12a
1004
(K12a
1004
)
A knot diagram
1
Linearized knot diagam
4 6 12 10 2 9 1 11 5 7 3 8
Solving Sequence
8,12 1,4
3 7 11 9 6 2 10 5
c
12
c
3
c
7
c
11
c
8
c
6
c
2
c
10
c
4
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.50144 × 10
15
u
30
+ 1.24069 × 10
15
u
29
+ ··· + 2.15585 × 10
16
b + 1.38288 × 10
16
,
− 5.21559 × 10
15
u
30
+ 7.73030 × 10
12
u
29
+ ··· + 2.15585 × 10
16
a − 2.45094 × 10
16
,
u
31
+ 11u
29
+ ··· + 12u + 4i
I
u
2
= h1.75494 × 10
735
u
149
+ 8.27613 × 10
735
u
148
+ ··· + 4.56524 × 10
736
b + 8.92522 × 10
738
,
− 1.97153 × 10
738
u
149
− 3.62879 × 10
738
u
148
+ ··· + 1.39848 × 10
739
a − 5.96878 × 10
740
,
u
150
+ 2u
149
+ ··· − 2018u + 919i
I
u
3
= hu
5
+ u
4
+ 2u
3
+ u
2
+ 2b + u − 1, −u
5
− u
4
− 2u
3
+ u
2
+ 2a − u + 3, u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1i
I
u
4
= h4.40374 × 10
51
u
45
− 8.43737 × 10
51
u
44
+ ··· + 5.41181 × 10
50
b − 4.27132 × 10
52
,
− 3.42335 × 10
52
u
45
+ 1.28492 × 10
52
u
44
+ ··· + 1.08236 × 10
51
a − 1.08479 × 10
53
, u
46
− u
45
+ ··· + 12u + 4i
* 4 irreducible components of dim
C
= 0, with total 233 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
= h2.50 × 10
15
u
30
+ 1.24 × 10
15
u
29
+ · · · + 2.16 × 10
16
b + 1.38 ×
10
16
, −5.22 × 10
15
u
30
+ 7.73 × 10
12
u
29
+ · · · + 2.16 × 10
16
a − 2.45 ×
10
16
, u
31
+ 11u
29
+ · · · + 12u + 4i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
0.241927u
30
− 0.000358573u
29
+ ··· + 1.43030u + 1.13688
−0.116030u
30
− 0.0575497u
29
+ ··· − 2.58346u − 0.641452
a
3
=
0.125897u
30
− 0.0579082u
29
+ ··· − 1.15316u + 0.495428
−0.116030u
30
− 0.0575497u
29
+ ··· − 2.58346u − 0.641452
a
7
=
u
u
3
+ u
a
11
=
0.267306u
30
− 0.0879097u
29
+ ··· + 1.72413u + 0.957239
−0.0656034u
30
− 0.0724256u
29
+ ··· − 0.829228u − 0.181723
a
9
=
0.187341u
30
− 0.218241u
29
+ ··· + 0.377796u + 0.202808
−0.111050u
30
− 0.0423717u
29
+ ··· + 0.523194u + 0.118533
a
6
=
0.0594148u
30
+ 0.278830u
29
+ ··· + 2.92868u + 0.485553
0.144722u
30
− 0.0776651u
29
+ ··· − 0.277149u − 0.426960
a
2
=
−0.146036u
30
− 0.204690u
29
+ ··· − 5.94370u − 0.605131
−0.0842819u
30
+ 0.0793837u
29
+ ··· − 0.316602u + 0.243659
a
10
=
0.303630u
30
− 0.0612345u
29
+ ··· + 2.62375u + 0.925578
−0.0609509u
30
+ 0.00637618u
29
+ ··· − 0.395007u − 0.320084
a
5
=
0.180693u
30
− 0.116290u
29
+ ··· − 1.28768u − 0.0776417
−0.109654u
30
− 0.0500993u
29
+ ··· − 2.17214u − 0.397648
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
9688058052053989
62715688746323008
u
30
+
39488066647219475
62715688746323008
u
29
+···+
22360344283783987
3919730546645188
u−
238434930063801187
15678922186580752
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 10u
30
+ ··· + 3180u + 792
c
2
, c
3
, c
5
c
11
2(2u
31
+ u
30
+ ··· + 6u + 1)
c
4
, c
7
, c
9
c
12
u
31
+ 11u
29
+ ··· + 12u + 4
c
6
, c
8
u
31
− 2u
30
+ ··· + 17u + 4
c
10
4(4u
31
+ 67u
30
+ ··· + 1040u + 104)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 2y
30
+ ··· + 13128336y −627264
c
2
, c
3
, c
5
c
11
4(4y
31
− 61y
30
+ ··· + 20y −1)
c
4
, c
7
, c
9
c
12
y
31
+ 22y
30
+ ··· + 96y −16
c
6
, c
8
y
31
+ 14y
30
+ ··· + 105y −16
c
10
16(16y
31
− 49y
30
+ ··· + 106912y −10816)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383328 + 0.813662I
a = 0.490897 + 0.768652I
b = 0.884559 − 0.136812I
−1.59008 − 1.84478I −16.5634 + 3.3949I
u = 0.383328 − 0.813662I
a = 0.490897 − 0.768652I
b = 0.884559 + 0.136812I
−1.59008 + 1.84478I −16.5634 − 3.3949I
u = 1.070470 + 0.329267I
a = −0.1172980 − 0.0191354I
b = −1.260470 + 0.477995I
−6.38658 + 8.07639I −17.3230 − 5.6061I
u = 1.070470 − 0.329267I
a = −0.1172980 + 0.0191354I
b = −1.260470 − 0.477995I
−6.38658 − 8.07639I −17.3230 + 5.6061I
u = −0.038964 + 0.879008I
a = 0.26251 + 2.53537I
b = −0.968074 − 0.655155I
0.53762 − 4.18229I −8.93395 + 4.77809I
u = −0.038964 − 0.879008I
a = 0.26251 − 2.53537I
b = −0.968074 + 0.655155I
0.53762 + 4.18229I −8.93395 − 4.77809I
u = −0.807575 + 0.281045I
a = 0.354252 − 0.171232I
b = −1.266270 − 0.341594I
−5.89222 − 2.10069I −18.4399 + 0.8290I
u = −0.807575 − 0.281045I
a = 0.354252 + 0.171232I
b = −1.266270 + 0.341594I
−5.89222 + 2.10069I −18.4399 − 0.8290I
u = −0.509694 + 1.139090I
a = 0.15388 − 1.50487I
b = −0.649674 + 0.372347I
0.79845 + 6.17925I −12.61058 − 5.13272I
u = −0.509694 − 1.139090I
a = 0.15388 + 1.50487I
b = −0.649674 − 0.372347I
0.79845 − 6.17925I −12.61058 + 5.13272I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258230 + 1.244910I
a = −0.41437 − 2.09862I
b = −0.981776 + 0.445465I
3.58488 + 8.85757I −8.38851 − 10.74241I
u = −0.258230 − 1.244910I
a = −0.41437 + 2.09862I
b = −0.981776 − 0.445465I
3.58488 − 8.85757I −8.38851 + 10.74241I
u = −0.558604 + 1.155740I
a = −0.366123 − 0.135434I
b = 0.899543 + 0.557800I
2.74768 − 0.19116I −7.37244 + 2.08773I
u = −0.558604 − 1.155740I
a = −0.366123 + 0.135434I
b = 0.899543 − 0.557800I
2.74768 + 0.19116I −7.37244 − 2.08773I
u = 0.383183 + 1.225150I
a = −0.64267 − 1.59359I
b = 1.34293 + 0.84208I
0.23602 − 10.85600I −10.2697 + 11.6694I
u = 0.383183 − 1.225150I
a = −0.64267 + 1.59359I
b = 1.34293 − 0.84208I
0.23602 + 10.85600I −10.2697 − 11.6694I
u = 0.441579 + 1.215660I
a = 0.279092 − 1.192030I
b = −0.192360 + 1.107890I
6.66804 − 7.94380I −5.46409 + 6.49661I
u = 0.441579 − 1.215660I
a = 0.279092 + 1.192030I
b = −0.192360 − 1.107890I
6.66804 + 7.94380I −5.46409 − 6.49661I
u = 0.700279 + 1.092210I
a = −0.66429 + 1.28471I
b = −0.824149 − 0.631671I
3.27893 − 9.24231I −7.94202 + 11.05232I
u = 0.700279 − 1.092210I
a = −0.66429 − 1.28471I
b = −0.824149 + 0.631671I
3.27893 + 9.24231I −7.94202 − 11.05232I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031247 + 1.321110I
a = −0.146418 + 0.997579I
b = −0.147308 − 0.798761I
8.82763 − 2.25729I −0.71517 + 3.43143I
u = 0.031247 − 1.321110I
a = −0.146418 − 0.997579I
b = −0.147308 + 0.798761I
8.82763 + 2.25729I −0.71517 − 3.43143I
u = 0.113033 + 1.391790I
a = −1.41835 + 0.33002I
b = 0.764199 − 0.058208I
6.32535 − 3.39686I −18.8474 + 2.2372I
u = 0.113033 − 1.391790I
a = −1.41835 − 0.33002I
b = 0.764199 + 0.058208I
6.32535 + 3.39686I −18.8474 − 2.2372I
u = −0.588800 + 0.060054I
a = 0.889305 + 0.058898I
b = 0.385009 + 0.352343I
−0.533538 + 0.055476I −12.22757 + 0.28015I
u = −0.588800 − 0.060054I
a = 0.889305 − 0.058898I
b = 0.385009 − 0.352343I
−0.533538 − 0.055476I −12.22757 − 0.28015I
u = 0.498181 + 0.318586I
a = 2.21809 − 0.66774I
b = 0.776069 − 0.373133I
−2.64416 + 2.93302I −20.2796 − 2.5092I
u = 0.498181 − 0.318586I
a = 2.21809 + 0.66774I
b = 0.776069 + 0.373133I
−2.64416 − 2.93302I −20.2796 + 2.5092I
u = −0.66403 + 1.33370I
a = −0.12218 + 1.55945I
b = 1.31916 − 0.68794I
−0.0102 + 20.8448I −11.8902 − 10.7471I
u = −0.66403 − 1.33370I
a = −0.12218 − 1.55945I
b = 1.31916 + 0.68794I
−0.0102 − 20.8448I −11.8902 + 10.7471I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.390808
a = 0.987357
b = 0.337219
−0.641880 −14.9490
8
II. I
u
2
= h1.75 × 10
735
u
149
+ 8.28 × 10
735
u
148
+ · · · + 4.57 × 10
736
b + 8.93 ×
10
738
, −1.97 × 10
738
u
149
− 3.63 × 10
738
u
148
+ · · · + 1.40 × 10
739
a − 5.97 ×
10
740
, u
150
+ 2u
149
+ · · · − 2018u + 919i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
0.140976u
149
+ 0.259480u
148
+ ··· + 82.9270u + 42.6804
−0.0384414u
149
− 0.181286u
148
+ ··· + 172.135u − 195.504
a
3
=
0.102535u
149
+ 0.0781942u
148
+ ··· + 255.062u − 152.823
−0.0384414u
149
− 0.181286u
148
+ ··· + 172.135u − 195.504
a
7
=
u
u
3
+ u
a
11
=
0.0527453u
149
+ 0.135239u
148
+ ··· − 205.782u + 94.4901
−0.124909u
149
− 0.285605u
148
+ ··· − 435.520u + 80.3466
a
9
=
−0.191319u
149
− 1.05657u
148
+ ··· + 1145.26u − 817.448
−0.154653u
149
− 0.481473u
148
+ ··· − 54.1775u − 24.3770
a
6
=
0.286348u
149
+ 0.609107u
148
+ ··· + 253.359u + 104.157
−0.0788148u
149
− 0.229913u
148
+ ··· − 125.252u + 5.41964
a
2
=
−0.648465u
149
− 1.52286u
148
+ ··· − 771.712u − 73.5282
0.0450857u
149
+ 0.0633439u
148
+ ··· + 404.505u − 140.573
a
10
=
0.0777436u
149
+ 0.213415u
148
+ ··· − 186.573u + 133.827
−0.0882209u
149
− 0.186805u
148
+ ··· − 382.419u + 93.7867
a
5
=
0.358685u
149
+ 1.26422u
148
+ ··· − 822.439u + 754.747
0.0215969u
149
+ 0.0830095u
148
+ ··· + 94.3670u − 104.822
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.246889u
149
− 1.99031u
148
+ ··· + 2745.00u − 2218.10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
75
+ u
74
+ ··· − 8855u + 8613)
2
c
2
, c
3
, c
5
c
11
u
150
+ 2u
149
+ ··· + 1677010u + 170479
c
4
, c
7
, c
9
c
12
u
150
+ 2u
149
+ ··· − 2018u + 919
c
6
, c
8
u
150
− 11u
149
+ ··· − 497109u + 23211
c
10
(u
75
− 14u
74
+ ··· + 3u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
75
− 5y
74
+ ··· − 714208913y −74183769)
2
c
2
, c
3
, c
5
c
11
y
150
− 90y
149
+ ··· − 927470682466y + 29063089441
c
4
, c
7
, c
9
c
12
y
150
+ 80y
149
+ ··· + 32014968y + 844561
c
6
, c
8
y
150
− 25y
149
+ ··· − 6938889327y + 538750521
c
10
(y
75
− 40y
74
+ ··· − 283y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.250266 + 0.977052I
a = 0.80676 − 1.47322I
b = −0.760581 + 0.919565I
2.08475 0
u = −0.250266 − 0.977052I
a = 0.80676 + 1.47322I
b = −0.760581 − 0.919565I
2.08475 0
u = 0.655265 + 0.743088I
a = 0.387229 − 1.131810I
b = 0.923417 − 0.212960I
−2.72280 + 3.03687I 0
u = 0.655265 − 0.743088I
a = 0.387229 + 1.131810I
b = 0.923417 + 0.212960I
−2.72280 − 3.03687I 0
u = −0.400769 + 0.901756I
a = 0.706701 + 0.969647I
b = 0.759020 − 0.470826I
0.183461 − 0.643254I 0
u = −0.400769 − 0.901756I
a = 0.706701 − 0.969647I
b = 0.759020 + 0.470826I
0.183461 + 0.643254I 0
u = −0.036000 + 0.978779I
a = −0.436667 + 0.213218I
b = 0.456001 − 0.628144I
1.28163 + 4.74782I 0
u = −0.036000 − 0.978779I
a = −0.436667 − 0.213218I
b = 0.456001 + 0.628144I
1.28163 − 4.74782I 0
u = −0.546343 + 0.804601I
a = −0.62861 + 1.63725I
b = 1.36068 − 0.45263I
−3.91595 − 4.23228I 0
u = −0.546343 − 0.804601I
a = −0.62861 − 1.63725I
b = 1.36068 + 0.45263I
−3.91595 + 4.23228I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.216397 + 0.943779I
a = −0.74672 + 1.91237I
b = 0.24646 − 1.52907I
7.63312 − 0.89997I 0
u = 0.216397 − 0.943779I
a = −0.74672 − 1.91237I
b = 0.24646 + 1.52907I
7.63312 + 0.89997I 0
u = 0.349373 + 0.899365I
a = −0.16996 − 2.06139I
b = 1.407160 + 0.040470I
−5.99442 − 2.26352I 0
u = 0.349373 − 0.899365I
a = −0.16996 + 2.06139I
b = 1.407160 − 0.040470I
−5.99442 + 2.26352I 0
u = 0.441210 + 0.941201I
a = −0.57467 − 1.77607I
b = 1.40592 + 0.41005I
−6.53345 − 2.32464I 0
u = 0.441210 − 0.941201I
a = −0.57467 + 1.77607I
b = 1.40592 − 0.41005I
−6.53345 + 2.32464I 0
u = −0.188199 + 1.057230I
a = 1.32209 − 2.15726I
b = −1.53250 + 1.80873I
2.35174 0
u = −0.188199 − 1.057230I
a = 1.32209 + 2.15726I
b = −1.53250 − 1.80873I
2.35174 0
u = 0.408850 + 1.007140I
a = −0.16808 + 1.42574I
b = 0.235347 − 0.899173I
−1.02208 − 2.05598I 0
u = 0.408850 − 1.007140I
a = −0.16808 − 1.42574I
b = 0.235347 + 0.899173I
−1.02208 + 2.05598I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.006600 + 0.438885I
a = 0.393281 − 0.145454I
b = 1.047080 − 0.364356I
−2.45707 + 3.31723I 0
u = 1.006600 − 0.438885I
a = 0.393281 + 0.145454I
b = 1.047080 + 0.364356I
−2.45707 − 3.31723I 0
u = 0.352204 + 0.825566I
a = 0.25726 + 2.29475I
b = −0.799291 − 0.233085I
−1.98483 − 1.30642I 0
u = 0.352204 − 0.825566I
a = 0.25726 − 2.29475I
b = −0.799291 + 0.233085I
−1.98483 + 1.30642I 0
u = 0.686439 + 0.578140I
a = −0.427492 + 1.035030I
b = 0.570528 − 0.667568I
−2.17590 − 1.99776I 0
u = 0.686439 − 0.578140I
a = −0.427492 − 1.035030I
b = 0.570528 + 0.667568I
−2.17590 + 1.99776I 0
u = −0.390466 + 1.057110I
a = 0.42845 − 2.10170I
b = −1.008840 + 0.388689I
1.22970 + 5.73765I 0
u = −0.390466 − 1.057110I
a = 0.42845 + 2.10170I
b = −1.008840 − 0.388689I
1.22970 − 5.73765I 0
u = 0.690066 + 0.891775I
a = 0.570034 − 0.418838I
b = −1.180320 + 0.478317I
−1.31289 − 1.98120I 0
u = 0.690066 − 0.891775I
a = 0.570034 + 0.418838I
b = −1.180320 − 0.478317I
−1.31289 + 1.98120I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855453 + 0.164095I
a = −0.010839 − 0.625499I
b = 0.495355 + 0.458806I
−1.98483 − 1.30642I 0
u = −0.855453 − 0.164095I
a = −0.010839 + 0.625499I
b = 0.495355 − 0.458806I
−1.98483 + 1.30642I 0
u = −0.143310 + 0.855821I
a = −0.73462 − 1.57560I
b = 1.36640 + 0.80674I
1.37427 + 1.78291I 0
u = −0.143310 − 0.855821I
a = −0.73462 + 1.57560I
b = 1.36640 − 0.80674I
1.37427 − 1.78291I 0
u = −0.447485 + 0.730129I
a = −0.55154 − 1.88716I
b = −1.026360 + 0.533608I
1.28163 + 4.74782I 0
u = −0.447485 − 0.730129I
a = −0.55154 + 1.88716I
b = −1.026360 − 0.533608I
1.28163 − 4.74782I 0
u = 0.323505 + 0.787742I
a = 0.40619 + 2.39052I
b = −0.633653 − 0.516123I
−1.80519 − 1.37797I 0
u = 0.323505 − 0.787742I
a = 0.40619 − 2.39052I
b = −0.633653 + 0.516123I
−1.80519 + 1.37797I 0
u = −0.271186 + 1.121900I
a = 0.73438 + 1.46158I
b = 1.109690 − 0.265505I
4.56771 + 4.91013I 0
u = −0.271186 − 1.121900I
a = 0.73438 − 1.46158I
b = 1.109690 + 0.265505I
4.56771 − 4.91013I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.262446 + 0.799550I
a = −0.97084 + 1.71487I
b = −1.46685 − 0.09403I
−6.45947 − 0.53044I 0
u = 0.262446 − 0.799550I
a = −0.97084 − 1.71487I
b = −1.46685 + 0.09403I
−6.45947 + 0.53044I 0
u = 0.181012 + 1.145580I
a = 0.420619 − 0.818133I
b = −0.498012 + 0.701152I
3.32569 + 0.65529I 0
u = 0.181012 − 1.145580I
a = 0.420619 + 0.818133I
b = −0.498012 − 0.701152I
3.32569 − 0.65529I 0
u = −0.769142 + 0.335251I
a = 0.414701 − 0.652623I
b = 0.656441 − 0.016514I
−1.80519 − 1.37797I 0
u = −0.769142 − 0.335251I
a = 0.414701 + 0.652623I
b = 0.656441 + 0.016514I
−1.80519 + 1.37797I 0
u = 0.247354 + 1.136450I
a = 0.86297 + 1.68247I
b = −0.777734 − 1.089730I
1.37427 − 1.78291I 0
u = 0.247354 − 1.136450I
a = 0.86297 − 1.68247I
b = −0.777734 + 1.089730I
1.37427 + 1.78291I 0
u = 0.379505 + 0.739562I
a = 0.892661 − 0.151906I
b = 1.176190 + 0.092279I
−2.17590 − 1.99776I 0
u = 0.379505 − 0.739562I
a = 0.892661 + 0.151906I
b = 1.176190 − 0.092279I
−2.17590 + 1.99776I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.300646 + 1.132930I
a = −1.23861 + 2.25342I
b = 1.146840 − 0.271611I
−1.21344 + 9.83163I 0
u = −0.300646 − 1.132930I
a = −1.23861 − 2.25342I
b = 1.146840 + 0.271611I
−1.21344 − 9.83163I 0
u = −0.450164 + 1.093910I
a = −0.63467 − 1.36529I
b = 0.284143 + 1.328500I
−0.03753 + 7.18574I 0
u = −0.450164 − 1.093910I
a = −0.63467 + 1.36529I
b = 0.284143 − 1.328500I
−0.03753 − 7.18574I 0
u = −0.402909 + 0.708552I
a = 0.803206 − 0.484338I
b = −1.68528 − 0.02177I
−4.26915 + 8.26207I 0
u = −0.402909 − 0.708552I
a = 0.803206 + 0.484338I
b = −1.68528 + 0.02177I
−4.26915 − 8.26207I 0
u = 0.843514 + 0.850015I
a = 0.739905 − 0.777530I
b = 0.625540 + 0.403159I
3.59312 − 3.90956I 0
u = 0.843514 − 0.850015I
a = 0.739905 + 0.777530I
b = 0.625540 − 0.403159I
3.59312 + 3.90956I 0
u = 0.256490 + 1.187730I
a = 0.78680 − 1.33207I
b = −0.454776 + 1.149360I
6.19587 + 1.47709I 0
u = 0.256490 − 1.187730I
a = 0.78680 + 1.33207I
b = −0.454776 − 1.149360I
6.19587 − 1.47709I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554540 + 1.088720I
a = −0.259263 − 1.328640I
b = −0.998413 + 0.555368I
1.83771 + 4.15446I 0
u = −0.554540 − 1.088720I
a = −0.259263 + 1.328640I
b = −0.998413 − 0.555368I
1.83771 − 4.15446I 0
u = 0.768907 + 0.115120I
a = −1.109670 + 0.765255I
b = −0.008615 − 0.858346I
0.07161 + 9.29331I 0
u = 0.768907 − 0.115120I
a = −1.109670 − 0.765255I
b = −0.008615 + 0.858346I
0.07161 − 9.29331I 0
u = −0.462373 + 1.141140I
a = −0.13970 + 1.63210I
b = 1.41592 − 0.58875I
3.21020 + 7.96938I 0
u = −0.462373 − 1.141140I
a = −0.13970 − 1.63210I
b = 1.41592 + 0.58875I
3.21020 − 7.96938I 0
u = −0.387293 + 1.181570I
a = 0.479022 + 0.905676I
b = −0.329614 − 0.909267I
2.94502 + 3.75977I 0
u = −0.387293 − 1.181570I
a = 0.479022 − 0.905676I
b = −0.329614 + 0.909267I
2.94502 − 3.75977I 0
u = 0.422255 + 0.626342I
a = 0.432656 + 0.749631I
b = −1.59437 + 0.11877I
−7.50514 − 1.37117I 0
u = 0.422255 − 0.626342I
a = 0.432656 − 0.749631I
b = −1.59437 − 0.11877I
−7.50514 + 1.37117I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.751881 + 0.054661I
a = 0.776209 + 0.365607I
b = 0.985866 − 0.530921I
0.183461 + 0.643254I 0
u = −0.751881 − 0.054661I
a = 0.776209 − 0.365607I
b = 0.985866 + 0.530921I
0.183461 − 0.643254I 0
u = 0.072438 + 0.748710I
a = 0.04199 + 3.88290I
b = 0.646521 − 0.073430I
0.90150 − 8.00755I 0
u = 0.072438 − 0.748710I
a = 0.04199 − 3.88290I
b = 0.646521 + 0.073430I
0.90150 + 8.00755I 0
u = −1.252590 + 0.223473I
a = −0.100363 + 0.250425I
b = −1.240240 − 0.498985I
−3.5371 − 14.1696I 0
u = −1.252590 − 0.223473I
a = −0.100363 − 0.250425I
b = −1.240240 + 0.498985I
−3.5371 + 14.1696I 0
u = −0.448926 + 1.198050I
a = −0.07328 − 1.78279I
b = −1.202550 + 0.678910I
3.71261 + 4.93092I 0
u = −0.448926 − 1.198050I
a = −0.07328 + 1.78279I
b = −1.202550 − 0.678910I
3.71261 − 4.93092I 0
u = 0.698619 + 0.137185I
a = 1.301690 + 0.042161I
b = 0.041138 − 0.388436I
2.94502 − 3.75977I 0
u = 0.698619 − 0.137185I
a = 1.301690 − 0.042161I
b = 0.041138 + 0.388436I
2.94502 + 3.75977I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461652 + 1.209270I
a = 0.692743 + 0.557834I
b = −0.723844 − 0.803902I
3.59312 + 3.90956I 0
u = −0.461652 − 1.209270I
a = 0.692743 − 0.557834I
b = −0.723844 + 0.803902I
3.59312 − 3.90956I 0
u = −0.713496 + 1.081450I
a = −0.21277 + 1.54177I
b = 1.150550 − 0.689190I
−3.68004 + 7.53499I 0
u = −0.713496 − 1.081450I
a = −0.21277 − 1.54177I
b = 1.150550 + 0.689190I
−3.68004 − 7.53499I 0
u = 0.502553 + 1.205120I
a = −0.54022 + 1.34157I
b = 0.296891 − 1.263300I
3.2751 − 14.0412I 0
u = 0.502553 − 1.205120I
a = −0.54022 − 1.34157I
b = 0.296891 + 1.263300I
3.2751 + 14.0412I 0
u = 1.254340 + 0.395241I
a = −0.195623 + 0.399096I
b = −1.139310 + 0.031343I
−6.53345 − 2.32464I 0
u = 1.254340 − 0.395241I
a = −0.195623 − 0.399096I
b = −1.139310 − 0.031343I
−6.53345 + 2.32464I 0
u = 0.563330 + 0.374444I
a = 0.367906 + 0.121104I
b = 0.392380 − 0.747287I
1.83771 + 4.15446I −12.00000 − 4.45837I
u = 0.563330 − 0.374444I
a = 0.367906 − 0.121104I
b = 0.392380 + 0.747287I
1.83771 − 4.15446I −12.00000 + 4.45837I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.035474 + 0.674379I
a = 0.73673 − 3.21244I
b = −0.727123 + 0.121587I
2.62009 − 3.15258I −7.30516 − 1.86749I
u = −0.035474 − 0.674379I
a = 0.73673 + 3.21244I
b = −0.727123 − 0.121587I
2.62009 + 3.15258I −7.30516 + 1.86749I
u = −1.292450 + 0.297044I
a = 0.140330 − 0.094987I
b = 1.147030 + 0.395623I
−0.03753 − 7.18574I 0
u = −1.292450 − 0.297044I
a = 0.140330 + 0.094987I
b = 1.147030 − 0.395623I
−0.03753 + 7.18574I 0
u = 0.493976 + 0.457694I
a = 0.253734 − 0.205322I
b = −0.197489 + 0.627814I
3.32569 − 0.65529I −6.71791 + 2.75531I
u = 0.493976 − 0.457694I
a = 0.253734 + 0.205322I
b = −0.197489 − 0.627814I
3.32569 + 0.65529I −6.71791 − 2.75531I
u = −0.420753 + 1.273170I
a = −0.198239 − 1.064800I
b = 0.285083 + 0.464077I
1.22970 + 5.73765I 0
u = −0.420753 − 1.273170I
a = −0.198239 + 1.064800I
b = 0.285083 − 0.464077I
1.22970 − 5.73765I 0
u = −0.408294 + 1.284780I
a = −0.992362 + 0.925617I
b = 0.929801 + 0.024442I
−1.31289 + 1.98120I 0
u = −0.408294 − 1.284780I
a = −0.992362 − 0.925617I
b = 0.929801 − 0.024442I
−1.31289 − 1.98120I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.318560 + 0.327432I
a = 0.0119743 − 0.1206620I
b = −1.189920 − 0.156849I
−7.50514 − 1.37117I 0
u = −1.318560 − 0.327432I
a = 0.0119743 + 0.1206620I
b = −1.189920 + 0.156849I
−7.50514 + 1.37117I 0
u = 0.083023 + 0.635682I
a = −0.03057 + 1.71932I
b = 1.089820 − 0.686141I
−0.551162 −4.22170 + 0.I
u = 0.083023 − 0.635682I
a = −0.03057 − 1.71932I
b = 1.089820 + 0.686141I
−0.551162 −4.22170 + 0.I
u = 0.461487 + 1.278340I
a = 0.633716 − 0.857699I
b = 0.736078 + 0.367160I
3.71261 + 4.93092I 0
u = 0.461487 − 1.278340I
a = 0.633716 + 0.857699I
b = 0.736078 − 0.367160I
3.71261 − 4.93092I 0
u = 0.635937 + 1.206620I
a = −0.141131 + 1.397990I
b = −1.228840 − 0.582408I
0.07161 − 9.29331I 0
u = 0.635937 − 1.206620I
a = −0.141131 − 1.397990I
b = −1.228840 + 0.582408I
0.07161 + 9.29331I 0
u = −0.402012 + 1.313960I
a = 0.692889 + 0.794692I
b = −0.484017 − 0.675496I
2.62009 + 3.15258I 0
u = −0.402012 − 1.313960I
a = 0.692889 − 0.794692I
b = −0.484017 + 0.675496I
2.62009 − 3.15258I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.675199 + 1.199990I
a = −0.083026 − 0.945417I
b = 1.315650 + 0.361753I
−3.91595 − 4.23228I 0
u = 0.675199 − 1.199990I
a = −0.083026 + 0.945417I
b = 1.315650 − 0.361753I
−3.91595 + 4.23228I 0
u = −0.559368 + 0.267785I
a = −0.612320 − 1.069500I
b = −1.248960 − 0.291886I
0.59207 − 3.84639I −16.3412 + 6.1087I
u = −0.559368 − 0.267785I
a = −0.612320 + 1.069500I
b = −1.248960 + 0.291886I
0.59207 + 3.84639I −16.3412 − 6.1087I
u = 0.640578 + 1.232330I
a = −0.08096 − 1.57782I
b = 1.35280 + 0.68528I
−3.5371 − 14.1696I 0
u = 0.640578 − 1.232330I
a = −0.08096 + 1.57782I
b = 1.35280 − 0.68528I
−3.5371 + 14.1696I 0
u = 0.487495 + 1.304020I
a = −0.208277 + 0.851270I
b = −0.985837 − 0.388487I
6.19587 − 1.47709I 0
u = 0.487495 − 1.304020I
a = −0.208277 − 0.851270I
b = −0.985837 + 0.388487I
6.19587 + 1.47709I 0
u = 0.500404 + 0.319118I
a = 1.03061 − 2.45334I
b = 0.805428 + 0.693717I
−2.72280 − 3.03687I −18.8978 + 3.7986I
u = 0.500404 − 0.319118I
a = 1.03061 + 2.45334I
b = 0.805428 − 0.693717I
−2.72280 + 3.03687I −18.8978 − 3.7986I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57488 + 1.31082I
a = −0.24084 + 1.64866I
b = −1.059500 − 0.572660I
0.90150 − 8.00755I 0
u = 0.57488 − 1.31082I
a = −0.24084 − 1.64866I
b = −1.059500 + 0.572660I
0.90150 + 8.00755I 0
u = −0.513014 + 0.229311I
a = 0.627065 − 0.718822I
b = 1.230040 + 0.148177I
−1.02208 − 2.05598I −15.0654 + 0.2508I
u = −0.513014 − 0.229311I
a = 0.627065 + 0.718822I
b = 1.230040 − 0.148177I
−1.02208 + 2.05598I −15.0654 − 0.2508I
u = 0.441975 + 0.340142I
a = −0.958567 − 0.445390I
b = −1.311680 − 0.324396I
−3.68004 − 7.53499I −17.8449 + 6.7090I
u = 0.441975 − 0.340142I
a = −0.958567 + 0.445390I
b = −1.311680 + 0.324396I
−3.68004 + 7.53499I −17.8449 − 6.7090I
u = 0.18678 + 1.43477I
a = 1.10945 − 0.90922I
b = −0.667207 + 0.521091I
4.56771 − 4.91013I 0
u = 0.18678 − 1.43477I
a = 1.10945 + 0.90922I
b = −0.667207 − 0.521091I
4.56771 + 4.91013I 0
u = −0.79123 + 1.21455I
a = −0.19125 + 1.41279I
b = 1.158130 − 0.612879I
−3.73630 + 7.55536I 0
u = −0.79123 − 1.21455I
a = −0.19125 − 1.41279I
b = 1.158130 + 0.612879I
−3.73630 − 7.55536I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.69068 + 1.30818I
a = −0.342924 + 1.139810I
b = 1.34710 − 0.51490I
−4.26915 + 8.26207I 0
u = −0.69068 − 1.30818I
a = −0.342924 − 1.139810I
b = 1.34710 + 0.51490I
−4.26915 − 8.26207I 0
u = −0.68673 + 1.32005I
a = 0.064725 − 1.366140I
b = −1.28534 + 0.61833I
3.2751 + 14.0412I 0
u = −0.68673 − 1.32005I
a = 0.064725 + 1.366140I
b = −1.28534 − 0.61833I
3.2751 − 14.0412I 0
u = −0.464434 + 0.187179I
a = −2.09409 − 0.59676I
b = 0.113747 + 0.848755I
−2.45707 − 3.31723I −16.2672 + 3.7814I
u = −0.464434 − 0.187179I
a = −2.09409 + 0.59676I
b = 0.113747 − 0.848755I
−2.45707 + 3.31723I −16.2672 − 3.7814I
u = 0.00030 + 1.51994I
a = −0.687857 + 0.192593I
b = 0.808043 − 0.228187I
0.59207 + 3.84639I 0
u = 0.00030 − 1.51994I
a = −0.687857 − 0.192593I
b = 0.808043 + 0.228187I
0.59207 − 3.84639I 0
u = 0.034618 + 0.409937I
a = −2.11467 − 0.07409I
b = −1.364660 − 0.266765I
−3.73630 − 7.55536I −20.7272 + 3.7806I
u = 0.034618 − 0.409937I
a = −2.11467 + 0.07409I
b = −1.364660 + 0.266765I
−3.73630 + 7.55536I −20.7272 − 3.7806I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60159 + 0.07335I
a = −0.402181 − 0.379049I
b = −0.945404 + 0.203727I
−5.99442 + 2.26352I 0
u = 1.60159 − 0.07335I
a = −0.402181 + 0.379049I
b = −0.945404 − 0.203727I
−5.99442 − 2.26352I 0
u = 0.68463 + 1.47823I
a = −0.136931 − 1.359930I
b = 1.121570 + 0.483815I
−1.21344 − 9.83163I 0
u = 0.68463 − 1.47823I
a = −0.136931 + 1.359930I
b = 1.121570 − 0.483815I
−1.21344 + 9.83163I 0
u = −1.63060 + 0.48529I
a = −0.111402 + 0.347942I
b = −1.020230 − 0.272083I
−6.45947 + 0.53044I 0
u = −1.63060 − 0.48529I
a = −0.111402 − 0.347942I
b = −1.020230 + 0.272083I
−6.45947 − 0.53044I 0
u = −0.23104 + 1.72150I
a = −0.558279 − 0.316774I
b = 0.914287 + 0.325735I
3.21020 − 7.96938I 0
u = −0.23104 − 1.72150I
a = −0.558279 + 0.316774I
b = 0.914287 − 0.325735I
3.21020 + 7.96938I 0
u = −0.15583 + 1.82679I
a = 0.370491 + 0.090013I
b = −0.778719 − 0.119365I
7.63312 − 0.89997I 0
u = −0.15583 − 1.82679I
a = 0.370491 − 0.090013I
b = −0.778719 + 0.119365I
7.63312 + 0.89997I 0
26
III. I
u
3
= hu
5
+ u
4
+ 2u
3
+ u
2
+ 2b + u − 1, −u
5
− u
4
− 2u
3
+ u
2
+ 2a − u +
3, u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
1
2
u
5
+
1
2
u
4
+ ··· +
1
2
u −
3
2
−
1
2
u
5
−
1
2
u
4
+ ··· −
1
2
u +
1
2
a
3
=
−u
2
− 1
−
1
2
u
5
−
1
2
u
4
+ ··· −
1
2
u +
1
2
a
7
=
u
u
3
+ u
a
11
=
−u
3
− 2u + 1
−
1
4
u
5
+
1
4
u
4
+ ··· −
3
4
u −
3
4
a
9
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u
−u
4
− 2u
2
+ u
a
6
=
u
5
+ 2u
4
+ 2u
3
+ u
2
− 1
−u
5
− u
4
+ 3u + 1
a
2
=
3
2
u
5
+
1
2
u
4
+ ··· −
1
2
u −
1
2
−
1
2
u
5
+
1
2
u
4
+ ··· +
1
2
u +
1
2
a
10
=
−
1
4
u
5
−
3
4
u
4
+ ··· −
3
4
u +
5
4
1
4
u
5
+
3
4
u
4
+ ··· −
5
4
u −
5
4
a
5
=
5
4
u
5
+
3
4
u
4
+ ··· −
1
4
u −
5
4
−
5
4
u
5
+
1
4
u
4
+ ··· +
1
4
u +
1
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =
339
64
u
5
−
203
64
u
4
+
127
16
u
3
−
815
64
u
2
−
19
64
u −
1051
64
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− u
5
− 2u
4
+ u
3
+ 15u
2
+ 3u − 13
c
2
, c
11
2(2u
6
− u
5
− 5u
4
+ 3u
3
+ 4u
2
− u − 1)
c
3
, c
5
2(2u
6
+ u
5
− 5u
4
− 3u
3
+ 4u
2
+ u − 1)
c
4
, c
7
u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1
c
6
, c
8
u
6
+ 2u
5
+ 3u
4
− 8u
2
− 3u + 4
c
9
, c
12
u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1
c
10
4(4u
6
+ 9u
5
+ 10u
4
+ 5u
3
+ 4u
2
+ 4u + 1)
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 5y
5
+ 36y
4
− 81y
3
+ 271y
2
− 399y + 169
c
2
, c
3
, c
5
c
11
4(4y
6
− 21y
5
+ 47y
4
− 55y
3
+ 32y
2
− 9y + 1)
c
4
, c
7
, c
9
c
12
y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1
c
6
, c
8
y
6
+ 2y
5
− 7y
4
− 28y
3
+ 88y
2
− 73y + 16
c
10
16(16y
6
− y
5
+ 42y
4
− 9y
3
− 4y
2
− 8y + 1)
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841864
a = −0.374188
b = −1.33455
−8.17258 −20.3140
u = 0.126468 + 1.352400I
a = 1.40195 − 0.45857I
b = −0.588959 + 0.116497I
6.71880 − 3.39374I 2.08996 + 1.93495I
u = 0.126468 − 1.352400I
a = 1.40195 + 0.45857I
b = −0.588959 − 0.116497I
6.71880 + 3.39374I 2.08996 − 1.93495I
u = −0.376468 + 1.319680I
a = −0.58244 + 1.44801I
b = 1.182250 − 0.454374I
0.12319 + 8.77346I −11.09361 − 6.96195I
u = −0.376468 − 1.319680I
a = −0.58244 − 1.44801I
b = 1.182250 + 0.454374I
0.12319 − 8.77346I −11.09361 + 6.96195I
u = −0.341865
a = −1.76483
b = 0.647956
−2.22153 −18.1940
30
IV.
I
u
4
= h4.40×10
51
u
45
−8.44×10
51
u
44
+· · ·+5.41×10
50
b−4.27×10
52
, −3.42×
10
52
u
45
+1.28×10
52
u
44
+· · ·+1.08×10
51
a−1.08×10
53
, u
46
−u
45
+· · ·+12u+4i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
31.6285u
45
− 11.8715u
44
+ ··· + 537.388u + 100.225
−8.13729u
45
+ 15.5907u
44
+ ··· + 195.982u + 78.9260
a
3
=
23.4912u
45
+ 3.71922u
44
+ ··· + 733.369u + 179.151
−8.13729u
45
+ 15.5907u
44
+ ··· + 195.982u + 78.9260
a
7
=
u
u
3
+ u
a
11
=
29.5760u
45
− 13.3326u
44
+ ··· + 617.752u + 113.976
−9.64980u
45
+ 27.5793u
44
+ ··· + 434.033u + 155.556
a
9
=
45.4243u
45
− 62.3283u
44
+ ··· − 212.470u − 191.008
22.9703u
45
− 28.5063u
44
+ ··· − 85.6937u − 90.0526
a
6
=
−13.3814u
45
+ 58.4735u
44
+ ··· + 1038.19u + 356.014
−4.41878u
45
+ 18.7774u
44
+ ··· + 358.045u + 128.384
a
2
=
19.7640u
45
− 45.5939u
44
+ ··· − 702.479u − 251.614
−10.7564u
45
− 8.87510u
44
+ ··· − 570.703u − 148.811
a
10
=
44.5405u
45
− 31.1466u
44
+ ··· + 598.656u + 71.7825
−2.97301u
45
+ 17.7030u
44
+ ··· + 389.272u + 124.760
a
5
=
−21.8041u
45
+ 27.9798u
44
+ ··· − 44.9663u + 49.2717
−34.9052u
45
+ 30.0647u
44
+ ··· − 292.715u + 1.25918
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9.48329u
45
− 53.2188u
44
+ ··· − 1217.89u − 404.995
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
23
− 3u
22
+ ··· + 151u − 25)
2
c
2
, c
11
u
46
+ 5u
45
+ ··· − 4u + 1
c
3
, c
5
u
46
− 5u
45
+ ··· + 4u + 1
c
4
, c
7
u
46
+ u
45
+ ··· − 12u + 4
c
6
, c
8
u
46
− 6u
45
+ ··· − 99u + 11
c
9
, c
12
u
46
− u
45
+ ··· + 12u + 4
c
10
(u
23
+ 5u
22
+ ··· + 2u + 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 9y
22
+ ··· − 5799y −625)
2
c
2
, c
3
, c
5
c
11
y
46
− 27y
45
+ ··· − 40y + 1
c
4
, c
7
, c
9
c
12
y
46
+ 25y
45
+ ··· + 416y + 16
c
6
, c
8
y
46
− 24y
45
+ ··· − 5995y + 121
c
10
(y
23
− 45y
22
+ ··· − 14y −1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.131845 + 0.978857I
a = 0.67246 − 1.82940I
b = −0.15795 + 1.43214I
7.82326 − 0.53653I −4.13730 − 5.24725I
u = 0.131845 − 0.978857I
a = 0.67246 + 1.82940I
b = −0.15795 − 1.43214I
7.82326 + 0.53653I −4.13730 + 5.24725I
u = 0.896198 + 0.476953I
a = 0.870986 − 0.150250I
b = 0.881003 − 0.361673I
−1.84009 + 3.24020I −9.52863 − 6.89276I
u = 0.896198 − 0.476953I
a = 0.870986 + 0.150250I
b = 0.881003 + 0.361673I
−1.84009 − 3.24020I −9.52863 + 6.89276I
u = 0.357790 + 0.912103I
a = −0.23483 − 1.80763I
b = 1.48597 + 0.04181I
−5.77540 − 2.30938I 3.60017 + 10.56143I
u = 0.357790 − 0.912103I
a = −0.23483 + 1.80763I
b = 1.48597 − 0.04181I
−5.77540 + 2.30938I 3.60017 − 10.56143I
u = 0.175393 + 1.057290I
a = 1.44993 + 2.26567I
b = −1.64967 − 1.92523I
2.33184 −249.889 + 0.I
u = 0.175393 − 1.057290I
a = 1.44993 − 2.26567I
b = −1.64967 + 1.92523I
2.33184 −249.889 + 0.I
u = −0.314974 + 0.856411I
a = −0.29088 − 3.34048I
b = −0.668525 + 0.261913I
0.95192 + 8.74138I −12.5922 − 12.9338I
u = −0.314974 − 0.856411I
a = −0.29088 + 3.34048I
b = −0.668525 − 0.261913I
0.95192 − 8.74138I −12.5922 + 12.9338I
34
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.245397 + 0.814683I
a = −0.57924 + 1.78892I
b = −1.51112 − 0.12500I
−6.31804 − 0.41537I 0.5403 − 14.4576I
u = 0.245397 − 0.814683I
a = −0.57924 − 1.78892I
b = −1.51112 + 0.12500I
−6.31804 + 0.41537I 0.5403 + 14.4576I
u = −0.304618 + 1.155010I
a = 0.562109 − 1.008460I
b = −0.125668 + 0.675542I
0.57175 + 2.34177I 0
u = −0.304618 − 1.155010I
a = 0.562109 + 1.008460I
b = −0.125668 − 0.675542I
0.57175 − 2.34177I 0
u = −0.364563 + 1.148240I
a = −0.22605 − 1.79969I
b = −1.228100 + 0.504496I
3.49555 + 6.29451I 0
u = −0.364563 − 1.148240I
a = −0.22605 + 1.79969I
b = −1.228100 − 0.504496I
3.49555 − 6.29451I 0
u = −0.459751 + 0.626740I
a = 1.56966 + 2.06593I
b = 0.815623 − 0.193608I
2.21969 + 4.00523I −12.62158 − 5.18160I
u = −0.459751 − 0.626740I
a = 1.56966 − 2.06593I
b = 0.815623 + 0.193608I
2.21969 − 4.00523I −12.62158 + 5.18160I
u = 0.463220 + 0.603361I
a = −0.756411 + 0.424958I
b = 1.157190 − 0.305670I
0.57175 − 2.34177I −11.22455 + 2.79967I
u = 0.463220 − 0.603361I
a = −0.756411 − 0.424958I
b = 1.157190 + 0.305670I
0.57175 + 2.34177I −11.22455 − 2.79967I
35
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.081360 + 0.735029I
a = 0.81812 + 3.30002I
b = −0.580140 − 0.643427I
−1.84009 − 3.24020I −9.52863 + 6.89276I
u = 0.081360 − 0.735029I
a = 0.81812 − 3.30002I
b = −0.580140 + 0.643427I
−1.84009 + 3.24020I −9.52863 − 6.89276I
u = 0.049943 + 0.694222I
a = −0.453160 − 0.308938I
b = −1.48075 − 0.20224I
−3.23627 − 7.73169I −6.25642 + 7.41688I
u = 0.049943 − 0.694222I
a = −0.453160 + 0.308938I
b = −1.48075 + 0.20224I
−3.23627 + 7.73169I −6.25642 − 7.41688I
u = −0.406323 + 1.269900I
a = 0.808009 + 0.646630I
b = −0.592483 − 0.684078I
2.21969 + 4.00523I 0
u = −0.406323 − 1.269900I
a = 0.808009 − 0.646630I
b = −0.592483 + 0.684078I
2.21969 − 4.00523I 0
u = −0.654251 + 0.013991I
a = −0.186552 − 0.036628I
b = 0.842704 − 0.393872I
−1.82461 − 0.02654I −14.7661 + 0.5460I
u = −0.654251 − 0.013991I
a = −0.186552 + 0.036628I
b = 0.842704 + 0.393872I
−1.82461 + 0.02654I −14.7661 − 0.5460I
u = −0.143948 + 1.353480I
a = 0.070610 − 0.184025I
b = 0.312840 − 0.106831I
1.12137 + 3.21807I 0
u = −0.143948 − 1.353480I
a = 0.070610 + 0.184025I
b = 0.312840 + 0.106831I
1.12137 − 3.21807I 0
36
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601361 + 1.273960I
a = −0.36765 + 1.58478I
b = −1.015330 − 0.548591I
0.95192 − 8.74138I 0
u = 0.601361 − 1.273960I
a = −0.36765 − 1.58478I
b = −1.015330 + 0.548591I
0.95192 + 8.74138I 0
u = −0.369655 + 0.401631I
a = 0.57718 + 1.92042I
b = 1.068430 + 0.193875I
1.12137 − 3.21807I −10.70427 − 0.14049I
u = −0.369655 − 0.401631I
a = 0.57718 − 1.92042I
b = 1.068430 − 0.193875I
1.12137 + 3.21807I −10.70427 + 0.14049I
u = −0.076941 + 0.527831I
a = −0.11008 − 2.98398I
b = 0.710838 + 0.441013I
−1.82461 − 0.02654I −14.7661 + 0.5460I
u = −0.076941 − 0.527831I
a = −0.11008 + 2.98398I
b = 0.710838 − 0.441013I
−1.82461 + 0.02654I −14.7661 − 0.5460I
u = −0.09756 + 1.47144I
a = −0.161127 + 0.881883I
b = 0.611162 − 0.036365I
3.49555 − 6.29451I 0
u = −0.09756 − 1.47144I
a = −0.161127 − 0.881883I
b = 0.611162 + 0.036365I
3.49555 + 6.29451I 0
u = 0.79501 + 1.30236I
a = −0.223692 − 1.289510I
b = 1.188870 + 0.590006I
−3.23627 − 7.73169I 0
u = 0.79501 − 1.30236I
a = −0.223692 + 1.289510I
b = 1.188870 − 0.590006I
−3.23627 + 7.73169I 0
37
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67530 + 0.03765I
a = −0.383637 + 0.298946I
b = −0.897619 − 0.190346I
−5.77540 − 2.30938I 0
u = −1.67530 − 0.03765I
a = −0.383637 − 0.298946I
b = −0.897619 + 0.190346I
−5.77540 + 2.30938I 0
u = 1.66358 + 0.48122I
a = −0.123714 − 0.283288I
b = −1.005550 + 0.269722I
−6.31804 − 0.41537I 0
u = 1.66358 − 0.48122I
a = −0.123714 + 0.283288I
b = −1.005550 − 0.269722I
−6.31804 + 0.41537I 0
u = −0.09321 + 1.75383I
a = 0.197963 − 0.174427I
b = −0.661737 + 0.007795I
7.82326 − 0.53653I 0
u = −0.09321 − 1.75383I
a = 0.197963 + 0.174427I
b = −0.661737 − 0.007795I
7.82326 + 0.53653I 0
38
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− u
5
+ ··· + 3u − 13)(u
23
− 3u
22
+ ··· + 151u − 25)
2
· (u
31
− 10u
30
+ ··· + 3180u + 792)(u
75
+ u
74
+ ··· − 8855u + 8613)
2
c
2
, c
11
4(2u
6
− u
5
+ ··· − u − 1)(2u
31
+ u
30
+ ··· + 6u + 1)
· (u
46
+ 5u
45
+ ··· − 4u + 1)(u
150
+ 2u
149
+ ··· + 1677010u + 170479)
c
3
, c
5
4(2u
6
+ u
5
+ ··· + u − 1)(2u
31
+ u
30
+ ··· + 6u + 1)
· (u
46
− 5u
45
+ ··· + 4u + 1)(u
150
+ 2u
149
+ ··· + 1677010u + 170479)
c
4
, c
7
(u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1)(u
31
+ 11u
29
+ ··· + 12u + 4)
· (u
46
+ u
45
+ ··· − 12u + 4)(u
150
+ 2u
149
+ ··· − 2018u + 919)
c
6
, c
8
(u
6
+ 2u
5
+ 3u
4
− 8u
2
− 3u + 4)(u
31
− 2u
30
+ ··· + 17u + 4)
· (u
46
− 6u
45
+ ··· − 99u + 11)(u
150
− 11u
149
+ ··· − 497109u + 23211)
c
9
, c
12
(u
6
+ 3u
4
− u
3
+ 2u
2
− 2u − 1)(u
31
+ 11u
29
+ ··· + 12u + 4)
· (u
46
− u
45
+ ··· + 12u + 4)(u
150
+ 2u
149
+ ··· − 2018u + 919)
c
10
16(4u
6
+ 9u
5
+ 10u
4
+ 5u
3
+ 4u
2
+ 4u + 1)
· ((u
23
+ 5u
22
+ ··· + 2u + 1)
2
)(4u
31
+ 67u
30
+ ··· + 1040u + 104)
· (u
75
− 14u
74
+ ··· + 3u − 1)
2
39
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 5y
5
+ 36y
4
− 81y
3
+ 271y
2
− 399y + 169)
· (y
23
+ 9y
22
+ ··· − 5799y −625)
2
· (y
31
+ 2y
30
+ ··· + 13128336y −627264)
· (y
75
− 5y
74
+ ··· − 714208913y −74183769)
2
c
2
, c
3
, c
5
c
11
16(4y
6
− 21y
5
+ 47y
4
− 55y
3
+ 32y
2
− 9y + 1)
· (4y
31
− 61y
30
+ ··· + 20y −1)(y
46
− 27y
45
+ ··· − 40y + 1)
· (y
150
− 90y
149
+ ··· − 927470682466y + 29063089441)
c
4
, c
7
, c
9
c
12
(y
6
+ 6y
5
+ ··· − 8y + 1)(y
31
+ 22y
30
+ ··· + 96y −16)
· (y
46
+ 25y
45
+ ··· + 416y + 16)
· (y
150
+ 80y
149
+ ··· + 32014968y + 844561)
c
6
, c
8
(y
6
+ 2y
5
− 7y
4
− 28y
3
+ 88y
2
− 73y + 16)
· (y
31
+ 14y
30
+ ··· + 105y −16)(y
46
− 24y
45
+ ··· − 5995y + 121)
· (y
150
− 25y
149
+ ··· − 6938889327y + 538750521)
c
10
256(16y
6
− y
5
+ 42y
4
− 9y
3
− 4y
2
− 8y + 1)
· (y
23
− 45y
22
+ ··· − 14y −1)
2
· (16y
31
− 49y
30
+ ··· + 106912y −10816)
· (y
75
− 40y
74
+ ··· − 283y −1)
2
40
