12n
0875
(K12n
0875
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 10 11 12 3 6 2 7 6
Solving Sequence
7,11
12
2,8
3 6 1 10 5 4 9
c
11
c
7
c
2
c
6
c
12
c
10
c
5
c
4
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−41u
26
+ 353u
25
+ ··· + 8b + 776, −421u
26
+ 3271u
25
+ ··· + 16a + 5248,
u
27
− 9u
26
+ ··· + 32u + 16i
I
u
2
= h5.05025 × 10
19
a
7
u
4
+ 2.52836 × 10
19
a
6
u
4
+ ··· − 5.62996 × 10
20
a − 3.53454 × 10
20
,
a
7
u
4
+ 2a
6
u
4
+ ··· + 2a + 8, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
3
= h−u
17
+ u
16
+ ··· + b − 1, −u
17
+ 2u
16
+ ··· + a + 1, u
18
− 10u
16
+ ··· + 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 85 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−41u
26
+ 353u
25
+ · · · + 8b + 776, −421u
26
+ 3271u
25
+ · · · + 16a +
5248, u
27
− 9u
26
+ · · · + 32u + 16i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
421
16
u
26
−
3271
16
u
25
+ ··· − 900u − 328
41
8
u
26
−
353
8
u
25
+ ··· − 287u − 97
a
8
=
−u
−u
3
+ u
a
3
=
389
16
u
26
−
2911
16
u
25
+ ··· − 639u − 246
185
8
u
26
−
1413
8
u
25
+ ··· − 660u − 251
a
6
=
u
u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
10
=
−9.50000u
26
+ 71.5000u
25
+ ··· + 263.500u + 100.500
−6u
26
+
93
2
u
25
+ ··· +
393
2
u + 72
a
5
=
95
4
u
26
−
689
4
u
25
+ ··· −
2027
4
u − 204
143
4
u
26
− 267u
25
+ ··· − 951u − 364
a
4
=
−34u
26
+
997
4
u
25
+ ··· +
3177
4
u + 312
−
61
4
u
26
+ 114u
25
+ ··· + 409u + 156
a
9
=
2u
26
−
25
2
u
25
+ ··· −
1
2
u −
7
2
11
2
u
26
−
75
2
u
25
+ ··· −
135
2
u − 32
(ii) Obstruction class = −1
(iii) Cusp Shapes =
21
2
u
26
−
155
2
u
25
+ ··· − 328u − 122
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
27
− 12u
26
+ ··· + 208u − 32
c
2
, c
8
, c
10
u
27
− u
26
+ ··· − u
2
+ 1
c
3
u
27
+ 14u
25
+ ··· + 15u + 6
c
5
, c
9
u
27
+ u
26
+ ··· + 3u + 1
c
6
, c
7
, c
11
u
27
− 9u
26
+ ··· + 32u + 16
c
12
u
27
+ 27u
26
+ ··· + 69984u + 2544
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
27
+ 12y
26
+ ··· + 2816y − 1024
c
2
, c
8
, c
10
y
27
− 11y
26
+ ··· + 2y − 1
c
3
y
27
+ 28y
26
+ ··· − 735y − 36
c
5
, c
9
y
27
− 39y
26
+ ··· − 23y − 1
c
6
, c
7
, c
11
y
27
− 25y
26
+ ··· − 896y − 256
c
12
y
27
− 5y
26
+ ··· + 1414291584y − 6471936
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.964369
a = −0.318344
b = −0.603064
−1.76934 −4.68310
u = −0.803711 + 0.683866I
a = 0.491705 + 0.343530I
b = 1.095410 − 0.539428I
−0.57691 − 5.99392I −1.84311 + 4.05619I
u = −0.803711 − 0.683866I
a = 0.491705 − 0.343530I
b = 1.095410 + 0.539428I
−0.57691 + 5.99392I −1.84311 − 4.05619I
u = −0.370454 + 0.864963I
a = 0.583628 − 0.747382I
b = −1.26577 − 0.69912I
0.74691 + 11.25370I −0.99031 − 7.88400I
u = −0.370454 − 0.864963I
a = 0.583628 + 0.747382I
b = −1.26577 + 0.69912I
0.74691 − 11.25370I −0.99031 + 7.88400I
u = −0.771780 + 0.532650I
a = −0.558602 − 0.144325I
b = −0.800896 + 0.600402I
−2.49843 + 0.05140I −5.15323 − 0.12545I
u = −0.771780 − 0.532650I
a = −0.558602 + 0.144325I
b = −0.800896 − 0.600402I
−2.49843 − 0.05140I −5.15323 + 0.12545I
u = −0.041989 + 0.912394I
a = 0.651675 − 0.346284I
b = −0.856463 − 0.371397I
6.42911 + 1.54622I −1.38870 − 4.76643I
u = −0.041989 − 0.912394I
a = 0.651675 + 0.346284I
b = −0.856463 + 0.371397I
6.42911 − 1.54622I −1.38870 + 4.76643I
u = −0.313750 + 0.820442I
a = −0.691743 + 0.655778I
b = 1.056140 + 0.752548I
−0.95670 + 4.64749I −3.11625 − 4.28962I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.313750 − 0.820442I
a = −0.691743 − 0.655778I
b = 1.056140 − 0.752548I
−0.95670 − 4.64749I −3.11625 + 4.28962I
u = 1.291790 + 0.132006I
a = 0.39275 + 1.80597I
b = −0.236326 + 0.731369I
−4.71486 − 2.66219I −10.24513 + 2.16538I
u = 1.291790 − 0.132006I
a = 0.39275 − 1.80597I
b = −0.236326 − 0.731369I
−4.71486 + 2.66219I −10.24513 − 2.16538I
u = −1.235650 + 0.498505I
a = 0.272822 + 0.119393I
b = 0.892468 − 0.171957I
2.75085 + 3.44962I −3.04006 − 0.75559I
u = −1.235650 − 0.498505I
a = 0.272822 − 0.119393I
b = 0.892468 + 0.171957I
2.75085 − 3.44962I −3.04006 + 0.75559I
u = 1.304880 + 0.416381I
a = −0.322702 − 1.316720I
b = 0.810130 − 0.511841I
2.23251 − 6.28195I −4.42614 + 9.81569I
u = 1.304880 − 0.416381I
a = −0.322702 + 1.316720I
b = 0.810130 + 0.511841I
2.23251 + 6.28195I −4.42614 − 9.81569I
u = 1.44686 + 0.33023I
a = −0.06455 + 1.78314I
b = −1.14982 + 0.91803I
−6.58526 − 8.82619I −6.63229 + 4.83886I
u = 1.44686 − 0.33023I
a = −0.06455 − 1.78314I
b = −1.14982 − 0.91803I
−6.58526 + 8.82619I −6.63229 − 4.83886I
u = 1.47459 + 0.33777I
a = 0.27730 − 1.78435I
b = 1.33721 − 0.86260I
−5.1650 − 15.6109I −4.73031 + 8.36235I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47459 − 0.33777I
a = 0.27730 + 1.78435I
b = 1.33721 + 0.86260I
−5.1650 + 15.6109I −4.73031 − 8.36235I
u = 1.56344 + 0.10077I
a = 0.666759 + 0.733427I
b = 0.423378 + 0.781537I
−10.26540 − 2.14143I −10.01123 − 1.60680I
u = 1.56344 − 0.10077I
a = 0.666759 − 0.733427I
b = 0.423378 − 0.781537I
−10.26540 + 2.14143I −10.01123 + 1.60680I
u = −0.207167 + 0.338394I
a = −0.807617 + 0.644314I
b = 0.198877 + 0.473880I
−0.191214 + 0.917747I −4.07825 − 7.40992I
u = −0.207167 − 0.338394I
a = −0.807617 − 0.644314I
b = 0.198877 − 0.473880I
−0.191214 − 0.917747I −4.07825 + 7.40992I
u = 1.64512 + 0.10744I
a = −0.732246 − 0.267743I
b = −0.702805 − 0.461250I
−9.10720 + 3.18920I −2.50344 − 8.37472I
u = 1.64512 − 0.10744I
a = −0.732246 + 0.267743I
b = −0.702805 + 0.461250I
−9.10720 − 3.18920I −2.50344 + 8.37472I
7
II. I
u
2
= h5.05 × 10
19
a
7
u
4
+ 2.53 × 10
19
a
6
u
4
+ · · · − 5.63 × 10
20
a − 3.53 ×
10
20
, a
7
u
4
+ 2a
6
u
4
+ · · · + 2a + 8, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
a
−0.122834a
7
u
4
− 0.0614957a
6
u
4
+ ··· + 1.36934a + 0.859686
a
8
=
−u
−u
3
+ u
a
3
=
0.0599628a
7
u
4
− 0.0892303a
6
u
4
+ ··· + 0.480015a − 0.153698
−0.0963330a
7
u
4
+ 0.0655129a
6
u
4
+ ··· + 0.468860a + 0.984014
a
6
=
u
u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
10
=
0.00880396a
7
u
4
+ 0.0745605a
6
u
4
+ ··· − 0.0852193a + 1.19688
−0.102685a
7
u
4
+ 0.0867561a
6
u
4
+ ··· + 0.183710a + 0.753308
a
5
=
0.0864621a
7
u
4
− 0.0164718a
6
u
4
+ ··· − 0.406676a + 0.181351
−0.0228102a
7
u
4
+ 0.150985a
6
u
4
+ ··· + 0.872274a − 0.350649
a
4
=
0.0542117a
7
u
4
− 0.181136a
6
u
4
+ ··· + 2.21194a + 1.16802
0.0222538a
7
u
4
+ 0.109064a
6
u
4
+ ··· + 1.48393a + 0.181306
a
9
=
0.0452252a
7
u
4
− 0.158091a
6
u
4
+ ··· + 0.0512540a + 2.19986
−0.0662635a
7
u
4
− 0.145896a
6
u
4
+ ··· + 0.320183a + 1.75629
(ii) Obstruction class = −1
(iii) Cusp Shapes =
161487074628025476936
411143306059987191701
a
7
u
4
+
242282595791648428492
411143306059987191701
a
6
u
4
+ ··· −
2121485914457092581344
411143306059987191701
a −
2877275927809975425030
411143306059987191701
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
+ u
3
+ u
2
+ 1)
10
c
2
, c
8
, c
10
u
40
+ u
39
+ ··· − 2070u + 277
c
3
u
40
+ u
39
+ ··· + 19056u + 6533
c
5
, c
9
u
40
+ 3u
39
+ ··· + 2230u + 179
c
6
, c
7
, c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
c
12
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
8
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
c
2
, c
8
, c
10
y
40
− 21y
39
+ ··· − 2195212y + 76729
c
3
y
40
− y
39
+ ··· + 822647562y + 42680089
c
5
, c
9
y
40
− 13y
39
+ ··· − 585968y + 32041
c
6
, c
7
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
8
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
8
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0.013355 + 0.679058I
b = 1.42762 + 0.04887I
2.74473 − 1.41510I 0.34560 + 4.90874I
u = 1.21774
a = 0.013355 − 0.679058I
b = 1.42762 − 0.04887I
2.74473 + 1.41510I 0.34560 − 4.90874I
u = 1.21774
a = −1.156090 + 0.786785I
b = −1.73061 + 0.33980I
2.74473 − 1.41510I 0.34560 + 4.90874I
u = 1.21774
a = −1.156090 − 0.786785I
b = −1.73061 − 0.33980I
2.74473 + 1.41510I 0.34560 − 4.90874I
u = 1.21774
a = −0.02233 + 2.04699I
b = 0.309062 + 0.060548I
−4.25702 − 3.16396I −3.30788 + 2.56480I
u = 1.21774
a = −0.02233 − 2.04699I
b = 0.309062 − 0.060548I
−4.25702 + 3.16396I −3.30788 − 2.56480I
u = 1.21774
a = −0.28099 + 2.44297I
b = −0.389484 + 1.129940I
−4.25702 − 3.16396I −3.30788 + 2.56480I
u = 1.21774
a = −0.28099 − 2.44297I
b = −0.389484 − 1.129940I
−4.25702 + 3.16396I −3.30788 − 2.56480I
u = 0.309916 + 0.549911I
a = 0.146171 − 1.055970I
b = 1.055970 − 0.619228I
4.81671 − 2.94568I 1.31162 + 9.33939I
u = 0.309916 + 0.549911I
a = −0.346370 − 1.015430I
b = 1.46492 − 0.16034I
4.81671 − 0.11547I 1.311623 − 0.478094I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309916 + 0.549911I
a = 0.315118 − 0.341217I
b = −0.330723 − 1.174280I
−2.18504 − 4.69454I −2.34185 + 6.99545I
u = 0.309916 + 0.549911I
a = −0.391964 + 0.132667I
b = 0.693402 + 0.981583I
−2.18504 + 1.63338I −2.34185 + 1.86585I
u = 0.309916 + 0.549911I
a = −0.46708 + 1.64131I
b = −0.914109 + 0.007273I
4.81671 − 0.11547I 1.311623 − 0.478094I
u = 0.309916 + 0.549911I
a = 0.65926 + 1.69213I
b = −1.338800 + 0.122412I
4.81671 − 2.94568I 1.31162 + 9.33939I
u = 0.309916 + 0.549911I
a = −2.08847 + 0.01907I
b = 0.618894 − 0.541366I
−2.18504 + 1.63338I −2.34185 + 1.86585I
u = 0.309916 + 0.549911I
a = 2.16319 + 0.52446I
b = −0.910444 + 0.561565I
−2.18504 − 4.69454I −2.34185 + 6.99545I
u = 0.309916 − 0.549911I
a = 0.146171 + 1.055970I
b = 1.055970 + 0.619228I
4.81671 + 2.94568I 1.31162 − 9.33939I
u = 0.309916 − 0.549911I
a = −0.346370 + 1.015430I
b = 1.46492 + 0.16034I
4.81671 + 0.11547I 1.311623 + 0.478094I
u = 0.309916 − 0.549911I
a = 0.315118 + 0.341217I
b = −0.330723 + 1.174280I
−2.18504 + 4.69454I −2.34185 − 6.99545I
u = 0.309916 − 0.549911I
a = −0.391964 − 0.132667I
b = 0.693402 − 0.981583I
−2.18504 − 1.63338I −2.34185 − 1.86585I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309916 − 0.549911I
a = −0.46708 − 1.64131I
b = −0.914109 − 0.007273I
4.81671 + 0.11547I 1.311623 + 0.478094I
u = 0.309916 − 0.549911I
a = 0.65926 − 1.69213I
b = −1.338800 − 0.122412I
4.81671 + 2.94568I 1.31162 − 9.33939I
u = 0.309916 − 0.549911I
a = −2.08847 − 0.01907I
b = 0.618894 + 0.541366I
−2.18504 − 1.63338I −2.34185 − 1.86585I
u = 0.309916 − 0.549911I
a = 2.16319 − 0.52446I
b = −0.910444 − 0.561565I
−2.18504 + 4.69454I −2.34185 − 6.99545I
u = −1.41878 + 0.21917I
a = 0.365290 − 1.160210I
b = −1.073010 − 0.613252I
−7.72850 + 1.23687I −6.57105 − 0.93379I
u = −1.41878 + 0.21917I
a = 0.71484 + 1.27508I
b = 0.589674 + 0.279437I
−0.72676 + 2.98573I −2.91758 + 1.41016I
u = −1.41878 + 0.21917I
a = −0.25095 + 1.45980I
b = 1.226260 + 0.624039I
−7.72850 + 7.56480I −6.57105 − 6.06338I
u = −1.41878 + 0.21917I
a = −0.93744 + 1.18988I
b = −0.83801 + 1.19485I
−7.72850 + 1.23687I −6.57105 − 0.93379I
u = −1.41878 + 0.21917I
a = −0.91744 − 1.39733I
b = −1.37802 − 0.52268I
−0.72676 + 2.98573I −2.91758 + 1.41016I
u = −1.41878 + 0.21917I
a = 0.70648 + 1.58918I
b = 1.227650 + 0.310123I
−0.72676 + 5.81594I −2.91758 − 8.40733I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41878 + 0.21917I
a = 0.81391 − 1.56615I
b = 0.58917 − 1.45737I
−7.72850 + 7.56480I −6.57105 − 6.06338I
u = −1.41878 + 0.21917I
a = −0.53850 − 1.75583I
b = −0.799412 − 1.015300I
−0.72676 + 5.81594I −2.91758 − 8.40733I
u = −1.41878 − 0.21917I
a = 0.365290 + 1.160210I
b = −1.073010 + 0.613252I
−7.72850 − 1.23687I −6.57105 + 0.93379I
u = −1.41878 − 0.21917I
a = 0.71484 − 1.27508I
b = 0.589674 − 0.279437I
−0.72676 − 2.98573I −2.91758 − 1.41016I
u = −1.41878 − 0.21917I
a = −0.25095 − 1.45980I
b = 1.226260 − 0.624039I
−7.72850 − 7.56480I −6.57105 + 6.06338I
u = −1.41878 − 0.21917I
a = −0.93744 − 1.18988I
b = −0.83801 − 1.19485I
−7.72850 − 1.23687I −6.57105 + 0.93379I
u = −1.41878 − 0.21917I
a = −0.91744 + 1.39733I
b = −1.37802 + 0.52268I
−0.72676 − 2.98573I −2.91758 − 1.41016I
u = −1.41878 − 0.21917I
a = 0.70648 − 1.58918I
b = 1.227650 − 0.310123I
−0.72676 − 5.81594I −2.91758 + 8.40733I
u = −1.41878 − 0.21917I
a = 0.81391 + 1.56615I
b = 0.58917 + 1.45737I
−7.72850 − 7.56480I −6.57105 + 6.06338I
u = −1.41878 − 0.21917I
a = −0.53850 + 1.75583I
b = −0.799412 + 1.015300I
−0.72676 − 5.81594I −2.91758 + 8.40733I
14
III.
I
u
3
= h−u
17
+u
16
+· · ·+b−1, −u
17
+2u
16
+· · ·+a+1, u
18
−10u
16
+· · ·+2u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
u
17
− 2u
16
+ ··· + 2u − 1
u
17
− u
16
+ ··· − 5u
2
+ 1
a
8
=
−u
−u
3
+ u
a
3
=
−u
16
+ 2u
15
+ ··· + u − 2
u
17
− 9u
15
+ ··· − 4u
2
+ 1
a
6
=
u
u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
17
− u
16
+ ··· − 3u + 4
u
15
− 8u
13
+ ··· − 2u
2
+ 2u
a
5
=
−u
17
− 2u
16
+ ··· + 3u − 4
−2u
16
+ 17u
14
+ ··· + 2u + 2
a
4
=
−2u
16
+ 2u
15
+ ··· + u − 2
−u
16
+ 9u
14
+ ··· + u + 2
a
9
=
u
17
− 9u
15
+ ··· − 4u + 3
u
16
+ u
15
+ ··· + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
17
+ 9u
16
+ 24u
15
− 78u
14
− 71u
13
+ 270u
12
+ 65u
11
−
443u
10
+ 105u
9
+ 266u
8
− 278u
7
+ 136u
6
+ 173u
5
− 194u
4
+ 5u
3
+ 8u
2
− 4u − 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 3u
17
+ ··· + 7u
2
+ 1
c
2
, c
10
u
18
− u
17
+ ··· − u + 1
c
3
u
18
− 4u
15
+ ··· + 72u + 89
c
4
u
18
+ 3u
17
+ ··· + 7u
2
+ 1
c
5
u
18
+ u
17
+ ··· + 4u
2
+ 1
c
6
, c
7
u
18
− 10u
16
+ ··· − 2u + 1
c
8
u
18
+ u
17
+ ··· + u + 1
c
9
u
18
− u
17
+ ··· + 4u
2
+ 1
c
11
u
18
− 10u
16
+ ··· + 2u + 1
c
12
u
18
− 2u
16
+ ··· + 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
18
+ 11y
17
+ ··· + 14y + 1
c
2
, c
8
, c
10
y
18
− 15y
17
+ ··· + 3y + 1
c
3
y
18
+ 18y
16
+ ··· + 13506y + 7921
c
5
, c
9
y
18
− 3y
17
+ ··· + 8y + 1
c
6
, c
7
, c
11
y
18
− 20y
17
+ ··· − 12y + 1
c
12
y
18
− 4y
17
+ ··· − 20y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.150560 + 0.836512I
a = −0.533179 − 0.729886I
b = 1.075140 − 0.196010I
7.45701 − 0.86946I 5.92156 + 0.65299I
u = 0.150560 − 0.836512I
a = −0.533179 + 0.729886I
b = 1.075140 + 0.196010I
7.45701 + 0.86946I 5.92156 − 0.65299I
u = 1.168950 + 0.333469I
a = −0.464909 + 0.152055I
b = −1.296280 − 0.148875I
4.40486 − 3.34214I 1.38697 + 3.55930I
u = 1.168950 − 0.333469I
a = −0.464909 − 0.152055I
b = −1.296280 + 0.148875I
4.40486 + 3.34214I 1.38697 − 3.55930I
u = −1.235970 + 0.060491I
a = 0.03532 + 2.77384I
b = 0.257150 + 0.795688I
−5.01572 + 3.63551I −13.7646 − 8.6540I
u = −1.235970 − 0.060491I
a = 0.03532 − 2.77384I
b = 0.257150 − 0.795688I
−5.01572 − 3.63551I −13.7646 + 8.6540I
u = 1.239720 + 0.079694I
a = 0.573148 + 0.001579I
b = 1.58735 + 0.16330I
2.15137 + 0.50360I −5.12126 + 2.00101I
u = 1.239720 − 0.079694I
a = 0.573148 − 0.001579I
b = 1.58735 − 0.16330I
2.15137 − 0.50360I −5.12126 − 2.00101I
u = −1.38028 + 0.40167I
a = −0.176194 − 1.167390I
b = −0.889583 − 0.299807I
2.62231 + 5.36601I 0.26863 − 2.79489I
u = −1.38028 − 0.40167I
a = −0.176194 + 1.167390I
b = −0.889583 + 0.299807I
2.62231 − 5.36601I 0.26863 + 2.79489I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44054 + 0.19476I
a = 0.93259 + 1.49794I
b = 1.105240 + 0.552133I
−0.52793 + 4.33231I −1.41553 − 3.95185I
u = −1.44054 − 0.19476I
a = 0.93259 − 1.49794I
b = 1.105240 − 0.552133I
−0.52793 − 4.33231I −1.41553 + 3.95185I
u = 0.280243 + 0.395808I
a = −0.21841 + 2.05894I
b = −1.315850 + 0.281244I
5.17187 − 1.97060I 5.62846 + 1.71237I
u = 0.280243 − 0.395808I
a = −0.21841 − 2.05894I
b = −1.315850 − 0.281244I
5.17187 + 1.97060I 5.62846 − 1.71237I
u = 1.59243 + 0.02692I
a = 0.0586212 + 0.1050240I
b = 0.230133 + 0.440093I
−9.22204 + 2.50043I −4.24190 + 1.59514I
u = 1.59243 − 0.02692I
a = 0.0586212 − 0.1050240I
b = 0.230133 − 0.440093I
−9.22204 − 2.50043I −4.24190 − 1.59514I
u = −0.375129 + 0.106964I
a = 1.29301 − 2.41807I
b = −0.253290 + 0.629019I
−2.10693 − 3.00421I −1.16234 + 3.79276I
u = −0.375129 − 0.106964I
a = 1.29301 + 2.41807I
b = −0.253290 − 0.629019I
−2.10693 + 3.00421I −1.16234 − 3.79276I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
4
+ u
3
+ u
2
+ 1)
10
)(u
18
− 3u
17
+ ··· + 7u
2
+ 1)
· (u
27
− 12u
26
+ ··· + 208u − 32)
c
2
, c
10
(u
18
− u
17
+ ··· − u + 1)(u
27
− u
26
+ ··· − u
2
+ 1)
· (u
40
+ u
39
+ ··· − 2070u + 277)
c
3
(u
18
− 4u
15
+ ··· + 72u + 89)(u
27
+ 14u
25
+ ··· + 15u + 6)
· (u
40
+ u
39
+ ··· + 19056u + 6533)
c
4
((u
4
+ u
3
+ u
2
+ 1)
10
)(u
18
+ 3u
17
+ ··· + 7u
2
+ 1)
· (u
27
− 12u
26
+ ··· + 208u − 32)
c
5
(u
18
+ u
17
+ ··· + 4u
2
+ 1)(u
27
+ u
26
+ ··· + 3u + 1)
· (u
40
+ 3u
39
+ ··· + 2230u + 179)
c
6
, c
7
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
)(u
18
− 10u
16
+ ··· − 2u + 1)
· (u
27
− 9u
26
+ ··· + 32u + 16)
c
8
(u
18
+ u
17
+ ··· + u + 1)(u
27
− u
26
+ ··· − u
2
+ 1)
· (u
40
+ u
39
+ ··· − 2070u + 277)
c
9
(u
18
− u
17
+ ··· + 4u
2
+ 1)(u
27
+ u
26
+ ··· + 3u + 1)
· (u
40
+ 3u
39
+ ··· + 2230u + 179)
c
11
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
)(u
18
− 10u
16
+ ··· + 2u + 1)
· (u
27
− 9u
26
+ ··· + 32u + 16)
c
12
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
8
)(u
18
− 2u
16
+ ··· + 2u + 1)
· (u
27
+ 27u
26
+ ··· + 69984u + 2544)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
)(y
18
+ 11y
17
+ ··· + 14y + 1)
· (y
27
+ 12y
26
+ ··· + 2816y − 1024)
c
2
, c
8
, c
10
(y
18
− 15y
17
+ ··· + 3y + 1)(y
27
− 11y
26
+ ··· + 2y − 1)
· (y
40
− 21y
39
+ ··· − 2195212y + 76729)
c
3
(y
18
+ 18y
16
+ ··· + 13506y + 7921)(y
27
+ 28y
26
+ ··· − 735y − 36)
· (y
40
− y
39
+ ··· + 822647562y + 42680089)
c
5
, c
9
(y
18
− 3y
17
+ ··· + 8y + 1)(y
27
− 39y
26
+ ··· − 23y − 1)
· (y
40
− 13y
39
+ ··· − 585968y + 32041)
c
6
, c
7
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
8
)(y
18
− 20y
17
+ ··· − 12y + 1)
· (y
27
− 25y
26
+ ··· − 896y − 256)
c
12
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
8
)(y
18
− 4y
17
+ ··· − 20y + 1)
· (y
27
− 5y
26
+ ··· + 1414291584y − 6471936)
21
