12a
0513
(K12a
0513
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 1 5 4 12 6 10
Solving Sequence
4,10
9 5 8
1,3
7 2 12 11 6
c
9
c
4
c
8
c
3
c
7
c
2
c
12
c
10
c
5
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.92594 × 10
42
u
79
− 6.66950 × 10
42
u
78
+ ··· + 7.86358 × 10
42
b − 2.35601 × 10
43
,
5.36807 × 10
42
u
79
− 2.27727 × 10
43
u
78
+ ··· + 7.86358 × 10
42
a − 1.74971 × 10
44
, u
80
− 4u
79
+ ··· − 52u + 4i
I
u
2
= h−au + b + 1, a
2
+ au − 1, u
2
+ 1i
I
u
3
= h−602a
4
u
2
− 112a
3
u
2
+ ··· − 678a + 1654,
2a
4
u
2
+ a
5
+ 2a
4
u + 4a
4
− 3a
3
u − 8a
2
u
2
− 3a
3
− 6a
2
u + 5u
2
a − 12a
2
+ 4au + 11u
2
+ 9a + 5u + 18,
u
3
+ u
2
+ 2u + 1i
I
u
4
= hau + b, a
2
+ au − 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 103 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
=
h1.93×10
42
u
79
−6.67×10
42
u
78
+· · ·+7.86×10
42
b−2.36×10
43
, 5.37×10
42
u
79
−
2.28 × 10
43
u
78
+ · · · + 7.86 × 10
42
a − 1.75 × 10
44
, u
80
− 4u
79
+ · · · − 52u + 4i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
5
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−0.682650u
79
+ 2.89597u
78
+ ··· − 176.929u + 22.2508
−0.244918u
79
+ 0.848150u
78
+ ··· − 31.1691u + 2.99611
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
0.284048u
79
− 1.00384u
78
+ ··· + 100.169u − 16.0275
0.259001u
79
− 1.01996u
78
+ ··· + 36.9256u − 4.27465
a
2
=
−0.595274u
79
+ 2.67307u
78
+ ··· − 170.692u + 21.3726
−0.245575u
79
+ 0.838980u
78
+ ··· − 34.0566u + 3.54660
a
12
=
−0.437731u
79
+ 2.04782u
78
+ ··· − 145.760u + 19.2547
−0.244918u
79
+ 0.848150u
78
+ ··· − 31.1691u + 2.99611
a
11
=
0.211687u
79
− 0.839912u
78
+ ··· + 3.89957u + 5.74577
−0.381115u
79
+ 1.41021u
78
+ ··· − 36.1654u + 4.19766
a
6
=
1.04592u
79
− 4.04767u
78
+ ··· + 105.753u − 6.02938
−0.123990u
79
+ 0.478152u
78
+ ··· − 0.617434u + 1.20681
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.35269u
79
+ 7.88005u
78
+ ··· − 272.741u + 41.4718
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
+ 39u
79
+ ··· + 6u + 1
c
2
, c
6
u
80
− u
79
+ ··· − 3u
2
+ 1
c
3
u
80
− 4u
79
+ ··· + 16384u + 1024
c
4
, c
8
, c
9
u
80
+ 4u
79
+ ··· + 52u + 4
c
5
, c
11
u
80
− u
79
+ ··· + 6u + 1
c
7
u
80
− 3u
79
+ ··· + 1122u + 989
c
10
, c
12
u
80
− 27u
79
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
+ 9y
79
+ ··· + 18y + 1
c
2
, c
6
y
80
− 39y
79
+ ··· − 6y + 1
c
3
y
80
− 20y
79
+ ··· − 70254592y + 1048576
c
4
, c
8
, c
9
y
80
+ 68y
79
+ ··· − 632y + 16
c
5
, c
11
y
80
− 27y
79
+ ··· − 22y + 1
c
7
y
80
+ 21y
79
+ ··· + 14907310y + 978121
c
10
, c
12
y
80
+ 57y
79
+ ··· − 54y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.551136 + 0.802488I
a = 0.554036 − 0.632918I
b = −0.296637 − 1.259010I
−4.73746 + 0.08999I 0
u = −0.551136 − 0.802488I
a = 0.554036 + 0.632918I
b = −0.296637 + 1.259010I
−4.73746 − 0.08999I 0
u = −0.208379 + 1.008740I
a = 0.1249350 − 0.0323541I
b = −0.226657 + 0.715830I
−1.88182 − 2.17157I 0
u = −0.208379 − 1.008740I
a = 0.1249350 + 0.0323541I
b = −0.226657 − 0.715830I
−1.88182 + 2.17157I 0
u = −0.106567 + 1.055930I
a = 0.842709 − 0.235495I
b = −0.0559371 + 0.0534132I
−1.50643 − 2.08258I 0
u = −0.106567 − 1.055930I
a = 0.842709 + 0.235495I
b = −0.0559371 − 0.0534132I
−1.50643 + 2.08258I 0
u = 0.596084 + 0.710997I
a = −0.493767 − 0.447695I
b = −0.163120 − 1.208000I
−4.92608 + 5.37940I 0
u = 0.596084 − 0.710997I
a = −0.493767 + 0.447695I
b = −0.163120 + 1.208000I
−4.92608 − 5.37940I 0
u = 0.521840 + 0.938751I
a = −0.055226 − 0.427953I
b = 0.013258 − 1.063850I
−4.08872 − 1.79777I 0
u = 0.521840 − 0.938751I
a = −0.055226 + 0.427953I
b = 0.013258 + 1.063850I
−4.08872 + 1.79777I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.408175 + 1.010050I
a = 0.171639 + 0.544181I
b = −0.509729 + 1.240020I
−1.18830 − 2.70563I 0
u = 0.408175 − 1.010050I
a = 0.171639 − 0.544181I
b = −0.509729 − 1.240020I
−1.18830 + 2.70563I 0
u = −0.879762 + 0.227693I
a = −1.51369 + 1.09263I
b = −0.55379 + 1.42889I
−0.91388 − 12.22470I 6.00000 + 9.71272I
u = −0.879762 − 0.227693I
a = −1.51369 − 1.09263I
b = −0.55379 − 1.42889I
−0.91388 + 12.22470I 6.00000 − 9.71272I
u = 0.838234 + 0.262017I
a = 1.27745 + 0.85390I
b = 0.199465 + 1.029370I
−2.02492 + 6.59780I 3.40984 − 5.16517I
u = 0.838234 − 0.262017I
a = 1.27745 − 0.85390I
b = 0.199465 − 1.029370I
−2.02492 − 6.59780I 3.40984 + 5.16517I
u = −0.305412 + 0.799433I
a = −0.1368440 + 0.0226105I
b = −0.215314 + 0.977607I
−1.84711 − 2.26526I 3.71962 + 4.08071I
u = −0.305412 − 0.799433I
a = −0.1368440 − 0.0226105I
b = −0.215314 − 0.977607I
−1.84711 + 2.26526I 3.71962 − 4.08071I
u = −0.528719 + 1.021590I
a = 0.227668 − 0.723744I
b = −0.47028 − 1.34644I
−3.33066 + 7.25011I 0
u = −0.528719 − 1.021590I
a = 0.227668 + 0.723744I
b = −0.47028 + 1.34644I
−3.33066 − 7.25011I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823129 + 0.204152I
a = −1.60401 − 1.00000I
b = −0.56137 − 1.37914I
1.28021 + 7.17762I 8.76583 − 5.85883I
u = 0.823129 − 0.204152I
a = −1.60401 + 1.00000I
b = −0.56137 + 1.37914I
1.28021 − 7.17762I 8.76583 + 5.85883I
u = −0.765302 + 0.332337I
a = −1.36288 + 0.78683I
b = −0.45279 + 1.35433I
−3.33691 − 4.71601I 1.93926 + 4.79761I
u = −0.765302 − 0.332337I
a = −1.36288 − 0.78683I
b = −0.45279 − 1.35433I
−3.33691 + 4.71601I 1.93926 − 4.79761I
u = 0.709218 + 0.403703I
a = 1.139150 + 0.747614I
b = 0.018638 + 1.087730I
−4.06181 − 0.78432I 0.213330 + 0.601164I
u = 0.709218 − 0.403703I
a = 1.139150 − 0.747614I
b = 0.018638 − 1.087730I
−4.06181 + 0.78432I 0.213330 − 0.601164I
u = −0.330389 + 1.137220I
a = −0.553942 − 1.234000I
b = −0.941219 − 0.028962I
0.99595 + 2.18968I 0
u = −0.330389 − 1.137220I
a = −0.553942 + 1.234000I
b = −0.941219 + 0.028962I
0.99595 − 2.18968I 0
u = −0.761131 + 0.226648I
a = 1.29441 − 0.79477I
b = 0.146142 − 0.958477I
0.18029 − 1.72517I 6.96648 + 1.19694I
u = −0.761131 − 0.226648I
a = 1.29441 + 0.79477I
b = 0.146142 + 0.958477I
0.18029 + 1.72517I 6.96648 − 1.19694I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769110 + 0.124508I
a = −2.01859 + 0.33682I
b = −1.140500 + 0.180943I
4.05517 − 6.19535I 11.24164 + 6.13913I
u = −0.769110 − 0.124508I
a = −2.01859 − 0.33682I
b = −1.140500 − 0.180943I
4.05517 + 6.19535I 11.24164 − 6.13913I
u = 0.220897 + 1.201700I
a = −0.221048 + 0.378026I
b = −0.755621 + 1.106820I
−1.01320 − 1.61452I 0
u = 0.220897 − 1.201700I
a = −0.221048 − 0.378026I
b = −0.755621 − 1.106820I
−1.01320 + 1.61452I 0
u = 0.763645 + 0.064433I
a = −1.96075 − 0.18144I
b = −1.126830 − 0.094815I
5.81886 + 1.20518I 14.4550 − 0.8575I
u = 0.763645 − 0.064433I
a = −1.96075 + 0.18144I
b = −1.126830 + 0.094815I
5.81886 − 1.20518I 14.4550 + 0.8575I
u = 0.327694 + 1.195580I
a = −0.696454 + 1.008560I
b = −1.033350 − 0.080637I
2.36178 + 2.75003I 0
u = 0.327694 − 1.195580I
a = −0.696454 − 1.008560I
b = −1.033350 + 0.080637I
2.36178 − 2.75003I 0
u = 0.147606 + 1.296040I
a = 1.63223 − 1.23495I
b = −0.037662 + 1.042620I
−3.72526 − 2.52051I 0
u = 0.147606 − 1.296040I
a = 1.63223 + 1.23495I
b = −0.037662 − 1.042620I
−3.72526 + 2.52051I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.049107 + 1.308430I
a = −0.502531 − 0.144008I
b = −0.949755 − 0.904347I
−4.24144 + 4.07906I 0
u = −0.049107 − 1.308430I
a = −0.502531 + 0.144008I
b = −0.949755 + 0.904347I
−4.24144 − 4.07906I 0
u = 0.670555 + 0.086690I
a = −2.05137 − 0.81648I
b = −0.613705 − 1.242710I
2.33556 + 4.87257I 10.70507 − 5.88102I
u = 0.670555 − 0.086690I
a = −2.05137 + 0.81648I
b = −0.613705 + 1.242710I
2.33556 − 4.87257I 10.70507 + 5.88102I
u = 0.315351 + 1.304030I
a = −0.921696 + 0.699551I
b = −1.203010 − 0.251403I
1.54253 + 5.09315I 0
u = 0.315351 − 1.304030I
a = −0.921696 − 0.699551I
b = −1.203010 + 0.251403I
1.54253 − 5.09315I 0
u = 0.266524 + 1.325000I
a = −1.62612 + 1.19602I
b = −0.51362 − 1.36083I
−2.10689 + 8.26650I 0
u = 0.266524 − 1.325000I
a = −1.62612 − 1.19602I
b = −0.51362 + 1.36083I
−2.10689 − 8.26650I 0
u = 0.585654 + 0.221603I
a = 1.32826 − 0.55799I
b = 0.211347 − 0.394465I
−0.36980 + 4.43761I 4.75087 − 6.66233I
u = 0.585654 − 0.221603I
a = 1.32826 + 0.55799I
b = 0.211347 + 0.394465I
−0.36980 − 4.43761I 4.75087 + 6.66233I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121476 + 1.374030I
a = 0.776792 − 0.099407I
b = 0.497170 − 0.215952I
−7.00972 − 0.03580I 0
u = 0.121476 − 1.374030I
a = 0.776792 + 0.099407I
b = 0.497170 + 0.215952I
−7.00972 + 0.03580I 0
u = −0.319084 + 1.344980I
a = −1.014690 − 0.624204I
b = −1.275130 + 0.292082I
−0.57753 − 10.12060I 0
u = −0.319084 − 1.344980I
a = −1.014690 + 0.624204I
b = −1.275130 − 0.292082I
−0.57753 + 10.12060I 0
u = 0.245398 + 1.369620I
a = 0.722283 − 0.225370I
b = 0.505471 − 0.436922I
−5.38272 + 7.52809I 0
u = 0.245398 − 1.369620I
a = 0.722283 + 0.225370I
b = 0.505471 + 0.436922I
−5.38272 − 7.52809I 0
u = −0.31258 + 1.39281I
a = 1.48142 + 0.38881I
b = 0.264823 − 1.069660I
−4.95968 − 5.61831I 0
u = −0.31258 − 1.39281I
a = 1.48142 − 0.38881I
b = 0.264823 + 1.069660I
−4.95968 + 5.61831I 0
u = 0.34340 + 1.39206I
a = −1.60088 + 0.60509I
b = −0.56567 − 1.47569I
−3.78107 + 11.38600I 0
u = 0.34340 − 1.39206I
a = −1.60088 − 0.60509I
b = −0.56567 + 1.47569I
−3.78107 − 11.38600I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02337 + 1.45374I
a = 0.149541 − 1.005020I
b = −0.150773 + 1.367660I
−8.93138 − 2.93585I 0
u = −0.02337 − 1.45374I
a = 0.149541 + 1.005020I
b = −0.150773 − 1.367660I
−8.93138 + 2.93585I 0
u = −0.29501 + 1.42781I
a = −1.30790 − 0.65861I
b = −0.49197 + 1.49263I
−8.94290 − 8.53329I 0
u = −0.29501 − 1.42781I
a = −1.30790 + 0.65861I
b = −0.49197 − 1.49263I
−8.94290 + 8.53329I 0
u = 0.34014 + 1.41816I
a = 1.45611 − 0.29908I
b = 0.319417 + 1.089870I
−7.36888 + 10.84370I 0
u = 0.34014 − 1.41816I
a = 1.45611 + 0.29908I
b = 0.319417 − 1.089870I
−7.36888 − 10.84370I 0
u = 0.25771 + 1.43558I
a = 1.292160 − 0.461107I
b = 0.212673 + 1.164040I
−9.91847 + 2.66208I 0
u = 0.25771 − 1.43558I
a = 1.292160 + 0.461107I
b = 0.212673 − 1.164040I
−9.91847 − 2.66208I 0
u = −0.36648 + 1.41215I
a = −1.59384 − 0.46201I
b = −0.58244 + 1.50990I
−6.1192 − 16.7066I 0
u = −0.36648 − 1.41215I
a = −1.59384 + 0.46201I
b = −0.58244 − 1.50990I
−6.1192 + 16.7066I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267652 + 0.469417I
a = 1.287930 − 0.150939I
b = 0.155923 − 0.055103I
−1.47309 − 1.47748I 0.853173 + 0.501389I
u = 0.267652 − 0.469417I
a = 1.287930 + 0.150939I
b = 0.155923 + 0.055103I
−1.47309 + 1.47748I 0.853173 − 0.501389I
u = −0.03028 + 1.50039I
a = 0.383013 + 0.722409I
b = −0.053416 − 1.393890I
−12.59510 − 1.27716I 0
u = −0.03028 − 1.50039I
a = 0.383013 − 0.722409I
b = −0.053416 + 1.393890I
−12.59510 + 1.27716I 0
u = 0.07316 + 1.49993I
a = −0.118714 + 0.762219I
b = −0.18506 − 1.45576I
−12.4175 + 7.3131I 0
u = 0.07316 − 1.49993I
a = −0.118714 − 0.762219I
b = −0.18506 + 1.45576I
−12.4175 − 7.3131I 0
u = −0.410317 + 0.068593I
a = 0.076036 + 0.775710I
b = −0.417482 + 0.255970I
0.972335 − 0.113438I 11.49870 + 0.99619I
u = −0.410317 − 0.068593I
a = 0.076036 − 0.775710I
b = −0.417482 − 0.255970I
0.972335 + 0.113438I 11.49870 − 0.99619I
u = 0.168606 + 0.085574I
a = 1.38717 − 5.08704I
b = −0.501486 − 0.738647I
0.08992 + 4.10562I 9.80690 − 7.22475I
u = 0.168606 − 0.085574I
a = 1.38717 + 5.08704I
b = −0.501486 + 0.738647I
0.08992 − 4.10562I 9.80690 + 7.22475I
12
II. I
u
2
= h−au + b + 1, a
2
+ au − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−1
a
5
=
u
0
a
8
=
0
−1
a
1
=
a
au − 1
a
3
=
0
u
a
7
=
−au + 1
u − 1
a
2
=
a
au − a − 1
a
12
=
−au + a + 1
au − 1
a
11
=
−au − u + 1
au
a
6
=
−au
a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8au
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
2
− u + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
u
4
− u
2
+ 1
c
3
u
4
c
4
, c
8
, c
9
(u
2
+ 1)
2
c
10
(u
2
+ u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
(y
2
− y + 1)
2
c
3
y
4
c
4
, c
8
, c
9
(y + 1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.866025 − 0.500000I
b = −0.500000 − 0.866025I
−1.64493 − 4.05977I 4.00000 + 6.92820I
u = 1.000000I
a = 0.866025 − 0.500000I
b = −0.500000 + 0.866025I
−1.64493 + 4.05977I 4.00000 − 6.92820I
u = − 1.000000I
a = −0.866025 + 0.500000I
b = −0.500000 + 0.866025I
−1.64493 + 4.05977I 4.00000 − 6.92820I
u = − 1.000000I
a = 0.866025 + 0.500000I
b = −0.500000 − 0.866025I
−1.64493 − 4.05977I 4.00000 + 6.92820I
16
III. I
u
3
= h−602a
4
u
2
− 112a
3
u
2
+ · · · − 678a + 1654, 2a
4
u
2
− 8a
2
u
2
+ · · · +
9a + 18, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
5
=
u
−u
2
− u − 1
a
8
=
u
2
+ 1
u
2
+ u + 1
a
1
=
a
0.523023a
4
u
2
+ 0.0973067a
3
u
2
+ ··· + 0.589053a − 1.43701
a
3
=
1
0
a
7
=
0.0225891a
4
u
2
− 0.112076a
3
u
2
+ ··· − 0.874891a + 2.13727
0.0816681a
4
u
2
− 0.635969a
3
u
2
+ ··· − 0.778454a + 2.03475
a
2
=
−0.523023a
4
u
2
− 0.0973067a
3
u
2
+ ··· + 0.410947a + 1.43701
0.523023a
4
u
2
+ 0.0973067a
3
u
2
+ ··· + 0.589053a − 1.43701
a
12
=
−0.523023a
4
u
2
− 0.0973067a
3
u
2
+ ··· + 0.410947a + 1.43701
0.523023a
4
u
2
+ 0.0973067a
3
u
2
+ ··· + 0.589053a − 1.43701
a
11
=
−0.901825a
4
u
2
+ 0.320591a
3
u
2
+ ··· − 0.148566a + 2.21199
0.960904a
4
u
2
− 0.844483a
3
u
2
+ ··· + 0.245004a − 2.31451
a
6
=
0.0877498a
4
u
2
+ 0.295395a
3
u
2
+ ··· + 0.716768a − 2.00521
−0.435274a
4
u
2
+ 0.198089a
3
u
2
+ ··· − 0.872285a − 0.568202
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 6u
14
+ ··· + 2u + 1
c
2
, c
5
, c
6
c
11
u
15
− 3u
13
+ ··· + u
2
− 1
c
3
(u
3
+ u
2
− 1)
5
c
4
, c
8
, c
9
(u
3
− u
2
+ 2u − 1)
5
c
7
u
15
− 3u
13
+ ··· + 6u − 1
c
10
, c
12
u
15
− 6u
14
+ ··· + 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
15
+ 6y
14
+ ··· − 6y −1
c
2
, c
5
, c
6
c
11
y
15
− 6y
14
+ ··· + 2y −1
c
3
(y
3
− y
2
+ 2y −1)
5
c
4
, c
8
, c
9
(y
3
+ 3y
2
+ 2y −1)
5
c
7
y
15
− 6y
14
+ ··· + 26y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.743485 − 0.454988I
b = −1.099900 + 0.434905I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = 0.667721 + 0.158832I
b = 0.386904 + 0.394695I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = −0.393785 − 0.432427I
b = −0.88734 − 1.13381I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = 1.68366 + 0.81495I
b = 0.067189 − 1.008200I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = −1.45923 − 1.57609I
b = −0.466851 + 1.312400I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = −0.743485 + 0.454988I
b = −1.099900 − 0.434905I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.667721 − 0.158832I
b = 0.386904 − 0.394695I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = −0.393785 + 0.432427I
b = −0.88734 + 1.13381I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 1.68366 − 0.81495I
b = 0.067189 + 1.008200I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = −1.45923 + 1.57609I
b = −0.466851 − 1.312400I
−3.02413 + 2.82812I 2.49024 − 2.97945I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569840
a = −1.17678
b = −0.803523
1.11345 9.01950
u = −0.569840
a = 1.32386 + 0.76221I
b = 0.045572 + 0.634784I
1.11345 9.01950
u = −0.569840
a = 1.32386 − 0.76221I
b = 0.045572 − 0.634784I
1.11345 9.01950
u = −0.569840
a = −2.49035 + 0.78497I
b = −0.643810 + 1.156050I
1.11345 9.01950
u = −0.569840
a = −2.49035 − 0.78497I
b = −0.643810 − 1.156050I
1.11345 9.01950
21
IV. I
u
4
= hau + b, a
2
+ au − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
−1
a
5
=
u
0
a
8
=
0
−1
a
1
=
a
−au
a
3
=
0
u
a
7
=
−au + 1
−a − u − 1
a
2
=
a
−au − a
a
12
=
au + a
−au
a
11
=
au + a + u
−au + 1
a
6
=
−au
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
2
− u + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
u
4
− u
2
+ 1
c
3
u
4
c
4
, c
8
, c
9
(u
2
+ 1)
2
c
10
(u
2
+ u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
5
, c
6
c
7
, c
11
(y
2
− y + 1)
2
c
3
y
4
c
4
, c
8
, c
9
(y + 1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.866025 − 0.500000I
b = −0.500000 + 0.866025I
−1.64493 4.00000
u = 1.000000I
a = 0.866025 − 0.500000I
b = −0.500000 − 0.866025I
−1.64493 4.00000
u = − 1.000000I
a = −0.866025 + 0.500000I
b = −0.500000 − 0.866025I
−1.64493 4.00000
u = − 1.000000I
a = 0.866025 + 0.500000I
b = −0.500000 + 0.866025I
−1.64493 4.00000
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
15
+ 6u
14
+ ··· + 2u + 1)(u
80
+ 39u
79
+ ··· + 6u + 1)
c
2
, c
6
((u
4
− u
2
+ 1)
2
)(u
15
− 3u
13
+ ··· + u
2
− 1)(u
80
− u
79
+ ··· − 3u
2
+ 1)
c
3
u
8
(u
3
+ u
2
− 1)
5
(u
80
− 4u
79
+ ··· + 16384u + 1024)
c
4
, c
8
, c
9
((u
2
+ 1)
4
)(u
3
− u
2
+ 2u − 1)
5
(u
80
+ 4u
79
+ ··· + 52u + 4)
c
5
, c
11
((u
4
− u
2
+ 1)
2
)(u
15
− 3u
13
+ ··· + u
2
− 1)(u
80
− u
79
+ ··· + 6u + 1)
c
7
((u
4
− u
2
+ 1)
2
)(u
15
− 3u
13
+ ··· + 6u − 1)
· (u
80
− 3u
79
+ ··· + 1122u + 989)
c
10
((u
2
+ u + 1)
4
)(u
15
− 6u
14
+ ··· + 2u − 1)(u
80
− 27u
79
+ ··· − 22u + 1)
c
12
((u
2
− u + 1)
4
)(u
15
− 6u
14
+ ··· + 2u − 1)(u
80
− 27u
79
+ ··· − 22u + 1)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
15
+ 6y
14
+ ··· − 6y −1)(y
80
+ 9y
79
+ ··· + 18y + 1)
c
2
, c
6
((y
2
− y + 1)
4
)(y
15
− 6y
14
+ ··· + 2y −1)(y
80
− 39y
79
+ ··· − 6y + 1)
c
3
y
8
(y
3
− y
2
+ 2y −1)
5
(y
80
− 20y
79
+ ··· − 7.02546 × 10
7
y + 1048576)
c
4
, c
8
, c
9
((y + 1)
8
)(y
3
+ 3y
2
+ 2y −1)
5
(y
80
+ 68y
79
+ ··· − 632y + 16)
c
5
, c
11
((y
2
− y + 1)
4
)(y
15
− 6y
14
+ ··· + 2y −1)(y
80
− 27y
79
+ ··· − 22y + 1)
c
7
((y
2
− y + 1)
4
)(y
15
− 6y
14
+ ··· + 26y −1)
· (y
80
+ 21y
79
+ ··· + 14907310y + 978121)
c
10
, c
12
((y
2
+ y + 1)
4
)(y
15
+ 6y
14
+ ··· − 6y −1)(y
80
+ 57y
79
+ ··· − 54y + 1)
27
