12a
0267
(K12a
0267
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 10 11 1 12 5 4 9
Solving Sequence
2,5
6
3,10
7 11 8 1 4 12 9
c
5
c
2
c
6
c
10
c
7
c
1
c
4
c
11
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.48175 × 10
423
u
145
+ 6.47417 × 10
423
u
144
+ ··· + 2.60431 × 10
425
b − 4.75085 × 10
426
,
1.32031 × 10
428
u
145
+ 5.69757 × 10
428
u
144
+ ··· + 7.55251 × 10
427
a − 5.42178 × 10
430
,
u
146
+ 4u
145
+ ··· − 333u + 145i
I
u
2
= h−22u
28
+ 63u
27
+ ··· + b + 40, 23u
28
− 38u
27
+ ··· + a − 9, u
29
− 3u
28
+ ··· − 3u + 1i
I
u
3
= h−8a
5
+ 5a
4
+ 4a
3
− 31a
2
+ 69b − 64a + 78, a
6
− 2a
5
+ 6a
3
− 2a
2
− 15a + 17, u + 1i
* 3 irreducible components of dim
C
= 0, with total 181 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
= h2.48 × 10
423
u
145
+ 6.47 × 10
423
u
144
+ · · · + 2.60 × 10
425
b − 4.75 ×
10
426
, 1.32 × 10
428
u
145
+ 5.70 × 10
428
u
144
+ · · · + 7.55 × 10
427
a − 5.42 ×
10
430
, u
146
+ 4u
145
+ · · · − 333u + 145i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−1.74818u
145
− 7.54395u
144
+ ··· + 409.136u + 717.878
−0.00952937u
145
− 0.0248594u
144
+ ··· + 17.2071u + 18.2422
a
7
=
−0.435446u
145
− 1.88667u
144
+ ··· + 130.906u + 250.926
0.114455u
145
+ 0.546935u
144
+ ··· + 7.79061u − 52.6943
a
11
=
−1.73865u
145
− 7.51909u
144
+ ··· + 391.929u + 699.635
−0.00952937u
145
− 0.0248594u
144
+ ··· + 17.2071u + 18.2422
a
8
=
1.22486u
145
+ 5.37461u
144
+ ··· − 224.823u − 480.791
0.0428686u
145
+ 0.227799u
144
+ ··· + 11.5021u − 11.9860
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
0.391087u
145
+ 1.84118u
144
+ ··· − 36.1350u − 159.522
0.223870u
145
+ 0.982120u
144
+ ··· − 18.3317u − 65.0821
a
12
=
0.120587u
145
+ 0.503240u
144
+ ··· − 24.4200u − 68.1190
0.120621u
145
+ 0.526531u
144
+ ··· − 34.8729u − 61.0393
a
9
=
1.24939u
145
+ 5.50261u
144
+ ··· − 217.275u − 493.079
0.194473u
145
+ 0.884878u
144
+ ··· − 14.3452u − 60.1351
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.772054u
145
− 3.28462u
144
+ ··· − 30.4527u + 140.299
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
146
+ 56u
145
+ ··· + 723369u + 21025
c
2
, c
5
u
146
+ 4u
145
+ ··· − 333u + 145
c
3
u
146
+ 4u
145
+ ··· + 2468988890u + 899654983
c
4
u
146
+ 12u
145
+ ··· + 18u + 1
c
6
u
146
− u
145
+ ··· + 13382u − 2117
c
7
u
146
− 4u
144
+ ··· + 672u + 320
c
8
, c
9
, c
12
u
146
+ 5u
145
+ ··· + 24u − 1
c
10
u
146
− u
145
+ ··· + 1200u + 145
c
11
u
146
− 5u
145
+ ··· − 1206u + 145
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
146
+ 76y
145
+ ··· − 56026237661y + 442050625
c
2
, c
5
y
146
− 56y
145
+ ··· − 723369y + 21025
c
3
y
146
+ 48y
145
+ ··· − 8.05 × 10
19
y + 8.09 × 10
17
c
4
y
146
+ 4y
145
+ ··· + 274y + 1
c
6
y
146
+ 31y
145
+ ··· + 165806780y + 4481689
c
7
y
146
− 8y
145
+ ··· − 3339264y + 102400
c
8
, c
9
, c
12
y
146
+ 147y
145
+ ··· + 14y + 1
c
10
y
146
+ 17y
145
+ ··· + 1475950y + 21025
c
11
y
146
− 7y
145
+ ··· − 324306y + 21025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.717312 + 0.699409I
a = −2.34714 − 1.26596I
b = −0.079322 + 0.544577I
9.86898 − 3.45452I 0
u = −0.717312 − 0.699409I
a = −2.34714 + 1.26596I
b = −0.079322 − 0.544577I
9.86898 + 3.45452I 0
u = 0.751663 + 0.666797I
a = −0.724199 − 0.469522I
b = −0.572940 + 1.018600I
4.66153 + 3.56872I 0
u = 0.751663 − 0.666797I
a = −0.724199 + 0.469522I
b = −0.572940 − 1.018600I
4.66153 − 3.56872I 0
u = 1.002600 + 0.195131I
a = 2.13983 + 0.28539I
b = 0.482851 + 0.453150I
0.85295 − 5.12362I 0
u = 1.002600 − 0.195131I
a = 2.13983 − 0.28539I
b = 0.482851 − 0.453150I
0.85295 + 5.12362I 0
u = 0.783873 + 0.582905I
a = −0.71241 + 2.00247I
b = −1.98372 + 0.05552I
−0.191919 + 0.970948I 0
u = 0.783873 − 0.582905I
a = −0.71241 − 2.00247I
b = −1.98372 − 0.05552I
−0.191919 − 0.970948I 0
u = −0.723954 + 0.736563I
a = −0.170958 + 0.108878I
b = 0.89695 + 1.32014I
3.10050 − 3.62856I 0
u = −0.723954 − 0.736563I
a = −0.170958 − 0.108878I
b = 0.89695 − 1.32014I
3.10050 + 3.62856I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.797875 + 0.656098I
a = 1.167590 + 0.442098I
b = 0.972968 + 0.380891I
0.107696 − 0.580505I 0
u = −0.797875 − 0.656098I
a = 1.167590 − 0.442098I
b = 0.972968 − 0.380891I
0.107696 + 0.580505I 0
u = 0.583336 + 0.856509I
a = 0.174856 + 0.109704I
b = 0.083596 − 0.849372I
4.28577 + 1.52049I 0
u = 0.583336 − 0.856509I
a = 0.174856 − 0.109704I
b = 0.083596 + 0.849372I
4.28577 − 1.52049I 0
u = −1.027870 + 0.186062I
a = 2.17640 − 0.35403I
b = 1.40942 − 1.24508I
−3.22736 − 0.23964I 0
u = −1.027870 − 0.186062I
a = 2.17640 + 0.35403I
b = 1.40942 + 1.24508I
−3.22736 + 0.23964I 0
u = 0.955093 + 0.003365I
a = −1.72619 + 1.44767I
b = −1.036130 + 0.751399I
−1.92739 + 4.08568I 0
u = 0.955093 − 0.003365I
a = −1.72619 − 1.44767I
b = −1.036130 − 0.751399I
−1.92739 − 4.08568I 0
u = −0.351932 + 0.984589I
a = 0.092783 − 0.200915I
b = −0.545899 + 0.665342I
1.45577 + 4.86741I 0
u = −0.351932 − 0.984589I
a = 0.092783 + 0.200915I
b = −0.545899 − 0.665342I
1.45577 − 4.86741I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545918 + 0.782116I
a = 0.43363 − 1.50600I
b = 1.52469 + 0.52897I
7.78027 + 5.16500I 0
u = 0.545918 − 0.782116I
a = 0.43363 + 1.50600I
b = 1.52469 − 0.52897I
7.78027 − 5.16500I 0
u = 0.866478 + 0.591952I
a = −1.77016 + 0.59900I
b = −0.19223 − 1.69763I
−0.48155 − 2.33988I 0
u = 0.866478 − 0.591952I
a = −1.77016 − 0.59900I
b = −0.19223 + 1.69763I
−0.48155 + 2.33988I 0
u = 0.943710 + 0.103188I
a = −0.738796 − 0.840429I
b = −0.400481 + 0.993970I
5.60767 + 3.55011I 0
u = 0.943710 − 0.103188I
a = −0.738796 + 0.840429I
b = −0.400481 − 0.993970I
5.60767 − 3.55011I 0
u = −1.039070 + 0.180991I
a = 0.52614 + 1.82921I
b = 0.323777 + 0.640515I
0.96939 − 3.33538I 0
u = −1.039070 − 0.180991I
a = 0.52614 − 1.82921I
b = 0.323777 − 0.640515I
0.96939 + 3.33538I 0
u = −0.876289 + 0.351593I
a = −0.69058 − 1.43780I
b = −0.765163 − 0.920942I
−1.81241 + 1.71386I 0
u = −0.876289 − 0.351593I
a = −0.69058 + 1.43780I
b = −0.765163 + 0.920942I
−1.81241 − 1.71386I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850854 + 0.402864I
a = −2.64553 − 0.68802I
b = −1.44440 + 0.94266I
−0.82398 + 4.32637I 0
u = −0.850854 − 0.402864I
a = −2.64553 + 0.68802I
b = −1.44440 − 0.94266I
−0.82398 − 4.32637I 0
u = 0.930828 + 0.018677I
a = −2.12552 + 1.00341I
b = −0.630981 + 0.098833I
−4.02304 + 1.06856I 0
u = 0.930828 − 0.018677I
a = −2.12552 − 1.00341I
b = −0.630981 − 0.098833I
−4.02304 − 1.06856I 0
u = −0.616483 + 0.873993I
a = 0.072867 + 0.126550I
b = −0.86988 − 1.25529I
3.03814 − 9.09734I 0
u = −0.616483 − 0.873993I
a = 0.072867 − 0.126550I
b = −0.86988 + 1.25529I
3.03814 + 9.09734I 0
u = 0.680944 + 0.828876I
a = −0.86122 + 1.39805I
b = 0.164437 − 0.912029I
8.81877 − 2.41807I 0
u = 0.680944 − 0.828876I
a = −0.86122 − 1.39805I
b = 0.164437 + 0.912029I
8.81877 + 2.41807I 0
u = −0.852601 + 0.652615I
a = 1.64036 + 0.74160I
b = 0.071893 − 0.436529I
2.32733 − 0.87919I 0
u = −0.852601 − 0.652615I
a = 1.64036 − 0.74160I
b = 0.071893 + 0.436529I
2.32733 + 0.87919I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780971 + 0.742856I
a = 0.232829 − 0.157510I
b = −0.094111 + 1.009100I
3.52936 − 2.28901I 0
u = 0.780971 − 0.742856I
a = 0.232829 + 0.157510I
b = −0.094111 − 1.009100I
3.52936 + 2.28901I 0
u = −0.689959 + 0.608093I
a = 0.032715 + 1.229640I
b = 0.484351 + 0.845214I
3.81022 + 3.81839I 0
u = −0.689959 − 0.608093I
a = 0.032715 − 1.229640I
b = 0.484351 − 0.845214I
3.81022 − 3.81839I 0
u = −0.859691 + 0.657191I
a = −0.512576 + 0.995728I
b = 0.032009 − 0.682643I
2.30507 + 5.97578I 0
u = −0.859691 − 0.657191I
a = −0.512576 − 0.995728I
b = 0.032009 + 0.682643I
2.30507 − 5.97578I 0
u = −0.815653 + 0.734411I
a = 2.03170 + 1.16713I
b = 1.11060 − 1.14783I
10.83000 + 5.19918I 0
u = −0.815653 − 0.734411I
a = 2.03170 − 1.16713I
b = 1.11060 + 1.14783I
10.83000 − 5.19918I 0
u = −0.724535 + 0.830904I
a = −0.794990 + 0.278518I
b = −0.703464 − 0.616085I
7.60813 − 4.48816I 0
u = −0.724535 − 0.830904I
a = −0.794990 − 0.278518I
b = −0.703464 + 0.616085I
7.60813 + 4.48816I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.944102 + 0.608604I
a = 0.68731 − 1.69640I
b = 2.06292 − 0.40586I
−0.73934 − 5.69919I 0
u = 0.944102 − 0.608604I
a = 0.68731 + 1.69640I
b = 2.06292 + 0.40586I
−0.73934 + 5.69919I 0
u = −1.100140 + 0.236992I
a = −0.654771 − 1.247530I
b = −0.496947 − 0.600281I
−3.40640 − 0.64916I 0
u = −1.100140 − 0.236992I
a = −0.654771 + 1.247530I
b = −0.496947 + 0.600281I
−3.40640 + 0.64916I 0
u = 0.865788 + 0.728011I
a = 0.791746 − 0.828220I
b = 0.015922 + 0.987668I
2.99302 − 2.77400I 0
u = 0.865788 − 0.728011I
a = 0.791746 + 0.828220I
b = 0.015922 − 0.987668I
2.99302 + 2.77400I 0
u = 0.448442 + 0.732258I
a = 0.269708 − 0.445502I
b = −0.570422 + 1.153250I
3.42380 + 1.90527I 0
u = 0.448442 − 0.732258I
a = 0.269708 + 0.445502I
b = −0.570422 − 1.153250I
3.42380 − 1.90527I 0
u = −0.929973 + 0.667074I
a = −1.79299 − 0.78709I
b = −0.949166 + 0.276522I
−0.32097 + 5.73154I 0
u = −0.929973 − 0.667074I
a = −1.79299 + 0.78709I
b = −0.949166 − 0.276522I
−0.32097 − 5.73154I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925352 + 0.696312I
a = 1.180240 − 0.330252I
b = 0.248804 + 0.874632I
3.08550 − 3.19478I 0
u = 0.925352 − 0.696312I
a = 1.180240 + 0.330252I
b = 0.248804 − 0.874632I
3.08550 + 3.19478I 0
u = 0.958288 + 0.653774I
a = 2.30704 − 0.58891I
b = 0.672339 + 0.916215I
4.01195 − 8.70770I 0
u = 0.958288 − 0.653774I
a = 2.30704 + 0.58891I
b = 0.672339 − 0.916215I
4.01195 + 8.70770I 0
u = −0.911350 + 0.724923I
a = −0.096637 − 0.263627I
b = −0.95510 − 1.29492I
10.54000 + 0.35533I 0
u = −0.911350 − 0.724923I
a = −0.096637 + 0.263627I
b = −0.95510 + 1.29492I
10.54000 − 0.35533I 0
u = 1.036340 + 0.539959I
a = −2.17866 + 0.23890I
b = −0.732179 − 0.945162I
−1.54255 − 7.41509I 0
u = 1.036340 − 0.539959I
a = −2.17866 − 0.23890I
b = −0.732179 + 0.945162I
−1.54255 + 7.41509I 0
u = 0.804131 + 0.196781I
a = 1.63599 − 1.35164I
b = 0.861544 + 0.425394I
−1.84482 − 3.79193I 0
u = 0.804131 − 0.196781I
a = 1.63599 + 1.35164I
b = 0.861544 − 0.425394I
−1.84482 + 3.79193I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.977193 + 0.662468I
a = 0.651879 − 1.038750I
b = 0.117675 + 0.764877I
9.06594 + 8.71802I 0
u = −0.977193 − 0.662468I
a = 0.651879 + 1.038750I
b = 0.117675 − 0.764877I
9.06594 − 8.71802I 0
u = 0.841321 + 0.839641I
a = −0.974740 + 0.296884I
b = −0.431739 − 0.975195I
9.07418 − 0.01157I 0
u = 0.841321 − 0.839641I
a = −0.974740 − 0.296884I
b = −0.431739 + 0.975195I
9.07418 + 0.01157I 0
u = −0.627394 + 1.009860I
a = 0.057245 − 0.154601I
b = 0.89466 + 1.22131I
9.8836 − 13.0615I 0
u = −0.627394 − 1.009860I
a = 0.057245 + 0.154601I
b = 0.89466 − 1.22131I
9.8836 + 13.0615I 0
u = 0.604209 + 0.540416I
a = 0.821630 − 0.997718I
b = −0.274803 + 1.293460I
3.36586 + 2.04358I 0
u = 0.604209 − 0.540416I
a = 0.821630 + 0.997718I
b = −0.274803 − 1.293460I
3.36586 − 2.04358I 0
u = −0.974105 + 0.690922I
a = −2.01905 − 0.78783I
b = −1.07905 + 1.30600I
2.33836 + 9.08534I 0
u = −0.974105 − 0.690922I
a = −2.01905 + 0.78783I
b = −1.07905 − 1.30600I
2.33836 − 9.08534I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.141470 + 0.355948I
a = 0.652636 + 0.431142I
b = 0.796747 + 0.083578I
−2.15783 + 0.47274I 0
u = −1.141470 − 0.355948I
a = 0.652636 − 0.431142I
b = 0.796747 − 0.083578I
−2.15783 − 0.47274I 0
u = −1.19608
a = −0.117728
b = 0.106639
−2.16845 0
u = 1.188120 + 0.138968I
a = 1.57314 + 0.69630I
b = 0.996363 + 0.874980I
−3.98425 − 8.00183I 0
u = 1.188120 − 0.138968I
a = 1.57314 − 0.69630I
b = 0.996363 − 0.874980I
−3.98425 + 8.00183I 0
u = 0.573498 + 1.052730I
a = −0.208464 + 0.063402I
b = −0.126410 + 0.761614I
10.84240 + 4.19994I 0
u = 0.573498 − 1.052730I
a = −0.208464 − 0.063402I
b = −0.126410 − 0.761614I
10.84240 − 4.19994I 0
u = −1.20457
a = 1.25998
b = 1.28139
−2.29042 0
u = −0.924917 + 0.772626I
a = −0.510780 − 0.815666I
b = −0.136400 + 0.394155I
0.39823 + 2.97064I 0
u = −0.924917 − 0.772626I
a = −0.510780 + 0.815666I
b = −0.136400 − 0.394155I
0.39823 − 2.97064I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.211270 + 0.065690I
a = −1.39811 + 0.41631I
b = −1.12136 + 1.38456I
2.01877 − 3.27988I 0
u = −1.211270 − 0.065690I
a = −1.39811 − 0.41631I
b = −1.12136 − 1.38456I
2.01877 + 3.27988I 0
u = −1.018490 + 0.661123I
a = −0.607336 − 0.209676I
b = −0.786040 + 0.277425I
2.70677 + 1.18376I 0
u = −1.018490 − 0.661123I
a = −0.607336 + 0.209676I
b = −0.786040 − 0.277425I
2.70677 − 1.18376I 0
u = 0.626628 + 1.043640I
a = −0.244716 − 0.109112I
b = 0.98256 − 1.14932I
11.28110 + 3.15961I 0
u = 0.626628 − 1.043640I
a = −0.244716 + 0.109112I
b = 0.98256 + 1.14932I
11.28110 − 3.15961I 0
u = 1.104500 + 0.515664I
a = 1.97248 − 0.25552I
b = 0.662522 + 1.080330I
1.40489 − 6.40274I 0
u = 1.104500 − 0.515664I
a = 1.97248 + 0.25552I
b = 0.662522 − 1.080330I
1.40489 + 6.40274I 0
u = 0.917205 + 0.806471I
a = −0.202384 − 0.247972I
b = 0.315295 − 1.057050I
8.83751 − 6.09791I 0
u = 0.917205 − 0.806471I
a = −0.202384 + 0.247972I
b = 0.315295 + 1.057050I
8.83751 + 6.09791I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.179720 + 0.318102I
a = 0.820981 + 0.995675I
b = 0.652857 + 0.704724I
0.20487 + 1.42751I 0
u = −1.179720 − 0.318102I
a = 0.820981 − 0.995675I
b = 0.652857 − 0.704724I
0.20487 − 1.42751I 0
u = 1.036700 + 0.650543I
a = 1.79157 − 0.52989I
b = 0.84396 + 1.50469I
1.90387 − 7.08754I 0
u = 1.036700 − 0.650543I
a = 1.79157 + 0.52989I
b = 0.84396 − 1.50469I
1.90387 + 7.08754I 0
u = −0.654689 + 0.392271I
a = 0.298988 + 0.601962I
b = 0.762877 + 0.836639I
−0.307473 − 0.908053I 0
u = −0.654689 − 0.392271I
a = 0.298988 − 0.601962I
b = 0.762877 − 0.836639I
−0.307473 + 0.908053I 0
u = −1.002750 + 0.742942I
a = 1.75731 + 0.93699I
b = 0.732421 − 0.570435I
6.75352 + 10.37920I 0
u = −1.002750 − 0.742942I
a = 1.75731 − 0.93699I
b = 0.732421 + 0.570435I
6.75352 − 10.37920I 0
u = 1.064050 + 0.676398I
a = −0.494160 + 1.258780I
b = −1.80412 + 0.71872I
6.26797 − 10.69380I 0
u = 1.064050 − 0.676398I
a = −0.494160 − 1.258780I
b = −1.80412 − 0.71872I
6.26797 + 10.69380I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.020640 + 0.741876I
a = −0.528153 + 0.894894I
b = −0.014774 − 1.081540I
7.80410 − 3.46305I 0
u = 1.020640 − 0.741876I
a = −0.528153 − 0.894894I
b = −0.014774 + 1.081540I
7.80410 + 3.46305I 0
u = 0.015470 + 0.719101I
a = −0.739835 − 0.441853I
b = −0.554711 + 0.786758I
4.01829 + 2.28197I 0
u = 0.015470 − 0.719101I
a = −0.739835 + 0.441853I
b = −0.554711 − 0.786758I
4.01829 − 2.28197I 0
u = 1.072250 + 0.704229I
a = −1.203790 + 0.050774I
b = −0.316168 − 0.789491I
2.81137 − 7.33191I 0
u = 1.072250 − 0.704229I
a = −1.203790 − 0.050774I
b = −0.316168 + 0.789491I
2.81137 + 7.33191I 0
u = −1.064020 + 0.720248I
a = 1.86456 + 0.66153I
b = 0.99984 − 1.30916I
1.6749 + 15.0128I 0
u = −1.064020 − 0.720248I
a = 1.86456 − 0.66153I
b = 0.99984 + 1.30916I
1.6749 − 15.0128I 0
u = 0.619429 + 0.355417I
a = 0.976203 + 0.498064I
b = 0.529728 − 0.970025I
0.05861 + 3.28511I 0
u = 0.619429 − 0.355417I
a = 0.976203 − 0.498064I
b = 0.529728 + 0.970025I
0.05861 − 3.28511I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211348 + 1.273640I
a = 0.017221 + 0.147212I
b = 0.727165 − 0.627290I
7.20516 + 6.10676I 0
u = −0.211348 − 1.273640I
a = 0.017221 − 0.147212I
b = 0.727165 + 0.627290I
7.20516 − 6.10676I 0
u = −1.118810 + 0.770554I
a = −1.73652 − 0.63855I
b = −0.96940 + 1.28485I
8.3272 + 19.5300I 0
u = −1.118810 − 0.770554I
a = −1.73652 + 0.63855I
b = −0.96940 − 1.28485I
8.3272 − 19.5300I 0
u = −0.852842 + 1.063010I
a = 0.135865 + 0.407023I
b = 0.372485 − 0.363029I
4.42543 + 5.17117I 0
u = −0.852842 − 1.063010I
a = 0.135865 − 0.407023I
b = 0.372485 + 0.363029I
4.42543 − 5.17117I 0
u = 1.123240 + 0.789966I
a = −1.48344 + 0.58122I
b = −1.16989 − 1.34831I
9.71395 − 9.76955I 0
u = 1.123240 − 0.789966I
a = −1.48344 − 0.58122I
b = −1.16989 + 1.34831I
9.71395 + 9.76955I 0
u = 1.352670 + 0.237321I
a = −1.40255 − 0.38503I
b = −1.021460 − 0.929167I
1.34036 − 11.09600I 0
u = 1.352670 − 0.237321I
a = −1.40255 + 0.38503I
b = −1.021460 + 0.929167I
1.34036 + 11.09600I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.150560 + 0.763047I
a = 1.089060 + 0.045709I
b = 0.346968 + 0.761374I
9.02146 − 10.73960I 0
u = 1.150560 − 0.763047I
a = 1.089060 − 0.045709I
b = 0.346968 − 0.761374I
9.02146 + 10.73960I 0
u = −1.339970 + 0.352179I
a = 0.312800 − 0.071554I
b = −0.0361016 − 0.1163310I
1.99227 + 1.49520I 0
u = −1.339970 − 0.352179I
a = 0.312800 + 0.071554I
b = −0.0361016 + 0.1163310I
1.99227 − 1.49520I 0
u = −0.529964 + 0.262897I
a = 1.254970 − 0.280525I
b = −0.296314 + 0.993222I
2.93103 + 5.26061I −3.71177 − 8.49168I
u = −0.529964 − 0.262897I
a = 1.254970 + 0.280525I
b = −0.296314 − 0.993222I
2.93103 − 5.26061I −3.71177 + 8.49168I
u = 0.164122 + 0.493858I
a = 0.530993 − 0.239220I
b = 0.541150 − 0.939625I
0.28061 + 3.26037I −8.37838 − 3.30675I
u = 0.164122 − 0.493858I
a = 0.530993 + 0.239220I
b = 0.541150 + 0.939625I
0.28061 − 3.26037I −8.37838 + 3.30675I
u = −1.48761 + 0.30426I
a = −0.783072 − 0.156790I
b = −1.086000 + 0.037885I
2.14579 + 0.41787I 0
u = −1.48761 − 0.30426I
a = −0.783072 + 0.156790I
b = −1.086000 − 0.037885I
2.14579 − 0.41787I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.314789 + 0.222246I
a = 1.161900 − 0.410180I
b = 0.424500 − 0.553519I
−0.821941 + 0.839879I −7.00670 − 5.24574I
u = −0.314789 − 0.222246I
a = 1.161900 + 0.410180I
b = 0.424500 + 0.553519I
−0.821941 − 0.839879I −7.00670 + 5.24574I
u = 0.355411 + 0.003002I
a = 1.72894 − 7.95506I
b = 0.744773 − 0.245230I
7.70434 + 4.10760I −12.27056 − 1.05216I
u = 0.355411 − 0.003002I
a = 1.72894 + 7.95506I
b = 0.744773 + 0.245230I
7.70434 − 4.10760I −12.27056 + 1.05216I
u = 0.079327 + 0.315653I
a = 2.24173 + 0.75887I
b = −0.810366 − 0.262073I
−0.21366 + 2.11606I −6.00885 − 3.78588I
u = 0.079327 − 0.315653I
a = 2.24173 − 0.75887I
b = −0.810366 + 0.262073I
−0.21366 − 2.11606I −6.00885 + 3.78588I
19
II. I
u
2
=
h−22u
28
+63u
27
+· · ·+b+40, 23u
28
−38u
27
+· · ·+a−9, u
29
−3u
28
+· · ·−3u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−23u
28
+ 38u
27
+ ··· − 41u + 9
22u
28
− 63u
27
+ ··· + 72u − 40
a
7
=
u
28
+ 5u
27
+ ··· − 4u + 17
−u
28
+ 2u
27
+ ··· − u
2
− 3u
a
11
=
−45u
28
+ 101u
27
+ ··· − 113u + 49
22u
28
− 63u
27
+ ··· + 72u − 40
a
8
=
39u
28
− 80u
27
+ ··· + 85u − 28
−16u
28
+ 21u
27
+ ··· − 18u + 1
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−47u
28
+ 95u
27
+ ··· − 104u + 33
11u
28
− 23u
27
+ ··· + 25u − 11
a
12
=
34u
28
− 89u
27
+ ··· + 92u − 57
4u
28
− 3u
27
+ ··· + 3u + 10
a
9
=
32u
28
− 78u
27
+ ··· + 87u − 37
−8u
28
+ 4u
27
+ ··· + 27u
2
− 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −30u
27
+ 30u
26
+ 157u
25
− 234u
24
− 386u
23
+ 713u
22
+ 611u
21
− 1352u
20
− 986u
19
+
2153u
18
+ 1363u
17
− 3142u
16
− 1303u
15
+ 3621u
14
+ 840u
13
− 3346u
12
− 504u
11
+
2575u
10
+ 261u
9
− 1854u
8
+ 38u
7
+ 934u
6
− 106u
5
− 373u
4
+ 37u
3
+ 78u
2
+ 18u − 38
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 13u
28
+ ··· + 7u − 1
c
2
u
29
+ 3u
28
+ ··· − 3u − 1
c
3
u
29
− 5u
27
+ ··· + 12u − 1
c
4
u
29
− u
27
+ ··· − 4u
2
− 1
c
5
u
29
− 3u
28
+ ··· − 3u + 1
c
6
u
29
+ 2u
28
+ ··· + 8u
2
− 1
c
7
u
29
− u
28
+ ··· − 30u + 35
c
8
, c
9
u
29
− 6u
28
+ ··· + 4u − 1
c
10
u
29
− 5u
27
+ ··· + 3u
2
− 1
c
11
u
29
− 3u
27
+ ··· + 5u
2
− 1
c
12
u
29
+ 6u
28
+ ··· + 4u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 7y
28
+ ··· − 25y −1
c
2
, c
5
y
29
− 13y
28
+ ··· + 7y −1
c
3
y
29
− 10y
28
+ ··· + 24y −1
c
4
y
29
− 2y
28
+ ··· − 8y −1
c
6
y
29
+ 22y
28
+ ··· + 16y −1
c
7
y
29
+ 13y
28
+ ··· + 10350y −1225
c
8
, c
9
, c
12
y
29
+ 30y
28
+ ··· − 26y −1
c
10
y
29
− 10y
28
+ ··· + 6y −1
c
11
y
29
− 6y
28
+ ··· + 10y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603979 + 0.758503I
a = −0.853063 + 0.992538I
b = −0.742925 + 0.396876I
8.88525 + 3.99076I 0.14446 − 2.94436I
u = 0.603979 − 0.758503I
a = −0.853063 − 0.992538I
b = −0.742925 − 0.396876I
8.88525 − 3.99076I 0.14446 + 2.94436I
u = 0.809799 + 0.645934I
a = 1.06316 − 1.04956I
b = 1.270230 − 0.277462I
0.560298 + 0.654606I 2.63934 − 2.40355I
u = 0.809799 − 0.645934I
a = 1.06316 + 1.04956I
b = 1.270230 + 0.277462I
0.560298 − 0.654606I 2.63934 + 2.40355I
u = −0.990375 + 0.369439I
a = −0.88962 − 1.19823I
b = −1.257750 − 0.409646I
−1.94545 − 0.59072I −11.29662 + 3.04823I
u = −0.990375 − 0.369439I
a = −0.88962 + 1.19823I
b = −1.257750 + 0.409646I
−1.94545 + 0.59072I −11.29662 − 3.04823I
u = −0.540273 + 0.748686I
a = −0.232531 + 0.556382I
b = 0.431449 − 0.681053I
1.26086 + 4.36994I −7.81233 − 4.10632I
u = −0.540273 − 0.748686I
a = −0.232531 − 0.556382I
b = 0.431449 + 0.681053I
1.26086 − 4.36994I −7.81233 + 4.10632I
u = 0.923343 + 0.645596I
a = −1.46577 + 0.82768I
b = −1.259210 − 0.245149I
0.19514 − 5.69192I −0.11025 + 8.57297I
u = 0.923343 − 0.645596I
a = −1.46577 − 0.82768I
b = −1.259210 + 0.245149I
0.19514 + 5.69192I −0.11025 − 8.57297I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.030400 + 0.511587I
a = −2.10531 + 0.22494I
b = −0.888420 − 0.939075I
−0.83926 − 7.04364I −4.54902 + 6.58787I
u = 1.030400 − 0.511587I
a = −2.10531 − 0.22494I
b = −0.888420 + 0.939075I
−0.83926 + 7.04364I −4.54902 − 6.58787I
u = 1.071310 + 0.449170I
a = 2.24231 + 0.08581I
b = 0.631284 + 0.976916I
1.36154 − 7.41260I −5.66969 + 10.49828I
u = 1.071310 − 0.449170I
a = 2.24231 − 0.08581I
b = 0.631284 − 0.976916I
1.36154 + 7.41260I −5.66969 − 10.49828I
u = −0.761627 + 0.334872I
a = 1.75452 + 1.63145I
b = 1.263110 − 0.309630I
−1.10598 + 3.57442I −7.61817 − 2.46604I
u = −0.761627 − 0.334872I
a = 1.75452 − 1.63145I
b = 1.263110 + 0.309630I
−1.10598 − 3.57442I −7.61817 + 2.46604I
u = −0.658517 + 0.969435I
a = 0.0936036 − 0.0082906I
b = −0.214901 + 0.639805I
5.02914 + 5.15670I 3.74856 − 7.07707I
u = −0.658517 − 0.969435I
a = 0.0936036 + 0.0082906I
b = −0.214901 − 0.639805I
5.02914 − 5.15670I 3.74856 + 7.07707I
u = 0.651359 + 0.447890I
a = 0.812864 − 0.001307I
b = 0.651736 − 0.964731I
0.49961 + 3.00268I −0.177166 + 0.645446I
u = 0.651359 − 0.447890I
a = 0.812864 + 0.001307I
b = 0.651736 + 0.964731I
0.49961 − 3.00268I −0.177166 − 0.645446I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22387
a = −0.917542
b = −0.837300
−2.55545 −22.7140
u = 0.670037 + 0.328739I
a = −0.50275 − 1.37469I
b = −0.379319 + 1.050880I
2.93642 + 4.03665I −4.98365 − 3.48684I
u = 0.670037 − 0.328739I
a = −0.50275 + 1.37469I
b = −0.379319 − 1.050880I
2.93642 − 4.03665I −4.98365 + 3.48684I
u = 1.048350 + 0.709611I
a = 1.351230 − 0.360180I
b = 0.853412 + 0.354777I
7.58140 − 9.62710I −1.49140 + 6.93719I
u = 1.048350 − 0.709611I
a = 1.351230 + 0.360180I
b = 0.853412 − 0.354777I
7.58140 + 9.62710I −1.49140 − 6.93719I
u = −0.299203 + 0.481809I
a = 2.70786 − 2.40692I
b = −0.551224 + 0.439249I
8.13165 + 4.30275I 4.34905 − 7.80104I
u = −0.299203 − 0.481809I
a = 2.70786 + 2.40692I
b = −0.551224 − 0.439249I
8.13165 − 4.30275I 4.34905 + 7.80104I
u = −1.44665 + 0.32614I
a = 0.482265 + 0.274236I
b = 0.611179 + 0.227807I
1.62579 + 1.29613I −12.31614 + 1.51557I
u = −1.44665 − 0.32614I
a = 0.482265 − 0.274236I
b = 0.611179 − 0.227807I
1.62579 − 1.29613I −12.31614 − 1.51557I
25
III. I
u
3
=
h−8a
5
+5a
4
+4a
3
−31a
2
+69b−64a+78, a
6
−2a
5
+6a
3
−2a
2
−15a+17, u+1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
10
=
a
0.115942a
5
− 0.0724638a
4
+ ··· + 0.927536a − 1.13043
a
7
=
0.159420a
5
− 0.0579710a
4
+ ··· + 0.608696a − 0.971014
0.00483092a
5
− 0.0724638a
4
+ ··· − 0.183575a + 0.314010
a
11
=
−0.115942a
5
+ 0.0724638a
4
+ ··· + 0.0724638a + 1.13043
0.115942a
5
− 0.0724638a
4
+ ··· + 0.927536a − 1.13043
a
8
=
0.159420a
5
− 0.0579710a
4
+ ··· + 0.608696a − 0.971014
0.00483092a
5
− 0.0724638a
4
+ ··· − 0.183575a + 0.314010
a
1
=
−1
−1
a
4
=
0.0289855a
5
+ 0.231884a
4
+ ··· + 0.231884a + 2.21739
0.159420a
5
− 0.0579710a
4
+ ··· + 0.608696a − 0.971014
a
12
=
0.207729a
5
− 0.115942a
4
+ ··· + 2.10628a − 1.49758
0.169082a
5
− 0.202899a
4
+ ··· + 1.24155a − 2.34300
a
9
=
0.314010a
5
− 0.0434783a
4
+ ··· + 1.40097a − 2.25604
0.159420a
5
− 0.0579710a
4
+ ··· + 0.608696a − 0.971014
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
25
207
a
5
−
13
69
a
4
−
38
69
a
3
−
13
23
a
2
+
122
207
a −
1832
207
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
4
u
6
− 3u
5
+ 4u
4
− 3u
3
+ 3u
2
− 2u + 1
c
5
(u + 1)
6
c
6
(u
3
+ u
2
− 1)
2
c
7
u
6
c
8
, c
9
(u
3
− u
2
+ 2u − 1)
2
c
10
, c
11
u
6
+ 2u
4
− u
3
+ 2u
2
+ 1
c
12
(u
3
+ u
2
+ 2u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1
c
6
(y
3
− y
2
+ 2y −1)
2
c
7
y
6
c
8
, c
9
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
10
, c
11
y
6
+ 4y
5
+ 8y
4
+ 9y
3
+ 8y
2
+ 4y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.302760 + 0.525329I
b = 0.425318 + 1.270190I
1.37919 + 2.82812I −9.31314 − 3.21164I
u = −1.00000
a = 1.302760 − 0.525329I
b = 0.425318 − 1.270190I
1.37919 − 2.82812I −9.31314 + 3.21164I
u = −1.00000
a = −1.41724 + 0.74919I
b = −0.662359 + 0.749187I
−2.75839 −10.76463 − 0.28829I
u = −1.00000
a = −1.41724 − 0.74919I
b = −0.662359 − 0.749187I
−2.75839 −10.76463 + 0.28829I
u = −1.00000
a = 1.11448 + 1.45277I
b = 0.237041 + 0.707911I
1.37919 − 2.82812I −2.42222 + 1.25753I
u = −1.00000
a = 1.11448 − 1.45277I
b = 0.237041 − 0.707911I
1.37919 + 2.82812I −2.42222 − 1.25753I
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
29
− 13u
28
+ ··· + 7u − 1)
· (u
146
+ 56u
145
+ ··· + 723369u + 21025)
c
2
((u − 1)
6
)(u
29
+ 3u
28
+ ··· − 3u − 1)(u
146
+ 4u
145
+ ··· − 333u + 145)
c
3
(u
6
− 3u
5
+ ··· − 2u + 1)(u
29
− 5u
27
+ ··· + 12u − 1)
· (u
146
+ 4u
145
+ ··· + 2468988890u + 899654983)
c
4
(u
6
− 3u
5
+ ··· − 2u + 1)(u
29
− u
27
+ ··· − 4u
2
− 1)
· (u
146
+ 12u
145
+ ··· + 18u + 1)
c
5
((u + 1)
6
)(u
29
− 3u
28
+ ··· − 3u + 1)(u
146
+ 4u
145
+ ··· − 333u + 145)
c
6
((u
3
+ u
2
− 1)
2
)(u
29
+ 2u
28
+ ··· + 8u
2
− 1)
· (u
146
− u
145
+ ··· + 13382u − 2117)
c
7
u
6
(u
29
− u
28
+ ··· − 30u + 35)(u
146
− 4u
144
+ ··· + 672u + 320)
c
8
, c
9
((u
3
− u
2
+ 2u − 1)
2
)(u
29
− 6u
28
+ ··· + 4u − 1)
· (u
146
+ 5u
145
+ ··· + 24u − 1)
c
10
(u
6
+ 2u
4
− u
3
+ 2u
2
+ 1)(u
29
− 5u
27
+ ··· + 3u
2
− 1)
· (u
146
− u
145
+ ··· + 1200u + 145)
c
11
(u
6
+ 2u
4
− u
3
+ 2u
2
+ 1)(u
29
− 3u
27
+ ··· + 5u
2
− 1)
· (u
146
− 5u
145
+ ··· − 1206u + 145)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
29
+ 6u
28
+ ··· + 4u + 1)
· (u
146
+ 5u
145
+ ··· + 24u − 1)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
29
+ 7y
28
+ ··· − 25y −1)
· (y
146
+ 76y
145
+ ··· − 56026237661y + 442050625)
c
2
, c
5
((y −1)
6
)(y
29
− 13y
28
+ ··· + 7y −1)
· (y
146
− 56y
145
+ ··· − 723369y + 21025)
c
3
(y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1)(y
29
− 10y
28
+ ··· + 24y −1)
· (y
146
+ 48y
145
+ ··· − 8.05 × 10
19
y + 8.09 × 10
17
)
c
4
(y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1)(y
29
− 2y
28
+ ··· − 8y −1)
· (y
146
+ 4y
145
+ ··· + 274y + 1)
c
6
((y
3
− y
2
+ 2y −1)
2
)(y
29
+ 22y
28
+ ··· + 16y −1)
· (y
146
+ 31y
145
+ ··· + 165806780y + 4481689)
c
7
y
6
(y
29
+ 13y
28
+ ··· + 10350y −1225)
· (y
146
− 8y
145
+ ··· − 3339264y + 102400)
c
8
, c
9
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
29
+ 30y
28
+ ··· − 26y −1)
· (y
146
+ 147y
145
+ ··· + 14y + 1)
c
10
(y
6
+ 4y
5
+ ··· + 4y + 1)(y
29
− 10y
28
+ ··· + 6y −1)
· (y
146
+ 17y
145
+ ··· + 1475950y + 21025)
c
11
(y
6
+ 4y
5
+ ··· + 4y + 1)(y
29
− 6y
28
+ ··· + 10y −1)
· (y
146
− 7y
145
+ ··· − 324306y + 21025)
31
