12a
0308
(K12a
0308
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 9 2 11 1 5 12 7 4
Solving Sequence
2,7
6 3
1,12
11 8 4 9 5 10
c
6
c
2
c
1
c
11
c
7
c
3
c
8
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.76624 × 10
219
u
125
− 7.53327 × 10
220
u
124
+ ··· + 1.14785 × 10
220
b − 1.35671 × 10
222
,
5.17876 × 10
220
u
125
+ 9.23238 × 10
220
u
124
+ ··· + 1.14785 × 10
220
a + 4.07465 × 10
219
,
u
126
+ u
125
+ ··· + 34u + 14i
I
u
2
= h6u
25
+ 6u
24
+ ··· + b − 1, u
25
+ 18u
24
+ ··· + 2a + 13, u
26
+ 2u
25
+ ··· − u + 2i
* 2 irreducible components of dim
C
= 0, with total 152 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−6.77 × 10
219
u
125
− 7.53 × 10
220
u
124
+ · · · + 1.15 × 10
220
b − 1.36 ×
10
222
, 5.18 × 10
220
u
125
+ 9.23 × 10
220
u
124
+ · · · + 1.15 × 10
220
a + 4.07 ×
10
219
, u
126
+ u
125
+ · · · + 34u + 14i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−4.51170u
125
− 8.04318u
124
+ ··· − 101.412u − 0.354980
0.589470u
125
+ 6.56293u
124
+ ··· + 423.567u + 118.196
a
11
=
−3.92223u
125
− 1.48025u
124
+ ··· + 322.156u + 117.841
0.589470u
125
+ 6.56293u
124
+ ··· + 423.567u + 118.196
a
8
=
7.01915u
125
+ 19.5025u
124
+ ··· + 898.354u + 202.158
8.43261u
125
+ 15.8836u
124
+ ··· + 368.196u + 47.8751
a
4
=
−2.62980u
125
+ 4.50769u
124
+ ··· + 787.361u + 248.392
3.00244u
125
+ 4.62029u
124
+ ··· + 102.275u − 1.00353
a
9
=
0.644228u
125
+ 10.4261u
124
+ ··· + 960.436u + 252.392
9.68437u
125
+ 16.5822u
124
+ ··· + 165.488u − 14.2616
a
5
=
13.8031u
125
+ 19.2938u
124
+ ··· + 47.9164u − 83.2406
1.57376u
125
− 3.66048u
124
+ ··· − 575.216u − 172.232
a
10
=
−6.91614u
125
− 4.39988u
124
+ ··· + 460.066u + 175.560
11.6019u
125
+ 20.7193u
124
+ ··· + 386.020u + 26.6522
(ii) Obstruction class = −1
(iii) Cusp Shapes = 15.9613u
125
+ 42.3387u
124
+ ··· + 2087.62u + 494.323
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
126
+ 59u
125
+ ··· + 3632u + 196
c
2
, c
6
u
126
+ u
125
+ ··· + 34u + 14
c
3
u
126
− u
125
+ ··· + 6u + 1
c
4
, c
5
, c
9
u
126
− u
125
+ ··· + 34u + 1
c
7
, c
11
u
126
− u
125
+ ··· − 210u + 25
c
8
u
126
+ 5u
125
+ ··· + 5198u + 1187
c
10
u
126
− 49u
125
+ ··· − 9850u + 625
c
12
u
126
+ 11u
125
+ ··· + 13400628u + 1597649
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
126
+ 27y
125
+ ··· + 566600y + 38416
c
2
, c
6
y
126
+ 59y
125
+ ··· + 3632y + 196
c
3
y
126
+ 5y
125
+ ··· − 28y + 1
c
4
, c
5
, c
9
y
126
+ 131y
125
+ ··· − 88y + 1
c
7
, c
11
y
126
+ 49y
125
+ ··· + 9850y + 625
c
8
y
126
− 13y
125
+ ··· − 64950976y + 1408969
c
10
y
126
+ 69y
125
+ ··· + 767141250y + 390625
c
12
y
126
+ 35y
125
+ ··· + 85429733377584y + 2552482327201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.304196 + 0.959223I
a = 2.28081 + 1.15437I
b = −0.686197 − 0.904816I
−2.73498 − 1.55888I 0
u = 0.304196 − 0.959223I
a = 2.28081 − 1.15437I
b = −0.686197 + 0.904816I
−2.73498 + 1.55888I 0
u = 0.835395 + 0.525075I
a = 0.437355 + 0.524666I
b = 0.054811 + 1.345080I
0.15817 − 4.07041I 0
u = 0.835395 − 0.525075I
a = 0.437355 − 0.524666I
b = 0.054811 − 1.345080I
0.15817 + 4.07041I 0
u = 0.905705 + 0.352784I
a = 0.762337 − 0.007198I
b = −0.953667 + 0.521074I
−6.99810 − 6.61558I 0
u = 0.905705 − 0.352784I
a = 0.762337 + 0.007198I
b = −0.953667 − 0.521074I
−6.99810 + 6.61558I 0
u = 0.969208 + 0.360630I
a = 0.913373 − 0.340051I
b = −0.707578 − 1.128780I
−5.12736 − 12.68230I 0
u = 0.969208 − 0.360630I
a = 0.913373 + 0.340051I
b = −0.707578 + 1.128780I
−5.12736 + 12.68230I 0
u = −0.848700 + 0.435657I
a = −0.800966 − 0.689324I
b = 0.636397 − 1.061860I
1.42651 + 8.48211I 0
u = −0.848700 − 0.435657I
a = −0.800966 + 0.689324I
b = 0.636397 + 1.061860I
1.42651 − 8.48211I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050120 + 0.037194I
a = 1.173120 + 0.083746I
b = −0.567799 + 0.859104I
−1.59844 + 2.26243I 0
u = −1.050120 − 0.037194I
a = 1.173120 − 0.083746I
b = −0.567799 − 0.859104I
−1.59844 − 2.26243I 0
u = 0.340011 + 0.995050I
a = −0.81522 − 1.56936I
b = 1.147330 + 0.260847I
−10.22130 + 1.04149I 0
u = 0.340011 − 0.995050I
a = −0.81522 + 1.56936I
b = 1.147330 − 0.260847I
−10.22130 − 1.04149I 0
u = 0.901643 + 0.279369I
a = −0.839003 + 0.471236I
b = 0.354250 + 0.969985I
3.37819 − 1.16988I 0
u = 0.901643 − 0.279369I
a = −0.839003 − 0.471236I
b = 0.354250 − 0.969985I
3.37819 + 1.16988I 0
u = 0.344085 + 1.003400I
a = 2.15546 − 1.37714I
b = −0.691262 + 0.806098I
−3.03452 + 3.74633I 0
u = 0.344085 − 1.003400I
a = 2.15546 + 1.37714I
b = −0.691262 − 0.806098I
−3.03452 − 3.74633I 0
u = 0.526490 + 0.922044I
a = −0.63637 − 1.38200I
b = −0.167355 − 1.003850I
1.94319 + 2.02809I 0
u = 0.526490 − 0.922044I
a = −0.63637 + 1.38200I
b = −0.167355 + 1.003850I
1.94319 − 2.02809I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424964 + 0.974873I
a = 0.748390 − 0.889163I
b = −0.828851 + 0.240308I
−2.91148 − 1.45412I 0
u = −0.424964 − 0.974873I
a = 0.748390 + 0.889163I
b = −0.828851 − 0.240308I
−2.91148 + 1.45412I 0
u = −0.314358 + 0.878335I
a = 0.71504 − 1.30889I
b = −0.810491 + 0.942201I
−2.16981 + 1.68101I 0
u = −0.314358 − 0.878335I
a = 0.71504 + 1.30889I
b = −0.810491 − 0.942201I
−2.16981 − 1.68101I 0
u = 0.851989 + 0.652954I
a = −1.006300 − 0.748571I
b = 0.493176 − 0.973939I
2.47505 + 4.56930I 0
u = 0.851989 − 0.652954I
a = −1.006300 + 0.748571I
b = 0.493176 + 0.973939I
2.47505 − 4.56930I 0
u = −0.706857 + 0.589361I
a = −0.736621 + 1.130370I
b = 0.067933 + 1.153670I
5.12221 + 1.40859I 0
u = −0.706857 − 0.589361I
a = −0.736621 − 1.130370I
b = 0.067933 − 1.153670I
5.12221 − 1.40859I 0
u = −0.423882 + 0.993862I
a = 1.70686 − 0.16242I
b = −0.892735 − 0.675362I
−2.92658 − 4.55745I 0
u = −0.423882 − 0.993862I
a = 1.70686 + 0.16242I
b = −0.892735 + 0.675362I
−2.92658 + 4.55745I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533387 + 0.733395I
a = 1.97686 + 1.93477I
b = −0.274635 + 0.962055I
2.53888 + 2.26690I 0
u = 0.533387 − 0.733395I
a = 1.97686 − 1.93477I
b = −0.274635 − 0.962055I
2.53888 − 2.26690I 0
u = −0.425119 + 1.008190I
a = −3.68859 + 1.35003I
b = 0.608252 + 0.809673I
−9.49093 − 2.85656I 0
u = −0.425119 − 1.008190I
a = −3.68859 − 1.35003I
b = 0.608252 − 0.809673I
−9.49093 + 2.85656I 0
u = 0.458143 + 1.005260I
a = −2.57796 − 0.68475I
b = 0.79730 − 1.24790I
−7.35715 + 7.96493I 0
u = 0.458143 − 1.005260I
a = −2.57796 + 0.68475I
b = 0.79730 + 1.24790I
−7.35715 − 7.96493I 0
u = 0.453612 + 1.013820I
a = −0.69279 − 1.39501I
b = 0.87394 + 1.12724I
−7.36705 − 1.88885I 0
u = 0.453612 − 1.013820I
a = −0.69279 + 1.39501I
b = 0.87394 − 1.12724I
−7.36705 + 1.88885I 0
u = −0.772036 + 0.805400I
a = 1.017510 − 0.300048I
b = −0.722220 + 0.162618I
−4.18688 − 2.83461I 0
u = −0.772036 − 0.805400I
a = 1.017510 + 0.300048I
b = −0.722220 − 0.162618I
−4.18688 + 2.83461I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.775339 + 0.391438I
a = −0.440764 + 0.060943I
b = 0.745303 + 0.499574I
−0.20476 + 3.21443I 0
u = −0.775339 − 0.391438I
a = −0.440764 − 0.060943I
b = 0.745303 − 0.499574I
−0.20476 − 3.21443I 0
u = −0.582289 + 0.975879I
a = 1.96224 − 0.61659I
b = −0.619094 − 1.159990I
−0.25292 − 6.81367I 0
u = −0.582289 − 0.975879I
a = 1.96224 + 0.61659I
b = −0.619094 + 1.159990I
−0.25292 + 6.81367I 0
u = −0.474415 + 1.041910I
a = −1.72373 + 1.55779I
b = 0.773142 − 0.805714I
−9.07944 − 3.46227I 0
u = −0.474415 − 1.041910I
a = −1.72373 − 1.55779I
b = 0.773142 + 0.805714I
−9.07944 + 3.46227I 0
u = −1.013480 + 0.533271I
a = 0.341574 + 0.204784I
b = −0.289449 + 1.112600I
−0.213684 + 0.352415I 0
u = −1.013480 − 0.533271I
a = 0.341574 − 0.204784I
b = −0.289449 − 1.112600I
−0.213684 − 0.352415I 0
u = 0.484142 + 1.041240I
a = −0.564084 − 0.414274I
b = 0.137177 + 0.113148I
−0.58867 + 3.12037I 0
u = 0.484142 − 1.041240I
a = −0.564084 + 0.414274I
b = 0.137177 − 0.113148I
−0.58867 − 3.12037I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707695 + 0.906471I
a = −0.121184 + 0.196638I
b = 0.362119 + 0.903655I
1.70584 + 1.20788I 0
u = 0.707695 − 0.906471I
a = −0.121184 − 0.196638I
b = 0.362119 − 0.903655I
1.70584 − 1.20788I 0
u = −0.131365 + 1.147900I
a = −1.66961 − 0.67260I
b = 0.732817 + 0.682786I
−5.24479 + 0.80749I 0
u = −0.131365 − 1.147900I
a = −1.66961 + 0.67260I
b = 0.732817 − 0.682786I
−5.24479 − 0.80749I 0
u = −0.399143 + 1.087450I
a = −0.29038 + 2.41435I
b = 0.622390 − 0.900391I
−9.19545 + 1.98580I 0
u = −0.399143 − 1.087450I
a = −0.29038 − 2.41435I
b = 0.622390 + 0.900391I
−9.19545 − 1.98580I 0
u = 0.519304 + 1.043880I
a = −1.91361 − 0.37497I
b = 1.163260 − 0.594506I
−8.97936 + 5.29000I 0
u = 0.519304 − 1.043880I
a = −1.91361 + 0.37497I
b = 1.163260 + 0.594506I
−8.97936 − 5.29000I 0
u = −0.525237 + 0.640775I
a = −0.214135 + 0.364457I
b = −0.491152 + 1.068160I
0.72408 + 2.24593I 0
u = −0.525237 − 0.640775I
a = −0.214135 − 0.364457I
b = −0.491152 − 1.068160I
0.72408 − 2.24593I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821774 + 0.096755I
a = 0.239620 − 0.704210I
b = −0.373706 − 0.774922I
−0.50789 − 1.40777I 0
u = −0.821774 − 0.096755I
a = 0.239620 + 0.704210I
b = −0.373706 + 0.774922I
−0.50789 + 1.40777I 0
u = −0.269837 + 0.777842I
a = −0.23956 − 3.56077I
b = 0.433067 − 0.667520I
−8.37304 − 0.20240I 0
u = −0.269837 − 0.777842I
a = −0.23956 + 3.56077I
b = 0.433067 + 0.667520I
−8.37304 + 0.20240I 0
u = 0.520987 + 1.057250I
a = −0.19299 + 1.66603I
b = −0.614214 − 0.677469I
−1.77476 + 2.74434I 0
u = 0.520987 − 1.057250I
a = −0.19299 − 1.66603I
b = −0.614214 + 0.677469I
−1.77476 − 2.74434I 0
u = −0.611604 + 1.009500I
a = 1.020410 − 0.503159I
b = −0.014759 − 1.212880I
3.86311 − 6.47822I 0
u = −0.611604 − 1.009500I
a = 1.020410 + 0.503159I
b = −0.014759 + 1.212880I
3.86311 + 6.47822I 0
u = −0.471025 + 1.084340I
a = −2.58576 − 0.79138I
b = 0.735297 + 0.925885I
−8.70606 − 9.15996I 0
u = −0.471025 − 1.084340I
a = −2.58576 + 0.79138I
b = 0.735297 − 0.925885I
−8.70606 + 9.15996I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636890 + 0.511863I
a = 0.74959 − 1.47990I
b = −0.573979 − 0.942697I
0.74250 − 2.88378I 0
u = 0.636890 − 0.511863I
a = 0.74959 + 1.47990I
b = −0.573979 + 0.942697I
0.74250 + 2.88378I 0
u = 0.567044 + 1.042860I
a = 2.64752 + 1.24214I
b = −0.616376 + 0.981556I
−0.83584 + 7.62976I 0
u = 0.567044 − 1.042860I
a = 2.64752 − 1.24214I
b = −0.616376 − 0.981556I
−0.83584 − 7.62976I 0
u = −0.036002 + 1.195090I
a = −1.63505 + 0.76040I
b = 0.670385 − 0.971002I
−4.38425 + 6.16299I 0
u = −0.036002 − 1.195090I
a = −1.63505 − 0.76040I
b = 0.670385 + 0.971002I
−4.38425 − 6.16299I 0
u = −0.131478 + 1.205920I
a = 0.177343 − 1.128170I
b = 0.083717 + 1.014730I
−6.34893 − 2.68074I 0
u = −0.131478 − 1.205920I
a = 0.177343 + 1.128170I
b = 0.083717 − 1.014730I
−6.34893 + 2.68074I 0
u = 0.557839 + 0.554982I
a = −0.556401 + 0.145950I
b = 0.299730 + 0.189693I
0.95342 + 1.08564I 0
u = 0.557839 − 0.554982I
a = −0.556401 − 0.145950I
b = 0.299730 − 0.189693I
0.95342 − 1.08564I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280401 + 0.708667I
a = −0.12271 + 2.58036I
b = −0.217797 − 0.658045I
1.263390 + 0.011603I 0
u = 0.280401 − 0.708667I
a = −0.12271 − 2.58036I
b = −0.217797 + 0.658045I
1.263390 − 0.011603I 0
u = 0.487908 + 1.144920I
a = −0.666693 − 0.826521I
b = 0.373759 + 0.584029I
−0.64550 + 2.94420I 0
u = 0.487908 − 1.144920I
a = −0.666693 + 0.826521I
b = 0.373759 − 0.584029I
−0.64550 − 2.94420I 0
u = −0.594137 + 1.106220I
a = −0.478963 + 1.203270I
b = 0.831555 − 0.515269I
−2.30659 − 8.36936I 0
u = −0.594137 − 1.106220I
a = −0.478963 − 1.203270I
b = 0.831555 + 0.515269I
−2.30659 + 8.36936I 0
u = 0.651493 + 1.073880I
a = −1.248870 + 0.019696I
b = 0.14468 − 1.41085I
−1.50580 + 9.60697I 0
u = 0.651493 − 1.073880I
a = −1.248870 − 0.019696I
b = 0.14468 + 1.41085I
−1.50580 − 9.60697I 0
u = 0.291352 + 0.669817I
a = 0.884379 + 0.348991I
b = 0.659985 + 1.207210I
−6.07876 − 4.48676I 0
u = 0.291352 − 0.669817I
a = 0.884379 − 0.348991I
b = 0.659985 − 1.207210I
−6.07876 + 4.48676I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629631 + 1.116680I
a = −2.33694 + 0.68964I
b = 0.668433 + 1.081720I
−0.62430 − 13.96600I 0
u = −0.629631 − 1.116680I
a = −2.33694 − 0.68964I
b = 0.668433 − 1.081720I
−0.62430 + 13.96600I 0
u = −0.542063 + 1.174470I
a = 0.959436 + 0.167740I
b = −0.177783 − 0.689107I
−3.71958 − 6.22307I 0
u = −0.542063 − 1.174470I
a = 0.959436 − 0.167740I
b = −0.177783 + 0.689107I
−3.71958 + 6.22307I 0
u = 0.079711 + 0.681310I
a = −0.301740 − 0.241630I
b = −0.212829 + 0.854997I
0.52498 + 1.77054I 0. − 5.80320I
u = 0.079711 − 0.681310I
a = −0.301740 + 0.241630I
b = −0.212829 − 0.854997I
0.52498 − 1.77054I 0. + 5.80320I
u = 0.156654 + 1.305020I
a = 1.94065 − 0.39633I
b = −0.849380 + 0.603867I
−12.69900 − 3.25347I 0
u = 0.156654 − 1.305020I
a = 1.94065 + 0.39633I
b = −0.849380 − 0.603867I
−12.69900 + 3.25347I 0
u = 0.622854 + 1.165200I
a = 0.83578 + 1.29620I
b = −1.002120 − 0.560547I
−9.4523 + 12.2086I 0
u = 0.622854 − 1.165200I
a = 0.83578 − 1.29620I
b = −1.002120 + 0.560547I
−9.4523 − 12.2086I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535144 + 0.378549I
a = −0.235413 − 0.308562I
b = −0.528077 + 0.759982I
0.11385 + 1.59214I 0. − 2.55317I
u = 0.535144 − 0.378549I
a = −0.235413 + 0.308562I
b = −0.528077 − 0.759982I
0.11385 − 1.59214I 0. + 2.55317I
u = 0.660437 + 1.171900I
a = −1.86787 − 0.29289I
b = 0.501676 − 1.015110I
0.77594 + 6.92005I 0
u = 0.660437 − 1.171900I
a = −1.86787 + 0.29289I
b = 0.501676 + 1.015110I
0.77594 − 6.92005I 0
u = 0.504091 + 0.411221I
a = −0.372730 − 1.037780I
b = 0.993826 + 0.604779I
−7.20638 − 1.02009I −3.78196 + 1.33795I
u = 0.504091 − 0.411221I
a = −0.372730 + 1.037780I
b = 0.993826 − 0.604779I
−7.20638 + 1.02009I −3.78196 − 1.33795I
u = 0.644273 + 1.186310I
a = 2.35727 + 0.33796I
b = −0.739089 + 1.135070I
−7.6558 + 18.5267I 0
u = 0.644273 − 1.186310I
a = 2.35727 − 0.33796I
b = −0.739089 − 1.135070I
−7.6558 − 18.5267I 0
u = −0.941667 + 0.995385I
a = 1.318860 − 0.260251I
b = −0.499825 − 1.102660I
−1.53422 − 7.22718I 0
u = −0.941667 − 0.995385I
a = 1.318860 + 0.260251I
b = −0.499825 + 1.102660I
−1.53422 + 7.22718I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.683019 + 1.196580I
a = 0.247859 + 0.205266I
b = −0.300909 + 0.800064I
−3.57489 − 4.29690I 0
u = −0.683019 − 1.196580I
a = 0.247859 − 0.205266I
b = −0.300909 − 0.800064I
−3.57489 + 4.29690I 0
u = 0.271330 + 0.559407I
a = −2.23515 − 0.14009I
b = 0.792809 − 1.049630I
−5.87626 + 5.39033I −2.10230 − 5.90723I
u = 0.271330 − 0.559407I
a = −2.23515 + 0.14009I
b = 0.792809 + 1.049630I
−5.87626 − 5.39033I −2.10230 + 5.90723I
u = 0.128595 + 1.378630I
a = 1.45318 + 0.96911I
b = −0.692080 − 1.060420I
−11.2967 − 9.0005I 0
u = 0.128595 − 1.378630I
a = 1.45318 − 0.96911I
b = −0.692080 + 1.060420I
−11.2967 + 9.0005I 0
u = −0.57287 + 1.30084I
a = 0.866018 − 1.041620I
b = −0.610847 + 0.819014I
−5.61110 − 3.39745I 0
u = −0.57287 − 1.30084I
a = 0.866018 + 1.041620I
b = −0.610847 − 0.819014I
−5.61110 + 3.39745I 0
u = −0.417130 + 0.378694I
a = −2.06822 − 0.98502I
b = 0.808920 + 0.701599I
−7.22150 − 0.41680I −1.77411 + 1.64915I
u = −0.417130 − 0.378694I
a = −2.06822 + 0.98502I
b = 0.808920 − 0.701599I
−7.22150 + 0.41680I −1.77411 − 1.64915I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555168 + 0.048198I
a = −0.207751 + 0.542664I
b = −0.435086 + 0.585368I
−0.53927 + 1.51210I −0.49571 − 4.96444I
u = −0.555168 − 0.048198I
a = −0.207751 − 0.542664I
b = −0.435086 − 0.585368I
−0.53927 − 1.51210I −0.49571 + 4.96444I
u = −0.61987 + 1.30527I
a = 2.09542 − 0.12149I
b = −0.605488 − 0.890439I
−5.38226 − 8.18906I 0
u = −0.61987 − 1.30527I
a = 2.09542 + 0.12149I
b = −0.605488 + 0.890439I
−5.38226 + 8.18906I 0
u = −0.467426 + 0.127639I
a = −1.04294 + 1.28363I
b = 0.699402 − 0.994643I
−6.29152 + 5.26183I −0.82354 − 4.38830I
u = −0.467426 − 0.127639I
a = −1.04294 − 1.28363I
b = 0.699402 + 0.994643I
−6.29152 − 5.26183I −0.82354 + 4.38830I
17
II.
I
u
2
= h6u
25
+6u
24
+· · ·+b−1, u
25
+18u
24
+· · ·+2a+13, u
26
+2u
25
+· · ·−u+2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−
1
2
u
25
− 9u
24
+ ··· + 17u −
13
2
−6u
25
− 6u
24
+ ··· − 22u + 1
a
11
=
−
13
2
u
25
− 15u
24
+ ··· − 5u −
11
2
−6u
25
− 6u
24
+ ··· − 22u + 1
a
8
=
9
2
u
25
+ 3u
24
+ ··· + 15u +
3
2
15u
25
+ 24u
24
+ ··· + 31u − 1
a
4
=
−
9
2
u
25
− 13u
24
+ ··· − 9u −
35
2
5u
25
+ 15u
24
+ ··· + 3u + 19
a
9
=
−
5
2
u
25
− 14u
24
+ ··· + 23u −
29
2
17u
25
+ 31u
24
+ ··· + 21u + 9
a
5
=
7
2
u
25
+ 5u
24
+ ··· + 7u −
11
2
−4u
25
− 7u
24
+ ··· − 10u + 3
a
10
=
−2u
25
− 12u
23
+ ··· − 21u + 18
−15u
25
− 24u
24
+ ··· − 22u − 18
(ii) Obstruction class = 1
(iii) Cusp Shapes = 20u
25
+ 38u
24
+ 159u
23
+ 239u
22
+ 606u
21
+ 821u
20
+ 1469u
19
+
1842u
18
+ 2477u
17
+ 2968u
16
+ 3088u
15
+ 3502u
14
+ 3037u
13
+ 3039u
12
+ 2611u
11
+
1896u
10
+ 2067u
9
+ 879u
8
+ 1367u
7
+ 377u
6
+ 608u
5
+ 217u
4
+ 125u
3
+ 104u
2
−5u + 26
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 14u
25
+ ··· − 55u + 4
c
2
u
26
− 2u
25
+ ··· + u + 2
c
3
u
26
+ 2u
24
+ ··· + 3u
2
+ 1
c
4
, c
5
u
26
+ 15u
24
+ ··· + 3u
2
+ 1
c
6
u
26
+ 2u
25
+ ··· − u + 2
c
7
u
26
+ 2u
25
+ ··· + 2u + 1
c
8
u
26
− u
24
+ ··· + 3u
2
+ 1
c
9
u
26
+ 15u
24
+ ··· + 3u
2
+ 1
c
10
u
26
+ 12u
25
+ ··· + 12u + 1
c
11
u
26
− 2u
25
+ ··· − 2u + 1
c
12
u
26
− 2u
25
+ ··· − 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 6y
25
+ ··· + 15y + 16
c
2
, c
6
y
26
+ 14y
25
+ ··· + 55y + 4
c
3
y
26
+ 4y
25
+ ··· + 6y + 1
c
4
, c
5
, c
9
y
26
+ 30y
25
+ ··· + 6y + 1
c
7
, c
11
y
26
+ 12y
25
+ ··· + 12y + 1
c
8
y
26
− 2y
25
+ ··· + 6y + 1
c
10
y
26
+ 16y
25
+ ··· + 8y + 1
c
12
y
26
− 6y
25
+ ··· + 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311363 + 0.971289I
a = 0.93024 − 2.57231I
b = −0.745520 + 0.534570I
−9.17363 − 0.88936I −4.93601 + 1.60159I
u = −0.311363 − 0.971289I
a = 0.93024 + 2.57231I
b = −0.745520 − 0.534570I
−9.17363 + 0.88936I −4.93601 − 1.60159I
u = 0.375794 + 0.954475I
a = −1.67639 + 0.56906I
b = 0.719884 − 0.780166I
−2.11427 + 4.30092I 2.41287 − 7.32267I
u = 0.375794 − 0.954475I
a = −1.67639 − 0.56906I
b = 0.719884 + 0.780166I
−2.11427 − 4.30092I 2.41287 + 7.32267I
u = −0.272339 + 0.899544I
a = −0.913395 − 0.477071I
b = −0.604124 − 0.459331I
−8.85848 − 1.51225I −4.02718 + 3.79819I
u = −0.272339 − 0.899544I
a = −0.913395 + 0.477071I
b = −0.604124 + 0.459331I
−8.85848 + 1.51225I −4.02718 − 3.79819I
u = 0.347205 + 0.859675I
a = −1.23638 − 1.35564I
b = 0.742168 + 0.901627I
−1.73422 − 1.30806I 4.15272 − 3.08898I
u = 0.347205 − 0.859675I
a = −1.23638 + 1.35564I
b = 0.742168 − 0.901627I
−1.73422 + 1.30806I 4.15272 + 3.08898I
u = −1.105820 + 0.219089I
a = 0.542514 + 0.442281I
b = −0.251337 + 0.961536I
0.351589 + 1.005860I 10.59379 − 1.99592I
u = −1.105820 − 0.219089I
a = 0.542514 − 0.442281I
b = −0.251337 − 0.961536I
0.351589 − 1.005860I 10.59379 + 1.99592I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392891 + 1.058220I
a = 2.62373 + 0.01042I
b = −0.811857 − 1.019200I
−7.74983 − 6.96656I −4.83921 + 5.14449I
u = −0.392891 − 1.058220I
a = 2.62373 − 0.01042I
b = −0.811857 + 1.019200I
−7.74983 + 6.96656I −4.83921 − 5.14449I
u = −0.289219 + 0.785918I
a = 0.222056 − 0.107860I
b = −0.763366 + 1.156230I
−6.61413 + 4.14195I −7.67026 − 0.14275I
u = −0.289219 − 0.785918I
a = 0.222056 + 0.107860I
b = −0.763366 − 1.156230I
−6.61413 − 4.14195I −7.67026 + 0.14275I
u = 0.680588 + 0.469144I
a = −0.649317 + 1.086000I
b = 0.304944 + 0.994889I
2.55820 − 0.90955I 4.89733 + 0.42106I
u = 0.680588 − 0.469144I
a = −0.649317 − 1.086000I
b = 0.304944 − 0.994889I
2.55820 + 0.90955I 4.89733 − 0.42106I
u = 0.481364 + 1.092720I
a = −0.310521 − 1.317850I
b = 0.401811 + 0.674449I
−0.59446 + 2.29256I 2.00284 + 3.27741I
u = 0.481364 − 1.092720I
a = −0.310521 + 1.317850I
b = 0.401811 − 0.674449I
−0.59446 − 2.29256I 2.00284 − 3.27741I
u = 0.630042 + 1.048530I
a = −1.94868 − 0.60778I
b = 0.495091 − 1.058770I
0.85668 + 6.06573I 4.11993 − 3.89880I
u = 0.630042 − 1.048530I
a = −1.94868 + 0.60778I
b = 0.495091 + 1.058770I
0.85668 − 6.06573I 4.11993 + 3.89880I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.235477 + 0.562989I
a = 0.48637 + 2.25669I
b = 0.187849 − 0.722521I
1.52018 + 1.18551I 4.64794 − 3.74193I
u = 0.235477 − 0.562989I
a = 0.48637 − 2.25669I
b = 0.187849 + 0.722521I
1.52018 − 1.18551I 4.64794 + 3.74193I
u = −0.773189 + 1.158700I
a = 1.362920 − 0.154630I
b = −0.407507 − 1.120730I
−2.29395 − 7.62574I −1.44841 + 9.42563I
u = −0.773189 − 1.158700I
a = 1.362920 + 0.154630I
b = −0.407507 + 1.120730I
−2.29395 + 7.62574I −1.44841 − 9.42563I
u = −0.60565 + 1.28237I
a = 0.316861 − 0.188890I
b = −0.268038 + 0.710837I
−3.98716 − 4.77328I −2.40635 + 7.58295I
u = −0.60565 − 1.28237I
a = 0.316861 + 0.188890I
b = −0.268038 − 0.710837I
−3.98716 + 4.77328I −2.40635 − 7.58295I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 14u
25
+ ··· − 55u + 4)(u
126
+ 59u
125
+ ··· + 3632u + 196)
c
2
(u
26
− 2u
25
+ ··· + u + 2)(u
126
+ u
125
+ ··· + 34u + 14)
c
3
(u
26
+ 2u
24
+ ··· + 3u
2
+ 1)(u
126
− u
125
+ ··· + 6u + 1)
c
4
, c
5
(u
26
+ 15u
24
+ ··· + 3u
2
+ 1)(u
126
− u
125
+ ··· + 34u + 1)
c
6
(u
26
+ 2u
25
+ ··· − u + 2)(u
126
+ u
125
+ ··· + 34u + 14)
c
7
(u
26
+ 2u
25
+ ··· + 2u + 1)(u
126
− u
125
+ ··· − 210u + 25)
c
8
(u
26
− u
24
+ ··· + 3u
2
+ 1)(u
126
+ 5u
125
+ ··· + 5198u + 1187)
c
9
(u
26
+ 15u
24
+ ··· + 3u
2
+ 1)(u
126
− u
125
+ ··· + 34u + 1)
c
10
(u
26
+ 12u
25
+ ··· + 12u + 1)(u
126
− 49u
125
+ ··· − 9850u + 625)
c
11
(u
26
− 2u
25
+ ··· − 2u + 1)(u
126
− u
125
+ ··· − 210u + 25)
c
12
(u
26
− 2u
25
+ ··· − 2u + 1)
· (u
126
+ 11u
125
+ ··· + 13400628u + 1597649)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 6y
25
+ ··· + 15y + 16)(y
126
+ 27y
125
+ ··· + 566600y + 38416)
c
2
, c
6
(y
26
+ 14y
25
+ ··· + 55y + 4)(y
126
+ 59y
125
+ ··· + 3632y + 196)
c
3
(y
26
+ 4y
25
+ ··· + 6y + 1)(y
126
+ 5y
125
+ ··· − 28y + 1)
c
4
, c
5
, c
9
(y
26
+ 30y
25
+ ··· + 6y + 1)(y
126
+ 131y
125
+ ··· − 88y + 1)
c
7
, c
11
(y
26
+ 12y
25
+ ··· + 12y + 1)(y
126
+ 49y
125
+ ··· + 9850y + 625)
c
8
(y
26
− 2y
25
+ ··· + 6y + 1)
· (y
126
− 13y
125
+ ··· − 64950976y + 1408969)
c
10
(y
26
+ 16y
25
+ ··· + 8y + 1)
· (y
126
+ 69y
125
+ ··· + 767141250y + 390625)
c
12
(y
26
− 6y
25
+ ··· + 2y + 1)
· (y
126
+ 35y
125
+ ··· + 85429733377584y + 2552482327201)
25
