12a
1106
(K12a
1106
)
A knot diagram
1
Linearized knot diagam
4 7 11 1 8 3 10 5 12 6 2 9
Solving Sequence
3,6 7,10
8 11 4 2 12 1 5 9
c
6
c
7
c
10
c
3
c
2
c
11
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.60339 × 10
20
u
45
− 6.13256 × 10
21
u
44
+ ··· + 3.13338 × 10
20
b − 5.65347 × 10
22
,
− 8.14927 × 10
21
u
45
− 9.80301 × 10
22
u
44
+ ··· + 4.07340 × 10
21
a − 3.64681 × 10
23
,
u
46
+ 13u
45
+ ··· + 528u + 52i
I
u
2
= h−2.52311 × 10
41
au
48
+ 4.74776 × 10
45
u
48
+ ··· + 1.26156 × 10
42
a − 1.24713 × 10
46
,
− 2.57277 × 10
43
au
48
− 5.51496 × 10
43
u
48
+ ··· − 6.30524 × 10
44
a − 2.26929 × 10
44
,
u
49
− 5u
48
+ ··· − 24u + 5i
I
u
3
= h39u
23
− 272u
22
+ ··· + 2b + 298, −227u
23
+ 1814u
22
+ ··· + 4a − 104, u
24
− 8u
23
+ ··· − 14u + 4i
I
u
4
= h−u
8
a − 2u
8
+ ··· − a + 12, −2u
8
a + 4u
8
+ ··· − 5a + 4,
u
9
+ 3u
8
+ 8u
7
+ 11u
6
+ 15u
5
+ 12u
4
+ 12u
3
+ 6u
2
+ 4u + 1i
* 4 irreducible components of dim
C
= 0, with total 186 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−4.60 × 10
20
u
45
− 6.13 × 10
21
u
44
+ · · · + 3.13 × 10
20
b − 5.65 ×
10
22
, −8.15 × 10
21
u
45
− 9.80 × 10
22
u
44
+ · · · + 4.07 × 10
21
a − 3.65 ×
10
23
, u
46
+ 13u
45
+ · · · + 528u + 52i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
2.00061u
45
+ 24.0659u
44
+ ··· + 818.429u + 89.5274
1.46914u
45
+ 19.5717u
44
+ ··· + 1562.07u + 180.427
a
8
=
−4.00772u
45
− 51.8972u
44
+ ··· − 2075.81u − 216.751
−1.86528u
45
− 22.5866u
44
+ ··· − 2577.80u − 305.396
a
11
=
3.46975u
45
+ 43.6376u
44
+ ··· + 2380.50u + 269.954
1.46914u
45
+ 19.5717u
44
+ ··· + 1562.07u + 180.427
a
4
=
−6.58633u
45
− 80.4182u
44
+ ··· − 5130.89u − 595.022
−5.20411u
45
− 63.1627u
44
+ ··· − 2881.56u − 342.489
a
2
=
u
u
3
+ u
a
12
=
2.09825u
45
+ 27.7764u
44
+ ··· + 2050.58u + 229.638
−0.444574u
45
− 6.01583u
44
+ ··· + 264.191u + 37.7574
a
1
=
−9.79082u
45
− 125.313u
44
+ ··· − 5041.79u − 538.637
−3.63013u
45
− 47.9190u
44
+ ··· − 5309.39u − 606.117
a
5
=
5.55453u
45
+ 70.1876u
44
+ ··· + 3099.66u + 331.686
−2.63800u
45
− 30.8944u
44
+ ··· − 683.228u − 70.7210
a
9
=
8.06685u
45
+ 102.106u
44
+ ··· + 5565.75u + 618.858
1.02710u
45
+ 14.1539u
44
+ ··· + 2593.21u + 305.374
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1739513054631728078213
156669125128683693623
u
45
−
19720374536040326128317
156669125128683693623
u
44
+ ··· +
65726012224390325344578
156669125128683693623
u +
6323936967181692502404
156669125128683693623
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
46
− u
45
+ ··· + 4u + 1
c
2
, c
6
u
46
+ 13u
45
+ ··· + 528u + 52
c
3
, c
10
u
46
− u
45
+ ··· − u + 1
c
7
, c
11
u
46
+ 3u
45
+ ··· + 44u + 19
c
9
, c
12
u
46
− 16u
45
+ ··· − 4284u + 356
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
46
+ 51y
45
+ ··· + 46y + 1
c
2
, c
6
y
46
+ 25y
45
+ ··· + 38416y + 2704
c
3
, c
10
y
46
− 31y
45
+ ··· − 37y + 1
c
7
, c
11
y
46
− 11y
45
+ ··· − 74y + 361
c
9
, c
12
y
46
+ 28y
45
+ ··· + 6976y + 126736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.807598 + 0.595089I
a = 0.145048 − 0.406650I
b = −0.139471 + 0.179847I
2.14007 − 2.35023I 0
u = 0.807598 − 0.595089I
a = 0.145048 + 0.406650I
b = −0.139471 − 0.179847I
2.14007 + 2.35023I 0
u = 0.231176 + 0.989385I
a = −1.43994 + 0.06005I
b = 0.753112 + 0.540664I
1.24241 − 3.60901I 0
u = 0.231176 − 0.989385I
a = −1.43994 − 0.06005I
b = 0.753112 − 0.540664I
1.24241 + 3.60901I 0
u = −0.958272 + 0.171846I
a = −0.139418 − 0.213175I
b = −1.218050 + 0.694851I
6.01083 − 6.65776I 0
u = −0.958272 − 0.171846I
a = −0.139418 + 0.213175I
b = −1.218050 − 0.694851I
6.01083 + 6.65776I 0
u = −0.133424 + 0.931610I
a = −1.83866 − 0.63682I
b = 0.48794 + 1.35404I
1.87823 + 0.64171I 7.20970 + 0.I
u = −0.133424 − 0.931610I
a = −1.83866 + 0.63682I
b = 0.48794 − 1.35404I
1.87823 − 0.64171I 7.20970 + 0.I
u = −0.850515 + 0.368554I
a = 0.199127 + 0.211355I
b = 0.481513 − 0.475580I
−1.68076 + 0.65406I −4.00000 + 0.I
u = −0.850515 − 0.368554I
a = 0.199127 − 0.211355I
b = 0.481513 + 0.475580I
−1.68076 − 0.65406I −4.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.079950 + 1.109550I
a = 1.71790 − 0.71105I
b = −1.273120 − 0.404326I
12.79600 + 1.32693I 0
u = 0.079950 − 1.109550I
a = 1.71790 + 0.71105I
b = −1.273120 + 0.404326I
12.79600 − 1.32693I 0
u = −0.123378 + 0.876834I
a = −1.62741 + 1.21693I
b = 1.39351 + 0.40523I
11.46350 − 1.33067I 5.54801 + 0.I
u = −0.123378 − 0.876834I
a = −1.62741 − 1.21693I
b = 1.39351 − 0.40523I
11.46350 + 1.33067I 5.54801 + 0.I
u = −1.136830 + 0.116641I
a = −0.090473 + 0.188791I
b = 1.154570 − 0.661441I
10.9076 − 13.1169I 0
u = −1.136830 − 0.116641I
a = −0.090473 − 0.188791I
b = 1.154570 + 0.661441I
10.9076 + 13.1169I 0
u = −1.177030 + 0.246057I
a = 0.100844 − 0.173825I
b = −0.760628 + 0.238675I
−0.28329 − 2.46940I 0
u = −1.177030 − 0.246057I
a = 0.100844 + 0.173825I
b = −0.760628 − 0.238675I
−0.28329 + 2.46940I 0
u = −0.553395 + 1.117580I
a = 0.674037 − 1.222200I
b = −1.40922 + 0.32528I
13.4569 + 4.5178I 0
u = −0.553395 − 1.117580I
a = 0.674037 + 1.222200I
b = −1.40922 − 0.32528I
13.4569 − 4.5178I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587105 + 1.105440I
a = 0.597505 + 0.241208I
b = −0.272732 − 0.315437I
7.07812 − 0.91875I 0
u = 0.587105 − 1.105440I
a = 0.597505 − 0.241208I
b = −0.272732 + 0.315437I
7.07812 + 0.91875I 0
u = −0.225696 + 0.704958I
a = 1.345580 − 0.046479I
b = −0.425277 − 0.851426I
−0.34086 + 1.39531I −7.67124 − 3.20232I
u = −0.225696 − 0.704958I
a = 1.345580 + 0.046479I
b = −0.425277 + 0.851426I
−0.34086 − 1.39531I −7.67124 + 3.20232I
u = −0.410569 + 1.212210I
a = 2.01084 − 0.24207I
b = −1.52000 − 1.17808I
14.4173 + 3.8759I 0
u = −0.410569 − 1.212210I
a = 2.01084 + 0.24207I
b = −1.52000 + 1.17808I
14.4173 − 3.8759I 0
u = 1.114170 + 0.678095I
a = −0.373922 + 0.123021I
b = 0.230477 − 0.018824I
5.21462 − 5.32991I 0
u = 1.114170 − 0.678095I
a = −0.373922 − 0.123021I
b = 0.230477 + 0.018824I
5.21462 + 5.32991I 0
u = −0.677172 + 0.036174I
a = 0.490434 + 0.446612I
b = 1.163000 + 0.751547I
10.79730 − 0.17282I 2.61634 − 1.42688I
u = −0.677172 − 0.036174I
a = 0.490434 − 0.446612I
b = 1.163000 − 0.751547I
10.79730 + 0.17282I 2.61634 + 1.42688I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.315606 + 1.283940I
a = −1.034810 + 0.862364I
b = 1.223300 + 0.044072I
10.86770 − 2.33603I 0
u = −0.315606 − 1.283940I
a = −1.034810 − 0.862364I
b = 1.223300 − 0.044072I
10.86770 + 2.33603I 0
u = −0.519948 + 1.222880I
a = 1.245960 − 0.257027I
b = −1.081520 − 0.697292I
1.18366 + 4.44726I 0
u = −0.519948 − 1.222880I
a = 1.245960 + 0.257027I
b = −1.081520 + 0.697292I
1.18366 − 4.44726I 0
u = −0.550737 + 1.253470I
a = −1.79269 + 0.41681I
b = 1.63311 + 0.95618I
9.3517 + 12.1022I 0
u = −0.550737 − 1.253470I
a = −1.79269 − 0.41681I
b = 1.63311 − 0.95618I
9.3517 − 12.1022I 0
u = −0.286358 + 1.351340I
a = −1.179040 + 0.177372I
b = 0.921389 + 0.559060I
5.63593 + 2.22264I 0
u = −0.286358 − 1.351340I
a = −1.179040 − 0.177372I
b = 0.921389 − 0.559060I
5.63593 − 2.22264I 0
u = −0.58550 + 1.33618I
a = 1.67084 − 0.31304I
b = −1.53069 − 0.89395I
14.7508 + 19.1920I 0
u = −0.58550 − 1.33618I
a = 1.67084 + 0.31304I
b = −1.53069 + 0.89395I
14.7508 − 19.1920I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60654 + 1.32680I
a = −1.223140 + 0.285432I
b = 1.169600 + 0.620562I
3.28252 + 8.78274I 0
u = −0.60654 − 1.32680I
a = −1.223140 − 0.285432I
b = 1.169600 − 0.620562I
3.28252 − 8.78274I 0
u = −0.38466 + 1.48180I
a = 0.857403 − 0.686288I
b = −1.047490 + 0.028732I
16.2619 − 7.4805I 0
u = −0.38466 − 1.48180I
a = 0.857403 + 0.686288I
b = −1.047490 − 0.028732I
16.2619 + 7.4805I 0
u = 0.175636 + 0.397553I
a = 1.72245 − 0.09939I
b = −0.433330 − 0.421079I
−0.163355 + 1.344400I −0.935383 − 1.030188I
u = 0.175636 − 0.397553I
a = 1.72245 + 0.09939I
b = −0.433330 + 0.421079I
−0.163355 − 1.344400I −0.935383 + 1.030188I
9
II. I
u
2
= h−2.52 × 10
41
au
48
+ 4.75 × 10
45
u
48
+ · · · + 1.26 × 10
42
a − 1.25 ×
10
46
, −2.57 × 10
43
au
48
− 5.51 × 10
43
u
48
+ · · · − 6.31 × 10
44
a − 2.27 ×
10
44
, u
49
− 5u
48
+ · · · − 24u + 5i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
a
0.000388350au
48
− 7.30759u
48
+ ··· − 0.00194175a + 19.1954
a
8
=
0.558404au
48
− 4.16725u
48
+ ··· − 21.6247a − 4.70757
−0.798041au
48
− 0.836990u
48
+ ··· − 14.9132a + 38.8839
a
11
=
0.000388350au
48
− 7.30759u
48
+ ··· + 0.998058a + 19.1954
0.000388350au
48
− 7.30759u
48
+ ··· − 0.00194175a + 19.1954
a
4
=
7.30759au
48
− 8.39539u
48
+ ··· − 19.1954a − 12.6628
−7.06522u
48
+ 35.5339u
47
+ ··· − 142.655u + 24.4019
a
2
=
u
u
3
+ u
a
12
=
−4.28213u
48
+ 22.8488u
47
+ ··· + a + 21.9874
−0.000388350au
48
− 6.31628u
48
+ ··· + 0.00194175a + 15.9948
a
1
=
−4.17147au
48
+ 5.85731u
48
+ ··· + 29.7650a − 59.5141
0.878342au
48
+ 0.836990u
48
+ ··· + 5.90205a − 37.8839
a
5
=
−3.32947au
48
− 1.66919u
48
+ ··· + 7.94493a − 43.2952
0.897083au
48
+ 2.34292u
48
+ ··· + 16.2745a − 40.3382
a
9
=
−3.75017au
48
+ 3.58649u
48
+ ··· − 10.6560a − 8.10556
−0.917110au
48
− 1.49781u
48
+ ··· + 12.6166a + 7.49436
(ii) Obstruction class = −1
(iii) Cusp Shapes = −24.6678u
48
+ 121.656u
47
+ ··· − 316.868u − 8.44978
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
98
− 8u
97
+ ··· − 1622u + 113
c
2
, c
6
(u
49
− 5u
48
+ ··· − 24u + 5)
2
c
3
, c
10
u
98
− 2u
97
+ ··· − 1030836u + 176389
c
7
, c
11
u
98
+ 14u
97
+ ··· + 155699u + 22103
c
9
, c
12
(u
49
+ 12u
48
+ ··· + 257u + 59)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
98
+ 86y
97
+ ··· + 162250y + 12769
c
2
, c
6
(y
49
+ 33y
48
+ ··· − 624y −25)
2
c
3
, c
10
y
98
− 12y
97
+ ··· + 591541541430y + 31113079321
c
7
, c
11
y
98
− 14y
97
+ ··· − 3878773113y + 488542609
c
9
, c
12
(y
49
+ 40y
48
+ ··· + 20383y −3481)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957418 + 0.137707I
a = 0.286955 + 0.026555I
b = 0.770591 + 0.427917I
0.78697 + 3.63609I −6.16185 − 3.13365I
u = 0.957418 + 0.137707I
a = 0.098397 + 0.256279I
b = −0.949930 − 0.580750I
0.78697 + 3.63609I −6.16185 − 3.13365I
u = 0.957418 − 0.137707I
a = 0.286955 − 0.026555I
b = 0.770591 − 0.427917I
0.78697 − 3.63609I −6.16185 + 3.13365I
u = 0.957418 − 0.137707I
a = 0.098397 − 0.256279I
b = −0.949930 + 0.580750I
0.78697 − 3.63609I −6.16185 + 3.13365I
u = 0.264760 + 1.006070I
a = −0.52326 + 1.53050I
b = 0.02032 − 2.33382I
10.39620 − 9.45799I 0
u = 0.264760 + 1.006070I
a = 2.83956 − 0.12888I
b = −0.675041 + 0.718691I
10.39620 − 9.45799I 0
u = 0.264760 − 1.006070I
a = −0.52326 − 1.53050I
b = 0.02032 + 2.33382I
10.39620 + 9.45799I 0
u = 0.264760 − 1.006070I
a = 2.83956 + 0.12888I
b = −0.675041 − 0.718691I
10.39620 + 9.45799I 0
u = 0.226346 + 0.929253I
a = −0.148134 + 0.600625I
b = −0.020547 + 0.894164I
0.67276 − 3.75122I −4.00000 + 10.38124I
u = 0.226346 + 0.929253I
a = −2.33048 − 0.06053I
b = 1.42722 − 0.18159I
0.67276 − 3.75122I −4.00000 + 10.38124I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.226346 − 0.929253I
a = −0.148134 − 0.600625I
b = −0.020547 − 0.894164I
0.67276 + 3.75122I −4.00000 − 10.38124I
u = 0.226346 − 0.929253I
a = −2.33048 + 0.06053I
b = 1.42722 + 0.18159I
0.67276 + 3.75122I −4.00000 − 10.38124I
u = −0.091513 + 0.935745I
a = −0.456898 − 0.674035I
b = −0.18764 + 1.53444I
1.92899 + 0.49464I 3.10942 + 0.I
u = −0.091513 + 0.935745I
a = −2.38983 − 0.72163I
b = 0.746133 + 0.681858I
1.92899 + 0.49464I 3.10942 + 0.I
u = −0.091513 − 0.935745I
a = −0.456898 + 0.674035I
b = −0.18764 − 1.53444I
1.92899 − 0.49464I 3.10942 + 0.I
u = −0.091513 − 0.935745I
a = −2.38983 + 0.72163I
b = 0.746133 − 0.681858I
1.92899 − 0.49464I 3.10942 + 0.I
u = −0.156773 + 1.055540I
a = −1.012630 + 0.946873I
b = 1.08233 − 1.74068I
6.66499 + 3.79319I 0
u = −0.156773 + 1.055540I
a = 2.58947 + 0.96162I
b = −0.826969 − 0.198015I
6.66499 + 3.79319I 0
u = −0.156773 − 1.055540I
a = −1.012630 − 0.946873I
b = 1.08233 + 1.74068I
6.66499 − 3.79319I 0
u = −0.156773 − 1.055540I
a = 2.58947 − 0.96162I
b = −0.826969 + 0.198015I
6.66499 − 3.79319I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346619 + 1.023320I
a = 0.016055 − 0.908875I
b = −0.22570 + 1.48864I
4.55239 + 5.49253I 0
u = −0.346619 + 1.023320I
a = −1.89262 − 0.17132I
b = 0.520618 + 0.415489I
4.55239 + 5.49253I 0
u = −0.346619 − 1.023320I
a = 0.016055 + 0.908875I
b = −0.22570 − 1.48864I
4.55239 − 5.49253I 0
u = −0.346619 − 1.023320I
a = −1.89262 + 0.17132I
b = 0.520618 − 0.415489I
4.55239 − 5.49253I 0
u = 0.255872 + 0.810452I
a = −2.33454 − 0.40118I
b = 0.036356 − 1.193870I
3.99300 − 1.28672I −2.49363 + 5.09640I
u = 0.255872 + 0.810452I
a = 2.03137 − 1.80698I
b = −0.70468 + 2.27070I
3.99300 − 1.28672I −2.49363 + 5.09640I
u = 0.255872 − 0.810452I
a = −2.33454 + 0.40118I
b = 0.036356 + 1.193870I
3.99300 + 1.28672I −2.49363 − 5.09640I
u = 0.255872 − 0.810452I
a = 2.03137 + 1.80698I
b = −0.70468 − 2.27070I
3.99300 + 1.28672I −2.49363 − 5.09640I
u = 0.650362 + 0.441524I
a = 0.677266 + 1.068720I
b = −1.096870 + 0.194713I
5.53096 − 2.47656I 1.49723 + 2.71117I
u = 0.650362 + 0.441524I
a = 0.184610 − 0.352276I
b = 0.830729 − 0.636420I
5.53096 − 2.47656I 1.49723 + 2.71117I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650362 − 0.441524I
a = 0.677266 − 1.068720I
b = −1.096870 − 0.194713I
5.53096 + 2.47656I 1.49723 − 2.71117I
u = 0.650362 − 0.441524I
a = 0.184610 + 0.352276I
b = 0.830729 + 0.636420I
5.53096 + 2.47656I 1.49723 − 2.71117I
u = 1.217590 + 0.050320I
a = −0.380129 − 0.100856I
b = 0.987499 + 0.498459I
3.96783 + 6.46429I 0
u = 1.217590 + 0.050320I
a = −0.107019 + 0.139455I
b = −0.719519 − 0.514679I
3.96783 + 6.46429I 0
u = 1.217590 − 0.050320I
a = −0.380129 + 0.100856I
b = 0.987499 − 0.498459I
3.96783 − 6.46429I 0
u = 1.217590 − 0.050320I
a = −0.107019 − 0.139455I
b = −0.719519 + 0.514679I
3.96783 − 6.46429I 0
u = −0.943010 + 0.818382I
a = −1.130180 + 0.715066I
b = 1.347900 − 0.119643I
8.64456 + 5.11693I 0
u = −0.943010 + 0.818382I
a = 0.185523 + 0.251875I
b = 0.692592 + 0.383315I
8.64456 + 5.11693I 0
u = −0.943010 − 0.818382I
a = −1.130180 − 0.715066I
b = 1.347900 + 0.119643I
8.64456 − 5.11693I 0
u = −0.943010 − 0.818382I
a = 0.185523 − 0.251875I
b = 0.692592 − 0.383315I
8.64456 − 5.11693I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662579 + 0.318199I
a = −1.42153 + 0.15838I
b = 0.494020 + 0.798046I
2.47935 − 1.74491I −2.56195 + 1.08924I
u = −0.662579 + 0.318199I
a = 0.446052 + 0.340850I
b = −0.310211 + 0.928842I
2.47935 − 1.74491I −2.56195 + 1.08924I
u = −0.662579 − 0.318199I
a = −1.42153 − 0.15838I
b = 0.494020 − 0.798046I
2.47935 + 1.74491I −2.56195 − 1.08924I
u = −0.662579 − 0.318199I
a = 0.446052 − 0.340850I
b = −0.310211 − 0.928842I
2.47935 + 1.74491I −2.56195 − 1.08924I
u = −0.719602
a = −0.388671 + 1.087390I
b = −0.997469 − 0.455040I
5.21368 −1.16360
u = −0.719602
a = −0.388671 − 1.087390I
b = −0.997469 + 0.455040I
5.21368 −1.16360
u = 0.329381 + 1.249470I
a = −1.42789 − 0.56714I
b = 1.009110 − 0.770169I
10.11660 − 5.76726I 0
u = 0.329381 + 1.249470I
a = 1.91025 − 0.05665I
b = −1.53298 + 0.96374I
10.11660 − 5.76726I 0
u = 0.329381 − 1.249470I
a = −1.42789 + 0.56714I
b = 1.009110 + 0.770169I
10.11660 + 5.76726I 0
u = 0.329381 − 1.249470I
a = 1.91025 + 0.05665I
b = −1.53298 − 0.96374I
10.11660 + 5.76726I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396490 + 1.239700I
a = −0.873184 − 0.814822I
b = 0.874312 − 0.185924I
5.25338 − 0.75552I 0
u = 0.396490 + 1.239700I
a = 1.172500 + 0.287941I
b = −1.241080 + 0.395387I
5.25338 − 0.75552I 0
u = 0.396490 − 1.239700I
a = −0.873184 + 0.814822I
b = 0.874312 + 0.185924I
5.25338 + 0.75552I 0
u = 0.396490 − 1.239700I
a = 1.172500 − 0.287941I
b = −1.241080 − 0.395387I
5.25338 + 0.75552I 0
u = −0.224605 + 0.658535I
a = 1.037960 + 0.472207I
b = −0.341084 − 1.075920I
−0.38164 + 1.40636I −7.90709 − 4.60491I
u = −0.224605 + 0.658535I
a = 1.54635 − 0.36863I
b = −0.241044 − 0.594512I
−0.38164 + 1.40636I −7.90709 − 4.60491I
u = −0.224605 − 0.658535I
a = 1.037960 − 0.472207I
b = −0.341084 + 1.075920I
−0.38164 − 1.40636I −7.90709 + 4.60491I
u = −0.224605 − 0.658535I
a = 1.54635 + 0.36863I
b = −0.241044 + 0.594512I
−0.38164 − 1.40636I −7.90709 + 4.60491I
u = −0.563956 + 1.217970I
a = −0.407390 + 0.754967I
b = 0.727020 + 0.391576I
8.40264 + 4.63276I 0
u = −0.563956 + 1.217970I
a = −1.61386 + 0.35681I
b = 1.57671 + 0.25730I
8.40264 + 4.63276I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563956 − 1.217970I
a = −0.407390 − 0.754967I
b = 0.727020 − 0.391576I
8.40264 − 4.63276I 0
u = −0.563956 − 1.217970I
a = −1.61386 − 0.35681I
b = 1.57671 − 0.25730I
8.40264 − 4.63276I 0
u = −0.253681 + 1.320130I
a = 1.20869 − 1.20917I
b = −0.783841 − 0.186625I
14.9725 + 8.1096I 0
u = −0.253681 + 1.320130I
a = 1.76114 + 0.31613I
b = −1.73484 − 0.91494I
14.9725 + 8.1096I 0
u = −0.253681 − 1.320130I
a = 1.20869 + 1.20917I
b = −0.783841 + 0.186625I
14.9725 − 8.1096I 0
u = −0.253681 − 1.320130I
a = 1.76114 − 0.31613I
b = −1.73484 + 0.91494I
14.9725 − 8.1096I 0
u = 0.008742 + 0.639353I
a = −0.147556 − 1.227300I
b = 0.719465 − 0.763198I
5.23017 − 2.51958I 1.241083 − 0.357010I
u = 0.008742 + 0.639353I
a = 2.45573 + 1.48966I
b = −1.277630 − 0.348252I
5.23017 − 2.51958I 1.241083 − 0.357010I
u = 0.008742 − 0.639353I
a = −0.147556 + 1.227300I
b = 0.719465 + 0.763198I
5.23017 + 2.51958I 1.241083 + 0.357010I
u = 0.008742 − 0.639353I
a = 2.45573 − 1.48966I
b = −1.277630 + 0.348252I
5.23017 + 2.51958I 1.241083 + 0.357010I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531201 + 1.269820I
a = 1.337790 + 0.287032I
b = −1.21857 + 0.88759I
4.30856 − 9.00359I 0
u = 0.531201 + 1.269820I
a = −1.68147 − 0.29022I
b = 1.42823 − 0.77535I
4.30856 − 9.00359I 0
u = 0.531201 − 1.269820I
a = 1.337790 − 0.287032I
b = −1.21857 − 0.88759I
4.30856 + 9.00359I 0
u = 0.531201 − 1.269820I
a = −1.68147 + 0.29022I
b = 1.42823 + 0.77535I
4.30856 + 9.00359I 0
u = 0.324351 + 0.493941I
a = 0.515496 + 1.077260I
b = 0.647626 + 1.092120I
8.96981 + 6.76225I −1.16496 − 1.32686I
u = 0.324351 + 0.493941I
a = −2.84073 + 1.17981I
b = 0.69428 − 1.27815I
8.96981 + 6.76225I −1.16496 − 1.32686I
u = 0.324351 − 0.493941I
a = 0.515496 − 1.077260I
b = 0.647626 − 1.092120I
8.96981 − 6.76225I −1.16496 + 1.32686I
u = 0.324351 − 0.493941I
a = −2.84073 − 1.17981I
b = 0.69428 + 1.27815I
8.96981 − 6.76225I −1.16496 + 1.32686I
u = 0.72262 + 1.25115I
a = −1.029400 − 0.615681I
b = 1.240690 + 0.008012I
7.38957 − 3.44269I 0
u = 0.72262 + 1.25115I
a = 0.478696 + 0.566053I
b = −0.912969 + 0.174762I
7.38957 − 3.44269I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.72262 − 1.25115I
a = −1.029400 + 0.615681I
b = 1.240690 − 0.008012I
7.38957 + 3.44269I 0
u = 0.72262 − 1.25115I
a = 0.478696 − 0.566053I
b = −0.912969 − 0.174762I
7.38957 + 3.44269I 0
u = 0.155829 + 0.518115I
a = 1.000180 + 0.818212I
b = −0.664836 − 0.869546I
−0.29520 + 1.46947I −6.37279 − 1.95675I
u = 0.155829 + 0.518115I
a = 1.97184 − 0.54810I
b = −0.078854 − 0.165747I
−0.29520 + 1.46947I −6.37279 − 1.95675I
u = 0.155829 − 0.518115I
a = 1.000180 − 0.818212I
b = −0.664836 + 0.869546I
−0.29520 − 1.46947I −6.37279 + 1.95675I
u = 0.155829 − 0.518115I
a = 1.97184 + 0.54810I
b = −0.078854 + 0.165747I
−0.29520 − 1.46947I −6.37279 + 1.95675I
u = 0.57926 + 1.36321I
a = −1.312240 − 0.075466I
b = 1.23560 − 0.94753I
8.1120 − 12.6788I 0
u = 0.57926 + 1.36321I
a = 1.61270 + 0.32089I
b = −1.35017 + 0.69705I
8.1120 − 12.6788I 0
u = 0.57926 − 1.36321I
a = −1.312240 + 0.075466I
b = 1.23560 + 0.94753I
8.1120 + 12.6788I 0
u = 0.57926 − 1.36321I
a = 1.61270 − 0.32089I
b = −1.35017 − 0.69705I
8.1120 + 12.6788I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27071 + 1.54654I
a = −0.733979 + 0.068037I
b = 0.853269 − 0.629295I
9.84990 + 0.22502I 0
u = 0.27071 + 1.54654I
a = 1.201400 + 0.636983I
b = −0.900300 − 0.032549I
9.84990 + 0.22502I 0
u = 0.27071 − 1.54654I
a = −0.733979 − 0.068037I
b = 0.853269 + 0.629295I
9.84990 − 0.22502I 0
u = 0.27071 − 1.54654I
a = 1.201400 − 0.636983I
b = −0.900300 + 0.032549I
9.84990 − 0.22502I 0
u = −0.78839 + 1.49937I
a = 1.379970 − 0.308325I
b = −1.283850 − 0.199748I
10.60110 + 2.92501I 0
u = −0.78839 + 1.49937I
a = 0.437662 − 0.180997I
b = −0.686011 − 0.544678I
10.60110 + 2.92501I 0
u = −0.78839 − 1.49937I
a = 1.379970 + 0.308325I
b = −1.283850 + 0.199748I
10.60110 − 2.92501I 0
u = −0.78839 − 1.49937I
a = 0.437662 + 0.180997I
b = −0.686011 + 0.544678I
10.60110 − 2.92501I 0
22
III. I
u
3
= h39u
23
− 272u
22
+ · · · + 2b + 298, −227u
23
+ 1814u
22
+ · · · + 4a −
104, u
24
− 8u
23
+ · · · − 14u + 4i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
227
4
u
23
−
907
2
u
22
+ ··· +
1255
4
u + 26
−
39
2
u
23
+ 136u
22
+ ··· +
797
2
u − 149
a
8
=
−67u
23
+
1195
2
u
22
+ ··· − 2016u +
841
2
121
2
u
23
− 485u
22
+ ··· +
709
2
u + 26
a
11
=
149
4
u
23
−
635
2
u
22
+ ··· +
2849
4
u − 123
−
39
2
u
23
+ 136u
22
+ ··· +
797
2
u − 149
a
4
=
−70u
23
+
1047
2
u
22
+ ··· + 601u −
623
2
−
73
2
u
23
+ 332u
22
+ ··· −
2581
2
u + 280
a
2
=
u
u
3
+ u
a
12
=
233
4
u
23
−
959
2
u
22
+ ··· +
2737
4
u − 73
−
21
2
u
23
+ 67u
22
+ ··· +
741
2
u − 123
a
1
=
135
4
u
23
−
389
2
u
22
+ ··· −
7481
4
u + 583
153
2
u
23
− 604u
22
+ ··· +
367
2
u + 107
a
5
=
271
4
u
23
−
1141
2
u
22
+ ··· +
4527
4
u − 174
−
57
2
u
23
+ 193u
22
+ ··· +
1549
2
u − 271
a
9
=
−
487
4
u
23
+
1901
2
u
22
+ ··· −
171
4
u − 236
−
49
2
u
23
+ 231u
22
+ ··· −
2137
2
u + 245
(ii) Obstruction class = 1
(iii) Cusp Shapes =
339u
23
−2735u
22
+12886u
21
−42800u
20
+109894u
19
−227540u
18
+388966u
17
−554634u
16
+
658690u
15
− 638936u
14
+ 477445u
13
− 219740u
12
− 41389u
11
+ 214969u
10
− 260392u
9
+
199498u
8
− 96701u
7
+ 10689u
6
+ 30944u
5
− 34906u
4
+ 22284u
3
− 9152u
2
+ 2542u − 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
24
− u
23
+ ··· − 3u + 1
c
2
u
24
+ 8u
23
+ ··· + 14u + 4
c
3
, c
10
u
24
+ u
23
+ ··· − 2u + 1
c
4
, c
8
u
24
+ u
23
+ ··· + 3u + 1
c
6
u
24
− 8u
23
+ ··· − 14u + 4
c
7
, c
11
u
24
+ 3u
23
+ ··· + 5u + 1
c
9
u
24
− 11u
23
+ ··· − 20u + 4
c
12
u
24
+ 11u
23
+ ··· + 20u + 4
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
24
+ 21y
23
+ ··· + 15y + 1
c
2
, c
6
y
24
+ 12y
23
+ ··· + 132y + 16
c
3
, c
10
y
24
+ 3y
23
+ ··· + 70y
2
+ 1
c
7
, c
11
y
24
− 9y
23
+ ··· − y + 1
c
9
, c
12
y
24
+ 11y
23
+ ··· + 248y + 16
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671893 + 0.698108I
a = 0.630740 − 0.226012I
b = −0.017757 + 0.841412I
1.37035 − 2.33264I −4.26323 + 3.17988I
u = 0.671893 − 0.698108I
a = 0.630740 + 0.226012I
b = −0.017757 − 0.841412I
1.37035 + 2.33264I −4.26323 − 3.17988I
u = −0.213205 + 1.019810I
a = −1.46281 − 0.25645I
b = 0.860408 − 0.461305I
1.64116 + 3.68159I 9.96979 − 4.33803I
u = −0.213205 − 1.019810I
a = −1.46281 + 0.25645I
b = 0.860408 + 0.461305I
1.64116 − 3.68159I 9.96979 + 4.33803I
u = 0.183939 + 0.915684I
a = −2.13851 + 0.97533I
b = 0.38486 − 1.74790I
4.79771 − 0.83920I 7.64954 − 0.48429I
u = 0.183939 − 0.915684I
a = −2.13851 − 0.97533I
b = 0.38486 + 1.74790I
4.79771 + 0.83920I 7.64954 + 0.48429I
u = 1.076920 + 0.061933I
a = 0.0447211 + 0.0825541I
b = −0.921732 − 0.449679I
1.89157 + 4.09183I 2.63483 − 6.27018I
u = 1.076920 − 0.061933I
a = 0.0447211 − 0.0825541I
b = −0.921732 + 0.449679I
1.89157 − 4.09183I 2.63483 + 6.27018I
u = 0.219761 + 1.205810I
a = 1.74443 − 0.35533I
b = −0.87688 + 1.24065I
12.2333 − 8.5328I 5.43258 + 6.23459I
u = 0.219761 − 1.205810I
a = 1.74443 + 0.35533I
b = −0.87688 − 1.24065I
12.2333 + 8.5328I 5.43258 − 6.23459I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.033498 + 0.738278I
a = 1.72752 + 0.41856I
b = −0.812320 + 0.640206I
0.33135 − 2.06974I 2.21463 + 6.39372I
u = −0.033498 − 0.738278I
a = 1.72752 − 0.41856I
b = −0.812320 − 0.640206I
0.33135 + 2.06974I 2.21463 − 6.39372I
u = −0.030881 + 0.735264I
a = 1.81388 − 1.41254I
b = 0.000148 + 1.336150I
9.95503 + 7.68910I 4.31056 − 5.22133I
u = −0.030881 − 0.735264I
a = 1.81388 + 1.41254I
b = 0.000148 − 1.336150I
9.95503 − 7.68910I 4.31056 + 5.22133I
u = −0.715028 + 0.076885I
a = 0.496566 − 0.598033I
b = −0.192008 + 0.262985I
−0.97820 − 1.68051I −7.67857 + 3.11334I
u = −0.715028 − 0.076885I
a = 0.496566 + 0.598033I
b = −0.192008 − 0.262985I
−0.97820 + 1.68051I −7.67857 − 3.11334I
u = 1.207490 + 0.553328I
a = −0.260037 − 0.109262I
b = 0.587657 − 0.237837I
5.46235 − 5.70006I 7.21757 + 10.78890I
u = 1.207490 − 0.553328I
a = −0.260037 + 0.109262I
b = 0.587657 + 0.237837I
5.46235 + 5.70006I 7.21757 − 10.78890I
u = 0.54072 + 1.31322I
a = −1.51712 − 0.30994I
b = 1.36741 − 0.79297I
5.80764 − 9.75826I 0. + 7.29101I
u = 0.54072 − 1.31322I
a = −1.51712 + 0.30994I
b = 1.36741 + 0.79297I
5.80764 + 9.75826I 0. − 7.29101I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38454 + 1.39270I
a = −1.029150 − 0.440987I
b = 1.020860 − 0.294308I
6.85863 − 1.24969I 0
u = 0.38454 − 1.39270I
a = −1.029150 + 0.440987I
b = 1.020860 + 0.294308I
6.85863 + 1.24969I 0
u = 0.70735 + 1.32860I
a = 0.699775 + 0.433953I
b = −0.900639 + 0.136993I
8.20180 − 1.36390I 0
u = 0.70735 − 1.32860I
a = 0.699775 − 0.433953I
b = −0.900639 − 0.136993I
8.20180 + 1.36390I 0
28
IV.
I
u
4
= h−u
8
a−2u
8
+· · ·−a+12, −2u
8
a+4u
8
+· · ·−5a+4, u
9
+3u
8
+· · ·+ 4u+1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
a
1
7
u
8
a +
2
7
u
8
+ ··· +
1
7
a −
12
7
a
8
=
−
5
7
u
8
a +
11
7
u
8
+ ··· −
5
7
a +
25
7
3
7
u
8
a −
1
7
u
8
+ ··· +
3
7
a −
1
7
a
11
=
1
7
u
8
a +
2
7
u
8
+ ··· +
8
7
a −
12
7
1
7
u
8
a +
2
7
u
8
+ ··· +
1
7
a −
12
7
a
4
=
2
7
u
8
a +
4
7
u
8
+ ··· −
12
7
a +
39
7
−u
8
− 3u
7
− 7u
6
− 9u
5
− 10u
4
− 8u
3
− 6u
2
− 3u
a
2
=
u
u
3
+ u
a
12
=
u
7
+ u
6
+ 2u
5
− u
3
a − u
4
− au − 2u
2
+ a − 1
−
1
7
u
8
a −
9
7
u
8
+ ··· −
1
7
a −
16
7
a
1
=
u
4
a + u
3
a + 2u
2
a + a + u − 1
−
3
7
u
8
a +
1
7
u
8
+ ··· −
3
7
a −
6
7
a
5
=
−
1
7
u
8
a +
5
7
u
8
+ ··· −
15
7
a +
19
7
4
7
u
8
a +
1
7
u
8
+ ··· −
3
7
a +
8
7
a
9
=
u
7
a + 3u
6
a + 6u
5
a + 7u
4
a + 6u
3
a + u
4
+ 4u
2
a + 2au + a − u
−
1
7
u
8
a −
2
7
u
8
+ ··· −
1
7
a −
9
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
+ 2u
7
− 20u
5
− 26u
4
− 32u
3
− 16u
2
− 17u − 9
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
18
+ u
17
+ ··· − 22u + 7
c
2
(u
9
− 3u
8
+ 8u
7
− 11u
6
+ 15u
5
− 12u
4
+ 12u
3
− 6u
2
+ 4u − 1)
2
c
3
, c
10
u
18
+ u
17
+ ··· + 4u + 7
c
4
, c
8
u
18
− u
17
+ ··· + 22u + 7
c
6
(u
9
+ 3u
8
+ 8u
7
+ 11u
6
+ 15u
5
+ 12u
4
+ 12u
3
+ 6u
2
+ 4u + 1)
2
c
7
, c
11
u
18
+ u
17
+ ··· + u + 1
c
9
(u
9
− 2u
8
+ 5u
7
− 8u
6
+ 10u
5
− 12u
4
+ 10u
3
− 7u
2
+ 5u − 1)
2
c
12
(u
9
+ 2u
8
+ 5u
7
+ 8u
6
+ 10u
5
+ 12u
4
+ 10u
3
+ 7u
2
+ 5u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
18
+ 23y
17
+ ··· + 622y + 49
c
2
, c
6
(y
9
+ 7y
8
+ 28y
7
+ 71y
6
+ 125y
5
+ 142y
4
+ 98y
3
+ 36y
2
+ 4y −1)
2
c
3
, c
10
y
18
+ y
17
+ ··· + 82y + 49
c
7
, c
11
y
18
+ 11y
17
+ ··· + 7y + 1
c
9
, c
12
(y
9
+ 6y
8
+ 13y
7
+ 8y
6
− 10y
5
− 10y
4
+ 16y
3
+ 27y
2
+ 11y −1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170099 + 0.870195I
a = −2.28493 + 0.33363I
b = 0.218125 + 0.934153I
1.39270 + 0.93298I −8.29333 − 7.88039I
u = −0.170099 + 0.870195I
a = 1.73845 + 1.57062I
b = −0.75166 − 2.01417I
1.39270 + 0.93298I −8.29333 − 7.88039I
u = −0.170099 − 0.870195I
a = −2.28493 − 0.33363I
b = 0.218125 − 0.934153I
1.39270 − 0.93298I −8.29333 + 7.88039I
u = −0.170099 − 0.870195I
a = 1.73845 − 1.57062I
b = −0.75166 + 2.01417I
1.39270 − 0.93298I −8.29333 + 7.88039I
u = 0.298286 + 0.823118I
a = 0.989385 − 0.331156I
b = 0.327124 − 0.639862I
5.25230 − 3.55910I −0.46414 + 5.94305I
u = 0.298286 + 0.823118I
a = −1.75178 − 1.39429I
b = 1.19196 + 0.79400I
5.25230 − 3.55910I −0.46414 + 5.94305I
u = 0.298286 − 0.823118I
a = 0.989385 + 0.331156I
b = 0.327124 + 0.639862I
5.25230 + 3.55910I −0.46414 − 5.94305I
u = 0.298286 − 0.823118I
a = −1.75178 + 1.39429I
b = 1.19196 − 0.79400I
5.25230 + 3.55910I −0.46414 − 5.94305I
u = −0.89957 + 1.19167I
a = −1.256460 + 0.455280I
b = 1.400940 + 0.053360I
9.15358 + 4.87540I 13.3950 − 4.9499I
u = −0.89957 + 1.19167I
a = 0.199311 − 0.485010I
b = −0.736096 − 0.285391I
9.15358 + 4.87540I 13.3950 − 4.9499I
32
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89957 − 1.19167I
a = −1.256460 − 0.455280I
b = 1.400940 − 0.053360I
9.15358 − 4.87540I 13.3950 + 4.9499I
u = −0.89957 − 1.19167I
a = 0.199311 + 0.485010I
b = −0.736096 + 0.285391I
9.15358 − 4.87540I 13.3950 + 4.9499I
u = −0.56414 + 1.39451I
a = −0.424477 + 0.161312I
b = 0.568251 + 0.712301I
10.37290 + 2.46792I 3.97641 + 2.17917I
u = −0.56414 + 1.39451I
a = 1.59666 − 0.23541I
b = −1.299370 − 0.292344I
10.37290 + 2.46792I 3.97641 + 2.17917I
u = −0.56414 − 1.39451I
a = −0.424477 − 0.161312I
b = 0.568251 − 0.712301I
10.37290 − 2.46792I 3.97641 − 2.17917I
u = −0.56414 − 1.39451I
a = 1.59666 + 0.23541I
b = −1.299370 + 0.292344I
10.37290 − 2.46792I 3.97641 − 2.17917I
u = −0.328953
a = 1.69385 + 1.68878I
b = −0.419275 + 0.827856I
0.294884 −4.22790
u = −0.328953
a = 1.69385 − 1.68878I
b = −0.419275 − 0.827856I
0.294884 −4.22790
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
18
+ u
17
+ ··· − 22u + 7)(u
24
− u
23
+ ··· − 3u + 1)
· (u
46
− u
45
+ ··· + 4u + 1)(u
98
− 8u
97
+ ··· − 1622u + 113)
c
2
(u
9
− 3u
8
+ 8u
7
− 11u
6
+ 15u
5
− 12u
4
+ 12u
3
− 6u
2
+ 4u − 1)
2
· (u
24
+ 8u
23
+ ··· + 14u + 4)(u
46
+ 13u
45
+ ··· + 528u + 52)
· (u
49
− 5u
48
+ ··· − 24u + 5)
2
c
3
, c
10
(u
18
+ u
17
+ ··· + 4u + 7)(u
24
+ u
23
+ ··· − 2u + 1)
· (u
46
− u
45
+ ··· − u + 1)(u
98
− 2u
97
+ ··· − 1030836u + 176389)
c
4
, c
8
(u
18
− u
17
+ ··· + 22u + 7)(u
24
+ u
23
+ ··· + 3u + 1)
· (u
46
− u
45
+ ··· + 4u + 1)(u
98
− 8u
97
+ ··· − 1622u + 113)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 11u
6
+ 15u
5
+ 12u
4
+ 12u
3
+ 6u
2
+ 4u + 1)
2
· (u
24
− 8u
23
+ ··· − 14u + 4)(u
46
+ 13u
45
+ ··· + 528u + 52)
· (u
49
− 5u
48
+ ··· − 24u + 5)
2
c
7
, c
11
(u
18
+ u
17
+ ··· + u + 1)(u
24
+ 3u
23
+ ··· + 5u + 1)
· (u
46
+ 3u
45
+ ··· + 44u + 19)(u
98
+ 14u
97
+ ··· + 155699u + 22103)
c
9
(u
9
− 2u
8
+ 5u
7
− 8u
6
+ 10u
5
− 12u
4
+ 10u
3
− 7u
2
+ 5u − 1)
2
· (u
24
− 11u
23
+ ··· − 20u + 4)(u
46
− 16u
45
+ ··· − 4284u + 356)
· (u
49
+ 12u
48
+ ··· + 257u + 59)
2
c
12
(u
9
+ 2u
8
+ 5u
7
+ 8u
6
+ 10u
5
+ 12u
4
+ 10u
3
+ 7u
2
+ 5u + 1)
2
· (u
24
+ 11u
23
+ ··· + 20u + 4)(u
46
− 16u
45
+ ··· − 4284u + 356)
· (u
49
+ 12u
48
+ ··· + 257u + 59)
2
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
(y
18
+ 23y
17
+ ··· + 622y + 49)(y
24
+ 21y
23
+ ··· + 15y + 1)
· (y
46
+ 51y
45
+ ··· + 46y + 1)(y
98
+ 86y
97
+ ··· + 162250y + 12769)
c
2
, c
6
(y
9
+ 7y
8
+ 28y
7
+ 71y
6
+ 125y
5
+ 142y
4
+ 98y
3
+ 36y
2
+ 4y −1)
2
· (y
24
+ 12y
23
+ ··· + 132y + 16)(y
46
+ 25y
45
+ ··· + 38416y + 2704)
· (y
49
+ 33y
48
+ ··· − 624y −25)
2
c
3
, c
10
(y
18
+ y
17
+ ··· + 82y + 49)(y
24
+ 3y
23
+ ··· + 70y
2
+ 1)
· (y
46
− 31y
45
+ ··· − 37y + 1)
· (y
98
− 12y
97
+ ··· + 591541541430y + 31113079321)
c
7
, c
11
(y
18
+ 11y
17
+ ··· + 7y + 1)(y
24
− 9y
23
+ ··· − y + 1)
· (y
46
− 11y
45
+ ··· − 74y + 361)
· (y
98
− 14y
97
+ ··· − 3878773113y + 488542609)
c
9
, c
12
(y
9
+ 6y
8
+ 13y
7
+ 8y
6
− 10y
5
− 10y
4
+ 16y
3
+ 27y
2
+ 11y −1)
2
· (y
24
+ 11y
23
+ ··· + 248y + 16)(y
46
+ 28y
45
+ ··· + 6976y + 126736)
· (y
49
+ 40y
48
+ ··· + 20383y −3481)
2
35
