12n
0320
(K12n
0320
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 9 10 12 5 4 8 9
Solving Sequence
6,9 3,7
2 1 5 10 4 12 8 11
c
6
c
2
c
1
c
5
c
9
c
4
c
12
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.94964 × 10
382
u
72
+ 1.20690 × 10
383
u
71
+ ··· + 5.33896 × 10
384
b − 1.10225 × 10
386
,
− 1.84504 × 10
385
u
72
− 1.15557 × 10
386
u
71
+ ··· + 1.20981 × 10
387
a + 8.26575 × 10
388
,
u
73
+ 6u
72
+ ··· − 18561u + 1133i
I
u
2
= h−362677236u
12
+ 287880043u
11
+ ··· + 2896442647b + 2924763966,
− 938151764u
12
− 1358804549u
11
+ ··· + 2896442647a − 4249866059,
u
13
+ u
11
+ 11u
10
+ 2u
9
+ 8u
8
+ 62u
7
− 17u
6
+ 25u
5
− 7u
4
− 10u
3
+ 2u
2
+ 1i
I
u
3
= hu
4
+ 2u
3
− u
2
+ b − 2u, 2u
5
+ 5u
4
− 2u
3
− 9u
2
+ a + u + 4, u
6
+ 3u
5
− 5u
3
− u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 92 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
= h1.95 × 10
382
u
72
+ 1.21 × 10
383
u
71
+ · · · + 5.34 × 10
384
b − 1.10 ×
10
386
, −1.85 × 10
385
u
72
− 1.16 × 10
386
u
71
+ · · · + 1.21 × 10
387
a + 8.27 ×
10
388
, u
73
+ 6u
72
+ · · · − 18561u + 1133i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
0.0152507u
72
+ 0.0955166u
71
+ ··· + 844.480u − 68.3229
−0.00365172u
72
− 0.0226055u
71
+ ··· − 241.555u + 20.6453
a
7
=
1
u
2
a
2
=
0.0115990u
72
+ 0.0729111u
71
+ ··· + 602.925u − 47.6775
−0.00365172u
72
− 0.0226055u
71
+ ··· − 241.555u + 20.6453
a
1
=
−0.0167624u
72
− 0.103452u
71
+ ··· − 1190.73u + 109.121
0.00289105u
72
+ 0.0179807u
71
+ ··· + 190.095u − 18.3749
a
5
=
0.0184116u
72
+ 0.114807u
71
+ ··· + 1089.39u − 91.6124
−0.00601210u
72
− 0.0371863u
71
+ ··· − 388.300u + 34.2741
a
10
=
−0.00271928u
72
− 0.0151351u
71
+ ··· − 390.211u + 41.7955
0.00573011u
72
+ 0.0357021u
71
+ ··· + 366.128u − 31.6795
a
4
=
0.0255847u
72
+ 0.159203u
71
+ ··· + 1537.33u − 130.800
−0.00565886u
72
− 0.0350883u
71
+ ··· − 371.217u + 32.7353
a
12
=
−0.0167624u
72
− 0.103452u
71
+ ··· − 1190.73u + 109.121
0.00250121u
72
+ 0.0155056u
71
+ ··· + 155.679u − 15.1148
a
8
=
0.0117290u
72
+ 0.0727452u
71
+ ··· + 719.230u − 62.4670
−0.00246932u
72
− 0.0152327u
71
+ ··· − 178.421u + 16.4833
a
11
=
−0.0182906u
72
− 0.113075u
71
+ ··· − 1255.70u + 113.788
0.000808248u
72
+ 0.00493055u
71
+ ··· + 38.6483u − 5.11399
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0291619u
72
+ 0.179368u
71
+ ··· + 1994.61u − 181.670
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 40u
72
+ ··· + 26772u + 121
c
2
, c
5
u
73
+ 2u
72
+ ··· + 146u − 11
c
3
u
73
+ 3u
72
+ ··· + 31u − 1
c
4
u
73
+ 7u
72
+ ··· − 96u + 64
c
6
u
73
− 6u
72
+ ··· − 18561u − 1133
c
7
u
73
− 3u
72
+ ··· − 12u − 1
c
8
, c
11
, c
12
u
73
− u
72
+ ··· − 11u − 1
c
9
u
73
− u
72
+ ··· − 11u − 19
c
10
u
73
+ 3u
72
+ ··· − 23u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 8y
72
+ ··· + 632441220y −14641
c
2
, c
5
y
73
− 40y
72
+ ··· + 26772y −121
c
3
y
73
− 71y
72
+ ··· − 323y −1
c
4
y
73
+ 29y
72
+ ··· − 1084416y −4096
c
6
y
73
− 34y
72
+ ··· + 64177063y −1283689
c
7
y
73
− 19y
72
+ ··· + 32y −1
c
8
, c
11
, c
12
y
73
− 17y
72
+ ··· − 37y −1
c
9
y
73
+ 21y
72
+ ··· − 26327y −361
c
10
y
73
+ 53y
72
+ ··· + 217y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031340 + 0.008433I
a = −0.069808 + 1.084620I
b = 1.375400 − 0.230767I
−8.53900 − 6.42718I 0
u = −1.031340 − 0.008433I
a = −0.069808 − 1.084620I
b = 1.375400 + 0.230767I
−8.53900 + 6.42718I 0
u = 1.016880 + 0.247438I
a = 0.18301 + 1.43687I
b = −1.134700 − 0.389357I
−3.48643 − 1.34087I 0
u = 1.016880 − 0.247438I
a = 0.18301 − 1.43687I
b = −1.134700 + 0.389357I
−3.48643 + 1.34087I 0
u = −0.698200 + 0.781658I
a = −0.086270 − 0.883147I
b = 0.143676 + 0.967502I
2.76121 + 4.17164I 0
u = −0.698200 − 0.781658I
a = −0.086270 + 0.883147I
b = 0.143676 − 0.967502I
2.76121 − 4.17164I 0
u = 0.923453 + 0.507277I
a = −0.711008 − 0.775964I
b = 0.052883 + 0.873653I
−3.09395 − 3.25435I 0
u = 0.923453 − 0.507277I
a = −0.711008 + 0.775964I
b = 0.052883 − 0.873653I
−3.09395 + 3.25435I 0
u = 0.320327 + 1.015200I
a = 0.345566 + 1.000120I
b = 0.139397 − 0.696765I
1.29497 − 2.48132I 0
u = 0.320327 − 1.015200I
a = 0.345566 − 1.000120I
b = 0.139397 + 0.696765I
1.29497 + 2.48132I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.102722 + 0.909943I
a = 1.58395 − 1.09523I
b = −0.999021 + 0.236970I
−0.52366 + 1.44354I 0
u = −0.102722 − 0.909943I
a = 1.58395 + 1.09523I
b = −0.999021 − 0.236970I
−0.52366 − 1.44354I 0
u = −1.080410 + 0.103383I
a = −0.551852 + 0.897401I
b = −0.020100 − 0.900171I
−4.24460 − 3.95976I 0
u = −1.080410 − 0.103383I
a = −0.551852 − 0.897401I
b = −0.020100 + 0.900171I
−4.24460 + 3.95976I 0
u = −0.972563 + 0.495097I
a = −0.18790 + 1.67102I
b = 1.258500 − 0.462677I
−8.13571 + 8.75720I 0
u = −0.972563 − 0.495097I
a = −0.18790 − 1.67102I
b = 1.258500 + 0.462677I
−8.13571 − 8.75720I 0
u = 0.845098 + 0.817919I
a = 0.223034 + 0.772508I
b = 0.195678 − 0.647035I
0.02539 − 2.06580I 0
u = 0.845098 − 0.817919I
a = 0.223034 − 0.772508I
b = 0.195678 + 0.647035I
0.02539 + 2.06580I 0
u = 0.704242 + 0.317833I
a = −0.59265 − 2.07838I
b = 1.251460 + 0.483613I
−6.73334 − 1.65613I −2.92629 + 0.79234I
u = 0.704242 − 0.317833I
a = −0.59265 + 2.07838I
b = 1.251460 − 0.483613I
−6.73334 + 1.65613I −2.92629 − 0.79234I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556762 + 0.475035I
a = 0.324680 + 0.714527I
b = −1.215180 − 0.518061I
−1.72177 − 1.34235I 1.77903 + 5.54028I
u = 0.556762 − 0.475035I
a = 0.324680 − 0.714527I
b = −1.215180 + 0.518061I
−1.72177 + 1.34235I 1.77903 − 5.54028I
u = −0.457882 + 1.231170I
a = −0.082528 − 0.200066I
b = 0.705147 + 0.340560I
1.30339 − 1.96383I 0
u = −0.457882 − 1.231170I
a = −0.082528 + 0.200066I
b = 0.705147 − 0.340560I
1.30339 + 1.96383I 0
u = 1.327210 + 0.201548I
a = −0.032088 − 0.895329I
b = 1.295440 + 0.256609I
−9.63449 − 0.84683I 0
u = 1.327210 − 0.201548I
a = −0.032088 + 0.895329I
b = 1.295440 − 0.256609I
−9.63449 + 0.84683I 0
u = 1.279340 + 0.555895I
a = 0.041703 − 1.054370I
b = −0.324932 + 0.913616I
−4.31900 − 2.85477I 0
u = 1.279340 − 0.555895I
a = 0.041703 + 1.054370I
b = −0.324932 − 0.913616I
−4.31900 + 2.85477I 0
u = −1.293390 + 0.552574I
a = 0.307125 − 0.021259I
b = 0.769443 + 0.511761I
3.52478 − 2.09880I 0
u = −1.293390 − 0.552574I
a = 0.307125 + 0.021259I
b = 0.769443 − 0.511761I
3.52478 + 2.09880I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564547
a = 1.46692
b = 0.0693710
1.42881 7.52280
u = −1.19035 + 0.80455I
a = −0.040182 + 1.009980I
b = −0.285323 − 1.026970I
−2.73397 + 10.71610I 0
u = −1.19035 − 0.80455I
a = −0.040182 − 1.009980I
b = −0.285323 + 1.026970I
−2.73397 − 10.71610I 0
u = 0.82644 + 1.17623I
a = 0.666106 − 1.183330I
b = 0.932325 + 0.388293I
−0.79582 − 6.86751I 0
u = 0.82644 − 1.17623I
a = 0.666106 + 1.183330I
b = 0.932325 − 0.388293I
−0.79582 + 6.86751I 0
u = −0.529293 + 0.181821I
a = −0.639919 − 1.224910I
b = −1.275540 + 0.261362I
−2.37007 + 0.33063I −5.36190 + 8.76599I
u = −0.529293 − 0.181821I
a = −0.639919 + 1.224910I
b = −1.275540 − 0.261362I
−2.37007 − 0.33063I −5.36190 − 8.76599I
u = −1.42533 + 0.24670I
a = 0.050785 − 0.805780I
b = 0.891619 + 0.767472I
3.06820 − 2.89868I 0
u = −1.42533 − 0.24670I
a = 0.050785 + 0.805780I
b = 0.891619 − 0.767472I
3.06820 + 2.89868I 0
u = −1.19516 + 0.92757I
a = 0.115452 + 1.011240I
b = 1.249180 − 0.552747I
−0.61277 + 9.60861I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19516 − 0.92757I
a = 0.115452 − 1.011240I
b = 1.249180 + 0.552747I
−0.61277 − 9.60861I 0
u = −1.40807 + 0.66939I
a = 0.460393 + 0.498489I
b = 0.913659 − 0.284641I
0.829050 + 0.928279I 0
u = −1.40807 − 0.66939I
a = 0.460393 − 0.498489I
b = 0.913659 + 0.284641I
0.829050 − 0.928279I 0
u = −0.37186 + 1.51517I
a = −0.603407 − 0.886155I
b = −0.791457 + 0.373687I
−0.66969 − 3.07517I 0
u = −0.37186 − 1.51517I
a = −0.603407 + 0.886155I
b = −0.791457 − 0.373687I
−0.66969 + 3.07517I 0
u = 0.168757 + 0.338708I
a = −1.39461 − 1.59302I
b = 0.849357 − 0.685739I
7.96391 + 2.63534I 10.53738 − 3.36691I
u = 0.168757 − 0.338708I
a = −1.39461 + 1.59302I
b = 0.849357 + 0.685739I
7.96391 − 2.63534I 10.53738 + 3.36691I
u = −1.60775 + 0.25073I
a = −0.058800 − 0.535382I
b = −1.270170 + 0.471642I
−8.07804 + 0.96725I 0
u = −1.60775 − 0.25073I
a = −0.058800 + 0.535382I
b = −1.270170 − 0.471642I
−8.07804 − 0.96725I 0
u = −1.62701 + 0.14118I
a = 0.057887 + 1.157310I
b = −0.885594 − 0.751718I
4.19772 − 2.84969I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62701 − 0.14118I
a = 0.057887 − 1.157310I
b = −0.885594 + 0.751718I
4.19772 + 2.84969I 0
u = 0.332878 + 0.028795I
a = −6.64477 + 4.14556I
b = −0.856356 + 0.076377I
0.469074 + 0.132162I −52.8630 − 35.7017I
u = 0.332878 − 0.028795I
a = −6.64477 − 4.14556I
b = −0.856356 − 0.076377I
0.469074 − 0.132162I −52.8630 + 35.7017I
u = 0.61123 + 1.63936I
a = −0.364083 + 0.786880I
b = 0.676939 − 0.447545I
0.01496 − 3.34458I 0
u = 0.61123 − 1.63936I
a = −0.364083 − 0.786880I
b = 0.676939 + 0.447545I
0.01496 + 3.34458I 0
u = 0.077199 + 0.194945I
a = −1.045320 + 0.356695I
b = −0.680238 + 1.054680I
0.55649 + 4.84325I −9.6053 − 10.7522I
u = 0.077199 − 0.194945I
a = −1.045320 − 0.356695I
b = −0.680238 − 1.054680I
0.55649 − 4.84325I −9.6053 + 10.7522I
u = 0.190020 + 0.008741I
a = 3.18173 + 0.88298I
b = −0.832237 − 0.401743I
−1.68584 − 0.75262I −4.20696 + 3.02462I
u = 0.190020 − 0.008741I
a = 3.18173 − 0.88298I
b = −0.832237 + 0.401743I
−1.68584 + 0.75262I −4.20696 − 3.02462I
u = 1.14874 + 1.41502I
a = −0.090176 − 0.812042I
b = 1.172430 + 0.484972I
−1.69151 − 6.95731I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14874 − 1.41502I
a = −0.090176 + 0.812042I
b = 1.172430 − 0.484972I
−1.69151 + 6.95731I 0
u = −1.72102 + 0.61105I
a = −0.084879 − 0.409811I
b = −0.915829 − 0.198212I
4.61519 − 0.89594I 0
u = −1.72102 − 0.61105I
a = −0.084879 + 0.409811I
b = −0.915829 + 0.198212I
4.61519 + 0.89594I 0
u = 1.69805 + 0.77805I
a = 0.034519 + 1.038170I
b = −1.197940 − 0.626774I
−6.94494 − 8.52178I 0
u = 1.69805 − 0.77805I
a = 0.034519 − 1.038170I
b = −1.197940 + 0.626774I
−6.94494 + 8.52178I 0
u = 1.78485 + 0.62481I
a = −0.035007 + 0.478103I
b = −1.246140 − 0.443705I
−7.01799 − 7.84696I 0
u = 1.78485 − 0.62481I
a = −0.035007 − 0.478103I
b = −1.246140 + 0.443705I
−7.01799 + 7.84696I 0
u = −1.64823 + 1.00779I
a = 0.019327 − 0.971347I
b = −1.246010 + 0.626078I
−5.7190 + 16.6662I 0
u = −1.64823 − 1.00779I
a = 0.019327 + 0.971347I
b = −1.246010 − 0.626078I
−5.7190 − 16.6662I 0
u = 1.64963 + 1.05225I
a = 0.079258 − 0.840196I
b = 1.137360 + 0.514079I
−2.59231 − 6.57079I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64963 − 1.05225I
a = 0.079258 + 0.840196I
b = 1.137360 − 0.514079I
−2.59231 + 6.57079I 0
u = 0.18175 + 2.19918I
a = 0.299156 + 0.533354I
b = −0.867813 − 0.323965I
−0.85745 − 6.14484I 0
u = 0.18175 − 2.19918I
a = 0.299156 − 0.533354I
b = −0.867813 + 0.323965I
−0.85745 + 6.14484I 0
12
II.
I
u
2
= h−3.63 × 10
8
u
12
+ 2.88 × 10
8
u
11
+ · · · + 2.90 × 10
9
b + 2.92 × 10
9
, −9.38 ×
10
8
u
12
−1.36×10
9
u
11
+· · · +2.90×10
9
a−4.25×10
9
, u
13
+u
11
+· · · +2u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
0.323898u
12
+ 0.469129u
11
+ ··· − 1.53927u + 1.46727
0.125215u
12
− 0.0993909u
11
+ ··· + 0.800156u − 1.00978
a
7
=
1
u
2
a
2
=
0.449113u
12
+ 0.369738u
11
+ ··· − 0.739109u + 0.457493
0.125215u
12
− 0.0993909u
11
+ ··· + 0.800156u − 1.00978
a
1
=
0.728746u
12
− 0.224556u
11
+ ··· + 6.06123u + 0.869555
−0.0551268u
12
+ 0.0473930u
11
+ ··· − 0.349385u − 1.07001
a
5
=
0.224507u
12
+ 0.453099u
11
+ ··· − 3.54904u + 1.34206
0.200391u
12
− 0.149232u
11
+ ··· + 1.25064u − 0.641494
a
10
=
−0.728746u
12
+ 0.224556u
11
+ ··· − 6.06123u − 0.869555
0.462877u
12
+ 0.0898353u
11
+ ··· + 0.207205u + 0.575649
a
4
=
−0.0112639u
12
+ 0.631242u
11
+ ··· − 5.02419u + 1.53045
0.243853u
12
− 0.165387u
11
+ ··· + 1.48641u − 0.819637
a
12
=
0.728746u
12
− 0.224556u
11
+ ··· + 6.06123u + 0.869555
−0.239996u
12
+ 0.0841438u
11
+ ··· − 1.07813u − 0.845449
a
8
=
1.80021u
12
− 0.278008u
11
+ ··· + 8.51205u + 1.52154
−0.477728u
12
+ 0.0168202u
11
+ ··· − 1.73086u − 1.17273
a
11
=
−2.02476u
12
+ 0.0931390u
11
+ ··· − 7.64250u − 1.25029
0.737360u
12
+ 0.126794u
11
+ ··· + 1.08449u + 1.08780
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
829234359
2896442647
u
12
+
370579677
413777521
u
11
+ ··· −
19569538353
2896442647
u −
2261800129
2896442647
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 7u
12
+ ··· + 7u − 1
c
2
u
13
− u
12
+ ··· − u − 1
c
3
u
13
+ 2u
12
+ ··· − 4u − 1
c
4
u
13
+ 4u
11
+ ··· + 317u − 19
c
5
u
13
+ u
12
+ ··· − u + 1
c
6
u
13
+ u
11
+ ··· + 2u
2
+ 1
c
7
u
13
+ u
12
+ ··· + 5u + 1
c
8
u
13
− 8u
12
+ ··· − 4u + 1
c
9
u
13
+ 4u
11
+ 5u
9
+ u
8
+ 2u
7
+ 3u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1
c
10
u
13
+ 2u
11
− 2u
10
+ 3u
9
− u
8
+ 3u
7
+ 2u
6
+ u
5
+ 5u
4
+ 4u
2
+ 1
c
11
, c
12
u
13
+ 8u
12
+ ··· − 4u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ y
12
+ ··· − 5y −1
c
2
, c
5
y
13
− 7y
12
+ ··· + 7y −1
c
3
y
13
− 14y
12
+ ··· + 20y −1
c
4
y
13
+ 8y
12
+ ··· + 106151y −361
c
6
y
13
+ 2y
12
+ ··· − 4y −1
c
7
y
13
− 7y
12
+ ··· + 9y −1
c
8
, c
11
, c
12
y
13
− 12y
12
+ ··· − 4y −1
c
9
y
13
+ 8y
12
+ ··· − 4y −1
c
10
y
13
+ 4y
12
+ ··· − 8y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.034638 + 0.808086I
a = 0.111409 + 0.893993I
b = −0.526985 − 0.893318I
1.01859 − 4.74508I 7.57177 + 6.41095I
u = 0.034638 − 0.808086I
a = 0.111409 − 0.893993I
b = −0.526985 + 0.893318I
1.01859 + 4.74508I 7.57177 − 6.41095I
u = −0.551883
a = −2.82392
b = −0.786174
0.523382 −4.29060
u = 0.511807 + 0.159844I
a = 0.02485 + 1.62930I
b = −1.269700 − 0.400560I
−2.26904 − 0.89336I −4.11638 + 1.75348I
u = 0.511807 − 0.159844I
a = 0.02485 − 1.62930I
b = −1.269700 + 0.400560I
−2.26904 + 0.89336I −4.11638 − 1.75348I
u = −0.137123 + 0.367985I
a = 3.01835 − 0.41849I
b = −0.876022 + 0.657317I
7.06478 + 2.55494I 0.70865 − 2.59980I
u = −0.137123 − 0.367985I
a = 3.01835 + 0.41849I
b = −0.876022 − 0.657317I
7.06478 − 2.55494I 0.70865 + 2.59980I
u = 0.42965 + 1.86940I
a = 0.045461 + 0.869498I
b = 0.559964 − 0.334651I
−0.38012 − 4.16412I −0.22979 + 8.48801I
u = 0.42965 − 1.86940I
a = 0.045461 − 0.869498I
b = 0.559964 + 0.334651I
−0.38012 + 4.16412I −0.22979 − 8.48801I
u = −1.91064 + 0.61379I
a = 0.171924 + 0.034388I
b = 0.881456 + 0.333147I
5.04599 − 1.42504I 7.51174 + 5.79280I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.91064 − 0.61379I
a = 0.171924 − 0.034388I
b = 0.881456 − 0.333147I
5.04599 + 1.42504I 7.51174 − 5.79280I
u = 1.34760 + 1.54920I
a = 0.039967 − 0.870494I
b = 1.124380 + 0.455563I
−2.51722 − 7.71156I −3.80070 + 11.12971I
u = 1.34760 − 1.54920I
a = 0.039967 + 0.870494I
b = 1.124380 − 0.455563I
−2.51722 + 7.71156I −3.80070 − 11.12971I
17
III. I
u
3
= hu
4
+ 2u
3
− u
2
+ b − 2u, 2u
5
+ 5u
4
− 2u
3
− 9u
2
+ a + u + 4, u
6
+
3u
5
− 5u
3
− u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−2u
5
− 5u
4
+ 2u
3
+ 9u
2
− u − 4
−u
4
− 2u
3
+ u
2
+ 2u
a
7
=
1
u
2
a
2
=
−2u
5
− 6u
4
+ 10u
2
+ u − 4
−u
4
− 2u
3
+ u
2
+ 2u
a
1
=
−u
5
− 3u
4
+ 5u
2
+ u − 2
u
2
+ u
a
5
=
−u
5
− 2u
4
+ 3u
3
+ 6u
2
− 2u − 3
u
4
+ 2u
3
− u − 1
a
10
=
u
5
+ 2u
4
− 3u
3
− 5u
2
+ 4u + 3
2u + 1
a
4
=
−u
5
− 2u
4
+ 3u
3
+ 6u
2
− 2u − 3
u
4
+ 2u
3
− u − 1
a
12
=
−u
5
− 3u
4
+ 5u
2
+ u − 2
u
2
+ 2u
a
8
=
u
5
+ 3u
4
− 5u
2
− u + 2
−u
2
− u
a
11
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
− 10u
4
− 8u
3
+ 14u
2
+ 7u + 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
, c
7
u
6
+ 3u
5
− 5u
3
− u
2
+ 2u + 1
c
8
(u + 1)
6
c
9
, c
10
u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 4u
2
+ 2u + 1
c
11
, c
12
(u − 1)
6
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
4
y
6
c
6
, c
7
y
6
− 9y
5
+ 28y
4
− 35y
3
+ 21y
2
− 6y + 1
c
8
, c
11
, c
12
(y −1)
6
c
9
, c
10
y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897438 + 0.201182I
a = 0.347054 + 0.067998I
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 7.93937 − 4.05868I
u = 0.897438 − 0.201182I
a = 0.347054 − 0.067998I
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 7.93937 + 4.05868I
u = −0.500000 + 0.273346I
a = −1.82472 − 1.95694I
b = −0.754878
0.531480 0.40089 − 2.50363I
u = −0.500000 − 0.273346I
a = −1.82472 + 1.95694I
b = −0.754878
0.531480 0.40089 + 2.50363I
u = −1.89744 + 0.20118I
a = −0.022336 − 1.056560I
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 13.15973 + 2.26538I
u = −1.89744 − 0.20118I
a = −0.022336 + 1.056560I
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 13.15973 − 2.26538I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
2
)(u
13
− 7u
12
+ ··· + 7u − 1)
· (u
73
+ 40u
72
+ ··· + 26772u + 121)
c
2
((u
3
+ u
2
− 1)
2
)(u
13
− u
12
+ ··· − u − 1)(u
73
+ 2u
72
+ ··· + 146u − 11)
c
3
((u
3
− u
2
+ 2u − 1)
2
)(u
13
+ 2u
12
+ ··· − 4u − 1)
· (u
73
+ 3u
72
+ ··· + 31u − 1)
c
4
u
6
(u
13
+ 4u
11
+ ··· + 317u − 19)(u
73
+ 7u
72
+ ··· − 96u + 64)
c
5
((u
3
− u
2
+ 1)
2
)(u
13
+ u
12
+ ··· − u + 1)(u
73
+ 2u
72
+ ··· + 146u − 11)
c
6
(u
6
+ 3u
5
− 5u
3
− u
2
+ 2u + 1)(u
13
+ u
11
+ ··· + 2u
2
+ 1)
· (u
73
− 6u
72
+ ··· − 18561u − 1133)
c
7
(u
6
+ 3u
5
− 5u
3
− u
2
+ 2u + 1)(u
13
+ u
12
+ ··· + 5u + 1)
· (u
73
− 3u
72
+ ··· − 12u − 1)
c
8
((u + 1)
6
)(u
13
− 8u
12
+ ··· − 4u + 1)(u
73
− u
72
+ ··· − 11u − 1)
c
9
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 4u
2
+ 2u + 1)
· (u
13
+ 4u
11
+ 5u
9
+ u
8
+ 2u
7
+ 3u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1)
· (u
73
− u
72
+ ··· − 11u − 19)
c
10
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 4u
2
+ 2u + 1)
· (u
13
+ 2u
11
− 2u
10
+ 3u
9
− u
8
+ 3u
7
+ 2u
6
+ u
5
+ 5u
4
+ 4u
2
+ 1)
· (u
73
+ 3u
72
+ ··· − 23u − 1)
c
11
, c
12
((u − 1)
6
)(u
13
+ 8u
12
+ ··· − 4u − 1)(u
73
− u
72
+ ··· − 11u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
2
)(y
13
+ y
12
+ ··· − 5y −1)
· (y
73
− 8y
72
+ ··· + 632441220y −14641)
c
2
, c
5
((y
3
− y
2
+ 2y −1)
2
)(y
13
− 7y
12
+ ··· + 7y −1)
· (y
73
− 40y
72
+ ··· + 26772y −121)
c
3
((y
3
+ 3y
2
+ 2y −1)
2
)(y
13
− 14y
12
+ ··· + 20y −1)
· (y
73
− 71y
72
+ ··· − 323y −1)
c
4
y
6
(y
13
+ 8y
12
+ ··· + 106151y −361)
· (y
73
+ 29y
72
+ ··· − 1084416y −4096)
c
6
(y
6
− 9y
5
+ ··· − 6y + 1)(y
13
+ 2y
12
+ ··· − 4y −1)
· (y
73
− 34y
72
+ ··· + 64177063y −1283689)
c
7
(y
6
− 9y
5
+ ··· − 6y + 1)(y
13
− 7y
12
+ ··· + 9y −1)
· (y
73
− 19y
72
+ ··· + 32y −1)
c
8
, c
11
, c
12
((y −1)
6
)(y
13
− 12y
12
+ ··· − 4y −1)(y
73
− 17y
72
+ ··· − 37y −1)
c
9
(y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1)(y
13
+ 8y
12
+ ··· − 4y −1)
· (y
73
+ 21y
72
+ ··· − 26327y −361)
c
10
(y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1)(y
13
+ 4y
12
+ ··· − 8y −1)
· (y
73
+ 53y
72
+ ··· + 217y −1)
23
