12n
0254
(K12n
0254
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 9 12 3 6 1 8 6
Solving Sequence
3,8 9,12
7 6 1 11 5 2 4 10
c
8
c
7
c
6
c
12
c
11
c
5
c
2
c
4
c
10
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.85386 × 10
22
u
20
− 1.50646 × 10
23
u
19
+ ··· + 1.12972 × 10
24
b + 1.18141 × 10
25
,
4.93819 × 10
24
u
20
− 2.24476 × 10
25
u
19
+ ··· + 2.48538 × 10
25
a + 6.80715 × 10
26
,
u
21
− 5u
20
+ ··· + 528u − 64i
I
u
2
= h−271u
5
a
3
− 2553u
5
a
2
+ ··· + 3664a − 2027, −2u
5
a
3
+ u
5
a
2
+ ··· − 4a − 2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h−17u
10
+ 21u
9
+ 46u
8
+ 6u
7
− 188u
6
− 125u
5
+ 284u
4
+ 136u
3
+ 86u
2
+ 356b − 512u + 71,
− 617u
10
+ 202u
9
+ ··· + 178a − 1470, u
11
− 3u
9
+ 2u
7
+ 5u
6
+ u
5
− 4u
4
+ 6u
3
− 2u
2
+ u + 1i
I
v
1
= ha, b + 2v + 2, 4v
2
+ 6v + 1i
* 4 irreducible components of dim
C
= 0, with total 58 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
=
h2.85×10
22
u
20
−1.51×10
23
u
19
+· · ·+1.13×10
24
b+1.18×10
25
, 4.94×10
24
u
20
−
2.24 × 10
25
u
19
+ · · · + 2.49 × 10
25
a + 6.81 × 10
26
, u
21
− 5u
20
+ · · · + 528u − 64i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
−0.198690u
20
+ 0.903187u
19
+ ··· + 168.839u − 27.3888
−0.0252617u
20
+ 0.133349u
19
+ ··· + 44.8453u − 10.4576
a
7
=
−0.0389223u
20
+ 0.169523u
19
+ ··· + 22.6922u − 1.25931
−0.204843u
20
+ 0.945787u
19
+ ··· + 195.515u − 36.3690
a
6
=
−0.256774u
20
+ 1.17458u
19
+ ··· + 228.962u − 39.2339
−0.169105u
20
+ 0.785773u
19
+ ··· + 165.000u − 30.9802
a
1
=
−0.126591u
20
+ 0.558334u
19
+ ··· + 86.6544u − 10.5130
0.416280u
20
− 1.91677u
19
+ ··· − 391.813u + 72.1250
a
11
=
−0.223951u
20
+ 1.03654u
19
+ ··· + 213.684u − 37.8464
−0.0252617u
20
+ 0.133349u
19
+ ··· + 44.8453u − 10.4576
a
5
=
−0.500539u
20
+ 2.28989u
19
+ ··· + 447.169u − 77.8622
−0.373948u
20
+ 1.73156u
19
+ ··· + 360.515u − 67.3492
a
2
=
−0.126591u
20
+ 0.558334u
19
+ ··· + 86.6544u − 10.5130
0.373948u
20
− 1.73156u
19
+ ··· − 360.515u + 67.3492
a
4
=
−u
−u
a
10
=
0.0720983u
20
− 0.344853u
19
+ ··· − 82.1841u + 17.8758
0.441542u
20
− 2.05012u
19
+ ··· − 436.659u + 82.5826
(ii) Obstruction class = −1
(iii) Cusp Shapes =
59011690898372144363232697
49707567109353239097754688
u
20
−
278177987921238114159260841
49707567109353239097754688
u
19
+
··· −
15717053070456132195264300185
12426891777338309774438672
u +
380289254330637407319519649
1553361472167288721804834
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 11u
20
+ ··· + 2416u + 256
c
2
, c
4
u
21
− 3u
20
+ ··· − 12u + 16
c
3
, c
8
u
21
+ 5u
20
+ ··· + 528u + 64
c
5
, c
7
, c
11
u
21
− u
20
+ ··· − 2u + 1
c
6
, c
9
, c
12
u
21
− 15u
19
+ ··· + 3u − 1
c
10
u
21
− 19u
20
+ ··· + 96u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ y
20
+ ··· − 37120y −65536
c
2
, c
4
y
21
− 11y
20
+ ··· + 2416y −256
c
3
, c
8
y
21
− 9y
20
+ ··· + 54016y −4096
c
5
, c
7
, c
11
y
21
+ 13y
20
+ ··· + 46y
2
− 1
c
6
, c
9
, c
12
y
21
− 30y
20
+ ··· + 41y −1
c
10
y
21
− 11y
20
+ ··· + 115712y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121943 + 0.682474I
a = 0.563394 − 0.200224I
b = 0.242967 + 0.329112I
−0.472540 − 0.941822I −7.59562 + 7.26185I
u = −0.121943 − 0.682474I
a = 0.563394 + 0.200224I
b = 0.242967 − 0.329112I
−0.472540 + 0.941822I −7.59562 − 7.26185I
u = 0.603944
a = 0.453168
b = 0.799712
−1.50093 −5.01190
u = 0.536882 + 1.288830I
a = 0.332371 + 0.204687I
b = −0.203835 − 0.523003I
−7.32268 + 3.73921I −2.18512 − 2.93436I
u = 0.536882 − 1.288830I
a = 0.332371 − 0.204687I
b = −0.203835 + 0.523003I
−7.32268 − 3.73921I −2.18512 + 2.93436I
u = −0.45031 + 1.42697I
a = 0.401321 − 0.196262I
b = −0.169622 + 1.002850I
−0.856656 + 0.283512I −6.72739 − 0.35031I
u = −0.45031 − 1.42697I
a = 0.401321 + 0.196262I
b = −0.169622 − 1.002850I
−0.856656 − 0.283512I −6.72739 + 0.35031I
u = 1.39749 + 0.58008I
a = 0.000890 + 1.116300I
b = 0.416233 − 1.089790I
−3.89482 + 3.14186I −8.38778 − 3.45220I
u = 1.39749 − 0.58008I
a = 0.000890 − 1.116300I
b = 0.416233 + 1.089790I
−3.89482 − 3.14186I −8.38778 + 3.45220I
u = 0.452501
a = 2.15908
b = −0.287661
−2.05646 −0.974600
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.68409 + 1.39512I
a = 0.435024 + 0.190053I
b = −0.549126 − 1.238180I
−2.93350 − 6.63406I −8.79219 + 4.92171I
u = 0.68409 − 1.39512I
a = 0.435024 − 0.190053I
b = −0.549126 + 1.238180I
−2.93350 + 6.63406I −8.79219 − 4.92171I
u = 1.30096 + 0.91198I
a = 0.393242 + 1.276420I
b = 0.90620 − 1.50613I
−0.8291 + 14.7385I −8.45146 − 7.52643I
u = 1.30096 − 0.91198I
a = 0.393242 − 1.276420I
b = 0.90620 + 1.50613I
−0.8291 − 14.7385I −8.45146 + 7.52643I
u = −1.42639 + 0.82761I
a = 0.254534 − 1.154900I
b = 0.63940 + 1.47836I
2.34232 − 8.31871I −5.94131 + 4.58592I
u = −1.42639 − 0.82761I
a = 0.254534 + 1.154900I
b = 0.63940 − 1.47836I
2.34232 + 8.31871I −5.94131 − 4.58592I
u = 0.334496
a = 0.508543
b = −1.69359
−10.4004 21.7570
u = 1.62920 + 0.48052I
a = −0.319293 − 1.001180I
b = −0.737374 + 0.986244I
5.91302 + 6.12351I −10.80009 − 6.57387I
u = 1.62920 − 0.48052I
a = −0.319293 + 1.001180I
b = −0.737374 − 0.986244I
5.91302 − 6.12351I −10.80009 + 6.57387I
u = −1.74543 + 0.04421I
a = −0.121882 + 0.958359I
b = −0.454067 − 1.159470I
6.80819 + 0.98118I −9.12937 − 0.92113I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74543 − 0.04421I
a = −0.121882 − 0.958359I
b = −0.454067 + 1.159470I
6.80819 − 0.98118I −9.12937 + 0.92113I
7
II. I
u
2
= h−271u
5
a
3
− 2553u
5
a
2
+ · · · + 3664a − 2027, −2u
5
a
3
+ u
5
a
2
+ · · · −
4a − 2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
a
0.110657a
3
u
5
+ 1.04247a
2
u
5
+ ··· − 1.49612a + 0.827685
a
7
=
0.518579a
3
u
5
+ 0.461004a
2
u
5
+ ··· + 0.0661494a + 0.956309
−1.96366a
3
u
5
− 0.801552a
2
u
5
+ ··· − 1.76072a − 1.99755
a
6
=
−0.518579a
3
u
5
− 0.461004a
2
u
5
+ ··· − 0.0661494a − 0.956309
−0.110657a
3
u
5
− 1.04247a
2
u
5
+ ··· + 1.49612a + 0.172315
a
1
=
u
2
− 1
u
2
a
11
=
0.110657a
3
u
5
+ 1.04247a
2
u
5
+ ··· − 0.496121a + 0.827685
0.110657a
3
u
5
+ 1.04247a
2
u
5
+ ··· − 1.49612a + 0.827685
a
5
=
−u
4
+ u
2
− 1
−u
4
a
2
=
u
2
− 1
u
4
a
4
=
−u
−u
a
10
=
−1.32993a
3
u
5
+ 1.68150a
2
u
5
+ ··· − 2.77909a + 0.292364
−1.44059a
3
u
5
+ 0.639036a
2
u
5
+ ··· − 2.28297a − 0.535321
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
c
2
, c
3
, c
4
c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
4
c
5
, c
7
, c
11
u
24
+ 3u
23
+ ··· + 418u + 319
c
6
, c
9
, c
12
u
24
− 3u
23
+ ··· − 38u + 181
c
10
(u
2
+ u − 1)
12
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
4
c
2
, c
3
, c
4
c
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
c
5
, c
7
, c
11
y
24
+ 11y
23
+ ··· + 621500y + 101761
c
6
, c
9
, c
12
y
24
− 13y
23
+ ··· − 152760y + 32761
c
10
(y
2
− 3y + 1)
12
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.642556 − 0.992563I
b = −0.61676 + 1.29086I
5.83845 + 0.92430I −4.28328 − 0.79423I
u = 1.002190 + 0.295542I
a = 0.85932 − 1.36236I
b = 0.022966 + 0.740302I
−2.05724 + 0.92430I −4.28328 − 0.79423I
u = 1.002190 + 0.295542I
a = 0.30955 + 1.60690I
b = 0.04999 − 1.65697I
5.83845 + 0.92430I −4.28328 − 0.79423I
u = 1.002190 + 0.295542I
a = 0.012501 − 0.246000I
b = 1.46084 + 0.21819I
−2.05724 + 0.92430I −4.28328 − 0.79423I
u = 1.002190 − 0.295542I
a = −0.642556 + 0.992563I
b = −0.61676 − 1.29086I
5.83845 − 0.92430I −4.28328 + 0.79423I
u = 1.002190 − 0.295542I
a = 0.85932 + 1.36236I
b = 0.022966 − 0.740302I
−2.05724 − 0.92430I −4.28328 + 0.79423I
u = 1.002190 − 0.295542I
a = 0.30955 − 1.60690I
b = 0.04999 + 1.65697I
5.83845 − 0.92430I −4.28328 + 0.79423I
u = 1.002190 − 0.295542I
a = 0.012501 + 0.246000I
b = 1.46084 − 0.21819I
−2.05724 − 0.92430I −4.28328 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.40914 + 1.08956I
b = 0.634044 − 0.520697I
−5.83845 + 0.92430I −11.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = −0.93092 − 1.84591I
b = 0.192218 − 1.006480I
2.05724 + 0.92430I −11.71672 − 0.79423I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = 2.36603 + 0.04486I
b = −0.032636 + 1.358240I
2.05724 + 0.92430I −11.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = −2.34802 + 3.62566I
b = −1.051840 − 0.400227I
−5.83845 + 0.92430I −11.71672 − 0.79423I
u = −0.428243 − 0.664531I
a = −1.40914 − 1.08956I
b = 0.634044 + 0.520697I
−5.83845 − 0.92430I −11.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = −0.93092 + 1.84591I
b = 0.192218 + 1.006480I
2.05724 − 0.92430I −11.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = 2.36603 − 0.04486I
b = −0.032636 − 1.358240I
2.05724 − 0.92430I −11.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = −2.34802 − 3.62566I
b = −1.051840 + 0.400227I
−5.83845 − 0.92430I −11.71672 + 0.79423I
u = −1.073950 + 0.558752I
a = 0.461962 − 1.241720I
b = 0.48362 + 1.59891I
3.94784 − 5.69302I −8.00000 + 5.51057I
u = −1.073950 + 0.558752I
a = −0.327999 + 0.551063I
b = −1.003490 − 0.857180I
3.94784 − 5.69302I −8.00000 + 5.51057I
u = −1.073950 + 0.558752I
a = −0.370228 + 0.210083I
b = 1.67733 − 0.62104I
−3.94784 − 5.69302I −8.00000 + 5.51057I
u = −1.073950 + 0.558752I
a = 0.01951 + 1.59808I
b = −0.316295 − 1.320830I
−3.94784 − 5.69302I −8.00000 + 5.51057I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.461962 + 1.241720I
b = 0.48362 − 1.59891I
3.94784 + 5.69302I −8.00000 − 5.51057I
u = −1.073950 − 0.558752I
a = −0.327999 − 0.551063I
b = −1.003490 + 0.857180I
3.94784 + 5.69302I −8.00000 − 5.51057I
u = −1.073950 − 0.558752I
a = −0.370228 − 0.210083I
b = 1.67733 + 0.62104I
−3.94784 + 5.69302I −8.00000 − 5.51057I
u = −1.073950 − 0.558752I
a = 0.01951 − 1.59808I
b = −0.316295 + 1.320830I
−3.94784 + 5.69302I −8.00000 − 5.51057I
13
III. I
u
3
= h−17u
10
+ 21u
9
+ · · · + 356b + 71, −617u
10
+ 202u
9
+ · · · + 178a −
1470, u
11
− 3u
9
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
3.46629u
10
− 1.13483u
9
+ ··· − 13.9270u + 8.25843
0.0477528u
10
− 0.0589888u
9
+ ··· + 1.43820u − 0.199438
a
7
=
2.36798u
10
− 0.278090u
9
+ ··· − 9.50562u + 8.34551
−0.00842697u
10
+ 0.216292u
9
+ ··· + 0.893258u + 0.0646067
a
6
=
2.99719u
10
− 0.261236u
9
+ ··· − 10.7022u + 8.68820
−0.0758427u
10
+ 0.446629u
9
+ ··· + 1.53933u + 0.0814607
a
1
=
−0.705056u
10
+ 0.429775u
9
+ ··· + 2.73596u − 1.26124
−0.0365169u
10
+ 0.103933u
9
+ ··· + 0.370787u + 0.446629
a
11
=
3.51404u
10
− 1.19382u
9
+ ··· − 12.4888u + 8.05899
0.0477528u
10
− 0.0589888u
9
+ ··· + 1.43820u − 0.199438
a
5
=
0.637640u
10
− 0.199438u
9
+ ··· − 2.08989u + 1.27809
−0.0674157u
10
+ 0.230337u
9
+ ··· + 0.646067u + 0.0168539
a
2
=
−0.705056u
10
+ 0.429775u
9
+ ··· + 2.73596u − 1.26124
−0.0674157u
10
+ 0.230337u
9
+ ··· + 0.646067u + 0.0168539
a
4
=
u
u
a
10
=
4.17135u
10
− 1.56461u
9
+ ··· − 16.6629u + 10.5197
0.0842697u
10
− 0.162921u
9
+ ··· + 1.06742u − 0.646067
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1809
356
u
10
−
507
356
u
9
−
2437
178
u
8
+
665
178
u
7
+
410
89
u
6
+
8485
356
u
5
+
653
178
u
4
−
2875
178
u
3
+
3149
89
u
2
−
4741
178
u+
2863
356
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 6u
10
+ ··· − 3u − 1
c
2
u
11
+ 4u
10
+ 5u
9
− 2u
8
− 11u
7
− 8u
6
+ 4u
5
+ 8u
4
+ 2u
3
− 2u
2
− u − 1
c
3
u
11
− 3u
9
+ 2u
7
− 5u
6
+ u
5
+ 4u
4
+ 6u
3
+ 2u
2
+ u − 1
c
4
u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
+ 4u
5
− 8u
4
+ 2u
3
+ 2u
2
− u + 1
c
5
, c
11
u
11
+ 3u
9
+ 3u
8
+ 3u
7
+ 6u
6
+ 3u
5
+ 2u
4
+ 2u
3
− 2u
2
− 3u − 1
c
6
, c
12
u
11
− 3u
10
+ 2u
9
+ 2u
8
− 2u
7
+ 3u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
+ 1
c
7
u
11
+ 3u
9
− 3u
8
+ 3u
7
− 6u
6
+ 3u
5
− 2u
4
+ 2u
3
+ 2u
2
− 3u + 1
c
8
u
11
− 3u
9
+ 2u
7
+ 5u
6
+ u
5
− 4u
4
+ 6u
3
− 2u
2
+ u + 1
c
9
u
11
+ 3u
10
+ 2u
9
− 2u
8
− 2u
7
− 3u
6
− 6u
5
− 3u
4
− 3u
3
− 3u
2
− 1
c
10
u
11
− 5u
10
+ ··· − 3u − 9
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 2y
10
+ ··· + 25y − 1
c
2
, c
4
y
11
− 6y
10
+ ··· − 3y − 1
c
3
, c
8
y
11
− 6y
10
+ ··· + 5y − 1
c
5
, c
7
, c
11
y
11
+ 6y
10
+ ··· + 5y − 1
c
6
, c
9
, c
12
y
11
− 5y
10
+ ··· − 6y − 1
c
10
y
11
− 5y
10
+ ··· + 369y − 81
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625397 + 0.494839I
a = 0.438748 − 1.244100I
b = 0.821829 + 0.139209I
−3.46083 + 0.46362I −10.64211 + 0.77158I
u = 0.625397 − 0.494839I
a = 0.438748 + 1.244100I
b = 0.821829 − 0.139209I
−3.46083 − 0.46362I −10.64211 − 0.77158I
u = −0.564447 + 1.125840I
a = −0.247928 + 0.345446I
b = 0.522992 − 0.276078I
−7.82119 − 3.76164I −18.6525 + 4.0849I
u = −0.564447 − 1.125840I
a = −0.247928 − 0.345446I
b = 0.522992 + 0.276078I
−7.82119 + 3.76164I −18.6525 − 4.0849I
u = 0.145041 + 0.670202I
a = 0.32779 + 2.44730I
b = 0.101556 + 1.234860I
2.75970 − 0.49193I −4.46246 − 4.43880I
u = 0.145041 − 0.670202I
a = 0.32779 − 2.44730I
b = 0.101556 − 1.234860I
2.75970 + 0.49193I −4.46246 + 4.43880I
u = −1.50834 + 0.06577I
a = −0.223191 + 1.141650I
b = −0.44883 − 1.38945I
7.91909 + 0.79075I −1.37905 − 0.86737I
u = −1.50834 − 0.06577I
a = −0.223191 − 1.141650I
b = −0.44883 + 1.38945I
7.91909 − 0.79075I −1.37905 + 0.86737I
u = 1.48572 + 0.56088I
a = −0.448099 − 0.943396I
b = −0.619533 + 1.131030I
6.75307 + 5.68255I −2.50294 − 2.90690I
u = 1.48572 − 0.56088I
a = −0.448099 + 0.943396I
b = −0.619533 − 1.131030I
6.75307 − 5.68255I −2.50294 + 2.90690I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366747
a = 17.3054
b = −0.756037
−5.71995 23.2780
18
IV. I
v
1
= ha, b + 2v + 2, 4v
2
+ 6v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
−2v − 2
a
7
=
1
−2v − 3
a
6
=
−2v − 2
−2v − 3
a
1
=
4v + 5
4v + 6
a
11
=
−2v − 2
−2v − 2
a
5
=
−4v − 5
−4v − 6
a
2
=
5v + 5
4v + 6
a
4
=
v
0
a
10
=
4v + 6
6v + 8
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
45
2
v −
183
4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
8
u
2
c
4
(u + 1)
2
c
5
, c
7
, c
10
u
2
+ u − 1
c
6
u
2
− 3u + 1
c
9
, c
12
u
2
+ 3u + 1
c
11
u
2
− u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
8
y
2
c
5
, c
7
, c
10
c
11
y
2
− 3y + 1
c
6
, c
9
, c
12
y
2
− 7y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.30902
a = 0
b = 0.618034
−2.63189 −16.2970
v = −0.190983
a = 0
b = −1.61803
−10.5276 −41.4530
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
4
· (u
11
− 6u
10
+ ··· − 3u − 1)(u
21
+ 11u
20
+ ··· + 2416u + 256)
c
2
(u − 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
4
· (u
11
+ 4u
10
+ 5u
9
− 2u
8
− 11u
7
− 8u
6
+ 4u
5
+ 8u
4
+ 2u
3
− 2u
2
− u − 1)
· (u
21
− 3u
20
+ ··· − 12u + 16)
c
3
u
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
4
· (u
11
− 3u
9
+ 2u
7
− 5u
6
+ u
5
+ 4u
4
+ 6u
3
+ 2u
2
+ u − 1)
· (u
21
+ 5u
20
+ ··· + 528u + 64)
c
4
(u + 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
4
· (u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
+ 4u
5
− 8u
4
+ 2u
3
+ 2u
2
− u + 1)
· (u
21
− 3u
20
+ ··· − 12u + 16)
c
5
(u
2
+ u − 1)
· (u
11
+ 3u
9
+ 3u
8
+ 3u
7
+ 6u
6
+ 3u
5
+ 2u
4
+ 2u
3
− 2u
2
− 3u − 1)
· (u
21
− u
20
+ ··· − 2u + 1)(u
24
+ 3u
23
+ ··· + 418u + 319)
c
6
(u
2
− 3u + 1)
· (u
11
− 3u
10
+ 2u
9
+ 2u
8
− 2u
7
+ 3u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
+ 1)
· (u
21
− 15u
19
+ ··· + 3u − 1)(u
24
− 3u
23
+ ··· − 38u + 181)
c
7
(u
2
+ u − 1)
· (u
11
+ 3u
9
− 3u
8
+ 3u
7
− 6u
6
+ 3u
5
− 2u
4
+ 2u
3
+ 2u
2
− 3u + 1)
· (u
21
− u
20
+ ··· − 2u + 1)(u
24
+ 3u
23
+ ··· + 418u + 319)
c
8
u
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
4
· (u
11
− 3u
9
+ 2u
7
+ 5u
6
+ u
5
− 4u
4
+ 6u
3
− 2u
2
+ u + 1)
· (u
21
+ 5u
20
+ ··· + 528u + 64)
c
9
(u
2
+ 3u + 1)
· (u
11
+ 3u
10
+ 2u
9
− 2u
8
− 2u
7
− 3u
6
− 6u
5
− 3u
4
− 3u
3
− 3u
2
− 1)
· (u
21
− 15u
19
+ ··· + 3u − 1)(u
24
− 3u
23
+ ··· − 38u + 181)
c
10
((u
2
+ u − 1)
13
)(u
11
− 5u
10
+ ··· − 3u − 9)(u
21
− 19u
20
+ ··· + 96u − 64)
c
11
(u
2
− u − 1)
· (u
11
+ 3u
9
+ 3u
8
+ 3u
7
+ 6u
6
+ 3u
5
+ 2u
4
+ 2u
3
− 2u
2
− 3u − 1)
· (u
21
− u
20
+ ··· − 2u + 1)(u
24
+ 3u
23
+ ··· + 418u + 319)
c
12
(u
2
+ 3u + 1)
· (u
11
− 3u
10
+ 2u
9
+ 2u
8
− 2u
7
+ 3u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
+ 1)
· (u
21
− 15u
19
+ ··· + 3u − 1)(u
24
− 3u
23
+ ··· − 38u + 181)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
6
+ y
5
+ ··· + 3y + 1)
4
(y
11
+ 2y
10
+ ··· + 25y − 1)
· (y
21
+ y
20
+ ··· − 37120y − 65536)
c
2
, c
4
(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
4
· (y
11
− 6y
10
+ ··· − 3y − 1)(y
21
− 11y
20
+ ··· + 2416y − 256)
c
3
, c
8
y
2
(y
6
− 3y
5
+ ··· − y + 1)
4
(y
11
− 6y
10
+ ··· + 5y − 1)
· (y
21
− 9y
20
+ ··· + 54016y − 4096)
c
5
, c
7
, c
11
(y
2
− 3y + 1)(y
11
+ 6y
10
+ ··· + 5y − 1)(y
21
+ 13y
20
+ ··· + 46y
2
− 1)
· (y
24
+ 11y
23
+ ··· + 621500y + 101761)
c
6
, c
9
, c
12
(y
2
− 7y + 1)(y
11
− 5y
10
+ ··· − 6y − 1)(y
21
− 30y
20
+ ··· + 41y − 1)
· (y
24
− 13y
23
+ ··· − 152760y + 32761)
c
10
((y
2
− 3y + 1)
13
)(y
11
− 5y
10
+ ··· + 369y − 81)
· (y
21
− 11y
20
+ ··· + 115712y − 4096)
24
