11a
351
(K11a
351
)
A knot diagram
1
Linearized knot diagam
7 6 1 10 11 9 4 3 2 5 8
Solving Sequence
6,9 3,7
2 10 1 4 8 11 5
c
6
c
2
c
9
c
1
c
3
c
8
c
11
c
5
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
15
+ 60u
14
+ ··· + b + 130, 35u
15
+ 195u
14
+ ··· + 19a − 844, u
16
+ 11u
15
+ ··· + 85u + 19i
I
u
2
= h4u
11
+ 38u
10
+ ··· + b + 71, 3u
11
− 4u
10
+ ··· + 17a − 272, u
12
+ 10u
11
+ ··· + 102u + 17i
I
u
3
= h−779024089a
9
u − 1957109432a
8
u + ··· + 3952254721a + 13062915505,
2a
9
u + 3a
8
u + ··· − 24a
2
− 5, u
2
− u + 1i
I
u
4
= h10206521a
9
u
3
+ 21936282a
8
u
3
+ ··· − 55249693a − 29498003, a
9
u
3
− 7a
8
u
3
+ ··· + 50a + 317,
u
4
− u
3
+ 2u + 1i
I
u
5
= h9901203u
19
− 97655512u
18
+ ··· + 45127189b − 2967898,
− 6933305u
19
+ 80845633u
18
+ ··· + 45127189a − 67619382, u
20
− 9u
19
+ ··· − 3u
2
+ 1i
I
u
6
= h−a
4
− a
2
+ b + a, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u − 1i
I
u
7
= ha
4
+ a
2
+ b, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u − 1i
I
u
8
= hb + 1, a, u − 1i
I
v
1
= ha, b
5
− b
4
+ 2b
3
− b
2
+ b − 1, v −1i
* 9 irreducible components of dim
C
= 0, with total 124 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
= h5u
15
+ 60u
14
+ · · · + b + 130, 35u
15
+ 195u
14
+ · · · + 19a −
844, u
16
+ 11u
15
+ · · · + 85u + 19i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−1.84211u
15
− 10.2632u
14
+ ··· + 138.789u + 44.4211
−5u
15
− 60u
14
+ ··· − 496u − 130
a
7
=
1
u
2
a
2
=
−6.84211u
15
− 70.2632u
14
+ ··· − 357.211u − 85.5789
−5u
15
− 60u
14
+ ··· − 496u − 130
a
10
=
0.473684u
15
+ 4.21053u
14
+ ··· − 2.63158u − 2.73684
u
15
+ 10u
14
+ ··· + 44u + 9
a
1
=
3.15789u
15
+ 20.7368u
14
+ ··· − 156.211u − 50.5789
15u
15
+ 160u
14
+ ··· + 929u + 231
a
4
=
12.1579u
15
+ 118.737u
14
+ ··· + 457.789u + 104.421
21u
14
+ 180u
13
+ ··· + 548u + 155
a
8
=
−0.526316u
15
− 4.78947u
14
+ ··· − 12.6316u − 1.73684
−u
14
− 9u
13
+ ··· − 32u − 10
a
11
=
2.57895u
15
+ 37.3684u
14
+ ··· + 428.895u + 117.211
−10u
15
− 94u
14
+ ··· − 302u − 65
a
5
=
−1.63158u
15
− 23.9474u
14
+ ··· − 287.158u − 77.6842
7u
15
+ 71u
14
+ ··· + 343u + 83
a
5
=
−1.63158u
15
− 23.9474u
14
+ ··· − 287.158u − 77.6842
7u
15
+ 71u
14
+ ··· + 343u + 83
(ii) Obstruction class = −1
(iii) Cusp Shapes = 20u
15
+ 204u
14
+ 914u
13
+ 2234u
12
+ 2754u
11
−94u
10
−6024u
9
−
9048u
8
− 3284u
7
+ 8196u
6
+ 15768u
5
+ 14640u
4
+ 8642u
3
+ 3488u
2
+ 1062u + 264
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ u
15
+ ··· + 2u + 2
c
2
, c
7
, c
9
c
11
u
16
+ u
15
+ ··· + u + 1
c
3
, c
6
u
16
− 11u
15
+ ··· − 85u + 19
c
4
, c
5
, c
10
u
16
+ 6u
15
+ ··· + 8u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
16
+ 9y
15
+ ··· + 48y + 4
c
2
, c
7
, c
9
c
11
y
16
+ 7y
15
+ ··· + 21y + 1
c
3
, c
6
y
16
− 11y
15
+ ··· + 3795y + 361
c
4
, c
5
, c
10
y
16
− 12y
15
+ ··· + 160y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.380977 + 0.787211I
a = −1.029130 − 0.000584I
b = 0.393453 + 0.808033I
5.25768 − 4.77897I 4.31247 + 4.75614I
u = −0.380977 − 0.787211I
a = −1.029130 + 0.000584I
b = 0.393453 − 0.808033I
5.25768 + 4.77897I 4.31247 − 4.75614I
u = 1.279880 + 0.358721I
a = 0.170555 + 0.671225I
b = −0.052349 − 0.395411I
−2.56459 − 2.34570I −6.28872 + 0.46963I
u = 1.279880 − 0.358721I
a = 0.170555 − 0.671225I
b = −0.052349 + 0.395411I
−2.56459 + 2.34570I −6.28872 − 0.46963I
u = −1.22875 + 0.75885I
a = 0.284860 + 0.655547I
b = 0.403315 − 1.238380I
8.29097 + 6.33547I 5.46130 − 6.31546I
u = −1.22875 − 0.75885I
a = 0.284860 − 0.655547I
b = 0.403315 + 1.238380I
8.29097 − 6.33547I 5.46130 + 6.31546I
u = −1.16827 + 1.01352I
a = 0.104611 − 1.132590I
b = −1.20879 + 1.21269I
2.8802 + 18.5253I 0.82769 − 9.63606I
u = −1.16827 − 1.01352I
a = 0.104611 + 1.132590I
b = −1.20879 − 1.21269I
2.8802 − 18.5253I 0.82769 + 9.63606I
u = −1.54277 + 0.30640I
a = −0.064517 − 0.349095I
b = −0.120682 + 0.887722I
−0.76511 + 3.23091I 8.87467 − 5.88690I
u = −1.54277 − 0.30640I
a = −0.064517 + 0.349095I
b = −0.120682 − 0.887722I
−0.76511 − 3.23091I 8.87467 + 5.88690I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20852 + 1.02268I
a = −0.121691 + 1.002120I
b = 1.08577 − 1.07970I
−2.9800 + 13.9622I −2.59981 − 9.26713I
u = −1.20852 − 1.02268I
a = −0.121691 − 1.002120I
b = 1.08577 + 1.07970I
−2.9800 − 13.9622I −2.59981 + 9.26713I
u = 0.035423 + 0.412947I
a = 1.80300 + 0.46760I
b = −0.145251 − 0.677138I
0.27480 − 1.44128I 1.93375 + 5.30960I
u = 0.035423 − 0.412947I
a = 1.80300 − 0.46760I
b = −0.145251 + 0.677138I
0.27480 + 1.44128I 1.93375 − 5.30960I
u = −1.28602 + 0.99596I
a = 0.062844 − 0.836469I
b = −0.855461 + 1.000990I
−1.34679 + 8.40080I −0.52134 − 6.47139I
u = −1.28602 − 0.99596I
a = 0.062844 + 0.836469I
b = −0.855461 − 1.000990I
−1.34679 − 8.40080I −0.52134 + 6.47139I
6
II. I
u
2
= h4u
11
+ 38u
10
+ · · · + b + 71, 3u
11
− 4u
10
+ · · · + 17a − 272, u
12
+
10u
11
+ · · · + 102u + 17i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−0.176471u
11
+ 0.235294u
10
+ ··· + 70.2353u + 16
−4u
11
− 38u
10
+ ··· − 371u − 71
a
7
=
1
u
2
a
2
=
−4.17647u
11
− 37.7647u
10
+ ··· − 300.765u − 55
−4u
11
− 38u
10
+ ··· − 371u − 71
a
10
=
−1.47059u
11
− 12.7059u
10
+ ··· − 80.7059u − 13
−2u
11
− 18u
10
+ ··· − 136u − 25
a
1
=
−2.17647u
11
− 21.7647u
10
+ ··· − 266.765u − 52
u
11
+ 8u
10
+ ··· + 3u − 3
a
4
=
−8.17647u
11
− 71.7647u
10
+ ··· − 476.765u − 83
−7u
11
− 67u
10
+ ··· − 714u − 139
a
8
=
0.529412u
11
+ 4.29412u
10
+ ··· + 14.2941u + 3
u
10
+ 8u
9
+ ··· + 43u + 9
a
11
=
−1.76471u
11
− 19.6471u
10
+ ··· − 338.647u − 68
3u
11
+ 26u
10
+ ··· + 136u + 21
a
5
=
−0.0588235u
11
+ 2.41176u
10
+ ··· + 156.412u + 35
−4u
11
− 36u
10
+ ··· − 289u − 52
a
5
=
−0.0588235u
11
+ 2.41176u
10
+ ··· + 156.412u + 35
−4u
11
− 36u
10
+ ··· − 289u − 52
(ii) Obstruction class = −1
(iii) Cusp Shapes = −15u
11
− 131u
10
− 625u
9
− 1949u
8
− 4347u
7
− 7138u
6
−
8765u
5
− 8007u
4
− 5383u
3
− 2560u
2
− 816u − 127
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
6
− u
4
+ u
3
+ u
2
− 1)
2
c
2
, c
7
, c
9
c
11
u
12
+ u
10
− u
9
+ 8u
8
+ u
7
+ 8u
6
− 8u
5
+ 4u
4
+ u
3
+ 4u
2
− 3u + 1
c
3
, c
6
u
12
− 10u
11
+ ··· − 102u + 17
c
4
, c
5
, c
10
(u
6
+ 3u
5
+ 2u
4
+ u
2
− 2u − 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
6
− 2y
5
+ 3y
4
− 5y
3
+ 3y
2
− 2y + 1)
2
c
2
, c
7
, c
9
c
11
y
12
+ 2y
11
+ ··· − y + 1
c
3
, c
6
y
12
+ 6y
11
+ ··· + 918y + 289
c
4
, c
5
, c
10
(y
6
− 5y
5
+ 6y
4
+ 8y
3
− 15y
2
− 12y + 16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014560 + 0.523445I
a = −0.208887 − 0.713790I
b = −1.14261 + 1.15043I
−1.71358 + 4.97819I 0.7768 − 21.8821I
u = −1.014560 − 0.523445I
a = −0.208887 + 0.713790I
b = −1.14261 − 1.15043I
−1.71358 − 4.97819I 0.7768 + 21.8821I
u = −0.681059 + 0.947774I
a = −0.626037 − 0.871204I
b = −0.399338 + 1.186680I
10.0009 7.28456 + 0.I
u = −0.681059 − 0.947774I
a = −0.626037 + 0.871204I
b = −0.399338 − 1.186680I
10.0009 7.28456 + 0.I
u = −1.011620 + 0.702683I
a = 0.146588 + 0.944898I
b = 1.19430 − 1.17568I
3.78738 + 10.11610I 0.74000 − 10.55076I
u = −1.011620 − 0.702683I
a = 0.146588 − 0.944898I
b = 1.19430 + 1.17568I
3.78738 − 10.11610I 0.74000 + 10.55076I
u = −0.216157 + 0.620958I
a = 0.399338 + 1.147190I
b = 0.626037 − 0.495944I
2.30081 4.68187 + 0.I
u = −0.216157 − 0.620958I
a = 0.399338 − 1.147190I
b = 0.626037 + 0.495944I
2.30081 4.68187 + 0.I
u = −1.02353 + 1.42273I
a = 0.665667 + 0.092024I
b = −0.608739 − 0.560847I
3.78738 − 10.11610I 0.74000 + 10.55076I
u = −1.02353 − 1.42273I
a = 0.665667 − 0.092024I
b = −0.608739 + 0.560847I
3.78738 + 10.11610I 0.74000 − 10.55076I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.05308 + 1.90895I
a = −0.376670 − 0.098951I
b = 0.330356 + 0.297557I
−1.71358 − 4.97819I 0.7768 + 21.8821I
u = −1.05308 − 1.90895I
a = −0.376670 + 0.098951I
b = 0.330356 − 0.297557I
−1.71358 + 4.97819I 0.7768 − 21.8821I
11
III. I
u
3
= h−7.79 × 10
8
a
9
u − 1.96 × 10
9
a
8
u + · · · + 3.95 × 10
9
a + 1.31 ×
10
10
, 2a
9
u + 3a
8
u + · · · − 24a
2
− 5, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
a
0.0624042a
9
u + 0.156775a
8
u + ··· − 0.316598a − 1.04641
a
7
=
1
u − 1
a
2
=
0.0624042a
9
u + 0.156775a
8
u + ··· + 0.683402a − 1.04641
0.0624042a
9
u + 0.156775a
8
u + ··· − 0.316598a − 1.04641
a
10
=
0.125388a
9
u − 0.0120961a
8
u + ··· − 1.79526a − 0.515904
0.234099a
9
u − 0.232380a
8
u + ··· − 1.93225a − 0.405863
a
1
=
−0.0155084a
9
u − 0.125977a
8
u + ··· − 0.624139a + 1.47218
0.0310168a
9
u + 0.251955a
8
u + ··· + 1.24828a − 2.94436
a
4
=
0.0624042a
9
u + 0.156775a
8
u + ··· + 1.68340a − 1.04641
−0.0624042a
9
u − 0.156775a
8
u + ··· − 0.683402a + 1.04641
a
8
=
−a
2
u
−0.108711a
9
u + 0.220284a
8
u + ··· + 0.136985a − 0.110041
a
11
=
0.0627102a
9
u − 0.0703413a
8
u + ··· + 0.570348a + 1.12072
−0.182654a
9
u + 0.0102801a
8
u + ··· − 4.10199a − 0.770574
a
5
=
0.197356a
9
u − 0.278756a
8
u + ··· + 2.01543a + 0.720538
0.0883103a
9
u − 0.662405a
8
u + ··· − 3.40104a + 1.50629
a
5
=
0.197356a
9
u − 0.278756a
8
u + ··· + 2.01543a + 0.720538
0.0883103a
9
u − 0.662405a
8
u + ··· − 3.40104a + 1.50629
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
20810162524
12483517597
a
9
u +
12117017480
12483517597
a
8
u + ··· −
108344247808
12483517597
a +
6755523522
12483517597
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
20
+ 3u
19
+ ··· − 12u + 61
c
2
, c
7
, c
9
c
11
u
20
+ u
19
+ ··· − 6u + 1
c
3
, c
6
(u
2
+ u + 1)
10
c
4
, c
5
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
20
− 13y
19
+ ··· + 17912y + 3721
c
2
, c
7
, c
9
c
11
y
20
− y
19
+ ··· + 8y + 1
c
3
, c
6
(y
2
+ y + 1)
10
c
4
, c
5
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.448982 − 0.894591I
b = 1.33834 + 0.88084I
0.32910 − 5.59035I 2.51511 + 11.35885I
u = 0.500000 + 0.866025I
a = −0.301250 − 0.932572I
b = 0.50256 + 1.40555I
5.87256 + 0.34107I 6.74431 + 3.42962I
u = 0.500000 + 0.866025I
a = 0.972249 − 0.372860I
b = 0.175892 + 0.206047I
0.32910 − 2.52919I 2.51511 + 2.49755I
u = 0.500000 + 0.866025I
a = 0.452147 + 0.960216I
b = −0.718535 − 0.910912I
0.32910 − 2.52919I 2.51511 + 2.49755I
u = 0.500000 + 0.866025I
a = 0.550143 + 0.975912I
b = −1.57593 − 1.21167I
5.87256 − 8.46060I 6.74431 + 10.42679I
u = 0.500000 + 0.866025I
a = 0.232340 + 0.431805I
b = −1.256950 − 0.014690I
2.40108 − 4.05977I 3.48114 + 6.92820I
u = 0.500000 + 0.866025I
a = −0.97541 + 1.48195I
b = −0.456587 − 0.763331I
0.32910 − 5.59035I 2.51511 + 11.35885I
u = 0.500000 + 0.866025I
a = −0.23234 − 1.75999I
b = 0.873537 + 0.678780I
2.40108 − 4.05977I 3.48114 + 6.92820I
u = 0.500000 + 0.866025I
a = −1.77747 + 0.14328I
b = 0.308955 − 0.410827I
5.87256 + 0.34107I 6.74431 + 3.42962I
u = 0.500000 + 0.866025I
a = 1.52858 − 1.76520I
b = 0.308723 + 1.006240I
5.87256 − 8.46060I 6.74431 + 10.42679I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −0.448982 + 0.894591I
b = 1.33834 − 0.88084I
0.32910 + 5.59035I 2.51511 − 11.35885I
u = 0.500000 − 0.866025I
a = −0.301250 + 0.932572I
b = 0.50256 − 1.40555I
5.87256 − 0.34107I 6.74431 − 3.42962I
u = 0.500000 − 0.866025I
a = 0.972249 + 0.372860I
b = 0.175892 − 0.206047I
0.32910 + 2.52919I 2.51511 − 2.49755I
u = 0.500000 − 0.866025I
a = 0.452147 − 0.960216I
b = −0.718535 + 0.910912I
0.32910 + 2.52919I 2.51511 − 2.49755I
u = 0.500000 − 0.866025I
a = 0.550143 − 0.975912I
b = −1.57593 + 1.21167I
5.87256 + 8.46060I 6.74431 − 10.42679I
u = 0.500000 − 0.866025I
a = 0.232340 − 0.431805I
b = −1.256950 + 0.014690I
2.40108 + 4.05977I 3.48114 − 6.92820I
u = 0.500000 − 0.866025I
a = −0.97541 − 1.48195I
b = −0.456587 + 0.763331I
0.32910 + 5.59035I 2.51511 − 11.35885I
u = 0.500000 − 0.866025I
a = −0.23234 + 1.75999I
b = 0.873537 − 0.678780I
2.40108 + 4.05977I 3.48114 − 6.92820I
u = 0.500000 − 0.866025I
a = −1.77747 − 0.14328I
b = 0.308955 + 0.410827I
5.87256 − 0.34107I 6.74431 − 3.42962I
u = 0.500000 − 0.866025I
a = 1.52858 + 1.76520I
b = 0.308723 − 1.006240I
5.87256 + 8.46060I 6.74431 − 10.42679I
16
IV. I
u
4
= h1.02 × 10
7
a
9
u
3
+ 2.19 × 10
7
a
8
u
3
+ · · · − 5.52 × 10
7
a − 2.95 ×
10
7
, a
9
u
3
− 7a
8
u
3
+ · · · + 50a + 317, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
a
−0.771383a
9
u
3
− 1.65789a
8
u
3
+ ··· + 4.17563a + 2.22938
a
7
=
1
u
2
a
2
=
−0.771383a
9
u
3
− 1.65789a
8
u
3
+ ··· + 5.17563a + 2.22938
−0.771383a
9
u
3
− 1.65789a
8
u
3
+ ··· + 4.17563a + 2.22938
a
10
=
−2.38899a
9
u
3
− 1.48429a
8
u
3
+ ··· + 0.191963a + 0.432924
−3.26466a
9
u
3
− 1.33077a
8
u
3
+ ··· + 0.127827a − 1.90249
a
1
=
−3.45130a
9
u
3
− 1.73595a
8
u
3
+ ··· + 3.15566a − 1.38448
5.95147a
9
u
3
+ 8.73616a
8
u
3
+ ··· + 4.17563a + 1.71700
a
4
=
−1.85369a
9
u
3
− 0.341548a
8
u
3
+ ··· − 3.58272a + 4.48596
3.94220a
9
u
3
+ 3.86768a
8
u
3
+ ··· − 3.42705a + 5.69058
a
8
=
−a
2
u
0.875666a
9
u
3
− 0.153515a
8
u
3
+ ··· + 0.0641357a + 2.33541
a
11
=
−5.23127a
9
u
3
− 4.21557a
8
u
3
+ ··· + 1.83391a − 0.272488
2.39529a
9
u
3
+ 2.70451a
8
u
3
+ ··· − 0.144882a + 1.16474
a
5
=
−7.86359a
9
u
3
− 7.45546a
8
u
3
+ ··· − 2.31526a + 3.05851
−1.07236a
9
u
3
− 0.0986639a
8
u
3
+ ··· − 0.769606a + 0.360690
a
5
=
−7.86359a
9
u
3
− 7.45546a
8
u
3
+ ··· − 2.31526a + 3.05851
−1.07236a
9
u
3
− 0.0986639a
8
u
3
+ ··· − 0.769606a + 0.360690
(ii) Obstruction class = −1
(iii) Cusp Shapes =
99852548
4410487
a
9
u
3
+
71190288
4410487
a
8
u
3
+ ··· −
4811112
4410487
a −
25276838
4410487
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
20
− u
19
+ ··· − 40u + 7)
2
c
2
, c
7
, c
9
c
11
u
40
− u
39
+ ··· − 24u + 1
c
3
, c
6
(u
4
+ u
3
− 2u + 1)
10
c
4
, c
5
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
8
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
20
+ 15y
19
+ ··· + 136y + 49)
2
c
2
, c
7
, c
9
c
11
y
40
− 19y
39
+ ··· − 140y + 1
c
3
, c
6
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
c
4
, c
5
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
8
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = −0.719862 + 1.116280I
b = −1.058220 − 0.214730I
−2.96077 + 2.52919I −9.48489 − 2.49755I
u = −0.621964 + 0.187730I
a = 0.590718 + 1.260270I
b = −1.91701 − 1.41092I
2.58269 + 8.46060I −5.25569 − 10.42679I
u = −0.621964 + 0.187730I
a = −0.21396 − 1.42839I
b = 1.27174 + 1.23977I
−2.96077 + 5.59035I −9.4849 − 11.3589I
u = −0.621964 + 0.187730I
a = 0.277604 + 0.458266I
b = 1.68999 − 0.50252I
2.58269 − 0.34107I −5.25569 − 3.42962I
u = −0.621964 + 0.187730I
a = 1.49834 + 0.40807I
b = 1.215460 − 0.396898I
2.58269 − 0.34107I −5.25569 − 3.42962I
u = −0.621964 + 0.187730I
a = −0.52719 − 1.68162I
b = −0.936656 + 0.894531I
−2.96077 + 2.52919I −9.48489 − 2.49755I
u = −0.621964 + 0.187730I
a = 0.13210 + 1.90315I
b = 0.01117 − 1.83111I
−0.88879 + 4.05977I −8.51886 − 6.92820I
u = −0.621964 + 0.187730I
a = 0.70008 + 2.70840I
b = 0.622489 − 0.315887I
−2.96077 + 5.59035I −9.4849 − 11.3589I
u = −0.621964 + 0.187730I
a = 0.72825 − 2.71120I
b = 0.1026320 + 0.0179107I
−0.88879 + 4.05977I −8.51886 − 6.92820I
u = −0.621964 + 0.187730I
a = −1.34411 − 3.08700I
b = −0.853187 + 0.155291I
2.58269 + 8.46060I −5.25569 − 10.42679I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 − 0.187730I
a = −0.719862 − 1.116280I
b = −1.058220 + 0.214730I
−2.96077 − 2.52919I −9.48489 + 2.49755I
u = −0.621964 − 0.187730I
a = 0.590718 − 1.260270I
b = −1.91701 + 1.41092I
2.58269 − 8.46060I −5.25569 + 10.42679I
u = −0.621964 − 0.187730I
a = −0.21396 + 1.42839I
b = 1.27174 − 1.23977I
−2.96077 − 5.59035I −9.4849 + 11.3589I
u = −0.621964 − 0.187730I
a = 0.277604 − 0.458266I
b = 1.68999 + 0.50252I
2.58269 + 0.34107I −5.25569 + 3.42962I
u = −0.621964 − 0.187730I
a = 1.49834 − 0.40807I
b = 1.215460 + 0.396898I
2.58269 + 0.34107I −5.25569 + 3.42962I
u = −0.621964 − 0.187730I
a = −0.52719 + 1.68162I
b = −0.936656 − 0.894531I
−2.96077 − 2.52919I −9.48489 + 2.49755I
u = −0.621964 − 0.187730I
a = 0.13210 − 1.90315I
b = 0.01117 + 1.83111I
−0.88879 − 4.05977I −8.51886 + 6.92820I
u = −0.621964 − 0.187730I
a = 0.70008 − 2.70840I
b = 0.622489 + 0.315887I
−2.96077 − 5.59035I −9.4849 + 11.3589I
u = −0.621964 − 0.187730I
a = 0.72825 + 2.71120I
b = 0.1026320 − 0.0179107I
−0.88879 − 4.05977I −8.51886 + 6.92820I
u = −0.621964 − 0.187730I
a = −1.34411 + 3.08700I
b = −0.853187 − 0.155291I
2.58269 − 8.46060I −5.25569 + 10.42679I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 + 1.05376I
a = 0.243796 + 1.155300I
b = −1.015060 − 0.944107I
−2.96077 − 5.59035I −9.4849 + 11.3589I
u = 1.12196 + 1.05376I
a = −0.784279 − 0.888215I
b = 1.50413 + 0.48312I
−0.88879 − 4.05977I −8.51886 + 6.92820I
u = 1.12196 + 1.05376I
a = 0.307340 + 0.744258I
b = −1.234520 − 0.304051I
−0.88879 − 4.05977I −8.51886 + 6.92820I
u = 1.12196 + 1.05376I
a = −0.116394 − 0.734680I
b = 0.654122 + 0.391067I
−2.96077 − 2.52919I −9.48489 + 2.49755I
u = 1.12196 + 1.05376I
a = −0.489819 + 0.435548I
b = 0.382798 − 0.494752I
2.58269 + 0.34107I −5.25569 + 3.42962I
u = 1.12196 + 1.05376I
a = −0.187266 − 0.580148I
b = 1.087870 + 0.575772I
−2.96077 − 5.59035I −9.4849 + 11.3589I
u = 1.12196 + 1.05376I
a = 0.013279 + 0.587324I
b = −1.046510 − 0.808228I
2.58269 − 8.46060I −5.25569 + 10.42679I
u = 1.12196 + 1.05376I
a = −0.07140 − 1.41932I
b = 0.92646 + 1.33661I
2.58269 − 8.46060I −5.25569 + 10.42679I
u = 1.12196 + 1.05376I
a = 0.481693 + 0.286853I
b = −0.965395 − 0.181113I
−2.96077 − 2.52919I −9.48489 + 2.49755I
u = 1.12196 + 1.05376I
a = −0.018914 + 0.225356I
b = 0.057687 + 0.179198I
2.58269 + 0.34107I −5.25569 + 3.42962I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 − 1.05376I
a = 0.243796 − 1.155300I
b = −1.015060 + 0.944107I
−2.96077 + 5.59035I −9.4849 − 11.3589I
u = 1.12196 − 1.05376I
a = −0.784279 + 0.888215I
b = 1.50413 − 0.48312I
−0.88879 + 4.05977I −8.51886 − 6.92820I
u = 1.12196 − 1.05376I
a = 0.307340 − 0.744258I
b = −1.234520 + 0.304051I
−0.88879 + 4.05977I −8.51886 − 6.92820I
u = 1.12196 − 1.05376I
a = −0.116394 + 0.734680I
b = 0.654122 − 0.391067I
−2.96077 + 2.52919I −9.48489 − 2.49755I
u = 1.12196 − 1.05376I
a = −0.489819 − 0.435548I
b = 0.382798 + 0.494752I
2.58269 − 0.34107I −5.25569 − 3.42962I
u = 1.12196 − 1.05376I
a = −0.187266 + 0.580148I
b = 1.087870 − 0.575772I
−2.96077 + 5.59035I −9.4849 − 11.3589I
u = 1.12196 − 1.05376I
a = 0.013279 − 0.587324I
b = −1.046510 + 0.808228I
2.58269 + 8.46060I −5.25569 − 10.42679I
u = 1.12196 − 1.05376I
a = −0.07140 + 1.41932I
b = 0.92646 − 1.33661I
2.58269 + 8.46060I −5.25569 − 10.42679I
u = 1.12196 − 1.05376I
a = 0.481693 − 0.286853I
b = −0.965395 + 0.181113I
−2.96077 + 2.52919I −9.48489 − 2.49755I
u = 1.12196 − 1.05376I
a = −0.018914 − 0.225356I
b = 0.057687 − 0.179198I
2.58269 − 0.34107I −5.25569 − 3.42962I
23
V.
I
u
5
= h9.90 × 10
6
u
19
− 9.77 × 10
7
u
18
+ · · · + 4.51 × 10
7
b − 2.97 × 10
6
, −6.93 ×
10
6
u
19
+8.08×10
7
u
18
+· · ·+4.51×10
7
a−6.76×10
7
, u
20
−9u
19
+· · ·−3u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
0.153639u
19
− 1.79151u
18
+ ··· + 2.24516u + 1.49842
−0.219407u
19
+ 2.16401u
18
+ ··· + 1.56419u + 0.0657674
a
7
=
1
u
2
a
2
=
−0.0657674u
19
+ 0.372500u
18
+ ··· + 3.80934u + 1.56419
−0.219407u
19
+ 2.16401u
18
+ ··· + 1.56419u + 0.0657674
a
10
=
−0.862994u
19
+ 7.09186u
18
+ ··· + 1.03984u − 0.290444
−0.675088u
19
+ 5.31678u
18
+ ··· + 0.709556u + 0.862994
a
1
=
0.342986u
19
− 3.06182u
18
+ ··· + 2.31093u + 1.71782
0.107949u
19
− 0.626322u
18
+ ··· + 1.15543u − 0.178694
a
4
=
−3.20937u
19
+ 27.2035u
18
+ ··· + 5.85762u + 1.67985
−1.35831u
19
+ 11.4178u
18
+ ··· + 3.23433u + 2.85186
a
8
=
−0.271837u
19
+ 2.92517u
18
+ ··· + 2.48372u − 1.34134
0.0839308u
19
− 1.15008u
18
+ ··· − 0.153439u + 0.187906
a
11
=
0.119355u
19
− 1.14339u
18
+ ··· − 3.89881u + 3.26977
0.0404788u
19
+ 0.0678868u
18
+ ··· + 1.91295u + 0.197670
a
5
=
−1.66613u
19
+ 15.1247u
18
+ ··· + 8.18078u − 2.09281
0.0199111u
19
− 0.114853u
18
+ ··· − 0.736002u + 1.34910
a
5
=
−1.66613u
19
+ 15.1247u
18
+ ··· + 8.18078u − 2.09281
0.0199111u
19
− 0.114853u
18
+ ··· − 0.736002u + 1.34910
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
566889690
45127189
u
19
+
4768864478
45127189
u
18
+ ··· +
1705220671
45127189
u +
1179786730
45127189
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
20
+ 5u
18
+ ··· − 14u
2
+ 5
c
2
, c
9
u
20
+ 3u
19
+ ··· + 5u + 1
c
3
u
20
+ 9u
19
+ ··· − 3u
2
+ 1
c
4
, c
5
, c
10
u
20
− 11u
18
+ ··· − 26u
2
+ 5
c
6
u
20
− 9u
19
+ ··· − 3u
2
+ 1
c
7
, c
11
u
20
− 3u
19
+ ··· − 5u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
10
+ 5y
9
+ 12y
8
+ 22y
7
+ 39y
6
+ 39y
5
+ 16y
4
− 3y
3
− y
2
− 14y + 5)
2
c
2
, c
7
, c
9
c
11
y
20
− 9y
19
+ ··· + y + 1
c
3
, c
6
y
20
− 3y
19
+ ··· − 6y + 1
c
4
, c
5
, c
10
(y
10
− 11y
9
+ ··· − 26y + 5)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821430 + 0.174947I
a = −0.09635 − 1.43572I
b = 0.118953 + 0.649652I
−2.73306 + 4.26272I −8.25212 − 5.64920I
u = −0.821430 − 0.174947I
a = −0.09635 + 1.43572I
b = 0.118953 − 0.649652I
−2.73306 − 4.26272I −8.25212 + 5.64920I
u = 0.973474 + 0.672727I
a = −0.120474 + 0.775350I
b = −1.037340 − 0.908780I
−1.82255 − 4.54196I −4.29864 + 3.11401I
u = 0.973474 − 0.672727I
a = −0.120474 − 0.775350I
b = −1.037340 + 0.908780I
−1.82255 + 4.54196I −4.29864 − 3.11401I
u = −0.490238 + 1.134900I
a = −0.705233 − 0.258301I
b = 0.489256 − 0.079506I
−1.82255 − 4.54196I −4.29864 + 3.11401I
u = −0.490238 − 1.134900I
a = −0.705233 + 0.258301I
b = 0.489256 + 0.079506I
−1.82255 + 4.54196I −4.29864 − 3.11401I
u = 0.947805 + 0.931675I
a = 0.117417 − 1.009620I
b = 0.96989 + 1.07473I
3.55383 − 7.96405I 2.92507 + 6.02428I
u = 0.947805 − 0.931675I
a = 0.117417 + 1.009620I
b = 0.96989 − 1.07473I
3.55383 + 7.96405I 2.92507 − 6.02428I
u = 0.624760 + 0.114740I
a = 1.015600 − 0.186789I
b = 1.59870 + 0.48840I
2.89253 + 0.54689I 18.6210 − 11.9306I
u = 0.624760 − 0.114740I
a = 1.015600 + 0.186789I
b = 1.59870 − 0.48840I
2.89253 − 0.54689I 18.6210 + 11.9306I
27
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05532 + 1.04300I
a = −0.530965 − 0.863445I
b = 1.38342 + 0.39958I
−0.24582 − 3.85817I 5.50469 + 2.33081I
u = 1.05532 − 1.04300I
a = −0.530965 + 0.863445I
b = 1.38342 − 0.39958I
−0.24582 + 3.85817I 5.50469 − 2.33081I
u = −0.116259 + 0.447931I
a = 2.34373 + 1.74010I
b = −1.074080 + 0.328248I
3.55383 − 7.96405I 2.92507 + 6.02428I
u = −0.116259 − 0.447931I
a = 2.34373 − 1.74010I
b = −1.074080 − 0.328248I
3.55383 + 7.96405I 2.92507 − 6.02428I
u = −0.404943 + 0.173477I
a = −0.59962 + 3.36092I
b = −0.111711 − 1.056540I
−0.24582 + 3.85817I 5.50469 − 2.33081I
u = −0.404943 − 0.173477I
a = −0.59962 − 3.36092I
b = −0.111711 + 1.056540I
−0.24582 − 3.85817I 5.50469 + 2.33081I
u = 1.19409 + 1.04649I
a = 0.326099 + 0.687739I
b = −1.017300 − 0.504325I
−2.73306 − 4.26272I −8.25212 + 5.64920I
u = 1.19409 − 1.04649I
a = 0.326099 − 0.687739I
b = −1.017300 + 0.504325I
−2.73306 + 4.26272I −8.25212 − 5.64920I
u = 1.53742 + 1.29075I
a = −0.250200 + 0.210167I
b = 0.180215 − 0.433147I
2.89253 + 0.54689I 18.6210 − 11.9306I
u = 1.53742 − 1.29075I
a = −0.250200 − 0.210167I
b = 0.180215 + 0.433147I
2.89253 − 0.54689I 18.6210 + 11.9306I
28
VI. I
u
6
= h−a
4
− a
2
+ b + a, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
1
a
3
=
a
a
4
+ a
2
− a
a
7
=
1
1
a
2
=
a
4
+ a
2
a
4
+ a
2
− a
a
10
=
a
4
+ a
3
+ a
−a
2
a
1
=
a
4
+ a
2
+ a
a
4
+ a
2
a
4
=
−a
4
− a
2
−a
a
8
=
−a
2
a
4
+ a
3
+ 2a
2
+ a + 2
a
11
=
a
4
+ a
3
+ a
2
+ a + 1
a
3
+ a
a
5
=
a
4
+ a
3
+ a + 1
a
4
+ a
3
+ a
2
+ 1
a
5
=
a
4
+ a
3
+ a + 1
a
4
+ a
3
+ a
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4a
3
+ 4a
2
+ 4a − 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
, c
7
u
5
+ u
4
− u
3
− 4u
2
− 3u − 1
c
3
, c
6
(u + 1)
5
c
4
, c
5
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
, c
11
u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
2
, c
7
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y − 1
c
3
, c
6
(y − 1)
5
c
4
, c
5
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
9
, c
11
y
5
+ 2y
4
+ 7y
3
− 15y
2
+ 7y − 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.339110 + 0.822375I
b = −0.896438 − 0.890762I
−2.96077 − 1.53058I −9.48489 + 4.43065I
u = 1.00000
a = 0.339110 − 0.822375I
b = −0.896438 + 0.890762I
−2.96077 + 1.53058I −9.48489 − 4.43065I
u = 1.00000
a = −0.766826
b = 1.70062
−0.888787 −8.51890
u = 1.00000
a = −0.455697 + 1.200150I
b = −0.453870 + 0.402731I
2.58269 + 4.40083I −5.25569 − 3.49859I
u = 1.00000
a = −0.455697 − 1.200150I
b = −0.453870 − 0.402731I
2.58269 − 4.40083I −5.25569 + 3.49859I
32
VII. I
u
7
= ha
4
+ a
2
+ b, a
5
+ a
4
+ 2a
3
+ a
2
+ a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
1
a
3
=
a
−a
4
− a
2
a
7
=
1
1
a
2
=
−a
4
− a
2
+ a
−a
4
− a
2
a
10
=
−a
4
− a
3
− 3a
2
− a − 2
−a
2
a
1
=
−a
4
− a
2
+ 2a
−a
4
− a
2
+ a
a
4
=
a
4
+ a
2
− a
−a
a
8
=
−a
2
−a
4
− a
3
− a
2
− a
a
11
=
−a
4
− a
2
+ 2a − 1
a
3
+ a
a
5
=
2a
4
+ 3a
2
− a + 2
a
4
+ a
3
+ a
2
+ 1
a
5
=
2a
4
+ 3a
2
− a + 2
a
4
+ a
3
+ a
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4a
3
+ 4a
2
+ 4a − 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
, c
7
u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1
c
3
, c
6
(u + 1)
5
c
4
, c
5
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
, c
11
u
5
+ u
4
− u
3
− 4u
2
− 3u − 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
2
, c
7
y
5
+ 2y
4
+ 7y
3
− 15y
2
+ 7y − 1
c
3
, c
6
(y − 1)
5
c
4
, c
5
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
9
, c
11
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y − 1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.339110 + 0.822375I
b = 0.557328 + 0.068387I
−2.96077 − 1.53058I −9.48489 + 4.43065I
u = 1.00000
a = 0.339110 − 0.822375I
b = 0.557328 − 0.068387I
−2.96077 + 1.53058I −9.48489 − 4.43065I
u = 1.00000
a = −0.766826
b = −0.933791
−0.888787 −8.51890
u = 1.00000
a = −0.455697 + 1.200150I
b = 0.90957 − 1.60288I
2.58269 + 4.40083I −5.25569 − 3.49859I
u = 1.00000
a = −0.455697 − 1.200150I
b = 0.90957 + 1.60288I
2.58269 − 4.40083I −5.25569 + 3.49859I
36
VIII. I
u
8
= hb + 1, a, u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
1
a
3
=
0
−1
a
7
=
1
1
a
2
=
−1
−1
a
10
=
−1
0
a
1
=
−1
−1
a
4
=
1
0
a
8
=
0
1
a
11
=
−1
0
a
5
=
1
0
a
5
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
10
u
c
2
, c
6
, c
9
u − 1
c
3
, c
7
, c
11
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
10
y
c
2
, c
3
, c
6
c
7
, c
9
, c
11
y − 1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
40
IX. I
v
1
= ha, b
5
− b
4
+ 2b
3
− b
2
+ b − 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
1
0
a
3
=
0
b
a
7
=
1
0
a
2
=
b
b
a
10
=
b
2
+ 1
b
2
a
1
=
0
b
a
4
=
0
b
a
8
=
1
b
2
a
11
=
b
b
3
+ b
a
5
=
b
4
+ b
2
+ 1
b
4
− b
3
+ b
2
+ 1
a
5
=
b
4
+ b
2
+ 1
b
4
− b
3
+ b
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
3
+ 4b
2
− 4b + 6
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
9
, c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
6
u
5
c
4
, c
5
, c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
9
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
3
, c
6
y
5
c
4
, c
5
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.339110 + 0.822375I
0.32910 + 1.53058I 2.51511 − 4.43065I
v = 1.00000
a = 0
b = −0.339110 − 0.822375I
0.32910 − 1.53058I 2.51511 + 4.43065I
v = 1.00000
a = 0
b = 0.766826
2.40108 3.48110
v = 1.00000
a = 0
b = 0.455697 + 1.200150I
5.87256 − 4.40083I 6.74431 + 3.49859I
v = 1.00000
a = 0
b = 0.455697 − 1.200150I
5.87256 + 4.40083I 6.74431 − 3.49859I
44
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
(u
6
− u
4
+ u
3
+ u
2
− 1)
2
· (u
16
+ u
15
+ ··· + 2u + 2)(u
20
+ 5u
18
+ ··· − 14u
2
+ 5)
· ((u
20
− u
19
+ ··· − 40u + 7)
2
)(u
20
+ 3u
19
+ ··· − 12u + 61)
c
2
, c
9
(u − 1)(u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
5
+ u
4
− u
3
− 4u
2
− 3u − 1)
· (u
12
+ u
10
− u
9
+ 8u
8
+ u
7
+ 8u
6
− 8u
5
+ 4u
4
+ u
3
+ 4u
2
− 3u + 1)
· (u
16
+ u
15
+ ··· + u + 1)(u
20
+ u
19
+ ··· − 6u + 1)
· (u
20
+ 3u
19
+ ··· + 5u + 1)(u
40
− u
39
+ ··· − 24u + 1)
c
3
u
5
(u + 1)
11
(u
2
+ u + 1)
10
(u
4
+ u
3
− 2u + 1)
10
· (u
12
− 10u
11
+ ··· − 102u + 17)(u
16
− 11u
15
+ ··· − 85u + 19)
· (u
20
+ 9u
19
+ ··· − 3u
2
+ 1)
c
4
, c
5
, c
10
u(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
14
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· ((u
6
+ 3u
5
+ 2u
4
+ u
2
− 2u − 4)
2
)(u
16
+ 6u
15
+ ··· + 8u + 8)
· (u
20
− 11u
18
+ ··· − 26u
2
+ 5)
c
6
u
5
(u − 1)(u + 1)
10
(u
2
+ u + 1)
10
(u
4
+ u
3
− 2u + 1)
10
· (u
12
− 10u
11
+ ··· − 102u + 17)(u
16
− 11u
15
+ ··· − 85u + 19)
· (u
20
− 9u
19
+ ··· − 3u
2
+ 1)
c
7
, c
11
(u + 1)(u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
5
+ u
4
− u
3
− 4u
2
− 3u − 1)
· (u
12
+ u
10
− u
9
+ 8u
8
+ u
7
+ 8u
6
− 8u
5
+ 4u
4
+ u
3
+ 4u
2
− 3u + 1)
· (u
16
+ u
15
+ ··· + u + 1)(u
20
− 3u
19
+ ··· − 5u + 1)
· (u
20
+ u
19
+ ··· − 6u + 1)(u
40
− u
39
+ ··· − 24u + 1)
45
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
· (y
6
− 2y
5
+ 3y
4
− 5y
3
+ 3y
2
− 2y + 1)
2
· (y
10
+ 5y
9
+ 12y
8
+ 22y
7
+ 39y
6
+ 39y
5
+ 16y
4
− 3y
3
− y
2
− 14y + 5)
2
· (y
16
+ 9y
15
+ ··· + 48y + 4)(y
20
− 13y
19
+ ··· + 17912y + 3721)
· (y
20
+ 15y
19
+ ··· + 136y + 49)
2
c
2
, c
7
, c
9
c
11
(y − 1)(y
5
− 3y
4
+ ··· + y − 1)(y
5
+ 2y
4
+ ··· + 7y − 1)
· (y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)(y
12
+ 2y
11
+ ··· − y + 1)
· (y
16
+ 7y
15
+ ··· + 21y + 1)(y
20
− 9y
19
+ ··· + y + 1)
· (y
20
− y
19
+ ··· + 8y + 1)(y
40
− 19y
39
+ ··· − 140y + 1)
c
3
, c
6
y
5
(y − 1)
11
(y
2
+ y + 1)
10
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
· (y
12
+ 6y
11
+ ··· + 918y + 289)(y
16
− 11y
15
+ ··· + 3795y + 361)
· (y
20
− 3y
19
+ ··· − 6y + 1)
c
4
, c
5
, c
10
y(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
15
· (y
6
− 5y
5
+ 6y
4
+ 8y
3
− 15y
2
− 12y + 16)
2
· ((y
10
− 11y
9
+ ··· − 26y + 5)
2
)(y
16
− 12y
15
+ ··· + 160y + 64)
46
