12n
0865
(K12n
0865
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 11 12 3 1 7 4 6 9
Solving Sequence
1,8 3,9
2 7 10 4 12 6 11 5
c
8
c
2
c
7
c
9
c
3
c
12
c
6
c
11
c
5
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.21913 × 10
261
u
74
− 9.56885 × 10
261
u
73
+ ··· + 2.67203 × 10
264
b + 1.08376 × 10
265
,
− 1.00658 × 10
265
u
74
+ 2.74878 × 10
266
u
73
+ ··· + 6.32123 × 10
268
a − 6.89423 × 10
270
,
u
75
− 2u
74
+ ··· − 55407u − 23657i
I
u
2
= h2.91037 × 10
16
u
25
+ 4.54222 × 10
16
u
24
+ ··· + 3.82887 × 10
16
b + 3.01035 × 10
16
,
4.61911 × 10
16
u
25
+ 3.17301 × 10
16
u
24
+ ··· + 3.82887 × 10
16
a + 1.83622 × 10
17
, u
26
+ u
25
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 101 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
= h5.22 × 10
261
u
74
− 9.57 × 10
261
u
73
+ · · · + 2.67 × 10
264
b + 1.08 ×
10
265
, −1.01 × 10
265
u
74
+ 2.75 × 10
266
u
73
+ · · · + 6.32 × 10
268
a − 6.89 ×
10
270
, u
75
− 2u
74
+ · · · − 55407u − 23657i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
3
=
0.000159238u
74
− 0.00434850u
73
+ ··· + 263.739u + 109.065
−0.00195324u
74
+ 0.00358111u
73
+ ··· + 5.27007u − 4.05594
a
9
=
1
u
2
a
2
=
−0.00179400u
74
− 0.000767386u
73
+ ··· + 269.009u + 105.009
−0.00195324u
74
+ 0.00358111u
73
+ ··· + 5.27007u − 4.05594
a
7
=
−0.000680792u
74
− 0.00431212u
73
+ ··· + 427.714u + 166.774
−0.00413535u
74
+ 0.00928373u
73
+ ··· − 54.5059u − 43.0394
a
10
=
0.000787410u
74
+ 0.00462093u
73
+ ··· − 432.170u − 181.460
0.00222760u
74
− 0.00102269u
73
+ ··· − 245.378u − 100.388
a
4
=
0.00134340u
74
− 0.00259924u
73
+ ··· − 135.966u − 59.0588
0.00268652u
74
− 0.00468443u
73
+ ··· − 198.293u − 54.9937
a
12
=
u
u
3
+ u
a
6
=
−0.00484735u
74
+ 0.00544928u
73
+ ··· + 371.990u + 115.623
−0.00332545u
74
+ 0.00836454u
73
+ ··· − 129.661u − 60.4015
a
11
=
−0.0000623277u
74
+ 0.000890244u
73
+ ··· − 13.0980u − 12.5219
−0.00713482u
74
+ 0.0130749u
73
+ ··· + 224.237u + 0.410665
a
5
=
−0.00134340u
74
+ 0.00259924u
73
+ ··· + 135.966u + 59.0588
−0.00115084u
74
+ 0.0000836745u
73
+ ··· + 161.660u + 52.9222
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0123355u
74
− 0.0295724u
73
+ ··· + 5.38788u + 130.186
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
75
− 5u
74
+ ··· − 5u − 1
c
2
, c
7
u
75
− u
74
+ ··· − 8219u + 2154
c
3
, c
10
u
75
− u
74
+ ··· + 7742u + 871
c
5
, c
6
, c
11
u
75
+ u
74
+ ··· − 261u − 38
c
8
, c
12
u
75
+ 2u
74
+ ··· − 55407u + 23657
c
9
u
75
− 32u
73
+ ··· + 255320u + 43933
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
75
− 41y
74
+ ··· − 1603y −1
c
2
, c
7
y
75
+ 43y
74
+ ··· − 85114943y −4639716
c
3
, c
10
y
75
− 41y
74
+ ··· + 127801658y −758641
c
5
, c
6
, c
11
y
75
− 75y
74
+ ··· − 54087y −1444
c
8
, c
12
y
75
+ 46y
74
+ ··· − 10823394625y −559653649
c
9
y
75
− 64y
74
+ ··· + 57837081376y −1930108489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511183 + 0.869827I
a = −0.419361 − 0.809039I
b = 0.420218 + 0.808317I
13.27380 − 3.79908I 0
u = 0.511183 − 0.869827I
a = −0.419361 + 0.809039I
b = 0.420218 − 0.808317I
13.27380 + 3.79908I 0
u = 0.104480 + 0.979928I
a = −0.487830 + 1.092380I
b = −0.921395 − 0.828476I
2.88960 − 2.99924I 0
u = 0.104480 − 0.979928I
a = −0.487830 − 1.092380I
b = −0.921395 + 0.828476I
2.88960 + 2.99924I 0
u = −0.719155 + 0.654606I
a = −0.916349 + 0.244548I
b = 0.291221 + 1.266280I
2.19050 − 4.12293I 0
u = −0.719155 − 0.654606I
a = −0.916349 − 0.244548I
b = 0.291221 − 1.266280I
2.19050 + 4.12293I 0
u = −0.951833 + 0.405463I
a = 0.325014 − 0.059797I
b = 0.61564 + 1.28372I
0.23121 − 5.24301I 0
u = −0.951833 − 0.405463I
a = 0.325014 + 0.059797I
b = 0.61564 − 1.28372I
0.23121 + 5.24301I 0
u = 0.105252 + 0.958516I
a = 1.006380 − 0.197424I
b = −0.965324 + 0.714891I
2.78360 + 2.13158I 5.83242 + 0.I
u = 0.105252 − 0.958516I
a = 1.006380 + 0.197424I
b = −0.965324 − 0.714891I
2.78360 − 2.13158I 5.83242 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06089
a = 1.62559
b = 1.31782
−3.08335 0
u = 0.135481 + 1.054220I
a = −0.48758 + 2.48428I
b = −0.657388 − 1.149370I
4.42124 − 3.94617I 0
u = 0.135481 − 1.054220I
a = −0.48758 − 2.48428I
b = −0.657388 + 1.149370I
4.42124 + 3.94617I 0
u = 0.350665 + 0.854397I
a = −1.99985 + 3.03274I
b = −0.197313 − 0.765054I
−1.48854 − 3.29434I 7.48156 + 7.38153I
u = 0.350665 − 0.854397I
a = −1.99985 − 3.03274I
b = −0.197313 + 0.765054I
−1.48854 + 3.29434I 7.48156 − 7.38153I
u = −0.345273 + 0.854044I
a = −0.984101 − 0.681820I
b = 0.066866 − 0.805142I
9.05899 + 1.64001I 10.85898 − 4.17615I
u = −0.345273 − 0.854044I
a = −0.984101 + 0.681820I
b = 0.066866 + 0.805142I
9.05899 − 1.64001I 10.85898 + 4.17615I
u = 0.705323 + 0.845543I
a = 0.287297 + 0.069028I
b = −0.326209 + 0.901624I
−0.812023 − 0.611465I 0
u = 0.705323 − 0.845543I
a = 0.287297 − 0.069028I
b = −0.326209 − 0.901624I
−0.812023 + 0.611465I 0
u = 0.758649 + 0.798057I
a = −0.517700 − 0.536390I
b = −0.465139 + 0.778563I
−1.67054 − 1.21029I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758649 − 0.798057I
a = −0.517700 + 0.536390I
b = −0.465139 − 0.778563I
−1.67054 + 1.21029I 0
u = −0.248465 + 1.077060I
a = −1.08986 − 2.54027I
b = −0.419327 + 1.083180I
6.37591 + 3.06208I 0
u = −0.248465 − 1.077060I
a = −1.08986 + 2.54027I
b = −0.419327 − 1.083180I
6.37591 − 3.06208I 0
u = 0.794516 + 0.774647I
a = −0.850628 + 0.384075I
b = −0.440996 − 0.929377I
−1.12250 − 4.94354I 0
u = 0.794516 − 0.774647I
a = −0.850628 − 0.384075I
b = −0.440996 + 0.929377I
−1.12250 + 4.94354I 0
u = −0.413012 + 1.057260I
a = 0.795418 + 0.507722I
b = 0.596653 − 1.011430I
3.48939 + 8.28532I 0
u = −0.413012 − 1.057260I
a = 0.795418 − 0.507722I
b = 0.596653 + 1.011430I
3.48939 − 8.28532I 0
u = −0.944332 + 0.653830I
a = 0.978690 + 0.474204I
b = 0.108588 − 0.808629I
2.09898 + 1.03718I 0
u = −0.944332 − 0.653830I
a = 0.978690 − 0.474204I
b = 0.108588 + 0.808629I
2.09898 − 1.03718I 0
u = −0.270614 + 0.799128I
a = −0.016859 − 0.980728I
b = −0.468669 − 0.799439I
5.16849 − 0.70436I 5.72629 − 4.08050I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270614 − 0.799128I
a = −0.016859 + 0.980728I
b = −0.468669 + 0.799439I
5.16849 + 0.70436I 5.72629 + 4.08050I
u = 0.005654 + 0.817770I
a = 0.134044 − 0.321095I
b = −0.707093 + 0.936838I
3.39522 + 3.07685I 7.17303 − 2.60816I
u = 0.005654 − 0.817770I
a = 0.134044 + 0.321095I
b = −0.707093 − 0.936838I
3.39522 − 3.07685I 7.17303 + 2.60816I
u = −0.344432 + 1.153890I
a = −0.92417 − 2.45111I
b = 0.035520 + 1.086570I
10.28840 + 1.28609I 0
u = −0.344432 − 1.153890I
a = −0.92417 + 2.45111I
b = 0.035520 − 1.086570I
10.28840 − 1.28609I 0
u = 0.476100 + 1.149580I
a = −0.57736 + 1.68816I
b = 0.387664 − 1.078130I
14.3526 − 0.3907I 0
u = 0.476100 − 1.149580I
a = −0.57736 − 1.68816I
b = 0.387664 + 1.078130I
14.3526 + 0.3907I 0
u = −0.290476 + 0.669460I
a = 0.135376 − 0.783012I
b = −0.507919 + 0.840529I
3.54366 + 3.13776I 7.61659 − 5.61372I
u = −0.290476 − 0.669460I
a = 0.135376 + 0.783012I
b = −0.507919 − 0.840529I
3.54366 − 3.13776I 7.61659 + 5.61372I
u = −0.666899 + 0.273019I
a = 1.47056 + 0.83535I
b = 0.965151 − 0.289411I
−2.93144 + 0.56702I −3.12772 + 0.55892I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666899 − 0.273019I
a = 1.47056 − 0.83535I
b = 0.965151 + 0.289411I
−2.93144 − 0.56702I −3.12772 − 0.55892I
u = −0.392778 + 1.233820I
a = −0.467158 + 0.321435I
b = 1.306830 + 0.469679I
0.13421 + 3.44719I 0
u = −0.392778 − 1.233820I
a = −0.467158 − 0.321435I
b = 1.306830 − 0.469679I
0.13421 − 3.44719I 0
u = 0.635415 + 0.279119I
a = −2.65731 − 1.31024I
b = −0.389296 − 0.211756I
−1.97277 − 3.13568I −4.47969 + 10.61839I
u = 0.635415 − 0.279119I
a = −2.65731 + 1.31024I
b = −0.389296 + 0.211756I
−1.97277 + 3.13568I −4.47969 − 10.61839I
u = −0.180180 + 1.306870I
a = 0.413334 − 0.331089I
b = 0.883170 + 0.676952I
2.37632 + 2.86198I 0
u = −0.180180 − 1.306870I
a = 0.413334 + 0.331089I
b = 0.883170 − 0.676952I
2.37632 − 2.86198I 0
u = −0.543058 + 1.224000I
a = 1.04247 + 1.66721I
b = 0.74590 − 1.30736I
2.96892 + 10.67880I 0
u = −0.543058 − 1.224000I
a = 1.04247 − 1.66721I
b = 0.74590 + 1.30736I
2.96892 − 10.67880I 0
u = −0.629714 + 1.222400I
a = 0.0776503 − 0.0540011I
b = 0.398225 + 0.534595I
4.24733 + 4.78659I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629714 − 1.222400I
a = 0.0776503 + 0.0540011I
b = 0.398225 − 0.534595I
4.24733 − 4.78659I 0
u = 0.314578 + 0.476986I
a = −0.094362 − 0.551096I
b = 0.215787 + 0.477288I
0.081149 − 0.980104I 1.59159 + 6.68499I
u = 0.314578 − 0.476986I
a = −0.094362 + 0.551096I
b = 0.215787 − 0.477288I
0.081149 + 0.980104I 1.59159 − 6.68499I
u = −1.30828 + 0.58916I
a = 0.312227 − 0.663397I
b = 0.217080 + 1.085900I
3.29323 − 0.45591I 0
u = −1.30828 − 0.58916I
a = 0.312227 + 0.663397I
b = 0.217080 − 1.085900I
3.29323 + 0.45591I 0
u = −0.562667
a = 0.589903
b = −0.367718
1.77914 4.46500
u = 1.01188 + 1.05851I
a = 0.366442 − 0.296992I
b = 0.946313 − 0.997142I
10.40690 − 0.26071I 0
u = 1.01188 − 1.05851I
a = 0.366442 + 0.296992I
b = 0.946313 + 0.997142I
10.40690 + 0.26071I 0
u = 0.84420 + 1.25393I
a = 1.23810 − 1.08437I
b = 0.78131 + 1.18814I
11.30420 − 7.23486I 0
u = 0.84420 − 1.25393I
a = 1.23810 + 1.08437I
b = 0.78131 − 1.18814I
11.30420 + 7.23486I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74519 + 1.34261I
a = 1.00802 + 1.48284I
b = 0.353123 − 1.081330I
5.99761 + 7.90570I 0
u = −0.74519 − 1.34261I
a = 1.00802 − 1.48284I
b = 0.353123 + 1.081330I
5.99761 − 7.90570I 0
u = −0.04853 + 1.60376I
a = −0.11926 − 1.50581I
b = 0.17633 + 1.63943I
8.17405 − 1.89172I 0
u = −0.04853 − 1.60376I
a = −0.11926 + 1.50581I
b = 0.17633 − 1.63943I
8.17405 + 1.89172I 0
u = −0.13866 + 1.65730I
a = 0.05286 − 1.55805I
b = −0.05126 + 1.58160I
12.02590 + 4.38057I 0
u = −0.13866 − 1.65730I
a = 0.05286 + 1.55805I
b = −0.05126 − 1.58160I
12.02590 − 4.38057I 0
u = 0.77641 + 1.51662I
a = −0.85410 + 1.22196I
b = −0.75448 − 1.43700I
9.3327 − 16.0128I 0
u = 0.77641 − 1.51662I
a = −0.85410 − 1.22196I
b = −0.75448 + 1.43700I
9.3327 + 16.0128I 0
u = 1.68879 + 0.30055I
a = −0.309838 − 0.248663I
b = −0.54887 + 1.55886I
5.24750 + 7.57788I 0
u = 1.68879 − 0.30055I
a = −0.309838 + 0.248663I
b = −0.54887 − 1.55886I
5.24750 − 7.57788I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55982 + 1.63014I
a = 0.099724 + 0.263898I
b = −1.53326 + 0.28524I
5.54758 − 8.17895I 0
u = 0.55982 − 1.63014I
a = 0.099724 − 0.263898I
b = −1.53326 − 0.28524I
5.54758 + 8.17895I 0
u = 1.83510
a = −0.883746
b = −1.70115
−0.530763 0
u = 0.29670 + 1.93221I
a = 0.134528 − 1.114210I
b = −0.28215 + 1.84615I
13.17690 − 0.66579I 0
u = 0.29670 − 1.93221I
a = 0.134528 + 1.114210I
b = −0.28215 − 1.84615I
13.17690 + 0.66579I 0
12
II.
I
u
2
= h2.91 × 10
16
u
25
+ 4.54 × 10
16
u
24
+ · · · + 3.83 × 10
16
b + 3.01 × 10
16
, 4.62 ×
10
16
u
25
+3.17×10
16
u
24
+· · ·+3.83×10
16
a+1.84×10
17
, u
26
+u
25
+· · ·+2u−1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
3
=
−1.20639u
25
− 0.828706u
24
+ ··· + 1.73262u − 4.79572
−0.760112u
25
− 1.18631u
24
+ ··· + 0.958027u − 0.786224
a
9
=
1
u
2
a
2
=
−1.96650u
25
− 2.01501u
24
+ ··· + 2.69064u − 5.58194
−0.760112u
25
− 1.18631u
24
+ ··· + 0.958027u − 0.786224
a
7
=
−1.21642u
25
− 1.65800u
24
+ ··· + 5.13990u − 0.269556
−0.349076u
25
− 0.479614u
24
+ ··· + 0.400726u − 0.201686
a
10
=
1.78308u
25
+ 2.35335u
24
+ ··· − 5.51137u + 2.67400
0.667069u
25
+ 1.03486u
24
+ ··· − 0.913447u + 0.959951
a
4
=
−0.587265u
25
− 0.150117u
24
+ ··· + 4.51193u − 2.36445
0.343491u
25
+ 0.719740u
24
+ ··· + 0.776310u − 0.0574895
a
12
=
u
u
3
+ u
a
6
=
−1.08773u
25
− 1.48220u
24
+ ··· + 5.02109u − 0.605262
−0.288867u
25
− 0.351748u
24
+ ··· + 0.316391u − 0.490286
a
11
=
−0.216918u
25
− 0.646654u
24
+ ··· + 2.48863u + 1.67400
0.237853u
25
+ 0.384292u
24
+ ··· + 0.936192u + 0.323441
a
5
=
−0.587265u
25
− 0.150117u
24
+ ··· + 4.51193u − 2.36445
0.973066u
25
+ 1.61974u
24
+ ··· − 0.685252u + 0.379659
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
99120760696784782
38288701182749165
u
25
+
156882915669688696
38288701182749165
u
24
+···−
288719780225598979
38288701182749165
u+
292380986892480686
38288701182749165
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 6u
25
+ ··· + 6u
2
+ 1
c
2
u
26
+ 8u
24
+ ··· − 5u
2
− 1
c
3
u
26
− 8u
24
+ ··· − u − 1
c
4
u
26
+ 6u
25
+ ··· + 6u
2
+ 1
c
5
, c
6
u
26
− 15u
24
+ ··· + 6u + 5
c
7
u
26
+ 8u
24
+ ··· − 5u
2
− 1
c
8
u
26
+ u
25
+ ··· + 2u − 1
c
9
u
26
− 7u
25
+ ··· + u + 1
c
10
u
26
− 8u
24
+ ··· + u − 1
c
11
u
26
− 15u
24
+ ··· − 6u + 5
c
12
u
26
− u
25
+ ··· − 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
26
− 12y
25
+ ··· + 12y + 1
c
2
, c
7
y
26
+ 16y
25
+ ··· + 10y + 1
c
3
, c
10
y
26
− 16y
25
+ ··· − 13y + 1
c
5
, c
6
, c
11
y
26
− 30y
25
+ ··· − 186y + 25
c
8
, c
12
y
26
+ 15y
25
+ ··· + 2y + 1
c
9
y
26
− 27y
25
+ ··· − 15y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.590338 + 0.822308I
a = −0.653984 + 0.298112I
b = −0.538989 + 0.321894I
−1.82169 − 2.18919I 0.71594 + 4.52010I
u = 0.590338 − 0.822308I
a = −0.653984 − 0.298112I
b = −0.538989 − 0.321894I
−1.82169 + 2.18919I 0.71594 − 4.52010I
u = −0.557582 + 0.811780I
a = −0.939860 − 0.765220I
b = −0.394713 − 0.799564I
8.44513 + 0.58228I 5.42167 + 1.05599I
u = −0.557582 − 0.811780I
a = −0.939860 + 0.765220I
b = −0.394713 + 0.799564I
8.44513 − 0.58228I 5.42167 − 1.05599I
u = −0.707692 + 0.742232I
a = −0.362984 − 0.288573I
b = 0.668229 + 0.896349I
1.25227 − 1.24373I 1.52510 + 0.51708I
u = −0.707692 − 0.742232I
a = −0.362984 + 0.288573I
b = 0.668229 − 0.896349I
1.25227 + 1.24373I 1.52510 − 0.51708I
u = 0.483441 + 0.822664I
a = 0.761342 + 0.842929I
b = −0.372992 − 0.771746I
13.38500 − 3.45757I 11.87393 − 5.98331I
u = 0.483441 − 0.822664I
a = 0.761342 − 0.842929I
b = −0.372992 + 0.771746I
13.38500 + 3.45757I 11.87393 + 5.98331I
u = 1.08679
a = −1.58066
b = −1.47725
−2.80705 16.8370
u = 0.045717 + 0.769529I
a = −0.950994 − 1.030120I
b = 0.410209 − 0.705964I
5.25690 + 1.40544I 7.78165 − 5.67202I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045717 − 0.769529I
a = −0.950994 + 1.030120I
b = 0.410209 + 0.705964I
5.25690 − 1.40544I 7.78165 + 5.67202I
u = 0.642147 + 0.048358I
a = −0.419788 + 1.064220I
b = −0.538855 + 1.302890I
2.16901 + 5.99916I 5.67527 − 5.94920I
u = 0.642147 − 0.048358I
a = −0.419788 − 1.064220I
b = −0.538855 − 1.302890I
2.16901 − 5.99916I 5.67527 + 5.94920I
u = −0.600554 + 0.170802I
a = 1.38453 + 0.96038I
b = 0.566860 − 1.040450I
2.02423 + 3.48369I 2.43057 − 3.98201I
u = −0.600554 − 0.170802I
a = 1.38453 − 0.96038I
b = 0.566860 + 1.040450I
2.02423 − 3.48369I 2.43057 + 3.98201I
u = −0.522844 + 1.292900I
a = 0.406590 + 0.413033I
b = 0.602021 − 0.151872I
3.96287 + 5.81407I 5.34419 − 5.82137I
u = −0.522844 − 1.292900I
a = 0.406590 − 0.413033I
b = 0.602021 + 0.151872I
3.96287 − 5.81407I 5.34419 + 5.82137I
u = −0.03051 + 1.50118I
a = −0.07962 − 1.68896I
b = 0.24430 + 1.51368I
8.69381 − 1.77690I 13.20778 + 0.66664I
u = −0.03051 − 1.50118I
a = −0.07962 + 1.68896I
b = 0.24430 − 1.51368I
8.69381 + 1.77690I 13.20778 − 0.66664I
u = 0.41159 + 1.44584I
a = 0.36105 − 1.47823I
b = −0.314006 + 1.374820I
15.7218 − 0.4856I 11.71944 + 0.11882I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.41159 − 1.44584I
a = 0.36105 + 1.47823I
b = −0.314006 − 1.374820I
15.7218 + 0.4856I 11.71944 − 0.11882I
u = 0.263927 + 0.407365I
a = −4.99855 + 0.90395I
b = −0.082774 + 0.451542I
−1.74954 − 2.69727I 3.12762 − 4.76260I
u = 0.263927 − 0.407365I
a = −4.99855 − 0.90395I
b = −0.082774 − 0.451542I
−1.74954 + 2.69727I 3.12762 + 4.76260I
u = −1.55396
a = 0.975493
b = 1.31730
−1.20091 −0.133790
u = −0.28440 + 1.64109I
a = −0.20515 − 1.56996I
b = −0.16931 + 1.58057I
12.10650 + 3.82226I 10.32517 + 2.41347I
u = −0.28440 − 1.64109I
a = −0.20515 + 1.56996I
b = −0.16931 − 1.58057I
12.10650 − 3.82226I 10.32517 − 2.41347I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 6u
25
+ ··· + 6u
2
+ 1)(u
75
− 5u
74
+ ··· − 5u − 1)
c
2
(u
26
+ 8u
24
+ ··· − 5u
2
− 1)(u
75
− u
74
+ ··· − 8219u + 2154)
c
3
(u
26
− 8u
24
+ ··· − u − 1)(u
75
− u
74
+ ··· + 7742u + 871)
c
4
(u
26
+ 6u
25
+ ··· + 6u
2
+ 1)(u
75
− 5u
74
+ ··· − 5u − 1)
c
5
, c
6
(u
26
− 15u
24
+ ··· + 6u + 5)(u
75
+ u
74
+ ··· − 261u − 38)
c
7
(u
26
+ 8u
24
+ ··· − 5u
2
− 1)(u
75
− u
74
+ ··· − 8219u + 2154)
c
8
(u
26
+ u
25
+ ··· + 2u − 1)(u
75
+ 2u
74
+ ··· − 55407u + 23657)
c
9
(u
26
− 7u
25
+ ··· + u + 1)(u
75
− 32u
73
+ ··· + 255320u + 43933)
c
10
(u
26
− 8u
24
+ ··· + u − 1)(u
75
− u
74
+ ··· + 7742u + 871)
c
11
(u
26
− 15u
24
+ ··· − 6u + 5)(u
75
+ u
74
+ ··· − 261u − 38)
c
12
(u
26
− u
25
+ ··· − 2u − 1)(u
75
+ 2u
74
+ ··· − 55407u + 23657)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
26
− 12y
25
+ ··· + 12y + 1)(y
75
− 41y
74
+ ··· − 1603y −1)
c
2
, c
7
(y
26
+ 16y
25
+ ··· + 10y + 1)
· (y
75
+ 43y
74
+ ··· − 85114943y −4639716)
c
3
, c
10
(y
26
− 16y
25
+ ··· − 13y + 1)
· (y
75
− 41y
74
+ ··· + 127801658y −758641)
c
5
, c
6
, c
11
(y
26
− 30y
25
+ ··· − 186y + 25)(y
75
− 75y
74
+ ··· − 54087y −1444)
c
8
, c
12
(y
26
+ 15y
25
+ ··· + 2y + 1)
· (y
75
+ 46y
74
+ ··· − 10823394625y −559653649)
c
9
(y
26
− 27y
25
+ ··· − 15y + 1)
· (y
75
− 64y
74
+ ··· + 57837081376y −1930108489)
20
