12n
0791
(K12n
0791
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 2 11 5 11 3 1 6 9
Solving Sequence
4,10 3,6
2 1 11 5 9 8 7 12
c
3
c
2
c
1
c
10
c
5
c
9
c
8
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.33940 × 10
221
u
77
+ 3.62622 × 10
220
u
76
+ ··· + 1.11812 × 10
223
b + 2.16286 × 10
224
,
1.25797 × 10
224
u
77
+ 2.59631 × 10
223
u
76
+ ··· + 7.97223 × 10
225
a − 1.18016 × 10
227
,
u
78
− u
77
+ ··· + 7307u − 713i
I
u
2
= h9.42636 × 10
15
u
31
− 1.03650 × 10
16
u
30
+ ··· + 2.60834 × 10
15
b + 8.63306 × 10
16
,
− 8.60928 × 10
16
u
31
+ 1.00029 × 10
17
u
30
+ ··· + 2.86917 × 10
16
a − 1.03993 × 10
18
,
u
32
− 12u
30
+ ··· + 14u + 11i
* 2 irreducible components of dim
C
= 0, with total 110 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
= h3.34 × 10
221
u
77
+ 3.63 × 10
220
u
76
+ · · · + 1.12 × 10
223
b + 2.16 ×
10
224
, 1.26 × 10
224
u
77
+ 2.60 × 10
223
u
76
+ · · · + 7.97 × 10
225
a − 1.18 ×
10
227
, u
78
− u
77
+ · · · + 7307u − 713i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
6
=
−0.0157793u
77
− 0.00325669u
76
+ ··· − 26.8738u + 14.8034
−0.0298661u
77
− 0.00324312u
76
+ ··· + 175.664u − 19.3436
a
2
=
0.0121080u
77
− 0.0122585u
76
+ ··· − 260.939u + 42.1759
0.0127688u
77
+ 0.000485058u
76
+ ··· − 101.992u + 11.9796
a
1
=
0.0248767u
77
− 0.0117734u
76
+ ··· − 362.931u + 54.1555
0.0127688u
77
+ 0.000485058u
76
+ ··· − 101.992u + 11.9796
a
11
=
0.0150625u
77
− 0.0141531u
76
+ ··· − 304.583u + 44.1204
0.00161713u
77
+ 0.00303149u
76
+ ··· + 21.4007u − 5.05900
a
5
=
−0.117342u
77
+ 0.0172410u
76
+ ··· + 835.872u − 90.0394
−0.0229477u
77
− 0.00152551u
76
+ ··· + 164.335u − 20.6918
a
9
=
u
−u
3
+ u
a
8
=
0.0594370u
77
− 0.0231347u
76
+ ··· − 617.741u + 82.9433
0.00163959u
77
− 0.00205736u
76
+ ··· − 58.1641u + 9.02172
a
7
=
−0.0839403u
77
+ 0.00200465u
76
+ ··· + 589.203u − 61.4125
−0.00229897u
77
− 0.00218375u
76
+ ··· − 22.8424u + 5.75187
a
12
=
0.00354460u
77
− 0.0181944u
76
+ ··· − 257.161u + 43.8462
0.0257467u
77
+ 0.00283761u
76
+ ··· − 183.805u + 21.4583
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0607658u
77
− 0.0336953u
76
+ ··· − 399.330u + 14.9628
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
78
− 9u
77
+ ··· − 30111u − 3476
c
2
, c
5
u
78
+ u
77
+ ··· + 25u − 1
c
3
, c
9
u
78
− u
77
+ ··· + 7307u − 713
c
4
, c
7
u
78
− 5u
77
+ ··· + 20u − 1
c
6
, c
11
u
78
+ 3u
77
+ ··· − 734300u + 685471
c
8
u
78
+ 5u
77
+ ··· + 107670903u + 34552577
c
10
u
78
+ u
77
+ ··· + 729u + 31
c
12
u
78
− 3u
77
+ ··· + 5399717u + 801148
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
78
− 27y
77
+ ··· + 17262383y + 12082576
c
2
, c
5
y
78
− 73y
77
+ ··· + 105y + 1
c
3
, c
9
y
78
− 67y
77
+ ··· − 15851373y + 508369
c
4
, c
7
y
78
+ 17y
77
+ ··· − 408y + 1
c
6
, c
11
y
78
− 83y
77
+ ··· − 10360427562352y + 469870491841
c
8
y
78
+ 69y
77
+ ··· − 21520300962268511y + 1193880577340929
c
10
y
78
+ 5y
77
+ ··· − 120505y + 961
c
12
y
78
+ 73y
77
+ ··· − 7450965034177y + 641838117904
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.942844 + 0.058139I
a = 0.387472 + 0.733615I
b = −0.195034 + 0.610856I
3.47891 − 1.49180I −6.00000 + 0.I
u = 0.942844 − 0.058139I
a = 0.387472 − 0.733615I
b = −0.195034 − 0.610856I
3.47891 + 1.49180I −6.00000 + 0.I
u = −0.233950 + 0.908933I
a = −0.417189 − 0.871468I
b = −0.705334 − 0.166427I
2.67343 + 2.46581I −6.00000 − 7.69832I
u = −0.233950 − 0.908933I
a = −0.417189 + 0.871468I
b = −0.705334 + 0.166427I
2.67343 − 2.46581I −6.00000 + 7.69832I
u = −1.052020 + 0.174510I
a = 0.301022 − 0.112833I
b = 0.098599 − 0.266687I
−2.28336 + 0.03067I 0
u = −1.052020 − 0.174510I
a = 0.301022 + 0.112833I
b = 0.098599 + 0.266687I
−2.28336 − 0.03067I 0
u = 0.985202 + 0.543560I
a = 0.344444 − 0.317962I
b = −0.725802 − 0.187739I
1.16693 − 4.65623I 0
u = 0.985202 − 0.543560I
a = 0.344444 + 0.317962I
b = −0.725802 + 0.187739I
1.16693 + 4.65623I 0
u = 0.512915 + 0.664507I
a = −0.019800 − 0.447055I
b = −0.502437 + 0.036527I
2.57696 − 0.05718I −1.84410 − 0.26283I
u = 0.512915 − 0.664507I
a = −0.019800 + 0.447055I
b = −0.502437 − 0.036527I
2.57696 + 0.05718I −1.84410 + 0.26283I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.117457 + 0.796160I
a = 0.799606 + 0.362909I
b = 1.54042 + 0.31597I
−1.82800 − 1.56177I −11.06612 + 4.95728I
u = −0.117457 − 0.796160I
a = 0.799606 − 0.362909I
b = 1.54042 − 0.31597I
−1.82800 + 1.56177I −11.06612 − 4.95728I
u = 0.788310 + 0.067667I
a = 0.34762 + 1.53388I
b = −0.222137 + 0.211517I
4.10212 + 0.95252I −6.69747 − 11.08186I
u = 0.788310 − 0.067667I
a = 0.34762 − 1.53388I
b = −0.222137 − 0.211517I
4.10212 − 0.95252I −6.69747 + 11.08186I
u = −1.181570 + 0.296006I
a = −1.25923 − 1.88608I
b = 1.53208 + 1.70546I
−9.81204 + 5.88301I 0
u = −1.181570 − 0.296006I
a = −1.25923 + 1.88608I
b = 1.53208 − 1.70546I
−9.81204 − 5.88301I 0
u = 0.370228 + 0.671180I
a = 0.426280 − 0.076400I
b = −0.016730 − 0.393794I
1.81907 + 1.89583I 1.064668 + 0.345602I
u = 0.370228 − 0.671180I
a = 0.426280 + 0.076400I
b = −0.016730 + 0.393794I
1.81907 − 1.89583I 1.064668 − 0.345602I
u = −0.262253 + 0.715559I
a = −0.814627 + 0.211044I
b = 1.082170 − 0.442549I
−7.06075 − 2.20723I −7.08678 + 2.81313I
u = −0.262253 − 0.715559I
a = −0.814627 − 0.211044I
b = 1.082170 + 0.442549I
−7.06075 + 2.20723I −7.08678 − 2.81313I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115340 + 0.560449I
a = −0.169288 − 0.244756I
b = −0.165686 + 0.541919I
−0.34731 − 6.68579I 0
u = 1.115340 − 0.560449I
a = −0.169288 + 0.244756I
b = −0.165686 − 0.541919I
−0.34731 + 6.68579I 0
u = 1.228540 + 0.240197I
a = −0.702013 − 1.070830I
b = 0.51943 + 2.25418I
−6.10822 − 3.54460I 0
u = 1.228540 − 0.240197I
a = −0.702013 + 1.070830I
b = 0.51943 − 2.25418I
−6.10822 + 3.54460I 0
u = 1.262970 + 0.047018I
a = 1.55368 − 0.40771I
b = −1.53769 + 1.10929I
−3.54474 − 4.39179I 0
u = 1.262970 − 0.047018I
a = 1.55368 + 0.40771I
b = −1.53769 − 1.10929I
−3.54474 + 4.39179I 0
u = −1.191080 + 0.473505I
a = −0.103272 + 0.395239I
b = 0.250583 + 0.278590I
−0.35015 + 2.38063I 0
u = −1.191080 − 0.473505I
a = −0.103272 − 0.395239I
b = 0.250583 − 0.278590I
−0.35015 − 2.38063I 0
u = −1.277390 + 0.110090I
a = −2.20740 − 0.08937I
b = 1.97105 − 0.56101I
−4.35623 + 3.03953I 0
u = −1.277390 − 0.110090I
a = −2.20740 + 0.08937I
b = 1.97105 + 0.56101I
−4.35623 − 3.03953I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.291280 + 0.159820I
a = 1.98881 + 1.23832I
b = −2.27722 − 1.32574I
−11.24160 − 1.94282I 0
u = −1.291280 − 0.159820I
a = 1.98881 − 1.23832I
b = −2.27722 + 1.32574I
−11.24160 + 1.94282I 0
u = 1.317320 + 0.121357I
a = 0.177970 + 1.254660I
b = −0.06318 − 2.60422I
−5.17676 + 4.17039I 0
u = 1.317320 − 0.121357I
a = 0.177970 − 1.254660I
b = −0.06318 + 2.60422I
−5.17676 − 4.17039I 0
u = 1.263750 + 0.446195I
a = 1.94787 − 0.98680I
b = −2.78785 − 0.16314I
−1.79519 − 7.98956I 0
u = 1.263750 − 0.446195I
a = 1.94787 + 0.98680I
b = −2.78785 + 0.16314I
−1.79519 + 7.98956I 0
u = 1.333270 + 0.154113I
a = −2.17809 − 0.01089I
b = 2.72516 + 0.87884I
−6.73250 − 1.36559I 0
u = 1.333270 − 0.154113I
a = −2.17809 + 0.01089I
b = 2.72516 − 0.87884I
−6.73250 + 1.36559I 0
u = −0.247106 + 1.366830I
a = 0.286312 + 0.222429I
b = 1.88034 + 0.30072I
−8.58231 + 2.86666I 0
u = −0.247106 − 1.366830I
a = 0.286312 − 0.222429I
b = 1.88034 − 0.30072I
−8.58231 − 2.86666I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146469 + 0.591338I
a = 1.169670 − 0.079543I
b = −1.066960 + 0.481680I
−7.60805 + 4.49193I −8.55555 − 2.21842I
u = −0.146469 − 0.591338I
a = 1.169670 + 0.079543I
b = −1.066960 − 0.481680I
−7.60805 − 4.49193I −8.55555 + 2.21842I
u = 0.297121 + 1.371380I
a = −0.371698 − 0.504760I
b = −2.17012 − 0.07122I
1.90547 + 2.10501I 0
u = 0.297121 − 1.371380I
a = −0.371698 + 0.504760I
b = −2.17012 + 0.07122I
1.90547 − 2.10501I 0
u = −0.266211 + 1.384610I
a = −0.228160 − 0.202664I
b = −1.84539 − 0.24540I
−7.80585 + 10.06730I 0
u = −0.266211 − 1.384610I
a = −0.228160 + 0.202664I
b = −1.84539 + 0.24540I
−7.80585 − 10.06730I 0
u = −1.399680 + 0.173379I
a = 0.334409 − 0.519138I
b = −0.111903 − 0.458529I
−8.31581 + 1.61430I 0
u = −1.399680 − 0.173379I
a = 0.334409 + 0.519138I
b = −0.111903 + 0.458529I
−8.31581 − 1.61430I 0
u = −1.37866 + 0.36295I
a = −1.64976 − 0.50953I
b = 1.80542 − 0.82492I
−6.03995 + 5.96238I 0
u = −1.37866 − 0.36295I
a = −1.64976 + 0.50953I
b = 1.80542 + 0.82492I
−6.03995 − 5.96238I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40559 + 0.25706I
a = 1.64134 − 0.25262I
b = −1.55258 + 0.17099I
−12.6770 − 7.6946I 0
u = 1.40559 − 0.25706I
a = 1.64134 + 0.25262I
b = −1.55258 − 0.17099I
−12.6770 + 7.6946I 0
u = −1.45079 + 0.18447I
a = −0.289984 + 0.565798I
b = 0.120076 + 0.470255I
−7.53186 + 8.23802I 0
u = −1.45079 − 0.18447I
a = −0.289984 − 0.565798I
b = 0.120076 − 0.470255I
−7.53186 − 8.23802I 0
u = 0.210864 + 0.491337I
a = 1.94925 + 1.15029I
b = 0.515472 − 0.844495I
−3.08975 + 0.76544I −5.09780 − 0.03360I
u = 0.210864 − 0.491337I
a = 1.94925 − 1.15029I
b = 0.515472 + 0.844495I
−3.08975 − 0.76544I −5.09780 + 0.03360I
u = −0.357502 + 0.389914I
a = 1.057850 − 0.269178I
b = 1.216960 + 0.412368I
−1.18445 − 1.39735I −10.38498 − 7.63627I
u = −0.357502 − 0.389914I
a = 1.057850 + 0.269178I
b = 1.216960 − 0.412368I
−1.18445 + 1.39735I −10.38498 + 7.63627I
u = 1.45944 + 0.24660I
a = −1.60374 + 0.25242I
b = 1.67036 − 0.13168I
−12.74980 − 1.29840I 0
u = 1.45944 − 0.24660I
a = −1.60374 − 0.25242I
b = 1.67036 + 0.13168I
−12.74980 + 1.29840I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47987 + 0.09429I
a = 1.64800 − 0.11539I
b = −1.92274 + 0.85333I
−6.22918 + 4.98031I 0
u = −1.47987 − 0.09429I
a = 1.64800 + 0.11539I
b = −1.92274 − 0.85333I
−6.22918 − 4.98031I 0
u = 0.268582 + 0.388279I
a = −2.50694 − 2.55703I
b = −0.609144 + 1.104730I
−1.75519 − 5.95991I −1.96592 + 6.04253I
u = 0.268582 − 0.388279I
a = −2.50694 + 2.55703I
b = −0.609144 − 1.104730I
−1.75519 + 5.95991I −1.96592 − 6.04253I
u = −0.421212
a = 0.897582
b = 0.341691
−0.747108 −13.2570
u = 1.58306
a = −1.63258
b = 2.46027
−8.82351 0
u = −1.59892 + 0.25190I
a = 1.392980 + 0.180687I
b = −1.91042 + 0.74588I
−5.56562 + 3.33736I 0
u = −1.59892 − 0.25190I
a = 1.392980 − 0.180687I
b = −1.91042 − 0.74588I
−5.56562 − 3.33736I 0
u = 1.53550 + 0.51590I
a = −1.52077 + 0.57665I
b = 2.45062 + 0.56733I
−14.3064 − 9.3860I 0
u = 1.53550 − 0.51590I
a = −1.52077 − 0.57665I
b = 2.45062 − 0.56733I
−14.3064 + 9.3860I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54978 + 0.53968I
a = 1.48248 − 0.57690I
b = −2.38130 − 0.59597I
−13.5587 − 16.7600I 0
u = 1.54978 − 0.53968I
a = 1.48248 + 0.57690I
b = −2.38130 + 0.59597I
−13.5587 + 16.7600I 0
u = 0.267828 + 0.052884I
a = 0.09300 − 3.41499I
b = −1.013240 − 0.178283I
−0.14166 − 4.08705I −7.04533 + 7.48783I
u = 0.267828 − 0.052884I
a = 0.09300 + 3.41499I
b = −1.013240 + 0.178283I
−0.14166 + 4.08705I −7.04533 − 7.48783I
u = −1.58752 + 0.74757I
a = −1.048890 − 0.614073I
b = 1.92049 − 1.18239I
−12.66830 + 5.03933I 0
u = −1.58752 − 0.74757I
a = −1.048890 + 0.614073I
b = 1.92049 + 1.18239I
−12.66830 − 5.03933I 0
u = −1.67659 + 0.87833I
a = 0.915811 + 0.565877I
b = −1.91733 + 1.36586I
−11.65830 − 1.69347I 0
u = −1.67659 − 0.87833I
a = 0.915811 − 0.565877I
b = −1.91733 − 1.36586I
−11.65830 + 1.69347I 0
12
II. I
u
2
= h9.43 × 10
15
u
31
− 1.04 × 10
16
u
30
+ · · · + 2.61 × 10
15
b + 8.63 ×
10
16
, −8.61 × 10
16
u
31
+ 1.00 × 10
17
u
30
+ · · · + 2.87 × 10
16
a − 1.04 ×
10
18
, u
32
− 12u
30
+ · · · + 14u + 11i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
6
=
3.00062u
31
− 3.48635u
30
+ ··· + 16.9894u + 36.2451
−3.61394u
31
+ 3.97380u
30
+ ··· − 9.33313u − 33.0980
a
2
=
0.673654u
31
− 0.202721u
30
+ ··· − 1.38111u + 6.42284
0.436104u
31
− 0.802754u
30
+ ··· + 4.55569u + 3.93941
a
1
=
1.10976u
31
− 1.00548u
30
+ ··· + 3.17457u + 10.3622
0.436104u
31
− 0.802754u
30
+ ··· + 4.55569u + 3.93941
a
11
=
−0.551853u
31
+ 1.15430u
30
+ ··· − 4.09676u − 14.1990
−0.260882u
31
+ 0.703792u
30
+ ··· − 1.69474u + 0.574746
a
5
=
2.29143u
31
− 3.63005u
30
+ ··· + 35.4371u + 40.5356
−3.03963u
31
+ 3.45383u
30
+ ··· − 7.45780u − 30.2115
a
9
=
u
−u
3
+ u
a
8
=
0.227355u
31
− 2.01232u
30
+ ··· + 5.94324u + 7.33651
−1.19027u
31
+ 1.68925u
30
+ ··· − 11.2608u − 16.4565
a
7
=
3.83119u
31
− 3.80169u
30
+ ··· − 5.28595u + 35.2770
−4.36810u
31
+ 4.86030u
30
+ ··· − 16.0382u − 45.6150
a
12
=
−0.592703u
31
+ 1.96262u
30
+ ··· − 9.25022u − 6.20976
2.14537u
31
− 3.17011u
30
+ ··· + 14.9572u + 20.0165
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8803823690177608
2608335035160577
u
31
+
27671018694520353
2608335035160577
u
30
+···−
228493900103964694
2608335035160577
u−
259489611336058185
2608335035160577
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
32
− 4u
31
+ ··· − 60u + 9
c
2
u
32
− 9u
30
+ ··· − 2u + 1
c
3
u
32
− 12u
30
+ ··· + 14u + 11
c
4
u
32
− 8u
31
+ ··· − 7u + 1
c
5
u
32
− 9u
30
+ ··· + 2u + 1
c
6
u
32
− 2u
30
+ ··· + 21u + 11
c
7
u
32
+ 8u
31
+ ··· + 7u + 1
c
8
u
32
+ 4u
30
+ ··· + 104u + 31
c
9
u
32
− 12u
30
+ ··· − 14u + 11
c
10
u
32
+ 16u
31
+ ··· + 4u + 1
c
11
u
32
− 2u
30
+ ··· − 21u + 11
c
12
u
32
+ 4u
31
+ ··· − 53u + 5
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 8y
30
+ ··· + 684y + 81
c
2
, c
5
y
32
− 18y
31
+ ··· − 14y + 1
c
3
, c
9
y
32
− 24y
31
+ ··· − 1164y + 121
c
4
, c
7
y
32
+ 12y
31
+ ··· + 29y + 1
c
6
, c
11
y
32
− 4y
31
+ ··· + 593y + 121
c
8
y
32
+ 8y
31
+ ··· − 5794y + 961
c
10
y
32
− 8y
31
+ ··· − 8y + 1
c
12
y
32
+ 16y
31
+ ··· − 229y + 25
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.608550 + 0.702570I
a = 0.054998 − 0.773982I
b = 0.028720 − 0.337814I
1.10440 + 2.37787I −8.44125 − 4.16468I
u = 0.608550 − 0.702570I
a = 0.054998 + 0.773982I
b = 0.028720 + 0.337814I
1.10440 − 2.37787I −8.44125 + 4.16468I
u = 0.393505 + 1.055530I
a = −0.378271 + 0.727602I
b = −0.564637 + 0.479550I
2.95553 − 1.85219I −2.71010 − 2.33872I
u = 0.393505 − 1.055530I
a = −0.378271 − 0.727602I
b = −0.564637 − 0.479550I
2.95553 + 1.85219I −2.71010 + 2.33872I
u = 1.149900 + 0.127905I
a = −0.126713 − 0.886278I
b = 0.029846 − 0.370064I
2.90185 − 1.95756I −10.84834 + 6.93834I
u = 1.149900 − 0.127905I
a = −0.126713 + 0.886278I
b = 0.029846 + 0.370064I
2.90185 + 1.95756I −10.84834 − 6.93834I
u = 0.792279 + 0.213841I
a = −0.257736 − 1.275920I
b = −0.020489 − 0.337783I
4.30341 + 0.61589I 4.66315 + 6.19858I
u = 0.792279 − 0.213841I
a = −0.257736 + 1.275920I
b = −0.020489 + 0.337783I
4.30341 − 0.61589I 4.66315 − 6.19858I
u = 1.123130 + 0.364207I
a = −1.00348 + 1.50445I
b = 0.903409 − 1.071170I
−9.60306 − 5.39034I −9.79295 − 0.61492I
u = 1.123130 − 0.364207I
a = −1.00348 − 1.50445I
b = 0.903409 + 1.071170I
−9.60306 + 5.39034I −9.79295 + 0.61492I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062610 + 0.540756I
a = −0.301171 + 0.165537I
b = −0.006583 − 0.183056I
−0.34395 − 7.11061I −6.1757 + 16.1016I
u = 1.062610 − 0.540756I
a = −0.301171 − 0.165537I
b = −0.006583 + 0.183056I
−0.34395 + 7.11061I −6.1757 − 16.1016I
u = −0.731631 + 0.286301I
a = 0.52628 − 1.91649I
b = 1.094140 + 0.871235I
−4.27035 − 0.78775I −13.76747 + 0.79111I
u = −0.731631 − 0.286301I
a = 0.52628 + 1.91649I
b = 1.094140 − 0.871235I
−4.27035 + 0.78775I −13.76747 − 0.79111I
u = −0.770679 + 0.148242I
a = 0.08527 + 3.02934I
b = −1.05799 − 1.31030I
−2.61922 + 5.83665I −12.12805 − 5.23486I
u = −0.770679 − 0.148242I
a = 0.08527 − 3.02934I
b = −1.05799 + 1.31030I
−2.61922 − 5.83665I −12.12805 + 5.23486I
u = 1.068010 + 0.613139I
a = −0.080989 − 0.362274I
b = 0.291002 + 0.024258I
0.84523 − 3.87440I −7.28635 + 0.99100I
u = 1.068010 − 0.613139I
a = −0.080989 + 0.362274I
b = 0.291002 − 0.024258I
0.84523 + 3.87440I −7.28635 − 0.99100I
u = −0.455603 + 1.225610I
a = −0.367004 + 0.445859I
b = −2.03913 − 0.37515I
2.13581 − 2.36751I −0.13711 + 10.90887I
u = −0.455603 − 1.225610I
a = −0.367004 − 0.445859I
b = −2.03913 + 0.37515I
2.13581 + 2.36751I −0.13711 − 10.90887I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.311760 + 0.096882I
a = −1.85773 + 0.62801I
b = 2.09422 − 1.84300I
−6.92946 + 2.50095I −15.7221 − 2.9652I
u = −1.311760 − 0.096882I
a = −1.85773 − 0.62801I
b = 2.09422 + 1.84300I
−6.92946 − 2.50095I −15.7221 + 2.9652I
u = −1.326920 + 0.040818I
a = 0.862918 + 1.085500I
b = −1.10833 − 2.42545I
−5.10653 + 5.11428I −11.6019 − 9.0253I
u = −1.326920 − 0.040818I
a = 0.862918 − 1.085500I
b = −1.10833 + 2.42545I
−5.10653 − 5.11428I −11.6019 + 9.0253I
u = −1.286370 + 0.411422I
a = 1.96528 + 0.76818I
b = −2.57628 + 0.34784I
−1.23130 + 7.74404I −2.80593 − 4.22492I
u = −1.286370 − 0.411422I
a = 1.96528 − 0.76818I
b = −2.57628 − 0.34784I
−1.23130 − 7.74404I −2.80593 + 4.22492I
u = 1.38689 + 0.41154I
a = 1.32731 − 0.85356I
b = −1.70308 + 0.12392I
−10.20550 + 1.53886I −8.62767 − 1.93246I
u = 1.38689 − 0.41154I
a = 1.32731 + 0.85356I
b = −1.70308 − 0.12392I
−10.20550 − 1.53886I −8.62767 + 1.93246I
u = −1.47647 + 0.19240I
a = −1.64111 − 0.12983I
b = 1.88472 − 0.73358I
−5.86392 + 4.22756I −7.45717 − 3.66135I
u = −1.47647 − 0.19240I
a = −1.64111 + 0.12983I
b = 1.88472 + 0.73358I
−5.86392 − 4.22756I −7.45717 + 3.66135I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.225427 + 0.412274I
a = 1.51033 + 0.38729I
b = 1.250440 + 0.341656I
−0.97158 − 1.70215I 2.83896 + 9.34419I
u = −0.225427 − 0.412274I
a = 1.51033 − 0.38729I
b = 1.250440 − 0.341656I
−0.97158 + 1.70215I 2.83896 − 9.34419I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
32
− 4u
31
+ ··· − 60u + 9)(u
78
− 9u
77
+ ··· − 30111u − 3476)
c
2
(u
32
− 9u
30
+ ··· − 2u + 1)(u
78
+ u
77
+ ··· + 25u − 1)
c
3
(u
32
− 12u
30
+ ··· + 14u + 11)(u
78
− u
77
+ ··· + 7307u − 713)
c
4
(u
32
− 8u
31
+ ··· − 7u + 1)(u
78
− 5u
77
+ ··· + 20u − 1)
c
5
(u
32
− 9u
30
+ ··· + 2u + 1)(u
78
+ u
77
+ ··· + 25u − 1)
c
6
(u
32
− 2u
30
+ ··· + 21u + 11)(u
78
+ 3u
77
+ ··· − 734300u + 685471)
c
7
(u
32
+ 8u
31
+ ··· + 7u + 1)(u
78
− 5u
77
+ ··· + 20u − 1)
c
8
(u
32
+ 4u
30
+ ··· + 104u + 31)
· (u
78
+ 5u
77
+ ··· + 107670903u + 34552577)
c
9
(u
32
− 12u
30
+ ··· − 14u + 11)(u
78
− u
77
+ ··· + 7307u − 713)
c
10
(u
32
+ 16u
31
+ ··· + 4u + 1)(u
78
+ u
77
+ ··· + 729u + 31)
c
11
(u
32
− 2u
30
+ ··· − 21u + 11)(u
78
+ 3u
77
+ ··· − 734300u + 685471)
c
12
(u
32
+ 4u
31
+ ··· − 53u + 5)(u
78
− 3u
77
+ ··· + 5399717u + 801148)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
32
− 8y
30
+ ··· + 684y + 81)
· (y
78
− 27y
77
+ ··· + 17262383y + 12082576)
c
2
, c
5
(y
32
− 18y
31
+ ··· − 14y + 1)(y
78
− 73y
77
+ ··· + 105y + 1)
c
3
, c
9
(y
32
− 24y
31
+ ··· − 1164y + 121)
· (y
78
− 67y
77
+ ··· − 15851373y + 508369)
c
4
, c
7
(y
32
+ 12y
31
+ ··· + 29y + 1)(y
78
+ 17y
77
+ ··· − 408y + 1)
c
6
, c
11
(y
32
− 4y
31
+ ··· + 593y + 121)
· (y
78
− 83y
77
+ ··· − 10360427562352y + 469870491841)
c
8
(y
32
+ 8y
31
+ ··· − 5794y + 961)
· (y
78
+ 69y
77
+ ··· − 21520300962268511y + 1193880577340929)
c
10
(y
32
− 8y
31
+ ··· − 8y + 1)(y
78
+ 5y
77
+ ··· − 120505y + 961)
c
12
(y
32
+ 16y
31
+ ··· − 229y + 25)
· (y
78
+ 73y
77
+ ··· − 7450965034177y + 641838117904)
23
