12a
0218
(K12a
0218
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 10 2 12 5 4 1 8 11
Solving Sequence
5,8
9 4 10
6,12
7 3 2 11 1
c
8
c
4
c
9
c
5
c
7
c
3
c
2
c
11
c
12
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.83761 × 10
47
u
83
+ 6.75612 × 10
47
u
82
+ ··· + 1.51134 × 10
48
b − 6.34548 × 10
47
,
7.37805 × 10
46
u
83
+ 2.42262 × 10
47
u
82
+ ··· + 7.55672 × 10
47
a + 6.02649 × 10
48
, u
84
+ 4u
83
+ ··· + 96u + 16i
I
u
2
= h4b + 2a − u + 2, 2a
2
− 2au + 5, u
2
+ 2i
I
u
3
= h−12751a
4
u
2
− 3476a
3
u
2
+ ··· + 134987a − 145138,
2a
4
u
2
+ a
5
− 2a
3
u
2
+ 2a
4
+ 3a
3
u + 4a
2
u
2
+ a
3
+ 2a
2
u + 5u
2
a − 4a
2
− 2au − 3u
2
+ 9a + 5u − 7,
u
3
− u
2
+ 2u − 1i
I
u
4
= hau + 9b + 4a + u + 4, 2a
2
+ au − 3u + 5, u
2
+ 2i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
I
v
2
= ha, b
2
− b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 111 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
=
h1.84×10
47
u
83
+6.76×10
47
u
82
+· · ·+1.51×10
48
b−6.35×10
47
, 7.38×10
46
u
83
+
2.42 × 10
47
u
82
+ · · · + 7.56 × 10
47
a + 6.03 × 10
48
, u
84
+ 4u
83
+ · · · + 96u + 16i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
12
=
−0.0976356u
83
− 0.320592u
82
+ ··· − 30.0041u − 7.97502
−0.121588u
83
− 0.447027u
82
+ ··· − 3.28280u + 0.419857
a
7
=
0.198396u
83
+ 0.413274u
82
+ ··· + 2.76813u + 0.709068
0.112403u
83
+ 0.314145u
82
+ ··· − 2.45717u − 1.02935
a
3
=
0.405056u
83
+ 1.56056u
82
+ ··· + 59.3006u + 12.8650
0.138509u
83
+ 0.543278u
82
+ ··· + 26.3533u + 5.30097
a
2
=
0.411073u
83
+ 1.58363u
82
+ ··· + 39.6138u + 7.75297
0.123419u
83
+ 0.481396u
82
+ ··· + 31.0917u + 6.38943
a
11
=
−0.219223u
83
− 0.767619u
82
+ ··· − 33.2869u − 7.55516
−0.121588u
83
− 0.447027u
82
+ ··· − 3.28280u + 0.419857
a
1
=
0.325649u
83
+ 1.35250u
82
+ ··· + 47.3100u + 8.96150
0.0405219u
83
+ 0.178471u
82
+ ··· + 36.9975u + 8.48326
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.25888u
83
− 3.47330u
82
+ ··· − 45.0684u − 15.7517
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 43u
83
+ ··· + 80u + 9
c
2
, c
6
u
84
− 3u
83
+ ··· − 8u + 3
c
3
u
84
+ 3u
83
+ ··· + 44270u + 12039
c
4
, c
8
, c
9
u
84
− 4u
83
+ ··· − 96u + 16
c
5
u
84
+ 4u
83
+ ··· + 192992u + 185296
c
7
, c
11
u
84
+ 3u
83
+ ··· − 22u + 3
c
10
, c
12
u
84
− 27u
83
+ ··· − 80u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
+ 3y
83
+ ··· + 1988y + 81
c
2
, c
6
y
84
+ 43y
83
+ ··· + 80y + 9
c
3
y
84
− 37y
83
+ ··· + 1982120948y + 144937521
c
4
, c
8
, c
9
y
84
+ 76y
83
+ ··· + 9728y
2
+ 256
c
5
y
84
− 4y
83
+ ··· + 562686205952y + 34334607616
c
7
, c
11
y
84
+ 27y
83
+ ··· + 80y + 9
c
10
, c
12
y
84
+ 67y
83
+ ··· + 35684y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.350754 + 0.942596I
a = 0.642858 − 0.879615I
b = 0.771585 + 0.815019I
−2.14146 − 2.52752I 0
u = 0.350754 − 0.942596I
a = 0.642858 + 0.879615I
b = 0.771585 − 0.815019I
−2.14146 + 2.52752I 0
u = 0.540304 + 0.822649I
a = −0.042257 + 0.688019I
b = 0.755822 − 0.974029I
−4.62886 + 7.84102I 0
u = 0.540304 − 0.822649I
a = −0.042257 − 0.688019I
b = 0.755822 + 0.974029I
−4.62886 − 7.84102I 0
u = −0.495294 + 0.887879I
a = 0.473834 + 0.922359I
b = 0.821705 − 0.771878I
−5.25459 − 1.93039I 0
u = −0.495294 − 0.887879I
a = 0.473834 − 0.922359I
b = 0.821705 + 0.771878I
−5.25459 + 1.93039I 0
u = −0.408826 + 0.824363I
a = 0.073344 − 0.595451I
b = 0.731673 + 0.929862I
−1.78240 − 3.16007I 0
u = −0.408826 − 0.824363I
a = 0.073344 + 0.595451I
b = 0.731673 − 0.929862I
−1.78240 + 3.16007I 0
u = 0.449775 + 0.998287I
a = −0.107414 + 0.446418I
b = 0.793035 − 0.902515I
−5.77493 − 0.50478I 0
u = 0.449775 − 0.998287I
a = −0.107414 − 0.446418I
b = 0.793035 + 0.902515I
−5.77493 + 0.50478I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826469 + 0.301584I
a = −1.43413 + 1.02708I
b = −0.752423 − 1.020840I
−6.29688 − 12.60120I −7.95324 + 9.37514I
u = 0.826469 − 0.301584I
a = −1.43413 − 1.02708I
b = −0.752423 + 1.020840I
−6.29688 + 12.60120I −7.95324 − 9.37514I
u = −0.829199 + 0.256834I
a = −0.196573 − 0.451034I
b = −0.858127 − 0.711648I
−7.24866 + 6.60173I −9.74629 − 4.48762I
u = −0.829199 − 0.256834I
a = −0.196573 + 0.451034I
b = −0.858127 + 0.711648I
−7.24866 − 6.60173I −9.74629 + 4.48762I
u = 0.834377 + 0.184117I
a = −1.35063 + 0.57913I
b = −0.779630 − 0.965446I
−8.29808 − 4.07556I −10.87765 + 3.19682I
u = 0.834377 − 0.184117I
a = −1.35063 − 0.57913I
b = −0.779630 + 0.965446I
−8.29808 + 4.07556I −10.87765 − 3.19682I
u = −0.839410 + 0.127426I
a = −0.581311 − 0.311001I
b = −0.839261 − 0.795078I
−8.82615 − 1.96225I −11.76893 + 2.26917I
u = −0.839410 − 0.127426I
a = −0.581311 + 0.311001I
b = −0.839261 + 0.795078I
−8.82615 + 1.96225I −11.76893 − 2.26917I
u = −0.433217 + 1.076530I
a = 0.663567 + 1.117850I
b = 0.814296 − 0.862710I
−5.90386 + 6.51028I 0
u = −0.433217 − 1.076530I
a = 0.663567 − 1.117850I
b = 0.814296 + 0.862710I
−5.90386 − 6.51028I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783250 + 0.264115I
a = −1.60999 − 0.87791I
b = −0.739512 + 0.994581I
−3.62130 + 7.46949I −5.36276 − 6.04622I
u = −0.783250 − 0.264115I
a = −1.60999 + 0.87791I
b = −0.739512 − 0.994581I
−3.62130 − 7.46949I −5.36276 + 6.04622I
u = 0.068050 + 1.173920I
a = 0.11077 − 2.34272I
b = −0.412731 + 1.054140I
2.11004 + 4.12289I 0
u = 0.068050 − 1.173920I
a = 0.11077 + 2.34272I
b = −0.412731 − 1.054140I
2.11004 − 4.12289I 0
u = −0.239259 + 1.168840I
a = 0.380988 − 0.383419I
b = −0.714493 + 0.091333I
−0.762339 − 0.275947I 0
u = −0.239259 − 1.168840I
a = 0.380988 + 0.383419I
b = −0.714493 − 0.091333I
−0.762339 + 0.275947I 0
u = 0.777544 + 0.209804I
a = −0.362630 + 0.599070I
b = −0.815410 + 0.732335I
−4.42446 − 1.63033I −7.06387 + 0.91981I
u = 0.777544 − 0.209804I
a = −0.362630 − 0.599070I
b = −0.815410 − 0.732335I
−4.42446 + 1.63033I −7.06387 − 0.91981I
u = −0.168003 + 1.255030I
a = −0.019540 + 0.607170I
b = 0.711034 + 0.763554I
2.47373 − 2.56298I 0
u = −0.168003 − 1.255030I
a = −0.019540 − 0.607170I
b = 0.711034 − 0.763554I
2.47373 + 2.56298I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713006 + 0.095615I
a = 0.334802 + 0.120967I
b = 0.722210 − 0.106046I
−3.96162 + 3.79092I −11.61122 − 4.56726I
u = −0.713006 − 0.095615I
a = 0.334802 − 0.120967I
b = 0.722210 + 0.106046I
−3.96162 − 3.79092I −11.61122 + 4.56726I
u = 0.668399 + 0.237900I
a = 0.67448 − 1.39382I
b = 0.213868 + 1.083920I
−0.04595 − 6.79511I −4.41057 + 8.39005I
u = 0.668399 − 0.237900I
a = 0.67448 + 1.39382I
b = 0.213868 − 1.083920I
−0.04595 + 6.79511I −4.41057 − 8.39005I
u = −0.288293 + 1.320130I
a = 0.367736 − 0.623675I
b = −0.776388 + 0.237242I
0.47634 + 7.41480I 0
u = −0.288293 − 1.320130I
a = 0.367736 + 0.623675I
b = −0.776388 − 0.237242I
0.47634 − 7.41480I 0
u = −0.576067 + 0.282806I
a = 0.82703 + 1.32861I
b = 0.165831 − 1.001990I
2.06976 + 2.29339I −0.00881 − 4.82687I
u = −0.576067 − 0.282806I
a = 0.82703 − 1.32861I
b = 0.165831 + 1.001990I
2.06976 − 2.29339I −0.00881 + 4.82687I
u = −0.132078 + 1.355200I
a = 0.22554 + 2.00262I
b = −0.514621 − 1.021830I
5.19651 − 1.43194I 0
u = −0.132078 − 1.355200I
a = 0.22554 − 2.00262I
b = −0.514621 + 1.021830I
5.19651 + 1.43194I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247258 + 1.348180I
a = 1.55578 + 1.82417I
b = 0.698833 − 0.975302I
3.79061 + 8.31615I 0
u = −0.247258 − 1.348180I
a = 1.55578 − 1.82417I
b = 0.698833 + 0.975302I
3.79061 − 8.31615I 0
u = −0.362756 + 1.332060I
a = −0.581243 + 0.024357I
b = 0.851771 + 0.728928I
−4.25572 + 2.35314I 0
u = −0.362756 − 1.332060I
a = −0.581243 − 0.024357I
b = 0.851771 − 0.728928I
−4.25572 − 2.35314I 0
u = 0.038709 + 1.381560I
a = −0.681056 + 0.333747I
b = −0.200806 − 0.178820I
4.96495 − 2.19922I 0
u = 0.038709 − 1.381560I
a = −0.681056 − 0.333747I
b = −0.200806 + 0.178820I
4.96495 + 2.19922I 0
u = −0.600064 + 0.128543I
a = −2.60142 + 0.17153I
b = −0.673393 + 0.902935I
−0.89912 + 5.19420I −7.11874 − 7.76852I
u = −0.600064 − 0.128543I
a = −2.60142 − 0.17153I
b = −0.673393 − 0.902935I
−0.89912 − 5.19420I −7.11874 + 7.76852I
u = −0.454019 + 0.410951I
a = 1.32194 + 1.40913I
b = −0.032813 − 0.909390I
2.60505 + 0.90512I 2.28754 − 4.05492I
u = −0.454019 − 0.410951I
a = 1.32194 − 1.40913I
b = −0.032813 + 0.909390I
2.60505 − 0.90512I 2.28754 + 4.05492I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23621 + 1.39451I
a = −0.71816 − 2.47299I
b = −0.144636 + 1.099660I
7.38356 + 5.30799I 0
u = −0.23621 − 1.39451I
a = −0.71816 + 2.47299I
b = −0.144636 − 1.099660I
7.38356 − 5.30799I 0
u = 0.35405 + 1.37132I
a = 1.00055 − 1.87993I
b = 0.757561 + 1.008790I
−3.39478 − 8.35215I 0
u = 0.35405 − 1.37132I
a = 1.00055 + 1.87993I
b = 0.757561 − 1.008790I
−3.39478 + 8.35215I 0
u = 0.27368 + 1.39259I
a = −0.67813 + 2.52469I
b = −0.157124 − 1.142510I
5.14150 − 10.24960I 0
u = 0.27368 − 1.39259I
a = −0.67813 − 2.52469I
b = −0.157124 + 1.142510I
5.14150 + 10.24960I 0
u = 0.354969 + 0.458153I
a = 1.89488 − 1.64861I
b = −0.181249 + 0.882030I
1.20125 + 3.56606I 0.00892 − 1.69990I
u = 0.354969 − 0.458153I
a = 1.89488 + 1.64861I
b = −0.181249 − 0.882030I
1.20125 − 3.56606I 0.00892 + 1.69990I
u = 0.31969 + 1.38632I
a = −0.720461 − 0.134519I
b = 0.839786 − 0.673215I
0.63547 − 5.59776I 0
u = 0.31969 − 1.38632I
a = −0.720461 + 0.134519I
b = 0.839786 + 0.673215I
0.63547 + 5.59776I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16228 + 1.42710I
a = −0.95852 − 2.33237I
b = −0.069061 + 0.988963I
8.46071 + 3.17427I 0
u = −0.16228 − 1.42710I
a = −0.95852 + 2.33237I
b = −0.069061 − 0.988963I
8.46071 − 3.17427I 0
u = 0.07272 + 1.44133I
a = −0.081833 + 1.365030I
b = −0.512649 − 0.683277I
4.65094 − 2.50593I 0
u = 0.07272 − 1.44133I
a = −0.081833 − 1.365030I
b = −0.512649 + 0.683277I
4.65094 + 2.50593I 0
u = 0.13184 + 1.43845I
a = −1.17422 + 2.21897I
b = −0.018498 − 0.919588I
7.23839 + 1.71145I 0
u = 0.13184 − 1.43845I
a = −1.17422 − 2.21897I
b = −0.018498 + 0.919588I
7.23839 − 1.71145I 0
u = −0.31835 + 1.41515I
a = 1.08570 + 2.10712I
b = 0.728768 − 1.031050I
1.72641 + 11.46270I 0
u = −0.31835 − 1.41515I
a = 1.08570 − 2.10712I
b = 0.728768 + 1.031050I
1.72641 − 11.46270I 0
u = −0.34234 + 1.41472I
a = −0.781229 + 0.066281I
b = 0.870421 + 0.660227I
−1.93901 + 10.83450I 0
u = −0.34234 − 1.41472I
a = −0.781229 − 0.066281I
b = 0.870421 − 0.660227I
−1.93901 − 10.83450I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07678 + 1.47131I
a = 0.25274 + 1.75932I
b = −0.604385 − 0.938277I
5.41135 − 2.06230I 0
u = −0.07678 − 1.47131I
a = 0.25274 − 1.75932I
b = −0.604385 + 0.938277I
5.41135 + 2.06230I 0
u = 0.33452 + 1.43819I
a = 0.97375 − 2.16552I
b = 0.735962 + 1.048690I
−0.7474 − 16.8065I 0
u = 0.33452 − 1.43819I
a = 0.97375 + 2.16552I
b = 0.735962 − 1.048690I
−0.7474 + 16.8065I 0
u = 0.409816 + 0.325133I
a = 0.638033 − 0.588897I
b = 0.475752 + 0.559238I
−1.05079 − 0.99662I −8.88984 + 5.17874I
u = 0.409816 − 0.325133I
a = 0.638033 + 0.588897I
b = 0.475752 − 0.559238I
−1.05079 + 0.99662I −8.88984 − 5.17874I
u = 0.226772 + 0.416872I
a = 1.164160 + 0.133562I
b = −0.317397 + 0.274980I
−0.50948 − 1.44830I −5.05239 + 5.14744I
u = 0.226772 − 0.416872I
a = 1.164160 − 0.133562I
b = −0.317397 − 0.274980I
−0.50948 + 1.44830I −5.05239 − 5.14744I
u = −0.02923 + 1.54028I
a = 0.29040 − 1.47834I
b = −0.696662 + 0.798330I
2.96237 − 0.76259I 0
u = −0.02923 − 1.54028I
a = 0.29040 + 1.47834I
b = −0.696662 − 0.798330I
2.96237 + 0.76259I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.367236 + 0.275592I
a = 0.364861 − 0.926737I
b = 0.540306 + 0.956806I
0.03876 − 3.21058I −4.83770 − 1.13154I
u = −0.367236 − 0.275592I
a = 0.364861 + 0.926737I
b = 0.540306 − 0.956806I
0.03876 + 3.21058I −4.83770 + 1.13154I
u = 0.06999 + 1.54596I
a = 0.36301 − 1.66914I
b = −0.688951 + 0.926678I
3.36051 + 6.09970I 0
u = 0.06999 − 1.54596I
a = 0.36301 + 1.66914I
b = −0.688951 − 0.926678I
3.36051 − 6.09970I 0
13
II. I
u
2
= h4b + 2a − u + 2, 2a
2
− 2au + 5, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−2
a
4
=
u
−u
a
10
=
−1
0
a
6
=
−u
u
a
12
=
a
−
1
2
a +
1
4
u −
1
2
a
7
=
1
4
au +
1
2
a −
1
4
−
1
2
a +
1
4
u +
1
2
a
3
=
1
4
au +
3
4
u −
3
4
−u + 1
a
2
=
3
4
au +
1
4
u −
1
4
−
1
2
au −
1
2
u +
1
2
a
11
=
1
2
a +
1
4
u −
1
2
−
1
2
a +
1
4
u −
1
2
a
1
=
1
4
au +
1
2
a −
1
4
−
1
2
a +
1
4
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 2u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
10
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
+ 2)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y + 2)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = − 1.024940I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I − 6.92820I
u = 1.414210I
a = 2.43916I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 6.92820I
u = − 1.414210I
a = 1.024940I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 6.92820I
u = − 1.414210I
a = − 2.43916I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I − 6.92820I
17
III. I
u
3
= h−1.28 × 10
4
a
4
u
2
− 3476a
3
u
2
+ · · · + 1.35 × 10
5
a − 1.45 ×
10
5
, 2a
4
u
2
− 2a
3
u
2
+ · · · + 9a − 7, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
u
u
2
− u + 1
a
10
=
u
2
+ 1
u
2
− u + 1
a
6
=
−1
0
a
12
=
a
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· − 0.862157a + 0.926991
a
7
=
0.0462799a
4
u
2
+ 0.214908a
3
u
2
+ ··· − 0.0906182a + 0.639309
−0.156046a
4
u
2
− 0.152054a
3
u
2
+ ··· + 0.525174a − 0.606940
a
3
=
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· + 0.137843a + 0.926991
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· − 0.862157a + 0.926991
a
2
=
a
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· − 0.862157a + 0.926991
a
11
=
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· + 0.137843a + 0.926991
0.0814401a
4
u
2
+ 0.0222011a
3
u
2
+ ··· − 0.862157a + 0.926991
a
1
=
0.100799a
4
u
2
+ 0.139817a
3
u
2
+ ··· + 0.601377a + 0.480325
0.0848572a
4
u
2
+ 0.182661a
3
u
2
+ ··· − 0.604583a + 0.979083
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
+ 4u − 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 6u
14
+ ··· + 2u − 1
c
2
, c
6
, c
7
c
11
u
15
+ 3u
13
+ ··· − u
2
+ 1
c
3
u
15
+ 3u
13
+ ··· + 12u + 5
c
4
, c
8
, c
9
(u
3
+ u
2
+ 2u + 1)
5
c
5
(u
3
− u
2
+ 1)
5
c
10
, c
12
u
15
− 6u
14
+ ··· + 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
15
+ 6y
14
+ ··· + 10y −1
c
2
, c
6
, c
7
c
11
y
15
+ 6y
14
+ ··· + 2y −1
c
3
y
15
+ 6y
14
+ ··· + 214y −25
c
4
, c
8
, c
9
(y
3
+ 3y
2
+ 2y −1)
5
c
5
(y
3
− y
2
+ 2y −1)
5
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.408569 − 0.516978I
b = 0.736794 − 0.720585I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = 0.232241 + 0.578143I
b = −0.683915 − 0.233449I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = 0.33425 − 2.10096I
b = −0.502216 + 1.085210I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = 1.72552 − 1.49654I
b = 0.692676 + 0.944809I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.55873 + 2.41178I
b = −0.243339 − 1.075990I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.408569 + 0.516978I
b = 0.736794 + 0.720585I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.232241 − 0.578143I
b = −0.683915 + 0.233449I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.33425 + 2.10096I
b = −0.502216 − 1.085210I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = 1.72552 + 1.49654I
b = 0.692676 − 0.944809I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.55873 − 2.41178I
b = −0.243339 + 1.075990I
3.02413 + 2.82812I −2.49024 − 2.97945I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = 0.486937 + 1.149840I
b = 0.395722 − 1.025370I
−1.11345 −9.01950
u = 0.569840
a = 0.486937 − 1.149840I
b = 0.395722 + 1.025370I
−1.11345 −9.01950
u = 0.569840
a = 0.528223
b = 0.544964
−1.11345 −9.01950
u = 0.569840
a = −2.07577 + 1.38334I
b = −0.668204 + 0.836779I
−1.11345 −9.01950
u = 0.569840
a = −2.07577 − 1.38334I
b = −0.668204 − 0.836779I
−1.11345 −9.01950
22
IV. I
u
4
= hau + 9b + 4a + u + 4, 2a
2
+ au − 3u + 5, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−2
a
4
=
u
−u
a
10
=
−1
0
a
6
=
−u
u
a
12
=
a
−
1
9
au −
4
9
a −
1
9
u −
4
9
a
7
=
−
1
9
au +
5
9
a +
7
18
u −
4
9
−
1
9
au −
4
9
a −
1
9
u +
5
9
a
3
=
−
1
9
au +
5
9
a +
8
9
u +
5
9
−
1
9
au −
4
9
a −
10
9
u −
4
9
a
2
=
−
5
9
au +
7
9
a +
4
9
u +
7
9
1
3
au −
2
3
a −
2
3
u −
2
3
a
11
=
−
1
9
au +
5
9
a −
1
9
u −
4
9
−
1
9
au −
4
9
a −
1
9
u −
4
9
a
1
=
−
1
9
au +
5
9
a +
7
18
u −
4
9
−
1
9
au −
4
9
a −
1
9
u +
5
9
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
10
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
+ 2)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y + 2)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.61237 + 1.37850I
b = −0.500000 − 0.866025I
4.93480 0
u = 1.414210I
a = −0.61237 − 2.08560I
b = −0.500000 + 0.866025I
4.93480 0
u = − 1.414210I
a = 0.61237 − 1.37850I
b = −0.500000 + 0.866025I
4.93480 0
u = − 1.414210I
a = −0.61237 + 2.08560I
b = −0.500000 − 0.866025I
4.93480 0
26
V. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
4
=
v
0
a
10
=
1
0
a
6
=
v
0
a
12
=
0
v + 1
a
7
=
1
−v
a
3
=
−1
−1
a
2
=
−v − 2
−1
a
11
=
v + 1
v + 1
a
1
=
−1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v − 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
− 4.05977I −6.00000 + 6.92820I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
4.05977I −6.00000 − 6.92820I
30
VI. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
1
0
a
9
=
1
0
a
4
=
1
0
a
10
=
1
0
a
6
=
1
0
a
12
=
0
b
a
7
=
1
−b + 1
a
3
=
b
b
a
2
=
0
b
a
11
=
b
b
a
1
=
−1
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
0 0
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
0 0
34
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
15
+ 6u
14
+ ··· + 2u − 1)(u
84
+ 43u
83
+ ··· + 80u + 9)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
15
+ 3u
13
+ ··· − u
2
+ 1)
· (u
84
− 3u
83
+ ··· − 8u + 3)
c
3
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
15
+ 3u
13
+ ··· + 12u + 5)
· (u
84
+ 3u
83
+ ··· + 44270u + 12039)
c
4
, c
8
, c
9
u
4
(u
2
+ 2)
4
(u
3
+ u
2
+ 2u + 1)
5
(u
84
− 4u
83
+ ··· − 96u + 16)
c
5
u
4
(u
2
+ 2)
4
(u
3
− u
2
+ 1)
5
(u
84
+ 4u
83
+ ··· + 192992u + 185296)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
15
+ 3u
13
+ ··· − u
2
+ 1)
· (u
84
− 3u
83
+ ··· − 8u + 3)
c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
15
+ 3u
13
+ ··· − u
2
+ 1)
· (u
84
+ 3u
83
+ ··· − 22u + 3)
c
10
((u
2
+ u + 1)
6
)(u
15
− 6u
14
+ ··· + 2u + 1)(u
84
− 27u
83
+ ··· − 80u + 9)
c
11
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
15
+ 3u
13
+ ··· − u
2
+ 1)
· (u
84
+ 3u
83
+ ··· − 22u + 3)
c
12
((u
2
− u + 1)
6
)(u
15
− 6u
14
+ ··· + 2u + 1)(u
84
− 27u
83
+ ··· − 80u + 9)
35
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
15
+ 6y
14
+ ··· + 10y − 1)
· (y
84
+ 3y
83
+ ··· + 1988y + 81)
c
2
, c
6
((y
2
+ y + 1)
6
)(y
15
+ 6y
14
+ ··· + 2y − 1)(y
84
+ 43y
83
+ ··· + 80y + 9)
c
3
((y
2
+ y + 1)
6
)(y
15
+ 6y
14
+ ··· + 214y − 25)
· (y
84
− 37y
83
+ ··· + 1982120948y + 144937521)
c
4
, c
8
, c
9
y
4
(y + 2)
8
(y
3
+ 3y
2
+ 2y − 1)
5
(y
84
+ 76y
83
+ ··· + 9728y
2
+ 256)
c
5
y
4
(y + 2)
8
(y
3
− y
2
+ 2y − 1)
5
· (y
84
− 4y
83
+ ··· + 562686205952y + 34334607616)
c
7
, c
11
((y
2
+ y + 1)
6
)(y
15
+ 6y
14
+ ··· + 2y − 1)(y
84
+ 27y
83
+ ··· + 80y + 9)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
15
+ 6y
14
+ ··· + 10y − 1)
· (y
84
+ 67y
83
+ ··· + 35684y + 81)
36
