12a
0280
(K12a
0280
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 12 11 10 4 5 1 7
Solving Sequence
4,9 2,5
6 10 11 8 3 1 7 12
c
4
c
5
c
9
c
10
c
8
c
3
c
1
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
38
+ 3u
37
+ ··· + b − 3, 3u
39
− 7u
38
+ ··· + 2a − 4, u
40
− 3u
39
+ ··· − 6u + 2i
I
u
2
= h205u
31
a − 187u
31
+ ··· − 343a + 410, −u
31
− 2u
30
+ ··· − 4a + 4, u
32
+ u
31
+ ··· − 2u − 1i
I
u
3
= h−u
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a − 2, u
4
+ 2u
2
+ 2i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 109 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−u
38
+ 3 u
37
+· · ·+b−3, 3u
39
−7u
38
+· · ·+2a−4, u
40
−3u
39
+· · ·−6u+2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−
3
2
u
39
+
7
2
u
38
+ ··· − 4u + 2
u
38
− 3u
37
+ ··· − 5u + 3
a
5
=
1
u
2
a
6
=
−
1
2
u
39
+
3
2
u
38
+ ··· − 4u + 3
−u
38
+ 2u
37
+ ··· + 3u − 1
a
10
=
−u
u
a
11
=
u
3
u
5
+ u
3
+ u
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
−
7
2
u
39
+
17
2
u
38
+ ··· − 10u + 3
2u
38
− 7u
37
+ ··· − 11u + 7
a
7
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
12
=
3
2
u
39
−
7
2
u
38
+ ··· + 4u − 1
−u
38
+ 3u
37
+ ··· + 6u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
39
−6u
38
+ 20u
37
−54u
36
+ 90u
35
−238u
34
+ 238u
33
−648u
32
+ 384u
31
−1158u
30
+
312u
29
−1278u
28
−154u
27
−492u
26
−898u
25
+ 1018u
24
−1550u
23
+ 2192u
22
−1746u
21
+
2064u
20
− 1346u
19
+ 876u
18
− 498u
17
− 254u
16
+ 320u
15
− 624u
14
+ 616u
13
− 464u
12
+
388u
11
− 200u
10
+ 68u
9
− 16u
8
− 38u
7
+ 56u
6
− 38u
5
+ 40u
4
− 30u
3
+ 8u
2
− 14u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
40
+ 19u
39
+ ··· + 8u + 1
c
2
, c
5
, c
6
c
12
u
40
+ u
39
+ ··· − 4u
2
+ 1
c
3
, c
10
u
40
+ 3u
39
+ ··· + 62u + 2
c
4
, c
9
u
40
− 3u
39
+ ··· − 6u + 2
c
7
u
40
+ 3u
39
+ ··· − 256u + 256
c
8
u
40
− 21u
39
+ ··· − 4u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
40
+ 13y
39
+ ··· − 8y + 1
c
2
, c
5
, c
6
c
12
y
40
− 19y
39
+ ··· − 8y + 1
c
3
, c
10
y
40
− 27y
39
+ ··· − 1244y + 4
c
4
, c
9
y
40
+ 21y
39
+ ··· + 4y + 4
c
7
y
40
+ 17y
39
+ ··· − 1441792y + 65536
c
8
y
40
− 3y
39
+ ··· + 80y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.032066 + 0.987972I
a = 0.79918 − 1.21680I
b = −0.098470 + 0.680905I
2.63292 + 1.38793I 3.69460 − 3.72098I
u = 0.032066 − 0.987972I
a = 0.79918 + 1.21680I
b = −0.098470 − 0.680905I
2.63292 − 1.38793I 3.69460 + 3.72098I
u = −0.603533 + 0.828822I
a = −1.69497 − 1.57214I
b = 0.15771 + 1.68881I
−6.26949 + 10.98300I −9.24065 − 9.80825I
u = −0.603533 − 0.828822I
a = −1.69497 + 1.57214I
b = 0.15771 − 1.68881I
−6.26949 − 10.98300I −9.24065 + 9.80825I
u = −0.621730 + 0.712285I
a = 1.139040 + 0.396240I
b = −0.95556 − 1.55078I
−6.60486 − 6.20651I −10.15571 + 3.67210I
u = −0.621730 − 0.712285I
a = 1.139040 − 0.396240I
b = −0.95556 + 1.55078I
−6.60486 + 6.20651I −10.15571 − 3.67210I
u = −0.481507 + 0.789783I
a = 0.648708 + 0.018988I
b = −0.141348 + 0.130562I
−0.36391 + 1.99287I −2.40004 − 3.73815I
u = −0.481507 − 0.789783I
a = 0.648708 − 0.018988I
b = −0.141348 − 0.130562I
−0.36391 − 1.99287I −2.40004 + 3.73815I
u = 0.491208 + 0.978630I
a = −0.81937 + 1.39099I
b = 0.109214 − 1.360820I
−0.16272 − 6.27605I −4.06803 + 10.74221I
u = 0.491208 − 0.978630I
a = −0.81937 − 1.39099I
b = 0.109214 + 1.360820I
−0.16272 + 6.27605I −4.06803 − 10.74221I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231511 + 1.113940I
a = 0.38329 + 1.48578I
b = −0.133956 − 1.058470I
−0.38661 − 7.27037I −2.50119 + 7.55106I
u = 0.231511 − 1.113940I
a = 0.38329 − 1.48578I
b = −0.133956 + 1.058470I
−0.38661 + 7.27037I −2.50119 − 7.55106I
u = 0.810351 + 0.193335I
a = −1.06622 − 1.29812I
b = 0.94040 − 1.69712I
−3.06749 + 12.23140I −7.51087 − 7.91346I
u = 0.810351 − 0.193335I
a = −1.06622 + 1.29812I
b = 0.94040 + 1.69712I
−3.06749 − 12.23140I −7.51087 + 7.91346I
u = −0.482698 + 1.065100I
a = −0.201840 − 0.655189I
b = 0.187841 + 0.901163I
0.58711 + 3.31811I −0.88906 − 1.84785I
u = −0.482698 − 1.065100I
a = −0.201840 + 0.655189I
b = 0.187841 − 0.901163I
0.58711 − 3.31811I −0.88906 + 1.84785I
u = 0.735874 + 0.291866I
a = 1.005670 + 0.058018I
b = −0.688345 − 0.001466I
−4.71000 − 4.49018I −9.32153 + 4.94666I
u = 0.735874 − 0.291866I
a = 1.005670 − 0.058018I
b = −0.688345 + 0.001466I
−4.71000 + 4.49018I −9.32153 − 4.94666I
u = −0.789239 + 0.057041I
a = −0.060699 + 1.159700I
b = 0.92550 + 1.37773I
3.56585 − 5.08226I −1.98598 + 6.14285I
u = −0.789239 − 0.057041I
a = −0.060699 − 1.159700I
b = 0.92550 − 1.37773I
3.56585 + 5.08226I −1.98598 − 6.14285I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762371 + 0.132104I
a = 0.507160 + 0.391032I
b = 0.517802 + 1.069740I
2.25804 + 2.12425I −0.766744 − 0.783432I
u = 0.762371 − 0.132104I
a = 0.507160 − 0.391032I
b = 0.517802 − 1.069740I
2.25804 − 2.12425I −0.766744 + 0.783432I
u = 0.538422 + 1.126370I
a = 0.287354 + 0.772248I
b = −0.106299 − 0.840485I
−2.27245 − 0.32612I −6.24945 − 1.38108I
u = 0.538422 − 1.126370I
a = 0.287354 − 0.772248I
b = −0.106299 + 0.840485I
−2.27245 + 0.32612I −6.24945 + 1.38108I
u = 0.388105 + 1.189300I
a = −0.30780 − 1.56210I
b = 1.45365 + 0.93184I
6.10895 − 1.76564I 3.66057 + 2.94812I
u = 0.388105 − 1.189300I
a = −0.30780 + 1.56210I
b = 1.45365 − 0.93184I
6.10895 + 1.76564I 3.66057 − 2.94812I
u = 0.337429 + 1.206360I
a = −0.76113 + 1.19834I
b = −1.13289 − 1.65527I
1.21656 + 8.48940I −2.44558 − 5.23918I
u = 0.337429 − 1.206360I
a = −0.76113 − 1.19834I
b = −1.13289 + 1.65527I
1.21656 − 8.48940I −2.44558 + 5.23918I
u = 0.555044 + 0.497691I
a = 0.945907 − 0.128380I
b = −0.639235 + 0.882559I
−1.53333 + 2.02570I −6.72849 − 5.03536I
u = 0.555044 − 0.497691I
a = 0.945907 + 0.128380I
b = −0.639235 − 0.882559I
−1.53333 − 2.02570I −6.72849 + 5.03536I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423526 + 1.205050I
a = −1.32062 − 1.13513I
b = −0.30701 + 2.10725I
7.28327 − 0.83841I 2.11651 + 2.51174I
u = −0.423526 − 1.205050I
a = −1.32062 + 1.13513I
b = −0.30701 − 2.10725I
7.28327 + 0.83841I 2.11651 − 2.51174I
u = 0.502221 + 1.179890I
a = −1.38981 + 0.79030I
b = 0.34238 − 1.75306I
5.30301 − 6.80866I 2.17056 + 4.01789I
u = 0.502221 − 1.179890I
a = −1.38981 − 0.79030I
b = 0.34238 + 1.75306I
5.30301 + 6.80866I 2.17056 − 4.01789I
u = −0.474723 + 1.200460I
a = −0.12740 + 2.43272I
b = 2.04029 − 2.13554I
6.92248 + 9.66949I 1.06879 − 9.19482I
u = −0.474723 − 1.200460I
a = −0.12740 − 2.43272I
b = 2.04029 + 2.13554I
6.92248 − 9.66949I 1.06879 + 9.19482I
u = 0.532636 + 1.182860I
a = 0.58956 − 2.71881I
b = 1.56465 + 3.20864I
−0.1411 − 17.1898I −4.00000 + 11.05603I
u = 0.532636 − 1.182860I
a = 0.58956 + 2.71881I
b = 1.56465 − 3.20864I
−0.1411 + 17.1898I −4.00000 − 11.05603I
u = −0.540282 + 0.409606I
a = 0.943993 − 0.013383I
b = −0.536333 − 0.185294I
−1.31907 + 0.83318I −6.05634 − 4.23853I
u = −0.540282 − 0.409606I
a = 0.943993 + 0.013383I
b = −0.536333 + 0.185294I
−1.31907 − 0.83318I −6.05634 + 4.23853I
8
II. I
u
2
= h205u
31
a − 187u
31
+ · · · − 343a + 410, −u
31
− 2u
30
+ · · · − 4a +
4, u
32
+ u
31
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
a
−2.38372au
31
+ 2.17442u
31
+ ··· + 3.98837a − 4.76744
a
5
=
1
u
2
a
6
=
−2.17442au
31
+ 2.48837u
31
+ ··· + 4.76744a − 4.84884
1.30233au
31
− 1.04651u
31
+ ··· − 1.93023a + 2.60465
a
10
=
−u
u
a
11
=
u
3
u
5
+ u
3
+ u
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
−2.33721au
31
+ 2.74419u
31
+ ··· + 4.88372a − 4.17442
−4.06977au
31
+ 3.89535u
31
+ ··· + 6.40698a − 7.63953
a
7
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
12
=
−2.38372au
31
+ 2.17442u
31
+ ··· + 4.98837a − 4.76744
−0.918605au
31
+ 0.872093u
31
+ ··· + 1.94186a − 2.83721
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
30
− 4u
29
− 32u
28
− 32u
27
− 124u
26
− 128u
25
− 292u
24
− 316u
23
− 448u
22
−
516u
21
− 440u
20
− 540u
19
− 232u
18
− 292u
17
+ 20u
16
+ 64u
15
+ 140u
14
+ 232u
13
+
108u
12
+ 144u
11
+ 24u
10
−16u
9
−28u
8
−64u
7
−24u
6
−28u
5
−8u
4
+ 12u
3
+ 8u
2
+ 12u + 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
64
+ 37u
63
+ ··· − 24u
2
+ 1
c
2
, c
5
, c
6
c
12
u
64
+ u
63
+ ··· − 2u − 1
c
3
, c
10
(u
32
− u
31
+ ··· + 14u − 5)
2
c
4
, c
9
(u
32
+ u
31
+ ··· − 2u − 1)
2
c
7
(u
32
+ 3u
31
+ ··· − 4u
4
+ 1)
2
c
8
(u
32
− 17u
31
+ ··· − 8u
2
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
64
− 21y
63
+ ··· − 48y + 1
c
2
, c
5
, c
6
c
12
y
64
− 37y
63
+ ··· − 24y
2
+ 1
c
3
, c
10
(y
32
− 23y
31
+ ··· − 296y + 25)
2
c
4
, c
9
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
c
7
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
c
8
(y
32
− 3y
31
+ ··· − 16y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.565288 + 0.826638I
a = 0.626478 + 0.116978I
b = −0.192527 − 0.250322I
−3.22871 − 6.17510I −6.26933 + 6.90538I
u = 0.565288 + 0.826638I
a = −1.61740 + 1.74426I
b = 0.09474 − 1.67827I
−3.22871 − 6.17510I −6.26933 + 6.90538I
u = 0.565288 − 0.826638I
a = 0.626478 − 0.116978I
b = −0.192527 + 0.250322I
−3.22871 + 6.17510I −6.26933 − 6.90538I
u = 0.565288 − 0.826638I
a = −1.61740 − 1.74426I
b = 0.09474 + 1.67827I
−3.22871 + 6.17510I −6.26933 − 6.90538I
u = −0.180753 + 1.016980I
a = 0.521524 + 0.939074I
b = 0.184906 − 0.499212I
1.71612 + 2.81562I 1.51638 − 3.82546I
u = −0.180753 + 1.016980I
a = 0.52552 − 1.67676I
b = −0.216370 + 1.014450I
1.71612 + 2.81562I 1.51638 − 3.82546I
u = −0.180753 − 1.016980I
a = 0.521524 − 0.939074I
b = 0.184906 + 0.499212I
1.71612 − 2.81562I 1.51638 + 3.82546I
u = −0.180753 − 1.016980I
a = 0.52552 + 1.67676I
b = −0.216370 − 1.014450I
1.71612 − 2.81562I 1.51638 + 3.82546I
u = −0.561289 + 0.769750I
a = 1.320700 + 0.336643I
b = −1.28891 − 1.60281I
−7.30442 + 2.24194I −11.34310 − 3.79727I
u = −0.561289 + 0.769750I
a = −1.90844 − 1.90270I
b = 0.06984 + 1.78121I
−7.30442 + 2.24194I −11.34310 − 3.79727I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561289 − 0.769750I
a = 1.320700 − 0.336643I
b = −1.28891 + 1.60281I
−7.30442 − 2.24194I −11.34310 + 3.79727I
u = −0.561289 − 0.769750I
a = −1.90844 + 1.90270I
b = 0.06984 − 1.78121I
−7.30442 − 2.24194I −11.34310 + 3.79727I
u = 0.570562 + 0.700867I
a = 1.170860 − 0.296591I
b = −1.08158 + 1.40420I
−3.58638 + 1.65231I −7.40697 − 0.15309I
u = 0.570562 + 0.700867I
a = 0.770876 + 0.069511I
b = −0.296211 − 0.127275I
−3.58638 + 1.65231I −7.40697 − 0.15309I
u = 0.570562 − 0.700867I
a = 1.170860 + 0.296591I
b = −1.08158 − 1.40420I
−3.58638 − 1.65231I −7.40697 + 0.15309I
u = 0.570562 − 0.700867I
a = 0.770876 − 0.069511I
b = −0.296211 + 0.127275I
−3.58638 − 1.65231I −7.40697 + 0.15309I
u = −0.792800 + 0.172177I
a = 0.445791 − 0.255610I
b = 0.417388 − 1.139860I
−0.15402 − 7.01747I −4.33777 + 4.88322I
u = −0.792800 + 0.172177I
a = −0.90083 + 1.44235I
b = 0.98440 + 1.65747I
−0.15402 − 7.01747I −4.33777 + 4.88322I
u = −0.792800 − 0.172177I
a = 0.445791 + 0.255610I
b = 0.417388 + 1.139860I
−0.15402 + 7.01747I −4.33777 − 4.88322I
u = −0.792800 − 0.172177I
a = −0.90083 − 1.44235I
b = 0.98440 − 1.65747I
−0.15402 + 7.01747I −4.33777 − 4.88322I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362087 + 1.159290I
a = 0.251876 + 1.266260I
b = −0.111636 − 1.060770I
−0.945525 − 0.397373I −4.16402 − 0.58140I
u = 0.362087 + 1.159290I
a = −0.78876 + 1.68341I
b = −1.52186 − 2.26685I
−0.945525 − 0.397373I −4.16402 − 0.58140I
u = 0.362087 − 1.159290I
a = 0.251876 − 1.266260I
b = −0.111636 + 1.060770I
−0.945525 + 0.397373I −4.16402 + 0.58140I
u = 0.362087 − 1.159290I
a = −0.78876 − 1.68341I
b = −1.52186 + 2.26685I
−0.945525 + 0.397373I −4.16402 + 0.58140I
u = −0.433982 + 1.139380I
a = 0.161663 − 1.092680I
b = −0.076534 + 1.012240I
0.99219 + 3.88889I −1.10872 − 4.90467I
u = −0.433982 + 1.139380I
a = −1.44549 + 1.30887I
b = 2.44483 + 0.25840I
0.99219 + 3.88889I −1.10872 − 4.90467I
u = −0.433982 − 1.139380I
a = 0.161663 + 1.092680I
b = −0.076534 − 1.012240I
0.99219 − 3.88889I −1.10872 + 4.90467I
u = −0.433982 − 1.139380I
a = −1.44549 − 1.30887I
b = 2.44483 − 0.25840I
0.99219 − 3.88889I −1.10872 + 4.90467I
u = 0.192477 + 0.755088I
a = 0.992213 + 0.146819I
b = −1.71332 + 0.31259I
−2.78881 − 1.03498I −4.81241 + 6.41402I
u = 0.192477 + 0.755088I
a = 1.40705 + 3.44547I
b = −0.85803 − 1.20724I
−2.78881 − 1.03498I −4.81241 + 6.41402I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192477 − 0.755088I
a = 0.992213 − 0.146819I
b = −1.71332 − 0.31259I
−2.78881 + 1.03498I −4.81241 − 6.41402I
u = 0.192477 − 0.755088I
a = 1.40705 − 3.44547I
b = −0.85803 + 1.20724I
−2.78881 + 1.03498I −4.81241 − 6.41402I
u = 0.778647
a = 0.238256 + 0.927510I
b = 0.84157 + 1.23904I
4.02976 −0.517490
u = 0.778647
a = 0.238256 − 0.927510I
b = 0.84157 − 1.23904I
4.02976 −0.517490
u = 0.747372 + 0.188735I
a = 1.025140 + 0.038278I
b = −0.732319 + 0.001696I
−4.85609 + 3.15266I −9.32272 − 3.41480I
u = 0.747372 + 0.188735I
a = −1.06088 − 1.87811I
b = 1.09181 − 1.72211I
−4.85609 + 3.15266I −9.32272 − 3.41480I
u = 0.747372 − 0.188735I
a = 1.025140 − 0.038278I
b = −0.732319 − 0.001696I
−4.85609 − 3.15266I −9.32272 + 3.41480I
u = 0.747372 − 0.188735I
a = −1.06088 + 1.87811I
b = 1.09181 + 1.72211I
−4.85609 − 3.15266I −9.32272 + 3.41480I
u = −0.492704 + 1.133860I
a = 0.198910 − 0.896949I
b = −0.073037 + 0.921498I
0.60843 + 3.89503I −2.64939 − 2.90091I
u = −0.492704 + 1.133860I
a = −1.34942 − 0.57930I
b = 0.65246 + 1.62226I
0.60843 + 3.89503I −2.64939 − 2.90091I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492704 − 1.133860I
a = 0.198910 + 0.896949I
b = −0.073037 − 0.921498I
0.60843 − 3.89503I −2.64939 + 2.90091I
u = −0.492704 − 1.133860I
a = −1.34942 + 0.57930I
b = 0.65246 − 1.62226I
0.60843 − 3.89503I −2.64939 + 2.90091I
u = −0.357265 + 1.197710I
a = −0.13206 + 1.45967I
b = 1.16104 − 0.93427I
3.96080 − 3.23058I 0.64791 + 1.85611I
u = −0.357265 + 1.197710I
a = −0.87084 − 1.30274I
b = −1.08042 + 1.88128I
3.96080 − 3.23058I 0.64791 + 1.85611I
u = −0.357265 − 1.197710I
a = −0.13206 − 1.45967I
b = 1.16104 + 0.93427I
3.96080 + 3.23058I 0.64791 − 1.85611I
u = −0.357265 − 1.197710I
a = −0.87084 + 1.30274I
b = −1.08042 − 1.88128I
3.96080 + 3.23058I 0.64791 − 1.85611I
u = 0.514933 + 1.164400I
a = 0.312133 + 0.896388I
b = −0.133391 − 0.910523I
−2.01515 − 7.88151I −5.80444 + 6.68910I
u = 0.514933 + 1.164400I
a = 0.46489 − 3.12097I
b = 2.11990 + 3.49281I
−2.01515 − 7.88151I −5.80444 + 6.68910I
u = 0.514933 − 1.164400I
a = 0.312133 − 0.896388I
b = −0.133391 + 0.910523I
−2.01515 + 7.88151I −5.80444 − 6.68910I
u = 0.514933 − 1.164400I
a = 0.46489 + 3.12097I
b = 2.11990 − 3.49281I
−2.01515 + 7.88151I −5.80444 − 6.68910I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.450235 + 1.200350I
a = −1.41612 + 1.00160I
b = −0.00388 − 2.05017I
7.53680 − 4.39858I 2.80847 + 3.53545I
u = 0.450235 + 1.200350I
a = −0.30788 − 2.18180I
b = 1.99857 + 1.67012I
7.53680 − 4.39858I 2.80847 + 3.53545I
u = 0.450235 − 1.200350I
a = −1.41612 − 1.00160I
b = −0.00388 + 2.05017I
7.53680 + 4.39858I 2.80847 − 3.53545I
u = 0.450235 − 1.200350I
a = −0.30788 + 2.18180I
b = 1.99857 − 1.67012I
7.53680 + 4.39858I 2.80847 − 3.53545I
u = −0.521034 + 1.182060I
a = −1.35096 − 0.79083I
b = 0.32647 + 1.66351I
2.81659 + 11.87580I −1.22046 − 7.99531I
u = −0.521034 + 1.182060I
a = 0.45108 + 2.79230I
b = 1.78779 − 3.13635I
2.81659 + 11.87580I −1.22046 − 7.99531I
u = −0.521034 − 1.182060I
a = −1.35096 + 0.79083I
b = 0.32647 − 1.66351I
2.81659 − 11.87580I −1.22046 + 7.99531I
u = −0.521034 − 1.182060I
a = 0.45108 − 2.79230I
b = 1.78779 + 3.13635I
2.81659 − 11.87580I −1.22046 + 7.99531I
u = −0.649942 + 0.248644I
a = 0.999339 − 0.033712I
b = −0.710884 − 0.045639I
−1.96053 + 0.52783I −6.40552 − 0.64788I
u = −0.649942 + 0.248644I
a = 0.767259 − 0.110823I
b = 0.166974 − 0.813857I
−1.96053 + 0.52783I −6.40552 − 0.64788I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649942 − 0.248644I
a = 0.999339 + 0.033712I
b = −0.710884 + 0.045639I
−1.96053 − 0.52783I −6.40552 + 0.64788I
u = −0.649942 − 0.248644I
a = 0.767259 + 0.110823I
b = 0.166974 + 0.813857I
−1.96053 − 0.52783I −6.40552 + 0.64788I
u = −0.605013
a = 1.01438
b = −0.783099
−2.06165 −3.73830
u = −0.605013
a = 1.98066
b = 1.27956
−2.06165 −3.73830
18
III. I
u
3
= h−u
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a − 2, u
4
+ 2u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−
1
2
u
3
+ u
2
+ 1
u
3
− u
2
+ u − 1
a
5
=
1
u
2
a
6
=
−
1
2
u
3
+ u
2
+ 2
u
3
+ u − 1
a
10
=
−u
u
a
11
=
u
3
−u
3
− u
a
8
=
−u
3
u
3
+ u
a
3
=
−1
−u
2
a
1
=
−
1
2
u
3
+ u
2
+ 2
u
3
+ u − 1
a
7
=
−u
3
u
3
+ u
a
12
=
1
2
u
3
+ u
2
+ 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
10
u
4
− 2u
2
+ 2
c
4
, c
9
u
4
+ 2u
2
+ 2
c
7
u
4
c
8
(u
2
+ 2u + 2)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
10
(y
2
− 2y + 2)
2
c
4
, c
9
(y
2
+ 2y + 2)
2
c
7
y
4
c
8
(y
2
+ 4)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455090 + 1.098680I
a = 0.77689 + 1.32180I
b = −1.098680 − 0.544910I
−0.82247 − 3.66386I −8.00000 + 4.00000I
u = 0.455090 − 1.098680I
a = 0.77689 − 1.32180I
b = −1.098680 + 0.544910I
−0.82247 + 3.66386I −8.00000 − 4.00000I
u = −0.455090 + 1.098680I
a = −0.776887 − 0.678203I
b = 1.09868 + 1.45509I
−0.82247 + 3.66386I −8.00000 − 4.00000I
u = −0.455090 − 1.098680I
a = −0.776887 + 0.678203I
b = 1.09868 − 1.45509I
−0.82247 − 3.66386I −8.00000 + 4.00000I
22
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
−1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
10
=
−1
0
a
11
=
−1
0
a
8
=
−1
0
a
3
=
1
0
a
1
=
−1
−1
a
7
=
−1
0
a
12
=
−2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y −1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
5
)(u
40
+ 19u
39
+ ··· + 8u + 1)(u
64
+ 37u
63
+ ··· − 24u
2
+ 1)
c
2
, c
6
(u − 1)(u + 1)
4
(u
40
+ u
39
+ ··· − 4u
2
+ 1)(u
64
+ u
63
+ ··· − 2u − 1)
c
3
, c
10
u(u
4
− 2u
2
+ 2)(u
32
− u
31
+ ··· + 14u − 5)
2
(u
40
+ 3u
39
+ ··· + 62u + 2)
c
4
, c
9
u(u
4
+ 2u
2
+ 2)(u
32
+ u
31
+ ··· − 2u − 1)
2
(u
40
− 3u
39
+ ··· − 6u + 2)
c
5
, c
12
((u − 1)
4
)(u + 1)(u
40
+ u
39
+ ··· − 4u
2
+ 1)(u
64
+ u
63
+ ··· − 2u − 1)
c
7
u
5
(u
32
+ 3u
31
+ ··· − 4u
4
+ 1)
2
(u
40
+ 3u
39
+ ··· − 256u + 256)
c
8
u(u
2
+ 2u + 2)
2
(u
32
− 17u
31
+ ··· − 8u
2
+ 1)
2
· (u
40
− 21u
39
+ ··· − 4u + 4)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
5
)(y
40
+ 13y
39
+ ··· − 8y + 1)(y
64
− 21y
63
+ ··· − 48y + 1)
c
2
, c
5
, c
6
c
12
((y −1)
5
)(y
40
− 19y
39
+ ··· − 8y + 1)(y
64
− 37y
63
+ ··· − 24y
2
+ 1)
c
3
, c
10
y(y
2
− 2y + 2)
2
(y
32
− 23y
31
+ ··· − 296y + 25)
2
· (y
40
− 27y
39
+ ··· − 1244y + 4)
c
4
, c
9
y(y
2
+ 2y + 2)
2
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
· (y
40
+ 21y
39
+ ··· + 4y + 4)
c
7
y
5
(y
32
+ 17y
31
+ ··· − 8y
2
+ 1)
2
· (y
40
+ 17y
39
+ ··· − 1441792y + 65536)
c
8
y(y
2
+ 4)
2
(y
32
− 3y
31
+ ··· − 16y + 1)
2
(y
40
− 3y
39
+ ··· + 80y + 16)
28
