12a
0273
(K12a
0273
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 5 11 1 12 7 10 4
Solving Sequence
7,10
11 8
4,12
1 3 9 5 6 2
c
10
c
7
c
11
c
12
c
3
c
9
c
4
c
6
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4.11782 × 10
111
u
107
− 1.72896 × 10
112
u
106
+ ··· + 2.70657 × 10
109
b + 5.15017 × 10
111
,
− 9.18604 × 10
110
u
107
+ 3.85195 × 10
111
u
106
+ ··· + 1.35329 × 10
109
a − 1.19005 × 10
111
,
u
108
− 5u
107
+ ··· − 4u − 1i
I
u
2
= hb
3
− b
2
+ 2b − 1, a, u − 1i
I
u
3
= hb, a − u − 1, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 114 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
= h4.12 × 10
111
u
107
− 1.73 × 10
112
u
106
+ · · · + 2.71 × 10
109
b + 5.15 ×
10
111
, −9.19 × 10
110
u
107
+ 3.85 × 10
111
u
106
+ · · · + 1.35 × 10
109
a − 1.19 ×
10
111
, u
108
− 5u
107
+ · · · − 4u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
4
=
67.8795u
107
− 284.637u
106
+ ··· + 399.400u + 87.9382
−152.142u
107
+ 638.802u
106
+ ··· − 1002.39u − 190.284
a
12
=
−u
2
+ 1
−u
2
a
1
=
6.01771u
107
− 24.3208u
106
+ ··· + 36.1965u + 2.67705
−5.22248u
107
+ 26.6576u
106
+ ··· − 58.8780u − 11.2402
a
3
=
−48.5904u
107
+ 202.556u
106
+ ··· − 350.712u − 55.3704
−190.876u
107
+ 800.455u
106
+ ··· − 1255.40u − 238.436
a
9
=
u
4
− u
2
+ 1
u
4
a
5
=
−48.3647u
107
+ 201.869u
106
+ ··· − 350.353u − 54.7783
−216.521u
107
+ 905.574u
106
+ ··· − 1403.65u − 267.141
a
6
=
16.3787u
107
− 67.4197u
106
+ ··· + 101.379u + 11.9449
46.8149u
107
− 192.264u
106
+ ··· + 275.135u + 52.5332
a
2
=
−12.7836u
107
+ 52.3966u
106
+ ··· − 69.4987u − 11.0363
−42.8242u
107
+ 178.501u
106
+ ··· − 268.820u − 51.4147
(ii) Obstruction class = −1
(iii) Cusp Shapes = −359.027u
107
+ 1549.26u
106
+ ··· − 2737.10u − 515.927
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
108
+ 35u
107
+ ··· + 146u + 1
c
2
, c
5
u
108
+ 5u
107
+ ··· + 4u − 1
c
3
u
108
+ u
107
+ ··· − 163u − 383
c
4
u
108
− u
107
+ ··· + 163u − 383
c
7
, c
10
u
108
− 5u
107
+ ··· − 4u − 1
c
8
u
108
− 10u
107
+ ··· − 12u + 8
c
9
, c
11
u
108
− 35u
107
+ ··· − 146u + 1
c
12
u
108
+ 10u
107
+ ··· + 12u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
y
108
+ 81y
107
+ ··· − 19954y + 1
c
2
, c
5
, c
7
c
10
y
108
− 35y
107
+ ··· − 146y + 1
c
3
, c
4
y
108
+ 123y
107
+ ··· − 3629833y + 146689
c
8
, c
12
y
108
+ 18y
107
+ ··· + 1904y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979728 + 0.166940I
a = −1.038070 + 0.480900I
b = 0.136075 + 0.665202I
3.19306 − 3.71797I 0
u = −0.979728 − 0.166940I
a = −1.038070 − 0.480900I
b = 0.136075 − 0.665202I
3.19306 + 3.71797I 0
u = −0.605005 + 0.787681I
a = 0.845635 − 0.095086I
b = 0.962946 + 0.612440I
−2.14715 − 1.03507I 0
u = −0.605005 − 0.787681I
a = 0.845635 + 0.095086I
b = 0.962946 − 0.612440I
−2.14715 + 1.03507I 0
u = 0.715108 + 0.670386I
a = 0.771317 + 0.384628I
b = 0.157147 − 1.104620I
2.14715 + 1.03507I 0
u = 0.715108 − 0.670386I
a = 0.771317 − 0.384628I
b = 0.157147 + 1.104620I
2.14715 − 1.03507I 0
u = −0.973353 + 0.047519I
a = −1.02470 − 1.12942I
b = −0.075717 − 1.064180I
7.14796 + 0.81738I 0
u = −0.973353 − 0.047519I
a = −1.02470 + 1.12942I
b = −0.075717 + 1.064180I
7.14796 − 0.81738I 0
u = −0.956601 + 0.099212I
a = 0.99426 + 1.23398I
b = 0.124520 + 1.135330I
6.35502 − 5.36585I 0
u = −0.956601 − 0.099212I
a = 0.99426 − 1.23398I
b = 0.124520 − 1.135330I
6.35502 + 5.36585I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745810 + 0.744346I
a = −1.027490 − 0.410866I
b = −0.451934 + 1.247910I
0.82383 − 4.62628I 0
u = 0.745810 − 0.744346I
a = −1.027490 + 0.410866I
b = −0.451934 − 1.247910I
0.82383 + 4.62628I 0
u = 0.850637 + 0.406962I
a = 0.080872 + 0.341351I
b = −0.238152 − 0.726384I
1.82900 + 1.35958I 0
u = 0.850637 − 0.406962I
a = 0.080872 − 0.341351I
b = −0.238152 + 0.726384I
1.82900 − 1.35958I 0
u = −1.019000 + 0.284607I
a = 0.769824 − 0.155699I
b = −0.374588 − 0.510091I
− 7.09355I 0
u = −1.019000 − 0.284607I
a = 0.769824 + 0.155699I
b = −0.374588 + 0.510091I
7.09355I 0
u = 0.862762 + 0.622752I
a = −1.58251 − 1.51375I
b = −2.86284 + 0.83647I
3.75903 − 0.77126I 0
u = 0.862762 − 0.622752I
a = −1.58251 + 1.51375I
b = −2.86284 − 0.83647I
3.75903 + 0.77126I 0
u = −0.616674 + 0.874327I
a = −0.865658 + 0.308655I
b = −1.042850 − 0.462236I
−2.85537 + 4.21466I 0
u = −0.616674 − 0.874327I
a = −0.865658 − 0.308655I
b = −1.042850 + 0.462236I
−2.85537 − 4.21466I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814404 + 0.714383I
a = 1.00553 + 2.14684I
b = −0.52002 + 1.34231I
− 4.57359I 0
u = −0.814404 − 0.714383I
a = 1.00553 − 2.14684I
b = −0.52002 − 1.34231I
4.57359I 0
u = 0.744550 + 0.799387I
a = −1.43674 − 1.59030I
b = −2.50978 − 0.05086I
−3.11037 − 2.87230I 0
u = 0.744550 − 0.799387I
a = −1.43674 + 1.59030I
b = −2.50978 + 0.05086I
−3.11037 + 2.87230I 0
u = 0.907254 + 0.638959I
a = 1.66458 + 1.44541I
b = 2.94097 − 0.92211I
3.93257 + 5.67737I 0
u = 0.907254 − 0.638959I
a = 1.66458 − 1.44541I
b = 2.94097 + 0.92211I
3.93257 − 5.67737I 0
u = −0.821570 + 0.746772I
a = −1.20102 − 2.36279I
b = 0.40213 − 1.66223I
−0.298325 + 0.873313I 0
u = −0.821570 − 0.746772I
a = −1.20102 + 2.36279I
b = 0.40213 + 1.66223I
−0.298325 − 0.873313I 0
u = 0.693031 + 0.877224I
a = −1.53841 − 1.50089I
b = −2.30877 − 0.13072I
− 6.29181I 0
u = 0.693031 − 0.877224I
a = −1.53841 + 1.50089I
b = −2.30877 + 0.13072I
6.29181I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.870551 + 0.703926I
a = −0.881042 + 0.605315I
b = 0.58910 + 2.04797I
−3.89287 + 2.70030I 0
u = 0.870551 − 0.703926I
a = −0.881042 − 0.605315I
b = 0.58910 − 2.04797I
−3.89287 − 2.70030I 0
u = −0.816700 + 0.769783I
a = 1.72760 − 0.26942I
b = 1.63286 + 0.89494I
−3.53829 − 1.78224I 0
u = −0.816700 − 0.769783I
a = 1.72760 + 0.26942I
b = 1.63286 − 0.89494I
−3.53829 + 1.78224I 0
u = 0.803722 + 0.787733I
a = 1.32736 + 1.65587I
b = 2.73483 + 0.18727I
−6.28442 + 1.49926I 0
u = 0.803722 − 0.787733I
a = 1.32736 − 1.65587I
b = 2.73483 − 0.18727I
−6.28442 − 1.49926I 0
u = 1.112550 + 0.201315I
a = 0.154894 − 0.326872I
b = 0.202520 + 0.144144I
0.629927 − 0.566671I 0
u = 1.112550 − 0.201315I
a = 0.154894 + 0.326872I
b = 0.202520 − 0.144144I
0.629927 + 0.566671I 0
u = 0.866946
a = 0.530489
b = −0.445872
1.43135 0
u = 0.700693 + 0.895805I
a = 1.54343 + 1.47096I
b = 2.30224 + 0.16065I
−1.06026 − 12.34350I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.700693 − 0.895805I
a = 1.54343 − 1.47096I
b = 2.30224 − 0.16065I
−1.06026 + 12.34350I 0
u = 0.752822 + 0.857130I
a = 1.43527 + 1.49045I
b = 2.41571 + 0.18143I
−7.40743 − 6.11835I 0
u = 0.752822 − 0.857130I
a = 1.43527 − 1.49045I
b = 2.41571 − 0.18143I
−7.40743 + 6.11835I 0
u = −1.126570 + 0.214725I
a = −0.564137 + 0.491665I
b = 0.450345 + 0.778573I
7.40743 − 6.11835I 0
u = −1.126570 − 0.214725I
a = −0.564137 − 0.491665I
b = 0.450345 − 0.778573I
7.40743 + 6.11835I 0
u = 0.107937 + 0.844817I
a = −0.365482 − 0.693695I
b = 0.131212 + 0.293224I
2.38418 + 8.65987I 0
u = 0.107937 − 0.844817I
a = −0.365482 + 0.693695I
b = 0.131212 − 0.293224I
2.38418 − 8.65987I 0
u = −0.912663 + 0.707599I
a = 2.08182 + 1.46268I
b = 0.95698 + 2.07662I
0.298325 − 0.873313I 0
u = −0.912663 − 0.707599I
a = 2.08182 − 1.46268I
b = 0.95698 − 2.07662I
0.298325 + 0.873313I 0
u = −0.878636 + 0.753546I
a = −2.34831 − 3.13274I
b = 0.00650 − 3.16279I
−4.37927 − 2.85474I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.878636 − 0.753546I
a = −2.34831 + 3.13274I
b = 0.00650 + 3.16279I
−4.37927 + 2.85474I 0
u = −0.752213 + 0.881864I
a = −1.149800 + 0.436361I
b = −1.329100 − 0.473314I
−7.14796 − 0.81738I 0
u = −0.752213 − 0.881864I
a = −1.149800 − 0.436361I
b = −1.329100 + 0.473314I
−7.14796 + 0.81738I 0
u = −1.140280 + 0.239475I
a = 0.499762 − 0.446388I
b = −0.505072 − 0.759246I
6.64063 − 12.17460I 0
u = −1.140280 − 0.239475I
a = 0.499762 + 0.446388I
b = −0.505072 + 0.759246I
6.64063 + 12.17460I 0
u = 0.829074 + 0.011014I
a = −0.07425 − 1.42512I
b = −0.16570 + 4.05652I
4.37927 + 2.85474I 0
u = 0.829074 − 0.011014I
a = −0.07425 + 1.42512I
b = −0.16570 − 4.05652I
4.37927 − 2.85474I 0
u = −0.918379 + 0.727605I
a = −2.14206 − 1.70389I
b = −0.85806 − 2.22807I
− 6.47878I 0
u = −0.918379 − 0.727605I
a = −2.14206 + 1.70389I
b = −0.85806 + 2.22807I
6.47878I 0
u = −0.819143 + 0.114490I
a = 1.78431 − 0.53842I
b = 0.292058 − 0.533870I
−0.629927 − 0.566671I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819143 − 0.114490I
a = 1.78431 + 0.53842I
b = 0.292058 + 0.533870I
−0.629927 + 0.566671I 0
u = 0.958471 + 0.677586I
a = 0.012558 − 0.529487I
b = −1.14801 − 1.14971I
2.85537 + 4.21466I 0
u = 0.958471 − 0.677586I
a = 0.012558 + 0.529487I
b = −1.14801 + 1.14971I
2.85537 − 4.21466I 0
u = 0.146172 + 0.809684I
a = 0.429990 + 0.687130I
b = −0.097622 − 0.338027I
3.11037 + 2.87230I 0
u = 0.146172 − 0.809684I
a = 0.429990 − 0.687130I
b = −0.097622 + 0.338027I
3.11037 − 2.87230I 0
u = −0.935562 + 0.738376I
a = −0.74515 + 1.49429I
b = −1.68440 + 0.26171I
−3.16513 − 3.92976I 0
u = −0.935562 − 0.738376I
a = −0.74515 − 1.49429I
b = −1.68440 − 0.26171I
−3.16513 + 3.92976I 0
u = 0.963977 + 0.711243I
a = 0.112037 + 0.707021I
b = 1.39808 + 1.15135I
1.48137 + 10.17620I 0
u = 0.963977 − 0.711243I
a = 0.112037 − 0.707021I
b = 1.39808 − 1.15135I
1.48137 − 10.17620I 0
u = 0.943219 + 0.748695I
a = −1.91135 − 1.20561I
b = −2.71010 + 1.24978I
−5.85299 + 4.29300I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943219 − 0.748695I
a = −1.91135 + 1.20561I
b = −2.71010 − 1.24978I
−5.85299 − 4.29300I 0
u = 1.138430 + 0.405967I
a = −0.245790 + 0.237091I
b = −0.558583 − 0.249422I
6.28442 + 1.49926I 0
u = 1.138430 − 0.405967I
a = −0.245790 − 0.237091I
b = −0.558583 + 0.249422I
6.28442 − 1.49926I 0
u = 1.165830 + 0.377480I
a = 0.253866 − 0.276152I
b = 0.523546 + 0.178040I
5.85299 − 4.29300I 0
u = 1.165830 − 0.377480I
a = 0.253866 + 0.276152I
b = 0.523546 − 0.178040I
5.85299 + 4.29300I 0
u = 0.982453 + 0.737148I
a = 1.81148 + 1.22461I
b = 2.71926 − 1.02344I
−2.38418 + 8.65987I 0
u = 0.982453 − 0.737148I
a = 1.81148 − 1.22461I
b = 2.71926 + 1.02344I
−2.38418 − 8.65987I 0
u = 1.228270 + 0.025249I
a = 0.023097 − 0.406949I
b = 0.0309378 − 0.0677333I
3.89287 + 2.70030I 0
u = 1.228270 − 0.025249I
a = 0.023097 + 0.406949I
b = 0.0309378 + 0.0677333I
3.89287 − 2.70030I 0
u = −0.873340 + 0.892543I
a = −1.209720 + 0.689510I
b = −1.55362 − 0.32280I
−3.93257 − 5.67737I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873340 − 0.892543I
a = −1.209720 − 0.689510I
b = −1.55362 + 0.32280I
−3.93257 + 5.67737I 0
u = 1.000250 + 0.769183I
a = −1.78545 − 1.18517I
b = −2.58944 + 0.94144I
−6.64063 + 12.17460I 0
u = 1.000250 − 0.769183I
a = −1.78545 + 1.18517I
b = −2.58944 − 0.94144I
−6.64063 − 12.17460I 0
u = −1.052770 + 0.702532I
a = −0.448401 + 0.782629I
b = −1.317170 − 0.072692I
−0.82383 − 4.62628I 0
u = −1.052770 − 0.702532I
a = −0.448401 − 0.782629I
b = −1.317170 + 0.072692I
−0.82383 + 4.62628I 0
u = −0.926658 + 0.863457I
a = 1.15989 − 0.81420I
b = 1.62405 + 0.23900I
−3.75903 − 0.77126I 0
u = −0.926658 − 0.863457I
a = 1.15989 + 0.81420I
b = 1.62405 − 0.23900I
−3.75903 + 0.77126I 0
u = 0.728160 + 0.046370I
a = −0.66850 − 1.61942I
b = −0.14823 + 2.49858I
0.189074I 0. + 28.3801I
u = 0.728160 − 0.046370I
a = −0.66850 + 1.61942I
b = −0.14823 − 2.49858I
− 0.189074I 0. − 28.3801I
u = −0.040621 + 0.727326I
a = −0.307045 − 0.417238I
b = 0.282641 + 0.401543I
−3.19306 + 3.71797I −7.99700 − 6.03379I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040621 − 0.727326I
a = −0.307045 + 0.417238I
b = 0.282641 − 0.401543I
−3.19306 − 3.71797I −7.99700 + 6.03379I
u = −1.008830 + 0.787104I
a = 0.809220 − 0.908283I
b = 1.53280 + 0.07933I
−6.35502 − 5.36585I 0
u = −1.008830 − 0.787104I
a = 0.809220 + 0.908283I
b = 1.53280 − 0.07933I
−6.35502 + 5.36585I 0
u = 1.036810 + 0.752906I
a = 1.76373 + 1.20388I
b = 2.68109 − 0.82580I
1.06026 + 12.34350I 0
u = 1.036810 − 0.752906I
a = 1.76373 − 1.20388I
b = 2.68109 + 0.82580I
1.06026 − 12.34350I 0
u = 1.042110 + 0.763618I
a = −1.76085 − 1.20027I
b = −2.65325 + 0.79823I
18.4856I 0
u = 1.042110 − 0.763618I
a = −1.76085 + 1.20027I
b = −2.65325 − 0.79823I
− 18.4856I 0
u = −1.070750 + 0.729666I
a = 0.557130 − 0.725560I
b = 1.369710 + 0.123145I
−1.48137 − 10.17620I 0
u = −1.070750 − 0.729666I
a = 0.557130 + 0.725560I
b = 1.369710 − 0.123145I
−1.48137 + 10.17620I 0
u = −0.389762 + 0.419664I
a = −0.003557 + 0.670504I
b = 0.383901 + 0.766173I
−1.82900 − 1.35958I −6.75012 + 4.20503I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.389762 − 0.419664I
a = −0.003557 − 0.670504I
b = 0.383901 − 0.766173I
−1.82900 + 1.35958I −6.75012 − 4.20503I
u = 0.081768 + 0.490352I
a = 0.807289 + 0.395788I
b = −0.204785 − 0.561810I
1.56023I 0. − 4.13499I
u = 0.081768 − 0.490352I
a = 0.807289 − 0.395788I
b = −0.204785 + 0.561810I
− 1.56023I 0. + 4.13499I
u = 0.289293 + 0.350302I
a = −1.33071 − 2.46775I
b = −1.131410 + 0.476487I
3.53829 − 1.78224I 0.68145 + 3.51053I
u = 0.289293 − 0.350302I
a = −1.33071 + 2.46775I
b = −1.131410 − 0.476487I
3.53829 + 1.78224I 0.68145 − 3.51053I
u = 0.156084 + 0.371239I
a = 1.74465 + 2.65310I
b = 1.025570 − 0.251004I
3.16513 + 3.92976I −0.15289 − 2.12894I
u = 0.156084 − 0.371239I
a = 1.74465 − 2.65310I
b = 1.025570 + 0.251004I
3.16513 − 3.92976I −0.15289 + 2.12894I
u = −0.0841052
a = 8.43911
b = 0.504757
−1.43135 −6.90500
15
II. I
u
2
= hb
3
− b
2
+ 2b − 1, a, u − 1i
(i) Arc colorings
a
7
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
8
=
1
0
a
4
=
0
b
a
12
=
0
−1
a
1
=
0
−1
a
3
=
b
b
a
9
=
1
1
a
5
=
b
2b
a
6
=
b
2
2b
2
+ 1
a
2
=
b
2
b
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7b
2
+ 5b − 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
, c
6
u
3
+ u
2
+ 2u + 1
c
5
u
3
− u
2
+ 1
c
7
, c
8
, c
9
(u + 1)
3
c
10
, c
11
(u − 1)
3
c
12
u
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
7
, c
8
, c
9
c
10
, c
11
(y −1)
3
c
12
y
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 0.215080 + 1.307140I
4.66906 − 2.82812I 7.71191 + 2.59975I
u = 1.00000
a = 0
b = 0.215080 − 1.307140I
4.66906 + 2.82812I 7.71191 − 2.59975I
u = 1.00000
a = 0
b = 0.569840
0.531480 −4.42380
19
III. I
u
3
= hb, a − u − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
u
2
+ u − 1
a
4
=
u + 1
0
a
12
=
−u
2
+ 1
−u
2
a
1
=
−u
2
− u
−u
2
a
3
=
u
2
+ u
u
2
− u
a
9
=
u
u
2
+ u − 1
a
5
=
u
2
+ u
u
2
− u
a
6
=
u
2
+ u
u
2
a
2
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
+ 7u − 2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
3
c
3
, c
4
, c
11
u
3
− u
2
+ 2u − 1
c
5
, c
6
(u + 1)
3
c
7
u
3
− u
2
+ 1
c
8
u
3
c
9
u
3
+ u
2
+ 2u + 1
c
10
u
3
+ u
2
− 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
12
(y −1)
3
c
3
, c
4
, c
9
c
11
y
3
+ 3y
2
+ 2y −1
c
7
, c
10
y
3
− y
2
+ 2y −1
c
8
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.122561 + 0.744862I
b = 0
−4.66906 − 2.82812I −7.71191 + 2.59975I
u = −0.877439 − 0.744862I
a = 0.122561 − 0.744862I
b = 0
−4.66906 + 2.82812I −7.71191 − 2.59975I
u = 0.754878
a = 1.75488
b = 0
−0.531480 4.42380
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)(u
108
+ 35u
107
+ ··· + 146u + 1)
c
2
((u − 1)
3
)(u
3
+ u
2
− 1)(u
108
+ 5u
107
+ ··· + 4u − 1)
c
3
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)(u
108
+ u
107
+ ··· − 163u − 383)
c
4
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)(u
108
− u
107
+ ··· + 163u − 383)
c
5
((u + 1)
3
)(u
3
− u
2
+ 1)(u
108
+ 5u
107
+ ··· + 4u − 1)
c
6
((u + 1)
3
)(u
3
+ u
2
+ 2u + 1)(u
108
+ 35u
107
+ ··· + 146u + 1)
c
7
((u + 1)
3
)(u
3
− u
2
+ 1)(u
108
− 5u
107
+ ··· − 4u − 1)
c
8
u
3
(u + 1)
3
(u
108
− 10u
107
+ ··· − 12u + 8)
c
9
((u + 1)
3
)(u
3
+ u
2
+ 2u + 1)(u
108
− 35u
107
+ ··· − 146u + 1)
c
10
((u − 1)
3
)(u
3
+ u
2
− 1)(u
108
− 5u
107
+ ··· − 4u − 1)
c
11
((u − 1)
3
)(u
3
− u
2
+ 2u − 1)(u
108
− 35u
107
+ ··· − 146u + 1)
c
12
u
3
(u − 1)
3
(u
108
+ 10u
107
+ ··· + 12u + 8)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
((y −1)
3
)(y
3
+ 3y
2
+ 2y −1)(y
108
+ 81y
107
+ ··· − 19954y + 1)
c
2
, c
5
, c
7
c
10
((y −1)
3
)(y
3
− y
2
+ 2y −1)(y
108
− 35y
107
+ ··· − 146y + 1)
c
3
, c
4
((y
3
+ 3y
2
+ 2y −1)
2
)(y
108
+ 123y
107
+ ··· − 3629833y + 146689)
c
8
, c
12
y
3
(y −1)
3
(y
108
+ 18y
107
+ ··· + 1904y + 64)
25
