12a
1199
(K12a
1199
)
A knot diagram
1
Linearized knot diagam
4 10 12 9 2 11 3 1 5 6 7 8
Solving Sequence
6,10
11
3,7
8 12 2 5 9 4 1
c
10
c
6
c
7
c
11
c
2
c
5
c
9
c
4
c
1
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1107u
29
− 7807u
28
+ ··· + 74b − 1824, 609u
29
+ 5328u
28
+ ··· + 74a + 3095,
u
30
+ 9u
29
+ ··· − 18u + 4i
I
u
2
= h−2.24569 × 10
16
u
41
+ 3.59238 × 10
16
u
40
+ ··· + 1.87613 × 10
15
b + 8.64633 × 10
15
,
− 8.64633 × 10
15
au
41
+ 5.57822 × 10
15
u
41
+ ··· + 1.84596 × 10
16
a − 3.64956 × 10
16
,
u
42
− 3u
41
+ ··· − 3u + 1i
I
u
3
= h5u
9
+ 2u
8
− 24u
7
+ 3u
6
+ 49u
5
− 23u
4
− 46u
3
+ 15u
2
+ b − 4,
5u
9
+ u
8
− 24u
7
+ 7u
6
+ 47u
5
− 29u
4
− 41u
3
+ 18u
2
+ a − u − 1,
u
10
+ 2u
9
− 4u
8
− 7u
7
+ 10u
6
+ 11u
5
− 15u
4
− 12u
3
+ 3u
2
− u − 1i
I
u
4
= h−u
2
a + au + b − u + 1, −u
5
a + u
4
a − u
5
+ 3u
3
a − 3u
2
a + 3u
3
+ a
2
− au − u + 1,
u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 136 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−1107u
29
− 7807u
28
+ · · · + 74b − 1824, 609u
29
+ 5328u
28
+ · · · +
74a + 3095, u
30
+ 9u
29
+ · · · − 18u + 4i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
−8.22973u
29
− 72u
28
+ ··· + 207.662u − 41.8243
14.9595u
29
+ 105.500u
28
+ ··· − 119.824u + 24.6486
a
7
=
−u
−u
3
+ u
a
8
=
23.4797u
29
+ 179.250u
28
+ ··· − 322.412u + 67.3243
10.0405u
29
+ 78.5000u
28
+ ··· − 180.176u + 34.3514
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−23.1892u
29
− 177.500u
28
+ ··· + 327.486u − 66.4730
14.9595u
29
+ 105.500u
28
+ ··· − 119.824u + 24.6486
a
5
=
−0.695946u
29
− 4.25000u
28
+ ··· + 11.6824u + 3.13514
−20.2027u
29
− 149.500u
28
+ ··· + 275.878u − 53.7568
a
9
=
3.44595u
29
+ 25u
28
+ ··· − 32.9324u + 14.3649
−2.47297u
29
− 15.5000u
28
+ ··· + 19.7162u − 4.43243
a
4
=
13.4865u
29
+ 101.500u
28
+ ··· − 177.108u + 30.7162
−22.4459u
29
− 164.500u
28
+ ··· + 266.932u − 52.8649
a
1
=
−52.9459u
29
− 399.500u
28
+ ··· + 713.432u − 146.365
−14.0135u
29
− 110.500u
28
+ ··· + 252.392u − 47.7838
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2517
37
u
29
− 485u
28
+ ··· +
30702
37
u −
5978
37
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 21u
29
+ ··· + 5664u − 576
c
2
, c
7
u
30
+ u
29
+ ··· + 3u + 1
c
3
, c
5
u
30
− 2u
29
+ ··· − 3u − 1
c
4
, c
8
, c
9
c
12
u
30
− u
29
+ ··· − 2u − 1
c
6
, c
10
, c
11
u
30
− 9u
29
+ ··· + 18u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ y
29
+ ··· + 625536y + 331776
c
2
, c
7
y
30
− 11y
29
+ ··· − 35y + 1
c
3
, c
5
y
30
− 6y
29
+ ··· − 35y + 1
c
4
, c
8
, c
9
c
12
y
30
− 31y
29
+ ··· − 38y + 1
c
6
, c
10
, c
11
y
30
− 31y
29
+ ··· − 380y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.410944 + 0.926981I
a = 0.213674 − 0.522235I
b = 0.822263 + 0.506816I
7.92023 + 8.26844I 5.79297 − 6.61407I
u = 0.410944 − 0.926981I
a = 0.213674 + 0.522235I
b = 0.822263 − 0.506816I
7.92023 − 8.26844I 5.79297 + 6.61407I
u = 0.657234 + 0.795413I
a = 0.286158 + 0.703110I
b = −1.16376 + 0.84778I
7.1697 − 13.8650I 3.50716 + 9.23776I
u = 0.657234 − 0.795413I
a = 0.286158 − 0.703110I
b = −1.16376 − 0.84778I
7.1697 + 13.8650I 3.50716 − 9.23776I
u = 0.732455 + 0.792176I
a = −0.171279 − 0.350284I
b = 0.574121 − 0.559120I
−2.28093 − 3.33714I −4.29262 + 9.83023I
u = 0.732455 − 0.792176I
a = −0.171279 + 0.350284I
b = 0.574121 + 0.559120I
−2.28093 + 3.33714I −4.29262 − 9.83023I
u = −1.192540 + 0.100004I
a = 0.823536 + 0.923814I
b = 0.308812 + 0.088803I
3.52040 + 2.10334I 2.60337 − 1.43319I
u = −1.192540 − 0.100004I
a = 0.823536 − 0.923814I
b = 0.308812 − 0.088803I
3.52040 − 2.10334I 2.60337 + 1.43319I
u = 0.565305 + 0.498449I
a = −0.152381 − 1.331500I
b = 1.31707 − 1.00922I
7.03863 − 3.47674I 6.16302 + 6.46879I
u = 0.565305 − 0.498449I
a = −0.152381 + 1.331500I
b = 1.31707 + 1.00922I
7.03863 + 3.47674I 6.16302 − 6.46879I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39387
a = 0.516557
b = 1.72362
3.76346 2.09680
u = 0.285170 + 0.476222I
a = 0.543085 + 0.598691I
b = −0.371848 + 0.489775I
0.036666 − 1.100320I 0.47503 + 5.63568I
u = 0.285170 − 0.476222I
a = 0.543085 − 0.598691I
b = −0.371848 − 0.489775I
0.036666 + 1.100320I 0.47503 − 5.63568I
u = 0.258913 + 0.478977I
a = −0.64282 + 1.46951I
b = −1.130390 − 0.325482I
7.79400 + 0.09205I 8.11865 + 0.48091I
u = 0.258913 − 0.478977I
a = −0.64282 − 1.46951I
b = −1.130390 + 0.325482I
7.79400 − 0.09205I 8.11865 − 0.48091I
u = −1.46966 + 0.13793I
a = −0.01513 + 1.70633I
b = 0.446291 + 1.149380I
−5.80438 + 3.26443I 0
u = −1.46966 − 0.13793I
a = −0.01513 − 1.70633I
b = 0.446291 − 1.149380I
−5.80438 − 3.26443I 0
u = 1.51744
a = −0.334350
b = −1.27724
−8.85903 −14.0970
u = 1.52403
a = 0.187267
b = 0.720364
−4.39987 0
u = −1.31833 + 0.78111I
a = −0.087798 − 0.207422I
b = −0.248448 + 0.151750I
2.43027 − 2.71202I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31833 − 0.78111I
a = −0.087798 + 0.207422I
b = −0.248448 − 0.151750I
2.43027 + 2.71202I 0
u = −1.54699 + 0.14661I
a = −0.77311 − 2.25751I
b = −1.33063 − 1.62440I
−0.01415 + 5.81789I 0
u = −1.54699 − 0.14661I
a = −0.77311 + 2.25751I
b = −1.33063 + 1.62440I
−0.01415 − 5.81789I 0
u = −0.423303
a = −2.12564
b = 0.518907
−2.26077 −15.8440
u = −1.58801 + 0.25775I
a = −0.131982 − 1.342510I
b = −0.867432 − 1.090380I
−9.82577 + 7.23018I 0
u = −1.58801 − 0.25775I
a = −0.131982 + 1.342510I
b = −0.867432 + 1.090380I
−9.82577 − 7.23018I 0
u = −1.58710 + 0.27028I
a = 0.42992 + 1.68609I
b = 1.36000 + 1.19527I
−0.2004 + 17.8372I 0
u = −1.58710 − 0.27028I
a = 0.42992 − 1.68609I
b = 1.36000 − 1.19527I
−0.2004 − 17.8372I 0
u = −1.65285
a = 1.19651
b = 1.29111
0.937751 0
u = 0.226022
a = −5.08409
b = −1.40884
8.14855 10.8180
7
II. I
u
2
= h−2.25 × 10
16
u
41
+ 3.59 × 10
16
u
40
+ · · · + 1.88 × 10
15
b + 8.65 ×
10
15
, −8.65 × 10
15
au
41
+ 5.58 × 10
15
u
41
+ · · · + 1.85 × 10
16
a − 3.65 ×
10
16
, u
42
− 3u
41
+ · · · − 3u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
a
11.9698u
41
− 19.1478u
40
+ ··· + 3.98658u − 4.60860
a
7
=
−u
−u
3
+ u
a
8
=
11.9698au
41
− 1.27352u
41
+ ··· − 4.60860a + 4.17129
−8.91385u
41
+ 14.0830u
40
+ ··· − 10.5039u + 3.92034
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−11.9698u
41
+ 19.1478u
40
+ ··· + a + 4.60860
11.9698u
41
− 19.1478u
40
+ ··· + 3.98658u − 4.60860
a
5
=
−7.67033au
41
− 8.03946u
41
+ ··· + 7.20165a + 7.93907
−6.00468au
41
+ 7.46200u
41
+ ··· + 4.95139a − 3.69228
a
9
=
−4.66809au
41
+ 5.31562u
41
+ ··· + 2.79353a − 9.59020
−2.22390au
41
+ 10.2324u
41
+ ··· + 1.44296a − 7.05505
a
4
=
−17.9745u
41
+ 27.7658u
40
+ ··· + a + 9.56000
4.08623u
41
− 6.98101u
40
+ ··· − 5.04797u − 0.163919
a
1
=
4.07196au
41
+ 4.18561u
41
+ ··· − 1.15846a − 2.98736
3.99634au
41
+ 7.46200u
41
+ ··· − 2.71991a − 4.69228
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
60686684670471694
938063624650451
u
41
−
88213372387653101
938063624650451
u
40
+ ···+
149849712719378746
938063624650451
u −
60672440054349689
938063624650451
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
42
+ 15u
41
+ ··· + 185u + 25)
2
c
2
, c
7
u
84
+ 2u
83
+ ··· + 7u − 1
c
3
, c
5
u
84
− 5u
82
+ ··· + 1628u − 151
c
4
, c
8
, c
9
c
12
u
84
+ u
83
+ ··· + 13u − 7
c
6
, c
10
, c
11
(u
42
+ 3u
41
+ ··· + 3u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
42
+ 19y
41
+ ··· + 10575y + 625)
2
c
2
, c
7
y
84
+ 16y
83
+ ··· − 965y + 1
c
3
, c
5
y
84
− 10y
83
+ ··· − 808486y + 22801
c
4
, c
8
, c
9
c
12
y
84
− 59y
83
+ ··· + 699y + 49
c
6
, c
10
, c
11
(y
42
− 45y
41
+ ··· − 37y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863764 + 0.522671I
a = −1.136370 + 0.489074I
b = −0.753370 − 0.394863I
5.82176 + 1.45109I 2.57813 − 2.42981I
u = 0.863764 + 0.522671I
a = 0.396273 + 0.223203I
b = −1.251320 + 0.291856I
5.82176 + 1.45109I 2.57813 − 2.42981I
u = 0.863764 − 0.522671I
a = −1.136370 − 0.489074I
b = −0.753370 + 0.394863I
5.82176 − 1.45109I 2.57813 + 2.42981I
u = 0.863764 − 0.522671I
a = 0.396273 − 0.223203I
b = −1.251320 − 0.291856I
5.82176 − 1.45109I 2.57813 + 2.42981I
u = −0.607177 + 0.810150I
a = −0.494044 + 0.609480I
b = 1.002410 + 0.742946I
1.39005 + 8.17887I 0. − 9.88270I
u = −0.607177 + 0.810150I
a = 0.187223 − 0.462069I
b = −0.702247 − 0.821575I
1.39005 + 8.17887I 0. − 9.88270I
u = −0.607177 − 0.810150I
a = −0.494044 − 0.609480I
b = 1.002410 − 0.742946I
1.39005 − 8.17887I 0. + 9.88270I
u = −0.607177 − 0.810150I
a = 0.187223 + 0.462069I
b = −0.702247 + 0.821575I
1.39005 − 8.17887I 0. + 9.88270I
u = −0.566268 + 0.921130I
a = 0.374671 + 0.124812I
b = 0.174252 − 0.314893I
1.65272 − 2.50366I −6.09925 + 11.01891I
u = −0.566268 + 0.921130I
a = −0.005360 − 0.259215I
b = −0.594720 + 0.416855I
1.65272 − 2.50366I −6.09925 + 11.01891I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566268 − 0.921130I
a = 0.374671 − 0.124812I
b = 0.174252 + 0.314893I
1.65272 + 2.50366I −6.09925 − 11.01891I
u = −0.566268 − 0.921130I
a = −0.005360 + 0.259215I
b = −0.594720 − 0.416855I
1.65272 + 2.50366I −6.09925 − 11.01891I
u = 0.141252 + 0.807812I
a = 1.122350 − 0.174833I
b = −0.728441 + 0.456399I
1.84859 − 0.65986I −1.04077 − 3.49741I
u = 0.141252 + 0.807812I
a = 0.0954544 + 0.0888990I
b = 0.219094 + 0.847500I
1.84859 − 0.65986I −1.04077 − 3.49741I
u = 0.141252 − 0.807812I
a = 1.122350 + 0.174833I
b = −0.728441 − 0.456399I
1.84859 + 0.65986I −1.04077 + 3.49741I
u = 0.141252 − 0.807812I
a = 0.0954544 − 0.0888990I
b = 0.219094 − 0.847500I
1.84859 + 0.65986I −1.04077 + 3.49741I
u = −0.605442 + 0.415115I
a = 1.045290 + 0.709146I
b = 0.748270 − 0.387756I
2.93139 − 0.78383I 4.56702 − 3.86421I
u = −0.605442 + 0.415115I
a = −0.212152 − 0.145332I
b = −1.041500 + 0.082980I
2.93139 − 0.78383I 4.56702 − 3.86421I
u = −0.605442 − 0.415115I
a = 1.045290 − 0.709146I
b = 0.748270 + 0.387756I
2.93139 + 0.78383I 4.56702 + 3.86421I
u = −0.605442 − 0.415115I
a = −0.212152 + 0.145332I
b = −1.041500 − 0.082980I
2.93139 + 0.78383I 4.56702 + 3.86421I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.258937 + 0.664390I
a = −0.342925 − 0.085855I
b = 1.16644 − 0.86498I
7.59159 − 5.61854I 7.27003 + 5.73638I
u = 0.258937 + 0.664390I
a = −0.50447 − 1.71458I
b = 0.747037 + 0.218239I
7.59159 − 5.61854I 7.27003 + 5.73638I
u = 0.258937 − 0.664390I
a = −0.342925 + 0.085855I
b = 1.16644 + 0.86498I
7.59159 + 5.61854I 7.27003 − 5.73638I
u = 0.258937 − 0.664390I
a = −0.50447 + 1.71458I
b = 0.747037 − 0.218239I
7.59159 + 5.61854I 7.27003 − 5.73638I
u = −0.411667 + 0.530873I
a = 0.623616 − 0.694387I
b = −1.105310 − 0.878796I
3.49440 + 4.19968I 4.41465 − 6.29777I
u = −0.411667 + 0.530873I
a = −0.13742 + 1.48491I
b = 0.776383 + 0.510140I
3.49440 + 4.19968I 4.41465 − 6.29777I
u = −0.411667 − 0.530873I
a = 0.623616 + 0.694387I
b = −1.105310 + 0.878796I
3.49440 − 4.19968I 4.41465 + 6.29777I
u = −0.411667 − 0.530873I
a = −0.13742 − 1.48491I
b = 0.776383 − 0.510140I
3.49440 − 4.19968I 4.41465 + 6.29777I
u = 1.325230 + 0.121163I
a = −0.33845 − 1.40772I
b = 0.0717567 − 0.0317378I
−1.60110 − 2.37215I 0
u = 1.325230 + 0.121163I
a = 0.32948 + 1.87790I
b = −0.30721 + 1.46972I
−1.60110 − 2.37215I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.325230 − 0.121163I
a = −0.33845 + 1.40772I
b = 0.0717567 + 0.0317378I
−1.60110 + 2.37215I 0
u = 1.325230 − 0.121163I
a = 0.32948 − 1.87790I
b = −0.30721 − 1.46972I
−1.60110 + 2.37215I 0
u = 0.565388 + 0.238251I
a = −0.387349 + 0.361291I
b = 0.316356 + 0.976830I
−0.30835 − 2.48253I −3.85775 + 6.40077I
u = 0.565388 + 0.238251I
a = 1.39851 + 1.15497I
b = −0.248572 + 0.792395I
−0.30835 − 2.48253I −3.85775 + 6.40077I
u = 0.565388 − 0.238251I
a = −0.387349 − 0.361291I
b = 0.316356 − 0.976830I
−0.30835 + 2.48253I −3.85775 − 6.40077I
u = 0.565388 − 0.238251I
a = 1.39851 − 1.15497I
b = −0.248572 − 0.792395I
−0.30835 + 2.48253I −3.85775 − 6.40077I
u = −1.41609 + 0.17675I
a = −0.36241 − 1.44279I
b = −0.160821 − 0.085750I
2.26163 + 8.51393I 0
u = −1.41609 + 0.17675I
a = −0.66383 − 1.90549I
b = −1.49610 − 1.45020I
2.26163 + 8.51393I 0
u = −1.41609 − 0.17675I
a = −0.36241 + 1.44279I
b = −0.160821 + 0.085750I
2.26163 − 8.51393I 0
u = −1.41609 − 0.17675I
a = −0.66383 + 1.90549I
b = −1.49610 + 1.45020I
2.26163 − 8.51393I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45653 + 0.03615I
a = 0.26001 − 1.51590I
b = −1.025060 − 0.747723I
−4.04142 + 2.69160I 0
u = −1.45653 + 0.03615I
a = 1.01452 − 1.68684I
b = 1.64938 − 1.46587I
−4.04142 + 2.69160I 0
u = −1.45653 − 0.03615I
a = 0.26001 + 1.51590I
b = −1.025060 + 0.747723I
−4.04142 − 2.69160I 0
u = −1.45653 − 0.03615I
a = 1.01452 + 1.68684I
b = 1.64938 + 1.46587I
−4.04142 − 2.69160I 0
u = 1.49131 + 0.14297I
a = −0.31406 + 1.83068I
b = −0.379398 + 1.070490I
−2.77120 − 6.54818I 0
u = 1.49131 + 0.14297I
a = 0.54619 − 1.94977I
b = 1.30490 − 1.37833I
−2.77120 − 6.54818I 0
u = 1.49131 − 0.14297I
a = −0.31406 − 1.83068I
b = −0.379398 − 1.070490I
−2.77120 + 6.54818I 0
u = 1.49131 − 0.14297I
a = 0.54619 + 1.94977I
b = 1.30490 + 1.37833I
−2.77120 + 6.54818I 0
u = 1.49885
a = −0.311540 + 0.980370I
b = −1.166850 + 0.733030I
−8.66282 0
u = 1.49885
a = −0.311540 − 0.980370I
b = −1.166850 − 0.733030I
−8.66282 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50805 + 0.06162I
a = −0.15996 + 1.54499I
b = 0.652969 + 1.020330I
−7.08373 + 3.55162I 0
u = −1.50805 + 0.06162I
a = −0.55068 + 1.64664I
b = −0.79820 + 1.50112I
−7.08373 + 3.55162I 0
u = −1.50805 − 0.06162I
a = −0.15996 − 1.54499I
b = 0.652969 − 1.020330I
−7.08373 − 3.55162I 0
u = −1.50805 − 0.06162I
a = −0.55068 − 1.64664I
b = −0.79820 − 1.50112I
−7.08373 − 3.55162I 0
u = 1.51088
a = 0.184782 + 0.402102I
b = 0.700993 + 0.310371I
−4.39160 0
u = 1.51088
a = 0.184782 − 0.402102I
b = 0.700993 − 0.310371I
−4.39160 0
u = −0.464315 + 0.152179I
a = 0.826498 + 1.010610I
b = −0.02611 + 1.65946I
4.22300 + 6.38749I −2.86967 − 7.52420I
u = −0.464315 + 0.152179I
a = 1.64608 − 2.86720I
b = −0.625983 − 1.127820I
4.22300 + 6.38749I −2.86967 − 7.52420I
u = −0.464315 − 0.152179I
a = 0.826498 − 1.010610I
b = −0.02611 − 1.65946I
4.22300 − 6.38749I −2.86967 + 7.52420I
u = −0.464315 − 0.152179I
a = 1.64608 + 2.86720I
b = −0.625983 + 1.127820I
4.22300 − 6.38749I −2.86967 + 7.52420I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51736 + 0.06881I
a = 0.12838 − 2.16534I
b = 0.93134 − 1.30155I
−2.46728 − 7.30353I 0
u = 1.51736 + 0.06881I
a = 0.22992 + 2.39296I
b = 0.37237 + 2.26942I
−2.46728 − 7.30353I 0
u = 1.51736 − 0.06881I
a = 0.12838 + 2.16534I
b = 0.93134 + 1.30155I
−2.46728 + 7.30353I 0
u = 1.51736 − 0.06881I
a = 0.22992 − 2.39296I
b = 0.37237 − 2.26942I
−2.46728 + 7.30353I 0
u = −1.48180 + 0.33629I
a = −0.133886 + 1.152100I
b = 1.104390 + 0.677706I
−3.51695 + 5.02150I 0
u = −1.48180 + 0.33629I
a = −0.421044 + 1.156400I
b = 0.086561 + 1.075800I
−3.51695 + 5.02150I 0
u = −1.48180 − 0.33629I
a = −0.133886 − 1.152100I
b = 1.104390 − 0.677706I
−3.51695 − 5.02150I 0
u = −1.48180 − 0.33629I
a = −0.421044 − 1.156400I
b = 0.086561 − 1.075800I
−3.51695 − 5.02150I 0
u = 1.56729 + 0.27366I
a = −0.23094 + 1.54795I
b = −1.23064 + 1.03994I
−5.72649 − 12.16830I 0
u = 1.56729 + 0.27366I
a = 0.13601 − 1.58594I
b = 0.89879 − 1.29737I
−5.72649 − 12.16830I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56729 − 0.27366I
a = −0.23094 − 1.54795I
b = −1.23064 − 1.03994I
−5.72649 + 12.16830I 0
u = 1.56729 − 0.27366I
a = 0.13601 + 1.58594I
b = 0.89879 + 1.29737I
−5.72649 + 12.16830I 0
u = −0.407892
a = −2.08788 + 0.51861I
b = 0.504258 + 0.297819I
−2.24512 −11.7400
u = −0.407892
a = −2.08788 − 0.51861I
b = 0.504258 − 0.297819I
−2.24512 −11.7400
u = 1.61172 + 0.26088I
a = 0.151617 − 0.867656I
b = 0.853272 − 0.684710I
−5.78754 − 1.93458I 0
u = 1.61172 + 0.26088I
a = −0.021830 + 0.861367I
b = −0.308860 + 0.801667I
−5.78754 − 1.93458I 0
u = 1.61172 − 0.26088I
a = 0.151617 + 0.867656I
b = 0.853272 + 0.684710I
−5.78754 + 1.93458I 0
u = 1.61172 − 0.26088I
a = −0.021830 − 0.861367I
b = −0.308860 − 0.801667I
−5.78754 + 1.93458I 0
u = −1.63736
a = 1.18397
b = 2.01301
−3.44170 0
u = −1.63736
a = 0.709156
b = −0.0373655
−3.44170 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192853 + 0.119529I
a = 1.96792 − 2.44007I
b = −0.92266 − 1.14868I
1.58994 − 2.14839I −5.01662 + 8.36358I
u = 0.192853 + 0.119529I
a = −6.79477 − 1.92552I
b = 0.604319 − 0.592713I
1.58994 − 2.14839I −5.01662 + 8.36358I
u = 0.192853 − 0.119529I
a = 1.96792 + 2.44007I
b = −0.92266 + 1.14868I
1.58994 + 2.14839I −5.01662 − 8.36358I
u = 0.192853 − 0.119529I
a = −6.79477 + 1.92552I
b = 0.604319 + 0.592713I
1.58994 + 2.14839I −5.01662 − 8.36358I
19
III.
I
u
3
= h5u
9
+ 2u
8
+ · · · + b − 4, 5u
9
+ u
8
+ · · · + a − 1, u
10
+ 2u
9
+ · · · − u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
−5u
9
− u
8
+ 24u
7
− 7u
6
− 47u
5
+ 29u
4
+ 41u
3
− 18u
2
+ u + 1
−5u
9
− 2u
8
+ 24u
7
− 3u
6
− 49u
5
+ 23u
4
+ 46u
3
− 15u
2
+ 4
a
7
=
−u
−u
3
+ u
a
8
=
u
9
− u
8
− 4u
7
+ 6u
6
+ 5u
5
− 12u
4
− u
3
+ 8u
2
− 2u − 3
3u
9
+ u
8
− 13u
7
+ 2u
6
+ 24u
5
− 11u
4
− 21u
3
+ 3u
2
− 3u − 2
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
8
− 4u
6
+ 2u
5
+ 6u
4
− 5u
3
− 3u
2
+ u − 3
−5u
9
− 2u
8
+ 24u
7
− 3u
6
− 49u
5
+ 23u
4
+ 46u
3
− 15u
2
+ 4
a
5
=
3u
9
+ 2u
8
− 15u
7
− 2u
6
+ 34u
5
− 8u
4
− 38u
3
+ 7u
2
+ 7u − 4
2u
9
+ u
8
− 10u
7
+ u
6
+ 21u
5
− 11u
4
− 19u
3
+ 9u
2
− 2u − 2
a
9
=
4u
9
+ 3u
8
− 18u
7
− 4u
6
+ 37u
5
− 5u
4
− 37u
3
− 2u
2
− 3u − 3
3u
9
+ 2u
8
− 14u
7
− 2u
6
+ 29u
5
− 6u
4
− 29u
3
+ u
2
− 1
a
4
=
−2u
9
+ 10u
7
− 5u
6
− 19u
5
+ 17u
4
+ 14u
3
− 12u
2
+ 3u − 1
−u
9
+ 5u
7
− 2u
6
− 10u
5
+ 7u
4
+ 9u
3
− 6u
2
− u + 1
a
1
=
−u
9
− u
8
+ 3u
7
+ 4u
6
− 5u
5
− 10u
4
+ 8u
3
+ 15u
2
− 3u − 1
−3u
9
− u
8
+ 14u
7
− 2u
6
− 28u
5
+ 12u
4
+ 27u
3
− 5u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −16u
9
− 14u
8
+ 72u
7
+ 28u
6
− 153u
5
− 2u
4
+ 166u
3
+ 18u
2
− 4u + 23
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 8u
9
+ ··· − 88u + 13
c
2
, c
7
u
10
− u
9
+ 4u
8
− u
7
+ 5u
6
− 9u
5
− 7u
4
− 5u
3
+ u − 1
c
3
, c
5
u
10
+ 2u
9
+ 2u
8
+ 5u
7
+ 7u
6
+ 6u
5
+ 6u
4
+ 6u
3
+ 4u
2
+ u + 1
c
4
, c
8
u
10
+ u
9
− 4u
8
− 4u
7
+ 8u
6
+ 6u
5
− 9u
4
− 3u
3
+ 6u
2
− 1
c
6
u
10
− 2u
9
− 4u
8
+ 7u
7
+ 10u
6
− 11u
5
− 15u
4
+ 12u
3
+ 3u
2
+ u − 1
c
9
, c
12
u
10
− u
9
− 4u
8
+ 4u
7
+ 8u
6
− 6u
5
− 9u
4
+ 3u
3
+ 6u
2
− 1
c
10
, c
11
u
10
+ 2u
9
− 4u
8
− 7u
7
+ 10u
6
+ 11u
5
− 15u
4
− 12u
3
+ 3u
2
− u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 12y
9
+ ··· − 464y + 169
c
2
, c
7
y
10
+ 7y
9
+ 24y
8
+ 7y
7
− 59y
6
− 161y
5
− 47y
4
− 17y
3
+ 24y
2
− y + 1
c
3
, c
5
y
10
− 2y
8
− 9y
7
− 3y
6
+ 2y
5
+ 14y
4
+ 14y
3
+ 16y
2
+ 7y + 1
c
4
, c
8
, c
9
c
12
y
10
− 9y
9
+ ··· − 12y + 1
c
6
, c
10
, c
11
y
10
− 12y
9
+ ··· − 7y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.123500 + 0.840732I
a = −0.1339860 + 0.0357723I
b = −0.322604 − 0.305704I
2.31865 + 2.84134I −4.4104 − 24.6107I
u = 1.123500 − 0.840732I
a = −0.1339860 − 0.0357723I
b = −0.322604 + 0.305704I
2.31865 − 2.84134I −4.4104 + 24.6107I
u = −1.45178 + 0.24453I
a = −0.156567 + 1.065310I
b = 0.402562 + 0.707908I
−4.52753 + 2.30900I −1.28825 − 2.99143I
u = −1.45178 − 0.24453I
a = −0.156567 − 1.065310I
b = 0.402562 − 0.707908I
−4.52753 − 2.30900I −1.28825 + 2.99143I
u = −1.50421 + 0.09962I
a = −0.36862 − 2.65968I
b = −0.80804 − 1.91705I
−0.97937 + 7.97248I 2.33266 − 8.09152I
u = −1.50421 − 0.09962I
a = −0.36862 + 2.65968I
b = −0.80804 + 1.91705I
−0.97937 − 7.97248I 2.33266 + 8.09152I
u = 1.51106
a = −0.361955
b = −1.37339
−8.44475 5.79620
u = 0.255179 + 0.355404I
a = −1.76332 − 1.74462I
b = 0.59443 − 1.28495I
5.13832 − 6.43552I 7.94486 + 8.35380I
u = 0.255179 − 0.355404I
a = −1.76332 + 1.74462I
b = 0.59443 + 1.28495I
5.13832 + 6.43552I 7.94486 − 8.35380I
u = −0.356433
a = −2.79306
b = 0.640696
−2.03513 20.0460
23
IV. I
u
4
=
h−u
2
a+au+b−u+1, −u
5
a−u
5
+· · ·+a
2
+1, u
6
−u
5
−3u
4
+3u
3
+u
2
−u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
a
u
2
a − au + u − 1
a
7
=
−u
−u
3
+ u
a
8
=
au + u
2
− a − u
u
4
− u
3
− 2u
2
+ 2u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−u
2
a + au + a − u + 1
u
2
a − au + u − 1
a
5
=
u
5
a − u
4
a − 3u
3
a + u
4
+ 3u
2
a + au − 2u
2
− a + u − 1
−u
5
a + u
4
a + u
5
+ 2u
3
a − u
4
− 2u
2
a − 2u
3
+ 2u
2
a
9
=
u
5
a − 2u
4
a − u
5
− 2u
3
a + u
4
+ 5u
2
a + u
3
− 2u
2
− a + 2u
u
3
a − u
2
a − au + u
2
+ a − u
a
4
=
u
5
a − u
4
a − u
5
− 2u
3
a + u
4
+ u
2
a + 2u
3
+ au − 2u
2
+ a − u + 1
−u
4
a + u
3
a + 2u
2
a − u
3
− 2au + u
2
+ 2u − 1
a
1
=
u
5
− u
3
a − u
4
+ u
2
a − 2u
3
+ au + u
2
+ 1
−u
5
+ u
2
a + 3u
3
− 2au − u
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
5
− u
4
− 3u
3
+ u
2
− u + 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− u
5
+ u
4
− u
3
− u
2
+ u − 1)
2
c
2
, c
7
u
12
+ u
11
+ ··· − 7u + 1
c
3
, c
5
u
12
− 5u
11
+ ··· − 2u − 1
c
4
, c
8
u
12
− 5u
10
− 2u
9
+ 8u
8
+ 7u
7
− 2u
6
− 5u
5
− 5u
4
− 6u
3
+ 2u
2
+ 7u + 1
c
6
(u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1)
2
c
9
, c
12
u
12
− 5u
10
+ 2u
9
+ 8u
8
− 7u
7
− 2u
6
+ 5u
5
− 5u
4
+ 6u
3
+ 2u
2
− 7u + 1
c
10
, c
11
(u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
− 3y
4
− 3y
3
+ y
2
+ y + 1)
2
c
2
, c
7
y
12
− 3y
11
+ ··· − 29y + 1
c
3
, c
5
y
12
− 5y
11
+ ··· − 10y + 1
c
4
, c
8
, c
9
c
12
y
12
− 10y
11
+ ··· − 45y + 1
c
6
, c
10
, c
11
(y
6
− 7y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847445
a = 0.235955
b = −1.47803
6.86480 4.00150
u = −0.847445
a = 1.94406
b = 1.19619
6.86480 4.00150
u = 0.251489 + 0.528716I
a = −0.311088 − 0.168531I
b = −0.647276 + 0.689301I
1.98554 + 1.63935I 2.25076 − 0.08848I
u = 0.251489 + 0.528716I
a = 0.57743 + 1.71093I
b = −0.569018 − 0.423369I
1.98554 + 1.63935I 2.25076 − 0.08848I
u = 0.251489 − 0.528716I
a = −0.311088 + 0.168531I
b = −0.647276 − 0.689301I
1.98554 − 1.63935I 2.25076 + 0.08848I
u = 0.251489 − 0.528716I
a = 0.57743 − 1.71093I
b = −0.569018 + 0.423369I
1.98554 − 1.63935I 2.25076 + 0.08848I
u = 1.46321 + 0.18726I
a = −0.06132 − 1.65441I
b = 1.020610 − 0.898165I
−2.65234 − 4.33255I 0.80689 + 2.76702I
u = 1.46321 + 0.18726I
a = 0.38891 + 1.74046I
b = 0.08531 + 1.44617I
−2.65234 − 4.33255I 0.80689 + 2.76702I
u = 1.46321 − 0.18726I
a = −0.06132 + 1.65441I
b = 1.020610 + 0.898165I
−2.65234 + 4.33255I 0.80689 − 2.76702I
u = 1.46321 − 0.18726I
a = 0.38891 − 1.74046I
b = 0.08531 − 1.44617I
−2.65234 + 4.33255I 0.80689 − 2.76702I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58196
a = 1.04686
b = 1.69397
−5.53118 −8.11680
u = −1.58196
a = 0.585273
b = −0.191384
−5.53118 −8.11680
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
− u
5
+ u
4
− u
3
− u
2
+ u − 1)
2
)(u
10
− 8u
9
+ ··· − 88u + 13)
· (u
30
− 21u
29
+ ··· + 5664u − 576)(u
42
+ 15u
41
+ ··· + 185u + 25)
2
c
2
, c
7
(u
10
− u
9
+ 4u
8
− u
7
+ 5u
6
− 9u
5
− 7u
4
− 5u
3
+ u − 1)
· (u
12
+ u
11
+ ··· − 7u + 1)(u
30
+ u
29
+ ··· + 3u + 1)
· (u
84
+ 2u
83
+ ··· + 7u − 1)
c
3
, c
5
(u
10
+ 2u
9
+ 2u
8
+ 5u
7
+ 7u
6
+ 6u
5
+ 6u
4
+ 6u
3
+ 4u
2
+ u + 1)
· (u
12
− 5u
11
+ ··· − 2u − 1)(u
30
− 2u
29
+ ··· − 3u − 1)
· (u
84
− 5u
82
+ ··· + 1628u − 151)
c
4
, c
8
(u
10
+ u
9
− 4u
8
− 4u
7
+ 8u
6
+ 6u
5
− 9u
4
− 3u
3
+ 6u
2
− 1)
· (u
12
− 5u
10
− 2u
9
+ 8u
8
+ 7u
7
− 2u
6
− 5u
5
− 5u
4
− 6u
3
+ 2u
2
+ 7u + 1)
· (u
30
− u
29
+ ··· − 2u − 1)(u
84
+ u
83
+ ··· + 13u − 7)
c
6
(u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1)
2
· (u
10
− 2u
9
− 4u
8
+ 7u
7
+ 10u
6
− 11u
5
− 15u
4
+ 12u
3
+ 3u
2
+ u − 1)
· (u
30
− 9u
29
+ ··· + 18u + 4)(u
42
+ 3u
41
+ ··· + 3u + 1)
2
c
9
, c
12
(u
10
− u
9
− 4u
8
+ 4u
7
+ 8u
6
− 6u
5
− 9u
4
+ 3u
3
+ 6u
2
− 1)
· (u
12
− 5u
10
+ 2u
9
+ 8u
8
− 7u
7
− 2u
6
+ 5u
5
− 5u
4
+ 6u
3
+ 2u
2
− 7u + 1)
· (u
30
− u
29
+ ··· − 2u − 1)(u
84
+ u
83
+ ··· + 13u − 7)
c
10
, c
11
(u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1)
2
· (u
10
+ 2u
9
− 4u
8
− 7u
7
+ 10u
6
+ 11u
5
− 15u
4
− 12u
3
+ 3u
2
− u − 1)
· (u
30
− 9u
29
+ ··· + 18u + 4)(u
42
+ 3u
41
+ ··· + 3u + 1)
2
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
− 3y
4
− 3y
3
+ y
2
+ y + 1)
2
)(y
10
+ 12y
9
+ ··· − 464y + 169)
· (y
30
+ y
29
+ ··· + 625536y + 331776)
· (y
42
+ 19y
41
+ ··· + 10575y + 625)
2
c
2
, c
7
(y
10
+ 7y
9
+ 24y
8
+ 7y
7
− 59y
6
− 161y
5
− 47y
4
− 17y
3
+ 24y
2
− y + 1)
· (y
12
− 3y
11
+ ··· − 29y + 1)(y
30
− 11y
29
+ ··· − 35y + 1)
· (y
84
+ 16y
83
+ ··· − 965y + 1)
c
3
, c
5
(y
10
− 2y
8
− 9y
7
− 3y
6
+ 2y
5
+ 14y
4
+ 14y
3
+ 16y
2
+ 7y + 1)
· (y
12
− 5y
11
+ ··· − 10y + 1)(y
30
− 6y
29
+ ··· − 35y + 1)
· (y
84
− 10y
83
+ ··· − 808486y + 22801)
c
4
, c
8
, c
9
c
12
(y
10
− 9y
9
+ ··· − 12y + 1)(y
12
− 10y
11
+ ··· − 45y + 1)
· (y
30
− 31y
29
+ ··· − 38y + 1)(y
84
− 59y
83
+ ··· + 699y + 49)
c
6
, c
10
, c
11
((y
6
− 7y
5
+ ··· + y + 1)
2
)(y
10
− 12y
9
+ ··· − 7y + 1)
· (y
30
− 31y
29
+ ··· − 380y + 16)(y
42
− 45y
41
+ ··· − 37y + 1)
2
30
