12a
0494
(K12a
0494
)
A knot diagram
1
Linearized knot diagam
3 6 12 10 8 2 11 1 5 4 7 9
Solving Sequence
5,9 10,12
1 4 11 3 8 6 2 7
c
9
c
12
c
4
c
10
c
3
c
8
c
5
c
2
c
7
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.59322 × 10
61
u
45
− 6.46819 × 10
61
u
44
+ ··· + 5.94180 × 10
62
b − 7.19573 × 10
62
,
− 5.17566 × 10
61
u
45
+ 1.21957 × 10
62
u
44
+ ··· + 4.75344 × 10
63
a − 2.87479 × 10
61
,
u
46
− 3u
45
+ ··· − 224u + 32i
I
u
2
= h95u
32
a − 243u
32
+ ··· + 483a − 3272, 30u
32
a − 55u
32
+ ··· + 33a − 86, u
33
+ u
32
+ ··· + 3u + 1i
I
u
3
= h−u
5
+ b − u, u
5
− 4u
4
− u
3
− 3u
2
+ 7a + 4u − 9, u
6
+ u
4
+ 2u
2
+ 1i
I
u
4
= hb − 1, 8a
2
− 2au + 24a − 3u + 17, u
2
+ 2i
I
v
1
= ha, b + 1, 4v
2
− 2v + 1i
* 5 irreducible components of dim
C
= 0, with total 124 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
= h2.59 × 10
61
u
45
− 6.47 × 10
61
u
44
+ · · · + 5.94 × 10
62
b − 7.20 ×
10
62
, −5.18 × 10
61
u
45
+ 1.22 × 10
62
u
44
+ · · · + 4.75 × 10
63
a − 2.87 ×
10
61
, u
46
− 3u
45
+ · · · − 224u + 32i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
12
=
0.0108883u
45
− 0.0256565u
44
+ ··· + 2.71425u + 0.00604782
−0.0436437u
45
+ 0.108859u
44
+ ··· − 11.8294u + 1.21104
a
1
=
−0.0327555u
45
+ 0.0832026u
44
+ ··· − 9.11514u + 1.21708
−0.0436437u
45
+ 0.108859u
44
+ ··· − 11.8294u + 1.21104
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
0.0404758u
45
− 0.0994274u
44
+ ··· + 13.5494u − 2.27268
−0.0314148u
45
+ 0.0849635u
44
+ ··· − 11.6220u + 2.15240
a
8
=
0.0566730u
45
− 0.138814u
44
+ ··· + 15.7651u − 1.42925
0.0599305u
45
− 0.148388u
44
+ ··· + 18.2271u − 2.43384
a
6
=
−0.0811578u
45
+ 0.209282u
44
+ ··· − 28.8041u + 5.12908
−0.0530046u
45
+ 0.138397u
44
+ ··· − 20.3166u + 3.95052
a
2
=
0.0304632u
45
− 0.0783396u
44
+ ··· + 13.8672u − 3.59282
−0.0360975u
45
+ 0.0959193u
44
+ ··· − 13.5985u + 1.99297
a
7
=
0.00825991u
45
− 0.0153222u
44
+ ··· + 0.388121u + 0.488092
0.0450341u
45
− 0.106499u
44
+ ··· + 11.3574u − 1.03163
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.447426u
45
− 1.30981u
44
+ ··· + 236.624u − 56.0043
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 24u
45
+ ··· + 1295u + 576
c
2
, c
6
u
46
− 2u
45
+ ··· − 71u + 24
c
3
, c
5
64(64u
46
− 160u
45
+ ··· + 146u + 11)
c
4
, c
9
, c
10
u
46
+ 3u
45
+ ··· + 224u + 32
c
7
, c
8
, c
11
c
12
u
46
+ 2u
45
+ ··· + 8u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 16y
44
+ ··· + 13494815y + 331776
c
2
, c
6
y
46
+ 24y
45
+ ··· + 1295y + 576
c
3
, c
5
4096(4096y
46
+ 60416y
45
+ ··· + 3104y + 121)
c
4
, c
9
, c
10
y
46
+ 41y
45
+ ··· − 5120y + 1024
c
7
, c
8
, c
11
c
12
y
46
+ 14y
45
+ ··· + 302y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.879927 + 0.422250I
a = −1.002480 − 0.651826I
b = 0.561540 − 1.266480I
−5.3080 − 13.9989I −4.18038 + 9.68220I
u = 0.879927 − 0.422250I
a = −1.002480 + 0.651826I
b = 0.561540 + 1.266480I
−5.3080 + 13.9989I −4.18038 − 9.68220I
u = −0.884396 + 0.372933I
a = −0.864488 + 0.759473I
b = 0.533136 + 1.175940I
−2.75455 + 8.29717I −1.70737 − 6.58630I
u = −0.884396 − 0.372933I
a = −0.864488 − 0.759473I
b = 0.533136 − 1.175940I
−2.75455 − 8.29717I −1.70737 + 6.58630I
u = 1.005690 + 0.347417I
a = −0.592795 − 0.569917I
b = 0.354628 − 1.155160I
−8.53774 − 4.63661I −7.26779 + 6.24429I
u = 1.005690 − 0.347417I
a = −0.592795 + 0.569917I
b = 0.354628 + 1.155160I
−8.53774 + 4.63661I −7.26779 − 6.24429I
u = 0.757476 + 0.798859I
a = −0.138023 + 0.165827I
b = −0.458745 − 1.156100I
−4.22061 + 8.47102I −3.55506 − 6.39259I
u = 0.757476 − 0.798859I
a = −0.138023 − 0.165827I
b = −0.458745 + 1.156100I
−4.22061 − 8.47102I −3.55506 + 6.39259I
u = −0.677203 + 0.890151I
a = −0.1047750 − 0.0770628I
b = −0.426999 + 1.020500I
−1.24313 − 2.90152I 0. + 4.04088I
u = −0.677203 − 0.890151I
a = −0.1047750 + 0.0770628I
b = −0.426999 − 1.020500I
−1.24313 + 2.90152I 0. − 4.04088I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754848 + 0.065218I
a = −0.005515 + 1.244420I
b = 0.435207 + 0.754548I
0.39391 + 4.28987I −0.46705 − 7.97221I
u = −0.754848 − 0.065218I
a = −0.005515 − 1.244420I
b = 0.435207 − 0.754548I
0.39391 − 4.28987I −0.46705 + 7.97221I
u = −0.899443 + 0.871931I
a = 0.417382 − 0.332407I
b = −0.087635 − 0.831168I
−5.56613 + 3.24368I 0
u = −0.899443 − 0.871931I
a = 0.417382 + 0.332407I
b = −0.087635 + 0.831168I
−5.56613 − 3.24368I 0
u = 0.053471 + 1.326470I
a = −2.00960 − 0.27769I
b = 1.397470 + 0.175373I
5.26321 + 1.38773I 0
u = 0.053471 − 1.326470I
a = −2.00960 + 0.27769I
b = 1.397470 − 0.175373I
5.26321 − 1.38773I 0
u = 0.348272 + 1.303000I
a = 1.089410 + 0.524655I
b = −0.515748 + 0.904481I
4.21026 − 2.45289I 0
u = 0.348272 − 1.303000I
a = 1.089410 − 0.524655I
b = −0.515748 − 0.904481I
4.21026 + 2.45289I 0
u = 0.785322 + 1.112070I
a = −0.189157 + 0.017429I
b = −0.244145 − 0.990574I
−6.40579 − 1.59325I 0
u = 0.785322 − 1.112070I
a = −0.189157 − 0.017429I
b = −0.244145 + 0.990574I
−6.40579 + 1.59325I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146892 + 1.387240I
a = −1.75835 − 0.81715I
b = 1.34196 + 0.58047I
6.66740 − 4.38324I 0
u = 0.146892 − 1.387240I
a = −1.75835 + 0.81715I
b = 1.34196 − 0.58047I
6.66740 + 4.38324I 0
u = −0.34923 + 1.38244I
a = 1.349640 − 0.348220I
b = −0.570864 − 1.015940I
5.05332 + 8.42012I 0
u = −0.34923 − 1.38244I
a = 1.349640 + 0.348220I
b = −0.570864 + 1.015940I
5.05332 − 8.42012I 0
u = −0.12544 + 1.43283I
a = −1.49007 + 0.74151I
b = 1.133480 − 0.604428I
8.14786 − 0.11264I 0
u = −0.12544 − 1.43283I
a = −1.49007 − 0.74151I
b = 1.133480 + 0.604428I
8.14786 + 0.11264I 0
u = 0.545297 + 0.078664I
a = 0.83525 + 1.15694I
b = 0.339032 + 0.466799I
0.445010 − 1.185620I −1.75729 − 0.29982I
u = 0.545297 − 0.078664I
a = 0.83525 − 1.15694I
b = 0.339032 − 0.466799I
0.445010 + 1.185620I −1.75729 + 0.29982I
u = −0.05409 + 1.45463I
a = −0.840100 − 0.001476I
b = 0.128963 + 0.320779I
4.81424 − 1.83892I 0
u = −0.05409 − 1.45463I
a = −0.840100 + 0.001476I
b = 0.128963 − 0.320779I
4.81424 + 1.83892I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271343 + 0.437430I
a = 0.674777 + 0.345785I
b = −0.143974 + 0.371385I
0.079000 − 0.909335I 2.05664 + 7.20006I
u = 0.271343 − 0.437430I
a = 0.674777 − 0.345785I
b = −0.143974 − 0.371385I
0.079000 + 0.909335I 2.05664 − 7.20006I
u = −0.287009 + 0.385178I
a = 0.422708 − 0.041305I
b = −0.918597 + 0.410101I
2.29870 − 1.77899I 6.01313 − 3.03294I
u = −0.287009 − 0.385178I
a = 0.422708 + 0.041305I
b = −0.918597 − 0.410101I
2.29870 + 1.77899I 6.01313 + 3.03294I
u = −0.33737 + 1.48238I
a = 1.70844 + 0.12166I
b = −0.646202 − 1.244350I
3.20888 + 12.70970I 0
u = −0.33737 − 1.48238I
a = 1.70844 − 0.12166I
b = −0.646202 + 1.244350I
3.20888 − 12.70970I 0
u = −0.06899 + 1.52703I
a = −0.969248 + 0.549033I
b = 0.669287 − 0.651303I
7.27063 − 1.16863I 0
u = −0.06899 − 1.52703I
a = −0.969248 − 0.549033I
b = 0.669287 + 0.651303I
7.27063 + 1.16863I 0
u = 0.38401 + 1.48415I
a = 1.41083 − 0.19362I
b = −0.513706 + 1.238240I
−2.67740 − 9.58899I 0
u = 0.38401 − 1.48415I
a = 1.41083 + 0.19362I
b = −0.513706 − 1.238240I
−2.67740 + 9.58899I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.33179 + 1.50033I
a = 1.78862 − 0.24742I
b = −0.66692 + 1.30465I
0.8798 − 18.3922I 0
u = 0.33179 − 1.50033I
a = 1.78862 + 0.24742I
b = −0.66692 − 1.30465I
0.8798 + 18.3922I 0
u = 0.349735 + 0.181130I
a = 0.516188 + 0.059087I
b = −1.173810 − 0.239503I
1.57408 − 2.45072I −5.4120 + 13.0814I
u = 0.349735 − 0.181130I
a = 0.516188 − 0.059087I
b = −1.173810 + 0.239503I
1.57408 + 2.45072I −5.4120 − 13.0814I
u = 0.07879 + 1.62688I
a = −0.623636 − 0.621149I
b = 0.472651 + 0.872181I
4.50126 + 5.50730I 0
u = 0.07879 − 1.62688I
a = −0.623636 + 0.621149I
b = 0.472651 − 0.872181I
4.50126 − 5.50730I 0
9
II. I
u
2
= h95u
32
a − 243u
32
+ · · · + 483a − 3272, 30u
32
a − 55u
32
+ · · · + 33a −
86, u
33
+ u
32
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
12
=
a
−0.0387913au
32
+ 0.0992242u
32
+ ··· − 0.197223a + 1.33606
a
1
=
−0.0387913au
32
+ 0.0992242u
32
+ ··· + 0.802777a + 1.33606
−0.0387913au
32
+ 0.0992242u
32
+ ··· − 0.197223a + 1.33606
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
1.86661au
32
− 0.313779u
32
+ ··· + 2.56744a − 3.08421
0.138832au
32
+ 0.469443u
32
+ ··· + 0.0216415a + 3.39377
a
8
=
−0.0387913au
32
− 2.56744u
32
+ ··· − 1.19722a − 2.99728
0.0604328au
32
− 0.0387913u
32
+ ··· + 0.138832a − 1.19722
a
6
=
0.191779au
32
+ 2.84161u
32
+ ··· + 3.35048a − 3.60410
−0.277664au
32
+ 1.72778u
32
+ ··· − 0.0432830a + 2.54580
a
2
=
0.748741au
32
− 1.53391u
32
+ ··· + 2.41377a + 0.163831
−0.246223au
32
− 0.731591u
32
+ ··· − 0.241323a + 1.84184
a
7
=
−0.0992242au
32
− 2.52865u
32
+ ··· − 1.33606a − 3.80005
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
32
− 4u
31
− 64u
30
− 56u
29
− 448u
28
− 340u
27
− 1788u
26
−
1156u
25
− 4432u
24
− 2356u
23
− 6940u
22
− 2804u
21
− 6652u
20
− 1616u
19
− 3660u
18
−
8u
17
− 1380u
16
+ 364u
15
− 932u
14
+ 156u
13
− 380u
12
+ 360u
11
+ 224u
10
+ 328u
9
+
40u
8
+ 4u
7
− 56u
6
− 4u
5
+ 48u
4
+ 32u
3
− 12u
2
− 20u − 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
33
+ 15u
32
+ ··· + u − 1)
2
c
2
, c
6
(u
33
− u
32
+ ··· − u + 1)
2
c
3
, c
5
9(9u
66
+ 129u
65
+ ··· + 233684u + 29567)
c
4
, c
9
, c
10
(u
33
− u
32
+ ··· + 3u − 1)
2
c
7
, c
8
, c
11
c
12
u
66
− 5u
65
+ ··· − 804u + 125
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
33
+ 7y
32
+ ··· + 17y − 1)
2
c
2
, c
6
(y
33
+ 15y
32
+ ··· + y − 1)
2
c
3
, c
5
81(81y
66
− 1701y
65
+ ··· − 4.02404 × 10
10
y + 8.74207 × 10
8
)
c
4
, c
9
, c
10
(y
33
+ 31y
32
+ ··· + y − 1)
2
c
7
, c
8
, c
11
c
12
y
66
+ 39y
65
+ ··· + 129584y + 15625
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.138722 + 1.178260I
a = 0.646725 + 0.922454I
b = −0.34986 − 1.41730I
−3.68002 + 0.57246I −4.31906 − 0.48605I
u = 0.138722 + 1.178260I
a = 1.89541 − 0.83665I
b = −0.620802 + 1.176010I
−3.68002 + 0.57246I −4.31906 − 0.48605I
u = 0.138722 − 1.178260I
a = 0.646725 − 0.922454I
b = −0.34986 + 1.41730I
−3.68002 − 0.57246I −4.31906 + 0.48605I
u = 0.138722 − 1.178260I
a = 1.89541 + 0.83665I
b = −0.620802 − 1.176010I
−3.68002 − 0.57246I −4.31906 + 0.48605I
u = −0.679432 + 0.391507I
a = 0.967832 − 0.605627I
b = −0.580882 − 1.258950I
−1.82082 + 8.41845I −1.65597 − 8.08731I
u = −0.679432 + 0.391507I
a = −0.492379 + 0.153513I
b = 1.009630 − 0.133152I
−1.82082 + 8.41845I −1.65597 − 8.08731I
u = −0.679432 − 0.391507I
a = 0.967832 + 0.605627I
b = −0.580882 + 1.258950I
−1.82082 − 8.41845I −1.65597 + 8.08731I
u = −0.679432 − 0.391507I
a = −0.492379 − 0.153513I
b = 1.009630 + 0.133152I
−1.82082 − 8.41845I −1.65597 + 8.08731I
u = 0.649750 + 0.407780I
a = 0.961232 + 0.680322I
b = −0.526453 + 1.104150I
0.09121 − 3.30675I 1.55576 + 3.71770I
u = 0.649750 + 0.407780I
a = −0.320653 − 0.049837I
b = 0.822908 + 0.226871I
0.09121 − 3.30675I 1.55576 + 3.71770I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.649750 − 0.407780I
a = 0.961232 − 0.680322I
b = −0.526453 − 1.104150I
0.09121 + 3.30675I 1.55576 − 3.71770I
u = 0.649750 − 0.407780I
a = −0.320653 + 0.049837I
b = 0.822908 − 0.226871I
0.09121 + 3.30675I 1.55576 − 3.71770I
u = −0.552937 + 0.519363I
a = 0.910395 + 0.295741I
b = 0.356991 − 1.066940I
−1.29130 − 4.30723I −0.15179 + 2.03529I
u = −0.552937 + 0.519363I
a = 0.72843 − 1.28598I
b = −0.613572 − 0.123118I
−1.29130 − 4.30723I −0.15179 + 2.03529I
u = −0.552937 − 0.519363I
a = 0.910395 − 0.295741I
b = 0.356991 + 1.066940I
−1.29130 + 4.30723I −0.15179 − 2.03529I
u = −0.552937 − 0.519363I
a = 0.72843 + 1.28598I
b = −0.613572 + 0.123118I
−1.29130 + 4.30723I −0.15179 − 2.03529I
u = 0.578988 + 0.474023I
a = 0.703739 + 0.930950I
b = −0.406968 + 0.442807I
0.382723 − 0.728314I 2.50985 + 3.12560I
u = 0.578988 + 0.474023I
a = 0.566060 + 0.034191I
b = 0.338945 + 0.776348I
0.382723 − 0.728314I 2.50985 + 3.12560I
u = 0.578988 − 0.474023I
a = 0.703739 − 0.930950I
b = −0.406968 − 0.442807I
0.382723 + 0.728314I 2.50985 − 3.12560I
u = 0.578988 − 0.474023I
a = 0.566060 − 0.034191I
b = 0.338945 − 0.776348I
0.382723 + 0.728314I 2.50985 − 3.12560I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.214004 + 1.270020I
a = −0.191089 + 0.920763I
b = −0.12595 − 1.55585I
−2.78381 − 6.56196I −2.35976 + 7.19745I
u = 0.214004 + 1.270020I
a = 2.06381 − 0.68885I
b = −0.847874 + 0.939274I
−2.78381 − 6.56196I −2.35976 + 7.19745I
u = 0.214004 − 1.270020I
a = −0.191089 − 0.920763I
b = −0.12595 + 1.55585I
−2.78381 + 6.56196I −2.35976 − 7.19745I
u = 0.214004 − 1.270020I
a = 2.06381 + 0.68885I
b = −0.847874 − 0.939274I
−2.78381 + 6.56196I −2.35976 − 7.19745I
u = −0.150986 + 1.283520I
a = 0.004911 − 0.404260I
b = −0.139375 + 1.388990I
−0.32048 + 2.39560I 1.63078 − 3.31266I
u = −0.150986 + 1.283520I
a = 2.00230 + 0.72485I
b = −0.620697 − 0.904803I
−0.32048 + 2.39560I 1.63078 − 3.31266I
u = −0.150986 − 1.283520I
a = 0.004911 + 0.404260I
b = −0.139375 − 1.388990I
−0.32048 − 2.39560I 1.63078 + 3.31266I
u = −0.150986 − 1.283520I
a = 2.00230 − 0.72485I
b = −0.620697 + 0.904803I
−0.32048 − 2.39560I 1.63078 + 3.31266I
u = −0.596688 + 0.315979I
a = −0.801138 − 0.348679I
b = 0.610189 + 0.315745I
−4.72027 + 1.50384I −5.59059 − 3.60616I
u = −0.596688 + 0.315979I
a = 0.819943 − 0.823377I
b = −0.174356 − 1.263120I
−4.72027 + 1.50384I −5.59059 − 3.60616I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596688 − 0.315979I
a = −0.801138 + 0.348679I
b = 0.610189 − 0.315745I
−4.72027 − 1.50384I −5.59059 + 3.60616I
u = −0.596688 − 0.315979I
a = 0.819943 + 0.823377I
b = −0.174356 + 1.263120I
−4.72027 − 1.50384I −5.59059 + 3.60616I
u = 0.632184 + 0.066503I
a = −0.489244 + 0.745012I
b = 0.34059 + 1.39699I
−6.89729 − 3.47782I −8.61515 + 4.95314I
u = 0.632184 + 0.066503I
a = −1.058740 − 0.395233I
b = 0.599015 − 1.162350I
−6.89729 − 3.47782I −8.61515 + 4.95314I
u = 0.632184 − 0.066503I
a = −0.489244 − 0.745012I
b = 0.34059 − 1.39699I
−6.89729 + 3.47782I −8.61515 − 4.95314I
u = 0.632184 − 0.066503I
a = −1.058740 + 0.395233I
b = 0.599015 + 1.162350I
−6.89729 + 3.47782I −8.61515 − 4.95314I
u = −0.036115 + 1.379920I
a = −0.14525 + 3.73600I
b = −0.071145 + 1.092410I
1.67010 + 2.19825I 4.55384 − 3.61625I
u = −0.036115 + 1.379920I
a = 4.97603 + 1.10355I
b = −0.123593 − 0.912424I
1.67010 + 2.19825I 4.55384 − 3.61625I
u = −0.036115 − 1.379920I
a = −0.14525 − 3.73600I
b = −0.071145 − 1.092410I
1.67010 − 2.19825I 4.55384 + 3.61625I
u = −0.036115 − 1.379920I
a = 4.97603 − 1.10355I
b = −0.123593 + 0.912424I
1.67010 − 2.19825I 4.55384 + 3.61625I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22801 + 1.42935I
a = 1.328190 − 0.115314I
b = −0.917469 + 0.029790I
0.90165 + 4.53523I 0. − 3.09222I
u = −0.22801 + 1.42935I
a = −1.40186 − 0.44308I
b = 0.474786 + 1.262170I
0.90165 + 4.53523I 0. − 3.09222I
u = −0.22801 − 1.42935I
a = 1.328190 + 0.115314I
b = −0.917469 − 0.029790I
0.90165 − 4.53523I 0. + 3.09222I
u = −0.22801 − 1.42935I
a = −1.40186 + 0.44308I
b = 0.474786 − 1.262170I
0.90165 − 4.53523I 0. + 3.09222I
u = 0.24113 + 1.46019I
a = 1.27404 + 0.62357I
b = −1.073110 − 0.325646I
6.10656 − 6.56751I 5.02440 + 3.41838I
u = 0.24113 + 1.46019I
a = −1.72095 + 0.33539I
b = 0.730734 − 1.186940I
6.10656 − 6.56751I 5.02440 + 3.41838I
u = 0.24113 − 1.46019I
a = 1.27404 − 0.62357I
b = −1.073110 + 0.325646I
6.10656 + 6.56751I 5.02440 − 3.41838I
u = 0.24113 − 1.46019I
a = −1.72095 − 0.33539I
b = 0.730734 + 1.186940I
6.10656 + 6.56751I 5.02440 − 3.41838I
u = −0.25408 + 1.45840I
a = 1.47015 − 0.66625I
b = −1.199750 + 0.285349I
4.13478 + 11.82880I 0. − 7.75337I
u = −0.25408 + 1.45840I
a = −1.79532 − 0.46400I
b = 0.77918 + 1.28933I
4.13478 + 11.82880I 0. − 7.75337I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25408 − 1.45840I
a = 1.47015 + 0.66625I
b = −1.199750 − 0.285349I
4.13478 − 11.82880I 0. + 7.75337I
u = −0.25408 − 1.45840I
a = −1.79532 + 0.46400I
b = 0.77918 − 1.28933I
4.13478 − 11.82880I 0. + 7.75337I
u = 0.20598 + 1.46844I
a = 0.604492 + 0.502279I
b = −0.688196 − 0.471575I
6.63262 − 3.59396I 5.77642 + 3.03909I
u = 0.20598 + 1.46844I
a = −1.45652 − 0.02095I
b = 0.563003 − 0.876122I
6.63262 − 3.59396I 5.77642 + 3.03909I
u = 0.20598 − 1.46844I
a = 0.604492 − 0.502279I
b = −0.688196 + 0.471575I
6.63262 + 3.59396I 5.77642 − 3.03909I
u = 0.20598 − 1.46844I
a = −1.45652 + 0.02095I
b = 0.563003 + 0.876122I
6.63262 + 3.59396I 5.77642 − 3.03909I
u = −0.18821 + 1.47294I
a = −1.203080 + 0.217482I
b = 0.423043 + 0.674782I
5.11137 − 1.63491I 3.54097 + 0.I
u = −0.18821 + 1.47294I
a = 0.116775 − 0.439727I
b = −0.444172 + 0.582855I
5.11137 − 1.63491I 3.54097 + 0.I
u = −0.18821 − 1.47294I
a = −1.203080 − 0.217482I
b = 0.423043 − 0.674782I
5.11137 + 1.63491I 3.54097 + 0.I
u = −0.18821 − 1.47294I
a = 0.116775 + 0.439727I
b = −0.444172 − 0.582855I
5.11137 + 1.63491I 3.54097 + 0.I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.514867
a = −1.33310 + 1.24762I
b = 0.300224 + 1.127120I
−4.29591 −5.72740
u = −0.514867
a = −1.33310 − 1.24762I
b = 0.300224 − 1.127120I
−4.29591 −5.72740
u = −0.216864 + 0.450093I
a = 3.54053 + 0.64125I
b = −0.082306 − 1.166920I
−3.83648 + 1.45331I −1.02647 − 4.36257I
u = −0.216864 + 0.450093I
a = 0.66167 − 3.58318I
b = −0.242715 + 0.837214I
−3.83648 + 1.45331I −1.02647 − 4.36257I
u = −0.216864 − 0.450093I
a = 3.54053 − 0.64125I
b = −0.082306 + 1.166920I
−3.83648 − 1.45331I −1.02647 + 4.36257I
u = −0.216864 − 0.450093I
a = 0.66167 + 3.58318I
b = −0.242715 − 0.837214I
−3.83648 − 1.45331I −1.02647 + 4.36257I
19
III. I
u
3
= h−u
5
+ b − u, u
5
− 4u
4
− u
3
− 3u
2
+ 7a + 4u − 9, u
6
+ u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
12
=
−
1
7
u
5
+
4
7
u
4
+ ··· −
4
7
u +
9
7
u
5
+ u
a
1
=
6
7
u
5
+
4
7
u
4
+ ··· +
3
7
u +
9
7
u
5
+ u
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
29
49
u
4
+
6
49
u
2
+ u +
60
49
4
7
u
5
−
2
7
u
4
+ ··· +
16
7
u −
1
7
a
8
=
6
7
u
5
+
3
7
u
4
+ ··· +
10
7
u +
5
7
−1
a
6
=
4
7
u
5
+
20
49
u
4
+ ··· +
9
7
u +
38
49
3
7
u
5
−
5
7
u
4
+ ··· +
12
7
u −
6
7
a
2
=
−
1
7
u
5
+
3
49
u
4
+ ··· +
3
7
u +
40
49
5
7
u
5
+
1
7
u
4
+ ··· +
13
7
u +
4
7
a
7
=
6
7
u
5
+
3
7
u
4
+ ··· +
10
7
u +
5
7
2u
5
+ u
3
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
+ 4u
2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 2u + 1)
2
c
2
(u
3
+ u
2
+ 2u + 1)
2
c
3
49(49u
6
+ 14u
5
− 68u
4
− 30u
3
+ 35u
2
+ 12u + 5)
c
4
, c
9
, c
10
u
6
+ u
4
+ 2u
2
+ 1
c
5
49(49u
6
− 14u
5
− 68u
4
+ 30u
3
+ 35u
2
− 12u + 5)
c
6
(u
3
− u
2
+ 2u − 1)
2
c
7
, c
8
, c
11
c
12
(u
2
+ 1)
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 10y − 1)
2
c
2
, c
6
(y
3
+ 3y
2
+ 2y − 1)
2
c
3
, c
5
2401(2401y
6
− 6860y
5
+ ··· + 206y + 25)
c
4
, c
9
, c
10
(y
3
+ y
2
+ 2y + 1)
2
c
7
, c
8
, c
11
c
12
(y + 1)
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744862 + 0.877439I
a = −0.262343 + 0.117844I
b = − 1.000000I
−6.31400 − 2.82812I −7.50976 + 2.97945I
u = 0.744862 − 0.877439I
a = −0.262343 − 0.117844I
b = 1.000000I
−6.31400 + 2.82812I −7.50976 − 2.97945I
u = −0.744862 + 0.877439I
a = 0.749579 − 0.359957I
b = − 1.000000I
−6.31400 + 2.82812I −7.50976 − 2.97945I
u = −0.744862 − 0.877439I
a = 0.749579 + 0.359957I
b = 1.000000I
−6.31400 − 2.82812I −7.50976 + 2.97945I
u = 0.754878I
a = 1.227050 − 0.527828I
b = 1.000000I
−2.17641 −0.980490
u = − 0.754878I
a = 1.227050 + 0.527828I
b = − 1.000000I
−2.17641 −0.980490
23
IV. I
u
4
= hb − 1, 8a
2
− 2au + 24a − 3u + 17, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−2
a
12
=
a
1
a
1
=
a + 1
1
a
4
=
u
−u
a
11
=
−1
0
a
3
=
2au +
1
2
a +
25
8
u +
3
4
−au − 2u
a
8
=
a + 2
1
a
6
=
−au +
1
2
a −
15
8
u +
3
4
−au − u
a
2
=
2au + 2a +
23
8
u +
7
2
−au − 2a −
3
2
u −
5
2
a
7
=
a + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8au − 12u + 4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
16(16u
4
+ 16u
3
+ 28u
2
+ 12u + 3)
c
4
, c
9
, c
10
(u
2
+ 2)
2
c
5
16(16u
4
− 16u
3
+ 28u
2
− 12u + 3)
c
6
(u
2
+ u + 1)
2
c
7
, c
8
(u − 1)
4
c
11
, c
12
(u + 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
256(256y
4
+ 640y
3
+ 496y
2
+ 24y + 9)
c
4
, c
9
, c
10
(y + 2)
4
c
7
, c
8
, c
11
c
12
(y − 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.193810 + 0.176777I
b = 1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 1.414210I
a = −1.80619 + 0.17678I
b = 1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
u = − 1.414210I
a = −1.193810 − 0.176777I
b = 1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
u = − 1.414210I
a = −1.80619 − 0.17678I
b = 1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
27
V. I
v
1
= ha, b + 1, 4v
2
− 2v + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
10
=
1
0
a
12
=
0
−1
a
1
=
−1
−1
a
4
=
v
0
a
11
=
1
0
a
3
=
v
−v
a
8
=
2
1
a
6
=
3v
v
a
2
=
v −
3
2
−v −
1
2
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7v −
1
2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
4(4u
2
+ 2u + 1)
c
4
, c
9
, c
10
u
2
c
5
4(4u
2
− 2u + 1)
c
7
, c
8
(u + 1)
2
c
11
, c
12
(u − 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
+ y + 1
c
3
, c
5
16(16y
2
+ 4y + 1)
c
4
, c
9
, c
10
y
2
c
7
, c
8
, c
11
c
12
(y − 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.250000 + 0.433013I
a = 0
b = −1.00000
1.64493 − 2.02988I −2.25000 − 3.03109I
v = 0.250000 − 0.433013I
a = 0
b = −1.00000
1.64493 + 2.02988I −2.25000 + 3.03109I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
3
− 3u
2
+ 2u + 1)
2
(u
33
+ 15u
32
+ ··· + u − 1)
2
· (u
46
+ 24u
45
+ ··· + 1295u + 576)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
33
− u
32
+ ··· − u + 1)
2
· (u
46
− 2u
45
+ ··· − 71u + 24)
c
3
1806336(4u
2
+ 2u + 1)(16u
4
+ 16u
3
+ 28u
2
+ 12u + 3)
· (49u
6
+ 14u
5
− 68u
4
− 30u
3
+ 35u
2
+ 12u + 5)
· (64u
46
− 160u
45
+ ··· + 146u + 11)
· (9u
66
+ 129u
65
+ ··· + 233684u + 29567)
c
4
, c
9
, c
10
u
2
(u
2
+ 2)
2
(u
6
+ u
4
+ 2u
2
+ 1)(u
33
− u
32
+ ··· + 3u − 1)
2
· (u
46
+ 3u
45
+ ··· + 224u + 32)
c
5
1806336(4u
2
− 2u + 1)(16u
4
− 16u
3
+ 28u
2
− 12u + 3)
· (49u
6
− 14u
5
− 68u
4
+ 30u
3
+ 35u
2
− 12u + 5)
· (64u
46
− 160u
45
+ ··· + 146u + 11)
· (9u
66
+ 129u
65
+ ··· + 233684u + 29567)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
3
− u
2
+ 2u − 1)
2
(u
33
− u
32
+ ··· − u + 1)
2
· (u
46
− 2u
45
+ ··· − 71u + 24)
c
7
, c
8
((u − 1)
4
)(u + 1)
2
(u
2
+ 1)
3
(u
46
+ 2u
45
+ ··· + 8u + 3)
· (u
66
− 5u
65
+ ··· − 804u + 125)
c
11
, c
12
((u − 1)
2
)(u + 1)
4
(u
2
+ 1)
3
(u
46
+ 2u
45
+ ··· + 8u + 3)
· (u
66
− 5u
65
+ ··· − 804u + 125)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
3
− 5y
2
+ 10y − 1)
2
(y
33
+ 7y
32
+ ··· + 17y − 1)
2
· (y
46
+ 16y
44
+ ··· + 13494815y + 331776)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
33
+ 15y
32
+ ··· + y − 1)
2
· (y
46
+ 24y
45
+ ··· + 1295y + 576)
c
3
, c
5
3262849744896(16y
2
+ 4y + 1)(256y
4
+ 640y
3
+ ··· + 24y + 9)
· (2401y
6
− 6860y
5
+ 8894y
4
− 5506y
3
+ 1265y
2
+ 206y + 25)
· (4096y
46
+ 60416y
45
+ ··· + 3104y + 121)
· (81y
66
− 1701y
65
+ ··· − 40240423876y + 874207489)
c
4
, c
9
, c
10
y
2
(y + 2)
4
(y
3
+ y
2
+ 2y + 1)
2
(y
33
+ 31y
32
+ ··· + y − 1)
2
· (y
46
+ 41y
45
+ ··· − 5120y + 1024)
c
7
, c
8
, c
11
c
12
((y − 1)
6
)(y + 1)
6
(y
46
+ 14y
45
+ ··· + 302y + 9)
· (y
66
+ 39y
65
+ ··· + 129584y + 15625)
33
