 4.39035I
u = −0.694921 + 0.997432I
a = 1.171340 − 0.252976I
b = −0.691218 + 1.072320I
−4.61773 − 5.57768I 0.56138 + 4.39035I
u = −0.694921 − 0.997432I
a = −0.476422 + 0.744456I
b = 0.794289 + 0.972074I
−4.61773 + 5.57768I 0.56138 − 4.39035I
u = −0.694921 − 0.997432I
a = 1.171340 + 0.252976I
b = −0.691218 − 1.072320I
−4.61773 + 5.57768I 0.56138 − 4.39035I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723170 + 0.999501I
a = 0.441305 − 0.786301I
b = −0.892771 − 0.882669I
0.03312 + 8.17729I 7.05192 − 5.82128I
u = 0.723170 + 0.999501I
a = −1.164480 − 0.213199I
b = 0.777102 + 1.138390I
0.03312 + 8.17729I 7.05192 − 5.82128I
u = 0.723170 − 0.999501I
a = 0.441305 + 0.786301I
b = −0.892771 + 0.882669I
0.03312 − 8.17729I 7.05192 + 5.82128I
u = 0.723170 − 0.999501I
a = −1.164480 + 0.213199I
b = 0.777102 − 1.138390I
0.03312 − 8.17729I 7.05192 + 5.82128I
u = −0.723431 + 1.012350I
a = −0.458988 − 0.803160I
b = 0.937952 − 0.925811I
−2.22064 − 13.23980I 3.80297 + 9.63322I
u = −0.723431 + 1.012350I
a = 1.182420 − 0.209193I
b = −0.750286 + 1.182330I
−2.22064 − 13.23980I 3.80297 + 9.63322I
u = −0.723431 − 1.012350I
a = −0.458988 + 0.803160I
b = 0.937952 + 0.925811I
−2.22064 + 13.23980I 3.80297 − 9.63322I
u = −0.723431 − 1.012350I
a = 1.182420 + 0.209193I
b = −0.750286 − 1.182330I
−2.22064 + 13.23980I 3.80297 − 9.63322I
u = 0.497642 + 0.392565I
a = 0.638573 + 1.002530I
b = 0.93207 − 2.32293I
−5.16819 − 1.42866I 2.24523 + 0.64534I
u = 0.497642 + 0.392565I
a = −1.13622 − 1.39510I
b = 1.93608 + 0.99240I
−5.16819 − 1.42866I 2.24523 + 0.64534I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.497642 − 0.392565I
a = 0.638573 − 1.002530I
b = 0.93207 + 2.32293I
−5.16819 + 1.42866I 2.24523 − 0.64534I
u = 0.497642 − 0.392565I
a = −1.13622 + 1.39510I
b = 1.93608 − 0.99240I
−5.16819 + 1.42866I 2.24523 − 0.64534I
u = 0.604024 + 0.174435I
a = 0.07218 + 1.50377I
b = 1.74868 − 2.46317I
−3.80642 + 5.28641I 5.70674 − 5.92677I
u = 0.604024 + 0.174435I
a = −0.67621 − 1.67820I
b = 2.07682 + 1.94062I
−3.80642 + 5.28641I 5.70674 − 5.92677I
u = 0.604024 − 0.174435I
a = 0.07218 − 1.50377I
b = 1.74868 + 2.46317I
−3.80642 − 5.28641I 5.70674 + 5.92677I
u = 0.604024 − 0.174435I
a = −0.67621 + 1.67820I
b = 2.07682 − 1.94062I
−3.80642 − 5.28641I 5.70674 + 5.92677I
u = −0.537810 + 0.103864I
a = −0.04488 + 1.79215I
b = −1.93537 − 2.64238I
−1.85361 − 0.71721I 10.03452 + 1.24829I
u = −0.537810 + 0.103864I
a = 0.58269 − 1.89602I
b = −2.32566 + 2.14288I
−1.85361 − 0.71721I 10.03452 + 1.24829I
u = −0.537810 − 0.103864I
a = −0.04488 − 1.79215I
b = −1.93537 + 2.64238I
−1.85361 + 0.71721I 10.03452 − 1.24829I
u = −0.537810 − 0.103864I
a = 0.58269 + 1.89602I
b = −2.32566 − 2.14288I
−1.85361 + 0.71721I 10.03452 − 1.24829I
20
III. I
u
3
= hb + u − 1, a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
1
a
8
=
−1
−u + 1
a
9
=
−u
−u + 1
a
11
=
u
−1
a
12
=
−1
−u − 2
a
1
=
0
−1
a
7
=
0
1
a
3
=
1
1
a
6
=
0
1
a
2
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u − 1)
2
c
4
, c
7
, c
9
c
10
, c
12
u
2
+ 1
c
5
(u + 1)
2
c
6
u
2
c
8
u
2
+ 2u + 2
c
11
u
2
− 2u + 2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y −1)
2
c
4
, c
7
, c
9
c
10
, c
12
(y + 1)
2
c
6
y
2
c
8
, c
11
y
2
+ 4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = 1.00000 − 1.00000I
−4.93480 −4.00000
u = − 1.000000I
a = −1.00000
b = 1.00000 + 1.00000I
−4.93480 −4.00000
24
IV.
I
v
1
= ha, v
5
− 2v
4
+ 16v
2
+ 64b − 16v − 32, v
6
− 2v
5
+ 16v
3
− 16v
2
− 32v + 64i
(i) Arc colorings
a
4
=
1
0
a
10
=
v
0
a
5
=
1
0
a
8
=
0
−
1
64
v
5
+
1
32
v
4
+ ··· +
1
4
v +
1
2
a
9
=
−
1
64
v
5
+
1
32
v
4
+ ··· +
1
4
v +
1
2
−
1
64
v
5
+
1
32
v
4
+ ··· +
1
4
v +
1
2
a
11
=
v
1
64
v
5
−
1
32
v
4
+ ··· −
1
4
v −
1
2
a
12
=
1
64
v
5
−
1
32
v
4
+ ··· +
3
4
v −
1
2
1
64
v
5
−
1
32
v
4
+ ··· −
1
4
v −
1
2
a
1
=
1
32
v
5
−
1
16
v
4
+ ··· +
1
2
v − 1
1
32
v
5
−
1
16
v
4
+ ··· −
1
2
v − 1
a
7
=
−v
−
1
32
v
5
+
1
16
v
4
+ ··· +
1
2
v + 1
a
3
=
−1
−
1
32
v
5
+
1
8
v
3
+ ··· −
1
2
v + 2
a
6
=
1
16
v
4
−
1
4
v
2
+ 1
1
32
v
5
+
1
4
v
2
+
1
2
v
a
2
=
−
1
16
v
4
+
1
4
v
2
− 1
1
8
v
3
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
128
v
5
−
1
32
v
3
+
9
8
v
2
+
1
8
v +
11
2
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
5
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
4
u
6
c
7
, c
9
(u + 1)
6
c
8
64(64u
6
+ 32u
5
− 16u
4
− 16u
3
+ 2u + 1)
c
10
, c
12
(u − 1)
6
c
11
64(64u
6
− 32u
5
− 16u
4
+ 16u
3
− 2u + 1)
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
5
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
4
y
6
c
7
, c
9
, c
10
c
12
(y − 1)
6
c
8
, c
11
4096(4096y
6
− 3072y
5
+ 1280y
4
− 256y
3
+ 32y
2
− 4y + 1)
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.46557 + 0.76250I
a = 0
b = 0.536975 − 0.279376I
1.64493 − 5.69302I 6.22322 + 3.57560I
v = 1.46557 − 0.76250I
a = 0
b = 0.536975 + 0.279376I
1.64493 + 5.69302I 6.22322 − 3.57560I
v = −1.83596 + 0.54142I
a = 0
b = −0.501096 − 0.147771I
3.53554 + 0.92430I 8.40983 + 1.04572I
v = −1.83596 − 0.54142I
a = 0
b = −0.501096 + 0.147771I
3.53554 − 0.92430I 8.40983 − 1.04572I
v = 1.37039 + 2.12652I
a = 0
b = 0.214122 − 0.332266I
−0.245672 + 0.924305I 6.99195 − 6.48027I
v = 1.37039 − 2.12652I
a = 0
b = 0.214122 + 0.332266I
−0.245672 − 0.924305I 6.99195 + 6.48027I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· ((u
40
+ 19u
39
+ ··· + 2u
2
+ 1)
2
)(u
49
+ 24u
48
+ ··· + 209u + 16)
c
2
((u − 1)
2
)(u
6
+ u
5
+ ··· + u + 1)(u
40
+ u
39
+ ··· + 2u + 1)
2
· (u
49
+ 2u
48
+ ··· + 5u − 4)
c
3
((u − 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
40
− u
39
+ ··· + 70u + 25)
2
· (u
49
+ 2u
48
+ ··· + 11533u − 1348)
c
4
u
6
(u
2
+ 1)(u
40
+ u
39
+ ··· + 2u
3
+ 1)
2
· (u
49
− 3u
48
+ ··· + 22528u − 8192)
c
5
((u + 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
40
+ u
39
+ ··· + 2u + 1)
2
· (u
49
+ 2u
48
+ ··· + 5u − 4)
c
6
u
2
(u
6
− 3u
5
+ ··· − u + 1)(u
40
+ 3u
39
+ ··· + 61u + 16)
2
· (u
49
+ 5u
47
+ ··· + 3280u − 704)
c
7
, c
9
((u + 1)
6
)(u
2
+ 1)(u
49
− 6u
48
+ ··· − 3u − 1)(u
80
+ 13u
79
+ ··· − 5u + 2)
c
8
4096(u
2
+ 2u + 2)(64u
6
+ 32u
5
− 16u
4
− 16u
3
+ 2u + 1)
· (64u
49
+ 32u
48
+ ··· + 2u − 2)(u
80
− u
79
+ ··· − 801912u + 50408)
c
10
, c
12
((u − 1)
6
)(u
2
+ 1)(u
49
− 6u
48
+ ··· − 3u − 1)(u
80
+ 13u
79
+ ··· − 5u + 2)
c
11
4096(u
2
− 2u + 2)(64u
6
− 32u
5
− 16u
4
+ 16u
3
− 2u + 1)
· (64u
49
+ 32u
48
+ ··· + 2u − 2)(u
80
− u
79
+ ··· − 801912u + 50408)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
6
+ y
5
+ ··· + 3y + 1)(y
40
+ 5y
39
+ ··· + 4y + 1)
2
· (y
49
+ 4y
48
+ ··· + 19265y − 256)
c
2
, c
5
(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· ((y
40
− 19y
39
+ ··· + 2y
2
+ 1)
2
)(y
49
− 24y
48
+ ··· + 209y − 16)
c
3
(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
40
− 11y
39
+ ··· − 11300y + 625)
2
· (y
49
− 16y
48
+ ··· − 79033007y − 1817104)
c
4
y
6
(y + 1)
2
(y
40
+ 13y
39
+ ··· − 2y
2
+ 1)
2
· (y
49
+ 15y
48
+ ··· − 1312817152y − 67108864)
c
6
y
2
(y
6
+ y
5
+ ··· + 3y + 1)(y
40
+ 9y
39
+ ··· + 4695y + 256)
2
· (y
49
+ 10y
48
+ ··· + 2659584y − 495616)
c
7
, c
9
, c
10
c
12
((y − 1)
6
)(y + 1)
2
(y
49
+ 20y
48
+ ··· − 3y − 1)
· (y
80
+ 51y
79
+ ··· − 165y + 4)
c
8
, c
11
16777216(y
2
+ 4)
· (4096y
6
− 3072y
5
+ 1280y
4
− 256y
3
+ 32y
2
− 4y + 1)
· (4096y
49
+ 13312y
48
+ ··· + 92y − 4)
· (y
80
+ 35y
79
+ ··· + 31771018144y + 2540966464)
30
