12n
0533
(K12n
0533
)
A knot diagram
1
Linearized knot diagam
3 6 12 7 2 9 11 4 6 3 8 10
Solving Sequence
2,6 3,9
7 10 11 1 5 4 8 12
c
2
c
6
c
9
c
10
c
1
c
5
c
4
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 685852313u
18
− 556454916u
17
+ ··· + 653732120a + 7160013, u
19
− u
18
+ ··· − u − 1i
I
u
2
= h−5.47513 × 10
57
u
27
− 1.03765 × 10
58
u
26
+ ··· + 1.25931 × 10
60
b + 3.43121 × 10
60
,
2.52837 × 10
60
u
27
+ 8.41887 × 10
58
u
26
+ ··· + 3.70867 × 10
62
a − 9.79223 × 10
62
,
2u
28
− 31u
26
+ ··· − 1810u + 589i
I
u
3
= hb + u, 2u
8
+ 8u
7
+ 6u
6
− 13u
5
− 23u
4
− 10u
3
+ 3u
2
+ a + 3u + 1,
u
9
+ 4u
8
+ 3u
7
− 7u
6
− 13u
5
− 5u
4
+ 5u
3
+ 4u
2
− 1i
I
u
4
= hb + 1, 3a − 4u − 2, 2u
2
+ 4u + 3i
I
u
5
= hb + 1, a
2
+ 2, u − 1i
I
u
6
= h2b − a − 2, a
2
+ 2, u − 1i
I
u
7
= hb + 1, a, u − 1i
* 7 irreducible components of dim
C
= 0, with total 63 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
= hb − u, 6.86 × 10
8
u
18
− 5.56 × 10
8
u
17
+ · · · + 6.54 × 10
8
a + 7.16 ×
10
6
, u
19
− u
18
+ · · · − u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−1.04913u
18
+ 0.851197u
17
+ ··· + 7.34496u − 0.0109525
u
a
7
=
0.158099u
18
+ 0.275222u
17
+ ··· − 2.08930u − 3.03953
−0.293094u
18
+ 0.271534u
17
+ ··· + 2.24707u + 0.197936
a
10
=
−1.04913u
18
+ 0.851197u
17
+ ··· + 7.34496u − 0.0109525
0.293094u
18
− 0.271534u
17
+ ··· − 0.247070u − 0.197936
a
11
=
−1.04913u
18
+ 0.851197u
17
+ ··· + 6.34496u − 0.0109525
0.293094u
18
− 0.271534u
17
+ ··· − 0.247070u − 0.197936
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−0.0634274u
18
− 0.299411u
17
+ ··· − 0.158823u + 2.17783
0.309916u
18
− 0.197991u
17
+ ··· − 0.689516u − 0.693690
a
8
=
−0.489325u
18
+ 0.908085u
17
+ ··· + 2.86952u − 2.02077
0.146260u
18
− 0.320706u
17
+ ··· + 1.12146u + 0.224248
a
12
=
0.652817u
18
− 1.22239u
17
+ ··· − 1.72619u + 2.50033
−0.0560035u
18
+ 0.251833u
17
+ ··· − 0.0119146u − 0.862668
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
98599477
81716515
u
18
+
19045887
32686606
u
17
+ ··· +
1773159057
163433030
u +
96551023
32686606
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 29u
18
+ ··· − 21u + 1
c
2
, c
5
, c
10
u
19
+ u
18
+ ··· − u + 1
c
3
u
19
− 12u
18
+ ··· − 112u + 8
c
4
u
19
+ u
18
+ ··· + 38u + 19
c
6
, c
9
u
19
− 11u
18
+ ··· + 192u − 16
c
7
, c
8
, c
11
u
19
− 6u
17
+ ··· + 2u + 1
c
12
u
19
− 2u
18
+ ··· + 640u + 206
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 89y
18
+ ··· + 167y −1
c
2
, c
5
, c
10
y
19
− 29y
18
+ ··· − 21y −1
c
3
y
19
+ 4y
18
+ ··· + 2272y −64
c
4
y
19
+ 17y
18
+ ··· + 342y −361
c
6
, c
9
y
19
+ 9y
18
+ ··· + 10112y −256
c
7
, c
8
, c
11
y
19
− 12y
18
+ ··· + 20y −1
c
12
y
19
− 44y
18
+ ··· + 39624y −42436
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.011380 + 0.313488I
a = 0.32432 + 1.42243I
b = 1.011380 + 0.313488I
3.19066 + 0.85534I −5.53948 − 2.70144I
u = 1.011380 − 0.313488I
a = 0.32432 − 1.42243I
b = 1.011380 − 0.313488I
3.19066 − 0.85534I −5.53948 + 2.70144I
u = −0.563817 + 0.542216I
a = −1.26815 + 1.02395I
b = −0.563817 + 0.542216I
7.09944 + 1.17461I 4.73931 − 3.05170I
u = −0.563817 − 0.542216I
a = −1.26815 − 1.02395I
b = −0.563817 − 0.542216I
7.09944 − 1.17461I 4.73931 + 3.05170I
u = 0.678408
a = 0.230292
b = 0.678408
−1.17152 −9.47840
u = −0.102826 + 0.584964I
a = 1.67025 − 1.13096I
b = −0.102826 + 0.584964I
4.80007 − 6.25425I 1.28229 + 2.73136I
u = −0.102826 − 0.584964I
a = 1.67025 + 1.13096I
b = −0.102826 − 0.584964I
4.80007 + 6.25425I 1.28229 − 2.73136I
u = −0.263709 + 0.494501I
a = −0.994354 − 0.913393I
b = −0.263709 + 0.494501I
2.36863 − 1.74565I −1.37224 + 0.88301I
u = −0.263709 − 0.494501I
a = −0.994354 + 0.913393I
b = −0.263709 − 0.494501I
2.36863 + 1.74565I −1.37224 − 0.88301I
u = −0.006101 + 0.333119I
a = −2.12160 + 1.28521I
b = −0.006101 + 0.333119I
0.09772 − 1.41403I 1.26259 + 3.76239I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.006101 − 0.333119I
a = −2.12160 − 1.28521I
b = −0.006101 − 0.333119I
0.09772 + 1.41403I 1.26259 − 3.76239I
u = −1.82852 + 0.27307I
a = −0.568825 + 0.667950I
b = −1.82852 + 0.27307I
−9.74488 + 5.38592I −1.90391 − 4.79888I
u = −1.82852 − 0.27307I
a = −0.568825 − 0.667950I
b = −1.82852 − 0.27307I
−9.74488 − 5.38592I −1.90391 + 4.79888I
u = 1.90401 + 0.14512I
a = 0.798373 + 0.448929I
b = 1.90401 + 0.14512I
−8.63257 + 5.48554I −4.82467 − 3.57754I
u = 1.90401 − 0.14512I
a = 0.798373 − 0.448929I
b = 1.90401 − 0.14512I
−8.63257 − 5.48554I −4.82467 + 3.57754I
u = −1.90239 + 0.21588I
a = −0.651528 + 0.330559I
b = −1.90239 + 0.21588I
−11.79520 + 2.21872I −6.42414 + 1.59237I
u = −1.90239 − 0.21588I
a = −0.651528 − 0.330559I
b = −1.90239 − 0.21588I
−11.79520 − 2.21872I −6.42414 − 1.59237I
u = 1.91277 + 0.40668I
a = 0.696362 + 0.544185I
b = 1.91277 + 0.40668I
−7.3598 − 14.6056I −3.48053 + 6.86328I
u = 1.91277 − 0.40668I
a = 0.696362 − 0.544185I
b = 1.91277 − 0.40668I
−7.3598 + 14.6056I −3.48053 − 6.86328I
6
II. I
u
2
= h−5.48 × 10
57
u
27
− 1.04 × 10
58
u
26
+ · · · + 1.26 × 10
60
b + 3.43 ×
10
60
, 2.53 × 10
60
u
27
+ 8.42 × 10
58
u
26
+ · · · + 3.71 × 10
62
a − 9.79 ×
10
62
, 2u
28
− 31u
26
+ · · · − 1810u + 589i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−0.00681744u
27
− 0.000227005u
26
+ ··· − 8.46563u + 2.64036
0.00434772u
27
+ 0.00823983u
26
+ ··· + 3.63527u − 2.72467
a
7
=
0.00201318u
27
+ 0.000373266u
26
+ ··· + 1.62410u + 3.93942
0.00381269u
27
+ 0.000556062u
26
+ ··· − 0.710321u + 1.46510
a
10
=
−0.00681744u
27
− 0.000227005u
26
+ ··· − 8.46563u + 2.64036
0.00232347u
27
+ 0.00897606u
26
+ ··· + 5.43757u − 2.65782
a
11
=
−0.0111652u
27
− 0.00846684u
26
+ ··· − 12.1009u + 5.36503
−0.000787486u
27
+ 0.00285253u
26
+ ··· − 0.739078u − 0.231186
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−0.00531622u
27
− 0.00441396u
26
+ ··· − 13.8077u + 0.531340
0.00187207u
27
− 0.00379823u
26
+ ··· − 6.50788u + 0.163980
a
8
=
−0.0119948u
27
− 0.00659420u
26
+ ··· − 10.2083u + 8.38054
0.00447526u
27
+ 0.000556236u
26
+ ··· − 3.48973u + 1.29218
a
12
=
−0.00515768u
27
+ 0.00174483u
26
+ ··· − 2.12442u + 4.32190
−0.00281226u
27
+ 0.00400340u
26
+ ··· + 4.13143u − 0.354315
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0000410394u
27
− 0.0223862u
26
+ ··· − 14.9786u + 4.40670
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
28
+ 124u
27
+ ··· + 3496386u + 346921)
c
2
, c
5
, c
10
2(2u
28
− 31u
26
+ ··· + 1810u + 589)
c
3
(u
14
+ 3u
13
+ ··· + 6u + 2)
2
c
4
4(4u
28
+ 4u
27
+ ··· + 2910u + 1318)
c
6
, c
9
(u
14
+ 4u
13
+ ··· + 6u + 2)
2
c
7
, c
8
, c
11
2(2u
28
− 3u
26
+ ··· + 18u + 143)
c
12
4(4u
28
+ 4u
27
+ ··· − 331822u + 51386)
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
28
− 1192y
27
+ ··· + 1.12038 × 10
13
y + 1.20354 × 10
11
)
c
2
, c
5
, c
10
4(4y
28
− 124y
27
+ ··· − 3496386y + 346921)
c
3
(y
14
+ 7y
13
+ ··· + 40y + 4)
2
c
4
16(16y
28
+ 120y
27
+ ··· + 3.30726 × 10
7
y + 1737124)
c
6
, c
9
(y
14
+ 14y
12
+ ··· − 16y + 4)
2
c
7
, c
8
, c
11
4(4y
28
− 12y
27
+ ··· − 208818y + 20449)
c
12
16(16y
28
− 872y
27
+ ··· + 9.39179 × 10
9
y + 2.64052 × 10
9
)
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966382 + 0.110966I
a = −0.828099 − 0.574299I
b = −0.89736 − 1.22031I
1.97484 − 7.76173I −3.86929 + 6.38577I
u = −0.966382 − 0.110966I
a = −0.828099 + 0.574299I
b = −0.89736 + 1.22031I
1.97484 + 7.76173I −3.86929 − 6.38577I
u = 0.851893 + 0.576043I
a = 0.774805 + 0.118277I
b = 1.41322 − 0.39522I
−0.285405 − 1.292740I −2.58201 + 4.98724I
u = 0.851893 − 0.576043I
a = 0.774805 − 0.118277I
b = 1.41322 + 0.39522I
−0.285405 + 1.292740I −2.58201 − 4.98724I
u = 0.809296 + 0.758852I
a = −0.701976 + 0.470898I
b = −0.656408 + 0.320572I
−1.78597 − 2.14155I −6.76179 + 4.84545I
u = 0.809296 − 0.758852I
a = −0.701976 − 0.470898I
b = −0.656408 − 0.320572I
−1.78597 + 2.14155I −6.76179 − 4.84545I
u = 0.820658 + 0.108803I
a = −0.497392 − 0.319928I
b = −0.69832 + 1.71552I
0.227845 − 0.102984I −1.99347 − 4.00034I
u = 0.820658 − 0.108803I
a = −0.497392 + 0.319928I
b = −0.69832 − 1.71552I
0.227845 + 0.102984I −1.99347 + 4.00034I
u = −0.656408 + 0.320572I
a = 1.047290 + 0.742422I
b = 0.809296 + 0.758852I
−1.78597 − 2.14155I −6.76179 + 4.84545I
u = −0.656408 − 0.320572I
a = 1.047290 − 0.742422I
b = 0.809296 − 0.758852I
−1.78597 + 2.14155I −6.76179 − 4.84545I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.130570 + 0.630186I
a = 0.307163 − 1.004640I
b = 0.261322 − 0.276894I
5.45172 + 3.41582I 0.19962 − 2.07440I
u = −1.130570 − 0.630186I
a = 0.307163 + 1.004640I
b = 0.261322 + 0.276894I
5.45172 − 3.41582I 0.19962 + 2.07440I
u = 1.41322 + 0.39522I
a = 0.288054 − 0.467672I
b = 0.851893 − 0.576043I
−0.285405 + 1.292740I −2.58201 − 4.98724I
u = 1.41322 − 0.39522I
a = 0.288054 + 0.467672I
b = 0.851893 + 0.576043I
−0.285405 − 1.292740I −2.58201 + 4.98724I
u = −0.89736 + 1.22031I
a = −0.584215 − 0.278401I
b = −0.966382 − 0.110966I
1.97484 + 7.76173I −3.86929 − 6.38577I
u = −0.89736 − 1.22031I
a = −0.584215 + 0.278401I
b = −0.966382 + 0.110966I
1.97484 − 7.76173I −3.86929 + 6.38577I
u = 0.261322 + 0.276894I
a = −2.02402 − 2.94250I
b = −1.130570 − 0.630186I
5.45172 − 3.41582I 0.19962 + 2.07440I
u = 0.261322 − 0.276894I
a = −2.02402 + 2.94250I
b = −1.130570 + 0.630186I
5.45172 + 3.41582I 0.19962 − 2.07440I
u = −1.77785 + 0.35616I
a = 0.794821 − 0.439524I
b = 2.03221 − 0.27091I
−10.49050 + 7.03206I −4.68824 − 5.11742I
u = −1.77785 − 0.35616I
a = 0.794821 + 0.439524I
b = 2.03221 + 0.27091I
−10.49050 − 7.03206I −4.68824 + 5.11742I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.78768 + 0.39075I
a = −0.782070 − 0.541782I
b = −1.84939 − 0.11154I
−9.89698 − 1.84815I −3.80483 − 0.45512I
u = 1.78768 − 0.39075I
a = −0.782070 + 0.541782I
b = −1.84939 + 0.11154I
−9.89698 + 1.84815I −3.80483 + 0.45512I
u = −0.69832 + 1.71552I
a = −0.082350 + 0.251169I
b = 0.820658 + 0.108803I
0.227845 − 0.102984I −1.99347 − 4.00034I
u = −0.69832 − 1.71552I
a = −0.082350 − 0.251169I
b = 0.820658 − 0.108803I
0.227845 + 0.102984I −1.99347 + 4.00034I
u = −1.84939 + 0.11154I
a = 0.680577 − 0.647893I
b = 1.78768 − 0.39075I
−9.89698 + 1.84815I −3.80483 + 0.45512I
u = −1.84939 − 0.11154I
a = 0.680577 + 0.647893I
b = 1.78768 + 0.39075I
−9.89698 − 1.84815I −3.80483 − 0.45512I
u = 2.03221 + 0.27091I
a = −0.676121 − 0.433678I
b = −1.77785 − 0.35616I
−10.49050 − 7.03206I −4.00000 + 5.11742I
u = 2.03221 − 0.27091I
a = −0.676121 + 0.433678I
b = −1.77785 + 0.35616I
−10.49050 + 7.03206I −4.00000 − 5.11742I
12
III. I
u
3
= hb + u, 2u
8
+ 8u
7
+ · · · + a + 1, u
9
+ 4u
8
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−2u
8
− 8u
7
− 6u
6
+ 13u
5
+ 23u
4
+ 10u
3
− 3u
2
− 3u − 1
−u
a
7
=
u
8
+ 3u
7
− u
6
− 10u
5
− 6u
4
+ 7u
3
+ 9u
2
+ u − 2
−u
7
− 3u
6
+ 7u
4
+ 5u
3
− u
2
− u
a
10
=
−2u
8
− 8u
7
− 6u
6
+ 13u
5
+ 23u
4
+ 10u
3
− 3u
2
− 3u − 1
−u
7
− 3u
6
+ 7u
4
+ 5u
3
− u
2
− 3u
a
11
=
−2u
8
− 8u
7
− 6u
6
+ 13u
5
+ 23u
4
+ 10u
3
− 3u
2
− 2u − 1
−u
7
− 3u
6
+ 7u
4
+ 6u
3
− u
2
− 3u
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−u
8
− 3u
7
+ u
6
+ 10u
5
+ 6u
4
− 8u
3
− 9u
2
+ 2u + 2
2u
8
+ 7u
7
+ 2u
6
− 16u
5
− 16u
4
+ 2u
3
+ 8u
2
+ u − 1
a
8
=
2u
8
+ 5u
7
− 5u
6
− 19u
5
− 3u
4
+ 19u
3
+ 13u
2
− 4u − 3
u
2
+ u − 1
a
12
=
−u
7
− 4u
6
− 3u
5
+ 7u
4
+ 12u
3
+ 3u
2
− 3u
−u
8
− 3u
7
+ 6u
5
+ 4u
4
+ u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
8
+ 22u
7
+ 14u
6
− 35u
5
− 59u
4
− 26u
3
+ 10u
2
− 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 10u
8
+ 39u
7
− 77u
6
+ 97u
5
− 91u
4
+ 51u
3
− 26u
2
+ 8u − 1
c
2
, c
10
u
9
+ 4u
8
+ 3u
7
− 7u
6
− 13u
5
− 5u
4
+ 5u
3
+ 4u
2
− 1
c
3
u
9
+ 2u
8
+ 3u
7
− 4u
5
− 6u
4
+ 7u
2
+ 5u + 1
c
4
u
9
− u
6
+ 5u
5
− 14u
4
− 3u
3
+ 3u
2
+ u − 1
c
5
u
9
− 4u
8
+ 3u
7
+ 7u
6
− 13u
5
+ 5u
4
+ 5u
3
− 4u
2
+ 1
c
6
u
9
− 2u
8
+ 5u
7
− 6u
6
+ 11u
5
− 8u
4
+ 10u
3
− 5u
2
+ 4u − 1
c
7
u
9
+ u
8
− 2u
7
− 2u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1
c
8
, c
11
u
9
− u
8
− 2u
7
+ 2u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u
2
+ u − 1
c
9
u
9
+ 2u
8
+ 5u
7
+ 6u
6
+ 11u
5
+ 8u
4
+ 10u
3
+ 5u
2
+ 4u + 1
c
12
u
9
+ 2u
8
− 6u
7
− 7u
6
+ 15u
5
+ 4u
4
− 8u
3
− 3u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 22y
8
+ ··· + 12y −1
c
2
, c
5
, c
10
y
9
− 10y
8
+ 39y
7
− 77y
6
+ 97y
5
− 91y
4
+ 51y
3
− 26y
2
+ 8y −1
c
3
y
9
+ 2y
8
+ y
7
− 2y
5
− 10y
4
+ 44y
3
− 37y
2
+ 11y −1
c
4
y
9
+ 10y
7
− 7y
6
− y
5
− 220y
4
+ 101y
3
− 43y
2
+ 7y −1
c
6
, c
9
y
9
+ 6y
8
+ 23y
7
+ 62y
6
+ 113y
5
+ 132y
4
+ 96y
3
+ 39y
2
+ 6y −1
c
7
, c
8
, c
11
y
9
− 5y
8
+ 12y
7
− 14y
6
+ 6y
5
+ y
4
− 6y
2
− 3y −1
c
12
y
9
− 16y
8
+ 94y
7
− 261y
6
+ 393y
5
− 318y
4
+ 134y
3
− 33y
2
− 2y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.865294 + 0.634244I
a = 0.435521 − 1.098430I
b = 0.865294 − 0.634244I
5.42733 + 5.08303I 0.17320 − 7.12597I
u = −0.865294 − 0.634244I
a = 0.435521 + 1.098430I
b = 0.865294 + 0.634244I
5.42733 − 5.08303I 0.17320 + 7.12597I
u = −0.538784 + 0.553717I
a = −1.116470 + 0.596317I
b = 0.538784 − 0.553717I
4.45461 + 7.56243I −0.11124 − 7.39319I
u = −0.538784 − 0.553717I
a = −1.116470 − 0.596317I
b = 0.538784 + 0.553717I
4.45461 − 7.56243I −0.11124 + 7.39319I
u = 1.45391
a = −0.210908
b = −1.45391
−0.245409 0.377120
u = 0.526629 + 0.094661I
a = −0.38098 + 1.63789I
b = −0.526629 − 0.094661I
−0.68115 + 1.57729I −9.12272 − 4.78889I
u = 0.526629 − 0.094661I
a = −0.38098 − 1.63789I
b = −0.526629 + 0.094661I
−0.68115 − 1.57729I −9.12272 + 4.78889I
u = −1.84951 + 0.27593I
a = 0.667388 − 0.551500I
b = 1.84951 − 0.27593I
−10.72300 + 4.06248I −5.12780 − 2.06389I
u = −1.84951 − 0.27593I
a = 0.667388 + 0.551500I
b = 1.84951 + 0.27593I
−10.72300 − 4.06248I −5.12780 + 2.06389I
16
IV. I
u
4
= hb + 1, 3a − 4u − 2, 2u
2
+ 4u + 3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−2u −
3
2
a
9
=
4
3
u +
2
3
−1
a
7
=
−
4
3
u −
8
3
−u − 2
a
10
=
4
3
u +
2
3
2u + 2
a
11
=
4
3
u +
5
3
0.5
a
1
=
2u +
5
2
2u +
15
4
a
5
=
u
u
a
4
=
5
3
u +
4
3
3
2
u + 1
a
8
=
−
1
3
u −
2
3
−
3
2
u − 2
a
12
=
4
3
u +
13
6
u +
11
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4u
2
− 4u + 9
c
2
, c
7
2u
2
+ 4u + 3
c
3
, c
6
, c
9
u
2
+ 2
c
4
(2u + 1)
2
c
5
, c
11
2u
2
− 4u + 3
c
8
(u + 1)
2
c
10
(u − 1)
2
c
12
(2u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16y
2
+ 56y + 81
c
2
, c
5
, c
7
c
11
4y
2
− 4y + 9
c
3
, c
6
, c
9
(y + 2)
2
c
4
, c
12
(4y −1)
2
c
8
, c
10
(y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.000000 + 0.707107I
a = −0.666667 + 0.942809I
b = −1.00000
4.93480 0
u = −1.000000 − 0.707107I
a = −0.666667 − 0.942809I
b = −1.00000
4.93480 0
20
V. I
u
5
= hb + 1, a
2
+ 2, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
a
−1
a
7
=
2
a + 1
a
10
=
a
a − 1
a
11
=
a + 1
a
a
1
=
0
−1
a
5
=
1
1
a
4
=
2a − 1
−2
a
8
=
−a + 1
1
a
12
=
2
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
10
(u − 1)
2
c
3
, c
4
u
2
+ 2u + 3
c
5
, c
8
, c
11
(u + 1)
2
c
6
, c
9
, c
12
u
2
+ 2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
+ 2y + 9
c
6
, c
9
, c
12
(y + 2)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.414210I
b = −1.00000
4.93480 0
u = 1.00000
a = − 1.414210I
b = −1.00000
4.93480 0
24
VI. I
u
6
= h2b − a − 2, a
2
+ 2, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
a
1
2
a + 1
a
7
=
2
−a + 2
a
10
=
a
3
2
a + 1
a
11
=
1
2
a − 1
a
a
1
=
0
−1
a
5
=
1
1
a
4
=
−2a + 1
−2a − 1
a
8
=
−
1
2
a + 3
−2a + 2
a
12
=
2
−a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
, c
4
, c
6
c
9
, c
12
u
2
+ 2
c
5
, c
11
(u + 1)
2
c
8
2(2u
2
− 4u + 3)
c
10
2(2u
2
+ 4u + 3)
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
11
(y −1)
2
c
3
, c
4
, c
6
c
9
, c
12
(y + 2)
2
c
8
, c
10
4(4y
2
− 4y + 9)
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.414210I
b = 1.000000 + 0.707107I
4.93480 0
u = 1.00000
a = − 1.414210I
b = 1.000000 − 0.707107I
4.93480 0
28
VII. I
u
7
= hb + 1, a, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
0
−1
a
7
=
0
1
a
10
=
0
−1
a
11
=
1
0
a
1
=
0
−1
a
5
=
1
1
a
4
=
1
2
a
8
=
1
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
, c
11
u − 1
c
3
, c
5
, c
7
u + 1
c
6
, c
9
, c
12
u
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
11
y −1
c
6
, c
9
, c
12
y
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
0 0
32
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
(4u
2
− 4u + 9)
· (u
9
− 10u
8
+ 39u
7
− 77u
6
+ 97u
5
− 91u
4
+ 51u
3
− 26u
2
+ 8u − 1)
· (u
19
+ 29u
18
+ ··· − 21u + 1)
· (4u
28
+ 124u
27
+ ··· + 3496386u + 346921)
c
2
(u − 1)
5
(2u
2
+ 4u + 3)
· (u
9
+ 4u
8
+ 3u
7
− 7u
6
− 13u
5
− 5u
4
+ 5u
3
+ 4u
2
− 1)
· (u
19
+ u
18
+ ··· − u + 1)(2u
28
− 31u
26
+ ··· + 1810u + 589)
c
3
(u + 1)(u
2
+ 2)
2
(u
2
+ 2u + 3)(u
9
+ 2u
8
+ ··· + 5u + 1)
· ((u
14
+ 3u
13
+ ··· + 6u + 2)
2
)(u
19
− 12u
18
+ ··· − 112u + 8)
c
4
(u − 1)(2u + 1)
2
(u
2
+ 2)(u
2
+ 2u + 3)
· (u
9
− u
6
+ ··· + u − 1)(u
19
+ u
18
+ ··· + 38u + 19)
· (4u
28
+ 4u
27
+ ··· + 2910u + 1318)
c
5
(u + 1)
5
(2u
2
− 4u + 3)
· (u
9
− 4u
8
+ 3u
7
+ 7u
6
− 13u
5
+ 5u
4
+ 5u
3
− 4u
2
+ 1)
· (u
19
+ u
18
+ ··· − u + 1)(2u
28
− 31u
26
+ ··· + 1810u + 589)
c
6
u(u
2
+ 2)
3
(u
9
− 2u
8
+ ··· + 4u − 1)
· ((u
14
+ 4u
13
+ ··· + 6u + 2)
2
)(u
19
− 11u
18
+ ··· + 192u − 16)
c
7
(u − 1)
4
(u + 1)(2u
2
+ 4u + 3)
· (u
9
+ u
8
− 2u
7
− 2u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
19
− 6u
17
+ ··· + 2u + 1)(2u
28
− 3u
26
+ ··· + 18u + 143)
c
8
4(u − 1)(u + 1)
4
(2u
2
− 4u + 3)
· (u
9
− u
8
− 2u
7
+ 2u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u
2
+ u − 1)
· (u
19
− 6u
17
+ ··· + 2u + 1)(2u
28
− 3u
26
+ ··· + 18u + 143)
c
9
u(u
2
+ 2)
3
(u
9
+ 2u
8
+ ··· + 4u + 1)
· ((u
14
+ 4u
13
+ ··· + 6u + 2)
2
)(u
19
− 11u
18
+ ··· + 192u − 16)
c
10
4(u − 1)
5
(2u
2
+ 4u + 3)
· (u
9
+ 4u
8
+ 3u
7
− 7u
6
− 13u
5
− 5u
4
+ 5u
3
+ 4u
2
− 1)
· (u
19
+ u
18
+ ··· − u + 1)(2u
28
− 31u
26
+ ··· + 1810u + 589)
c
11
(u − 1)(u + 1)
4
(2u
2
− 4u + 3)
· (u
9
− u
8
− 2u
7
+ 2u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u
2
+ u − 1)
· (u
19
− 6u
17
+ ··· + 2u + 1)(2u
28
− 3u
26
+ ··· + 18u + 143)
c
12
u(2u − 1)
2
(u
2
+ 2)
2
· (u
9
+ 2u
8
− 6u
7
− 7u
6
+ 15u
5
+ 4u
4
− 8u
3
− 3u
2
+ 2u − 1)
· (u
19
− 2u
18
+ ··· + 640u + 206)
· (4u
28
+ 4u
27
+ ··· − 331822u + 51386)
33
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(16y
2
+ 56y + 81)(y
9
− 22y
8
+ ··· + 12y −1)
· (y
19
− 89y
18
+ ··· + 167y −1)
· (16y
28
− 1192y
27
+ ··· + 11203834917014y + 120354180241)
c
2
, c
5
(y −1)
5
(4y
2
− 4y + 9)
· (y
9
− 10y
8
+ 39y
7
− 77y
6
+ 97y
5
− 91y
4
+ 51y
3
− 26y
2
+ 8y −1)
· (y
19
− 29y
18
+ ··· − 21y −1)
· (4y
28
− 124y
27
+ ··· − 3496386y + 346921)
c
3
(y −1)(y + 2)
4
(y
2
+ 2y + 9)
· (y
9
+ 2y
8
+ y
7
− 2y
5
− 10y
4
+ 44y
3
− 37y
2
+ 11y −1)
· ((y
14
+ 7y
13
+ ··· + 40y + 4)
2
)(y
19
+ 4y
18
+ ··· + 2272y −64)
c
4
(y −1)(y + 2)
2
(4y −1)
2
(y
2
+ 2y + 9)
· (y
9
+ 10y
7
− 7y
6
− y
5
− 220y
4
+ 101y
3
− 43y
2
+ 7y −1)
· (y
19
+ 17y
18
+ ··· + 342y −361)
· (16y
28
+ 120y
27
+ ··· + 33072624y + 1737124)
c
6
, c
9
y(y + 2)
6
· (y
9
+ 6y
8
+ 23y
7
+ 62y
6
+ 113y
5
+ 132y
4
+ 96y
3
+ 39y
2
+ 6y −1)
· ((y
14
+ 14y
12
+ ··· − 16y + 4)
2
)(y
19
+ 9y
18
+ ··· + 10112y −256)
c
7
, c
11
(y −1)
5
(4y
2
− 4y + 9)
· (y
9
− 5y
8
+ 12y
7
− 14y
6
+ 6y
5
+ y
4
− 6y
2
− 3y −1)
· (y
19
− 12y
18
+ ··· + 20y −1)(4y
28
− 12y
27
+ ··· − 208818y + 20449)
c
8
16(y −1)
5
(4y
2
− 4y + 9)
· (y
9
− 5y
8
+ 12y
7
− 14y
6
+ 6y
5
+ y
4
− 6y
2
− 3y −1)
· (y
19
− 12y
18
+ ··· + 20y −1)(4y
28
− 12y
27
+ ··· − 208818y + 20449)
c
10
16(y −1)
5
(4y
2
− 4y + 9)
· (y
9
− 10y
8
+ 39y
7
− 77y
6
+ 97y
5
− 91y
4
+ 51y
3
− 26y
2
+ 8y −1)
· (y
19
− 29y
18
+ ··· − 21y −1)
· (4y
28
− 124y
27
+ ··· − 3496386y + 346921)
c
12
y(y + 2)
4
(4y −1)
2
· (y
9
− 16y
8
+ 94y
7
− 261y
6
+ 393y
5
− 318y
4
+ 134y
3
− 33y
2
− 2y −1)
· (y
19
− 44y
18
+ ··· + 39624y −42436)
· (16y
28
− 872y
27
+ ··· + 9391789456y + 2640520996)
34
