12n
0840
(K12n
0840
)
A knot diagram
1
Linearized knot diagam
4 10 6 9 1 2 10 5 12 6 2 8
Solving Sequence
2,10 3,6
4 7 8 11 12 1 5 9
c
2
c
3
c
6
c
7
c
10
c
11
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.20855 × 10
14
u
23
+ 4.72872 × 10
15
u
22
+ ··· + 1.51654 × 10
16
b + 1.15899 × 10
17
,
9.05460 × 10
14
u
23
− 1.58566 × 10
16
u
22
+ ··· + 3.03307 × 10
16
a − 3.94363 × 10
17
,
u
24
− 18u
23
+ ··· − 1792u + 256i
I
u
2
= h−9209872u
16
− 47227765u
15
+ ··· + 25630152b + 19575099,
− 6525033u
16
− 41835037u
15
+ ··· + 25630152a − 88967192, u
17
+ 5u
16
+ ··· − 7u + 3i
I
u
3
= h50u
28
+ 444u
27
+ ··· + 64b + 198, −198u
28
a + 743u
28
+ ··· + 3432a − 21508,
u
29
+ 10u
28
+ ··· − 32u − 2i
I
u
4
= hau + b + u − 1, 6a
2
+ 3au + 6a + 2u − 1, u
2
+ 2i
I
v
1
= ha, b + v, v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 105 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−2.21 × 10
14
u
23
+ 4.73 × 10
15
u
22
+ · · · + 1.52 × 10
16
b + 1.16 ×
10
17
, 9.05 × 10
14
u
23
− 1.59 × 10
16
u
22
+ · · · + 3.03 × 10
16
a − 3.94 ×
10
17
, u
24
− 18u
23
+ · · · − 1792u + 256i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
6
=
−0.0298529u
23
+ 0.522789u
22
+ ··· − 64.9055u + 13.0021
0.0145631u
23
− 0.311811u
22
+ ··· + 40.4943u − 7.64234
a
4
=
−0.00905264u
23
+ 0.149935u
22
+ ··· − 33.0279u + 6.96109
0.0130124u
23
− 0.201731u
22
+ ··· + 10.2612u − 2.31748
a
7
=
−0.0152898u
23
+ 0.210978u
22
+ ··· − 24.4112u + 5.35977
0.0145631u
23
− 0.311811u
22
+ ··· + 40.4943u − 7.64234
a
8
=
−0.0152898u
23
+ 0.210978u
22
+ ··· − 24.4112u + 5.35977
0.205024u
23
− 3.31073u
22
+ ··· + 151.694u − 24.0872
a
11
=
−0.0521967u
23
+ 0.896396u
22
+ ··· − 107.241u + 19.3234
0.0431440u
23
− 0.746461u
22
+ ··· + 75.2130u − 13.3623
a
12
=
−0.00905264u
23
+ 0.149935u
22
+ ··· − 32.0279u + 5.96109
0.0431440u
23
− 0.746461u
22
+ ··· + 75.2130u − 13.3623
a
1
=
−0.00666547u
23
+ 0.0871674u
22
+ ··· − 0.179325u + 0.846328
0.0610145u
23
− 0.974137u
22
+ ··· + 45.9929u − 6.69328
a
5
=
0.0545990u
23
− 0.928564u
22
+ ··· + 37.7724u − 3.48734
0.146921u
23
− 2.29092u
22
+ ··· + 73.7072u − 11.6542
a
9
=
−0.0261456u
23
+ 0.409607u
22
+ ··· − 10.9189u + 0.860033
0.0481684u
23
− 0.847385u
22
+ ··· + 96.6167u − 15.6932
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
261339848863265
1421751842414568
u
23
+
151465938324859
50776851514806
u
22
+ ··· −
76152219280730
533690631537
u +
3978648810812680
177718980301821
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
24
− 3u
23
+ ··· − 12u + 3
c
2
u
24
− 18u
23
+ ··· − 1792u + 256
c
3
, c
7
u
24
+ 2u
23
+ ··· + 9u − 3
c
4
, c
8
u
24
− 9u
23
+ ··· + 44u − 8
c
5
, c
12
3(3u
24
+ 3u
23
+ ··· − 6u + 1)
c
6
, c
10
3(3u
24
− 3u
23
+ ··· − u − 1)
c
11
9(9u
24
+ 141u
23
+ ··· + 14728u + 1960)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
24
+ 3y
23
+ ··· + 66y + 9
c
2
y
24
− 18y
23
+ ··· + 262144y + 65536
c
3
, c
7
y
24
− 20y
23
+ ··· + 57y + 9
c
4
, c
8
y
24
+ 11y
23
+ ··· + 176y + 64
c
5
, c
12
9(9y
24
− 87y
23
+ ··· − 66y + 1)
c
6
, c
10
9(9y
24
− 303y
23
+ ··· − 17y + 1)
c
11
81(81y
24
− 369y
23
+ ··· + 1.23041 × 10
7
y + 3841600)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530777 + 0.640777I
a = 0.265857 + 0.440018I
b = 0.140843 − 0.403906I
0.26899 + 1.49716I 3.11954 − 2.07751I
u = 0.530777 − 0.640777I
a = 0.265857 − 0.440018I
b = 0.140843 + 0.403906I
0.26899 − 1.49716I 3.11954 + 2.07751I
u = 0.688395 + 1.068310I
a = 0.206159 − 0.248091I
b = −0.406957 − 0.049457I
−1.49200 + 3.53503I 6.33355 − 5.98826I
u = 0.688395 − 1.068310I
a = 0.206159 + 0.248091I
b = −0.406957 + 0.049457I
−1.49200 − 3.53503I 6.33355 + 5.98826I
u = −0.154209 + 1.284530I
a = −0.262592 + 0.372209I
b = 0.437620 + 0.394705I
−5.06511 + 1.65286I −0.70806 − 3.88591I
u = −0.154209 − 1.284530I
a = −0.262592 − 0.372209I
b = 0.437620 − 0.394705I
−5.06511 − 1.65286I −0.70806 + 3.88591I
u = 1.278810 + 0.409856I
a = −0.843748 + 0.488093I
b = 1.279040 − 0.278361I
0.75060 + 2.39087I 2.55581 − 0.50009I
u = 1.278810 − 0.409856I
a = −0.843748 − 0.488093I
b = 1.279040 + 0.278361I
0.75060 − 2.39087I 2.55581 + 0.50009I
u = 1.42403
a = 1.18251
b = −1.68393
3.38392 2.10530
u = −0.376695 + 0.432151I
a = 0.796902 + 0.859648I
b = 0.671687 − 0.020557I
−0.73124 + 4.01940I 4.26636 − 3.12077I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.376695 − 0.432151I
a = 0.796902 − 0.859648I
b = 0.671687 + 0.020557I
−0.73124 − 4.01940I 4.26636 + 3.12077I
u = −0.38587 + 1.39561I
a = 0.132291 − 0.512227I
b = −0.663821 − 0.382280I
1.35141 − 3.47627I 4.76400 + 8.33538I
u = −0.38587 − 1.39561I
a = 0.132291 + 0.512227I
b = −0.663821 + 0.382280I
1.35141 + 3.47627I 4.76400 − 8.33538I
u = 0.298932 + 0.404251I
a = 0.38457 − 1.82839I
b = −0.854090 + 0.391104I
1.36425 − 1.12274I 2.97626 + 1.52454I
u = 0.298932 − 0.404251I
a = 0.38457 + 1.82839I
b = −0.854090 − 0.391104I
1.36425 + 1.12274I 2.97626 − 1.52454I
u = −0.44722 + 1.43798I
a = −0.070696 + 0.446274I
b = 0.610116 + 0.301240I
−2.42080 − 9.85876I 4.00000 + 7.00757I
u = −0.44722 − 1.43798I
a = −0.070696 − 0.446274I
b = 0.610116 − 0.301240I
−2.42080 + 9.85876I 4.00000 − 7.00757I
u = 1.83440 + 0.51876I
a = 1.046860 − 0.052839I
b = −1.94776 − 0.44614I
5.0719 + 17.4667I 0. − 8.41645I
u = 1.83440 − 0.51876I
a = 1.046860 + 0.052839I
b = −1.94776 + 0.44614I
5.0719 − 17.4667I 0. + 8.41645I
u = 1.84303 + 0.56018I
a = −1.017100 + 0.103953I
b = 1.93278 + 0.37817I
8.5754 + 11.2460I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.84303 − 0.56018I
a = −1.017100 − 0.103953I
b = 1.93278 − 0.37817I
8.5754 − 11.2460I 0
u = 1.94698 + 0.52145I
a = 0.908100 − 0.084492I
b = −1.81211 − 0.30903I
2.43712 + 5.84189I 0
u = 1.94698 − 0.52145I
a = 0.908100 + 0.084492I
b = −1.81211 + 0.30903I
2.43712 − 5.84189I 0
u = 2.46132
a = −0.775702
b = 1.90925
10.9388 0
7
II.
I
u
2
= h−9.21 × 10
6
u
16
− 4.72 × 10
7
u
15
+ · · · + 2.56 × 10
7
b + 1.96 × 10
7
, −6.53 ×
10
6
u
16
−4.18×10
7
u
15
+· · · +2.56×10
7
a−8.90×10
7
, u
17
+5u
16
+· · · − 7u +3i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
6
=
0.254584u
16
+ 1.63226u
15
+ ··· − 0.198028u + 3.47119
0.359337u
16
+ 1.84266u
15
+ ··· + 5.25328u − 0.763753
a
4
=
−0.0880697u
16
− 0.334155u
15
+ ··· − 5.22509u + 4.77122
0.106193u
16
+ 0.569279u
15
+ ··· + 3.15474u + 0.264209
a
7
=
0.613922u
16
+ 3.47492u
15
+ ··· + 5.05525u + 2.70744
0.359337u
16
+ 1.84266u
15
+ ··· + 5.25328u − 0.763753
a
8
=
0.613922u
16
+ 3.47492u
15
+ ··· + 5.05525u + 2.70744
0.400116u
16
+ 2.15432u
15
+ ··· + 4.25784u + 0.452191
a
11
=
0.171796u
16
+ 0.775254u
15
+ ··· + 7.27835u − 3.25584
−0.0837263u
16
− 0.441098u
15
+ ··· − 1.05326u − 0.515388
a
12
=
0.0880697u
16
+ 0.334155u
15
+ ··· + 6.22509u − 3.77122
−0.0837263u
16
− 0.441098u
15
+ ··· − 1.05326u − 0.515388
a
1
=
−0.351457u
16
− 1.90179u
15
+ ··· − 7.26298u − 1.70210
−0.127546u
16
− 0.667421u
15
+ ··· − 4.20513u + 0.620853
a
5
=
−0.689667u
16
− 3.43906u
15
+ ··· − 8.87737u + 1.25219
−0.147048u
16
− 0.564321u
15
+ ··· − 3.95783u + 1.01883
a
9
=
0.206951u
16
+ 1.16230u
15
+ ··· + 3.10068u + 2.75647
0.0662469u
16
+ 0.354221u
15
+ ··· + 3.83737u − 0.103532
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17990383
25630152
u
16
+
100459123
25630152
u
15
+ ··· +
531682607
25630152
u −
2019718
1067923
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
17
− 3u
16
+ ··· − 28u + 12
c
2
u
17
+ 5u
16
+ ··· − 7u + 3
c
3
, c
7
u
17
+ 2u
16
+ ··· + 60u + 36
c
4
u
17
− 4u
16
+ ··· + 2u − 3
c
5
, c
12
4(4u
17
− 4u
16
+ ··· + 2u − 1)
c
6
, c
10
4(4u
17
+ 4u
16
+ ··· − 3u + 1)
c
8
u
17
+ 4u
16
+ ··· + 2u + 3
c
11
16(16u
17
+ 112u
16
+ ··· + 33u + 33)
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
17
+ 3y
16
+ ··· − 32y −144
c
2
y
17
− 17y
16
+ ··· − 137y −9
c
3
, c
7
y
17
− 12y
16
+ ··· − 3168y −1296
c
4
, c
8
y
17
+ 8y
16
+ ··· − 62y −9
c
5
, c
12
16(16y
17
− 64y
16
+ ··· − 4y −1)
c
6
, c
10
16(16y
17
− 192y
16
+ ··· − 17y −1)
c
11
256(256y
17
− 1408y
16
+ ··· + 1749y −1089)
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202685 + 0.958929I
a = −0.101984 + 0.631097I
b = −0.625848 + 0.030119I
1.15527 + 2.33712I 4.92657 − 5.08042I
u = 0.202685 − 0.958929I
a = −0.101984 − 0.631097I
b = −0.625848 − 0.030119I
1.15527 − 2.33712I 4.92657 + 5.08042I
u = 0.442788 + 0.854378I
a = −0.605348 − 0.519672I
b = 0.175955 − 0.747300I
−6.09745 + 0.34180I −6.54411 + 0.10551I
u = 0.442788 − 0.854378I
a = −0.605348 + 0.519672I
b = 0.175955 + 0.747300I
−6.09745 − 0.34180I −6.54411 − 0.10551I
u = 0.933842 + 0.546353I
a = −0.320613 − 0.343229I
b = −0.111878 − 0.495690I
−1.10631 + 1.98360I −1.30446 − 2.82949I
u = 0.933842 − 0.546353I
a = −0.320613 + 0.343229I
b = −0.111878 + 0.495690I
−1.10631 − 1.98360I −1.30446 + 2.82949I
u = 0.844311 + 0.930797I
a = 0.286806 + 0.217633I
b = 0.039581 + 0.450708I
−2.00645 + 3.18660I −4.32554 + 0.79064I
u = 0.844311 − 0.930797I
a = 0.286806 − 0.217633I
b = 0.039581 − 0.450708I
−2.00645 − 3.18660I −4.32554 − 0.79064I
u = −0.116566 + 0.581560I
a = −1.71456 + 0.09351I
b = 0.145475 − 1.008020I
−4.77665 − 10.19610I −2.01174 + 7.98398I
u = −0.116566 − 0.581560I
a = −1.71456 − 0.09351I
b = 0.145475 + 1.008020I
−4.77665 + 10.19610I −2.01174 − 7.98398I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135915 + 0.400426I
a = 1.80918 + 1.26166I
b = −0.259307 + 0.895924I
−1.32003 − 4.67660I −0.03284 + 6.45930I
u = 0.135915 − 0.400426I
a = 1.80918 − 1.26166I
b = −0.259307 − 0.895924I
−1.32003 + 4.67660I −0.03284 − 6.45930I
u = −1.66080 + 0.20153I
a = −1.167840 + 0.110611I
b = 1.91726 − 0.41906I
7.89276 − 6.13727I 5.32681 + 4.36806I
u = −1.66080 − 0.20153I
a = −1.167840 − 0.110611I
b = 1.91726 + 0.41906I
7.89276 + 6.13727I 5.32681 − 4.36806I
u = −2.02550 + 0.14114I
a = 0.861774 − 0.051839I
b = −1.73821 + 0.22663I
4.12908 − 6.62683I 4.11488 + 6.30699I
u = −2.02550 − 0.14114I
a = 0.861774 + 0.051839I
b = −1.73821 − 0.22663I
4.12908 + 6.62683I 4.11488 − 6.30699I
u = −2.51334
a = −0.761514
b = 1.91394
10.8393 −38.2990
12
III. I
u
3
= h50u
28
+ 444u
27
+ · · · + 64b + 198, −198u
28
a + 743u
28
+ · · · +
3432a − 21508, u
29
+ 10u
28
+ · · · − 32u − 2i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
6
=
a
−0.781250u
28
− 6.93750u
27
+ ··· − 22.6875u − 3.09375
a
4
=
0.875000au
28
+ 0.343750u
28
+ ··· − 1.56250a + 14.1875
−0.875000au
28
+ 0.695313u
28
+ ··· + 1.56250a − 1.07813
a
7
=
−0.781250u
28
− 6.93750u
27
+ ··· + a − 3.09375
−0.781250u
28
− 6.93750u
27
+ ··· − 22.6875u − 3.09375
a
8
=
−0.781250u
28
− 6.93750u
27
+ ··· + a − 3.09375
−0.140625u
28
− 0.968750u
27
+ ··· − 49.1250u − 4.84375
a
11
=
0.781250au
28
− 0.789063u
28
+ ··· + 3.09375a − 11.6094
0.445313u
28
+ 4.37500u
27
+ ··· − 35.8594u − 1.57813
a
12
=
0.781250au
28
− 0.343750u
28
+ ··· + 3.09375a − 13.1875
0.445313u
28
+ 4.37500u
27
+ ··· − 35.8594u − 1.57813
a
1
=
0.250000au
28
− 1.92188u
28
+ ··· + 4.59375a − 18.5000
5
32
u
28
a −
9
8
u
28
+ ··· −
7
32
a +
67
32
a
5
=
0.453125au
28
− 2.57031u
28
+ ··· − 0.750000a + 61.4063
0.281250au
28
+ 1.63281u
28
+ ··· − 0.625000a − 1.26563
a
9
=
−0.109375au
28
+ 1.07813u
28
+ ··· − 5.09375a + 21.3125
0.937500au
28
− 0.242188u
28
+ ··· − 3.62500a − 0.0156250
(ii) Obstruction class = −1
(iii) Cusp Shapes =
77
32
u
28
+
169
8
u
27
+ ··· +
1
16
u +
15
8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
58
− 8u
57
+ ··· − 7380u + 484
c
2
(u
29
+ 10u
28
+ ··· − 32u − 2)
2
c
3
, c
7
u
58
+ 12u
57
+ ··· + 3588u + 3484
c
4
, c
8
(u
29
+ 4u
28
+ ··· + 10u + 2)
2
c
5
, c
12
4(4u
58
+ 8u
57
+ ··· + 623u + 131)
c
6
, c
10
4(4u
58
− 8u
57
+ ··· + 16111u + 3551)
c
11
16(4u
29
− 54u
28
+ ··· − 525u + 167)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
58
+ 2y
57
+ ··· + 1251744y + 234256
c
2
(y
29
− 38y
28
+ ··· + 144y −4)
2
c
3
, c
7
y
58
− 30y
57
+ ··· − 6839456y + 12138256
c
4
, c
8
(y
29
+ 20y
28
+ ··· − 44y −4)
2
c
5
, c
12
16(16y
58
+ 48y
57
+ ··· − 58009y + 17161)
c
6
, c
10
16(16y
58
− 976y
57
+ ··· + 3.82329 × 10
8
y + 1.26096 × 10
7
)
c
11
256(16y
29
− 428y
28
+ ··· + 272619y −27889)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.912216 + 0.585428I
a = 0.675374 − 0.268010I
b = −0.261923 + 0.728143I
−1.57846 + 4.29036I −0.46910 − 8.73987I
u = 0.912216 + 0.585428I
a = −0.159461 − 0.695877I
b = −0.772988 − 0.150900I
−1.57846 + 4.29036I −0.46910 − 8.73987I
u = 0.912216 − 0.585428I
a = 0.675374 + 0.268010I
b = −0.261923 − 0.728143I
−1.57846 − 4.29036I −0.46910 + 8.73987I
u = 0.912216 − 0.585428I
a = −0.159461 + 0.695877I
b = −0.772988 + 0.150900I
−1.57846 − 4.29036I −0.46910 + 8.73987I
u = 0.618541 + 0.519711I
a = 0.666375 + 0.683260I
b = 0.182291 − 0.200504I
0.26701 + 1.60185I 5.56020 − 2.94171I
u = 0.618541 + 0.519711I
a = −0.013100 + 0.335163I
b = −0.057082 − 0.768947I
0.26701 + 1.60185I 5.56020 − 2.94171I
u = 0.618541 − 0.519711I
a = 0.666375 − 0.683260I
b = 0.182291 + 0.200504I
0.26701 − 1.60185I 5.56020 + 2.94171I
u = 0.618541 − 0.519711I
a = −0.013100 − 0.335163I
b = −0.057082 + 0.768947I
0.26701 − 1.60185I 5.56020 + 2.94171I
u = −0.637964 + 0.411709I
a = −0.223297 + 0.131875I
b = −0.57825 − 1.30385I
−0.23811 + 4.12161I 7.82602 − 2.63486I
u = −0.637964 + 0.411709I
a = 0.29124 − 1.85581I
b = −0.088162 + 0.176065I
−0.23811 + 4.12161I 7.82602 − 2.63486I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637964 − 0.411709I
a = −0.223297 − 0.131875I
b = −0.57825 + 1.30385I
−0.23811 − 4.12161I 7.82602 + 2.63486I
u = −0.637964 − 0.411709I
a = 0.29124 + 1.85581I
b = −0.088162 − 0.176065I
−0.23811 − 4.12161I 7.82602 + 2.63486I
u = −0.624381 + 0.324404I
a = 0.599713 − 0.357478I
b = 0.56058 + 1.50487I
−3.46043 + 9.57152I 4.68334 − 5.35627I
u = −0.624381 + 0.324404I
a = −0.27908 + 2.26519I
b = 0.258482 − 0.417751I
−3.46043 + 9.57152I 4.68334 − 5.35627I
u = −0.624381 − 0.324404I
a = 0.599713 + 0.357478I
b = 0.56058 − 1.50487I
−3.46043 − 9.57152I 4.68334 + 5.35627I
u = −0.624381 − 0.324404I
a = −0.27908 − 2.26519I
b = 0.258482 + 0.417751I
−3.46043 − 9.57152I 4.68334 + 5.35627I
u = −0.445198 + 0.435124I
a = 0.413859 + 0.679908I
b = 0.176153 + 1.266900I
−5.07047 − 0.16816I 2.60672 − 1.18920I
u = −0.445198 + 0.435124I
a = −1.22011 + 1.65319I
b = 0.480093 + 0.122614I
−5.07047 − 0.16816I 2.60672 − 1.18920I
u = −0.445198 − 0.435124I
a = 0.413859 − 0.679908I
b = 0.176153 − 1.266900I
−5.07047 + 0.16816I 2.60672 + 1.18920I
u = −0.445198 − 0.435124I
a = −1.22011 − 1.65319I
b = 0.480093 − 0.122614I
−5.07047 + 0.16816I 2.60672 + 1.18920I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040804 + 1.377650I
a = −1.056440 + 0.006297I
b = 0.677724 + 0.153812I
−4.92375 + 0.51981I 0.77865 − 14.11985I
u = −0.040804 + 1.377650I
a = −0.096993 + 0.494816I
b = −0.03443 + 1.45565I
−4.92375 + 0.51981I 0.77865 − 14.11985I
u = −0.040804 − 1.377650I
a = −1.056440 − 0.006297I
b = 0.677724 − 0.153812I
−4.92375 − 0.51981I 0.77865 + 14.11985I
u = −0.040804 − 1.377650I
a = −0.096993 − 0.494816I
b = −0.03443 − 1.45565I
−4.92375 − 0.51981I 0.77865 + 14.11985I
u = 0.595003 + 0.172391I
a = −0.238046 + 1.232310I
b = −0.220914 − 0.822274I
0.79583 + 1.58851I 8.05301 − 4.96467I
u = 0.595003 + 0.172391I
a = 0.711919 + 1.175700I
b = 0.354077 − 0.692191I
0.79583 + 1.58851I 8.05301 − 4.96467I
u = 0.595003 − 0.172391I
a = −0.238046 − 1.232310I
b = −0.220914 + 0.822274I
0.79583 − 1.58851I 8.05301 + 4.96467I
u = 0.595003 − 0.172391I
a = 0.711919 − 1.175700I
b = 0.354077 + 0.692191I
0.79583 − 1.58851I 8.05301 + 4.96467I
u = −1.39792 + 0.49312I
a = −0.889514 − 0.603962I
b = 1.65241 − 0.35905I
5.42820 + 1.19904I 8.46180 + 0.I
u = −1.39792 + 0.49312I
a = 1.131820 + 0.142409I
b = −1.54129 − 0.40565I
5.42820 + 1.19904I 8.46180 + 0.I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39792 − 0.49312I
a = −0.889514 + 0.603962I
b = 1.65241 + 0.35905I
5.42820 − 1.19904I 8.46180 + 0.I
u = −1.39792 − 0.49312I
a = 1.131820 − 0.142409I
b = −1.54129 + 0.40565I
5.42820 − 1.19904I 8.46180 + 0.I
u = −1.62739 + 0.37476I
a = 0.950086 + 0.262975I
b = −1.88014 + 0.44823I
7.16635 − 4.11940I 0
u = −1.62739 + 0.37476I
a = −1.157360 + 0.008903I
b = 1.64471 + 0.07190I
7.16635 − 4.11940I 0
u = −1.62739 − 0.37476I
a = 0.950086 − 0.262975I
b = −1.88014 − 0.44823I
7.16635 + 4.11940I 0
u = −1.62739 − 0.37476I
a = −1.157360 − 0.008903I
b = 1.64471 − 0.07190I
7.16635 + 4.11940I 0
u = −1.70107 + 0.22060I
a = 1.131150 + 0.020130I
b = −1.91034 + 0.46562I
8.43792 − 4.79047I 0
u = −1.70107 + 0.22060I
a = −1.139360 + 0.125968I
b = 1.92860 − 0.21529I
8.43792 − 4.79047I 0
u = −1.70107 − 0.22060I
a = 1.131150 − 0.020130I
b = −1.91034 − 0.46562I
8.43792 + 4.79047I 0
u = −1.70107 − 0.22060I
a = −1.139360 − 0.125968I
b = 1.92860 + 0.21529I
8.43792 + 4.79047I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74292 + 0.20742I
a = 1.041960 − 0.156952I
b = −2.01087 + 0.35947I
7.62859 − 7.68544I 0
u = −1.74292 + 0.20742I
a = −1.161830 + 0.067978I
b = 1.78350 − 0.48968I
7.62859 − 7.68544I 0
u = −1.74292 − 0.20742I
a = 1.041960 + 0.156952I
b = −2.01087 − 0.35947I
7.62859 + 7.68544I 0
u = −1.74292 − 0.20742I
a = −1.161830 − 0.067978I
b = 1.78350 + 0.48968I
7.62859 + 7.68544I 0
u = −0.1103580 + 0.0869906I
a = −0.31613 − 7.51279I
b = 0.535049 − 1.059640I
−1.30167 − 0.70742I 0.34305 + 1.38757I
u = −0.1103580 + 0.0869906I
a = 7.65845 − 3.56497I
b = −0.688429 − 0.801592I
−1.30167 − 0.70742I 0.34305 + 1.38757I
u = −0.1103580 − 0.0869906I
a = −0.31613 + 7.51279I
b = 0.535049 + 1.059640I
−1.30167 + 0.70742I 0.34305 − 1.38757I
u = −0.1103580 − 0.0869906I
a = 7.65845 + 3.56497I
b = −0.688429 + 0.801592I
−1.30167 + 0.70742I 0.34305 − 1.38757I
u = −1.83815 + 0.38020I
a = 1.079450 − 0.054355I
b = −1.405120 + 0.141930I
2.19953 − 7.64350I 0
u = −1.83815 + 0.38020I
a = −0.748373 − 0.077577I
b = 1.96353 − 0.51032I
2.19953 − 7.64350I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.83815 − 0.38020I
a = 1.079450 + 0.054355I
b = −1.405120 − 0.141930I
2.19953 + 7.64350I 0
u = −1.83815 − 0.38020I
a = −0.748373 + 0.077577I
b = 1.96353 + 0.51032I
2.19953 + 7.64350I 0
u = 2.01903
a = −0.873906 + 0.128847I
b = 1.76444 + 0.26015I
10.1337 0
u = 2.01903
a = −0.873906 − 0.128847I
b = 1.76444 − 0.26015I
10.1337 0
u = 2.03087 + 0.14541I
a = 0.965885 + 0.090036I
b = −1.56320 + 0.28729I
5.90158 − 5.80201I 0
u = 2.03087 + 0.14541I
a = 0.755716 − 0.195570I
b = −1.94850 − 0.32330I
5.90158 − 5.80201I 0
u = 2.03087 − 0.14541I
a = 0.965885 − 0.090036I
b = −1.56320 − 0.28729I
5.90158 + 5.80201I 0
u = 2.03087 − 0.14541I
a = 0.755716 + 0.195570I
b = −1.94850 + 0.32330I
5.90158 + 5.80201I 0
21
IV. I
u
4
= hau + b + u − 1, 6a
2
+ 3au + 6a + 2u − 1, u
2
+ 2i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
2
a
6
=
a
−au − u + 1
a
4
=
−au − 2a −
1
2
u + 2
au + 2a + u + 2
a
7
=
−au + a − u + 1
−au − u + 1
a
8
=
−au + a − u + 1
−3au + 2a − 3u + 3
a
11
=
−au + a +
1
6
u +
2
3
1
3
u +
1
3
a
12
=
−au + a +
1
2
u + 1
1
3
u +
1
3
a
1
=
−2au − a − u − 1
−3au − 6a − 4u − 5
a
5
=
2au + 4a +
3
2
u
au + 4a + 2u + 4
a
9
=
3au − 3a − u − 2
au + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
4
− 6u
3
+ 11u
2
− 6u + 3
c
2
, c
4
, c
8
(u
2
+ 2)
2
c
5
, c
12
3(3u
4
− 6u
3
+ 11u
2
− 10u + 3)
c
6
, c
10
3(3u
4
+ 6u
3
+ 11u
2
+ 10u + 3)
c
11
9(3u
2
+ 2u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
y
4
− 14y
3
+ 55y
2
+ 30y + 9
c
2
, c
4
, c
8
(y + 2)
4
c
5
, c
6
, c
10
c
12
9(9y
4
+ 30y
3
+ 19y
2
− 34y + 9)
c
11
81(9y
2
+ 2y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.050570 − 0.246526I
b = 0.651360 + 0.071509I
−4.93480 0
u = 1.414210I
a = 0.050565 − 0.460581I
b = 0.34864 − 1.48572I
−4.93480 0
u = − 1.414210I
a = −1.050570 + 0.246526I
b = 0.651360 − 0.071509I
−4.93480 0
u = − 1.414210I
a = 0.050565 + 0.460581I
b = 0.34864 + 1.48572I
−4.93480 0
25
V. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
2
=
1
0
a
10
=
v
0
a
3
=
1
0
a
6
=
0
−v
a
4
=
1
−v + 1
a
7
=
−v
−v
a
8
=
−v + 1
−v
a
11
=
v
1
a
12
=
v + 1
1
a
1
=
v
v
a
5
=
1
−v + 1
a
9
=
−v + 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
u
2
− u + 1
c
2
, c
4
, c
8
u
2
c
3
, c
5
, c
7
c
12
u
2
+ u + 1
c
11
(u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
9
c
10
, c
12
y
2
+ y + 1
c
2
, c
4
, c
8
y
2
c
11
(y − 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
0 6.00000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
0 6.00000
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
2
− u + 1)(u
4
− 6u
3
+ ··· − 6u + 3)(u
17
− 3u
16
+ ··· − 28u + 12)
· (u
24
− 3u
23
+ ··· − 12u + 3)(u
58
− 8u
57
+ ··· − 7380u + 484)
c
2
u
2
(u
2
+ 2)
2
(u
17
+ 5u
16
+ ··· − 7u + 3)
· (u
24
− 18u
23
+ ··· − 1792u + 256)(u
29
+ 10u
28
+ ··· − 32u − 2)
2
c
3
, c
7
(u
2
+ u + 1)(u
4
− 6u
3
+ ··· − 6u + 3)(u
17
+ 2u
16
+ ··· + 60u + 36)
· (u
24
+ 2u
23
+ ··· + 9u − 3)(u
58
+ 12u
57
+ ··· + 3588u + 3484)
c
4
u
2
(u
2
+ 2)
2
(u
17
− 4u
16
+ ··· + 2u − 3)(u
24
− 9u
23
+ ··· + 44u − 8)
· (u
29
+ 4u
28
+ ··· + 10u + 2)
2
c
5
, c
12
144(u
2
+ u + 1)(3u
4
− 6u
3
+ ··· − 10u + 3)(4u
17
− 4u
16
+ ··· + 2u − 1)
· (3u
24
+ 3u
23
+ ··· − 6u + 1)(4u
58
+ 8u
57
+ ··· + 623u + 131)
c
6
, c
10
144(u
2
− u + 1)(3u
4
+ 6u
3
+ ··· + 10u + 3)(4u
17
+ 4u
16
+ ··· − 3u + 1)
· (3u
24
− 3u
23
+ ··· − u − 1)(4u
58
− 8u
57
+ ··· + 16111u + 3551)
c
8
u
2
(u
2
+ 2)
2
(u
17
+ 4u
16
+ ··· + 2u + 3)(u
24
− 9u
23
+ ··· + 44u − 8)
· (u
29
+ 4u
28
+ ··· + 10u + 2)
2
c
11
20736(u + 1)
2
(3u
2
+ 2u + 1)
2
(16u
17
+ 112u
16
+ ··· + 33u + 33)
· (9u
24
+ 141u
23
+ ··· + 14728u + 1960)
· (4u
29
− 54u
28
+ ··· − 525u + 167)
2
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
2
+ y + 1)(y
4
− 14y
3
+ ··· + 30y + 9)(y
17
+ 3y
16
+ ··· − 32y − 144)
· (y
24
+ 3y
23
+ ··· + 66y + 9)(y
58
+ 2y
57
+ ··· + 1251744y + 234256)
c
2
y
2
(y + 2)
4
(y
17
− 17y
16
+ ··· − 137y − 9)
· (y
24
− 18y
23
+ ··· + 262144y + 65536)
· (y
29
− 38y
28
+ ··· + 144y − 4)
2
c
3
, c
7
(y
2
+ y + 1)(y
4
− 14y
3
+ 55y
2
+ 30y + 9)
· (y
17
− 12y
16
+ ··· − 3168y − 1296)(y
24
− 20y
23
+ ··· + 57y + 9)
· (y
58
− 30y
57
+ ··· − 6839456y + 12138256)
c
4
, c
8
y
2
(y + 2)
4
(y
17
+ 8y
16
+ ··· − 62y − 9)(y
24
+ 11y
23
+ ··· + 176y + 64)
· (y
29
+ 20y
28
+ ··· − 44y − 4)
2
c
5
, c
12
20736(y
2
+ y + 1)(9y
4
+ 30y
3
+ 19y
2
− 34y + 9)
· (16y
17
− 64y
16
+ ··· − 4y − 1)(9y
24
− 87y
23
+ ··· − 66y + 1)
· (16y
58
+ 48y
57
+ ··· − 58009y + 17161)
c
6
, c
10
20736(y
2
+ y + 1)(9y
4
+ 30y
3
+ 19y
2
− 34y + 9)
· (16y
17
− 192y
16
+ ··· − 17y − 1)(9y
24
− 303y
23
+ ··· − 17y + 1)
· (16y
58
− 976y
57
+ ··· + 382328643y + 12609601)
c
11
429981696(y − 1)
2
(9y
2
+ 2y + 1)
2
· (256y
17
− 1408y
16
+ ··· + 1749y − 1089)
· (81y
24
− 369y
23
+ ··· + 12304096y + 3841600)
· (16y
29
− 428y
28
+ ··· + 272619y − 27889)
2
31
