12a
0040
(K12a
0040
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 10 4 12 11 6 1 9
Solving Sequence
8,12
9
1,4
7 3 11 10 6 5 2
c
8
c
12
c
7
c
3
c
11
c
9
c
6
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.52476 × 10
40
u
119
+ 1.85032 × 10
41
u
118
+ ··· + 3.97571 × 10
38
b + 3.69260 × 10
40
,
1.98154 × 10
40
u
119
+ 1.49672 × 10
41
u
118
+ ··· + 1.98786 × 10
38
a + 3.56279 × 10
40
, u
120
+ 8u
119
+ ··· + 8u + 1i
I
u
2
= hb, u
8
+ 2u
7
− u
6
− 4u
5
− u
4
+ 3u
3
+ 3u
2
+ a + 2u, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
u
3
= h2a
5
− 2a
4
+ 7a
3
− 5a
2
+ 3b + a − 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 135 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
= h2.52 × 10
40
u
119
+ 1.85 × 10
41
u
118
+ · · · + 3.98 × 10
38
b + 3.69 ×
10
40
, 1.98 × 10
40
u
119
+ 1.50 × 10
41
u
118
+ · · · + 1.99 × 10
38
a + 3.56 ×
10
40
, u
120
+ 8u
119
+ · · · + 8u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−99.6821u
119
− 752.933u
118
+ ··· − 1132.22u − 179.228
−63.5047u
119
− 465.406u
118
+ ··· − 610.082u − 92.8790
a
7
=
−87.8357u
119
− 646.404u
118
+ ··· − 906.733u − 143.815
−72.6685u
119
− 538.693u
118
+ ··· − 759.203u − 119.616
a
3
=
−58.4140u
119
− 454.008u
118
+ ··· − 741.967u − 116.664
−11.7388u
119
− 99.1517u
118
+ ··· − 221.718u − 34.2318
a
11
=
u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
6
=
−142.741u
119
− 1051.82u
118
+ ··· − 1483.16u − 234.293
−79.4077u
119
− 581.716u
118
+ ··· − 788.076u − 124.403
a
5
=
−63.3338u
119
− 470.103u
118
+ ··· − 695.081u − 109.889
−79.4077u
119
− 581.716u
118
+ ··· − 788.076u − 124.403
a
2
=
−101.184u
119
− 771.740u
118
+ ··· − 1234.87u − 197.448
−73.1735u
119
− 538.032u
118
+ ··· − 737.816u − 115.113
(ii) Obstruction class = −1
(iii) Cusp Shapes = 155.044u
119
+ 1104.19u
118
+ ··· + 1214.15u + 168.050
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
+ 57u
119
+ ··· + 451u + 1
c
2
, c
4
u
120
− 11u
119
+ ··· + 27u − 1
c
3
, c
7
u
120
− 2u
119
+ ··· − 512u + 512
c
5
u
120
+ 3u
119
+ ··· − 3758933u − 444601
c
6
, c
10
u
120
+ 2u
119
+ ··· − 128u − 64
c
8
, c
12
u
120
− 8u
119
+ ··· − 8u + 1
c
9
u
120
− 42u
119
+ ··· − 106496u + 4096
c
11
u
120
+ 64u
119
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
+ 23y
119
+ ··· − 187035y + 1
c
2
, c
4
y
120
− 57y
119
+ ··· − 451y + 1
c
3
, c
7
y
120
− 60y
119
+ ··· − 11796480y + 262144
c
5
y
120
− 21y
119
+ ··· − 9546190035499y + 197670049201
c
6
, c
10
y
120
+ 42y
119
+ ··· + 106496y + 4096
c
8
, c
12
y
120
− 64y
119
+ ··· − 8y + 1
c
9
y
120
+ 62y
119
+ ··· − 511705088y + 16777216
c
11
y
120
− 8y
119
+ ··· − 64y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781703 + 0.626996I
a = 2.53481 − 0.75078I
b = −0.897256 − 0.066842I
1.45619 + 2.43204I 0
u = −0.781703 − 0.626996I
a = 2.53481 + 0.75078I
b = −0.897256 + 0.066842I
1.45619 − 2.43204I 0
u = −0.688922 + 0.732659I
a = 1.61210 − 0.53654I
b = −1.277420 + 0.530341I
6.62514 − 5.23780I 0
u = −0.688922 − 0.732659I
a = 1.61210 + 0.53654I
b = −1.277420 − 0.530341I
6.62514 + 5.23780I 0
u = −0.739899 + 0.655965I
a = 0.767226 + 0.255470I
b = −0.164900 − 1.010320I
3.04826 + 0.29752I 0
u = −0.739899 − 0.655965I
a = 0.767226 − 0.255470I
b = −0.164900 + 1.010320I
3.04826 − 0.29752I 0
u = −0.733582 + 0.717890I
a = −1.83320 + 0.64066I
b = 1.305000 − 0.285363I
8.21310 + 0.50687I 0
u = −0.733582 − 0.717890I
a = −1.83320 − 0.64066I
b = 1.305000 + 0.285363I
8.21310 − 0.50687I 0
u = 0.930786 + 0.465334I
a = −1.02154 − 1.67472I
b = 1.180540 + 0.406202I
0.64675 + 2.54597I 0
u = 0.930786 − 0.465334I
a = −1.02154 + 1.67472I
b = 1.180540 − 0.406202I
0.64675 − 2.54597I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819870 + 0.648210I
a = −0.568752 − 0.480301I
b = −0.257485 + 1.034380I
2.81901 + 4.71117I 0
u = −0.819870 − 0.648210I
a = −0.568752 + 0.480301I
b = −0.257485 − 1.034380I
2.81901 − 4.71117I 0
u = 1.072720 + 0.077721I
a = −0.20436 − 2.27899I
b = −0.211326 − 0.578062I
−3.19317 − 0.58424I 0
u = 1.072720 − 0.077721I
a = −0.20436 + 2.27899I
b = −0.211326 + 0.578062I
−3.19317 + 0.58424I 0
u = −0.226064 + 0.885039I
a = 1.57130 + 0.52144I
b = −1.221930 + 0.677956I
2.10205 − 12.84790I 0
u = −0.226064 − 0.885039I
a = 1.57130 − 0.52144I
b = −1.221930 − 0.677956I
2.10205 + 12.84790I 0
u = −0.841471 + 0.691793I
a = −2.07690 + 1.04697I
b = 1.296310 + 0.355054I
7.89915 + 4.80277I 0
u = −0.841471 − 0.691793I
a = −2.07690 − 1.04697I
b = 1.296310 − 0.355054I
7.89915 − 4.80277I 0
u = −0.248169 + 0.867541I
a = −1.72098 − 0.45454I
b = 1.237400 − 0.490795I
4.40266 − 7.18738I 0
u = −0.248169 − 0.867541I
a = −1.72098 + 0.45454I
b = 1.237400 + 0.490795I
4.40266 + 7.18738I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798069 + 0.417778I
a = −0.028492 − 0.471920I
b = −0.661694 − 0.043069I
1.21358 + 1.83340I 0
u = −0.798069 − 0.417778I
a = −0.028492 + 0.471920I
b = −0.661694 + 0.043069I
1.21358 − 1.83340I 0
u = 1.004720 + 0.468278I
a = 1.28653 + 1.75341I
b = −1.221750 − 0.109820I
1.69311 − 2.74237I 0
u = 1.004720 − 0.468278I
a = 1.28653 − 1.75341I
b = −1.221750 + 0.109820I
1.69311 + 2.74237I 0
u = −0.878883 + 0.685866I
a = 2.04246 − 1.14516I
b = −1.272340 − 0.584117I
6.07322 + 10.56780I 0
u = −0.878883 − 0.685866I
a = 2.04246 + 1.14516I
b = −1.272340 + 0.584117I
6.07322 − 10.56780I 0
u = −0.344653 + 0.812462I
a = −1.85816 − 0.05813I
b = 1.296950 + 0.114963I
6.09868 − 3.26636I 0
u = −0.344653 − 0.812462I
a = −1.85816 + 0.05813I
b = 1.296950 − 0.114963I
6.09868 + 3.26636I 0
u = −0.401546 + 0.783989I
a = 1.75354 − 0.06110I
b = −1.259800 − 0.384650I
5.11752 + 2.33858I 0
u = −0.401546 − 0.783989I
a = 1.75354 + 0.06110I
b = −1.259800 + 0.384650I
5.11752 − 2.33858I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233066 + 0.838650I
a = 0.082248 + 0.246084I
b = −0.431383 − 1.042700I
−0.41671 − 6.60155I 0
u = −0.233066 − 0.838650I
a = 0.082248 − 0.246084I
b = −0.431383 + 1.042700I
−0.41671 + 6.60155I 0
u = 0.863965
a = −0.644795
b = 0.219021
−1.25564 0
u = −1.082180 + 0.408010I
a = −0.060771 + 0.358868I
b = −1.056880 + 0.541010I
−0.617111 + 1.136830I 0
u = −1.082180 − 0.408010I
a = −0.060771 − 0.358868I
b = −1.056880 − 0.541010I
−0.617111 − 1.136830I 0
u = −0.228884 + 0.809806I
a = 2.14403 + 0.63084I
b = −0.913467 + 0.317981I
−1.37934 − 4.06817I 0
u = −0.228884 − 0.809806I
a = 2.14403 − 0.63084I
b = −0.913467 − 0.317981I
−1.37934 + 4.06817I 0
u = 1.091890 + 0.407398I
a = −1.225800 − 0.382164I
b = −0.106806 − 0.841935I
−3.25950 − 1.43414I 0
u = 1.091890 − 0.407398I
a = −1.225800 + 0.382164I
b = −0.106806 + 0.841935I
−3.25950 + 1.43414I 0
u = −1.114220 + 0.383038I
a = 0.298421 − 0.602605I
b = 1.117930 − 0.678993I
−3.13753 − 4.01738I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114220 − 0.383038I
a = 0.298421 + 0.602605I
b = 1.117930 + 0.678993I
−3.13753 + 4.01738I 0
u = −0.114192 + 0.811962I
a = 0.195578 + 0.002860I
b = −0.774547 − 0.295093I
−1.84565 − 1.28021I 0
u = −0.114192 − 0.811962I
a = 0.195578 − 0.002860I
b = −0.774547 + 0.295093I
−1.84565 + 1.28021I 0
u = −0.263583 + 0.772995I
a = 0.048817 − 0.164759I
b = 0.062093 + 0.937483I
0.77417 − 2.19825I 0
u = −0.263583 − 0.772995I
a = 0.048817 + 0.164759I
b = 0.062093 − 0.937483I
0.77417 + 2.19825I 0
u = 1.145450 + 0.314699I
a = −0.630962 − 1.037490I
b = 0.172083 − 0.746812I
−3.47727 − 0.99083I 0
u = 1.145450 − 0.314699I
a = −0.630962 + 1.037490I
b = 0.172083 + 0.746812I
−3.47727 + 0.99083I 0
u = −1.108160 + 0.433990I
a = −0.355791 + 1.337260I
b = 0.570690 + 0.939425I
−4.90498 + 1.93971I 0
u = −1.108160 − 0.433990I
a = −0.355791 − 1.337260I
b = 0.570690 − 0.939425I
−4.90498 − 1.93971I 0
u = 1.118830 + 0.445202I
a = −1.95584 − 2.05447I
b = 0.869061 − 0.363739I
−5.50041 − 3.10765I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.118830 − 0.445202I
a = −1.95584 + 2.05447I
b = 0.869061 + 0.363739I
−5.50041 + 3.10765I 0
u = −1.119840 + 0.453707I
a = −0.521942 − 0.703698I
b = 0.849724 − 0.535024I
−5.43931 + 4.53491I 0
u = −1.119840 − 0.453707I
a = −0.521942 + 0.703698I
b = 0.849724 + 0.535024I
−5.43931 − 4.53491I 0
u = −0.777873 + 0.136267I
a = 0.441442 + 1.221480I
b = 1.019780 + 0.579374I
−1.06043 + 6.07967I 0
u = −0.777873 − 0.136267I
a = 0.441442 − 1.221480I
b = 1.019780 − 0.579374I
−1.06043 − 6.07967I 0
u = 1.116780 + 0.468489I
a = 1.380320 − 0.108317I
b = 0.451699 + 1.005900I
−4.64482 − 5.60149I 0
u = 1.116780 − 0.468489I
a = 1.380320 + 0.108317I
b = 0.451699 − 1.005900I
−4.64482 + 5.60149I 0
u = 0.617737 + 0.488236I
a = −2.91600 − 0.23481I
b = 1.193780 − 0.512097I
1.56344 − 6.54073I 0
u = 0.617737 − 0.488236I
a = −2.91600 + 0.23481I
b = 1.193780 + 0.512097I
1.56344 + 6.54073I 0
u = 1.108140 + 0.494518I
a = 1.60623 + 2.13884I
b = −1.200220 + 0.485456I
0.04434 − 6.17641I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.108140 − 0.494518I
a = 1.60623 − 2.13884I
b = −1.200220 − 0.485456I
0.04434 + 6.17641I 0
u = −1.121190 + 0.486520I
a = 0.532816 − 0.923881I
b = −0.373734 − 0.813785I
−2.64934 + 6.07508I 0
u = −1.121190 − 0.486520I
a = 0.532816 + 0.923881I
b = −0.373734 + 0.813785I
−2.64934 − 6.07508I 0
u = 1.224670 + 0.160747I
a = −0.065857 − 0.607777I
b = 1.163270 − 0.153221I
0.928537 + 0.392500I 0
u = 1.224670 − 0.160747I
a = −0.065857 + 0.607777I
b = 1.163270 + 0.153221I
0.928537 − 0.392500I 0
u = −1.090900 + 0.581156I
a = 0.667582 − 0.986969I
b = −1.279380 + 0.305378I
3.07488 + 2.77369I 0
u = −1.090900 − 0.581156I
a = 0.667582 + 0.986969I
b = −1.279380 − 0.305378I
3.07488 − 2.77369I 0
u = 1.130050 + 0.504249I
a = −1.59951 − 2.24133I
b = 1.200410 − 0.671678I
−2.26176 − 11.72400I 0
u = 1.130050 − 0.504249I
a = −1.59951 + 2.24133I
b = 1.200410 + 0.671678I
−2.26176 + 11.72400I 0
u = 1.240540 + 0.097824I
a = −0.114954 + 0.943587I
b = −1.158460 + 0.463847I
−0.36881 − 4.75701I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.240540 − 0.097824I
a = −0.114954 − 0.943587I
b = −1.158460 − 0.463847I
−0.36881 + 4.75701I 0
u = 1.205540 + 0.311353I
a = 0.787036 − 0.684011I
b = −0.825731 − 0.396066I
−5.80900 + 0.49213I 0
u = 1.205540 − 0.311353I
a = 0.787036 + 0.684011I
b = −0.825731 + 0.396066I
−5.80900 − 0.49213I 0
u = −0.014569 + 0.745385I
a = −0.132373 + 0.263093I
b = 0.852646 − 0.399361I
−2.28381 − 4.26886I −4.00000 + 7.23139I
u = −0.014569 − 0.745385I
a = −0.132373 − 0.263093I
b = 0.852646 + 0.399361I
−2.28381 + 4.26886I −4.00000 − 7.23139I
u = −0.676491 + 0.294104I
a = 0.092796 − 0.977502I
b = −0.769091 − 0.387965I
1.10898 + 1.72747I 2.65279 − 4.70086I
u = −0.676491 − 0.294104I
a = 0.092796 + 0.977502I
b = −0.769091 + 0.387965I
1.10898 − 1.72747I 2.65279 + 4.70086I
u = −1.179610 + 0.459342I
a = 0.185176 + 0.934182I
b = 0.800243 + 0.459866I
−5.61132 + 8.60634I 0
u = −1.179610 − 0.459342I
a = 0.185176 − 0.934182I
b = 0.800243 − 0.459866I
−5.61132 − 8.60634I 0
u = 1.230470 + 0.297887I
a = 0.198205 + 1.323250I
b = −0.459486 + 0.970631I
−5.03723 + 2.93363I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.230470 − 0.297887I
a = 0.198205 − 1.323250I
b = −0.459486 − 0.970631I
−5.03723 − 2.93363I 0
u = 1.191720 + 0.436251I
a = 0.796656 − 0.555080I
b = 0.789045 + 0.341843I
−5.77673 + 0.02106I 0
u = 1.191720 − 0.436251I
a = 0.796656 + 0.555080I
b = 0.789045 − 0.341843I
−5.77673 − 0.02106I 0
u = −1.129220 + 0.581695I
a = −0.96045 + 1.24949I
b = 1.324340 − 0.051025I
3.76758 + 8.45005I 0
u = −1.129220 − 0.581695I
a = −0.96045 − 1.24949I
b = 1.324340 + 0.051025I
3.76758 − 8.45005I 0
u = −1.153540 + 0.544827I
a = 0.973644 − 0.345979I
b = 0.137809 − 0.980748I
−1.84822 + 7.13621I 0
u = −1.153540 − 0.544827I
a = 0.973644 + 0.345979I
b = 0.137809 + 0.980748I
−1.84822 − 7.13621I 0
u = 1.227000 + 0.386133I
a = −0.294669 + 0.951287I
b = −0.808514 + 0.369592I
−5.89085 − 2.84747I 0
u = 1.227000 − 0.386133I
a = −0.294669 − 0.951287I
b = −0.808514 − 0.369592I
−5.89085 + 2.84747I 0
u = 1.257270 + 0.278547I
a = −0.004685 + 0.408350I
b = 1.171660 + 0.468968I
−0.45388 + 3.46501I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.257270 − 0.278547I
a = −0.004685 − 0.408350I
b = 1.171660 − 0.468968I
−0.45388 − 3.46501I 0
u = −1.172770 + 0.546681I
a = 1.68702 − 1.69167I
b = −0.961413 − 0.359816I
−4.16973 + 9.09296I 0
u = −1.172770 − 0.546681I
a = 1.68702 + 1.69167I
b = −0.961413 + 0.359816I
−4.16973 − 9.09296I 0
u = −1.196940 + 0.506293I
a = −0.643195 − 0.390538I
b = −0.714462 + 0.313692I
−5.03212 + 6.08894I 0
u = −1.196940 − 0.506293I
a = −0.643195 + 0.390538I
b = −0.714462 − 0.313692I
−5.03212 − 6.08894I 0
u = 0.520939 + 0.466359I
a = 3.01766 + 0.01392I
b = −1.184520 + 0.244481I
3.11618 − 1.21036I 0.73938 + 2.05412I
u = 0.520939 − 0.466359I
a = 3.01766 − 0.01392I
b = −1.184520 − 0.244481I
3.11618 + 1.21036I 0.73938 − 2.05412I
u = −1.180790 + 0.555828I
a = −1.122070 + 0.075223I
b = −0.466595 + 1.068750I
−3.23739 + 11.73660I 0
u = −1.180790 − 0.555828I
a = −1.122070 − 0.075223I
b = −0.466595 − 1.068750I
−3.23739 − 11.73660I 0
u = 1.274470 + 0.300341I
a = −0.191230 − 0.651809I
b = −1.185770 − 0.660462I
−2.72898 + 8.92074I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.274470 − 0.300341I
a = −0.191230 + 0.651809I
b = −1.185770 + 0.660462I
−2.72898 − 8.92074I 0
u = −1.186380 + 0.569612I
a = −1.30423 + 1.84761I
b = 1.240130 + 0.529876I
1.59168 + 12.45610I 0
u = −1.186380 − 0.569612I
a = −1.30423 − 1.84761I
b = 1.240130 − 0.529876I
1.59168 − 12.45610I 0
u = 0.218013 + 0.644463I
a = −2.18699 + 0.73008I
b = 1.176600 + 0.628728I
0.32142 + 7.26034I −3.12276 − 4.25340I
u = 0.218013 − 0.644463I
a = −2.18699 − 0.73008I
b = 1.176600 − 0.628728I
0.32142 − 7.26034I −3.12276 + 4.25340I
u = −1.199900 + 0.566803I
a = 1.29789 − 1.99136I
b = −1.219960 − 0.702540I
−0.8252 + 18.1477I 0
u = −1.199900 − 0.566803I
a = 1.29789 + 1.99136I
b = −1.219960 + 0.702540I
−0.8252 − 18.1477I 0
u = −0.187391 + 0.606350I
a = −0.0996893 + 0.0375649I
b = −0.332098 + 0.642698I
−0.05579 − 1.79813I −0.85726 + 4.29000I
u = −0.187391 − 0.606350I
a = −0.0996893 − 0.0375649I
b = −0.332098 − 0.642698I
−0.05579 + 1.79813I −0.85726 − 4.29000I
u = 0.632989
a = −4.83215
b = 0.540597
−2.53994 3.84450
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556173 + 0.283448I
a = −0.385281 − 1.342290I
b = 0.228525 + 0.822863I
−1.42904 − 1.60232I −4.26980 + 4.78073I
u = 0.556173 − 0.283448I
a = −0.385281 + 1.342290I
b = 0.228525 − 0.822863I
−1.42904 + 1.60232I −4.26980 − 4.78073I
u = 0.254734 + 0.567111I
a = 2.51572 − 0.73225I
b = −1.154150 − 0.407412I
2.43994 + 1.89866I 0.169019 − 0.013106I
u = 0.254734 − 0.567111I
a = 2.51572 + 0.73225I
b = −1.154150 + 0.407412I
2.43994 − 1.89866I 0.169019 + 0.013106I
u = −0.561395 + 0.088207I
a = 0.20179 − 1.71648I
b = 0.589833 − 0.700153I
−2.37909 + 1.13832I −2.91664 − 1.12450I
u = −0.561395 − 0.088207I
a = 0.20179 + 1.71648I
b = 0.589833 + 0.700153I
−2.37909 − 1.13832I −2.91664 + 1.12450I
u = 0.128372 + 0.511693I
a = 0.389966 + 0.703377I
b = 0.431553 − 0.892472I
−2.01742 + 1.58305I −5.13335 − 1.24333I
u = 0.128372 − 0.511693I
a = 0.389966 − 0.703377I
b = 0.431553 + 0.892472I
−2.01742 − 1.58305I −5.13335 + 1.24333I
u = −0.019560 + 0.524337I
a = −2.28586 + 1.65876I
b = 0.713656 + 0.450896I
−2.64124 − 0.66798I −4.60713 − 0.98427I
u = −0.019560 − 0.524337I
a = −2.28586 − 1.65876I
b = 0.713656 − 0.450896I
−2.64124 + 0.66798I −4.60713 + 0.98427I
16
II. I
u
2
= hb, u
8
+ 2u
7
− u
6
− 4u
5
− u
4
+ 3u
3
+ 3u
2
+ a + 2u, u
9
+ u
8
− 2u
7
−
3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−u
8
− 2u
7
+ u
6
+ 4u
5
+ u
4
− 3u
3
− 3u
2
− 2u
0
a
7
=
1
0
a
3
=
−u
8
− 2u
7
+ u
6
+ 4u
5
+ u
4
− 3u
3
− 3u
2
− 2u
0
a
11
=
u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
6
=
u
3
u
3
− u
a
5
=
u
u
3
− u
a
2
=
−u
8
− 2u
7
+ u
6
+ 4u
5
+ u
4
− 3u
3
− 3u
2
− 3u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
8
− 9u
7
+ 17u
5
+ 12u
4
− 11u
3
− 15u
2
− 12u − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
8
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
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 1.004430 − 0.297869I
b = 0
0.13850 + 2.09337I −5.16894 − 4.06115I
u = −0.772920 − 0.510351I
a = 1.004430 + 0.297869I
b = 0
0.13850 − 2.09337I −5.16894 + 4.06115I
u = 0.825933
a = −3.80937
b = 0
−2.84338 −27.2330
u = 1.173910 + 0.391555I
a = −0.070080 − 0.850995I
b = 0
−6.01628 − 1.33617I −9.21174 + 0.80685I
u = 1.173910 − 0.391555I
a = −0.070080 + 0.850995I
b = 0
−6.01628 + 1.33617I −9.21174 − 0.80685I
u = −0.141484 + 0.739668I
a = 0.275254 + 0.816341I
b = 0
−2.26187 − 2.45442I −4.66498 + 3.27944I
u = −0.141484 − 0.739668I
a = 0.275254 − 0.816341I
b = 0
−2.26187 + 2.45442I −4.66498 − 3.27944I
u = −1.172470 + 0.500383I
a = 0.195086 − 0.635552I
b = 0
−5.24306 + 7.08493I −7.33806 − 6.93476I
u = −1.172470 − 0.500383I
a = 0.195086 + 0.635552I
b = 0
−5.24306 − 7.08493I −7.33806 + 6.93476I
20
III. I
u
3
= h2a
5
− 2a
4
+ 7a
3
− 5a
2
+ 3b + a − 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
4
=
a
−
2
3
a
5
+
2
3
a
4
+ ··· −
1
3
a +
4
3
a
7
=
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
a
3
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
−
1
3
a
5
+
1
3
a
4
+ ··· −
5
3
a +
2
3
a
11
=
1
1
a
10
=
1
1
a
6
=
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
a
5
=
0
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
a
2
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
a
5
+ 3a
3
+ 2a
2
+ a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
5
+ a
4
− 12a
3
− 4a − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
, c
9
, c
10
u
6
c
8
, c
11
(u − 1)
6
c
12
(u + 1)
6
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
, c
9
, c
10
y
6
c
8
, c
11
, c
12
(y −1)
6
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.341164 + 0.940004I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −8.89162 + 3.92918I
u = 1.00000
a = −0.341164 − 0.940004I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −8.89162 − 3.92918I
u = 1.00000
a = 0.084211 + 0.566250I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −3.44826 − 0.47256I
u = 1.00000
a = 0.084211 − 0.566250I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −3.44826 + 0.47256I
u = 1.00000
a = 0.25695 + 1.72779I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −13.66012 − 2.42665I
u = 1.00000
a = 0.25695 − 1.72779I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −13.66012 + 2.42665I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
120
+ 57u
119
+ ··· + 451u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)(u
120
− 11u
119
+ ··· + 27u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)(u
120
− 2u
119
+ ··· − 512u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)(u
120
− 11u
119
+ ··· + 27u − 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
120
+ 3u
119
+ ··· − 3758933u − 444601)
c
6
u
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
120
+ 2u
119
+ ··· − 128u − 64)
c
7
u
9
(u
6
+ u
5
+ ··· + u + 1)(u
120
− 2u
119
+ ··· − 512u + 512)
c
8
(u − 1)
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
120
− 8u
119
+ ··· − 8u + 1)
c
9
u
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
120
− 42u
119
+ ··· − 106496u + 4096)
c
10
u
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
120
+ 2u
119
+ ··· − 128u − 64)
c
11
(u − 1)
6
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
120
+ 64u
119
+ ··· + 8u + 1)
c
12
(u + 1)
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
120
− 8u
119
+ ··· − 8u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
120
+ 23y
119
+ ··· − 187035y + 1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
120
− 57y
119
+ ··· − 451y + 1)
c
3
, c
7
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
120
− 60y
119
+ ··· − 11796480y + 262144)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
120
− 21y
119
+ ··· − 9546190035499y + 197670049201)
c
6
, c
10
y
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
120
+ 42y
119
+ ··· + 106496y + 4096)
c
8
, c
12
(y −1)
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
120
− 64y
119
+ ··· − 8y + 1)
c
9
y
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
120
+ 62y
119
+ ··· − 511705088y + 16777216)
c
11
(y −1)
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
120
− 8y
119
+ ··· − 64y + 1)
26
