12n
0204
(K12n
0204
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 4 12 1 5 1 6
Solving Sequence
3,5
2
1,11
12 4 10 6 7 9 8
c
2
c
1
c
11
c
4
c
10
c
5
c
6
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−409562441u
28
− 633138331u
27
+ ··· + 1278981878b + 1495358594,
− 649542429u
28
− 1056906370u
27
+ ··· + 2557963756a − 48242973, u
29
+ 2u
28
+ ··· + 5u − 4i
I
u
2
= hu
14
a − u
14
+ ··· + b − 1, −2u
14
− u
13
+ ··· − a + 3,
u
15
+ u
14
− 4u
13
− 5u
12
+ 6u
11
+ 10u
10
− 7u
8
− 8u
7
− 4u
6
+ 6u
5
+ 8u
4
+ 2u
3
− 2u
2
− 2u − 1i
I
u
3
= hu
4
a + u
3
a − u
4
− u
3
− au + b − a + u, u
5
− 2u
3
+ a
2
− u
2
+ 2u + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
4
= h2b + 3, a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 72 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−4.10 × 10
8
u
28
− 6.33 × 10
8
u
27
+ · · · + 1.28 × 10
9
b + 1.50 × 10
9
, −6.50 ×
10
8
u
28
−1.06×10
9
u
27
+· · · +2.56×10
9
a−4.82×10
7
, u
29
+2u
28
+· · · +5u −4i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
11
=
0.253929u
28
+ 0.413183u
27
+ ··· + 3.78605u + 0.0188599
0.320225u
28
+ 0.495033u
27
+ ··· + 1.86204u − 1.16918
a
12
=
0.253151u
28
+ 0.268291u
27
+ ··· + 2.54838u + 0.206314
0.0347611u
28
+ 0.0691866u
27
+ ··· − 0.718788u − 0.0155112
a
4
=
u
−u
3
+ u
a
10
=
0.253929u
28
+ 0.413183u
27
+ ··· + 3.78605u + 0.0188599
0.265953u
28
+ 0.469651u
27
+ ··· + 0.372941u − 0.790474
a
6
=
−0.241553u
28
− 0.198421u
27
+ ··· − 2.06949u + 0.135383
0.0507414u
28
+ 0.0659434u
27
+ ··· + 1.51952u − 0.265184
a
7
=
−0.482352u
28
− 0.389873u
27
+ ··· − 4.05885u + 0.333349
0.0518322u
28
+ 0.0860020u
27
+ ··· + 1.78896u − 0.341645
a
9
=
0.246071u
28
+ 0.0868173u
27
+ ··· + 1.21395u + 0.481140
−0.0746592u
28
− 0.176612u
27
+ ··· − 2.68612u + 0.591964
a
8
=
0.487395u
28
+ 0.426835u
27
+ ··· + 3.80650u − 0.325257
−0.00202308u
28
− 0.00908992u
27
+ ··· − 1.92712u + 0.242240
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1071754917
2557963756
u
28
−
75682913
2557963756
u
27
+ ··· +
8446888807
2557963756
u −
9796598069
639490939
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 16u
28
+ ··· + 209u + 16
c
2
, c
4
u
29
− 2u
28
+ ··· + 5u + 4
c
3
, c
7
u
29
+ 3u
28
+ ··· + 18u + 8
c
5
, c
6
, c
10
c
12
u
29
+ u
28
+ ··· + 2u + 1
c
8
, c
11
u
29
− 5u
28
+ ··· − 6u + 1
c
9
u
29
+ 26u
28
+ ··· + 376832u + 32768
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 4y
28
+ ··· + 21313y −256
c
2
, c
4
y
29
− 16y
28
+ ··· + 209y −16
c
3
, c
7
y
29
+ 9y
28
+ ··· − 140y −64
c
5
, c
6
, c
10
c
12
y
29
+ 5y
28
+ ··· − 6y −1
c
8
, c
11
y
29
+ 45y
28
+ ··· + 6y −1
c
9
y
29
− 16y
28
+ ··· + 6174015488y −1073741824
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960613 + 0.170294I
a = −1.129440 − 0.468149I
b = −1.63701 − 0.14149I
−3.34627 + 0.60911I −7.67402 − 10.34191I
u = −0.960613 − 0.170294I
a = −1.129440 + 0.468149I
b = −1.63701 + 0.14149I
−3.34627 − 0.60911I −7.67402 + 10.34191I
u = 0.829481 + 0.498753I
a = 0.851038 + 0.266459I
b = 1.25630 − 0.93003I
−0.95125 − 3.42018I −9.12436 + 7.13905I
u = 0.829481 − 0.498753I
a = 0.851038 − 0.266459I
b = 1.25630 + 0.93003I
−0.95125 + 3.42018I −9.12436 − 7.13905I
u = −0.555934 + 0.787790I
a = −0.385011 + 0.878403I
b = −0.547815 − 0.259593I
3.91212 − 3.07296I −3.58580 + 5.16956I
u = −0.555934 − 0.787790I
a = −0.385011 − 0.878403I
b = −0.547815 + 0.259593I
3.91212 + 3.07296I −3.58580 − 5.16956I
u = −0.133622 + 0.942757I
a = −1.05744 + 1.03712I
b = −0.400359 − 0.621002I
−3.40148 − 10.10230I −5.65840 + 6.34779I
u = −0.133622 − 0.942757I
a = −1.05744 − 1.03712I
b = −0.400359 + 0.621002I
−3.40148 + 10.10230I −5.65840 − 6.34779I
u = −0.482129 + 0.757528I
a = 0.760914 − 0.157398I
b = 0.683226 + 0.243077I
3.66760 − 0.05333I −4.59541 − 3.69602I
u = −0.482129 − 0.757528I
a = 0.760914 + 0.157398I
b = 0.683226 − 0.243077I
3.66760 + 0.05333I −4.59541 + 3.69602I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.819144 + 0.362327I
a = 0.087730 − 0.590172I
b = −0.776429 + 0.138255I
−0.751059 − 0.353134I −9.39424 − 1.40493I
u = 0.819144 − 0.362327I
a = 0.087730 + 0.590172I
b = −0.776429 − 0.138255I
−0.751059 + 0.353134I −9.39424 + 1.40493I
u = 0.121290 + 0.842756I
a = −1.00456 − 1.22447I
b = −0.539181 + 0.622092I
−4.45862 + 3.60692I −7.22386 − 2.01130I
u = 0.121290 − 0.842756I
a = −1.00456 + 1.22447I
b = −0.539181 − 0.622092I
−4.45862 − 3.60692I −7.22386 + 2.01130I
u = −1.002290 + 0.666485I
a = 0.794138 − 0.363712I
b = 1.64106 + 0.14073I
2.60025 + 8.50017I −5.17138 − 9.83055I
u = −1.002290 − 0.666485I
a = 0.794138 + 0.363712I
b = 1.64106 − 0.14073I
2.60025 − 8.50017I −5.17138 + 9.83055I
u = −1.064380 + 0.598303I
a = −0.159509 + 0.533064I
b = −0.638339 − 0.004258I
1.93242 + 5.18468I −8.47176 − 2.14374I
u = −1.064380 − 0.598303I
a = −0.159509 − 0.533064I
b = −0.638339 + 0.004258I
1.93242 − 5.18468I −8.47176 + 2.14374I
u = 1.230540 + 0.053330I
a = −0.440769 + 0.411058I
b = −1.154760 + 0.333664I
−2.23909 + 1.32557I −7.93584 − 5.22491I
u = 1.230540 − 0.053330I
a = −0.440769 − 0.411058I
b = −1.154760 − 0.333664I
−2.23909 − 1.32557I −7.93584 + 5.22491I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.243450 + 0.397204I
a = −0.541600 − 0.973717I
b = −1.67988 − 0.94005I
−8.59540 + 0.64697I −11.02522 − 1.67463I
u = −1.243450 − 0.397204I
a = −0.541600 + 0.973717I
b = −1.67988 + 0.94005I
−8.59540 − 0.64697I −11.02522 + 1.67463I
u = 1.215230 + 0.518861I
a = 0.943218 + 0.506066I
b = 2.90492 + 0.42900I
−7.70776 − 8.57292I −9.65881 + 5.33629I
u = 1.215230 − 0.518861I
a = 0.943218 − 0.506066I
b = 2.90492 − 0.42900I
−7.70776 + 8.57292I −9.65881 − 5.33629I
u = −1.252950 + 0.545209I
a = 0.925713 − 0.557598I
b = 2.79765 − 0.77731I
−6.8135 + 15.4607I −8.47000 − 9.06787I
u = −1.252950 − 0.545209I
a = 0.925713 + 0.557598I
b = 2.79765 + 0.77731I
−6.8135 − 15.4607I −8.47000 + 9.06787I
u = 1.313260 + 0.385635I
a = −0.416958 + 0.934515I
b = −1.47424 + 1.05397I
−8.00289 + 5.49028I −9.85377 − 4.12172I
u = 1.313260 − 0.385635I
a = −0.416958 − 0.934515I
b = −1.47424 − 1.05397I
−8.00289 − 5.49028I −9.85377 + 4.12172I
u = 0.332840
a = 1.29507
b = −0.370297
−0.777392 −12.5640
7
II.
I
u
2
= hu
14
a−u
14
+· · ·+b−1, −2u
14
−u
13
+· · ·−a+3, u
15
+u
14
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
11
=
a
−u
14
a + u
14
+ ··· + u + 1
a
12
=
u
6
a − 2u
4
a + u
2
a − u
2
+ a + 1
−u
14
a + u
14
+ ··· + u + 1
a
4
=
u
−u
3
+ u
a
10
=
a
−u
14
a + u
14
+ ··· + u + 1
a
6
=
u
14
+ u
13
+ ··· − u − 2
−u
13
a − u
13
+ ··· − a − 1
a
7
=
−u
11
+ 4u
9
− 6u
7
+ 2u
5
+ 3u
3
− 2u
−u
11
+ 3u
9
− 4u
7
+ u
5
+ u
3
− u
a
9
=
−u
2
+ a + 1
−u
14
a + u
14
+ ··· + u + 1
a
8
=
u
14
− 5u
12
+ 10u
10
− 7u
8
− 4u
6
+ 8u
4
− 2u
2
− 1
u
14
− 4u
12
+ 7u
10
− 4u
8
− 2u
6
+ 4u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
13
+ 16u
11
+ 4u
10
− 28u
9
− 12u
8
+ 12u
7
+ 16u
6
+ 16u
5
− 24u
3
− 8u
2
− 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 9u
14
+ ··· − 4u
2
+ 1)
2
c
2
, c
4
(u
15
− u
14
+ ··· − 2u + 1)
2
c
3
, c
7
(u
15
− u
14
+ ··· + 2u − 1)
2
c
5
, c
6
, c
10
c
12
u
30
− 3u
29
+ ··· − 30u + 9
c
8
, c
11
u
30
− 11u
29
+ ··· − 1296u + 81
c
9
(u − 1)
30
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 5y
14
+ ··· + 8y −1)
2
c
2
, c
4
(y
15
− 9y
14
+ ··· + 4y
2
− 1)
2
c
3
, c
7
(y
15
+ 3y
14
+ ··· + 8y
2
− 1)
2
c
5
, c
6
, c
10
c
12
y
30
+ 11y
29
+ ··· + 1296y + 81
c
8
, c
11
y
30
+ 15y
29
+ ··· − 73224y + 6561
c
9
(y −1)
30
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.023100 + 0.900040I
a = 0.825316 + 1.129310I
b = 0.286301 − 0.445204I
−4.73497 − 3.25615I −7.67133 + 2.40088I
u = −0.023100 + 0.900040I
a = 0.98422 − 1.08773I
b = 0.164746 + 0.352495I
−4.73497 − 3.25615I −7.67133 + 2.40088I
u = −0.023100 − 0.900040I
a = 0.825316 − 1.129310I
b = 0.286301 + 0.445204I
−4.73497 + 3.25615I −7.67133 − 2.40088I
u = −0.023100 − 0.900040I
a = 0.98422 + 1.08773I
b = 0.164746 − 0.352495I
−4.73497 + 3.25615I −7.67133 − 2.40088I
u = 0.863978
a = 0.126771 + 1.178080I
b = 3.66551 − 2.58901I
2.03422 −12.4840
u = 0.863978
a = 0.126771 − 1.178080I
b = 3.66551 + 2.58901I
2.03422 −12.4840
u = 1.093890 + 0.311098I
a = −0.297631 − 0.955829I
b = −1.62293 − 0.54486I
−0.109911 − 1.108490I −11.51398 + 0.68443I
u = 1.093890 + 0.311098I
a = 0.197813 + 0.275213I
b = 0.45469 + 1.92439I
−0.109911 − 1.108490I −11.51398 + 0.68443I
u = 1.093890 − 0.311098I
a = −0.297631 + 0.955829I
b = −1.62293 + 0.54486I
−0.109911 + 1.108490I −11.51398 − 0.68443I
u = 1.093890 − 0.311098I
a = 0.197813 − 0.275213I
b = 0.45469 − 1.92439I
−0.109911 + 1.108490I −11.51398 − 0.68443I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747479 + 0.391613I
a = 1.023110 − 0.862412I
b = 1.63828 − 1.05509I
4.53214 + 1.75942I −1.14915 − 5.01461I
u = −0.747479 + 0.391613I
a = −0.42847 + 1.44786I
b = 0.248041 − 0.151767I
4.53214 + 1.75942I −1.14915 − 5.01461I
u = −0.747479 − 0.391613I
a = 1.023110 + 0.862412I
b = 1.63828 + 1.05509I
4.53214 − 1.75942I −1.14915 + 5.01461I
u = −0.747479 − 0.391613I
a = −0.42847 − 1.44786I
b = 0.248041 + 0.151767I
4.53214 − 1.75942I −1.14915 + 5.01461I
u = −1.070290 + 0.443484I
a = −0.592827 + 0.959612I
b = −1.162130 + 0.705596I
0.87635 + 5.68434I −8.20490 − 7.47679I
u = −1.070290 + 0.443484I
a = 0.643980 − 0.010296I
b = 1.27621 − 1.00477I
0.87635 + 5.68434I −8.20490 − 7.47679I
u = −1.070290 − 0.443484I
a = −0.592827 − 0.959612I
b = −1.162130 − 0.705596I
0.87635 − 5.68434I −8.20490 + 7.47679I
u = −1.070290 − 0.443484I
a = 0.643980 + 0.010296I
b = 1.27621 + 1.00477I
0.87635 − 5.68434I −8.20490 + 7.47679I
u = 1.268720 + 0.457284I
a = −0.923717 − 0.340768I
b = −2.59581 − 0.49906I
−8.68612 − 1.54935I −11.09602 + 0.66420I
u = 1.268720 + 0.457284I
a = 0.523167 − 0.819566I
b = 1.44899 − 1.21103I
−8.68612 − 1.54935I −11.09602 + 0.66420I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.268720 − 0.457284I
a = −0.923717 + 0.340768I
b = −2.59581 + 0.49906I
−8.68612 + 1.54935I −11.09602 − 0.66420I
u = 1.268720 − 0.457284I
a = 0.523167 + 0.819566I
b = 1.44899 + 1.21103I
−8.68612 + 1.54935I −11.09602 − 0.66420I
u = −1.260410 + 0.482704I
a = 0.621138 + 0.785123I
b = 1.74021 + 0.98052I
−8.49724 + 8.19235I −10.69502 − 5.35870I
u = −1.260410 + 0.482704I
a = −0.976755 + 0.431682I
b = −2.53986 + 0.80421I
−8.49724 + 8.19235I −10.69502 − 5.35870I
u = −1.260410 − 0.482704I
a = 0.621138 − 0.785123I
b = 1.74021 − 0.98052I
−8.49724 − 8.19235I −10.69502 + 5.35870I
u = −1.260410 − 0.482704I
a = −0.976755 − 0.431682I
b = −2.53986 − 0.80421I
−8.49724 − 8.19235I −10.69502 + 5.35870I
u = −0.193328 + 0.557909I
a = −0.687123 + 0.933709I
b = 0.869302 − 0.104344I
3.26563 − 1.73642I −4.42769 + 4.08118I
u = −0.193328 + 0.557909I
a = 1.96101 − 0.71799I
b = 0.628452 − 0.272272I
3.26563 − 1.73642I −4.42769 + 4.08118I
u = −0.193328 − 0.557909I
a = −0.687123 − 0.933709I
b = 0.869302 + 0.104344I
3.26563 + 1.73642I −4.42769 − 4.08118I
u = −0.193328 − 0.557909I
a = 1.96101 + 0.71799I
b = 0.628452 + 0.272272I
3.26563 + 1.73642I −4.42769 − 4.08118I
13
III. I
u
3
= hu
4
a + u
3
a − u
4
− u
3
− au + b − a + u, u
5
− 2u
3
+ a
2
− u
2
+ 2u +
1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
11
=
a
−u
4
a − u
3
a + u
4
+ u
3
+ au + a − u
a
12
=
−u
2
+ a + 1
−u
4
a − u
3
a + u
4
+ u
3
+ au − u
2
+ a − u
a
4
=
u
−u
3
+ u
a
10
=
a
−u
4
a − u
3
a + u
4
− u
2
a + u
3
+ au + a − u
a
6
=
−u
5
− u
4
+ u
3
+ 2u
2
− 1
−u
5
a − u
4
a − u
5
− u
4
+ u
2
a + u
2
a
7
=
−u
3
a + au
−u
3
a
a
9
=
u
5
a + u
4
a − 2u
3
a − u
2
a + au − u
2
+ 2a + 1
u
5
a − u
4
a − 3u
3
a + u
4
− u
2
a + u
3
+ 2au − u
2
+ 2a − u
a
8
=
u
5
a + u
4
a − 2u
3
a − u
2
a + au + a
u
5
a − 2u
3
a − u
2
a + au + a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 4u
2
− 4u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
7
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
, c
6
, c
10
c
12
(u
2
+ 1)
6
c
8
, c
11
(u + 1)
12
c
9
u
12
+ 12u
11
+ ··· + 60u + 9
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
7
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
5
, c
6
, c
10
c
12
(y + 1)
12
c
8
, c
11
(y −1)
12
c
9
y
12
− 14y
11
+ ··· − 108y + 81
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.270708 − 0.917982I
b = −1.49594 + 1.39869I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = 1.002190 + 0.295542I
a = 0.270708 + 0.917982I
b = 1.95964 + 1.91259I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = 1.002190 − 0.295542I
a = −0.270708 + 0.917982I
b = −1.49594 − 1.39869I
1.39926 + 0.92430I −5.71672 − 0.79423I
u = 1.002190 − 0.295542I
a = 0.270708 − 0.917982I
b = 1.95964 − 1.91259I
1.39926 + 0.92430I −5.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = 1.063260 − 0.685196I
b = 1.226020 − 0.214242I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.063260 + 0.685196I
b = 0.093522 − 0.382665I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = 1.063260 + 0.685196I
b = 1.226020 + 0.214242I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = −0.428243 − 0.664531I
a = −1.063260 − 0.685196I
b = 0.093522 + 0.382665I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = −1.073950 + 0.558752I
a = 0.381252 − 0.732786I
b = 1.04838 − 1.16005I
3.28987 + 5.69302I −2.00000 − 5.51057I
u = −1.073950 + 0.558752I
a = −0.381252 + 0.732786I
b = −0.831626 − 0.477727I
3.28987 + 5.69302I −2.00000 − 5.51057I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.381252 + 0.732786I
b = 1.04838 + 1.16005I
3.28987 − 5.69302I −2.00000 + 5.51057I
u = −1.073950 − 0.558752I
a = −0.381252 − 0.732786I
b = −0.831626 + 0.477727I
3.28987 − 5.69302I −2.00000 + 5.51057I
18
IV. I
u
4
= h2b + 3, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
11
=
−1
−1.5
a
12
=
−1
−0.5
a
4
=
1
0
a
10
=
−1
−0.5
a
6
=
−1
0.5
a
7
=
−2
0
a
9
=
−1
0.5
a
8
=
−2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9.75
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
, c
9
c
11
u − 1
c
3
, c
7
u
c
4
, c
10
, c
12
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y −1
c
3
, c
7
y
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.50000
−3.28987 −9.75000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· ((u
15
+ 9u
14
+ ··· − 4u
2
+ 1)
2
)(u
29
+ 16u
28
+ ··· + 209u + 16)
c
2
(u − 1)(u
6
+ u
5
+ ··· + u + 1)
2
(u
15
− u
14
+ ··· − 2u + 1)
2
· (u
29
− 2u
28
+ ··· + 5u + 4)
c
3
, c
7
u(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
15
− u
14
+ ··· + 2u − 1)
2
· (u
29
+ 3u
28
+ ··· + 18u + 8)
c
4
(u + 1)(u
6
− u
5
+ ··· − u + 1)
2
(u
15
− u
14
+ ··· − 2u + 1)
2
· (u
29
− 2u
28
+ ··· + 5u + 4)
c
5
, c
6
(u − 1)(u
2
+ 1)
6
(u
29
+ u
28
+ ··· + 2u + 1)(u
30
− 3u
29
+ ··· − 30u + 9)
c
8
, c
11
(u − 1)(u + 1)
12
(u
29
− 5u
28
+ ··· − 6u + 1)
· (u
30
− 11u
29
+ ··· − 1296u + 81)
c
9
((u − 1)
31
)(u
12
+ 12u
11
+ ··· + 60u + 9)
· (u
29
+ 26u
28
+ ··· + 376832u + 32768)
c
10
, c
12
(u + 1)(u
2
+ 1)
6
(u
29
+ u
28
+ ··· + 2u + 1)(u
30
− 3u
29
+ ··· − 30u + 9)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
6
+ y
5
+ ··· + 3y + 1)
2
(y
15
− 5y
14
+ ··· + 8y −1)
2
· (y
29
− 4y
28
+ ··· + 21313y −256)
c
2
, c
4
(y −1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
15
− 9y
14
+ ··· + 4y
2
− 1)
2
)(y
29
− 16y
28
+ ··· + 209y −16)
c
3
, c
7
y(y
6
+ 3y
5
+ ··· + y + 1)
2
(y
15
+ 3y
14
+ ··· + 8y
2
− 1)
2
· (y
29
+ 9y
28
+ ··· − 140y −64)
c
5
, c
6
, c
10
c
12
(y −1)(y + 1)
12
(y
29
+ 5y
28
+ ··· − 6y −1)
· (y
30
+ 11y
29
+ ··· + 1296y + 81)
c
8
, c
11
((y −1)
13
)(y
29
+ 45y
28
+ ··· + 6y −1)
· (y
30
+ 15y
29
+ ··· − 73224y + 6561)
c
9
((y −1)
31
)(y
12
− 14y
11
+ ··· − 108y + 81)
· (y
29
− 16y
28
+ ··· + 6174015488y −1073741824)
24
