12a
0907
(K12a
0907
)
A knot diagram
1
Linearized knot diagam
4 6 8 1 12 10 11 5 2 7 3 9
Solving Sequence
6,10
7 11
3,8
4 12 2 1 5 9
c
6
c
10
c
7
c
3
c
11
c
2
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.36776 × 10
26
u
53
+ 3.91730 × 10
27
u
52
+ ··· + 2.24514 × 10
23
b − 9.81393 × 10
26
,
− 1.27427 × 10
27
u
53
+ 1.48006 × 10
28
u
52
+ ··· + 4.49027 × 10
23
a − 3.66919 × 10
27
,
u
54
− 13u
53
+ ··· + 34u − 4i
I
u
2
= h686725223456u
23
a
3
− 53855889828079u
23
a
2
+ ··· − 122527711835341a − 257682162174646,
7u
23
a
3
− 30u
23
a
2
+ ··· + 101a + 65, u
24
+ 3u
23
+ ··· − 3u − 1i
I
u
3
= h−1133664u
29
− 7205220u
28
+ ··· + 38189b − 689951,
− 233434u
29
− 944087u
28
+ ··· + 38189a + 273567, u
30
+ 8u
29
+ ··· + 6u + 1i
I
u
4
= h−2a
7
+ 19a
6
+ 18a
5
− 57a
4
− 111a
3
+ 159a
2
+ 55b + 6a − 61,
a
8
− 3a
6
− 2a
5
+ 10a
4
− 6a
3
− 2a
2
+ 2a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 188 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−3.37 × 10
26
u
53
+ 3.92 × 10
27
u
52
+ · · · + 2.25 × 10
23
b − 9.81 ×
10
26
, −1.27 × 10
27
u
53
+ 1.48 × 10
28
u
52
+ · · · + 4.49 × 10
23
a − 3.67 ×
10
27
, u
54
− 13u
53
+ · · · + 34u − 4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
2837.85u
53
− 32961.4u
52
+ ··· − 63640.3u + 8171.42
1500.03u
53
− 17447.9u
52
+ ··· − 33975.2u + 4371.20
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
1040.34u
53
− 12078.0u
52
+ ··· − 23374.2u + 2997.45
1765.41u
53
− 20426.7u
52
+ ··· − 38653.6u + 4959.58
a
12
=
700.056u
53
− 8023.67u
52
+ ··· − 14095.8u + 1795.50
561.272u
53
− 6465.23u
52
+ ··· − 11812.3u + 1508.00
a
2
=
1337.82u
53
− 15513.4u
52
+ ··· − 29665.1u + 3800.22
1500.03u
53
− 17447.9u
52
+ ··· − 33975.2u + 4371.20
a
1
=
1322.69u
53
− 15354.9u
52
+ ··· − 29533.0u + 3779.67
1634.57u
53
− 18951.8u
52
+ ··· − 36197.1u + 4648.23
a
5
=
−1168.57u
53
+ 13437.1u
52
+ ··· + 24303.1u − 3094.58
−1266.34u
53
+ 14590.7u
52
+ ··· + 26781.1u − 3423.17
a
9
=
264.065u
53
− 3140.74u
52
+ ··· − 6974.68u + 915.893
−245.749u
53
+ 2782.17u
52
+ ··· + 4432.15u − 555.135
(ii) Obstruction class = −1
(iii) Cusp Shapes =
589994116974512942783147236
112256792457085332631919
u
53
−
6776033072646746153986440530
112256792457085332631919
u
52
+
··· −
12142947172972580665078190700
112256792457085332631919
u +
1547202967534202217337683890
112256792457085332631919
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
54
− 22u
53
+ ··· − 4312u + 448
c
2
, c
11
u
54
− u
53
+ ··· + 13u + 2
c
3
, c
9
u
54
− u
53
+ ··· + 28u − 4
c
5
u
54
− 45u
53
+ ··· − 144703488u + 8388608
c
6
, c
7
, c
10
u
54
+ 13u
53
+ ··· − 34u − 4
c
8
, c
12
u
54
+ u
53
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
54
+ 36y
53
+ ··· + 1750336y + 200704
c
2
, c
11
y
54
+ 9y
53
+ ··· + 83y + 4
c
3
, c
9
y
54
− 27y
53
+ ··· − 896y + 16
c
5
y
54
+ 5y
53
+ ··· − 532163627843584y + 70368744177664
c
6
, c
7
, c
10
y
54
− 55y
53
+ ··· − 908y + 16
c
8
, c
12
y
54
+ 23y
53
+ ··· + 31y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441312 + 0.889865I
a = 0.480858 + 0.262881I
b = 0.365486 − 0.846526I
−3.91979 − 4.10130I 0
u = −0.441312 − 0.889865I
a = 0.480858 − 0.262881I
b = 0.365486 + 0.846526I
−3.91979 + 4.10130I 0
u = −0.570988 + 0.834174I
a = 0.608929 − 0.543849I
b = −0.84924 − 1.19743I
−1.0568 + 15.5175I 0
u = −0.570988 − 0.834174I
a = 0.608929 + 0.543849I
b = −0.84924 + 1.19743I
−1.0568 − 15.5175I 0
u = −0.637135 + 0.741301I
a = −0.476946 + 0.620063I
b = 0.809980 + 1.110120I
−4.60432 + 9.42368I 0
u = −0.637135 − 0.741301I
a = −0.476946 − 0.620063I
b = 0.809980 − 1.110120I
−4.60432 − 9.42368I 0
u = −0.608693 + 0.871804I
a = −0.547448 − 0.169996I
b = −0.448601 + 1.021030I
−1.09490 − 9.86752I 0
u = −0.608693 − 0.871804I
a = −0.547448 + 0.169996I
b = −0.448601 − 1.021030I
−1.09490 + 9.86752I 0
u = 0.900779 + 0.233525I
a = −0.574933 + 0.544624I
b = −0.019206 − 0.185995I
−0.294416 − 0.269624I 0
u = 0.900779 − 0.233525I
a = −0.574933 − 0.544624I
b = −0.019206 + 0.185995I
−0.294416 + 0.269624I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990203 + 0.557417I
a = 0.284165 + 0.146019I
b = 0.714298 − 0.229702I
3.53531 + 5.84821I 0
u = −0.990203 − 0.557417I
a = 0.284165 − 0.146019I
b = 0.714298 + 0.229702I
3.53531 − 5.84821I 0
u = −0.637541 + 0.994808I
a = −0.267203 + 0.183692I
b = 0.401222 + 0.614737I
2.70452 + 6.50099I 0
u = −0.637541 − 0.994808I
a = −0.267203 − 0.183692I
b = 0.401222 − 0.614737I
2.70452 − 6.50099I 0
u = −0.232302 + 0.697717I
a = −0.546747 + 0.697335I
b = 0.822239 + 0.418863I
5.64709 − 1.46866I 0
u = −0.232302 − 0.697717I
a = −0.546747 − 0.697335I
b = 0.822239 − 0.418863I
5.64709 + 1.46866I 0
u = −0.910231 + 0.907970I
a = 0.175775 − 0.131869I
b = −0.176983 − 0.570715I
1.99463 + 0.20661I 0
u = −0.910231 − 0.907970I
a = 0.175775 + 0.131869I
b = −0.176983 + 0.570715I
1.99463 − 0.20661I 0
u = 1.339880 + 0.030929I
a = 1.23977 + 1.88630I
b = 0.465396 + 0.921605I
−2.39574 + 1.99510I 0
u = 1.339880 − 0.030929I
a = 1.23977 − 1.88630I
b = 0.465396 − 0.921605I
−2.39574 − 1.99510I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.476300 + 0.421762I
a = 0.402419 − 1.333210I
b = −0.886558 − 1.031710I
1.45632 + 3.89302I 6.55672 − 9.08244I
u = −0.476300 − 0.421762I
a = 0.402419 + 1.333210I
b = −0.886558 + 1.031710I
1.45632 − 3.89302I 6.55672 + 9.08244I
u = 1.378770 + 0.190230I
a = 0.08077 − 1.62497I
b = 0.582543 − 0.762799I
0.56954 − 1.63715I 0
u = 1.378770 − 0.190230I
a = 0.08077 + 1.62497I
b = 0.582543 + 0.762799I
0.56954 + 1.63715I 0
u = −0.503257 + 0.340699I
a = −0.308311 − 0.871589I
b = −0.793291 − 0.347440I
1.42449 + 1.40957I 1.24500 − 4.46886I
u = −0.503257 − 0.340699I
a = −0.308311 + 0.871589I
b = −0.793291 + 0.347440I
1.42449 − 1.40957I 1.24500 + 4.46886I
u = −1.42698 + 0.05858I
a = −0.411356 − 0.061254I
b = −1.43704 − 0.11906I
−3.13163 + 3.14235I 0
u = −1.42698 − 0.05858I
a = −0.411356 + 0.061254I
b = −1.43704 + 0.11906I
−3.13163 − 3.14235I 0
u = 0.565586
a = −0.656550
b = 0.161313
−0.821914 −12.3890
u = −1.44155 + 0.03373I
a = 0.431824 − 0.086075I
b = 1.50809 − 0.35940I
−3.83782 − 1.54660I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44155 − 0.03373I
a = 0.431824 + 0.086075I
b = 1.50809 + 0.35940I
−3.83782 + 1.54660I 0
u = 1.44478 + 0.02804I
a = −0.49400 + 1.70003I
b = −0.407113 + 1.064940I
−4.61801 − 2.16208I 0
u = 1.44478 − 0.02804I
a = −0.49400 − 1.70003I
b = −0.407113 − 1.064940I
−4.61801 + 2.16208I 0
u = −0.502533 + 0.069201I
a = −1.248020 + 0.506640I
b = −0.866071 + 0.553290I
1.43237 − 1.61761I 1.66182 + 0.91579I
u = −0.502533 − 0.069201I
a = −1.248020 − 0.506640I
b = −0.866071 − 0.553290I
1.43237 + 1.61761I 1.66182 − 0.91579I
u = 1.52443 + 0.12641I
a = −0.41871 + 2.19083I
b = −0.89545 + 1.60801I
−5.24335 − 5.87061I 0
u = 1.52443 − 0.12641I
a = −0.41871 − 2.19083I
b = −0.89545 − 1.60801I
−5.24335 + 5.87061I 0
u = −1.56753
a = 0.225076
b = 0.905857
−8.29018 0
u = 1.55862 + 0.28807I
a = 0.04358 + 1.83178I
b = −1.08291 + 1.46947I
−8.0087 − 19.6385I 0
u = 1.55862 − 0.28807I
a = 0.04358 − 1.83178I
b = −1.08291 − 1.46947I
−8.0087 + 19.6385I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57042 + 0.24408I
a = 0.09505 − 1.82694I
b = 1.03413 − 1.47804I
−11.8661 − 13.0652I 0
u = 1.57042 − 0.24408I
a = 0.09505 + 1.82694I
b = 1.03413 + 1.47804I
−11.8661 + 13.0652I 0
u = 1.59876 + 0.19161I
a = −0.293276 + 1.351160I
b = −0.838910 + 1.120330I
−6.50546 − 3.58269I 0
u = 1.59876 − 0.19161I
a = −0.293276 − 1.351160I
b = −0.838910 − 1.120330I
−6.50546 + 3.58269I 0
u = 1.59272 + 0.30489I
a = 0.060084 − 1.200020I
b = 0.850742 − 0.981285I
−4.61524 − 11.13620I 0
u = 1.59272 − 0.30489I
a = 0.060084 + 1.200020I
b = 0.850742 + 0.981285I
−4.61524 + 11.13620I 0
u = 1.58609 + 0.34471I
a = 0.413350 + 0.767749I
b = −0.239741 + 0.931967I
−10.50980 − 0.61947I 0
u = 1.58609 − 0.34471I
a = 0.413350 − 0.767749I
b = −0.239741 − 0.931967I
−10.50980 + 0.61947I 0
u = 0.115403 + 0.350211I
a = 0.91938 − 1.99231I
b = −0.743304 + 0.200073I
2.00199 − 2.00819I 0.25947 + 4.80616I
u = 0.115403 − 0.350211I
a = 0.91938 + 1.99231I
b = −0.743304 − 0.200073I
2.00199 + 2.00819I 0.25947 − 4.80616I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62567 + 0.25031I
a = −0.421902 − 0.972033I
b = 0.145063 − 1.165550I
−8.62255 + 5.60885I 0
u = 1.62567 − 0.25031I
a = −0.421902 + 0.972033I
b = 0.145063 + 1.165550I
−8.62255 − 5.60885I 0
u = 0.143684 + 0.069902I
a = −7.76137 − 0.82758I
b = 0.951650 + 0.492495I
1.60698 + 1.98880I 0.07500 − 3.30992I
u = 0.143684 − 0.069902I
a = −7.76137 + 0.82758I
b = 0.951650 − 0.492495I
1.60698 − 1.98880I 0.07500 + 3.30992I
10
II. I
u
2
= h6.87 × 10
11
a
3
u
23
− 5.39 × 10
13
a
2
u
23
+ · · · − 1.23 × 10
14
a − 2.58 ×
10
14
, 7u
23
a
3
− 30u
23
a
2
+ · · · + 101a + 65, u
24
+ 3u
23
+ · · · − 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
a
−0.00885799a
3
u
23
+ 0.694681a
2
u
23
+ ··· + 1.58047a + 3.32381
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−0.0882291a
3
u
23
− 1.02761a
2
u
23
+ ··· − 0.472149a − 1.45990
0.0913234a
3
u
23
+ 0.736611a
2
u
23
+ ··· + 1.58495a + 1.70083
a
12
=
−0.833699a
3
u
23
− 0.114091a
2
u
23
+ ··· + 1.66166a + 0.0746337
−0.127483a
3
u
23
− 0.0212748a
2
u
23
+ ··· − 0.869253a + 0.0822611
a
2
=
0.00885799a
3
u
23
− 0.694681a
2
u
23
+ ··· − 0.580470a − 3.32381
−0.00885799a
3
u
23
+ 0.694681a
2
u
23
+ ··· + 1.58047a + 3.32381
a
1
=
0.158340a
3
u
23
+ 0.200905a
2
u
23
+ ··· − 1.35850a + 1.27461
−0.228069a
3
u
23
− 0.232662a
2
u
23
+ ··· + 1.54683a + 0.596958
a
5
=
−0.196421a
3
u
23
− 0.0357957a
2
u
23
+ ··· − 2.36347a + 2.88251
−0.127483a
3
u
23
− 0.0212748a
2
u
23
+ ··· − 0.869253a − 0.917739
a
9
=
0.579542a
3
u
23
+ 0.217953a
2
u
23
+ ··· − 2.47214a − 0.551645
0.254156a
3
u
23
− 0.103863a
2
u
23
+ ··· + 0.810479a + 0.477011
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
19766575345996
38763058577429
u
23
a
3
+
3298705036766
38763058577429
u
23
a
2
+ ··· +
134779543741642
38763058577429
a −
981831227284727
38763058577429
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
24
+ 7u
23
+ ··· + 15u + 3)
4
c
2
, c
11
u
96
− 7u
95
+ ··· − 1069888u + 802048
c
3
, c
9
u
96
+ u
95
+ ··· − 364694380u + 80529475
c
5
(u
2
+ u + 1)
48
c
6
, c
7
, c
10
(u
24
− 3u
23
+ ··· + 3u − 1)
4
c
8
, c
12
u
96
+ u
95
+ ··· + 44u + 4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
24
+ 15y
23
+ ··· + 69y + 9)
4
c
2
, c
11
y
96
+ 51y
95
+ ··· + 30481927393280y + 643280994304
c
3
, c
9
y
96
− 47y
95
+ ··· − 312805919734027100y + 6484996343775625
c
5
(y
2
+ y + 1)
48
c
6
, c
7
, c
10
(y
24
− 25y
23
+ ··· − 15y + 1)
4
c
8
, c
12
y
96
− 15y
95
+ ··· − 1080y + 16
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501824 + 0.827967I
a = −0.941728 − 0.506405I
b = 0.94344 − 1.10114I
−2.09646 − 5.93902I −10.0595 + 11.8785I
u = 0.501824 + 0.827967I
a = 0.673618 + 0.241303I
b = −0.008927 + 0.741066I
−2.09646 − 1.87925I −10.05947 + 4.95027I
u = 0.501824 + 0.827967I
a = −0.511557 + 0.274202I
b = −0.144242 − 1.222840I
−2.09646 − 1.87925I −10.05947 + 4.95027I
u = 0.501824 + 0.827967I
a = 0.414257 + 0.389001I
b = −0.449624 + 1.209380I
−2.09646 − 5.93902I −10.0595 + 11.8785I
u = 0.501824 − 0.827967I
a = −0.941728 + 0.506405I
b = 0.94344 + 1.10114I
−2.09646 + 5.93902I −10.0595 − 11.8785I
u = 0.501824 − 0.827967I
a = 0.673618 − 0.241303I
b = −0.008927 − 0.741066I
−2.09646 + 1.87925I −10.05947 − 4.95027I
u = 0.501824 − 0.827967I
a = −0.511557 − 0.274202I
b = −0.144242 + 1.222840I
−2.09646 + 1.87925I −10.05947 − 4.95027I
u = 0.501824 − 0.827967I
a = 0.414257 − 0.389001I
b = −0.449624 − 1.209380I
−2.09646 + 5.93902I −10.0595 − 11.8785I
u = 0.627517 + 0.736102I
a = −0.862281 − 0.115013I
b = −0.087494 − 0.919950I
−2.54142 + 0.67389I −12.20233 − 4.65914I
u = 0.627517 + 0.736102I
a = 0.774125 + 0.314012I
b = −0.70822 + 1.26921I
−2.54142 − 3.38588I −12.20233 + 2.26907I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.627517 + 0.736102I
a = −0.268923 − 0.641558I
b = 0.377880 − 0.920328I
−2.54142 − 3.38588I −12.20233 + 2.26907I
u = 0.627517 + 0.736102I
a = 0.326018 − 0.158732I
b = 0.554803 + 1.031590I
−2.54142 + 0.67389I −12.20233 − 4.65914I
u = 0.627517 − 0.736102I
a = −0.862281 + 0.115013I
b = −0.087494 + 0.919950I
−2.54142 − 0.67389I −12.20233 + 4.65914I
u = 0.627517 − 0.736102I
a = 0.774125 − 0.314012I
b = −0.70822 − 1.26921I
−2.54142 + 3.38588I −12.20233 − 2.26907I
u = 0.627517 − 0.736102I
a = −0.268923 + 0.641558I
b = 0.377880 + 0.920328I
−2.54142 + 3.38588I −12.20233 − 2.26907I
u = 0.627517 − 0.736102I
a = 0.326018 + 0.158732I
b = 0.554803 − 1.031590I
−2.54142 − 0.67389I −12.20233 + 4.65914I
u = 1.054250 + 0.290340I
a = −1.091580 + 0.475704I
b = −0.618246 − 0.144581I
−0.215066 − 0.620694I −8.00295 − 1.70887I
u = 1.054250 + 0.290340I
a = −0.708721 + 0.161940I
b = 0.461816 − 0.452114I
−0.215066 − 0.620694I −8.00295 − 1.70887I
u = 1.054250 + 0.290340I
a = 1.24279 + 0.75488I
b = 0.734389 + 0.963603I
−0.21507 + 3.43907I −8.00295 − 8.63707I
u = 1.054250 + 0.290340I
a = 0.209578 + 0.485403I
b = −1.172930 − 0.529783I
−0.21507 + 3.43907I −8.00295 − 8.63707I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.054250 − 0.290340I
a = −1.091580 − 0.475704I
b = −0.618246 + 0.144581I
−0.215066 + 0.620694I −8.00295 + 1.70887I
u = 1.054250 − 0.290340I
a = −0.708721 − 0.161940I
b = 0.461816 + 0.452114I
−0.215066 + 0.620694I −8.00295 + 1.70887I
u = 1.054250 − 0.290340I
a = 1.24279 − 0.75488I
b = 0.734389 − 0.963603I
−0.21507 − 3.43907I −8.00295 + 8.63707I
u = 1.054250 − 0.290340I
a = 0.209578 − 0.485403I
b = −1.172930 + 0.529783I
−0.21507 − 3.43907I −8.00295 + 8.63707I
u = 0.515675 + 0.430762I
a = 0.555106 + 0.172159I
b = −0.752740 + 1.185000I
−1.82150 − 3.66074I −10.9992 + 8.9039I
u = 0.515675 + 0.430762I
a = −1.55196 + 0.28820I
b = −0.194016 − 0.676593I
−1.82150 + 0.39903I −10.99918 + 1.97568I
u = 0.515675 + 0.430762I
a = −0.05876 − 1.74381I
b = 0.557900 − 0.494143I
−1.82150 − 3.66074I −10.9992 + 8.9039I
u = 0.515675 + 0.430762I
a = −0.0572993 + 0.0677786I
b = 0.889737 + 0.499900I
−1.82150 + 0.39903I −10.99918 + 1.97568I
u = 0.515675 − 0.430762I
a = 0.555106 − 0.172159I
b = −0.752740 − 1.185000I
−1.82150 + 3.66074I −10.9992 − 8.9039I
u = 0.515675 − 0.430762I
a = −1.55196 − 0.28820I
b = −0.194016 + 0.676593I
−1.82150 − 0.39903I −10.99918 − 1.97568I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.515675 − 0.430762I
a = −0.05876 + 1.74381I
b = 0.557900 + 0.494143I
−1.82150 + 3.66074I −10.9992 − 8.9039I
u = 0.515675 − 0.430762I
a = −0.0572993 − 0.0677786I
b = 0.889737 − 0.499900I
−1.82150 − 0.39903I −10.99918 − 1.97568I
u = −1.388310 + 0.136000I
a = −0.098431 + 1.233460I
b = −0.384677 + 0.209710I
−2.29923 + 5.09220I −5.75594 − 4.07307I
u = −1.388310 + 0.136000I
a = −0.32020 − 1.60308I
b = −1.18550 − 1.21341I
−2.29923 + 5.09220I −5.75594 − 4.07307I
u = −1.388310 + 0.136000I
a = 0.10983 − 2.26454I
b = −0.569343 − 0.430488I
−2.29923 + 9.15197I −5.75594 − 11.00127I
u = −1.388310 + 0.136000I
a = −0.22061 + 2.81189I
b = 0.48520 + 2.29215I
−2.29923 + 9.15197I −5.75594 − 11.00127I
u = −1.388310 − 0.136000I
a = −0.098431 − 1.233460I
b = −0.384677 − 0.209710I
−2.29923 − 5.09220I −5.75594 + 4.07307I
u = −1.388310 − 0.136000I
a = −0.32020 + 1.60308I
b = −1.18550 + 1.21341I
−2.29923 − 5.09220I −5.75594 + 4.07307I
u = −1.388310 − 0.136000I
a = 0.10983 + 2.26454I
b = −0.569343 + 0.430488I
−2.29923 − 9.15197I −5.75594 + 11.00127I
u = −1.388310 − 0.136000I
a = −0.22061 − 2.81189I
b = 0.48520 − 2.29215I
−2.29923 − 9.15197I −5.75594 + 11.00127I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134959 + 0.586695I
a = 0.467337 − 0.398311I
b = −0.912342 + 0.692340I
2.51254 − 2.68858I −0.20958 + 2.79925I
u = 0.134959 + 0.586695I
a = −0.517171 − 0.284910I
b = 0.63884 − 1.43472I
2.51254 − 6.74834I −0.20958 + 9.72745I
u = 0.134959 + 0.586695I
a = −0.48427 − 1.51429I
b = 0.100913 + 0.196536I
2.51254 − 2.68858I −0.20958 + 2.79925I
u = 0.134959 + 0.586695I
a = 2.18199 + 1.22655I
b = −1.002920 + 0.287562I
2.51254 − 6.74834I −0.20958 + 9.72745I
u = 0.134959 − 0.586695I
a = 0.467337 + 0.398311I
b = −0.912342 − 0.692340I
2.51254 + 2.68858I −0.20958 − 2.79925I
u = 0.134959 − 0.586695I
a = −0.517171 + 0.284910I
b = 0.63884 + 1.43472I
2.51254 + 6.74834I −0.20958 − 9.72745I
u = 0.134959 − 0.586695I
a = −0.48427 + 1.51429I
b = 0.100913 − 0.196536I
2.51254 + 2.68858I −0.20958 − 2.79925I
u = 0.134959 − 0.586695I
a = 2.18199 − 1.22655I
b = −1.002920 − 0.287562I
2.51254 + 6.74834I −0.20958 − 9.72745I
u = 1.47990 + 0.06437I
a = −1.14142 − 1.07909I
b = 0.568701 − 0.551179I
−5.91170 − 8.68883I −13.6665 + 11.0201I
u = 1.47990 + 0.06437I
a = −0.02579 + 1.94910I
b = 0.37013 + 1.41279I
−5.91170 − 4.62906I −13.6665 + 4.0919I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47990 + 0.06437I
a = −0.45472 + 1.94082I
b = −1.20015 + 1.27309I
−5.91170 − 4.62906I −13.6665 + 4.0919I
u = 1.47990 + 0.06437I
a = −1.98710 − 1.28200I
b = −2.47973 − 1.51058I
−5.91170 − 8.68883I −13.6665 + 11.0201I
u = 1.47990 − 0.06437I
a = −1.14142 + 1.07909I
b = 0.568701 + 0.551179I
−5.91170 + 8.68883I −13.6665 − 11.0201I
u = 1.47990 − 0.06437I
a = −0.02579 − 1.94910I
b = 0.37013 − 1.41279I
−5.91170 + 4.62906I −13.6665 − 4.0919I
u = 1.47990 − 0.06437I
a = −0.45472 − 1.94082I
b = −1.20015 − 1.27309I
−5.91170 + 4.62906I −13.6665 − 4.0919I
u = 1.47990 − 0.06437I
a = −1.98710 + 1.28200I
b = −2.47973 + 1.51058I
−5.91170 + 8.68883I −13.6665 − 11.0201I
u = 1.48763
a = 0.78072 + 1.74517I
b = −0.371914 + 0.809926I
−10.05140 − 2.02988I −19.8585 + 3.4641I
u = 1.48763
a = 0.78072 − 1.74517I
b = −0.371914 − 0.809926I
−10.05140 + 2.02988I −19.8585 − 3.4641I
u = 1.48763
a = 1.41142 + 2.05173I
b = 1.96212 + 1.94440I
−10.05140 − 2.02988I −19.8585 + 3.4641I
u = 1.48763
a = 1.41142 − 2.05173I
b = 1.96212 − 1.94440I
−10.05140 + 2.02988I −19.8585 − 3.4641I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50771 + 0.06276I
a = −0.583794 + 1.007180I
b = 0.437480 + 0.686134I
−8.56715 + 1.04981I −15.6111 − 1.4870I
u = −1.50771 + 0.06276I
a = 1.08772 − 1.08882I
b = 1.44525 − 1.12148I
−8.56715 + 1.04981I −15.6111 − 1.4870I
u = −1.50771 + 0.06276I
a = 0.50300 + 1.78783I
b = 0.097892 + 0.721670I
−8.56715 + 5.10957I −15.6111 − 8.4152I
u = −1.50771 + 0.06276I
a = −0.82567 − 2.18343I
b = −1.41628 − 2.13449I
−8.56715 + 5.10957I −15.6111 − 8.4152I
u = −1.50771 − 0.06276I
a = −0.583794 − 1.007180I
b = 0.437480 − 0.686134I
−8.56715 − 1.04981I −15.6111 + 1.4870I
u = −1.50771 − 0.06276I
a = 1.08772 + 1.08882I
b = 1.44525 + 1.12148I
−8.56715 − 1.04981I −15.6111 + 1.4870I
u = −1.50771 − 0.06276I
a = 0.50300 − 1.78783I
b = 0.097892 − 0.721670I
−8.56715 − 5.10957I −15.6111 + 8.4152I
u = −1.50771 − 0.06276I
a = −0.82567 + 2.18343I
b = −1.41628 + 2.13449I
−8.56715 − 5.10957I −15.6111 + 8.4152I
u = −1.53906 + 0.29450I
a = 0.468849 − 1.130790I
b = −0.401363 − 0.868130I
−8.75286 + 5.99693I −11.10804 − 4.58319I
u = −1.53906 + 0.29450I
a = −0.536018 + 1.286150I
b = 0.33129 + 1.54241I
−8.75286 + 5.99693I −11.10804 − 4.58319I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53906 + 0.29450I
a = −0.10981 + 1.71530I
b = 1.22120 + 1.26198I
−8.75286 + 10.05670I −11.1080 − 11.5114I
u = −1.53906 + 0.29450I
a = 0.27794 − 1.73481I
b = −0.60222 − 1.53843I
−8.75286 + 10.05670I −11.1080 − 11.5114I
u = −1.53906 − 0.29450I
a = 0.468849 + 1.130790I
b = −0.401363 + 0.868130I
−8.75286 − 5.99693I −11.10804 + 4.58319I
u = −1.53906 − 0.29450I
a = −0.536018 − 1.286150I
b = 0.33129 − 1.54241I
−8.75286 − 5.99693I −11.10804 + 4.58319I
u = −1.53906 − 0.29450I
a = −0.10981 − 1.71530I
b = 1.22120 − 1.26198I
−8.75286 − 10.05670I −11.1080 + 11.5114I
u = −1.53906 − 0.29450I
a = 0.27794 + 1.73481I
b = −0.60222 + 1.53843I
−8.75286 − 10.05670I −11.1080 + 11.5114I
u = −1.55630 + 0.23462I
a = −0.392822 + 1.170440I
b = 0.498753 + 1.040900I
−9.71144 + 2.85087I −13.61294 + 3.46181I
u = −1.55630 + 0.23462I
a = 0.551496 − 1.212510I
b = 0.083179 − 1.359070I
−9.71144 + 2.85087I −13.61294 + 3.46181I
u = −1.55630 + 0.23462I
a = −0.10432 + 1.70199I
b = 0.551562 + 1.277580I
−9.71144 + 6.91064I −13.61294 − 3.46639I
u = −1.55630 + 0.23462I
a = −0.01145 − 1.81837I
b = −1.11807 − 1.62246I
−9.71144 + 6.91064I −13.61294 − 3.46639I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55630 − 0.23462I
a = −0.392822 − 1.170440I
b = 0.498753 − 1.040900I
−9.71144 − 2.85087I −13.61294 − 3.46181I
u = −1.55630 − 0.23462I
a = 0.551496 + 1.212510I
b = 0.083179 + 1.359070I
−9.71144 − 2.85087I −13.61294 − 3.46181I
u = −1.55630 − 0.23462I
a = −0.10432 − 1.70199I
b = 0.551562 − 1.277580I
−9.71144 − 6.91064I −13.61294 + 3.46639I
u = −1.55630 − 0.23462I
a = −0.01145 + 1.81837I
b = −1.11807 + 1.62246I
−9.71144 − 6.91064I −13.61294 + 3.46639I
u = −0.381299 + 0.182721I
a = 1.024320 + 0.205900I
b = −1.34020 + 1.14539I
0.27813 + 7.73674I −13.1616 − 14.7688I
u = −0.381299 + 0.182721I
a = −1.00657 − 1.70526I
b = −0.128729 − 1.076670I
0.27813 + 3.67697I −13.1616 − 7.8406I
u = −0.381299 + 0.182721I
a = 1.52126 − 1.96163I
b = −0.798346 − 0.897976I
0.27813 + 3.67697I −13.1616 − 7.8406I
u = −0.381299 + 0.182721I
a = −4.45729 + 1.18181I
b = 0.093646 + 0.644800I
0.27813 + 7.73674I −13.1616 − 14.7688I
u = −0.381299 − 0.182721I
a = 1.024320 − 0.205900I
b = −1.34020 − 1.14539I
0.27813 − 7.73674I −13.1616 + 14.7688I
u = −0.381299 − 0.182721I
a = −1.00657 + 1.70526I
b = −0.128729 + 1.076670I
0.27813 − 3.67697I −13.1616 + 7.8406I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381299 − 0.182721I
a = 1.52126 + 1.96163I
b = −0.798346 + 0.897976I
0.27813 − 3.67697I −13.1616 + 7.8406I
u = −0.381299 − 0.182721I
a = −4.45729 − 1.18181I
b = 0.093646 − 0.644800I
0.27813 − 7.73674I −13.1616 + 14.7688I
u = −0.370541
a = −0.975477 + 0.794014I
b = 1.06082 + 1.25813I
−3.81259 − 2.02988I −23.3624 + 3.4641I
u = −0.370541
a = −0.975477 − 0.794014I
b = 1.06082 − 1.25813I
−3.81259 + 2.02988I −23.3624 − 3.4641I
u = −0.370541
a = 3.22436 + 3.10117I
b = 0.081252 + 0.720006I
−3.81259 − 2.02988I −23.3624 + 3.4641I
u = −0.370541
a = 3.22436 − 3.10117I
b = 0.081252 − 0.720006I
−3.81259 + 2.02988I −23.3624 − 3.4641I
23
III.
I
u
3
= h−1.13 × 10
6
u
29
− 7.21 × 10
6
u
28
+ · · · + 3.82 × 10
4
b − 6.90 × 10
5
, −2.33 ×
10
5
u
29
−9.44×10
5
u
28
+· · · +3.82×10
4
a+2.74×10
5
, u
30
+8u
29
+· · · +6u +1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
6.11260u
29
+ 24.7214u
28
+ ··· − 20.4687u − 7.16350
29.6856u
29
+ 188.673u
28
+ ··· + 95.1244u + 18.0667
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
4.53989u
29
+ 21.0029u
28
+ ··· − 10.8574u − 5.66119
−15.2280u
29
− 111.435u
28
+ ··· − 82.3008u − 15.8717
a
12
=
−52.5830u
29
− 340.295u
28
+ ··· − 193.529u − 34.2780
−45.4567u
29
− 289.745u
28
+ ··· − 147.412u − 27.7861
a
2
=
−23.5730u
29
− 163.951u
28
+ ··· − 115.593u − 25.2302
29.6856u
29
+ 188.673u
28
+ ··· + 95.1244u + 18.0667
a
1
=
−84.0584u
29
− 549.976u
28
+ ··· − 306.194u − 64.0743
−40.6236u
29
− 263.315u
28
+ ··· − 143.881u − 25.7792
a
5
=
259.328u
29
+ 1680.90u
28
+ ··· + 926.254u + 175.912
161.259u
29
+ 1048.40u
28
+ ··· + 568.927u + 105.945
a
9
=
26.4432u
29
+ 177.739u
28
+ ··· + 90.6277u + 19.2857
6.46073u
29
+ 45.4625u
28
+ ··· + 37.2660u + 7.12632
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
6206476
38189
u
29
−
44334803
38189
u
28
+ ··· −
29935284
38189
u −
5980763
38189
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 13u
29
+ ··· − 85u + 13
c
2
, c
11
u
30
+ 3u
29
+ ··· + 6u + 1
c
3
, c
9
u
30
− u
29
+ ··· − 2u + 4
c
4
u
30
+ 13u
29
+ ··· + 85u + 13
c
5
u
30
+ 10u
29
+ ··· + 8u + 4
c
6
, c
7
u
30
+ 8u
29
+ ··· + 6u + 1
c
8
, c
12
u
30
− u
29
+ ··· + u + 1
c
10
u
30
− 8u
29
+ ··· − 6u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
+ 23y
29
+ ··· + 4163y + 169
c
2
, c
11
y
30
+ 19y
29
+ ··· + 18y + 1
c
3
, c
9
y
30
− 13y
29
+ ··· + 36y + 16
c
5
y
30
+ 4y
29
+ ··· + 216y + 16
c
6
, c
7
, c
10
y
30
− 32y
29
+ ··· − 4y + 1
c
8
, c
12
y
30
− 3y
29
+ ··· − 13y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642245 + 0.763853I
a = −0.555321 − 0.043797I
b = −0.185269 − 0.989682I
−2.27847 − 0.51362I −10.61612 + 0.72082I
u = 0.642245 − 0.763853I
a = −0.555321 + 0.043797I
b = −0.185269 + 0.989682I
−2.27847 + 0.51362I −10.61612 − 0.72082I
u = 0.527835 + 0.820250I
a = 0.642437 + 0.412311I
b = −0.609373 + 1.138350I
−1.94765 − 4.85354I −7.71248 + 4.30986I
u = 0.527835 − 0.820250I
a = 0.642437 − 0.412311I
b = −0.609373 − 1.138350I
−1.94765 + 4.85354I −7.71248 − 4.30986I
u = 0.879905 + 0.235691I
a = 0.461677 + 0.226265I
b = 0.590853 + 0.662007I
−0.44942 + 1.73476I −9.02190 − 3.44309I
u = 0.879905 − 0.235691I
a = 0.461677 − 0.226265I
b = 0.590853 − 0.662007I
−0.44942 − 1.73476I −9.02190 + 3.44309I
u = −0.801178 + 0.792132I
a = −0.349606 − 0.004829I
b = 0.272753 + 0.170612I
2.74186 + 5.92630I −8.64032 − 1.11570I
u = −0.801178 − 0.792132I
a = −0.349606 + 0.004829I
b = 0.272753 − 0.170612I
2.74186 − 5.92630I −8.64032 + 1.11570I
u = −0.985363 + 0.781065I
a = 0.270446 + 0.170416I
b = −0.039680 − 0.311474I
2.21624 − 0.05351I 0. + 9.20699I
u = −0.985363 − 0.781065I
a = 0.270446 − 0.170416I
b = −0.039680 + 0.311474I
2.21624 + 0.05351I 0. − 9.20699I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.365490 + 0.075077I
a = 1.02354 − 2.23453I
b = 0.214666 − 1.235630I
−3.29773 + 8.08131I 0. − 5.40847I
u = −1.365490 − 0.075077I
a = 1.02354 + 2.23453I
b = 0.214666 + 1.235630I
−3.29773 − 8.08131I 0. + 5.40847I
u = 0.375697 + 0.392763I
a = −0.79229 − 1.46902I
b = 0.723248 − 1.077650I
1.00820 − 4.13658I −5.7915 + 14.7595I
u = 0.375697 − 0.392763I
a = −0.79229 + 1.46902I
b = 0.723248 + 1.077650I
1.00820 + 4.13658I −5.7915 − 14.7595I
u = −1.48400 + 0.06467I
a = −0.41893 + 1.93998I
b = −0.05224 + 1.43862I
−8.66650 + 3.37784I 0
u = −1.48400 − 0.06467I
a = −0.41893 − 1.93998I
b = −0.05224 − 1.43862I
−8.66650 − 3.37784I 0
u = 1.50386 + 0.04313I
a = 0.316735 + 0.074482I
b = 1.179190 + 0.335072I
−5.60166 − 7.25627I 0
u = 1.50386 − 0.04313I
a = 0.316735 − 0.074482I
b = 1.179190 − 0.335072I
−5.60166 + 7.25627I 0
u = −1.51308 + 0.11947I
a = 0.33672 + 2.25100I
b = 0.80151 + 1.63388I
−5.40316 + 5.95865I 0
u = −1.51308 − 0.11947I
a = 0.33672 − 2.25100I
b = 0.80151 − 1.63388I
−5.40316 − 5.95865I 0
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52723 + 0.07696I
a = −0.243823 + 0.082893I
b = −0.965498 + 0.243372I
−8.79839 + 0.44060I 0
u = 1.52723 − 0.07696I
a = −0.243823 − 0.082893I
b = −0.965498 − 0.243372I
−8.79839 − 0.44060I 0
u = −1.54602 + 0.23911I
a = −0.419980 + 1.278380I
b = 0.308955 + 1.216150I
−9.45733 + 4.02263I 0
u = −1.54602 − 0.23911I
a = −0.419980 − 1.278380I
b = 0.308955 − 1.216150I
−9.45733 − 4.02263I 0
u = −1.54315 + 0.28532I
a = 0.21164 − 1.70333I
b = −0.85375 − 1.41497I
−8.70767 + 8.89911I 0
u = −1.54315 − 0.28532I
a = 0.21164 + 1.70333I
b = −0.85375 + 1.41497I
−8.70767 − 8.89911I 0
u = 0.010566 + 0.322840I
a = −1.86779 + 1.71826I
b = −0.391718 − 0.776480I
−3.11479 − 2.03526I −8.49725 + 3.17405I
u = 0.010566 − 0.322840I
a = −1.86779 − 1.71826I
b = −0.391718 + 0.776480I
−3.11479 + 2.03526I −8.49725 − 3.17405I
u = −0.229059 + 0.123829I
a = −1.11546 − 4.35585I
b = 0.506364 + 0.761147I
0.76351 − 7.25820I −2.86716 + 4.27850I
u = −0.229059 − 0.123829I
a = −1.11546 + 4.35585I
b = 0.506364 − 0.761147I
0.76351 + 7.25820I −2.86716 − 4.27850I
29
IV.
I
u
4
= h−2a
7
+55b+· · ·+6a−61, a
8
−3a
6
−2a
5
+10a
4
−6a
3
−2a
2
+2a+1, u−1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
−1
0
a
3
=
a
0.0363636a
7
− 0.345455a
6
+ ··· − 0.109091a + 1.10909
a
8
=
0
1
a
4
=
a
0.0363636a
7
− 0.345455a
6
+ ··· + 0.890909a + 1.10909
a
12
=
−0.345455a
7
− 0.218182a
6
+ ··· + 1.03636a − 1.03636
0.618182a
7
+ 0.127273a
6
+ ··· + 0.145455a + 0.854545
a
2
=
−0.0363636a
7
+ 0.345455a
6
+ ··· + 1.10909a − 1.10909
0.0363636a
7
− 0.345455a
6
+ ··· − 0.109091a + 1.10909
a
1
=
−0.127273a
7
+ 0.709091a
6
+ ··· + 1.38182a − 1.38182
0.563636a
7
+ 0.145455a
6
+ ··· + 0.309091a + 0.690909
a
5
=
−0.709091a
7
+ 0.236364a
6
+ ··· + 0.127273a − 0.127273
0.618182a
7
+ 0.127273a
6
+ ··· + 0.145455a − 0.145455
a
9
=
1.30909a
7
+ 0.563636a
6
+ ··· − 1.92727a + 0.927273
−0.963636a
7
− 0.345455a
6
+ ··· + 0.890909a + 0.109091
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
136
55
a
7
−
28
55
a
6
+
344
55
a
5
+
304
55
a
4
−
1168
55
a
3
+
692
55
a
2
−
32
55
a −
408
55
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
+ 1)
4
c
2
, c
11
(u
4
− u
2
+ 1)
2
c
3
, c
9
u
8
− 3u
6
− 2u
5
+ 10u
4
− 6u
3
− 2u
2
+ 2u + 1
c
5
(u
2
− u + 1)
4
c
6
, c
7
(u − 1)
8
c
8
, c
12
u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 6u
4
+ 6u
2
+ 2u + 1
c
10
(u + 1)
8
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y + 1)
8
c
2
, c
11
(y
2
− y + 1)
4
c
3
, c
9
y
8
− 6y
7
+ 29y
6
− 68y
5
+ 90y
4
− 74y
3
+ 48y
2
− 8y + 1
c
5
(y
2
+ y + 1)
4
c
6
, c
7
, c
10
(y −1)
8
c
8
, c
12
y
8
+ 6y
7
+ 29y
6
+ 68y
5
+ 90y
4
+ 74y
3
+ 48y
2
+ 8y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.750055 + 0.630141I
b = −0.866025 − 0.500000I
2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 0.750055 − 0.630141I
b = −0.866025 + 0.500000I
− 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 1.225300 + 0.302085I
b = 0.866025 + 0.500000I
2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 1.225300 − 0.302085I
b = 0.866025 − 0.500000I
− 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −0.359271 + 0.197915I
b = 0.866025 + 0.500000I
2.02988I −6.00000 − 3.46410I
u = 1.00000
a = −0.359271 − 0.197915I
b = 0.866025 − 0.500000I
− 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −1.61608 + 1.13014I
b = −0.866025 + 0.500000I
− 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −1.61608 − 1.13014I
b = −0.866025 − 0.500000I
2.02988I −6.00000 − 3.46410I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 1)
4
)(u
24
+ 7u
23
+ ··· + 15u + 3)
4
(u
30
− 13u
29
+ ··· − 85u + 13)
· (u
54
− 22u
53
+ ··· − 4312u + 448)
c
2
, c
11
((u
4
− u
2
+ 1)
2
)(u
30
+ 3u
29
+ ··· + 6u + 1)(u
54
− u
53
+ ··· + 13u + 2)
· (u
96
− 7u
95
+ ··· − 1069888u + 802048)
c
3
, c
9
(u
8
− 3u
6
+ ··· + 2u + 1)(u
30
− u
29
+ ··· − 2u + 4)
· (u
54
− u
53
+ ··· + 28u − 4)
· (u
96
+ u
95
+ ··· − 364694380u + 80529475)
c
4
((u
2
+ 1)
4
)(u
24
+ 7u
23
+ ··· + 15u + 3)
4
(u
30
+ 13u
29
+ ··· + 85u + 13)
· (u
54
− 22u
53
+ ··· − 4312u + 448)
c
5
((u
2
− u + 1)
4
)(u
2
+ u + 1)
48
(u
30
+ 10u
29
+ ··· + 8u + 4)
· (u
54
− 45u
53
+ ··· − 144703488u + 8388608)
c
6
, c
7
((u − 1)
8
)(u
24
− 3u
23
+ ··· + 3u − 1)
4
(u
30
+ 8u
29
+ ··· + 6u + 1)
· (u
54
+ 13u
53
+ ··· − 34u − 4)
c
8
, c
12
(u
8
+ 2u
7
+ ··· + 2u + 1)(u
30
− u
29
+ ··· + u + 1)
· (u
54
+ u
53
+ ··· − u − 1)(u
96
+ u
95
+ ··· + 44u + 4)
c
10
((u + 1)
8
)(u
24
− 3u
23
+ ··· + 3u − 1)
4
(u
30
− 8u
29
+ ··· − 6u + 1)
· (u
54
+ 13u
53
+ ··· − 34u − 4)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y + 1)
8
)(y
24
+ 15y
23
+ ··· + 69y + 9)
4
· (y
30
+ 23y
29
+ ··· + 4163y + 169)
· (y
54
+ 36y
53
+ ··· + 1750336y + 200704)
c
2
, c
11
((y
2
− y + 1)
4
)(y
30
+ 19y
29
+ ··· + 18y + 1)(y
54
+ 9y
53
+ ··· + 83y + 4)
· (y
96
+ 51y
95
+ ··· + 30481927393280y + 643280994304)
c
3
, c
9
(y
8
− 6y
7
+ 29y
6
− 68y
5
+ 90y
4
− 74y
3
+ 48y
2
− 8y + 1)
· (y
30
− 13y
29
+ ··· + 36y + 16)(y
54
− 27y
53
+ ··· − 896y + 16)
· (y
96
− 47y
95
+ ··· − 312805919734027100y + 6484996343775625)
c
5
((y
2
+ y + 1)
52
)(y
30
+ 4y
29
+ ··· + 216y + 16)
· (y
54
+ 5y
53
+ ··· − 532163627843584y + 70368744177664)
c
6
, c
7
, c
10
((y −1)
8
)(y
24
− 25y
23
+ ··· − 15y + 1)
4
(y
30
− 32y
29
+ ··· − 4y + 1)
· (y
54
− 55y
53
+ ··· − 908y + 16)
c
8
, c
12
(y
8
+ 6y
7
+ 29y
6
+ 68y
5
+ 90y
4
+ 74y
3
+ 48y
2
+ 8y + 1)
· (y
30
− 3y
29
+ ··· − 13y + 1)(y
54
+ 23y
53
+ ··· + 31y + 1)
· (y
96
− 15y
95
+ ··· − 1080y + 16)
35
