12n
0420
(K12n
0420
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 11 1 12 5 6 9 4
Solving Sequence
2,6 3,11
7 1 8 5 4 10 9 12
c
2
c
6
c
1
c
7
c
5
c
4
c
10
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h364223527493u
32
− 2361609064840u
31
+ ··· + 171190334071b + 90526252853,
671951659745u
32
− 4453002864896u
31
+ ··· + 342380668142a − 1160832184987,
u
33
− 8u
32
+ ··· − 11u + 2i
I
u
2
= h−u
18
− 6u
17
+ ··· + b + 3, 2u
18
+ 7u
17
+ ··· + a + 2, u
19
+ 5u
18
+ ··· − 2u − 1i
I
u
3
= hu
14
a + 39u
14
+ ··· + a + 69, 12u
14
a + 4u
14
+ ··· + 19a + 12,
u
15
+ 3u
14
+ 3u
13
− 4u
12
− 9u
11
− 2u
10
+ 11u
9
+ 5u
8
− 6u
7
− 2u
6
+ 10u
5
+ 3u
4
− 5u
3
+ 3u + 1i
I
u
4
= hb
2
− 3ba + a − 1, a
2
+ 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 86 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
=
h3.64×10
11
u
32
−2.36×10
12
u
31
+· · ·+1.71×10
11
b+9.05×10
10
, 6.72×10
11
u
32
−
4.45 × 10
12
u
31
+ · · · + 3.42 × 10
11
a − 1.16 × 10
12
, u
33
− 8u
32
+ · · · − 11u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
11
=
−1.96259u
32
+ 13.0060u
31
+ ··· − 22.5803u + 3.39047
−2.12759u
32
+ 13.7952u
31
+ ··· − 2.47506u − 0.528805
a
7
=
1.18113u
32
− 6.74280u
31
+ ··· − 5.72215u + 4.99723
2.30591u
32
− 15.5550u
31
+ ··· + 7.17397u − 1.80465
a
1
=
−u
2
+ 1
−u
4
a
8
=
−0.716291u
32
+ 1.55456u
31
+ ··· + 4.09153u + 1.50206
−7.10380u
32
+ 48.6587u
31
+ ··· − 37.9303u + 6.10199
a
5
=
u
u
a
4
=
−1.12478u
32
+ 8.81217u
31
+ ··· − 10.8961u + 6.80188
−1.14806u
32
+ 10.3781u
31
+ ··· − 22.6370u + 4.15836
a
10
=
−1.96259u
32
+ 13.0060u
31
+ ··· − 22.5803u + 3.39047
0.996508u
32
− 9.67025u
31
+ ··· + 23.2414u − 5.91819
a
9
=
−0.264402u
32
+ 4.24281u
31
+ ··· − 27.6237u + 5.38349
2.69469u
32
− 18.4334u
31
+ ··· + 18.1980u − 3.92517
a
12
=
−1.35910u
32
+ 12.0492u
31
+ ··· − 33.5143u + 3.10913
3.64636u
32
− 25.3633u
31
+ ··· + 26.2232u − 4.54568
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
71232541821
171190334071
u
32
+
136288968420
171190334071
u
31
+ ··· +
5957445668473
171190334071
u −
448061765060
171190334071
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
+ 8u
32
+ ··· + 13u + 4
c
2
, c
5
u
33
+ 8u
32
+ ··· − 11u − 2
c
3
, c
12
u
33
− 9u
31
+ ··· + 11u + 1
c
4
u
33
− 16u
31
+ ··· + 868u + 259
c
6
, c
10
u
33
+ u
32
+ ··· + 29u + 2
c
7
u
33
− 29u
32
+ ··· − 159744u + 16384
c
8
, c
11
u
33
− 11u
32
+ ··· − 57u + 4
c
9
u
33
+ u
32
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
+ 40y
32
+ ··· − 2383y −16
c
2
, c
5
y
33
− 8y
32
+ ··· + 13y −4
c
3
, c
12
y
33
− 18y
32
+ ··· + 59y −1
c
4
y
33
− 32y
32
+ ··· + 556584y −67081
c
6
, c
10
y
33
+ 53y
32
+ ··· + 33y −4
c
7
y
33
− 9y
32
+ ··· − 1459617792y −268435456
c
8
, c
11
y
33
+ 23y
32
+ ··· + 177y −16
c
9
y
33
− 53y
32
+ ··· − 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.703285 + 0.636850I
a = 1.106170 + 0.251999I
b = 0.909144 − 1.059290I
4.30952 + 3.14688I 2.88697 − 4.88211I
u = −0.703285 − 0.636850I
a = 1.106170 − 0.251999I
b = 0.909144 + 1.059290I
4.30952 − 3.14688I 2.88697 + 4.88211I
u = −0.417059 + 1.000070I
a = −0.648249 − 0.662444I
b = −0.580122 + 0.953178I
5.17920 − 2.64024I 3.71273 + 1.48167I
u = −0.417059 − 1.000070I
a = −0.648249 + 0.662444I
b = −0.580122 − 0.953178I
5.17920 + 2.64024I 3.71273 − 1.48167I
u = 1.030280 + 0.369979I
a = −0.005672 − 0.234478I
b = −0.462951 − 0.491884I
−1.92686 − 1.50296I −0.206389 + 1.352839I
u = 1.030280 − 0.369979I
a = −0.005672 + 0.234478I
b = −0.462951 + 0.491884I
−1.92686 + 1.50296I −0.206389 − 1.352839I
u = 1.100340 + 0.181053I
a = 0.180870 + 0.010838I
b = 0.858956 − 0.643211I
−0.342656 + 0.092474I −4.88343 + 1.19512I
u = 1.100340 − 0.181053I
a = 0.180870 − 0.010838I
b = 0.858956 + 0.643211I
−0.342656 − 0.092474I −4.88343 − 1.19512I
u = −0.759456 + 0.391806I
a = 0.009616 + 1.198430I
b = 0.866202 + 1.049840I
3.92702 + 0.90107I 3.65109 − 2.09842I
u = −0.759456 − 0.391806I
a = 0.009616 − 1.198430I
b = 0.866202 − 1.049840I
3.92702 − 0.90107I 3.65109 + 2.09842I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.075450 + 0.453106I
a = −0.361831 + 0.442964I
b = −0.063445 + 1.049590I
−1.12678 + 5.28243I −1.72426 − 8.87772I
u = −1.075450 − 0.453106I
a = −0.361831 − 0.442964I
b = −0.063445 − 1.049590I
−1.12678 − 5.28243I −1.72426 + 8.87772I
u = 0.617486 + 0.446217I
a = 0.750133 + 0.203711I
b = 0.207012 − 0.540399I
−0.66765 − 1.55785I −3.86335 + 5.45533I
u = 0.617486 − 0.446217I
a = 0.750133 − 0.203711I
b = 0.207012 + 0.540399I
−0.66765 + 1.55785I −3.86335 − 5.45533I
u = −0.268250 + 0.672707I
a = 0.777671 + 0.095093I
b = 0.068519 − 0.534112I
1.35635 − 1.05663I 4.19428 + 2.46182I
u = −0.268250 − 0.672707I
a = 0.777671 − 0.095093I
b = 0.068519 + 0.534112I
1.35635 + 1.05663I 4.19428 − 2.46182I
u = 0.868458 + 0.964205I
a = −1.45868 − 0.78756I
b = −0.48302 − 1.49770I
12.95180 − 2.19664I 5.82474 + 2.27919I
u = 0.868458 − 0.964205I
a = −1.45868 + 0.78756I
b = −0.48302 + 1.49770I
12.95180 + 2.19664I 5.82474 − 2.27919I
u = 0.916626 + 0.950177I
a = −1.06864 − 1.17969I
b = −0.08093 − 1.74309I
9.06275 + 2.60903I 0.48775 − 2.35974I
u = 0.916626 − 0.950177I
a = −1.06864 + 1.17969I
b = −0.08093 + 1.74309I
9.06275 − 2.60903I 0.48775 + 2.35974I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.023220 + 0.876693I
a = 0.87894 + 1.19241I
b = 0.37002 + 2.13539I
12.43740 − 4.58287I 4.99508 + 2.38247I
u = 1.023220 − 0.876693I
a = 0.87894 − 1.19241I
b = 0.37002 − 2.13539I
12.43740 + 4.58287I 4.99508 − 2.38247I
u = 0.990802 + 0.915834I
a = 1.36449 + 0.89241I
b = 0.89932 + 1.99675I
8.82668 − 9.47341I 0. + 6.83895I
u = 0.990802 − 0.915834I
a = 1.36449 − 0.89241I
b = 0.89932 − 1.99675I
8.82668 + 9.47341I 0. − 6.83895I
u = −1.241080 + 0.559280I
a = −0.055515 − 0.655838I
b = −1.07954 − 1.10250I
2.34090 + 8.49049I 2.07804 − 5.32543I
u = −1.241080 − 0.559280I
a = −0.055515 + 0.655838I
b = −1.07954 + 1.10250I
2.34090 − 8.49049I 2.07804 + 5.32543I
u = 0.893546 + 1.073000I
a = 1.11701 + 1.10394I
b = −0.47751 + 1.72433I
14.6502 + 8.3217I 2.61160 − 3.46041I
u = 0.893546 − 1.073000I
a = 1.11701 − 1.10394I
b = −0.47751 − 1.72433I
14.6502 − 8.3217I 2.61160 + 3.46041I
u = 1.08079 + 0.94085I
a = −1.30612 − 0.84939I
b = −0.96271 − 2.44484I
14.0051 − 15.6492I 1.72340 + 7.56042I
u = 1.08079 − 0.94085I
a = −1.30612 + 0.84939I
b = −0.96271 + 2.44484I
14.0051 + 15.6492I 1.72340 − 7.56042I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530622
a = −2.30551
b = −1.44839
−2.29787 −17.6560
u = 0.208352 + 0.257728I
a = −2.37744 − 2.48596I
b = −0.264747 + 1.039230I
3.34739 − 0.13046I 5.79773 + 0.03563I
u = 0.208352 − 0.257728I
a = −2.37744 + 2.48596I
b = −0.264747 − 1.039230I
3.34739 + 0.13046I 5.79773 − 0.03563I
8
II.
I
u
2
= h−u
18
−6u
17
+· · ·+b+3, 2u
18
+7u
17
+· · ·+a+2, u
19
+5u
18
+· · ·−2u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
11
=
−2u
18
− 7u
17
+ ··· + u − 2
u
18
+ 6u
17
+ ··· − 4u − 3
a
7
=
−2u
17
− 8u
16
+ ··· − 4u + 1
−u
17
− 4u
16
+ ··· − 4u
3
− 6u
2
a
1
=
−u
2
+ 1
−u
4
a
8
=
−u
18
− 4u
17
+ ··· − 4u − 1
−3u
18
− 12u
17
+ ··· + 3u + 1
a
5
=
u
u
a
4
=
−u
17
− 4u
16
+ ··· − 2u + 1
−4u
18
− 17u
17
+ ··· + 5u + 4
a
10
=
−2u
18
− 7u
17
+ ··· + u − 2
4u
18
+ 19u
17
+ ··· − 8u − 6
a
9
=
−3u
18
− 14u
17
+ ··· + 3u + 2
3u
18
+ 12u
17
+ ··· − 6u − 2
a
12
=
−3u
18
− 12u
17
+ ··· + 5u + 3
2u
18
+ 11u
17
+ ··· − 3u − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14u
18
− 57u
17
− 68u
16
+ 85u
15
+ 290u
14
+ 126u
13
− 418u
12
−
544u
11
+ 95u
10
+ 567u
9
+ 182u
8
−289u
7
−164u
6
+ 78u
5
+ u
4
−101u
3
−31u
2
+ 35u + 22
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 7u
18
+ ··· + 8u − 1
c
2
u
19
+ 5u
18
+ ··· − 2u − 1
c
3
, c
12
u
19
+ 2u
16
+ ··· + 3u + 1
c
4
u
19
− 7u
17
+ ··· + 2u − 1
c
5
u
19
− 5u
18
+ ··· − 2u + 1
c
6
u
19
+ u
18
+ ··· − u − 1
c
7
u
19
− 8u
18
+ ··· + 2u − 1
c
8
u
19
− 8u
18
+ ··· + 103u − 13
c
9
u
19
− u
18
+ ··· + 2u + 1
c
10
u
19
− u
18
+ ··· − u + 1
c
11
u
19
+ 8u
18
+ ··· + 103u + 13
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 17y
18
+ ··· + 4y −1
c
2
, c
5
y
19
− 7y
18
+ ··· + 8y −1
c
3
, c
12
y
19
+ 10y
17
+ ··· + 3y −1
c
4
y
19
− 14y
18
+ ··· − 4y −1
c
6
, c
10
y
19
+ 7y
18
+ ··· + 15y −1
c
7
y
19
− 8y
18
+ ··· − 6y −1
c
8
, c
11
y
19
+ 12y
18
+ ··· − 25y −169
c
9
y
19
− 11y
18
+ ··· + 12y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932201 + 0.382585I
a = −0.652447 + 0.235364I
b = −0.990085 − 0.241494I
−2.78530 − 1.52808I −10.73635 + 2.82089I
u = 0.932201 − 0.382585I
a = −0.652447 − 0.235364I
b = −0.990085 + 0.241494I
−2.78530 + 1.52808I −10.73635 − 2.82089I
u = −0.624787 + 0.658264I
a = 1.003060 + 0.151577I
b = 0.255285 + 0.371052I
−0.002497 + 0.784497I 2.96024 + 1.59105I
u = −0.624787 − 0.658264I
a = 1.003060 − 0.151577I
b = 0.255285 − 0.371052I
−0.002497 − 0.784497I 2.96024 − 1.59105I
u = −1.021020 + 0.575808I
a = 0.239601 + 0.502383I
b = 0.144505 + 1.025180I
−1.25834 + 4.04878I −0.84230 − 4.09364I
u = −1.021020 − 0.575808I
a = 0.239601 − 0.502383I
b = 0.144505 − 1.025180I
−1.25834 − 4.04878I −0.84230 + 4.09364I
u = −1.067510 + 0.498451I
a = −0.488686 − 0.116550I
b = −0.948978 − 0.694197I
0.84328 + 8.76402I −3.62315 − 7.96043I
u = −1.067510 − 0.498451I
a = −0.488686 + 0.116550I
b = −0.948978 + 0.694197I
0.84328 − 8.76402I −3.62315 + 7.96043I
u = 1.169200 + 0.389254I
a = 0.304496 − 0.673763I
b = 1.20589 − 0.89024I
0.243599 + 1.379440I −1.72015 − 3.05492I
u = 1.169200 − 0.389254I
a = 0.304496 + 0.673763I
b = 1.20589 + 0.89024I
0.243599 − 1.379440I −1.72015 + 3.05492I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371084 + 0.611861I
a = 1.24272 − 1.18831I
b = 1.054910 + 0.717314I
3.06976 − 5.52425I 0.98196 + 6.56688I
u = 0.371084 − 0.611861I
a = 1.24272 + 1.18831I
b = 1.054910 − 0.717314I
3.06976 + 5.52425I 0.98196 − 6.56688I
u = −0.555549 + 0.399589I
a = −1.021540 − 0.577214I
b = 0.486749 − 0.634203I
2.60739 − 4.81529I 1.74304 + 2.99283I
u = −0.555549 − 0.399589I
a = −1.021540 + 0.577214I
b = 0.486749 + 0.634203I
2.60739 + 4.81529I 1.74304 − 2.99283I
u = −0.876351 + 1.033240I
a = −1.20703 + 0.83058I
b = 0.00403 + 1.52107I
10.98580 + 1.99614I 1.00063 − 2.24339I
u = −0.876351 − 1.033240I
a = −1.20703 − 0.83058I
b = 0.00403 − 1.52107I
10.98580 − 1.99614I 1.00063 + 2.24339I
u = −1.063610 + 0.923538I
a = 1.021470 − 0.912245I
b = 0.57254 − 2.13980I
10.36830 + 5.14621I 0.49469 − 2.50743I
u = −1.063610 − 0.923538I
a = 1.021470 + 0.912245I
b = 0.57254 + 2.13980I
10.36830 − 5.14621I 0.49469 + 2.50743I
u = 0.472695
a = −2.88328
b = −1.56969
−2.08591 20.4830
13
III. I
u
3
=
hu
14
a+39u
14
+· · ·+a+69, 12u
14
a+4u
14
+· · ·+19a+12, u
15
+3u
14
+· · ·+3u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
11
=
a
−
1
4
u
14
a −
39
4
u
14
+ ··· −
1
4
a −
69
4
a
7
=
−7u
14
a − u
14
+ ··· − 12a − 4
3
4
u
14
a +
1
4
u
14
+ ··· +
5
4
a +
5
4
a
1
=
−u
2
+ 1
−u
4
a
8
=
−7u
14
a − u
14
+ ··· − 12a − 3
3
4
u
14
a +
1
4
u
14
+ ··· +
5
4
a +
5
4
a
5
=
u
u
a
4
=
−7.75000au
14
− 1.25000u
14
+ ··· − 13.2500a − 5.25000
−
5
2
u
14
a − 7u
13
a + ··· −
11
2
a − 1
a
10
=
a
−
1
4
u
14
a −
39
4
u
14
+ ··· −
1
4
a −
69
4
a
9
=
1
4
u
14
a +
11
4
u
14
+ ··· +
5
4
a +
21
4
−7u
14
− 17u
13
+ ··· − 17u − 12
a
12
=
−
11
4
u
14
a −
3
4
u
14
+ ··· −
9
4
a −
11
4
1
4
u
14
a −
11
4
u
14
+ ··· +
1
4
a −
9
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −17u
14
− 44u
13
− 31u
12
+ 85u
11
+ 122u
10
− 24u
9
− 191u
8
−
12u
7
+ 126u
6
− 8u
5
− 174u
4
+ 11u
3
+ 96u
2
− 32u − 45
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 3u
14
+ ··· + 9u + 1)
2
c
2
, c
5
(u
15
− 3u
14
+ ··· + 3u − 1)
2
c
3
, c
12
u
30
+ 3u
29
+ ··· + 8u + 2
c
4
u
30
− u
29
+ ··· + 72516u + 14102
c
6
, c
10
u
30
− 3u
29
+ ··· + 8468u + 872
c
7
(u + 1)
30
c
8
, c
11
(u
15
+ 3u
14
+ ··· + u + 3)
2
c
9
u
30
− u
29
+ ··· + 47532u + 25406
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 21y
14
+ ··· + 9y −1)
2
c
2
, c
5
(y
15
− 3y
14
+ ··· + 9y −1)
2
c
3
, c
12
y
30
− 3y
29
+ ··· + 316y
2
+ 4
c
4
y
30
− 27y
29
+ ··· − 960449880y + 198866404
c
6
, c
10
y
30
+ 39y
29
+ ··· − 9306704y + 760384
c
7
(y −1)
30
c
8
, c
11
(y
15
+ 13y
14
+ ··· + 49y −9)
2
c
9
y
30
− 39y
29
+ ··· + 4154402864y + 645464836
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455780 + 0.742288I
a = 0.374894 − 0.055630I
b = 0.80444 + 1.32107I
4.49075 − 5.71085I 6.46241 + 7.10367I
u = 0.455780 + 0.742288I
a = −2.14568 + 1.13593I
b = −0.614258 − 0.952191I
4.49075 − 5.71085I 6.46241 + 7.10367I
u = 0.455780 − 0.742288I
a = 0.374894 + 0.055630I
b = 0.80444 − 1.32107I
4.49075 + 5.71085I 6.46241 − 7.10367I
u = 0.455780 − 0.742288I
a = −2.14568 − 1.13593I
b = −0.614258 + 0.952191I
4.49075 + 5.71085I 6.46241 − 7.10367I
u = 1.138960 + 0.300791I
a = −0.103181 − 0.773806I
b = 0.554576 − 0.429686I
1.96309 + 1.51473I 3.34538 − 3.96091I
u = 1.138960 + 0.300791I
a = −0.365344 + 1.172340I
b = −1.36268 + 2.77623I
1.96309 + 1.51473I 3.34538 − 3.96091I
u = 1.138960 − 0.300791I
a = −0.103181 + 0.773806I
b = 0.554576 + 0.429686I
1.96309 − 1.51473I 3.34538 + 3.96091I
u = 1.138960 − 0.300791I
a = −0.365344 − 1.172340I
b = −1.36268 − 2.77623I
1.96309 − 1.51473I 3.34538 + 3.96091I
u = 0.679943 + 0.425075I
a = 1.288550 + 0.270756I
b = 0.310334 − 0.078658I
−0.68938 − 1.70420I −3.28110 + 6.20426I
u = 0.679943 + 0.425075I
a = 0.176983 − 0.279271I
b = −0.096624 − 1.275770I
−0.68938 − 1.70420I −3.28110 + 6.20426I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679943 − 0.425075I
a = 1.288550 − 0.270756I
b = 0.310334 + 0.078658I
−0.68938 + 1.70420I −3.28110 − 6.20426I
u = 0.679943 − 0.425075I
a = 0.176983 + 0.279271I
b = −0.096624 + 1.275770I
−0.68938 + 1.70420I −3.28110 − 6.20426I
u = −0.966502 + 0.945831I
a = 1.230920 − 0.689205I
b = 0.90511 − 1.88788I
8.07776 + 3.48053I −1.20552 − 1.99086I
u = −0.966502 + 0.945831I
a = −0.95957 + 1.09544I
b = 0.08832 + 1.59239I
8.07776 + 3.48053I −1.20552 − 1.99086I
u = −0.966502 − 0.945831I
a = 1.230920 + 0.689205I
b = 0.90511 + 1.88788I
8.07776 − 3.48053I −1.20552 + 1.99086I
u = −0.966502 − 0.945831I
a = −0.95957 − 1.09544I
b = 0.08832 − 1.59239I
8.07776 − 3.48053I −1.20552 + 1.99086I
u = −0.572435 + 0.216966I
a = 1.54766 − 0.25368I
b = 2.07813 + 0.63415I
1.75184 + 5.76927I −5.27590 − 9.59925I
u = −0.572435 + 0.216966I
a = 1.59367 + 1.91830I
b = 0.541087 − 0.592067I
1.75184 + 5.76927I −5.27590 − 9.59925I
u = −0.572435 − 0.216966I
a = 1.54766 + 0.25368I
b = 2.07813 − 0.63415I
1.75184 − 5.76927I −5.27590 + 9.59925I
u = −0.572435 − 0.216966I
a = 1.59367 − 1.91830I
b = 0.541087 + 0.592067I
1.75184 − 5.76927I −5.27590 + 9.59925I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862360 + 1.093580I
a = −1.045040 + 0.596115I
b = −0.319838 + 1.263430I
12.51580 + 1.19189I 6.81331 + 0.30242I
u = −0.862360 + 1.093580I
a = 1.27746 − 1.33704I
b = −1.21684 − 1.86631I
12.51580 + 1.19189I 6.81331 + 0.30242I
u = −0.862360 − 1.093580I
a = −1.045040 − 0.596115I
b = −0.319838 − 1.263430I
12.51580 − 1.19189I 6.81331 − 0.30242I
u = −0.862360 − 1.093580I
a = 1.27746 + 1.33704I
b = −1.21684 + 1.86631I
12.51580 − 1.19189I 6.81331 − 0.30242I
u = −1.11139 + 0.94100I
a = 0.803051 − 0.849353I
b = 0.41663 − 1.67373I
11.69180 + 6.19707I 5.35055 − 5.75816I
u = −1.11139 + 0.94100I
a = −1.44943 + 0.77049I
b = −1.21250 + 3.06428I
11.69180 + 6.19707I 5.35055 − 5.75816I
u = −1.11139 − 0.94100I
a = 0.803051 + 0.849353I
b = 0.41663 + 1.67373I
11.69180 − 6.19707I 5.35055 + 5.75816I
u = −1.11139 − 0.94100I
a = −1.44943 − 0.77049I
b = −1.21250 − 3.06428I
11.69180 − 6.19707I 5.35055 + 5.75816I
u = −0.523988
a = −2.22494 + 0.27610I
b = −1.375880 − 0.228118I
−2.29134 −14.4180
u = −0.523988
a = −2.22494 − 0.27610I
b = −1.375880 + 0.228118I
−2.29134 −14.4180
19
IV. I
u
4
= hb
2
− 3ba + a − 1, a
2
+ 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
11
=
a
b
a
7
=
1
−ba + 1
a
1
=
0
−1
a
8
=
1
−ba
a
5
=
1
1
a
4
=
ba + 2
2ba − a + 2
a
10
=
a
b − a
a
9
=
−b + 3a
a
a
12
=
ba + a + 3
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
12
u
4
− 2u
3
− u
2
+ 2u + 2
c
4
, c
9
u
4
+ 3u
2
− 2u + 2
c
5
, c
7
(u + 1)
4
c
6
, c
8
, c
10
c
11
(u
2
+ 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
(y −1)
4
c
3
, c
12
y
4
− 6y
3
+ 13y
2
− 8y + 4
c
4
, c
9
y
4
+ 6y
3
+ 13y
2
+ 8y + 4
c
6
, c
8
, c
10
c
11
(y + 1)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.000000I
b = 0.418797 + 0.306103I
1.64493 0
u = 1.00000
a = 1.000000I
b = −0.41880 + 2.69390I
1.64493 0
u = 1.00000
a = − 1.000000I
b = 0.418797 − 0.306103I
1.64493 0
u = 1.00000
a = − 1.000000I
b = −0.41880 − 2.69390I
1.64493 0
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
15
+ 3u
14
+ ··· + 9u + 1)
2
(u
19
− 7u
18
+ ··· + 8u − 1)
· (u
33
+ 8u
32
+ ··· + 13u + 4)
c
2
((u − 1)
4
)(u
15
− 3u
14
+ ··· + 3u − 1)
2
(u
19
+ 5u
18
+ ··· − 2u − 1)
· (u
33
+ 8u
32
+ ··· − 11u − 2)
c
3
, c
12
(u
4
− 2u
3
− u
2
+ 2u + 2)(u
19
+ 2u
16
+ ··· + 3u + 1)
· (u
30
+ 3u
29
+ ··· + 8u + 2)(u
33
− 9u
31
+ ··· + 11u + 1)
c
4
(u
4
+ 3u
2
− 2u + 2)(u
19
− 7u
17
+ ··· + 2u − 1)
· (u
30
− u
29
+ ··· + 72516u + 14102)(u
33
− 16u
31
+ ··· + 868u + 259)
c
5
((u + 1)
4
)(u
15
− 3u
14
+ ··· + 3u − 1)
2
(u
19
− 5u
18
+ ··· − 2u + 1)
· (u
33
+ 8u
32
+ ··· − 11u − 2)
c
6
((u
2
+ 1)
2
)(u
19
+ u
18
+ ··· − u − 1)(u
30
− 3u
29
+ ··· + 8468u + 872)
· (u
33
+ u
32
+ ··· + 29u + 2)
c
7
((u + 1)
34
)(u
19
− 8u
18
+ ··· + 2u − 1)
· (u
33
− 29u
32
+ ··· − 159744u + 16384)
c
8
((u
2
+ 1)
2
)(u
15
+ 3u
14
+ ··· + u + 3)
2
(u
19
− 8u
18
+ ··· + 103u − 13)
· (u
33
− 11u
32
+ ··· − 57u + 4)
c
9
(u
4
+ 3u
2
− 2u + 2)(u
19
− u
18
+ ··· + 2u + 1)
· (u
30
− u
29
+ ··· + 47532u + 25406)(u
33
+ u
32
+ ··· + 2u + 1)
c
10
((u
2
+ 1)
2
)(u
19
− u
18
+ ··· − u + 1)(u
30
− 3u
29
+ ··· + 8468u + 872)
· (u
33
+ u
32
+ ··· + 29u + 2)
c
11
((u
2
+ 1)
2
)(u
15
+ 3u
14
+ ··· + u + 3)
2
(u
19
+ 8u
18
+ ··· + 103u + 13)
· (u
33
− 11u
32
+ ··· − 57u + 4)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
15
+ 21y
14
+ ··· + 9y −1)
2
(y
19
+ 17y
18
+ ··· + 4y −1)
· (y
33
+ 40y
32
+ ··· − 2383y −16)
c
2
, c
5
((y −1)
4
)(y
15
− 3y
14
+ ··· + 9y −1)
2
(y
19
− 7y
18
+ ··· + 8y −1)
· (y
33
− 8y
32
+ ··· + 13y −4)
c
3
, c
12
(y
4
− 6y
3
+ 13y
2
− 8y + 4)(y
19
+ 10y
17
+ ··· + 3y −1)
· (y
30
− 3y
29
+ ··· + 316y
2
+ 4)(y
33
− 18y
32
+ ··· + 59y −1)
c
4
(y
4
+ 6y
3
+ 13y
2
+ 8y + 4)(y
19
− 14y
18
+ ··· − 4y −1)
· (y
30
− 27y
29
+ ··· − 960449880y + 198866404)
· (y
33
− 32y
32
+ ··· + 556584y −67081)
c
6
, c
10
((y + 1)
4
)(y
19
+ 7y
18
+ ··· + 15y −1)
· (y
30
+ 39y
29
+ ··· − 9306704y + 760384)
· (y
33
+ 53y
32
+ ··· + 33y −4)
c
7
((y −1)
34
)(y
19
− 8y
18
+ ··· − 6y −1)
· (y
33
− 9y
32
+ ··· − 1459617792y −268435456)
c
8
, c
11
((y + 1)
4
)(y
15
+ 13y
14
+ ··· + 49y −9)
2
· (y
19
+ 12y
18
+ ··· − 25y −169)(y
33
+ 23y
32
+ ··· + 177y −16)
c
9
(y
4
+ 6y
3
+ 13y
2
+ 8y + 4)(y
19
− 11y
18
+ ··· + 12y −1)
· (y
30
− 39y
29
+ ··· + 4154402864y + 645464836)
· (y
33
− 53y
32
+ ··· − 8y −1)
25
