12a
1174
(K12a
1174
)
A knot diagram
1
Linearized knot diagam
4 10 7 1 9 3 11 12 2 6 8 5
Solving Sequence
3,6
7
4,11
8 12 10 2 1 9 5
c
6
c
3
c
7
c
11
c
10
c
2
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.79172 × 10
293
u
92
+ 5.18538 × 10
293
u
91
+ ··· + 5.07764 × 10
292
b + 2.25779 × 10
296
,
− 2.37870 × 10
296
u
92
+ 7.02532 × 10
296
u
91
+ ··· + 5.48893 × 10
295
a + 2.78497 × 10
299
,
u
93
− 2u
92
+ ··· + 2191u − 1081i
I
u
2
= h−32320u
20
+ 116817u
19
+ ··· + 14919b − 48202, 12963u
20
+ 67496u
19
+ ··· + 14919a − 214943,
u
21
− 3u
20
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 114 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−1.79 × 10
293
u
92
+ 5.19 × 10
293
u
91
+ · · · + 5.08 × 10
292
b + 2.26 ×
10
296
, −2.38 × 10
296
u
92
+ 7.03 × 10
296
u
91
+ · · · + 5.49 × 10
295
a + 2.78 ×
10
299
, u
93
− 2u
92
+ · · · + 2191u − 1081i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
4.33363u
92
− 12.7991u
91
+ ··· + 15938.8u − 5073.80
3.52865u
92
− 10.2122u
91
+ ··· + 14118.3u − 4446.54
a
8
=
−0.294962u
92
+ 0.652560u
91
+ ··· − 3271.15u + 901.397
−2.28531u
92
+ 6.61498u
91
+ ··· − 9727.95u + 3065.58
a
12
=
1.38877u
92
− 3.49286u
91
+ ··· + 5890.99u − 1513.44
−1.10004u
92
+ 3.10829u
91
+ ··· − 5830.00u + 1865.50
a
10
=
0.804989u
92
− 2.58688u
91
+ ··· + 1820.44u − 627.253
3.52865u
92
− 10.2122u
91
+ ··· + 14118.3u − 4446.54
a
2
=
−1.54792u
92
+ 4.79711u
91
+ ··· − 4518.22u + 1695.55
0.788795u
92
− 2.14540u
91
+ ··· + 3223.00u − 926.289
a
1
=
−1.06239u
92
+ 3.58010u
91
+ ··· − 2164.67u + 1046.92
0.454016u
92
− 1.20759u
91
+ ··· + 1933.22u − 543.550
a
9
=
1.40660u
92
− 3.76007u
91
+ ··· + 7861.74u − 2444.89
1.43867u
92
− 4.20929u
91
+ ··· + 5481.94u − 1756.79
a
5
=
−1.81351u
92
+ 5.12931u
91
+ ··· − 6832.74u + 2194.88
2.31351u
92
− 6.77939u
91
+ ··· + 8527.69u − 2737.03
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.43488u
92
− 3.65079u
91
+ ··· + 6204.45u − 1887.76
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
93
− 3u
92
+ ··· + 12u − 1
c
2
, c
9
u
93
− 34u
91
+ ··· − 4634u + 2071
c
3
, c
6
u
93
− 2u
92
+ ··· + 2191u − 1081
c
5
u
93
− 7u
92
+ ··· + 245345u + 714407
c
7
, c
8
, c
11
u
93
− 7u
92
+ ··· − 14u − 4
c
10
u
93
+ 7u
91
+ ··· + 21184u − 3499
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
93
+ 95y
92
+ ··· + 230y −1
c
2
, c
9
y
93
− 68y
92
+ ··· + 77411666y −4289041
c
3
, c
6
y
93
− 58y
92
+ ··· + 28900295y −1168561
c
5
y
93
− 35y
92
+ ··· + 27772503205947y −510377361649
c
7
, c
8
, c
11
y
93
− 103y
92
+ ··· + 1372y −16
c
10
y
93
+ 14y
92
+ ··· − 580713924y −12243001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493220 + 0.865157I
a = 0.381752 − 0.204747I
b = 1.229960 − 0.447001I
14.4991 − 4.6980I 0
u = −0.493220 − 0.865157I
a = 0.381752 + 0.204747I
b = 1.229960 + 0.447001I
14.4991 + 4.6980I 0
u = −0.999193 + 0.206178I
a = −0.81805 + 1.25971I
b = 0.60869 + 1.28232I
−3.17135 + 0.93926I 0
u = −0.999193 − 0.206178I
a = −0.81805 − 1.25971I
b = 0.60869 − 1.28232I
−3.17135 − 0.93926I 0
u = −0.957998 + 0.358983I
a = −0.20807 + 1.83442I
b = 0.482838 + 0.488493I
5.24104 + 4.96610I 0
u = −0.957998 − 0.358983I
a = −0.20807 − 1.83442I
b = 0.482838 − 0.488493I
5.24104 − 4.96610I 0
u = 0.941539 + 0.247200I
a = 0.70673 − 1.39465I
b = −0.101345 − 0.424981I
1.74388 − 1.76077I 0
u = 0.941539 − 0.247200I
a = 0.70673 + 1.39465I
b = −0.101345 + 0.424981I
1.74388 + 1.76077I 0
u = 1.004200 + 0.244501I
a = 0.06367 − 1.54106I
b = 0.462032 − 0.656917I
−1.04854 − 3.13751I 0
u = 1.004200 − 0.244501I
a = 0.06367 + 1.54106I
b = 0.462032 + 0.656917I
−1.04854 + 3.13751I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931604 + 0.243587I
a = −1.48753 + 2.26052I
b = −0.76730 + 1.22144I
10.18600 + 4.17288I 0
u = 0.931604 − 0.243587I
a = −1.48753 − 2.26052I
b = −0.76730 − 1.22144I
10.18600 − 4.17288I 0
u = −0.945716 + 0.448641I
a = −0.18841 + 1.50162I
b = −0.126174 + 1.037660I
2.23609 + 2.02110I 0
u = −0.945716 − 0.448641I
a = −0.18841 − 1.50162I
b = −0.126174 − 1.037660I
2.23609 − 2.02110I 0
u = −0.927769 + 0.198246I
a = 0.760639 + 0.112021I
b = −1.157820 + 0.065675I
8.08998 − 0.30173I 0
u = −0.927769 − 0.198246I
a = 0.760639 − 0.112021I
b = −1.157820 − 0.065675I
8.08998 + 0.30173I 0
u = −0.922638 + 0.013782I
a = 0.607351 − 1.268960I
b = 0.418728 − 0.759155I
−1.47830 + 0.09644I 0
u = −0.922638 − 0.013782I
a = 0.607351 + 1.268960I
b = 0.418728 + 0.759155I
−1.47830 − 0.09644I 0
u = 0.900637 + 0.166565I
a = 1.094280 + 0.849188I
b = 2.22704 + 0.89576I
10.45250 − 5.98256I 0
u = 0.900637 − 0.166565I
a = 1.094280 − 0.849188I
b = 2.22704 − 0.89576I
10.45250 + 5.98256I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797331 + 0.740231I
a = −1.108150 − 0.676986I
b = −0.87426 − 1.30671I
11.46630 − 3.61096I 0
u = 0.797331 − 0.740231I
a = −1.108150 + 0.676986I
b = −0.87426 + 1.30671I
11.46630 + 3.61096I 0
u = −0.055022 + 0.905084I
a = 0.025792 − 0.394822I
b = 0.370767 + 0.799825I
−1.60208 + 3.45125I 0
u = −0.055022 − 0.905084I
a = 0.025792 + 0.394822I
b = 0.370767 − 0.799825I
−1.60208 − 3.45125I 0
u = −0.857480 + 0.183860I
a = 1.55300 + 1.77791I
b = 0.021598 + 0.223081I
8.33093 + 2.12160I 0
u = −0.857480 − 0.183860I
a = 1.55300 − 1.77791I
b = 0.021598 − 0.223081I
8.33093 − 2.12160I 0
u = −1.113040 + 0.284847I
a = −1.29160 − 1.55734I
b = −1.051500 − 0.915350I
3.59625 + 1.07886I 0
u = −1.113040 − 0.284847I
a = −1.29160 + 1.55734I
b = −1.051500 + 0.915350I
3.59625 − 1.07886I 0
u = 0.966274 + 0.629500I
a = −0.41670 − 1.77249I
b = 0.44013 − 1.49164I
10.87060 − 1.71491I 0
u = 0.966274 − 0.629500I
a = −0.41670 + 1.77249I
b = 0.44013 + 1.49164I
10.87060 + 1.71491I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15328
a = −0.528664
b = −1.46093
−2.43023 0
u = −0.839487
a = 1.65103
b = 2.74988
5.42501 −3.13060
u = 0.883008 + 0.754425I
a = 0.449816 + 0.330996I
b = 0.242674 + 0.604013I
3.94725 − 2.93006I 0
u = 0.883008 − 0.754425I
a = 0.449816 − 0.330996I
b = 0.242674 − 0.604013I
3.94725 + 2.93006I 0
u = 0.144101 + 1.157950I
a = −0.603621 + 0.290732I
b = −0.777671 − 0.730996I
4.63046 + 5.69476I 0
u = 0.144101 − 1.157950I
a = −0.603621 − 0.290732I
b = −0.777671 + 0.730996I
4.63046 − 5.69476I 0
u = 0.210658 + 0.801457I
a = 0.430928 + 0.084530I
b = 1.225280 + 0.183772I
7.81659 + 1.96154I 6.74178 + 0.I
u = 0.210658 − 0.801457I
a = 0.430928 − 0.084530I
b = 1.225280 − 0.183772I
7.81659 − 1.96154I 6.74178 + 0.I
u = 0.010973 + 1.171930I
a = 0.0279016 + 0.1302840I
b = 0.444660 − 0.805741I
4.72768 − 6.23749I 0
u = 0.010973 − 1.171930I
a = 0.0279016 − 0.1302840I
b = 0.444660 + 0.805741I
4.72768 + 6.23749I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.521607 + 0.638309I
a = 1.021990 + 0.648190I
b = −0.193682 + 0.955385I
4.63896 − 2.60617I 0
u = 0.521607 − 0.638309I
a = 1.021990 − 0.648190I
b = −0.193682 − 0.955385I
4.63896 + 2.60617I 0
u = 0.808996
a = 0.890695
b = −1.13803
3.01362 19.9250
u = −1.152100 + 0.402465I
a = 0.23414 − 1.55231I
b = −0.79506 − 1.59274I
−4.53697 + 3.39634I 0
u = −1.152100 − 0.402465I
a = 0.23414 + 1.55231I
b = −0.79506 + 1.59274I
−4.53697 − 3.39634I 0
u = 1.188090 + 0.303700I
a = −0.446730 − 1.057390I
b = 0.775271 − 0.984324I
−5.44087 − 3.46543I 0
u = 1.188090 − 0.303700I
a = −0.446730 + 1.057390I
b = 0.775271 + 0.984324I
−5.44087 + 3.46543I 0
u = −1.095180 + 0.568287I
a = −0.29331 − 1.74923I
b = −0.828115 − 0.843797I
12.5498 + 9.9708I 0
u = −1.095180 − 0.568287I
a = −0.29331 + 1.74923I
b = −0.828115 + 0.843797I
12.5498 − 9.9708I 0
u = 1.232980 + 0.122197I
a = −0.336685 − 0.619050I
b = −1.196950 − 0.645650I
2.00637 − 4.23616I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.232980 − 0.122197I
a = −0.336685 + 0.619050I
b = −1.196950 + 0.645650I
2.00637 + 4.23616I 0
u = 1.159470 + 0.468713I
a = −0.59929 + 1.51495I
b = −0.850517 + 0.823859I
4.89220 − 6.62233I 0
u = 1.159470 − 0.468713I
a = −0.59929 − 1.51495I
b = −0.850517 − 0.823859I
4.89220 + 6.62233I 0
u = −0.388822 + 0.606017I
a = 0.653073 + 0.206751I
b = −0.780994 + 0.330700I
6.79433 − 1.25102I 5.03730 + 1.40597I
u = −0.388822 − 0.606017I
a = 0.653073 − 0.206751I
b = −0.780994 − 0.330700I
6.79433 + 1.25102I 5.03730 − 1.40597I
u = −0.268356 + 0.661606I
a = −1.43984 − 0.64695I
b = −1.19354 + 0.78355I
4.40669 − 0.72719I 0.950513 + 0.183278I
u = −0.268356 − 0.661606I
a = −1.43984 + 0.64695I
b = −1.19354 − 0.78355I
4.40669 + 0.72719I 0.950513 − 0.183278I
u = −1.250230 + 0.328637I
a = −0.411455 + 1.094640I
b = 0.860122 + 0.847553I
−0.01907 + 5.71711I 0
u = −1.250230 − 0.328637I
a = −0.411455 − 1.094640I
b = 0.860122 − 0.847553I
−0.01907 − 5.71711I 0
u = −1.183020 + 0.523529I
a = 0.07747 + 1.93133I
b = 0.99024 + 1.94367I
1.66900 + 5.42826I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.183020 − 0.523529I
a = 0.07747 − 1.93133I
b = 0.99024 − 1.94367I
1.66900 − 5.42826I 0
u = 1.286270 + 0.468225I
a = 0.124109 + 1.336630I
b = −0.92387 + 1.34449I
−5.65977 − 8.34050I 0
u = 1.286270 − 0.468225I
a = 0.124109 − 1.336630I
b = −0.92387 − 1.34449I
−5.65977 + 8.34050I 0
u = −0.142049 + 0.574380I
a = 0.794922 + 0.815026I
b = 0.262591 − 0.776350I
−1.68799 + 0.40666I −4.08766 + 0.57840I
u = −0.142049 − 0.574380I
a = 0.794922 − 0.815026I
b = 0.262591 + 0.776350I
−1.68799 − 0.40666I −4.08766 − 0.57840I
u = −0.584513
a = 1.44672
b = 0.616268
−1.06007 −13.2570
u = −0.30460 + 1.38334I
a = −0.520117 − 0.087341I
b = −0.643508 + 0.824625I
11.3051 − 9.4157I 0
u = −0.30460 − 1.38334I
a = −0.520117 + 0.087341I
b = −0.643508 − 0.824625I
11.3051 + 9.4157I 0
u = 1.30757 + 0.60332I
a = 0.15218 − 1.54858I
b = 1.12343 − 1.60621I
0.99513 − 11.82820I 0
u = 1.30757 − 0.60332I
a = 0.15218 + 1.54858I
b = 1.12343 + 1.60621I
0.99513 + 11.82820I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35464 + 0.50483I
a = −0.208649 + 0.708455I
b = 0.612881 + 0.904430I
−5.34351 + 1.98352I 0
u = −1.35464 − 0.50483I
a = −0.208649 − 0.708455I
b = 0.612881 − 0.904430I
−5.34351 − 1.98352I 0
u = −1.34636 + 0.53316I
a = 0.131831 − 1.266200I
b = −0.95023 − 1.22871I
0.44368 + 12.08020I 0
u = −1.34636 − 0.53316I
a = 0.131831 + 1.266200I
b = −0.95023 + 1.22871I
0.44368 − 12.08020I 0
u = −1.34826 + 0.69353I
a = 0.043561 + 1.394630I
b = 1.06566 + 1.47988I
7.8476 + 16.5231I 0
u = −1.34826 − 0.69353I
a = 0.043561 − 1.394630I
b = 1.06566 − 1.47988I
7.8476 − 16.5231I 0
u = 1.49310 + 0.30944I
a = −0.035631 − 0.798458I
b = 0.590963 − 0.949456I
−0.727333 + 0.157658I 0
u = 1.49310 − 0.30944I
a = −0.035631 + 0.798458I
b = 0.590963 + 0.949456I
−0.727333 − 0.157658I 0
u = 1.29993 + 0.86389I
a = −0.236875 − 0.413569I
b = 0.544137 − 0.825950I
−1.67635 − 4.00277I 0
u = 1.29993 − 0.86389I
a = −0.236875 + 0.413569I
b = 0.544137 + 0.825950I
−1.67635 + 4.00277I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417218 + 0.008728I
a = 2.36201 − 2.71549I
b = 0.318240 − 0.856868I
4.68957 + 2.88584I 0.97095 + 1.99776I
u = 0.417218 − 0.008728I
a = 2.36201 + 2.71549I
b = 0.318240 + 0.856868I
4.68957 − 2.88584I 0.97095 − 1.99776I
u = −1.58461
a = 0.315412
b = −0.467132
−1.98786 0
u = 0.173797 + 0.361664I
a = 0.701705 − 0.109675I
b = −0.592919 − 0.173738I
1.059400 + 0.567180I 6.46224 − 2.40973I
u = 0.173797 − 0.361664I
a = 0.701705 + 0.109675I
b = −0.592919 + 0.173738I
1.059400 − 0.567180I 6.46224 + 2.40973I
u = 1.51072 + 0.54787I
a = 0.220888 − 0.180105I
b = −0.508833 + 0.053803I
1.82375 − 3.68778I 0
u = 1.51072 − 0.54787I
a = 0.220888 + 0.180105I
b = −0.508833 − 0.053803I
1.82375 + 3.68778I 0
u = −1.30165 + 0.95853I
a = 0.274672 − 0.772887I
b = −0.400158 − 1.144420I
−1.18766 + 4.19203I 0
u = −1.30165 − 0.95853I
a = 0.274672 + 0.772887I
b = −0.400158 + 1.144420I
−1.18766 − 4.19203I 0
u = 1.40617 + 0.81755I
a = 0.150305 + 0.770760I
b = −0.349946 + 1.025780I
3.25425 − 3.89917I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40617 − 0.81755I
a = 0.150305 − 0.770760I
b = −0.349946 − 1.025780I
3.25425 + 3.89917I 0
u = 1.29654 + 1.08535I
a = 0.308610 + 0.717193I
b = −0.403588 + 1.194610I
3.93308 − 4.47908I 0
u = 1.29654 − 1.08535I
a = 0.308610 − 0.717193I
b = −0.403588 − 1.194610I
3.93308 + 4.47908I 0
14
II. I
u
2
= h−3.23 × 10
4
u
20
+ 1.17 × 10
5
u
19
+ · · · + 1.49 × 10
4
b − 4.82 ×
10
4
, 12963u
20
+ 67496u
19
+ · · · + 14919a − 214943, u
21
− 3u
20
+ · · · − u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
−0.868892u
20
− 4.52416u
19
+ ··· − 24.9788u + 14.4073
2.16637u
20
− 7.83008u
19
+ ··· − 15.3797u + 3.23091
a
8
=
−14.7261u
20
+ 36.2327u
19
+ ··· + 23.6956u + 10.3162
−3.16637u
20
+ 10.8301u
19
+ ··· + 16.3797u − 4.23091
a
12
=
8.64193u
20
− 15.7334u
19
+ ··· + 7.53536u − 15.3984
−3.90777u
20
+ 9.82077u
19
+ ··· + 8.86634u + 3.35472
a
10
=
−3.03526u
20
+ 3.30592u
19
+ ··· − 9.59910u + 11.1764
2.16637u
20
− 7.83008u
19
+ ··· − 15.3797u + 3.23091
a
2
=
−10.6472u
20
+ 25.0120u
19
+ ··· + 7.88404u + 8.84536
2.33099u
20
− 6.78953u
19
+ ··· + 0.602721u − 4.83363
a
1
=
−13.0975u
20
+ 29.4578u
19
+ ··· + 6.55305u + 11.0922
2.59863u
20
− 6.89637u
19
+ ··· + 1.47892u − 4.17541
a
9
=
12.1546u
20
− 26.1111u
19
+ ··· − 5.03271u − 12.2706
−0.774851u
20
− 0.722904u
19
+ ··· − 6.83451u + 5.37657
a
5
=
0.915879u
20
+ 0.499229u
19
+ ··· + 5.23091u + 4.91776
0.534419u
20
− 1.94504u
19
+ ··· − 1.89993u + 2.83538
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
61671
4973
u
20
+
561805
14919
u
19
+ ··· +
170057
14919
u −
107689
14919
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
21
− 2u
20
+ ··· + 3u
2
+ 1
c
2
u
21
+ u
20
+ ··· + 2u + 1
c
3
u
21
+ 3u
20
+ ··· − u − 1
c
4
u
21
+ 2u
20
+ ··· − 3u
2
− 1
c
5
u
21
+ 4u
19
+ ··· + 5u + 1
c
6
u
21
− 3u
20
+ ··· − u + 1
c
7
, c
8
u
21
− 14u
19
+ ··· + u − 1
c
9
u
21
− u
20
+ ··· + 2u − 1
c
10
u
21
+ u
20
+ ··· − 4u + 1
c
11
u
21
− 14u
19
+ ··· + u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
21
+ 22y
20
+ ··· − 6y −1
c
2
, c
9
y
21
− 21y
20
+ ··· + 10y −1
c
3
, c
6
y
21
− 15y
20
+ ··· + 19y −1
c
5
y
21
+ 8y
20
+ ··· + 11y −1
c
7
, c
8
, c
11
y
21
− 28y
20
+ ··· + 9y −1
c
10
y
21
− 3y
20
+ ··· − 20y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993975 + 0.256264I
a = 0.52588 + 1.47733I
b = −0.036527 + 0.847504I
1.19169 + 1.35193I −5.28800 + 1.11369I
u = −0.993975 − 0.256264I
a = 0.52588 − 1.47733I
b = −0.036527 − 0.847504I
1.19169 − 1.35193I −5.28800 − 1.11369I
u = −0.852337
a = 0.407214
b = −1.37095
2.76419 −13.7230
u = −1.123130 + 0.385031I
a = −0.394107 + 1.032940I
b = 0.665275 + 1.168610I
−4.43426 + 2.01026I −3.84315 − 1.41009I
u = −1.123130 − 0.385031I
a = −0.394107 − 1.032940I
b = 0.665275 − 1.168610I
−4.43426 − 2.01026I −3.84315 + 1.41009I
u = 0.704180 + 0.366426I
a = −1.41812 − 1.13657I
b = −0.419901 − 0.650984I
4.56727 − 3.68956I 0.48270 + 7.21520I
u = 0.704180 − 0.366426I
a = −1.41812 + 1.13657I
b = −0.419901 + 0.650984I
4.56727 + 3.68956I 0.48270 − 7.21520I
u = 0.785290 + 0.108148I
a = 1.26531 − 1.60821I
b = −0.722409 − 0.420929I
8.62553 − 1.55127I 6.74187 − 0.39361I
u = 0.785290 − 0.108148I
a = 1.26531 + 1.60821I
b = −0.722409 + 0.420929I
8.62553 + 1.55127I 6.74187 + 0.39361I
u = 1.029560 + 0.687392I
a = −0.071373 − 0.699939I
b = −0.064352 − 0.329319I
4.59193 − 3.18711I 7.00885 + 2.74110I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.029560 − 0.687392I
a = −0.071373 + 0.699939I
b = −0.064352 + 0.329319I
4.59193 + 3.18711I 7.00885 − 2.74110I
u = −0.593681
a = −1.91921
b = −1.09140
−0.667031 9.43560
u = 0.409546 + 0.386676I
a = 2.90773 + 0.46724I
b = 1.47022 + 0.81755I
11.62230 − 5.60544I 5.46888 + 4.11805I
u = 0.409546 − 0.386676I
a = 2.90773 − 0.46724I
b = 1.47022 − 0.81755I
11.62230 + 5.60544I 5.46888 − 4.11805I
u = −1.20544 + 0.79163I
a = 0.345951 − 1.061940I
b = −0.40954 − 1.40792I
−0.53899 + 3.58293I 0.204406 − 0.830422I
u = −1.20544 − 0.79163I
a = 0.345951 + 1.061940I
b = −0.40954 + 1.40792I
−0.53899 − 3.58293I 0.204406 + 0.830422I
u = 1.29520 + 0.63974I
a = −0.344878 − 0.357812I
b = 0.591845 − 0.668863I
−1.56010 − 3.41588I −1.70053 − 1.96092I
u = 1.29520 − 0.63974I
a = −0.344878 + 0.357812I
b = 0.591845 + 0.668863I
−1.56010 + 3.41588I −1.70053 + 1.96092I
u = −0.442244
a = 3.66401
b = 2.26536
6.17929 8.39950
u = 1.54290 + 1.10466I
a = 0.107599 + 0.547407I
b = −0.476118 + 0.873161I
1.40523 − 5.05089I −2.63101 + 6.73141I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54290 − 1.10466I
a = 0.107599 − 0.547407I
b = −0.476118 − 0.873161I
1.40523 + 5.05089I −2.63101 − 6.73141I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
21
− 2u
20
+ ··· + 3u
2
+ 1)(u
93
− 3u
92
+ ··· + 12u − 1)
c
2
(u
21
+ u
20
+ ··· + 2u + 1)(u
93
− 34u
91
+ ··· − 4634u + 2071)
c
3
(u
21
+ 3u
20
+ ··· − u − 1)(u
93
− 2u
92
+ ··· + 2191u − 1081)
c
4
(u
21
+ 2u
20
+ ··· − 3u
2
− 1)(u
93
− 3u
92
+ ··· + 12u − 1)
c
5
(u
21
+ 4u
19
+ ··· + 5u + 1)(u
93
− 7u
92
+ ··· + 245345u + 714407)
c
6
(u
21
− 3u
20
+ ··· − u + 1)(u
93
− 2u
92
+ ··· + 2191u − 1081)
c
7
, c
8
(u
21
− 14u
19
+ ··· + u − 1)(u
93
− 7u
92
+ ··· − 14u − 4)
c
9
(u
21
− u
20
+ ··· + 2u − 1)(u
93
− 34u
91
+ ··· − 4634u + 2071)
c
10
(u
21
+ u
20
+ ··· − 4u + 1)(u
93
+ 7u
91
+ ··· + 21184u − 3499)
c
11
(u
21
− 14u
19
+ ··· + u + 1)(u
93
− 7u
92
+ ··· − 14u − 4)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
21
+ 22y
20
+ ··· − 6y −1)(y
93
+ 95y
92
+ ··· + 230y −1)
c
2
, c
9
(y
21
− 21y
20
+ ··· + 10y −1)
· (y
93
− 68y
92
+ ··· + 77411666y −4289041)
c
3
, c
6
(y
21
− 15y
20
+ ··· + 19y −1)
· (y
93
− 58y
92
+ ··· + 28900295y −1168561)
c
5
(y
21
+ 8y
20
+ ··· + 11y −1)
· (y
93
− 35y
92
+ ··· + 27772503205947y −510377361649)
c
7
, c
8
, c
11
(y
21
− 28y
20
+ ··· + 9y −1)(y
93
− 103y
92
+ ··· + 1372y −16)
c
10
(y
21
− 3y
20
+ ··· − 20y −1)
· (y
93
+ 14y
92
+ ··· − 580713924y −12243001)
22
