12n
0353
(K12n
0353
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 10 2 12 3 11 5 7 9
Solving Sequence
3,12 4,9
5 1 2 8 7 6 11 10
c
3
c
4
c
12
c
1
c
8
c
7
c
6
c
11
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.19698 × 10
252
u
72
+ 4.10952 × 10
253
u
71
+ ··· + 1.58931 × 10
253
b + 8.73323 × 10
256
,
− 1.50404 × 10
255
u
72
+ 6.27835 × 10
255
u
71
+ ··· + 7.16781 × 10
255
a + 2.14004 × 10
259
,
u
73
− 4u
72
+ ··· − 7469u − 4961i
I
u
2
= h−9u
21
− 48u
20
+ ··· + b + 11, 28u
21
+ 177u
20
+ ··· + a + 3, u
22
+ 7u
21
+ ··· + 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 95 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−9.20 × 10
252
u
72
+ 4.11 × 10
253
u
71
+ · · · + 1.59 × 10
253
b + 8.73 ×
10
256
, −1.50 × 10
255
u
72
+ 6.28 × 10
255
u
71
+ · · · + 7.17 × 10
255
a + 2.14 ×
10
259
, u
73
− 4u
72
+ · · · − 7469u − 4961i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
9
=
0.209833u
72
− 0.875910u
71
+ ··· + 2329.47u − 2985.62
0.578676u
72
− 2.58572u
71
+ ··· + 2145.74u − 5494.97
a
5
=
−1.50718u
72
+ 6.92175u
71
+ ··· − 2293.79u + 12596.8
0.676487u
72
− 3.11685u
71
+ ··· + 970.426u − 5595.66
a
1
=
−0.754050u
72
+ 3.46435u
71
+ ··· − 1139.08u + 6262.26
−1.15917u
72
+ 5.32183u
71
+ ··· − 1731.26u + 9700.40
a
2
=
0.405124u
72
− 1.85748u
71
+ ··· + 592.184u − 3438.14
−1.15917u
72
+ 5.32183u
71
+ ··· − 1731.26u + 9700.40
a
8
=
−0.368843u
72
+ 1.70981u
71
+ ··· + 183.722u + 2509.35
0.578676u
72
− 2.58572u
71
+ ··· + 2145.74u − 5494.97
a
7
=
−0.368843u
72
+ 1.70981u
71
+ ··· + 183.722u + 2509.35
0.423437u
72
− 1.87140u
71
+ ··· + 2066.92u − 4331.94
a
6
=
−0.0556736u
72
+ 0.215818u
71
+ ··· − 1052.76u + 687.535
−0.208916u
72
+ 1.01482u
71
+ ··· + 1183.76u + 1059.07
a
11
=
−1.57181u
72
+ 7.22423u
71
+ ··· − 2235.05u + 13095.6
0.607582u
72
− 2.79839u
71
+ ··· + 843.580u − 5009.04
a
10
=
−1.51645u
72
+ 7.01530u
71
+ ··· − 1132.33u + 11925.2
1.75380u
72
− 7.99846u
71
+ ··· + 4270.33u − 15380.1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.97688u
72
− 27.3063u
71
+ ··· + 12628.2u − 52558.5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 42u
72
+ ··· + u − 1
c
2
, c
6
u
73
− 2u
72
+ ··· + 3u − 1
c
3
u
73
− 4u
72
+ ··· − 7469u − 4961
c
4
u
73
+ u
72
+ ··· + 504u − 34447
c
5
, c
10
u
73
− u
72
+ ··· + 6u − 19
c
7
, c
11
u
73
− 3u
72
+ ··· + 518u − 77
c
8
u
73
− u
72
+ ··· − 4184u − 2449
c
9
u
73
− 35u
72
+ ··· − 3270u + 361
c
12
u
73
+ u
72
+ ··· + 9112u − 2479
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 6y
72
+ ··· + 109y −1
c
2
, c
6
y
73
+ 42y
72
+ ··· + y −1
c
3
y
73
− 80y
72
+ ··· + 887378547y −24611521
c
4
y
73
− 5y
72
+ ··· + 9963979872y −1186595809
c
5
, c
10
y
73
+ 35y
72
+ ··· − 3270y −361
c
7
, c
11
y
73
− 25y
72
+ ··· − 47222y −5929
c
8
y
73
+ 83y
72
+ ··· − 316258558y −5997601
c
9
y
73
+ 15y
72
+ ··· − 1105302y −130321
c
12
y
73
+ 79y
72
+ ··· − 157637734y −6145441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960694 + 0.223002I
a = −0.31701 − 1.62689I
b = −0.06752 − 1.93464I
−5.68153 + 1.21562I 0
u = 0.960694 − 0.223002I
a = −0.31701 + 1.62689I
b = −0.06752 + 1.93464I
−5.68153 − 1.21562I 0
u = −0.800102 + 0.544363I
a = −1.340300 − 0.231886I
b = −0.229015 + 0.678752I
3.32889 + 1.44969I 0
u = −0.800102 − 0.544363I
a = −1.340300 + 0.231886I
b = −0.229015 − 0.678752I
3.32889 − 1.44969I 0
u = 0.164338 + 1.072630I
a = −0.568772 + 0.453403I
b = 0.067159 − 0.480853I
3.93954 + 2.04644I 0
u = 0.164338 − 1.072630I
a = −0.568772 − 0.453403I
b = 0.067159 + 0.480853I
3.93954 − 2.04644I 0
u = −0.436988 + 1.059720I
a = −0.333172 + 0.259820I
b = −0.045424 + 0.670574I
0.65478 + 1.74378I 0
u = −0.436988 − 1.059720I
a = −0.333172 − 0.259820I
b = −0.045424 − 0.670574I
0.65478 − 1.74378I 0
u = −0.795078 + 0.220539I
a = −1.98401 − 0.60795I
b = −0.300669 − 0.679598I
1.18619 − 7.05030I 0
u = −0.795078 − 0.220539I
a = −1.98401 + 0.60795I
b = −0.300669 + 0.679598I
1.18619 + 7.05030I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802130 + 0.134868I
a = −0.306467 + 0.314014I
b = −0.350471 − 0.748878I
−3.45310 + 2.18113I 0
u = −0.802130 − 0.134868I
a = −0.306467 − 0.314014I
b = −0.350471 + 0.748878I
−3.45310 − 2.18113I 0
u = −0.330029 + 1.180410I
a = 0.607699 − 0.317572I
b = 0.032457 − 0.739244I
2.70715 − 2.50353I 0
u = −0.330029 − 1.180410I
a = 0.607699 + 0.317572I
b = 0.032457 + 0.739244I
2.70715 + 2.50353I 0
u = −0.661879 + 1.045090I
a = 0.806091 + 0.004427I
b = 0.145525 − 0.713654I
3.77152 + 3.96149I 0
u = −0.661879 − 1.045090I
a = 0.806091 − 0.004427I
b = 0.145525 + 0.713654I
3.77152 − 3.96149I 0
u = 0.716179 + 0.098392I
a = 0.780594 − 0.817015I
b = −0.982012 − 0.581986I
4.73461 + 4.33640I 0
u = 0.716179 − 0.098392I
a = 0.780594 + 0.817015I
b = −0.982012 + 0.581986I
4.73461 − 4.33640I 0
u = 0.632663 + 0.312150I
a = 1.67667 − 0.35481I
b = −0.283393 + 0.257017I
5.10442 + 3.75309I 0
u = 0.632663 − 0.312150I
a = 1.67667 + 0.35481I
b = −0.283393 − 0.257017I
5.10442 − 3.75309I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697508 + 0.042276I
a = 0.320190 + 1.056290I
b = 1.293460 + 0.457104I
3.08996 + 0.50335I 0
u = −0.697508 − 0.042276I
a = 0.320190 − 1.056290I
b = 1.293460 − 0.457104I
3.08996 − 0.50335I 0
u = −1.344490 + 0.232038I
a = 0.222248 + 0.421654I
b = 0.107848 + 1.300160I
−3.26184 − 1.83723I 0
u = −1.344490 − 0.232038I
a = 0.222248 − 0.421654I
b = 0.107848 − 1.300160I
−3.26184 + 1.83723I 0
u = −0.629638 + 0.051553I
a = −0.506953 + 0.948183I
b = −1.270960 − 0.116190I
−0.96981 + 3.12263I 0. − 3.92838I
u = −0.629638 − 0.051553I
a = −0.506953 − 0.948183I
b = −1.270960 + 0.116190I
−0.96981 − 3.12263I 0. + 3.92838I
u = 0.623255 + 0.102892I
a = 0.812430 + 0.004182I
b = −1.051920 − 0.163847I
4.88061 + 4.25358I 7.95219 − 6.27359I
u = 0.623255 − 0.102892I
a = 0.812430 − 0.004182I
b = −1.051920 + 0.163847I
4.88061 − 4.25358I 7.95219 + 6.27359I
u = −0.570164 + 0.021414I
a = 0.589757 − 1.092380I
b = 1.64229 + 0.16254I
1.88323 + 7.93272I 1.77664 − 7.45810I
u = −0.570164 − 0.021414I
a = 0.589757 + 1.092380I
b = 1.64229 − 0.16254I
1.88323 − 7.93272I 1.77664 + 7.45810I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30805 + 1.39618I
a = 0.292611 + 0.126630I
b = 0.015318 + 0.602025I
−0.08107 + 3.31791I 0
u = −0.30805 − 1.39618I
a = 0.292611 − 0.126630I
b = 0.015318 − 0.602025I
−0.08107 − 3.31791I 0
u = −1.38600 + 0.44020I
a = 0.082384 − 0.995509I
b = −0.47298 − 1.51710I
0.98783 + 1.74704I 0
u = −1.38600 − 0.44020I
a = 0.082384 + 0.995509I
b = −0.47298 + 1.51710I
0.98783 − 1.74704I 0
u = 1.46506 + 0.00570I
a = −0.244949 + 0.905533I
b = 0.06859 + 1.83552I
−4.04293 − 0.08034I 0
u = 1.46506 − 0.00570I
a = −0.244949 − 0.905533I
b = 0.06859 − 1.83552I
−4.04293 + 0.08034I 0
u = −0.445112 + 0.281624I
a = 2.64254 + 1.30726I
b = 0.326600 + 0.664261I
−0.18113 − 2.12200I − 60.10 + 0.246955I
u = −0.445112 − 0.281624I
a = 2.64254 − 1.30726I
b = 0.326600 − 0.664261I
−0.18113 + 2.12200I − 60.10 − 0.246955I
u = 1.37711 + 0.55990I
a = −0.543341 − 1.220170I
b = −0.10757 − 1.80567I
−7.78936 − 4.71097I 0
u = 1.37711 − 0.55990I
a = −0.543341 + 1.220170I
b = −0.10757 + 1.80567I
−7.78936 + 4.71097I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503647
a = −0.984699
b = 0.808330
1.57161 5.96450
u = 0.463701 + 0.131323I
a = −1.78260 + 1.42853I
b = 0.591813 + 0.515091I
1.58882 − 0.32095I 2.16231 − 0.77182I
u = 0.463701 − 0.131323I
a = −1.78260 − 1.42853I
b = 0.591813 − 0.515091I
1.58882 + 0.32095I 2.16231 + 0.77182I
u = 1.48212 + 0.39520I
a = 0.466011 + 1.151950I
b = 0.06640 + 1.79340I
−9.37134 + 0.19549I 0
u = 1.48212 − 0.39520I
a = 0.466011 − 1.151950I
b = 0.06640 − 1.79340I
−9.37134 − 0.19549I 0
u = −0.14949 + 1.54080I
a = −0.489674 − 0.086157I
b = −0.047121 − 0.560015I
1.51048 + 8.25732I 0
u = −0.14949 − 1.54080I
a = −0.489674 + 0.086157I
b = −0.047121 + 0.560015I
1.51048 − 8.25732I 0
u = 1.56042 + 0.34674I
a = 0.010384 − 1.048110I
b = 0.67684 − 1.68437I
−1.26128 − 7.24457I 0
u = 1.56042 − 0.34674I
a = 0.010384 + 1.048110I
b = 0.67684 + 1.68437I
−1.26128 + 7.24457I 0
u = 1.65389 + 0.09304I
a = 0.414399 + 0.961671I
b = −0.02065 + 1.74832I
−8.67096 + 2.54106I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65389 − 0.09304I
a = 0.414399 − 0.961671I
b = −0.02065 − 1.74832I
−8.67096 − 2.54106I 0
u = −0.010648 + 0.336630I
a = −0.862000 + 0.884016I
b = 0.186715 + 0.375985I
0.391751 + 1.001410I 6.35526 − 6.56819I
u = −0.010648 − 0.336630I
a = −0.862000 − 0.884016I
b = 0.186715 − 0.375985I
0.391751 − 1.001410I 6.35526 + 6.56819I
u = 1.69732 + 0.15917I
a = −0.038668 + 1.110620I
b = 0.55120 + 1.40451I
−7.69355 − 0.16950I 0
u = 1.69732 − 0.15917I
a = −0.038668 − 1.110620I
b = 0.55120 − 1.40451I
−7.69355 + 0.16950I 0
u = 1.71266 + 0.01894I
a = −0.436259 + 0.898448I
b = 0.05204 + 1.71503I
−6.53777 − 7.64853I 0
u = 1.71266 − 0.01894I
a = −0.436259 − 0.898448I
b = 0.05204 − 1.71503I
−6.53777 + 7.64853I 0
u = −1.64149 + 0.52671I
a = −0.146618 + 0.979002I
b = 0.32106 + 1.60321I
−3.98213 + 4.52901I 0
u = −1.64149 − 0.52671I
a = −0.146618 − 0.979002I
b = 0.32106 − 1.60321I
−3.98213 − 4.52901I 0
u = −1.62388 + 0.66255I
a = 0.156149 − 1.005480I
b = −0.33974 − 1.66999I
−1.69099 + 9.76232I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62388 − 0.66255I
a = 0.156149 + 1.005480I
b = −0.33974 + 1.66999I
−1.69099 − 9.76232I 0
u = −1.75783 + 0.13522I
a = −0.154026 + 0.860113I
b = 0.14670 + 1.46011I
−5.44293 + 1.91638I 0
u = −1.75783 − 0.13522I
a = −0.154026 − 0.860113I
b = 0.14670 − 1.46011I
−5.44293 − 1.91638I 0
u = 1.77611 + 0.03947I
a = 0.016455 + 1.094850I
b = −0.54064 + 1.51324I
−8.82927 − 5.92695I 0
u = 1.77611 − 0.03947I
a = 0.016455 − 1.094850I
b = −0.54064 − 1.51324I
−8.82927 + 5.92695I 0
u = −1.80292 + 0.06963I
a = 0.205300 + 0.777815I
b = −0.03434 + 1.45649I
−4.37924 + 2.95785I 0
u = −1.80292 − 0.06963I
a = 0.205300 − 0.777815I
b = −0.03434 − 1.45649I
−4.37924 − 2.95785I 0
u = 1.75562 + 0.45978I
a = −0.028610 + 1.074530I
b = −0.55514 + 1.73413I
−7.12058 − 10.34450I 0
u = 1.75562 − 0.45978I
a = −0.028610 − 1.074530I
b = −0.55514 − 1.73413I
−7.12058 + 10.34450I 0
u = 1.73522 + 0.57056I
a = 0.041863 − 1.072980I
b = 0.55270 − 1.79198I
−4.7685 − 16.0285I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73522 − 0.57056I
a = 0.041863 + 1.072980I
b = 0.55270 + 1.79198I
−4.7685 + 16.0285I 0
u = −1.83475 + 0.17714I
a = −0.000375 + 0.827349I
b = −0.049312 + 0.996855I
−5.37639 + 2.89949I 0
u = −1.83475 − 0.17714I
a = −0.000375 − 0.827349I
b = −0.049312 − 0.996855I
−5.37639 − 2.89949I 0
12
II. I
u
2
=
h−9u
21
−48u
20
+· · ·+b+11, 28u
21
+177u
20
+· · ·+a+3, u
22
+7u
21
+· · ·+7u+1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
9
=
−28u
21
− 177u
20
+ ··· − 66u − 3
9u
21
+ 48u
20
+ ··· − 57u − 11
a
5
=
6u
21
+ 41u
20
+ ··· + 92u + 16
−15u
21
− 100u
20
+ ··· − 137u − 19
a
1
=
−u − 1
u
21
+ 7u
20
+ ··· + 28u + 6
a
2
=
−u
21
− 7u
20
+ ··· − 29u − 7
u
21
+ 7u
20
+ ··· + 28u + 6
a
8
=
−37u
21
− 225u
20
+ ··· − 9u + 8
9u
21
+ 48u
20
+ ··· − 57u − 11
a
7
=
−37u
21
− 225u
20
+ ··· − 9u + 8
3u
21
− 7u
20
+ ··· − 258u − 45
a
6
=
−53u
21
− 365u
20
+ ··· − 460u − 65
28u
21
+ 177u
20
+ ··· + 66u + 3
a
11
=
7u
21
+ 49u
20
+ ··· + 142u + 28
−7u
21
− 48u
20
+ ··· − 120u − 21
a
10
=
8u
21
+ 40u
20
+ ··· − 16u − 4
2u
21
+ 19u
20
+ ··· + 60u + 11
(ii) Obstruction class = 1
(iii) Cusp Shapes = 76u
21
+ 537u
20
+ 1268u
19
+ 254u
18
− 4506u
17
− 9416u
16
−
6062u
15
+ 8390u
14
+ 23885u
13
+ 25018u
12
+ 7101u
11
−17555u
10
−30785u
9
−25183u
8
−
8290u
7
+ 6877u
6
+ 12900u
5
+ 10927u
4
+ 6127u
3
+ 2402u
2
+ 611u + 94
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
22
− 15u
21
+ ··· − 17u + 1
c
2
u
22
− u
21
+ ··· − u + 1
c
3
u
22
+ 7u
21
+ ··· + 7u + 1
c
4
u
22
− 2u
20
+ ··· + 2u + 1
c
5
u
22
+ 6u
20
+ ··· + 4u
2
+ 1
c
6
u
22
+ u
21
+ ··· + u + 1
c
7
u
22
− 2u
21
+ ··· + 4u
2
+ 1
c
8
u
22
+ 8u
20
+ ··· − 8u
2
+ 1
c
9
u
22
+ 12u
21
+ ··· + 8u + 1
c
10
u
22
+ 6u
20
+ ··· + 4u
2
+ 1
c
11
u
22
+ 2u
21
+ ··· + 4u
2
+ 1
c
12
u
22
+ 4u
20
+ ··· + 2u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− y
21
+ ··· − 19y + 1
c
2
, c
6
y
22
+ 15y
21
+ ··· + 17y + 1
c
3
y
22
− 15y
21
+ ··· + 7y + 1
c
4
y
22
− 4y
21
+ ··· + 10y + 1
c
5
, c
10
y
22
+ 12y
21
+ ··· + 8y + 1
c
7
, c
11
y
22
− 12y
21
+ ··· + 8y + 1
c
8
y
22
+ 16y
21
+ ··· − 16y + 1
c
9
y
22
+ 4y
21
+ ··· − 8y + 1
c
12
y
22
+ 8y
21
+ ··· − 12y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.786340 + 0.565962I
a = −0.480702 − 0.627163I
b = 0.794404 − 0.189170I
5.03496 − 3.36076I 8.69178 − 1.68696I
u = −0.786340 − 0.565962I
a = −0.480702 + 0.627163I
b = 0.794404 + 0.189170I
5.03496 + 3.36076I 8.69178 + 1.68696I
u = −0.645075 + 0.696793I
a = 0.519121 + 0.744340I
b = −0.426535 − 0.029869I
2.08453 + 1.37373I 6.40548 − 4.04825I
u = −0.645075 − 0.696793I
a = 0.519121 − 0.744340I
b = −0.426535 + 0.029869I
2.08453 − 1.37373I 6.40548 + 4.04825I
u = 1.050430 + 0.104212I
a = 0.033541 + 1.394220I
b = 0.14477 + 2.02805I
−6.17325 + 1.44187I −4.49643 − 5.78362I
u = 1.050430 − 0.104212I
a = 0.033541 − 1.394220I
b = 0.14477 − 2.02805I
−6.17325 − 1.44187I −4.49643 + 5.78362I
u = −0.196664 + 0.874491I
a = 0.533665 + 1.019810I
b = 0.576578 − 0.060736I
1.15199 + 2.87768I 6.14711 − 2.75750I
u = −0.196664 − 0.874491I
a = 0.533665 − 1.019810I
b = 0.576578 + 0.060736I
1.15199 − 2.87768I 6.14711 + 2.75750I
u = −0.025945 + 0.804370I
a = −0.552142 − 1.124630I
b = −1.022830 + 0.014286I
3.28844 + 7.64426I 8.77312 − 6.57606I
u = −0.025945 − 0.804370I
a = −0.552142 + 1.124630I
b = −1.022830 − 0.014286I
3.28844 − 7.64426I 8.77312 + 6.57606I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552269 + 0.511977I
a = −0.662176 − 0.681665I
b = 0.762642 + 0.506834I
5.76722 + 5.07165I 11.26800 − 7.37230I
u = −0.552269 − 0.511977I
a = −0.662176 + 0.681665I
b = 0.762642 − 0.506834I
5.76722 − 5.07165I 11.26800 + 7.37230I
u = −0.320236 + 0.596503I
a = 0.719182 + 0.904753I
b = 0.136570 − 0.890708I
2.51715 + 2.73559I 3.06423 − 4.00239I
u = −0.320236 − 0.596503I
a = 0.719182 − 0.904753I
b = 0.136570 + 0.890708I
2.51715 − 2.73559I 3.06423 + 4.00239I
u = −0.160838 + 0.633062I
a = −0.702253 − 1.056490I
b = −0.866556 + 0.783842I
4.58448 + 0.25572I 9.66478 + 0.84740I
u = −0.160838 − 0.633062I
a = −0.702253 + 1.056490I
b = −0.866556 − 0.783842I
4.58448 − 0.25572I 9.66478 − 0.84740I
u = −1.42190 + 0.08708I
a = 0.039113 + 0.548518I
b = −0.13321 + 1.42787I
−2.62572 − 1.09341I 7.40708 − 0.45044I
u = −1.42190 − 0.08708I
a = 0.039113 − 0.548518I
b = −0.13321 − 1.42787I
−2.62572 + 1.09341I 7.40708 + 0.45044I
u = 1.52157 + 0.14127I
a = 0.023534 + 1.285360I
b = 0.07886 + 1.61385I
−8.18195 − 2.56207I 0.65909 + 2.77062I
u = 1.52157 − 0.14127I
a = 0.023534 − 1.285360I
b = 0.07886 − 1.61385I
−8.18195 + 2.56207I 0.65909 − 2.77062I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.96273 + 0.15882I
a = 0.029119 + 0.703327I
b = −0.044696 + 1.062180I
−5.80293 + 2.78792I 0
u = −1.96273 − 0.15882I
a = 0.029119 − 0.703327I
b = −0.044696 − 1.062180I
−5.80293 − 2.78792I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 15u
21
+ ··· − 17u + 1)(u
73
+ 42u
72
+ ··· + u − 1)
c
2
(u
22
− u
21
+ ··· − u + 1)(u
73
− 2u
72
+ ··· + 3u − 1)
c
3
(u
22
+ 7u
21
+ ··· + 7u + 1)(u
73
− 4u
72
+ ··· − 7469u − 4961)
c
4
(u
22
− 2u
20
+ ··· + 2u + 1)(u
73
+ u
72
+ ··· + 504u − 34447)
c
5
(u
22
+ 6u
20
+ ··· + 4u
2
+ 1)(u
73
− u
72
+ ··· + 6u − 19)
c
6
(u
22
+ u
21
+ ··· + u + 1)(u
73
− 2u
72
+ ··· + 3u − 1)
c
7
(u
22
− 2u
21
+ ··· + 4u
2
+ 1)(u
73
− 3u
72
+ ··· + 518u − 77)
c
8
(u
22
+ 8u
20
+ ··· − 8u
2
+ 1)(u
73
− u
72
+ ··· − 4184u − 2449)
c
9
(u
22
+ 12u
21
+ ··· + 8u + 1)(u
73
− 35u
72
+ ··· − 3270u + 361)
c
10
(u
22
+ 6u
20
+ ··· + 4u
2
+ 1)(u
73
− u
72
+ ··· + 6u − 19)
c
11
(u
22
+ 2u
21
+ ··· + 4u
2
+ 1)(u
73
− 3u
72
+ ··· + 518u − 77)
c
12
(u
22
+ 4u
20
+ ··· + 2u + 1)(u
73
+ u
72
+ ··· + 9112u − 2479)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− y
21
+ ··· − 19y + 1)(y
73
− 6y
72
+ ··· + 109y −1)
c
2
, c
6
(y
22
+ 15y
21
+ ··· + 17y + 1)(y
73
+ 42y
72
+ ··· + y −1)
c
3
(y
22
− 15y
21
+ ··· + 7y + 1)
· (y
73
− 80y
72
+ ··· + 887378547y −24611521)
c
4
(y
22
− 4y
21
+ ··· + 10y + 1)
· (y
73
− 5y
72
+ ··· + 9963979872y −1186595809)
c
5
, c
10
(y
22
+ 12y
21
+ ··· + 8y + 1)(y
73
+ 35y
72
+ ··· − 3270y −361)
c
7
, c
11
(y
22
− 12y
21
+ ··· + 8y + 1)(y
73
− 25y
72
+ ··· − 47222y −5929)
c
8
(y
22
+ 16y
21
+ ··· − 16y + 1)
· (y
73
+ 83y
72
+ ··· − 316258558y −5997601)
c
9
(y
22
+ 4y
21
+ ··· − 8y + 1)(y
73
+ 15y
72
+ ··· − 1105302y −130321)
c
12
(y
22
+ 8y
21
+ ··· − 12y + 1)
· (y
73
+ 79y
72
+ ··· − 157637734y −6145441)
22
