12n
0431
(K12n
0431
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 9 2 12 1 5 4 8 10
Solving Sequence
4,12 5,8
3 7 11 10 1 2 6 9
c
4
c
3
c
7
c
11
c
10
c
12
c
1
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.28741 × 10
479
u
73
− 2.87933 × 10
478
u
72
+ ··· + 8.18620 × 10
484
b + 8.77584 × 10
484
,
− 9.92062 × 10
484
u
73
− 8.13255 × 10
483
u
72
+ ··· + 1.40884 × 10
490
a − 5.50149 × 10
490
,
u
74
+ 17u
72
+ ··· + 566418u + 172099i
I
u
2
= h3.09881 × 10
32
u
23
− 1.01801 × 10
33
u
22
+ ··· + 2.58026 × 10
32
b + 5.97065 × 10
32
,
− 9.65284 × 10
32
u
23
+ 3.27534 × 10
33
u
22
+ ··· + 2.58026 × 10
32
a − 2.48109 × 10
33
, u
24
− 3u
23
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 98 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
= h3.29 × 10
479
u
73
− 2.88 × 10
478
u
72
+ · · · + 8.19 × 10
484
b + 8.78 ×
10
484
, −9.92 × 10
484
u
73
− 8.13 × 10
483
u
72
+ · · · + 1.41 × 10
490
a − 5.50 ×
10
490
, u
74
+ 17u
72
+ · · · + 566418u + 172099i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
7.04171 × 10
−6
u
73
+ 5.77253 × 10
−7
u
72
+ ··· + 22.2661u + 3.90499
−4.01579 × 10
−6
u
73
+ 3.51729 × 10
−7
u
72
+ ··· − 12.7786u − 1.07203
a
3
=
4.10227 × 10
−6
u
73
− 5.68165 × 10
−7
u
72
+ ··· + 9.97933u − 6.12982
2.46937 × 10
−6
u
73
− 9.40460 × 10
−7
u
72
+ ··· + 3.33975u + 4.81554
a
7
=
7.04171 × 10
−6
u
73
+ 5.77253 × 10
−7
u
72
+ ··· + 22.2661u + 3.90499
−5.02310 × 10
−6
u
73
+ 9.02842 × 10
−7
u
72
+ ··· − 14.3175u − 1.17137
a
11
=
3.03522 × 10
−6
u
73
− 5.96192 × 10
−7
u
72
+ ··· + 17.7584u + 3.27815
−5.68165 × 10
−7
u
73
+ 4.05095 × 10
−7
u
72
+ ··· − 8.45342u − 0.705996
a
10
=
2.46706 × 10
−6
u
73
− 1.91097 × 10
−7
u
72
+ ··· + 9.30498u + 2.57215
−5.68165 × 10
−7
u
73
+ 4.05095 × 10
−7
u
72
+ ··· − 8.45342u − 0.705996
a
1
=
−3.83456 × 10
−6
u
73
+ 2.72856 × 10
−6
u
72
+ ··· + 1.24718u + 1.08281
9.25604 × 10
−8
u
73
− 1.11084 × 10
−8
u
72
+ ··· − 3.16667u − 1.19214
a
2
=
−0.0000145703u
73
+ 3.10645 × 10
−6
u
72
+ ··· − 21.8387u + 2.58100
7.25950 × 10
−6
u
73
− 1.35849 × 10
−6
u
72
+ ··· + 7.69972u − 4.14218
a
6
=
3.33389 × 10
−6
u
73
+ 1.49484 × 10
−6
u
72
+ ··· + 15.6618u − 1.68488
2.06380 × 10
−6
u
73
− 3.06763 × 10
−6
u
72
+ ··· − 4.88783u + 1.52464
a
9
=
3.64252 × 10
−6
u
73
− 7.63769 × 10
−7
u
72
+ ··· + 17.4421u + 3.31103
−7.64708 × 10
−8
u
73
+ 8.94112 × 10
−7
u
72
+ ··· − 8.33134u − 0.607440
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −0.0000403389u
73
+ 0.0000203868u
72
+ ··· − 47.2240u + 0.0222812
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 34u
73
+ ··· + 340368u + 13456
c
2
, c
6
u
74
− 2u
73
+ ··· − 192u + 116
c
3
u
74
− 3u
73
+ ··· + 2408u + 184
c
4
u
74
+ 17u
72
+ ··· − 566418u + 172099
c
5
, c
9
u
74
− 4u
73
+ ··· − 69u + 131
c
7
, c
11
u
74
− u
73
+ ··· − 325282u + 19639
c
8
u
74
+ 3u
73
+ ··· − 8536u + 1093
c
10
u
74
− 2u
73
+ ··· + 49021u + 18569
c
12
u
74
− 9u
73
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 26y
73
+ ··· + 2544232064y + 181063936
c
2
, c
6
y
74
+ 34y
73
+ ··· + 340368y + 13456
c
3
y
74
+ 103y
73
+ ··· + 155040y + 33856
c
4
y
74
+ 34y
73
+ ··· + 998146334424y + 29618065801
c
5
, c
9
y
74
+ 44y
73
+ ··· + 371471y + 17161
c
7
, c
11
y
74
− 93y
73
+ ··· − 43352903060y + 385690321
c
8
y
74
+ 9y
73
+ ··· + 23967760y + 1194649
c
10
y
74
+ 90y
73
+ ··· + 2650383495y + 344807761
c
12
y
74
− 3y
73
+ ··· − 56y
2
+ 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.934779 + 0.503629I
a = −1.194160 − 0.295302I
b = −0.254337 − 0.211732I
−0.307331 − 1.010300I 0
u = 0.934779 − 0.503629I
a = −1.194160 + 0.295302I
b = −0.254337 + 0.211732I
−0.307331 + 1.010300I 0
u = −1.002250 + 0.372992I
a = −0.268943 − 0.748372I
b = 0.369189 + 0.429283I
−6.55930 + 3.70588I −5.57212 + 0.I
u = −1.002250 − 0.372992I
a = −0.268943 + 0.748372I
b = 0.369189 − 0.429283I
−6.55930 − 3.70588I −5.57212 + 0.I
u = −0.374952 + 0.843157I
a = −0.597418 − 0.434941I
b = −1.021630 − 0.003737I
−5.47234 + 0.86790I −3.59499 + 0.79812I
u = −0.374952 − 0.843157I
a = −0.597418 + 0.434941I
b = −1.021630 + 0.003737I
−5.47234 − 0.86790I −3.59499 − 0.79812I
u = 1.082250 + 0.107771I
a = −0.608665 + 0.566681I
b = −0.859754 − 0.446277I
−0.94736 − 5.88404I 0. + 8.12047I
u = 1.082250 − 0.107771I
a = −0.608665 − 0.566681I
b = −0.859754 + 0.446277I
−0.94736 + 5.88404I 0. − 8.12047I
u = −0.435194 + 0.774098I
a = 1.52616 + 0.04105I
b = 0.110382 − 0.125676I
0.58998 − 3.66458I 2.57268 + 0.26922I
u = −0.435194 − 0.774098I
a = 1.52616 − 0.04105I
b = 0.110382 + 0.125676I
0.58998 + 3.66458I 2.57268 − 0.26922I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.810830 + 0.337697I
a = 0.464928 + 0.856520I
b = 0.242275 − 0.682677I
1.26684 + 1.82853I 1.78603 − 4.52891I
u = −0.810830 − 0.337697I
a = 0.464928 − 0.856520I
b = 0.242275 + 0.682677I
1.26684 − 1.82853I 1.78603 + 4.52891I
u = −0.016733 + 0.853800I
a = −0.61995 − 2.02125I
b = −0.15930 + 1.56017I
8.24996 − 1.54945I 3.85987 + 1.93387I
u = −0.016733 − 0.853800I
a = −0.61995 + 2.02125I
b = −0.15930 − 1.56017I
8.24996 + 1.54945I 3.85987 − 1.93387I
u = 0.639477 + 0.519628I
a = 0.565407 + 0.564947I
b = 0.207804 − 0.033918I
−1.11297 − 1.12209I −5.31504 + 3.79418I
u = 0.639477 − 0.519628I
a = 0.565407 − 0.564947I
b = 0.207804 + 0.033918I
−1.11297 + 1.12209I −5.31504 − 3.79418I
u = −0.350425 + 0.723346I
a = 0.370401 − 0.209665I
b = 0.115118 + 0.975558I
0.72481 − 1.83639I 1.12069 + 4.87359I
u = −0.350425 − 0.723346I
a = 0.370401 + 0.209665I
b = 0.115118 − 0.975558I
0.72481 + 1.83639I 1.12069 − 4.87359I
u = 0.457795 + 0.617756I
a = 1.43093 − 1.15085I
b = 0.47311 + 1.48482I
2.48087 − 3.10809I 2.96786 + 1.73580I
u = 0.457795 − 0.617756I
a = 1.43093 + 1.15085I
b = 0.47311 − 1.48482I
2.48087 + 3.10809I 2.96786 − 1.73580I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.216764 + 0.727146I
a = 0.14023 − 2.38086I
b = 0.02763 + 1.51400I
5.47332 + 8.05912I 0.18543 − 6.05650I
u = −0.216764 − 0.727146I
a = 0.14023 + 2.38086I
b = 0.02763 − 1.51400I
5.47332 − 8.05912I 0.18543 + 6.05650I
u = 0.319181 + 1.202940I
a = 0.431572 − 0.366985I
b = 1.203360 + 0.711683I
−0.85478 − 3.82352I 0
u = 0.319181 − 1.202940I
a = 0.431572 + 0.366985I
b = 1.203360 − 0.711683I
−0.85478 + 3.82352I 0
u = −0.467790 + 0.563021I
a = 0.549943 + 1.084810I
b = −0.532295 − 1.238560I
1.58966 + 1.29211I 4.03888 + 5.21852I
u = −0.467790 − 0.563021I
a = 0.549943 − 1.084810I
b = −0.532295 + 1.238560I
1.58966 − 1.29211I 4.03888 − 5.21852I
u = −0.547174 + 0.464224I
a = −1.47110 + 1.20328I
b = −0.093733 + 0.616829I
−9.47431 + 0.30033I −4.15634 + 8.16557I
u = −0.547174 − 0.464224I
a = −1.47110 − 1.20328I
b = −0.093733 − 0.616829I
−9.47431 − 0.30033I −4.15634 − 8.16557I
u = 1.088520 + 0.716063I
a = 0.709402 + 0.222922I
b = −0.110085 + 0.256217I
−1.25400 − 2.51544I 0
u = 1.088520 − 0.716063I
a = 0.709402 − 0.222922I
b = −0.110085 − 0.256217I
−1.25400 + 2.51544I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518744 + 1.213760I
a = −0.419984 − 0.307566I
b = −1.64440 + 0.69687I
−3.28433 + 8.86378I 0
u = −0.518744 − 1.213760I
a = −0.419984 + 0.307566I
b = −1.64440 − 0.69687I
−3.28433 − 8.86378I 0
u = 0.512571 + 0.438202I
a = −0.691080 − 0.061151I
b = 1.050440 − 0.405546I
0.61911 + 3.11056I 3.75248 + 0.56298I
u = 0.512571 − 0.438202I
a = −0.691080 + 0.061151I
b = 1.050440 + 0.405546I
0.61911 − 3.11056I 3.75248 − 0.56298I
u = −0.521401 + 0.376721I
a = 1.142470 + 0.548301I
b = −1.154480 − 0.714467I
1.65020 + 1.37390I 18.4680 − 12.7347I
u = −0.521401 − 0.376721I
a = 1.142470 − 0.548301I
b = −1.154480 + 0.714467I
1.65020 − 1.37390I 18.4680 + 12.7347I
u = 0.329499 + 0.490134I
a = −0.151663 + 0.089033I
b = 0.744003 + 0.776343I
−0.25653 − 2.28963I −1.31647 + 4.44383I
u = 0.329499 − 0.490134I
a = −0.151663 − 0.089033I
b = 0.744003 − 0.776343I
−0.25653 + 2.28963I −1.31647 − 4.44383I
u = −1.29609 + 0.63868I
a = −0.714241 + 0.014858I
b = 0.224602 + 0.245414I
−2.18586 + 8.15624I 0
u = −1.29609 − 0.63868I
a = −0.714241 − 0.014858I
b = 0.224602 − 0.245414I
−2.18586 − 8.15624I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57675 + 1.33502I
a = −0.419449 − 1.215320I
b = −0.31506 + 1.85613I
10.81600 + 3.74825I 0
u = −0.57675 − 1.33502I
a = −0.419449 + 1.215320I
b = −0.31506 − 1.85613I
10.81600 − 3.74825I 0
u = 0.071209 + 0.532949I
a = −0.12914 + 2.57050I
b = −0.01065 − 2.13563I
2.73609 − 2.38466I −10.42559 + 0.76440I
u = 0.071209 − 0.532949I
a = −0.12914 − 2.57050I
b = −0.01065 + 2.13563I
2.73609 + 2.38466I −10.42559 − 0.76440I
u = 1.27357 + 0.72807I
a = −0.414781 − 0.349604I
b = −0.275822 + 0.512285I
−6.32359 − 3.97690I 0
u = 1.27357 − 0.72807I
a = −0.414781 + 0.349604I
b = −0.275822 − 0.512285I
−6.32359 + 3.97690I 0
u = 0.12017 + 1.51738I
a = 1.011970 − 0.315727I
b = 0.379110 + 0.559913I
−0.39783 + 1.72887I 0
u = 0.12017 − 1.51738I
a = 1.011970 + 0.315727I
b = 0.379110 − 0.559913I
−0.39783 − 1.72887I 0
u = 0.71828 + 1.39939I
a = 0.343326 − 1.136520I
b = 0.33207 + 1.92509I
9.56306 − 9.81975I 0
u = 0.71828 − 1.39939I
a = 0.343326 + 1.136520I
b = 0.33207 − 1.92509I
9.56306 + 9.81975I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.97511 + 1.28716I
a = −0.633764 + 1.006090I
b = −0.40476 − 1.67994I
0.54467 − 6.58007I 0
u = 0.97511 − 1.28716I
a = −0.633764 − 1.006090I
b = −0.40476 + 1.67994I
0.54467 + 6.58007I 0
u = −0.101175 + 0.268318I
a = 1.32347 + 2.96824I
b = 0.00255 − 1.97774I
1.15369 + 1.33003I 0.26910 − 8.47917I
u = −0.101175 − 0.268318I
a = 1.32347 − 2.96824I
b = 0.00255 + 1.97774I
1.15369 − 1.33003I 0.26910 + 8.47917I
u = 1.33047 + 1.16519I
a = 0.478417 − 0.613747I
b = 0.66765 + 1.86705I
3.05422 − 4.02557I 0
u = 1.33047 − 1.16519I
a = 0.478417 + 0.613747I
b = 0.66765 − 1.86705I
3.05422 + 4.02557I 0
u = 0.42249 + 1.74075I
a = −0.871746 − 0.415011I
b = −0.361054 + 0.602089I
−1.16452 − 7.75367I 0
u = 0.42249 − 1.74075I
a = −0.871746 + 0.415011I
b = −0.361054 − 0.602089I
−1.16452 + 7.75367I 0
u = −0.42488 + 1.77560I
a = 0.300223 + 1.183900I
b = 0.14185 − 1.70906I
9.45918 + 3.10998I 0
u = −0.42488 − 1.77560I
a = 0.300223 − 1.183900I
b = 0.14185 + 1.70906I
9.45918 − 3.10998I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07853 + 1.91814I
a = −0.171569 + 1.111140I
b = −0.07595 − 1.74382I
8.50999 + 3.70014I 0
u = 0.07853 − 1.91814I
a = −0.171569 − 1.111140I
b = −0.07595 + 1.74382I
8.50999 − 3.70014I 0
u = −1.84596 + 0.63181I
a = −0.469448 − 0.493054I
b = −0.62297 + 1.95623I
3.44928 + 1.73681I 0
u = −1.84596 − 0.63181I
a = −0.469448 + 0.493054I
b = −0.62297 − 1.95623I
3.44928 − 1.73681I 0
u = −1.32220 + 1.55486I
a = 0.440807 + 0.919591I
b = 0.35456 − 1.87560I
8.07490 + 10.29220I 0
u = −1.32220 − 1.55486I
a = 0.440807 − 0.919591I
b = 0.35456 + 1.87560I
8.07490 − 10.29220I 0
u = 1.48295 + 1.47987I
a = −0.415885 + 0.867026I
b = −0.38217 − 1.94494I
5.8809 − 16.7307I 0
u = 1.48295 − 1.47987I
a = −0.415885 − 0.867026I
b = −0.38217 + 1.94494I
5.8809 + 16.7307I 0
u = 2.27181 + 1.64904I
a = 0.460402 − 0.548295I
b = 0.54956 + 1.75108I
5.60799 − 0.31469I 0
u = 2.27181 − 1.64904I
a = 0.460402 + 0.548295I
b = 0.54956 − 1.75108I
5.60799 + 0.31469I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.49665 + 1.28593I
a = −0.451579 − 0.553382I
b = −0.50037 + 1.80564I
5.54289 + 5.38790I 0
u = −2.49665 − 1.28593I
a = −0.451579 + 0.553382I
b = −0.50037 − 1.80564I
5.54289 − 5.38790I 0
u = −0.78268 + 3.57446I
a = 0.064497 + 0.693383I
b = 0.08356 − 2.09334I
8.35485 + 3.17981I 0
u = −0.78268 − 3.57446I
a = 0.064497 − 0.693383I
b = 0.08356 + 2.09334I
8.35485 − 3.17981I 0
12
II.
I
u
2
= h3.10×10
32
u
23
−1.02×10
33
u
22
+· · ·+2.58×10
32
b+5.97×10
32
, −9.65×
10
32
u
23
+3.28×10
33
u
22
+· · ·+2.58×10
32
a−2.48×10
33
, u
24
−3u
23
+· · ·+3u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
3.74103u
23
− 12.6938u
22
+ ··· + 10.1999u + 9.61566
−1.20097u
23
+ 3.94538u
22
+ ··· − 4.41854u − 2.31397
a
3
=
−0.905445u
23
+ 3.08921u
22
+ ··· − 1.58493u − 3.29115
0.744548u
23
− 2.26904u
22
+ ··· + 3.33781u + 3.02014
a
7
=
3.74103u
23
− 12.6938u
22
+ ··· + 10.1999u + 9.61566
−0.495914u
23
+ 1.56323u
22
+ ··· − 3.74734u − 0.843228
a
11
=
2.50091u
23
− 8.64542u
22
+ ··· + 4.71165u + 5.73810
0.372873u
23
− 1.41387u
22
+ ··· − 0.574815u + 0.905445
a
10
=
2.87378u
23
− 10.0593u
22
+ ··· + 4.13684u + 6.64354
0.372873u
23
− 1.41387u
22
+ ··· − 0.574815u + 0.905445
a
1
=
−3.28358u
23
+ 11.2247u
22
+ ··· − 4.93024u − 7.38504
−0.132750u
23
+ 0.365444u
22
+ ··· + 1.06308u − 0.0278847
a
2
=
−3.04569u
23
+ 10.5278u
22
+ ··· − 5.14348u − 8.23501
0.415551u
23
− 1.42417u
22
+ ··· + 2.99968u + 2.58734
a
6
=
−1.13356u
23
+ 3.73009u
22
+ ··· − 1.83336u − 2.03684
−0.561956u
23
+ 2.08239u
22
+ ··· − 0.145765u − 0.429411
a
9
=
3.15671u
23
− 10.9173u
22
+ ··· + 6.15169u + 7.17604
0.289587u
23
− 1.13640u
22
+ ··· − 0.830127u + 0.914649
(ii) Obstruction class = 1
(iii) Cusp Shapes = −19.3109u
23
+ 64.5263u
22
+ ··· − 45.8349u − 32.8279
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
24
− 17u
23
+ ··· − 208u + 16
c
2
u
24
− 3u
23
+ ··· − 8u + 4
c
3
u
24
+ 2u
23
+ ··· − 24u + 104
c
4
u
24
− 3u
23
+ ··· + 3u + 1
c
5
u
24
+ u
23
+ ··· − 2u + 1
c
6
u
24
+ 3u
23
+ ··· + 8u + 4
c
7
u
24
− 4u
23
+ ··· + 3u + 1
c
8
u
24
+ 2u
23
+ ··· − u + 1
c
9
u
24
− u
23
+ ··· + 2u + 1
c
10
u
24
− u
23
+ ··· − 5u
2
+ 1
c
11
u
24
+ 4u
23
+ ··· − 3u + 1
c
12
u
24
+ 12u
23
+ ··· + 7u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 7y
23
+ ··· − 896y + 256
c
2
, c
6
y
24
+ 17y
23
+ ··· + 208y + 16
c
3
y
24
+ 26y
23
+ ··· + 115488y + 10816
c
4
y
24
+ 9y
23
+ ··· + 3y + 1
c
5
, c
9
y
24
+ 19y
23
+ ··· + 6y + 1
c
7
, c
11
y
24
− 14y
23
+ ··· + 15y + 1
c
8
y
24
− 8y
23
+ ··· + 11y + 1
c
10
y
24
+ 5y
23
+ ··· − 10y + 1
c
12
y
24
− 8y
23
+ ··· + 23y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.723024 + 0.782726I
a = 0.673808 − 0.302861I
b = 0.765613 − 0.566388I
−2.20701 + 3.69626I −3.43242 − 3.87608I
u = −0.723024 − 0.782726I
a = 0.673808 + 0.302861I
b = 0.765613 + 0.566388I
−2.20701 − 3.69626I −3.43242 + 3.87608I
u = 0.847397 + 0.882962I
a = −0.456499 − 0.214505I
b = −1.242050 − 0.428880I
−4.22629 − 9.01064I −6.66500 + 7.64370I
u = 0.847397 − 0.882962I
a = −0.456499 + 0.214505I
b = −1.242050 + 0.428880I
−4.22629 + 9.01064I −6.66500 − 7.64370I
u = −1.180080 + 0.537451I
a = 0.047185 − 0.458093I
b = 0.056612 + 0.723882I
−6.12630 + 4.80640I −2.33201 − 9.94746I
u = −1.180080 − 0.537451I
a = 0.047185 + 0.458093I
b = 0.056612 − 0.723882I
−6.12630 − 4.80640I −2.33201 + 9.94746I
u = 1.125420 + 0.707641I
a = −0.179275 − 0.371476I
b = −0.746357 + 0.726100I
−6.63349 − 2.50572I −4.31899 − 1.64120I
u = 1.125420 − 0.707641I
a = −0.179275 + 0.371476I
b = −0.746357 − 0.726100I
−6.63349 + 2.50572I −4.31899 + 1.64120I
u = 0.485255 + 0.418739I
a = −1.63375 − 1.33049I
b = −0.212253 − 0.680015I
−9.45464 − 0.62738I −2.4053 + 15.6637I
u = 0.485255 − 0.418739I
a = −1.63375 + 1.33049I
b = −0.212253 + 0.680015I
−9.45464 + 0.62738I −2.4053 − 15.6637I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317045 + 0.448646I
a = 1.01488 + 1.36223I
b = −1.15529 − 1.75240I
1.52490 + 1.48153I −2.0321 − 50.0105I
u = −0.317045 − 0.448646I
a = 1.01488 − 1.36223I
b = −1.15529 + 1.75240I
1.52490 − 1.48153I −2.0321 + 50.0105I
u = −0.005354 + 0.515723I
a = 0.48435 + 1.83018I
b = 0.78622 − 1.71522I
0.63974 + 1.78828I 4.77420 − 6.68732I
u = −0.005354 − 0.515723I
a = 0.48435 − 1.83018I
b = 0.78622 + 1.71522I
0.63974 − 1.78828I 4.77420 + 6.68732I
u = 0.195505 + 0.452685I
a = 1.41911 + 1.70966I
b = 0.046863 − 0.707692I
0.484096 − 0.031327I 1.40435 + 0.73990I
u = 0.195505 − 0.452685I
a = 1.41911 − 1.70966I
b = 0.046863 + 0.707692I
0.484096 + 0.031327I 1.40435 − 0.73990I
u = −1.31797 + 0.82434I
a = −0.757681 − 0.498561I
b = −0.68743 + 1.55050I
1.26248 + 4.42614I −1.29334 − 4.33015I
u = −1.31797 − 0.82434I
a = −0.757681 + 0.498561I
b = −0.68743 − 1.55050I
1.26248 − 4.42614I −1.29334 + 4.33015I
u = −0.444707 + 0.017789I
a = 0.83768 + 1.92404I
b = 0.586420 − 0.500844I
−0.16296 + 4.41575I −3.01988 − 6.24842I
u = −0.444707 − 0.017789I
a = 0.83768 − 1.92404I
b = 0.586420 + 0.500844I
−0.16296 − 4.41575I −3.01988 + 6.24842I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.92278 + 0.85994I
a = 0.438350 − 0.488629I
b = 0.66494 + 1.94897I
3.68223 − 2.53447I 0
u = 1.92278 − 0.85994I
a = 0.438350 + 0.488629I
b = 0.66494 − 1.94897I
3.68223 + 2.53447I 0
u = 0.91183 + 3.28463I
a = 0.111832 − 0.742734I
b = 0.13671 + 1.99524I
8.05775 − 3.34069I 0
u = 0.91183 − 3.28463I
a = 0.111832 + 0.742734I
b = 0.13671 − 1.99524I
8.05775 + 3.34069I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 17u
23
+ ··· − 208u + 16)
· (u
74
+ 34u
73
+ ··· + 340368u + 13456)
c
2
(u
24
− 3u
23
+ ··· − 8u + 4)(u
74
− 2u
73
+ ··· − 192u + 116)
c
3
(u
24
+ 2u
23
+ ··· − 24u + 104)(u
74
− 3u
73
+ ··· + 2408u + 184)
c
4
(u
24
− 3u
23
+ ··· + 3u + 1)(u
74
+ 17u
72
+ ··· − 566418u + 172099)
c
5
(u
24
+ u
23
+ ··· − 2u + 1)(u
74
− 4u
73
+ ··· − 69u + 131)
c
6
(u
24
+ 3u
23
+ ··· + 8u + 4)(u
74
− 2u
73
+ ··· − 192u + 116)
c
7
(u
24
− 4u
23
+ ··· + 3u + 1)(u
74
− u
73
+ ··· − 325282u + 19639)
c
8
(u
24
+ 2u
23
+ ··· − u + 1)(u
74
+ 3u
73
+ ··· − 8536u + 1093)
c
9
(u
24
− u
23
+ ··· + 2u + 1)(u
74
− 4u
73
+ ··· − 69u + 131)
c
10
(u
24
− u
23
+ ··· − 5u
2
+ 1)(u
74
− 2u
73
+ ··· + 49021u + 18569)
c
11
(u
24
+ 4u
23
+ ··· − 3u + 1)(u
74
− u
73
+ ··· − 325282u + 19639)
c
12
(u
24
+ 12u
23
+ ··· + 7u + 1)(u
74
− 9u
73
+ ··· − 22u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
− 7y
23
+ ··· − 896y + 256)
· (y
74
+ 26y
73
+ ··· + 2544232064y + 181063936)
c
2
, c
6
(y
24
+ 17y
23
+ ··· + 208y + 16)
· (y
74
+ 34y
73
+ ··· + 340368y + 13456)
c
3
(y
24
+ 26y
23
+ ··· + 115488y + 10816)
· (y
74
+ 103y
73
+ ··· + 155040y + 33856)
c
4
(y
24
+ 9y
23
+ ··· + 3y + 1)
· (y
74
+ 34y
73
+ ··· + 998146334424y + 29618065801)
c
5
, c
9
(y
24
+ 19y
23
+ ··· + 6y + 1)(y
74
+ 44y
73
+ ··· + 371471y + 17161)
c
7
, c
11
(y
24
− 14y
23
+ ··· + 15y + 1)
· (y
74
− 93y
73
+ ··· − 43352903060y + 385690321)
c
8
(y
24
− 8y
23
+ ··· + 11y + 1)
· (y
74
+ 9y
73
+ ··· + 23967760y + 1194649)
c
10
(y
24
+ 5y
23
+ ··· − 10y + 1)
· (y
74
+ 90y
73
+ ··· + 2650383495y + 344807761)
c
12
(y
24
− 8y
23
+ ··· + 23y + 1)(y
74
− 3y
73
+ ··· − 56y
2
+ 1)
22
