12a
0989
(K12a
0989
)
A knot diagram
1
Linearized knot diagam
4 6 11 10 9 3 12 1 5 2 8 7
Solving Sequence
4,10 2,5
11 1 3 9 6 7 8 12
c
4
c
10
c
1
c
3
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.17644 × 10
158
u
92
− 4.89354 × 10
158
u
91
+ ··· + 2.36703 × 10
158
b + 2.64156 × 10
160
,
− 1.71815 × 10
160
u
92
+ 2.80396 × 10
160
u
91
+ ··· + 7.33779 × 10
159
a − 2.19928 × 10
162
,
u
93
− 2u
92
+ ··· + 272u − 31i
I
u
2
= hu
20
− u
19
+ ··· + 2u
2
+ b, u
17
− u
16
+ ··· + a + 4, u
21
− u
20
+ ··· + 9u
2
+ 1i
I
u
3
= hu
2
+ b, a − 1, u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 129 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
= h2.18 × 10
158
u
92
− 4.89 × 10
158
u
91
+ · · · + 2.37 × 10
158
b + 2.64 ×
10
160
, −1.72 × 10
160
u
92
+ 2.80 × 10
160
u
91
+ · · · + 7.34 × 10
159
a − 2.20 ×
10
162
, u
93
− 2u
92
+ · · · + 272u − 31i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
2.34150u
92
− 3.82126u
91
+ ··· − 1537.23u + 299.720
−0.919480u
92
+ 2.06737u
91
+ ··· + 662.190u − 111.598
a
5
=
1
−u
2
a
11
=
−1.05704u
92
+ 2.58553u
91
+ ··· + 713.093u − 107.997
−1.32311u
92
+ 2.32703u
91
+ ··· + 778.565u − 142.988
a
1
=
1.42202u
92
− 1.75388u
91
+ ··· − 875.044u + 188.122
−0.919480u
92
+ 2.06737u
91
+ ··· + 662.190u − 111.598
a
3
=
1.34484u
92
− 1.75442u
91
+ ··· − 1040.40u + 221.242
−0.842160u
92
+ 1.62410u
91
+ ··· + 516.189u − 89.1519
a
9
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−3.75367u
92
+ 6.11615u
91
+ ··· + 2424.00u − 448.315
2.03760u
92
− 3.19078u
91
+ ··· − 1029.66u + 188.557
a
8
=
−3.68763u
92
+ 5.77130u
91
+ ··· + 2009.93u − 364.805
0.312514u
92
− 0.432786u
91
+ ··· − 141.093u + 24.4478
a
12
=
−2.67125u
92
+ 4.38356u
91
+ ··· + 1306.55u − 207.373
−2.16240u
92
+ 3.42633u
91
+ ··· + 1506.82u − 289.648
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.26141u
92
+ 4.72648u
91
+ ··· + 1127.48u − 174.399
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
− 9u
92
+ ··· + 5549u − 149
c
2
, c
6
u
93
− 4u
92
+ ··· − 16486u − 5639
c
3
u
93
+ 13u
91
+ ··· − 23676u − 2809
c
4
, c
5
, c
9
u
93
− 2u
92
+ ··· + 272u − 31
c
7
, c
11
, c
12
u
93
+ 5u
92
+ ··· − 230u − 28
c
8
u
93
− 5u
92
+ ··· − 978070u − 166348
c
10
u
93
+ 7u
92
+ ··· + 3131u − 509
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
− 7y
92
+ ··· + 30482673y −22201
c
2
, c
6
y
93
− 56y
92
+ ··· + 966106988y −31798321
c
3
y
93
+ 26y
92
+ ··· − 221556894y −7890481
c
4
, c
5
, c
9
y
93
+ 98y
92
+ ··· + 49928y −961
c
7
, c
11
, c
12
y
93
+ 81y
92
+ ··· + 1660y −784
c
8
y
93
− 27y
92
+ ··· + 59397369308y −27671657104
c
10
y
93
− 19y
92
+ ··· + 11519509y −259081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913602 + 0.442628I
a = −0.457622 + 1.243410I
b = 1.058510 − 0.914805I
−0.09995 + 12.96690I 0
u = 0.913602 − 0.442628I
a = −0.457622 − 1.243410I
b = 1.058510 + 0.914805I
−0.09995 − 12.96690I 0
u = 0.477137 + 0.859449I
a = −1.021430 − 0.010347I
b = 0.468897 + 0.485013I
1.63423 − 0.00473I 0
u = 0.477137 − 0.859449I
a = −1.021430 + 0.010347I
b = 0.468897 − 0.485013I
1.63423 + 0.00473I 0
u = −0.935734 + 0.449982I
a = −0.416168 + 0.107447I
b = 0.705075 − 0.315756I
−3.85014 − 0.96568I 0
u = −0.935734 − 0.449982I
a = −0.416168 − 0.107447I
b = 0.705075 + 0.315756I
−3.85014 + 0.96568I 0
u = −0.863338 + 0.408854I
a = −0.46911 − 1.34477I
b = 0.955959 + 0.919498I
5.07812 − 8.87462I 0
u = −0.863338 − 0.408854I
a = −0.46911 + 1.34477I
b = 0.955959 − 0.919498I
5.07812 + 8.87462I 0
u = −0.645207 + 0.651632I
a = 0.186968 − 1.274370I
b = 0.891416 + 0.487223I
−4.79645 − 4.22664I 0
u = −0.645207 − 0.651632I
a = 0.186968 + 1.274370I
b = 0.891416 − 0.487223I
−4.79645 + 4.22664I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735166 + 0.839615I
a = −0.777511 − 0.042973I
b = 0.659808 − 0.589993I
3.87469 + 3.43543I 0
u = −0.735166 − 0.839615I
a = −0.777511 + 0.042973I
b = 0.659808 + 0.589993I
3.87469 − 3.43543I 0
u = 0.764831 + 0.380631I
a = −0.43381 + 1.55356I
b = 0.799947 − 0.860704I
2.91231 + 4.47308I 0
u = 0.764831 − 0.380631I
a = −0.43381 − 1.55356I
b = 0.799947 + 0.860704I
2.91231 − 4.47308I 0
u = 0.832710 + 0.861085I
a = −0.709125 + 0.097582I
b = 0.751222 + 0.616665I
−1.21449 − 7.09054I 0
u = 0.832710 − 0.861085I
a = −0.709125 − 0.097582I
b = 0.751222 − 0.616665I
−1.21449 + 7.09054I 0
u = −0.599446 + 0.529611I
a = 0.200504 + 1.259710I
b = −1.03242 − 1.03698I
−3.75102 − 7.23646I 0
u = −0.599446 − 0.529611I
a = 0.200504 − 1.259710I
b = −1.03242 + 1.03698I
−3.75102 + 7.23646I 0
u = 0.530203 + 0.536247I
a = −0.848529 − 0.391549I
b = 0.635048 + 0.428441I
1.89674 − 0.16432I 0
u = 0.530203 − 0.536247I
a = −0.848529 + 0.391549I
b = 0.635048 − 0.428441I
1.89674 + 0.16432I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583719 + 0.435352I
a = 0.274470 − 1.263930I
b = −0.824406 + 0.986343I
0.96715 + 3.76112I 6.00000 − 7.79854I
u = 0.583719 − 0.435352I
a = 0.274470 + 1.263930I
b = −0.824406 − 0.986343I
0.96715 − 3.76112I 6.00000 + 7.79854I
u = 0.043409 + 1.292040I
a = −0.129329 + 1.260720I
b = −0.577513 − 1.162990I
−4.13101 − 4.56307I 0
u = 0.043409 − 1.292040I
a = −0.129329 − 1.260720I
b = −0.577513 + 1.162990I
−4.13101 + 4.56307I 0
u = −0.063260 + 1.309100I
a = −1.91793 − 0.51884I
b = −0.266745 − 0.059748I
0.82618 − 2.85276I 0
u = −0.063260 − 1.309100I
a = −1.91793 + 0.51884I
b = −0.266745 + 0.059748I
0.82618 + 2.85276I 0
u = −0.625101 + 0.280638I
a = 0.312212 + 1.130920I
b = −0.345387 − 1.035540I
−1.92190 − 0.78399I 6.00000 + 4.34634I
u = −0.625101 − 0.280638I
a = 0.312212 − 1.130920I
b = −0.345387 + 1.035540I
−1.92190 + 0.78399I 6.00000 − 4.34634I
u = 0.151548 + 1.312570I
a = −0.154828 − 0.278383I
b = 0.47612 + 2.10791I
−3.57737 + 7.92014I 0
u = 0.151548 − 1.312570I
a = −0.154828 + 0.278383I
b = 0.47612 − 2.10791I
−3.57737 − 7.92014I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122631 + 1.319250I
a = −0.098610 + 0.261745I
b = 0.81321 − 1.84355I
0.68667 − 3.90580I 0
u = −0.122631 − 1.319250I
a = −0.098610 − 0.261745I
b = 0.81321 + 1.84355I
0.68667 + 3.90580I 0
u = 0.086300 + 1.323190I
a = −0.033382 − 0.229889I
b = 1.17676 + 1.47463I
−2.79990 − 0.13216I 0
u = 0.086300 − 1.323190I
a = −0.033382 + 0.229889I
b = 1.17676 − 1.47463I
−2.79990 + 0.13216I 0
u = −0.102451 + 1.339250I
a = 0.10172 − 1.45870I
b = −0.122372 + 1.064720I
0.261156 − 0.373382I 0
u = −0.102451 − 1.339250I
a = 0.10172 + 1.45870I
b = −0.122372 − 1.064720I
0.261156 + 0.373382I 0
u = 0.380036 + 1.300450I
a = −0.056447 − 0.899311I
b = −1.277570 + 0.597971I
−6.84431 + 2.10476I 0
u = 0.380036 − 1.300450I
a = −0.056447 + 0.899311I
b = −1.277570 − 0.597971I
−6.84431 − 2.10476I 0
u = 0.108724 + 1.377210I
a = −1.45681 + 0.90106I
b = −0.484326 + 0.094880I
−5.29511 + 7.48084I 0
u = 0.108724 − 1.377210I
a = −1.45681 − 0.90106I
b = −0.484326 − 0.094880I
−5.29511 − 7.48084I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601998
a = 0.475355
b = 0.0274806
0.846249 13.8440
u = 0.162275 + 1.400340I
a = 0.50117 + 1.37602I
b = 0.400795 − 0.971210I
−2.65152 + 5.81739I 0
u = 0.162275 − 1.400340I
a = 0.50117 − 1.37602I
b = 0.400795 + 0.971210I
−2.65152 − 5.81739I 0
u = 0.512131 + 0.278620I
a = −0.40132 + 2.59528I
b = 0.429005 − 0.669047I
2.68816 + 3.40353I 11.5134 − 8.5198I
u = 0.512131 − 0.278620I
a = −0.40132 − 2.59528I
b = 0.429005 + 0.669047I
2.68816 − 3.40353I 11.5134 + 8.5198I
u = −0.23586 + 1.39895I
a = −0.331701 + 0.594399I
b = −1.00644 − 1.34411I
−7.24895 − 3.91169I 0
u = −0.23586 − 1.39895I
a = −0.331701 − 0.594399I
b = −1.00644 + 1.34411I
−7.24895 + 3.91169I 0
u = −0.15703 + 1.42035I
a = −0.450171 + 0.829493I
b = −1.23858 − 0.89464I
−6.63384 − 3.20290I 0
u = −0.15703 − 1.42035I
a = −0.450171 − 0.829493I
b = −1.23858 + 0.89464I
−6.63384 + 3.20290I 0
u = 0.545802 + 0.030068I
a = 0.12360 − 1.47805I
b = 0.89653 + 1.26313I
0.58881 + 5.47605I 10.85334 − 6.45978I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545802 − 0.030068I
a = 0.12360 + 1.47805I
b = 0.89653 − 1.26313I
0.58881 − 5.47605I 10.85334 + 6.45978I
u = −0.39220 + 1.40768I
a = −0.005970 + 0.835212I
b = −1.127310 − 0.377774I
−3.51071 − 4.89100I 0
u = −0.39220 − 1.40768I
a = −0.005970 − 0.835212I
b = −1.127310 + 0.377774I
−3.51071 + 4.89100I 0
u = 0.24694 + 1.45463I
a = −0.035778 − 0.663022I
b = −0.542421 + 0.600773I
−4.63718 + 3.26112I 0
u = 0.24694 − 1.45463I
a = −0.035778 + 0.663022I
b = −0.542421 − 0.600773I
−4.63718 − 3.26112I 0
u = 0.21190 + 1.46415I
a = −0.502395 − 0.696276I
b = −1.45367 + 1.07755I
−5.16038 + 6.68364I 0
u = 0.21190 − 1.46415I
a = −0.502395 + 0.696276I
b = −1.45367 − 1.07755I
−5.16038 − 6.68364I 0
u = 0.203352 + 0.478894I
a = −0.15094 − 1.89057I
b = −1.154220 + 0.296388I
−6.65054 + 0.51603I −2.97629 − 0.81890I
u = 0.203352 − 0.478894I
a = −0.15094 + 1.89057I
b = −1.154220 − 0.296388I
−6.65054 − 0.51603I −2.97629 + 0.81890I
u = 0.09622 + 1.47913I
a = −0.610858 − 0.868754I
b = −1.33232 + 0.62691I
−13.10280 + 1.77082I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09622 − 1.47913I
a = −0.610858 + 0.868754I
b = −1.33232 − 0.62691I
−13.10280 − 1.77082I 0
u = 0.17173 + 1.47790I
a = 0.338655 + 0.331113I
b = 0.899141 − 0.179238I
−4.77166 + 2.31742I 0
u = 0.17173 − 1.47790I
a = 0.338655 − 0.331113I
b = 0.899141 + 0.179238I
−4.77166 − 2.31742I 0
u = −0.04028 + 1.49084I
a = 0.263156 − 0.385197I
b = 0.762580 + 0.278955I
−4.89782 + 1.60324I 0
u = −0.04028 − 1.49084I
a = 0.263156 + 0.385197I
b = 0.762580 − 0.278955I
−4.89782 − 1.60324I 0
u = 0.28423 + 1.47284I
a = 0.539000 + 1.044640I
b = 1.09985 − 1.02283I
−3.07822 + 8.28484I 0
u = 0.28423 − 1.47284I
a = 0.539000 − 1.044640I
b = 1.09985 + 1.02283I
−3.07822 − 8.28484I 0
u = −0.395291 + 0.288983I
a = 0.71541 + 1.49210I
b = −0.674999 − 0.451166I
−1.12259 − 1.10724I −0.87157 + 3.08284I
u = −0.395291 − 0.288983I
a = 0.71541 − 1.49210I
b = −0.674999 + 0.451166I
−1.12259 + 1.10724I −0.87157 − 3.08284I
u = −0.21627 + 1.49749I
a = −0.555071 + 0.685058I
b = −1.60874 − 1.03760I
−10.3086 − 10.2526I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21627 − 1.49749I
a = −0.555071 − 0.685058I
b = −1.60874 + 1.03760I
−10.3086 + 10.2526I 0
u = 0.42246 + 1.46495I
a = 0.038625 − 0.826763I
b = −1.119850 + 0.181789I
−8.15205 + 8.05269I 0
u = 0.42246 − 1.46495I
a = 0.038625 + 0.826763I
b = −1.119850 − 0.181789I
−8.15205 − 8.05269I 0
u = −0.32088 + 1.49052I
a = 0.518975 − 1.006450I
b = 1.27865 + 1.03826I
−1.03771 − 13.15390I 0
u = −0.32088 − 1.49052I
a = 0.518975 + 1.006450I
b = 1.27865 − 1.03826I
−1.03771 + 13.15390I 0
u = −0.20586 + 1.53058I
a = 0.701032 − 0.996276I
b = 0.961366 + 0.620833I
−11.88910 − 7.29226I 0
u = −0.20586 − 1.53058I
a = 0.701032 + 0.996276I
b = 0.961366 − 0.620833I
−11.88910 + 7.29226I 0
u = −0.449276 + 0.042466I
a = −0.03422 + 1.73671I
b = 1.07255 − 1.01805I
4.94301 − 1.86722I 17.1351 + 4.2480I
u = −0.449276 − 0.042466I
a = −0.03422 − 1.73671I
b = 1.07255 + 1.01805I
4.94301 + 1.86722I 17.1351 − 4.2480I
u = 0.33771 + 1.51180I
a = 0.515098 + 0.984249I
b = 1.38685 − 0.99515I
−6.3932 + 17.4899I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.33771 − 1.51180I
a = 0.515098 − 0.984249I
b = 1.38685 + 0.99515I
−6.3932 − 17.4899I 0
u = −0.27620 + 1.54799I
a = 0.075848 + 0.702148I
b = −0.489239 − 0.122470I
−9.41833 − 1.36160I 0
u = −0.27620 − 1.54799I
a = 0.075848 − 0.702148I
b = −0.489239 + 0.122470I
−9.41833 + 1.36160I 0
u = 0.00946 + 1.58941I
a = 0.299789 + 0.498833I
b = 0.636869 − 0.079459I
−10.78520 − 4.40021I 0
u = 0.00946 − 1.58941I
a = 0.299789 − 0.498833I
b = 0.636869 + 0.079459I
−10.78520 + 4.40021I 0
u = −0.24751 + 1.57309I
a = 0.359834 − 0.311803I
b = 0.910200 + 0.119775I
−10.91280 − 5.38166I 0
u = −0.24751 − 1.57309I
a = 0.359834 + 0.311803I
b = 0.910200 − 0.119775I
−10.91280 + 5.38166I 0
u = −0.390226 + 0.057007I
a = −2.61524 − 3.45928I
b = −0.001314 + 0.642526I
4.67448 + 1.36905I 20.6717 − 3.3521I
u = −0.390226 − 0.057007I
a = −2.61524 + 3.45928I
b = −0.001314 − 0.642526I
4.67448 − 1.36905I 20.6717 + 3.3521I
u = 0.346986 + 0.103915I
a = −4.06340 − 1.50940I
b = −0.345849 + 0.679582I
−0.47838 + 5.84762I 9.7633 − 10.6724I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346986 − 0.103915I
a = −4.06340 + 1.50940I
b = −0.345849 − 0.679582I
−0.47838 − 5.84762I 9.7633 + 10.6724I
u = 0.294798 + 0.013504I
a = −0.08216 − 2.66607I
b = 1.38561 + 0.72652I
1.49403 − 1.59244I 14.2016 + 0.3191I
u = 0.294798 − 0.013504I
a = −0.08216 + 2.66607I
b = 1.38561 − 0.72652I
1.49403 + 1.59244I 14.2016 − 0.3191I
14
II.
I
u
2
= hu
20
−u
19
+· · ·+ 2 u
2
+b, u
17
−u
16
+· · ·+ a +4, u
21
−u
20
+· · ·+ 9 u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−u
17
+ u
16
+ ··· − 16u
2
− 4
−u
20
+ u
19
+ ··· − u
3
− 2u
2
a
5
=
1
−u
2
a
11
=
−4u
20
+ 4u
19
+ ··· − 2u
2
− 10u
−u
19
+ u
18
+ ··· + 2u − 1
a
1
=
−u
20
+ u
19
+ ··· − 18u
2
− 4
−u
20
+ u
19
+ ··· − u
3
− 2u
2
a
3
=
−u
17
+ u
16
+ ··· − 16u
2
− 3
u
18
− u
17
+ ··· − 4u
2
+ u
a
9
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−u
20
+ 2u
19
+ ··· − u + 5
−4u
20
+ 4u
19
+ ··· + 2u
2
− 5u
a
8
=
u
20
− 5u
19
+ ··· − 3u − 1
u
20
− 4u
19
+ ··· − 4u
2
+ 3u
a
12
=
−7u
20
+ 3u
19
+ ··· − 7u − 6
−u
20
− 4u
19
+ ··· + 4u − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
20
−u
19
−34u
18
−17u
17
−105u
16
−93u
15
−108u
14
−232u
13
+ 112u
12
−261u
11
+
327u
10
− 64u
9
+ 134u
8
+ 75u
7
− 201u
6
− 10u
5
− 205u
4
− 47u
3
− 60u
2
− 3u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 4u
19
+ ··· + 3u − 1
c
2
u
21
− 3u
20
+ ··· − 9u
2
+ 1
c
3
u
21
− u
20
+ ··· + 4u
3
+ 1
c
4
, c
5
u
21
− u
20
+ ··· + 9u
2
+ 1
c
6
u
21
+ 3u
20
+ ··· + 9u
2
− 1
c
7
u
21
− u
20
+ ··· − 5u
2
+ 1
c
8
u
21
+ u
20
+ ··· + 2u + 1
c
9
u
21
+ u
20
+ ··· − 9u
2
− 1
c
10
u
21
− 4u
18
+ ··· − u − 1
c
11
, c
12
u
21
+ u
20
+ ··· + 5u
2
− 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 8y
20
+ ··· + 3y −1
c
2
, c
6
y
21
− 21y
20
+ ··· + 18y −1
c
3
y
21
− 3y
20
+ ··· − 8y
2
− 1
c
4
, c
5
, c
9
y
21
+ 21y
20
+ ··· − 18y −1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 10y −1
c
8
y
21
− 7y
20
+ ··· + 10y −1
c
10
y
21
+ 8y
19
+ ··· + 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.942504 + 0.246260I
a = 0.631734 − 0.286008I
b = −0.752858 − 0.134198I
−4.31301 + 1.48475I −2.43515 − 3.09049I
u = 0.942504 − 0.246260I
a = 0.631734 + 0.286008I
b = −0.752858 + 0.134198I
−4.31301 − 1.48475I −2.43515 + 3.09049I
u = −0.867402
a = 0.846213
b = −0.674358
0.209182 −3.13540
u = −0.024819 + 1.260640I
a = 0.873577 + 0.193046I
b = 1.79051 − 0.60013I
−1.87183 + 1.42542I 6.45818 − 0.53250I
u = −0.024819 − 1.260640I
a = 0.873577 − 0.193046I
b = 1.79051 + 0.60013I
−1.87183 − 1.42542I 6.45818 + 0.53250I
u = 0.051916 + 1.310110I
a = 1.134780 − 0.699911I
b = 0.761655 + 0.696872I
0.60500 + 2.12401I 7.45502 − 0.61311I
u = 0.051916 − 1.310110I
a = 1.134780 + 0.699911I
b = 0.761655 − 0.696872I
0.60500 − 2.12401I 7.45502 + 0.61311I
u = −0.116459 + 1.317440I
a = 0.529330 + 0.945267I
b = 0.127554 − 1.169550I
−4.23054 − 6.68298I 3.09112 + 5.24011I
u = −0.116459 − 1.317440I
a = 0.529330 − 0.945267I
b = 0.127554 + 1.169550I
−4.23054 + 6.68298I 3.09112 − 5.24011I
u = 0.315230 + 1.339510I
a = −0.047136 − 0.641467I
b = −1.16096 + 0.82040I
−8.03930 + 2.94569I −3.03387 − 2.74900I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315230 − 1.339510I
a = −0.047136 + 0.641467I
b = −1.16096 − 0.82040I
−8.03930 − 2.94569I −3.03387 + 2.74900I
u = −0.313919 + 0.482198I
a = −0.35009 + 1.42347I
b = −0.070636 + 0.740220I
−1.00960 + 5.13706I 3.81791 − 2.57618I
u = −0.313919 − 0.482198I
a = −0.35009 − 1.42347I
b = −0.070636 − 0.740220I
−1.00960 − 5.13706I 3.81791 + 2.57618I
u = −0.077295 + 0.557233I
a = −1.226070 + 0.444963I
b = 0.974734 + 0.496814I
0.81376 − 1.77615I 1.80485 + 4.14303I
u = −0.077295 − 0.557233I
a = −1.226070 − 0.444963I
b = 0.974734 − 0.496814I
0.81376 + 1.77615I 1.80485 − 4.14303I
u = −0.27572 + 1.43267I
a = −0.199332 + 0.719503I
b = −0.867664 − 0.619835I
−4.77951 − 4.11317I 3.13796 + 6.16435I
u = −0.27572 − 1.43267I
a = −0.199332 − 0.719503I
b = −0.867664 + 0.619835I
−4.77951 + 4.11317I 3.13796 − 6.16435I
u = 0.162734 + 0.459737I
a = −1.36050 − 1.34511I
b = 0.361068 − 0.517119I
3.85234 − 1.38121I 8.78785 + 1.62457I
u = 0.162734 − 0.459737I
a = −1.36050 + 1.34511I
b = 0.361068 + 0.517119I
3.85234 + 1.38121I 8.78785 − 1.62457I
u = 0.26953 + 1.56759I
a = −0.409400 − 0.556126I
b = −0.826230 + 0.337958I
−10.74070 + 6.05778I 1.98382 − 7.58727I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26953 − 1.56759I
a = −0.409400 + 0.556126I
b = −0.826230 − 0.337958I
−10.74070 − 6.05778I 1.98382 + 7.58727I
20
III. I
u
3
= hu
2
+ b, a − 1, u
15
+ 3u
13
+ · · · − u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1
−u
2
a
5
=
1
−u
2
a
11
=
−u
u
3
+ u
a
1
=
−u
2
+ 1
−u
2
a
3
=
u
4
+ u
2
+ 1
−u
6
− 2u
4
− u
2
a
9
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
− 2u
2
a
8
=
−u
7
+ 2u
3
− 2u
−u
7
− u
5
+ 2u
3
+ u
a
12
=
u
12
+ u
11
+ u
10
+ 2u
9
− 3u
8
− u
7
− u
6
− 2u
5
+ 3u
4
+ u
3
− 2u
2
− u + 1
−u
13
+ u
12
− 3u
11
+ 2u
10
− u
9
− u
8
+ 3u
7
− 2u
6
+ u
5
+ u
4
− u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
5
− 4u
3
+ 4u + 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 6u
14
+ ··· + 2u + 1
c
2
, c
6
u
15
+ 6u
14
+ ··· + 2u − 1
c
3
u
15
− 3u
13
+ ··· + 4u + 5
c
4
, c
5
, c
9
c
10
u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1
c
7
, c
11
, c
12
(u
3
− u
2
+ 2u − 1)
5
c
8
(u
3
+ u
2
− 1)
5
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
15
− 18y
14
+ ··· − 6y −1
c
3
y
15
− 6y
14
+ ··· − 134y −25
c
4
, c
5
, c
9
c
10
y
15
+ 6y
14
+ ··· + 2y −1
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
5
c
8
(y
3
− y
2
+ 2y −1)
5
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.003770 + 0.106833I
a = 1.00000
b = −0.996143 − 0.214471I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 1.003770 − 0.106833I
a = 1.00000
b = −0.996143 + 0.214471I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.962445
a = 1.00000
b = −0.926301
1.11345 9.01950
u = −0.803235 + 0.362184I
a = 1.00000
b = −0.514010 + 0.581838I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.803235 − 0.362184I
a = 1.00000
b = −0.514010 − 0.581838I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = 0.168874 + 1.219270I
a = 1.00000
b = 1.45811 − 0.41181I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = 0.168874 − 1.219270I
a = 1.00000
b = 1.45811 + 0.41181I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.450135 + 0.619793I
a = 1.00000
b = 0.181522 + 0.557981I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.450135 − 0.619793I
a = 1.00000
b = 0.181522 − 0.557981I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.096333 + 1.293630I
a = 1.00000
b = 1.66419 + 0.24924I
1.11345 9.01951 + 0.I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096333 − 1.293630I
a = 1.00000
b = 1.66419 − 0.24924I
1.11345 9.01951 + 0.I
u = 0.577555 + 0.364050I
a = 1.00000
b = −0.201038 − 0.420518I
1.11345 9.01951 + 0.I
u = 0.577555 − 0.364050I
a = 1.00000
b = −0.201038 + 0.420518I
1.11345 9.01951 + 0.I
u = 0.080725 + 1.370050I
a = 1.00000
b = 1.87052 − 0.22119I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.080725 − 1.370050I
a = 1.00000
b = 1.87052 + 0.22119I
−3.02413 − 2.82812I 2.49024 + 2.97945I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 6u
14
+ ··· + 2u + 1)(u
21
− 4u
19
+ ··· + 3u − 1)
· (u
93
− 9u
92
+ ··· + 5549u − 149)
c
2
(u
15
+ 6u
14
+ ··· + 2u − 1)(u
21
− 3u
20
+ ··· − 9u
2
+ 1)
· (u
93
− 4u
92
+ ··· − 16486u − 5639)
c
3
(u
15
− 3u
13
+ ··· + 4u + 5)(u
21
− u
20
+ ··· + 4u
3
+ 1)
· (u
93
+ 13u
91
+ ··· − 23676u − 2809)
c
4
, c
5
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (u
21
− u
20
+ ··· + 9u
2
+ 1)(u
93
− 2u
92
+ ··· + 272u − 31)
c
6
(u
15
+ 6u
14
+ ··· + 2u − 1)(u
21
+ 3u
20
+ ··· + 9u
2
− 1)
· (u
93
− 4u
92
+ ··· − 16486u − 5639)
c
7
((u
3
− u
2
+ 2u − 1)
5
)(u
21
− u
20
+ ··· − 5u
2
+ 1)
· (u
93
+ 5u
92
+ ··· − 230u − 28)
c
8
((u
3
+ u
2
− 1)
5
)(u
21
+ u
20
+ ··· + 2u + 1)
· (u
93
− 5u
92
+ ··· − 978070u − 166348)
c
9
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (u
21
+ u
20
+ ··· − 9u
2
− 1)(u
93
− 2u
92
+ ··· + 272u − 31)
c
10
(u
15
+ 3u
13
− u
10
− 5u
9
− 2u
8
+ u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
+ 1)
· (u
21
− 4u
18
+ ··· − u − 1)(u
93
+ 7u
92
+ ··· + 3131u − 509)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
5
)(u
21
+ u
20
+ ··· + 5u
2
− 1)
· (u
93
+ 5u
92
+ ··· − 230u − 28)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 18y
14
+ ··· − 6y −1)(y
21
− 8y
20
+ ··· + 3y −1)
· (y
93
− 7y
92
+ ··· + 30482673y −22201)
c
2
, c
6
(y
15
− 18y
14
+ ··· − 6y −1)(y
21
− 21y
20
+ ··· + 18y −1)
· (y
93
− 56y
92
+ ··· + 966106988y −31798321)
c
3
(y
15
− 6y
14
+ ··· − 134y −25)(y
21
− 3y
20
+ ··· − 8y
2
− 1)
· (y
93
+ 26y
92
+ ··· − 221556894y −7890481)
c
4
, c
5
, c
9
(y
15
+ 6y
14
+ ··· + 2y −1)(y
21
+ 21y
20
+ ··· − 18y −1)
· (y
93
+ 98y
92
+ ··· + 49928y −961)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
5
)(y
21
+ 21y
20
+ ··· + 10y −1)
· (y
93
+ 81y
92
+ ··· + 1660y −784)
c
8
((y
3
− y
2
+ 2y −1)
5
)(y
21
− 7y
20
+ ··· + 10y −1)
· (y
93
− 27y
92
+ ··· + 59397369308y −27671657104)
c
10
(y
15
+ 6y
14
+ ··· + 2y −1)(y
21
+ 8y
19
+ ··· + 3y −1)
· (y
93
− 19y
92
+ ··· + 11519509y −259081)
27
