12n
0758
(K12n
0758
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 2 10 1 4 12 5 7 9
Solving Sequence
9,12
10
1,4
2 3 8 7 6 5 11
c
9
c
12
c
1
c
3
c
8
c
7
c
6
c
5
c
11
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h8.72942 × 10
279
u
83
− 3.70180 × 10
280
u
82
+ ··· + 2.19369 × 10
283
b + 5.24856 × 10
283
,
− 1.73871 × 10
284
u
83
+ 3.54688 × 10
284
u
82
+ ··· + 8.62121 × 10
285
a + 9.41097 × 10
286
,
u
84
− 2u
83
+ ··· − 931u + 393i
I
u
2
= h5.19189 × 10
21
u
32
− 9.68160 × 10
21
u
31
+ ··· + 1.69614 × 10
22
b − 1.88611 × 10
23
,
9.63063 × 10
21
u
32
− 6.63604 × 10
22
u
31
+ ··· + 2.66537 × 10
22
a + 9.17471 × 10
23
, u
33
− 3u
32
+ ··· − 3u − 11i
* 2 irreducible components of dim
C
= 0, with total 117 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
= h8.73 × 10
279
u
83
− 3.70 × 10
280
u
82
+ · · · + 2.19 × 10
283
b + 5.25 ×
10
283
, −1.74 × 10
284
u
83
+ 3.55 × 10
284
u
82
+ · · · + 8.62 × 10
285
a + 9.41 ×
10
286
, u
84
− 2u
83
+ · · · − 931u + 393i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
4
=
0.0201678u
83
− 0.0411413u
82
+ ··· + 37.2561u − 10.9161
−0.000397933u
83
+ 0.00168747u
82
+ ··· − 1.39648u − 2.39257
a
2
=
0.0161633u
83
− 0.0261933u
82
+ ··· + 26.1042u − 11.4528
0.00781208u
83
− 0.0178962u
82
+ ··· + 12.4153u − 7.75229
a
3
=
0.0197698u
83
− 0.0394538u
82
+ ··· + 35.8597u − 13.3086
−0.000397933u
83
+ 0.00168747u
82
+ ··· − 1.39648u − 2.39257
a
8
=
0.0206064u
83
− 0.0260386u
82
+ ··· + 19.3445u + 2.04760
−0.000880470u
83
− 0.00560114u
82
+ ··· + 7.71886u − 7.99711
a
7
=
0.0183344u
83
− 0.0267967u
82
+ ··· + 18.8652u − 1.02254
0.00139156u
83
− 0.00484311u
82
+ ··· + 8.19811u − 4.92696
a
6
=
0.0219774u
83
− 0.0304770u
82
+ ··· + 25.0778u − 2.06978
0.00306746u
83
− 0.00998246u
82
+ ··· + 10.1234u − 6.34404
a
5
=
0.0249425u
83
− 0.0285448u
82
+ ··· + 18.3761u + 11.2314
−0.00242622u
83
+ 0.0000518733u
82
+ ··· + 7.71179u − 4.90936
a
11
=
−0.0267748u
83
+ 0.0522669u
82
+ ··· − 49.2862u + 13.0525
0.00829693u
83
− 0.0131191u
82
+ ··· + 8.72583u + 0.990108
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0195060u
83
− 0.0235693u
82
+ ··· + 27.4576u − 11.4055
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
− 3u
83
+ ··· + 8464u + 8464
c
2
, c
5
u
84
+ 4u
83
+ ··· − 959u − 69
c
3
, c
8
u
84
− u
83
+ ··· − 231109u − 59333
c
4
, c
10
u
84
− u
83
+ ··· − 99u − 85
c
6
u
84
+ 8u
83
+ ··· + 13309u + 799
c
7
u
84
+ 2u
83
+ ··· − 28656216u − 9025047
c
9
, c
12
u
84
− 2u
83
+ ··· − 931u + 393
c
11
u
84
− 2u
83
+ ··· − 66u − 71
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
− 105y
83
+ ··· − 4667929856y + 71639296
c
2
, c
5
y
84
− 54y
83
+ ··· − 314551y + 4761
c
3
, c
8
y
84
− 91y
83
+ ··· − 79247924731y + 3520404889
c
4
, c
10
y
84
+ 43y
83
+ ··· + 129599y + 7225
c
6
y
84
+ 4y
83
+ ··· − 82932175y + 638401
c
7
y
84
− 108y
83
+ ··· − 5560618845808998y + 81451473352209
c
9
, c
12
y
84
+ 36y
83
+ ··· + 530747y + 154449
c
11
y
84
+ 20y
83
+ ··· − 234396y + 5041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294887 + 0.952377I
a = 0.440850 + 1.193960I
b = 0.495235 + 0.003125I
2.54954 + 5.24160I 0
u = 0.294887 − 0.952377I
a = 0.440850 − 1.193960I
b = 0.495235 − 0.003125I
2.54954 − 5.24160I 0
u = −0.694610 + 0.707656I
a = 1.008470 − 0.624427I
b = −1.97615 − 0.19025I
−7.38511 − 2.76283I 0
u = −0.694610 − 0.707656I
a = 1.008470 + 0.624427I
b = −1.97615 + 0.19025I
−7.38511 + 2.76283I 0
u = 0.500809 + 0.888563I
a = −0.38984 − 1.62928I
b = 1.67416 + 0.12811I
−8.76932 − 2.02840I 0
u = 0.500809 − 0.888563I
a = −0.38984 + 1.62928I
b = 1.67416 − 0.12811I
−8.76932 + 2.02840I 0
u = 0.554522 + 0.858130I
a = −0.899708 − 0.388618I
b = −0.730243 − 0.171302I
2.11870 − 9.06028I 0
u = 0.554522 − 0.858130I
a = −0.899708 + 0.388618I
b = −0.730243 + 0.171302I
2.11870 + 9.06028I 0
u = 0.661636 + 0.717303I
a = −0.55456 + 2.11719I
b = −0.11809 − 1.64544I
1.06596 − 8.36354I 0
u = 0.661636 − 0.717303I
a = −0.55456 − 2.11719I
b = −0.11809 + 1.64544I
1.06596 + 8.36354I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727502 + 0.631455I
a = 0.43599 + 1.99000I
b = 0.132082 − 1.308720I
−1.65955 + 2.50124I 0
u = −0.727502 − 0.631455I
a = 0.43599 − 1.99000I
b = 0.132082 + 1.308720I
−1.65955 − 2.50124I 0
u = 0.646116 + 0.813367I
a = −0.865057 − 1.114140I
b = 1.95306 + 0.07640I
−9.54811 − 1.92793I 0
u = 0.646116 − 0.813367I
a = −0.865057 + 1.114140I
b = 1.95306 − 0.07640I
−9.54811 + 1.92793I 0
u = 0.859691 + 0.384127I
a = 0.058309 + 1.043550I
b = −1.60144 − 0.20746I
−3.80926 + 3.22658I −12.00000 + 0.I
u = 0.859691 − 0.384127I
a = 0.058309 − 1.043550I
b = −1.60144 + 0.20746I
−3.80926 − 3.22658I −12.00000 + 0.I
u = −0.758174 + 0.486652I
a = 0.20809 + 1.59324I
b = 1.305480 − 0.526811I
−5.03724 + 1.13583I −16.8365 − 2.0066I
u = −0.758174 − 0.486652I
a = 0.20809 − 1.59324I
b = 1.305480 + 0.526811I
−5.03724 − 1.13583I −16.8365 + 2.0066I
u = −0.477920 + 0.729132I
a = −0.017678 − 0.832177I
b = −1.70255 − 0.02946I
−6.28978 + 5.06326I −14.0964 − 11.0858I
u = −0.477920 − 0.729132I
a = −0.017678 + 0.832177I
b = −1.70255 + 0.02946I
−6.28978 − 5.06326I −14.0964 + 11.0858I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724830 + 0.871030I
a = 0.188923 − 0.513292I
b = 0.800606 + 0.197504I
−0.97523 + 4.20327I 0
u = −0.724830 − 0.871030I
a = 0.188923 + 0.513292I
b = 0.800606 − 0.197504I
−0.97523 − 4.20327I 0
u = 0.431842 + 0.751226I
a = 0.035604 + 0.411641I
b = 0.930341 + 0.119546I
4.15608 − 3.39999I −8.12553 + 3.32156I
u = 0.431842 − 0.751226I
a = 0.035604 − 0.411641I
b = 0.930341 − 0.119546I
4.15608 + 3.39999I −8.12553 − 3.32156I
u = 0.130197 + 1.176620I
a = −0.452940 + 0.792535I
b = 0.335620 − 1.078210I
8.02881 − 0.15919I 0
u = 0.130197 − 1.176620I
a = −0.452940 − 0.792535I
b = 0.335620 + 1.078210I
8.02881 + 0.15919I 0
u = 0.633110 + 1.001470I
a = −0.86554 − 1.72536I
b = 1.69381 + 0.53177I
−8.92273 − 3.05638I 0
u = 0.633110 − 1.001470I
a = −0.86554 + 1.72536I
b = 1.69381 − 0.53177I
−8.92273 + 3.05638I 0
u = −0.166772 + 1.176770I
a = 0.025390 − 1.080680I
b = −0.058126 + 0.634635I
2.44569 + 1.97696I 0
u = −0.166772 − 1.176770I
a = 0.025390 + 1.080680I
b = −0.058126 − 0.634635I
2.44569 − 1.97696I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554951 + 0.582546I
a = −0.390319 − 1.179360I
b = −0.095466 + 0.110201I
3.77440 − 0.27401I −9.00425 + 3.62754I
u = 0.554951 − 0.582546I
a = −0.390319 + 1.179360I
b = −0.095466 − 0.110201I
3.77440 + 0.27401I −9.00425 − 3.62754I
u = −0.542964 + 1.077790I
a = 0.88186 − 1.75494I
b = −1.37004 + 0.37482I
−5.04156 − 0.89545I 0
u = −0.542964 − 1.077790I
a = 0.88186 + 1.75494I
b = −1.37004 − 0.37482I
−5.04156 + 0.89545I 0
u = 0.786924 + 0.071577I
a = −0.372606 − 0.083145I
b = −0.740135 + 0.590064I
−2.30274 − 1.98452I −14.0122 + 3.5761I
u = 0.786924 − 0.071577I
a = −0.372606 + 0.083145I
b = −0.740135 − 0.590064I
−2.30274 + 1.98452I −14.0122 − 3.5761I
u = −0.672532 + 1.053140I
a = 0.80649 − 1.86180I
b = −1.59182 + 0.83021I
−6.27265 + 8.07086I 0
u = −0.672532 − 1.053140I
a = 0.80649 + 1.86180I
b = −1.59182 − 0.83021I
−6.27265 − 8.07086I 0
u = −0.744362 + 0.073072I
a = 0.697845 + 0.302573I
b = 0.064934 − 0.638988I
−2.55097 + 1.64807I −14.0611 − 4.2086I
u = −0.744362 − 0.073072I
a = 0.697845 − 0.302573I
b = 0.064934 + 0.638988I
−2.55097 − 1.64807I −14.0611 + 4.2086I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173456 + 0.718283I
a = −0.032776 + 1.023540I
b = −0.777152 − 0.064260I
−0.042915 − 0.404585I −13.05213 + 0.11444I
u = −0.173456 − 0.718283I
a = −0.032776 − 1.023540I
b = −0.777152 + 0.064260I
−0.042915 + 0.404585I −13.05213 − 0.11444I
u = 0.641058 + 1.102710I
a = 0.249195 + 1.241840I
b = −1.311760 − 0.478156I
0.08416 − 2.58633I 0
u = 0.641058 − 1.102710I
a = 0.249195 − 1.241840I
b = −1.311760 + 0.478156I
0.08416 + 2.58633I 0
u = −0.290314 + 1.244790I
a = 0.275935 + 0.456597I
b = 0.373975 − 0.153030I
1.34700 + 5.25981I 0
u = −0.290314 − 1.244790I
a = 0.275935 − 0.456597I
b = 0.373975 + 0.153030I
1.34700 − 5.25981I 0
u = −0.617200 + 1.123120I
a = −0.097327 + 0.894259I
b = 1.297870 − 0.212302I
−2.08185 + 5.12268I 0
u = −0.617200 − 1.123120I
a = −0.097327 − 0.894259I
b = 1.297870 + 0.212302I
−2.08185 − 5.12268I 0
u = 0.480007 + 1.204710I
a = 0.87508 − 1.45094I
b = −0.733207 + 1.187610I
2.63050 + 3.51421I 0
u = 0.480007 − 1.204710I
a = 0.87508 + 1.45094I
b = −0.733207 − 1.187610I
2.63050 − 3.51421I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369350 + 1.258530I
a = −0.590165 − 0.607206I
b = 0.391473 + 0.703417I
1.10901 + 2.54970I 0
u = −0.369350 − 1.258530I
a = −0.590165 + 0.607206I
b = 0.391473 − 0.703417I
1.10901 − 2.54970I 0
u = −0.415634 + 0.543818I
a = 0.89412 + 2.48326I
b = 0.884750 − 0.112569I
−4.20056 − 0.60057I −16.6383 − 2.6615I
u = −0.415634 − 0.543818I
a = 0.89412 − 2.48326I
b = 0.884750 + 0.112569I
−4.20056 + 0.60057I −16.6383 + 2.6615I
u = −0.704625 + 1.145320I
a = −0.879881 + 0.787804I
b = 1.71635 − 0.09528I
−3.05789 + 4.55898I 0
u = −0.704625 − 1.145320I
a = −0.879881 − 0.787804I
b = 1.71635 + 0.09528I
−3.05789 − 4.55898I 0
u = 0.372324 + 1.313810I
a = 1.080030 − 0.158632I
b = −0.824823 + 0.643218I
2.02799 − 6.25953I 0
u = 0.372324 − 1.313810I
a = 1.080030 + 0.158632I
b = −0.824823 − 0.643218I
2.02799 + 6.25953I 0
u = 0.167980 + 0.608575I
a = 0.68138 − 2.97181I
b = −0.03290 + 1.56661I
5.82823 − 1.27096I −14.7250 + 7.1500I
u = 0.167980 − 0.608575I
a = 0.68138 + 2.97181I
b = −0.03290 − 1.56661I
5.82823 + 1.27096I −14.7250 − 7.1500I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687697 + 1.184100I
a = 0.98819 + 1.24337I
b = −1.86840 − 0.39246I
−1.48207 − 9.06979I 0
u = 0.687697 − 1.184100I
a = 0.98819 − 1.24337I
b = −1.86840 + 0.39246I
−1.48207 + 9.06979I 0
u = 0.513564 + 0.324791I
a = −0.74244 + 1.77974I
b = 0.491909 − 1.087890I
4.35293 + 1.81909I −12.5856 − 7.0446I
u = 0.513564 − 0.324791I
a = −0.74244 − 1.77974I
b = 0.491909 + 1.087890I
4.35293 − 1.81909I −12.5856 + 7.0446I
u = 0.249177 + 1.382250I
a = −0.314905 − 1.183540I
b = 0.249096 + 0.681502I
8.37804 − 4.78916I 0
u = 0.249177 − 1.382250I
a = −0.314905 + 1.183540I
b = 0.249096 − 0.681502I
8.37804 + 4.78916I 0
u = 0.29257 + 1.39174I
a = 0.543919 + 0.847268I
b = −0.906092 − 0.068662I
1.47257 − 1.02886I 0
u = 0.29257 − 1.39174I
a = 0.543919 − 0.847268I
b = −0.906092 + 0.068662I
1.47257 + 1.02886I 0
u = 1.43426 + 0.49546I
a = −0.818674 − 0.319409I
b = 1.87334 − 0.08896I
−8.06573 + 9.12714I 0
u = 1.43426 − 0.49546I
a = −0.818674 + 0.319409I
b = 1.87334 + 0.08896I
−8.06573 − 9.12714I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234443 + 0.380976I
a = −1.84626 + 2.80271I
b = −1.046060 − 0.024623I
−3.18480 − 2.73332I −12.05403 + 5.98503I
u = 0.234443 − 0.380976I
a = −1.84626 − 2.80271I
b = −1.046060 + 0.024623I
−3.18480 + 2.73332I −12.05403 − 5.98503I
u = 0.82750 + 1.34118I
a = −0.94562 − 1.44691I
b = 1.81256 + 0.64877I
−5.2595 − 16.9363I 0
u = 0.82750 − 1.34118I
a = −0.94562 + 1.44691I
b = 1.81256 − 0.64877I
−5.2595 + 16.9363I 0
u = −0.26128 + 1.64077I
a = −0.835871 − 1.085830I
b = 0.887576 + 0.676070I
1.73512 + 3.03684I 0
u = −0.26128 − 1.64077I
a = −0.835871 + 1.085830I
b = 0.887576 − 0.676070I
1.73512 − 3.03684I 0
u = −0.92014 + 1.38379I
a = 1.05538 − 1.29487I
b = −1.83164 + 0.57155I
−8.22061 + 10.14930I 0
u = −0.92014 − 1.38379I
a = 1.05538 + 1.29487I
b = −1.83164 − 0.57155I
−8.22061 − 10.14930I 0
u = 1.17080 + 1.22285I
a = −1.008100 − 0.971486I
b = 1.78040 + 0.43010I
−0.81519 − 4.49750I 0
u = 1.17080 − 1.22285I
a = −1.008100 + 0.971486I
b = 1.78040 − 0.43010I
−0.81519 + 4.49750I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238294
a = 1.10963
b = −0.360138
−0.555440 −17.7430
u = −1.68658 + 0.74957I
a = 1.071620 − 0.461588I
b = −1.94447 + 0.11664I
−10.77950 − 1.32110I 0
u = −1.68658 − 0.74957I
a = 1.071620 + 0.461588I
b = −1.94447 − 0.11664I
−10.77950 + 1.32110I 0
u = −2.11735
a = −0.666267
b = 1.59201
−7.38413 0
13
II. I
u
2
=
h5.19×10
21
u
32
−9.68×10
21
u
31
+· · ·+1.70×10
22
b−1.89×10
23
, 9.63×10
21
u
32
−
6.64 × 10
22
u
31
+ · · · + 2.67 × 10
22
a + 9.17 × 10
23
, u
33
− 3u
32
+ · · · − 3u − 11i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
4
=
−0.361324u
32
+ 2.48973u
31
+ ··· + 27.4713u − 34.4219
−0.306100u
32
+ 0.570801u
31
+ ··· + 6.12789u + 11.1200
a
2
=
−0.883120u
32
+ 2.84019u
31
+ ··· + 47.3126u − 15.8633
0.0177951u
32
+ 0.440778u
31
+ ··· + 2.04823u − 2.25569
a
3
=
−0.667424u
32
+ 3.06053u
31
+ ··· + 33.5992u − 23.3019
−0.306100u
32
+ 0.570801u
31
+ ··· + 6.12789u + 11.1200
a
8
=
−1.06983u
32
+ 2.82773u
31
+ ··· + 1.48987u + 8.00809
0.864764u
32
− 2.19475u
31
+ ··· − 10.8117u − 5.34467
a
7
=
−0.575663u
32
+ 1.30304u
31
+ ··· − 0.712432u + 8.20383
0.370601u
32
− 0.670060u
31
+ ··· − 8.60944u − 5.54041
a
6
=
−0.761489u
32
+ 2.09630u
31
+ ··· − 1.71773u + 7.32684
0.594062u
32
− 1.51722u
31
+ ··· − 9.94618u − 2.94683
a
5
=
−1.15234u
32
+ 4.53564u
31
+ ··· + 38.8556u − 30.8553
0.461484u
32
− 1.56817u
31
+ ··· − 5.73776u − 0.574177
a
11
=
0.844408u
32
− 4.18554u
31
+ ··· − 24.8597u + 32.7171
−0.233714u
32
+ 1.17394u
31
+ ··· + 7.38558u − 13.6829
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16825122534945883551404
16961432124929635941773
u
32
−
73487686778808495843325
16961432124929635941773
u
31
+ ··· −
49225530394429173931634
892706953943665049567
u +
166067436798213608922909
16961432124929635941773
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
33
− 12u
32
+ ··· − 104u + 16
c
2
u
33
+ 3u
32
+ ··· − 3u − 1
c
3
u
33
− 9u
31
+ ··· − 5u + 1
c
4
u
33
+ 10u
31
+ ··· − 3u − 1
c
5
u
33
− 3u
32
+ ··· − 3u + 1
c
6
u
33
− u
32
+ ··· + 177u + 41
c
7
u
33
+ u
32
+ ··· + 92u − 13
c
8
u
33
− 9u
31
+ ··· − 5u − 1
c
9
u
33
− 3u
32
+ ··· − 3u − 11
c
10
u
33
+ 10u
31
+ ··· − 3u + 1
c
11
u
33
+ u
32
+ ··· − 8u + 1
c
12
u
33
+ 3u
32
+ ··· − 3u + 11
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
− 40y
32
+ ··· − 4288y −256
c
2
, c
5
y
33
− 17y
32
+ ··· + 21y −1
c
3
, c
8
y
33
− 18y
32
+ ··· + 5y −1
c
4
, c
10
y
33
+ 20y
32
+ ··· + 19y −1
c
6
y
33
+ 9y
32
+ ··· + 333y −1681
c
7
y
33
− 23y
32
+ ··· − 4016y −169
c
9
, c
12
y
33
+ 21y
32
+ ··· − 2125y −121
c
11
y
33
+ 13y
32
+ ··· + 22y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.459052 + 0.905733I
a = −0.56066 − 1.70826I
b = 1.72209 + 0.16447I
−8.51907 − 1.87974I −1.03019 − 5.88561I
u = 0.459052 − 0.905733I
a = −0.56066 + 1.70826I
b = 1.72209 − 0.16447I
−8.51907 + 1.87974I −1.03019 + 5.88561I
u = −0.245360 + 1.061590I
a = 0.930247 − 0.636269I
b = 0.074224 + 0.799741I
3.51668 + 7.97897I −7.39109 − 6.52906I
u = −0.245360 − 1.061590I
a = 0.930247 + 0.636269I
b = 0.074224 − 0.799741I
3.51668 − 7.97897I −7.39109 + 6.52906I
u = −0.610076 + 0.668441I
a = −0.217068 − 1.379820I
b = 0.662456 + 1.019410I
4.64509 − 1.25556I −6.42802 − 3.34918I
u = −0.610076 − 0.668441I
a = −0.217068 + 1.379820I
b = 0.662456 − 1.019410I
4.64509 + 1.25556I −6.42802 + 3.34918I
u = 0.454768 + 0.770417I
a = 0.27414 + 2.29897I
b = −1.036150 − 0.409481I
−2.95118 + 1.41193I −9.56268 − 0.25561I
u = 0.454768 − 0.770417I
a = 0.27414 − 2.29897I
b = −1.036150 + 0.409481I
−2.95118 − 1.41193I −9.56268 + 0.25561I
u = −0.029969 + 1.160230I
a = −0.240386 + 0.550783I
b = −0.048969 − 1.022730I
7.83061 + 1.07084I −7.89231 − 6.76156I
u = −0.029969 − 1.160230I
a = −0.240386 − 0.550783I
b = −0.048969 + 1.022730I
7.83061 − 1.07084I −7.89231 + 6.76156I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046952 + 0.778136I
a = 0.18434 − 2.62639I
b = 0.05144 + 1.43505I
6.31075 − 0.74758I −5.46772 − 0.87004I
u = −0.046952 − 0.778136I
a = 0.18434 + 2.62639I
b = 0.05144 − 1.43505I
6.31075 + 0.74758I −5.46772 + 0.87004I
u = −0.333275 + 1.193090I
a = −0.27031 + 1.62232I
b = −0.277614 − 0.782132I
3.69256 − 5.45915I −5.46961 + 5.79594I
u = −0.333275 − 1.193090I
a = −0.27031 − 1.62232I
b = −0.277614 + 0.782132I
3.69256 + 5.45915I −5.46961 − 5.79594I
u = 0.553223 + 1.118550I
a = 0.197888 + 0.797204I
b = −1.350490 − 0.096338I
−1.51828 − 5.36008I −7.21231 + 8.64726I
u = 0.553223 − 1.118550I
a = 0.197888 − 0.797204I
b = −1.350490 + 0.096338I
−1.51828 + 5.36008I −7.21231 − 8.64726I
u = 0.285884 + 1.215990I
a = −0.187548 − 0.002564I
b = −0.228537 + 0.409155I
0.97377 − 3.53160I −11.50426 + 5.16930I
u = 0.285884 − 1.215990I
a = −0.187548 + 0.002564I
b = −0.228537 − 0.409155I
0.97377 + 3.53160I −11.50426 − 5.16930I
u = 0.665375
a = −0.938279
b = −0.233345
−2.65548 −15.0300
u = −0.373186 + 0.529413I
a = −0.24508 − 1.41919I
b = −1.71902 + 0.10927I
−6.11499 + 4.40709I −10.75692 − 0.28206I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373186 − 0.529413I
a = −0.24508 + 1.41919I
b = −1.71902 − 0.10927I
−6.11499 − 4.40709I −10.75692 + 0.28206I
u = 1.36215
a = −0.700896
b = 1.92850
−10.6105 −14.9290
u = 0.26216 + 1.39678I
a = −0.009915 + 1.296920I
b = 0.237993 − 0.526775I
1.50022 − 0.84587I −12.00000 + 0.I
u = 0.26216 − 1.39678I
a = −0.009915 − 1.296920I
b = 0.237993 + 0.526775I
1.50022 + 0.84587I −12.00000 + 0.I
u = −0.217483 + 0.524802I
a = 0.56077 + 3.45838I
b = 0.851151 − 0.357375I
−3.87405 + 1.39425I −10.67403 − 4.79504I
u = −0.217483 − 0.524802I
a = 0.56077 − 3.45838I
b = 0.851151 + 0.357375I
−3.87405 − 1.39425I −10.67403 + 4.79504I
u = 0.48836 + 1.34669I
a = 0.522857 − 0.665638I
b = −0.716644 + 0.590418I
0.77285 − 3.95768I −12.00000 + 4.64056I
u = 0.48836 − 1.34669I
a = 0.522857 + 0.665638I
b = −0.716644 − 0.590418I
0.77285 + 3.95768I −12.00000 − 4.64056I
u = −0.93001 + 1.09186I
a = −0.543452 + 0.798842I
b = 1.44498 − 0.28184I
0.88870 + 3.81447I −7.70305 − 4.44957I
u = −0.93001 − 1.09186I
a = −0.543452 − 0.798842I
b = 1.44498 + 0.28184I
0.88870 − 3.81447I −7.70305 + 4.44957I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27081 + 1.41098I
a = −0.338582 + 1.197300I
b = 0.268339 − 0.592788I
8.14231 + 4.67717I −20.9718 + 2.5564I
u = −0.27081 − 1.41098I
a = −0.338582 − 1.197300I
b = 0.268339 + 0.592788I
8.14231 − 4.67717I −20.9718 − 2.5564I
u = 2.07982
a = 0.615608
b = −1.56567
−7.45635 0
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
33
− 12u
32
+ ··· − 104u + 16)(u
84
− 3u
83
+ ··· + 8464u + 8464)
c
2
(u
33
+ 3u
32
+ ··· − 3u − 1)(u
84
+ 4u
83
+ ··· − 959u − 69)
c
3
(u
33
− 9u
31
+ ··· − 5u + 1)(u
84
− u
83
+ ··· − 231109u − 59333)
c
4
(u
33
+ 10u
31
+ ··· − 3u − 1)(u
84
− u
83
+ ··· − 99u − 85)
c
5
(u
33
− 3u
32
+ ··· − 3u + 1)(u
84
+ 4u
83
+ ··· − 959u − 69)
c
6
(u
33
− u
32
+ ··· + 177u + 41)(u
84
+ 8u
83
+ ··· + 13309u + 799)
c
7
(u
33
+ u
32
+ ··· + 92u − 13)
· (u
84
+ 2u
83
+ ··· − 28656216u − 9025047)
c
8
(u
33
− 9u
31
+ ··· − 5u − 1)(u
84
− u
83
+ ··· − 231109u − 59333)
c
9
(u
33
− 3u
32
+ ··· − 3u − 11)(u
84
− 2u
83
+ ··· − 931u + 393)
c
10
(u
33
+ 10u
31
+ ··· − 3u + 1)(u
84
− u
83
+ ··· − 99u − 85)
c
11
(u
33
+ u
32
+ ··· − 8u + 1)(u
84
− 2u
83
+ ··· − 66u − 71)
c
12
(u
33
+ 3u
32
+ ··· − 3u + 11)(u
84
− 2u
83
+ ··· − 931u + 393)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
33
− 40y
32
+ ··· − 4288y −256)
· (y
84
− 105y
83
+ ··· − 4667929856y + 71639296)
c
2
, c
5
(y
33
− 17y
32
+ ··· + 21y −1)(y
84
− 54y
83
+ ··· − 314551y + 4761)
c
3
, c
8
(y
33
− 18y
32
+ ··· + 5y −1)
· (y
84
− 91y
83
+ ··· − 79247924731y + 3520404889)
c
4
, c
10
(y
33
+ 20y
32
+ ··· + 19y −1)(y
84
+ 43y
83
+ ··· + 129599y + 7225)
c
6
(y
33
+ 9y
32
+ ··· + 333y −1681)
· (y
84
+ 4y
83
+ ··· − 82932175y + 638401)
c
7
(y
33
− 23y
32
+ ··· − 4016y −169)
· (y
84
− 108y
83
+ ··· − 5560618845808998y + 81451473352209)
c
9
, c
12
(y
33
+ 21y
32
+ ··· − 2125y −121)
· (y
84
+ 36y
83
+ ··· + 530747y + 154449)
c
11
(y
33
+ 13y
32
+ ··· + 22y −1)(y
84
+ 20y
83
+ ··· − 234396y + 5041)
24
