12n
0836
(K12n
0836
)
A knot diagram
1
Linearized knot diagam
4 6 12 9 2 9 1 11 4 7 3 8
Solving Sequence
8,12 1,4
3 7 11 9 5 6 2 10
c
12
c
3
c
7
c
11
c
8
c
4
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.01141 × 10
178
u
79
− 1.53427 × 10
179
u
78
+ ··· + 8.20723 × 10
178
b + 1.11833 × 10
181
,
− 8.82110 × 10
179
u
79
− 1.86815 × 10
180
u
78
+ ··· + 4.33810 × 10
179
a − 1.20564 × 10
182
,
u
80
+ 3u
79
+ ··· − 692u − 148i
I
u
2
= h−419743649u
22
+ 600334478u
21
+ ··· + 939590426b + 1322008284,
544158953u
22
− 1664036159u
21
+ ··· + 1879180852a − 3189273440, u
23
− u
22
+ ··· + 8u + 4i
I
u
3
= hb + 1, a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 104 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−2.01 × 10
178
u
79
− 1.53 × 10
179
u
78
+ · · · + 8.21 × 10
178
b + 1.12 ×
10
181
, −8.82 × 10
179
u
79
− 1.87 × 10
180
u
78
+ · · · + 4.34 × 10
179
a − 1.21 ×
10
182
, u
80
+ 3u
79
+ · · · − 692u − 148i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
2.03340u
79
+ 4.30637u
78
+ ··· + 1080.35u + 277.919
0.245078u
79
+ 1.86942u
78
+ ··· − 692.484u − 136.261
a
3
=
2.27848u
79
+ 6.17578u
78
+ ··· + 387.869u + 141.658
0.245078u
79
+ 1.86942u
78
+ ··· − 692.484u − 136.261
a
7
=
u
u
3
+ u
a
11
=
−0.261711u
79
− 0.131889u
78
+ ··· − 408.221u − 92.9224
−0.447967u
79
− 2.59603u
78
+ ··· + 801.323u + 153.979
a
9
=
0.937727u
79
+ 2.63334u
78
+ ··· + 85.3324u + 42.4994
−0.149265u
79
− 0.548385u
78
+ ··· + 52.3634u + 9.08703
a
5
=
10.1203u
79
+ 29.8622u
78
+ ··· + 201.630u + 315.128
0.0269954u
79
+ 2.97414u
78
+ ··· − 1810.20u − 372.735
a
6
=
−2.15415u
79
− 4.52646u
78
+ ··· − 1317.07u − 333.037
0.0899931u
79
− 0.186489u
78
+ ··· + 277.477u + 59.4733
a
2
=
−0.980754u
79
− 4.52806u
78
+ ··· + 1187.82u + 218.399
0.419539u
79
+ 0.305039u
78
+ ··· + 544.761u + 128.017
a
10
=
0.135237u
79
+ 2.49572u
78
+ ··· − 1315.46u − 271.021
−0.303249u
79
− 2.42157u
78
+ ··· + 947.070u + 188.521
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.02688u
79
+ 13.5179u
78
+ ··· − 913.018u − 91.2459
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
+ u
79
+ ··· + 121816053u + 10935405
c
2
, c
5
u
80
+ 5u
79
+ ··· − 9u + 1
c
3
, c
11
u
80
+ 2u
79
+ ··· − 488u − 91
c
4
, c
9
u
80
− 4u
79
+ ··· + 22580u + 3676
c
6
u
80
− 8u
79
+ ··· + 11892000u + 986616
c
7
, c
12
u
80
+ 3u
79
+ ··· − 692u − 148
c
8
u
80
− 11u
79
+ ··· + 258u − 11
c
10
u
80
− 4u
79
+ ··· + 9331040u + 665887
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
+ 59y
79
+ ··· + 3158025656114421y + 119583082514025
c
2
, c
5
y
80
− 21y
79
+ ··· − 63y + 1
c
3
, c
11
y
80
− 46y
79
+ ··· − 130946y + 8281
c
4
, c
9
y
80
− 80y
79
+ ··· − 1476835552y + 13512976
c
6
y
80
+ 58y
79
+ ··· − 53110665152640y + 973411131456
c
7
, c
12
y
80
+ 57y
79
+ ··· + 262912y + 21904
c
8
y
80
+ 3y
79
+ ··· − 8880y + 121
c
10
y
80
+ 46y
79
+ ··· − 72020481186584y + 443405496769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.046801 + 1.002510I
a = 0.98336 + 1.75820I
b = −0.573536 − 0.982987I
−0.176447 − 0.015979I 0
u = 0.046801 − 1.002510I
a = 0.98336 − 1.75820I
b = −0.573536 + 0.982987I
−0.176447 + 0.015979I 0
u = 0.822278 + 0.475094I
a = 0.732335 − 0.357721I
b = 0.957847 − 0.349248I
−2.53039 + 3.09745I 0
u = 0.822278 − 0.475094I
a = 0.732335 + 0.357721I
b = 0.957847 + 0.349248I
−2.53039 − 3.09745I 0
u = 0.091622 + 1.055600I
a = 0.24639 + 2.94466I
b = 0.822173 − 0.286394I
6.28320 − 3.62041I 0
u = 0.091622 − 1.055600I
a = 0.24639 − 2.94466I
b = 0.822173 + 0.286394I
6.28320 + 3.62041I 0
u = 0.279779 + 1.030260I
a = −0.01582 + 2.20267I
b = −1.160090 − 0.565372I
−2.43822 − 5.49446I 0
u = 0.279779 − 1.030260I
a = −0.01582 − 2.20267I
b = −1.160090 + 0.565372I
−2.43822 + 5.49446I 0
u = −0.255565 + 0.885376I
a = 1.192220 − 0.536184I
b = −1.74649 + 0.21439I
1.24011 + 5.04477I 0
u = −0.255565 − 0.885376I
a = 1.192220 + 0.536184I
b = −1.74649 − 0.21439I
1.24011 − 5.04477I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.105049 + 1.089820I
a = 0.41716 − 2.72556I
b = −0.757713 + 0.316934I
6.31846 + 2.49469I 0
u = 0.105049 − 1.089820I
a = 0.41716 + 2.72556I
b = −0.757713 − 0.316934I
6.31846 − 2.49469I 0
u = 0.081923 + 1.111640I
a = −0.93761 − 1.73433I
b = 1.45583 + 1.02764I
3.16613 − 5.16687I 0
u = 0.081923 − 1.111640I
a = −0.93761 + 1.73433I
b = 1.45583 − 1.02764I
3.16613 + 5.16687I 0
u = 0.306815 + 0.809611I
a = −0.59543 + 1.62433I
b = 0.680031 − 1.128500I
−1.13568 − 1.39327I 0. + 6.02870I
u = 0.306815 − 0.809611I
a = −0.59543 − 1.62433I
b = 0.680031 + 1.128500I
−1.13568 + 1.39327I 0. − 6.02870I
u = 0.850618 + 0.141619I
a = −0.603834 − 0.644927I
b = −0.082168 + 0.834234I
4.31948 − 6.02401I −8.00000 + 4.76540I
u = 0.850618 − 0.141619I
a = −0.603834 + 0.644927I
b = −0.082168 − 0.834234I
4.31948 + 6.02401I −8.00000 − 4.76540I
u = −0.393225 + 1.082950I
a = 0.149783 − 1.328200I
b = −1.077820 + 0.560087I
1.63816 + 3.25672I 0
u = −0.393225 − 1.082950I
a = 0.149783 + 1.328200I
b = −1.077820 − 0.560087I
1.63816 − 3.25672I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010130 + 0.814360I
a = 0.298622 + 1.013230I
b = 1.011000 − 0.400621I
−0.745254 − 0.723458I −9.33301 + 2.88959I
u = 0.010130 − 0.814360I
a = 0.298622 − 1.013230I
b = 1.011000 + 0.400621I
−0.745254 + 0.723458I −9.33301 − 2.88959I
u = 0.765524 + 0.242345I
a = 0.829280 + 0.521861I
b = 0.120637 − 0.711335I
5.10844 + 0.82388I −5.14125 − 0.25076I
u = 0.765524 − 0.242345I
a = 0.829280 − 0.521861I
b = 0.120637 + 0.711335I
5.10844 − 0.82388I −5.14125 + 0.25076I
u = 0.540193 + 0.561625I
a = 0.470096 − 0.502904I
b = 1.121930 − 0.386740I
−3.79395 + 2.22531I −15.1723 + 3.2449I
u = 0.540193 − 0.561625I
a = 0.470096 + 0.502904I
b = 1.121930 + 0.386740I
−3.79395 − 2.22531I −15.1723 − 3.2449I
u = 0.491737 + 1.117400I
a = −0.54139 + 1.52861I
b = −1.131240 − 0.476408I
−0.42712 − 8.03019I 0
u = 0.491737 − 1.117400I
a = −0.54139 − 1.52861I
b = −1.131240 + 0.476408I
−0.42712 + 8.03019I 0
u = −1.224740 + 0.000179I
a = 0.246321 + 0.350162I
b = 1.144690 − 0.486456I
2.22985 + 3.62423I 0
u = −1.224740 − 0.000179I
a = 0.246321 − 0.350162I
b = 1.144690 + 0.486456I
2.22985 − 3.62423I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.306758 + 1.193560I
a = 0.435738 + 0.477747I
b = −0.212987 − 0.588066I
2.19021 + 3.79104I 0
u = −0.306758 − 1.193560I
a = 0.435738 − 0.477747I
b = −0.212987 + 0.588066I
2.19021 − 3.79104I 0
u = −1.235680 + 0.050440I
a = −0.272628 − 0.464013I
b = −1.206980 + 0.505362I
1.01408 + 10.86440I 0
u = −1.235680 − 0.050440I
a = −0.272628 + 0.464013I
b = −1.206980 − 0.505362I
1.01408 − 10.86440I 0
u = 1.23866
a = −0.818757
b = −0.903518
−4.96766 0
u = 0.287804 + 1.205310I
a = −0.07226 − 1.48666I
b = 1.35004 + 0.46853I
−1.05609 − 7.02185I 0
u = 0.287804 − 1.205310I
a = −0.07226 + 1.48666I
b = 1.35004 − 0.46853I
−1.05609 + 7.02185I 0
u = −0.037339 + 1.249590I
a = 0.008119 − 1.158290I
b = −0.278270 + 0.933238I
3.92396 + 2.10466I 0
u = −0.037339 − 1.249590I
a = 0.008119 + 1.158290I
b = −0.278270 − 0.933238I
3.92396 − 2.10466I 0
u = −0.717179 + 0.064230I
a = 0.389771 − 0.052663I
b = 0.500055 − 0.258503I
−1.354540 − 0.079357I −5.49507 − 1.06068I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.717179 − 0.064230I
a = 0.389771 + 0.052663I
b = 0.500055 + 0.258503I
−1.354540 + 0.079357I −5.49507 + 1.06068I
u = −0.548102 + 0.419477I
a = −0.34153 + 1.63307I
b = 1.310210 − 0.401158I
0.18162 − 1.54489I −11.98300 + 1.73737I
u = −0.548102 − 0.419477I
a = −0.34153 − 1.63307I
b = 1.310210 + 0.401158I
0.18162 + 1.54489I −11.98300 − 1.73737I
u = −0.128278 + 1.308850I
a = 0.334243 − 1.179070I
b = −0.661054 + 0.678245I
3.31548 + 2.64034I 0
u = −0.128278 − 1.308850I
a = 0.334243 + 1.179070I
b = −0.661054 − 0.678245I
3.31548 − 2.64034I 0
u = 0.418017 + 1.260320I
a = 0.254230 − 1.347270I
b = 1.153920 + 0.328092I
−1.18466 − 4.83399I 0
u = 0.418017 − 1.260320I
a = 0.254230 + 1.347270I
b = 1.153920 − 0.328092I
−1.18466 + 4.83399I 0
u = −0.148559 + 1.327950I
a = −1.80054 + 1.36603I
b = 0.897881 − 0.303281I
6.00828 + 6.28936I 0
u = −0.148559 − 1.327950I
a = −1.80054 − 1.36603I
b = 0.897881 + 0.303281I
6.00828 − 6.28936I 0
u = −1.276820 + 0.458507I
a = 0.0642039 + 0.1102510I
b = −1.137630 − 0.262063I
−6.57602 − 0.89051I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276820 − 0.458507I
a = 0.0642039 − 0.1102510I
b = −1.137630 + 0.262063I
−6.57602 + 0.89051I 0
u = 0.375344 + 1.305330I
a = 0.45582 − 1.38696I
b = −0.316427 + 1.215260I
9.73007 − 3.25378I 0
u = 0.375344 − 1.305330I
a = 0.45582 + 1.38696I
b = −0.316427 − 1.215260I
9.73007 + 3.25378I 0
u = −0.156318 + 1.363940I
a = 1.34534 − 1.61897I
b = −0.905799 + 0.399198I
5.74714 + 0.69667I 0
u = −0.156318 − 1.363940I
a = 1.34534 + 1.61897I
b = −0.905799 − 0.399198I
5.74714 − 0.69667I 0
u = 0.419691 + 1.331690I
a = −0.51408 + 1.35772I
b = 0.280095 − 1.188640I
8.83649 − 10.61630I 0
u = 0.419691 − 1.331690I
a = −0.51408 − 1.35772I
b = 0.280095 + 1.188640I
8.83649 + 10.61630I 0
u = −0.127688 + 1.402740I
a = −1.017010 − 0.198866I
b = 0.712556 − 0.016753I
1.28019 + 3.07152I 0
u = −0.127688 − 1.402740I
a = −1.017010 + 0.198866I
b = 0.712556 + 0.016753I
1.28019 − 3.07152I 0
u = −0.69061 + 1.25085I
a = −0.287373 + 1.369720I
b = 1.233370 − 0.610545I
−3.79073 + 7.70099I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.69061 − 1.25085I
a = −0.287373 − 1.369720I
b = 1.233370 + 0.610545I
−3.79073 − 7.70099I 0
u = 0.509923 + 0.167049I
a = −1.18077 + 1.18242I
b = −1.183380 + 0.287450I
−4.27418 + 3.88356I −16.0855 − 8.1336I
u = 0.509923 − 0.167049I
a = −1.18077 − 1.18242I
b = −1.183380 − 0.287450I
−4.27418 − 3.88356I −16.0855 + 8.1336I
u = 0.73780 + 1.26578I
a = −0.619671 + 0.951801I
b = −0.805392 − 0.449705I
7.29022 − 6.62158I 0
u = 0.73780 − 1.26578I
a = −0.619671 − 0.951801I
b = −0.805392 + 0.449705I
7.29022 + 6.62158I 0
u = 0.81373 + 1.23958I
a = 0.665630 − 0.811391I
b = 0.683396 + 0.362604I
6.67626 + 0.49264I 0
u = 0.81373 − 1.23958I
a = 0.665630 + 0.811391I
b = 0.683396 − 0.362604I
6.67626 − 0.49264I 0
u = −0.55706 + 1.40052I
a = 0.15830 − 1.53976I
b = −1.26779 + 0.67703I
6.69796 + 9.82224I 0
u = −0.55706 − 1.40052I
a = 0.15830 + 1.53976I
b = −1.26779 − 0.67703I
6.69796 − 9.82224I 0
u = −0.55658 + 1.41662I
a = −0.14783 + 1.60393I
b = 1.28529 − 0.66239I
5.6492 + 17.0935I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55658 − 1.41662I
a = −0.14783 − 1.60393I
b = 1.28529 + 0.66239I
5.6492 − 17.0935I 0
u = −0.324715 + 0.300358I
a = 0.982844 − 0.479573I
b = 0.024182 − 0.478711I
−0.850668 + 1.089870I −8.28515 − 6.20149I
u = −0.324715 − 0.300358I
a = 0.982844 + 0.479573I
b = 0.024182 + 0.478711I
−0.850668 − 1.089870I −8.28515 + 6.20149I
u = −0.47290 + 1.51406I
a = 0.473897 + 0.321956I
b = −0.796617 − 0.473267I
7.30475 + 2.76610I 0
u = −0.47290 − 1.51406I
a = 0.473897 − 0.321956I
b = −0.796617 + 0.473267I
7.30475 − 2.76610I 0
u = −0.379685
a = 1.02008
b = 0.736668
−0.972157 −10.3410
u = −0.170182 + 0.315443I
a = 2.15961 − 1.70448I
b = −1.293230 + 0.398588I
1.08478 + 4.75218I −10.44225 − 3.54394I
u = −0.170182 − 0.315443I
a = 2.15961 + 1.70448I
b = −1.293230 − 0.398588I
1.08478 − 4.75218I −10.44225 + 3.54394I
u = −0.55597 + 1.61236I
a = −0.432708 − 0.309730I
b = 0.932914 + 0.420052I
5.84863 − 3.93774I 0
u = −0.55597 − 1.61236I
a = −0.432708 + 0.309730I
b = 0.932914 − 0.420052I
5.84863 + 3.93774I 0
12
II.
I
u
2
= h−4.20 × 10
8
u
22
+ 6.00 × 10
8
u
21
+ · · · + 9.40 × 10
8
b + 1.32 × 10
9
, 5.44 ×
10
8
u
22
− 1.66 × 10
9
u
21
+ · · · + 1.88 × 10
9
a − 3.19 × 10
9
, u
23
− u
22
+ · · · + 8u + 4i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−0.289572u
22
+ 0.885511u
21
+ ··· + 2.14028u + 1.69716
0.446730u
22
− 0.638932u
21
+ ··· − 1.35067u − 1.40700
a
3
=
0.157158u
22
+ 0.246579u
21
+ ··· + 0.789609u + 0.290157
0.446730u
22
− 0.638932u
21
+ ··· − 1.35067u − 1.40700
a
7
=
u
u
3
+ u
a
11
=
0.276363u
22
− 0.173920u
21
+ ··· + 2.11044u + 1.48875
0.765290u
22
− 0.962834u
21
+ ··· + 0.685442u − 0.921020
a
9
=
−0.167152u
22
− 0.278332u
21
+ ··· − 3.22268u − 0.798647
−0.132267u
22
− 0.326350u
21
+ ··· − 2.03671u − 1.02647
a
5
=
−0.574730u
22
+ 1.11722u
21
+ ··· + 5.10114u + 3.51895
0.571145u
22
+ 0.408285u
21
+ ··· + 9.08167u + 2.72101
a
6
=
−0.487679u
22
+ 0.809537u
21
+ ··· + 3.24767u + 1.15810
0.269230u
22
+ 0.475192u
21
+ ··· + 6.03127u + 1.81567
a
2
=
−0.378803u
22
+ 0.704466u
21
+ ··· − 2.22326u + 0.615635
−0.221457u
22
− 0.0125231u
21
+ ··· − 1.12963u − 0.278927
a
10
=
−0.723637u
22
+ 0.826080u
21
+ ··· − 0.889562u + 1.48875
0.765290u
22
− 0.962834u
21
+ ··· + 1.68544u − 0.921020
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1916934295
469795213
u
22
+
3433733587
469795213
u
21
+ ··· +
4938247538
469795213
u −
1506429838
469795213
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
23
− 2u
22
+ ··· + 311u − 97
c
2
u
23
+ u
22
+ ··· − 3u − 1
c
3
u
23
− 8u
21
+ ··· + 2u − 1
c
4
u
23
− 5u
21
+ ··· − 8u − 4
c
5
u
23
− u
22
+ ··· − 3u + 1
c
6
u
23
− u
22
+ ··· + 112u − 8
c
7
u
23
+ u
22
+ ··· + 8u − 4
c
8
u
23
− 7u
22
+ ··· − 4u + 1
c
9
u
23
− 5u
21
+ ··· − 8u + 4
c
10
u
23
+ 2u
22
+ ··· + 8u + 1
c
11
u
23
− 8u
21
+ ··· + 2u + 1
c
12
u
23
− u
22
+ ··· + 8u + 4
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 14y
22
+ ··· + 102929y −9409
c
2
, c
5
y
23
− 15y
22
+ ··· + 21y −1
c
3
, c
11
y
23
− 16y
22
+ ··· + 20y −1
c
4
, c
9
y
23
− 10y
22
+ ··· − 336y −16
c
6
y
23
+ 9y
22
+ ··· + 224y −64
c
7
, c
12
y
23
+ 15y
22
+ ··· − 16y −16
c
8
y
23
− 3y
22
+ ··· + 38y −1
c
10
y
23
+ 4y
22
+ ··· + 10y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.195695 + 0.905353I
a = 0.663809 + 1.111290I
b = −1.58112 − 0.64190I
1.80593 − 5.30609I −4.19368 + 10.52796I
u = 0.195695 − 0.905353I
a = 0.663809 − 1.111290I
b = −1.58112 + 0.64190I
1.80593 + 5.30609I −4.19368 − 10.52796I
u = −0.249720 + 0.815143I
a = −0.74167 − 1.92054I
b = 0.65124 + 1.31322I
−1.43107 + 1.29521I −23.7677 + 0.8270I
u = −0.249720 − 0.815143I
a = −0.74167 + 1.92054I
b = 0.65124 − 1.31322I
−1.43107 − 1.29521I −23.7677 − 0.8270I
u = 0.311236 + 1.186810I
a = −0.17688 + 1.72983I
b = −1.224100 − 0.449665I
−1.34450 − 6.20497I −10.76093 + 5.12215I
u = 0.311236 − 1.186810I
a = −0.17688 − 1.72983I
b = −1.224100 + 0.449665I
−1.34450 + 6.20497I −10.76093 − 5.12215I
u = 0.525423 + 0.535300I
a = 0.488288 − 1.047180I
b = 1.076500 − 0.325826I
−3.66567 + 2.95631I −13.7337 − 5.1643I
u = 0.525423 − 0.535300I
a = 0.488288 + 1.047180I
b = 1.076500 + 0.325826I
−3.66567 − 2.95631I −13.7337 + 5.1643I
u = −0.325767 + 1.238460I
a = 0.55023 − 1.85887I
b = −0.698035 + 0.081331I
6.29166 + 4.98444I −6.04423 − 4.91486I
u = −0.325767 − 1.238460I
a = 0.55023 + 1.85887I
b = −0.698035 − 0.081331I
6.29166 − 4.98444I −6.04423 + 4.91486I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.063849 + 1.280080I
a = −0.765281 + 0.991836I
b = 1.030940 − 0.647555I
3.41540 + 3.83887I −6.08616 − 5.69445I
u = 0.063849 − 1.280080I
a = −0.765281 − 0.991836I
b = 1.030940 + 0.647555I
3.41540 − 3.83887I −6.08616 + 5.69445I
u = −0.466124 + 1.219360I
a = 0.30524 + 1.67930I
b = 0.753830 − 0.116296I
5.78601 − 1.16137I −8.66700 + 0.78351I
u = −0.466124 − 1.219360I
a = 0.30524 − 1.67930I
b = 0.753830 + 0.116296I
5.78601 + 1.16137I −8.66700 − 0.78351I
u = −0.208317 + 1.310250I
a = 0.888196 + 0.303119I
b = −0.338193 − 0.237729I
1.87567 + 2.84881I −4.03264 + 0.76341I
u = −0.208317 − 1.310250I
a = 0.888196 − 0.303119I
b = −0.338193 + 0.237729I
1.87567 − 2.84881I −4.03264 − 0.76341I
u = 1.187760 + 0.606265I
a = 0.0365848 − 0.0492523I
b = −1.163490 + 0.305211I
−6.91288 + 1.35220I −16.3921 − 6.4530I
u = 1.187760 − 0.606265I
a = 0.0365848 + 0.0492523I
b = −1.163490 − 0.305211I
−6.91288 − 1.35220I −16.3921 + 6.4530I
u = 0.618783 + 1.194600I
a = −0.24896 − 1.47907I
b = 1.264580 + 0.564204I
−4.65670 − 7.69608I −15.2035 + 5.8609I
u = 0.618783 − 1.194600I
a = −0.24896 + 1.47907I
b = 1.264580 − 0.564204I
−4.65670 + 7.69608I −15.2035 − 5.8609I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44339
a = −0.670422
b = −0.776001
−4.63397 4.55600
u = −0.431125 + 0.126042I
a = −0.164338 − 1.136870I
b = 0.615858 − 0.308043I
−2.13675 − 0.30581I −17.3964 + 1.2323I
u = −0.431125 − 0.126042I
a = −0.164338 + 1.136870I
b = 0.615858 + 0.308043I
−2.13675 + 0.30581I −17.3964 − 1.2323I
20
III. I
u
3
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
12
=
1
0
a
1
=
1
1
a
4
=
−1
−1
a
3
=
−2
−1
a
7
=
1
2
a
11
=
−1
−1
a
9
=
−1
0
a
5
=
−2
−1
a
6
=
3
2
a
2
=
1
1
a
10
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
c
2
, c
4
, c
5
c
8
, c
9
, c
10
u + 1
c
3
, c
7
, c
11
c
12
u − 1
c
6
u + 2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y −1
c
6
y −4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−4.93480 −18.0000
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
23
− 2u
22
+ ··· + 311u − 97)
· (u
80
+ u
79
+ ··· + 121816053u + 10935405)
c
2
(u + 1)(u
23
+ u
22
+ ··· − 3u − 1)(u
80
+ 5u
79
+ ··· − 9u + 1)
c
3
(u − 1)(u
23
− 8u
21
+ ··· + 2u − 1)(u
80
+ 2u
79
+ ··· − 488u − 91)
c
4
(u + 1)(u
23
− 5u
21
+ ··· − 8u − 4)(u
80
− 4u
79
+ ··· + 22580u + 3676)
c
5
(u + 1)(u
23
− u
22
+ ··· − 3u + 1)(u
80
+ 5u
79
+ ··· − 9u + 1)
c
6
(u + 2)(u
23
− u
22
+ ··· + 112u − 8)
· (u
80
− 8u
79
+ ··· + 11892000u + 986616)
c
7
(u − 1)(u
23
+ u
22
+ ··· + 8u − 4)(u
80
+ 3u
79
+ ··· − 692u − 148)
c
8
(u + 1)(u
23
− 7u
22
+ ··· − 4u + 1)(u
80
− 11u
79
+ ··· + 258u − 11)
c
9
(u + 1)(u
23
− 5u
21
+ ··· − 8u + 4)(u
80
− 4u
79
+ ··· + 22580u + 3676)
c
10
(u + 1)(u
23
+ 2u
22
+ ··· + 8u + 1)
· (u
80
− 4u
79
+ ··· + 9331040u + 665887)
c
11
(u − 1)(u
23
− 8u
21
+ ··· + 2u + 1)(u
80
+ 2u
79
+ ··· − 488u − 91)
c
12
(u − 1)(u
23
− u
22
+ ··· + 8u + 4)(u
80
+ 3u
79
+ ··· − 692u − 148)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
23
+ 14y
22
+ ··· + 102929y −9409)
· (y
80
+ 59y
79
+ ··· + 3158025656114421y + 119583082514025)
c
2
, c
5
(y −1)(y
23
− 15y
22
+ ··· + 21y −1)(y
80
− 21y
79
+ ··· − 63y + 1)
c
3
, c
11
(y −1)(y
23
− 16y
22
+ ··· + 20y −1)
· (y
80
− 46y
79
+ ··· − 130946y + 8281)
c
4
, c
9
(y −1)(y
23
− 10y
22
+ ··· − 336y −16)
· (y
80
− 80y
79
+ ··· − 1476835552y + 13512976)
c
6
(y −4)(y
23
+ 9y
22
+ ··· + 224y −64)
· (y
80
+ 58y
79
+ ··· − 53110665152640y + 973411131456)
c
7
, c
12
(y −1)(y
23
+ 15y
22
+ ··· − 16y −16)
· (y
80
+ 57y
79
+ ··· + 262912y + 21904)
c
8
(y −1)(y
23
− 3y
22
+ ··· + 38y −1)(y
80
+ 3y
79
+ ··· − 8880y + 121)
c
10
(y −1)(y
23
+ 4y
22
+ ··· + 10y −1)
· (y
80
+ 46y
79
+ ··· − 72020481186584y + 443405496769)
26
