12n
0266
(K12n
0266
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 1 12 3 7 6 8 10
Solving Sequence
3,8 9,12
7 10 1 6 11 5 2 4
c
8
c
7
c
9
c
12
c
6
c
11
c
5
c
2
c
4
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.30470 × 10
57
u
29
− 8.04261 × 10
57
u
28
+ ··· + 3.78260 × 10
57
b − 1.44716 × 10
60
,
1.67303 × 10
56
u
29
− 2.36382 × 10
57
u
28
+ ··· + 3.02608 × 10
58
a − 1.98438 × 10
60
,
u
30
− 7u
29
+ ··· − 8960u + 1024i
I
u
2
= h85a
5
u
3
+ 81a
4
u
3
+ ··· − 914a − 116, 4a
5
u
3
+ 36a
4
u
3
+ ··· + 70a − 27, u
4
+ 3u
3
+ 3u
2
+ 2u + 2i
I
u
3
= h4147258u
15
+ 7664206u
14
+ ··· + 53503381b + 7608876,
− 151936201u
15
+ 44795175u
14
+ ··· + 53503381a − 367339747,
u
16
− 3u
14
− 4u
12
+ 5u
11
+ 23u
10
− 7u
9
− 13u
8
+ 6u
7
− 11u
6
− 12u
5
+ 13u
4
− 4u
3
+ 5u
2
+ u + 1i
I
u
4
= h9.10023 × 10
19
a
11
u + 1.90099 × 10
20
a
10
u + ··· + 3.63923 × 10
20
a + 7.09845 × 10
19
,
− a
11
u − 29a
10
u + ··· − 3954a + 1387, u
2
− u − 1i
I
v
1
= ha, 8v
3
+ 12v
2
+ b + 10v + 3, 8v
4
+ 12v
3
+ 12v
2
+ 5v + 1i
I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 104 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
=
h1.30×10
57
u
29
−8.04×10
57
u
28
+· · ·+3.78×10
57
b−1.45×10
60
, 1.67×10
56
u
29
−
2.36×10
57
u
28
+· · ·+3.03×10
58
a−1.98×10
60
, u
30
−7u
29
+· · ·−8960u+1024i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
−0.00552871u
29
+ 0.0781148u
28
+ ··· − 455.718u + 65.5759
−0.344921u
29
+ 2.12621u
28
+ ··· − 3000.66u + 382.582
a
7
=
−0.0965905u
29
+ 0.626567u
28
+ ··· − 1195.73u + 163.169
0.437196u
29
− 2.77353u
28
+ ··· + 5006.91u − 693.942
a
10
=
−0.199941u
29
+ 1.25377u
28
+ ··· − 2078.67u + 283.434
0.126079u
29
− 0.746114u
28
+ ··· + 510.964u − 30.8012
a
1
=
−0.237653u
29
+ 1.50770u
28
+ ··· − 2693.25u + 371.955
−0.0793898u
29
+ 0.480636u
28
+ ··· − 898.423u + 142.638
a
6
=
−0.393468u
29
+ 2.51203u
28
+ ··· − 4452.78u + 601.479
−0.252406u
29
+ 1.63090u
28
+ ··· − 2955.26u + 391.693
a
11
=
−0.350450u
29
+ 2.20433u
28
+ ··· − 3456.38u + 448.158
−0.344921u
29
+ 2.12621u
28
+ ··· − 3000.66u + 382.582
a
5
=
−0.0528628u
29
+ 0.365076u
28
+ ··· − 641.595u + 69.7063
0.184790u
29
− 1.14262u
28
+ ··· + 2051.66u − 302.249
a
2
=
−0.237653u
29
+ 1.50770u
28
+ ··· − 2693.25u + 371.955
−0.184790u
29
+ 1.14262u
28
+ ··· − 2051.66u + 302.249
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.780219u
29
+ 4.90701u
28
+ ··· − 10318.3u + 1584.28
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 15u
29
+ ··· + 5376u + 4096
c
2
, c
4
u
30
− 5u
29
+ ··· − 144u + 64
c
3
, c
8
u
30
+ 7u
29
+ ··· + 8960u + 1024
c
5
, c
7
, c
10
c
11
u
30
+ 16u
28
+ ··· − 4u + 1
c
6
, c
9
u
30
+ u
29
+ ··· − 3u + 1
c
12
u
30
+ 25u
29
+ ··· + 4224u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 5y
29
+ ··· + 918224896y + 16777216
c
2
, c
4
y
30
− 15y
29
+ ··· − 5376y + 4096
c
3
, c
8
y
30
− 15y
29
+ ··· − 7667712y + 1048576
c
5
, c
7
, c
10
c
11
y
30
+ 32y
29
+ ··· − 14y + 1
c
6
, c
9
y
30
− 13y
29
+ ··· + 5y + 1
c
12
y
30
+ 7y
29
+ ··· + 180224y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295304 + 0.827577I
a = 0.432685 + 0.180516I
b = 0.502251 − 0.079193I
−1.52614 − 1.54845I −7.05353 + 2.25516I
u = 0.295304 − 0.827577I
a = 0.432685 − 0.180516I
b = 0.502251 + 0.079193I
−1.52614 + 1.54845I −7.05353 − 2.25516I
u = −1.118510 + 0.267682I
a = 0.344821 + 0.251878I
b = −0.488387 − 0.036524I
2.84106 − 1.32814I −1.11844 − 2.01669I
u = −1.118510 − 0.267682I
a = 0.344821 − 0.251878I
b = −0.488387 + 0.036524I
2.84106 + 1.32814I −1.11844 + 2.01669I
u = 0.790526 + 0.025536I
a = 0.369046 + 0.400347I
b = 0.758312 − 0.591430I
−1.67774 + 2.21849I −1.35323 − 5.31460I
u = 0.790526 − 0.025536I
a = 0.369046 − 0.400347I
b = 0.758312 + 0.591430I
−1.67774 − 2.21849I −1.35323 + 5.31460I
u = 1.150710 + 0.487372I
a = 0.146682 − 0.393834I
b = −0.578991 + 0.126474I
1.25283 + 6.44217I −7.35418 − 5.48188I
u = 1.150710 − 0.487372I
a = 0.146682 + 0.393834I
b = −0.578991 − 0.126474I
1.25283 − 6.44217I −7.35418 + 5.48188I
u = 0.587875 + 0.294150I
a = 1.49596 − 0.54450I
b = −0.410397 − 0.248863I
−2.33932 − 0.29501I −4.95113 − 2.59003I
u = 0.587875 − 0.294150I
a = 1.49596 + 0.54450I
b = −0.410397 + 0.248863I
−2.33932 + 0.29501I −4.95113 + 2.59003I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.281814 + 0.580917I
a = 0.633016 − 0.523942I
b = 0.265637 + 0.486839I
−0.114599 − 1.183600I −1.52357 + 6.11116I
u = −0.281814 − 0.580917I
a = 0.633016 + 0.523942I
b = 0.265637 − 0.486839I
−0.114599 + 1.183600I −1.52357 − 6.11116I
u = 0.581579 + 0.213573I
a = −0.181652 − 0.352155I
b = −0.562214 + 1.036190I
1.23856 + 8.05442I 5.2311 − 14.4328I
u = 0.581579 − 0.213573I
a = −0.181652 + 0.352155I
b = −0.562214 − 1.036190I
1.23856 − 8.05442I 5.2311 + 14.4328I
u = −0.21710 + 1.53848I
a = 0.204399 + 0.699894I
b = 0.241334 − 0.976861I
−5.66421 + 0.94543I −11.8910 − 17.8120I
u = −0.21710 − 1.53848I
a = 0.204399 − 0.699894I
b = 0.241334 + 0.976861I
−5.66421 − 0.94543I −11.8910 + 17.8120I
u = 0.05187 + 1.70653I
a = −0.098466 + 0.394900I
b = −0.28890 − 1.53476I
7.74868 − 8.57967I 0
u = 0.05187 − 1.70653I
a = −0.098466 − 0.394900I
b = −0.28890 + 1.53476I
7.74868 + 8.57967I 0
u = 1.69998 + 0.25374I
a = −0.298306 − 1.350070I
b = 0.15069 + 1.46462I
5.39652 − 5.08088I 0
u = 1.69998 − 0.25374I
a = −0.298306 + 1.350070I
b = 0.15069 − 1.46462I
5.39652 + 5.08088I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61078 + 0.80572I
a = 0.68358 + 1.24119I
b = 0.61201 − 1.60557I
12.5033 + 17.2116I 0
u = 1.61078 − 0.80572I
a = 0.68358 − 1.24119I
b = 0.61201 + 1.60557I
12.5033 − 17.2116I 0
u = 0.47534 + 1.81581I
a = −0.048480 − 0.458166I
b = 0.00271 + 1.46604I
7.03462 + 1.24559I 0
u = 0.47534 − 1.81581I
a = −0.048480 + 0.458166I
b = 0.00271 − 1.46604I
7.03462 − 1.24559I 0
u = −1.87027 + 0.50681I
a = 0.337792 − 1.250370I
b = 0.45821 + 1.67495I
14.6658 − 9.7485I 0
u = −1.87027 − 0.50681I
a = 0.337792 + 1.250370I
b = 0.45821 − 1.67495I
14.6658 + 9.7485I 0
u = 1.69641 + 0.95826I
a = −0.604731 − 1.038330I
b = −0.42883 + 1.37214I
10.87200 + 8.65298I 0
u = 1.69641 − 0.95826I
a = −0.604731 + 1.038330I
b = −0.42883 − 1.37214I
10.87200 − 8.65298I 0
u = −1.95267 + 0.75510I
a = −0.416349 + 1.035550I
b = −0.23344 − 1.52553I
13.56600 − 0.76045I 0
u = −1.95267 − 0.75510I
a = −0.416349 − 1.035550I
b = −0.23344 + 1.52553I
13.56600 + 0.76045I 0
7
II. I
u
2
= h85a
5
u
3
+ 81a
4
u
3
+ · · · − 914a − 116, 4a
5
u
3
+ 36a
4
u
3
+ · · · + 70a −
27, u
4
+ 3u
3
+ 3u
2
+ 2u + 2i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
a
−0.702479a
5
u
3
− 0.669421a
4
u
3
+ ··· + 7.55372a + 0.958678
a
7
=
0.305785a
5
u
3
− 0.876033a
4
u
3
+ ··· + 1.58678a + 0.314050
0.834711a
5
u
3
+ 2.74380a
4
u
3
+ ··· − 8.47934a − 1.75207
a
10
=
0.239669a
4
u
3
− 0.909091a
3
u
3
+ ··· − 0.727273a + 1.32231
1.05785a
4
u
3
+ 1.54545a
3
u
3
+ ··· + 5.63636a + 0.595041
a
1
=
−
1
2
u
3
−
1
2
u
2
−
1
2
u − 1
u
3
+ 2u
2
+ u + 1
a
6
=
0.0826446a
5
u
3
+ 0.628099a
4
u
3
+ ··· − 5.76033a − 1.30579
−0.975207a
5
u
3
− 0.611570a
4
u
3
+ ··· − 4.62810a + 1.55372
a
11
=
−0.702479a
5
u
3
− 0.669421a
4
u
3
+ ··· + 8.55372a + 0.958678
−0.702479a
5
u
3
− 0.669421a
4
u
3
+ ··· + 7.55372a + 0.958678
a
5
=
1
2
u
3
+
1
2
u
2
−
1
2
u
u
3
+ u
2
+ 1
a
2
=
−
1
2
u
3
−
1
2
u
2
−
1
2
u − 1
−u
3
− u
2
− 1
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
148
121
a
4
u
3
+
28
11
a
3
u
3
+ ··· −
136
11
a +
68
121
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 4u
2
+ u + 1)
6
c
2
, c
4
(u
4
− u
3
+ u + 1)
6
c
3
, c
8
(u
4
− 3u
3
+ 3u
2
− 2u + 2)
6
c
5
, c
7
, c
10
c
11
u
24
+ u
23
+ ··· − 6u + 23
c
6
, c
9
u
24
+ 3u
23
+ ··· + 82u + 67
c
12
(u
3
− u
2
+ 1)
8
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 7y
3
+ 16y
2
+ 7y + 1)
6
c
2
, c
4
(y
4
− y
3
+ 4y
2
− y + 1)
6
c
3
, c
8
(y
4
− 3y
3
+ y
2
+ 8y + 4)
6
c
5
, c
7
, c
10
c
11
y
24
+ 21y
23
+ ··· + 24252y + 529
c
6
, c
9
y
24
− 7y
23
+ ··· − 56036y + 4489
c
12
(y
3
− y
2
+ 2y − 1)
8
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066121 + 0.864054I
a = 0.847489 − 0.409743I
b = 0.435029 + 1.039690I
1.24998 − 1.37790I −0.06985 − 1.74429I
u = 0.066121 + 0.864054I
a = −0.066440 + 1.227610I
b = 0.219486 − 1.053480I
1.24998 + 4.27835I −0.06985 − 7.70319I
u = 0.066121 + 0.864054I
a = −0.685301 + 1.029190I
b = −0.34890 + 1.62773I
5.38756 + 1.45022I 6.45941 − 4.72374I
u = 0.066121 + 0.864054I
a = 1.56525 − 0.14261I
b = 0.026299 − 1.366270I
5.38756 + 1.45022I 6.45941 − 4.72374I
u = 0.066121 + 0.864054I
a = 1.51833 − 1.27411I
b = 0.042954 − 0.201002I
1.24998 − 1.37790I −0.06985 − 1.74429I
u = 0.066121 + 0.864054I
a = −1.63512 + 1.12550I
b = −0.940992 + 0.412160I
1.24998 + 4.27835I −0.06985 − 7.70319I
u = 0.066121 − 0.864054I
a = 0.847489 + 0.409743I
b = 0.435029 − 1.039690I
1.24998 + 1.37790I −0.06985 + 1.74429I
u = 0.066121 − 0.864054I
a = −0.066440 − 1.227610I
b = 0.219486 + 1.053480I
1.24998 − 4.27835I −0.06985 + 7.70319I
u = 0.066121 − 0.864054I
a = −0.685301 − 1.029190I
b = −0.34890 − 1.62773I
5.38756 − 1.45022I 6.45941 + 4.72374I
u = 0.066121 − 0.864054I
a = 1.56525 + 0.14261I
b = 0.026299 + 1.366270I
5.38756 − 1.45022I 6.45941 + 4.72374I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066121 − 0.864054I
a = 1.51833 + 1.27411I
b = 0.042954 + 0.201002I
1.24998 + 1.37790I −0.06985 + 1.74429I
u = 0.066121 − 0.864054I
a = −1.63512 − 1.12550I
b = −0.940992 − 0.412160I
1.24998 − 4.27835I −0.06985 + 7.70319I
u = −1.56612 + 0.45882I
a = 0.446198 − 1.247430I
b = 0.95639 + 1.77228I
10.82130 − 6.78371I 7.57961 + 4.72374I
u = −1.56612 + 0.45882I
a = 0.352386 − 1.325540I
b = −0.05667 + 1.51321I
6.68371 − 3.95559I 1.05034 + 1.74429I
u = −1.56612 + 0.45882I
a = −1.04122 + 1.11468I
b = −0.348867 − 1.279900I
10.82130 − 6.78371I 7.57961 + 4.72374I
u = −1.56612 + 0.45882I
a = −0.123141 − 0.393851I
b = 1.61223 + 0.24522I
6.68371 − 9.61184I 1.05034 + 7.70319I
u = −1.56612 + 0.45882I
a = −0.272467 − 0.089477I
b = −0.843469 + 0.066206I
6.68371 − 3.95559I 1.05034 + 1.74429I
u = −1.56612 + 0.45882I
a = −0.40595 + 1.70866I
b = −0.25349 − 1.45295I
6.68371 − 9.61184I 1.05034 + 7.70319I
u = −1.56612 − 0.45882I
a = 0.446198 + 1.247430I
b = 0.95639 − 1.77228I
10.82130 + 6.78371I 7.57961 − 4.72374I
u = −1.56612 − 0.45882I
a = 0.352386 + 1.325540I
b = −0.05667 − 1.51321I
6.68371 + 3.95559I 1.05034 − 1.74429I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56612 − 0.45882I
a = −1.04122 − 1.11468I
b = −0.348867 + 1.279900I
10.82130 + 6.78371I 7.57961 − 4.72374I
u = −1.56612 − 0.45882I
a = −0.123141 + 0.393851I
b = 1.61223 − 0.24522I
6.68371 + 9.61184I 1.05034 − 7.70319I
u = −1.56612 − 0.45882I
a = −0.272467 + 0.089477I
b = −0.843469 − 0.066206I
6.68371 + 3.95559I 1.05034 − 1.74429I
u = −1.56612 − 0.45882I
a = −0.40595 − 1.70866I
b = −0.25349 + 1.45295I
6.68371 + 9.61184I 1.05034 − 7.70319I
13
III.
I
u
3
= h4.15 × 10
6
u
15
+ 7.66 × 10
6
u
14
+ · · · + 5.35 × 10
7
b + 7.61 × 10
6
, −1.52 ×
10
8
u
15
+ 4.48 × 10
7
u
14
+ · · · + 5.35 × 10
7
a − 3.67 × 10
8
, u
16
− 3u
14
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
2.83975u
15
− 0.837240u
14
+ ··· + 10.0880u + 6.86573
−0.0775139u
15
− 0.143247u
14
+ ··· + 1.48032u − 0.142213
a
7
=
1.46611u
15
+ 0.555277u
14
+ ··· − 7.60428u + 7.02320
0.342955u
15
− 0.0913471u
14
+ ··· + 0.412915u − 0.146361
a
10
=
2.10671u
15
+ 1.02973u
14
+ ··· + 1.90799u + 11.0945
0.202635u
15
+ 0.190332u
14
+ ··· + 2.50674u + 0.600158
a
1
=
−0.478951u
15
+ 0.274850u
14
+ ··· − 3.19806u − 1.01076
0.134911u
15
+ 0.189098u
14
+ ··· + 0.316322u + 0.253088
a
6
=
2.43159u
15
+ 0.321717u
14
+ ··· − 3.47288u + 6.86583
0.486533u
15
+ 0.0412901u
14
+ ··· + 0.933338u − 0.168123
a
11
=
2.76224u
15
− 0.980487u
14
+ ··· + 11.5683u + 6.72352
−0.0775139u
15
− 0.143247u
14
+ ··· + 1.48032u − 0.142213
a
5
=
0.622529u
15
− 0.142213u
14
+ ··· + 3.71848u + 0.988996
0.143578u
15
+ 0.132637u
14
+ ··· + 0.520422u − 0.0217622
a
2
=
−0.478951u
15
+ 0.274850u
14
+ ··· − 3.19806u − 1.01076
0.143578u
15
+ 0.132637u
14
+ ··· + 0.520422u − 0.0217622
a
4
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
119862154
53503381
u
15
−
50233104
53503381
u
14
+ ··· +
2012450980
53503381
u −
93776732
53503381
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 7u + 1
c
2
u
16
+ 6u
15
+ ··· − u + 1
c
3
u
16
− 3u
14
+ ··· − u + 1
c
4
u
16
− 6u
15
+ ··· + u + 1
c
5
, c
11
u
16
+ 8u
14
+ ··· + 3u + 1
c
6
, c
9
u
16
− 3u
15
+ ··· − 6u + 1
c
7
, c
10
u
16
+ 8u
14
+ ··· − 3u + 1
c
8
u
16
− 3u
14
+ ··· + u + 1
c
12
u
16
− 5u
15
+ ··· − 5u
3
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 2y
15
+ ··· + 61y + 1
c
2
, c
4
y
16
− 10y
15
+ ··· − 7y + 1
c
3
, c
8
y
16
− 6y
15
+ ··· + 9y + 1
c
5
, c
7
, c
10
c
11
y
16
+ 16y
15
+ ··· + 11y + 1
c
6
, c
9
y
16
− 5y
15
+ ··· − 14y + 1
c
12
y
16
+ 9y
15
+ ··· + 10y
2
+ 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978949 + 0.078957I
a = −0.453108 − 0.320975I
b = 0.445295 − 0.521652I
3.29193 + 2.08322I 4.28264 − 4.24407I
u = 0.978949 − 0.078957I
a = −0.453108 + 0.320975I
b = 0.445295 + 0.521652I
3.29193 − 2.08322I 4.28264 + 4.24407I
u = −0.996285 + 0.490791I
a = −0.353672 − 0.270556I
b = 0.279505 + 0.496867I
1.92823 − 6.43556I 5.05003 + 5.97847I
u = −0.996285 − 0.490791I
a = −0.353672 + 0.270556I
b = 0.279505 − 0.496867I
1.92823 + 6.43556I 5.05003 − 5.97847I
u = 0.196535 + 0.775710I
a = −0.14260 + 1.75182I
b = 0.08961 + 1.47734I
4.79804 − 0.70603I 0.45722 − 4.37222I
u = 0.196535 − 0.775710I
a = −0.14260 − 1.75182I
b = 0.08961 − 1.47734I
4.79804 + 0.70603I 0.45722 + 4.37222I
u = 0.172282 + 0.628783I
a = 2.18279 − 0.75635I
b = 0.405160 + 0.782797I
1.56983 − 2.39298I 2.54235 + 6.16314I
u = 0.172282 − 0.628783I
a = 2.18279 + 0.75635I
b = 0.405160 − 0.782797I
1.56983 + 2.39298I 2.54235 − 6.16314I
u = −0.206080 + 0.337926I
a = 10.45890 + 6.32490I
b = −0.380479 + 0.681918I
0.32266 + 2.98693I −4.4966 + 17.7278I
u = −0.206080 − 0.337926I
a = 10.45890 − 6.32490I
b = −0.380479 − 0.681918I
0.32266 − 2.98693I −4.4966 − 17.7278I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61349 + 0.06231I
a = −0.307309 + 1.257690I
b = −0.43055 − 1.58967I
10.48480 + 0.24679I 0.73600 − 1.75528I
u = −1.61349 − 0.06231I
a = −0.307309 − 1.257690I
b = −0.43055 + 1.58967I
10.48480 − 0.24679I 0.73600 + 1.75528I
u = −0.13825 + 1.62727I
a = 0.254873 + 0.700959I
b = 0.192282 − 1.004160I
−5.54863 + 0.76161I 8.2609 + 13.1613I
u = −0.13825 − 1.62727I
a = 0.254873 − 0.700959I
b = 0.192282 + 1.004160I
−5.54863 − 0.76161I 8.2609 − 13.1613I
u = 1.60635 + 0.50423I
a = −0.639909 − 1.085690I
b = −0.60082 + 1.36455I
9.47206 + 6.62853I 0.16748 − 3.62136I
u = 1.60635 − 0.50423I
a = −0.639909 + 1.085690I
b = −0.60082 − 1.36455I
9.47206 − 6.62853I 0.16748 + 3.62136I
18
IV. I
u
4
= h9.10 × 10
19
a
11
u + 1.90 × 10
20
a
10
u + · · · + 3.64 × 10
20
a + 7.10 ×
10
19
, −a
11
u − 29a
10
u + · · · − 3954a + 1387, u
2
− u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u − 1
a
12
=
a
−1.56829a
11
u − 3.27608a
10
u + ··· − 6.27166a − 1.22331
a
7
=
−0.460239a
11
u − 1.23068a
10
u + ··· − 5.15203a + 1.64031
2.83175a
11
u + 6.50769a
10
u + ··· + 17.3200a + 1.87860
a
10
=
−0.837001a
11
u − 1.69786a
10
u + ··· − 2.77220a − 2.20499
−1.53854a
11
u − 3.00157a
10
u + ··· − 9.06731a − 1.48673
a
1
=
1.83049a
11
u + 3.69414a
10
u + ··· + 10.1122a + 0.883061
−1.83049a
11
u − 3.69414a
10
u + ··· − 10.1122a − 1.88306
a
6
=
2.59830a
11
u + 5.43442a
10
u + ··· + 10.6594a + 4.31367
−0.401435a
11
u − 0.287843a
10
u + ··· − 1.58392a + 2.69916
a
11
=
−1.56829a
11
u − 3.27608a
10
u + ··· − 5.27166a − 1.22331
−1.56829a
11
u − 3.27608a
10
u + ··· − 6.27166a − 1.22331
a
5
=
−1.13131a
11
u − 2.28310a
10
u + ··· − 6.25174a − 0.296436
−2.96180a
11
u − 5.97724a
10
u + ··· − 16.3639a − 1.17950
a
2
=
1.83049a
11
u + 3.69414a
10
u + ··· + 10.1122a + 0.883061
2.96180a
11
u + 5.97724a
10
u + ··· + 16.3639a + 1.17950
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
460629544778988
234092030786251
a
11
u +
789216386414344
234092030786251
a
10
u + ··· −
2682835470744820
234092030786251
a +
2366946904870098
234092030786251
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 2u
2
+ 4u + 1)
6
c
2
, c
4
(u
4
− u
3
+ 2u − 1)
6
c
3
, c
8
(u
2
+ u − 1)
12
c
5
, c
7
, c
10
c
11
u
24
+ u
23
+ ··· − 30u + 59
c
6
, c
9
u
24
+ 3u
23
+ ··· + 226u + 59
c
12
(u
3
− u
2
+ 1)
8
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 3y
3
− 2y
2
− 12y + 1)
6
c
2
, c
4
(y
4
− y
3
+ 2y
2
− 4y + 1)
6
c
3
, c
8
(y
2
− 3y + 1)
12
c
5
, c
7
, c
10
c
11
y
24
+ 21y
23
+ ··· − 1844y + 3481
c
6
, c
9
y
24
− 7y
23
+ ··· − 22992y + 3481
c
12
(y
3
− y
2
+ 2y − 1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.150728 + 0.935298I
b = −0.837750 − 0.491196I
−0.39223 + 2.82812I 2.49024 − 2.97945I
u = −0.618034
a = −0.150728 − 0.935298I
b = −0.837750 + 0.491196I
−0.39223 − 2.82812I 2.49024 + 2.97945I
u = −0.618034
a = 0.423709 + 0.723737I
b = 0.589608 − 1.016880I
−0.39223 + 2.82812I 2.49024 − 2.97945I
u = −0.618034
a = 0.423709 − 0.723737I
b = 0.589608 + 1.016880I
−0.39223 − 2.82812I 2.49024 + 2.97945I
u = −0.618034
a = 0.361623 + 0.378726I
b = −0.328718 + 0.941057I
3.74535 9.01951 + 0.I
u = −0.618034
a = 0.361623 − 0.378726I
b = −0.328718 − 0.941057I
3.74535 9.01951 + 0.I
u = −0.618034
a = −2.38323 + 1.43737I
b = 0.492907 + 0.249410I
−0.39223 − 2.82812I 2.49024 + 2.97945I
u = −0.618034
a = −2.38323 − 1.43737I
b = 0.492907 − 0.249410I
−0.39223 + 2.82812I 2.49024 − 2.97945I
u = −0.618034
a = −1.67739 + 5.70634I
b = 0.15263 − 1.41932I
3.74535 9.01951 + 0.I
u = −0.618034
a = −1.67739 − 5.70634I
b = 0.15263 + 1.41932I
3.74535 9.01951 + 0.I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.11700 + 6.25809I
b = −0.377692 − 0.949629I
−0.39223 − 2.82812I 0
u = −0.618034
a = 1.11700 − 6.25809I
b = −0.377692 + 0.949629I
−0.39223 + 2.82812I 0
u = 1.61803
a = −0.047191 + 1.301750I
b = 0.73365 − 1.98613I
11.6410 9.01951 + 0.I
u = 1.61803
a = −0.047191 − 1.301750I
b = 0.73365 + 1.98613I
11.6410 9.01951 + 0.I
u = 1.61803
a = −0.07600 + 1.43046I
b = −0.37139 − 1.51467I
7.50345 − 2.82812I 2.49024 + 2.97945I
u = 1.61803
a = −0.07600 − 1.43046I
b = −0.37139 + 1.51467I
7.50345 + 2.82812I 2.49024 − 2.97945I
u = 1.61803
a = −0.483052 + 0.076488I
b = −0.737687 + 0.246052I
7.50345 − 2.82812I 2.49024 + 2.97945I
u = 1.61803
a = −0.483052 − 0.076488I
b = −0.737687 − 0.246052I
7.50345 + 2.82812I 2.49024 − 2.97945I
u = 1.61803
a = −0.63148 + 1.43380I
b = −0.27264 − 1.42678I
11.6410 9.01951 + 0.I
u = 1.61803
a = −0.63148 − 1.43380I
b = −0.27264 + 1.42678I
11.6410 9.01951 + 0.I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61803
a = −0.165330 + 0.160935I
b = 1.52448 − 0.54039I
7.50345 + 2.82812I 2.49024 − 2.97945I
u = 1.61803
a = −0.165330 − 0.160935I
b = 1.52448 + 0.54039I
7.50345 − 2.82812I 2.49024 + 2.97945I
u = 1.61803
a = 0.21207 + 1.76756I
b = −0.067397 − 1.386770I
7.50345 − 2.82812I 2.49024 + 2.97945I
u = 1.61803
a = 0.21207 − 1.76756I
b = −0.067397 + 1.386770I
7.50345 + 2.82812I 2.49024 − 2.97945I
24
V. I
v
1
= ha, 8v
3
+ 12v
2
+ b + 10v + 3, 8v
4
+ 12v
3
+ 12v
2
+ 5v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
−8v
3
− 12v
2
− 10v − 3
a
7
=
1
−8v
3
− 8v
2
− 8v − 1
a
10
=
8v
3
+ 8v
2
+ 8v + 2
16v
3
+ 20v
2
+ 18v + 5
a
1
=
8v
3
+ 12v
2
+ 12v + 4
8v
3
+ 12v
2
+ 12v + 5
a
6
=
−4v
2
− 4v − 3
−4v
2
− 4v − 4
a
11
=
−8v
3
− 12v
2
− 10v − 3
−8v
3
− 12v
2
− 10v − 3
a
5
=
−8v
3
− 12v
2
− 12v − 4
−8v
3
− 12v
2
− 12v − 5
a
2
=
8v
3
+ 12v
2
+ 13v + 4
8v
3
+ 12v
2
+ 12v + 5
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8v
3
− 5v
2
− 3
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
− u + 1
c
6
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
u
4
− 2u
3
+ 3u
2
− u + 1
c
10
, c
11
u
4
+ u
2
+ u + 1
c
12
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
9
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
12
y
4
− y
3
+ 2y
2
+ 7y + 4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.447562 + 0.776246I
a = 0
b = 0.547424 + 0.585652I
−2.62503 − 1.39709I −6.74392 + 3.48426I
v = −0.447562 − 0.776246I
a = 0
b = 0.547424 − 0.585652I
−2.62503 + 1.39709I −6.74392 − 3.48426I
v = −0.302438 + 0.253422I
a = 0
b = −0.547424 − 1.120870I
0.98010 − 7.64338I −3.38108 + 0.34032I
v = −0.302438 − 0.253422I
a = 0
b = −0.547424 + 1.120870I
0.98010 + 7.64338I −3.38108 − 0.34032I
28
VI. I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
b
a
7
=
1
−b
2
a
10
=
b
2
+ 1
−b
4
a
1
=
b
5
+ 2b
3
+ b
−1
a
6
=
−2b
5
− 3b
3
− b
2
− 2b − 1
−b
5
− b
3
− b
2
− b
a
11
=
b
b
a
5
=
−b
5
− 2b
3
− b
1
a
2
=
b
5
+ 2b
3
+ b + 1
−1
a
4
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
3
+ 4b − 4
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
10
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
12
(u
3
− u
2
+ 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
9
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
12
(y
3
− y
2
+ 2y − 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.498832 + 1.001300I
−1.37919 − 2.82812I −7.50976 + 2.97945I
v = 1.00000
a = 0
b = 0.498832 − 1.001300I
−1.37919 + 2.82812I −7.50976 − 2.97945I
v = 1.00000
a = 0
b = −0.284920 + 1.115140I
2.75839 −6 − 0.980489 + 0.10I
v = 1.00000
a = 0
b = −0.284920 − 1.115140I
2.75839 −6 − 0.980489 + 0.10I
v = 1.00000
a = 0
b = −0.713912 + 0.305839I
−1.37919 − 2.82812I −7.50976 + 2.97945I
v = 1.00000
a = 0
b = −0.713912 − 0.305839I
−1.37919 + 2.82812I −7.50976 − 2.97945I
32
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
4
+ u
3
+ 2u
2
+ 4u + 1)
6
(u
4
+ u
3
+ 4u
2
+ u + 1)
6
· (u
16
− 10u
15
+ ··· − 7u + 1)(u
30
+ 15u
29
+ ··· + 5376u + 4096)
c
2
(u − 1)
10
(u
4
− u
3
+ u + 1)
6
(u
4
− u
3
+ 2u − 1)
6
· (u
16
+ 6u
15
+ ··· − u + 1)(u
30
− 5u
29
+ ··· − 144u + 64)
c
3
u
10
(u
2
+ u − 1)
12
(u
4
− 3u
3
+ ··· − 2u + 2)
6
(u
16
− 3u
14
+ ··· − u + 1)
· (u
30
+ 7u
29
+ ··· + 8960u + 1024)
c
4
(u + 1)
10
(u
4
− u
3
+ u + 1)
6
(u
4
− u
3
+ 2u − 1)
6
· (u
16
− 6u
15
+ ··· + u + 1)(u
30
− 5u
29
+ ··· − 144u + 64)
c
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
16
+ 8u
14
+ ··· + 3u + 1)(u
24
+ u
23
+ ··· − 30u + 59)
· (u
24
+ u
23
+ ··· − 6u + 23)(u
30
+ 16u
28
+ ··· − 4u + 1)
c
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
16
− 3u
15
+ ··· − 6u + 1)(u
24
+ 3u
23
+ ··· + 226u + 59)
· (u
24
+ 3u
23
+ ··· + 82u + 67)(u
30
+ u
29
+ ··· − 3u + 1)
c
7
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
16
+ 8u
14
+ ··· − 3u + 1)(u
24
+ u
23
+ ··· − 30u + 59)
· (u
24
+ u
23
+ ··· − 6u + 23)(u
30
+ 16u
28
+ ··· − 4u + 1)
c
8
u
10
(u
2
+ u − 1)
12
(u
4
− 3u
3
+ ··· − 2u + 2)
6
(u
16
− 3u
14
+ ··· + u + 1)
· (u
30
+ 7u
29
+ ··· + 8960u + 1024)
c
9
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
16
− 3u
15
+ ··· − 6u + 1)(u
24
+ 3u
23
+ ··· + 226u + 59)
· (u
24
+ 3u
23
+ ··· + 82u + 67)(u
30
+ u
29
+ ··· − 3u + 1)
c
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
16
+ 8u
14
+ ··· − 3u + 1)(u
24
+ u
23
+ ··· − 30u + 59)
· (u
24
+ u
23
+ ··· − 6u + 23)(u
30
+ 16u
28
+ ··· − 4u + 1)
c
11
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
16
+ 8u
14
+ ··· + 3u + 1)(u
24
+ u
23
+ ··· − 30u + 59)
· (u
24
+ u
23
+ ··· − 6u + 23)(u
30
+ 16u
28
+ ··· − 4u + 1)
c
12
((u
3
− u
2
+ 1)
18
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
16
− 5u
15
+ ··· − 5u
3
+ 1)
· (u
30
+ 25u
29
+ ··· + 4224u + 256)
33
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
4
+ 3y
3
− 2y
2
− 12y + 1)
6
(y
4
+ 7y
3
+ 16y
2
+ 7y + 1)
6
· (y
16
− 2y
15
+ ··· + 61y + 1)
· (y
30
+ 5y
29
+ ··· + 918224896y + 16777216)
c
2
, c
4
(y − 1)
10
(y
4
− y
3
+ 2y
2
− 4y + 1)
6
(y
4
− y
3
+ 4y
2
− y + 1)
6
· (y
16
− 10y
15
+ ··· − 7y + 1)(y
30
− 15y
29
+ ··· − 5376y + 4096)
c
3
, c
8
y
10
(y
2
− 3y + 1)
12
(y
4
− 3y
3
+ ··· + 8y + 4)
6
(y
16
− 6y
15
+ ··· + 9y + 1)
· (y
30
− 15y
29
+ ··· − 7667712y + 1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
16
+ 16y
15
+ ··· + 11y + 1)(y
24
+ 21y
23
+ ··· + 24252y + 529)
· (y
24
+ 21y
23
+ ··· − 1844y + 3481)(y
30
+ 32y
29
+ ··· − 14y + 1)
c
6
, c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
16
− 5y
15
+ ··· − 14y + 1)(y
24
− 7y
23
+ ··· − 22992y + 3481)
· (y
24
− 7y
23
+ ··· − 56036y + 4489)(y
30
− 13y
29
+ ··· + 5y + 1)
c
12
((y
3
− y
2
+ 2y − 1)
18
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
16
+ 9y
15
+ ··· + 10y
2
+ 1)
· (y
30
+ 7y
29
+ ··· + 180224y + 65536)
34
