12a
0207
(K12a
0207
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 9 4 12 1 5 10
Solving Sequence
9,12
10 1
4,11
8 5 7 3 2 6
c
9
c
12
c
10
c
8
c
4
c
7
c
3
c
1
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.51570 × 10
15
u
34
− 5.53502 × 10
15
u
33
+ ··· + 1.20230 × 10
15
b + 4.04644 × 10
15
,
6.68182 × 10
15
u
34
+ 2.49675 × 10
16
u
33
+ ··· + 4.80919 × 10
15
a − 2.62648 × 10
16
, u
35
+ 5u
34
+ ··· − 13u − 4i
I
u
2
= h−1763u
28
a + 3881u
28
+ ··· − 1262a + 2496, 29u
28
a − 5u
28
+ ··· + 5a + 39, u
29
+ 4u
28
+ ··· + 2u + 1i
I
u
3
= h−2a
2
+ b + a + 1, 2a
4
− a
3
− 2a
2
+ a + 1, u − 1i
I
u
4
= ha
5
− a
4
− 3a
3
+ 4a
2
+ b + 4a − 2, a
6
− 2a
5
− a
4
+ 5a
3
− 3a + 1, u − 1i
I
u
5
= hau + b + u + 1, a
2
+ 2au + 4a + 4u + 7, u
2
+ u − 1i
* 5 irreducible components of dim
C
= 0, with total 107 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−1.52 × 10
15
u
34
− 5.54 × 10
15
u
33
+ · · · + 1.20 × 10
15
b + 4.05 ×
10
15
, 6.68 × 10
15
u
34
+ 2.50 × 10
16
u
33
+ · · · + 4.81 × 10
15
a − 2.63 ×
10
16
, u
35
+ 5u
34
+ · · · − 13u − 4i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−1.38939u
34
− 5.19162u
33
+ ··· + 16.4019u + 5.46137
1.26067u
34
+ 4.60371u
33
+ ··· − 11.0154u − 3.36559
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−0.955888u
34
− 3.63380u
33
+ ··· + 10.9509u + 4.67994
1.37755u
34
+ 5.16666u
33
+ ··· − 11.9980u − 4.33307
a
5
=
−1.18952u
34
− 4.52016u
33
+ ··· + 14.1974u + 5.74534
1.68537u
34
+ 6.13795u
33
+ ··· − 14.5486u − 4.33555
a
7
=
0.421659u
34
+ 1.53286u
33
+ ··· − 1.04716u + 0.346871
1.37755u
34
+ 5.16666u
33
+ ··· − 11.9980u − 4.33307
a
3
=
0.507830u
34
+ 1.85439u
33
+ ··· − 1.52833u − 0.397819
1.41127u
34
+ 5.28521u
33
+ ··· − 12.6990u − 4.42566
a
2
=
−0.624564u
34
− 2.20570u
33
+ ··· + 1.73779u + 1.68599
−0.299699u
34
− 1.03425u
33
+ ··· + 2.40823u + 0.469963
a
6
=
0.222426u
34
+ 0.604677u
33
+ ··· + 3.42434u + 2.44151
1.45957u
34
+ 5.39478u
33
+ ··· − 13.5630u − 4.01322
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
28600273364382339
9618382602850592
u
34
−
55866542605177373
4809191301425296
u
33
+···+
344438964453645221
9618382602850592
u+
38144347486615397
2404595650712648
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
35
+ 18u
34
+ ··· − 9u − 1
c
2
, c
4
, c
6
c
8
u
35
+ 9u
33
+ ··· − u − 1
c
3
u
35
+ 6u
34
+ ··· + 64u − 64
c
5
, c
11
u
35
+ 3u
34
+ ··· − 112u + 64
c
9
, c
10
, c
12
u
35
− 5u
34
+ ··· − 13u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
35
+ 6y
34
+ ··· + 3y −1
c
2
, c
4
, c
6
c
8
y
35
+ 18y
34
+ ··· − 9y −1
c
3
y
35
− 24y
34
+ ··· − 57344y −4096
c
5
, c
11
y
35
+ 27y
34
+ ··· − 7936y −4096
c
9
, c
10
, c
12
y
35
− 37y
34
+ ··· − 175y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959008 + 0.270609I
a = 0.823234 + 0.223651I
b = −0.173746 + 0.485732I
−1.84314 − 0.87084I −4.62038 + 1.34519I
u = 0.959008 − 0.270609I
a = 0.823234 − 0.223651I
b = −0.173746 − 0.485732I
−1.84314 + 0.87084I −4.62038 − 1.34519I
u = 0.512518 + 0.917994I
a = −1.70850 + 0.05834I
b = 0.517624 − 1.215310I
−7.59221 − 11.92590I −6.11495 + 8.82041I
u = 0.512518 − 0.917994I
a = −1.70850 − 0.05834I
b = 0.517624 + 1.215310I
−7.59221 + 11.92590I −6.11495 − 8.82041I
u = 0.954171 + 0.487790I
a = 0.010990 + 0.441890I
b = −0.416864 − 0.843498I
−2.25613 + 2.35480I −4.42628 − 5.78689I
u = 0.954171 − 0.487790I
a = 0.010990 − 0.441890I
b = −0.416864 + 0.843498I
−2.25613 − 2.35480I −4.42628 + 5.78689I
u = 0.721919 + 0.835340I
a = −0.372316 − 0.313834I
b = 0.476440 + 1.196050I
−8.22119 + 6.06183I −7.41980 − 3.98537I
u = 0.721919 − 0.835340I
a = −0.372316 + 0.313834I
b = 0.476440 − 1.196050I
−8.22119 − 6.06183I −7.41980 + 3.98537I
u = 0.495421 + 0.731154I
a = 1.122580 + 0.574754I
b = −0.732884 − 0.119482I
−1.27974 − 2.37099I 0.31894 + 3.15329I
u = 0.495421 − 0.731154I
a = 1.122580 − 0.574754I
b = −0.732884 + 0.119482I
−1.27974 + 2.37099I 0.31894 − 3.15329I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200040 + 0.713689I
a = 1.50067 − 1.01116I
b = −0.551950 + 0.938432I
0.02332 − 6.64372I −0.26642 + 9.39853I
u = 0.200040 − 0.713689I
a = 1.50067 + 1.01116I
b = −0.551950 − 0.938432I
0.02332 + 6.64372I −0.26642 − 9.39853I
u = 1.283430 + 0.258737I
a = −1.16481 − 0.94463I
b = 0.468567 − 0.922566I
−2.99912 − 4.93329I −3.82940 + 6.57606I
u = 1.283430 − 0.258737I
a = −1.16481 + 0.94463I
b = 0.468567 + 0.922566I
−2.99912 + 4.93329I −3.82940 − 6.57606I
u = −1.365140 + 0.043173I
a = −0.965795 + 0.425482I
b = 0.760139 − 0.637733I
−2.59101 − 0.97059I −3.20816 + 2.30460I
u = −1.365140 − 0.043173I
a = −0.965795 − 0.425482I
b = 0.760139 + 0.637733I
−2.59101 + 0.97059I −3.20816 − 2.30460I
u = 1.39159
a = 0.0610608
b = 0.727022
−3.41993 −0.649850
u = −1.389770 + 0.195625I
a = 1.45955 − 0.21134I
b = −0.651228 − 1.025580I
−4.98605 + 9.79445I −5.34481 − 8.93651I
u = −1.389770 − 0.195625I
a = 1.45955 + 0.21134I
b = −0.651228 + 1.025580I
−4.98605 − 9.79445I −5.34481 + 8.93651I
u = −0.481446 + 0.181091I
a = 1.21465 − 1.46620I
b = −0.528136 − 1.141240I
−3.37780 + 7.99798I 0.71148 − 7.40743I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.481446 − 0.181091I
a = 1.21465 + 1.46620I
b = −0.528136 + 1.141240I
−3.37780 − 7.99798I 0.71148 + 7.40743I
u = 1.51965 + 0.08089I
a = 0.71051 + 1.32043I
b = −0.495431 + 1.212500I
−10.12230 − 9.08658I 0
u = 1.51965 − 0.08089I
a = 0.71051 − 1.32043I
b = −0.495431 − 1.212500I
−10.12230 + 9.08658I 0
u = −0.100508 + 0.458939I
a = −2.27911 + 0.05270I
b = 0.543260 + 0.738488I
1.32849 + 2.20779I 4.23160 − 4.03649I
u = −0.100508 − 0.458939I
a = −2.27911 − 0.05270I
b = 0.543260 − 0.738488I
1.32849 − 2.20779I 4.23160 + 4.03649I
u = −1.52211 + 0.26355I
a = 0.493088 − 0.569107I
b = −0.872759 + 0.176459I
−7.85990 + 6.04546I 0
u = −1.52211 − 0.26355I
a = 0.493088 + 0.569107I
b = −0.872759 − 0.176459I
−7.85990 − 6.04546I 0
u = −1.55878 + 0.33189I
a = −1.50039 + 0.85083I
b = 0.543971 + 1.243490I
−14.3234 + 16.5120I 0
u = −1.55878 − 0.33189I
a = −1.50039 − 0.85083I
b = 0.543971 − 1.243490I
−14.3234 − 16.5120I 0
u = −1.63807 + 0.22494I
a = −0.012996 − 0.570463I
b = 0.408913 − 1.203980I
−16.1932 − 2.1173I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63807 − 0.22494I
a = −0.012996 + 0.570463I
b = 0.408913 + 1.203980I
−16.1932 + 2.1173I 0
u = −0.120066 + 0.311369I
a = 0.23634 + 1.50251I
b = 0.516750 − 0.437851I
1.051550 − 0.797647I 6.50655 + 3.66562I
u = −0.120066 − 0.311369I
a = 0.23634 − 1.50251I
b = 0.516750 + 0.437851I
1.051550 + 0.797647I 6.50655 − 3.66562I
u = −1.66607 + 0.03814I
a = 0.026783 + 0.627545I
b = −0.176178 + 0.879030I
−11.63190 − 0.88202I 0
u = −1.66607 − 0.03814I
a = 0.026783 − 0.627545I
b = −0.176178 − 0.879030I
−11.63190 + 0.88202I 0
8
II. I
u
2
= h−1763u
28
a + 3881u
28
+ · · · − 1262a + 2496, 29u
28
a − 5u
28
+ · · · +
5a + 39, u
29
+ 4u
28
+ · · · + 2u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
1.52773au
28
− 3.36308u
28
+ ··· + 1.09359a − 2.16291
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
3.11308au
28
− 0.363518u
28
+ ··· + 1.91291a − 0.0706239
−1.71274au
28
+ 2.52773u
28
+ ··· − 1.18674a + 0.593588
a
5
=
−
5
2
u
28
−
11
2
u
27
+ ··· −
11
2
u −
1
2
5
4
u
28
+
13
4
u
27
+ ··· +
1
4
u +
7
4
a
7
=
1.40035au
28
+ 2.16421u
28
+ ··· + 0.726170a + 0.522964
−1.71274au
28
+ 2.52773u
28
+ ··· − 1.18674a + 0.593588
a
3
=
2.86092au
28
− 2.45234u
28
+ ··· + 2.62435a − 3.15165
3.70147au
28
− 4.98960u
28
+ ··· + 2.58622a − 3.71490
a
2
=
−3.90945au
28
+ 1.96274u
28
+ ··· − 4.28813a + 2.43674
−6.43718au
28
+ 5.32582u
28
+ ··· − 4.88172a + 3.59965
a
6
=
9
2
u
28
+
25
2
u
27
+ ··· +
1
2
u +
9
2
19
4
u
28
+
51
4
u
27
+ ··· +
11
4
u +
17
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9u
28
+
49
2
u
27
+ ··· + 10u +
3
2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
58
+ 34u
57
+ ··· + 432u + 81
c
2
, c
4
, c
6
c
8
u
58
− 2u
57
+ ··· − 24u + 9
c
3
(u
29
− 2u
28
+ ··· − 15u + 9)
2
c
5
, c
11
(u
29
− u
28
+ ··· − 4u + 8)
2
c
9
, c
10
, c
12
(u
29
− 4u
28
+ ··· + 2u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
58
− 22y
57
+ ··· − 31428y + 6561
c
2
, c
4
, c
6
c
8
y
58
+ 34y
57
+ ··· + 432y + 81
c
3
(y
29
− 24y
28
+ ··· + 621y −81)
2
c
5
, c
11
(y
29
+ 21y
28
+ ··· + 144y −64)
2
c
9
, c
10
, c
12
(y
29
− 30y
28
+ ··· + 18y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.574714 + 0.809142I
a = −0.496285 − 0.329278I
b = 0.383823 + 1.246440I
−8.55101 − 2.70743I −7.83350 + 3.32702I
u = 0.574714 + 0.809142I
a = −2.02764 − 0.04424I
b = 0.430351 − 1.199840I
−8.55101 − 2.70743I −7.83350 + 3.32702I
u = 0.574714 − 0.809142I
a = −0.496285 + 0.329278I
b = 0.383823 − 1.246440I
−8.55101 + 2.70743I −7.83350 − 3.32702I
u = 0.574714 − 0.809142I
a = −2.02764 + 0.04424I
b = 0.430351 + 1.199840I
−8.55101 + 2.70743I −7.83350 − 3.32702I
u = 0.673518 + 0.754049I
a = −1.000040 − 0.560059I
b = 0.769255 − 0.056261I
−4.91068 + 1.51334I −4.49380 − 0.41799I
u = 0.673518 + 0.754049I
a = 0.406818 + 0.385726I
b = −0.411656 − 1.172770I
−4.91068 + 1.51334I −4.49380 − 0.41799I
u = 0.673518 − 0.754049I
a = −1.000040 + 0.560059I
b = 0.769255 + 0.056261I
−4.91068 − 1.51334I −4.49380 + 0.41799I
u = 0.673518 − 0.754049I
a = 0.406818 − 0.385726I
b = −0.411656 + 1.172770I
−4.91068 − 1.51334I −4.49380 + 0.41799I
u = 0.496046 + 0.855361I
a = −1.099850 − 0.481039I
b = 0.852937 + 0.125205I
−4.33597 − 6.94187I −3.09973 + 6.05967I
u = 0.496046 + 0.855361I
a = 1.84336 − 0.14503I
b = −0.491051 + 1.177580I
−4.33597 − 6.94187I −3.09973 + 6.05967I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.496046 − 0.855361I
a = −1.099850 + 0.481039I
b = 0.852937 − 0.125205I
−4.33597 + 6.94187I −3.09973 − 6.05967I
u = 0.496046 − 0.855361I
a = 1.84336 + 0.14503I
b = −0.491051 − 1.177580I
−4.33597 + 6.94187I −3.09973 − 6.05967I
u = 1.09947
a = −3.27542 + 2.45605I
b = 0.138638 + 1.028430I
−5.36254 1.86910
u = 1.09947
a = −3.27542 − 2.45605I
b = 0.138638 − 1.028430I
−5.36254 1.86910
u = 1.109450 + 0.283231I
a = 1.260760 + 0.513284I
b = −0.347220 + 0.737093I
−1.85262 − 1.10103I −2.03106 − 0.28755I
u = 1.109450 + 0.283231I
a = 0.187734 − 0.187443I
b = 0.397780 + 0.487721I
−1.85262 − 1.10103I −2.03106 − 0.28755I
u = 1.109450 − 0.283231I
a = 1.260760 − 0.513284I
b = −0.347220 − 0.737093I
−1.85262 + 1.10103I −2.03106 + 0.28755I
u = 1.109450 − 0.283231I
a = 0.187734 + 0.187443I
b = 0.397780 − 0.487721I
−1.85262 + 1.10103I −2.03106 + 0.28755I
u = −1.377160 + 0.122752I
a = 0.775794 − 0.486569I
b = −0.813747 + 0.500062I
−3.43590 + 4.37313I −3.64888 − 4.01970I
u = −1.377160 + 0.122752I
a = −1.396230 − 0.037221I
b = 0.666978 + 0.923318I
−3.43590 + 4.37313I −3.64888 − 4.01970I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.377160 − 0.122752I
a = 0.775794 + 0.486569I
b = −0.813747 − 0.500062I
−3.43590 − 4.37313I −3.64888 + 4.01970I
u = −1.377160 − 0.122752I
a = −1.396230 + 0.037221I
b = 0.666978 − 0.923318I
−3.43590 − 4.37313I −3.64888 + 4.01970I
u = 0.093803 + 0.571484I
a = 1.77937 + 0.48269I
b = −0.596648 − 0.524729I
1.17976 − 2.10537I 3.42367 + 3.98592I
u = 0.093803 + 0.571484I
a = −1.13444 + 1.49748I
b = 0.521180 − 0.791272I
1.17976 − 2.10537I 3.42367 + 3.98592I
u = 0.093803 − 0.571484I
a = 1.77937 − 0.48269I
b = −0.596648 + 0.524729I
1.17976 + 2.10537I 3.42367 − 3.98592I
u = 0.093803 − 0.571484I
a = −1.13444 − 1.49748I
b = 0.521180 + 0.791272I
1.17976 + 2.10537I 3.42367 − 3.98592I
u = 1.46649 + 0.06834I
a = −0.79189 − 1.39162I
b = 0.454670 − 1.185180I
−6.77922 − 4.29283I −4.53955 + 3.19264I
u = 1.46649 + 0.06834I
a = −0.0365899 + 0.0197419I
b = −0.824448 − 0.084249I
−6.77922 − 4.29283I −4.53955 + 3.19264I
u = 1.46649 − 0.06834I
a = −0.79189 + 1.39162I
b = 0.454670 + 1.185180I
−6.77922 + 4.29283I −4.53955 − 3.19264I
u = 1.46649 − 0.06834I
a = −0.0365899 − 0.0197419I
b = −0.824448 + 0.084249I
−6.77922 + 4.29283I −4.53955 − 3.19264I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46813
a = 0.70362 + 1.51889I
b = −0.412156 + 1.228670I
−10.7199 −8.58670
u = 1.46813
a = 0.70362 − 1.51889I
b = −0.412156 − 1.228670I
−10.7199 −8.58670
u = −1.46854 + 0.05369I
a = −0.000804 + 0.602797I
b = −0.077278 + 1.297810I
−9.63904 + 2.02688I −7.64196 − 3.46616I
u = −1.46854 + 0.05369I
a = 1.66820 + 0.63206I
b = −0.489594 − 0.791303I
−9.63904 + 2.02688I −7.64196 − 3.46616I
u = −1.46854 − 0.05369I
a = −0.000804 − 0.602797I
b = −0.077278 − 1.297810I
−9.63904 − 2.02688I −7.64196 + 3.46616I
u = −1.46854 − 0.05369I
a = 1.66820 − 0.63206I
b = −0.489594 + 0.791303I
−9.63904 − 2.02688I −7.64196 + 3.46616I
u = 0.332600 + 0.298296I
a = 1.17191 + 1.35445I
b = −0.078563 − 1.142090I
−3.67943 − 0.93878I −2.80996 + 7.32576I
u = 0.332600 + 0.298296I
a = 2.88434 − 4.02305I
b = −0.196086 + 0.856959I
−3.67943 − 0.93878I −2.80996 + 7.32576I
u = 0.332600 − 0.298296I
a = 1.17191 − 1.35445I
b = −0.078563 + 1.142090I
−3.67943 + 0.93878I −2.80996 − 7.32576I
u = 0.332600 − 0.298296I
a = 2.88434 + 4.02305I
b = −0.196086 − 0.856959I
−3.67943 + 0.93878I −2.80996 − 7.32576I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54068 + 0.30648I
a = −0.461477 + 0.542815I
b = 0.930068 − 0.139535I
−10.9685 + 11.1989I −5.19156 − 6.17598I
u = −1.54068 + 0.30648I
a = 1.56938 − 0.78799I
b = −0.541040 − 1.210840I
−10.9685 + 11.1989I −5.19156 − 6.17598I
u = −1.54068 − 0.30648I
a = −0.461477 − 0.542815I
b = 0.930068 + 0.139535I
−10.9685 − 11.1989I −5.19156 + 6.17598I
u = −1.54068 − 0.30648I
a = 1.56938 + 0.78799I
b = −0.541040 + 1.210840I
−10.9685 − 11.1989I −5.19156 + 6.17598I
u = −1.56175 + 0.26987I
a = 0.005904 − 0.572450I
b = 0.376897 − 1.308090I
−15.5682 + 6.6680I −9.30046 − 3.89200I
u = −1.56175 + 0.26987I
a = −1.71421 + 0.84034I
b = 0.496073 + 1.194220I
−15.5682 + 6.6680I −9.30046 − 3.89200I
u = −1.56175 − 0.26987I
a = 0.005904 + 0.572450I
b = 0.376897 + 1.308090I
−15.5682 − 6.6680I −9.30046 + 3.89200I
u = −1.56175 − 0.26987I
a = −1.71421 − 0.84034I
b = 0.496073 − 1.194220I
−15.5682 − 6.6680I −9.30046 + 3.89200I
u = −0.356186 + 0.206024I
a = −0.329572 − 0.575621I
b = −0.730042 + 0.234742I
−0.75685 + 3.25312I 3.53153 − 3.58405I
u = −0.356186 + 0.206024I
a = −1.75145 + 1.68560I
b = 0.474813 + 1.053290I
−0.75685 + 3.25312I 3.53153 − 3.58405I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356186 − 0.206024I
a = −0.329572 + 0.575621I
b = −0.730042 − 0.234742I
−0.75685 − 3.25312I 3.53153 + 3.58405I
u = −0.356186 − 0.206024I
a = −1.75145 − 1.68560I
b = 0.474813 − 1.053290I
−0.75685 − 3.25312I 3.53153 + 3.58405I
u = −1.57403 + 0.21687I
a = −0.455066 + 0.636664I
b = 0.779101 − 0.101681I
−12.38060 + 1.97634I −6.56391 + 0.I
u = −1.57403 + 0.21687I
a = 0.002336 + 0.579304I
b = −0.340208 + 1.254970I
−12.38060 + 1.97634I −6.56391 + 0.I
u = −1.57403 − 0.21687I
a = −0.455066 − 0.636664I
b = 0.779101 + 0.101681I
−12.38060 − 1.97634I −6.56391 + 0.I
u = −1.57403 − 0.21687I
a = 0.002336 − 0.579304I
b = −0.340208 − 1.254970I
−12.38060 − 1.97634I −6.56391 + 0.I
u = −0.304151
a = 0.71142 + 2.97196I
b = −0.322825 + 1.145710I
−4.79354 −1.88400
u = −0.304151
a = 0.71142 − 2.97196I
b = −0.322825 − 1.145710I
−4.79354 −1.88400
17
III. I
u
3
= h−2a
2
+ b + a + 1, 2a
4
− a
3
− 2a
2
+ a + 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
2a
2
− a − 1
a
11
=
0
1
a
8
=
2a
3
− a
2
− a + 1
−2a
3
+ a
2
− 1
a
5
=
0
−2a
3
+ 3a
2
+ a − 1
a
7
=
−a
−2a
3
+ a
2
− 1
a
3
=
−2a
3
+ a
2
+ a − 1
−2a
3
+ a
2
− 1
a
2
=
−2a
3
+ a
2
+ a − 1
−2a
3
− a
2
+ a + 1
a
6
=
0
−2a
3
+ 3a
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16a
3
− 9a
2
− 10a + 3
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
11
u
4
c
6
, c
8
u
4
+ u
2
− u + 1
c
9
, c
10
(u − 1)
4
c
12
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
6
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
5
, c
11
y
4
c
9
, c
10
, c
12
(y −1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.927958 + 0.413327I
b = −0.547424 + 1.120870I
−4.26996 − 7.64338I −7.31637 + 4.91712I
u = 1.00000
a = 0.927958 − 0.413327I
b = −0.547424 − 1.120870I
−4.26996 + 7.64338I −7.31637 − 4.91712I
u = 1.00000
a = −0.677958 + 0.157780I
b = 0.547424 − 0.585652I
−0.66484 − 1.39709I 1.69137 + 3.76574I
u = 1.00000
a = −0.677958 − 0.157780I
b = 0.547424 + 0.585652I
−0.66484 + 1.39709I 1.69137 − 3.76574I
21
IV.
I
u
4
= ha
5
− a
4
− 3a
3
+ 4a
2
+ b + 4a − 2, a
6
− 2a
5
− a
4
+ 5a
3
− 3a + 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
−a
5
+ a
4
+ 3a
3
− 4a
2
− 4a + 2
a
11
=
0
1
a
8
=
−a
5
+ 2a
4
+ a
3
− 4a
2
− a + 2
2a
5
− 3a
4
− 3a
3
+ 7a
2
+ 4a − 3
a
5
=
0
−3a
5
+ 4a
4
+ 6a
3
− 12a
2
− 7a + 5
a
7
=
a
5
− a
4
− 2a
3
+ 3a
2
+ 3a − 1
2a
5
− 3a
4
− 3a
3
+ 7a
2
+ 4a − 3
a
3
=
−4a
5
+ 6a
4
+ 7a
3
− 16a
2
− 8a + 7
−4a
5
+ 6a
4
+ 7a
3
− 16a
2
− 9a + 7
a
2
=
−4a
5
+ 6a
4
+ 7a
3
− 16a
2
− 8a + 7
−6a
5
+ 9a
4
+ 11a
3
− 25a
2
− 13a + 12
a
6
=
0
−3a
5
+ 4a
4
+ 6a
3
− 12a
2
− 7a + 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10a
5
− 13a
4
− 20a
3
+ 39a
2
+ 23a − 22
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
11
u
6
c
6
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
, c
10
(u − 1)
6
c
12
(u + 1)
6
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
6
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
11
y
6
c
9
, c
10
, c
12
(y − 1)
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.060970 + 0.237841I
b = 0.498832 + 1.001300I
−1.91067 + 2.82812I −2.82789 − 2.41717I
u = 1.00000
a = −1.060970 − 0.237841I
b = 0.498832 − 1.001300I
−1.91067 − 2.82812I −2.82789 + 2.41717I
u = 1.00000
a = 0.521167 + 0.055259I
b = −0.713912 − 0.305839I
−1.91067 − 2.82812I −2.82789 + 2.41717I
u = 1.00000
a = 0.521167 − 0.055259I
b = −0.713912 + 0.305839I
−1.91067 + 2.82812I −2.82789 − 2.41717I
u = 1.00000
a = 1.53980 + 0.84179I
b = −0.284920 + 1.115140I
−6.04826 −11.34423 + 0.I
u = 1.00000
a = 1.53980 − 0.84179I
b = −0.284920 − 1.115140I
−6.04826 −11.34423 + 0.I
25
V. I
u
5
= hau + b + u + 1, a
2
+ 2au + 4a + 4u + 7, u
2
+ u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u + 1
a
1
=
−u
−u + 1
a
4
=
a
−au − u − 1
a
11
=
u
u
a
8
=
au + a + 3u + 5
−1
a
5
=
−au − u − 1
0
a
7
=
au + a + 3u + 4
−1
a
3
=
a
−au − u − 1
a
2
=
a − u
−au − 2u
a
6
=
au − a − 1
2au − a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)
4
c
2
, c
4
, c
6
c
8
(u
2
+ 1)
2
c
3
u
4
c
5
, c
11
u
4
+ 3u
2
+ 1
c
9
, c
10
(u
2
+ u − 1)
2
c
12
(u
2
− u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y − 1)
4
c
2
, c
4
, c
6
c
8
(y + 1)
4
c
3
y
4
c
5
, c
11
(y
2
+ 3y + 1)
2
c
9
, c
10
, c
12
(y
2
− 3y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.61803 + 1.61803I
b = − 1.000000I
−4.27683 −12.0000
u = 0.618034
a = −2.61803 − 1.61803I
b = 1.000000I
−4.27683 −12.0000
u = −1.61803
a = −0.381966 + 0.618034I
b = 1.000000I
−12.1725 −12.0000
u = −1.61803
a = −0.381966 − 0.618034I
b = − 1.000000I
−12.1725 −12.0000
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)
4
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
35
+ 18u
34
+ ··· − 9u − 1)(u
58
+ 34u
57
+ ··· + 432u + 81)
c
2
, c
4
(u
2
+ 1)
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
35
+ 9u
33
+ ··· − u − 1)(u
58
− 2u
57
+ ··· − 24u + 9)
c
3
u
4
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ ··· + 3u + 2)(u
29
− 2u
28
+ ··· − 15u + 9)
2
· (u
35
+ 6u
34
+ ··· + 64u − 64)
c
5
, c
11
u
10
(u
4
+ 3u
2
+ 1)(u
29
− u
28
+ ··· − 4u + 8)
2
· (u
35
+ 3u
34
+ ··· − 112u + 64)
c
6
, c
8
(u
2
+ 1)
2
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
35
+ 9u
33
+ ··· − u − 1)(u
58
− 2u
57
+ ··· − 24u + 9)
c
9
, c
10
((u − 1)
10
)(u
2
+ u − 1)
2
(u
29
− 4u
28
+ ··· + 2u − 1)
2
· (u
35
− 5u
34
+ ··· − 13u + 4)
c
12
((u + 1)
10
)(u
2
− u − 1)
2
(u
29
− 4u
28
+ ··· + 2u − 1)
2
· (u
35
− 5u
34
+ ··· − 13u + 4)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y − 1)
4
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
35
+ 6y
34
+ ··· + 3y − 1)(y
58
− 22y
57
+ ··· − 31428y + 6561)
c
2
, c
4
, c
6
c
8
(y + 1)
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
35
+ 18y
34
+ ··· − 9y − 1)(y
58
+ 34y
57
+ ··· + 432y + 81)
c
3
y
4
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
29
− 24y
28
+ ··· + 621y − 81)
2
· (y
35
− 24y
34
+ ··· − 57344y − 4096)
c
5
, c
11
y
10
(y
2
+ 3y + 1)
2
(y
29
+ 21y
28
+ ··· + 144y − 64)
2
· (y
35
+ 27y
34
+ ··· − 7936y − 4096)
c
9
, c
10
, c
12
((y − 1)
10
)(y
2
− 3y + 1)
2
(y
29
− 30y
28
+ ··· + 18y − 1)
2
· (y
35
− 37y
34
+ ··· − 175y − 16)
31
