12n
0427
(K12n
0427
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 2 9 5 11 6 1 4 9
Solving Sequence
2,6 3,9
7 10 1 11 5 8 12 4
c
2
c
6
c
9
c
1
c
10
c
5
c
7
c
12
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.07936 × 10
110
u
78
+ 8.79010 × 10
109
u
77
+ ··· + 6.15846 × 10
109
b − 9.76189 × 10
110
,
5.98068 × 10
109
u
78
− 1.62667 × 10
110
u
77
+ ··· + 6.15846 × 10
109
a + 1.72158 × 10
110
, u
79
− u
78
+ ··· − 5u − 1i
I
u
2
= h−12u
22
+ 36u
21
+ ··· + 29b + 62, 17u
22
+ 65u
21
+ ··· + 29a + 178, u
23
− 6u
21
+ ··· + 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 102 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−9.08 × 10
110
u
78
+ 8.79 × 10
109
u
77
+ · · · + 6.16 × 10
109
b − 9.76 ×
10
110
, 5.98 × 10
109
u
78
− 1.63 × 10
110
u
77
+ · · · + 6.16 × 10
109
a + 1.72 ×
10
110
, u
79
− u
78
+ · · · − 5u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−0.971132u
78
+ 2.64136u
77
+ ··· + 6.04319u − 2.79547
14.7429u
78
− 1.42732u
77
+ ··· + 94.4842u + 15.8512
a
7
=
11.8768u
78
− 3.37720u
77
+ ··· + 83.6913u + 11.1756
11.9659u
78
− 4.59087u
77
+ ··· + 116.379u + 18.6517
a
10
=
−0.971132u
78
+ 2.64136u
77
+ ··· + 6.04319u − 2.79547
16.3558u
78
− 0.971234u
77
+ ··· + 101.864u + 17.5214
a
1
=
−u
2
+ 1
−u
4
a
11
=
−0.810554u
78
+ 3.36782u
77
+ ··· − 7.29319u − 4.32558
12.4497u
78
− 0.403268u
77
+ ··· + 72.5802u + 12.6725
a
5
=
u
u
a
8
=
12.8514u
78
− 3.04231u
77
+ ··· + 89.2245u + 12.3001
12.9406u
78
− 4.25598u
77
+ ··· + 121.912u + 19.7762
a
12
=
−14.4160u
78
+ 5.24384u
77
+ ··· − 95.6278u − 14.3701
−11.5538u
78
+ 3.34984u
77
+ ··· − 112.598u − 17.7373
a
4
=
17.1980u
78
− 7.17604u
77
+ ··· + 116.184u + 19.2207
6.15055u
78
− 3.28266u
77
+ ··· + 78.6335u + 11.8437
(ii) Obstruction class = −1
(iii) Cusp Shapes = 13.0730u
78
− 4.80433u
77
+ ··· + 106.377u + 11.6389
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 47u
78
+ ··· − 15u + 1
c
2
, c
5
u
79
+ u
78
+ ··· − 5u + 1
c
3
u
79
+ 2u
78
+ ··· − 1585u − 751
c
4
, c
11
u
79
+ u
78
+ ··· − 95u − 17
c
6
, c
9
u
79
+ 8u
78
+ ··· + 228781u + 27293
c
7
u
79
− 10u
78
+ ··· + 105789720u − 12203621
c
8
u
79
+ 9u
78
+ ··· + 87u + 1
c
10
u
79
+ 6u
78
+ ··· + 180673434u + 11333737
c
12
u
79
− 3u
78
+ ··· − 427561u + 16969
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
− 23y
78
+ ··· + 201y −1
c
2
, c
5
y
79
− 47y
78
+ ··· − 15y −1
c
3
y
79
− 18y
78
+ ··· + 14546249y −564001
c
4
, c
11
y
79
− 59y
78
+ ··· − 10729y −289
c
6
, c
9
y
79
− 86y
78
+ ··· + 37605309847y −744907849
c
7
y
79
− 74y
78
+ ··· + 3831097413487084y −148928365511641
c
8
y
79
+ 17y
78
+ ··· + 4035y −1
c
10
y
79
+ 72y
78
+ ··· + 6604146335611458y −128453594385169
c
12
y
79
+ 57y
78
+ ··· + 62831435943y −287946961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.124050 + 0.993308I
a = 0.04579 − 1.50731I
b = −0.099183 + 0.105938I
−3.53096 − 5.44418I 0
u = −0.124050 − 0.993308I
a = 0.04579 + 1.50731I
b = −0.099183 − 0.105938I
−3.53096 + 5.44418I 0
u = −1.00792
a = 1.83576
b = 3.13845
−6.57376 0
u = 0.124459 + 1.005840I
a = −0.20988 − 1.77449I
b = 0.0137860 − 0.0597242I
−8.55740 + 11.15110I 0
u = 0.124459 − 1.005840I
a = −0.20988 + 1.77449I
b = 0.0137860 + 0.0597242I
−8.55740 − 11.15110I 0
u = 0.144077 + 0.963515I
a = 0.42273 − 1.45073I
b = 0.385199 + 0.154386I
−7.42668 − 1.34593I 0
u = 0.144077 − 0.963515I
a = 0.42273 + 1.45073I
b = 0.385199 − 0.154386I
−7.42668 + 1.34593I 0
u = 0.860189 + 0.441139I
a = 1.057870 + 0.073073I
b = 0.93330 + 1.20699I
−3.06653 + 2.05333I 0
u = 0.860189 − 0.441139I
a = 1.057870 − 0.073073I
b = 0.93330 − 1.20699I
−3.06653 − 2.05333I 0
u = −0.996413 + 0.319112I
a = 0.650609 − 1.213410I
b = 0.649781 − 0.828840I
−0.44095 + 4.14481I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996413 − 0.319112I
a = 0.650609 + 1.213410I
b = 0.649781 + 0.828840I
−0.44095 − 4.14481I 0
u = 0.655543 + 0.819980I
a = 0.255857 + 0.086779I
b = 0.588626 − 0.201877I
−0.66585 + 2.44129I 0
u = 0.655543 − 0.819980I
a = 0.255857 − 0.086779I
b = 0.588626 + 0.201877I
−0.66585 − 2.44129I 0
u = 0.967265 + 0.427782I
a = −0.488566 − 0.371683I
b = 0.273554 + 0.305272I
−3.57853 − 3.77822I 0
u = 0.967265 − 0.427782I
a = −0.488566 + 0.371683I
b = 0.273554 − 0.305272I
−3.57853 + 3.77822I 0
u = −0.777640 + 0.524131I
a = 0.060922 + 1.178250I
b = −1.05995 + 1.07375I
−1.88772 − 1.48161I −6.00000 + 0.I
u = −0.777640 − 0.524131I
a = 0.060922 − 1.178250I
b = −1.05995 − 1.07375I
−1.88772 + 1.48161I −6.00000 + 0.I
u = 0.874391 + 0.252735I
a = 0.106856 + 0.911284I
b = 1.077430 + 0.356830I
−0.337925 − 0.256564I −8.30782 + 3.39103I
u = 0.874391 − 0.252735I
a = 0.106856 − 0.911284I
b = 1.077430 − 0.356830I
−0.337925 + 0.256564I −8.30782 − 3.39103I
u = −0.148498 + 1.081220I
a = −0.15032 + 1.59909I
b = −0.284344 + 0.412088I
−6.06830 − 1.45699I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148498 − 1.081220I
a = −0.15032 − 1.59909I
b = −0.284344 − 0.412088I
−6.06830 + 1.45699I 0
u = 0.111700 + 0.880869I
a = −0.27307 + 1.59148I
b = 0.148200 + 0.097888I
−2.96592 − 0.33851I −4.86982 + 0.I
u = 0.111700 − 0.880869I
a = −0.27307 − 1.59148I
b = 0.148200 − 0.097888I
−2.96592 + 0.33851I −4.86982 + 0.I
u = 1.095650 + 0.199276I
a = −0.233611 + 0.299177I
b = −0.413784 − 1.166340I
−1.65389 − 2.40002I 0
u = 1.095650 − 0.199276I
a = −0.233611 − 0.299177I
b = −0.413784 + 1.166340I
−1.65389 + 2.40002I 0
u = −0.870987 + 0.694280I
a = −0.242416 − 0.409787I
b = −0.672718 − 0.142168I
2.25413 + 2.59808I 0
u = −0.870987 − 0.694280I
a = −0.242416 + 0.409787I
b = −0.672718 + 0.142168I
2.25413 − 2.59808I 0
u = 1.090130 + 0.235481I
a = −0.99350 − 1.82783I
b = −1.34961 − 1.90635I
−4.58545 − 6.42996I 0
u = 1.090130 − 0.235481I
a = −0.99350 + 1.82783I
b = −1.34961 + 1.90635I
−4.58545 + 6.42996I 0
u = −1.087020 + 0.301405I
a = 0.377902 − 0.095022I
b = 1.47034 − 1.51852I
−4.52644 + 7.46779I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.087020 − 0.301405I
a = 0.377902 + 0.095022I
b = 1.47034 + 1.51852I
−4.52644 − 7.46779I 0
u = −0.870532 + 0.729133I
a = −0.408189 − 0.291159I
b = −0.415327 + 0.247680I
2.25574 + 2.83763I 0
u = −0.870532 − 0.729133I
a = −0.408189 + 0.291159I
b = −0.415327 − 0.247680I
2.25574 − 2.83763I 0
u = 0.854887 + 0.086205I
a = −0.824990 − 0.760452I
b = −2.18721 + 0.40335I
0.20270 − 1.63900I −6.18579 + 2.68412I
u = 0.854887 − 0.086205I
a = −0.824990 + 0.760452I
b = −2.18721 − 0.40335I
0.20270 + 1.63900I −6.18579 − 2.68412I
u = −0.011138 + 0.799292I
a = 0.75122 + 2.24520I
b = 0.0809696 + 0.0150184I
−6.90468 + 2.02476I −12.86621 − 3.49188I
u = −0.011138 − 0.799292I
a = 0.75122 − 2.24520I
b = 0.0809696 − 0.0150184I
−6.90468 − 2.02476I −12.86621 + 3.49188I
u = −1.205070 + 0.075848I
a = 0.352959 + 0.793234I
b = 0.249679 + 0.319589I
−6.98811 − 1.03838I 0
u = −1.205070 − 0.075848I
a = 0.352959 − 0.793234I
b = 0.249679 − 0.319589I
−6.98811 + 1.03838I 0
u = −0.714612 + 0.322053I
a = 1.17385 − 1.10692I
b = 1.122240 + 0.616705I
−1.62856 + 5.22847I −5.24615 − 6.25825I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714612 − 0.322053I
a = 1.17385 + 1.10692I
b = 1.122240 − 0.616705I
−1.62856 − 5.22847I −5.24615 + 6.25825I
u = 0.756993 + 0.152949I
a = 0.42209 − 2.06915I
b = 1.42709 − 0.91137I
−2.35393 − 5.09247I −5.03911 + 4.20229I
u = 0.756993 − 0.152949I
a = 0.42209 + 2.06915I
b = 1.42709 + 0.91137I
−2.35393 + 5.09247I −5.03911 − 4.20229I
u = −0.759300
a = 1.70752
b = 0.277959
−5.85282 −17.3230
u = 1.002520 + 0.747637I
a = 0.169318 − 0.323597I
b = −0.213329 + 0.028211I
−1.68225 − 8.27881I 0
u = 1.002520 − 0.747637I
a = 0.169318 + 0.323597I
b = −0.213329 − 0.028211I
−1.68225 + 8.27881I 0
u = −0.690200 + 0.252371I
a = −0.650362 − 1.021330I
b = −1.241910 − 0.053379I
1.59486 + 1.49978I −0.07297 − 3.73762I
u = −0.690200 − 0.252371I
a = −0.650362 + 1.021330I
b = −1.241910 + 0.053379I
1.59486 − 1.49978I −0.07297 + 3.73762I
u = −1.208530 + 0.474510I
a = 1.40585 + 0.74277I
b = 2.77928 + 1.38636I
−10.38010 + 2.53397I 0
u = −1.208530 − 0.474510I
a = 1.40585 − 0.74277I
b = 2.77928 − 1.38636I
−10.38010 − 2.53397I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.224290 + 0.452162I
a = −1.73180 − 0.11246I
b = −3.45824 − 0.11592I
−10.54610 − 6.52041I 0
u = 1.224290 − 0.452162I
a = −1.73180 + 0.11246I
b = −3.45824 + 0.11592I
−10.54610 + 6.52041I 0
u = 0.374424 + 0.557104I
a = −0.298573 + 0.266159I
b = 0.242278 + 0.712052I
−1.95304 − 0.10654I −6.12961 + 0.27546I
u = 0.374424 − 0.557104I
a = −0.298573 − 0.266159I
b = 0.242278 − 0.712052I
−1.95304 + 0.10654I −6.12961 − 0.27546I
u = −1.265280 + 0.418387I
a = 1.407490 + 0.110564I
b = 2.67014 + 0.03204I
−7.15565 + 4.82155I 0
u = −1.265280 − 0.418387I
a = 1.407490 − 0.110564I
b = 2.67014 − 0.03204I
−7.15565 − 4.82155I 0
u = 1.244170 + 0.526496I
a = −1.215800 + 0.223081I
b = −2.34833 + 0.63093I
−6.36388 − 4.79049I 0
u = 1.244170 − 0.526496I
a = −1.215800 − 0.223081I
b = −2.34833 − 0.63093I
−6.36388 + 4.79049I 0
u = −1.318950 + 0.404408I
a = −1.115090 + 0.101971I
b = −2.54344 − 0.28658I
−12.04730 + 6.05783I 0
u = −1.318950 − 0.404408I
a = −1.115090 − 0.101971I
b = −2.54344 + 0.28658I
−12.04730 − 6.05783I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.275450 + 0.561649I
a = 1.108870 − 0.514663I
b = 2.30481 − 0.53958I
−10.87960 − 4.18016I 0
u = 1.275450 − 0.561649I
a = 1.108870 + 0.514663I
b = 2.30481 + 0.53958I
−10.87960 + 4.18016I 0
u = 0.604300
a = −0.346901
b = 0.407027
−0.845319 −12.4810
u = −1.283240 + 0.553621I
a = −1.264520 − 0.190049I
b = −2.61620 − 0.22912I
−7.10608 + 10.99590I 0
u = −1.283240 − 0.553621I
a = −1.264520 + 0.190049I
b = −2.61620 + 0.22912I
−7.10608 − 10.99590I 0
u = 1.340750 + 0.402994I
a = 1.098720 − 0.190005I
b = 2.39136 − 0.49670I
−8.23565 + 0.56859I 0
u = 1.340750 − 0.402994I
a = 1.098720 + 0.190005I
b = 2.39136 + 0.49670I
−8.23565 − 0.56859I 0
u = 1.285480 + 0.558802I
a = 1.49634 − 0.09704I
b = 2.91711 − 0.19888I
−12.1399 − 16.7524I 0
u = 1.285480 − 0.558802I
a = 1.49634 + 0.09704I
b = 2.91711 + 0.19888I
−12.1399 + 16.7524I 0
u = −1.35867 + 0.40255I
a = −1.282670 − 0.351429I
b = −2.48277 − 0.74627I
−13.3361 − 6.1955I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35867 − 0.40255I
a = −1.282670 + 0.351429I
b = −2.48277 + 0.74627I
−13.3361 + 6.1955I 0
u = 1.37038 + 0.38850I
a = −1.53013 + 0.38050I
b = −2.45200 + 0.42466I
−11.12530 − 3.60644I 0
u = 1.37038 − 0.38850I
a = −1.53013 − 0.38050I
b = −2.45200 − 0.42466I
−11.12530 + 3.60644I 0
u = −1.32407 + 0.56602I
a = 1.383350 − 0.123531I
b = 2.40408 + 0.15262I
−9.81222 + 7.35945I 0
u = −1.32407 − 0.56602I
a = 1.383350 + 0.123531I
b = 2.40408 − 0.15262I
−9.81222 − 7.35945I 0
u = −0.253383 + 0.206686I
a = −1.85540 + 1.55580I
b = −0.751106 + 0.542245I
1.37257 − 1.37746I 0.75336 + 3.11081I
u = −0.253383 − 0.206686I
a = −1.85540 − 1.55580I
b = −0.751106 − 0.542245I
1.37257 + 1.37746I 0.75336 − 3.11081I
u = −0.063007 + 0.180194I
a = −5.07786 + 2.45613I
b = 0.548490 − 0.799172I
−1.92545 − 4.88532I −6.44213 + 5.94399I
u = −0.063007 − 0.180194I
a = −5.07786 − 2.45613I
b = 0.548490 + 0.799172I
−1.92545 + 4.88532I −6.44213 − 5.94399I
12
II. I
u
2
= h−12u
22
+ 36u
21
+ · · · + 29b + 62, 17u
22
+ 65u
21
+ · · · + 29a +
178, u
23
− 6u
21
+ · · · + 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−0.586207u
22
− 2.24138u
21
+ ··· − 4.20690u − 6.13793
0.413793u
22
− 1.24138u
21
+ ··· − 3.20690u − 2.13793
a
7
=
−1.06897u
22
− 2.79310u
21
+ ··· + 17.0345u − 14.3103
−5.79310u
22
+ 3.37931u
21
+ ··· − 8.10345u − 1.06897
a
10
=
−0.586207u
22
− 2.24138u
21
+ ··· − 4.20690u − 6.13793
4.13793u
22
− 4.41379u
21
+ ··· + 2.93103u − 4.37931
a
1
=
−u
2
+ 1
−u
4
a
11
=
−3.89655u
22
− 1.31034u
21
+ ··· − 12.5517u − 7.03448
−0.379310u
22
− 0.862069u
21
+ ··· − 10.3103u − 1.20690
a
5
=
u
u
a
8
=
3.44828u
22
− 6.34483u
21
+ ··· + 40.2759u − 20.4828
−1.27586u
22
− 0.172414u
21
+ ··· + 15.1379u − 7.24138
a
12
=
4.58621u
22
+ 2.24138u
21
+ ··· + 9.20690u + 7.13793
−2.03448u
22
+ 5.10345u
21
+ ··· − 8.48276u + 4.34483
a
4
=
6.51724u
22
+ 0.448276u
21
+ ··· + 13.2414u + 9.82759
2.86207u
22
− 2.58621u
21
+ ··· + 13.0690u − 0.620690
(ii) Obstruction class = 1
(iii) Cusp Shapes =
336
29
u
22
−
486
29
u
21
+ ··· +
1079
29
u −
605
29
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
23
− 12u
22
+ ··· + 17u − 1
c
2
u
23
− 6u
21
+ ··· + 3u − 1
c
3
u
23
+ u
22
+ ··· + u + 1
c
4
u
23
− 8u
21
+ ··· − u + 5
c
5
u
23
− 6u
21
+ ··· + 3u + 1
c
6
u
23
− 15u
22
+ ··· + 51u − 5
c
7
u
23
+ 3u
22
+ ··· − 24u + 19
c
8
u
23
+ 8u
22
+ ··· − 3u − 1
c
9
u
23
+ 15u
22
+ ··· + 51u + 5
c
10
u
23
− u
22
+ ··· + 40u − 19
c
11
u
23
− 8u
21
+ ··· − u − 5
c
12
u
23
+ 4u
22
+ ··· − 7u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 4y
22
+ ··· + 69y −1
c
2
, c
5
y
23
− 12y
22
+ ··· + 17y −1
c
3
y
23
+ y
22
+ ··· + y −1
c
4
, c
11
y
23
− 16y
22
+ ··· + 11y −25
c
6
, c
9
y
23
− 7y
22
+ ··· − 329y −25
c
7
y
23
− 19y
22
+ ··· + 1184y −361
c
8
y
23
+ 24y
21
+ ··· + 11y −1
c
10
y
23
+ 7y
22
+ ··· + 2018y −361
c
12
y
23
+ 12y
22
+ ··· + 11y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741033 + 0.707784I
a = 0.346463 + 0.724986I
b = 0.292617 + 0.066396I
0.01294 + 3.03667I −3.29385 − 4.70963I
u = 0.741033 − 0.707784I
a = 0.346463 − 0.724986I
b = 0.292617 − 0.066396I
0.01294 − 3.03667I −3.29385 + 4.70963I
u = 0.999976 + 0.286700I
a = −0.466877 − 0.796422I
b = −0.787607 + 0.431045I
−0.49287 − 2.88561I −6.13993 + 4.79776I
u = 0.999976 − 0.286700I
a = −0.466877 + 0.796422I
b = −0.787607 − 0.431045I
−0.49287 + 2.88561I −6.13993 − 4.79776I
u = −0.908909 + 0.291662I
a = −0.687671 + 1.171800I
b = −1.00814 + 2.16111I
−3.10340 − 3.51447I −10.21023 + 3.16506I
u = −0.908909 − 0.291662I
a = −0.687671 − 1.171800I
b = −1.00814 − 2.16111I
−3.10340 + 3.51447I −10.21023 − 3.16506I
u = −0.806475 + 0.679820I
a = 0.577898 + 0.014874I
b = 0.708260 − 0.504395I
2.69708 + 3.05485I 1.87315 − 8.21021I
u = −0.806475 − 0.679820I
a = 0.577898 − 0.014874I
b = 0.708260 + 0.504395I
2.69708 − 3.05485I 1.87315 + 8.21021I
u = −0.891878 + 0.236181I
a = 0.51820 − 1.71239I
b = −0.178682 − 0.443321I
−2.96370 + 5.82303I −10.5506 − 9.5130I
u = −0.891878 − 0.236181I
a = 0.51820 + 1.71239I
b = −0.178682 + 0.443321I
−2.96370 − 5.82303I −10.5506 + 9.5130I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.042903 + 0.915541I
a = −0.28646 + 1.73775I
b = −0.296665 + 0.230996I
−5.34196 − 1.12606I −6.62744 − 0.03733I
u = −0.042903 − 0.915541I
a = −0.28646 − 1.73775I
b = −0.296665 − 0.230996I
−5.34196 + 1.12606I −6.62744 + 0.03733I
u = 0.958656 + 0.645813I
a = −0.397487 − 0.543897I
b = −0.819521 − 0.826094I
−0.66948 − 8.24106I −4.12296 + 7.31736I
u = 0.958656 − 0.645813I
a = −0.397487 + 0.543897I
b = −0.819521 + 0.826094I
−0.66948 + 8.24106I −4.12296 − 7.31736I
u = −0.932276 + 0.684370I
a = 0.220474 + 0.637743I
b = 0.614045 + 0.246642I
2.30961 + 2.21517I −5.35115 + 8.29705I
u = −0.932276 − 0.684370I
a = 0.220474 − 0.637743I
b = 0.614045 − 0.246642I
2.30961 − 2.21517I −5.35115 − 8.29705I
u = 0.732993 + 0.234436I
a = 0.104383 + 0.620473I
b = 1.38315 + 0.95696I
0.500246 + 0.529647I −2.76731 + 1.70335I
u = 0.732993 − 0.234436I
a = 0.104383 − 0.620473I
b = 1.38315 − 0.95696I
0.500246 − 0.529647I −2.76731 − 1.70335I
u = 1.249510 + 0.470199I
a = −1.35976 + 0.50699I
b = −2.56148 + 0.64724I
−9.21032 − 3.62425I −10.21319 + 2.92816I
u = 1.249510 − 0.470199I
a = −1.35976 − 0.50699I
b = −2.56148 − 0.64724I
−9.21032 + 3.62425I −10.21319 − 2.92816I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.274960 + 0.459002I
a = 1.45276 − 0.13786I
b = 2.72479 − 0.00258I
−9.24494 + 6.08267I −10.44404 − 3.52440I
u = −1.274960 − 0.459002I
a = 1.45276 + 0.13786I
b = 2.72479 + 0.00258I
−9.24494 − 6.08267I −10.44404 + 3.52440I
u = 0.350478
a = −4.04386
b = −1.14153
−4.91416 −7.30480
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 12u
22
+ ··· + 17u − 1)(u
79
+ 47u
78
+ ··· − 15u + 1)
c
2
(u
23
− 6u
21
+ ··· + 3u − 1)(u
79
+ u
78
+ ··· − 5u + 1)
c
3
(u
23
+ u
22
+ ··· + u + 1)(u
79
+ 2u
78
+ ··· − 1585u − 751)
c
4
(u
23
− 8u
21
+ ··· − u + 5)(u
79
+ u
78
+ ··· − 95u − 17)
c
5
(u
23
− 6u
21
+ ··· + 3u + 1)(u
79
+ u
78
+ ··· − 5u + 1)
c
6
(u
23
− 15u
22
+ ··· + 51u − 5)(u
79
+ 8u
78
+ ··· + 228781u + 27293)
c
7
(u
23
+ 3u
22
+ ··· − 24u + 19)
· (u
79
− 10u
78
+ ··· + 105789720u − 12203621)
c
8
(u
23
+ 8u
22
+ ··· − 3u − 1)(u
79
+ 9u
78
+ ··· + 87u + 1)
c
9
(u
23
+ 15u
22
+ ··· + 51u + 5)(u
79
+ 8u
78
+ ··· + 228781u + 27293)
c
10
(u
23
− u
22
+ ··· + 40u − 19)
· (u
79
+ 6u
78
+ ··· + 180673434u + 11333737)
c
11
(u
23
− 8u
21
+ ··· − u − 5)(u
79
+ u
78
+ ··· − 95u − 17)
c
12
(u
23
+ 4u
22
+ ··· − 7u + 1)(u
79
− 3u
78
+ ··· − 427561u + 16969)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 4y
22
+ ··· + 69y −1)(y
79
− 23y
78
+ ··· + 201y −1)
c
2
, c
5
(y
23
− 12y
22
+ ··· + 17y −1)(y
79
− 47y
78
+ ··· − 15y −1)
c
3
(y
23
+ y
22
+ ··· + y −1)(y
79
− 18y
78
+ ··· + 1.45462 × 10
7
y −564001)
c
4
, c
11
(y
23
− 16y
22
+ ··· + 11y −25)(y
79
− 59y
78
+ ··· − 10729y −289)
c
6
, c
9
(y
23
− 7y
22
+ ··· − 329y −25)
· (y
79
− 86y
78
+ ··· + 37605309847y −744907849)
c
7
(y
23
− 19y
22
+ ··· + 1184y −361)
· (y
79
− 74y
78
+ ··· + 3831097413487084y −148928365511641)
c
8
(y
23
+ 24y
21
+ ··· + 11y −1)(y
79
+ 17y
78
+ ··· + 4035y −1)
c
10
(y
23
+ 7y
22
+ ··· + 2018y −361)
· (y
79
+ 72y
78
+ ··· + 6604146335611458y −128453594385169)
c
12
(y
23
+ 12y
22
+ ··· + 11y −1)
· (y
79
+ 57y
78
+ ··· + 62831435943y −287946961)
22
