12n
0845
(K12n
0845
)
A knot diagram
1
Linearized knot diagam
4 10 11 10 1 12 3 4 1 8 6 7
Solving Sequence
1,4 2,10
3 5 6 9 8 11 7 12
c
1
c
2
c
4
c
5
c
9
c
8
c
10
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.47941 × 10
24
u
27
+ 1.23843 × 10
26
u
26
+ ··· + 1.61992 × 10
22
b + 5.31574 × 10
27
,
1.03823 × 10
25
u
27
+ 1.71923 × 10
26
u
26
+ ··· + 3.23983 × 10
22
a + 7.38572 × 10
27
,
u
28
+ 18u
27
+ ··· + 1280u + 1024i
I
u
2
= h−7125076710u
18
+ 91561872113u
17
+ ··· + 543606477b − 93548383993,
− 93548383993u
18
+ 1209003915199u
17
+ ··· + 543606477a − 1268729042138,
u
19
− 13u
18
+ ··· + 29u − 1i
I
u
3
= h468422399a
9
u
3
+ 40467670a
8
u
3
+ ··· − 48741327a + 38855139,
− a
9
u
3
− 9a
8
u
3
+ ··· + 679a − 378, u
4
− 3u
3
+ u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 87 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
=
h7.48×10
24
u
27
+1.24×10
26
u
26
+· · ·+1.62×10
22
b+5.32×10
27
, 1.04×10
25
u
27
+
1.72×10
26
u
26
+· · ·+3.24×10
22
a+7.39×10
27
, u
28
+18u
27
+· · ·+1280u+1024 i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−320.458u
27
− 5306.53u
26
+ ··· − 126445.u − 227966.
−461.716u
27
− 7645.01u
26
+ ··· − 182220.u − 328149.
a
3
=
−37.8334u
27
− 632.042u
26
+ ··· − 14648.4u − 29529.5
−48.9592u
27
− 819.012u
26
+ ··· − 18896.2u − 38741.4
a
5
=
111.460u
27
+ 1856.99u
26
+ ··· + 43415.8u + 84604.4
149.293u
27
+ 2489.03u
26
+ ··· + 58065.3u + 114135.
a
6
=
−37.8334u
27
− 632.042u
26
+ ··· − 14649.4u − 29530.5
149.293u
27
+ 2489.03u
26
+ ··· + 58065.3u + 114135.
a
9
=
141.258u
27
+ 2338.48u
26
+ ··· + 55775.1u + 100183.
−461.716u
27
− 7645.01u
26
+ ··· − 182220.u − 328149.
a
8
=
141.258u
27
+ 2338.48u
26
+ ··· + 55775.1u + 100183.
−166.322u
27
− 2755.77u
26
+ ··· − 65538.3u − 119085.
a
11
=
−81.7198u
27
− 1353.54u
26
+ ··· − 32166.5u − 58365.7
−746.494u
27
− 12362.3u
26
+ ··· − 294547.u − 531430.
a
7
=
205.704u
27
+ 3402.49u
26
+ ··· + 81390.4u + 144506.
−145.362u
27
− 2412.32u
26
+ ··· − 56976.3u − 106020.
a
12
=
−103.259u
27
− 1702.27u
26
+ ··· − 41159.1u − 69833.4
−208.655u
27
− 3462.18u
26
+ ··· − 82098.9u − 151590.
(ii) Obstruction class = −1
(iii) Cusp Shapes =
13322328677737983134489147
8099581639968855113536
u
27
+
110674001941628848158963191
4049790819984427556768
u
26
+
··· +
81474007049283441507399205
126555963124513361149
u +
153623166708123437656283814
126555963124513361149
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 18u
27
+ ··· − 1280u + 1024
c
2
, c
8
u
28
+ u
27
+ ··· + 2u + 10
c
3
, c
7
u
28
− 3u
26
+ ··· − 4u + 1
c
4
, c
9
u
28
+ u
27
+ ··· + 2u + 1
c
5
u
28
+ 27u
27
+ ··· + 186016u + 13840
c
6
, c
11
, c
12
u
28
− 8u
27
+ ··· + 32u + 16
c
10
u
28
+ 21u
27
+ ··· + 432u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 28y
27
+ ··· + 2162688y + 1048576
c
2
, c
8
y
28
+ 17y
27
+ ··· + 1336y + 100
c
3
, c
7
y
28
− 6y
27
+ ··· − 22y + 1
c
4
, c
9
y
28
+ 45y
27
+ ··· + 16y + 1
c
5
y
28
+ 3y
27
+ ··· − 987913856y + 191545600
c
6
, c
11
, c
12
y
28
− 24y
27
+ ··· − 640y + 256
c
10
y
28
+ 5y
27
+ ··· + 13568y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425697 + 0.914932I
a = −0.312755 − 0.479893I
b = −0.305930 + 0.490439I
−3.34248 − 5.03502I 0. + 7.22973I
u = 0.425697 − 0.914932I
a = −0.312755 + 0.479893I
b = −0.305930 − 0.490439I
−3.34248 + 5.03502I 0. − 7.22973I
u = −0.105022 + 1.112840I
a = 0.381320 − 0.351416I
b = −0.351024 − 0.461256I
−0.514267 + 0.130456I 0
u = −0.105022 − 1.112840I
a = 0.381320 + 0.351416I
b = −0.351024 + 0.461256I
−0.514267 − 0.130456I 0
u = 1.130170 + 0.322911I
a = −0.317402 − 0.254746I
b = 0.276457 + 0.390398I
−6.73975 − 1.18993I 0
u = 1.130170 − 0.322911I
a = −0.317402 + 0.254746I
b = 0.276457 − 0.390398I
−6.73975 + 1.18993I 0
u = −1.324700 + 0.306113I
a = −0.621209 + 1.202590I
b = −0.45479 + 1.78323I
−5.26230 + 3.26030I 0
u = −1.324700 − 0.306113I
a = −0.621209 − 1.202590I
b = −0.45479 − 1.78323I
−5.26230 − 3.26030I 0
u = −1.41642 + 0.00861I
a = 0.253081 − 1.240320I
b = 0.34779 − 1.75900I
−3.54950 − 3.27899I 0
u = −1.41642 − 0.00861I
a = 0.253081 + 1.240320I
b = 0.34779 + 1.75900I
−3.54950 + 3.27899I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.040270 + 0.540835I
a = 0.764936 + 0.846392I
b = 0.426954 − 0.447789I
0.86405 − 1.47972I 0.04127 + 5.19835I
u = 0.040270 − 0.540835I
a = 0.764936 − 0.846392I
b = 0.426954 + 0.447789I
0.86405 + 1.47972I 0.04127 − 5.19835I
u = 0.31182 + 1.46661I
a = −0.308577 + 0.173644I
b = 0.350888 + 0.398418I
2.48566 − 3.77616I 0
u = 0.31182 − 1.46661I
a = −0.308577 − 0.173644I
b = 0.350888 − 0.398418I
2.48566 + 3.77616I 0
u = −1.52883 + 0.03670I
a = −0.339231 − 1.169130I
b = −0.56153 − 1.77495I
−9.73727 + 7.90821I 0
u = −1.52883 − 0.03670I
a = −0.339231 + 1.169130I
b = −0.56153 + 1.77495I
−9.73727 − 7.90821I 0
u = 0.332678 + 0.259381I
a = 1.059500 + 0.353725I
b = −0.260723 − 0.392490I
−1.017830 − 0.678910I −6.84852 + 2.35129I
u = 0.332678 − 0.259381I
a = 1.059500 − 0.353725I
b = −0.260723 + 0.392490I
−1.017830 + 0.678910I −6.84852 − 2.35129I
u = −1.73874 + 0.31279I
a = 0.195104 − 1.130570I
b = −0.01440 − 2.02680I
−15.5874 + 4.5388I 0
u = −1.73874 − 0.31279I
a = 0.195104 + 1.130570I
b = −0.01440 + 2.02680I
−15.5874 − 4.5388I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.62542 + 1.66377I
a = 0.263163 − 0.106601I
b = −0.341946 − 0.371174I
−2.13746 − 7.74211I 0
u = 0.62542 − 1.66377I
a = 0.263163 + 0.106601I
b = −0.341946 + 0.371174I
−2.13746 + 7.74211I 0
u = −1.83553 + 0.47211I
a = −0.097425 + 0.937524I
b = 0.26379 + 1.76685I
−7.04260 + 6.51785I 0
u = −1.83553 − 0.47211I
a = −0.097425 − 0.937524I
b = 0.26379 − 1.76685I
−7.04260 − 6.51785I 0
u = −1.93764 + 0.44814I
a = −0.023604 − 0.925470I
b = −0.46048 − 1.78265I
−5.47616 + 11.59450I 0
u = −1.93764 − 0.44814I
a = −0.023604 + 0.925470I
b = −0.46048 + 1.78265I
−5.47616 − 11.59450I 0
u = −1.97916 + 0.39645I
a = 0.103098 + 0.960765I
b = 0.58495 + 1.86064I
−11.2075 + 15.9109I 0
u = −1.97916 − 0.39645I
a = 0.103098 − 0.960765I
b = 0.58495 − 1.86064I
−11.2075 − 15.9109I 0
7
II. I
u
2
= h−7.13 × 10
9
u
18
+ 9.16 × 10
10
u
17
+ · · · + 5.44 × 10
8
b − 9.35 ×
10
10
, −9.35 × 10
10
u
18
+ 1.21 × 10
12
u
17
+ · · · + 5.44 × 10
8
a − 1.27 ×
10
12
, u
19
− 13u
18
+ · · · + 29u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
172.088u
18
− 2224.04u
17
+ ··· − 36002.5u + 2333.91
13.1070u
18
− 168.434u
17
+ ··· − 2656.65u + 172.088
a
3
=
−255.016u
18
+ 3296.25u
17
+ ··· + 53367.8u − 3449.13
−18.9607u
18
+ 244.839u
17
+ ··· + 3945.33u − 255.016
a
5
=
275.389u
18
− 3559.68u
17
+ ··· − 57628.5u + 3725.52
20.3725u
18
− 263.431u
17
+ ··· − 4259.75u + 275.389
a
6
=
255.016u
18
− 3296.25u
17
+ ··· − 53368.8u + 3450.13
20.3725u
18
− 263.431u
17
+ ··· − 4259.75u + 275.389
a
9
=
158.981u
18
− 2055.61u
17
+ ··· − 33345.8u + 2161.82
13.1070u
18
− 168.434u
17
+ ··· − 2656.65u + 172.088
a
8
=
158.981u
18
− 2055.61u
17
+ ··· − 33345.8u + 2161.82
12.7663u
18
− 166.395u
17
+ ··· − 2821.01u + 183.238
a
11
=
−386.578u
18
+ 4997.30u
17
+ ··· + 80922.8u − 5216.60
−34.7026u
18
+ 449.189u
17
+ ··· + 7326.27u − 472.582
a
7
=
239.348u
18
− 3094.91u
17
+ ··· − 50207.9u + 3243.13
21.1566u
18
− 274.000u
17
+ ··· − 4496.28u + 290.649
a
12
=
−155.007u
18
+ 2004.69u
17
+ ··· + 32544.1u − 2096.72
−14.7054u
18
+ 190.365u
17
+ ··· + 3100.48u − 199.857
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
119077780094
543606477
u
18
+
513494948917
181202159
u
17
+ ··· +
25027294000157
543606477
u −
1610829968363
543606477
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 13u
18
+ ··· + 29u − 1
c
2
, c
8
u
19
− u
18
+ ··· + 15u + 4
c
3
, c
7
u
19
+ 3u
17
+ ··· − 5u − 1
c
4
, c
9
u
19
− u
18
+ ··· − u − 1
c
5
u
19
+ 2u
17
+ ··· − u + 2
c
6
u
19
− u
18
+ ··· + u − 2
c
10
u
19
− 6u
18
+ ··· − u
2
− 1
c
11
, c
12
u
19
+ u
18
+ ··· + u + 2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 21y
18
+ ··· + 369y −1
c
2
, c
8
y
19
+ 9y
18
+ ··· + 313y −16
c
3
, c
7
y
19
+ 6y
18
+ ··· + 13y −1
c
4
, c
9
y
19
+ 13y
18
+ ··· + 15y −1
c
5
y
19
+ 4y
18
+ ··· − 7y −4
c
6
, c
11
, c
12
y
19
− 19y
18
+ ··· − 7y −4
c
10
y
19
+ 4y
18
+ ··· − 2y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.132656 + 1.126360I
a = 0.153669 + 0.574383I
b = −0.667344 + 0.096891I
3.32009 − 4.48223I 4.24188 + 6.09054I
u = −0.132656 − 1.126360I
a = 0.153669 − 0.574383I
b = −0.667344 − 0.096891I
3.32009 + 4.48223I 4.24188 − 6.09054I
u = 0.785063
a = −1.31667
b = −1.03366
−4.77237 −11.3350
u = −0.725595 + 0.990920I
a = −0.391337 − 0.324746I
b = 0.605750 − 0.152150I
0.045522 − 1.162280I −2.70106 + 1.05620I
u = −0.725595 − 0.990920I
a = −0.391337 + 0.324746I
b = 0.605750 + 0.152150I
0.045522 + 1.162280I −2.70106 − 1.05620I
u = −0.679401 + 0.189945I
a = 0.707865 + 0.676866I
b = −0.609492 − 0.325408I
−0.50830 + 4.64971I −2.08446 − 8.11285I
u = −0.679401 − 0.189945I
a = 0.707865 − 0.676866I
b = −0.609492 + 0.325408I
−0.50830 − 4.64971I −2.08446 + 8.11285I
u = 0.277340 + 1.346140I
a = 0.080380 − 0.492677I
b = 0.685506 − 0.028435I
−1.35162 − 8.11424I 0. + 8.05738I
u = 0.277340 − 1.346140I
a = 0.080380 + 0.492677I
b = 0.685506 + 0.028435I
−1.35162 + 8.11424I 0. − 8.05738I
u = 1.35264 + 0.41899I
a = −0.581509 − 0.936432I
b = −0.39421 − 1.51030I
−5.14116 − 3.04738I −5.23248 − 5.83675I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35264 − 0.41899I
a = −0.581509 + 0.936432I
b = −0.39421 + 1.51030I
−5.14116 + 3.04738I −5.23248 + 5.83675I
u = 1.89589 + 0.25753I
a = 0.001396 − 0.811646I
b = 0.21167 − 1.53843I
−5.14031 − 1.99928I 0
u = 1.89589 − 0.25753I
a = 0.001396 + 0.811646I
b = 0.21167 + 1.53843I
−5.14031 + 1.99928I 0
u = 0.0740689 + 0.0001641I
a = 10.82830 − 4.38594I
b = 0.802759 − 0.323084I
2.12947 − 2.13351I 7.28519 + 5.60767I
u = 0.0740689 − 0.0001641I
a = 10.82830 + 4.38594I
b = 0.802759 + 0.323084I
2.12947 + 2.13351I 7.28519 − 5.60767I
u = 1.93088 + 0.10553I
a = −0.111630 + 0.947120I
b = −0.31549 + 1.81699I
−10.73160 − 4.56238I 0
u = 1.93088 − 0.10553I
a = −0.111630 − 0.947120I
b = −0.31549 − 1.81699I
−10.73160 + 4.56238I 0
u = 2.11431 + 0.40872I
a = −0.028790 + 0.590712I
b = −0.302309 + 1.237180I
−8.19982 − 0.45166I 0
u = 2.11431 − 0.40872I
a = −0.028790 − 0.590712I
b = −0.302309 − 1.237180I
−8.19982 + 0.45166I 0
12
III. I
u
3
= h4.68 × 10
8
a
9
u
3
+ 4.05 × 10
7
a
8
u
3
+ · · · − 4.87 × 10
7
a + 3.89 ×
10
7
, −a
9
u
3
− 9a
8
u
3
+ · · · + 679a − 378, u
4
− 3u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
a
−22.1644a
9
u
3
− 1.91482a
8
u
3
+ ··· + 2.30630a − 1.83852
a
3
=
−1.51178a
9
u
3
− 8.84115a
8
u
3
+ ··· + 3.25676a + 1.69003
a
2
u
2
+ 2u
a
5
=
a
2
u
−4.63223a
9
u
3
+ 13.2533a
8
u
3
+ ··· − 5.43917a − 2.40270
a
6
=
4.63223a
9
u
3
− 13.2533a
8
u
3
+ ··· + 5.43917a + 2.40270
−4.63223a
9
u
3
+ 13.2533a
8
u
3
+ ··· − 5.43917a − 2.40270
a
9
=
22.1644a
9
u
3
+ 1.91482a
8
u
3
+ ··· − 1.30630a + 1.83852
−22.1644a
9
u
3
− 1.91482a
8
u
3
+ ··· + 2.30630a − 1.83852
a
8
=
22.1644a
9
u
3
+ 1.91482a
8
u
3
+ ··· − 1.30630a + 1.83852
38.6794a
9
u
3
+ 22.0734a
8
u
3
+ ··· − 9.55612a + 5.40766
a
11
=
15.1613a
9
u
3
− 7.57062a
8
u
3
+ ··· + 2.80685a + 0.756003
33.7491a
9
u
3
− 12.2037a
8
u
3
+ ··· + 2.40978a + 3.94988
a
7
=
20.9588a
9
u
3
− 3.95908a
8
u
3
+ ··· − 1.13897a + 3.09172
−31.4812a
9
u
3
+ 26.0516a
8
u
3
+ ··· − 5.58213a − 2.98326
a
12
=
41.8680a
9
u
3
+ 34.2555a
8
u
3
+ ··· − 7.45530a + 1.02267
−17.8033a
9
u
3
− 23.2306a
8
u
3
+ ··· + 6.33497a + 0.367516
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2269696784
21133951
a
9
u
3
+
1081914868
21133951
a
8
u
3
+ ··· −
12085268
21133951
a −
175881906
21133951
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ u
2
− 2u + 1)
10
c
2
, c
8
u
40
− u
39
+ ··· − 2252u + 10709
c
3
, c
7
u
40
− 3u
39
+ ··· − 94u + 19
c
4
, c
9
u
40
− u
39
+ ··· − 15778u + 2401
c
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
8
c
6
, c
11
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
c
10
(u
4
− u
3
+ u
2
+ 1)
10
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
10
c
2
, c
8
y
40
+ 19y
39
+ ··· + 1867654162y + 114682681
c
3
, c
7
y
40
+ 7y
39
+ ··· + 1044y + 361
c
4
, c
9
y
40
+ 39y
39
+ ··· − 51765560y + 5764801
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
8
c
6
, c
11
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399232 + 0.325640I
a = 0.824100 − 1.018670I
b = −1.309580 + 0.234829I
1.52684 − 4.69454I −2.68838 + 6.99545I
u = −0.399232 + 0.325640I
a = 0.477104 + 0.081474I
b = 1.024160 − 0.489876I
1.52684 − 1.63338I −2.68838 − 1.86585I
u = −0.399232 + 0.325640I
a = −1.37182 − 1.14774I
b = −0.894007 + 0.844829I
−4.01662 + 1.23687I −6.91758 − 0.93379I
u = −0.399232 + 0.325640I
a = 0.76466 + 1.68764I
b = −0.774417 + 0.765734I
−0.54514 − 3.16396I −3.65440 + 2.56480I
u = −0.399232 + 0.325640I
a = −0.71374 + 1.79710I
b = 1.61076 − 0.36829I
−4.01662 − 7.56480I −6.91758 + 6.06338I
u = −0.399232 + 0.325640I
a = −2.10425 + 0.20165I
b = 0.854840 + 0.424757I
−0.54514 − 3.16396I −3.65440 + 2.56480I
u = −0.399232 + 0.325640I
a = 2.14145 + 0.51967I
b = 0.217006 − 0.122837I
1.52684 − 1.63338I −2.68838 − 1.86585I
u = −0.399232 + 0.325640I
a = −2.38116 + 0.17390I
b = −0.921427 − 0.011495I
−4.01662 + 1.23687I −6.91758 − 0.93379I
u = −0.399232 + 0.325640I
a = −2.25785 − 1.25346I
b = −0.002714 − 0.675046I
1.52684 − 4.69454I −2.68838 + 6.99545I
u = −0.399232 + 0.325640I
a = 2.87459 + 1.42222I
b = 0.300259 + 0.949883I
−4.01662 − 7.56480I −6.91758 + 6.06338I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399232 − 0.325640I
a = 0.824100 + 1.018670I
b = −1.309580 − 0.234829I
1.52684 + 4.69454I −2.68838 − 6.99545I
u = −0.399232 − 0.325640I
a = 0.477104 − 0.081474I
b = 1.024160 + 0.489876I
1.52684 + 1.63338I −2.68838 + 1.86585I
u = −0.399232 − 0.325640I
a = −1.37182 + 1.14774I
b = −0.894007 − 0.844829I
−4.01662 − 1.23687I −6.91758 + 0.93379I
u = −0.399232 − 0.325640I
a = 0.76466 − 1.68764I
b = −0.774417 − 0.765734I
−0.54514 + 3.16396I −3.65440 − 2.56480I
u = −0.399232 − 0.325640I
a = −0.71374 − 1.79710I
b = 1.61076 + 0.36829I
−4.01662 + 7.56480I −6.91758 − 6.06338I
u = −0.399232 − 0.325640I
a = −2.10425 − 0.20165I
b = 0.854840 − 0.424757I
−0.54514 + 3.16396I −3.65440 − 2.56480I
u = −0.399232 − 0.325640I
a = 2.14145 − 0.51967I
b = 0.217006 + 0.122837I
1.52684 + 1.63338I −2.68838 + 1.86585I
u = −0.399232 − 0.325640I
a = −2.38116 − 0.17390I
b = −0.921427 + 0.011495I
−4.01662 − 1.23687I −6.91758 + 0.93379I
u = −0.399232 − 0.325640I
a = −2.25785 + 1.25346I
b = −0.002714 + 0.675046I
1.52684 + 4.69454I −2.68838 − 6.99545I
u = −0.399232 − 0.325640I
a = 2.87459 − 1.42222I
b = 0.300259 − 0.949883I
−4.01662 + 7.56480I −6.91758 − 6.06338I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.89923 + 0.40053I
a = 0.137171 + 0.934880I
b = 0.168897 + 1.333680I
−5.47491 + 0.11547I −6.34185 + 0.47809I
u = 1.89923 + 0.40053I
a = −0.220342 + 1.050850I
b = −0.05103 + 1.66432I
−11.01840 − 5.81594I −10.57105 + 8.40733I
u = 1.89923 + 0.40053I
a = 0.122676 − 0.897182I
b = 0.04153 − 1.50176I
−5.47491 − 2.94568I −6.34185 + 9.33939I
u = 1.89923 + 0.40053I
a = −0.196723 − 1.090910I
b = −0.36491 − 1.44551I
−11.01840 + 2.98573I −10.57105 + 1.41016I
u = 1.89923 + 0.40053I
a = −0.151210 − 0.844421I
b = 0.83938 − 1.90756I
−11.01840 − 5.81594I −10.57105 + 8.40733I
u = 1.89923 + 0.40053I
a = 0.138717 + 0.761464I
b = −0.59234 + 1.65482I
−5.47491 − 2.94568I −6.34185 + 9.33939I
u = 1.89923 + 0.40053I
a = 0.337630 + 0.689898I
b = −0.06332 + 2.15068I
−11.01840 + 2.98573I −10.57105 + 1.41016I
u = 1.89923 + 0.40053I
a = −0.146267 − 0.682718I
b = 0.298645 − 0.966564I
−7.54689 − 1.41510I −7.30788 + 4.90874I
u = 1.89923 + 0.40053I
a = −0.226929 − 0.654363I
b = 0.11393 − 1.83050I
−5.47491 + 0.11547I −6.34185 + 0.47809I
u = 1.89923 + 0.40053I
a = −0.047792 + 0.519003I
b = 0.004345 + 1.355230I
−7.54689 − 1.41510I −7.30788 + 4.90874I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.89923 − 0.40053I
a = 0.137171 − 0.934880I
b = 0.168897 − 1.333680I
−5.47491 − 0.11547I −6.34185 − 0.47809I
u = 1.89923 − 0.40053I
a = −0.220342 − 1.050850I
b = −0.05103 − 1.66432I
−11.01840 + 5.81594I −10.57105 − 8.40733I
u = 1.89923 − 0.40053I
a = 0.122676 + 0.897182I
b = 0.04153 + 1.50176I
−5.47491 + 2.94568I −6.34185 − 9.33939I
u = 1.89923 − 0.40053I
a = −0.196723 + 1.090910I
b = −0.36491 + 1.44551I
−11.01840 − 2.98573I −10.57105 − 1.41016I
u = 1.89923 − 0.40053I
a = −0.151210 + 0.844421I
b = 0.83938 + 1.90756I
−11.01840 + 5.81594I −10.57105 − 8.40733I
u = 1.89923 − 0.40053I
a = 0.138717 − 0.761464I
b = −0.59234 − 1.65482I
−5.47491 + 2.94568I −6.34185 − 9.33939I
u = 1.89923 − 0.40053I
a = 0.337630 − 0.689898I
b = −0.06332 − 2.15068I
−11.01840 − 2.98573I −10.57105 − 1.41016I
u = 1.89923 − 0.40053I
a = −0.146267 + 0.682718I
b = 0.298645 + 0.966564I
−7.54689 + 1.41510I −7.30788 − 4.90874I
u = 1.89923 − 0.40053I
a = −0.226929 + 0.654363I
b = 0.11393 + 1.83050I
−5.47491 − 0.11547I −6.34185 − 0.47809I
u = 1.89923 − 0.40053I
a = −0.047792 − 0.519003I
b = 0.004345 − 1.355230I
−7.54689 + 1.41510I −7.30788 − 4.90874I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
4
+ 3u
3
+ u
2
− 2u + 1)
10
)(u
19
− 13u
18
+ ··· + 29u − 1)
· (u
28
− 18u
27
+ ··· − 1280u + 1024)
c
2
, c
8
(u
19
− u
18
+ ··· + 15u + 4)(u
28
+ u
27
+ ··· + 2u + 10)
· (u
40
− u
39
+ ··· − 2252u + 10709)
c
3
, c
7
(u
19
+ 3u
17
+ ··· − 5u − 1)(u
28
− 3u
26
+ ··· − 4u + 1)
· (u
40
− 3u
39
+ ··· − 94u + 19)
c
4
, c
9
(u
19
− u
18
+ ··· − u − 1)(u
28
+ u
27
+ ··· + 2u + 1)
· (u
40
− u
39
+ ··· − 15778u + 2401)
c
5
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
8
)(u
19
+ 2u
17
+ ··· − u + 2)
· (u
28
+ 27u
27
+ ··· + 186016u + 13840)
c
6
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
)(u
19
− u
18
+ ··· + u − 2)
· (u
28
− 8u
27
+ ··· + 32u + 16)
c
10
((u
4
− u
3
+ u
2
+ 1)
10
)(u
19
− 6u
18
+ ··· − u
2
− 1)
· (u
28
+ 21u
27
+ ··· + 432u + 32)
c
11
, c
12
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
)(u
19
+ u
18
+ ··· + u + 2)
· (u
28
− 8u
27
+ ··· + 32u + 16)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
10
)(y
19
− 21y
18
+ ··· + 369y −1)
· (y
28
− 28y
27
+ ··· + 2162688y + 1048576)
c
2
, c
8
(y
19
+ 9y
18
+ ··· + 313y −16)(y
28
+ 17y
27
+ ··· + 1336y + 100)
· (y
40
+ 19y
39
+ ··· + 1867654162y + 114682681)
c
3
, c
7
(y
19
+ 6y
18
+ ··· + 13y −1)(y
28
− 6y
27
+ ··· − 22y + 1)
· (y
40
+ 7y
39
+ ··· + 1044y + 361)
c
4
, c
9
(y
19
+ 13y
18
+ ··· + 15y −1)(y
28
+ 45y
27
+ ··· + 16y + 1)
· (y
40
+ 39y
39
+ ··· − 51765560y + 5764801)
c
5
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
8
)(y
19
+ 4y
18
+ ··· − 7y −4)
· (y
28
+ 3y
27
+ ··· − 987913856y + 191545600)
c
6
, c
11
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
8
)(y
19
− 19y
18
+ ··· − 7y −4)
· (y
28
− 24y
27
+ ··· − 640y + 256)
c
10
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
)(y
19
+ 4y
18
+ ··· − 2y −1)
· (y
28
+ 5y
27
+ ··· + 13568y + 1024)
21
