12a
0166
(K12a
0166
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 12 1 10 4 11 8 7 6
Solving Sequence
4,8 9,10
11
1,3
2 5 7 6 12
c
8
c
10
c
3
c
1
c
4
c
7
c
6
c
12
c
2
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h458802669672u
24
+ 367351897733u
23
+ ··· + 7058049605558d − 1244576019090,
147880761515u
24
− 335144114156u
23
+ ··· + 28232198422232c − 35621876846456,
1278289196883u
24
+ 1997820239306u
23
+ ··· + 14116099211116b − 10424467040404,
377943683179u
24
+ 896277965838u
23
+ ··· + 28232198422232a − 14859817453240,
u
25
+ 2u
24
+ ··· − 16u − 8i
I
u
2
= h2u
10
a − u
10
+ ··· − 6a − 7, 10u
10
a + 5u
10
+ ··· − 18a − 34, 2u
9
a + 3u
10
+ ··· + b + 2a,
3u
10
a + 8u
10
+ ··· + 2a
2
− 6, u
11
− 3u
10
+ 6u
9
− 7u
8
+ 7u
7
− 3u
6
− 2u
5
+ 8u
4
− 7u
3
+ 5u
2
− 2u + 2i
I
u
3
= h−u
7
− u
5
− 2u
3
+ d − u, −u
7
− 2u
5
− 2u
3
+ c − 2u, u
8
a + 25u
8
+ ··· − 28a + 13,
− u
8
− 2u
7
− 3u
6
− 3u
5
− 3u
4
+ u
2
a − 2u
3
+ a
2
+ 2au − 3u
2
+ a,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
4
= hu
8
c + 5u
8
+ ··· − 27c + 10, 2u
8
c − 2u
8
+ ··· + 2c − 4, −u
2
+ b, −u
2
+ a − 1,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
5
= h−u
7
− u
5
− 2u
3
+ d − u, −u
7
− 2u
5
− 2u
3
+ c − 2u, −u
2
+ b, −u
2
+ a − 1,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
v
1
= ha, d − 1, c − a − 1, b − 1, v + 1i
I
v
2
= ha, d, c − 1, b + 1, v −1i
I
v
3
= hc, d − 1, b, a − 1, v −1i
I
v
4
= hc, d − 1, av + c −v −1, bv + 1i
* 8 irreducible components of dim
C
= 0, with total 95 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h4.59 × 10
11
u
24
+ 3.67 × 10
11
u
23
+ · · · + 7.06 × 10
12
d − 1.24 ×
10
12
, 1.48 × 10
11
u
24
− 3.35 × 10
11
u
23
+ · · · + 2.82 × 10
13
c − 3.56 × 10
13
, 1.28 ×
10
12
u
24
+ 2.00 × 10
12
u
23
+ · · · + 1.41 × 10
13
b − 1.04 × 10
13
, 3.78 × 10
11
u
24
+
8.96 × 10
11
u
23
+ · · · + 2.82 × 10
13
a − 1.49 × 10
13
, u
25
+ 2u
24
+ · · · − 16u − 8i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
−0.00523802u
24
+ 0.0118710u
23
+ ··· + 0.471795u + 1.26175
−0.0650042u
24
− 0.0520472u
23
+ ··· + 0.578878u + 0.176334
a
11
=
0.0597662u
24
+ 0.0639182u
23
+ ··· − 0.107083u + 1.08541
−0.0650042u
24
− 0.0520472u
23
+ ··· + 0.578878u + 0.176334
a
1
=
−0.0133870u
24
− 0.0317467u
23
+ ··· + 1.11820u + 0.526343
−0.0905554u
24
− 0.141528u
23
+ ··· + 1.83403u + 0.738481
a
3
=
u
u
3
+ u
a
2
=
0.0220418u
24
− 0.0209206u
23
+ ··· + 1.13918u + 0.226210
0.0223470u
24
− 0.0180859u
23
+ ··· + 1.17794u − 0.0419041
a
5
=
−0.0776559u
24
− 0.117795u
23
+ ··· + 0.902489u + 0.251920
−0.0910429u
24
− 0.149542u
23
+ ··· + 2.02069u + 0.778262
a
7
=
0.0972828u
24
+ 0.103523u
23
+ ··· − 1.09766u + 0.464165
0.0375166u
24
+ 0.0396045u
23
+ ··· − 0.990575u − 0.621247
a
6
=
0.151545u
24
+ 0.183512u
23
+ ··· − 2.01089u − 0.346355
0.119577u
24
+ 0.131747u
23
+ ··· − 2.07836u − 1.21236
a
12
=
0.0923101u
24
+ 0.0940648u
23
+ ··· − 0.785506u + 0.357069
−0.00497271u
24
− 0.00945799u
23
+ ··· + 0.312151u − 0.107096
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
8058725701665
7058049605558
u
24
+
10736954342885
7058049605558
u
23
+ ··· −
38478403451674
3529024802779
u −
29622418287164
3529024802779
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
25
+ 12u
24
+ ··· + 3u + 1
c
2
, c
4
, c
7
c
10
u
25
− 2u
24
+ ··· − u + 1
c
3
, c
8
u
25
− 2u
24
+ ··· − 16u + 8
c
5
, c
6
, c
12
u
25
+ 2u
24
+ ··· + 8u + 4
c
11
u
25
− 6u
24
+ ··· + 64u + 64
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
25
+ 8y
24
+ ··· − 13y −1
c
2
, c
4
, c
7
c
10
y
25
− 12y
24
+ ··· + 3y −1
c
3
, c
8
y
25
+ 6y
24
+ ··· + 64y −64
c
5
, c
6
, c
12
y
25
− 22y
24
+ ··· + 88y −16
c
11
y
25
+ 14y
24
+ ··· + 43008y −4096
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041130 + 0.234144I
a = 0.008394 + 0.208390I
b = −0.269928 + 1.383510I
c = 1.348140 − 0.409095I
d = 0.853442 − 0.558038I
3.14377 + 4.46824I −1.00511 − 6.27335I
u = 1.041130 − 0.234144I
a = 0.008394 − 0.208390I
b = −0.269928 − 1.383510I
c = 1.348140 + 0.409095I
d = 0.853442 + 0.558038I
3.14377 − 4.46824I −1.00511 + 6.27335I
u = −0.804646 + 0.457350I
a = −0.895367 + 0.386742I
b = −1.161700 + 0.803797I
c = 0.875912 − 0.274270I
d = 0.214886 − 0.601608I
2.41327 − 0.90505I 1.24488 − 0.76686I
u = −0.804646 − 0.457350I
a = −0.895367 − 0.386742I
b = −1.161700 − 0.803797I
c = 0.875912 + 0.274270I
d = 0.214886 + 0.601608I
2.41327 + 0.90505I 1.24488 + 0.76686I
u = −0.336133 + 1.048560I
a = −0.156441 − 0.276251I
b = 0.845749 + 0.298371I
c = −0.694150 − 1.216860I
d = −0.927060 + 0.554841I
0.70247 + 6.59785I −2.96140 − 9.56947I
u = −0.336133 − 1.048560I
a = −0.156441 + 0.276251I
b = 0.845749 − 0.298371I
c = −0.694150 + 1.216860I
d = −0.927060 − 0.554841I
0.70247 − 6.59785I −2.96140 + 9.56947I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926049 + 0.758012I
a = −1.42251 − 0.81155I
b = −0.87316 − 1.69108I
c = 1.62524 − 0.37230I
d = 1.187970 − 0.465287I
−7.68831 + 5.75962I −10.13195 − 4.49272I
u = 0.926049 − 0.758012I
a = −1.42251 + 0.81155I
b = −0.87316 + 1.69108I
c = 1.62524 + 0.37230I
d = 1.187970 + 0.465287I
−7.68831 − 5.75962I −10.13195 + 4.49272I
u = −0.759240 + 0.251838I
a = −0.264762 − 0.457484I
b = −0.051945 + 0.352201I
c = 1.384510 + 0.243604I
d = 0.865432 + 0.337523I
−2.09943 − 2.64913I −8.26724 + 7.08829I
u = −0.759240 − 0.251838I
a = −0.264762 + 0.457484I
b = −0.051945 − 0.352201I
c = 1.384510 − 0.243604I
d = 0.865432 − 0.337523I
−2.09943 + 2.64913I −8.26724 − 7.08829I
u = −0.169266 + 0.764490I
a = −0.128013 + 0.686745I
b = −0.303623 + 0.446468I
c = 0.734127 + 0.404802I
d = −0.420684 − 0.407489I
1.62680 − 1.08260I 3.35440 + 3.89731I
u = −0.169266 − 0.764490I
a = −0.128013 − 0.686745I
b = −0.303623 − 0.446468I
c = 0.734127 − 0.404802I
d = −0.420684 + 0.407489I
1.62680 + 1.08260I 3.35440 − 3.89731I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096683 + 1.217070I
a = −0.596071 + 0.850107I
b = 0.883990 − 0.599145I
c = −0.133481 − 0.336989I
d = −0.646064 + 0.751814I
8.85704 + 0.98974I 4.51267 − 2.53049I
u = 0.096683 − 1.217070I
a = −0.596071 − 0.850107I
b = 0.883990 + 0.599145I
c = −0.133481 + 0.336989I
d = −0.646064 − 0.751814I
8.85704 − 0.98974I 4.51267 + 2.53049I
u = −0.661369 + 1.057320I
a = −0.57589 + 1.50124I
b = 1.36579 + 0.96216I
c = 0.362414 − 0.234138I
d = −0.212320 − 0.866068I
4.06909 + 6.32284I 1.86961 − 4.09954I
u = −0.661369 − 1.057320I
a = −0.57589 − 1.50124I
b = 1.36579 − 0.96216I
c = 0.362414 + 0.234138I
d = −0.212320 + 0.866068I
4.06909 − 6.32284I 1.86961 + 4.09954I
u = −1.024310 + 0.754591I
a = 1.59421 − 0.47481I
b = 1.76886 − 1.85122I
c = 1.62073 + 0.41845I
d = 1.188320 + 0.521494I
−3.22783 − 10.10170I −5.60475 + 6.88322I
u = −1.024310 − 0.754591I
a = 1.59421 + 0.47481I
b = 1.76886 + 1.85122I
c = 1.62073 − 0.41845I
d = 1.188320 − 0.521494I
−3.22783 + 10.10170I −5.60475 − 6.88322I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425565 + 1.220260I
a = 0.635489 − 0.691012I
b = −0.588986 + 0.949659I
c = −1.004750 + 0.853367I
d = −1.001440 − 0.660540I
6.70868 − 9.75196I 0.64851 + 8.69449I
u = 0.425565 − 1.220260I
a = 0.635489 + 0.691012I
b = −0.588986 − 0.949659I
c = −1.004750 − 0.853367I
d = −1.001440 + 0.660540I
6.70868 + 9.75196I 0.64851 − 8.69449I
u = 0.797713 + 1.033120I
a = −0.52447 − 1.76199I
b = 1.27330 − 1.73823I
c = −1.87693 + 1.11019I
d = −1.213130 − 0.525024I
−6.80818 − 12.11480I −8.50713 + 8.67244I
u = 0.797713 − 1.033120I
a = −0.52447 + 1.76199I
b = 1.27330 + 1.73823I
c = −1.87693 − 1.11019I
d = −1.213130 + 0.525024I
−6.80818 + 12.11480I −8.50713 − 8.67244I
u = −0.832592 + 1.087810I
a = 0.39378 − 1.99462I
b = −2.07832 − 1.63190I
c = −1.88297 − 0.97500I
d = −1.234910 + 0.554337I
−2.1296 + 16.8657I −4.74649 − 10.33694I
u = −0.832592 − 1.087810I
a = 0.39378 + 1.99462I
b = −2.07832 + 1.63190I
c = −1.88297 + 0.97500I
d = −1.234910 − 0.554337I
−2.1296 − 16.8657I −4.74649 + 10.33694I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600838
a = 0.863277
b = 0.379944
c = 1.28245
d = 0.691126
−1.26593 −6.81200
10
II. I
u
2
= h2u
10
a − u
10
+ · · · − 6a − 7, 10u
10
a + 5u
10
+ · · · − 18a − 34, 2u
9
a +
3u
10
+ · · · + b + 2a, 3u
10
a + 8u
10
+ · · · + 2a
2
− 6, u
11
− 3u
10
+ · · · − 2u + 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
−5u
10
a −
5
2
u
10
+ ··· + 9a + 17
−2u
10
a + u
10
+ ··· + 6a + 7
a
11
=
−3u
10
a −
7
2
u
10
+ ··· + 3a + 10
−2u
10
a + u
10
+ ··· + 6a + 7
a
1
=
a
−2u
9
a − 3u
10
+ ··· − 2a − 3u
a
3
=
u
u
3
+ u
a
2
=
3u
10
a + 3u
10
+ ··· − 3a − 10
2u
10
a − 7u
10
+ ··· − 10a − 6
a
5
=
−2u
9
a − 3u
10
+ ··· − 3a − 3u
−2u
9
a − 3u
10
+ ··· − 2a − 3u
a
7
=
−u
10
a +
3
2
u
10
+ ··· + 3a + 1
2u
10
a + 5u
10
+ ··· + 6u − 9
a
6
=
u
9
a +
3
2
u
10
+ ··· + 2a + 1
u
10
a + 3u
10
+ ··· + 3u − 3
a
12
=
−u
10
a −
3
2
u
10
+ ··· + 3a + 4
−3u
10
+ 6u
9
+ ··· − 3u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
10
− 8u
9
+ 10u
8
− 10u
7
+ 4u
6
− 4u
5
− 14u
4
+ 12u
3
− 6u
2
− 8u − 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
22
+ 11u
21
+ ··· + 40u + 16
c
2
, c
4
, c
7
c
10
u
22
− u
21
+ ··· − 4u + 4
c
3
, c
8
(u
11
+ 3u
10
+ 6u
9
+ 7u
8
+ 7u
7
+ 3u
6
− 2u
5
− 8u
4
− 7u
3
− 5u
2
− 2u − 2)
2
c
5
, c
6
, c
12
(u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 4u
6
− 5u
5
+ 3u
4
− 3u
3
− 5u
2
+ 3u − 1)
2
c
11
(u
11
− 3u
10
+ ··· − 16u + 4)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
22
− 3y
21
+ ··· − 544y + 256
c
2
, c
4
, c
7
c
10
y
22
− 11y
21
+ ··· − 40y + 16
c
3
, c
8
(y
11
+ 3y
10
+ ··· − 16y −4)
2
c
5
, c
6
, c
12
(y
11
− 11y
10
+ ··· − y −1)
2
c
11
(y
11
+ 7y
10
+ ··· + 24y −16)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992754
a = −0.539348 + 0.169351I
b = −0.94293 + 1.07661I
c = 1.202080 − 0.374899I
d = 0.660661 − 0.556253I
3.69004 0.666830
u = −0.992754
a = −0.539348 − 0.169351I
b = −0.94293 − 1.07661I
c = 1.202080 + 0.374899I
d = 0.660661 + 0.556253I
3.69004 0.666830
u = 0.762686 + 0.875309I
a = −0.98257 − 1.33960I
b = −0.38116 − 2.19608I
c = 1.68434 − 0.30273I
d = 1.252300 − 0.374583I
−7.89368 − 2.87937I −10.41286 + 3.23335I
u = 0.762686 + 0.875309I
a = −1.44491 − 1.55956I
b = 0.70519 − 1.74288I
c = −2.02916 + 1.48909I
d = −1.190170 − 0.436468I
−7.89368 − 2.87937I −10.41286 + 3.23335I
u = 0.762686 − 0.875309I
a = −0.98257 + 1.33960I
b = −0.38116 + 2.19608I
c = 1.68434 + 0.30273I
d = 1.252300 + 0.374583I
−7.89368 + 2.87937I −10.41286 − 3.23335I
u = 0.762686 − 0.875309I
a = −1.44491 + 1.55956I
b = 0.70519 + 1.74288I
c = −2.02916 − 1.48909I
d = −1.190170 + 0.436468I
−7.89368 + 2.87937I −10.41286 − 3.23335I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958422 + 0.661375I
a = −1.166710 − 0.533776I
b = −1.25478 − 0.98207I
c = 0.744407 + 0.405064I
d = 0.164345 + 0.807203I
−0.20533 + 5.20915I −2.55774 − 3.72118I
u = 0.958422 + 0.661375I
a = 1.28394 + 0.64916I
b = 1.39078 + 2.09707I
c = 1.57823 − 0.38401I
d = 1.132380 − 0.485520I
−0.20533 + 5.20915I −2.55774 − 3.72118I
u = 0.958422 − 0.661375I
a = −1.166710 + 0.533776I
b = −1.25478 + 0.98207I
c = 0.744407 − 0.405064I
d = 0.164345 − 0.807203I
−0.20533 − 5.20915I −2.55774 + 3.72118I
u = 0.958422 − 0.661375I
a = 1.28394 − 0.64916I
b = 1.39078 − 2.09707I
c = 1.57823 + 0.38401I
d = 1.132380 + 0.485520I
−0.20533 − 5.20915I −2.55774 + 3.72118I
u = −0.273627 + 1.210650I
a = 0.376337 + 1.232810I
b = −0.055892 − 0.873986I
c = −0.687715 − 0.784193I
d = −0.901383 + 0.672173I
8.10965 + 4.33574I 3.31243 − 3.68401I
u = −0.273627 + 1.210650I
a = −0.680000 − 0.179254I
b = 1.163320 + 0.588782I
c = 0.0243773 + 0.1172880I
d = −0.522674 − 0.802934I
8.10965 + 4.33574I 3.31243 − 3.68401I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273627 − 1.210650I
a = 0.376337 − 1.232810I
b = −0.055892 + 0.873986I
c = −0.687715 + 0.784193I
d = −0.901383 − 0.672173I
8.10965 − 4.33574I 3.31243 + 3.68401I
u = −0.273627 − 1.210650I
a = −0.680000 + 0.179254I
b = 1.163320 − 0.588782I
c = 0.0243773 − 0.1172880I
d = −0.522674 + 0.802934I
8.10965 − 4.33574I 3.31243 + 3.68401I
u = 0.764438 + 1.080520I
a = −0.29279 − 1.73056I
b = 1.42979 − 1.08893I
c = 0.371944 + 0.333066I
d = −0.163987 + 0.927905I
1.11929 − 11.51290I −1.55919 + 7.44023I
u = 0.764438 + 1.080520I
a = 0.80955 + 1.63996I
b = −1.82005 + 1.63929I
c = −1.76532 + 1.05251I
d = −1.196120 − 0.553243I
1.11929 − 11.51290I −1.55919 + 7.44023I
u = 0.764438 − 1.080520I
a = −0.29279 + 1.73056I
b = 1.42979 + 1.08893I
c = 0.371944 − 0.333066I
d = −0.163987 − 0.927905I
1.11929 + 11.51290I −1.55919 − 7.44023I
u = 0.764438 − 1.080520I
a = 0.80955 − 1.63996I
b = −1.82005 − 1.63929I
c = −1.76532 − 1.05251I
d = −1.196120 + 0.553243I
1.11929 + 11.51290I −1.55919 − 7.44023I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215541 + 0.601634I
a = 0.704776 + 0.667690I
b = 1.56963 + 1.15126I
c = 1.60686 + 0.07009I
d = 1.140500 + 0.089613I
−2.97495 + 0.92758I −6.11605 − 7.40073I
u = −0.215541 + 0.601634I
a = −0.06827 − 2.46100I
b = −0.303895 + 0.345281I
c = 1.26996 − 3.35470I
d = −0.875845 + 0.206022I
−2.97495 + 0.92758I −6.11605 − 7.40073I
u = −0.215541 − 0.601634I
a = 0.704776 − 0.667690I
b = 1.56963 − 1.15126I
c = 1.60686 − 0.07009I
d = 1.140500 − 0.089613I
−2.97495 − 0.92758I −6.11605 + 7.40073I
u = −0.215541 − 0.601634I
a = −0.06827 + 2.46100I
b = −0.303895 − 0.345281I
c = 1.26996 + 3.35470I
d = −0.875845 − 0.206022I
−2.97495 − 0.92758I −6.11605 + 7.40073I
17
III. I
u
3
= h−u
7
− u
5
− 2u
3
+ d − u, −u
7
− 2u
5
− 2u
3
+ c − 2u, u
8
a + 25u
8
+
· · · − 28a + 13, −u
8
− 2u
7
+ · · · + a
2
+ a, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
11
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
1
=
a
−0.0322581au
8
− 0.806452u
8
+ ··· + 0.903226a − 0.419355
a
3
=
u
u
3
+ u
a
2
=
0.225806au
8
− 0.354839u
8
+ ··· + 0.677419a − 0.0645161
−0.225806au
8
− 1.64516u
8
+ ··· + 0.322581a − 0.935484
a
5
=
−0.0322581au
8
− 0.806452u
8
+ ··· − 0.0967742a − 0.419355
−0.0322581au
8
− 0.806452u
8
+ ··· + 0.903226a − 0.419355
a
7
=
−u
3
−u
5
− u
3
− u
a
6
=
0.451613au
8
+ 1.29032u
8
+ ··· + 0.354839a + 0.870968
0.387097au
8
+ 0.677419u
8
+ ··· − 0.838710a + 0.0322581
a
12
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 13u
17
+ ··· + 12u + 1
c
2
, c
4
, c
5
c
6
, c
12
u
18
+ u
17
+ ··· − 2u − 1
c
3
, c
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
2
c
7
, c
10
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
c
9
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
2
c
11
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 17y
17
+ ··· − 156y + 1
c
2
, c
4
, c
5
c
6
, c
12
y
18
− 13y
17
+ ··· − 12y + 1
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
c
7
, c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
2
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = −0.085582 + 0.757267I
b = 0.418870 + 0.086291I
c = −0.045155 + 1.125270I
d = −0.772920 − 0.510351I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 + 0.966856I
a = −0.27999 − 2.96236I
b = 0.70313 + 1.42788I
c = −0.045155 + 1.125270I
d = −0.772920 − 0.510351I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = −0.085582 − 0.757267I
b = 0.418870 − 0.086291I
c = −0.045155 − 1.125270I
d = −0.772920 + 0.510351I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.140343 − 0.966856I
a = −0.27999 + 2.96236I
b = 0.70313 − 1.42788I
c = −0.045155 − 1.125270I
d = −0.772920 + 0.510351I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = −0.739935 − 0.923677I
b = −0.747999 − 1.130940I
c = 0.527060 + 0.163673I
d = −0.141484 + 0.739668I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = −1.14609 − 1.92647I
b = 1.17043 − 0.94478I
c = 0.527060 + 0.163673I
d = −0.141484 + 0.739668I
−0.61694 − 2.45442I −2.32792 + 2.91298I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628449 − 0.875112I
a = −0.739935 + 0.923677I
b = −0.747999 + 1.130940I
c = 0.527060 − 0.163673I
d = −0.141484 − 0.739668I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = −1.14609 + 1.92647I
b = 1.17043 + 0.94478I
c = 0.527060 − 0.163673I
d = −0.141484 − 0.739668I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = −0.978726 + 0.854864I
b = −0.42218 + 1.69219I
c = 1.61946 + 0.31131I
d = 1.173910 + 0.391555I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 + 0.733148I
a = 1.47462 − 1.15398I
b = 1.71904 − 2.73838I
c = 1.61946 + 0.31131I
d = 1.173910 + 0.391555I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = −0.978726 − 0.854864I
b = −0.42218 − 1.69219I
c = 1.61946 − 0.31131I
d = 1.173910 − 0.391555I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −0.796005 − 0.733148I
a = 1.47462 + 1.15398I
b = 1.71904 + 2.73838I
c = 1.61946 − 0.31131I
d = 1.173910 − 0.391555I
−4.37135 + 1.33617I −7.28409 − 0.70175I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = −0.78241 + 1.38542I
b = 1.05246 + 1.54480I
c = −1.78816 − 1.28587I
d = −1.172470 + 0.500383I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 + 0.986295I
a = 1.68173 − 1.92006I
b = −1.66387 − 1.99378I
c = −1.78816 − 1.28587I
d = −1.172470 + 0.500383I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = −0.78241 − 1.38542I
b = 1.05246 − 1.54480I
c = −1.78816 + 1.28587I
d = −1.172470 − 0.500383I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = −0.728966 − 0.986295I
a = 1.68173 + 1.92006I
b = −1.66387 + 1.99378I
c = −1.78816 + 1.28587I
d = −1.172470 − 0.500383I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 0.516084
b = 0.492057
c = 1.37360
d = 0.825933
−1.19845 −8.65230
u = 0.512358
a = −2.80331
b = −5.95180
c = 1.37360
d = 0.825933
−1.19845 −8.65230
23
IV. I
u
4
= hu
8
c + 5u
8
+ · · · − 27c + 10, 2u
8
c − 2u
8
+ · · · + 2c − 4, −u
2
+
b, −u
2
+ a − 1, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
c
−0.0344828cu
8
− 0.172414u
8
+ ··· + 0.931034c − 0.344828
a
11
=
0.0344828cu
8
+ 0.172414u
8
+ ··· + 0.0689655c + 0.344828
−0.0344828cu
8
− 0.172414u
8
+ ··· + 0.931034c − 0.344828
a
1
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
5
=
−u
4
− u
2
− 1
−u
4
a
7
=
−0.172414cu
8
+ 0.137931u
8
+ ··· − 0.344828c + 0.275862
−0.206897cu
8
− 0.0344828u
8
+ ··· − 0.413793c − 0.0689655
a
6
=
0.0344828cu
8
+ 0.172414u
8
+ ··· + 0.0689655c + 0.344828
0.0344828cu
8
+ 0.172414u
8
+ ··· − 0.931034c + 0.344828
a
12
=
−0.758621cu
8
+ 0.206897u
8
+ ··· + 1.48276c − 0.586207
−0.586207cu
8
+ 0.0689655u
8
+ ··· + 1.82759c − 0.862069
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
2
c
2
, c
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
c
3
, c
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
2
c
5
, c
6
, c
7
c
10
, c
12
u
18
+ u
17
+ ··· − 2u − 1
c
9
u
18
+ 13u
17
+ ··· + 12u + 1
c
11
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
2
c
2
, c
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
c
5
, c
6
, c
7
c
10
, c
12
y
18
− 13y
17
+ ··· − 12y + 1
c
9
y
18
− 17y
17
+ ··· − 156y + 1
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.084886 + 0.271383I
b = −0.915114 + 0.271383I
c = 0.312641 − 0.476170I
d = −0.535620 + 0.576021I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 + 0.966856I
a = 0.084886 + 0.271383I
b = −0.915114 + 0.271383I
c = 1.74136 − 0.05336I
d = 1.308540 − 0.065670I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = 0.084886 − 0.271383I
b = −0.915114 − 0.271383I
c = 0.312641 + 0.476170I
d = −0.535620 − 0.576021I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.140343 − 0.966856I
a = 0.084886 − 0.271383I
b = −0.915114 − 0.271383I
c = 1.74136 + 0.05336I
d = 1.308540 + 0.065670I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = 0.629127 + 1.099930I
b = −0.370873 + 1.099930I
c = 1.68962 − 0.24481I
d = 1.253840 − 0.303492I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = 0.629127 + 1.099930I
b = −0.370873 + 1.099930I
c = −1.66618 + 1.71382I
d = −1.112360 − 0.436175I
−0.61694 − 2.45442I −2.32792 + 2.91298I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628449 − 0.875112I
a = 0.629127 − 1.099930I
b = −0.370873 − 1.099930I
c = 1.68962 + 0.24481I
d = 1.253840 + 0.303492I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = 0.629127 − 1.099930I
b = −0.370873 − 1.099930I
c = −1.66618 − 1.71382I
d = −1.112360 + 0.436175I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = 1.09612 − 1.16718I
b = 0.096118 − 1.167180I
c = 0.669579 − 0.290859I
d = 0.035822 − 0.749326I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 + 0.733148I
a = 1.09612 − 1.16718I
b = 0.096118 − 1.167180I
c = −2.42920 − 1.72243I
d = −1.209730 + 0.357771I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = 1.09612 + 1.16718I
b = 0.096118 + 1.167180I
c = 0.669579 + 0.290859I
d = 0.035822 + 0.749326I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −0.796005 − 0.733148I
a = 1.09612 + 1.16718I
b = 0.096118 + 1.167180I
c = −2.42920 + 1.72243I
d = −1.209730 − 0.357771I
−4.37135 + 1.33617I −7.28409 − 0.70175I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = 0.55861 − 1.43795I
b = −0.44139 − 1.43795I
c = 0.444675 − 0.276867I
d = −0.138557 − 0.857281I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 + 0.986295I
a = 0.55861 − 1.43795I
b = −0.44139 − 1.43795I
c = 1.73366 + 0.29163I
d = 1.311030 + 0.356898I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = 0.55861 + 1.43795I
b = −0.44139 + 1.43795I
c = 0.444675 + 0.276867I
d = −0.138557 + 0.857281I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = −0.728966 − 0.986295I
a = 0.55861 + 1.43795I
b = −0.44139 + 1.43795I
c = 1.73366 − 0.29163I
d = 1.311030 − 0.356898I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 1.26251
b = 0.262511
c = 1.06355
d = 0.285873
−1.19845 −8.65230
u = 0.512358
a = 1.26251
b = 0.262511
c = −10.0559
d = −1.11181
−1.19845 −8.65230
29
V. I
u
5
= h−u
7
− u
5
− 2u
3
+ d − u, −u
7
− 2u
5
− 2u
3
+ c − 2u, −u
2
+
b, −u
2
+ a − 1, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
11
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
1
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
5
=
−u
4
− u
2
− 1
−u
4
a
7
=
−u
3
−u
5
− u
3
− u
a
6
=
−u
8
− u
6
− u
4
+ 1
−u
8
− u
7
− u
6
− 2u
5
− u
4
− 2u
3
− 2u + 1
a
12
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
3
, c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
8
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.084886 + 0.271383I
b = −0.915114 + 0.271383I
c = −0.045155 + 1.125270I
d = −0.772920 − 0.510351I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = 0.084886 − 0.271383I
b = −0.915114 − 0.271383I
c = −0.045155 − 1.125270I
d = −0.772920 + 0.510351I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = 0.629127 + 1.099930I
b = −0.370873 + 1.099930I
c = 0.527060 + 0.163673I
d = −0.141484 + 0.739668I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 − 0.875112I
a = 0.629127 − 1.099930I
b = −0.370873 − 1.099930I
c = 0.527060 − 0.163673I
d = −0.141484 − 0.739668I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = 1.09612 − 1.16718I
b = 0.096118 − 1.167180I
c = 1.61946 + 0.31131I
d = 1.173910 + 0.391555I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = 1.09612 + 1.16718I
b = 0.096118 + 1.167180I
c = 1.61946 − 0.31131I
d = 1.173910 − 0.391555I
−4.37135 + 1.33617I −7.28409 − 0.70175I
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = 0.55861 − 1.43795I
b = −0.44139 − 1.43795I
c = −1.78816 − 1.28587I
d = −1.172470 + 0.500383I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = 0.55861 + 1.43795I
b = −0.44139 + 1.43795I
c = −1.78816 + 1.28587I
d = −1.172470 − 0.500383I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 1.26251
b = 0.262511
c = 1.37360
d = 0.825933
−1.19845 −8.65230
34
VI. I
v
1
= ha, d − 1, c − a − 1, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
1
a
11
=
0
1
a
1
=
0
1
a
3
=
−1
0
a
2
=
−1
1
a
5
=
0
−1
a
7
=
0
−1
a
6
=
0
−1
a
12
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
9
u − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
u
c
4
, c
10
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
9
, c
10
y −1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
y
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 1.00000
d = 1.00000
−3.28987 −12.0000
38
VII. I
v
2
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
0
a
11
=
1
0
a
1
=
0
−1
a
3
=
1
0
a
2
=
1
−1
a
5
=
0
1
a
7
=
1
0
a
6
=
1
1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
7
, c
8
c
9
, c
10
, c
11
u
c
4
, c
5
, c
6
u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
12
y −1
c
3
, c
7
, c
8
c
9
, c
10
, c
11
y
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 1.00000
d = 0
0 0
42
VIII. I
v
3
= hc, d − 1, b, a − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
1
a
11
=
−1
1
a
1
=
1
0
a
3
=
1
0
a
2
=
1
0
a
5
=
1
0
a
7
=
1
−1
a
6
=
2
−1
a
12
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
11
u
c
5
, c
6
, c
7
c
9
u − 1
c
10
, c
12
u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
11
y
c
5
, c
6
, c
7
c
9
, c
10
, c
12
y −1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
46
IX. I
v
4
= hc, d − 1, av + c − v − 1, bv + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
1
a
11
=
−1
1
a
1
=
a
−a + 1
a
3
=
v
0
a
2
=
a + v
−a + 1
a
5
=
−a
a − 1
a
7
=
1
−1
a
6
=
a + 1
−a
a
12
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = a
2
+ v
2
− 2a − 7
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
47
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−1.64493 −6.78092 + 0.05196I
48
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
u(u − 1)
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
· (u
18
+ 13u
17
+ ··· + 12u + 1)(u
22
+ 11u
21
+ ··· + 40u + 16)
· (u
25
+ 12u
24
+ ··· + 3u + 1)
c
2
, c
7
u(u − 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
18
+ u
17
+ ··· − 2u − 1)(u
22
− u
21
+ ··· − 4u + 4)
· (u
25
− 2u
24
+ ··· − u + 1)
c
3
, c
8
u
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
5
· (u
11
+ 3u
10
+ 6u
9
+ 7u
8
+ 7u
7
+ 3u
6
− 2u
5
− 8u
4
− 7u
3
− 5u
2
− 2u − 2)
2
· (u
25
− 2u
24
+ ··· − 16u + 8)
c
4
, c
10
u(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
18
+ u
17
+ ··· − 2u − 1)(u
22
− u
21
+ ··· − 4u + 4)
· (u
25
− 2u
24
+ ··· − u + 1)
c
5
, c
6
, c
12
u(u − 1)(u + 1)(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 4u
6
− 5u
5
+ 3u
4
− 3u
3
− 5u
2
+ 3u − 1)
2
· ((u
18
+ u
17
+ ··· − 2u − 1)
2
)(u
25
+ 2u
24
+ ··· + 8u + 4)
c
11
u
3
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
5
· ((u
11
− 3u
10
+ ··· − 16u + 4)
2
)(u
25
− 6u
24
+ ··· + 64u + 64)
49
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
y(y − 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
3
· (y
18
− 17y
17
+ ··· − 156y + 1)(y
22
− 3y
21
+ ··· − 544y + 256)
· (y
25
+ 8y
24
+ ··· − 13y −1)
c
2
, c
4
, c
7
c
10
y(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
· (y
18
− 13y
17
+ ··· − 12y + 1)(y
22
− 11y
21
+ ··· − 40y + 16)
· (y
25
− 12y
24
+ ··· + 3y −1)
c
3
, c
8
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
5
· ((y
11
+ 3y
10
+ ··· − 16y −4)
2
)(y
25
+ 6y
24
+ ··· + 64y −64)
c
5
, c
6
, c
12
y(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· ((y
11
− 11y
10
+ ··· − y −1)
2
)(y
18
− 13y
17
+ ··· − 12y + 1)
2
· (y
25
− 22y
24
+ ··· + 88y −16)
c
11
y
3
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
5
· ((y
11
+ 7y
10
+ ··· + 24y −16)
2
)(y
25
+ 14y
24
+ ··· + 43008y −4096)
50
