12a
0416
(K12a
0416
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 7 2 1 11 5 8 4 10
Solving Sequence
3,6
2 7 1
8,10
11 5 9 12 4
c
2
c
6
c
1
c
7
c
10
c
5
c
9
c
12
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.41786 × 10
58
u
106
+ 1.11346 × 10
59
u
105
+ ··· + 3.68055 × 10
58
b + 3.69355 × 10
58
,
5.68621 × 10
58
u
106
+ 8.00830 × 10
58
u
105
+ ··· + 3.68055 × 10
58
a + 2.33644 × 10
58
, u
107
+ 2u
106
+ ··· + 5u
2
+ 1i
I
u
2
= h3u
3
− 10u
2
+ 16b + 5u − 1, u
3
+ 2u
2
+ 16a − 9u + 5, u
4
− u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 111 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
= h6.42 × 10
58
u
106
+ 1.11 × 10
59
u
105
+ · · · + 3.68 × 10
58
b + 3.69 ×
10
58
, 5.69 × 10
58
u
106
+ 8.01 × 10
58
u
105
+ · · · + 3.68 × 10
58
a + 2.34 ×
10
58
, u
107
+ 2u
106
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
10
=
−1.54494u
106
− 2.17584u
105
+ ··· + 4.67915u − 0.634808
−1.74372u
106
− 3.02525u
105
+ ··· − 0.345092u − 1.00353
a
11
=
−1.61452u
106
− 2.12033u
105
+ ··· + 2.40127u − 0.833938
−1.79319u
106
− 3.10408u
105
+ ··· − 1.51075u − 1.20808
a
5
=
u
3
u
5
+ u
3
+ u
a
9
=
−1.30918u
106
− 1.99248u
105
+ ··· + 4.75193u − 0.619919
−1.49000u
106
− 2.55809u
105
+ ··· − 0.284829u − 0.785527
a
12
=
1.91247u
106
+ 1.68905u
105
+ ··· + 0.287353u − 2.38447
1.66556u
106
+ 3.26726u
105
+ ··· + 3.40325u + 0.816457
a
4
=
−0.193027u
106
+ 0.449266u
105
+ ··· − 2.00140u + 0.00824800
0.232615u
106
+ 0.0280210u
105
+ ··· + 4.32238u − 1.20722
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.124020u
106
− 0.719172u
105
+ ··· − 1.22907u − 7.39183
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
107
+ 36u
106
+ ··· − 10u − 1
c
2
, c
6
u
107
− 2u
106
+ ··· − 5u
2
− 1
c
3
16(16u
107
− 75u
106
+ ··· − 2.85939 × 10
8
u − 5.57740 × 10
7
)
c
4
, c
11
u
107
+ 2u
106
+ ··· + 4u + 1
c
7
u
107
+ 10u
106
+ ··· − 55360u − 60751
c
8
, c
10
u
107
− 5u
106
+ ··· + 3671u + 256
c
9
u
107
− 3u
106
+ ··· − 14208u − 4096
c
12
16(16u
107
+ 83u
106
+ ··· + 1.25403 × 10
8
u − 9972353)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
107
+ 72y
106
+ ··· − 22y −1
c
2
, c
6
y
107
+ 36y
106
+ ··· − 10y −1
c
3
256(256y
107
+ 25319y
106
+ ··· − 7.95186 × 10
16
y −3.11074 × 10
15
)
c
4
, c
11
y
107
− 72y
106
+ ··· − 10y −1
c
7
y
107
+ 36y
106
+ ··· − 86065371038y −3690684001
c
8
, c
10
y
107
− 85y
106
+ ··· + 5667729y −65536
c
9
y
107
+ 27y
106
+ ··· − 1042857984y −16777216
c
12
256
· (256y
107
− 3401y
106
+ ··· + 3072980132794765y −99447824356609)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572555 + 0.816228I
a = 2.52809 + 0.77404I
b = 0.51685 + 1.60831I
−2.67149 + 4.54950I 0
u = 0.572555 − 0.816228I
a = 2.52809 − 0.77404I
b = 0.51685 − 1.60831I
−2.67149 − 4.54950I 0
u = −0.739110 + 0.684442I
a = 1.64740 + 0.61961I
b = 1.54687 + 0.42061I
−0.333003 + 0.042241I 0
u = −0.739110 − 0.684442I
a = 1.64740 − 0.61961I
b = 1.54687 − 0.42061I
−0.333003 − 0.042241I 0
u = 0.693461 + 0.733009I
a = 0.96918 + 4.82361I
b = 0.47980 + 4.66509I
−1.47357 − 0.02935I 0
u = 0.693461 − 0.733009I
a = 0.96918 − 4.82361I
b = 0.47980 − 4.66509I
−1.47357 + 0.02935I 0
u = −0.647407 + 0.776662I
a = −1.38461 + 0.99050I
b = −0.48414 + 1.42730I
0.84772 − 2.11192I 0
u = −0.647407 − 0.776662I
a = −1.38461 − 0.99050I
b = −0.48414 − 1.42730I
0.84772 + 2.11192I 0
u = 0.046668 + 1.012190I
a = 1.11018 + 1.35436I
b = −1.68594 − 1.42232I
−5.79533 − 0.00929I 0
u = 0.046668 − 1.012190I
a = 1.11018 − 1.35436I
b = −1.68594 + 1.42232I
−5.79533 + 0.00929I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779058 + 0.650419I
a = 2.55013 − 1.30493I
b = 1.56781 − 1.66329I
−0.45641 + 6.27660I 0
u = −0.779058 − 0.650419I
a = 2.55013 + 1.30493I
b = 1.56781 + 1.66329I
−0.45641 − 6.27660I 0
u = −0.718616 + 0.656188I
a = 1.50113 − 0.25187I
b = 1.54019 − 1.12578I
−0.67697 + 1.53545I 0
u = −0.718616 − 0.656188I
a = 1.50113 + 0.25187I
b = 1.54019 + 1.12578I
−0.67697 − 1.53545I 0
u = 0.777566 + 0.672502I
a = −1.70061 − 0.94033I
b = −1.06308 − 1.09985I
3.07553 − 2.64129I 0
u = 0.777566 − 0.672502I
a = −1.70061 + 0.94033I
b = −1.06308 + 1.09985I
3.07553 + 2.64129I 0
u = −0.078882 + 1.030440I
a = −0.621536 + 0.191873I
b = 1.48564 + 0.21337I
−2.81526 − 2.54077I 0
u = −0.078882 − 1.030440I
a = −0.621536 − 0.191873I
b = 1.48564 − 0.21337I
−2.81526 + 2.54077I 0
u = 0.018006 + 1.038180I
a = 1.04825 − 1.03206I
b = −1.51635 + 0.37279I
−5.96646 + 1.12046I 0
u = 0.018006 − 1.038180I
a = 1.04825 + 1.03206I
b = −1.51635 − 0.37279I
−5.96646 − 1.12046I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727533 + 0.620282I
a = −2.21540 + 1.31033I
b = −1.97976 − 0.19879I
−5.08482 − 3.05325I 0
u = 0.727533 − 0.620282I
a = −2.21540 − 1.31033I
b = −1.97976 + 0.19879I
−5.08482 + 3.05325I 0
u = 0.837675 + 0.627096I
a = 1.61326 + 0.70242I
b = 1.42239 + 1.01685I
−0.72153 − 6.99583I 0
u = 0.837675 − 0.627096I
a = 1.61326 − 0.70242I
b = 1.42239 − 1.01685I
−0.72153 + 6.99583I 0
u = −0.833095 + 0.636825I
a = −2.29893 + 0.83993I
b = −1.98652 + 1.23353I
−5.55745 + 12.65750I 0
u = −0.833095 − 0.636825I
a = −2.29893 − 0.83993I
b = −1.98652 − 1.23353I
−5.55745 − 12.65750I 0
u = 0.663407 + 0.676201I
a = 1.72189 + 0.62515I
b = 0.962894 − 0.088589I
−1.161400 + 0.572745I 0
u = 0.663407 − 0.676201I
a = 1.72189 − 0.62515I
b = 0.962894 + 0.088589I
−1.161400 − 0.572745I 0
u = 0.072508 + 1.059040I
a = 0.718322 − 0.057892I
b = −2.23899 + 0.56383I
−6.38996 + 5.89641I 0
u = 0.072508 − 1.059040I
a = 0.718322 + 0.057892I
b = −2.23899 − 0.56383I
−6.38996 − 5.89641I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021482 + 1.065870I
a = −0.498349 − 0.295555I
b = 1.57487 − 1.20386I
−10.53900 − 2.34670I 0
u = −0.021482 − 1.065870I
a = −0.498349 + 0.295555I
b = 1.57487 + 1.20386I
−10.53900 + 2.34670I 0
u = −0.861913 + 0.640246I
a = −1.127330 − 0.215348I
b = −1.160100 + 0.147222I
−4.62472 + 0.42113I 0
u = −0.861913 − 0.640246I
a = −1.127330 + 0.215348I
b = −1.160100 − 0.147222I
−4.62472 − 0.42113I 0
u = −0.733935 + 0.841377I
a = −0.207227 − 0.928291I
b = −0.919580 + 0.275183I
2.46950 − 5.13290I 0
u = −0.733935 − 0.841377I
a = −0.207227 + 0.928291I
b = −0.919580 − 0.275183I
2.46950 + 5.13290I 0
u = 0.111769 + 1.113810I
a = −0.968189 − 0.007849I
b = 2.09870 − 0.48022I
−12.1009 + 12.0094I 0
u = 0.111769 − 1.113810I
a = −0.968189 + 0.007849I
b = 2.09870 + 0.48022I
−12.1009 − 12.0094I 0
u = 0.765238 + 0.818174I
a = −0.212152 − 0.487781I
b = 0.491573 + 0.001552I
5.25937 + 0.90397I 0
u = 0.765238 − 0.818174I
a = −0.212152 + 0.487781I
b = 0.491573 − 0.001552I
5.25937 − 0.90397I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.634185 + 0.597497I
a = −1.20096 + 2.39832I
b = 0.044086 + 0.934957I
−5.60148 − 1.35298I 0
u = −0.634185 − 0.597497I
a = −1.20096 − 2.39832I
b = 0.044086 − 0.934957I
−5.60148 + 1.35298I 0
u = −0.109524 + 1.125450I
a = 0.705092 + 0.077937I
b = −1.49776 − 0.36174I
−7.29613 − 6.22971I 0
u = −0.109524 − 1.125450I
a = 0.705092 − 0.077937I
b = −1.49776 + 0.36174I
−7.29613 + 6.22971I 0
u = 0.132569 + 1.127410I
a = −0.452270 − 0.144598I
b = 1.151400 + 0.385658I
−11.45990 − 0.25981I 0
u = 0.132569 − 1.127410I
a = −0.452270 + 0.144598I
b = 1.151400 − 0.385658I
−11.45990 + 0.25981I 0
u = −0.721484 + 0.881806I
a = 0.287036 + 0.095689I
b = 1.006650 − 0.068646I
2.34405 − 0.40468I 0
u = −0.721484 − 0.881806I
a = 0.287036 − 0.095689I
b = 1.006650 + 0.068646I
2.34405 + 0.40468I 0
u = −0.636751 + 0.946553I
a = −0.38190 + 1.89505I
b = 1.13597 + 1.16685I
0.30477 − 2.89231I 0
u = −0.636751 − 0.946553I
a = −0.38190 − 1.89505I
b = 1.13597 − 1.16685I
0.30477 + 2.89231I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605466 + 0.969047I
a = −0.47718 + 2.60038I
b = −1.75712 + 1.09425I
−3.29947 + 0.02397I 0
u = 0.605466 − 0.969047I
a = −0.47718 − 2.60038I
b = −1.75712 − 1.09425I
−3.29947 − 0.02397I 0
u = 0.501653 + 1.045680I
a = −0.76284 − 1.21835I
b = 0.416918 − 0.654919I
−9.20052 + 7.31020I 0
u = 0.501653 − 1.045680I
a = −0.76284 + 1.21835I
b = 0.416918 + 0.654919I
−9.20052 − 7.31020I 0
u = 0.531187 + 1.038580I
a = 0.38097 − 2.08084I
b = 1.352130 − 0.228748I
−9.54319 − 5.13852I 0
u = 0.531187 − 1.038580I
a = 0.38097 + 2.08084I
b = 1.352130 + 0.228748I
−9.54319 + 5.13852I 0
u = −0.245463 + 0.792676I
a = 0.199411 + 0.599935I
b = 0.271663 + 0.310043I
−0.56851 − 1.64515I 0. + 5.38816I
u = −0.245463 − 0.792676I
a = 0.199411 − 0.599935I
b = 0.271663 − 0.310043I
−0.56851 + 1.64515I 0. − 5.38816I
u = 0.665165 + 0.963024I
a = 3.68761 + 3.95714I
b = −1.50055 + 3.53640I
−2.17929 + 5.27880I 0
u = 0.665165 − 0.963024I
a = 3.68761 − 3.95714I
b = −1.50055 − 3.53640I
−2.17929 − 5.27880I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745883 + 0.914563I
a = −0.0171571 − 0.0566864I
b = −0.494211 − 0.276217I
4.96743 + 4.80385I 0
u = 0.745883 − 0.914563I
a = −0.0171571 + 0.0566864I
b = −0.494211 + 0.276217I
4.96743 − 4.80385I 0
u = −0.811697 + 0.857361I
a = 0.450118 − 0.099056I
b = −0.312448 − 0.472158I
−0.73668 + 3.73977I 0
u = −0.811697 − 0.857361I
a = 0.450118 + 0.099056I
b = −0.312448 + 0.472158I
−0.73668 − 3.73977I 0
u = −0.529166 + 1.057900I
a = −0.137429 − 1.371400I
b = −0.821551 − 0.155925I
−4.70260 − 0.83335I 0
u = −0.529166 − 1.057900I
a = −0.137429 + 1.371400I
b = −0.821551 + 0.155925I
−4.70260 + 0.83335I 0
u = 0.656100 + 0.987672I
a = −1.02169 + 2.13604I
b = −1.127310 + 0.026416I
−2.10121 + 4.59471I 0
u = 0.656100 − 0.987672I
a = −1.02169 − 2.13604I
b = −1.127310 − 0.026416I
−2.10121 − 4.59471I 0
u = −0.641946 + 1.002990I
a = −1.20790 + 2.08709I
b = 0.15928 + 1.79219I
−6.75012 − 3.71244I 0
u = −0.641946 − 1.002990I
a = −1.20790 − 2.08709I
b = 0.15928 − 1.79219I
−6.75012 + 3.71244I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749094 + 0.305561I
a = 1.051380 − 0.015805I
b = 0.884161 + 0.341399I
−2.47323 − 3.82700I −4.04906 + 6.12784I
u = −0.749094 − 0.305561I
a = 1.051380 + 0.015805I
b = 0.884161 − 0.341399I
−2.47323 + 3.82700I −4.04906 − 6.12784I
u = −0.794258 + 0.900063I
a = 0.0218861 + 0.0446674I
b = 0.161813 − 0.644801I
−0.87138 − 9.73384I 0
u = −0.794258 − 0.900063I
a = 0.0218861 − 0.0446674I
b = 0.161813 + 0.644801I
−0.87138 + 9.73384I 0
u = −0.672273 + 1.000660I
a = 0.36256 − 2.06486I
b = −1.85620 − 0.99758I
−1.70112 − 6.88767I 0
u = −0.672273 − 1.000660I
a = 0.36256 + 2.06486I
b = −1.85620 + 0.99758I
−1.70112 + 6.88767I 0
u = −0.688074 + 0.993783I
a = −1.68115 − 1.97202I
b = −1.87014 + 0.44496I
−1.26073 − 5.50150I 0
u = −0.688074 − 0.993783I
a = −1.68115 + 1.97202I
b = −1.87014 − 0.44496I
−1.26073 + 5.50150I 0
u = 0.667865 + 1.014470I
a = 1.59065 − 1.79707I
b = 2.56053 + 0.11805I
−6.24275 + 8.40853I 0
u = 0.667865 − 1.014470I
a = 1.59065 + 1.79707I
b = 2.56053 − 0.11805I
−6.24275 − 8.40853I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746220 + 0.243908I
a = −0.548011 − 0.781846I
b = −0.682427 − 0.253394I
−6.82390 − 2.87754I −7.55606 + 2.65618I
u = 0.746220 − 0.243908I
a = −0.548011 + 0.781846I
b = −0.682427 + 0.253394I
−6.82390 + 2.87754I −7.55606 − 2.65618I
u = 0.717094 + 0.295055I
a = −1.73531 − 0.02894I
b = −1.35567 + 0.43051I
−7.41312 + 9.67363I −4.73264 − 6.38997I
u = 0.717094 − 0.295055I
a = −1.73531 + 0.02894I
b = −1.35567 − 0.43051I
−7.41312 − 9.67363I −4.73264 + 6.38997I
u = 0.699336 + 1.008630I
a = −0.14409 − 2.25681I
b = 1.39931 − 1.21172I
2.06203 + 8.23607I 0
u = 0.699336 − 1.008630I
a = −0.14409 + 2.25681I
b = 1.39931 + 1.21172I
2.06203 − 8.23607I 0
u = −0.693869 + 1.018100I
a = 0.30703 − 3.14528I
b = −2.01636 − 1.87103I
−1.55940 − 11.85470I 0
u = −0.693869 − 1.018100I
a = 0.30703 + 3.14528I
b = −2.01636 + 1.87103I
−1.55940 + 11.85470I 0
u = 0.865077 + 0.912693I
a = −0.147695 − 0.056476I
b = 0.017267 − 0.336869I
5.02105 + 3.20233I 0
u = 0.865077 − 0.912693I
a = −0.147695 + 0.056476I
b = 0.017267 + 0.336869I
5.02105 − 3.20233I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.710551 + 1.042030I
a = 0.03854 + 2.97997I
b = 2.27288 + 1.28431I
−6.7863 − 18.4344I 0
u = −0.710551 − 1.042030I
a = 0.03854 − 2.97997I
b = 2.27288 − 1.28431I
−6.7863 + 18.4344I 0
u = 0.708638 + 1.046960I
a = 0.13873 + 2.21107I
b = −1.68135 + 1.06324I
−1.99428 + 12.77590I 0
u = 0.708638 − 1.046960I
a = 0.13873 − 2.21107I
b = −1.68135 − 1.06324I
−1.99428 − 12.77590I 0
u = −0.720384 + 1.052700I
a = 0.540882 + 1.306510I
b = 1.362950 + 0.189864I
−5.89103 − 6.31209I 0
u = −0.720384 − 1.052700I
a = 0.540882 − 1.306510I
b = 1.362950 − 0.189864I
−5.89103 + 6.31209I 0
u = −0.219769 + 0.626637I
a = −1.28173 + 2.73269I
b = 0.397565 − 0.307830I
−5.57963 − 1.60313I −10.66319 + 3.91153I
u = −0.219769 − 0.626637I
a = −1.28173 − 2.73269I
b = 0.397565 + 0.307830I
−5.57963 + 1.60313I −10.66319 − 3.91153I
u = 0.530510 + 0.326469I
a = 2.34754 + 0.32620I
b = 0.902410 − 0.116640I
−2.07804 + 4.29773I −3.00401 − 7.13446I
u = 0.530510 − 0.326469I
a = 2.34754 − 0.32620I
b = 0.902410 + 0.116640I
−2.07804 − 4.29773I −3.00401 + 7.13446I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492999 + 0.207407I
a = −1.344610 + 0.074414I
b = −0.509915 − 0.140971I
1.044660 − 0.934483I 4.99330 + 2.84480I
u = −0.492999 − 0.207407I
a = −1.344610 − 0.074414I
b = −0.509915 + 0.140971I
1.044660 + 0.934483I 4.99330 − 2.84480I
u = 0.405448 + 0.294968I
a = 0.58034 + 1.41016I
b = 0.634644 + 0.871857I
−1.95599 − 1.13377I −2.53809 − 1.17932I
u = 0.405448 − 0.294968I
a = 0.58034 − 1.41016I
b = 0.634644 − 0.871857I
−1.95599 + 1.13377I −2.53809 + 1.17932I
u = 0.190818 + 0.343308I
a = 0.80570 + 1.44261I
b = 0.599634 − 0.623946I
−1.77412 + 0.60929I −5.34675 + 2.38641I
u = 0.190818 − 0.343308I
a = 0.80570 − 1.44261I
b = 0.599634 + 0.623946I
−1.77412 − 0.60929I −5.34675 − 2.38641I
u = −0.340862
a = −1.81662
b = −2.49020
−3.83963 12.7780
15
II.
I
u
2
= h3u
3
− 10u
2
+ 16b + 5u − 1, u
3
+ 2u
2
+ 16a − 9u + 5, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
8
=
−2u
2
− 1
−u
2
a
10
=
−
1
16
u
3
−
1
8
u
2
+
9
16
u −
5
16
−
3
16
u
3
+
5
8
u
2
−
5
16
u +
1
16
a
11
=
−0.0625000u
3
+ 1.87500u
2
+ 0.562500u + 0.687500
−
3
16
u
3
+
13
8
u
2
−
5
16
u +
1
16
a
5
=
u
3
u
3
− u
2
− 1
a
9
=
−
1
16
u
3
−
1
8
u
2
+
9
16
u −
5
16
−
3
16
u
3
+
5
8
u
2
−
5
16
u +
1
16
a
12
=
−0.136719u
3
+ 0.976563u
2
+ 0.292969u + 0.628906
−0.160156u
3
+ 1.42969u
2
− 0.371094u + 0.136719
a
4
=
−0.269531u
3
+ 0.210938u
2
− 0.136719u + 0.839844
−0.0585938u
3
+ 0.132813u
2
− 0.160156u + 0.269531
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2223
256
u
3
+
625
128
u
2
+
2679
256
u +
805
256
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
16(16u
4
+ 5u
3
+ 8u
2
+ u + 1)
c
4
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
8
(u − 1)
4
c
9
u
4
c
10
(u + 1)
4
c
12
16(16u
4
+ 35u
3
+ 28u
2
+ 9u + 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
256(256y
4
+ 231y
3
+ 86y
2
+ 15y + 1)
c
7
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
8
, c
10
(y − 1)
4
c
9
y
4
c
12
256(256y
4
− 329y
3
+ 186y
2
− 25y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = −0.492508 + 0.475192I
b = −0.169032 − 0.521951I
−1.85594 − 1.41510I −6.84387 + 5.98661I
u = −0.351808 − 0.720342I
a = −0.492508 − 0.475192I
b = −0.169032 + 0.521951I
−1.85594 + 1.41510I −6.84387 − 5.98661I
u = 0.851808 + 0.911292I
a = 0.273758 + 0.241862I
b = 0.012782 + 0.455494I
5.14581 + 3.16396I 24.6075 + 6.4636I
u = 0.851808 − 0.911292I
a = 0.273758 − 0.241862I
b = 0.012782 − 0.455494I
5.14581 − 3.16396I 24.6075 − 6.4636I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
107
+ 36u
106
+ ··· − 10u − 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
107
− 2u
106
+ ··· − 5u
2
− 1)
c
3
256(16u
4
+ 5u
3
+ 8u
2
+ u + 1)
· (16u
107
− 75u
106
+ ··· − 285938817u − 55773989)
c
4
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
107
+ 2u
106
+ ··· + 4u + 1)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
107
− 2u
106
+ ··· − 5u
2
− 1)
c
7
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
107
+ 10u
106
+ ··· − 55360u − 60751)
c
8
((u − 1)
4
)(u
107
− 5u
106
+ ··· + 3671u + 256)
c
9
u
4
(u
107
− 3u
106
+ ··· − 14208u − 4096)
c
10
((u + 1)
4
)(u
107
− 5u
106
+ ··· + 3671u + 256)
c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
107
+ 2u
106
+ ··· + 4u + 1)
c
12
256(16u
4
+ 35u
3
+ 28u
2
+ 9u + 1)
· (16u
107
+ 83u
106
+ ··· + 125402807u − 9972353)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
107
+ 72y
106
+ ··· − 22y − 1)
c
2
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
107
+ 36y
106
+ ··· − 10y − 1)
c
3
65536(256y
4
+ 231y
3
+ 86y
2
+ 15y + 1)
· (256y
107
+ 2.53 × 10
4
y
106
+ ··· − 7.95 × 10
16
y − 3.11 × 10
15
)
c
4
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
107
− 72y
106
+ ··· − 10y − 1)
c
7
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)
· (y
107
+ 36y
106
+ ··· − 86065371038y − 3690684001)
c
8
, c
10
((y − 1)
4
)(y
107
− 85y
106
+ ··· + 5667729y − 65536)
c
9
y
4
(y
107
+ 27y
106
+ ··· − 1.04286 × 10
9
y − 1.67772 × 10
7
)
c
12
65536(256y
4
− 329y
3
+ 186y
2
− 25y + 1)
· (256y
107
− 3401y
106
+ ··· + 3072980132794765y − 99447824356609)
21
