12a
0029
(K12a
0029
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 4 11 8 1 7
Solving Sequence
4,9 2,5
3
6,11
10 1 8 7 12
c
4
c
2
c
5
c
9
c
1
c
8
c
7
c
12
c
3
, c
6
, c
10
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.48200 × 10
61
u
45
− 9.22155 × 10
61
u
44
+ ··· + 1.04756 × 10
63
d − 1.67459 × 10
63
,
7.62250 × 10
61
u
45
− 1.89258 × 10
62
u
44
+ ··· + 2.09512 × 10
63
c − 3.36115 × 10
63
,
1.37141 × 10
61
u
45
− 2.04563 × 10
61
u
44
+ ··· + 1.04756 × 10
63
b − 1.27647 × 10
63
,
7.65358 × 10
61
u
45
− 2.24209 × 10
62
u
44
+ ··· + 1.04756 × 10
63
a − 1.33042 × 10
62
, u
46
− 3u
45
+ ··· − 32u + 32i
I
u
2
= h−5.05017 × 10
19
cu
37
+ 2.57220 × 10
19
u
37
+ ··· + 1.77366 × 10
20
c + 1.40518 × 10
20
,
− 1.48141 × 10
20
cu
37
+ 8.78585 × 10
19
u
37
+ ··· + 1.69449 × 10
19
c − 1.02888 × 10
20
,
− 3.80860 × 10
20
u
37
− 1.22578 × 10
20
u
36
+ ··· + 3.70123 × 10
20
b + 1.73663 × 10
21
,
− 9.01587 × 10
20
u
37
− 1.40080 × 10
20
u
36
+ ··· + 7.40247 × 10
20
a + 2.56553 × 10
21
, u
38
+ u
37
+ ··· + 4u − 4i
I
v
1
= ha, d, c − v, b − v, v
2
− v + 1i
I
v
2
= ha, d − v + 1, −av + c + 1, b − v, v
2
− v + 1i
I
v
3
= hc, d − 1, b, a − 1, v + 1i
I
v
4
= ha, db + da − cb − d + b − 1, a
2
d − cba − da + cb + ba + d − c − a + 1, dv + 1, cv − ba − bv + b + a,
b
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
= h4.48 × 10
61
u
45
− 9.22 × 10
61
u
44
+ · · · + 1.05 × 10
63
d − 1.67 ×
10
63
, 7.62 × 10
61
u
45
− 1.89 × 10
62
u
44
+ · · · + 2.10 × 10
63
c − 3.36 × 10
63
, 1.37 ×
10
61
u
45
− 2.05 × 10
61
u
44
+ · · · + 1.05 × 10
63
b − 1.28 × 10
63
, 7.65 × 10
61
u
45
−
2.24 × 10
62
u
44
+ · · · + 1.05 × 10
63
a − 1.33 × 10
62
, u
46
− 3u
45
+ · · · − 32u + 32i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−0.0730608u
45
+ 0.214029u
44
+ ··· − 11.1865u + 0.127001
−0.0130915u
45
+ 0.0195275u
44
+ ··· + 0.982266u + 1.21851
a
5
=
1
u
2
a
3
=
−0.107506u
45
+ 0.286640u
44
+ ··· − 12.3773u + 1.18060
−0.0329822u
45
+ 0.0562768u
44
+ ··· + 1.10132u + 2.20169
a
6
=
−0.0337179u
45
+ 0.143074u
44
+ ··· − 8.46741u + 4.71002
0.0470900u
45
− 0.103838u
44
+ ··· + 1.16123u − 2.01452
a
11
=
−0.0363821u
45
+ 0.0903327u
44
+ ··· − 1.88200u + 1.60427
−0.0427850u
45
+ 0.0880286u
44
+ ··· + 0.686956u + 1.59856
a
10
=
−0.0168951u
45
+ 0.0465535u
44
+ ··· − 1.39848u + 0.915857
−0.0232980u
45
+ 0.0442495u
44
+ ··· + 1.17047u + 0.910145
a
1
=
−0.0808079u
45
+ 0.246912u
44
+ ··· − 9.62863u + 6.72455
−0.0570466u
45
+ 0.0968746u
44
+ ··· + 1.56827u + 1.87088
a
8
=
u
u
a
7
=
0.00655998u
45
− 0.0259377u
44
+ ··· + 2.00677u − 0.607746
−0.0298221u
45
+ 0.0643950u
44
+ ··· + 0.124764u + 0.996524
a
12
=
−0.0639128u
45
+ 0.200359u
44
+ ··· − 8.23015u + 5.80869
−0.0337486u
45
+ 0.0526252u
44
+ ··· + 1.39779u + 0.960739
(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
u
46
+ 21u
45
+ ··· − 40u + 16
c
2
, c
5
u
46
+ u
45
+ ··· − 4u + 4
c
3
u
46
− u
45
+ ··· − 2596u + 1252
c
4
, c
8
u
46
− 3u
45
+ ··· − 32u + 32
c
6
, c
7
, c
10
c
12
u
46
+ 5u
45
+ ··· + 2u + 1
c
9
, c
11
u
46
− 21u
45
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 9y
45
+ ··· − 5664y + 256
c
2
, c
5
y
46
+ 21y
45
+ ··· − 40y + 16
c
3
y
46
− 3y
45
+ ··· − 20408552y + 1567504
c
4
, c
8
y
46
− 15y
45
+ ··· + 4096y + 1024
c
6
, c
7
, c
10
c
12
y
46
− 21y
45
+ ··· + 4y + 1
c
9
, c
11
y
46
+ 19y
45
+ ··· − 72y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248116 + 0.949341I
a = 0.659883 − 0.533852I
b = 0.16697 + 1.82340I
c = −0.570373 + 0.029986I
d = −0.088362 + 0.621385I
−1.66114 + 2.12776I −0.422256 − 0.234121I
u = 0.248116 − 0.949341I
a = 0.659883 + 0.533852I
b = 0.16697 − 1.82340I
c = −0.570373 − 0.029986I
d = −0.088362 − 0.621385I
−1.66114 − 2.12776I −0.422256 + 0.234121I
u = −0.642875 + 0.814816I
a = 0.006254 + 1.275600I
b = 0.634122 + 0.252731I
c = −1.335160 − 0.293800I
d = −0.362590 + 0.315550I
5.93091 − 3.99675I 10.51051 + 4.44974I
u = −0.642875 − 0.814816I
a = 0.006254 − 1.275600I
b = 0.634122 − 0.252731I
c = −1.335160 + 0.293800I
d = −0.362590 − 0.315550I
5.93091 + 3.99675I 10.51051 − 4.44974I
u = −0.046642 + 1.050320I
a = 0.666501 + 0.584237I
b = −0.27294 − 1.79729I
c = −0.807442 − 0.110962I
d = −0.214208 + 0.539648I
−2.04690 − 4.94372I 0.16550 + 7.58166I
u = −0.046642 − 1.050320I
a = 0.666501 − 0.584237I
b = −0.27294 + 1.79729I
c = −0.807442 + 0.110962I
d = −0.214208 − 0.539648I
−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 = −3.11307 − 1.54198I
b = 1.05080 − 1.50344I
c = 1.39259 − 0.38277I
d = 0.334763 + 0.277573I
4.70063 − 1.01560I 8.78023 + 1.30126I
u = 0.614432 − 0.696436I
a = −3.11307 + 1.54198I
b = 1.05080 + 1.50344I
c = 1.39259 + 0.38277I
d = 0.334763 − 0.277573I
4.70063 + 1.01560I 8.78023 − 1.30126I
u = 0.904459 + 0.035006I
a = 0.684510 + 0.349167I
b = 1.217210 − 0.498628I
c = 0.226719 − 0.709857I
d = 0.94895 − 1.25909I
0.23417 − 4.06154I 0.42563 + 7.90074I
u = 0.904459 − 0.035006I
a = 0.684510 − 0.349167I
b = 1.217210 + 0.498628I
c = 0.226719 + 0.709857I
d = 0.94895 + 1.25909I
0.23417 + 4.06154I 0.42563 − 7.90074I
u = 0.517103 + 1.038360I
a = 0.728606 + 0.786743I
b = −1.25298 − 0.96152I
c = 1.178790 − 0.188129I
d = 0.361203 + 0.412386I
0.12548 + 4.11136I 2.46017 − 3.87123I
u = 0.517103 − 1.038360I
a = 0.728606 − 0.786743I
b = −1.25298 + 0.96152I
c = 1.178790 + 0.188129I
d = 0.361203 − 0.412386I
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 = 0.853788 + 0.005623I
b = −0.0664210 + 0.0072212I
c = 0.617736 − 0.298148I
d = 0.123361 + 0.470883I
0.79101 + 1.46703I 5.32252 − 4.75359I
u = 0.017678 − 0.820472I
a = 0.853788 − 0.005623I
b = −0.0664210 − 0.0072212I
c = 0.617736 + 0.298148I
d = 0.123361 − 0.470883I
0.79101 − 1.46703I 5.32252 + 4.75359I
u = 1.006520 + 0.624064I
a = 0.618102 − 0.412984I
b = 1.58573 + 1.52879I
c = 0.186343 − 1.252860I
d = 0.75459 − 2.11694I
3.52144 − 4.08819I 5.82465 + 4.54278I
u = 1.006520 − 0.624064I
a = 0.618102 + 0.412984I
b = 1.58573 − 1.52879I
c = 0.186343 + 1.252860I
d = 0.75459 + 2.11694I
3.52144 + 4.08819I 5.82465 − 4.54278I
u = −1.071740 + 0.508840I
a = 0.249412 + 0.451516I
b = −0.037567 + 0.421763I
c = 0.237093 + 0.582132I
d = −0.291926 + 1.082080I
−1.98761 + 2.55534I 0.98949 − 1.01939I
u = −1.071740 − 0.508840I
a = 0.249412 − 0.451516I
b = −0.037567 − 0.421763I
c = 0.237093 − 0.582132I
d = −0.291926 − 1.082080I
−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 = 0.701991 − 0.351361I
b = 1.056930 + 0.488868I
c = −0.192599 + 0.514963I
d = −0.891839 + 0.948808I
0.274017 + 1.087600I −0.651009 + 0.594713I
u = −0.807683 − 0.082878I
a = 0.701991 + 0.351361I
b = 1.056930 − 0.488868I
c = −0.192599 − 0.514963I
d = −0.891839 − 0.948808I
0.274017 − 1.087600I −0.651009 − 0.594713I
u = −0.668777 + 1.013930I
a = 0.733154 − 0.148233I
b = 0.143797 − 0.527077I
c = −1.276030 − 0.170948I
d = −0.403997 + 0.376312I
4.90536 − 6.51831I 8.90536 + 4.64881I
u = −0.668777 − 1.013930I
a = 0.733154 + 0.148233I
b = 0.143797 + 0.527077I
c = −1.276030 + 0.170948I
d = −0.403997 − 0.376312I
4.90536 + 6.51831I 8.90536 − 4.64881I
u = −1.035500 + 0.682470I
a = 0.691378 − 0.235874I
b = 0.882817 − 0.508436I
c = −0.156215 − 1.277950I
d = −0.69298 − 2.14399I
4.70874 + 9.62616I 7.79470 − 8.99124I
u = −1.035500 − 0.682470I
a = 0.691378 + 0.235874I
b = 0.882817 + 0.508436I
c = −0.156215 + 1.277950I
d = −0.69298 + 2.14399I
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 = 0.253462 − 0.169367I
b = −0.320531 − 0.225417I
c = 0.050461 − 0.989550I
d = 0.63809 − 1.66040I
−3.57586 − 5.30392I 1.93777 + 5.96454I
u = 1.224990 − 0.226721I
a = 0.253462 + 0.169367I
b = −0.320531 + 0.225417I
c = 0.050461 + 0.989550I
d = 0.63809 + 1.66040I
−3.57586 + 5.30392I 1.93777 − 5.96454I
u = 1.195740 + 0.364671I
a = 0.44005 + 1.75493I
b = −1.22042 + 1.50844I
c = −0.186101 + 0.688056I
d = 0.356273 + 1.213420I
−6.39735 + 0.44189I −4.43091 − 2.06201I
u = 1.195740 − 0.364671I
a = 0.44005 − 1.75493I
b = −1.22042 − 1.50844I
c = −0.186101 − 0.688056I
d = 0.356273 − 1.213420I
−6.39735 − 0.44189I −4.43091 + 2.06201I
u = 0.687704 + 1.079720I
a = 0.598930 − 0.485617I
b = 0.89116 + 2.33948I
c = 1.270960 − 0.132505I
d = 0.421173 + 0.392926I
2.74057 + 11.63170I 5.60201 − 8.64749I
u = 0.687704 − 1.079720I
a = 0.598930 + 0.485617I
b = 0.89116 − 2.33948I
c = 1.270960 + 0.132505I
d = 0.421173 − 0.392926I
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 = −1.27784 − 1.84483I
b = 0.63049 − 2.44257I
c = −0.292580 + 0.618138I
d = 0.226552 + 1.126520I
−4.42926 − 7.47789I −1.74286 + 4.84208I
u = 1.158970 − 0.578549I
a = −1.27784 + 1.84483I
b = 0.63049 + 2.44257I
c = −0.292580 − 0.618138I
d = 0.226552 − 1.126520I
−4.42926 + 7.47789I −1.74286 − 4.84208I
u = −1.311140 + 0.102134I
a = 0.00268 − 1.92087I
b = −0.86720 − 2.10727I
c = 0.030662 − 0.940031I
d = −0.53344 − 1.57008I
−7.51022 + 1.50301I −3.10935 − 2.27720I
u = −1.311140 − 0.102134I
a = 0.00268 + 1.92087I
b = −0.86720 + 2.10727I
c = 0.030662 + 0.940031I
d = −0.53344 + 1.57008I
−7.51022 − 1.50301I −3.10935 + 2.27720I
u = −0.435796 + 0.485308I
a = 0.873003 − 0.355186I
b = 0.215705 + 0.325189I
c = 0.168435 + 0.132484I
d = −0.223442 + 0.550785I
−0.084212 + 1.381070I −0.30299 − 4.86269I
u = −0.435796 − 0.485308I
a = 0.873003 + 0.355186I
b = 0.215705 − 0.325189I
c = 0.168435 − 0.132484I
d = −0.223442 − 0.550785I
−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 = −0.68441 + 1.94019I
b = −0.04666 + 2.56224I
c = −0.010549 − 1.050770I
d = −0.56280 − 1.73815I
−6.69471 + 9.89538I −1.12698 − 9.02462I
u = −1.316840 − 0.304432I
a = −0.68441 − 1.94019I
b = −0.04666 − 2.56224I
c = −0.010549 + 1.050770I
d = −0.56280 + 1.73815I
−6.69471 − 9.89538I −1.12698 + 9.02462I
u = −1.118430 + 0.781907I
a = 0.006550 + 0.558246I
b = 0.136959 + 0.741041I
c = −0.096143 − 1.306940I
d = −0.58055 − 2.15879I
3.44989 + 13.07100I 7.52581 − 7.90184I
u = −1.118430 − 0.781907I
a = 0.006550 − 0.558246I
b = 0.136959 − 0.741041I
c = −0.096143 + 1.306940I
d = −0.58055 + 2.15879I
3.44989 − 13.07100I 7.52581 + 7.90184I
u = 1.166960 + 0.709743I
a = 0.55758 + 1.32715I
b = −1.85153 + 0.87351I
c = 0.086648 − 1.266670I
d = 0.58757 − 2.09046I
−1.96462 − 10.42030I 0. + 7.01224I
u = 1.166960 − 0.709743I
a = 0.55758 − 1.32715I
b = −1.85153 − 0.87351I
c = 0.086648 + 1.266670I
d = 0.58757 + 2.09046I
−1.96462 + 10.42030I 0. − 7.01224I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.144720 + 0.813548I
a = −1.46199 − 1.44274I
b = 1.12386 − 2.52551I
c = 0.079457 − 1.315210I
d = 0.54947 − 2.16215I
1.2351 − 18.4885I 4.00000 + 11.60486I
u = 1.144720 − 0.813548I
a = −1.46199 + 1.44274I
b = 1.12386 + 2.52551I
c = 0.079457 + 1.315210I
d = 0.54947 + 2.16215I
1.2351 + 18.4885I 4.00000 − 11.60486I
u = 0.068034 + 0.485475I
a = −3.28852 − 7.48764I
b = 0.699694 + 0.686768I
c = 0.39729 − 1.46311I
d = 0.044140 + 0.259666I
2.91211 + 2.24138I 11.31463 − 3.80305I
u = 0.068034 − 0.485475I
a = −3.28852 + 7.48764I
b = 0.699694 − 0.686768I
c = 0.39729 + 1.46311I
d = 0.044140 − 0.259666I
2.91211 − 2.24138I 11.31463 + 3.80305I
12
II. I
u
2
= h−5.05 × 10
19
cu
37
+ 2.57 × 10
19
u
37
+ · · · + 1.77 × 10
20
c + 1.41 ×
10
20
, −1.48×10
20
cu
37
+8.79×10
19
u
37
+· · ·+1.69×10
19
c−1.03×10
20
, −3.81×
10
20
u
37
− 1.23 × 10
20
u
36
+ · · · + 3.70 × 10
20
b + 1.74 × 10
21
, −9.02 × 10
20
u
37
−
1.40 × 10
20
u
36
+ · · · + 7.40 × 10
20
a + 2.57 × 10
21
, u
38
+ u
37
+ · · · + 4u − 4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
1.21795u
37
+ 0.189235u
36
+ ··· + 8.79024u − 3.46578
1.02901u
37
+ 0.331181u
36
+ ··· + 9.83857u − 4.69204
a
5
=
1
u
2
a
3
=
1.53590u
37
+ 0.295833u
36
+ ··· + 9.64211u − 4.04294
1.20001u
37
+ 0.438425u
36
+ ··· + 11.9557u − 5.53741
a
6
=
0.904497u
37
− 0.262263u
36
+ ··· + 5.27517u − 2.04692
0.358591u
37
− 0.434315u
36
+ ··· + 1.07020u − 1.14792
a
11
=
c
0.272891cu
37
− 0.138991u
37
+ ··· − 0.958415c − 0.759301
a
10
=
−0.395649cu
37
+ 0.295906u
37
+ ··· + 3.20198c − 1.89901
−0.122758cu
37
+ 0.156914u
37
+ ··· + 1.24357c − 2.65831
a
1
=
0.545906u
37
+ 0.172052u
36
+ ··· + 4.20498u − 0.899010
−0.0826896u
37
+ 0.291100u
36
+ ··· + 2.60884u − 0.347500
a
8
=
u
u
a
7
=
0.272891cu
37
− 0.138991u
37
+ ··· − 1.95842c − 0.759301
0.272891cu
37
− 0.138991u
37
+ ··· − 0.958415c − 0.759301
a
12
=
0.373854cu
37
+ 1.39231u
37
+ ··· − 1.18362c − 3.88958
−0.100899cu
37
+ 0.624721u
37
+ ··· − 0.627657c − 4.09737
(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
38
+ 18u
37
+ ··· − 5u + 1)
2
c
2
(u
38
+ 2u
37
+ ··· + 5u + 1)
2
c
3
(u
38
− 2u
37
+ ··· − 37u + 17)
2
c
4
(u
38
+ u
37
+ ··· + 4u − 4)
2
c
5
(u
38
− 2u
37
+ ··· − 5u + 1)
2
c
6
, c
7
u
76
+ 3u
75
+ ··· − 104u − 16
c
8
(u
38
− u
37
+ ··· − 4u − 4)
2
c
9
u
76
− 43u
75
+ ··· − 800u + 256
c
10
, c
12
− u
76
+ 3u
75
+ ··· − 104u + 16
c
11
u
76
+ 43u
75
+ ··· + 800u + 256
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 6y
37
+ ··· − 61y + 1)
2
c
2
, c
5
(y
38
+ 18y
37
+ ··· − 5y + 1)
2
c
3
(y
38
− 6y
37
+ ··· − 6333y + 289)
2
c
4
, c
8
(y
38
− 15y
37
+ ··· − 72y + 16)
2
c
6
, c
7
, c
10
c
12
y
76
− 43y
75
+ ··· − 800y + 256
c
9
, c
11
y
76
− 23y
75
+ ··· − 1516032y + 65536
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718175 + 0.689913I
a = 0.759326 − 0.224057I
b = 0.474987 − 0.230385I
c = −0.31772 − 1.41713I
d = −0.91042 − 2.46929I
6.09366 + 1.46931I 10.87065 − 3.08473I
u = −0.718175 + 0.689913I
a = 0.759326 − 0.224057I
b = 0.474987 − 0.230385I
c = −1.44823 − 0.31091I
d = −0.371242 + 0.261333I
6.09366 + 1.46931I 10.87065 − 3.08473I
u = −0.718175 − 0.689913I
a = 0.759326 + 0.224057I
b = 0.474987 + 0.230385I
c = −0.31772 + 1.41713I
d = −0.91042 + 2.46929I
6.09366 − 1.46931I 10.87065 + 3.08473I
u = −0.718175 − 0.689913I
a = 0.759326 + 0.224057I
b = 0.474987 + 0.230385I
c = −1.44823 + 0.31091I
d = −0.371242 − 0.261333I
6.09366 − 1.46931I 10.87065 + 3.08473I
u = −0.257524 + 0.984493I
a = 0.730146 − 0.660359I
b = −0.70295 + 1.28730I
c = −0.967410 − 0.240606I
d = −0.263329 + 0.455019I
−1.60581 + 0.49664I −0.272784 − 1.115032I
u = −0.257524 + 0.984493I
a = 0.730146 − 0.660359I
b = −0.70295 + 1.28730I
c = 0.593095 + 0.049873I
d = 0.100752 + 0.635092I
−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 = 0.730146 + 0.660359I
b = −0.70295 − 1.28730I
c = −0.967410 + 0.240606I
d = −0.263329 − 0.455019I
−1.60581 − 0.49664I −0.272784 + 1.115032I
u = −0.257524 − 0.984493I
a = 0.730146 + 0.660359I
b = −0.70295 − 1.28730I
c = 0.593095 − 0.049873I
d = 0.100752 − 0.635092I
−1.60581 − 0.49664I −0.272784 + 1.115032I
u = −0.924425 + 0.450549I
a = −1.61291 + 2.52841I
b = 0.52794 + 1.92562I
c = 0.171561 + 0.498961I
d = −0.364946 + 0.973548I
0.88516 + 3.95746I 1.72480 − 4.57056I
u = −0.924425 + 0.450549I
a = −1.61291 + 2.52841I
b = 0.52794 + 1.92562I
c = −1.63227 − 0.20134I
d = −0.419779 + 0.157998I
0.88516 + 3.95746I 1.72480 − 4.57056I
u = −0.924425 − 0.450549I
a = −1.61291 − 2.52841I
b = 0.52794 − 1.92562I
c = 0.171561 − 0.498961I
d = −0.364946 − 0.973548I
0.88516 − 3.95746I 1.72480 + 4.57056I
u = −0.924425 − 0.450549I
a = −1.61291 − 2.52841I
b = 0.52794 − 1.92562I
c = −1.63227 + 0.20134I
d = −0.419779 − 0.157998I
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 = 0.779777 + 0.149134I
b = 0.134208 + 0.296022I
c = 1.227900 − 0.296771I
d = 0.335612 + 0.358410I
2.26472 + 1.90334I 6.18021 − 1.07076I
u = 0.531079 + 0.883531I
a = 0.779777 + 0.149134I
b = 0.134208 + 0.296022I
c = −0.458700 + 0.220577I
d = 0.014532 + 0.739994I
2.26472 + 1.90334I 6.18021 − 1.07076I
u = 0.531079 − 0.883531I
a = 0.779777 − 0.149134I
b = 0.134208 − 0.296022I
c = 1.227900 + 0.296771I
d = 0.335612 − 0.358410I
2.26472 − 1.90334I 6.18021 + 1.07076I
u = 0.531079 − 0.883531I
a = 0.779777 − 0.149134I
b = 0.134208 − 0.296022I
c = −0.458700 − 0.220577I
d = 0.014532 − 0.739994I
2.26472 − 1.90334I 6.18021 + 1.07076I
u = −0.860778 + 0.429023I
a = 0.649690 + 0.406518I
b = 1.31432 − 1.20770I
c = −0.351705 − 1.146920I
d = −1.07373 − 1.99897I
1.135440 − 0.390890I 2.15175 − 1.14697I
u = −0.860778 + 0.429023I
a = 0.649690 + 0.406518I
b = 1.31432 − 1.20770I
c = 0.145196 + 0.457097I
d = −0.391254 + 0.916323I
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 = 0.649690 − 0.406518I
b = 1.31432 + 1.20770I
c = −0.351705 + 1.146920I
d = −1.07373 + 1.99897I
1.135440 + 0.390890I 2.15175 + 1.14697I
u = −0.860778 − 0.429023I
a = 0.649690 − 0.406518I
b = 1.31432 + 1.20770I
c = 0.145196 − 0.457097I
d = −0.391254 − 0.916323I
1.135440 + 0.390890I 2.15175 + 1.14697I
u = 0.959864 + 0.423605I
a = 0.91740 + 1.74027I
b = −0.949339 + 0.978173I
c = 0.262143 − 1.119880I
d = 0.93067 − 1.92567I
0.93346 − 1.43399I 1.64648 + 2.88902I
u = 0.959864 + 0.423605I
a = 0.91740 + 1.74027I
b = −0.949339 + 0.978173I
c = 1.64185 − 0.17843I
d = 0.430009 + 0.146452I
0.93346 − 1.43399I 1.64648 + 2.88902I
u = 0.959864 − 0.423605I
a = 0.91740 − 1.74027I
b = −0.949339 − 0.978173I
c = 0.262143 + 1.119880I
d = 0.93067 + 1.92567I
0.93346 + 1.43399I 1.64648 − 2.88902I
u = 0.959864 − 0.423605I
a = 0.91740 − 1.74027I
b = −0.949339 − 0.978173I
c = 1.64185 + 0.17843I
d = 0.430009 − 0.146452I
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 = 0.647196 − 0.465482I
b = 0.84895 + 1.68623I
c = 1.344230 − 0.369647I
d = 0.333035 + 0.298147I
4.63851 + 3.34557I 8.53398 − 2.94107I
u = 0.590924 + 0.743055I
a = 0.647196 − 0.465482I
b = 0.84895 + 1.68623I
c = 0.32357 − 1.52942I
d = 0.87033 − 2.69031I
4.63851 + 3.34557I 8.53398 − 2.94107I
u = 0.590924 − 0.743055I
a = 0.647196 + 0.465482I
b = 0.84895 − 1.68623I
c = 1.344230 + 0.369647I
d = 0.333035 − 0.298147I
4.63851 − 3.34557I 8.53398 + 2.94107I
u = 0.590924 − 0.743055I
a = 0.647196 + 0.465482I
b = 0.84895 − 1.68623I
c = 0.32357 + 1.52942I
d = 0.87033 + 2.69031I
4.63851 − 3.34557I 8.53398 + 2.94107I
u = −0.944268 + 0.080074I
a = 0.47872 − 2.76266I
b = −0.35670 − 1.46996I
c = −0.105277 + 0.649327I
d = −0.762060 + 1.161940I
−0.25240 − 2.75914I −1.19764 + 4.35912I
u = −0.944268 + 0.080074I
a = 0.47872 − 2.76266I
b = −0.35670 − 1.46996I
c = −1.77987 − 0.04841I
d = −0.411287 + 0.028167I
−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 = 0.47872 + 2.76266I
b = −0.35670 + 1.46996I
c = −0.105277 − 0.649327I
d = −0.762060 − 1.161940I
−0.25240 + 2.75914I −1.19764 − 4.35912I
u = −0.944268 − 0.080074I
a = 0.47872 + 2.76266I
b = −0.35670 + 1.46996I
c = −1.77987 + 0.04841I
d = −0.411287 − 0.028167I
−0.25240 + 2.75914I −1.19764 − 4.35912I
u = 0.932230 + 0.544110I
a = 0.711056 + 0.261382I
b = 0.873920 + 0.226986I
c = 0.256252 − 1.221400I
d = 0.88507 − 2.09363I
2.05024 − 4.86305I 4.53119 + 6.13263I
u = 0.932230 + 0.544110I
a = 0.711056 + 0.261382I
b = 0.873920 + 0.226986I
c = −0.235604 + 0.489367I
d = 0.285549 + 0.970591I
2.05024 − 4.86305I 4.53119 + 6.13263I
u = 0.932230 − 0.544110I
a = 0.711056 − 0.261382I
b = 0.873920 − 0.226986I
c = 0.256252 + 1.221400I
d = 0.88507 + 2.09363I
2.05024 + 4.86305I 4.53119 − 6.13263I
u = 0.932230 − 0.544110I
a = 0.711056 − 0.261382I
b = 0.873920 − 0.226986I
c = −0.235604 − 0.489367I
d = 0.285549 − 0.970591I
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 = 0.675134 − 0.882504I
b = 0.244504 − 0.127412I
c = −0.208049 + 0.334490I
d = 0.283657 + 0.784026I
2.72088 + 0.47986I 5.93461 + 0.48126I
u = 0.708662 + 0.534244I
a = 0.675134 − 0.882504I
b = 0.244504 − 0.127412I
c = 1.57174 − 0.36447I
d = 0.350066 + 0.206079I
2.72088 + 0.47986I 5.93461 + 0.48126I
u = 0.708662 − 0.534244I
a = 0.675134 + 0.882504I
b = 0.244504 + 0.127412I
c = −0.208049 − 0.334490I
d = 0.283657 − 0.784026I
2.72088 − 0.47986I 5.93461 − 0.48126I
u = 0.708662 − 0.534244I
a = 0.675134 + 0.882504I
b = 0.244504 + 0.127412I
c = 1.57174 + 0.36447I
d = 0.350066 − 0.206079I
2.72088 − 0.47986I 5.93461 − 0.48126I
u = −0.947945 + 0.635897I
a = 0.229415 + 0.658277I
b = 0.175268 + 0.437196I
c = −0.217424 − 1.276340I
d = −0.79602 − 2.17049I
5.38662 + 3.65224I 8.95361 − 3.74887I
u = −0.947945 + 0.635897I
a = 0.229415 + 0.658277I
b = 0.175268 + 0.437196I
c = −1.53314 − 0.18806I
d = −0.442998 + 0.217877I
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 = 0.229415 − 0.658277I
b = 0.175268 − 0.437196I
c = −0.217424 + 1.276340I
d = −0.79602 + 2.17049I
5.38662 − 3.65224I 8.95361 + 3.74887I
u = −0.947945 − 0.635897I
a = 0.229415 − 0.658277I
b = 0.175268 − 0.437196I
c = −1.53314 + 0.18806I
d = −0.442998 − 0.217877I
5.38662 − 3.65224I 8.95361 + 3.74887I
u = −0.538756 + 1.020250I
a = 0.619031 + 0.499374I
b = 0.63204 − 2.14935I
c = −1.196440 − 0.196554I
d = −0.364434 + 0.402323I
0.15070 − 6.61979I 2.54938 + 5.39938I
u = −0.538756 + 1.020250I
a = 0.619031 + 0.499374I
b = 0.63204 − 2.14935I
c = 0.545739 + 0.245695I
d = 0.052704 + 0.770717I
0.15070 − 6.61979I 2.54938 + 5.39938I
u = −0.538756 − 1.020250I
a = 0.619031 − 0.499374I
b = 0.63204 + 2.14935I
c = −1.196440 + 0.196554I
d = −0.364434 − 0.402323I
0.15070 + 6.61979I 2.54938 − 5.39938I
u = −0.538756 − 1.020250I
a = 0.619031 − 0.499374I
b = 0.63204 + 2.14935I
c = 0.545739 − 0.245695I
d = 0.052704 − 0.770717I
0.15070 + 6.61979I 2.54938 − 5.39938I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20232
a = 0.295778
b = −0.330847
c = 0.007353 + 0.846402I
d = −0.58336 + 1.44227I
−4.04432 0.509520
u = −1.20232
a = 0.295778
b = −0.330847
c = 0.007353 − 0.846402I
d = −0.58336 − 1.44227I
−4.04432 0.509520
u = 1.034470 + 0.639555I
a = −1.59290 − 1.84692I
b = 0.81702 − 2.22810I
c = 0.166717 − 1.255100I
d = 0.72123 − 2.11158I
3.29566 − 8.62980I 5.39171 + 7.80256I
u = 1.034470 + 0.639555I
a = −1.59290 − 1.84692I
b = 0.81702 − 2.22810I
c = 1.53962 − 0.14913I
d = 0.470945 + 0.211132I
3.29566 − 8.62980I 5.39171 + 7.80256I
u = 1.034470 − 0.639555I
a = −1.59290 + 1.84692I
b = 0.81702 + 2.22810I
c = 0.166717 + 1.255100I
d = 0.72123 + 2.11158I
3.29566 + 8.62980I 5.39171 − 7.80256I
u = 1.034470 − 0.639555I
a = −1.59290 + 1.84692I
b = 0.81702 + 2.22810I
c = 1.53962 + 0.14913I
d = 0.470945 − 0.211132I
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 = 0.097757 − 0.529135I
b = 0.057337 − 0.616881I
c = 0.120703 − 1.260900I
d = 0.64408 − 2.09872I
0.49001 − 7.69321I 4.38087 + 4.90752I
u = 1.106900 + 0.677869I
a = 0.097757 − 0.529135I
b = 0.057337 − 0.616881I
c = −0.338125 + 0.575068I
d = 0.173339 + 1.077430I
0.49001 − 7.69321I 4.38087 + 4.90752I
u = 1.106900 − 0.677869I
a = 0.097757 + 0.529135I
b = 0.057337 + 0.616881I
c = 0.120703 + 1.260900I
d = 0.64408 + 2.09872I
0.49001 + 7.69321I 4.38087 − 4.90752I
u = 1.106900 − 0.677869I
a = 0.097757 + 0.529135I
b = 0.057337 + 0.616881I
c = −0.338125 − 0.575068I
d = 0.173339 − 1.077430I
0.49001 + 7.69321I 4.38087 − 4.90752I
u = −1.174770 + 0.565730I
a = 0.54948 − 1.48780I
b = −1.57912 − 1.14053I
c = −0.099407 − 1.192690I
d = −0.64241 − 1.98202I
−4.51708 + 4.93169I −1.83206 − 3.23906I
u = −1.174770 + 0.565730I
a = 0.54948 − 1.48780I
b = −1.57912 − 1.14053I
c = 0.288625 + 0.628881I
d = −0.231233 + 1.139200I
−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 = 0.54948 + 1.48780I
b = −1.57912 + 1.14053I
c = −0.099407 + 1.192690I
d = −0.64241 + 1.98202I
−4.51708 − 4.93169I −1.83206 + 3.23906I
u = −1.174770 − 0.565730I
a = 0.54948 + 1.48780I
b = −1.57912 + 1.14053I
c = 0.288625 − 0.628881I
d = −0.231233 − 1.139200I
−4.51708 − 4.93169I −1.83206 + 3.23906I
u = 1.307610 + 0.109024I
a = −0.34714 − 2.01472I
b = −0.43751 − 2.35043I
c = −0.026803 − 0.942642I
d = 0.53828 − 1.57459I
−7.49754 − 4.17106I −3.10533 + 3.69910I
u = 1.307610 + 0.109024I
a = −0.34714 − 2.01472I
b = −0.43751 − 2.35043I
c = −0.104395 + 0.836665I
d = 0.45070 + 1.41497I
−7.49754 − 4.17106I −3.10533 + 3.69910I
u = 1.307610 − 0.109024I
a = −0.34714 + 2.01472I
b = −0.43751 + 2.35043I
c = −0.026803 + 0.942642I
d = 0.53828 + 1.57459I
−7.49754 + 4.17106I −3.10533 − 3.69910I
u = 1.307610 − 0.109024I
a = −0.34714 + 2.01472I
b = −0.43751 + 2.35043I
c = −0.104395 − 0.836665I
d = 0.45070 − 1.41497I
−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 = −1.40371 + 1.59813I
b = 0.92356 + 2.51029I
c = −0.090116 − 1.273270I
d = −0.58952 − 2.10255I
−1.81705 + 12.92960I 1.59130 − 8.57718I
u = −1.155970 + 0.720501I
a = −1.40371 + 1.59813I
b = 0.92356 + 2.51029I
c = 0.366569 + 0.595652I
d = −0.141563 + 1.100900I
−1.81705 + 12.92960I 1.59130 − 8.57718I
u = −1.155970 − 0.720501I
a = −1.40371 − 1.59813I
b = 0.92356 − 2.51029I
c = −0.090116 + 1.273270I
d = −0.58952 + 2.10255I
−1.81705 − 12.92960I 1.59130 + 8.57718I
u = −1.155970 − 0.720501I
a = −1.40371 − 1.59813I
b = 0.92356 − 2.51029I
c = 0.366569 − 0.595652I
d = −0.141563 − 1.100900I
−1.81705 − 12.92960I 1.59130 + 8.57718I
u = 0.620359
a = 0.850291
b = −0.0134746
c = 0.526910
d = 1.44852
2.31973 2.07640
u = 0.620359
a = 0.850291
b = −0.0134746
c = 2.14922
d = 0.287912
2.31973 2.07640
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141853 + 0.491513I
a = 0.789501 + 0.479357I
b = 0.173722 − 0.874524I
c = 0.76489 − 1.34869I
d = 0.089447 + 0.255868I
2.95645 − 1.74546I 9.67431 + 3.49934I
u = 0.141853 + 0.491513I
a = 0.789501 + 0.479357I
b = 0.173722 − 0.874524I
c = 0.43488 − 2.33014I
d = 0.93136 − 4.42466I
2.95645 − 1.74546I 9.67431 + 3.49934I
u = 0.141853 − 0.491513I
a = 0.789501 − 0.479357I
b = 0.173722 + 0.874524I
c = 0.76489 + 1.34869I
d = 0.089447 − 0.255868I
2.95645 + 1.74546I 9.67431 − 3.49934I
u = 0.141853 − 0.491513I
a = 0.789501 − 0.479357I
b = 0.173722 + 0.874524I
c = 0.43488 + 2.33014I
d = 0.93136 + 4.42466I
2.95645 + 1.74546I 9.67431 − 3.49934I
28
III. I
v
1
= ha, d, c − v, b − v, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
v
a
5
=
1
0
a
3
=
v
v
a
6
=
1
−v + 1
a
11
=
v
0
a
10
=
v
0
a
1
=
−1
v − 1
a
8
=
v
0
a
7
=
v
0
a
12
=
v − 1
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 5
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
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 = 0.500000 + 0.866025I
c = 0.500000 + 0.866025I
d = 0
1.64493 + 2.02988I 3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = 0.500000 − 0.866025I
d = 0
1.64493 − 2.02988I 3.00000 + 3.46410I
32
IV. I
v
2
= ha, d − v + 1, −av + c + 1, b − v, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
v
a
5
=
1
0
a
3
=
v
v
a
6
=
1
−v + 1
a
11
=
−1
v − 1
a
10
=
v − 1
v − 1
a
1
=
−1
v − 1
a
8
=
v
0
a
7
=
1
−v + 1
a
12
=
−1
v − 1
(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
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
8
c
11
, c
12
u
2
c
7
, c
9
(u + 1)
2
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
5
y
2
+ y + 1
c
4
, c
6
, c
8
c
11
, c
12
y
2
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 = 0
b = 0.500000 + 0.866025I
c = −1.00000
d = −0.500000 + 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = −1.00000
d = −0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
36
V. I
v
3
= hc, d − 1, b, a − 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
−1
0
a
2
=
1
0
a
5
=
1
0
a
3
=
1
0
a
6
=
1
0
a
11
=
0
1
a
10
=
−1
1
a
1
=
1
0
a
8
=
−1
0
a
7
=
0
−1
a
12
=
1
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
3
c
4
, c
5
, c
8
u
c
6
, c
10
u − 1
c
7
, c
9
, c
11
c
12
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
39
(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
3.28987 12.0000
40
VI. I
v
4
=
ha, db+da+· · ·+b−1, a
2
d−da+· · ·−a+1, dv+1, cv−ba−bv+b+a, b
2
−b+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
b
a
5
=
1
0
a
3
=
b
b
a
6
=
1
−b + 1
a
11
=
c
−cb + c − 1
a
10
=
c + v
−cb + c − 1
a
1
=
−1
b − 1
a
8
=
v
0
a
7
=
−c
cb − c + 1
a
12
=
c − 1
−cb + c + b − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −c
2
b + 2cb + v
2
− 2c − 4b + 13
(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 8.56933 + 3.58827I
42
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
46
+ 21u
45
+ ··· − 40u + 16)
c
2
u(u
2
+ u + 1)
2
(u
46
+ u
45
+ ··· − 4u + 4)
c
3
u(u
2
− u + 1)
2
(u
46
− u
45
+ ··· − 2596u + 1252)
c
4
, c
8
u
5
(u
46
− 3u
45
+ ··· − 32u + 32)
c
5
u(u
2
− u + 1)
2
(u
46
+ u
45
+ ··· − 4u + 4)
c
6
u
2
(u − 1)(u + 1)
2
(u
46
+ 5u
45
+ ··· + 2u + 1)
c
7
u
2
(u + 1)
3
(u
46
+ 5u
45
+ ··· + 2u + 1)
c
9
, c
11
u
2
(u + 1)
3
(u
46
− 21u
45
+ ··· + 4u + 1)
c
10
u
2
(u − 1)
3
(u
46
+ 5u
45
+ ··· + 2u + 1)
c
12
u
2
(u − 1)
2
(u + 1)(u
46
+ 5u
45
+ ··· + 2u + 1)
43
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
46
+ 9y
45
+ ··· − 5664y + 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
46
+ 21y
45
+ ··· − 40y + 16)
c
3
y(y
2
+ y + 1)
2
(y
46
− 3y
45
+ ··· − 2.04086 × 10
7
y + 1567504)
c
4
, c
8
y
5
(y
46
− 15y
45
+ ··· + 4096y + 1024)
c
6
, c
7
, c
10
c
12
y
2
(y − 1)
3
(y
46
− 21y
45
+ ··· + 4y + 1)
c
9
, c
11
y
2
(y − 1)
3
(y
46
+ 19y
45
+ ··· − 72y + 1)
44
