12n
0212
(K12n
0212
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 11 3 6 12 5 8 10
Solving Sequence
6,11 3,7
8 9 12 5 2 1 4 10
c
6
c
7
c
8
c
11
c
5
c
2
c
1
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.43322 × 10
268
u
64
+ 4.87957 × 10
268
u
63
+ ··· + 4.09619 × 10
272
b + 8.91816 × 10
272
,
2.78500 × 10
270
u
64
− 6.50544 × 10
270
u
63
+ ··· + 7.37313 × 10
273
a − 4.93581 × 10
274
,
u
65
− 2u
64
+ ··· − 19008u + 5184i
I
u
2
= hu
6
− u
4
+ u
2
+ b − u, u
7
+ u
6
− u
5
− 3u
4
+ u
3
+ 3u
2
+ a − 3, u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
v
1
= ha, −18315v
5
+ 20514v
4
− 76517v
3
+ 68962v
2
+ 11867b + 4895v + 9310,
9v
6
− 3v
5
+ 38v
4
− 6v
3
+ 7v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 79 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−1.43 × 10
268
u
64
+ 4.88 × 10
268
u
63
+ · · · + 4.10 × 10
272
b + 8.92 ×
10
272
, 2.79 × 10
270
u
64
− 6.51 × 10
270
u
63
+ · · · + 7.37 × 10
273
a − 4.94 ×
10
274
, u
65
− 2u
64
+ · · · − 19008u + 5184i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.000377723u
64
+ 0.000882317u
63
+ ··· − 24.2190u + 6.69432
0.0000349893u
64
− 0.000119125u
63
+ ··· + 6.31596u − 2.17719
a
7
=
1
−u
2
a
8
=
−0.000281496u
64
+ 0.000444213u
63
+ ··· − 2.66344u − 1.87984
0.0000716784u
64
− 0.0000602668u
63
+ ··· − 2.06803u + 1.30681
a
9
=
−0.000209817u
64
+ 0.000383947u
63
+ ··· − 4.73147u − 0.573035
0.0000716784u
64
− 0.0000602668u
63
+ ··· − 2.06803u + 1.30681
a
12
=
0.000110706u
64
− 0.000268775u
63
+ ··· + 6.05995u − 1.93909
0.000214065u
64
− 0.000335465u
63
+ ··· + 2.94068u + 0.325061
a
5
=
0.0000382070u
64
+ 0.0000348721u
63
+ ··· − 4.30269u + 2.47351
0.000100912u
64
− 0.000304602u
63
+ ··· + 8.12093u − 1.65906
a
2
=
−0.000284710u
64
+ 0.000546492u
63
+ ··· − 12.1877u + 2.72060
0.000172387u
64
− 0.000396564u
63
+ ··· + 8.99806u − 2.35482
a
1
=
0.000100309u
64
− 0.000149136u
63
+ ··· + 0.894466u − 0.119551
−0.000143803u
64
+ 0.000150522u
63
+ ··· + 1.65869u − 1.49182
a
4
=
−0.000313975u
64
+ 0.000618260u
63
+ ··· − 13.5334u + 3.85944
0.0000715938u
64
− 0.000222008u
63
+ ··· + 9.24221u − 2.88513
a
10
=
0.000148358u
64
− 0.000310823u
63
+ ··· + 4.46935u − 2.06733
0.000108769u
64
− 0.000131377u
63
+ ··· + 0.525836u + 0.505205
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00132072u
64
+ 0.00246498u
63
+ ··· − 45.0317u + 16.1770
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 68u
64
+ ··· + 59u + 1
c
2
, c
4
u
65
− 10u
64
+ ··· − 11u + 1
c
3
, c
7
u
65
− 2u
64
+ ··· + 640u − 256
c
5
, c
8
u
65
+ 3u
64
+ ··· + 3u + 1
c
6
u
65
+ 2u
64
+ ··· − 19008u − 5184
c
9
, c
12
u
65
+ 8u
64
+ ··· + 1080u + 81
c
10
9(9u
65
+ 18u
64
+ ··· − 294572u − 29917)
c
11
9(9u
65
+ 42u
64
+ ··· + 608293u + 315227)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 132y
64
+ ··· + 7503y −1
c
2
, c
4
y
65
− 68y
64
+ ··· + 59y −1
c
3
, c
7
y
65
+ 48y
64
+ ··· + 901120y −65536
c
5
, c
8
y
65
+ 37y
64
+ ··· + 11y −1
c
6
y
65
+ 36y
64
+ ··· − 462827520y −26873856
c
9
, c
12
y
65
− 30y
64
+ ··· + 422172y −6561
c
10
81(81y
65
+ 5796y
64
+ ··· + 1.08032 × 10
10
y −8.95027 × 10
8
)
c
11
81(81y
65
− 558y
64
+ ··· − 1.06335 × 10
12
y −9.93681 × 10
10
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.987989 + 0.000953I
a = −2.12082 + 1.54640I
b = 1.33246 − 1.66976I
−2.66486 − 2.32248I 5.14580 + 2.29349I
u = −0.987989 − 0.000953I
a = −2.12082 − 1.54640I
b = 1.33246 + 1.66976I
−2.66486 + 2.32248I 5.14580 − 2.29349I
u = −0.748540 + 0.696645I
a = 0.226780 + 1.145830I
b = −0.874173 − 0.089609I
1.04936 + 1.32007I 10.95788 − 0.41796I
u = −0.748540 − 0.696645I
a = 0.226780 − 1.145830I
b = −0.874173 + 0.089609I
1.04936 − 1.32007I 10.95788 + 0.41796I
u = 0.055143 + 1.022190I
a = 0.05532 − 1.41633I
b = −0.271016 − 0.120884I
−2.21134 + 0.65096I 2.94304 − 0.27515I
u = 0.055143 − 1.022190I
a = 0.05532 + 1.41633I
b = −0.271016 + 0.120884I
−2.21134 − 0.65096I 2.94304 + 0.27515I
u = 0.963379
a = −0.0469319
b = 0.578355
5.22479 24.0830
u = −0.286459 + 1.010510I
a = 0.78431 + 1.39006I
b = −0.316087 + 1.221670I
1.45815 + 1.19485I 9.19775 − 4.74594I
u = −0.286459 − 1.010510I
a = 0.78431 − 1.39006I
b = −0.316087 − 1.221670I
1.45815 − 1.19485I 9.19775 + 4.74594I
u = 0.726229 + 0.814196I
a = −0.121481 − 0.226198I
b = −0.807017 + 0.074160I
−2.55567 + 2.51492I 6.00000 − 3.00902I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726229 − 0.814196I
a = −0.121481 + 0.226198I
b = −0.807017 − 0.074160I
−2.55567 − 2.51492I 6.00000 + 3.00902I
u = −0.891332 + 0.686560I
a = 0.0513899 − 0.0389433I
b = −0.565696 + 0.133789I
1.17561 − 6.59366I 15.1731 + 8.7497I
u = −0.891332 − 0.686560I
a = 0.0513899 + 0.0389433I
b = −0.565696 − 0.133789I
1.17561 + 6.59366I 15.1731 − 8.7497I
u = 0.218273 + 1.185850I
a = −0.011907 − 0.174978I
b = −1.58075 + 0.11150I
−3.79735 + 2.57206I 0
u = 0.218273 − 1.185850I
a = −0.011907 + 0.174978I
b = −1.58075 − 0.11150I
−3.79735 − 2.57206I 0
u = −0.627540 + 0.484254I
a = 1.321520 + 0.352976I
b = −0.573718 + 0.068027I
1.19155 + 0.95389I 10.21513 − 0.37317I
u = −0.627540 − 0.484254I
a = 1.321520 − 0.352976I
b = −0.573718 − 0.068027I
1.19155 − 0.95389I 10.21513 + 0.37317I
u = −0.485202 + 1.151820I
a = 0.294894 + 1.249500I
b = −0.567218 + 0.263601I
−0.92912 − 5.51849I 0
u = −0.485202 − 1.151820I
a = 0.294894 − 1.249500I
b = −0.567218 − 0.263601I
−0.92912 + 5.51849I 0
u = −0.001950 + 1.261610I
a = −0.529291 + 1.160890I
b = −1.249780 + 0.587678I
−5.91253 + 0.89151I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.001950 − 1.261610I
a = −0.529291 − 1.160890I
b = −1.249780 − 0.587678I
−5.91253 − 0.89151I 0
u = −0.181767 + 1.284800I
a = 0.394438 + 1.295480I
b = 0.520041 + 0.490473I
−13.75280 + 0.18156I 0
u = −0.181767 − 1.284800I
a = 0.394438 − 1.295480I
b = 0.520041 − 0.490473I
−13.75280 − 0.18156I 0
u = 0.666243 + 0.215627I
a = 0.63298 + 3.14043I
b = 0.528259 + 0.129647I
−9.22847 − 0.59840I 0.51834 − 6.09970I
u = 0.666243 − 0.215627I
a = 0.63298 − 3.14043I
b = 0.528259 − 0.129647I
−9.22847 + 0.59840I 0.51834 + 6.09970I
u = 0.667926 + 0.125084I
a = 3.07822 − 0.34270I
b = −1.44314 + 0.42007I
−1.45078 − 0.59119I 2.85675 − 3.51070I
u = 0.667926 − 0.125084I
a = 3.07822 + 0.34270I
b = −1.44314 − 0.42007I
−1.45078 + 0.59119I 2.85675 + 3.51070I
u = 0.375714 + 1.275330I
a = −0.01142 − 1.46097I
b = −1.39649 − 0.60732I
−5.14289 + 4.65238I 0
u = 0.375714 − 1.275330I
a = −0.01142 + 1.46097I
b = −1.39649 + 0.60732I
−5.14289 − 4.65238I 0
u = 1.370430 + 0.169263I
a = −0.311596 + 0.742406I
b = 1.14616 − 2.08345I
−0.61197 − 3.88642I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.370430 − 0.169263I
a = −0.311596 − 0.742406I
b = 1.14616 + 2.08345I
−0.61197 + 3.88642I 0
u = 0.224303 + 0.571448I
a = 1.08323 − 6.98590I
b = −1.15343 − 1.78571I
−0.766193 − 0.710691I −8.2875 − 12.4812I
u = 0.224303 − 0.571448I
a = 1.08323 + 6.98590I
b = −1.15343 + 1.78571I
−0.766193 + 0.710691I −8.2875 + 12.4812I
u = −0.271460 + 0.550386I
a = 0.171011 − 0.156416I
b = −1.073610 + 0.399773I
1.52187 − 6.09633I 2.3393 + 14.1949I
u = −0.271460 − 0.550386I
a = 0.171011 + 0.156416I
b = −1.073610 − 0.399773I
1.52187 + 6.09633I 2.3393 − 14.1949I
u = 0.553293 + 1.271240I
a = 0.553265 − 0.871213I
b = 0.249245 − 0.493678I
−12.27680 + 5.48243I 0
u = 0.553293 − 1.271240I
a = 0.553265 + 0.871213I
b = 0.249245 + 0.493678I
−12.27680 − 5.48243I 0
u = 0.060757 + 0.566257I
a = −0.169552 + 0.223408I
b = 1.169990 − 0.272700I
3.05269 − 0.72062I −0.37252 − 2.34749I
u = 0.060757 − 0.566257I
a = −0.169552 − 0.223408I
b = 1.169990 + 0.272700I
3.05269 + 0.72062I −0.37252 + 2.34749I
u = −0.541890
a = 0.432973
b = 0.203067
0.709590 14.3470
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22284 + 1.47296I
a = 0.233664 + 0.102031I
b = 1.89702 + 0.23201I
−8.45370 + 1.77642I 0
u = 0.22284 − 1.47296I
a = 0.233664 − 0.102031I
b = 1.89702 − 0.23201I
−8.45370 − 1.77642I 0
u = −0.53597 + 1.39821I
a = −0.146182 − 0.038643I
b = 1.399900 − 0.050013I
−7.04530 − 8.03742I 0
u = −0.53597 − 1.39821I
a = −0.146182 + 0.038643I
b = 1.399900 + 0.050013I
−7.04530 + 8.03742I 0
u = 0.497138
a = 6.35919
b = −1.12723
−0.408756 31.3810
u = 0.72094 + 1.40121I
a = −0.313940 + 1.369360I
b = 1.89330 + 1.11991I
−4.34514 + 11.16830I 0
u = 0.72094 − 1.40121I
a = −0.313940 − 1.369360I
b = 1.89330 − 1.11991I
−4.34514 − 11.16830I 0
u = 0.097484 + 0.387248I
a = 0.01203 − 2.23100I
b = −0.493159 + 0.407995I
−1.70444 + 0.86317I −1.80335 − 2.14625I
u = 0.097484 − 0.387248I
a = 0.01203 + 2.23100I
b = −0.493159 − 0.407995I
−1.70444 − 0.86317I −1.80335 + 2.14625I
u = −0.88341 + 1.34912I
a = −0.447992 − 1.029800I
b = 1.177480 − 0.641815I
−7.46828 − 10.68780I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.88341 − 1.34912I
a = −0.447992 + 1.029800I
b = 1.177480 + 0.641815I
−7.46828 + 10.68780I 0
u = −0.51591 + 1.53296I
a = 0.030967 − 1.340990I
b = 2.10343 − 1.45671I
−6.56044 − 4.64446I 0
u = −0.51591 − 1.53296I
a = 0.030967 + 1.340990I
b = 2.10343 + 1.45671I
−6.56044 + 4.64446I 0
u = 0.82368 + 1.39986I
a = −0.450753 + 0.978865I
b = 1.237730 + 0.645893I
−10.53090 + 4.21781I 0
u = 0.82368 − 1.39986I
a = −0.450753 − 0.978865I
b = 1.237730 − 0.645893I
−10.53090 − 4.21781I 0
u = −1.52984 + 0.86914I
a = −0.354905 − 0.297066I
b = 1.52741 + 0.94608I
−5.31966 + 2.30754I 0
u = −1.52984 − 0.86914I
a = −0.354905 + 0.297066I
b = 1.52741 − 0.94608I
−5.31966 − 2.30754I 0
u = 0.99000 + 1.57649I
a = 0.478911 − 1.130600I
b = −2.01241 − 1.65324I
−11.1904 + 16.3453I 0
u = 0.99000 − 1.57649I
a = 0.478911 + 1.130600I
b = −2.01241 + 1.65324I
−11.1904 − 16.3453I 0
u = −0.65125 + 2.02422I
a = −0.213696 − 0.852249I
b = 1.51737 − 2.34323I
−4.34300 + 1.86014I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.65125 − 2.02422I
a = −0.213696 + 0.852249I
b = 1.51737 + 2.34323I
−4.34300 − 1.86014I 0
u = −0.90018 + 2.02783I
a = 0.247259 + 0.974849I
b = −2.21700 + 2.52211I
−14.1808 − 8.5511I 0
u = −0.90018 − 2.02783I
a = 0.247259 − 0.974849I
b = −2.21700 − 2.52211I
−14.1808 + 8.5511I 0
u = 2.26622 + 0.12631I
a = −0.013705 − 0.386355I
b = −0.43221 + 3.40125I
−7.12119 − 6.12750I 0
u = 2.26622 − 0.12631I
a = −0.013705 + 0.386355I
b = −0.43221 − 3.40125I
−7.12119 + 6.12750I 0
11
II. I
u
2
= hu
6
− u
4
+ u
2
+ b − u, u
7
+ u
6
− u
5
− 3u
4
+ u
3
+ 3u
2
+ a − 3, u
8
+
u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
7
− u
6
+ u
5
+ 3u
4
− u
3
− 3u
2
+ 3
−u
6
+ u
4
− u
2
+ u
a
7
=
1
−u
2
a
8
=
1
−u
2
a
9
=
−u
2
+ 1
−u
2
a
12
=
u
−u
3
+ u
a
5
=
u
4
− u
2
+ 1
u
4
a
2
=
−u
7
− u
6
+ u
5
+ 2u
4
− u
3
− 2u
2
+ 2
−u
6
− u
2
+ u
a
1
=
−u
4
+ u
2
− 1
−u
4
a
4
=
−u
7
− u
6
+ u
5
+ 3u
4
− u
3
− 3u
2
+ 3
−u
6
+ u
4
− u
2
+ u
a
10
=
−u
6
+ u
4
− 2u
2
+ 1
−u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
− 2u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
+ 4u
6
− 2u
5
− 5u
4
+ 3u
3
+ 5u
2
− 5u − 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
9
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
, c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = 1.21928 + 2.03110I
b = −1.44082 + 1.43962I
−0.604279 + 1.131230I 6.13774 − 5.30650I
u = −0.570868 − 0.730671I
a = 1.21928 − 2.03110I
b = −1.44082 − 1.43962I
−0.604279 − 1.131230I 6.13774 + 5.30650I
u = 0.855237 + 0.665892I
a = −1.230330 + 0.083902I
b = 0.44992 + 1.37717I
−3.80435 + 2.57849I −1.88107 − 3.45077I
u = 0.855237 − 0.665892I
a = −1.230330 − 0.083902I
b = 0.44992 − 1.37717I
−3.80435 − 2.57849I −1.88107 + 3.45077I
u = 1.09818
a = 0.337834
b = −0.407427
4.85780 0.988100
u = −1.031810 + 0.655470I
a = −0.370895 + 0.073482I
b = 0.136119 − 0.548347I
0.73474 − 6.44354I −1.17016 + 2.68172I
u = −1.031810 − 0.655470I
a = −0.370895 − 0.073482I
b = 0.136119 + 0.548347I
0.73474 + 6.44354I −1.17016 − 2.68172I
u = −0.603304
a = 2.42604
b = −0.883019
−0.799899 1.83890
15
III. I
v
1
= ha, −18315v
5
+ 20514v
4
+ · · · + 11867b + 9310, 9v
6
− 3v
5
+ 38v
4
−
6v
3
+ 7v
2
− 3v + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
3
=
0
1.54336v
5
− 1.72866v
4
+ ··· − 0.412488v − 0.784529
a
7
=
1
0
a
8
=
1
−3.02073v
5
+ 0.380467v
4
+ ··· − 3.21968v − 0.339176
a
9
=
−3.02073v
5
+ 0.380467v
4
+ ··· − 3.21968v + 0.660824
−3.02073v
5
+ 0.380467v
4
+ ··· − 3.21968v − 0.339176
a
12
=
0.626443v
5
+ 0.0634533v
4
+ ··· + 2.34609v − 0.335637
−0.861549v
5
− 0.0654757v
4
+ ··· − 0.715682v + 0.732788
a
5
=
3.57437v
5
− 0.956350v
4
+ ··· + 2.47712v − 0.821859
6.59510v
5
− 1.33682v
4
+ ··· + 5.69681v − 1.48268
a
2
=
3.02073v
5
− 0.380467v
4
+ ··· + 3.21968v − 0.660824
6.59510v
5
− 1.33682v
4
+ ··· + 5.69681v − 1.48268
a
1
=
3.02073v
5
− 0.380467v
4
+ ··· + 3.21968v − 0.660824
3.02073v
5
− 0.380467v
4
+ ··· + 3.21968v + 0.339176
a
4
=
1.54336v
5
− 1.72866v
4
+ ··· − 0.412488v − 0.784529
1.54336v
5
− 1.72866v
4
+ ··· − 0.412488v − 0.784529
a
10
=
−2.39429v
5
+ 0.443920v
4
+ ··· − 0.873599v + 0.325187
−3.88228v
5
+ 0.314991v
4
+ ··· − 3.93537v + 0.393613
(ii) Obstruction class = 1
(iii) Cusp Shapes =
224001
11867
v
5
−
36660
11867
v
4
+
906833
11867
v
3
+
26609
11867
v
2
+
40841
11867
v +
96708
11867
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
u
6
c
9
(u + 1)
6
c
10
9(9u
6
+ 12u
5
+ 2u
4
− u
3
+ 4u
2
+ 4u + 1)
c
11
9(9u
6
− 30u
5
+ 41u
4
− 30u
3
+ 15u
2
− 5u + 1)
c
12
(u − 1)
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
y
6
c
9
, c
12
(y − 1)
6
c
10
81(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
c
11
81(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.178337 + 0.463585I
a = 0
b = 1.002190 + 0.295542I
3.53554 + 0.92430I 14.9081 − 3.3454I
v = −0.178337 − 0.463585I
a = 0
b = 1.002190 − 0.295542I
3.53554 − 0.92430I 14.9081 + 3.3454I
v = 0.246749 + 0.226622I
a = 0
b = −1.073950 − 0.558752I
1.64493 + 5.69302I 7.23419 + 3.25470I
v = 0.246749 − 0.226622I
a = 0
b = −1.073950 + 0.558752I
1.64493 − 5.69302I 7.23419 − 3.25470I
v = 0.09825 + 2.00069I
a = 0
b = −0.428243 − 0.664531I
−0.245672 − 0.924305I 8.52440 + 0.42550I
v = 0.09825 − 2.00069I
a = 0
b = −0.428243 + 0.664531I
−0.245672 + 0.924305I 8.52440 − 0.42550I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
65
+ 68u
64
+ ··· + 59u + 1)
c
2
((u − 1)
8
)(u
6
+ u
5
+ ··· + u + 1)(u
65
− 10u
64
+ ··· − 11u + 1)
c
3
u
8
(u
6
− u
5
+ ··· − u + 1)(u
65
− 2u
64
+ ··· + 640u − 256)
c
4
((u + 1)
8
)(u
6
− u
5
+ ··· − u + 1)(u
65
− 10u
64
+ ··· − 11u + 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
65
+ 3u
64
+ ··· + 3u + 1)
c
6
u
6
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
65
+ 2u
64
+ ··· − 19008u − 5184)
c
7
u
8
(u
6
+ u
5
+ ··· + u + 1)(u
65
− 2u
64
+ ··· + 640u − 256)
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
65
+ 3u
64
+ ··· + 3u + 1)
c
9
(u + 1)
6
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
65
+ 8u
64
+ ··· + 1080u + 81)
c
10
81(9u
6
+ 12u
5
+ 2u
4
− u
3
+ 4u
2
+ 4u + 1)
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (9u
65
+ 18u
64
+ ··· − 294572u − 29917)
c
11
81(9u
6
− 30u
5
+ 41u
4
− 30u
3
+ 15u
2
− 5u + 1)
· (u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (9u
65
+ 42u
64
+ ··· + 608293u + 315227)
c
12
(u − 1)
6
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
65
+ 8u
64
+ ··· + 1080u + 81)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
6
+ y
5
+ ··· + 3y + 1)(y
65
− 132y
64
+ ··· + 7503y − 1)
c
2
, c
4
(y − 1)
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
65
− 68y
64
+ ··· + 59y − 1)
c
3
, c
7
y
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
65
+ 48y
64
+ ··· + 901120y − 65536)
c
5
, c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
65
+ 37y
64
+ ··· + 11y − 1)
c
6
y
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
65
+ 36y
64
+ ··· − 462827520y − 26873856)
c
9
, c
12
(y − 1)
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
65
− 30y
64
+ ··· + 422172y − 6561)
c
10
6561(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (81y
65
+ 5796y
64
+ ··· + 10803168570y − 895026889)
c
11
6561(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (81y
65
− 558y
64
+ ··· − 1063347056943y − 99368061529)
21
