12a
1209
(K12a
1209
)
A knot diagram
1
Linearized knot diagam
5 6 7 8 2 10 11 12 1 3 4 9
Solving Sequence
1,5
2 6
3,9
10 7 12 8 4 11
c
1
c
5
c
2
c
9
c
6
c
12
c
8
c
4
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.48893 × 10
298
u
111
− 4.47573 × 10
299
u
110
+ ··· + 3.13728 × 10
299
b − 4.27963 × 10
300
,
4.44331 × 10
302
u
111
− 2.47868 × 10
303
u
110
+ ··· + 1.02338 × 10
303
a − 2.27353 × 10
304
,
u
112
− 4u
111
+ ··· − 55u − 7i
I
u
2
= h3u
13
− u
12
− 26u
11
+ 2u
10
+ 78u
9
+ 11u
8
− 79u
7
− 32u
6
− 23u
5
+ 18u
4
+ 58u
3
+ 12u
2
+ b + 13u + 1,
− u
13
+ 8u
11
+ 4u
10
− 22u
9
− 22u
8
+ 17u
7
+ 36u
6
+ 17u
5
− 9u
4
− 22u
3
− 17u
2
+ a − 6u − 1,
u
14
+ u
13
− 9u
12
− 11u
11
+ 26u
10
+ 39u
9
− 19u
8
− 47u
7
− 24u
6
− 4u
5
+ 26u
4
+ 31u
3
+ 12u
2
+ 6u + 1i
I
u
3
= ha
3
− 2a
2
+ b − a + 2, a
4
− 3a
3
+ 4a − 1, u − 1i
I
u
4
= hb − 1, a
2
+ au + 2a − u − 2, u
2
+ u − 1i
* 4 irreducible components of dim
C
= 0, with total 134 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
= h7.49 × 10
298
u
111
− 4.48 × 10
299
u
110
+ · · · + 3.14 × 10
299
b − 4.28 ×
10
300
, 4.44 × 10
302
u
111
− 2.48 × 10
303
u
110
+ · · · + 1.02 × 10
303
a − 2.27 ×
10
304
, u
112
− 4u
111
+ · · · − 55u − 7i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−0.434180u
111
+ 2.42206u
110
+ ··· + 77.6450u + 22.2159
−0.238708u
111
+ 1.42663u
110
+ ··· + 65.6634u + 13.6412
a
10
=
−0.672888u
111
+ 3.84868u
110
+ ··· + 143.308u + 35.8571
−0.238708u
111
+ 1.42663u
110
+ ··· + 65.6634u + 13.6412
a
7
=
−0.799898u
111
+ 3.60747u
110
+ ··· + 114.720u + 26.3507
−0.436005u
111
+ 1.72349u
110
+ ··· + 28.8713u + 6.86379
a
12
=
0.697419u
111
− 2.48429u
110
+ ··· + 3.78721u − 4.87783
0.995487u
111
− 3.33126u
110
+ ··· − 20.6507u − 6.74406
a
8
=
0.549522u
111
− 2.63485u
110
+ ··· − 79.2880u − 21.7160
−0.483500u
111
+ 0.733367u
110
+ ··· − 78.0141u − 13.2688
a
4
=
−1.92915u
111
+ 8.16559u
110
+ ··· + 238.894u + 50.0542
−0.674264u
111
+ 3.03349u
110
+ ··· + 73.4607u + 17.5378
a
11
=
−0.788999u
111
+ 3.82299u
110
+ ··· + 101.778u + 28.1283
0.0637123u
111
+ 0.566343u
110
+ ··· + 76.1515u + 14.4215
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.05210u
111
− 10.3041u
110
+ ··· − 50.8805u − 13.6156
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
112
+ 4u
111
+ ··· + 55u − 7
c
3
u
112
+ 5u
111
+ ··· − 376u + 16
c
4
u
112
+ 2u
111
+ ··· + 403u − 61
c
6
u
112
− 2u
111
+ ··· − 403u − 61
c
7
u
112
− 5u
111
+ ··· + 376u + 16
c
8
, c
9
, c
12
u
112
− 4u
111
+ ··· − 55u − 7
c
10
u
112
− 24u
110
+ ··· + 1642u − 3505
c
11
u
112
− 24u
110
+ ··· − 1642u − 3505
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
9
, c
12
y
112
− 116y
111
+ ··· − 1625y + 49
c
3
, c
7
y
112
− 29y
111
+ ··· − 62016y + 256
c
4
, c
6
y
112
+ 4y
111
+ ··· − 334917y + 3721
c
10
, c
11
y
112
− 48y
111
+ ··· − 513627024y + 12285025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321679 + 0.955410I
a = −2.48730 − 0.40966I
b = 1.44602 − 0.14963I
3.88943 − 4.41203I 0
u = 0.321679 − 0.955410I
a = −2.48730 + 0.40966I
b = 1.44602 + 0.14963I
3.88943 + 4.41203I 0
u = −0.405419 + 0.846552I
a = −0.040244 − 0.553258I
b = −0.344832 + 0.366948I
0.51401 − 4.74927I 0
u = −0.405419 − 0.846552I
a = −0.040244 + 0.553258I
b = −0.344832 − 0.366948I
0.51401 + 4.74927I 0
u = −0.547671 + 0.952094I
a = −1.99606 + 0.66515I
b = 1.52327 + 0.24630I
6.7615 + 13.1536I 0
u = −0.547671 − 0.952094I
a = −1.99606 − 0.66515I
b = 1.52327 − 0.24630I
6.7615 − 13.1536I 0
u = −0.556694 + 0.699427I
a = 0.695091 + 0.018015I
b = −0.556694 − 0.699427I
9.67295I 0
u = −0.556694 − 0.699427I
a = 0.695091 − 0.018015I
b = −0.556694 + 0.699427I
− 9.67295I 0
u = 0.838087 + 0.304732I
a = 0.924454 + 0.042715I
b = −0.551175 − 0.110613I
−1.167220 + 0.162853I 0
u = 0.838087 − 0.304732I
a = 0.924454 − 0.042715I
b = −0.551175 + 0.110613I
−1.167220 − 0.162853I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551002 + 0.686614I
a = 0.776150 − 0.007145I
b = −0.328491 + 0.467072I
−1.88406 − 2.20530I 0
u = 0.551002 − 0.686614I
a = 0.776150 + 0.007145I
b = −0.328491 − 0.467072I
−1.88406 + 2.20530I 0
u = 0.871319 + 0.097886I
a = 1.204680 − 0.009200I
b = 0.405993 + 0.099359I
−0.792868 + 0.014090I 0
u = 0.871319 − 0.097886I
a = 1.204680 + 0.009200I
b = 0.405993 − 0.099359I
−0.792868 − 0.014090I 0
u = 0.483629 + 0.729393I
a = −0.128824 + 0.158406I
b = 0.079070 − 0.525923I
−1.64840 − 2.53965I 0
u = 0.483629 − 0.729393I
a = −0.128824 − 0.158406I
b = 0.079070 + 0.525923I
−1.64840 + 2.53965I 0
u = −0.506988 + 0.711723I
a = 1.85722 − 1.07160I
b = −1.52140 − 0.22264I
8.66599 + 5.50260I 0
u = −0.506988 − 0.711723I
a = 1.85722 + 1.07160I
b = −1.52140 + 0.22264I
8.66599 − 5.50260I 0
u = 0.306485 + 1.115190I
a = 1.99195 + 0.40121I
b = −1.317420 + 0.100162I
2.53996 − 4.69116I 0
u = 0.306485 − 1.115190I
a = 1.99195 − 0.40121I
b = −1.317420 − 0.100162I
2.53996 + 4.69116I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.040390 + 0.527001I
a = 0.887183 + 0.696092I
b = −1.47232 − 0.13274I
5.47290 + 1.48951I 0
u = 1.040390 − 0.527001I
a = 0.887183 − 0.696092I
b = −1.47232 + 0.13274I
5.47290 − 1.48951I 0
u = −0.533311 + 0.624626I
a = 1.55211 − 0.93488I
b = −1.51214 + 0.07926I
8.52713 − 0.93448I 0
u = −0.533311 − 0.624626I
a = 1.55211 + 0.93488I
b = −1.51214 − 0.07926I
8.52713 + 0.93448I 0
u = 0.171948 + 0.794989I
a = 2.24121 + 0.38931I
b = −1.50281 + 0.25807I
8.09567 − 6.13786I 0
u = 0.171948 − 0.794989I
a = 2.24121 − 0.38931I
b = −1.50281 − 0.25807I
8.09567 + 6.13786I 0
u = 0.416047 + 0.685828I
a = −2.09609 − 1.79075I
b = 1.48957 + 0.00500I
7.38069 − 3.65080I 0
u = 0.416047 − 0.685828I
a = −2.09609 + 1.79075I
b = 1.48957 − 0.00500I
7.38069 + 3.65080I 0
u = 0.760960
a = −2.05033
b = 1.65282
6.71801 0
u = 1.265270 + 0.034808I
a = 0.423245 + 0.826019I
b = 0.091380 + 0.347715I
−2.44897 + 0.28218I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.265270 − 0.034808I
a = 0.423245 − 0.826019I
b = 0.091380 − 0.347715I
−2.44897 − 0.28218I 0
u = 1.202520 + 0.425853I
a = −1.53659 − 1.21523I
b = 1.294470 − 0.019710I
1.12792 − 0.89446I 0
u = 1.202520 − 0.425853I
a = −1.53659 + 1.21523I
b = 1.294470 + 0.019710I
1.12792 + 0.89446I 0
u = −0.714941 + 1.068540I
a = −1.66011 + 0.53628I
b = 1.45359 − 0.14068I
6.42066 − 6.67264I 0
u = −0.714941 − 1.068540I
a = −1.66011 − 0.53628I
b = 1.45359 + 0.14068I
6.42066 + 6.67264I 0
u = 1.294470 + 0.019710I
a = −0.199984 − 1.223820I
b = 1.202520 − 0.425853I
−1.12792 − 0.89446I 0
u = 1.294470 − 0.019710I
a = −0.199984 + 1.223820I
b = 1.202520 + 0.425853I
−1.12792 + 0.89446I 0
u = 0.683717
a = 0.968888
b = −0.237400
−1.21099 −8.47520
u = −1.317420 + 0.100162I
a = −0.317926 + 0.663451I
b = 0.306485 + 1.115190I
−2.53996 + 4.69116I 0
u = −1.317420 − 0.100162I
a = −0.317926 − 0.663451I
b = 0.306485 − 1.115190I
−2.53996 − 4.69116I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.333370 + 0.034104I
a = 0.71226 − 1.76474I
b = −1.333370 − 0.034104I
− 5.25957I 0
u = −1.333370 − 0.034104I
a = 0.71226 + 1.76474I
b = −1.333370 + 0.034104I
5.25957I 0
u = 1.33647
a = −0.563365
b = 2.14347
3.34549 0
u = −1.34328
a = 1.66814
b = −1.71082
4.88748 0
u = −1.380120 + 0.088053I
a = −1.29268 + 0.86109I
b = 1.42691 + 0.18223I
−2.29797 + 1.74948I 0
u = −1.380120 − 0.088053I
a = −1.29268 − 0.86109I
b = 1.42691 − 0.18223I
−2.29797 − 1.74948I 0
u = −1.355270 + 0.283343I
a = 0.85616 − 1.19537I
b = −1.49734 − 0.39913I
3.28444 + 9.97047I 0
u = −1.355270 − 0.283343I
a = 0.85616 + 1.19537I
b = −1.49734 + 0.39913I
3.28444 − 9.97047I 0
u = −1.382200 + 0.144894I
a = −0.440287 + 0.676590I
b = 1.57137 + 0.57546I
1.27966 + 2.23912I 0
u = −1.382200 − 0.144894I
a = −0.440287 − 0.676590I
b = 1.57137 − 0.57546I
1.27966 − 2.23912I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169614 + 0.578662I
a = 1.44471 + 1.42829I
b = −0.434375 + 0.022634I
0.98397 − 3.56679I 7.85774 + 7.70365I
u = 0.169614 − 0.578662I
a = 1.44471 − 1.42829I
b = −0.434375 − 0.022634I
0.98397 + 3.56679I 7.85774 − 7.70365I
u = −1.404440 + 0.151869I
a = −0.008953 − 1.383810I
b = −0.113310 − 0.195536I
−4.05419 + 5.99508I 0
u = −1.404440 − 0.151869I
a = −0.008953 + 1.383810I
b = −0.113310 + 0.195536I
−4.05419 − 5.99508I 0
u = 1.41365 + 0.08564I
a = 1.17589 + 1.51053I
b = −1.49773 + 0.25118I
−1.12496 − 7.09143I 0
u = 1.41365 − 0.08564I
a = 1.17589 − 1.51053I
b = −1.49773 − 0.25118I
−1.12496 + 7.09143I 0
u = −0.328491 + 0.467072I
a = −0.872955 + 0.465938I
b = 0.551002 + 0.686614I
1.88406 + 2.20530I 7.62600 − 6.55616I
u = −0.328491 − 0.467072I
a = −0.872955 − 0.465938I
b = 0.551002 − 0.686614I
1.88406 − 2.20530I 7.62600 + 6.55616I
u = −0.551175 + 0.110613I
a = 0.601595 + 0.017597I
b = 0.838087 − 0.304732I
1.167220 + 0.162853I 6.34896 − 5.05762I
u = −0.551175 − 0.110613I
a = 0.601595 − 0.017597I
b = 0.838087 + 0.304732I
1.167220 − 0.162853I 6.34896 + 5.05762I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42691 + 0.18223I
a = 0.316859 + 0.960364I
b = −1.380120 + 0.088053I
2.29797 − 1.74948I 0
u = 1.42691 − 0.18223I
a = 0.316859 − 0.960364I
b = −1.380120 − 0.088053I
2.29797 + 1.74948I 0
u = 0.413365 + 0.362962I
a = −1.84869 − 0.43224I
b = 1.66446 − 0.15584I
6.75617 − 0.15175I 1.77908 + 7.36297I
u = 0.413365 − 0.362962I
a = −1.84869 + 0.43224I
b = 1.66446 + 0.15584I
6.75617 + 0.15175I 1.77908 − 7.36297I
u = 1.44602 + 0.14963I
a = −0.219608 − 0.789683I
b = 0.321679 − 0.955410I
−3.88943 − 4.41203I 0
u = 1.44602 − 0.14963I
a = −0.219608 + 0.789683I
b = 0.321679 + 0.955410I
−3.88943 + 4.41203I 0
u = 1.45359 + 0.14068I
a = 0.154262 − 0.361321I
b = −0.714941 − 1.068540I
−6.42066 − 6.67264I 0
u = 1.45359 − 0.14068I
a = 0.154262 + 0.361321I
b = −0.714941 + 1.068540I
−6.42066 + 6.67264I 0
u = 0.079070 + 0.525923I
a = −0.466179 + 0.393862I
b = 0.483629 − 0.729393I
1.64840 − 2.53965I 7.80985 + 5.36906I
u = 0.079070 − 0.525923I
a = −0.466179 − 0.393862I
b = 0.483629 + 0.729393I
1.64840 + 2.53965I 7.80985 − 5.36906I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47232 + 0.13274I
a = −0.593293 − 0.242129I
b = 1.040390 − 0.527001I
−5.47290 + 1.48951I 0
u = −1.47232 − 0.13274I
a = −0.593293 + 0.242129I
b = 1.040390 + 0.527001I
−5.47290 − 1.48951I 0
u = 1.48957 + 0.00500I
a = −0.650175 + 0.780207I
b = 0.416047 + 0.685828I
−7.38069 + 3.65080I 0
u = 1.48957 − 0.00500I
a = −0.650175 − 0.780207I
b = 0.416047 − 0.685828I
−7.38069 − 3.65080I 0
u = −0.344832 + 0.366948I
a = 0.789260 + 0.113577I
b = −0.405419 + 0.846552I
−0.51401 + 4.74927I −1.10748 − 10.25917I
u = −0.344832 − 0.366948I
a = 0.789260 − 0.113577I
b = −0.405419 − 0.846552I
−0.51401 − 4.74927I −1.10748 + 10.25917I
u = −1.51214 + 0.07926I
a = 0.321771 + 0.335141I
b = −0.533311 + 0.624626I
−8.52713 + 0.93448I 0
u = −1.51214 − 0.07926I
a = 0.321771 − 0.335141I
b = −0.533311 − 0.624626I
−8.52713 − 0.93448I 0
u = −1.49773 + 0.25118I
a = −0.66168 + 1.53344I
b = 1.41365 + 0.08564I
1.12496 + 7.09143I 0
u = −1.49773 − 0.25118I
a = −0.66168 − 1.53344I
b = 1.41365 − 0.08564I
1.12496 − 7.09143I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50281 + 0.25807I
a = −0.328105 + 0.408347I
b = 0.171948 + 0.794989I
−8.09567 + 6.13786I 0
u = −1.50281 − 0.25807I
a = −0.328105 − 0.408347I
b = 0.171948 − 0.794989I
−8.09567 − 6.13786I 0
u = −1.48639 + 0.34563I
a = −1.34811 + 1.09317I
b = 1.53017 + 0.25062I
−1.98950 + 9.04012I 0
u = −1.48639 − 0.34563I
a = −1.34811 − 1.09317I
b = 1.53017 − 0.25062I
−1.98950 − 9.04012I 0
u = −1.52140 + 0.22264I
a = 0.567500 − 0.505341I
b = −0.506988 − 0.711723I
−8.66599 + 5.50260I 0
u = −1.52140 − 0.22264I
a = 0.567500 + 0.505341I
b = −0.506988 + 0.711723I
−8.66599 − 5.50260I 0
u = 1.52327 + 0.24630I
a = 0.487720 + 0.544350I
b = −0.547671 + 0.952094I
−6.7615 − 13.1536I 0
u = 1.52327 − 0.24630I
a = 0.487720 − 0.544350I
b = −0.547671 − 0.952094I
−6.7615 + 13.1536I 0
u = −1.49734 + 0.39913I
a = 1.15254 − 1.01466I
b = −1.355270 − 0.283343I
−3.28444 + 9.97047I 0
u = −1.49734 − 0.39913I
a = 1.15254 + 1.01466I
b = −1.355270 + 0.283343I
−3.28444 − 9.97047I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53017 + 0.25062I
a = 0.669484 + 1.154560I
b = −1.48639 + 0.34563I
1.98950 − 9.04012I 0
u = 1.53017 − 0.25062I
a = 0.669484 − 1.154560I
b = −1.48639 − 0.34563I
1.98950 + 9.04012I 0
u = −0.434375 + 0.022634I
a = −1.63358 + 1.82737I
b = 0.169614 + 0.578662I
−0.98397 + 3.56679I −7.85774 − 7.70365I
u = −0.434375 − 0.022634I
a = −1.63358 − 1.82737I
b = 0.169614 − 0.578662I
−0.98397 − 3.56679I −7.85774 + 7.70365I
u = 0.405993 + 0.099359I
a = −3.37524 + 0.24419I
b = 0.871319 + 0.097886I
0.792868 − 0.014090I 14.9886 + 7.9999I
u = 0.405993 − 0.099359I
a = −3.37524 − 0.24419I
b = 0.871319 − 0.097886I
0.792868 + 0.014090I 14.9886 − 7.9999I
u = 1.55311 + 0.34453I
a = −1.05597 − 1.08729I
b = 1.55311 − 0.34453I
− 17.8765I 0
u = 1.55311 − 0.34453I
a = −1.05597 + 1.08729I
b = 1.55311 + 0.34453I
17.8765I 0
u = −1.59684
a = 0.697025
b = −0.277564
−8.75489 0
u = 0.091380 + 0.347715I
a = −4.47473 + 0.57917I
b = 1.265270 + 0.034808I
2.44897 − 0.28218I 0.405352 + 1.322822I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.091380 − 0.347715I
a = −4.47473 − 0.57917I
b = 1.265270 − 0.034808I
2.44897 + 0.28218I 0.405352 − 1.322822I
u = 1.65282
a = 0.183014
b = 0.760960
−6.71801 0
u = 1.66446 + 0.15584I
a = −0.099057 − 0.176948I
b = 0.413365 − 0.362962I
−6.75617 − 0.15175I 0
u = 1.66446 − 0.15584I
a = −0.099057 + 0.176948I
b = 0.413365 + 0.362962I
−6.75617 + 0.15175I 0
u = 1.57137 + 0.57546I
a = 1.301010 + 0.520573I
b = −1.382200 + 0.144894I
−1.27966 − 2.23912I 0
u = 1.57137 − 0.57546I
a = 1.301010 − 0.520573I
b = −1.382200 − 0.144894I
−1.27966 + 2.23912I 0
u = −1.71082
a = 0.0335132
b = −1.34328
−4.88748 0
u = −0.277564
a = −2.41318
b = −1.59684
8.75489 11.2650
u = −0.237400
a = 2.10670
b = 0.683717
1.21099 8.47520
u = −0.113310 + 0.195536I
a = 9.33406 − 3.30415I
b = −1.404440 − 0.151869I
4.05419 + 5.99508I −2.99141 − 8.55802I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113310 − 0.195536I
a = 9.33406 + 3.30415I
b = −1.404440 + 0.151869I
4.05419 − 5.99508I −2.99141 + 8.55802I
u = 2.14347
a = −0.985209
b = 1.33647
−3.34549 0
16
II.
I
u
2
= h3u
13
−u
12
+· · ·+b+1, −u
13
+8u
11
+· · ·+a−1, u
14
+u
13
+· · ·+6u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
13
− 8u
11
+ ··· + 6u + 1
−3u
13
+ u
12
+ ··· − 13u − 1
a
10
=
−2u
13
+ u
12
+ ··· + 5u
2
− 7u
−3u
13
+ u
12
+ ··· − 13u − 1
a
7
=
−u
13
+ 9u
11
+ ··· − 3u − 2
3u
13
− u
12
+ ··· + 13u + 1
a
12
=
3u
13
− u
12
+ ··· + 13u + 4
−10u
13
+ 5u
12
+ ··· − 35u − 4
a
8
=
−u
13
+ 9u
11
+ ··· − 3u − 3
11u
13
− 5u
12
+ ··· + 39u + 4
a
4
=
2u
13
− u
12
+ ··· + 10u + 1
−8u
13
+ 2u
12
+ ··· − 31u − 8
a
11
=
3u
13
− u
12
+ ··· + 14u + 3
−7u
13
+ 3u
12
+ ··· − 28u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12u
13
+ 5u
12
− 108u
11
− 69u
10
+ 327u
9
+ 273u
8
− 311u
7
−
362u
6
− 159u
5
+ 17u
4
+ 288u
3
+ 207u
2
+ 81u + 36
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u
14
+ u
13
+ ··· + 6u + 1
c
3
u
14
− 4u
13
+ ··· + 91u − 29
c
4
u
14
+ u
13
+ ··· + u − 1
c
5
, c
8
, c
9
u
14
− u
13
+ ··· − 6u + 1
c
6
u
14
− u
13
+ ··· − u − 1
c
7
u
14
+ 4u
13
+ ··· − 91u − 29
c
10
u
14
− u
13
+ ··· − u + 1
c
11
u
14
+ u
13
+ ··· + u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
9
, c
12
y
14
− 19y
13
+ ··· − 12y + 1
c
3
, c
7
y
14
− 6y
13
+ ··· − 1611y + 841
c
4
, c
6
y
14
+ 9y
13
+ ··· + y + 1
c
10
, c
11
y
14
− 7y
13
+ ··· − 7y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068732 + 0.763152I
a = 3.26573 − 0.25691I
b = −1.41455 + 0.12580I
4.88055 − 5.52492I 4.39718 + 5.23580I
u = −0.068732 − 0.763152I
a = 3.26573 + 0.25691I
b = −1.41455 − 0.12580I
4.88055 + 5.52492I 4.39718 − 5.23580I
u = 1.311340 + 0.253442I
a = −0.863185 − 0.946981I
b = 1.311340 − 0.253442I
− 1.71554I − 60.10 − 0.147212I
u = 1.311340 − 0.253442I
a = −0.863185 + 0.946981I
b = 1.311340 + 0.253442I
1.71554I − 60.10 + 0.147212I
u = −1.35049
a = −0.818895
b = 2.02006
3.04921 −9.67630
u = −1.41455 + 0.12580I
a = −0.107751 + 0.995504I
b = −0.068732 + 0.763152I
−4.88055 + 5.52492I −4.39718 − 5.23580I
u = −1.41455 − 0.12580I
a = −0.107751 − 0.995504I
b = −0.068732 − 0.763152I
−4.88055 − 5.52492I −4.39718 + 5.23580I
u = −1.44062 + 0.23762I
a = 1.00474 − 1.60565I
b = −1.44062 − 0.23762I
8.84538I 0. − 8.04036I
u = −1.44062 − 0.23762I
a = 1.00474 + 1.60565I
b = −1.44062 + 0.23762I
− 8.84538I 0. + 8.04036I
u = −0.020694 + 0.453060I
a = −1.56710 + 0.29858I
b = −0.020694 − 0.453060I
− 3.66683I 0. + 5.82256I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.020694 − 0.453060I
a = −1.56710 − 0.29858I
b = −0.020694 + 0.453060I
3.66683I 0. − 5.82256I
u = −0.218049
a = 0.297239
b = 1.81498
7.07035 25.2800
u = 1.81498
a = 0.253759
b = −0.218049
−7.07035 −25.2800
u = 2.02006
a = 0.803026
b = −1.35049
−3.04921 9.67630
21
III. I
u
3
= ha
3
− 2a
2
+ b − a + 2, a
4
− 3a
3
+ 4a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
6
=
−1
0
a
3
=
0
1
a
9
=
a
−a
3
+ 2a
2
+ a − 2
a
10
=
−a
3
+ 2a
2
+ 2a − 2
−a
3
+ 2a
2
+ a − 2
a
7
=
−a
2
+ a + 1
a
3
− 2a
2
− a + 3
a
12
=
−a
3
+ a
2
+ 2a
a
3
− 2a
2
− a + 3
a
8
=
−a
2
+ a + 1
a
3
− 2a
2
− a + 3
a
4
=
a
3
− a
2
− 2a + 2
−2a
2
+ a + 4
a
11
=
−a
3
+ 2a
2
+ 2a − 2
−2a
3
+ 4a
2
+ 3a − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17a
3
+ 28a
2
+ 36a − 7
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
u
4
− 2u
3
− 2u
2
+ 3u + 1
c
5
(u + 1)
4
c
6
, c
8
, c
9
(u
2
− u − 1)
2
c
7
u
4
c
10
, c
11
u
4
− u
3
− 3u
2
+ u + 1
c
12
(u
2
+ u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
y
4
− 8y
3
+ 18y
2
− 13y + 1
c
6
, c
8
, c
9
c
12
(y
2
− 3y + 1)
2
c
7
y
4
c
10
, c
11
y
4
− 7y
3
+ 13y
2
− 7y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.09529
b = 0.618034
−0.657974 9.49800
u = 1.00000
a = 1.47726
b = 0.618034
−0.657974 52.4810
u = 1.00000
a = 0.262360
b = −1.61803
7.23771 4.06530
u = 1.00000
a = 2.35567
b = −1.61803
7.23771 10.9560
25
IV. I
u
4
= hb − 1, a
2
+ au + 2a − u − 2, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u + 1
a
6
=
−u
−u + 1
a
3
=
u
u
a
9
=
a
1
a
10
=
a + 1
1
a
7
=
−au + a − u + 2
−au + a − u + 2
a
12
=
a + 1
1
a
8
=
−1
0
a
4
=
u
u
a
11
=
−au + 2a + 1
−au + a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7au + 6a − 4u − 15
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
2
+ u − 1)
2
c
3
u
4
c
5
(u
2
− u − 1)
2
c
6
, c
7
u
4
+ 2u
3
− 2u
2
− 3u + 1
c
8
, c
9
(u + 1)
4
c
10
, c
11
u
4
+ u
3
− 3u
2
− u + 1
c
12
(u − 1)
4
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
− 3y + 1)
2
c
3
y
4
c
6
, c
7
y
4
− 8y
3
+ 18y
2
− 13y + 1
c
8
, c
9
, c
12
(y −1)
4
c
10
, c
11
y
4
− 7y
3
+ 13y
2
− 7y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.772223
b = 1.00000
0.657974 −9.49800
u = 0.618034
a = −3.39026
b = 1.00000
0.657974 −52.4810
u = −1.61803
a = −0.837853
b = 1.00000
−7.23771 −4.06530
u = −1.61803
a = 0.455887
b = 1.00000
−7.23771 −10.9560
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
4
)(u
2
+ u − 1)
2
(u
14
+ u
13
+ ··· + 6u + 1)
· (u
112
+ 4u
111
+ ··· + 55u − 7)
c
3
u
4
(u
4
− 2u
3
+ ··· + 3u + 1)(u
14
− 4u
13
+ ··· + 91u − 29)
· (u
112
+ 5u
111
+ ··· − 376u + 16)
c
4
((u
2
+ u − 1)
2
)(u
4
− 2u
3
+ ··· + 3u + 1)(u
14
+ u
13
+ ··· + u − 1)
· (u
112
+ 2u
111
+ ··· + 403u − 61)
c
5
((u + 1)
4
)(u
2
− u − 1)
2
(u
14
− u
13
+ ··· − 6u + 1)
· (u
112
+ 4u
111
+ ··· + 55u − 7)
c
6
((u
2
− u − 1)
2
)(u
4
+ 2u
3
+ ··· − 3u + 1)(u
14
− u
13
+ ··· − u − 1)
· (u
112
− 2u
111
+ ··· − 403u − 61)
c
7
u
4
(u
4
+ 2u
3
+ ··· − 3u + 1)(u
14
+ 4u
13
+ ··· − 91u − 29)
· (u
112
− 5u
111
+ ··· + 376u + 16)
c
8
, c
9
((u + 1)
4
)(u
2
− u − 1)
2
(u
14
− u
13
+ ··· − 6u + 1)
· (u
112
− 4u
111
+ ··· − 55u − 7)
c
10
(u
4
− u
3
− 3u
2
+ u + 1)(u
4
+ u
3
− 3u
2
− u + 1)(u
14
− u
13
+ ··· − u + 1)
· (u
112
− 24u
110
+ ··· + 1642u − 3505)
c
11
(u
4
− u
3
− 3u
2
+ u + 1)(u
4
+ u
3
− 3u
2
− u + 1)(u
14
+ u
13
+ ··· + u + 1)
· (u
112
− 24u
110
+ ··· − 1642u − 3505)
c
12
((u − 1)
4
)(u
2
+ u − 1)
2
(u
14
+ u
13
+ ··· + 6u + 1)
· (u
112
− 4u
111
+ ··· − 55u − 7)
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
9
, c
12
((y −1)
4
)(y
2
− 3y + 1)
2
(y
14
− 19y
13
+ ··· − 12y + 1)
· (y
112
− 116y
111
+ ··· − 1625y + 49)
c
3
, c
7
y
4
(y
4
− 8y
3
+ ··· − 13y + 1)(y
14
− 6y
13
+ ··· − 1611y + 841)
· (y
112
− 29y
111
+ ··· − 62016y + 256)
c
4
, c
6
((y
2
− 3y + 1)
2
)(y
4
− 8y
3
+ ··· − 13y + 1)(y
14
+ 9y
13
+ ··· + y + 1)
· (y
112
+ 4y
111
+ ··· − 334917y + 3721)
c
10
, c
11
((y
4
− 7y
3
+ 13y
2
− 7y + 1)
2
)(y
14
− 7y
13
+ ··· − 7y + 1)
· (y
112
− 48y
111
+ ··· − 513627024y + 12285025)
31
