12a
0979
(K12a
0979
)
A knot diagram
1
Linearized knot diagam
4 6 11 8 2 10 1 5 12 3 7 9
Solving Sequence
5,9
8
1,4
2 6 7 12 10 11 3
c
8
c
4
c
1
c
5
c
7
c
12
c
9
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.28281 × 10
609
u
152
+ 5.70333 × 10
609
u
151
+ ··· + 1.62531 × 10
610
b + 4.43748 × 10
612
,
9.86064 × 10
612
u
152
+ 3.28103 × 10
613
u
151
+ ··· + 4.53298 × 10
613
a + 4.56455 × 10
616
,
u
153
+ 3u
152
+ ··· − 5927u − 2789i
I
u
2
= h−4.96325 × 10
19
u
36
− 1.68009 × 10
20
u
35
+ ··· + 5.82980 × 10
17
b + 9.18197 × 10
19
,
2.83565 × 10
19
u
36
+ 9.47056 × 10
19
u
35
+ ··· + 5.82980 × 10
17
a − 7.12118 × 10
19
, u
37
+ 4u
36
+ ··· − 8u − 1i
I
u
3
= hb, a − u − 1, u
3
+ u
2
− 1i
I
u
4
= hb, a − 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 194 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
= h1.28 × 10
609
u
152
+ 5.70 × 10
609
u
151
+ · · · + 1.63 × 10
610
b + 4.44 ×
10
612
, 9.86 × 10
612
u
152
+ 3.28 × 10
613
u
151
+ · · · + 4.53 × 10
613
a + 4.56 ×
10
616
, u
153
+ 3u
152
+ · · · − 5927u − 2789i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−0.217531u
152
− 0.723812u
151
+ ··· − 2983.07u − 1006.96
−0.0789275u
152
− 0.350907u
151
+ ··· − 1126.14u − 273.024
a
4
=
−u
−u
3
+ u
a
2
=
−0.104395u
152
− 0.284179u
151
+ ··· − 1526.20u − 473.627
−0.0380832u
152
− 0.244056u
151
+ ··· − 1673.44u − 526.835
a
6
=
1.88754u
152
+ 7.27310u
151
+ ··· + 19454.7u + 5679.34
−0.431277u
152
− 1.74643u
151
+ ··· − 5970.32u − 1834.41
a
7
=
2.38322u
152
+ 9.22443u
151
+ ··· + 26525.4u + 8607.01
−0.204594u
152
− 1.05976u
151
+ ··· − 5337.10u − 1970.55
a
12
=
−0.138603u
152
− 0.372904u
151
+ ··· − 1856.93u − 733.940
−0.0789275u
152
− 0.350907u
151
+ ··· − 1126.14u − 273.024
a
10
=
−0.501318u
152
− 2.22897u
151
+ ··· − 9009.17u − 2879.10
0.247246u
152
+ 1.06495u
151
+ ··· + 2246.96u + 849.901
a
11
=
6.22371u
152
+ 24.5377u
151
+ ··· + 57732.8u + 18511.5
−0.738844u
152
− 3.16251u
151
+ ··· − 6523.56u − 2353.66
a
3
=
−6.52573u
152
− 26.1053u
151
+ ··· − 59538.9u − 18890.0
0.571964u
152
+ 2.31321u
151
+ ··· + 3012.92u + 903.759
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.81594u
152
+ 24.7068u
151
+ ··· + 47717.7u + 16629.8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
153
− 12u
152
+ ··· − 56332u + 7874
c
2
, c
5
u
153
+ 9u
152
+ ··· − 508434u − 176401
c
3
, c
10
u
153
− 3u
152
+ ··· + 28708u − 3617
c
4
, c
8
u
153
+ 3u
152
+ ··· − 5927u − 2789
c
6
u
153
− 7u
152
+ ··· − 4234131617u − 264250321
c
7
u
153
+ 3u
152
+ ··· + 1096u − 428
c
9
, c
12
u
153
+ 10u
152
+ ··· + 6400u − 2432
c
11
u
153
+ 15u
152
+ ··· + 331308u − 100816
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
153
+ 20y
152
+ ··· + 105095636y −61999876
c
2
, c
5
y
153
− 193y
152
+ ··· + 755521653094y −31117312801
c
3
, c
10
y
153
− 105y
152
+ ··· + 1173688910y −13082689
c
4
, c
8
y
153
− 75y
152
+ ··· + 149372347y −7778521
c
6
y
153
+ 77y
152
+ ··· + 1847642535511061561y −69828232148603041
c
7
y
153
− 75y
152
+ ··· + 8936032y −183184
c
9
, c
12
y
153
+ 118y
152
+ ··· + 647831552y −5914624
c
11
y
153
− 35y
152
+ ··· + 290394396848y −10163865856
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997781
a = 8.75197
b = 0.0647899
−0.00219509 0
u = −0.341614 + 0.931233I
a = −0.370406 + 0.406647I
b = −0.185584 − 1.072250I
−3.61191 + 2.52822I 0
u = −0.341614 − 0.931233I
a = −0.370406 − 0.406647I
b = −0.185584 + 1.072250I
−3.61191 − 2.52822I 0
u = −0.072377 + 0.983268I
a = −0.318149 + 0.469174I
b = −0.300070 − 1.335890I
−5.26544 + 7.42458I 0
u = −0.072377 − 0.983268I
a = −0.318149 − 0.469174I
b = −0.300070 + 1.335890I
−5.26544 − 7.42458I 0
u = 0.864802 + 0.538644I
a = 1.02477 − 1.09021I
b = 0.244675 + 0.892365I
−0.76159 + 1.35256I 0
u = 0.864802 − 0.538644I
a = 1.02477 + 1.09021I
b = 0.244675 − 0.892365I
−0.76159 − 1.35256I 0
u = −0.827905 + 0.595560I
a = 1.304940 − 0.197851I
b = 0.12160 − 1.47494I
−8.89019 − 3.19697I 0
u = −0.827905 − 0.595560I
a = 1.304940 + 0.197851I
b = 0.12160 + 1.47494I
−8.89019 + 3.19697I 0
u = −0.025248 + 0.969006I
a = −0.299791 − 0.487821I
b = 0.906922 + 0.100199I
−2.14800 − 1.50633I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.025248 − 0.969006I
a = −0.299791 + 0.487821I
b = 0.906922 − 0.100199I
−2.14800 + 1.50633I 0
u = 0.989734 + 0.318008I
a = 0.22701 + 1.42246I
b = −0.70870 + 2.08315I
−7.32709 + 4.58957I 0
u = 0.989734 − 0.318008I
a = 0.22701 − 1.42246I
b = −0.70870 − 2.08315I
−7.32709 − 4.58957I 0
u = −0.902372 + 0.538652I
a = −1.090840 − 0.663576I
b = −0.13790 + 1.55018I
−9.00785 − 0.43770I 0
u = −0.902372 − 0.538652I
a = −1.090840 + 0.663576I
b = −0.13790 − 1.55018I
−9.00785 + 0.43770I 0
u = −0.862240 + 0.392691I
a = −0.29420 − 1.42358I
b = −0.161096 + 1.356630I
−9.38534 − 9.47300I 0
u = −0.862240 − 0.392691I
a = −0.29420 + 1.42358I
b = −0.161096 − 1.356630I
−9.38534 + 9.47300I 0
u = 0.832026 + 0.426042I
a = −0.293205 + 0.324712I
b = −0.48148 + 1.50098I
−9.63438 − 5.81743I 0
u = 0.832026 − 0.426042I
a = −0.293205 − 0.324712I
b = −0.48148 − 1.50098I
−9.63438 + 5.81743I 0
u = −0.119562 + 0.924520I
a = 0.096611 − 0.517704I
b = 0.349672 + 1.234820I
−2.18119 + 3.63455I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.119562 − 0.924520I
a = 0.096611 + 0.517704I
b = 0.349672 − 1.234820I
−2.18119 − 3.63455I 0
u = −0.826872 + 0.428150I
a = 0.252811 + 0.823012I
b = 0.093204 − 1.393210I
−5.75444 − 4.67554I 0
u = −0.826872 − 0.428150I
a = 0.252811 − 0.823012I
b = 0.093204 + 1.393210I
−5.75444 + 4.67554I 0
u = −0.726161 + 0.582004I
a = −0.737072 + 0.151735I
b = −0.00296 + 1.53384I
−9.17623 − 1.44438I 0
u = −0.726161 − 0.582004I
a = −0.737072 − 0.151735I
b = −0.00296 − 1.53384I
−9.17623 + 1.44438I 0
u = 0.882528 + 0.290522I
a = 1.85197 − 1.11541I
b = 0.383224 − 0.566013I
1.56920 + 3.18136I 0
u = 0.882528 − 0.290522I
a = 1.85197 + 1.11541I
b = 0.383224 + 0.566013I
1.56920 − 3.18136I 0
u = −0.899606 + 0.585036I
a = −0.394547 + 0.708643I
b = 0.043813 + 0.711490I
−0.935418 + 0.215869I 0
u = −0.899606 − 0.585036I
a = −0.394547 − 0.708643I
b = 0.043813 − 0.711490I
−0.935418 − 0.215869I 0
u = 0.861926 + 0.334675I
a = 2.55635 + 0.76486I
b = 0.56596 + 1.48467I
−5.08208 + 4.36622I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.861926 − 0.334675I
a = 2.55635 − 0.76486I
b = 0.56596 − 1.48467I
−5.08208 − 4.36622I 0
u = 0.088621 + 0.920266I
a = 0.031760 + 0.517902I
b = −0.981938 + 0.073899I
−6.10163 − 8.06042I 0
u = 0.088621 − 0.920266I
a = 0.031760 − 0.517902I
b = −0.981938 − 0.073899I
−6.10163 + 8.06042I 0
u = 0.824328 + 0.409646I
a = −2.59398 − 0.67280I
b = −0.69516 − 1.29223I
−9.66879 + 9.36370I 0
u = 0.824328 − 0.409646I
a = −2.59398 + 0.67280I
b = −0.69516 + 1.29223I
−9.66879 − 9.36370I 0
u = −0.800529 + 0.438940I
a = −2.50618 + 0.30716I
b = 0.081374 + 1.141410I
−5.83015 + 1.00845I 0
u = −0.800529 − 0.438940I
a = −2.50618 − 0.30716I
b = 0.081374 − 1.141410I
−5.83015 − 1.00845I 0
u = 1.045210 + 0.312312I
a = −1.042300 + 0.955080I
b = −0.333642 + 0.446226I
2.12407 − 0.35100I 0
u = 1.045210 − 0.312312I
a = −1.042300 − 0.955080I
b = −0.333642 − 0.446226I
2.12407 + 0.35100I 0
u = −0.247276 + 0.864800I
a = 0.349804 − 0.025716I
b = 0.427405 + 1.068930I
−5.34348 + 4.86562I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247276 − 0.864800I
a = 0.349804 + 0.025716I
b = 0.427405 − 1.068930I
−5.34348 − 4.86562I 0
u = −0.809279 + 0.390526I
a = 3.04826 − 0.42221I
b = −0.138789 − 1.089010I
−9.56347 + 6.10996I 0
u = −0.809279 − 0.390526I
a = 3.04826 + 0.42221I
b = −0.138789 + 1.089010I
−9.56347 − 6.10996I 0
u = 0.826940 + 0.333273I
a = −0.405508 + 0.051029I
b = 0.27071 − 1.58027I
−5.19468 − 1.39926I 0
u = 0.826940 − 0.333273I
a = −0.405508 − 0.051029I
b = 0.27071 + 1.58027I
−5.19468 + 1.39926I 0
u = 1.098250 + 0.159299I
a = −0.807502 + 0.315922I
b = −0.252210 + 0.472759I
2.04815 + 0.14892I 0
u = 1.098250 − 0.159299I
a = −0.807502 − 0.315922I
b = −0.252210 − 0.472759I
2.04815 − 0.14892I 0
u = 0.882448 + 0.078541I
a = −2.64840 + 3.64459I
b = −0.00259 − 1.43722I
−5.21371 + 0.20813I 0
u = 0.882448 − 0.078541I
a = −2.64840 − 3.64459I
b = −0.00259 + 1.43722I
−5.21371 − 0.20813I 0
u = 1.040800 + 0.455931I
a = 2.37266 + 0.10421I
b = 0.294268 + 1.152880I
−0.60098 + 5.99532I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.040800 − 0.455931I
a = 2.37266 − 0.10421I
b = 0.294268 − 1.152880I
−0.60098 − 5.99532I 0
u = 0.855047
a = 2.44653
b = 0.623171
0.683985 0
u = −1.052750 + 0.475909I
a = 1.17176 + 0.80525I
b = 0.947447 + 0.572850I
−0.93849 − 4.41930I 0
u = −1.052750 − 0.475909I
a = 1.17176 − 0.80525I
b = 0.947447 − 0.572850I
−0.93849 + 4.41930I 0
u = −0.829950 + 0.155484I
a = −1.56712 − 0.63356I
b = −1.007240 − 0.465181I
−1.68823 − 1.09179I 0
u = −0.829950 − 0.155484I
a = −1.56712 + 0.63356I
b = −1.007240 + 0.465181I
−1.68823 + 1.09179I 0
u = −0.693252 + 0.480222I
a = 2.25022 + 0.61354I
b = −0.188654 − 1.271180I
−9.65386 − 3.75737I 0
u = −0.693252 − 0.480222I
a = 2.25022 − 0.61354I
b = −0.188654 + 1.271180I
−9.65386 + 3.75737I 0
u = −0.823391 + 0.166420I
a = −0.403071 − 0.970330I
b = −0.21061 − 1.49328I
−1.05457 − 3.16951I 0
u = −0.823391 − 0.166420I
a = −0.403071 + 0.970330I
b = −0.21061 + 1.49328I
−1.05457 + 3.16951I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.074790 + 0.461713I
a = −0.872623 − 0.779579I
b = −0.651069 − 0.667330I
0.45680 − 4.19166I 0
u = −1.074790 − 0.461713I
a = −0.872623 + 0.779579I
b = −0.651069 + 0.667330I
0.45680 + 4.19166I 0
u = 1.068190 + 0.480580I
a = −1.80608 + 0.39287I
b = −0.321321 − 0.998354I
0.38913 + 2.69464I 0
u = 1.068190 − 0.480580I
a = −1.80608 − 0.39287I
b = −0.321321 + 0.998354I
0.38913 − 2.69464I 0
u = −1.183880 + 0.094998I
a = 1.054400 − 0.570452I
b = 0.738664 − 1.066100I
2.04139 − 3.66981I 0
u = −1.183880 − 0.094998I
a = 1.054400 + 0.570452I
b = 0.738664 + 1.066100I
2.04139 + 3.66981I 0
u = 0.364490 + 1.137200I
a = −0.077897 − 0.409675I
b = −0.48454 + 1.37028I
−10.6121 − 13.3462I 0
u = 0.364490 − 1.137200I
a = −0.077897 + 0.409675I
b = −0.48454 − 1.37028I
−10.6121 + 13.3462I 0
u = 1.113250 + 0.473616I
a = −1.64873 − 0.07451I
b = −0.223103 − 1.035910I
0.52843 + 2.52604I 0
u = 1.113250 − 0.473616I
a = −1.64873 + 0.07451I
b = −0.223103 + 1.035910I
0.52843 − 2.52604I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.097490 + 0.521943I
a = −0.509017 − 0.345882I
b = −0.285983 − 0.449083I
0.28557 − 4.65072I 0
u = −1.097490 − 0.521943I
a = −0.509017 + 0.345882I
b = −0.285983 + 0.449083I
0.28557 + 4.65072I 0
u = 1.168670 + 0.337131I
a = 1.63363 + 1.06823I
b = 0.058301 + 1.162300I
−3.04783 + 0.69043I 0
u = 1.168670 − 0.337131I
a = 1.63363 − 1.06823I
b = 0.058301 − 1.162300I
−3.04783 − 0.69043I 0
u = −1.182420 + 0.321253I
a = 1.42288 + 0.38962I
b = 1.102580 − 0.025907I
5.46132 − 3.10520I 0
u = −1.182420 − 0.321253I
a = 1.42288 − 0.38962I
b = 1.102580 + 0.025907I
5.46132 + 3.10520I 0
u = −0.236778 + 0.722749I
a = 0.278181 − 0.035120I
b = −0.292920 − 1.309310I
−7.12480 + 2.61572I 0
u = −0.236778 − 0.722749I
a = 0.278181 + 0.035120I
b = −0.292920 + 1.309310I
−7.12480 − 2.61572I 0
u = 0.734491 + 0.194000I
a = −3.26533 − 0.98574I
b = −1.22706 − 1.46656I
−8.38323 − 2.12065I 0
u = 0.734491 − 0.194000I
a = −3.26533 + 0.98574I
b = −1.22706 + 1.46656I
−8.38323 + 2.12065I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.162880 + 0.438073I
a = −1.133890 + 0.352910I
b = −1.261010 + 0.096086I
−4.34991 + 0.42060I 0
u = 1.162880 − 0.438073I
a = −1.133890 − 0.352910I
b = −1.261010 − 0.096086I
−4.34991 − 0.42060I 0
u = −1.134370 + 0.510920I
a = −1.56551 + 0.26888I
b = −0.627093 + 1.266570I
−4.52703 − 7.27671I 0
u = −1.134370 − 0.510920I
a = −1.56551 − 0.26888I
b = −0.627093 − 1.266570I
−4.52703 + 7.27671I 0
u = 0.443567 + 1.170040I
a = −0.045839 + 0.427843I
b = 0.50619 − 1.34115I
−6.11410 − 6.82150I 0
u = 0.443567 − 1.170040I
a = −0.045839 − 0.427843I
b = 0.50619 + 1.34115I
−6.11410 + 6.82150I 0
u = −1.188910 + 0.394190I
a = −1.43237 − 0.32360I
b = −0.928790 + 0.106605I
3.07922 − 7.88184I 0
u = −1.188910 − 0.394190I
a = −1.43237 + 0.32360I
b = −0.928790 − 0.106605I
3.07922 + 7.88184I 0
u = 1.083140 + 0.642497I
a = −0.632980 + 0.526468I
b = −0.220938 − 0.375852I
1.95588 + 0.17301I 0
u = 1.083140 − 0.642497I
a = −0.632980 − 0.526468I
b = −0.220938 + 0.375852I
1.95588 − 0.17301I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.230520 + 0.285456I
a = 0.303618 − 0.480615I
b = 0.531964 − 0.824565I
2.64938 + 0.52879I 0
u = 1.230520 − 0.285456I
a = 0.303618 + 0.480615I
b = 0.531964 + 0.824565I
2.64938 − 0.52879I 0
u = −0.057350 + 0.727652I
a = 0.572425 + 0.940772I
b = −0.584339 + 0.227450I
−7.73358 + 3.67399I 0
u = −0.057350 − 0.727652I
a = 0.572425 − 0.940772I
b = −0.584339 − 0.227450I
−7.73358 − 3.67399I 0
u = −0.911566 + 0.909547I
a = 0.561740 + 0.901315I
b = 0.048986 − 1.082890I
−2.08708 − 0.28521I 0
u = −0.911566 − 0.909547I
a = 0.561740 − 0.901315I
b = 0.048986 + 1.082890I
−2.08708 + 0.28521I 0
u = −1.198840 + 0.494811I
a = 0.456784 − 0.358729I
b = −0.009708 + 0.142361I
−4.46263 − 8.22652I 0
u = −1.198840 − 0.494811I
a = 0.456784 + 0.358729I
b = −0.009708 − 0.142361I
−4.46263 + 8.22652I 0
u = 1.278550 + 0.223642I
a = 0.238216 − 0.887311I
b = 0.272328 − 0.736728I
−0.318757 − 1.181500I 0
u = 1.278550 − 0.223642I
a = 0.238216 + 0.887311I
b = 0.272328 + 0.736728I
−0.318757 + 1.181500I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.178150 + 0.567079I
a = 1.76441 − 0.13756I
b = 0.600713 − 1.064050I
−2.56385 − 10.10150I 0
u = −1.178150 − 0.567079I
a = 1.76441 + 0.13756I
b = 0.600713 + 1.064050I
−2.56385 + 10.10150I 0
u = −1.172480 + 0.600215I
a = −1.67947 − 0.00210I
b = −0.373130 + 1.089400I
−1.04559 − 8.07744I 0
u = −1.172480 − 0.600215I
a = −1.67947 + 0.00210I
b = −0.373130 − 1.089400I
−1.04559 + 8.07744I 0
u = 0.048406 + 0.678959I
a = −0.461341 − 0.341300I
b = −0.630635 − 0.209529I
−0.50865 + 3.99134I 0
u = 0.048406 − 0.678959I
a = −0.461341 + 0.341300I
b = −0.630635 + 0.209529I
−0.50865 − 3.99134I 0
u = −1.217280 + 0.525243I
a = 1.66710 − 0.13015I
b = 0.51662 − 1.35832I
1.13115 − 8.76605I 0
u = −1.217280 − 0.525243I
a = 1.66710 + 0.13015I
b = 0.51662 + 1.35832I
1.13115 + 8.76605I 0
u = 0.386880 + 0.545795I
a = 0.019599 + 0.401864I
b = 0.535227 − 0.054926I
1.331330 + 0.135841I 0
u = 0.386880 − 0.545795I
a = 0.019599 − 0.401864I
b = 0.535227 + 0.054926I
1.331330 − 0.135841I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.229420 + 0.521834I
a = −1.300530 + 0.536723I
b = −1.347630 − 0.158698I
−2.67038 + 13.18000I 0
u = 1.229420 − 0.521834I
a = −1.300530 − 0.536723I
b = −1.347630 + 0.158698I
−2.67038 − 13.18000I 0
u = −1.083090 + 0.788286I
a = −1.159790 − 0.595573I
b = −0.121507 + 1.098270I
−1.40267 − 6.25997I 0
u = −1.083090 − 0.788286I
a = −1.159790 + 0.595573I
b = −0.121507 − 1.098270I
−1.40267 + 6.25997I 0
u = 0.658027
a = −0.0661940
b = 0.390696
1.05441 10.6590
u = 1.261740 + 0.483853I
a = 1.252050 − 0.506803I
b = 1.53286 + 0.17527I
1.76560 + 6.51802I 0
u = 1.261740 − 0.483853I
a = 1.252050 + 0.506803I
b = 1.53286 − 0.17527I
1.76560 − 6.51802I 0
u = −1.254690 + 0.529603I
a = −1.69639 + 0.23211I
b = −0.42223 + 1.38623I
−1.65727 − 12.74040I 0
u = −1.254690 − 0.529603I
a = −1.69639 − 0.23211I
b = −0.42223 − 1.38623I
−1.65727 + 12.74040I 0
u = −0.398298 + 0.486792I
a = 1.58074 + 0.64029I
b = 0.838778 − 0.238634I
−2.81335 + 0.38459I −2.77066 + 0.I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398298 − 0.486792I
a = 1.58074 − 0.64029I
b = 0.838778 + 0.238634I
−2.81335 − 0.38459I −2.77066 + 0.I
u = 0.471508 + 0.413069I
a = 0.48452 + 1.47249I
b = 0.149745 − 1.217450I
−2.31181 − 2.20262I 0
u = 0.471508 − 0.413069I
a = 0.48452 − 1.47249I
b = 0.149745 + 1.217450I
−2.31181 + 2.20262I 0
u = −0.417327 + 0.465612I
a = −1.263600 − 0.237117I
b = −0.338519 + 0.294274I
−1.49143 + 0.36154I −7.24646 + 0.I
u = −0.417327 − 0.465612I
a = −1.263600 + 0.237117I
b = −0.338519 − 0.294274I
−1.49143 − 0.36154I −7.24646 + 0.I
u = 1.211930 + 0.654448I
a = 0.993767 − 0.422852I
b = 0.717888 + 0.753620I
3.17466 + 5.34859I 0
u = 1.211930 − 0.654448I
a = 0.993767 + 0.422852I
b = 0.717888 − 0.753620I
3.17466 − 5.34859I 0
u = −1.336130 + 0.348625I
a = 1.142270 − 0.017239I
b = 0.99874 − 1.01771I
2.37925 − 3.65891I 0
u = −1.336130 − 0.348625I
a = 1.142270 + 0.017239I
b = 0.99874 + 1.01771I
2.37925 + 3.65891I 0
u = 0.285400 + 0.540991I
a = −0.463903 − 1.102900I
b = 0.066989 + 1.098600I
−1.81329 + 1.62957I 0. − 4.69464I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285400 − 0.540991I
a = −0.463903 + 1.102900I
b = 0.066989 − 1.098600I
−1.81329 − 1.62957I 0. + 4.69464I
u = −1.353580 + 0.334412I
a = −1.009290 − 0.311841I
b = −0.973841 + 0.517886I
−1.44753 + 3.36539I 0
u = −1.353580 − 0.334412I
a = −1.009290 + 0.311841I
b = −0.973841 − 0.517886I
−1.44753 − 3.36539I 0
u = 0.486407 + 1.311050I
a = 0.121664 − 0.290404I
b = −0.465339 + 1.205790I
−11.41490 − 0.01711I 0
u = 0.486407 − 1.311050I
a = 0.121664 + 0.290404I
b = −0.465339 − 1.205790I
−11.41490 + 0.01711I 0
u = 1.25083 + 0.67685I
a = −1.61549 + 0.08361I
b = −0.56865 − 1.47360I
−7.7816 + 19.7699I 0
u = 1.25083 − 0.67685I
a = −1.61549 − 0.08361I
b = −0.56865 + 1.47360I
−7.7816 − 19.7699I 0
u = 1.24419 + 0.70048I
a = 1.51849 − 0.16660I
b = 0.57430 + 1.48281I
−3.47835 + 13.44060I 0
u = 1.24419 − 0.70048I
a = 1.51849 + 0.16660I
b = 0.57430 − 1.48281I
−3.47835 − 13.44060I 0
u = 1.26926 + 0.72078I
a = −1.328030 + 0.112243I
b = −0.59703 − 1.43379I
−8.67684 + 7.04237I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26926 − 0.72078I
a = −1.328030 − 0.112243I
b = −0.59703 + 1.43379I
−8.67684 − 7.04237I 0
u = 1.43162 + 0.34643I
a = 0.000628 + 0.516965I
b = −0.243679 + 1.104630I
−0.39131 − 2.31110I 0
u = 1.43162 − 0.34643I
a = 0.000628 − 0.516965I
b = −0.243679 − 1.104630I
−0.39131 + 2.31110I 0
u = −1.47308 + 0.05715I
a = −0.607626 + 0.443165I
b = −0.573407 + 1.032710I
−3.15052 − 9.00420I 0
u = −1.47308 − 0.05715I
a = −0.607626 − 0.443165I
b = −0.573407 − 1.032710I
−3.15052 + 9.00420I 0
u = −0.51099 + 1.41149I
a = 0.003554 − 0.365713I
b = −0.000791 + 1.163130I
−10.88220 + 1.87551I 0
u = −0.51099 − 1.41149I
a = 0.003554 + 0.365713I
b = −0.000791 − 1.163130I
−10.88220 − 1.87551I 0
u = −1.30568 + 0.74372I
a = 1.094100 − 0.060933I
b = 0.144051 − 1.242120I
−8.00553 − 9.26939I 0
u = −1.30568 − 0.74372I
a = 1.094100 + 0.060933I
b = 0.144051 + 1.242120I
−8.00553 + 9.26939I 0
u = −0.25999 + 1.59207I
a = 0.145997 + 0.240124I
b = −0.191776 − 0.861933I
−9.30902 + 2.62774I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25999 − 1.59207I
a = 0.145997 − 0.240124I
b = −0.191776 + 0.861933I
−9.30902 − 2.62774I 0
u = −0.130832 + 0.284403I
a = −2.28871 − 0.88948I
b = −0.449867 + 0.501349I
−1.67842 + 0.58174I −3.95276 + 0.21148I
u = −0.130832 − 0.284403I
a = −2.28871 + 0.88948I
b = −0.449867 − 0.501349I
−1.67842 − 0.58174I −3.95276 − 0.21148I
20
II.
I
u
2
= h−4.96×10
19
u
36
−1.68×10
20
u
35
+· · ·+5.83×10
17
b+9.18×10
19
, 2.84×
10
19
u
36
+9.47×10
19
u
35
+· · ·+5.83×10
17
a−7.12×10
19
, u
37
+4u
36
+· · ·−8u−1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−48.6405u
36
− 162.451u
35
+ ··· + 769.079u + 122.151
85.1357u
36
+ 288.189u
35
+ ··· − 1002.32u − 157.500
a
4
=
−u
−u
3
+ u
a
2
=
−65.6089u
36
− 218.742u
35
+ ··· + 970.329u + 152.834
96.6233u
36
+ 327.400u
35
+ ··· − 1127.88u − 176.601
a
6
=
−179.908u
36
− 645.832u
35
+ ··· + 1638.84u + 279.067
112.631u
36
+ 390.482u
35
+ ··· − 1213.34u − 197.267
a
7
=
333.610u
36
+ 1121.78u
35
+ ··· − 4105.83u − 657.046
−25.4700u
36
− 80.8433u
35
+ ··· + 297.801u + 43.9902
a
12
=
−133.776u
36
− 450.640u
35
+ ··· + 1771.40u + 279.652
85.1357u
36
+ 288.189u
35
+ ··· − 1002.32u − 157.500
a
10
=
−213.983u
36
− 733.193u
35
+ ··· + 2408.13u + 388.746
−61.7426u
36
− 212.174u
35
+ ··· + 686.774u + 113.547
a
11
=
108.020u
36
+ 338.722u
35
+ ··· − 2089.45u − 312.093
−30.5461u
36
− 72.7620u
35
+ ··· + 760.104u + 106.365
a
3
=
317.979u
36
+ 1130.22u
35
+ ··· − 2710.24u − 457.688
−38.5625u
36
− 158.873u
35
+ ··· − 106.485u − 7.19371
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
309707479104250841599
582980292410531251
u
36
−
1084973529995227481957
582980292410531251
u
35
+ ··· +
8021401349665189962
1729911846915523
u +
448377740969530933741
582980292410531251
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
37
− 4u
36
+ ··· + 7u − 1
c
2
u
37
− 13u
35
+ ··· + 2u − 1
c
3
u
37
− 12u
35
+ ··· + 3u + 1
c
4
u
37
− 4u
36
+ ··· − 8u + 1
c
5
u
37
− 13u
35
+ ··· + 2u + 1
c
6
u
37
+ 7u
35
+ ··· + 11u
2
+ 1
c
7
u
37
+ 2u
36
+ ··· − 28u + 4
c
8
u
37
+ 4u
36
+ ··· − 8u − 1
c
9
u
37
+ 3u
36
+ ··· + 51u − 23
c
10
u
37
− 12u
35
+ ··· + 3u − 1
c
11
u
37
+ 4u
36
+ ··· − 10u − 1
c
12
u
37
− 3u
36
+ ··· + 51u + 23
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 8y
36
+ ··· − 9y −1
c
2
, c
5
y
37
− 26y
36
+ ··· − 6y −1
c
3
, c
10
y
37
− 24y
36
+ ··· + 11y −1
c
4
, c
8
y
37
− 14y
36
+ ··· + 20y −1
c
6
y
37
+ 14y
36
+ ··· − 22y −1
c
7
y
37
+ 12y
36
+ ··· + 48y −16
c
9
, c
12
y
37
+ 37y
36
+ ··· + 32087y −529
c
11
y
37
+ 16y
36
+ ··· + 6y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.944692
a = 2.02152
b = 0.116966
−0.0439988 −3.32010
u = −0.995422 + 0.355549I
a = −0.624297 + 1.073420I
b = 0.39959 + 1.90063I
−6.98931 − 4.64264I 6.35251 + 8.83665I
u = −0.995422 − 0.355549I
a = −0.624297 − 1.073420I
b = 0.39959 − 1.90063I
−6.98931 + 4.64264I 6.35251 − 8.83665I
u = −0.304941 + 0.853735I
a = −0.310767 + 0.341351I
b = −0.315612 − 1.183650I
−3.72043 + 3.83403I −3.12967 − 4.67200I
u = −0.304941 − 0.853735I
a = −0.310767 − 0.341351I
b = −0.315612 + 1.183650I
−3.72043 − 3.83403I −3.12967 + 4.67200I
u = 0.972411 + 0.567656I
a = 1.73240 − 0.63340I
b = 0.130997 + 0.904141I
0.48267 + 4.38413I 0. − 6.21715I
u = 0.972411 − 0.567656I
a = 1.73240 + 0.63340I
b = 0.130997 − 0.904141I
0.48267 − 4.38413I 0. + 6.21715I
u = −1.022940 + 0.485830I
a = −1.107660 − 0.855277I
b = −0.582738 − 0.522232I
1.12745 − 4.79266I 5.55418 + 7.95156I
u = −1.022940 − 0.485830I
a = −1.107660 + 0.855277I
b = −0.582738 + 0.522232I
1.12745 + 4.79266I 5.55418 − 7.95156I
u = 0.846816 + 0.081504I
a = 2.09679 − 3.48558I
b = −0.00268 + 1.43121I
−5.26168 + 0.21555I −64.1715 − 7.3346I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846816 − 0.081504I
a = 2.09679 + 3.48558I
b = −0.00268 − 1.43121I
−5.26168 − 0.21555I −64.1715 + 7.3346I
u = 0.797988 + 0.121711I
a = 0.786447 − 0.612142I
b = 0.137852 − 1.358060I
−0.90636 + 2.89655I 5.72453 + 4.24088I
u = 0.797988 − 0.121711I
a = 0.786447 + 0.612142I
b = 0.137852 + 1.358060I
−0.90636 − 2.89655I 5.72453 − 4.24088I
u = 0.995306 + 0.678343I
a = −0.970035 + 0.842092I
b = −0.162565 − 0.997622I
0.341123 + 0.738385I 0
u = 0.995306 − 0.678343I
a = −0.970035 − 0.842092I
b = −0.162565 + 0.997622I
0.341123 − 0.738385I 0
u = −0.774421 + 0.173860I
a = 3.13794 − 0.96170I
b = 0.98785 − 1.51125I
−8.17554 + 2.22695I 9.24303 − 9.12785I
u = −0.774421 − 0.173860I
a = 3.13794 + 0.96170I
b = 0.98785 + 1.51125I
−8.17554 − 2.22695I 9.24303 + 9.12785I
u = 1.173100 + 0.323813I
a = −0.069861 + 0.731728I
b = −0.188044 + 0.802950I
0.858771 − 0.851004I 0
u = 1.173100 − 0.323813I
a = −0.069861 − 0.731728I
b = −0.188044 − 0.802950I
0.858771 + 0.851004I 0
u = −0.109710 + 1.269750I
a = 0.075332 + 0.558562I
b = 0.206772 − 1.216090I
−10.67190 + 1.00730I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.109710 − 1.269750I
a = 0.075332 − 0.558562I
b = 0.206772 + 1.216090I
−10.67190 − 1.00730I 0
u = −1.160280 + 0.569290I
a = −1.83161 + 0.09277I
b = −0.462809 + 1.176410I
−1.13517 − 9.04893I 0
u = −1.160280 − 0.569290I
a = −1.83161 − 0.09277I
b = −0.462809 − 1.176410I
−1.13517 + 9.04893I 0
u = 1.243150 + 0.406209I
a = −1.302040 + 0.124095I
b = −0.874556 − 0.958317I
3.04009 + 3.47459I 0
u = 1.243150 − 0.406209I
a = −1.302040 − 0.124095I
b = −0.874556 + 0.958317I
3.04009 − 3.47459I 0
u = −0.308880 + 0.582581I
a = −0.810024 − 0.543350I
b = −0.639549 + 0.168643I
−0.618085 + 0.366189I 3.54182 − 0.00112I
u = −0.308880 − 0.582581I
a = −0.810024 + 0.543350I
b = −0.639549 − 0.168643I
−0.618085 − 0.366189I 3.54182 + 0.00112I
u = −1.256810 + 0.593453I
a = −0.991896 − 0.422756I
b = −1.028950 + 0.423412I
1.78377 − 5.63034I 0
u = −1.256810 − 0.593453I
a = −0.991896 + 0.422756I
b = −1.028950 − 0.423412I
1.78377 + 5.63034I 0
u = −1.32738 + 0.52407I
a = 1.062350 − 0.380731I
b = 0.491278 − 0.982868I
−4.96649 − 9.85576I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32738 − 0.52407I
a = 1.062350 + 0.380731I
b = 0.491278 + 0.982868I
−4.96649 + 9.85576I 0
u = −0.561994 + 0.029803I
a = 3.27360 + 0.53544I
b = 0.384731 − 1.292170I
−9.38890 − 7.70197I −2.24879 + 5.73769I
u = −0.561994 − 0.029803I
a = 3.27360 − 0.53544I
b = 0.384731 + 1.292170I
−9.38890 + 7.70197I −2.24879 − 5.73769I
u = −0.314756 + 0.254189I
a = −2.60345 − 1.73640I
b = −0.274771 + 1.366580I
−5.65730 − 3.00951I −0.73274 + 2.44772I
u = −0.314756 − 0.254189I
a = −2.60345 + 1.73640I
b = −0.274771 − 1.366580I
−5.65730 + 3.00951I −0.73274 − 2.44772I
u = −0.36357 + 1.60215I
a = −0.053977 − 0.188346I
b = 0.234713 + 0.881288I
−9.33829 + 2.86115I 0
u = −0.36357 − 1.60215I
a = −0.053977 + 0.188346I
b = 0.234713 − 0.881288I
−9.33829 − 2.86115I 0
29
III. I
u
3
= hb, a − u − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
u + 1
0
a
4
=
−u
u
2
+ u − 1
a
2
=
u
2
+ u
−u
2
+ u
a
6
=
−u
2
− u
u
2
a
7
=
−u
u
2
a
12
=
u + 1
0
a
10
=
1
0
a
11
=
1
u
2
a
3
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
− 3u + 2
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− u
2
+ 2u − 1
c
2
, c
11
(u − 1)
3
c
3
, c
4
u
3
− u
2
+ 1
c
5
, c
7
(u + 1)
3
c
6
u
3
+ u
2
+ 2u + 1
c
8
, c
10
u
3
+ u
2
− 1
c
9
, c
12
u
3
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
, c
7
c
11
(y −1)
3
c
3
, c
4
, c
8
c
10
y
3
− y
2
+ 2y −1
c
9
, c
12
y
3
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.122561 + 0.744862I
b = 0
0 4.20216 + 0.37970I
u = −0.877439 − 0.744862I
a = 0.122561 − 0.744862I
b = 0
0 4.20216 − 0.37970I
u = 0.754878
a = 1.75488
b = 0
0 −1.40430
33
IV. I
u
4
= hb, a − 1, u − 1i
(i) Arc colorings
a
5
=
0
1
a
9
=
1
0
a
8
=
1
1
a
1
=
1
0
a
4
=
−1
0
a
2
=
1
0
a
6
=
−1
1
a
7
=
0
1
a
12
=
1
0
a
10
=
1
0
a
11
=
1
1
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
u
c
2
, c
8
, c
10
c
11
u − 1
c
3
, c
4
, c
5
c
6
, c
7
u + 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
11
y −1
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
0 0
37
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
3
− u
2
+ 2u − 1)(u
37
− 4u
36
+ ··· + 7u − 1)
· (u
153
− 12u
152
+ ··· − 56332u + 7874)
c
2
((u − 1)
4
)(u
37
− 13u
35
+ ··· + 2u − 1)
· (u
153
+ 9u
152
+ ··· − 508434u − 176401)
c
3
(u + 1)(u
3
− u
2
+ 1)(u
37
− 12u
35
+ ··· + 3u + 1)
· (u
153
− 3u
152
+ ··· + 28708u − 3617)
c
4
(u + 1)(u
3
− u
2
+ 1)(u
37
− 4u
36
+ ··· − 8u + 1)
· (u
153
+ 3u
152
+ ··· − 5927u − 2789)
c
5
((u + 1)
4
)(u
37
− 13u
35
+ ··· + 2u + 1)
· (u
153
+ 9u
152
+ ··· − 508434u − 176401)
c
6
(u + 1)(u
3
+ u
2
+ 2u + 1)(u
37
+ 7u
35
+ ··· + 11u
2
+ 1)
· (u
153
− 7u
152
+ ··· − 4234131617u − 264250321)
c
7
((u + 1)
4
)(u
37
+ 2u
36
+ ··· − 28u + 4)(u
153
+ 3u
152
+ ··· + 1096u − 428)
c
8
(u − 1)(u
3
+ u
2
− 1)(u
37
+ 4u
36
+ ··· − 8u − 1)
· (u
153
+ 3u
152
+ ··· − 5927u − 2789)
c
9
u
4
(u
37
+ 3u
36
+ ··· + 51u − 23)(u
153
+ 10u
152
+ ··· + 6400u − 2432)
c
10
(u − 1)(u
3
+ u
2
− 1)(u
37
− 12u
35
+ ··· + 3u − 1)
· (u
153
− 3u
152
+ ··· + 28708u − 3617)
c
11
((u − 1)
4
)(u
37
+ 4u
36
+ ··· − 10u − 1)
· (u
153
+ 15u
152
+ ··· + 331308u − 100816)
c
12
u
4
(u
37
− 3u
36
+ ··· + 51u + 23)(u
153
+ 10u
152
+ ··· + 6400u − 2432)
38
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
3
+ 3y
2
+ 2y −1)(y
37
+ 8y
36
+ ··· − 9y −1)
· (y
153
+ 20y
152
+ ··· + 105095636y −61999876)
c
2
, c
5
((y −1)
4
)(y
37
− 26y
36
+ ··· − 6y −1)
· (y
153
− 193y
152
+ ··· + 755521653094y −31117312801)
c
3
, c
10
(y −1)(y
3
− y
2
+ 2y −1)(y
37
− 24y
36
+ ··· + 11y −1)
· (y
153
− 105y
152
+ ··· + 1173688910y −13082689)
c
4
, c
8
(y −1)(y
3
− y
2
+ 2y −1)(y
37
− 14y
36
+ ··· + 20y −1)
· (y
153
− 75y
152
+ ··· + 149372347y −7778521)
c
6
(y −1)(y
3
+ 3y
2
+ 2y −1)(y
37
+ 14y
36
+ ··· − 22y −1)
· (y
153
+ 77y
152
+ ··· + 1847642535511061561y −69828232148603041)
c
7
((y −1)
4
)(y
37
+ 12y
36
+ ··· + 48y −16)
· (y
153
− 75y
152
+ ··· + 8936032y −183184)
c
9
, c
12
y
4
(y
37
+ 37y
36
+ ··· + 32087y −529)
· (y
153
+ 118y
152
+ ··· + 647831552y −5914624)
c
11
((y −1)
4
)(y
37
+ 16y
36
+ ··· + 6y −1)
· (y
153
− 35y
152
+ ··· + 290394396848y −10163865856)
39
