12n
0263
(K12n
0263
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 1 10 3 12 6 8 7
Solving Sequence
5,11 3,6
2 1 7 4 10 8 12 9
c
5
c
2
c
1
c
6
c
4
c
10
c
7
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.10710 × 10
324
u
87
− 9.56312 × 10
325
u
86
+ ··· + 1.34371 × 10
329
b + 2.04185 × 10
329
,
1.04950 × 10
330
u
87
+ 1.94168 × 10
330
u
86
+ ··· + 2.37970 × 10
332
a − 5.85379 × 10
332
,
u
88
+ 2u
87
+ ··· + 4968u − 1771i
I
u
2
= hb + 1, 6u
8
+ 7u
7
+ 12u
6
+ 8u
5
+ 17u
4
+ 10u
3
+ 9u
2
+ 7a + 5u + 8,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
3
= h2u
15
− 2u
14
+ ··· + b − 2, 3u
15
− u
14
+ ··· + a + 5u, u
16
+ 8u
14
+ ··· + 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 113 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−5.11 × 10
324
u
87
− 9.56 × 10
325
u
86
+ · · · + 1.34 × 10
329
b + 2.04 ×
10
329
, 1.05 × 10
330
u
87
+ 1.94 × 10
330
u
86
+ · · · + 2.38 × 10
332
a − 5.85 ×
10
332
, u
88
+ 2u
87
+ · · · + 4968u − 1771i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.00441021u
87
− 0.00815934u
86
+ ··· + 21.8561u + 2.45988
0.0000380076u
87
+ 0.000711697u
86
+ ··· + 9.10028u − 1.51957
a
6
=
1
u
2
a
2
=
−0.00437220u
87
− 0.00744764u
86
+ ··· + 30.9564u + 0.940316
0.0000380076u
87
+ 0.000711697u
86
+ ··· + 9.10028u − 1.51957
a
1
=
−0.00153178u
87
− 0.00266896u
86
+ ··· + 23.2890u − 2.25667
−0.000996652u
87
− 0.00124794u
86
+ ··· + 14.3592u − 2.12843
a
7
=
−0.00142383u
87
− 0.00605369u
86
+ ··· − 33.0919u + 13.1203
−0.000364423u
87
− 0.00102860u
86
+ ··· − 28.1927u + 9.11040
a
4
=
−0.00292538u
87
− 0.00347282u
86
+ ··· + 53.4302u − 13.5553
−0.000932894u
87
+ 0.0000161336u
86
+ ··· + 34.8142u − 9.59675
a
10
=
u
u
3
+ u
a
8
=
−0.00119455u
87
− 0.00482926u
86
+ ··· − 31.9654u + 12.3640
−0.000562133u
87
− 0.00184393u
86
+ ··· − 30.4650u + 9.71045
a
12
=
0.00596932u
87
+ 0.0100899u
86
+ ··· − 21.3404u − 4.51265
0.00269198u
87
+ 0.00756739u
86
+ ··· + 12.7020u − 10.9619
a
9
=
0.00392308u
87
+ 0.00976005u
86
+ ··· − 4.05932u − 10.1331
0.00259711u
87
+ 0.00552722u
86
+ ··· + 16.4800u − 8.72611
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0135860u
87
− 0.0234158u
86
+ ··· + 148.906u − 31.3158
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 36u
87
+ ··· + 9016u + 2401
c
2
, c
4
u
88
− 16u
87
+ ··· + 504u − 49
c
3
, c
8
u
88
+ u
87
+ ··· + 14336u + 25088
c
5
, c
10
u
88
+ 2u
87
+ ··· + 4968u − 1771
c
6
, c
12
u
88
+ 3u
87
+ ··· − 1497u − 181
c
7
u
88
− 4u
87
+ ··· + 2u − 1
c
9
u
88
− 14u
87
+ ··· − 5848u + 1043
c
11
u
88
− u
87
+ ··· + 8558243u − 2435537
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 48y
87
+ ··· − 1539089020y + 5764801
c
2
, c
4
y
88
− 36y
87
+ ··· − 9016y + 2401
c
3
, c
8
y
88
− 63y
87
+ ··· − 10096214016y + 629407744
c
5
, c
10
y
88
+ 70y
87
+ ··· + 39623986y + 3136441
c
6
, c
12
y
88
+ 49y
87
+ ··· − 883509y + 32761
c
7
y
88
− 16y
87
+ ··· + 6y + 1
c
9
y
88
+ 2y
87
+ ··· + 12594048y + 1087849
c
11
y
88
+ 33y
87
+ ··· + 85934090519941y + 5931840478369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.805310 + 0.589984I
a = 0.939329 + 0.447844I
b = 1.000810 − 0.612397I
−0.95191 + 5.34222I 0
u = −0.805310 − 0.589984I
a = 0.939329 − 0.447844I
b = 1.000810 + 0.612397I
−0.95191 − 5.34222I 0
u = 0.992163 + 0.083390I
a = 0.306400 + 0.290281I
b = −0.860253 − 0.469883I
−3.57000 − 4.86222I 0
u = 0.992163 − 0.083390I
a = 0.306400 − 0.290281I
b = −0.860253 + 0.469883I
−3.57000 + 4.86222I 0
u = 0.948677 + 0.240901I
a = 0.257262 + 0.041899I
b = 0.816492 − 0.831232I
4.48132 + 0.68778I 0
u = 0.948677 − 0.240901I
a = 0.257262 − 0.041899I
b = 0.816492 + 0.831232I
4.48132 − 0.68778I 0
u = 0.139706 + 0.952235I
a = −0.925127 + 0.095450I
b = 1.61154 − 0.00181I
−8.88186 − 0.52240I 0
u = 0.139706 − 0.952235I
a = −0.925127 − 0.095450I
b = 1.61154 + 0.00181I
−8.88186 + 0.52240I 0
u = 0.517483 + 0.776305I
a = −1.78011 + 2.41840I
b = −0.936656 + 0.081694I
−2.86090 − 2.57918I 0
u = 0.517483 − 0.776305I
a = −1.78011 − 2.41840I
b = −0.936656 − 0.081694I
−2.86090 + 2.57918I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.919116 + 0.059965I
a = 0.926180 + 0.256722I
b = 0.955514 − 0.798995I
4.06052 + 5.39830I 0
u = 0.919116 − 0.059965I
a = 0.926180 − 0.256722I
b = 0.955514 + 0.798995I
4.06052 − 5.39830I 0
u = −0.740792 + 0.830928I
a = 0.971335 + 0.053984I
b = 0.063149 − 0.256272I
−0.52740 + 2.78156I 0
u = −0.740792 − 0.830928I
a = 0.971335 − 0.053984I
b = 0.063149 + 0.256272I
−0.52740 − 2.78156I 0
u = −0.248018 + 0.848575I
a = 4.78654 − 1.31097I
b = −0.711645 + 0.146889I
−2.35191 + 3.21223I −7.96555 − 6.35540I
u = −0.248018 − 0.848575I
a = 4.78654 + 1.31097I
b = −0.711645 − 0.146889I
−2.35191 − 3.21223I −7.96555 + 6.35540I
u = −0.079212 + 1.132010I
a = −0.24213 + 2.07975I
b = 0.808393 − 0.790949I
2.28913 − 1.10084I 0
u = −0.079212 − 1.132010I
a = −0.24213 − 2.07975I
b = 0.808393 + 0.790949I
2.28913 + 1.10084I 0
u = 0.319029 + 1.102470I
a = 0.16501 − 1.71908I
b = 1.18756 + 0.90857I
6.66068 − 5.31014I 0
u = 0.319029 − 1.102470I
a = 0.16501 + 1.71908I
b = 1.18756 − 0.90857I
6.66068 + 5.31014I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.174859 + 0.815548I
a = 0.677317 + 0.300319I
b = 0.575930 + 0.151275I
1.08551 + 1.92358I 4.64840 − 3.23156I
u = −0.174859 − 0.815548I
a = 0.677317 − 0.300319I
b = 0.575930 − 0.151275I
1.08551 − 1.92358I 4.64840 + 3.23156I
u = −0.767240 + 0.896651I
a = 0.121871 + 0.271621I
b = 0.760360 + 0.637175I
−0.156171 + 0.447897I 0
u = −0.767240 − 0.896651I
a = 0.121871 − 0.271621I
b = 0.760360 − 0.637175I
−0.156171 − 0.447897I 0
u = 0.237078 + 0.779145I
a = −1.16266 + 0.85834I
b = −1.135060 − 0.295927I
−2.63864 − 1.15581I −8.11133 + 0.I
u = 0.237078 − 0.779145I
a = −1.16266 − 0.85834I
b = −1.135060 + 0.295927I
−2.63864 + 1.15581I −8.11133 + 0.I
u = −0.451795 + 1.101000I
a = 0.528741 − 0.757913I
b = −0.311022 + 0.556483I
0.22772 + 2.36626I 0
u = −0.451795 − 1.101000I
a = 0.528741 + 0.757913I
b = −0.311022 − 0.556483I
0.22772 − 2.36626I 0
u = 0.938892 + 0.789370I
a = 0.381760 − 0.534102I
b = 0.744153 + 0.149516I
−5.45148 + 0.98119I 0
u = 0.938892 − 0.789370I
a = 0.381760 + 0.534102I
b = 0.744153 − 0.149516I
−5.45148 − 0.98119I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.785869 + 0.950757I
a = 0.384303 − 0.295118I
b = 0.839629 + 0.078942I
−4.90136 − 7.25149I 0
u = 0.785869 − 0.950757I
a = 0.384303 + 0.295118I
b = 0.839629 − 0.078942I
−4.90136 + 7.25149I 0
u = 0.135066 + 1.254400I
a = −0.86601 − 1.61832I
b = 0.951322 + 0.752407I
1.84545 − 6.92325I 0
u = 0.135066 − 1.254400I
a = −0.86601 + 1.61832I
b = 0.951322 − 0.752407I
1.84545 + 6.92325I 0
u = 0.166697 + 1.254150I
a = 0.45531 − 1.38825I
b = −0.879422 + 0.969350I
1.34449 − 3.11057I 0
u = 0.166697 − 1.254150I
a = 0.45531 + 1.38825I
b = −0.879422 − 0.969350I
1.34449 + 3.11057I 0
u = 0.128440 + 1.272930I
a = −0.271149 + 0.753744I
b = −1.331880 − 0.096691I
1.74481 − 1.77274I 0
u = 0.128440 − 1.272930I
a = −0.271149 − 0.753744I
b = −1.331880 + 0.096691I
1.74481 + 1.77274I 0
u = −0.696650 + 0.064826I
a = −0.85984 − 3.03345I
b = −1.216760 + 0.127728I
−4.59376 − 2.75184I −8.12364 + 4.75878I
u = −0.696650 − 0.064826I
a = −0.85984 + 3.03345I
b = −1.216760 − 0.127728I
−4.59376 + 2.75184I −8.12364 − 4.75878I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.112427 + 1.300630I
a = −0.610156 + 1.055710I
b = 0.671732 − 1.206590I
8.28391 + 2.17535I 0
u = 0.112427 − 1.300630I
a = −0.610156 − 1.055710I
b = 0.671732 + 1.206590I
8.28391 − 2.17535I 0
u = −0.313929 + 1.278860I
a = 0.149566 − 0.089877I
b = −1.57140 − 0.02860I
−0.73301 + 6.46230I 0
u = −0.313929 − 1.278860I
a = 0.149566 + 0.089877I
b = −1.57140 + 0.02860I
−0.73301 − 6.46230I 0
u = −0.266726 + 1.305550I
a = 0.20459 − 1.68443I
b = −0.771564 + 0.690828I
3.68905 + 4.17717I 0
u = −0.266726 − 1.305550I
a = 0.20459 + 1.68443I
b = −0.771564 − 0.690828I
3.68905 − 4.17717I 0
u = −0.021756 + 1.350550I
a = 0.54100 + 1.31164I
b = −1.064570 − 0.638718I
2.82569 − 0.98099I 0
u = −0.021756 − 1.350550I
a = 0.54100 − 1.31164I
b = −1.064570 + 0.638718I
2.82569 + 0.98099I 0
u = 0.018865 + 0.638570I
a = 0.311943 + 0.067730I
b = 0.240022 + 0.542471I
0.93570 + 1.73737I 2.01048 − 1.71572I
u = 0.018865 − 0.638570I
a = 0.311943 − 0.067730I
b = 0.240022 − 0.542471I
0.93570 − 1.73737I 2.01048 + 1.71572I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588985
a = 1.28655
b = 0.415532
−1.64409 −5.83610
u = −0.094002 + 0.577464I
a = −1.39684 + 1.25204I
b = −1.093430 − 0.334889I
−2.55730 − 1.15360I −7.35870 − 0.72400I
u = −0.094002 − 0.577464I
a = −1.39684 − 1.25204I
b = −1.093430 + 0.334889I
−2.55730 + 1.15360I −7.35870 + 0.72400I
u = 0.54155 + 1.31866I
a = 0.48355 − 1.60161I
b = 1.146830 + 0.768411I
7.90999 − 10.78390I 0
u = 0.54155 − 1.31866I
a = 0.48355 + 1.60161I
b = 1.146830 − 0.768411I
7.90999 + 10.78390I 0
u = 0.41333 + 1.36783I
a = 0.26044 + 1.47995I
b = −0.956288 − 0.865062I
1.05954 − 9.78750I 0
u = 0.41333 − 1.36783I
a = 0.26044 − 1.47995I
b = −0.956288 + 0.865062I
1.05954 + 9.78750I 0
u = −1.40756 + 0.26250I
a = 0.374109 − 0.401712I
b = 0.629173 + 0.870781I
1.45716 + 4.42701I 0
u = −1.40756 − 0.26250I
a = 0.374109 + 0.401712I
b = 0.629173 − 0.870781I
1.45716 − 4.42701I 0
u = 0.42686 + 1.41707I
a = −0.688198 + 0.711293I
b = 0.591567 − 1.025660I
9.65161 − 4.27098I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.42686 − 1.41707I
a = −0.688198 − 0.711293I
b = 0.591567 + 1.025660I
9.65161 + 4.27098I 0
u = −0.26866 + 1.45831I
a = −0.184670 + 1.371300I
b = 1.27277 − 0.73698I
5.43825 + 8.83857I 0
u = −0.26866 − 1.45831I
a = −0.184670 − 1.371300I
b = 1.27277 + 0.73698I
5.43825 − 8.83857I 0
u = −0.478957 + 0.175114I
a = 0.040374 − 1.124940I
b = −0.611656 + 0.327422I
−0.78467 + 1.23926I −5.32242 − 5.47295I
u = −0.478957 − 0.175114I
a = 0.040374 + 1.124940I
b = −0.611656 − 0.327422I
−0.78467 − 1.23926I −5.32242 + 5.47295I
u = −0.07800 + 1.49272I
a = −0.256225 − 1.188790I
b = 0.392465 + 1.111420I
8.16387 + 2.18472I 0
u = −0.07800 − 1.49272I
a = −0.256225 + 1.188790I
b = 0.392465 − 1.111420I
8.16387 − 2.18472I 0
u = −1.51183 + 0.01086I
a = 0.401307 − 0.477569I
b = 1.085220 + 0.734711I
0.06365 − 10.42840I 0
u = −1.51183 − 0.01086I
a = 0.401307 + 0.477569I
b = 1.085220 − 0.734711I
0.06365 + 10.42840I 0
u = 0.13980 + 1.52059I
a = 1.52559 + 1.25765I
b = −0.728958 − 0.092773I
1.66607 − 0.20314I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13980 − 1.52059I
a = 1.52559 − 1.25765I
b = −0.728958 + 0.092773I
1.66607 + 0.20314I 0
u = −0.030492 + 0.449001I
a = 1.60154 + 0.54119I
b = 1.080300 − 0.524113I
−1.21942 + 6.06914I −0.76059 + 2.63784I
u = −0.030492 − 0.449001I
a = 1.60154 − 0.54119I
b = 1.080300 + 0.524113I
−1.21942 − 6.06914I −0.76059 − 2.63784I
u = −0.50465 + 1.51967I
a = −0.517765 − 0.950862I
b = 0.493945 + 1.166180I
7.20481 + 10.90700I 0
u = −0.50465 − 1.51967I
a = −0.517765 + 0.950862I
b = 0.493945 − 1.166180I
7.20481 − 10.90700I 0
u = 0.378884
a = −3.47834
b = −1.11771
−2.22317 −0.252670
u = −0.64911 + 1.49897I
a = 0.19669 + 1.47748I
b = 1.24122 − 0.77052I
4.8344 + 17.8080I 0
u = −0.64911 − 1.49897I
a = 0.19669 − 1.47748I
b = 1.24122 + 0.77052I
4.8344 − 17.8080I 0
u = 0.71431 + 1.53469I
a = −0.359043 + 0.727090I
b = 0.856254 − 0.988984I
7.13913 − 0.48203I 0
u = 0.71431 − 1.53469I
a = −0.359043 − 0.727090I
b = 0.856254 + 0.988984I
7.13913 + 0.48203I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.92191 + 1.43934I
a = 0.308109 − 1.238810I
b = 1.030790 + 0.892722I
6.56818 − 7.36505I 0
u = 0.92191 − 1.43934I
a = 0.308109 + 1.238810I
b = 1.030790 − 0.892722I
6.56818 + 7.36505I 0
u = 0.237720 + 0.158364I
a = 0.93631 + 3.97152I
b = −0.294689 − 0.539934I
−2.23495 + 1.29247I −6.68617 + 1.38636I
u = 0.237720 − 0.158364I
a = 0.93631 − 3.97152I
b = −0.294689 + 0.539934I
−2.23495 − 1.29247I −6.68617 − 1.38636I
u = −0.62041 + 1.63980I
a = 0.299269 + 1.165990I
b = 0.920922 − 0.781821I
6.07321 + 3.61773I 0
u = −0.62041 − 1.63980I
a = 0.299269 − 1.165990I
b = 0.920922 + 0.781821I
6.07321 − 3.61773I 0
u = −0.43998 + 1.83287I
a = −0.332892 − 0.678022I
b = 0.858291 + 0.792146I
6.26435 − 2.30308I 0
u = −0.43998 − 1.83287I
a = −0.332892 + 0.678022I
b = 0.858291 − 0.792146I
6.26435 + 2.30308I 0
13
II.
I
u
2
= hb+1, 6u
8
+7u
7
+· · ·+7a+8, u
9
+u
8
+2u
7
+u
6
+3u
5
+u
4
+2u
3
+u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−
6
7
u
8
− u
7
+ ··· −
5
7
u −
8
7
−1
a
6
=
1
u
2
a
2
=
−
6
7
u
8
− u
7
+ ··· −
5
7
u −
15
7
−1
a
1
=
−1
0
a
7
=
u
2
+ 1
u
2
a
4
=
−
6
7
u
8
− u
7
+ ··· −
5
7
u −
8
7
−1
a
10
=
u
u
3
+ u
a
8
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
12
=
−u
4
− u
2
− 1
−u
4
a
9
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
5
49
u
8
−
16
7
u
7
−
241
49
u
6
−
184
49
u
5
−
307
49
u
4
−
342
49
u
3
−
361
49
u
2
+
95
49
u −
618
49
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = −0.636856 + 0.580378I
b = −1.00000
0.13850 − 2.09337I −5.47770 + 4.24226I
u = 0.140343 − 0.966856I
a = −0.636856 − 0.580378I
b = −1.00000
0.13850 + 2.09337I −5.47770 − 4.24226I
u = 0.628449 + 0.875112I
a = −1.064930 + 0.497852I
b = −1.00000
−2.26187 − 2.45442I −3.78210 + 4.39771I
u = 0.628449 − 0.875112I
a = −1.064930 − 0.497852I
b = −1.00000
−2.26187 + 2.45442I −3.78210 − 4.39771I
u = −0.796005 + 0.733148I
a = 0.031938 − 0.639952I
b = −1.00000
−6.01628 − 1.33617I −12.84367 + 3.27176I
u = −0.796005 − 0.733148I
a = 0.031938 + 0.639952I
b = −1.00000
−6.01628 + 1.33617I −12.84367 − 3.27176I
u = −0.728966 + 0.986295I
a = −0.256313 − 0.286999I
b = −1.00000
−5.24306 + 7.08493I −15.6193 − 1.7431I
u = −0.728966 − 0.986295I
a = −0.256313 + 0.286999I
b = −1.00000
−5.24306 − 7.08493I −15.6193 + 1.7431I
u = 0.512358
a = −2.29054
b = −1.00000
−2.84338 −15.1670
17
III.
I
u
3
= h2u
15
−2u
14
+· · ·+b−2, 3u
15
−u
14
+· · ·+a+5u, u
16
+8u
14
+· · ·+3u+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−3u
15
+ u
14
+ ··· − 8u
2
− 5u
−2u
15
+ 2u
14
+ ··· − 3u + 2
a
6
=
1
u
2
a
2
=
−5u
15
+ 3u
14
+ ··· − 8u + 2
−2u
15
+ 2u
14
+ ··· − 3u + 2
a
1
=
u
15
− u
14
+ ··· + 5u + 2
u
15
+ u
14
+ ··· + 12u + 4
a
7
=
−2u
15
+ u
14
+ ··· − 11u
2
− 13u
−4u
15
+ u
14
+ ··· − 19u
2
− 15u
a
4
=
7u
15
− 5u
14
+ ··· + 29u
2
+ 22u
3u
15
− 2u
14
+ ··· + 14u
2
+ 11u
a
10
=
u
u
3
+ u
a
8
=
−3u
15
+ u
14
+ ··· − 15u
2
− 14u
−4u
15
+ u
14
+ ··· − 20u
2
− 15u
a
12
=
u
15
− 3u
14
+ ··· − 6u − 11
u
15
− 3u
14
+ ··· − 7u − 11
a
9
=
−2u
15
+ 3u
14
+ ··· − u + 8
−2u
15
+ 3u
14
+ ··· + 28u
2
+ 8
(ii) Obstruction class = 1
(iii) Cusp Shapes = −35u
15
+ 12u
14
− 275u
13
− 18u
12
− 898u
11
− 348u
10
− 1661u
9
−
964u
8
− 1955u
7
− 1160u
6
− 1383u
5
− 706u
4
− 579u
3
− 256u
2
− 146u − 39
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 7u + 1
c
2
u
16
+ 6u
15
+ ··· − u + 1
c
3
u
16
− 3u
14
+ ··· − u + 1
c
4
u
16
− 6u
15
+ ··· + u + 1
c
5
u
16
+ 8u
14
+ ··· + 3u + 1
c
6
u
16
− 3u
15
+ ··· + 8u
2
+ 1
c
7
u
16
− 6u
15
+ ··· − 3u + 1
c
8
u
16
− 3u
14
+ ··· + u + 1
c
9
u
16
− 5u
13
+ ··· − 5u + 1
c
10
u
16
+ 8u
14
+ ··· − 3u + 1
c
11
u
16
+ 3u
15
+ ··· + 6u + 1
c
12
u
16
+ 3u
15
+ ··· + 8u
2
+ 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 2y
15
+ ··· + 61y + 1
c
2
, c
4
y
16
− 10y
15
+ ··· − 7y + 1
c
3
, c
8
y
16
− 6y
15
+ ··· + 9y + 1
c
5
, c
10
y
16
+ 16y
15
+ ··· + 11y + 1
c
6
, c
12
y
16
+ 11y
15
+ ··· + 16y + 1
c
7
y
16
− 14y
15
+ ··· − 5y + 1
c
9
y
16
+ 10y
14
+ ··· + 9y + 1
c
11
y
16
− 5y
15
+ ··· − 14y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192282 + 1.004160I
a = −0.846374 − 0.009443I
b = 1.62263 + 0.06526I
−8.83850 + 0.76161I −4.2680 − 18.7238I
u = −0.192282 − 1.004160I
a = −0.846374 + 0.009443I
b = 1.62263 − 0.06526I
−8.83850 − 0.76161I −4.2680 + 18.7238I
u = −0.405160 + 0.782797I
a = 2.19859 + 0.67570I
b = −0.322228 − 0.282076I
−1.72004 + 2.39298I −3.94028 − 2.30129I
u = −0.405160 − 0.782797I
a = 2.19859 − 0.67570I
b = −0.322228 + 0.282076I
−1.72004 − 2.39298I −3.94028 + 2.30129I
u = 0.380479 + 0.681918I
a = −2.94802 − 4.63492I
b = −0.971409 − 0.076314I
−2.96721 − 2.98693I −21.6572 − 12.8409I
u = 0.380479 − 0.681918I
a = −2.94802 + 4.63492I
b = −0.971409 + 0.076314I
−2.96721 + 2.98693I −21.6572 + 12.8409I
u = −0.445295 + 0.521652I
a = 1.099140 + 0.513773I
b = 0.590770 + 0.565876I
0.00207 + 2.08322I −6.76763 − 3.46484I
u = −0.445295 − 0.521652I
a = 1.099140 − 0.513773I
b = 0.590770 − 0.565876I
0.00207 − 2.08322I −6.76763 + 3.46484I
u = −0.279505 + 0.496867I
a = 1.118600 − 0.344839I
b = 1.028060 − 0.512541I
−1.36164 + 6.43556I −8.1558 − 16.1878I
u = −0.279505 − 0.496867I
a = 1.118600 + 0.344839I
b = 1.028060 + 0.512541I
−1.36164 − 6.43556I −8.1558 + 16.1878I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08961 + 1.47734I
a = 1.06198 − 1.18104I
b = −0.817120 + 0.344873I
1.50817 + 0.70603I −8.36846 − 5.87842I
u = −0.08961 − 1.47734I
a = 1.06198 + 1.18104I
b = −0.817120 − 0.344873I
1.50817 − 0.70603I −8.36846 + 5.87842I
u = 0.60082 + 1.36455I
a = 0.137422 − 1.400270I
b = 1.097750 + 0.880157I
6.18219 − 6.62853I −4.79477 + 3.23115I
u = 0.60082 − 1.36455I
a = 0.137422 + 1.400270I
b = 1.097750 − 0.880157I
6.18219 + 6.62853I −4.79477 − 3.23115I
u = 0.43055 + 1.58967I
a = −0.321336 + 0.878995I
b = 0.771549 − 0.994058I
7.19496 + 0.24679I −1.04785 − 3.22477I
u = 0.43055 − 1.58967I
a = −0.321336 − 0.878995I
b = 0.771549 + 0.994058I
7.19496 − 0.24679I −1.04785 + 3.22477I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
16
− 10u
15
+ ··· − 7u + 1)
· (u
88
+ 36u
87
+ ··· + 9016u + 2401)
c
2
((u − 1)
9
)(u
16
+ 6u
15
+ ··· − u + 1)(u
88
− 16u
87
+ ··· + 504u − 49)
c
3
u
9
(u
16
− 3u
14
+ ··· − u + 1)(u
88
+ u
87
+ ··· + 14336u + 25088)
c
4
((u + 1)
9
)(u
16
− 6u
15
+ ··· + u + 1)(u
88
− 16u
87
+ ··· + 504u − 49)
c
5
(u
9
+ u
8
+ ··· + u − 1)(u
16
+ 8u
14
+ ··· + 3u + 1)
· (u
88
+ 2u
87
+ ··· + 4968u − 1771)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
16
− 3u
15
+ ··· + 8u
2
+ 1)(u
88
+ 3u
87
+ ··· − 1497u − 181)
c
7
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
16
− 6u
15
+ ··· − 3u + 1)(u
88
− 4u
87
+ ··· + 2u − 1)
c
8
u
9
(u
16
− 3u
14
+ ··· + u + 1)(u
88
+ u
87
+ ··· + 14336u + 25088)
c
9
(u
9
+ u
8
+ ··· − u − 1)(u
16
− 5u
13
+ ··· − 5u + 1)
· (u
88
− 14u
87
+ ··· − 5848u + 1043)
c
10
(u
9
− u
8
+ ··· + u + 1)(u
16
+ 8u
14
+ ··· − 3u + 1)
· (u
88
+ 2u
87
+ ··· + 4968u − 1771)
c
11
(u
9
− u
8
+ ··· − u + 1)(u
16
+ 3u
15
+ ··· + 6u + 1)
· (u
88
− u
87
+ ··· + 8558243u − 2435537)
c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
16
+ 3u
15
+ ··· + 8u
2
+ 1)(u
88
+ 3u
87
+ ··· − 1497u − 181)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
16
− 2y
15
+ ··· + 61y + 1)
· (y
88
+ 48y
87
+ ··· − 1539089020y + 5764801)
c
2
, c
4
((y −1)
9
)(y
16
− 10y
15
+ ··· − 7y + 1)
· (y
88
− 36y
87
+ ··· − 9016y + 2401)
c
3
, c
8
y
9
(y
16
− 6y
15
+ ··· + 9y + 1)
· (y
88
− 63y
87
+ ··· − 10096214016y + 629407744)
c
5
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
16
+ 16y
15
+ ··· + 11y + 1)
· (y
88
+ 70y
87
+ ··· + 39623986y + 3136441)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
16
+ 11y
15
+ ··· + 16y + 1)(y
88
+ 49y
87
+ ··· − 883509y + 32761)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
16
− 14y
15
+ ··· − 5y + 1)(y
88
− 16y
87
+ ··· + 6y + 1)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
16
+ 10y
14
+ ··· + 9y + 1)
· (y
88
+ 2y
87
+ ··· + 12594048y + 1087849)
c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
16
− 5y
15
+ ··· − 14y + 1)
· (y
88
+ 33y
87
+ ··· + 85934090519941y + 5931840478369)
26
