12a
1108
(K12a
1108
)
A knot diagram
1
Linearized knot diagam
4 7 11 1 10 9 3 12 6 2 8 5
Solving Sequence
5,10 1,6
4 2 11 3 9 7 12 8
c
5
c
4
c
1
c
10
c
3
c
9
c
6
c
12
c
8
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.88369 × 10
219
u
103
− 3.46423 × 10
220
u
102
+ ··· + 1.55368 × 10
220
b + 9.10459 × 10
221
,
6.55031 × 10
220
u
103
− 1.41928 × 10
221
u
102
+ ··· + 3.57346 × 10
221
a + 1.01047 × 10
224
,
u
104
+ 4u
103
+ ··· − 4255u − 529i
I
u
2
= hu
25
+ 4u
24
+ ··· + b + 3, −u
25
− 3u
24
+ ··· + a + 1, u
27
+ 3u
26
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 131 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−8.88 × 10
219
u
103
− 3.46 × 10
220
u
102
+ · · · + 1.55 × 10
220
b + 9.10 ×
10
221
, 6.55 × 10
220
u
103
− 1.42 × 10
221
u
102
+ · · · + 3.57 × 10
221
a + 1.01 ×
10
224
, u
104
+ 4u
103
+ · · · − 4255u − 529i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
−0.183304u
103
+ 0.397174u
102
+ ··· − 2245.37u − 282.771
0.571785u
103
+ 2.22970u
102
+ ··· − 600.028u − 58.6003
a
6
=
1
−u
2
a
4
=
−0.371940u
103
− 1.83384u
102
+ ··· + 1047.48u + 109.993
0.155948u
103
+ 1.00054u
102
+ ··· − 985.578u − 114.243
a
2
=
0.386064u
103
+ 1.36986u
102
+ ··· − 214.929u − 22.7915
−0.285722u
103
− 1.16300u
102
+ ··· + 450.273u + 54.6246
a
11
=
0.0442397u
103
− 0.795827u
102
+ ··· + 2948.61u + 391.066
0.375507u
103
+ 2.42856u
102
+ ··· − 3062.77u − 379.760
a
3
=
0.396800u
103
+ 1.56173u
102
+ ··· − 404.122u − 41.2529
−0.283963u
103
− 1.23407u
102
+ ··· + 609.778u + 70.8958
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
0.388481u
103
+ 2.62687u
102
+ ··· − 2845.40u − 341.371
0.571785u
103
+ 2.22970u
102
+ ··· − 600.028u − 58.6003
a
8
=
0.201012u
103
+ 1.99070u
102
+ ··· − 3254.17u − 404.502
0.251586u
103
+ 0.498810u
102
+ ··· + 1127.65u + 152.910
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.72322u
103
− 10.0804u
102
+ ··· + 428.095u − 67.4251
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
104
− 4u
103
+ ··· + 30u − 4
c
2
, c
7
u
104
+ u
103
+ ··· + 795u + 2071
c
3
u
104
+ 26u
102
+ ··· + 8003385u − 1611677
c
5
, c
6
, c
9
u
104
+ 4u
103
+ ··· − 4255u − 529
c
8
, c
11
u
104
− 42u
102
+ ··· − 17433u + 11887
c
10
u
104
+ 7u
103
+ ··· + 3018333u − 281591
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
104
+ 106y
103
+ ··· − 1084y + 16
c
2
, c
7
y
104
− 71y
103
+ ··· − 59982743y + 4289041
c
3
y
104
+ 52y
103
+ ··· + 80900979801019y + 2597502752329
c
5
, c
6
, c
9
y
104
+ 96y
103
+ ··· − 1564253y + 279841
c
8
, c
11
y
104
− 84y
103
+ ··· − 776703027y + 141300769
c
10
y
104
+ 23y
103
+ ··· − 1658049684805y + 79293491281
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998404 + 0.066441I
a = 0.40664 + 2.25976I
b = 0.024542 − 1.362530I
5.41766 + 0.40969I 0
u = 0.998404 − 0.066441I
a = 0.40664 − 2.25976I
b = 0.024542 + 1.362530I
5.41766 − 0.40969I 0
u = −0.969486 + 0.282556I
a = 0.04918 − 2.23361I
b = −0.149167 + 1.248050I
5.89794 + 2.79943I 0
u = −0.969486 − 0.282556I
a = 0.04918 + 2.23361I
b = −0.149167 − 1.248050I
5.89794 − 2.79943I 0
u = 0.872225 + 0.386027I
a = −0.63402 − 1.93115I
b = −0.23272 + 1.53537I
8.77117 + 6.22222I 0
u = 0.872225 − 0.386027I
a = −0.63402 + 1.93115I
b = −0.23272 − 1.53537I
8.77117 − 6.22222I 0
u = −0.633735 + 0.860627I
a = −0.285219 − 0.398896I
b = 0.427811 − 0.402352I
4.64761 + 3.38555I 0
u = −0.633735 − 0.860627I
a = −0.285219 + 0.398896I
b = 0.427811 + 0.402352I
4.64761 − 3.38555I 0
u = 0.073852 + 1.066990I
a = 2.00678 − 0.01381I
b = 0.305195 − 1.270380I
6.26427 + 4.42302I 0
u = 0.073852 − 1.066990I
a = 2.00678 + 0.01381I
b = 0.305195 + 1.270380I
6.26427 − 4.42302I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.023460 + 0.312641I
a = 0.53307 − 2.07864I
b = 0.25526 + 1.51975I
12.9579 − 11.9173I 0
u = −1.023460 − 0.312641I
a = 0.53307 + 2.07864I
b = 0.25526 − 1.51975I
12.9579 + 11.9173I 0
u = −0.928373
a = 0.323165
b = −0.614916
2.21584 0
u = 0.785609 + 0.754829I
a = 0.81012 + 1.33339I
b = −0.08988 − 1.48205I
7.69660 − 0.76643I 0
u = 0.785609 − 0.754829I
a = 0.81012 − 1.33339I
b = −0.08988 + 1.48205I
7.69660 + 0.76643I 0
u = −0.822823 + 0.300153I
a = −0.136303 − 0.641555I
b = 0.729313 + 0.530280I
6.29249 − 8.31502I 0
u = −0.822823 − 0.300153I
a = −0.136303 + 0.641555I
b = 0.729313 − 0.530280I
6.29249 + 8.31502I 0
u = 0.651115 + 0.577237I
a = −0.40122 − 2.24284I
b = 0.169860 + 1.381650I
7.11747 − 1.89662I 0
u = 0.651115 − 0.577237I
a = −0.40122 + 2.24284I
b = 0.169860 − 1.381650I
7.11747 + 1.89662I 0
u = −0.181205 + 1.139620I
a = −0.111011 + 0.759565I
b = 0.14074 − 1.71793I
10.52570 − 2.57968I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.181205 − 1.139620I
a = −0.111011 − 0.759565I
b = 0.14074 + 1.71793I
10.52570 + 2.57968I 0
u = 0.082428 + 1.155290I
a = −2.21153 − 1.42249I
b = −0.027261 + 1.335620I
5.81144 − 3.37082I 0
u = 0.082428 − 1.155290I
a = −2.21153 + 1.42249I
b = −0.027261 − 1.335620I
5.81144 + 3.37082I 0
u = −0.098594 + 1.227330I
a = 0.06407 − 1.94244I
b = −0.01603 + 1.65998I
9.41869 + 0.21611I 0
u = −0.098594 − 1.227330I
a = 0.06407 + 1.94244I
b = −0.01603 − 1.65998I
9.41869 − 0.21611I 0
u = −0.196901 + 1.225630I
a = 1.163310 − 0.102328I
b = 0.834652 + 0.152457I
2.82236 + 0.39547I 0
u = −0.196901 − 1.225630I
a = 1.163310 + 0.102328I
b = 0.834652 − 0.152457I
2.82236 − 0.39547I 0
u = 0.136309 + 1.256230I
a = −0.543584 + 0.051104I
b = −0.796096 − 1.079340I
−1.41379 − 0.49702I 0
u = 0.136309 − 1.256230I
a = −0.543584 − 0.051104I
b = −0.796096 + 1.079340I
−1.41379 + 0.49702I 0
u = 0.571816 + 0.454044I
a = −0.216301 − 0.296006I
b = 0.443926 + 0.330981I
1.77754 + 0.38509I 4.38443 + 0.48534I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.571816 − 0.454044I
a = −0.216301 + 0.296006I
b = 0.443926 − 0.330981I
1.77754 − 0.38509I 4.38443 − 0.48534I
u = 0.667908 + 0.292392I
a = 0.96415 + 3.27127I
b = 0.15855 − 1.46104I
7.79155 + 5.85095I 9.05721 − 6.34260I
u = 0.667908 − 0.292392I
a = 0.96415 − 3.27127I
b = 0.15855 + 1.46104I
7.79155 − 5.85095I 9.05721 + 6.34260I
u = 0.573518 + 0.444519I
a = 0.217991 + 1.214100I
b = 0.503464 − 0.394630I
1.77117 + 3.47379I 4.30454 − 8.11372I
u = 0.573518 − 0.444519I
a = 0.217991 − 1.214100I
b = 0.503464 + 0.394630I
1.77117 − 3.47379I 4.30454 + 8.11372I
u = −0.130265 + 1.284020I
a = −1.66242 − 0.57082I
b = −0.161378 − 0.095670I
1.67702 − 4.00381I 0
u = −0.130265 − 1.284020I
a = −1.66242 + 0.57082I
b = −0.161378 + 0.095670I
1.67702 + 4.00381I 0
u = −0.672561 + 0.216268I
a = 1.00368 − 1.90578I
b = 0.25153 + 1.56236I
13.11990 − 0.50623I 12.21127 + 0.97407I
u = −0.672561 − 0.216268I
a = 1.00368 + 1.90578I
b = 0.25153 − 1.56236I
13.11990 + 0.50623I 12.21127 − 0.97407I
u = −0.172810 + 1.289970I
a = 1.03528 − 1.11652I
b = 0.119702 + 1.332210I
0.233186 + 0.396521I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.172810 − 1.289970I
a = 1.03528 + 1.11652I
b = 0.119702 − 1.332210I
0.233186 − 0.396521I 0
u = 0.671616
a = 0.393968
b = 0.121223
1.05986 13.1460
u = −0.207093 + 1.327860I
a = −1.29131 + 1.11059I
b = −0.29956 − 1.47499I
−0.26646 − 5.70650I 0
u = −0.207093 − 1.327860I
a = −1.29131 − 1.11059I
b = −0.29956 + 1.47499I
−0.26646 + 5.70650I 0
u = −0.810446 + 1.082160I
a = −0.518297 + 1.276570I
b = 0.16861 − 1.46801I
10.77610 + 5.67331I 0
u = −0.810446 − 1.082160I
a = −0.518297 − 1.276570I
b = 0.16861 + 1.46801I
10.77610 − 5.67331I 0
u = −0.250365 + 1.338370I
a = 0.281599 + 0.064221I
b = 0.862834 − 0.787889I
1.63639 − 6.53052I 0
u = −0.250365 − 1.338370I
a = 0.281599 − 0.064221I
b = 0.862834 + 0.787889I
1.63639 + 6.53052I 0
u = 0.393489 + 1.303500I
a = −0.68596 − 1.41890I
b = −0.14152 + 1.43341I
1.40965 + 4.51412I 0
u = 0.393489 − 1.303500I
a = −0.68596 + 1.41890I
b = −0.14152 − 1.43341I
1.40965 − 4.51412I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.539367 + 0.337757I
a = 0.975272 − 0.257796I
b = −0.064074 − 0.350230I
1.46743 + 0.10661I 5.93203 + 0.60348I
u = 0.539367 − 0.337757I
a = 0.975272 + 0.257796I
b = −0.064074 + 0.350230I
1.46743 − 0.10661I 5.93203 − 0.60348I
u = −0.625129 + 0.102895I
a = 0.138815 + 0.941849I
b = 0.778379 − 0.524859I
6.20399 − 3.33840I 9.20206 + 2.72693I
u = −0.625129 − 0.102895I
a = 0.138815 − 0.941849I
b = 0.778379 + 0.524859I
6.20399 + 3.33840I 9.20206 − 2.72693I
u = −0.072414 + 1.379240I
a = −0.640172 + 0.519110I
b = −0.786982 − 0.376868I
−6.25007 − 1.75695I 0
u = −0.072414 − 1.379240I
a = −0.640172 − 0.519110I
b = −0.786982 + 0.376868I
−6.25007 + 1.75695I 0
u = −0.229091 + 1.365350I
a = −0.037639 − 0.653313I
b = −0.382110 + 0.941592I
0.278441 − 0.737804I 0
u = −0.229091 − 1.365350I
a = −0.037639 + 0.653313I
b = −0.382110 − 0.941592I
0.278441 + 0.737804I 0
u = 0.567239 + 0.205735I
a = −0.064922 − 0.596855I
b = −0.763362 + 0.623857I
1.72979 + 2.71370I 8.69800 − 7.54641I
u = 0.567239 − 0.205735I
a = −0.064922 + 0.596855I
b = −0.763362 − 0.623857I
1.72979 − 2.71370I 8.69800 + 7.54641I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244641 + 1.378890I
a = −0.704509 − 0.351277I
b = −1.005120 + 0.397758I
−3.32666 + 5.76599I 0
u = 0.244641 − 1.378890I
a = −0.704509 + 0.351277I
b = −1.005120 − 0.397758I
−3.32666 − 5.76599I 0
u = −0.522796 + 1.301600I
a = −1.18192 + 1.47657I
b = −0.270766 − 1.344250I
2.56525 − 8.31671I 0
u = −0.522796 − 1.301600I
a = −1.18192 − 1.47657I
b = −0.270766 + 1.344250I
2.56525 + 8.31671I 0
u = −0.386313 + 1.358230I
a = −0.343760 + 0.501923I
b = −0.729258 − 0.163103I
−2.16914 − 4.72705I 0
u = −0.386313 − 1.358230I
a = −0.343760 − 0.501923I
b = −0.729258 + 0.163103I
−2.16914 + 4.72705I 0
u = −0.28742 + 1.39789I
a = 1.250790 − 0.364112I
b = 0.36538 + 1.43826I
7.95514 − 4.03865I 0
u = −0.28742 − 1.39789I
a = 1.250790 + 0.364112I
b = 0.36538 − 1.43826I
7.95514 + 4.03865I 0
u = 0.21370 + 1.41327I
a = 0.605805 + 0.166674I
b = 0.542202 − 0.063337I
−4.04218 + 2.97751I 0
u = 0.21370 − 1.41327I
a = 0.605805 − 0.166674I
b = 0.542202 + 0.063337I
−4.04218 − 2.97751I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21887 + 1.41889I
a = −1.68782 + 0.11155I
b = −0.06655 − 1.41986I
6.85407 − 4.86950I 0
u = −0.21887 − 1.41889I
a = −1.68782 − 0.11155I
b = −0.06655 + 1.41986I
6.85407 + 4.86950I 0
u = −0.501834 + 0.255964I
a = −2.79604 + 1.81261I
b = 0.00008 − 1.53491I
12.29450 − 2.11950I 13.9495 + 3.8281I
u = −0.501834 − 0.255964I
a = −2.79604 − 1.81261I
b = 0.00008 + 1.53491I
12.29450 + 2.11950I 13.9495 − 3.8281I
u = 0.07061 + 1.43505I
a = −0.287140 − 0.116310I
b = −0.445250 + 0.808015I
−4.94431 + 2.81434I 0
u = 0.07061 − 1.43505I
a = −0.287140 + 0.116310I
b = −0.445250 − 0.808015I
−4.94431 − 2.81434I 0
u = 0.27439 + 1.41169I
a = 1.35331 + 1.41659I
b = 0.22053 − 1.52889I
2.36733 + 9.32735I 0
u = 0.27439 − 1.41169I
a = 1.35331 − 1.41659I
b = 0.22053 + 1.52889I
2.36733 − 9.32735I 0
u = 0.01734 + 1.44545I
a = 0.396386 − 0.751706I
b = 0.268892 + 1.158060I
−0.534801 − 0.028205I 0
u = 0.01734 − 1.44545I
a = 0.396386 + 0.751706I
b = 0.268892 − 1.158060I
−0.534801 + 0.028205I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549662 + 0.041925I
a = −0.09236 + 3.36928I
b = −0.153243 − 1.394490I
4.09130 − 2.97513I 1.12422 + 4.10553I
u = −0.549662 − 0.041925I
a = −0.09236 − 3.36928I
b = −0.153243 + 1.394490I
4.09130 + 2.97513I 1.12422 − 4.10553I
u = 0.18947 + 1.45243I
a = 0.658336 + 0.700750I
b = 0.615723 − 0.503069I
−4.33718 + 6.21858I 0
u = 0.18947 − 1.45243I
a = 0.658336 − 0.700750I
b = 0.615723 + 0.503069I
−4.33718 − 6.21858I 0
u = −0.33054 + 1.42798I
a = 0.616003 − 0.560579I
b = 0.920195 + 0.479120I
0.79859 − 12.47880I 0
u = −0.33054 − 1.42798I
a = 0.616003 + 0.560579I
b = 0.920195 − 0.479120I
0.79859 + 12.47880I 0
u = 0.06538 + 1.47185I
a = 0.361525 − 0.221663I
b = 0.461071 + 0.284534I
−4.56537 + 2.56676I 0
u = 0.06538 − 1.47185I
a = 0.361525 + 0.221663I
b = 0.461071 − 0.284534I
−4.56537 − 2.56676I 0
u = 0.39903 + 1.42674I
a = 1.17849 + 1.06086I
b = 0.171298 − 1.352080I
0.49101 + 5.48323I 0
u = 0.39903 − 1.42674I
a = 1.17849 − 1.06086I
b = 0.171298 + 1.352080I
0.49101 − 5.48323I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472827 + 0.144736I
a = −1.58765 − 2.63391I
b = −0.026338 + 0.558642I
5.26654 + 1.96738I 14.2458 − 2.6393I
u = −0.472827 − 0.144736I
a = −1.58765 + 2.63391I
b = −0.026338 − 0.558642I
5.26654 − 1.96738I 14.2458 + 2.6393I
u = 0.15160 + 1.50309I
a = 0.023024 − 0.305139I
b = −0.070230 + 0.432947I
−4.71084 + 2.85923I 0
u = 0.15160 − 1.50309I
a = 0.023024 + 0.305139I
b = −0.070230 − 0.432947I
−4.71084 − 2.85923I 0
u = 0.35014 + 1.47046I
a = −1.130810 − 0.831992I
b = −0.36239 + 1.51575I
2.85832 + 10.65370I 0
u = 0.35014 − 1.47046I
a = −1.130810 + 0.831992I
b = −0.36239 − 1.51575I
2.85832 − 10.65370I 0
u = −0.41431 + 1.47342I
a = 1.23289 − 1.08392I
b = 0.33859 + 1.53104I
7.2848 − 17.0538I 0
u = −0.41431 − 1.47342I
a = 1.23289 + 1.08392I
b = 0.33859 − 1.53104I
7.2848 + 17.0538I 0
u = 0.113165 + 0.423487I
a = 0.246557 − 0.386479I
b = −0.306576 + 0.975377I
1.08545 + 2.15056I −3.09530 − 5.75751I
u = 0.113165 − 0.423487I
a = 0.246557 + 0.386479I
b = −0.306576 − 0.975377I
1.08545 − 2.15056I −3.09530 + 5.75751I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227567 + 0.261070I
a = 0.20134 + 1.41758I
b = −0.504243 − 0.205514I
−1.043770 − 0.672454I −5.80489 + 2.84262I
u = −0.227567 − 0.261070I
a = 0.20134 − 1.41758I
b = −0.504243 + 0.205514I
−1.043770 + 0.672454I −5.80489 − 2.84262I
u = 0.13415 + 1.72704I
a = 0.292858 + 0.442501I
b = 0.018613 − 1.343400I
−1.07790 + 3.06653I 0
u = 0.13415 − 1.72704I
a = 0.292858 − 0.442501I
b = 0.018613 + 1.343400I
−1.07790 − 3.06653I 0
15
II.
I
u
2
= hu
25
+4u
24
+· · ·+b+3, −u
25
−3u
24
+· · ·+a+1, u
27
+3u
26
+· · ·+6u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
u
25
+ 3u
24
+ ··· + 4u − 1
−u
25
− 4u
24
+ ··· − 15u − 3
a
6
=
1
−u
2
a
4
=
−3u
26
− 9u
25
+ ··· − 16u − 2
u
26
+ 6u
25
+ ··· + 9u + 2
a
2
=
−u
26
− 6u
25
+ ··· − 5u − 1
−3u
26
− 4u
25
+ ··· + 21u + 4
a
11
=
−u
26
− 5u
25
+ ··· − 7u − 1
7u
25
+ 21u
24
+ ··· + 38u + 6
a
3
=
−2u
26
− 9u
25
+ ··· − 13u − 2
5u
25
+ 16u
24
+ ··· + 23u + 4
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−u
24
− 3u
23
+ ··· − 11u − 4
−u
25
− 4u
24
+ ··· − 15u − 3
a
8
=
u
26
+ 4u
25
+ ··· + 17u + 5
u
26
+ u
25
+ ··· + 5u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
25
+ 13u
24
+ 85u
23
+ 182u
22
+ 610u
21
+ 1102u
20
+ 2453u
19
+ 3799u
18
+ 6173u
17
+
8267u
16
+ 10319u
15
+ 11931u
14
+ 12010u
13
+ 11760u
12
+ 10241u
11
+ 8170u
10
+
6609u
9
+ 4250u
8
+ 3054u
7
+ 1807u
6
+ 882u
5
+ 599u
4
+ 180u
3
+ 103u
2
+ 29u + 14
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
27
− 3u
26
+ ··· + 2u − 1
c
2
u
27
− 9u
25
+ ··· − 8u
2
+ 1
c
3
u
27
− u
26
+ ··· + 9u
2
+ 1
c
4
u
27
+ 3u
26
+ ··· + 2u + 1
c
5
, c
6
u
27
+ 3u
26
+ ··· + 6u + 1
c
7
u
27
− 9u
25
+ ··· + 8u
2
− 1
c
8
u
27
− 5u
26
+ ··· − 2u + 1
c
9
u
27
− 3u
26
+ ··· + 6u − 1
c
10
u
27
− 2u
24
+ ··· − 6u − 1
c
11
u
27
+ 5u
26
+ ··· − 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
27
+ 31y
26
+ ··· − 8y −1
c
2
, c
7
y
27
− 18y
26
+ ··· + 16y −1
c
3
y
27
+ 9y
26
+ ··· − 18y −1
c
5
, c
6
, c
9
y
27
+ 29y
26
+ ··· − 2y −1
c
8
, c
11
y
27
− 27y
26
+ ··· + 24y −1
c
10
y
27
− 4y
25
+ ··· − 26y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.953121 + 0.270021I
a = 0.21006 − 2.20597I
b = −0.138665 + 1.343430I
5.00078 + 1.91899I 3.53402 − 0.96985I
u = −0.953121 − 0.270021I
a = 0.21006 + 2.20597I
b = −0.138665 − 1.343430I
5.00078 − 1.91899I 3.53402 + 0.96985I
u = −0.844792
a = 0.232958
b = −0.401656
0.639115 −8.33940
u = 0.025992 + 1.215150I
a = 0.63219 − 1.63481I
b = 0.07781 + 1.66159I
9.28897 + 1.43370I 5.01219 − 4.00671I
u = 0.025992 − 1.215150I
a = 0.63219 + 1.63481I
b = 0.07781 − 1.66159I
9.28897 − 1.43370I 5.01219 + 4.00671I
u = 0.112036 + 1.269680I
a = 1.38122 − 0.60102I
b = 0.410532 + 0.372903I
1.65209 + 3.38872I 3.97132 + 1.99113I
u = 0.112036 − 1.269680I
a = 1.38122 + 0.60102I
b = 0.410532 − 0.372903I
1.65209 − 3.38872I 3.97132 − 1.99113I
u = 0.474983 + 0.534120I
a = −1.07777 − 3.50732I
b = 0.099942 + 1.298690I
7.86766 − 3.16902I 11.98247 + 2.71676I
u = 0.474983 − 0.534120I
a = −1.07777 + 3.50732I
b = 0.099942 − 1.298690I
7.86766 + 3.16902I 11.98247 − 2.71676I
u = 0.206747 + 1.299110I
a = 2.05472 + 0.24015I
b = 0.204486 − 1.302700I
4.93364 + 5.66240I 4.09828 − 6.00158I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206747 − 1.299110I
a = 2.05472 − 0.24015I
b = 0.204486 + 1.302700I
4.93364 − 5.66240I 4.09828 + 6.00158I
u = −0.101175 + 1.329440I
a = −0.455244 − 0.405502I
b = −0.604161 + 1.075950I
−2.47041 + 0.63128I −1.17981 − 1.34152I
u = −0.101175 − 1.329440I
a = −0.455244 + 0.405502I
b = −0.604161 − 1.075950I
−2.47041 − 0.63128I −1.17981 + 1.34152I
u = 0.064544 + 0.651511I
a = −0.562891 − 0.083563I
b = 0.04264 − 1.59060I
11.45130 − 1.10960I 9.17208 − 0.20764I
u = 0.064544 − 0.651511I
a = −0.562891 + 0.083563I
b = 0.04264 + 1.59060I
11.45130 + 1.10960I 9.17208 + 0.20764I
u = 0.261887 + 0.531153I
a = −0.84496 − 1.60343I
b = 0.205953 − 0.319778I
4.44858 − 2.02609I 3.57896 + 1.32740I
u = 0.261887 − 0.531153I
a = −0.84496 + 1.60343I
b = 0.205953 + 0.319778I
4.44858 + 2.02609I 3.57896 − 1.32740I
u = −0.399249 + 1.350510I
a = −1.15237 + 1.29768I
b = −0.22963 − 1.43459I
1.26374 − 6.84192I 4.75336 + 5.44208I
u = −0.399249 − 1.350510I
a = −1.15237 − 1.29768I
b = −0.22963 + 1.43459I
1.26374 + 6.84192I 4.75336 − 5.44208I
u = −0.23800 + 1.41045I
a = −0.507042 + 0.320211I
b = −0.606888 − 0.319468I
−4.36033 − 3.84066I −0.61771 + 6.76680I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23800 − 1.41045I
a = −0.507042 − 0.320211I
b = −0.606888 + 0.319468I
−4.36033 + 3.84066I −0.61771 − 6.76680I
u = −0.11037 + 1.51491I
a = −0.285999 − 0.066289I
b = −0.232289 − 0.749147I
−4.28572 − 3.34164I 6.49116 + 6.76473I
u = −0.11037 − 1.51491I
a = −0.285999 + 0.066289I
b = −0.232289 + 0.749147I
−4.28572 + 3.34164I 6.49116 − 6.76473I
u = −0.17455 + 1.64659I
a = 0.116623 − 0.702219I
b = −0.054303 + 1.228230I
−2.12873 − 2.36216I 0
u = −0.17455 − 1.64659I
a = 0.116623 + 0.702219I
b = −0.054303 − 1.228230I
−2.12873 + 2.36216I 0
u = −0.247316 + 0.147370I
a = −1.62502 − 0.18943I
b = −0.474585 − 0.911358I
1.56250 − 1.88777I 9.68720 − 1.71213I
u = −0.247316 − 0.147370I
a = −1.62502 + 0.18943I
b = −0.474585 + 0.911358I
1.56250 + 1.88777I 9.68720 + 1.71213I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
27
− 3u
26
+ ··· + 2u − 1)(u
104
− 4u
103
+ ··· + 30u − 4)
c
2
(u
27
− 9u
25
+ ··· − 8u
2
+ 1)(u
104
+ u
103
+ ··· + 795u + 2071)
c
3
(u
27
− u
26
+ ··· + 9u
2
+ 1)(u
104
+ 26u
102
+ ··· + 8003385u − 1611677)
c
4
(u
27
+ 3u
26
+ ··· + 2u + 1)(u
104
− 4u
103
+ ··· + 30u − 4)
c
5
, c
6
(u
27
+ 3u
26
+ ··· + 6u + 1)(u
104
+ 4u
103
+ ··· − 4255u − 529)
c
7
(u
27
− 9u
25
+ ··· + 8u
2
− 1)(u
104
+ u
103
+ ··· + 795u + 2071)
c
8
(u
27
− 5u
26
+ ··· − 2u + 1)(u
104
− 42u
102
+ ··· − 17433u + 11887)
c
9
(u
27
− 3u
26
+ ··· + 6u − 1)(u
104
+ 4u
103
+ ··· − 4255u − 529)
c
10
(u
27
− 2u
24
+ ··· − 6u − 1)(u
104
+ 7u
103
+ ··· + 3018333u − 281591)
c
11
(u
27
+ 5u
26
+ ··· − 2u − 1)(u
104
− 42u
102
+ ··· − 17433u + 11887)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
27
+ 31y
26
+ ··· − 8y −1)(y
104
+ 106y
103
+ ··· − 1084y + 16)
c
2
, c
7
(y
27
− 18y
26
+ ··· + 16y −1)
· (y
104
− 71y
103
+ ··· − 59982743y + 4289041)
c
3
(y
27
+ 9y
26
+ ··· − 18y −1)
· (y
104
+ 52y
103
+ ··· + 80900979801019y + 2597502752329)
c
5
, c
6
, c
9
(y
27
+ 29y
26
+ ··· − 2y −1)
· (y
104
+ 96y
103
+ ··· − 1564253y + 279841)
c
8
, c
11
(y
27
− 27y
26
+ ··· + 24y −1)
· (y
104
− 84y
103
+ ··· − 776703027y + 141300769)
c
10
(y
27
− 4y
25
+ ··· − 26y −1)
· (y
104
+ 23y
103
+ ··· − 1658049684805y + 79293491281)
23
