12a
0927
(K12a
0927
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 10 3 12 1 2 5 8 7
Solving Sequence
8,11 5,12
4 7 1 2 9 3 6 10
c
11
c
4
c
7
c
12
c
1
c
8
c
3
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.17204 × 10
92
u
100
+ 5.80593 × 10
92
u
99
+ ··· + 1.37181 × 10
93
b − 1.38998 × 10
93
,
1.34846 × 10
94
u
100
+ 5.39689 × 10
93
u
99
+ ··· + 9.60265 × 10
93
a + 1.74373 × 10
94
, u
101
+ 46u
99
+ ··· + u − 1i
I
u
2
= h−u
18
− u
17
+ ··· + b + 2u, u
18
+ 3u
17
+ ··· + a − 3, u
19
− u
18
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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
= h1.17 × 10
92
u
100
+ 5.81 × 10
92
u
99
+ · · · + 1.37 × 10
93
b − 1.39 ×
10
93
, 1.35 × 10
94
u
100
+ 5.40 × 10
93
u
99
+ · · · + 9.60 × 10
93
a + 1.74 ×
10
94
, u
101
+ 46u
99
+ · · · + u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
−1.40425u
100
− 0.562021u
99
+ ··· − 10.2436u − 1.81588
−0.0854374u
100
− 0.423232u
99
+ ··· − 1.90512u + 1.01325
a
12
=
1
u
2
a
4
=
−1.48969u
100
− 0.985252u
99
+ ··· − 12.1487u − 0.802639
−0.0854374u
100
− 0.423232u
99
+ ··· − 1.90512u + 1.01325
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−0.940964u
100
− 0.279768u
99
+ ··· − 5.22472u − 1.91292
−0.237618u
100
− 0.171606u
99
+ ··· − 0.697920u + 0.894695
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
−1.29125u
100
− 0.629929u
99
+ ··· − 11.0393u − 0.969058
−0.132061u
100
− 0.130376u
99
+ ··· − 2.32353u + 0.594206
a
6
=
−0.868953u
100
+ 1.16462u
99
+ ··· − 14.5751u − 2.32310
0.206049u
100
− 0.125342u
99
+ ··· − 0.0119723u + 0.0903791
a
10
=
0.482166u
100
+ 1.70715u
99
+ ··· + 4.91113u + 0.887370
−0.114195u
100
− 0.653840u
99
+ ··· − 0.298804u + 0.247379
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.59770u
100
− 1.50889u
99
+ ··· + 12.8990u + 3.67843
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
101
− 17u
100
+ ··· + 59829u − 3461
c
2
, c
6
u
101
+ 2u
100
+ ··· + 9256u − 1034
c
3
u
101
− u
100
+ ··· − 91u + 1
c
4
, c
5
, c
10
u
101
− u
100
+ ··· + 22u − 4
c
7
, c
11
, c
12
u
101
+ 46u
99
+ ··· + u − 1
c
8
u
101
− 2u
99
+ ··· + 712u − 232
c
9
u
101
+ 3u
100
+ ··· + 5282083u + 2372859
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
101
+ 15y
100
+ ··· + 43620123y −11978521
c
2
, c
6
y
101
− 84y
100
+ ··· + 41122612y −1069156
c
3
y
101
− 9y
100
+ ··· + 7531y −1
c
4
, c
5
, c
10
y
101
+ 107y
100
+ ··· − 708y −16
c
7
, c
11
, c
12
y
101
+ 92y
100
+ ··· + 19y −1
c
8
y
101
− 4y
100
+ ··· + 171472y −53824
c
9
y
101
− 39y
100
+ ··· + 211509629585425y −5630459833881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.338601 + 0.929957I
a = −0.796464 + 1.012730I
b = −0.022504 − 1.387680I
5.03799 − 2.07046I 0
u = 0.338601 − 0.929957I
a = −0.796464 − 1.012730I
b = −0.022504 + 1.387680I
5.03799 + 2.07046I 0
u = 0.813138 + 0.514209I
a = 0.90012 − 1.28023I
b = 0.02602 + 1.43752I
4.47550 − 2.65435I 0
u = 0.813138 − 0.514209I
a = 0.90012 + 1.28023I
b = 0.02602 − 1.43752I
4.47550 + 2.65435I 0
u = −0.560557 + 0.768072I
a = −0.421182 − 1.247580I
b = 0.25302 + 1.54034I
9.75188 − 8.20632I 0
u = −0.560557 − 0.768072I
a = −0.421182 + 1.247580I
b = 0.25302 − 1.54034I
9.75188 + 8.20632I 0
u = 0.128473 + 1.056460I
a = −0.503339 + 0.351516I
b = −0.444666 + 0.213037I
−0.200435 + 0.703668I 0
u = 0.128473 − 1.056460I
a = −0.503339 − 0.351516I
b = −0.444666 − 0.213037I
−0.200435 − 0.703668I 0
u = −0.055755 + 1.087090I
a = 0.269569 + 1.352040I
b = 0.645189 − 0.746095I
3.31819 + 0.06863I 0
u = −0.055755 − 1.087090I
a = 0.269569 − 1.352040I
b = 0.645189 + 0.746095I
3.31819 − 0.06863I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.321913 + 0.829241I
a = −0.045721 + 1.039040I
b = −0.10695 − 1.44066I
5.22244 − 2.50144I 0
u = −0.321913 − 0.829241I
a = −0.045721 − 1.039040I
b = −0.10695 + 1.44066I
5.22244 + 2.50144I 0
u = 0.406936 + 0.775815I
a = −0.300390 − 0.045936I
b = 0.734298 − 0.534377I
2.94013 + 4.57156I 0
u = 0.406936 − 0.775815I
a = −0.300390 + 0.045936I
b = 0.734298 + 0.534377I
2.94013 − 4.57156I 0
u = 0.787460 + 0.379801I
a = −0.855942 + 0.809852I
b = −0.140540 − 1.265200I
2.64686 − 2.47490I 0
u = 0.787460 − 0.379801I
a = −0.855942 − 0.809852I
b = −0.140540 + 1.265200I
2.64686 + 2.47490I 0
u = −0.345176 + 1.073310I
a = −0.012039 + 0.367281I
b = 0.639537 − 0.260559I
2.13144 + 4.10343I 0
u = −0.345176 − 1.073310I
a = −0.012039 − 0.367281I
b = 0.639537 + 0.260559I
2.13144 − 4.10343I 0
u = 0.844506 + 0.188748I
a = −0.535125 + 0.252887I
b = −0.087205 − 1.339120I
2.69324 − 2.22762I 0
u = 0.844506 − 0.188748I
a = −0.535125 − 0.252887I
b = −0.087205 + 1.339120I
2.69324 + 2.22762I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799774 + 0.329138I
a = −1.54547 − 0.83395I
b = −0.28641 + 1.56866I
8.3431 + 12.9028I 0. − 7.85868I
u = −0.799774 − 0.329138I
a = −1.54547 + 0.83395I
b = −0.28641 − 1.56866I
8.3431 − 12.9028I 0. + 7.85868I
u = −0.732389 + 0.383945I
a = 0.303247 + 0.402040I
b = 0.127737 − 0.125151I
−0.84943 + 2.18733I −11.7134 − 11.9875I
u = −0.732389 − 0.383945I
a = 0.303247 − 0.402040I
b = 0.127737 + 0.125151I
−0.84943 − 2.18733I −11.7134 + 11.9875I
u = 0.754882 + 0.273496I
a = −0.956345 + 0.605149I
b = −0.846330 − 0.599759I
1.25837 − 8.74577I −2.71147 + 8.57986I
u = 0.754882 − 0.273496I
a = −0.956345 − 0.605149I
b = −0.846330 + 0.599759I
1.25837 + 8.74577I −2.71147 − 8.57986I
u = −0.742037 + 0.242897I
a = 1.91043 + 0.22567I
b = 0.16250 − 1.46227I
3.30401 + 6.47041I −1.74126 − 7.20929I
u = −0.742037 − 0.242897I
a = 1.91043 − 0.22567I
b = 0.16250 + 1.46227I
3.30401 − 6.47041I −1.74126 + 7.20929I
u = −0.777007
a = −0.409554
b = −0.578616
−1.11245 −11.1750
u = −0.025748 + 1.236330I
a = 0.824447 − 0.076392I
b = −0.179975 + 1.350560I
10.93490 + 2.78038I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.025748 − 1.236330I
a = 0.824447 + 0.076392I
b = −0.179975 − 1.350560I
10.93490 − 2.78038I 0
u = −0.159559 + 1.251210I
a = −1.43728 − 1.79915I
b = −0.266877 + 1.026130I
2.17976 + 1.85998I 0
u = −0.159559 − 1.251210I
a = −1.43728 + 1.79915I
b = −0.266877 − 1.026130I
2.17976 − 1.85998I 0
u = 0.681119 + 0.191835I
a = 1.338130 − 0.230387I
b = 0.557811 + 0.339618I
−2.58528 − 3.94320I −8.28628 + 7.57752I
u = 0.681119 − 0.191835I
a = 1.338130 + 0.230387I
b = 0.557811 − 0.339618I
−2.58528 + 3.94320I −8.28628 − 7.57752I
u = −0.659379 + 0.224660I
a = −0.421405 − 0.382008I
b = −0.933561 − 0.630970I
1.19502 + 2.86675I −0.48560 − 5.63717I
u = −0.659379 − 0.224660I
a = −0.421405 + 0.382008I
b = −0.933561 + 0.630970I
1.19502 − 2.86675I −0.48560 + 5.63717I
u = 0.123790 + 1.319540I
a = −0.028371 + 1.029170I
b = 0.419572 − 0.634578I
4.45606 + 0.45152I 0
u = 0.123790 − 1.319540I
a = −0.028371 − 1.029170I
b = 0.419572 + 0.634578I
4.45606 − 0.45152I 0
u = −0.048734 + 1.338630I
a = 0.55365 − 2.90345I
b = 0.09844 + 1.58170I
11.89780 − 2.24580I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.048734 − 1.338630I
a = 0.55365 + 2.90345I
b = 0.09844 − 1.58170I
11.89780 + 2.24580I 0
u = 0.452314 + 1.270540I
a = 0.78602 − 1.48254I
b = 0.167551 + 1.383620I
7.24145 − 6.94635I 0
u = 0.452314 − 1.270540I
a = 0.78602 + 1.48254I
b = 0.167551 − 1.383620I
7.24145 + 6.94635I 0
u = −0.238627 + 1.333130I
a = 0.079299 + 0.683567I
b = 0.655029 − 0.237112I
3.08685 + 3.11452I 0
u = −0.238627 − 1.333130I
a = 0.079299 − 0.683567I
b = 0.655029 + 0.237112I
3.08685 − 3.11452I 0
u = 0.608901 + 0.192542I
a = −0.385198 + 1.115390I
b = −0.203404 − 0.637908I
1.37542 − 2.38581I 0.25318 + 6.68724I
u = 0.608901 − 0.192542I
a = −0.385198 − 1.115390I
b = −0.203404 + 0.637908I
1.37542 + 2.38581I 0.25318 − 6.68724I
u = −0.212837 + 1.348630I
a = 0.173204 + 0.342037I
b = −0.515624 − 0.729139I
3.32479 + 3.40667I 0
u = −0.212837 − 1.348630I
a = 0.173204 − 0.342037I
b = −0.515624 + 0.729139I
3.32479 − 3.40667I 0
u = −0.629319
a = −0.702050
b = −0.548156
−1.22681 −8.76370
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.160524 + 1.364360I
a = 1.76789 − 1.18203I
b = −0.009637 + 0.248297I
7.62385 − 1.80031I 0
u = 0.160524 − 1.364360I
a = 1.76789 + 1.18203I
b = −0.009637 − 0.248297I
7.62385 + 1.80031I 0
u = 0.551646 + 0.273553I
a = 2.47112 − 0.13182I
b = 0.33166 + 1.54527I
8.78897 − 4.29126I 1.52859 + 7.08794I
u = 0.551646 − 0.273553I
a = 2.47112 + 0.13182I
b = 0.33166 − 1.54527I
8.78897 + 4.29126I 1.52859 − 7.08794I
u = 0.030644 + 1.385460I
a = 0.44733 − 2.69168I
b = 0.04203 + 1.58721I
11.97780 − 2.24521I 0
u = 0.030644 − 1.385460I
a = 0.44733 + 2.69168I
b = 0.04203 − 1.58721I
11.97780 + 2.24521I 0
u = −0.151276 + 1.377880I
a = 0.125296 − 1.287730I
b = −1.080770 + 0.264270I
7.92835 + 1.55973I 0
u = −0.151276 − 1.377880I
a = 0.125296 + 1.287730I
b = −1.080770 − 0.264270I
7.92835 − 1.55973I 0
u = 0.250853 + 1.369630I
a = 0.06598 − 1.62169I
b = 0.055380 + 0.653130I
6.32441 − 5.55834I 0
u = 0.250853 − 1.369630I
a = 0.06598 + 1.62169I
b = 0.055380 − 0.653130I
6.32441 + 5.55834I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.270313 + 1.372210I
a = −0.659965 + 0.973165I
b = −0.619046 − 0.391720I
2.37745 − 7.40004I 0
u = 0.270313 − 1.372210I
a = −0.659965 − 0.973165I
b = −0.619046 + 0.391720I
2.37745 + 7.40004I 0
u = −0.551260 + 0.236529I
a = −3.45506 − 0.56029I
b = 0.04181 + 1.46447I
8.40226 − 0.97889I 1.86302 − 1.67471I
u = −0.551260 − 0.236529I
a = −3.45506 + 0.56029I
b = 0.04181 − 1.46447I
8.40226 + 0.97889I 1.86302 + 1.67471I
u = −0.200699 + 1.387680I
a = 0.54548 + 3.81886I
b = 0.03756 − 1.57332I
13.8987 + 6.0274I 0
u = −0.200699 − 1.387680I
a = 0.54548 − 3.81886I
b = 0.03756 + 1.57332I
13.8987 − 6.0274I 0
u = −0.221577 + 1.389650I
a = 2.67668 + 2.67309I
b = 0.01190 − 1.48145I
13.59660 + 1.89175I 0
u = −0.221577 − 1.389650I
a = 2.67668 − 2.67309I
b = 0.01190 + 1.48145I
13.59660 − 1.89175I 0
u = −0.261270 + 1.388330I
a = −0.916443 − 0.073681I
b = 1.047840 + 0.631466I
6.33302 + 6.22584I 0
u = −0.261270 − 1.388330I
a = −0.916443 + 0.073681I
b = 1.047840 − 0.631466I
6.33302 − 6.22584I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200751 + 1.399130I
a = −0.92911 + 2.47143I
b = 0.26421 − 1.70761I
14.4126 − 1.0864I 0
u = 0.200751 − 1.399130I
a = −0.92911 − 2.47143I
b = 0.26421 + 1.70761I
14.4126 + 1.0864I 0
u = 0.21988 + 1.40059I
a = −1.59795 + 2.30465I
b = −0.40144 − 1.59340I
14.1350 − 7.1569I 0
u = 0.21988 − 1.40059I
a = −1.59795 − 2.30465I
b = −0.40144 + 1.59340I
14.1350 + 7.1569I 0
u = −0.29630 + 1.39861I
a = −2.04244 − 1.97677I
b = −0.18413 + 1.48474I
8.52537 + 10.23280I 0
u = −0.29630 − 1.39861I
a = −2.04244 + 1.97677I
b = −0.18413 − 1.48474I
8.52537 − 10.23280I 0
u = −0.547687 + 0.105446I
a = 1.135650 + 0.577720I
b = 0.336961 + 0.799665I
−1.31790 + 0.62224I −7.09922 + 0.77597I
u = −0.547687 − 0.105446I
a = 1.135650 − 0.577720I
b = 0.336961 − 0.799665I
−1.31790 − 0.62224I −7.09922 − 0.77597I
u = 0.480019 + 0.282782I
a = 0.649807 − 0.476462I
b = −0.22688 + 1.63741I
9.05022 + 1.50195I 1.96716 + 2.77210I
u = 0.480019 − 0.282782I
a = 0.649807 + 0.476462I
b = −0.22688 − 1.63741I
9.05022 − 1.50195I 1.96716 − 2.77210I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30052 + 1.41380I
a = 0.21485 − 1.48584I
b = 0.889892 + 0.660149I
6.6355 − 12.5722I 0
u = 0.30052 − 1.41380I
a = 0.21485 + 1.48584I
b = 0.889892 − 0.660149I
6.6355 + 12.5722I 0
u = 0.04134 + 1.45689I
a = 0.700785 − 0.798334I
b = −0.531147 + 0.725633I
10.09610 + 3.53770I 0
u = 0.04134 − 1.45689I
a = 0.700785 + 0.798334I
b = −0.531147 − 0.725633I
10.09610 − 3.53770I 0
u = 0.30096 + 1.42621I
a = 1.11691 − 2.05682I
b = 0.24255 + 1.39901I
8.29004 − 6.40229I 0
u = 0.30096 − 1.42621I
a = 1.11691 + 2.05682I
b = 0.24255 − 1.39901I
8.29004 + 6.40229I 0
u = −0.473695 + 0.236439I
a = −0.86694 − 2.68749I
b = −0.07268 + 1.55428I
8.70674 + 3.45703I 2.44717 − 9.91200I
u = −0.473695 − 0.236439I
a = −0.86694 + 2.68749I
b = −0.07268 − 1.55428I
8.70674 − 3.45703I 2.44717 + 9.91200I
u = −0.30470 + 1.44424I
a = −0.402971 − 0.560318I
b = −0.161745 + 0.293715I
4.96437 + 6.03326I 0
u = −0.30470 − 1.44424I
a = −0.402971 + 0.560318I
b = −0.161745 − 0.293715I
4.96437 − 6.03326I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31504 + 1.44516I
a = 1.55186 + 2.38348I
b = 0.29560 − 1.59663I
14.0172 + 16.9441I 0
u = −0.31504 − 1.44516I
a = 1.55186 − 2.38348I
b = 0.29560 + 1.59663I
14.0172 − 16.9441I 0
u = 0.31481 + 1.51069I
a = −1.11031 + 2.32799I
b = −0.05247 − 1.47834I
10.97510 − 6.80865I 0
u = 0.31481 − 1.51069I
a = −1.11031 − 2.32799I
b = −0.05247 + 1.47834I
10.97510 + 6.80865I 0
u = −0.07125 + 1.54701I
a = 0.24035 + 2.66634I
b = −0.18266 − 1.56545I
17.6103 − 6.2593I 0
u = −0.07125 − 1.54701I
a = 0.24035 − 2.66634I
b = −0.18266 + 1.56545I
17.6103 + 6.2593I 0
u = −0.090348 + 0.422609I
a = −0.670633 + 0.126283I
b = −0.284960 + 0.359912I
−0.342899 + 1.083340I −5.49487 − 5.61803I
u = −0.090348 − 0.422609I
a = −0.670633 − 0.126283I
b = −0.284960 − 0.359912I
−0.342899 − 1.083340I −5.49487 + 5.61803I
u = −0.055576 + 0.292303I
a = 0.64785 + 3.69479I
b = 0.621082 − 0.277003I
2.82192 − 0.05355I 4.54835 − 0.89727I
u = −0.055576 − 0.292303I
a = 0.64785 − 3.69479I
b = 0.621082 + 0.277003I
2.82192 + 0.05355I 4.54835 + 0.89727I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167888
a = −8.08813
b = 0.399625
2.81213 8.15040
15
II.
I
u
2
= h−u
18
−u
17
+· · ·+b+2u, u
18
+3u
17
+· · ·+a−3, u
19
−u
18
+· · ·−2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
−u
18
− 3u
17
+ ··· + 3u + 3
u
18
+ u
17
+ ··· + 3u
2
− 2u
a
12
=
1
u
2
a
4
=
−2u
17
+ 2u
16
+ ··· + u + 3
u
18
+ u
17
+ ··· + 3u
2
− 2u
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
2u
18
+ u
17
+ ··· + u − 4
−u
18
− 8u
16
+ ··· − 2u − 1
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
−u
18
− u
17
+ ··· + u + 3
u
18
+ u
17
+ ··· + 5u
2
− 2u
a
6
=
2u
18
+ 19u
16
+ ··· − 11u − 3
−u
18
− 2u
17
+ ··· − 27u
3
− 2u
2
a
10
=
−2u
18
+ 2u
17
+ ··· − 3u + 2
−u
18
+ u
17
+ ··· + 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
18
+ 5u
17
− 44u
16
+ 40u
15
− 156u
14
+ 130u
13
− 276u
12
+
207u
11
− 244u
10
+ 141u
9
− 104u
8
− 8u
7
− 51u
6
− 36u
5
− 40u
4
+ 18u
3
− 8u
2
+ 13u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 2u
18
+ ··· − 4u + 1
c
2
u
19
− 3u
18
+ ··· + u + 2
c
3
u
19
− u
17
+ ··· + 2u
2
+ 1
c
4
, c
5
u
19
+ 11u
17
+ ··· + 2u
2
+ 1
c
6
u
19
+ 3u
18
+ ··· + u − 2
c
7
u
19
+ u
18
+ ··· − 2u − 1
c
8
u
19
− u
18
+ ··· − 7u − 2
c
9
u
19
+ 2u
17
+ ··· − u
2
+ 1
c
10
u
19
+ 11u
17
+ ··· − 2u
2
− 1
c
11
, c
12
u
19
− u
18
+ ··· − 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 2y
18
+ ··· + 4y −1
c
2
, c
6
y
19
− 21y
18
+ ··· + 49y −4
c
3
y
19
− 2y
18
+ ··· − 4y −1
c
4
, c
5
, c
10
y
19
+ 22y
18
+ ··· − 4y −1
c
7
, c
11
, c
12
y
19
+ 19y
18
+ ··· + 16y −1
c
8
y
19
− y
18
+ ··· + 37y −4
c
9
y
19
+ 4y
18
+ ··· + 2y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886443 + 0.453355I
a = −0.716598 + 0.909448I
b = −0.077183 − 1.278510I
2.38737 − 2.81719I −9.7675 + 12.6617I
u = 0.886443 − 0.453355I
a = −0.716598 − 0.909448I
b = −0.077183 + 1.278510I
2.38737 + 2.81719I −9.7675 − 12.6617I
u = −0.088895 + 1.160480I
a = 1.10669 + 1.03757I
b = 0.210413 − 0.837050I
1.67617 + 0.71995I −1.96518 + 0.21105I
u = −0.088895 − 1.160480I
a = 1.10669 − 1.03757I
b = 0.210413 + 0.837050I
1.67617 − 0.71995I −1.96518 − 0.21105I
u = −0.655190 + 0.282477I
a = −0.049085 − 0.233175I
b = −0.233097 − 0.515283I
−0.50072 + 1.73928I −1.86896 − 1.30041I
u = −0.655190 − 0.282477I
a = −0.049085 + 0.233175I
b = −0.233097 + 0.515283I
−0.50072 − 1.73928I −1.86896 + 1.30041I
u = 0.115166 + 1.323600I
a = −0.41987 − 1.81336I
b = −0.18953 + 1.55344I
12.45790 + 1.16993I 6.72713 + 1.16230I
u = 0.115166 − 1.323600I
a = −0.41987 + 1.81336I
b = −0.18953 − 1.55344I
12.45790 − 1.16993I 6.72713 − 1.16230I
u = −0.155593 + 1.346690I
a = −0.62452 − 1.29696I
b = −0.640183 + 0.101653I
6.87721 + 2.00897I −1.71426 − 3.94861I
u = −0.155593 − 1.346690I
a = −0.62452 + 1.29696I
b = −0.640183 − 0.101653I
6.87721 − 2.00897I −1.71426 + 3.94861I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169490 + 1.400430I
a = −1.14282 + 3.38727I
b = −0.10110 − 1.58854I
13.5666 − 4.7196I 5.48212 + 2.36816I
u = 0.169490 − 1.400430I
a = −1.14282 − 3.38727I
b = −0.10110 + 1.58854I
13.5666 + 4.7196I 5.48212 − 2.36816I
u = −0.27333 + 1.39440I
a = −0.341325 − 0.338769I
b = 0.420683 + 0.436838I
4.80685 + 5.19614I −0.17965 − 1.92409I
u = −0.27333 − 1.39440I
a = −0.341325 + 0.338769I
b = 0.420683 − 0.436838I
4.80685 − 5.19614I −0.17965 + 1.92409I
u = 0.36151 + 1.43875I
a = 0.99294 − 1.73689I
b = 0.170869 + 1.345600I
8.27633 − 7.37319I 4.02539 + 9.62777I
u = 0.36151 − 1.43875I
a = 0.99294 + 1.73689I
b = 0.170869 − 1.345600I
8.27633 + 7.37319I 4.02539 − 9.62777I
u = −0.395920
a = 3.91237
b = 0.595540
2.44142 −14.4680
u = 0.338351 + 0.119715I
a = 3.23840 − 2.07906I
b = 0.14136 + 1.55398I
8.44919 − 2.73166I −2.00535 + 0.64537I
u = 0.338351 − 0.119715I
a = 3.23840 + 2.07906I
b = 0.14136 − 1.55398I
8.44919 + 2.73166I −2.00535 − 0.64537I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
+ 2u
18
+ ··· − 4u + 1)(u
101
− 17u
100
+ ··· + 59829u − 3461)
c
2
(u
19
− 3u
18
+ ··· + u + 2)(u
101
+ 2u
100
+ ··· + 9256u − 1034)
c
3
(u
19
− u
17
+ ··· + 2u
2
+ 1)(u
101
− u
100
+ ··· − 91u + 1)
c
4
, c
5
(u
19
+ 11u
17
+ ··· + 2u
2
+ 1)(u
101
− u
100
+ ··· + 22u − 4)
c
6
(u
19
+ 3u
18
+ ··· + u − 2)(u
101
+ 2u
100
+ ··· + 9256u − 1034)
c
7
(u
19
+ u
18
+ ··· − 2u − 1)(u
101
+ 46u
99
+ ··· + u − 1)
c
8
(u
19
− u
18
+ ··· − 7u − 2)(u
101
− 2u
99
+ ··· + 712u − 232)
c
9
(u
19
+ 2u
17
+ ··· − u
2
+ 1)(u
101
+ 3u
100
+ ··· + 5282083u + 2372859)
c
10
(u
19
+ 11u
17
+ ··· − 2u
2
− 1)(u
101
− u
100
+ ··· + 22u − 4)
c
11
, c
12
(u
19
− u
18
+ ··· − 2u + 1)(u
101
+ 46u
99
+ ··· + u − 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 2y
18
+ ··· + 4y −1)
· (y
101
+ 15y
100
+ ··· + 43620123y −11978521)
c
2
, c
6
(y
19
− 21y
18
+ ··· + 49y −4)
· (y
101
− 84y
100
+ ··· + 41122612y −1069156)
c
3
(y
19
− 2y
18
+ ··· − 4y −1)(y
101
− 9y
100
+ ··· + 7531y −1)
c
4
, c
5
, c
10
(y
19
+ 22y
18
+ ··· − 4y −1)(y
101
+ 107y
100
+ ··· − 708y −16)
c
7
, c
11
, c
12
(y
19
+ 19y
18
+ ··· + 16y −1)(y
101
+ 92y
100
+ ··· + 19y −1)
c
8
(y
19
− y
18
+ ··· + 37y −4)(y
101
− 4y
100
+ ··· + 171472y −53824)
c
9
(y
19
+ 4y
18
+ ··· + 2y −1)
· (y
101
− 39y
100
+ ··· + 211509629585425y −5630459833881)
22
