10
121
(K10a
90
)
A knot diagram
1
Linearized knot diagam
6 5 1 8 9 4 10 2 3 7
Solving Sequence
2,5 3,9
6 10 1 8 4 7
c
2
c
5
c
9
c
1
c
8
c
4
c
7
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1260218947u
22
− 19109508090u
21
+ ··· + 984316106b + 5089661734,
− 2544830867u
22
− 38196855978u
21
+ ··· + 1968632212a + 17497959996,
u
23
+ 16u
22
+ ··· − 10u − 4i
I
u
2
= h111u
10
a
3
+ 343u
10
a
2
+ ··· − 317a − 203, −u
10
a
3
+ 5u
10
a
2
+ ··· + 9a
2
+ 12,
u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1i
I
u
3
= hu
9
− 5u
8
+ 11u
7
− 12u
6
+ 5u
5
+ 3u
4
− 5u
3
+ 3u
2
+ b + u − 2,
2u
9
− 9u
8
+ 19u
7
− 21u
6
+ 12u
5
− u
4
− 3u
3
+ 3u
2
+ a + u − 1,
u
10
− 5u
9
+ 12u
8
− 16u
7
+ 12u
6
− 3u
5
− 3u
4
+ 4u
3
− u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 77 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−1.26 × 10
9
u
22
− 1.91 × 10
10
u
21
+ · · · + 9.84× 10
8
b + 5.09 ×10
9
, −2.54 ×
10
9
u
22
−3.82×10
10
u
21
+· · ·+1.97×10
9
a+1.75×10
10
, u
23
+16u
22
+· · ·−10u−4i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
1.29269u
22
+ 19.4027u
21
+ ··· − 9.50831u − 8.88838
1.28030u
22
+ 19.4140u
21
+ ··· − 4.03851u − 5.17076
a
6
=
0.319249u
22
+ 5.03061u
21
+ ··· + 6.76619u − 4.03209
0.0773747u
22
+ 0.861665u
21
+ ··· + 1.83960u − 1.27700
a
10
=
1.08318u
22
+ 16.7864u
21
+ ··· − 13.1020u − 8.83882
−0.0242790u
22
− 0.125186u
21
+ ··· + 2.48170u − 2.22746
a
1
=
1.02071u
22
+ 13.6913u
21
+ ··· − 4.25396u + 6.74097
2.26372u
22
+ 33.8581u
21
+ ··· − 16.4513u − 3.77333
a
8
=
0.0123908u
22
− 0.0112566u
21
+ ··· − 5.46979u − 3.71763
1.28030u
22
+ 19.4140u
21
+ ··· − 4.03851u − 5.17076
a
4
=
0.540830u
22
+ 8.50923u
21
+ ··· + 5.59024u − 1.78760
−0.298956u
22
− 4.34029u
21
+ ··· + 1.33635u − 0.967496
a
7
=
−0.221415u
22
− 3.51881u
21
+ ··· − 1.62252u − 3.99396
0.519049u
22
+ 7.71688u
21
+ ··· + 1.74955u − 3.39079
(ii) Obstruction class = −1
(iii) Cusp Shap es = −
3396085143
492158053
u
22
−
53190862554
492158053
u
21
+ ··· +
29461471174
492158053
u +
13339530290
492158053
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 19u
22
+ ··· − 18432u + 2048
c
2
u
23
− 16u
22
+ ··· − 10u + 4
c
3
, c
6
u
23
+ u
22
+ ··· + 2u + 1
c
4
, c
9
u
23
+ u
22
+ ··· + u + 1
c
5
, c
8
u
23
− u
22
+ ··· + 2u + 1
c
7
, c
10
u
23
− 10u
22
+ ··· − 108u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 9y
22
+ ··· + 2097152y −4194304
c
2
y
23
− 2y
22
+ ··· + 252y −16
c
3
, c
6
y
23
+ 9y
22
+ ··· − 16y −1
c
4
, c
9
y
23
− 7y
22
+ ··· − y −1
c
5
, c
8
y
23
− 3y
22
+ ··· + 6y −1
c
7
, c
10
y
23
+ 16y
22
+ ··· − 1360y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799030 + 0.571303I
a = −0.12013 − 1.57743I
b = −0.99718 − 1.19178I
1.35281 + 4.50771I 12.5679 − 8.0453I
u = −0.799030 − 0.571303I
a = −0.12013 + 1.57743I
b = −0.99718 + 1.19178I
1.35281 − 4.50771I 12.5679 + 8.0453I
u = 0.924432
a = −0.417135
b = 0.385613
−1.38648 −7.37670
u = −0.517217 + 1.045830I
a = −0.047708 + 0.890847I
b = 0.906994 + 0.510655I
6.24675 − 0.93599I 3.26085 + 0.04991I
u = −0.517217 − 1.045830I
a = −0.047708 − 0.890847I
b = 0.906994 − 0.510655I
6.24675 + 0.93599I 3.26085 − 0.04991I
u = −1.119710 + 0.513718I
a = −0.452909 − 0.773390I
b = −0.904431 − 0.633306I
0.95729 + 2.04351I 2.51837 − 2.36281I
u = −1.119710 − 0.513718I
a = −0.452909 + 0.773390I
b = −0.904431 + 0.633306I
0.95729 − 2.04351I 2.51837 + 2.36281I
u = −0.587912 + 0.172198I
a = −0.88228 − 1.27862I
b = −0.738880 − 0.599789I
1.10859 + 1.69807I 0.99491 − 2.62569I
u = −0.587912 − 0.172198I
a = −0.88228 + 1.27862I
b = −0.738880 + 0.599789I
1.10859 − 1.69807I 0.99491 + 2.62569I
u = 0.267486 + 0.510215I
a = 0.57156 − 1.32428I
b = −0.828550 + 0.062607I
2.14619 − 2.15516I 1.26567 + 4.32711I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267486 − 0.510215I
a = 0.57156 + 1.32428I
b = −0.828550 − 0.062607I
2.14619 + 2.15516I 1.26567 − 4.32711I
u = −1.14560 + 0.90839I
a = 0.060381 + 1.065800I
b = 1.03734 + 1.16613I
−4.47926 + 10.82160I −7.18200 − 7.95225I
u = −1.14560 − 0.90839I
a = 0.060381 − 1.065800I
b = 1.03734 − 1.16613I
−4.47926 − 10.82160I −7.18200 + 7.95225I
u = −1.14496 + 1.09496I
a = 0.038158 − 1.004390I
b = −1.05609 − 1.19178I
−0.6004 + 16.9749I 0. − 9.34400I
u = −1.14496 − 1.09496I
a = 0.038158 + 1.004390I
b = −1.05609 + 1.19178I
−0.6004 − 16.9749I 0. + 9.34400I
u = 0.257593 + 0.139438I
a = −3.87302 + 0.15811I
b = 1.019710 + 0.499316I
1.57996 + 1.95049I 0.00371 − 3.34610I
u = 0.257593 − 0.139438I
a = −3.87302 − 0.15811I
b = 1.019710 − 0.499316I
1.57996 − 1.95049I 0.00371 + 3.34610I
u = −1.37621 + 1.06752I
a = 0.189943 + 0.547859I
b = 0.846254 + 0.551200I
3.21418 + 8.47524I 0
u = −1.37621 − 1.06752I
a = 0.189943 − 0.547859I
b = 0.846254 − 0.551200I
3.21418 − 8.47524I 0
u = −0.84300 + 1.61883I
a = 0.299587 − 0.003010I
b = 0.247680 − 0.487517I
−2.90076 − 2.91786I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.84300 − 1.61883I
a = 0.299587 + 0.003010I
b = 0.247680 + 0.487517I
−2.90076 + 2.91786I 0
u = −1.45365 + 1.27820I
a = −0.325009 + 0.193081I
b = −0.225654 + 0.696100I
−0.52992 − 8.08521I 0
u = −1.45365 − 1.27820I
a = −0.325009 − 0.193081I
b = −0.225654 − 0.696100I
−0.52992 + 8.08521I 0
7
II. I
u
2
= h111u
10
a
3
+ 343u
10
a
2
+ · · · − 317a − 203, −u
10
a
3
+ 5u
10
a
2
+ · · · +
9a
2
+ 12, u
11
− 5u
10
+ · · · − 3u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
a
−0.350158a
3
u
10
− 1.08202a
2
u
10
+ ··· + a + 0.640379
a
6
=
a
2
u
−0.0820189a
3
u
10
+ 0.350158a
2
u
10
+ ··· − a + 0.996845
a
10
=
0.350158a
3
u
10
+ 1.08202a
2
u
10
+ ··· − 1.04101a
2
− 0.640379
0.0504732a
3
u
10
− 0.753943a
2
u
10
+ ··· + 0.876972a
2
+ 0.0788644
a
1
=
0.0410095a
3
u
10
− 0.675079a
2
u
10
+ ··· + a + 0.501577
−0.0820189a
3
u
10
+ 0.350158a
2
u
10
+ ··· − a − 0.00315457
a
8
=
0.350158a
3
u
10
+ 1.08202a
2
u
10
+ ··· − 1.04101a
2
− 0.640379
−0.350158a
3
u
10
− 1.08202a
2
u
10
+ ··· + a + 0.640379
a
4
=
−0.328076a
3
u
10
+ 0.400631a
2
u
10
+ ··· − a − 0.0126183
0.410095a
3
u
10
− 0.750789a
2
u
10
+ ··· + 2a − 0.984227
a
7
=
−0.451104a
3
u
10
+ 0.425868a
2
u
10
+ ··· − 0.712934a
2
+ 0.482650
0.246057a
3
u
10
− 1.05047a
2
u
10
+ ··· + 2a + 0.00946372
(ii) Obstruction class = −1
(iii) Cusp Shapes =
104
317
u
10
a
3
−
444
317
u
10
a
2
+ ··· + 4a −
6970
317
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
22
c
2
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
4
c
3
, c
6
u
44
+ u
43
+ ··· − 8u + 1
c
4
, c
9
u
44
− u
43
+ ··· − 918u + 289
c
5
, c
8
u
44
− 3u
43
+ ··· + 14u + 1
c
7
, c
10
(u
11
+ 3u
10
+ ··· + 2u + 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
22
c
2
(y
11
− y
10
+ ··· + 6y −1)
4
c
3
, c
6
y
44
− 9y
43
+ ··· − 8y + 1
c
4
, c
9
y
44
− 13y
43
+ ··· − 899368y + 83521
c
5
, c
8
y
44
+ 15y
43
+ ··· − 56y + 1
c
7
, c
10
(y
11
+ 7y
10
+ ··· − 6y −1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326966 + 0.916688I
a = −0.038498 − 1.048450I
b = 0.80389 − 1.55903I
2.98579 − 7.03062I 1.84059 + 9.69161I
u = 0.326966 + 0.916688I
a = −0.281007 − 1.284950I
b = 0.1356230 + 0.0379857I
2.98579 − 2.97085I 1.84059 + 2.76341I
u = 0.326966 + 0.916688I
a = 1.23128 + 1.31612I
b = −0.948517 + 0.378099I
2.98579 − 7.03062I 1.84059 + 9.69161I
u = 0.326966 + 0.916688I
a = −0.083576 + 0.118139I
b = −1.086020 + 0.677732I
2.98579 − 2.97085I 1.84059 + 2.76341I
u = 0.326966 − 0.916688I
a = −0.038498 + 1.048450I
b = 0.80389 + 1.55903I
2.98579 + 7.03062I 1.84059 − 9.69161I
u = 0.326966 − 0.916688I
a = −0.281007 + 1.284950I
b = 0.1356230 − 0.0379857I
2.98579 + 2.97085I 1.84059 − 2.76341I
u = 0.326966 − 0.916688I
a = 1.23128 − 1.31612I
b = −0.948517 − 0.378099I
2.98579 + 7.03062I 1.84059 − 9.69161I
u = 0.326966 − 0.916688I
a = −0.083576 − 0.118139I
b = −1.086020 − 0.677732I
2.98579 + 2.97085I 1.84059 − 2.76341I
u = 0.864248 + 0.407709I
a = −0.129704 + 0.797794I
b = −1.09220 + 1.32253I
−2.06894 − 4.27767I −9.63582 + 8.52770I
u = 0.864248 + 0.407709I
a = −1.193510 − 0.275075I
b = 0.002110 − 0.500193I
−2.06894 − 0.21790I −9.63582 + 1.59949I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.864248 + 0.407709I
a = 0.221332 + 0.474348I
b = 0.919334 + 0.724336I
−2.06894 − 0.21790I −9.63582 + 1.59949I
u = 0.864248 + 0.407709I
a = 0.44322 − 1.73936I
b = 0.437365 − 0.636610I
−2.06894 − 4.27767I −9.63582 + 8.52770I
u = 0.864248 − 0.407709I
a = −0.129704 − 0.797794I
b = −1.09220 − 1.32253I
−2.06894 + 4.27767I −9.63582 − 8.52770I
u = 0.864248 − 0.407709I
a = −1.193510 + 0.275075I
b = 0.002110 + 0.500193I
−2.06894 + 0.21790I −9.63582 − 1.59949I
u = 0.864248 − 0.407709I
a = 0.221332 − 0.474348I
b = 0.919334 − 0.724336I
−2.06894 + 0.21790I −9.63582 − 1.59949I
u = 0.864248 − 0.407709I
a = 0.44322 + 1.73936I
b = 0.437365 + 0.636610I
−2.06894 + 4.27767I −9.63582 − 8.52770I
u = −0.577598 + 0.283449I
a = −0.081013 + 0.913235I
b = −1.57832 + 1.34962I
0.11530 + 7.95431I −9.1705 − 13.4876I
u = −0.577598 + 0.283449I
a = 0.76538 − 1.71451I
b = −0.918479 − 0.926010I
0.11530 + 3.89454I −9.17045 − 6.55945I
u = −0.577598 + 0.283449I
a = −0.64749 − 1.92095I
b = −0.043897 − 1.207240I
0.11530 + 3.89454I −9.17045 − 6.55945I
u = −0.577598 + 0.283449I
a = −3.12633 + 0.80240I
b = 0.212063 + 0.550445I
0.11530 + 7.95431I −9.1705 − 13.4876I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577598 − 0.283449I
a = −0.081013 − 0.913235I
b = −1.57832 − 1.34962I
0.11530 − 7.95431I −9.1705 + 13.4876I
u = −0.577598 − 0.283449I
a = 0.76538 + 1.71451I
b = −0.918479 + 0.926010I
0.11530 − 3.89454I −9.17045 + 6.55945I
u = −0.577598 − 0.283449I
a = −0.64749 + 1.92095I
b = −0.043897 + 1.207240I
0.11530 − 3.89454I −9.17045 + 6.55945I
u = −0.577598 − 0.283449I
a = −3.12633 − 0.80240I
b = 0.212063 − 0.550445I
0.11530 − 7.95431I −9.1705 + 13.4876I
u = 1.110200 + 0.862988I
a = 0.028627 − 1.133370I
b = 0.596743 − 0.983192I
−2.44783 − 4.73429I −9.46762 + 3.38077I
u = 1.110200 + 0.862988I
a = 0.094059 + 0.812487I
b = −1.00987 + 1.23356I
−2.44783 − 4.73429I −9.46762 + 3.38077I
u = 1.110200 + 0.862988I
a = −0.521303 − 0.385563I
b = 0.177376 − 0.645337I
−2.44783 − 0.67452I −9.46762 − 3.54743I
u = 1.110200 + 0.862988I
a = 0.182065 + 0.439757I
b = 0.246013 + 0.877929I
−2.44783 − 0.67452I −9.46762 − 3.54743I
u = 1.110200 − 0.862988I
a = 0.028627 + 1.133370I
b = 0.596743 + 0.983192I
−2.44783 + 4.73429I −9.46762 − 3.38077I
u = 1.110200 − 0.862988I
a = 0.094059 − 0.812487I
b = −1.00987 − 1.23356I
−2.44783 + 4.73429I −9.46762 − 3.38077I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.110200 − 0.862988I
a = −0.521303 + 0.385563I
b = 0.177376 + 0.645337I
−2.44783 + 0.67452I −9.46762 + 3.54743I
u = 1.110200 − 0.862988I
a = 0.182065 − 0.439757I
b = 0.246013 − 0.877929I
−2.44783 + 0.67452I −9.46762 + 3.54743I
u = −0.566454
a = −0.061706 + 1.273110I
b = 1.26958 + 1.41728I
−4.02369 − 2.02988I −18.2613 + 3.4641I
u = −0.566454
a = −0.061706 − 1.273110I
b = 1.26958 − 1.41728I
−4.02369 + 2.02988I −18.2613 − 3.4641I
u = −0.566454
a = 2.24127 + 2.50202I
b = −0.034953 + 0.721156I
−4.02369 − 2.02988I −18.2613 + 3.4641I
u = −0.566454
a = 2.24127 − 2.50202I
b = −0.034953 − 0.721156I
−4.02369 + 2.02988I −18.2613 − 3.4641I
u = 1.05941 + 1.17096I
a = 0.014454 + 0.953147I
b = −0.651229 + 1.243080I
−1.50728 − 7.24617I −6.43603 + 12.47688I
u = 1.05941 + 1.17096I
a = −0.307069 − 0.833969I
b = 1.10078 − 1.02670I
−1.50728 − 7.24617I −6.43603 + 12.47688I
u = 1.05941 + 1.17096I
a = 0.426989 + 0.526407I
b = −0.201428 + 0.560153I
−1.50728 − 3.18641I −6.43603 + 5.54868I
u = 1.05941 + 1.17096I
a = −0.177470 − 0.332583I
b = 0.164043 − 1.057670I
−1.50728 − 3.18641I −6.43603 + 5.54868I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05941 − 1.17096I
a = 0.014454 − 0.953147I
b = −0.651229 − 1.243080I
−1.50728 + 7.24617I −6.43603 − 12.47688I
u = 1.05941 − 1.17096I
a = −0.307069 + 0.833969I
b = 1.10078 + 1.02670I
−1.50728 + 7.24617I −6.43603 − 12.47688I
u = 1.05941 − 1.17096I
a = 0.426989 − 0.526407I
b = −0.201428 − 0.560153I
−1.50728 + 3.18641I −6.43603 − 5.54868I
u = 1.05941 − 1.17096I
a = −0.177470 + 0.332583I
b = 0.164043 + 1.057670I
−1.50728 + 3.18641I −6.43603 − 5.54868I
15
III.
I
u
3
= hu
9
− 5u
8
+ · · · + b − 2, 2u
9
− 9u
8
+ · · · + a − 1, u
10
− 5u
9
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
−2u
9
+ 9u
8
− 19u
7
+ 21u
6
− 12u
5
+ u
4
+ 3u
3
− 3u
2
− u + 1
−u
9
+ 5u
8
− 11u
7
+ 12u
6
− 5u
5
− 3u
4
+ 5u
3
− 3u
2
− u + 2
a
6
=
−u
9
+ 3u
8
− 4u
7
+ u
6
+ u
5
− 2u
3
+ u
2
− 2u − 1
−2u
9
+ 8u
8
− 15u
7
+ 13u
6
− 3u
5
− 5u
4
+ 5u
3
− 3u
2
− u + 1
a
10
=
−u
9
+ 5u
8
− 12u
7
+ 16u
6
− 13u
5
+ 6u
4
− u
3
− 2u
2
+ u
−u
9
+ 4u
8
− 8u
7
+ 8u
6
− 3u
5
− 3u
4
+ 4u
3
− 2u
2
− u + 1
a
1
=
4u
9
− 18u
8
+ 38u
7
− 42u
6
+ 23u
5
− 9u
3
+ 8u
2
+ u − 3
−u
8
+ 3u
7
− 4u
6
+ u
5
+ 2u
4
− 3u
3
+ 2u
2
− u − 2
a
8
=
−u
9
+ 4u
8
− 8u
7
+ 9u
6
− 7u
5
+ 4u
4
− 2u
3
− 1
−u
9
+ 5u
8
− 11u
7
+ 12u
6
− 5u
5
− 3u
4
+ 5u
3
− 3u
2
− u + 2
a
4
=
u
9
− 4u
8
+ 7u
7
− 4u
6
− 4u
5
+ 9u
4
− 7u
3
+ 3u
2
+ u − 1
−u
8
+ 4u
7
− 8u
6
+ 8u
5
− 4u
4
+ u
2
− 1
a
7
=
−u
9
+ 3u
8
− 4u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u
2
− 2
−u
9
+ 4u
8
− 7u
7
+ 5u
6
− 3u
4
+ 2u
3
− u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14u
9
−60u
8
+ 124u
7
−133u
6
+ 74u
5
−2u
4
−25u
3
+ 27u
2
+ 6u −16
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 4u
8
− u
7
+ 6u
6
− 3u
5
+ 6u
4
− 3u
3
+ 4u
2
− 2u + 1
c
2
u
10
− 5u
9
+ 12u
8
− 16u
7
+ 12u
6
− 3u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
3
, c
6
u
10
+ 3u
9
+ 3u
8
− u
7
− u
6
+ 7u
5
+ 11u
4
+ 3u
3
− 3u
2
− u + 1
c
4
, c
9
u
10
+ u
9
− u
8
− 2u
7
+ 3u
6
− 2u
4
− u
3
+ 5u
2
− 4u + 1
c
5
, c
8
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 7u
6
+ 5u
5
+ 8u
4
+ 4u
3
+ 4u
2
+ u + 1
c
7
u
10
− 3u
9
+ 9u
8
− 16u
7
+ 24u
6
− 27u
5
+ 24u
4
− 18u
3
+ 10u
2
− 4u + 1
c
10
u
10
+ 3u
9
+ 9u
8
+ 16u
7
+ 24u
6
+ 27u
5
+ 24u
4
+ 18u
3
+ 10u
2
+ 4u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 8y
9
+ ··· + 4y + 1
c
2
y
10
− y
9
+ 8y
8
− 4y
7
+ 14y
6
+ 15y
5
+ y
4
+ 8y
3
+ 3y
2
− 3y + 1
c
3
, c
6
y
10
− 3y
9
+ ··· − 7y + 1
c
4
, c
9
y
10
− 3y
9
+ ··· − 6y + 1
c
5
, c
8
y
10
+ 5y
9
+ ··· + 7y + 1
c
7
, c
10
y
10
+ 9y
9
+ 33y
8
+ 62y
7
+ 56y
6
+ 5y
5
− 26y
4
− 12y
3
+ 4y
2
+ 4y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689571 + 0.575966I
a = −0.12950 − 1.62825I
b = 0.84852 − 1.19738I
0.99844 − 4.62197I −7.4943 + 13.1842I
u = 0.689571 − 0.575966I
a = −0.12950 + 1.62825I
b = 0.84852 + 1.19738I
0.99844 + 4.62197I −7.4943 − 13.1842I
u = 0.117471 + 0.884570I
a = −0.748660 + 0.130004I
b = −0.202944 − 0.646971I
−2.84633 − 2.07393I −9.25779 + 2.43239I
u = 0.117471 − 0.884570I
a = −0.748660 − 0.130004I
b = −0.202944 + 0.646971I
−2.84633 + 2.07393I −9.25779 − 2.43239I
u = 1.171940 + 0.674004I
a = −0.240799 − 0.606453I
b = 0.126549 − 0.873027I
−2.30790 − 1.97177I −10.18714 + 3.25987I
u = 1.171940 − 0.674004I
a = −0.240799 + 0.606453I
b = 0.126549 + 0.873027I
−2.30790 + 1.97177I −10.18714 − 3.25987I
u = −0.561171 + 0.194255I
a = −0.531466 − 1.276610I
b = 0.546232 + 0.613157I
0.66134 − 7.13925I −2.98492 + 4.64046I
u = −0.561171 − 0.194255I
a = −0.531466 + 1.276610I
b = 0.546232 − 0.613157I
0.66134 + 7.13925I −2.98492 − 4.64046I
u = 1.08219 + 1.11471I
a = 0.150423 + 0.880176I
b = −0.818356 + 1.120190I
−1.44035 − 6.19794I −4.57589 + 3.75444I
u = 1.08219 − 1.11471I
a = 0.150423 − 0.880176I
b = −0.818356 − 1.120190I
−1.44035 + 6.19794I −4.57589 − 3.75444I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
22
)(u
10
+ 4u
8
+ ··· − 2u + 1)
· (u
23
− 19u
22
+ ··· − 18432u + 2048)
c
2
(u
10
− 5u
9
+ 12u
8
− 16u
7
+ 12u
6
− 3u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
4
· (u
23
− 16u
22
+ ··· − 10u + 4)
c
3
, c
6
(u
10
+ 3u
9
+ 3u
8
− u
7
− u
6
+ 7u
5
+ 11u
4
+ 3u
3
− 3u
2
− u + 1)
· (u
23
+ u
22
+ ··· + 2u + 1)(u
44
+ u
43
+ ··· − 8u + 1)
c
4
, c
9
(u
10
+ u
9
− u
8
− 2u
7
+ 3u
6
− 2u
4
− u
3
+ 5u
2
− 4u + 1)
· (u
23
+ u
22
+ ··· + u + 1)(u
44
− u
43
+ ··· − 918u + 289)
c
5
, c
8
(u
10
+ u
9
+ 3u
8
+ 2u
7
+ 7u
6
+ 5u
5
+ 8u
4
+ 4u
3
+ 4u
2
+ u + 1)
· (u
23
− u
22
+ ··· + 2u + 1)(u
44
− 3u
43
+ ··· + 14u + 1)
c
7
(u
10
− 3u
9
+ 9u
8
− 16u
7
+ 24u
6
− 27u
5
+ 24u
4
− 18u
3
+ 10u
2
− 4u + 1)
· ((u
11
+ 3u
10
+ ··· + 2u + 1)
4
)(u
23
− 10u
22
+ ··· − 108u + 16)
c
10
(u
10
+ 3u
9
+ 9u
8
+ 16u
7
+ 24u
6
+ 27u
5
+ 24u
4
+ 18u
3
+ 10u
2
+ 4u + 1)
· ((u
11
+ 3u
10
+ ··· + 2u + 1)
4
)(u
23
− 10u
22
+ ··· − 108u + 16)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
22
)(y
10
+ 8y
9
+ ··· + 4y + 1)
· (y
23
+ 9y
22
+ ··· + 2097152y −4194304)
c
2
(y
10
− y
9
+ 8y
8
− 4y
7
+ 14y
6
+ 15y
5
+ y
4
+ 8y
3
+ 3y
2
− 3y + 1)
· ((y
11
− y
10
+ ··· + 6y −1)
4
)(y
23
− 2y
22
+ ··· + 252y −16)
c
3
, c
6
(y
10
− 3y
9
+ ··· − 7y + 1)(y
23
+ 9y
22
+ ··· − 16y −1)
· (y
44
− 9y
43
+ ··· − 8y + 1)
c
4
, c
9
(y
10
− 3y
9
+ ··· − 6y + 1)(y
23
− 7y
22
+ ··· − y −1)
· (y
44
− 13y
43
+ ··· − 899368y + 83521)
c
5
, c
8
(y
10
+ 5y
9
+ ··· + 7y + 1)(y
23
− 3y
22
+ ··· + 6y −1)
· (y
44
+ 15y
43
+ ··· − 56y + 1)
c
7
, c
10
(y
10
+ 9y
9
+ 33y
8
+ 62y
7
+ 56y
6
+ 5y
5
− 26y
4
− 12y
3
+ 4y
2
+ 4y + 1)
· ((y
11
+ 7y
10
+ ··· − 6y −1)
4
)(y
23
+ 16y
22
+ ··· − 1360y −256)
21
