12a
0177
(K12a
0177
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 11 10 12 4 7 1 8
Solving Sequence
6,11 2,7
5 3 1 4 10 8 9 12
c
6
c
5
c
2
c
1
c
4
c
10
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.32498 × 10
64
u
73
+ 8.66991 × 10
64
u
72
+ ··· + 6.16277 × 10
65
b − 4.73818 × 10
66
,
− 1.00235 × 10
67
u
73
− 1.65925 × 10
67
u
72
+ ··· + 2.09534 × 10
67
a + 3.92221 × 10
68
,
u
74
+ 3u
73
+ ··· + 241u + 34i
I
u
2
= h−u
12
− 4u
10
+ 2u
9
− 6u
8
+ 6u
7
− 6u
6
+ 6u
5
− 5u
4
+ 2u
3
− 2u
2
+ b,
u
10
+ 3u
8
− 2u
7
+ 4u
6
− 4u
5
+ 5u
4
− 4u
3
+ 3u
2
+ a − 2u + 1, u
27
+ 9u
25
+ ··· + u − 1i
I
u
3
= hu
2
a + u
2
+ b + a + 1, 2u
3
a + 4u
2
a + 5u
3
+ 4a
2
+ 6au + 6u
2
+ 14a + 13u + 15, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
4
= h−a
2
− 2au + b + 2a + 2u − 1, a
4
+ 3a
3
u − 4a
3
− 9a
2
u + 5a
2
+ 11au − 2a − 5u + 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 117 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
= h7.32 × 10
64
u
73
+ 8.67 × 10
64
u
72
+ · · · + 6.16 × 10
65
b − 4.74 ×
10
66
, −1.00 × 10
67
u
73
− 1.66 × 10
67
u
72
+ · · · + 2.10 × 10
67
a + 3.92 ×
10
68
, u
74
+ 3u
73
+ · · · + 241u + 34i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
0.478370u
73
+ 0.791874u
72
+ ··· − 33.3429u − 18.7187
−0.118859u
73
− 0.140682u
72
+ ··· + 21.7836u + 7.68839
a
7
=
1
−u
2
a
5
=
−1.54482u
73
− 3.80613u
72
+ ··· − 519.075u − 88.4779
0.760024u
73
+ 1.86639u
72
+ ··· + 269.188u + 47.8263
a
3
=
0.570211u
73
+ 1.31506u
72
+ ··· + 144.190u + 26.0532
0.0702357u
73
+ 0.201359u
72
+ ··· − 19.1668u − 9.42275
a
1
=
0.737803u
73
+ 1.93511u
72
+ ··· + 256.366u + 47.4633
0.565372u
73
+ 1.35960u
72
+ ··· + 138.390u + 21.9622
a
4
=
−0.784791u
73
− 1.93974u
72
+ ··· − 249.887u − 40.6516
0.760024u
73
+ 1.86639u
72
+ ··· + 269.188u + 47.8263
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
1.26077u
73
+ 3.03039u
72
+ ··· + 376.302u + 61.5916
−1.04521u
73
− 2.74727u
72
+ ··· − 382.989u − 69.8736
a
12
=
1.61959u
73
+ 4.23678u
72
+ ··· + 593.454u + 111.477
0.435515u
73
+ 0.883326u
72
+ ··· + 44.5571u + 0.814681
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.202194u
73
+ 0.134817u
72
+ ··· − 112.657u − 17.5239
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
74
+ 24u
73
+ ··· − 225u + 16
c
2
, c
5
u
74
+ 4u
73
+ ··· + 35u + 4
c
3
, c
9
u
74
− 2u
73
+ ··· − 2560u + 2048
c
6
, c
7
, c
10
u
74
+ 3u
73
+ ··· + 241u + 34
c
8
, c
12
u
74
+ 3u
73
+ ··· + 243u + 34
c
11
u
74
− 31u
73
+ ··· − 29555u + 1156
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
74
+ 56y
73
+ ··· + 227743y + 256
c
2
, c
5
y
74
+ 24y
73
+ ··· − 225y + 16
c
3
, c
9
y
74
− 40y
73
+ ··· − 36438016y + 4194304
c
6
, c
7
, c
10
y
74
+ 75y
73
+ ··· + 36099y + 1156
c
8
, c
12
y
74
+ 31y
73
+ ··· + 29555y + 1156
c
11
y
74
+ 35y
73
+ ··· + 11195711y + 1336336
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944775 + 0.259860I
a = 2.05390 − 0.30574I
b = −0.743584 + 1.028880I
5.92126 − 12.56140I 0
u = −0.944775 − 0.259860I
a = 2.05390 + 0.30574I
b = −0.743584 − 1.028880I
5.92126 + 12.56140I 0
u = −0.921296 + 0.218016I
a = 1.35216 + 1.03131I
b = −0.857448 − 0.692852I
6.95372 − 6.59603I 0
u = −0.921296 − 0.218016I
a = 1.35216 − 1.03131I
b = −0.857448 + 0.692852I
6.95372 + 6.59603I 0
u = 0.701992 + 0.812926I
a = 0.745443 − 0.467058I
b = −0.711125 + 0.915757I
2.32200 − 1.76357I 0
u = 0.701992 − 0.812926I
a = 0.745443 + 0.467058I
b = −0.711125 − 0.915757I
2.32200 + 1.76357I 0
u = 0.633453 + 0.888233I
a = 1.49188 − 0.19124I
b = −0.734625 − 0.820944I
2.61817 + 3.75049I 0
u = 0.633453 − 0.888233I
a = 1.49188 + 0.19124I
b = −0.734625 + 0.820944I
2.61817 − 3.75049I 0
u = −0.784151 + 0.296355I
a = −0.632018 + 0.069860I
b = 0.190621 − 1.095890I
−0.13573 − 6.54057I 4.00000 + 8.07439I
u = −0.784151 − 0.296355I
a = −0.632018 − 0.069860I
b = 0.190621 + 1.095890I
−0.13573 + 6.54057I 4.00000 − 8.07439I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672265 + 0.482118I
a = 1.222840 + 0.018497I
b = −0.042473 − 0.877998I
−1.54681 + 2.12225I 0. − 3.10049I
u = 0.672265 − 0.482118I
a = 1.222840 − 0.018497I
b = −0.042473 + 0.877998I
−1.54681 − 2.12225I 0. + 3.10049I
u = −0.126360 + 1.199890I
a = 1.040200 + 0.208918I
b = −0.877658 − 0.958922I
6.07360 + 1.90106I 0
u = −0.126360 − 1.199890I
a = 1.040200 − 0.208918I
b = −0.877658 + 0.958922I
6.07360 − 1.90106I 0
u = 0.114557 + 0.782746I
a = 0.659521 + 0.464671I
b = 0.177178 + 0.779440I
−1.59283 + 1.64325I −3.33878 − 4.86673I
u = 0.114557 − 0.782746I
a = 0.659521 − 0.464671I
b = 0.177178 − 0.779440I
−1.59283 − 1.64325I −3.33878 + 4.86673I
u = −0.164572 + 1.204940I
a = 1.227960 − 0.069637I
b = −0.910018 + 0.882320I
6.31241 − 4.67571I 0
u = −0.164572 − 1.204940I
a = 1.227960 + 0.069637I
b = −0.910018 − 0.882320I
6.31241 + 4.67571I 0
u = 0.742648 + 0.206519I
a = −2.53072 − 1.14776I
b = 0.716663 + 0.940041I
2.97428 + 6.29652I 7.50844 − 6.68334I
u = 0.742648 − 0.206519I
a = −2.53072 + 1.14776I
b = 0.716663 − 0.940041I
2.97428 − 6.29652I 7.50844 + 6.68334I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.717121 + 0.158800I
a = −1.225590 + 0.380080I
b = 0.731356 − 0.145206I
3.98068 − 3.64075I 11.59299 + 4.80389I
u = −0.717121 − 0.158800I
a = −1.225590 − 0.380080I
b = 0.731356 + 0.145206I
3.98068 + 3.64075I 11.59299 − 4.80389I
u = 0.668164 + 0.154518I
a = −2.39850 + 1.57549I
b = 0.744333 − 0.790073I
3.43591 + 0.73188I 9.08233 − 1.08851I
u = 0.668164 − 0.154518I
a = −2.39850 − 1.57549I
b = 0.744333 + 0.790073I
3.43591 − 0.73188I 9.08233 + 1.08851I
u = −0.129344 + 1.322690I
a = −0.479899 − 0.769382I
b = 0.779061 + 0.657588I
−3.18435 + 0.63847I 0
u = −0.129344 − 1.322690I
a = −0.479899 + 0.769382I
b = 0.779061 − 0.657588I
−3.18435 − 0.63847I 0
u = 0.168573 + 1.321110I
a = −0.405207 + 0.035030I
b = 0.761529 + 0.328332I
−2.90837 + 2.42803I 0
u = 0.168573 − 1.321110I
a = −0.405207 − 0.035030I
b = 0.761529 − 0.328332I
−2.90837 − 2.42803I 0
u = −0.619119 + 0.176034I
a = 0.73745 + 1.54337I
b = −0.846329 − 0.820584I
9.31962 + 1.94114I 12.61811 − 2.00223I
u = −0.619119 − 0.176034I
a = 0.73745 − 1.54337I
b = −0.846329 + 0.820584I
9.31962 − 1.94114I 12.61811 + 2.00223I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.080972 + 1.372850I
a = −0.741831 − 0.900405I
b = 0.543374 − 1.089860I
−5.16943 − 2.42403I 0
u = 0.080972 − 1.372850I
a = −0.741831 + 0.900405I
b = 0.543374 + 1.089860I
−5.16943 + 2.42403I 0
u = −0.195770 + 1.365850I
a = −1.82469 − 0.71360I
b = 0.693804 − 1.006320I
−4.22851 − 4.92303I 0
u = −0.195770 − 1.365850I
a = −1.82469 + 0.71360I
b = 0.693804 + 1.006320I
−4.22851 + 4.92303I 0
u = 0.264758 + 1.357650I
a = −0.734404 + 0.940199I
b = 0.834563 − 0.756749I
−1.35573 + 4.11982I 0
u = 0.264758 − 1.357650I
a = −0.734404 − 0.940199I
b = 0.834563 + 0.756749I
−1.35573 − 4.11982I 0
u = −0.287291 + 1.361710I
a = −0.635754 − 0.259327I
b = 0.855562 − 0.209147I
−0.83655 − 7.27459I 0
u = −0.287291 − 1.361710I
a = −0.635754 + 0.259327I
b = 0.855562 + 0.209147I
−0.83655 + 7.27459I 0
u = −0.221792 + 1.376420I
a = −0.337020 + 0.630518I
b = 0.469813 + 1.138480I
−3.81286 − 2.52146I 0
u = −0.221792 − 1.376420I
a = −0.337020 − 0.630518I
b = 0.469813 − 1.138480I
−3.81286 + 2.52146I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.545845 + 0.228098I
a = 2.57811 + 0.51294I
b = −0.800509 + 0.954675I
8.90634 − 4.18645I 12.18887 + 3.45540I
u = −0.545845 − 0.228098I
a = 2.57811 − 0.51294I
b = −0.800509 − 0.954675I
8.90634 + 4.18645I 12.18887 − 3.45540I
u = −0.545719 + 0.215154I
a = −1.73543 − 0.37199I
b = 0.421570 + 1.033690I
1.244170 + 0.336310I 9.44086 + 1.14384I
u = −0.545719 − 0.215154I
a = −1.73543 + 0.37199I
b = 0.421570 − 1.033690I
1.244170 − 0.336310I 9.44086 − 1.14384I
u = 0.29962 + 1.38522I
a = −1.98098 + 0.41163I
b = 0.755945 + 0.990941I
−2.08327 + 10.07100I 0
u = 0.29962 − 1.38522I
a = −1.98098 − 0.41163I
b = 0.755945 − 0.990941I
−2.08327 − 10.07100I 0
u = 0.07395 + 1.42707I
a = 0.701838 − 0.037664I
b = −0.569204 + 0.123347I
−5.46924 + 2.64105I 0
u = 0.07395 − 1.42707I
a = 0.701838 + 0.037664I
b = −0.569204 − 0.123347I
−5.46924 − 2.64105I 0
u = 0.21382 + 1.43929I
a = −0.487788 + 1.212470I
b = 0.120316 + 1.133060I
−7.79078 + 4.88573I 0
u = 0.21382 − 1.43929I
a = −0.487788 − 1.212470I
b = 0.120316 − 1.133060I
−7.79078 − 4.88573I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31083 + 1.42891I
a = −0.828824 − 0.998794I
b = 0.177740 − 1.175180I
−5.64512 − 10.50590I 0
u = −0.31083 − 1.42891I
a = −0.828824 + 0.998794I
b = 0.177740 + 1.175180I
−5.64512 + 10.50590I 0
u = 0.33404 + 1.42646I
a = 0.275691 − 0.575217I
b = −0.839583 + 0.641379I
−1.11669 + 5.57868I 0
u = 0.33404 − 1.42646I
a = 0.275691 + 0.575217I
b = −0.839583 − 0.641379I
−1.11669 − 5.57868I 0
u = 0.343987 + 0.408307I
a = 1.259340 − 0.200200I
b = −0.164430 + 0.105291I
0.438180 + 1.277440I 4.77216 − 5.31124I
u = 0.343987 − 0.408307I
a = 1.259340 + 0.200200I
b = −0.164430 − 0.105291I
0.438180 − 1.277440I 4.77216 + 5.31124I
u = −0.38671 + 1.41560I
a = 0.358467 + 0.797877I
b = −0.900022 − 0.655211I
1.77264 − 11.28690I 0
u = −0.38671 − 1.41560I
a = 0.358467 − 0.797877I
b = −0.900022 + 0.655211I
1.77264 + 11.28690I 0
u = −0.39335 + 1.44216I
a = 1.78767 + 0.81460I
b = −0.744553 + 1.062820I
0.5121 − 17.3690I 0
u = −0.39335 − 1.44216I
a = 1.78767 − 0.81460I
b = −0.744553 − 1.062820I
0.5121 + 17.3690I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07337 + 1.49652I
a = 0.689010 + 1.074630I
b = −0.098684 + 1.018160I
−9.15376 + 0.69582I 0
u = −0.07337 − 1.49652I
a = 0.689010 − 1.074630I
b = −0.098684 − 1.018160I
−9.15376 − 0.69582I 0
u = 0.33300 + 1.47174I
a = 1.55926 − 0.90181I
b = −0.717365 − 1.043070I
−2.33369 + 11.39850I 0
u = 0.33300 − 1.47174I
a = 1.55926 + 0.90181I
b = −0.717365 + 1.043070I
−2.33369 − 11.39850I 0
u = 0.20232 + 1.50188I
a = 1.013920 − 0.861496I
b = −0.197794 − 0.951591I
−8.06757 + 5.26507I 0
u = 0.20232 − 1.50188I
a = 1.013920 + 0.861496I
b = −0.197794 + 0.951591I
−8.06757 − 5.26507I 0
u = −0.152162 + 0.459797I
a = −3.15294 + 1.05533I
b = 0.535113 − 0.935355I
0.28773 − 2.82692I 5.81058 − 1.66051I
u = −0.152162 − 0.459797I
a = −3.15294 − 1.05533I
b = 0.535113 + 0.935355I
0.28773 + 2.82692I 5.81058 + 1.66051I
u = 0.04801 + 1.62342I
a = 0.686356 − 0.660507I
b = −0.622151 − 0.909091I
−6.42773 + 5.85172I 0
u = 0.04801 − 1.62342I
a = 0.686356 + 0.660507I
b = −0.622151 + 0.909091I
−6.42773 − 5.85172I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11130 + 1.62165I
a = 0.478526 + 0.438391I
b = −0.614683 + 0.843469I
−6.20432 + 1.00932I 0
u = 0.11130 − 1.62165I
a = 0.478526 − 0.438391I
b = −0.614683 − 0.843469I
−6.20432 − 1.00932I 0
u = 0.012155 + 0.262876I
a = −2.05266 − 4.00172I
b = 0.483697 + 0.622554I
1.18616 + 1.37603I 10.47248 − 4.16898I
u = 0.012155 − 0.262876I
a = −2.05266 + 4.00172I
b = 0.483697 − 0.622554I
1.18616 − 1.37603I 10.47248 + 4.16898I
12
II.
I
u
2
= h−u
12
−4u
10
+· · ·−2u
2
+b, u
10
+3u
8
+· · ·+a+1, u
27
+9u
25
+· · ·+u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−u
10
− 3u
8
+ 2u
7
− 4u
6
+ 4u
5
− 5u
4
+ 4u
3
− 3u
2
+ 2u − 1
u
12
+ 4u
10
− 2u
9
+ 6u
8
− 6u
7
+ 6u
6
− 6u
5
+ 5u
4
− 2u
3
+ 2u
2
a
7
=
1
−u
2
a
5
=
−u
22
− 7u
20
+ ··· − 2u
2
+ 1
u
24
+ 8u
22
+ ··· − 8u
5
+ 4u
4
a
3
=
u
21
+ 8u
19
+ ··· + 6u
3
− u
−u
21
− 7u
19
+ ··· − u
3
+ u
a
1
=
−u
u
3
+ u
a
4
=
u
24
+ 7u
22
+ ··· − 2u
2
+ 1
u
24
+ 8u
22
+ ··· − 8u
5
+ 4u
4
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
4
− u
2
− 1
u
6
+ 2u
4
+ u
2
a
12
=
u
3
−u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
24
+ 32u
22
− 20u
21
+ 112u
20
− 140u
19
+ 268u
18
− 420u
17
+
544u
16
− 744u
15
+ 884u
14
− 920u
13
+ 1000u
12
− 860u
11
+ 724u
10
− 556u
9
+ 316u
8
−
168u
7
+ 60u
6
+ 28u
5
− 24u
4
+ 24u
3
− 16u
2
+ 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
c
2
, c
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
c
3
, c
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
6
, c
7
, c
8
c
10
, c
12
u
27
+ 9u
25
+ ··· + u − 1
c
11
u
27
− 18u
26
+ ··· + 5u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
3
c
2
, c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
3
c
3
, c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
c
6
, c
7
, c
8
c
10
, c
12
y
27
+ 18y
26
+ ··· + 5y −1
c
11
y
27
− 18y
26
+ ··· + 25y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269474 + 1.004760I
a = −0.82716 + 1.96998I
b = 0.628449 − 0.875112I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = 0.269474 − 1.004760I
a = −0.82716 − 1.96998I
b = 0.628449 + 0.875112I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.861055 + 0.381086I
a = 1.96932 + 0.07622I
b = −0.728966 − 0.986295I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 0.861055 − 0.381086I
a = 1.96932 − 0.07622I
b = −0.728966 + 0.986295I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −0.457598 + 0.805344I
a = 0.921794 + 0.293449I
b = 0.140343 + 0.966856I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.457598 − 0.805344I
a = 0.921794 − 0.293449I
b = 0.140343 − 0.966856I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = 0.846765 + 0.300344I
a = 1.11197 − 0.96313I
b = −0.796005 + 0.733148I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 0.846765 − 0.300344I
a = 1.11197 + 0.96313I
b = −0.796005 − 0.733148I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −0.265891 + 1.100950I
a = 0.098685 − 0.826899I
b = 0.512358
1.19845 8.65235 + 0.I
u = −0.265891 − 1.100950I
a = 0.098685 + 0.826899I
b = 0.512358
1.19845 8.65235 + 0.I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.186213 + 1.135090I
a = −3.15403 + 1.36709I
b = 0.628449 + 0.875112I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = 0.186213 − 1.135090I
a = −3.15403 − 1.36709I
b = 0.628449 − 0.875112I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.632288 + 1.029230I
a = 0.789222 + 0.418020I
b = −0.728966 − 0.986295I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = −0.632288 − 1.029230I
a = 0.789222 − 0.418020I
b = −0.728966 + 0.986295I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −0.579410 + 1.072300I
a = 1.46542 + 0.12702I
b = −0.796005 + 0.733148I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −0.579410 − 1.072300I
a = 1.46542 − 0.12702I
b = −0.796005 − 0.733148I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 0.543809 + 0.474736I
a = −0.277099 + 0.364720I
b = 0.140343 + 0.966856I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.543809 − 0.474736I
a = −0.277099 − 0.364720I
b = 0.140343 − 0.966856I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.086211 + 1.280080I
a = −0.09642 − 2.48041I
b = 0.140343 − 0.966856I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.086211 − 1.280080I
a = −0.09642 + 2.48041I
b = 0.140343 + 0.966856I
−1.78344 + 2.09337I −0.51499 − 4.16283I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267354 + 1.372650I
a = −0.193595 + 0.403575I
b = −0.796005 − 0.733148I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −0.267354 − 1.372650I
a = −0.193595 − 0.403575I
b = −0.796005 + 0.733148I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = −0.22877 + 1.41032I
a = 1.32551 + 1.36940I
b = −0.728966 + 0.986295I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −0.22877 − 1.41032I
a = 1.32551 − 1.36940I
b = −0.728966 − 0.986295I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = 0.531781
a = −0.500428
b = 0.512358
1.19845 8.65230
u = −0.455687 + 0.130328I
a = −2.88341 + 1.31485I
b = 0.628449 − 0.875112I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.455687 − 0.130328I
a = −2.88341 − 1.31485I
b = 0.628449 + 0.875112I
0.61694 + 2.45442I 2.32792 − 2.91298I
18
III.
I
u
3
= hu
2
a + u
2
+ b + a + 1, 2u
3
a + 5u
3
+ · · · + 14a + 15, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−u
2
a − u
2
− a − 1
a
7
=
1
−u
2
a
5
=
u
2
a +
1
2
u
3
+ 2u
2
+ 2a +
3
2
u +
9
2
−u
2
a − u
2
− a − 2
a
3
=
1
2
u
3
+ u
2
+ a +
3
2
u +
5
2
−u
2
a − u
2
− a − 2
a
1
=
−1
0
a
4
=
1
2
u
3
+ u
2
+ a +
3
2
u +
5
2
−u
2
a − u
2
− a − 2
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
9
=
−u
u
3
+ u
a
12
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7
2
u
3
a + u
2
a +
3
2
u
3
−
11
2
au + 7u
2
+
7
2
a +
15
2
u +
27
2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
3
, c
9
u
8
c
6
, c
7
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
8
(u
4
+ u
3
+ u
2
+ 1)
2
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
12
(u
4
− u
3
+ u
2
+ 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
4
c
3
, c
9
y
8
c
6
, c
7
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −1.10603 − 1.01030I
b = 0.500000 + 0.866025I
0.211005 + 0.614778I 1.372162 + 0.328352I
u = −0.395123 + 0.506844I
a = −1.82193 + 0.59697I
b = 0.500000 − 0.866025I
0.21101 − 3.44499I 3.71851 + 10.46973I
u = −0.395123 − 0.506844I
a = −1.10603 + 1.01030I
b = 0.500000 − 0.866025I
0.211005 − 0.614778I 1.372162 − 0.328352I
u = −0.395123 − 0.506844I
a = −1.82193 − 0.59697I
b = 0.500000 + 0.866025I
0.21101 + 3.44499I 3.71851 − 10.46973I
u = −0.10488 + 1.55249I
a = −0.797662 − 0.666019I
b = 0.500000 − 0.866025I
−6.79074 − 5.19385I 0.529613 + 1.243149I
u = −0.10488 + 1.55249I
a = −0.524380 + 0.508239I
b = 0.500000 + 0.866025I
−6.79074 − 1.13408I −4.49529 + 1.20873I
u = −0.10488 − 1.55249I
a = −0.797662 + 0.666019I
b = 0.500000 + 0.866025I
−6.79074 + 5.19385I 0.529613 − 1.243149I
u = −0.10488 − 1.55249I
a = −0.524380 − 0.508239I
b = 0.500000 − 0.866025I
−6.79074 + 1.13408I −4.49529 − 1.20873I
22
IV. I
u
4
= h−a
2
− 2au + b + 2a + 2u − 1, 3a
3
u − 9a
2
u + · · · − 2a + 1, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
a
2
+ 2au − 2a − 2u + 1
a
7
=
1
1
a
5
=
a
3
+ 2a
2
u − 2a
2
− 2au + a + 1
a
3
u − 3a
2
u − 3a
2
+ au + 6a + u − 4
a
3
=
a
3
u − 4a
2
u − 2a
2
+ 5au + 6a − 3u − 4
−a
3
u + 3a
2
u + 4a
2
− 8a − 2u + 6
a
1
=
−u
−au + u + 2
a
4
=
a
3
u + a
3
− a
2
u − 5a
2
− au + 7a + u − 3
a
3
u − 3a
2
u − 3a
2
+ au + 6a + u − 4
a
10
=
−u
0
a
8
=
0
1
a
9
=
1
a + 2u − 1
a
12
=
−u
−au + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
u + 12a
2
u + 8a
2
− 12au − 16a + 4u + 16
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
(u
4
− u
3
+ u
2
+ 1)
2
c
3
, c
9
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
5
(u
4
+ u
3
+ u
2
+ 1)
2
c
6
, c
7
, c
8
c
10
, c
12
(u
2
+ 1)
4
c
11
(u + 1)
8
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
9
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
6
, c
7
, c
8
c
10
, c
12
(y + 1)
8
c
11
(y − 1)
8
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.674360 + 0.399232I
b = −0.851808 − 0.911292I
6.79074 + 3.16396I 7.82674 − 2.56480I
u = 1.000000I
a = 1.325640 + 0.399232I
b = −0.851808 + 0.911292I
6.79074 − 3.16396I 7.82674 + 2.56480I
u = 1.000000I
a = 0.59947 − 1.89923I
b = 0.351808 + 0.720342I
−0.21101 + 1.41510I 4.17326 − 4.90874I
u = 1.000000I
a = 1.40053 − 1.89923I
b = 0.351808 − 0.720342I
−0.21101 − 1.41510I 4.17326 + 4.90874I
u = − 1.000000I
a = 0.674360 − 0.399232I
b = −0.851808 + 0.911292I
6.79074 − 3.16396I 7.82674 + 2.56480I
u = − 1.000000I
a = 1.325640 − 0.399232I
b = −0.851808 − 0.911292I
6.79074 + 3.16396I 7.82674 − 2.56480I
u = − 1.000000I
a = 0.59947 + 1.89923I
b = 0.351808 − 0.720342I
−0.21101 − 1.41510I 4.17326 + 4.90874I
u = − 1.000000I
a = 1.40053 + 1.89923I
b = 0.351808 + 0.720342I
−0.21101 + 1.41510I 4.17326 − 4.90874I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
4
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
74
+ 24u
73
+ ··· − 225u + 16)
c
2
(u
2
+ u + 1)
4
(u
4
− u
3
+ u
2
+ 1)
2
· (u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
74
+ 4u
73
+ ··· + 35u + 4)
c
3
, c
9
u
8
(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)
· (u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
74
− 2u
73
+ ··· − 2560u + 2048)
c
5
(u
2
− u + 1)
4
(u
4
+ u
3
+ u
2
+ 1)
2
· (u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
74
+ 4u
73
+ ··· + 35u + 4)
c
6
, c
7
((u
2
+ 1)
4
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
27
+ 9u
25
+ ··· + u − 1)
· (u
74
+ 3u
73
+ ··· + 241u + 34)
c
8
((u
2
+ 1)
4
)(u
4
+ u
3
+ u
2
+ 1)
2
(u
27
+ 9u
25
+ ··· + u − 1)
· (u
74
+ 3u
73
+ ··· + 243u + 34)
c
10
((u
2
+ 1)
4
)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
(u
27
+ 9u
25
+ ··· + u − 1)
· (u
74
+ 3u
73
+ ··· + 241u + 34)
c
11
((u + 1)
8
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
(u
27
− 18u
26
+ ··· + 5u + 1)
· (u
74
− 31u
73
+ ··· − 29555u + 1156)
c
12
((u
2
+ 1)
4
)(u
4
− u
3
+ u
2
+ 1)
2
(u
27
+ 9u
25
+ ··· + u − 1)
· (u
74
+ 3u
73
+ ··· + 243u + 34)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)
4
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
74
+ 56y
73
+ ··· + 227743y + 256)
c
2
, c
5
(y
2
+ y + 1)
4
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
74
+ 24y
73
+ ··· − 225y + 16)
c
3
, c
9
y
8
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
74
− 40y
73
+ ··· − 36438016y + 4194304)
c
6
, c
7
, c
10
((y + 1)
8
)(y
4
+ 5y
3
+ ··· + 2y + 1)
2
(y
27
+ 18y
26
+ ··· + 5y − 1)
· (y
74
+ 75y
73
+ ··· + 36099y + 1156)
c
8
, c
12
((y + 1)
8
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
27
+ 18y
26
+ ··· + 5y − 1)
· (y
74
+ 31y
73
+ ··· + 29555y + 1156)
c
11
((y − 1)
8
)(y
4
+ 5y
3
+ ··· + 2y + 1)
2
(y
27
− 18y
26
+ ··· + 25y − 1)
· (y
74
+ 35y
73
+ ··· + 11195711y + 1336336)
28
