12n
0445
(K12n
0445
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 9 11 1 5 8 7 4
Solving Sequence
7,11
8
5,12
4 1 3 10 9 6 2
c
7
c
11
c
4
c
12
c
3
c
10
c
9
c
6
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4.88127 × 10
25
u
40
− 6.12725 × 10
26
u
39
+ ··· + 1.13889 × 10
27
b + 1.45283 × 10
27
,
− 1.45283 × 10
27
u
40
− 1.60788 × 10
28
u
39
+ ··· + 2.27778 × 10
27
a + 3.79150 × 10
27
, u
41
+ 11u
40
+ ··· + u − 2i
I
u
2
= h−2u
21
+ 19u
20
+ ··· + b − 1, −2u
21
a − 3u
21
+ ··· + 34a − 19, u
22
− 9u
21
+ ··· − u + 2i
I
u
3
= hu
18
− 8u
17
+ ··· + b + 5, 5u
18
− 37u
17
+ ··· + 3a + 11, u
19
− 8u
18
+ ··· + 22u − 3i
I
v
1
= ha, b + v, v
2
− v + 1i
* 4 irreducible components of dim
C
= 0, with total 106 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
= h4.88×10
25
u
40
−6.13×10
26
u
39
+· · ·+1.14×10
27
b+1.45×10
27
, −1.45×
10
27
u
40
−1.61×10
28
u
39
+· · ·+2.28×10
27
a+3.79×10
27
, u
41
+11u
40
+· · ·+u−2i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
0.637828u
40
+ 7.05897u
39
+ ··· + 1.58542u − 1.66456
−0.0428599u
40
+ 0.538002u
39
+ ··· + 2.30239u − 1.27566
a
12
=
−u
u
a
4
=
0.680688u
40
+ 6.52097u
39
+ ··· − 0.716970u − 0.388904
−0.0428599u
40
+ 0.538002u
39
+ ··· + 2.30239u − 1.27566
a
1
=
0.207988u
40
+ 0.989850u
39
+ ··· − 7.34286u + 1.00547
0.819161u
40
+ 9.48963u
39
+ ··· + 3.07598u − 2.05430
a
3
=
0.296693u
40
+ 2.56331u
39
+ ··· − 0.742559u + 0.268642
0.281486u
40
+ 3.50776u
39
+ ··· + 1.26811u − 0.743072
a
10
=
u
u
3
+ u
a
9
=
−0.270868u
40
− 2.54290u
39
+ ··· − 2.46940u − 0.632851
−0.436658u
40
− 4.27983u
39
+ ··· + 1.36198u + 0.541737
a
6
=
0.0572819u
40
+ 0.783896u
39
+ ··· + 2.88773u + 2.45935
−0.0867526u
40
− 1.16787u
39
+ ··· − 2.34038u + 0.331579
a
2
=
−0.0310885u
40
− 0.596983u
39
+ ··· − 4.03552u − 1.81429
0.0740473u
40
+ 1.07368u
39
+ ··· + 2.39076u − 0.0351562
(ii) Obstruction class = −1
(iii) Cusp Shapes =
378478785869090728393822916
1138889945132180533501554689
u
40
+
11896145826997136075657447571
1138889945132180533501554689
u
39
+
··· +
19860747148497818423208281317
1138889945132180533501554689
u −
23171170042984224447109221988
1138889945132180533501554689
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 18u
40
+ ··· + 545u + 16
c
2
, c
5
u
41
+ 10u
40
+ ··· + 47u + 4
c
3
, c
9
u
41
− 5u
39
+ ··· + 84u + 19
c
4
, c
12
u
41
+ 2u
40
+ ··· − 2u + 1
c
6
, c
8
u
41
+ u
40
+ ··· − 10u
2
+ 1
c
7
, c
10
, c
11
u
41
− 11u
40
+ ··· + u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 18y
40
+ ··· + 181953y −256
c
2
, c
5
y
41
− 18y
40
+ ··· + 545y −16
c
3
, c
9
y
41
− 10y
40
+ ··· + 4814y −361
c
4
, c
12
y
41
+ 54y
40
+ ··· + 14y −1
c
6
, c
8
y
41
− 13y
40
+ ··· + 20y −1
c
7
, c
10
, c
11
y
41
+ 15y
40
+ ··· + 53y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706689 + 0.696257I
a = −0.44253 + 1.82957I
b = 0.96112 + 1.60105I
−4.16406 − 0.45245I −25.4999 + 8.2253I
u = −0.706689 − 0.696257I
a = −0.44253 − 1.82957I
b = 0.96112 − 1.60105I
−4.16406 + 0.45245I −25.4999 − 8.2253I
u = 0.054180 + 1.030020I
a = −0.205903 − 0.584165I
b = −0.590549 + 0.243735I
2.74291 − 1.39069I −3.13201 + 4.53829I
u = 0.054180 − 1.030020I
a = −0.205903 + 0.584165I
b = −0.590549 − 0.243735I
2.74291 + 1.39069I −3.13201 − 4.53829I
u = −0.662735 + 0.842868I
a = −1.20996 + 0.98701I
b = 0.03003 + 1.67396I
−2.14687 − 1.05402I −7.74942 + 6.28637I
u = −0.662735 − 0.842868I
a = −1.20996 − 0.98701I
b = 0.03003 − 1.67396I
−2.14687 + 1.05402I −7.74942 − 6.28637I
u = 0.439686 + 1.004910I
a = −0.227962 + 0.447265I
b = 0.549691 + 0.032423I
0.53392 − 5.39252I −5.32610 + 6.80273I
u = 0.439686 − 1.004910I
a = −0.227962 − 0.447265I
b = 0.549691 − 0.032423I
0.53392 + 5.39252I −5.32610 − 6.80273I
u = −0.715109 + 0.936991I
a = 0.89217 − 1.39574I
b = −0.66980 − 1.83406I
−1.83014 + 6.43547I −5.1590 − 14.1797I
u = −0.715109 − 0.936991I
a = 0.89217 + 1.39574I
b = −0.66980 + 1.83406I
−1.83014 − 6.43547I −5.1590 + 14.1797I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.639753 + 1.021650I
a = 1.36343 − 0.56041I
b = 0.29972 − 1.75146I
−3.15249 + 5.67349I −22.3042 − 5.1134I
u = −0.639753 − 1.021650I
a = 1.36343 + 0.56041I
b = 0.29972 + 1.75146I
−3.15249 − 5.67349I −22.3042 + 5.1134I
u = 0.749226 + 0.080309I
a = 0.634776 − 0.408448I
b = −0.508392 + 0.255042I
−1.77251 − 3.09207I −9.97234 + 6.78819I
u = 0.749226 − 0.080309I
a = 0.634776 + 0.408448I
b = −0.508392 − 0.255042I
−1.77251 + 3.09207I −9.97234 − 6.78819I
u = −1.077050 + 0.731963I
a = −0.755315 + 0.956096I
b = −0.11369 + 1.58263I
−3.86757 − 4.67435I 0
u = −1.077050 − 0.731963I
a = −0.755315 − 0.956096I
b = −0.11369 − 1.58263I
−3.86757 + 4.67435I 0
u = −0.991014 + 0.898447I
a = 0.853887 − 0.830660I
b = 0.09991 − 1.59037I
−9.50663 − 2.07425I 0
u = −0.991014 − 0.898447I
a = 0.853887 + 0.830660I
b = 0.09991 + 1.59037I
−9.50663 + 2.07425I 0
u = −0.909466 + 1.012270I
a = −0.610859 + 1.219880I
b = 0.67929 + 1.72779I
−9.11357 + 9.02534I 0
u = −0.909466 − 1.012270I
a = −0.610859 − 1.219880I
b = 0.67929 − 1.72779I
−9.11357 − 9.02534I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317085 + 1.324460I
a = 0.167071 − 0.176954I
b = −0.287344 − 0.165168I
1.91772 − 2.11217I 0
u = 0.317085 − 1.324460I
a = 0.167071 + 0.176954I
b = −0.287344 + 0.165168I
1.91772 + 2.11217I 0
u = 0.551588 + 0.303342I
a = −0.685929 + 0.484409I
b = 0.525291 − 0.059123I
−1.096810 + 0.369586I −7.78047 + 1.64670I
u = 0.551588 − 0.303342I
a = −0.685929 − 0.484409I
b = 0.525291 + 0.059123I
−1.096810 − 0.369586I −7.78047 − 1.64670I
u = 0.598810 + 0.171732I
a = 0.774821 + 0.711251I
b = −0.341827 − 0.558966I
−1.91659 − 1.91366I −9.00153 + 2.78248I
u = 0.598810 − 0.171732I
a = 0.774821 − 0.711251I
b = −0.341827 + 0.558966I
−1.91659 + 1.91366I −9.00153 − 2.78248I
u = −1.165560 + 0.768008I
a = 0.698856 − 0.909733I
b = 0.11588 − 1.59708I
−5.97721 − 10.12420I 0
u = −1.165560 − 0.768008I
a = 0.698856 + 0.909733I
b = 0.11588 + 1.59708I
−5.97721 + 10.12420I 0
u = −0.86763 + 1.13055I
a = 0.672250 − 1.107310I
b = −0.66860 − 1.72074I
−2.60013 + 11.71520I 0
u = −0.86763 − 1.13055I
a = 0.672250 + 1.107310I
b = −0.66860 + 1.72074I
−2.60013 − 11.71520I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08068 + 1.45257I
a = −0.349159 − 0.015316I
b = 0.005923 + 0.508414I
5.17956 − 2.13402I 0
u = 0.08068 − 1.45257I
a = −0.349159 + 0.015316I
b = 0.005923 − 0.508414I
5.17956 + 2.13402I 0
u = 0.530027
a = −0.611909
b = 0.324328
−0.845057 −11.6180
u = −0.90994 + 1.16307I
a = −0.635453 + 1.076980I
b = 0.67438 + 1.71907I
−4.6756 + 17.5700I 0
u = −0.90994 − 1.16307I
a = −0.635453 − 1.076980I
b = 0.67438 − 1.71907I
−4.6756 − 17.5700I 0
u = 0.16583 + 1.51682I
a = 0.330656 − 0.061308I
b = −0.147825 − 0.491380I
4.13932 − 6.99541I 0
u = 0.16583 − 1.51682I
a = 0.330656 + 0.061308I
b = −0.147825 + 0.491380I
4.13932 + 6.99541I 0
u = −0.379598 + 0.214574I
a = −1.36798 + 2.33209I
b = −0.018879 + 1.178790I
−1.67453 − 1.71586I −7.00815 + 4.04385I
u = −0.379598 − 0.214574I
a = −1.36798 − 2.33209I
b = −0.018879 − 1.178790I
−1.67453 + 1.71586I −7.00815 − 4.04385I
u = 0.302462 + 0.289728I
a = −1.84091 − 1.08136I
b = 0.243505 + 0.860433I
−1.71950 + 1.88942I −7.73833 − 4.11458I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302462 − 0.289728I
a = −1.84091 + 1.08136I
b = 0.243505 − 0.860433I
−1.71950 − 1.88942I −7.73833 + 4.11458I
9
II. I
u
2
=
h−2u
21
+19u
20
+· · ·+b−1, −2u
21
a−3u
21
+· · ·+34a−19, u
22
−9u
21
+· · ·−u+2i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
a
2u
21
− 19u
20
+ ··· + 8u + 1
a
12
=
−u
u
a
4
=
−2u
21
+ 19u
20
+ ··· + a − 1
2u
21
− 19u
20
+ ··· + 8u + 1
a
1
=
−2u
21
a +
1
2
u
21
+ ··· − a −
1
2
−1
a
3
=
u
20
− 9u
19
+ ··· + a + 2
2u
21
− 18u
20
+ ··· + 4u + 1
a
10
=
u
u
3
+ u
a
9
=
−2u
21
a +
1
2
u
21
+ ··· − 3a −
1
2
−u
20
a + 9u
19
a + ··· − 2a + 1
a
6
=
1
2
u
21
−
9
2
u
20
+ ··· − a −
1
2
−u
18
a + 7u
17
a + ··· − 2a − 1
a
2
=
−u
21
a +
1
2
u
21
+ ··· +
7
2
u −
1
2
u
21
− 9u
20
+ ··· + au + 6u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
21
+ 29u
20
− 144u
19
+ 471u
18
− 1127u
17
+ 2093u
16
−
3160u
15
+ 4048u
14
− 4576u
13
+ 4688u
12
− 4396u
11
+ 3795u
10
− 3049u
9
+ 2299u
8
−
1600u
7
+ 1028u
6
− 621u
5
+ 359u
4
− 176u
3
+ 83u
2
− 39u + 7
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
22
+ 10u
21
+ ··· + 6u
2
+ 1)
2
c
2
, c
5
(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
c
3
, c
9
u
44
+ 2u
43
+ ··· − 5637u + 2363
c
4
, c
12
u
44
+ 4u
43
+ ··· + 42835u + 8921
c
6
, c
8
u
44
− 3u
43
+ ··· − 64u + 23
c
7
, c
10
, c
11
(u
22
+ 9u
21
+ ··· + u + 2)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 6y
21
+ ··· + 12y + 1)
2
c
2
, c
5
(y
22
− 10y
21
+ ··· + 6y
2
+ 1)
2
c
3
, c
9
y
44
− 20y
43
+ ··· − 96091903y + 5583769
c
4
, c
12
y
44
+ 28y
43
+ ··· + 190747193y + 79584241
c
6
, c
8
y
44
+ 13y
43
+ ··· − 10582y + 529
c
7
, c
10
, c
11
(y
22
+ 3y
21
+ ··· + 43y + 4)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.082505 + 0.876862I
a = −0.994227 + 0.559616I
b = 1.168570 − 0.479238I
2.57347 − 6.33920I −4.37211 + 3.75640I
u = −0.082505 + 0.876862I
a = 0.66603 + 1.27001I
b = 0.408677 + 0.917971I
2.57347 − 6.33920I −4.37211 + 3.75640I
u = −0.082505 − 0.876862I
a = −0.994227 − 0.559616I
b = 1.168570 + 0.479238I
2.57347 + 6.33920I −4.37211 − 3.75640I
u = −0.082505 − 0.876862I
a = 0.66603 − 1.27001I
b = 0.408677 − 0.917971I
2.57347 + 6.33920I −4.37211 − 3.75640I
u = 1.051620 + 0.552954I
a = −0.254635 − 0.923856I
b = 0.08978 − 1.86403I
−5.78853 + 0.61650I −17.5868 − 1.7638I
u = 1.051620 + 0.552954I
a = 0.66327 + 1.42377I
b = −0.243071 + 1.112350I
−5.78853 + 0.61650I −17.5868 − 1.7638I
u = 1.051620 − 0.552954I
a = −0.254635 + 0.923856I
b = 0.08978 + 1.86403I
−5.78853 − 0.61650I −17.5868 + 1.7638I
u = 1.051620 − 0.552954I
a = 0.66327 − 1.42377I
b = −0.243071 − 1.112350I
−5.78853 − 0.61650I −17.5868 + 1.7638I
u = −0.182575 + 0.789359I
a = 0.771291 − 0.798362I
b = −1.230910 + 0.284989I
4.00164 − 0.70655I −2.19340 − 2.74214I
u = −0.182575 + 0.789359I
a = −0.68507 − 1.40092I
b = −0.489376 − 0.754586I
4.00164 − 0.70655I −2.19340 − 2.74214I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182575 − 0.789359I
a = 0.771291 + 0.798362I
b = −1.230910 − 0.284989I
4.00164 + 0.70655I −2.19340 + 2.74214I
u = −0.182575 − 0.789359I
a = −0.68507 + 1.40092I
b = −0.489376 + 0.754586I
4.00164 + 0.70655I −2.19340 + 2.74214I
u = 0.888328 + 0.821810I
a = 0.401655 + 0.956499I
b = −0.10086 + 1.63729I
−3.58480 − 2.91734I −9.58143 + 2.23849I
u = 0.888328 + 0.821810I
a = −0.857594 − 1.049740I
b = 0.429259 − 1.179770I
−3.58480 − 2.91734I −9.58143 + 2.23849I
u = 0.888328 − 0.821810I
a = 0.401655 − 0.956499I
b = −0.10086 − 1.63729I
−3.58480 + 2.91734I −9.58143 − 2.23849I
u = 0.888328 − 0.821810I
a = −0.857594 + 1.049740I
b = 0.429259 + 1.179770I
−3.58480 + 2.91734I −9.58143 − 2.23849I
u = −0.502606 + 0.558420I
a = −0.049171 + 0.545384I
b = 1.81734 + 0.03703I
1.09964 + 8.87036I −9.8963 − 11.1459I
u = −0.502606 + 0.558420I
a = 1.58159 + 1.83091I
b = 0.279840 + 0.301571I
1.09964 + 8.87036I −9.8963 − 11.1459I
u = −0.502606 − 0.558420I
a = −0.049171 − 0.545384I
b = 1.81734 − 0.03703I
1.09964 − 8.87036I −9.8963 + 11.1459I
u = −0.502606 − 0.558420I
a = 1.58159 − 1.83091I
b = 0.279840 − 0.301571I
1.09964 − 8.87036I −9.8963 + 11.1459I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.422081 + 0.604834I
a = 0.114470 − 0.665679I
b = −1.67854 − 0.04798I
3.16775 + 3.23482I −5.63518 − 6.95069I
u = −0.422081 + 0.604834I
a = −1.24905 − 1.90355I
b = −0.354310 − 0.350206I
3.16775 + 3.23482I −5.63518 − 6.95069I
u = −0.422081 − 0.604834I
a = 0.114470 + 0.665679I
b = −1.67854 + 0.04798I
3.16775 − 3.23482I −5.63518 + 6.95069I
u = −0.422081 − 0.604834I
a = −1.24905 + 1.90355I
b = −0.354310 + 0.350206I
3.16775 − 3.23482I −5.63518 + 6.95069I
u = 0.802265 + 1.111960I
a = −0.783193 − 0.659087I
b = 0.69440 − 1.33953I
−2.65613 − 3.32247I −7.06262 + 4.78079I
u = 0.802265 + 1.111960I
a = 0.495942 + 0.982294I
b = −0.104553 + 1.399650I
−2.65613 − 3.32247I −7.06262 + 4.78079I
u = 0.802265 − 1.111960I
a = −0.783193 + 0.659087I
b = 0.69440 + 1.33953I
−2.65613 + 3.32247I −7.06262 − 4.78079I
u = 0.802265 − 1.111960I
a = 0.495942 − 0.982294I
b = −0.104553 − 1.399650I
−2.65613 + 3.32247I −7.06262 − 4.78079I
u = −0.233653 + 0.464879I
a = 0.284498 + 0.968652I
b = 1.59386 + 0.60943I
−2.74656 + 0.64646I −4.58105 − 11.49115I
u = −0.233653 + 0.464879I
a = 0.32914 + 3.26313I
b = 0.516780 + 0.094072I
−2.74656 + 0.64646I −4.58105 − 11.49115I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233653 − 0.464879I
a = 0.284498 − 0.968652I
b = 1.59386 − 0.60943I
−2.74656 − 0.64646I −4.58105 + 11.49115I
u = −0.233653 − 0.464879I
a = 0.32914 − 3.26313I
b = 0.516780 − 0.094072I
−2.74656 − 0.64646I −4.58105 + 11.49115I
u = 1.19187 + 0.88971I
a = −0.372278 − 0.787230I
b = 0.33790 − 1.79489I
−5.90168 − 5.56778I −18.6777 + 6.1462I
u = 1.19187 + 0.88971I
a = 0.539838 + 1.102960I
b = −0.256700 + 1.269500I
−5.90168 − 5.56778I −18.6777 + 6.1462I
u = 1.19187 − 0.88971I
a = −0.372278 + 0.787230I
b = 0.33790 + 1.79489I
−5.90168 + 5.56778I −18.6777 − 6.1462I
u = 1.19187 − 0.88971I
a = 0.539838 − 1.102960I
b = −0.256700 − 1.269500I
−5.90168 + 5.56778I −18.6777 − 6.1462I
u = 0.89170 + 1.22557I
a = −0.503664 − 0.972041I
b = 0.150661 − 1.350040I
−3.78159 − 7.76222I −11.1837 + 10.9706I
u = 0.89170 + 1.22557I
a = 0.661786 + 0.604432I
b = −0.74219 + 1.48405I
−3.78159 − 7.76222I −11.1837 + 10.9706I
u = 0.89170 − 1.22557I
a = −0.503664 + 0.972041I
b = 0.150661 + 1.350040I
−3.78159 + 7.76222I −11.1837 − 10.9706I
u = 0.89170 − 1.22557I
a = 0.661786 − 0.604432I
b = −0.74219 − 1.48405I
−3.78159 + 7.76222I −11.1837 − 10.9706I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09763 + 1.08982I
a = 0.503463 + 0.723010I
b = −0.52189 + 1.65424I
−5.29996 − 2.56491I −17.7298 + 4.0042I
u = 1.09763 + 1.08982I
a = −0.514092 − 0.996661I
b = 0.235329 − 1.342280I
−5.29996 − 2.56491I −17.7298 + 4.0042I
u = 1.09763 − 1.08982I
a = 0.503463 − 0.723010I
b = −0.52189 − 1.65424I
−5.29996 + 2.56491I −17.7298 − 4.0042I
u = 1.09763 − 1.08982I
a = −0.514092 + 0.996661I
b = 0.235329 + 1.342280I
−5.29996 + 2.56491I −17.7298 − 4.0042I
17
III. I
u
3
=
hu
18
−8u
17
+· · · +b+5, 5u
18
−37u
17
+· · · +3a+11, u
19
−8u
18
+· · · +22u−3i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
−
5
3
u
18
+
37
3
u
17
+ ··· + 13u −
11
3
−u
18
+ 8u
17
+ ··· + 33u − 5
a
12
=
−u
u
a
4
=
−
2
3
u
18
+
13
3
u
17
+ ··· − 20u +
4
3
−u
18
+ 8u
17
+ ··· + 33u − 5
a
1
=
−
2
3
u
18
+
16
3
u
17
+ ··· − 6u +
7
3
u
18
− 7u
17
+ ··· − 3u + 1
a
3
=
−
5
3
u
18
+
37
3
u
17
+ ··· − 7u −
2
3
u
17
− 8u
16
+ ··· + 30u − 5
a
10
=
u
u
3
+ u
a
9
=
1
3
u
18
−
8
3
u
17
+ ··· − 25u +
16
3
u
2
− u + 1
a
6
=
−
1
3
u
18
+
8
3
u
17
+ ··· + 22u −
10
3
−u
4
+ 2u
3
− 3u
2
+ 2u − 1
a
2
=
−
1
3
u
18
+
8
3
u
17
+ ··· + 25u −
16
3
u
9
− 3u
8
+ 7u
7
− 10u
6
+ 13u
5
− 11u
4
+ 10u
3
− 6u
2
+ 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
18
+44u
17
−217u
16
+750u
15
−2012u
14
+4389u
13
−8018u
12
+12471u
11
−16700u
10
+
19364u
9
−19501u
8
+ 17059u
7
−12932u
6
+ 8454u
5
−4715u
4
+ 2208u
3
−830u
2
+ 234u −45
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 9u
18
+ ··· + 169u − 25
c
2
u
19
+ 3u
18
+ ··· − 13u − 5
c
3
, c
9
u
19
− 6u
17
+ ··· − 2u − 1
c
4
, c
12
u
19
− 2u
18
+ ··· + 4u − 1
c
5
u
19
− 3u
18
+ ··· − 13u + 5
c
6
, c
8
u
19
+ u
18
+ ··· + 2u − 1
c
7
u
19
− 8u
18
+ ··· + 22u − 3
c
10
, c
11
u
19
+ 8u
18
+ ··· + 22u + 3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 11y
18
+ ··· − 1139y −625
c
2
, c
5
y
19
− 9y
18
+ ··· + 169y −25
c
3
, c
9
y
19
− 12y
18
+ ··· + 10y −1
c
4
, c
12
y
19
+ 8y
18
+ ··· − 2y −1
c
6
, c
8
y
19
+ 9y
18
+ ··· − 4y −1
c
7
, c
10
, c
11
y
19
+ 12y
18
+ ··· − 2y −9
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773741 + 0.615757I
a = 0.24873 + 1.43202I
b = −0.68932 + 1.26117I
−3.86357 + 0.16314I −9.77303 + 4.53952I
u = 0.773741 − 0.615757I
a = 0.24873 − 1.43202I
b = −0.68932 − 1.26117I
−3.86357 − 0.16314I −9.77303 − 4.53952I
u = 0.039910 + 1.250850I
a = −0.068408 − 0.556985I
b = 0.693972 − 0.107797I
6.19767 − 2.13666I 1.33946 + 1.38403I
u = 0.039910 − 1.250850I
a = −0.068408 + 0.556985I
b = 0.693972 + 0.107797I
6.19767 + 2.13666I 1.33946 − 1.38403I
u = 0.721180 + 1.040720I
a = −0.991865 − 0.825716I
b = 0.14402 − 1.62774I
−2.62148 − 5.85923I −7.22644 + 7.45241I
u = 0.721180 − 1.040720I
a = −0.991865 + 0.825716I
b = 0.14402 + 1.62774I
−2.62148 + 5.85923I −7.22644 − 7.45241I
u = −0.011190 + 0.730118I
a = −0.15129 − 1.57639I
b = 1.152650 − 0.092823I
4.06604 + 2.04452I 0.28047 − 4.71022I
u = −0.011190 − 0.730118I
a = −0.15129 + 1.57639I
b = 1.152650 + 0.092823I
4.06604 − 2.04452I 0.28047 + 4.71022I
u = −0.150676 + 0.642563I
a = 0.56785 + 1.62118I
b = −1.127270 + 0.120608I
1.98975 + 7.97545I −3.92964 − 7.09376I
u = −0.150676 − 0.642563I
a = 0.56785 − 1.62118I
b = −1.127270 − 0.120608I
1.98975 − 7.97545I −3.92964 + 7.09376I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.035331 + 1.343980I
a = 0.170224 + 0.479774I
b = −0.638791 + 0.245728I
5.03084 − 7.46362I −1.18346 + 7.65699I
u = 0.035331 − 1.343980I
a = 0.170224 − 0.479774I
b = −0.638791 − 0.245728I
5.03084 + 7.46362I −1.18346 − 7.65699I
u = 0.231018 + 1.346920I
a = 0.221009 + 0.141498I
b = −0.139530 + 0.330370I
1.74668 − 2.43305I −12.4850 + 10.8155I
u = 0.231018 − 1.346920I
a = 0.221009 − 0.141498I
b = −0.139530 − 0.330370I
1.74668 + 2.43305I −12.4850 − 10.8155I
u = 1.13685 + 0.95705I
a = 0.438459 + 0.886064I
b = −0.34954 + 1.42695I
−4.88243 − 5.70418I −8.20039 + 6.89287I
u = 1.13685 − 0.95705I
a = 0.438459 − 0.886064I
b = −0.34954 − 1.42695I
−4.88243 + 5.70418I −8.20039 − 6.89287I
u = 1.07213 + 1.08467I
a = −0.513113 − 0.815633I
b = 0.33456 − 1.43102I
−4.49067 − 2.22049I −6.78328 − 1.40884I
u = 1.07213 − 1.08467I
a = −0.513113 + 0.815633I
b = 0.33456 + 1.43102I
−4.49067 + 2.22049I −6.78328 + 1.40884I
u = 0.303402
a = −2.50986
b = −0.761496
−3.05579 −14.0770
22
IV. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
v
0
a
8
=
1
0
a
5
=
0
−v
a
12
=
v
0
a
4
=
v
−v
a
1
=
v − 1
1
a
3
=
0
−v
a
10
=
v
0
a
9
=
v
1
a
6
=
−v + 1
−1
a
2
=
v − 1
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(u − 1)
2
c
3
, c
4
, c
9
c
12
u
2
− u + 1
c
5
(u + 1)
2
c
7
, c
10
, c
11
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
(y − 1)
2
c
3
, c
4
, c
9
c
12
y
2
+ y + 1
c
7
, c
10
, c
11
y
2
25
(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
−3.28987 −15.0000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
−3.28987 −15.0000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
19
− 9u
18
+ ··· + 169u − 25)(u
22
+ 10u
21
+ ··· + 6u
2
+ 1)
2
· (u
41
+ 18u
40
+ ··· + 545u + 16)
c
2
((u − 1)
2
)(u
19
+ 3u
18
+ ··· − 13u − 5)(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
· (u
41
+ 10u
40
+ ··· + 47u + 4)
c
3
, c
9
(u
2
− u + 1)(u
19
− 6u
17
+ ··· − 2u − 1)(u
41
− 5u
39
+ ··· + 84u + 19)
· (u
44
+ 2u
43
+ ··· − 5637u + 2363)
c
4
, c
12
(u
2
− u + 1)(u
19
− 2u
18
+ ··· + 4u − 1)(u
41
+ 2u
40
+ ··· − 2u + 1)
· (u
44
+ 4u
43
+ ··· + 42835u + 8921)
c
5
((u + 1)
2
)(u
19
− 3u
18
+ ··· − 13u + 5)(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
· (u
41
+ 10u
40
+ ··· + 47u + 4)
c
6
, c
8
((u − 1)
2
)(u
19
+ u
18
+ ··· + 2u − 1)(u
41
+ u
40
+ ··· − 10u
2
+ 1)
· (u
44
− 3u
43
+ ··· − 64u + 23)
c
7
u
2
(u
19
− 8u
18
+ ··· + 22u − 3)(u
22
+ 9u
21
+ ··· + u + 2)
2
· (u
41
− 11u
40
+ ··· + u + 2)
c
10
, c
11
u
2
(u
19
+ 8u
18
+ ··· + 22u + 3)(u
22
+ 9u
21
+ ··· + u + 2)
2
· (u
41
− 11u
40
+ ··· + u + 2)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
19
+ 11y
18
+ ··· − 1139y − 625)
· ((y
22
+ 6y
21
+ ··· + 12y + 1)
2
)(y
41
+ 18y
40
+ ··· + 181953y − 256)
c
2
, c
5
((y − 1)
2
)(y
19
− 9y
18
+ ··· + 169y − 25)(y
22
− 10y
21
+ ··· + 6y
2
+ 1)
2
· (y
41
− 18y
40
+ ··· + 545y − 16)
c
3
, c
9
(y
2
+ y + 1)(y
19
− 12y
18
+ ··· + 10y − 1)
· (y
41
− 10y
40
+ ··· + 4814y − 361)
· (y
44
− 20y
43
+ ··· − 96091903y + 5583769)
c
4
, c
12
(y
2
+ y + 1)(y
19
+ 8y
18
+ ··· − 2y − 1)(y
41
+ 54y
40
+ ··· + 14y − 1)
· (y
44
+ 28y
43
+ ··· + 190747193y + 79584241)
c
6
, c
8
((y − 1)
2
)(y
19
+ 9y
18
+ ··· − 4y − 1)(y
41
− 13y
40
+ ··· + 20y − 1)
· (y
44
+ 13y
43
+ ··· − 10582y + 529)
c
7
, c
10
, c
11
y
2
(y
19
+ 12y
18
+ ··· − 2y − 9)(y
22
+ 3y
21
+ ··· + 43y + 4)
2
· (y
41
+ 15y
40
+ ··· + 53y − 4)
28
