12a
0547
(K12a
0547
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 9 12 2 5 1 6 4 10
Solving Sequence
2,8
7 3
4,11
5 9 12 1 6 10
c
7
c
2
c
3
c
4
c
8
c
11
c
1
c
6
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.82820 × 10
271
u
152
+ 1.44234 × 10
271
u
151
+ ··· + 2.04979 × 10
271
b + 3.56914 × 10
272
,
4.13842 × 10
272
u
152
+ 4.80709 × 10
272
u
151
+ ··· + 2.25477 × 10
272
a + 5.49438 × 10
273
,
u
153
+ u
152
+ ··· + 28u + 11i
I
u
2
= h−15u
36
+ 4u
35
+ ··· + b + 12, 3u
36
− u
35
+ ··· + a + 4, u
37
+ 10u
35
+ ··· + 7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 190 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−1.83 × 10
271
u
152
+ 1.44 × 10
271
u
151
+ · · · + 2.05 × 10
271
b + 3.57 ×
10
272
, 4.14 × 10
272
u
152
+ 4.81 × 10
272
u
151
+ · · · + 2.25 × 10
272
a + 5.49 ×
10
273
, u
153
+ u
152
+ · · · + 28u + 11i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−1.83540u
152
− 2.13196u
151
+ ··· − 55.6512u − 24.3678
0.891895u
152
− 0.703650u
151
+ ··· − 15.7291u − 17.4122
a
5
=
−3.07699u
152
+ 0.677463u
151
+ ··· − 31.4818u − 0.617562
−0.627358u
152
− 1.90774u
151
+ ··· − 44.2921u − 19.0364
a
9
=
0.541198u
152
− 4.00467u
151
+ ··· − 73.7467u − 47.3026
1.32157u
152
+ 0.752987u
151
+ ··· + 18.8733u − 1.48239
a
12
=
−2.06938u
152
− 1.82937u
151
+ ··· − 53.0326u − 22.5137
0.934884u
152
− 1.02868u
151
+ ··· − 17.9375u − 17.6217
a
1
=
u
3
u
5
+ u
3
+ u
a
6
=
−2.75509u
152
+ 0.779317u
151
+ ··· − 25.6683u − 2.59189
−1.43719u
152
− 3.10153u
151
+ ··· − 82.2229u − 39.1923
a
10
=
−1.72401u
152
− 2.92931u
151
+ ··· − 75.4883u − 35.5372
1.63954u
152
− 0.541052u
151
+ ··· + 7.50025u − 9.41830
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.17995u
152
− 1.07008u
151
+ ··· + 20.1517u − 47.8921
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
153
+ 77u
152
+ ··· − 1548u − 121
c
2
, c
7
u
153
+ u
152
+ ··· + 28u + 11
c
3
u
153
− u
152
+ ··· + 13334880u + 1770791
c
4
, c
11
u
153
+ 2u
152
+ ··· + 3u + 1
c
5
, c
8
u
153
− 50u
151
+ ··· + 8395u + 10331
c
6
u
153
+ u
152
+ ··· + 869544u + 253007
c
9
, c
12
u
153
− 4u
152
+ ··· − 52195u + 4961
c
10
u
153
− u
152
+ ··· + 35046u + 9439
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
153
+ 5y
152
+ ··· − 286508y −14641
c
2
, c
7
y
153
+ 77y
152
+ ··· − 1548y −121
c
3
y
153
− 67y
152
+ ··· − 141584742282518y −3135700765681
c
4
, c
11
y
153
+ 84y
152
+ ··· − 39y −1
c
5
, c
8
y
153
− 100y
152
+ ··· + 4473444915y −106729561
c
6
y
153
+ 25y
152
+ ··· − 1962648262454y −64012542049
c
9
, c
12
y
153
+ 80y
152
+ ··· − 798994097y −24611521
c
10
y
153
+ 17y
152
+ ··· − 7057634132y −89094721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803169 + 0.577760I
a = 0.654727 − 0.658081I
b = −2.16547 + 0.07601I
2.89636 + 2.62923I 0
u = −0.803169 − 0.577760I
a = 0.654727 + 0.658081I
b = −2.16547 − 0.07601I
2.89636 − 2.62923I 0
u = −1.004370 + 0.112798I
a = −0.307076 − 0.833264I
b = 0.592813 + 1.118070I
−1.59495 + 1.22097I 0
u = −1.004370 − 0.112798I
a = −0.307076 + 0.833264I
b = 0.592813 − 1.118070I
−1.59495 − 1.22097I 0
u = −0.420378 + 0.885705I
a = 1.45676 + 0.24596I
b = −1.23957 − 0.84798I
1.16632 + 2.69264I 0
u = −0.420378 − 0.885705I
a = 1.45676 − 0.24596I
b = −1.23957 + 0.84798I
1.16632 − 2.69264I 0
u = −0.169016 + 1.013590I
a = 1.214710 + 0.245532I
b = −0.462782 − 0.735315I
−1.48405 + 1.57407I 0
u = −0.169016 − 1.013590I
a = 1.214710 − 0.245532I
b = −0.462782 + 0.735315I
−1.48405 − 1.57407I 0
u = 0.661362 + 0.709297I
a = 0.463802 − 0.665196I
b = 1.51391 + 0.38433I
1.30435 + 5.87704I 0
u = 0.661362 − 0.709297I
a = 0.463802 + 0.665196I
b = 1.51391 − 0.38433I
1.30435 − 5.87704I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.661394 + 0.698725I
a = −0.054834 + 0.347458I
b = 1.60907 + 0.63444I
7.98668 − 5.17937I 0
u = −0.661394 − 0.698725I
a = −0.054834 − 0.347458I
b = 1.60907 − 0.63444I
7.98668 + 5.17937I 0
u = 0.926965 + 0.468778I
a = −0.899004 + 0.412334I
b = 2.08791 − 1.45289I
0.49601 − 3.67330I 0
u = 0.926965 − 0.468778I
a = −0.899004 − 0.412334I
b = 2.08791 + 1.45289I
0.49601 + 3.67330I 0
u = 0.922348 + 0.250824I
a = 0.432284 − 1.050650I
b = −1.42601 + 1.70545I
0.69176 − 1.30939I 0
u = 0.922348 − 0.250824I
a = 0.432284 + 1.050650I
b = −1.42601 − 1.70545I
0.69176 + 1.30939I 0
u = 0.599653 + 0.866993I
a = −0.12882 − 1.44661I
b = 1.282060 − 0.139973I
0.836296 − 0.978230I 0
u = 0.599653 − 0.866993I
a = −0.12882 + 1.44661I
b = 1.282060 + 0.139973I
0.836296 + 0.978230I 0
u = 0.024048 + 1.060330I
a = 1.70255 + 0.01296I
b = −0.953502 − 0.444769I
0.19382 + 2.04626I 0
u = 0.024048 − 1.060330I
a = 1.70255 − 0.01296I
b = −0.953502 + 0.444769I
0.19382 − 2.04626I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885318 + 0.300352I
a = 0.282592 + 0.613095I
b = −1.86384 − 1.14675I
2.3619 + 14.1579I 0
u = −0.885318 − 0.300352I
a = 0.282592 − 0.613095I
b = −1.86384 + 1.14675I
2.3619 − 14.1579I 0
u = −0.538737 + 0.761034I
a = −0.809151 − 1.144800I
b = −1.272290 + 0.084596I
4.31832 − 2.17917I 0
u = −0.538737 − 0.761034I
a = −0.809151 + 1.144800I
b = −1.272290 − 0.084596I
4.31832 + 2.17917I 0
u = 0.265107 + 1.037410I
a = −0.391450 − 0.151234I
b = 0.808245 + 0.272149I
1.63828 + 3.80010I 0
u = 0.265107 − 1.037410I
a = −0.391450 + 0.151234I
b = 0.808245 − 0.272149I
1.63828 − 3.80010I 0
u = −0.529733 + 0.745288I
a = 0.27196 − 1.60407I
b = −0.847186 + 0.569319I
1.48585 − 6.62716I 0
u = −0.529733 − 0.745288I
a = 0.27196 + 1.60407I
b = −0.847186 − 0.569319I
1.48585 + 6.62716I 0
u = −0.626068 + 0.894564I
a = 0.64894 + 2.15812I
b = 1.34997 − 1.01960I
7.41917 + 0.20736I 0
u = −0.626068 − 0.894564I
a = 0.64894 − 2.15812I
b = 1.34997 + 1.01960I
7.41917 − 0.20736I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.113240 + 1.098040I
a = −2.40907 + 1.47465I
b = 1.004810 − 0.952987I
−5.34213 − 1.63294I 0
u = 0.113240 − 1.098040I
a = −2.40907 − 1.47465I
b = 1.004810 + 0.952987I
−5.34213 + 1.63294I 0
u = 0.737210 + 0.499189I
a = 0.035993 − 0.473925I
b = −1.232050 + 0.370722I
5.42547 + 0.75189I 0
u = 0.737210 − 0.499189I
a = 0.035993 + 0.473925I
b = −1.232050 − 0.370722I
5.42547 − 0.75189I 0
u = −0.427201 + 1.025550I
a = 1.46652 − 2.59746I
b = −2.03822 − 0.26994I
−0.07991 + 1.48262I 0
u = −0.427201 − 1.025550I
a = 1.46652 + 2.59746I
b = −2.03822 + 0.26994I
−0.07991 − 1.48262I 0
u = 0.524046 + 0.983672I
a = −0.204309 + 0.610614I
b = 0.244671 − 0.234525I
2.01558 + 2.87049I 0
u = 0.524046 − 0.983672I
a = −0.204309 − 0.610614I
b = 0.244671 + 0.234525I
2.01558 − 2.87049I 0
u = 0.795132 + 0.784678I
a = 0.418719 + 1.070430I
b = −2.11529 − 0.37904I
5.30275 + 10.77780I 0
u = 0.795132 − 0.784678I
a = 0.418719 − 1.070430I
b = −2.11529 + 0.37904I
5.30275 − 10.77780I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.467919 + 1.030120I
a = −0.486150 + 0.390238I
b = 1.266510 + 0.358123I
−4.17331 − 3.13943I 0
u = −0.467919 − 1.030120I
a = −0.486150 − 0.390238I
b = 1.266510 − 0.358123I
−4.17331 + 3.13943I 0
u = −0.422936 + 1.051470I
a = −1.64652 − 2.71399I
b = −0.279492 + 1.009320I
2.80395 − 0.18184I 0
u = −0.422936 − 1.051470I
a = −1.64652 + 2.71399I
b = −0.279492 − 1.009320I
2.80395 + 0.18184I 0
u = −0.728290 + 0.455821I
a = −0.255788 − 0.431460I
b = −1.71113 − 0.25408I
5.24838 + 3.35209I 0
u = −0.728290 − 0.455821I
a = −0.255788 + 0.431460I
b = −1.71113 + 0.25408I
5.24838 − 3.35209I 0
u = −0.805772 + 0.293840I
a = 0.125125 − 0.537652I
b = 1.59272 + 0.94279I
−0.88656 + 8.08747I 0
u = −0.805772 − 0.293840I
a = 0.125125 + 0.537652I
b = 1.59272 − 0.94279I
−0.88656 − 8.08747I 0
u = −0.415484 + 1.068520I
a = −1.264150 + 0.217576I
b = 1.020550 + 0.631809I
−3.51137 − 3.38573I 0
u = −0.415484 − 1.068520I
a = −1.264150 − 0.217576I
b = 1.020550 − 0.631809I
−3.51137 + 3.38573I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.436413 + 1.062230I
a = −2.81312 + 1.71557I
b = 1.01179 − 1.77752I
−3.07142 + 1.23078I 0
u = 0.436413 − 1.062230I
a = −2.81312 − 1.71557I
b = 1.01179 + 1.77752I
−3.07142 − 1.23078I 0
u = 0.214188 + 0.812689I
a = 0.522372 + 0.212518I
b = −0.129247 − 0.290374I
−0.573771 + 1.117010I 0
u = 0.214188 − 0.812689I
a = 0.522372 − 0.212518I
b = −0.129247 + 0.290374I
−0.573771 − 1.117010I 0
u = 0.791592 + 0.279934I
a = 0.010624 + 0.208496I
b = 1.83748 − 0.03341I
5.85581 − 7.23825I 0
u = 0.791592 − 0.279934I
a = 0.010624 − 0.208496I
b = 1.83748 + 0.03341I
5.85581 + 7.23825I 0
u = 0.484218 + 1.074660I
a = 0.80584 − 3.69106I
b = 1.57664 + 1.61174I
−2.70678 + 5.64464I 0
u = 0.484218 − 1.074660I
a = 0.80584 + 3.69106I
b = 1.57664 − 1.61174I
−2.70678 − 5.64464I 0
u = 0.355257 + 1.125980I
a = −1.022580 + 0.111630I
b = 0.030616 + 0.297694I
−7.39263 + 2.02832I 0
u = 0.355257 − 1.125980I
a = −1.022580 − 0.111630I
b = 0.030616 − 0.297694I
−7.39263 − 2.02832I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.495307 + 1.075110I
a = 1.37526 + 2.72517I
b = 0.313367 − 1.252430I
3.36604 − 6.63400I 0
u = −0.495307 − 1.075110I
a = 1.37526 − 2.72517I
b = 0.313367 + 1.252430I
3.36604 + 6.63400I 0
u = −0.498143 + 1.073910I
a = −1.19365 + 1.96600I
b = 1.73648 − 0.00647I
−2.99168 − 3.47198I 0
u = −0.498143 − 1.073910I
a = −1.19365 − 1.96600I
b = 1.73648 + 0.00647I
−2.99168 + 3.47198I 0
u = 0.336033 + 1.135300I
a = 1.59010 − 0.29813I
b = −1.084310 + 0.461830I
−1.70702 + 0.20417I 0
u = 0.336033 − 1.135300I
a = 1.59010 + 0.29813I
b = −1.084310 − 0.461830I
−1.70702 − 0.20417I 0
u = 0.777805 + 0.238252I
a = 0.736978 − 0.649162I
b = −0.129376 + 0.136119I
−0.91343 − 7.83033I −8.00000 + 5.36238I
u = 0.777805 − 0.238252I
a = 0.736978 + 0.649162I
b = −0.129376 − 0.136119I
−0.91343 + 7.83033I −8.00000 − 5.36238I
u = 0.800176 + 0.877926I
a = 0.88752 + 1.47851I
b = −2.10313 − 0.10183I
5.06004 − 4.90030I 0
u = 0.800176 − 0.877926I
a = 0.88752 − 1.47851I
b = −2.10313 + 0.10183I
5.06004 + 4.90030I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518758 + 1.070880I
a = −0.419405 − 1.157740I
b = 1.076190 − 0.340141I
3.16301 + 2.84324I 0
u = 0.518758 − 1.070880I
a = −0.419405 + 1.157740I
b = 1.076190 + 0.340141I
3.16301 − 2.84324I 0
u = 0.604831 + 0.537268I
a = 0.153128 − 0.747016I
b = −0.170830 + 0.266794I
3.31184 + 1.61796I −8.00000 + 0.I
u = 0.604831 − 0.537268I
a = 0.153128 + 0.747016I
b = −0.170830 − 0.266794I
3.31184 − 1.61796I −8.00000 + 0.I
u = −0.804054 + 0.028913I
a = 0.0738268 + 0.0031876I
b = 0.342861 + 0.482325I
−1.96641 + 1.44396I −10.10047 − 1.74700I
u = −0.804054 − 0.028913I
a = 0.0738268 − 0.0031876I
b = 0.342861 − 0.482325I
−1.96641 − 1.44396I −10.10047 + 1.74700I
u = −0.529515 + 1.072320I
a = 1.36972 − 0.52815I
b = −1.43026 − 0.35470I
0.80352 − 7.91545I 0
u = −0.529515 − 1.072320I
a = 1.36972 + 0.52815I
b = −1.43026 + 0.35470I
0.80352 + 7.91545I 0
u = 0.278954 + 1.170680I
a = −2.04057 − 0.50987I
b = 1.53105 − 0.21670I
1.35908 − 4.03523I 0
u = 0.278954 − 1.170680I
a = −2.04057 + 0.50987I
b = 1.53105 + 0.21670I
1.35908 + 4.03523I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254270 + 1.185540I
a = −2.13863 − 1.09344I
b = 1.28167 + 0.96987I
−5.56411 + 4.90770I 0
u = −0.254270 − 1.185540I
a = −2.13863 + 1.09344I
b = 1.28167 − 0.96987I
−5.56411 − 4.90770I 0
u = 0.607861 + 1.049160I
a = −0.01178 + 1.98308I
b = −0.921894 − 0.660627I
3.80249 + 4.36928I 0
u = 0.607861 − 1.049160I
a = −0.01178 − 1.98308I
b = −0.921894 + 0.660627I
3.80249 − 4.36928I 0
u = −0.581277 + 1.070960I
a = 0.41404 − 2.18203I
b = −1.87012 + 0.52084I
3.42627 − 8.35156I 0
u = −0.581277 − 1.070960I
a = 0.41404 + 2.18203I
b = −1.87012 − 0.52084I
3.42627 + 8.35156I 0
u = 0.396784 + 1.155950I
a = 2.89958 − 1.26714I
b = −1.40518 + 1.46228I
−3.41797 − 1.17717I 0
u = 0.396784 − 1.155950I
a = 2.89958 + 1.26714I
b = −1.40518 − 1.46228I
−3.41797 + 1.17717I 0
u = 0.304939 + 1.184940I
a = 0.987353 − 0.056795I
b = −0.158035 − 0.252883I
−5.24129 − 4.41690I 0
u = 0.304939 − 1.184940I
a = 0.987353 + 0.056795I
b = −0.158035 + 0.252883I
−5.24129 + 4.41690I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626569 + 1.062030I
a = 0.97901 − 2.18234I
b = −2.04671 + 0.62504I
1.38311 − 8.00166I 0
u = −0.626569 − 1.062030I
a = 0.97901 + 2.18234I
b = −2.04671 − 0.62504I
1.38311 + 8.00166I 0
u = −0.652876 + 0.399979I
a = −0.042548 − 0.783913I
b = −0.959350 + 0.188021I
2.75263 + 3.31067I −4.78268 − 2.44794I
u = −0.652876 − 0.399979I
a = −0.042548 + 0.783913I
b = −0.959350 − 0.188021I
2.75263 − 3.31067I −4.78268 + 2.44794I
u = 0.513181 + 1.127210I
a = −0.494940 − 0.841920I
b = −0.075096 + 0.195869I
−6.29750 + 5.72449I 0
u = 0.513181 − 1.127210I
a = −0.494940 + 0.841920I
b = −0.075096 − 0.195869I
−6.29750 − 5.72449I 0
u = 0.716816 + 0.223428I
a = −0.319148 − 0.645624I
b = −1.273520 + 0.282810I
2.20690 − 3.05991I −4.94983 + 2.95032I
u = 0.716816 − 0.223428I
a = −0.319148 + 0.645624I
b = −1.273520 − 0.282810I
2.20690 + 3.05991I −4.94983 − 2.95032I
u = 0.492970 + 1.148300I
a = 0.02850 + 3.84157I
b = −1.78955 − 1.50932I
−2.73820 + 9.28492I 0
u = 0.492970 − 1.148300I
a = 0.02850 − 3.84157I
b = −1.78955 + 1.50932I
−2.73820 − 9.28492I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520803 + 1.141260I
a = 0.51173 + 2.15597I
b = −1.40784 − 0.36801I
−0.43649 + 7.74062I 0
u = 0.520803 − 1.141260I
a = 0.51173 − 2.15597I
b = −1.40784 + 0.36801I
−0.43649 − 7.74062I 0
u = 0.249185 + 1.240000I
a = 2.54342 − 1.62987I
b = −1.21371 + 1.26680I
−4.38413 + 2.37619I 0
u = 0.249185 − 1.240000I
a = 2.54342 + 1.62987I
b = −1.21371 − 1.26680I
−4.38413 − 2.37619I 0
u = −0.733805 + 0.033596I
a = −0.389271 + 0.173878I
b = 0.343342 + 0.651786I
−2.11339 + 1.38961I −8.75300 − 4.56908I
u = −0.733805 − 0.033596I
a = −0.389271 − 0.173878I
b = 0.343342 − 0.651786I
−2.11339 − 1.38961I −8.75300 + 4.56908I
u = −0.491152 + 1.169130I
a = 0.049291 + 0.730421I
b = 0.082986 − 0.647105I
−5.26325 − 5.85056I 0
u = −0.491152 − 1.169130I
a = 0.049291 − 0.730421I
b = 0.082986 + 0.647105I
−5.26325 + 5.85056I 0
u = −0.317102 + 1.228990I
a = −1.384350 + 0.052888I
b = 0.683499 + 0.023809I
−6.26076 − 3.02281I 0
u = −0.317102 − 1.228990I
a = −1.384350 − 0.052888I
b = 0.683499 − 0.023809I
−6.26076 + 3.02281I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.543168 + 1.157210I
a = 0.422446 + 0.532579I
b = 0.110553 − 0.147833I
−3.60234 + 12.75860I 0
u = 0.543168 − 1.157210I
a = 0.422446 − 0.532579I
b = 0.110553 + 0.147833I
−3.60234 − 12.75860I 0
u = −0.223301 + 1.259190I
a = 2.60164 + 1.04394I
b = −1.54079 − 0.98551I
−2.84117 + 10.66610I 0
u = −0.223301 − 1.259190I
a = 2.60164 − 1.04394I
b = −1.54079 + 0.98551I
−2.84117 − 10.66610I 0
u = 0.558687 + 1.153750I
a = −1.26378 − 2.21148I
b = 1.96014 + 0.19747I
3.27547 + 12.28210I 0
u = 0.558687 − 1.153750I
a = −1.26378 + 2.21148I
b = 1.96014 − 0.19747I
3.27547 − 12.28210I 0
u = −0.443636 + 1.204070I
a = −0.843315 − 0.160289I
b = 0.309435 + 0.592095I
−5.66176 − 2.88998I 0
u = −0.443636 − 1.204070I
a = −0.843315 + 0.160289I
b = 0.309435 − 0.592095I
−5.66176 + 2.88998I 0
u = −0.568214 + 1.152690I
a = −0.04655 + 2.88528I
b = 1.64677 − 1.11729I
−3.42925 − 13.20540I 0
u = −0.568214 − 1.152690I
a = −0.04655 − 2.88528I
b = 1.64677 + 1.11729I
−3.42925 + 13.20540I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.249040 + 0.667944I
a = −2.87581 − 0.55560I
b = −0.301550 − 0.257994I
4.41673 − 2.94301I −7.72377 − 2.80983I
u = −0.249040 − 0.667944I
a = −2.87581 + 0.55560I
b = −0.301550 + 0.257994I
4.41673 + 2.94301I −7.72377 + 2.80983I
u = −0.449897 + 1.211370I
a = −0.489003 − 0.295317I
b = 0.318179 + 0.497734I
−5.61132 − 2.98647I 0
u = −0.449897 − 1.211370I
a = −0.489003 + 0.295317I
b = 0.318179 − 0.497734I
−5.61132 + 2.98647I 0
u = −0.467643 + 1.211860I
a = 0.070724 + 0.767974I
b = 0.395979 − 0.539772I
−5.45282 − 6.02890I 0
u = −0.467643 − 1.211860I
a = 0.070724 − 0.767974I
b = 0.395979 + 0.539772I
−5.45282 + 6.02890I 0
u = −0.348227 + 0.603564I
a = −1.85480 − 0.85300I
b = −1.92973 + 0.73724I
1.33390 − 4.92038I −2.96903 + 7.20510I
u = −0.348227 − 0.603564I
a = −1.85480 + 0.85300I
b = −1.92973 − 0.73724I
1.33390 + 4.92038I −2.96903 − 7.20510I
u = 0.656745 + 0.220774I
a = −0.95862 + 1.04655I
b = 0.203938 − 0.105601I
−3.74502 − 1.20259I −7.76392 + 5.48574I
u = 0.656745 − 0.220774I
a = −0.95862 − 1.04655I
b = 0.203938 + 0.105601I
−3.74502 + 1.20259I −7.76392 − 5.48574I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416436 + 0.551040I
a = 0.55337 + 2.11407I
b = 0.806600 − 0.306418I
−2.64830 − 0.66881I 1.13261 + 10.21227I
u = −0.416436 − 0.551040I
a = 0.55337 − 2.11407I
b = 0.806600 + 0.306418I
−2.64830 + 0.66881I 1.13261 − 10.21227I
u = 0.669051 + 0.129996I
a = −0.086872 − 1.143820I
b = −1.67120 + 1.28658I
0.10169 − 4.86501I −6.23365 + 7.74181I
u = 0.669051 − 0.129996I
a = −0.086872 + 1.143820I
b = −1.67120 − 1.28658I
0.10169 + 4.86501I −6.23365 − 7.74181I
u = 0.579276 + 0.358982I
a = 1.350700 + 0.202255I
b = 0.869778 + 0.493481I
5.17720 + 1.57032I −1.58318 − 2.26362I
u = 0.579276 − 0.358982I
a = 1.350700 − 0.202255I
b = 0.869778 − 0.493481I
5.17720 − 1.57032I −1.58318 + 2.26362I
u = 0.644270 + 1.150770I
a = 0.08994 − 3.28212I
b = 1.70427 + 1.81284I
−1.66120 + 9.45022I 0
u = 0.644270 − 1.150770I
a = 0.08994 + 3.28212I
b = 1.70427 − 1.81284I
−1.66120 − 9.45022I 0
u = −0.593287 + 1.178580I
a = 0.26963 − 3.16414I
b = −1.83640 + 1.33864I
−0.2864 − 19.5811I 0
u = −0.593287 − 1.178580I
a = 0.26963 + 3.16414I
b = −1.83640 − 1.33864I
−0.2864 + 19.5811I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561028 + 0.372602I
a = 0.343687 − 0.119766I
b = 1.52319 − 0.41698I
−0.985320 − 0.794515I −7.89002 + 1.41192I
u = −0.561028 − 0.372602I
a = 0.343687 + 0.119766I
b = 1.52319 + 0.41698I
−0.985320 + 0.794515I −7.89002 − 1.41192I
u = 0.562698 + 1.204090I
a = −0.33535 + 3.24093I
b = −1.23686 − 1.67317I
−2.25908 + 6.69261I 0
u = 0.562698 − 1.204090I
a = −0.33535 − 3.24093I
b = −1.23686 + 1.67317I
−2.25908 − 6.69261I 0
u = −0.436059 + 1.288710I
a = 0.879936 + 1.019690I
b = −0.177384 − 0.607356I
−5.55889 − 6.39241I 0
u = −0.436059 − 1.288710I
a = 0.879936 − 1.019690I
b = −0.177384 + 0.607356I
−5.55889 + 6.39241I 0
u = −0.494635 + 0.385298I
a = 1.25666 − 1.50464I
b = 0.467833 + 0.879146I
5.37889 + 2.47470I −4.33792 − 4.94559I
u = −0.494635 − 0.385298I
a = 1.25666 + 1.50464I
b = 0.467833 − 0.879146I
5.37889 − 2.47470I −4.33792 + 4.94559I
u = 0.241418 + 0.555776I
a = −1.05287 − 1.30742I
b = 0.71230 + 1.33021I
−1.21452 + 2.10656I −2.73296 − 4.39387I
u = 0.241418 − 0.555776I
a = −1.05287 + 1.30742I
b = 0.71230 − 1.33021I
−1.21452 − 2.10656I −2.73296 + 4.39387I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.445195 + 0.397840I
a = 1.044290 + 0.085184I
b = 1.43864 − 1.16421I
−0.69479 − 1.62339I −7.51539 − 1.89786I
u = 0.445195 − 0.397840I
a = 1.044290 − 0.085184I
b = 1.43864 + 1.16421I
−0.69479 + 1.62339I −7.51539 + 1.89786I
u = −0.458239
a = 0.601847
b = 0.560207
−0.900948 −11.0700
20
II. I
u
2
=
h−15u
36
+4u
35
+· · ·+b+12, 3u
36
−u
35
+· · ·+a+4, u
37
+10u
35
+· · ·+7u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−3u
36
+ u
35
+ ··· − 4u − 4
15u
36
− 4u
35
+ ··· + 20u − 12
a
5
=
−6u
36
+ 3u
35
+ ··· + 69u
2
+ 16
−u
36
− 9u
34
+ ··· − u − 1
a
9
=
15u
36
+ 2u
35
+ ··· + 15u − 9
7u
36
+ 2u
35
+ ··· + 8u + 3
a
12
=
u
36
+ 2u
35
+ ··· + 2u − 3
17u
36
− 4u
35
+ ··· + 23u − 12
a
1
=
u
3
u
5
+ u
3
+ u
a
6
=
7u
36
+ 9u
35
+ ··· + 23u + 15
15u
36
+ 14u
35
+ ··· + 22u + 16
a
10
=
21u
36
+ 7u
35
+ ··· + 26u − 4
−3u
35
− 3u
34
+ ··· − 12u
2
− 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −43u
36
− 50u
35
+ ··· − 96u − 74
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
37
− 20u
36
+ ··· − 14u + 1
c
2
u
37
+ 10u
35
+ ··· − 7u
2
− 1
c
3
u
37
− 10u
35
+ ··· + 4u − 1
c
4
u
37
− u
36
+ ··· − u + 1
c
5
u
37
+ 3u
36
+ ··· − 3u − 1
c
6
u
37
+ 2u
35
+ ··· − 16u
2
+ 1
c
7
u
37
+ 10u
35
+ ··· + 7u
2
+ 1
c
8
u
37
− 3u
36
+ ··· − 3u + 1
c
9
u
37
− 7u
36
+ ··· + 7u − 1
c
10
u
37
+ 8u
31
+ ··· − 2u + 1
c
11
u
37
+ u
36
+ ··· − u − 1
c
12
u
37
+ 7u
36
+ ··· + 7u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 40y
35
+ ··· + 6y −1
c
2
, c
7
y
37
+ 20y
36
+ ··· − 14y −1
c
3
y
37
− 20y
36
+ ··· − 24y −1
c
4
, c
11
y
37
+ 23y
36
+ ··· − 21y −1
c
5
, c
8
y
37
− 33y
36
+ ··· + 29y −1
c
6
y
37
+ 4y
36
+ ··· + 32y −1
c
9
, c
12
y
37
+ 15y
36
+ ··· − 23y −1
c
10
y
37
+ 16y
34
+ ··· + 30y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952212 + 0.090311I
a = −0.104007 − 0.655366I
b = 0.208410 + 0.522362I
−1.17932 + 0.96611I 0.27254 + 2.52102I
u = −0.952212 − 0.090311I
a = −0.104007 + 0.655366I
b = 0.208410 − 0.522362I
−1.17932 − 0.96611I 0.27254 − 2.52102I
u = 0.319819 + 0.996719I
a = 2.65049 + 0.61977I
b = −1.59562 + 1.02330I
−0.45140 − 2.56507I −11.02853 + 5.16547I
u = 0.319819 − 0.996719I
a = 2.65049 − 0.61977I
b = −1.59562 − 1.02330I
−0.45140 + 2.56507I −11.02853 − 5.16547I
u = 0.740520 + 0.585878I
a = 0.663276 + 0.775081I
b = −2.40811 + 0.48918I
3.15523 − 3.56081I −4.03686 + 6.43106I
u = 0.740520 − 0.585878I
a = 0.663276 − 0.775081I
b = −2.40811 − 0.48918I
3.15523 + 3.56081I −4.03686 − 6.43106I
u = −0.416499 + 0.972612I
a = 0.88128 + 2.03607I
b = 0.595763 − 0.127531I
3.64739 + 0.16584I −2.88358 − 0.96832I
u = −0.416499 − 0.972612I
a = 0.88128 − 2.03607I
b = 0.595763 + 0.127531I
3.64739 − 0.16584I −2.88358 + 0.96832I
u = 0.831452 + 0.345027I
a = −0.429239 + 0.777863I
b = 1.66786 − 1.60998I
0.47473 − 2.75973I −5.24795 + 1.41911I
u = 0.831452 − 0.345027I
a = −0.429239 − 0.777863I
b = 1.66786 + 1.60998I
0.47473 + 2.75973I −5.24795 − 1.41911I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.458141 + 1.028050I
a = −0.869327 − 0.706073I
b = 1.51754 − 0.42557I
−4.46888 + 3.15544I −26.5881 − 4.0517I
u = 0.458141 − 1.028050I
a = −0.869327 + 0.706073I
b = 1.51754 + 0.42557I
−4.46888 − 3.15544I −26.5881 + 4.0517I
u = −0.566830 + 0.661005I
a = −1.332300 − 0.304883I
b = −0.626582 + 0.321553I
5.59318 + 1.34355I −3.36632 + 1.17381I
u = −0.566830 − 0.661005I
a = −1.332300 + 0.304883I
b = −0.626582 − 0.321553I
5.59318 − 1.34355I −3.36632 − 1.17381I
u = −0.538094 + 0.996131I
a = −0.69125 − 1.56159I
b = −0.415061 + 0.357911I
4.51353 − 5.77883I −3.50165 + 5.87210I
u = −0.538094 − 0.996131I
a = −0.69125 + 1.56159I
b = −0.415061 − 0.357911I
4.51353 + 5.77883I −3.50165 − 5.87210I
u = 0.342528 + 1.111330I
a = −2.97687 + 1.70899I
b = 1.10784 − 1.57583I
−3.72281 + 0.02504I −11.46828 + 0.I
u = 0.342528 − 1.111330I
a = −2.97687 − 1.70899I
b = 1.10784 + 1.57583I
−3.72281 − 0.02504I −11.46828 + 0.I
u = 0.196424 + 0.810077I
a = −0.071376 + 1.329080I
b = −1.34633 − 0.67267I
0.42538 + 4.86711I −12.3973 − 6.8417I
u = 0.196424 − 0.810077I
a = −0.071376 − 1.329080I
b = −1.34633 + 0.67267I
0.42538 − 4.86711I −12.3973 + 6.8417I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340917 + 0.742877I
a = 2.68410 + 1.31226I
b = 0.653111 − 0.504954I
4.51247 − 3.44104I −4.31509 + 12.23106I
u = −0.340917 − 0.742877I
a = 2.68410 − 1.31226I
b = 0.653111 + 0.504954I
4.51247 + 3.44104I −4.31509 − 12.23106I
u = 0.604712 + 1.052990I
a = 0.79485 + 2.85404I
b = −2.42269 − 0.96027I
1.68369 + 8.70603I −6.3309 − 12.6711I
u = 0.604712 − 1.052990I
a = 0.79485 − 2.85404I
b = −2.42269 + 0.96027I
1.68369 − 8.70603I −6.3309 + 12.6711I
u = −0.453958 + 1.153080I
a = −0.514883 + 0.395782I
b = −0.033508 − 0.222257I
−6.72491 − 4.05872I −14.5319 + 3.6037I
u = −0.453958 − 1.153080I
a = −0.514883 − 0.395782I
b = −0.033508 + 0.222257I
−6.72491 + 4.05872I −14.5319 − 3.6037I
u = 0.087285 + 0.738567I
a = −1.156660 − 0.183774I
b = 0.76662 + 1.20592I
−1.79055 + 1.99497I −17.4589 − 1.8946I
u = 0.087285 − 0.738567I
a = −1.156660 + 0.183774I
b = 0.76662 − 1.20592I
−1.79055 − 1.99497I −17.4589 + 1.8946I
u = 0.552094 + 1.164430I
a = 0.33534 − 3.50860I
b = 1.44777 + 1.73879I
−2.09762 + 7.91089I −7.69267 − 6.67021I
u = 0.552094 − 1.164430I
a = 0.33534 + 3.50860I
b = 1.44777 − 1.73879I
−2.09762 − 7.91089I −7.69267 + 6.67021I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.401506 + 1.227270I
a = −0.240017 + 0.236492I
b = 0.295463 − 0.357562I
−5.42342 − 3.43861I −6.21564 + 7.48749I
u = −0.401506 − 1.227270I
a = −0.240017 − 0.236492I
b = 0.295463 + 0.357562I
−5.42342 + 3.43861I −6.21564 − 7.48749I
u = −0.467703 + 1.250830I
a = 0.566324 + 0.107385I
b = −0.429435 − 0.045642I
−4.92900 − 5.98878I 0
u = −0.467703 − 1.250830I
a = 0.566324 − 0.107385I
b = −0.429435 + 0.045642I
−4.92900 + 5.98878I 0
u = 0.313789 + 0.564788I
a = 0.43343 − 2.21104I
b = 0.891963 + 0.402792I
−2.91040 + 0.42992I −16.9096 + 4.9698I
u = 0.313789 − 0.564788I
a = 0.43343 + 2.21104I
b = 0.891963 − 0.402792I
−2.91040 − 0.42992I −16.9096 − 4.9698I
u = −0.618091
a = −1.24632
b = 0.249980
−3.64366 −10.0020
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
37
− 20u
36
+ ··· − 14u + 1)(u
153
+ 77u
152
+ ··· − 1548u − 121)
c
2
(u
37
+ 10u
35
+ ··· − 7u
2
− 1)(u
153
+ u
152
+ ··· + 28u + 11)
c
3
(u
37
− 10u
35
+ ··· + 4u − 1)
· (u
153
− u
152
+ ··· + 13334880u + 1770791)
c
4
(u
37
− u
36
+ ··· − u + 1)(u
153
+ 2u
152
+ ··· + 3u + 1)
c
5
(u
37
+ 3u
36
+ ··· − 3u − 1)(u
153
− 50u
151
+ ··· + 8395u + 10331)
c
6
(u
37
+ 2u
35
+ ··· − 16u
2
+ 1)(u
153
+ u
152
+ ··· + 869544u + 253007)
c
7
(u
37
+ 10u
35
+ ··· + 7u
2
+ 1)(u
153
+ u
152
+ ··· + 28u + 11)
c
8
(u
37
− 3u
36
+ ··· − 3u + 1)(u
153
− 50u
151
+ ··· + 8395u + 10331)
c
9
(u
37
− 7u
36
+ ··· + 7u − 1)(u
153
− 4u
152
+ ··· − 52195u + 4961)
c
10
(u
37
+ 8u
31
+ ··· − 2u + 1)(u
153
− u
152
+ ··· + 35046u + 9439)
c
11
(u
37
+ u
36
+ ··· − u − 1)(u
153
+ 2u
152
+ ··· + 3u + 1)
c
12
(u
37
+ 7u
36
+ ··· + 7u + 1)(u
153
− 4u
152
+ ··· − 52195u + 4961)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
37
+ 40y
35
+ ··· + 6y −1)(y
153
+ 5y
152
+ ··· − 286508y −14641)
c
2
, c
7
(y
37
+ 20y
36
+ ··· − 14y −1)(y
153
+ 77y
152
+ ··· − 1548y −121)
c
3
(y
37
− 20y
36
+ ··· − 24y −1)
· (y
153
− 67y
152
+ ··· − 141584742282518y −3135700765681)
c
4
, c
11
(y
37
+ 23y
36
+ ··· − 21y −1)(y
153
+ 84y
152
+ ··· − 39y −1)
c
5
, c
8
(y
37
− 33y
36
+ ··· + 29y −1)
· (y
153
− 100y
152
+ ··· + 4473444915y −106729561)
c
6
(y
37
+ 4y
36
+ ··· + 32y −1)
· (y
153
+ 25y
152
+ ··· − 1962648262454y −64012542049)
c
9
, c
12
(y
37
+ 15y
36
+ ··· − 23y −1)
· (y
153
+ 80y
152
+ ··· − 798994097y −24611521)
c
10
(y
37
+ 16y
34
+ ··· + 30y −1)
· (y
153
+ 17y
152
+ ··· − 7057634132y −89094721)
31
