12a
0113
(K12a
0113
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 12 10 4 7 9 1 6
Solving Sequence
3,8
4
5,9
2
1,11
12 10 7 6
c
3
c
8
c
2
c
1
c
11
c
10
c
7
c
6
c
4
, c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.57614 × 10
61
u
45
− 5.16765 × 10
61
u
44
+ ··· + 1.04756 × 10
63
d − 8.34150 × 10
62
,
− 1.37440 × 10
61
u
45
+ 5.43427 × 10
61
u
44
+ ··· + 2.09512 × 10
63
c + 1.27330 × 10
63
,
− 2.25361 × 10
61
u
45
+ 4.71945 × 10
61
u
44
+ ··· + 1.04756 × 10
63
b + 2.14640 × 10
62
,
1.04662 × 10
62
u
45
− 2.24346 × 10
62
u
44
+ ··· + 2.09512 × 10
63
a − 4.78844 × 10
63
, u
46
− 3u
45
+ ··· − 32u + 32i
I
u
2
= h−2.67306 × 10
20
au
37
+ 1.38721 × 10
19
u
37
+ ··· + 1.33819 × 10
21
a − 9.87299 × 10
20
,
3.11246 × 10
20
au
37
− 2.82340 × 10
20
u
37
+ ··· + 4.88853 × 10
19
a + 1.51002 × 10
20
,
− 6.51406 × 10
19
au
37
+ 1.38360 × 10
20
u
37
+ ··· + 2.42874 × 10
20
a − 6.50377 × 10
20
,
− 8.51184 × 10
19
au
37
+ 2.87125 × 10
20
u
37
+ ··· − 2.71211 × 10
21
a + 1.26240 × 10
21
, u
38
+ u
37
+ ··· + 4u − 4i
I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, a
2
d + c
2
v − 2ca + cv − a + v, dv − 1, c
2
v
2
− 2cav + v
2
c + a
2
− av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 127 representations.
* 1 irreducible components of dim
C
= 1
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h2.58×10
61
u
45
−5.17×10
61
u
44
+· · ·+1.05×10
63
d−8.34×10
62
, −1.37×
10
61
u
45
+ 5.43 × 10
61
u
44
+ · · · + 2.10 × 10
63
c + 1.27 × 10
63
, −2.25 ×
10
61
u
45
+ 4.72 × 10
61
u
44
+ · · · + 1.05 × 10
63
b + 2.15 × 10
62
, 1.05 × 10
62
u
45
−
2.24 × 10
62
u
44
+ · · · + 2.10 × 10
63
a − 4.79 × 10
63
, u
46
− 3u
45
+ · · · − 32u + 32i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
−0.0499550u
45
+ 0.107080u
44
+ ··· + 0.105000u + 2.28551
0.0215129u
45
− 0.0450517u
44
+ ··· + 0.210607u − 0.204895
a
9
=
u
−u
3
+ u
a
2
=
−0.0499550u
45
+ 0.107080u
44
+ ··· + 0.105000u + 2.28551
0.0188136u
45
− 0.0434778u
44
+ ··· − 0.440044u − 1.16423
a
1
=
−0.0311414u
45
+ 0.0636021u
44
+ ··· − 0.335044u + 1.12129
0.0188136u
45
− 0.0434778u
44
+ ··· − 0.440044u − 1.16423
a
11
=
0.00655998u
45
− 0.0259377u
44
+ ··· + 2.00677u − 0.607746
−0.0245918u
45
+ 0.0493302u
44
+ ··· + 0.534931u + 0.796277
a
12
=
−0.00367220u
45
− 0.0105532u
44
+ ··· + 1.80694u + 0.0421140
−0.0300186u
45
+ 0.0694063u
44
+ ··· − 0.0507359u + 1.20714
a
10
=
−0.00640297u
45
− 0.00230401u
44
+ ··· + 2.56896u − 0.00571168
−0.0232980u
45
+ 0.0442495u
44
+ ··· + 1.17047u + 0.910145
a
7
=
−0.0363821u
45
+ 0.0903327u
44
+ ··· − 1.88200u + 1.60427
−0.0298221u
45
+ 0.0643950u
44
+ ··· + 0.124764u + 0.996524
a
6
=
−0.0377231u
45
+ 0.0831509u
44
+ ··· − 1.46595u + 1.15640
0.0215698u
45
− 0.0484849u
44
+ ··· + 0.0753964u − 0.117510
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.247381u
45
+ 0.445802u
44
+ ··· + 4.44172u + 0.790830
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
46
+ 21u
45
+ ··· − 4u + 1
c
2
, c
4
, c
7
c
9
u
46
− 5u
45
+ ··· − 2u + 1
c
3
, c
8
u
46
+ 3u
45
+ ··· + 32u + 32
c
5
u
46
+ u
45
+ ··· + 2596u + 1252
c
6
, c
12
u
46
− u
45
+ ··· + 4u + 4
c
11
u
46
− 21u
45
+ ··· + 40u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
46
+ 19y
45
+ ··· − 72y + 1
c
2
, c
4
, c
7
c
9
y
46
− 21y
45
+ ··· + 4y + 1
c
3
, c
8
y
46
− 15y
45
+ ··· + 4096y + 1024
c
5
y
46
− 3y
45
+ ··· − 20408552y + 1567504
c
6
, c
12
y
46
+ 21y
45
+ ··· − 40y + 16
c
11
y
46
+ 9y
45
+ ··· − 5664y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248116 + 0.949341I
a = 0.589922 + 0.247257I
b = 0.441845 − 0.604328I
c = 0.017203 + 0.885277I
d = −0.12168 + 1.65051I
1.66114 − 2.12776I 0.422256 + 0.234121I
u = 0.248116 − 0.949341I
a = 0.589922 − 0.247257I
b = 0.441845 + 0.604328I
c = 0.017203 − 0.885277I
d = −0.12168 − 1.65051I
1.66114 + 2.12776I 0.422256 − 0.234121I
u = −0.642875 + 0.814816I
a = 0.455077 + 0.085949I
b = 1.121750 − 0.400729I
c = 0.945725 − 0.863065I
d = 0.751792 − 0.382393I
−5.93091 + 3.99675I −10.51051 − 4.44974I
u = −0.642875 − 0.814816I
a = 0.455077 − 0.085949I
b = 1.121750 + 0.400729I
c = 0.945725 + 0.863065I
d = 0.751792 + 0.382393I
−5.93091 − 3.99675I −10.51051 + 4.44974I
u = −0.046642 + 1.050320I
a = 0.521824 + 0.180773I
b = 0.711017 − 0.592739I
c = −0.284880 + 0.449331I
d = −1.45000 + 0.80516I
2.04690 + 4.94372I −0.16550 − 7.58166I
u = −0.046642 − 1.050320I
a = 0.521824 − 0.180773I
b = 0.711017 + 0.592739I
c = −0.284880 − 0.449331I
d = −1.45000 − 0.80516I
2.04690 − 4.94372I −0.16550 + 7.58166I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.614432 + 0.696436I
a = 0.462583 − 0.072566I
b = 1.109850 + 0.330974I
c = −1.235720 − 0.572618I
d = −0.466020 + 0.040614I
−4.70063 + 1.01560I −8.78023 − 1.30126I
u = 0.614432 − 0.696436I
a = 0.462583 + 0.072566I
b = 1.109850 − 0.330974I
c = −1.235720 + 0.572618I
d = −0.466020 − 0.040614I
−4.70063 − 1.01560I −8.78023 + 1.30126I
u = 0.904459 + 0.035006I
a = 0.99383 − 1.43056I
b = −0.672458 + 0.471479I
c = 0.492096 + 0.016232I
d = 0.317889 − 0.738045I
−0.23417 + 4.06154I −0.42563 − 7.90074I
u = 0.904459 − 0.035006I
a = 0.99383 + 1.43056I
b = −0.672458 − 0.471479I
c = 0.492096 − 0.016232I
d = 0.317889 + 0.738045I
−0.23417 − 4.06154I −0.42563 + 7.90074I
u = 0.517103 + 1.038360I
a = 0.457040 − 0.120254I
b = 1.046330 + 0.538419I
c = −0.063868 − 0.817891I
d = 0.18483 − 1.60057I
−0.12548 − 4.11136I −2.46017 + 3.87123I
u = 0.517103 − 1.038360I
a = 0.457040 + 0.120254I
b = 1.046330 − 0.538419I
c = −0.063868 + 0.817891I
d = 0.18483 + 1.60057I
−0.12548 + 4.11136I −2.46017 − 3.87123I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017678 + 0.820472I
a = 0.576889 − 0.137924I
b = 0.639709 + 0.392026I
c = −0.087372 + 0.550499I
d = 0.487544 + 0.625296I
−0.79101 − 1.46703I −5.32252 + 4.75359I
u = 0.017678 − 0.820472I
a = 0.576889 + 0.137924I
b = 0.639709 − 0.392026I
c = −0.087372 − 0.550499I
d = 0.487544 − 0.625296I
−0.79101 + 1.46703I −5.32252 − 4.75359I
u = 1.006520 + 0.624064I
a = −0.40042 − 1.85496I
b = −1.111190 + 0.515094I
c = −1.121880 − 0.316865I
d = −0.633971 + 0.037265I
−3.52144 + 4.08819I −5.82465 − 4.54278I
u = 1.006520 − 0.624064I
a = −0.40042 + 1.85496I
b = −1.111190 − 0.515094I
c = −1.121880 + 0.316865I
d = −0.633971 − 0.037265I
−3.52144 − 4.08819I −5.82465 + 4.54278I
u = −1.071740 + 0.508840I
a = 0.613457 − 0.718385I
b = −0.312581 + 0.804998I
c = −1.374890 + 0.240606I
d = −0.176960 − 0.890915I
1.98761 − 2.55534I −0.98949 + 1.01939I
u = −1.071740 − 0.508840I
a = 0.613457 + 0.718385I
b = −0.312581 − 0.804998I
c = −1.374890 − 0.240606I
d = −0.176960 + 0.890915I
1.98761 + 2.55534I −0.98949 − 1.01939I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807683 + 0.082878I
a = 1.21197 − 1.05036I
b = −0.528808 + 0.408361I
c = −0.643863 + 0.075660I
d = −0.430989 + 0.455586I
−0.274017 − 1.087600I 0.651009 − 0.594713I
u = −0.807683 − 0.082878I
a = 1.21197 + 1.05036I
b = −0.528808 − 0.408361I
c = −0.643863 − 0.075660I
d = −0.430989 − 0.455586I
−0.274017 + 1.087600I 0.651009 + 0.594713I
u = −0.668777 + 1.013930I
a = 0.441760 + 0.107066I
b = 1.138080 − 0.518189I
c = 0.362758 − 1.282570I
d = 1.03682 − 1.70646I
−4.90536 + 6.51831I −8.90536 − 4.64881I
u = −0.668777 − 1.013930I
a = 0.441760 − 0.107066I
b = 1.138080 + 0.518189I
c = 0.362758 + 1.282570I
d = 1.03682 + 1.70646I
−4.90536 − 6.51831I −8.90536 + 4.64881I
u = −1.035500 + 0.682470I
a = −0.48479 + 1.75097I
b = −1.146870 − 0.530449I
c = 1.364230 − 0.311759I
d = 0.821257 + 0.527558I
−4.70874 − 9.62616I −7.79470 + 8.99124I
u = −1.035500 − 0.682470I
a = −0.48479 − 1.75097I
b = −1.146870 + 0.530449I
c = 1.364230 + 0.311759I
d = 0.821257 − 0.527558I
−4.70874 + 9.62616I −7.79470 − 8.99124I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.224990 + 0.226721I
a = 0.26109 − 1.40376I
b = −0.871935 + 0.688553I
c = −0.035155 + 0.735172I
d = 0.474612 − 1.300260I
3.57586 + 5.30392I −1.93777 − 5.96454I
u = 1.224990 − 0.226721I
a = 0.26109 + 1.40376I
b = −0.871935 − 0.688553I
c = −0.035155 − 0.735172I
d = 0.474612 + 1.300260I
3.57586 − 5.30392I −1.93777 + 5.96454I
u = 1.195740 + 0.364671I
a = 0.555749 + 0.845299I
b = −0.456951 − 0.825982I
c = 1.383760 − 0.204608I
d = −0.775236 − 0.457994I
6.39735 − 0.44189I 4.43091 + 2.06201I
u = 1.195740 − 0.364671I
a = 0.555749 − 0.845299I
b = −0.456951 + 0.825982I
c = 1.383760 + 0.204608I
d = −0.775236 + 0.457994I
6.39735 + 0.44189I 4.43091 − 2.06201I
u = 0.687704 + 1.079720I
a = 0.435637 − 0.112607I
b = 1.151720 + 0.556193I
c = −0.16597 − 1.45383I
d = −1.16901 − 2.34716I
−2.74057 − 11.63170I −5.60201 + 8.64749I
u = 0.687704 − 1.079720I
a = 0.435637 + 0.112607I
b = 1.151720 − 0.556193I
c = −0.16597 + 1.45383I
d = −1.16901 + 2.34716I
−2.74057 + 11.63170I −5.60201 − 8.64749I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.158970 + 0.578549I
a = 0.544904 + 0.699989I
b = −0.307535 − 0.889547I
c = 1.64315 + 0.27736I
d = 0.06540 − 1.58776I
4.42926 + 7.47789I 1.74286 − 4.84208I
u = 1.158970 − 0.578549I
a = 0.544904 − 0.699989I
b = −0.307535 + 0.889547I
c = 1.64315 − 0.27736I
d = 0.06540 + 1.58776I
4.42926 − 7.47789I 1.74286 + 4.84208I
u = −1.311140 + 0.102134I
a = 0.311679 + 1.221780I
b = −0.803961 − 0.768470I
c = −0.364729 + 0.984342I
d = 0.02550 − 1.73526I
7.51022 − 1.50301I 3.10935 + 2.27720I
u = −1.311140 − 0.102134I
a = 0.311679 − 1.221780I
b = −0.803961 + 0.768470I
c = −0.364729 − 0.984342I
d = 0.02550 + 1.73526I
7.51022 + 1.50301I 3.10935 − 2.27720I
u = −0.435796 + 0.485308I
a = 0.857168 − 0.309306I
b = 0.032227 + 0.372475I
c = −0.440235 + 0.495589I
d = −0.501506 + 0.464460I
0.084212 − 1.381070I 0.30299 + 4.86269I
u = −0.435796 − 0.485308I
a = 0.857168 + 0.309306I
b = 0.032227 − 0.372475I
c = −0.440235 − 0.495589I
d = −0.501506 − 0.464460I
0.084212 + 1.381070I 0.30299 − 4.86269I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.316840 + 0.304432I
a = 0.116039 + 1.346760I
b = −0.936495 − 0.737050I
c = 0.307546 + 1.028890I
d = −1.03275 − 1.46411I
6.69471 − 9.89538I 1.12698 + 9.02462I
u = −1.316840 − 0.304432I
a = 0.116039 − 1.346760I
b = −0.936495 + 0.737050I
c = 0.307546 − 1.028890I
d = −1.03275 + 1.46411I
6.69471 + 9.89538I 1.12698 − 9.02462I
u = −1.118430 + 0.781907I
a = −0.55775 + 1.54027I
b = −1.207840 − 0.573976I
c = 1.86293 − 0.18421I
d = 0.89762 + 1.88496I
−3.44989 − 13.07100I −7.52581 + 7.90184I
u = −1.118430 − 0.781907I
a = −0.55775 − 1.54027I
b = −1.207840 + 0.573976I
c = 1.86293 + 0.18421I
d = 0.89762 − 1.88496I
−3.44989 + 13.07100I −7.52581 − 7.90184I
u = 1.166960 + 0.709743I
a = −0.42776 − 1.53120I
b = −1.169240 + 0.605803I
c = −1.67165 + 0.11957I
d = 0.04746 + 1.51937I
1.96462 + 10.42030I 0. − 7.01224I
u = 1.166960 − 0.709743I
a = −0.42776 + 1.53120I
b = −1.169240 − 0.605803I
c = −1.67165 − 0.11957I
d = 0.04746 − 1.51937I
1.96462 − 10.42030I 0. + 7.01224I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.144720 + 0.813548I
a = −0.57296 − 1.48160I
b = −1.227060 + 0.587138I
c = −2.03119 − 0.14199I
d = −0.89891 + 2.41812I
−1.2351 + 18.4885I −4.00000 − 11.60486I
u = 1.144720 − 0.813548I
a = −0.57296 + 1.48160I
b = −1.227060 − 0.587138I
c = −2.03119 + 0.14199I
d = −0.89891 − 2.41812I
−1.2351 − 18.4885I −4.00000 + 11.60486I
u = 0.068034 + 0.485475I
a = 0.537064 − 0.015658I
b = 0.860393 + 0.054239I
c = −0.358003 + 1.358470I
d = 0.046305 + 0.232893I
−2.91211 − 2.24138I −11.31463 + 3.80305I
u = 0.068034 − 0.485475I
a = 0.537064 + 0.015658I
b = 0.860393 − 0.054239I
c = −0.358003 − 1.358470I
d = 0.046305 − 0.232893I
−2.91211 + 2.24138I −11.31463 − 3.80305I
12
II. I
u
2
= h−2.67 × 10
20
au
37
+ 1.39 × 10
19
u
37
+ · · · + 1.34 × 10
21
a − 9.87 ×
10
20
, 3.11×10
20
au
37
−2.82×10
20
u
37
+· · ·+4.89×10
19
a+1.51×10
20
, −6.51×
10
19
au
37
+1.38×10
20
u
37
+· · · + 2.43 × 10
20
a−6.50×10
20
, −8.51×10
19
au
37
+
2.87 × 10
20
u
37
+ · · · − 2.71 × 10
21
a + 1.26 × 10
21
, u
38
+ u
37
+ · · · + 4u − 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
a
0.351994au
37
− 0.747643u
37
+ ··· − 1.31240a + 3.51438
a
9
=
u
−u
3
+ u
a
2
=
a
−0.351994au
37
+ 0.747643u
37
+ ··· + 1.31240a − 3.51438
a
1
=
−0.351994au
37
+ 0.747643u
37
+ ··· + 2.31240a − 3.51438
−0.351994au
37
+ 0.747643u
37
+ ··· + 1.31240a − 3.51438
a
11
=
−0.840926au
37
+ 0.762827u
37
+ ··· − 0.132078a − 0.407976
0.722207au
37
− 0.0374795u
37
+ ··· − 3.61552a + 2.66749
a
12
=
0.717046au
37
− 0.375927u
37
+ ··· − 6.28667a + 4.45469
1.61990au
37
− 1.17623u
37
+ ··· − 6.25098a + 7.53015
a
10
=
−0.328099au
37
+ 0.250000u
37
+ ··· − 1.54005a + 1
0.512827au
37
+ 0.171901u
37
+ ··· − 1.40798a + 0.459946
a
7
=
0.328099au
37
− 0.0780990u
37
+ ··· + 1.54005a − 0.540054
−0.512827au
37
+ 0.684728u
37
+ ··· + 1.40798a − 0.948030
a
6
=
1.56275au
37
− 0.842508u
37
+ ··· − 1.04475a + 2.32445
−0.332058au
37
− 0.0145277u
37
+ ··· + 2.86819a + 1.41585
(ii) Obstruction class = −1
(iii) Cusp Shapes =
125334397169543797937
92530874909565185306
u
37
+
144830212205814099033
92530874909565185306
u
36
+ ··· +
34223567447539124627
92530874909565185306
u −
228286816014379276432
46265437454782592653
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 43u
75
+ ··· + 800u + 256
c
2
, c
7
u
76
− 3u
75
+ ··· + 104u − 16
c
3
(u
38
− u
37
+ ··· − 4u − 4)
2
c
4
, c
9
− u
76
− 3u
75
+ ··· + 104u + 16
c
5
(u
38
+ 2u
37
+ ··· + 37u + 17)
2
c
6
(u
38
− 2u
37
+ ··· − 5u + 1)
2
c
8
(u
38
+ u
37
+ ··· + 4u − 4)
2
c
10
u
76
− 43u
75
+ ··· − 800u + 256
c
11
(u
38
+ 18u
37
+ ··· − 5u + 1)
2
c
12
(u
38
+ 2u
37
+ ··· + 5u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
76
− 23y
75
+ ··· − 1516032y + 65536
c
2
, c
4
, c
7
c
9
y
76
− 43y
75
+ ··· − 800y + 256
c
3
, c
8
(y
38
− 15y
37
+ ··· − 72y + 16)
2
c
5
(y
38
− 6y
37
+ ··· − 6333y + 289)
2
c
6
, c
12
(y
38
+ 18y
37
+ ··· − 5y + 1)
2
c
11
(y
38
+ 6y
37
+ ··· − 61y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718175 + 0.689913I
a = 0.450629 + 0.069011I
b = 1.168270 − 0.332058I
c = 0.82426 − 1.31061I
d = 1.77249 − 1.85878I
−6.09366 − 1.46931I −10.87065 + 3.08473I
u = −0.718175 + 0.689913I
a = −1.05848 + 2.42146I
b = −1.151560 − 0.346723I
c = 1.44273 − 0.85052I
d = 0.779906 + 0.302096I
−6.09366 − 1.46931I −10.87065 + 3.08473I
u = −0.718175 − 0.689913I
a = 0.450629 − 0.069011I
b = 1.168270 + 0.332058I
c = 0.82426 + 1.31061I
d = 1.77249 + 1.85878I
−6.09366 + 1.46931I −10.87065 − 3.08473I
u = −0.718175 − 0.689913I
a = −1.05848 − 2.42146I
b = −1.151560 + 0.346723I
c = 1.44273 + 0.85052I
d = 0.779906 − 0.302096I
−6.09366 + 1.46931I −10.87065 − 3.08473I
u = −0.257524 + 0.984493I
a = 0.578727 − 0.253722I
b = 0.449354 + 0.635417I
c = −0.0473997 − 0.0121555I
d = −1.051440 − 0.287772I
1.60581 − 0.49664I 0.272784 + 1.115032I
u = −0.257524 + 0.984493I
a = 0.498072 + 0.137191I
b = 0.866155 − 0.514022I
c = 0.017878 + 0.930985I
d = 0.15505 + 1.83052I
1.60581 − 0.49664I 0.272784 + 1.115032I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.257524 − 0.984493I
a = 0.578727 + 0.253722I
b = 0.449354 − 0.635417I
c = −0.0473997 + 0.0121555I
d = −1.051440 + 0.287772I
1.60581 + 0.49664I 0.272784 − 1.115032I
u = −0.257524 − 0.984493I
a = 0.498072 − 0.137191I
b = 0.866155 + 0.514022I
c = 0.017878 − 0.930985I
d = 0.15505 − 1.83052I
1.60581 + 0.49664I 0.272784 − 1.115032I
u = −0.924425 + 0.450549I
a = 0.733764 − 0.695514I
b = −0.282136 + 0.680443I
c = 2.44374 − 0.86916I
d = −0.05679 + 1.53145I
−0.88516 − 3.95746I −1.72480 + 4.57056I
u = −0.924425 + 0.450549I
a = 0.434246 + 0.040729I
b = 1.282760 − 0.214107I
c = −1.063930 + 0.292390I
d = −0.442706 − 0.285409I
−0.88516 − 3.95746I −1.72480 + 4.57056I
u = −0.924425 − 0.450549I
a = 0.733764 + 0.695514I
b = −0.282136 − 0.680443I
c = 2.44374 + 0.86916I
d = −0.05679 − 1.53145I
−0.88516 + 3.95746I −1.72480 − 4.57056I
u = −0.924425 − 0.450549I
a = 0.434246 − 0.040729I
b = 1.282760 + 0.214107I
c = −1.063930 − 0.292390I
d = −0.442706 + 0.285409I
−0.88516 + 3.95746I −1.72480 − 4.57056I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531079 + 0.883531I
a = 0.622511 + 0.357737I
b = 0.207598 − 0.693967I
c = −0.558583 − 0.645103I
d = −0.214583 − 0.739308I
−2.26472 − 1.90334I −6.18021 + 1.07076I
u = 0.531079 + 0.883531I
a = 0.465715 − 0.099917I
b = 1.052750 + 0.440407I
c = 0.451533 + 1.059860I
d = 1.21258 + 1.38512I
−2.26472 − 1.90334I −6.18021 + 1.07076I
u = 0.531079 − 0.883531I
a = 0.622511 − 0.357737I
b = 0.207598 + 0.693967I
c = −0.558583 + 0.645103I
d = −0.214583 + 0.739308I
−2.26472 + 1.90334I −6.18021 − 1.07076I
u = 0.531079 − 0.883531I
a = 0.465715 + 0.099917I
b = 1.052750 − 0.440407I
c = 0.451533 − 1.059860I
d = 1.21258 − 1.38512I
−2.26472 + 1.90334I −6.18021 − 1.07076I
u = −0.860778 + 0.429023I
a = 0.789089 − 0.671236I
b = −0.264746 + 0.625441I
c = 0.320925 − 0.473124I
d = 0.139948 − 1.119540I
−1.135440 + 0.390890I −2.15175 + 1.14697I
u = −0.860778 + 0.429023I
a = 0.07205 + 2.35819I
b = −0.987057 − 0.423659I
c = −0.954913 + 0.311920I
d = −0.508328 − 0.109971I
−1.135440 + 0.390890I −2.15175 + 1.14697I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860778 − 0.429023I
a = 0.789089 + 0.671236I
b = −0.264746 − 0.625441I
c = 0.320925 + 0.473124I
d = 0.139948 + 1.119540I
−1.135440 − 0.390890I −2.15175 − 1.14697I
u = −0.860778 − 0.429023I
a = 0.07205 − 2.35819I
b = −0.987057 + 0.423659I
c = −0.954913 − 0.311920I
d = −0.508328 + 0.109971I
−1.135440 − 0.390890I −2.15175 − 1.14697I
u = 0.959864 + 0.423605I
a = 0.431319 − 0.037774I
b = 1.300820 + 0.201498I
c = −0.436644 − 0.188137I
d = −0.003550 − 0.813354I
−0.93346 + 1.43399I −1.64648 − 2.88902I
u = 0.959864 + 0.423605I
a = 0.07049 − 2.03730I
b = −0.983037 + 0.490258I
c = −2.57502 − 0.87790I
d = 0.26331 + 1.68900I
−0.93346 + 1.43399I −1.64648 − 2.88902I
u = 0.959864 − 0.423605I
a = 0.431319 + 0.037774I
b = 1.300820 − 0.201498I
c = −0.436644 + 0.188137I
d = −0.003550 + 0.813354I
−0.93346 − 1.43399I −1.64648 + 2.88902I
u = 0.959864 − 0.423605I
a = 0.07049 + 2.03730I
b = −0.983037 − 0.490258I
c = −2.57502 + 0.87790I
d = 0.26331 − 1.68900I
−0.93346 − 1.43399I −1.64648 + 2.88902I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.590924 + 0.743055I
a = 0.464137 − 0.079085I
b = 1.093750 + 0.356756I
c = −0.73068 − 1.75542I
d = −2.09697 − 2.99942I
−4.63851 − 3.34557I −8.53398 + 2.94107I
u = 0.590924 + 0.743055I
a = −1.64730 − 2.48133I
b = −1.185700 + 0.279725I
c = −1.063010 − 0.587695I
d = −0.450613 − 0.143094I
−4.63851 − 3.34557I −8.53398 + 2.94107I
u = 0.590924 − 0.743055I
a = 0.464137 + 0.079085I
b = 1.093750 − 0.356756I
c = −0.73068 + 1.75542I
d = −2.09697 + 2.99942I
−4.63851 + 3.34557I −8.53398 − 2.94107I
u = 0.590924 − 0.743055I
a = −1.64730 + 2.48133I
b = −1.185700 − 0.279725I
c = −1.063010 + 0.587695I
d = −0.450613 + 0.143094I
−4.63851 + 3.34557I −8.53398 − 2.94107I
u = −0.944268 + 0.080074I
a = 0.90488 − 1.15379I
b = −0.579133 + 0.536637I
c = 2.95149 − 0.14973I
d = −1.41848 + 0.38074I
0.25240 + 2.75914I 1.19764 − 4.35912I
u = −0.944268 + 0.080074I
a = 0.434964 + 0.007055I
b = 1.298440 − 0.037280I
c = −0.661782 − 0.078108I
d = −0.169418 + 0.540287I
0.25240 + 2.75914I 1.19764 − 4.35912I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944268 − 0.080074I
a = 0.90488 + 1.15379I
b = −0.579133 − 0.536637I
c = 2.95149 + 0.14973I
d = −1.41848 − 0.38074I
0.25240 − 2.75914I 1.19764 + 4.35912I
u = −0.944268 − 0.080074I
a = 0.434964 − 0.007055I
b = 1.298440 + 0.037280I
c = −0.661782 + 0.078108I
d = −0.169418 − 0.540287I
0.25240 − 2.75914I 1.19764 + 4.35912I
u = 0.932230 + 0.544110I
a = 0.681744 + 0.643239I
b = −0.223996 − 0.732175I
c = −0.757090 − 0.432327I
d = −0.505611 − 0.637960I
−2.05024 + 4.86305I −4.53119 − 6.13263I
u = 0.932230 + 0.544110I
a = −0.26957 − 2.08849I
b = −1.060790 + 0.470969I
c = 1.152600 + 0.439830I
d = 0.702756 − 0.492106I
−2.05024 + 4.86305I −4.53119 − 6.13263I
u = 0.932230 − 0.544110I
a = 0.681744 − 0.643239I
b = −0.223996 + 0.732175I
c = −0.757090 + 0.432327I
d = −0.505611 + 0.637960I
−2.05024 − 4.86305I −4.53119 + 6.13263I
u = 0.932230 − 0.544110I
a = −0.26957 + 2.08849I
b = −1.060790 − 0.470969I
c = 1.152600 − 0.439830I
d = 0.702756 + 0.492106I
−2.05024 − 4.86305I −4.53119 + 6.13263I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708662 + 0.534244I
a = 0.787028 + 0.513024I
b = −0.108292 − 0.581260I
c = −1.83838 − 0.54055I
d = −0.277411 + 0.604173I
−2.72088 − 0.47986I −5.93461 − 0.48126I
u = 0.708662 + 0.534244I
a = 0.454757 − 0.052031I
b = 1.170560 + 0.248344I
c = 0.790083 + 0.534557I
d = 0.815520 + 0.154915I
−2.72088 − 0.47986I −5.93461 − 0.48126I
u = 0.708662 − 0.534244I
a = 0.787028 − 0.513024I
b = −0.108292 + 0.581260I
c = −1.83838 + 0.54055I
d = −0.277411 − 0.604173I
−2.72088 + 0.47986I −5.93461 + 0.48126I
u = 0.708662 − 0.534244I
a = 0.454757 + 0.052031I
b = 1.170560 − 0.248344I
c = 0.790083 − 0.534557I
d = 0.815520 − 0.154915I
−2.72088 + 0.47986I −5.93461 + 0.48126I
u = −0.947945 + 0.635897I
a = 0.428626 + 0.057689I
b = 1.291520 − 0.308415I
c = 1.067620 − 0.525455I
d = 0.956024 − 0.254994I
−5.38662 − 3.65224I −8.95361 + 3.74887I
u = −0.947945 + 0.635897I
a = −0.48016 + 1.96758I
b = −1.117060 − 0.479673I
c = 2.07459 − 1.34946I
d = 1.14302 + 1.63054I
−5.38662 − 3.65224I −8.95361 + 3.74887I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.947945 − 0.635897I
a = 0.428626 − 0.057689I
b = 1.291520 + 0.308415I
c = 1.067620 + 0.525455I
d = 0.956024 + 0.254994I
−5.38662 + 3.65224I −8.95361 − 3.74887I
u = −0.947945 − 0.635897I
a = −0.48016 − 1.96758I
b = −1.117060 + 0.479673I
c = 2.07459 + 1.34946I
d = 1.14302 − 1.63054I
−5.38662 + 3.65224I −8.95361 − 3.74887I
u = −0.538756 + 1.020250I
a = 0.569371 − 0.352320I
b = 0.270030 + 0.785880I
c = 0.149966 − 0.863957I
d = 0.01588 − 1.54419I
−0.15070 + 6.61979I −2.54938 − 5.39938I
u = −0.538756 + 1.020250I
a = 0.455847 + 0.116484I
b = 1.059250 − 0.526209I
c = −0.353472 + 1.309410I
d = −1.51255 + 2.14943I
−0.15070 + 6.61979I −2.54938 − 5.39938I
u = −0.538756 − 1.020250I
a = 0.569371 + 0.352320I
b = 0.270030 − 0.785880I
c = 0.149966 + 0.863957I
d = 0.01588 + 1.54419I
−0.15070 − 6.61979I −2.54938 + 5.39938I
u = −0.538756 − 1.020250I
a = 0.455847 − 0.116484I
b = 1.059250 + 0.526209I
c = −0.353472 − 1.309410I
d = −1.51255 − 2.14943I
−0.15070 − 6.61979I −2.54938 + 5.39938I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20232
a = 0.485197 + 1.199570I
b = −0.710226 − 0.716423I
c = −0.601344 − 0.627663I
d = 0.275293 + 1.126070I
4.04432 −0.509520
u = −1.20232
a = 0.485197 − 1.199570I
b = −0.710226 + 0.716423I
c = −0.601344 + 0.627663I
d = 0.275293 − 1.126070I
4.04432 −0.509520
u = 1.034470 + 0.639555I
a = 0.420652 − 0.055969I
b = 1.335910 + 0.310802I
c = −1.216440 − 0.247352I
d = −0.572842 + 0.270664I
−3.29566 + 8.62980I −5.39171 − 7.80256I
u = 1.034470 + 0.639555I
a = −0.40860 − 1.78861I
b = −1.121390 + 0.531363I
c = −2.28382 − 1.57837I
d = −1.32289 + 2.33789I
−3.29566 + 8.62980I −5.39171 − 7.80256I
u = 1.034470 − 0.639555I
a = 0.420652 + 0.055969I
b = 1.335910 − 0.310802I
c = −1.216440 + 0.247352I
d = −0.572842 − 0.270664I
−3.29566 − 8.62980I −5.39171 + 7.80256I
u = 1.034470 − 0.639555I
a = −0.40860 + 1.78861I
b = −1.121390 − 0.531363I
c = −2.28382 + 1.57837I
d = −1.32289 − 2.33789I
−3.29566 − 8.62980I −5.39171 + 7.80256I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.106900 + 0.677869I
a = 0.547401 + 0.638144I
b = −0.225605 − 0.902768I
c = −1.46124 − 0.05347I
d = −0.301873 + 0.919404I
−0.49001 + 7.69321I −4.38087 − 4.90752I
u = 1.106900 + 0.677869I
a = −0.42127 − 1.63805I
b = −1.147260 + 0.572609I
c = 1.63336 + 0.56943I
d = 0.89907 − 1.74265I
−0.49001 + 7.69321I −4.38087 − 4.90752I
u = 1.106900 − 0.677869I
a = 0.547401 − 0.638144I
b = −0.225605 + 0.902768I
c = −1.46124 + 0.05347I
d = −0.301873 − 0.919404I
−0.49001 − 7.69321I −4.38087 + 4.90752I
u = 1.106900 − 0.677869I
a = −0.42127 + 1.63805I
b = −1.147260 − 0.572609I
c = 1.63336 − 0.56943I
d = 0.89907 + 1.74265I
−0.49001 − 7.69321I −4.38087 + 4.90752I
u = −1.174770 + 0.565730I
a = 0.538852 − 0.710226I
b = −0.322013 + 0.893610I
c = 1.147710 + 0.342848I
d = −0.624036 + 0.312274I
4.51708 − 4.93169I 1.83206 + 3.23906I
u = −1.174770 + 0.565730I
a = −0.21563 + 1.58331I
b = −1.084450 − 0.620088I
c = −1.66173 + 0.22732I
d = 0.08624 − 1.59356I
4.51708 − 4.93169I 1.83206 + 3.23906I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.174770 − 0.565730I
a = 0.538852 + 0.710226I
b = −0.322013 − 0.893610I
c = 1.147710 − 0.342848I
d = −0.624036 − 0.312274I
4.51708 + 4.93169I 1.83206 − 3.23906I
u = −1.174770 − 0.565730I
a = −0.21563 − 1.58331I
b = −1.084450 + 0.620088I
c = −1.66173 − 0.22732I
d = 0.08624 + 1.59356I
4.51708 + 4.93169I 1.83206 − 3.23906I
u = 1.307610 + 0.109024I
a = 0.431895 + 1.046090I
b = −0.662804 − 0.816722I
c = 0.341826 + 0.976264I
d = 0.01297 − 1.72150I
7.49754 + 4.17106I 3.10533 − 3.69910I
u = 1.307610 + 0.109024I
a = 0.309103 − 1.229950I
b = −0.807809 + 0.764743I
c = 0.970909 − 0.812558I
d = −1.01374 + 1.12698I
7.49754 + 4.17106I 3.10533 − 3.69910I
u = 1.307610 − 0.109024I
a = 0.431895 − 1.046090I
b = −0.662804 + 0.816722I
c = 0.341826 − 0.976264I
d = 0.01297 + 1.72150I
7.49754 − 4.17106I 3.10533 + 3.69910I
u = 1.307610 − 0.109024I
a = 0.309103 + 1.229950I
b = −0.807809 − 0.764743I
c = 0.970909 + 0.812558I
d = −1.01374 − 1.12698I
7.49754 − 4.17106I 3.10533 + 3.69910I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.155970 + 0.720501I
a = 0.515710 − 0.630924I
b = −0.223354 + 0.950156I
c = 1.69519 + 0.06105I
d = 0.11817 + 1.56166I
1.81705 − 12.92960I −1.59130 + 8.57718I
u = −1.155970 + 0.720501I
a = −0.44919 + 1.53889I
b = −1.174790 − 0.598801I
c = −1.79988 + 0.62913I
d = −1.01052 − 2.28746I
1.81705 − 12.92960I −1.59130 + 8.57718I
u = −1.155970 − 0.720501I
a = 0.515710 + 0.630924I
b = −0.223354 − 0.950156I
c = 1.69519 − 0.06105I
d = 0.11817 − 1.56166I
1.81705 + 12.92960I −1.59130 − 8.57718I
u = −1.155970 − 0.720501I
a = −0.44919 − 1.53889I
b = −1.174790 + 0.598801I
c = −1.79988 − 0.62913I
d = −1.01052 + 2.28746I
1.81705 + 12.92960I −1.59130 − 8.57718I
u = 0.620359
a = 0.464106
b = 1.15468
c = 0.718830
d = 0.969102
−2.31973 −2.07640
u = 0.620359
a = 2.33497
b = −0.571729
c = −2.68843
d = 0.495424
−2.31973 −2.07640
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141853 + 0.491513I
a = 0.529029 − 0.029302I
b = 0.884474 + 0.104376I
c = 0.26786 − 2.67120I
d = 0.38957 − 5.63026I
−2.95645 + 1.74546I −9.67431 − 3.49934I
u = 0.141853 + 0.491513I
a = −7.80514 − 4.14749I
b = −1.099910 + 0.053090I
c = −0.694116 + 1.199210I
d = 0.084276 + 0.212896I
−2.95645 + 1.74546I −9.67431 − 3.49934I
u = 0.141853 − 0.491513I
a = 0.529029 + 0.029302I
b = 0.884474 − 0.104376I
c = 0.26786 + 2.67120I
d = 0.38957 + 5.63026I
−2.95645 − 1.74546I −9.67431 + 3.49934I
u = 0.141853 − 0.491513I
a = −7.80514 + 4.14749I
b = −1.099910 − 0.053090I
c = −0.694116 − 1.199210I
d = 0.084276 − 0.212896I
−2.95645 − 1.74546I −9.67431 + 3.49934I
28
III. I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
9
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v
0
a
12
=
v
−v
a
10
=
v
0
a
7
=
v
0
a
6
=
v − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 1
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
u
2
c
4
(u + 1)
2
c
5
, c
11
, c
12
u
2
+ u + 1
c
6
u
2
− u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0.500000 + 0.866025I
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
32
IV. I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
1
0
a
9
=
v
0
a
2
=
1
0
a
1
=
1
0
a
11
=
0
−v + 1
a
12
=
−v + 1
−v + 1
a
10
=
v
−v + 1
a
7
=
0
v − 1
a
6
=
1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 5
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
12
u
2
− u + 1
c
6
, c
11
u
2
+ u + 1
c
7
(u − 1)
2
c
9
, c
10
(u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
c
7
, c
9
, c
10
(y − 1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
36
V. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
0
−1
a
12
=
0
−1
a
10
=
−1
−1
a
7
=
0
1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
u
c
4
, c
9
, c
10
u + 1
38
(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
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
40
VI.
I
v
4
= ha, c
2
v + cv + · · · − 2ca − a, dv − 1, c
2
v
2
+ v
2
c + · · · + a
2
− av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
9
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
c
d
a
12
=
c
d − c
a
10
=
c + v
d
a
7
=
−c
−d
a
6
=
−c − 1
dc + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
+ 4c − 8
(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.
41
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 − 2.02988I −12.31897 + 3.83889I
42
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
46
+ 21u
45
+ ··· − 4u + 1)
c
2
, c
7
u
2
(u − 1)
3
(u
46
− 5u
45
+ ··· − 2u + 1)
c
3
, c
8
u
5
(u
46
+ 3u
45
+ ··· + 32u + 32)
c
4
, c
9
u
2
(u + 1)
3
(u
46
− 5u
45
+ ··· − 2u + 1)
c
5
u(u
2
− u + 1)(u
2
+ u + 1)(u
46
+ u
45
+ ··· + 2596u + 1252)
c
6
, c
12
u(u
2
− u + 1)(u
2
+ u + 1)(u
46
− u
45
+ ··· + 4u + 4)
c
10
u
2
(u + 1)
3
(u
46
+ 21u
45
+ ··· − 4u + 1)
c
11
u(u
2
+ u + 1)
2
(u
46
− 21u
45
+ ··· + 40u + 16)
43
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
(y − 1)
3
(y
46
+ 19y
45
+ ··· − 72y + 1)
c
2
, c
4
, c
7
c
9
y
2
(y − 1)
3
(y
46
− 21y
45
+ ··· + 4y + 1)
c
3
, c
8
y
5
(y
46
− 15y
45
+ ··· + 4096y + 1024)
c
5
y(y
2
+ y + 1)
2
(y
46
− 3y
45
+ ··· − 2.04086 × 10
7
y + 1567504)
c
6
, c
12
y(y
2
+ y + 1)
2
(y
46
+ 21y
45
+ ··· − 40y + 16)
c
11
y(y
2
+ y + 1)
2
(y
46
+ 9y
45
+ ··· − 5664y + 256)
44
