12a
1101
(K12a
1101
)
A knot diagram
1
Linearized knot diagam
4 7 11 9 12 10 3 1 6 2 8 5
Solving Sequence
2,7
3
8,10
11 4 12 1 6 5 9
c
2
c
7
c
10
c
3
c
11
c
1
c
6
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.20156 × 10
826
u
157
− 1.46744 × 10
828
u
156
+ ··· + 7.17053 × 10
829
b − 9.65577 × 10
830
,
2.89627 × 10
830
u
157
− 3.51152 × 10
830
u
156
+ ··· + 9.35037 × 10
831
a − 3.38511 × 10
833
,
u
158
− u
157
+ ··· − 2697u − 163i
I
u
2
= h8.79895 × 10
26
u
39
− 1.14601 × 10
27
u
38
+ ··· + 7.82938 × 10
24
b + 6.82482 × 10
26
,
3.10296 × 10
27
u
39
− 4.02963 × 10
27
u
38
+ ··· + 1.56588 × 10
25
a + 2.38940 × 10
27
, u
40
− 11u
38
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 198 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
= h4.20 × 10
826
u
157
− 1.47 × 10
828
u
156
+ · · · + 7.17 × 10
829
b − 9.66 ×
10
830
, 2.90 × 10
830
u
157
− 3.51 × 10
830
u
156
+ · · · + 9.35 × 10
831
a − 3.39 ×
10
833
, u
158
− u
157
+ · · · − 2697u − 163i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
10
=
−0.0309749u
157
+ 0.0375549u
156
+ ··· + 326.486u + 36.2030
−0.000585948u
157
+ 0.0204648u
156
+ ··· + 140.491u + 13.4659
a
11
=
−0.0303889u
157
+ 0.0170901u
156
+ ··· + 185.995u + 22.7371
−0.000585948u
157
+ 0.0204648u
156
+ ··· + 140.491u + 13.4659
a
4
=
−0.0472203u
157
+ 0.0619381u
156
+ ··· + 583.791u + 58.0681
−0.0201682u
157
+ 0.0280384u
156
+ ··· + 257.010u + 25.1093
a
12
=
−0.0234350u
157
+ 0.0270363u
156
+ ··· + 211.541u + 24.1368
−0.00474923u
157
+ 0.0153554u
156
+ ··· + 119.324u + 12.1108
a
1
=
0.107539u
157
− 0.136689u
156
+ ··· − 1241.05u − 119.312
0.0481404u
157
− 0.0530366u
156
+ ··· − 492.326u − 47.5686
a
6
=
−0.0398818u
157
+ 0.0361639u
156
+ ··· + 281.333u + 31.2174
−0.0144608u
157
+ 0.00568183u
156
+ ··· + 91.0633u + 10.1594
a
5
=
−0.0855294u
157
+ 0.110350u
156
+ ··· + 960.430u + 93.9086
−0.0333719u
157
+ 0.0414586u
156
+ ··· + 395.243u + 38.6279
a
9
=
0.00240024u
157
+ 0.0117237u
156
+ ··· + 188.798u + 18.4530
−0.00256341u
157
+ 0.00167084u
156
+ ··· + 35.6458u + 4.07512
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000109904u
157
− 0.00588549u
156
+ ··· − 275.257u − 34.1483
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
158
− 11u
157
+ ··· − 6874340367u + 404850059
c
2
, c
7
u
158
+ u
157
+ ··· + 2697u − 163
c
3
4(4u
158
− 12u
157
+ ··· + 3747366u + 276277)
c
4
u
158
+ 2u
157
+ ··· − 16u − 16
c
5
, c
12
u
158
− 3u
157
+ ··· − 68508u + 5048
c
6
, c
9
4(4u
158
− 32u
157
+ ··· − 1649929u − 86329)
c
8
4(4u
158
− 4u
157
+ ··· − 245u + 11)
c
10
u
158
+ 9u
157
+ ··· + 92598104u + 15966368
c
11
u
158
+ 3u
157
+ ··· + 104047000685u + 19423529740
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
158
+ 63y
157
+ ··· + 1.55 × 10
18
y + 1.64 × 10
17
c
2
, c
7
y
158
− 113y
157
+ ··· − 2010213y + 26569
c
3
16(16y
158
+ 824y
157
+ ··· − 4.73888 × 10
12
y + 7.63290 × 10
10
)
c
4
y
158
− 4y
157
+ ··· − 8896y + 256
c
5
, c
12
y
158
+ 93y
157
+ ··· − 3359381776y + 25482304
c
6
, c
9
16(16y
158
− 2328y
157
+ ··· − 3.44551 × 10
11
y + 7.45270 × 10
9
)
c
8
16(16y
158
+ 216y
157
+ ··· − 669y + 121)
c
10
y
158
+ 79y
157
+ ··· − 33590848646406208y + 254924907111424
c
11
y
158
− 85y
157
+ ··· − 3.42 × 10
22
y + 3.77 × 10
20
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972496 + 0.176994I
a = −0.073541 + 0.876303I
b = −0.57216 − 1.40449I
−1.69003 − 5.70181I 0
u = −0.972496 − 0.176994I
a = −0.073541 − 0.876303I
b = −0.57216 + 1.40449I
−1.69003 + 5.70181I 0
u = 0.524096 + 0.819167I
a = 0.594120 − 1.147880I
b = −0.52115 − 1.34476I
0.58624 − 5.07304I 0
u = 0.524096 − 0.819167I
a = 0.594120 + 1.147880I
b = −0.52115 + 1.34476I
0.58624 + 5.07304I 0
u = 0.892950 + 0.303249I
a = 0.173154 − 1.065080I
b = −0.174260 + 0.435076I
−3.04707 − 2.27103I 0
u = 0.892950 − 0.303249I
a = 0.173154 + 1.065080I
b = −0.174260 − 0.435076I
−3.04707 + 2.27103I 0
u = −1.048140 + 0.190695I
a = −1.58091 + 0.91977I
b = 0.011945 − 0.609301I
2.57946 + 0.04227I 0
u = −1.048140 − 0.190695I
a = −1.58091 − 0.91977I
b = 0.011945 + 0.609301I
2.57946 − 0.04227I 0
u = 1.006040 + 0.431525I
a = −1.203940 + 0.189020I
b = −0.26780 + 2.24989I
2.12257 + 9.84038I 0
u = 1.006040 − 0.431525I
a = −1.203940 − 0.189020I
b = −0.26780 − 2.24989I
2.12257 − 9.84038I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886316 + 0.136831I
a = 2.84905 + 1.23233I
b = −0.016301 − 0.449801I
3.26182 + 0.52209I 0
u = 0.886316 − 0.136831I
a = 2.84905 − 1.23233I
b = −0.016301 + 0.449801I
3.26182 − 0.52209I 0
u = −0.520804 + 0.719046I
a = −0.559338 − 1.265560I
b = 0.482395 − 0.572738I
0.56865 + 1.56704I 0
u = −0.520804 − 0.719046I
a = −0.559338 + 1.265560I
b = 0.482395 + 0.572738I
0.56865 − 1.56704I 0
u = −0.182545 + 1.108990I
a = −0.370635 + 0.572715I
b = −0.456034 + 0.397160I
−4.80667 − 1.90727I 0
u = −0.182545 − 1.108990I
a = −0.370635 − 0.572715I
b = −0.456034 − 0.397160I
−4.80667 + 1.90727I 0
u = 0.209754 + 1.109620I
a = 0.482782 − 1.310490I
b = 0.382311 − 1.073030I
5.02998 + 1.75266I 0
u = 0.209754 − 1.109620I
a = 0.482782 + 1.310490I
b = 0.382311 + 1.073030I
5.02998 − 1.75266I 0
u = −1.087210 + 0.344346I
a = 1.224740 + 0.088820I
b = 1.08024 + 1.44995I
2.35644 − 5.67072I 0
u = −1.087210 − 0.344346I
a = 1.224740 − 0.088820I
b = 1.08024 − 1.44995I
2.35644 + 5.67072I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131001 + 0.843040I
a = 1.209090 − 0.413809I
b = 0.907246 − 0.711468I
−1.89484 + 8.93030I 0
u = −0.131001 − 0.843040I
a = 1.209090 + 0.413809I
b = 0.907246 + 0.711468I
−1.89484 − 8.93030I 0
u = −1.154430 + 0.169353I
a = −0.666205 + 0.461464I
b = 0.099171 − 0.835807I
2.74617 + 0.23020I 0
u = −1.154430 − 0.169353I
a = −0.666205 − 0.461464I
b = 0.099171 + 0.835807I
2.74617 − 0.23020I 0
u = 1.135510 + 0.274743I
a = 1.00468 + 1.56112I
b = 0.591744 − 0.615130I
1.95988 − 0.09410I 0
u = 1.135510 − 0.274743I
a = 1.00468 − 1.56112I
b = 0.591744 + 0.615130I
1.95988 + 0.09410I 0
u = −1.166460 + 0.090330I
a = 1.299070 + 0.189538I
b = 1.323790 − 0.126033I
3.58747 − 2.79067I 0
u = −1.166460 − 0.090330I
a = 1.299070 − 0.189538I
b = 1.323790 + 0.126033I
3.58747 + 2.79067I 0
u = −0.116066 + 0.812332I
a = −0.897072 − 0.201798I
b = −0.784145 − 0.592525I
1.21129 − 4.40721I 0
u = −0.116066 − 0.812332I
a = −0.897072 + 0.201798I
b = −0.784145 + 0.592525I
1.21129 + 4.40721I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.179580 + 0.029736I
a = −1.32946 + 0.52017I
b = −1.148630 − 0.110588I
4.54299 + 0.54773I 0
u = 1.179580 − 0.029736I
a = −1.32946 − 0.52017I
b = −1.148630 + 0.110588I
4.54299 − 0.54773I 0
u = 1.180930 + 0.044499I
a = 1.068350 + 0.124337I
b = 2.82651 + 1.24716I
5.17203 + 9.21722I 0
u = 1.180930 − 0.044499I
a = 1.068350 − 0.124337I
b = 2.82651 − 1.24716I
5.17203 − 9.21722I 0
u = 0.536868 + 0.616169I
a = −1.078980 + 0.276097I
b = −0.933898 − 0.044945I
−4.20059 + 5.90431I 0
u = 0.536868 − 0.616169I
a = −1.078980 − 0.276097I
b = −0.933898 + 0.044945I
−4.20059 − 5.90431I 0
u = 0.259597 + 1.158670I
a = −0.475211 + 1.081420I
b = −0.543486 + 0.985503I
6.36687 + 7.91230I 0
u = 0.259597 − 1.158670I
a = −0.475211 − 1.081420I
b = −0.543486 − 0.985503I
6.36687 − 7.91230I 0
u = 1.175410 + 0.202419I
a = −0.0600927 + 0.0711441I
b = −0.86941 − 1.19621I
5.22153 + 2.39646I 0
u = 1.175410 − 0.202419I
a = −0.0600927 − 0.0711441I
b = −0.86941 + 1.19621I
5.22153 − 2.39646I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.200440 + 0.064067I
a = −1.074530 − 0.025046I
b = −2.22782 − 2.13888I
9.40499 + 1.88060I 0
u = −1.200440 − 0.064067I
a = −1.074530 + 0.025046I
b = −2.22782 + 2.13888I
9.40499 − 1.88060I 0
u = −0.141766 + 1.197420I
a = −0.562048 − 1.039970I
b = −0.478009 − 1.016290I
4.37943 − 5.11985I 0
u = −0.141766 − 1.197420I
a = −0.562048 + 1.039970I
b = −0.478009 + 1.016290I
4.37943 + 5.11985I 0
u = −1.153430 + 0.352973I
a = −0.126504 − 0.441810I
b = 0.99858 − 1.40863I
2.01105 − 6.84612I 0
u = −1.153430 − 0.352973I
a = −0.126504 + 0.441810I
b = 0.99858 + 1.40863I
2.01105 + 6.84612I 0
u = 1.198370 + 0.227073I
a = 0.466174 + 0.359694I
b = 0.68893 − 1.24429I
1.95646 + 4.00929I 0
u = 1.198370 − 0.227073I
a = 0.466174 − 0.359694I
b = 0.68893 + 1.24429I
1.95646 − 4.00929I 0
u = −1.209880 + 0.201266I
a = 1.072660 + 0.145832I
b = 1.53815 + 2.37422I
8.00150 − 5.00996I 0
u = −1.209880 − 0.201266I
a = 1.072660 − 0.145832I
b = 1.53815 − 2.37422I
8.00150 + 5.00996I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.231880 + 0.008491I
a = −0.998482 + 0.167959I
b = −0.74436 − 1.56845I
5.03180 + 3.49129I 0
u = −1.231880 − 0.008491I
a = −0.998482 − 0.167959I
b = −0.74436 + 1.56845I
5.03180 − 3.49129I 0
u = 0.170038 + 1.222920I
a = −0.320527 + 0.215257I
b = −0.307318 + 0.027207I
−4.70136 − 1.98621I 0
u = 0.170038 − 1.222920I
a = −0.320527 − 0.215257I
b = −0.307318 − 0.027207I
−4.70136 + 1.98621I 0
u = −0.694239 + 0.307579I
a = −0.552988 + 0.227283I
b = −1.152400 + 0.801745I
−2.57390 + 3.50364I 0
u = −0.694239 − 0.307579I
a = −0.552988 − 0.227283I
b = −1.152400 − 0.801745I
−2.57390 − 3.50364I 0
u = −0.108940 + 1.238290I
a = −0.047728 − 1.125060I
b = 0.285890 − 1.129490I
4.30242 + 3.38275I 0
u = −0.108940 − 1.238290I
a = −0.047728 + 1.125060I
b = 0.285890 + 1.129490I
4.30242 − 3.38275I 0
u = 0.664175 + 0.355810I
a = 0.576003 + 0.778348I
b = 0.717451 − 0.332543I
−2.39540 + 1.85956I 0
u = 0.664175 − 0.355810I
a = 0.576003 − 0.778348I
b = 0.717451 + 0.332543I
−2.39540 − 1.85956I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607564 + 0.438868I
a = 0.588777 + 0.455203I
b = 1.048600 − 0.069155I
−2.70359 + 1.56793I 0
u = 0.607564 − 0.438868I
a = 0.588777 − 0.455203I
b = 1.048600 + 0.069155I
−2.70359 − 1.56793I 0
u = −0.135834 + 1.247920I
a = 0.445245 + 1.095000I
b = 0.537035 + 1.051880I
3.2775 − 14.0624I 0
u = −0.135834 − 1.247920I
a = 0.445245 − 1.095000I
b = 0.537035 − 1.051880I
3.2775 + 14.0624I 0
u = 1.247020 + 0.160701I
a = 1.050930 + 0.207259I
b = 1.18198 − 1.70202I
5.53116 + 5.99526I 0
u = 1.247020 − 0.160701I
a = 1.050930 − 0.207259I
b = 1.18198 + 1.70202I
5.53116 − 5.99526I 0
u = 1.266680 + 0.000702I
a = −0.898403 − 0.104619I
b = −1.89802 − 1.29012I
7.29221 + 1.25319I 0
u = 1.266680 − 0.000702I
a = −0.898403 + 0.104619I
b = −1.89802 + 1.29012I
7.29221 − 1.25319I 0
u = −1.261130 + 0.138936I
a = −0.254687 − 0.734299I
b = 0.485281 + 1.004630I
1.88739 − 2.47937I 0
u = −1.261130 − 0.138936I
a = −0.254687 + 0.734299I
b = 0.485281 − 1.004630I
1.88739 + 2.47937I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.250090 + 0.241877I
a = −0.080927 + 0.896505I
b = −0.234905 − 0.962361I
5.46473 − 2.84011I 0
u = −1.250090 − 0.241877I
a = −0.080927 − 0.896505I
b = −0.234905 + 0.962361I
5.46473 + 2.84011I 0
u = −1.263360 + 0.200311I
a = −0.113462 − 0.425456I
b = 0.306504 + 0.663413I
2.05238 − 1.32981I 0
u = −1.263360 − 0.200311I
a = −0.113462 + 0.425456I
b = 0.306504 − 0.663413I
2.05238 + 1.32981I 0
u = −1.199950 + 0.470520I
a = −0.894677 + 0.262000I
b = −0.772532 − 1.042120I
−1.56522 − 3.38023I 0
u = −1.199950 − 0.470520I
a = −0.894677 − 0.262000I
b = −0.772532 + 1.042120I
−1.56522 + 3.38023I 0
u = 1.289730 + 0.065499I
a = 1.250570 + 0.372455I
b = 0.423635 − 1.053610I
10.69750 + 3.82655I 0
u = 1.289730 − 0.065499I
a = 1.250570 − 0.372455I
b = 0.423635 + 1.053610I
10.69750 − 3.82655I 0
u = 1.239890 + 0.363577I
a = 0.412526 + 0.411125I
b = 0.310240 − 1.324370I
2.52060 + 6.53191I 0
u = 1.239890 − 0.363577I
a = 0.412526 − 0.411125I
b = 0.310240 + 1.324370I
2.52060 − 6.53191I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.233350 + 0.406634I
a = 0.782995 − 0.925735I
b = 0.734911 + 0.940159I
1.55342 − 13.45400I 0
u = −1.233350 − 0.406634I
a = 0.782995 + 0.925735I
b = 0.734911 − 0.940159I
1.55342 + 13.45400I 0
u = −0.089749 + 0.694593I
a = 0.30094 + 1.45572I
b = 0.659706 + 1.027540I
−0.29199 − 3.17931I 0. + 6.67643I
u = −0.089749 − 0.694593I
a = 0.30094 − 1.45572I
b = 0.659706 − 1.027540I
−0.29199 + 3.17931I 0. − 6.67643I
u = 0.027364 + 0.694608I
a = 0.04426 − 2.08651I
b = 0.498891 − 1.001460I
4.25937 + 2.05166I 9.86825 − 3.99888I
u = 0.027364 − 0.694608I
a = 0.04426 + 2.08651I
b = 0.498891 + 1.001460I
4.25937 − 2.05166I 9.86825 + 3.99888I
u = −1.239290 + 0.427582I
a = 0.094661 + 0.185977I
b = −0.562354 + 0.696633I
4.55768 − 0.18030I 0
u = −1.239290 − 0.427582I
a = 0.094661 − 0.185977I
b = −0.562354 − 0.696633I
4.55768 + 0.18030I 0
u = −1.311730 + 0.112851I
a = −1.38563 + 0.36984I
b = −0.455582 − 0.897722I
7.33792 − 10.12360I 0
u = −1.311730 − 0.112851I
a = −1.38563 − 0.36984I
b = −0.455582 + 0.897722I
7.33792 + 10.12360I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.082464 + 1.319310I
a = −0.043371 − 0.926541I
b = −0.218391 − 0.994642I
3.59690 − 0.82728I 0
u = −0.082464 − 1.319310I
a = −0.043371 + 0.926541I
b = −0.218391 + 0.994642I
3.59690 + 0.82728I 0
u = 1.243230 + 0.481417I
a = −0.328977 − 0.468734I
b = −0.316688 + 0.593529I
−1.13878 + 7.49614I 0
u = 1.243230 − 0.481417I
a = −0.328977 + 0.468734I
b = −0.316688 − 0.593529I
−1.13878 − 7.49614I 0
u = 0.124803 + 0.644685I
a = 0.032379 + 0.363993I
b = 0.513510 + 0.736845I
−0.92261 − 2.62985I 4.21753 + 4.40726I
u = 0.124803 − 0.644685I
a = 0.032379 − 0.363993I
b = 0.513510 − 0.736845I
−0.92261 + 2.62985I 4.21753 − 4.40726I
u = 1.311880 + 0.329941I
a = −0.477865 − 0.655221I
b = −0.629737 + 1.029840I
5.67724 + 8.45520I 0
u = 1.311880 − 0.329941I
a = −0.477865 + 0.655221I
b = −0.629737 − 1.029840I
5.67724 − 8.45520I 0
u = 1.323920 + 0.303669I
a = 0.887984 + 0.035456I
b = 0.99042 − 1.99909I
4.14211 + 6.83802I 0
u = 1.323920 − 0.303669I
a = 0.887984 − 0.035456I
b = 0.99042 + 1.99909I
4.14211 − 6.83802I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.358770 + 0.155274I
a = 0.050662 + 0.171830I
b = 0.663872 + 1.150450I
3.24320 − 5.27212I 0
u = 1.358770 − 0.155274I
a = 0.050662 − 0.171830I
b = 0.663872 − 1.150450I
3.24320 + 5.27212I 0
u = 1.352840 + 0.216916I
a = −1.145330 + 0.010321I
b = −0.496026 + 0.846466I
8.78920 + 1.55715I 0
u = 1.352840 − 0.216916I
a = −1.145330 − 0.010321I
b = −0.496026 − 0.846466I
8.78920 − 1.55715I 0
u = 0.224820 + 0.587817I
a = 0.624793 − 1.170690I
b = −0.333869 + 0.265909I
1.67631 + 1.08555I 11.12651 − 5.08174I
u = 0.224820 − 0.587817I
a = 0.624793 + 1.170690I
b = −0.333869 − 0.265909I
1.67631 − 1.08555I 11.12651 + 5.08174I
u = 0.018477 + 0.599029I
a = 1.82913 + 0.39746I
b = 0.676478 + 0.759055I
−1.23861 + 3.38808I 5.09987 − 3.91185I
u = 0.018477 − 0.599029I
a = 1.82913 − 0.39746I
b = 0.676478 − 0.759055I
−1.23861 − 3.38808I 5.09987 + 3.91185I
u = −1.406480 + 0.012457I
a = 0.912512 − 0.310317I
b = 0.280328 + 0.894705I
7.90395 + 2.90748I 0
u = −1.406480 − 0.012457I
a = 0.912512 + 0.310317I
b = 0.280328 − 0.894705I
7.90395 − 2.90748I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42327
a = −0.934980
b = −1.39459
7.59081 0
u = −1.41147 + 0.45996I
a = 1.137190 + 0.107640I
b = 0.99473 + 1.59165I
10.11070 − 7.17354I 0
u = −1.41147 − 0.45996I
a = 1.137190 − 0.107640I
b = 0.99473 − 1.59165I
10.11070 + 7.17354I 0
u = −0.027917 + 0.510011I
a = 0.625937 + 0.766897I
b = 0.821473 + 0.311864I
−1.54343 − 1.25994I −0.90756 + 4.15364I
u = −0.027917 − 0.510011I
a = 0.625937 − 0.766897I
b = 0.821473 − 0.311864I
−1.54343 + 1.25994I −0.90756 − 4.15364I
u = −0.031821 + 0.507487I
a = −1.185640 − 0.454865I
b = −0.589764 + 0.575921I
1.75476 − 0.00881I 9.25065 + 0.20424I
u = −0.031821 − 0.507487I
a = −1.185640 + 0.454865I
b = −0.589764 − 0.575921I
1.75476 + 0.00881I 9.25065 − 0.20424I
u = 1.43160 + 0.50110I
a = −1.152710 − 0.047862I
b = −0.97736 + 1.39351I
9.3803 + 11.0084I 0
u = 1.43160 − 0.50110I
a = −1.152710 + 0.047862I
b = −0.97736 − 1.39351I
9.3803 − 11.0084I 0
u = −0.316065 + 0.362795I
a = −1.35281 − 2.00326I
b = 0.0807781 + 0.0430423I
1.08480 + 1.35011I 7.86429 + 4.10908I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.316065 − 0.362795I
a = −1.35281 + 2.00326I
b = 0.0807781 − 0.0430423I
1.08480 − 1.35011I 7.86429 − 4.10908I
u = −1.45399 + 0.46764I
a = −1.017860 − 0.050164I
b = −1.00969 − 1.57753I
11.7618 − 13.5679I 0
u = −1.45399 − 0.46764I
a = −1.017860 + 0.050164I
b = −1.00969 + 1.57753I
11.7618 + 13.5679I 0
u = 1.45012 + 0.52667I
a = 1.091200 − 0.048739I
b = 0.98501 − 1.54394I
8.3083 + 20.2211I 0
u = 1.45012 − 0.52667I
a = 1.091200 + 0.048739I
b = 0.98501 + 1.54394I
8.3083 − 20.2211I 0
u = 1.41217 + 0.63611I
a = −0.899446 + 0.448745I
b = −0.466691 + 1.260560I
8.74406 + 4.82722I 0
u = 1.41217 − 0.63611I
a = −0.899446 − 0.448745I
b = −0.466691 − 1.260560I
8.74406 − 4.82722I 0
u = −1.43009 + 0.60638I
a = 0.941449 + 0.215775I
b = 0.65181 + 1.55927I
8.54213 − 9.98741I 0
u = −1.43009 − 0.60638I
a = 0.941449 − 0.215775I
b = 0.65181 − 1.55927I
8.54213 + 9.98741I 0
u = 1.48102 + 0.48582I
a = −0.944532 + 0.186449I
b = −0.523837 + 1.039610I
9.49782 + 2.72844I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48102 − 0.48582I
a = −0.944532 − 0.186449I
b = −0.523837 − 1.039610I
9.49782 − 2.72844I 0
u = 1.49218 + 0.51974I
a = −0.812465 + 0.101790I
b = −0.65610 + 1.43526I
8.77165 + 7.29520I 0
u = 1.49218 − 0.51974I
a = −0.812465 − 0.101790I
b = −0.65610 − 1.43526I
8.77165 − 7.29520I 0
u = −0.419362
a = −1.15392
b = −0.179600
0.733985 13.9250
u = −1.48119 + 0.60190I
a = 0.699727 + 0.380594I
b = 0.307076 + 1.179410I
8.61838 − 1.63934I 0
u = −1.48119 − 0.60190I
a = 0.699727 − 0.380594I
b = 0.307076 − 1.179410I
8.61838 + 1.63934I 0
u = 1.55440 + 0.38829I
a = 0.792212 − 0.091477I
b = 1.03536 − 1.17689I
5.36976 + 3.67718I 0
u = 1.55440 − 0.38829I
a = 0.792212 + 0.091477I
b = 1.03536 + 1.17689I
5.36976 − 3.67718I 0
u = −0.339824 + 0.172306I
a = −4.54248 + 0.60166I
b = −0.654412 + 0.480759I
2.66144 − 0.90561I 8.87778 + 3.44537I
u = −0.339824 − 0.172306I
a = −4.54248 − 0.60166I
b = −0.654412 − 0.480759I
2.66144 + 0.90561I 8.87778 − 3.44537I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51459 + 0.57605I
a = 0.867845 + 0.134554I
b = 0.472778 + 0.998305I
8.31088 − 6.11794I 0
u = −1.51459 − 0.57605I
a = 0.867845 − 0.134554I
b = 0.472778 − 0.998305I
8.31088 + 6.11794I 0
u = −1.56637 + 0.54685I
a = −0.860530 − 0.113138I
b = −0.919502 − 1.032930I
4.03489 − 11.20490I 0
u = −1.56637 − 0.54685I
a = −0.860530 + 0.113138I
b = −0.919502 + 1.032930I
4.03489 + 11.20490I 0
u = −1.58210 + 0.63538I
a = −0.703750 − 0.373404I
b = −0.319120 − 0.967375I
7.66634 + 6.87529I 0
u = −1.58210 − 0.63538I
a = −0.703750 + 0.373404I
b = −0.319120 + 0.967375I
7.66634 − 6.87529I 0
u = 1.52417 + 0.77909I
a = 0.714408 − 0.393402I
b = 0.335005 − 0.839056I
9.79703 − 0.61756I 0
u = 1.52417 − 0.77909I
a = 0.714408 + 0.393402I
b = 0.335005 + 0.839056I
9.79703 + 0.61756I 0
u = −0.068387 + 0.279446I
a = 1.66125 + 3.63079I
b = 0.347019 + 1.141660I
1.56097 − 4.17167I 10.7930 + 10.9520I
u = −0.068387 − 0.279446I
a = 1.66125 − 3.63079I
b = 0.347019 − 1.141660I
1.56097 + 4.17167I 10.7930 − 10.9520I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.263119 + 0.093851I
a = −4.99663 − 0.00442I
b = 0.745352 + 1.086500I
2.47935 + 9.02049I 6.50503 − 3.40743I
u = 0.263119 − 0.093851I
a = −4.99663 + 0.00442I
b = 0.745352 − 1.086500I
2.47935 − 9.02049I 6.50503 + 3.40743I
u = −0.136885 + 0.213031I
a = 3.51690 + 3.81197I
b = −0.603176 + 1.138650I
6.29263 − 2.85998I 11.50676 + 2.78422I
u = −0.136885 − 0.213031I
a = 3.51690 − 3.81197I
b = −0.603176 − 1.138650I
6.29263 + 2.85998I 11.50676 − 2.78422I
u = −0.15269 + 1.74787I
a = 0.009292 + 0.728608I
b = −0.005764 + 0.677667I
−1.46647 + 3.34301I 0
u = −0.15269 − 1.74787I
a = 0.009292 − 0.728608I
b = −0.005764 − 0.677667I
−1.46647 − 3.34301I 0
u = −0.160810 + 0.011492I
a = 3.27215 + 1.61623I
b = 1.105650 + 0.459270I
−1.88768 − 1.27148I −12.53468 − 0.26382I
u = −0.160810 − 0.011492I
a = 3.27215 − 1.61623I
b = 1.105650 − 0.459270I
−1.88768 + 1.27148I −12.53468 + 0.26382I
20
II. I
u
2
=
h8.80×10
26
u
39
−1.15×10
27
u
38
+· · ·+7.83×10
24
b+6.82×10
26
, 3.10×10
27
u
39
−
4.03 × 10
27
u
38
+ · · · + 1.57 × 10
25
a + 2.39 × 10
27
, u
40
− 11u
38
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
10
=
−198.161u
39
+ 257.340u
38
+ ··· − 189.503u − 152.592
−112.384u
39
+ 146.373u
38
+ ··· − 104.131u − 87.1694
a
11
=
−85.7776u
39
+ 110.967u
38
+ ··· − 85.3718u − 65.4224
−112.384u
39
+ 146.373u
38
+ ··· − 104.131u − 87.1694
a
4
=
−27.0117u
39
+ 34.5709u
38
+ ··· − 15.5111u − 14.9920
366.337u
39
− 481.374u
38
+ ··· + 343.186u + 280.837
a
12
=
−383.226u
39
+ 500.717u
38
+ ··· − 367.520u − 292.885
100.565u
39
− 132.469u
38
+ ··· + 95.7729u + 75.1178
a
1
=
−287.526u
39
+ 388.585u
38
+ ··· − 291.596u − 231.470
672.260u
39
− 885.850u
38
+ ··· + 637.953u + 508.779
a
6
=
368.415u
39
− 479.619u
38
+ ··· + 345.052u + 279.655
259.056u
39
− 338.430u
38
+ ··· + 241.787u + 198.136
a
5
=
−824.624u
39
+ 1086.66u
38
+ ··· − 777.991u − 623.044
176.401u
39
− 228.868u
38
+ ··· + 159.288u + 136.809
a
9
=
557.142u
39
− 721.095u
38
+ ··· + 495.212u + 411.860
467.817u
39
− 612.671u
38
+ ··· + 435.884u + 352.534
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
44986684399660635698516854661
15658758159275251011365702
u
39
+
29489410211352808863632682782
7829379079637625505682851
u
38
+ ··· −
42491430590740029645550764887
15658758159275251011365702
u −
16980280580749417169886998014
7829379079637625505682851
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
40
− 6u
39
+ ··· − 58u + 7
c
2
u
40
− 11u
38
+ ··· + 2u + 1
c
3
4(4u
40
− 32u
39
+ ··· − 7u + 1)
c
4
u
40
+ u
39
+ ··· + 44u + 8
c
5
u
40
+ 14u
38
+ ··· − 16u + 8
c
6
4(4u
40
+ 28u
39
+ ··· + 244u + 29)
c
7
u
40
− 11u
38
+ ··· − 2u + 1
c
8
4(4u
40
+ 8u
39
+ ··· + 4u + 1)
c
9
4(4u
40
− 28u
39
+ ··· − 244u + 29)
c
10
u
40
− 4u
39
+ ··· + 20u + 8
c
11
u
40
+ 6u
39
+ ··· + 342u + 459
c
12
u
40
+ 14u
38
+ ··· + 16u + 8
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 2y
39
+ ··· − 270y + 49
c
2
, c
7
y
40
− 22y
39
+ ··· + 4y + 1
c
3
16(16y
40
− 280y
39
+ ··· + 43y + 1)
c
4
y
40
− y
39
+ ··· + 288y + 64
c
5
, c
12
y
40
+ 28y
39
+ ··· + 1824y + 64
c
6
, c
9
16(16y
40
− 1192y
39
+ ··· − 29318y + 841)
c
8
16(16y
40
+ 648y
39
+ ··· + 16y + 1)
c
10
y
40
+ 22y
39
+ ··· + 1568y + 64
c
11
y
40
− 22y
39
+ ··· − 4267242y + 210681
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885821 + 0.261488I
a = 1.381710 − 0.092326I
b = −0.91396 + 1.59533I
3.18361 − 9.70369I 12.8707 + 9.4890I
u = −0.885821 − 0.261488I
a = 1.381710 + 0.092326I
b = −0.91396 − 1.59533I
3.18361 + 9.70369I 12.8707 − 9.4890I
u = −1.055710 + 0.304501I
a = −0.452103 + 0.593617I
b = 0.398254 − 0.522821I
4.26352 − 1.26858I 0
u = −1.055710 − 0.304501I
a = −0.452103 − 0.593617I
b = 0.398254 + 0.522821I
4.26352 + 1.26858I 0
u = 0.864055 + 0.056711I
a = 4.92614 − 0.29652I
b = 0.197618 − 0.268041I
3.05844 − 0.25163I 23.1978 − 17.4445I
u = 0.864055 − 0.056711I
a = 4.92614 + 0.29652I
b = 0.197618 + 0.268041I
3.05844 + 0.25163I 23.1978 + 17.4445I
u = 1.135600 + 0.262958I
a = −1.115230 + 0.095083I
b = −0.31519 + 1.82125I
7.94101 + 3.99745I 0
u = 1.135600 − 0.262958I
a = −1.115230 − 0.095083I
b = −0.31519 − 1.82125I
7.94101 − 3.99745I 0
u = −0.021446 + 1.242590I
a = 0.103787 − 1.134760I
b = 0.291129 − 1.081620I
4.11209 + 2.77736I 0
u = −0.021446 − 1.242590I
a = 0.103787 + 1.134760I
b = 0.291129 + 1.081620I
4.11209 − 2.77736I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.234230 + 0.350762I
a = 0.220618 − 0.065174I
b = 0.056753 − 1.393890I
0.37655 + 6.69384I 0
u = 1.234230 − 0.350762I
a = 0.220618 + 0.065174I
b = 0.056753 + 1.393890I
0.37655 − 6.69384I 0
u = −1.282100 + 0.160821I
a = 0.002455 + 0.577590I
b = −0.540239 − 0.895100I
1.82283 − 2.01960I 0
u = −1.282100 − 0.160821I
a = 0.002455 − 0.577590I
b = −0.540239 + 0.895100I
1.82283 + 2.01960I 0
u = −1.311010 + 0.009235I
a = 0.794975 − 0.117286I
b = 0.90592 + 1.21994I
6.38031 + 2.01596I 0
u = −1.311010 − 0.009235I
a = 0.794975 + 0.117286I
b = 0.90592 − 1.21994I
6.38031 − 2.01596I 0
u = −1.314430 + 0.000742I
a = −1.013060 − 0.219499I
b = −1.71966 + 0.05362I
5.30111 + 8.12301I 0
u = −1.314430 − 0.000742I
a = −1.013060 + 0.219499I
b = −1.71966 − 0.05362I
5.30111 − 8.12301I 0
u = 1.289330 + 0.294980I
a = −0.921582 − 0.039029I
b = −0.91865 + 2.08075I
4.34706 + 6.96401I 0
u = 1.289330 − 0.294980I
a = −0.921582 + 0.039029I
b = −0.91865 − 2.08075I
4.34706 − 6.96401I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.305940 + 0.276596I
a = 0.990124 − 0.245024I
b = 1.227810 − 0.679905I
8.33097 − 0.99541I 0
u = 1.305940 − 0.276596I
a = 0.990124 + 0.245024I
b = 1.227810 + 0.679905I
8.33097 + 0.99541I 0
u = 0.230244 + 0.622617I
a = 0.37498 − 1.65707I
b = −0.539842 − 1.179840I
0.78946 − 3.48348I 6.42936 + 4.05909I
u = 0.230244 − 0.622617I
a = 0.37498 + 1.65707I
b = −0.539842 + 1.179840I
0.78946 + 3.48348I 6.42936 − 4.05909I
u = 0.064133 + 1.361480I
a = −0.216705 + 0.345135I
b = −0.093899 + 0.348838I
−4.48688 − 1.96389I 0
u = 0.064133 − 1.361480I
a = −0.216705 − 0.345135I
b = −0.093899 − 0.348838I
−4.48688 + 1.96389I 0
u = −0.089545 + 0.593125I
a = 0.44927 − 1.64525I
b = 0.552277 + 0.234868I
1.323320 + 0.174545I 5.28001 + 2.10756I
u = −0.089545 − 0.593125I
a = 0.44927 + 1.64525I
b = 0.552277 − 0.234868I
1.323320 − 0.174545I 5.28001 − 2.10756I
u = 0.520326 + 0.208882I
a = 0.088072 − 0.865583I
b = 0.923469 + 0.741691I
−2.78307 − 4.17570I 2.65404 + 9.06688I
u = 0.520326 − 0.208882I
a = 0.088072 + 0.865583I
b = 0.923469 − 0.741691I
−2.78307 + 4.17570I 2.65404 − 9.06688I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.467636 + 0.030089I
a = −1.213680 − 0.584586I
b = −1.140850 − 0.431614I
−1.61725 − 1.29593I 17.6870 + 1.4584I
u = −0.467636 − 0.030089I
a = −1.213680 + 0.584586I
b = −1.140850 + 0.431614I
−1.61725 + 1.29593I 17.6870 − 1.4584I
u = −0.15909 + 1.53066I
a = 0.007528 + 0.809600I
b = −0.010230 + 0.514414I
−1.77257 + 3.34526I 0
u = −0.15909 − 1.53066I
a = 0.007528 − 0.809600I
b = −0.010230 − 0.514414I
−1.77257 − 3.34526I 0
u = 1.46056 + 0.52455I
a = −0.890542 + 0.271471I
b = −0.517763 + 1.167590I
8.97944 + 3.55354I 0
u = 1.46056 − 0.52455I
a = −0.890542 − 0.271471I
b = −0.517763 − 1.167590I
8.97944 − 3.55354I 0
u = −1.45175 + 0.56091I
a = 0.978747 + 0.127049I
b = 0.73549 + 1.46098I
8.72748 − 9.21510I 0
u = −1.45175 − 0.56091I
a = 0.978747 − 0.127049I
b = 0.73549 − 1.46098I
8.72748 + 9.21510I 0
u = −0.065876 + 0.286330I
a = −0.99550 − 3.73079I
b = −0.578451 + 0.270275I
0.94020 + 1.88067I 3.98517 − 9.07011I
u = −0.065876 − 0.286330I
a = −0.99550 + 3.73079I
b = −0.578451 − 0.270275I
0.94020 − 1.88067I 3.98517 + 9.07011I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
40
− 6u
39
+ ··· − 58u + 7)
· (u
158
− 11u
157
+ ··· − 6874340367u + 404850059)
c
2
(u
40
− 11u
38
+ ··· + 2u + 1)(u
158
+ u
157
+ ··· + 2697u − 163)
c
3
16(4u
40
− 32u
39
+ ··· − 7u + 1)
· (4u
158
− 12u
157
+ ··· + 3747366u + 276277)
c
4
(u
40
+ u
39
+ ··· + 44u + 8)(u
158
+ 2u
157
+ ··· − 16u − 16)
c
5
(u
40
+ 14u
38
+ ··· − 16u + 8)(u
158
− 3u
157
+ ··· − 68508u + 5048)
c
6
16(4u
40
+ 28u
39
+ ··· + 244u + 29)
· (4u
158
− 32u
157
+ ··· − 1649929u − 86329)
c
7
(u
40
− 11u
38
+ ··· − 2u + 1)(u
158
+ u
157
+ ··· + 2697u − 163)
c
8
16(4u
40
+ 8u
39
+ ··· + 4u + 1)(4u
158
− 4u
157
+ ··· − 245u + 11)
c
9
16(4u
40
− 28u
39
+ ··· − 244u + 29)
· (4u
158
− 32u
157
+ ··· − 1649929u − 86329)
c
10
(u
40
− 4u
39
+ ··· + 20u + 8)
· (u
158
+ 9u
157
+ ··· + 92598104u + 15966368)
c
11
(u
40
+ 6u
39
+ ··· + 342u + 459)
· (u
158
+ 3u
157
+ ··· + 104047000685u + 19423529740)
c
12
(u
40
+ 14u
38
+ ··· + 16u + 8)(u
158
− 3u
157
+ ··· − 68508u + 5048)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
40
+ 2y
39
+ ··· − 270y + 49)
· (y
158
+ 63y
157
+ ··· + 1.55 × 10
18
y + 1.64 × 10
17
)
c
2
, c
7
(y
40
− 22y
39
+ ··· + 4y + 1)
· (y
158
− 113y
157
+ ··· − 2010213y + 26569)
c
3
256(16y
40
− 280y
39
+ ··· + 43y + 1)
· (16y
158
+ 824y
157
+ ··· − 4738880286642y + 76328980729)
c
4
(y
40
− y
39
+ ··· + 288y + 64)(y
158
− 4y
157
+ ··· − 8896y + 256)
c
5
, c
12
(y
40
+ 28y
39
+ ··· + 1824y + 64)
· (y
158
+ 93y
157
+ ··· − 3359381776y + 25482304)
c
6
, c
9
256(16y
40
− 1192y
39
+ ··· − 29318y + 841)
· (16y
158
− 2328y
157
+ ··· − 344551467095y + 7452696241)
c
8
256(16y
40
+ 648y
39
+ ··· + 16y + 1)
· (16y
158
+ 216y
157
+ ··· − 669y + 121)
c
10
(y
40
+ 22y
39
+ ··· + 1568y + 64)
· (y
158
+ 79y
157
+ ··· − 33590848646406208y + 254924907111424)
c
11
(y
40
− 22y
39
+ ··· − 4267242y + 210681)
· (y
158
− 85y
157
+ ··· − 3.42 × 10
22
y + 3.77 × 10
20
)
31
