12a
0220
(K12a
0220
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 10 2 12 1 11 5 4 8
Solving Sequence
7,12
8 1
4,9
5 3 2 6 11 10
c
7
c
12
c
8
c
4
c
3
c
1
c
6
c
11
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.49096 × 10
181
u
106
+ 9.13411 × 10
180
u
105
+ ··· + 5.06627 × 10
181
b − 7.23078 × 10
182
,
6.06637 × 10
182
u
106
− 1.74049 × 10
183
u
105
+ ··· + 1.31723 × 10
183
a − 2.71243 × 10
184
,
u
107
− 3u
106
+ ··· − 111u − 13i
I
u
2
= hb
2
− b + 1, a
4
− 2a
2
+ 2, u + 1i
I
u
3
= hb
2
+ b + 1, a
3
, u − 1i
* 3 irreducible components of dim
C
= 0, with total 121 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−1.49 × 10
181
u
106
+ 9.13 × 10
180
u
105
+ · · · + 5.07 × 10
181
b − 7.23 ×
10
182
, 6.07 × 10
182
u
106
− 1.74 × 10
183
u
105
+ · · · + 1.32 × 10
183
a − 2.71 ×
10
184
, u
107
− 3u
106
+ · · · − 111u − 13i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−0.460540u
106
+ 1.32132u
105
+ ··· + 177.538u + 20.5919
0.294291u
106
− 0.180293u
105
+ ··· + 132.884u + 14.2724
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
−0.339961u
106
+ 1.59337u
105
+ ··· + 324.599u + 34.4376
0.183891u
106
− 0.141636u
105
+ ··· + 110.762u + 12.7655
a
3
=
−0.166249u
106
+ 1.14103u
105
+ ··· + 310.421u + 34.8643
0.294291u
106
− 0.180293u
105
+ ··· + 132.884u + 14.2724
a
2
=
−0.813218u
106
+ 2.47693u
105
+ ··· + 392.711u + 41.8323
−0.137167u
106
+ 0.176247u
105
+ ··· − 14.8599u − 0.292318
a
6
=
0.455592u
106
− 2.01489u
105
+ ··· + 4.63244u + 13.1807
0.102062u
106
+ 0.00933752u
105
+ ··· − 49.6066u − 10.5866
a
11
=
−0.832717u
106
+ 1.95875u
105
+ ··· + 267.318u + 30.0119
−0.325817u
106
+ 0.776598u
105
+ ··· + 23.5117u + 1.24472
a
10
=
−0.816162u
106
+ 2.12713u
105
+ ··· + 317.788u + 27.2416
0.127653u
106
− 0.129996u
105
+ ··· − 43.6773u − 7.17967
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.703236u
106
+ 1.11367u
105
+ ··· + 8.19553u + 10.4291
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
107
+ 54u
106
+ ··· − 8u − 1
c
2
, c
6
u
107
− 2u
106
+ ··· + 2u − 1
c
3
u
107
+ 2u
106
+ ··· − 188610u − 36209
c
4
u
107
+ u
106
+ ··· + 3876u + 3764
c
5
, c
10
u
107
− u
106
+ ··· + 4u + 4
c
7
, c
8
, c
12
u
107
+ 3u
106
+ ··· − 111u + 13
c
9
u
107
− 51u
106
+ ··· − 80u + 16
c
11
u
107
− 5u
106
+ ··· − 692004u + 563884
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
107
+ 6y
106
+ ··· + 40y −1
c
2
, c
6
y
107
+ 54y
106
+ ··· − 8y −1
c
3
y
107
− 42y
106
+ ··· + 2264493656y −1311091681
c
4
y
107
− 21y
106
+ ··· + 424757360y −14167696
c
5
, c
10
y
107
+ 51y
106
+ ··· − 80y −16
c
7
, c
8
, c
12
y
107
− 103y
106
+ ··· − 9207y −169
c
9
y
107
+ 15y
106
+ ··· − 2304y −256
c
11
y
107
+ 39y
106
+ ··· − 10755598905296y −317965165456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904262 + 0.431584I
a = −0.133296 − 0.339278I
b = 0.530938 − 0.189035I
−1.99885 + 5.17052I 0
u = −0.904262 − 0.431584I
a = −0.133296 + 0.339278I
b = 0.530938 + 0.189035I
−1.99885 − 5.17052I 0
u = 0.787760 + 0.643206I
a = 0.871626 + 0.708841I
b = −1.096750 + 0.335060I
−4.40852 + 2.42869I 0
u = 0.787760 − 0.643206I
a = 0.871626 − 0.708841I
b = −1.096750 − 0.335060I
−4.40852 − 2.42869I 0
u = −0.956946 + 0.360565I
a = −0.597535 + 0.227282I
b = 0.958606 + 0.767416I
−0.373093 − 0.971380I 0
u = −0.956946 − 0.360565I
a = −0.597535 − 0.227282I
b = 0.958606 − 0.767416I
−0.373093 + 0.971380I 0
u = −0.358282 + 0.896448I
a = −1.10747 + 1.21913I
b = 1.41980 − 0.65124I
−1.00079 + 12.66400I 0
u = −0.358282 − 0.896448I
a = −1.10747 − 1.21913I
b = 1.41980 + 0.65124I
−1.00079 − 12.66400I 0
u = 0.992483 + 0.309368I
a = −0.160962 − 0.486626I
b = −0.269567 − 0.291149I
−3.00656 − 1.10116I 0
u = 0.992483 − 0.309368I
a = −0.160962 + 0.486626I
b = −0.269567 + 0.291149I
−3.00656 + 1.10116I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.608114 + 0.728544I
a = −0.691648 + 0.449361I
b = 1.128540 − 0.315477I
−2.81110 + 0.44680I 0
u = −0.608114 − 0.728544I
a = −0.691648 − 0.449361I
b = 1.128540 + 0.315477I
−2.81110 − 0.44680I 0
u = 1.033090 + 0.207124I
a = −0.748487 − 0.391269I
b = 0.001488 − 0.410585I
−1.89971 − 0.44446I 0
u = 1.033090 − 0.207124I
a = −0.748487 + 0.391269I
b = 0.001488 + 0.410585I
−1.89971 + 0.44446I 0
u = 0.391004 + 0.857866I
a = 0.99548 + 1.11660I
b = −1.36178 − 0.60152I
−3.15539 − 7.60366I 0
u = 0.391004 − 0.857866I
a = 0.99548 − 1.11660I
b = −1.36178 + 0.60152I
−3.15539 + 7.60366I 0
u = −0.541436 + 0.770509I
a = −0.741344 + 1.076260I
b = 0.858958 − 0.011904I
−2.59503 + 4.68959I 0
u = −0.541436 − 0.770509I
a = −0.741344 − 1.076260I
b = 0.858958 + 0.011904I
−2.59503 − 4.68959I 0
u = 0.606025 + 0.712743I
a = 0.766219 + 0.966722I
b = −0.916895 + 0.108302I
−4.40673 + 0.22528I 0
u = 0.606025 − 0.712743I
a = 0.766219 − 0.966722I
b = −0.916895 − 0.108302I
−4.40673 − 0.22528I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.023130 + 0.308756I
a = 0.835122 + 0.060413I
b = −0.362952 − 0.673846I
1.30429 + 3.26731I 0
u = −1.023130 − 0.308756I
a = 0.835122 − 0.060413I
b = −0.362952 + 0.673846I
1.30429 − 3.26731I 0
u = 0.517016 + 0.772169I
a = 0.775725 + 0.721111I
b = −1.220000 − 0.429494I
−4.10761 − 5.28481I 0
u = 0.517016 − 0.772169I
a = 0.775725 − 0.721111I
b = −1.220000 + 0.429494I
−4.10761 + 5.28481I 0
u = −0.873419 + 0.646269I
a = −0.961755 + 0.599798I
b = 1.201530 + 0.414908I
−2.58534 − 7.32575I 0
u = −0.873419 − 0.646269I
a = −0.961755 − 0.599798I
b = 1.201530 − 0.414908I
−2.58534 + 7.32575I 0
u = −1.073390 + 0.173489I
a = 1.185970 − 0.495544I
b = 0.025415 − 0.404365I
0.62750 − 3.83015I 0
u = −1.073390 − 0.173489I
a = 1.185970 + 0.495544I
b = 0.025415 + 0.404365I
0.62750 + 3.83015I 0
u = −0.347205 + 0.789149I
a = 0.98779 − 1.36315I
b = −0.998853 + 0.689661I
1.55865 + 7.81274I 0
u = −0.347205 − 0.789149I
a = 0.98779 + 1.36315I
b = −0.998853 − 0.689661I
1.55865 − 7.81274I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697681 + 0.486866I
a = 1.017260 − 0.382052I
b = −0.787593 − 0.084239I
0.26585 − 3.31149I 0
u = −0.697681 − 0.486866I
a = 1.017260 + 0.382052I
b = −0.787593 + 0.084239I
0.26585 + 3.31149I 0
u = −0.305416 + 0.776614I
a = −0.73060 + 1.37269I
b = 1.24517 − 0.72111I
1.49738 + 5.20503I 0
u = −0.305416 − 0.776614I
a = −0.73060 − 1.37269I
b = 1.24517 + 0.72111I
1.49738 − 5.20503I 0
u = 0.366231 + 0.724436I
a = −0.89880 − 1.21010I
b = 0.918174 + 0.589822I
−0.58468 − 2.93122I 0
u = 0.366231 − 0.724436I
a = −0.89880 + 1.21010I
b = 0.918174 − 0.589822I
−0.58468 + 2.93122I 0
u = −1.193830 + 0.133951I
a = 1.186440 + 0.254501I
b = 0.478845 − 0.410517I
1.09290 + 3.87383I 0
u = −1.193830 − 0.133951I
a = 1.186440 − 0.254501I
b = 0.478845 + 0.410517I
1.09290 − 3.87383I 0
u = 1.201360 + 0.183444I
a = 0.419710 − 0.338240I
b = −0.79913 + 1.21442I
−0.18627 + 3.28365I 0
u = 1.201360 − 0.183444I
a = 0.419710 + 0.338240I
b = −0.79913 − 1.21442I
−0.18627 − 3.28365I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24303
a = −0.920747
b = −0.643030
−2.16232 0
u = −0.222910 + 0.706813I
a = 0.57898 − 1.45300I
b = −0.731318 + 0.783769I
3.66702 + 0.52581I 4.89543 − 0.81246I
u = −0.222910 − 0.706813I
a = 0.57898 + 1.45300I
b = −0.731318 − 0.783769I
3.66702 − 0.52581I 4.89543 + 0.81246I
u = 0.504839 + 0.540212I
a = −0.851823 − 0.684157I
b = 0.771656 + 0.223252I
−1.33042 − 1.16536I −4.57238 + 3.59666I
u = 0.504839 − 0.540212I
a = −0.851823 + 0.684157I
b = 0.771656 − 0.223252I
−1.33042 + 1.16536I −4.57238 − 3.59666I
u = 1.245520 + 0.201441I
a = −0.458006 + 0.563615I
b = 0.050412 − 1.311980I
0.58850 − 1.75903I 0
u = 1.245520 − 0.201441I
a = −0.458006 − 0.563615I
b = 0.050412 + 1.311980I
0.58850 + 1.75903I 0
u = −1.346650 + 0.022218I
a = −0.127155 − 0.744802I
b = 0.49820 + 1.55717I
−3.79047 − 1.76476I 0
u = −1.346650 − 0.022218I
a = −0.127155 + 0.744802I
b = 0.49820 − 1.55717I
−3.79047 + 1.76476I 0
u = −1.349610 + 0.062394I
a = −1.345650 + 0.408342I
b = −1.030110 + 0.398339I
−1.64321 − 0.63614I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.349610 − 0.062394I
a = −1.345650 − 0.408342I
b = −1.030110 − 0.398339I
−1.64321 + 0.63614I 0
u = −1.356410 + 0.112287I
a = 0.202197 + 0.820758I
b = 0.17434 − 1.59862I
−3.53567 + 3.73820I 0
u = −1.356410 − 0.112287I
a = 0.202197 − 0.820758I
b = 0.17434 + 1.59862I
−3.53567 − 3.73820I 0
u = −1.358470 + 0.143026I
a = −1.353580 − 0.228884I
b = −1.160700 + 0.526570I
−1.26765 + 7.94095I 0
u = −1.358470 − 0.143026I
a = −1.353580 + 0.228884I
b = −1.160700 − 0.526570I
−1.26765 − 7.94095I 0
u = 1.368360 + 0.085834I
a = 0.290701 − 0.765642I
b = −0.64968 + 1.59002I
−2.02551 − 3.00487I 0
u = 1.368360 − 0.085834I
a = 0.290701 + 0.765642I
b = −0.64968 − 1.59002I
−2.02551 + 3.00487I 0
u = 1.379890 + 0.160353I
a = −0.317648 + 0.896210I
b = −0.05306 − 1.66215I
−1.56942 − 8.60645I 0
u = 1.379890 − 0.160353I
a = −0.317648 − 0.896210I
b = −0.05306 + 1.66215I
−1.56942 + 8.60645I 0
u = 1.390970 + 0.096096I
a = 1.103970 + 0.103885I
b = 1.152920 + 0.397138I
−4.97509 − 3.82300I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.390970 − 0.096096I
a = 1.103970 − 0.103885I
b = 1.152920 − 0.397138I
−4.97509 + 3.82300I 0
u = −0.037503 + 0.596397I
a = 0.36414 − 1.92620I
b = 0.261674 + 1.022480I
4.52566 − 1.15109I 6.23436 + 0.38594I
u = −0.037503 − 0.596397I
a = 0.36414 + 1.92620I
b = 0.261674 − 1.022480I
4.52566 + 1.15109I 6.23436 − 0.38594I
u = 1.40667 + 0.26184I
a = −0.485247 + 0.970070I
b = −1.141110 − 0.816619I
−1.56131 − 4.01030I 0
u = 1.40667 − 0.26184I
a = −0.485247 − 0.970070I
b = −1.141110 + 0.816619I
−1.56131 + 4.01030I 0
u = −0.298161 + 0.443295I
a = −0.549122 + 0.963108I
b = 0.444626 + 0.356044I
−0.15371 − 1.58994I −1.42624 + 1.98288I
u = −0.298161 − 0.443295I
a = −0.549122 − 0.963108I
b = 0.444626 − 0.356044I
−0.15371 + 1.58994I −1.42624 − 1.98288I
u = 1.46362 + 0.17385I
a = 0.304404 − 1.032320I
b = 0.846992 + 0.221001I
−6.17519 − 0.76182I 0
u = 1.46362 − 0.17385I
a = 0.304404 + 1.032320I
b = 0.846992 − 0.221001I
−6.17519 + 0.76182I 0
u = −0.155990 + 0.497529I
a = 1.04483 − 2.35071I
b = 0.015047 + 1.085040I
3.36815 + 6.26844I 3.96391 − 7.68382I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.155990 − 0.497529I
a = 1.04483 + 2.35071I
b = 0.015047 − 1.085040I
3.36815 − 6.26844I 3.96391 + 7.68382I
u = 1.44935 + 0.30104I
a = 0.526429 − 1.065710I
b = 1.52911 + 0.71038I
−4.15695 − 9.12120I 0
u = 1.44935 − 0.30104I
a = 0.526429 + 1.065710I
b = 1.52911 − 0.71038I
−4.15695 + 9.12120I 0
u = −1.46542 + 0.27690I
a = 0.254920 + 1.037850I
b = 1.32007 − 0.86889I
−6.50073 + 6.60004I 0
u = −1.46542 − 0.27690I
a = 0.254920 − 1.037850I
b = 1.32007 + 0.86889I
−6.50073 − 6.60004I 0
u = 1.46386 + 0.30484I
a = −0.263373 + 1.147230I
b = −1.31153 − 0.95461I
−4.27302 − 11.79580I 0
u = 1.46386 − 0.30484I
a = −0.263373 − 1.147230I
b = −1.31153 + 0.95461I
−4.27302 + 11.79580I 0
u = −1.48495 + 0.19479I
a = 0.167816 + 0.722945I
b = 1.38966 − 0.61548I
−7.76705 + 3.90228I 0
u = −1.48495 − 0.19479I
a = 0.167816 − 0.722945I
b = 1.38966 + 0.61548I
−7.76705 − 3.90228I 0
u = 1.49176 + 0.14550I
a = −0.134205 + 0.537263I
b = −1.41496 − 0.46095I
−6.68330 + 1.19848I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49176 − 0.14550I
a = −0.134205 − 0.537263I
b = −1.41496 + 0.46095I
−6.68330 − 1.19848I 0
u = 0.066760 + 0.486078I
a = −0.41695 + 2.46615I
b = −0.881052 − 0.937770I
3.30433 − 5.76662I 3.79923 + 6.91273I
u = 0.066760 − 0.486078I
a = −0.41695 − 2.46615I
b = −0.881052 + 0.937770I
3.30433 + 5.76662I 3.79923 − 6.91273I
u = 1.48454 + 0.34898I
a = 0.254201 − 1.213360I
b = 1.65526 + 0.76856I
−6.9227 − 17.1759I 0
u = 1.48454 − 0.34898I
a = 0.254201 + 1.213360I
b = 1.65526 − 0.76856I
−6.9227 + 17.1759I 0
u = −1.49146 + 0.32588I
a = −0.272333 − 1.094210I
b = −1.64360 + 0.71264I
−9.2253 + 11.9036I 0
u = −1.49146 − 0.32588I
a = −0.272333 + 1.094210I
b = −1.64360 − 0.71264I
−9.2253 − 11.9036I 0
u = 0.066503 + 0.460813I
a = −1.13702 − 1.73349I
b = −0.034938 + 0.934134I
0.95866 − 1.83427I 0.73406 + 3.89858I
u = 0.066503 − 0.460813I
a = −1.13702 + 1.73349I
b = −0.034938 − 0.934134I
0.95866 + 1.83427I 0.73406 − 3.89858I
u = −1.52227 + 0.25706I
a = −0.251276 − 0.717849I
b = −1.62467 + 0.53247I
−10.77400 + 9.01109I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52227 − 0.25706I
a = −0.251276 + 0.717849I
b = −1.62467 − 0.53247I
−10.77400 − 9.01109I 0
u = 1.53098 + 0.21479I
a = 0.265871 − 0.505711I
b = 1.58794 + 0.43363I
−9.84860 − 3.77356I 0
u = 1.53098 − 0.21479I
a = 0.265871 + 0.505711I
b = 1.58794 − 0.43363I
−9.84860 + 3.77356I 0
u = 1.52612 + 0.24737I
a = 0.153500 − 1.100690I
b = 0.833157 + 0.473629I
−9.36969 − 8.34998I 0
u = 1.52612 − 0.24737I
a = 0.153500 + 1.100690I
b = 0.833157 − 0.473629I
−9.36969 + 8.34998I 0
u = −1.53189 + 0.21291I
a = −0.156064 − 1.042910I
b = −0.907267 + 0.417953I
−11.43450 + 3.06093I 0
u = −1.53189 − 0.21291I
a = −0.156064 + 1.042910I
b = −0.907267 − 0.417953I
−11.43450 − 3.06093I 0
u = −1.55684 + 0.12305I
a = −0.148490 − 0.836226I
b = −1.116250 + 0.286900I
−12.31450 + 0.01828I 0
u = −1.55684 − 0.12305I
a = −0.148490 + 0.836226I
b = −1.116250 − 0.286900I
−12.31450 − 0.01828I 0
u = 1.56528 + 0.07740I
a = 0.149063 − 0.704571I
b = 1.211780 + 0.210713I
−11.02690 + 5.25826I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56528 − 0.07740I
a = 0.149063 + 0.704571I
b = 1.211780 − 0.210713I
−11.02690 − 5.25826I 0
u = −0.154957 + 0.386807I
a = −0.836798 + 0.702949I
b = 0.264901 + 0.471924I
−0.14462 − 1.60637I −1.48281 + 3.72848I
u = −0.154957 − 0.386807I
a = −0.836798 − 0.702949I
b = 0.264901 − 0.471924I
−0.14462 + 1.60637I −1.48281 − 3.72848I
u = −0.156750 + 0.282652I
a = 2.02349 + 1.65973I
b = 0.732640 − 0.821272I
0.05214 + 2.40475I −0.47032 − 3.52067I
u = −0.156750 − 0.282652I
a = 2.02349 − 1.65973I
b = 0.732640 + 0.821272I
0.05214 − 2.40475I −0.47032 + 3.52067I
u = −0.048155 + 0.266320I
a = −1.69653 + 4.39859I
b = −0.672555 − 0.967240I
2.63765 + 1.71529I 3.42382 − 0.87900I
u = −0.048155 − 0.266320I
a = −1.69653 − 4.39859I
b = −0.672555 + 0.967240I
2.63765 − 1.71529I 3.42382 + 0.87900I
15
II. I
u
2
= hb
2
− b + 1, a
4
− 2a
2
+ 2, u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
−1
a
8
=
1
1
a
1
=
1
0
a
4
=
a
b
a
9
=
0
1
a
5
=
a
b − a
a
3
=
b + a
b
a
2
=
ba + b
b − 1
a
6
=
−a
−b
a
11
=
a
2
ba − 1
a
10
=
2a
2
− 2
a
3
b − a
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 4b
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
4
c
3
, c
6
(u
2
+ u + 1)
4
c
4
, c
11
(u
4
− 2u
2
+ 2)
2
c
5
, c
10
(u
4
+ 2u
2
+ 2)
2
c
7
, c
8
(u + 1)
8
c
9
(u
2
+ 2u + 2)
4
c
12
(u − 1)
8
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
11
(y
2
− 2y + 2)
4
c
5
, c
10
(y
2
+ 2y + 2)
4
c
7
, c
8
, c
12
(y −1)
8
c
9
(y
2
+ 4)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.098680 + 0.455090I
b = 0.500000 + 0.866025I
0.82247 + 1.63398I −2.00000 − 0.53590I
u = −1.00000
a = 1.098680 + 0.455090I
b = 0.500000 − 0.866025I
0.82247 + 5.69375I −2.00000 − 7.46410I
u = −1.00000
a = 1.098680 − 0.455090I
b = 0.500000 + 0.866025I
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −1.00000
a = 1.098680 − 0.455090I
b = 0.500000 − 0.866025I
0.82247 − 1.63398I −2.00000 + 0.53590I
u = −1.00000
a = −1.098680 + 0.455090I
b = 0.500000 + 0.866025I
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −1.00000
a = −1.098680 + 0.455090I
b = 0.500000 − 0.866025I
0.82247 − 1.63398I −2.00000 + 0.53590I
u = −1.00000
a = −1.098680 − 0.455090I
b = 0.500000 + 0.866025I
0.82247 + 1.63398I −2.00000 − 0.53590I
u = −1.00000
a = −1.098680 − 0.455090I
b = 0.500000 − 0.866025I
0.82247 + 5.69375I −2.00000 − 7.46410I
19
III. I
u
3
= hb
2
+ b + 1, a
3
, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
8
=
1
1
a
1
=
−1
0
a
4
=
a
b
a
9
=
0
1
a
5
=
a
b − a
a
3
=
b + a
b
a
2
=
−ba + b
b + 1
a
6
=
a
b
a
11
=
−a
2
−ba + 1
a
10
=
0
−a
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2a
2
− 4b − 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
5
, c
9
c
10
, c
11
u
6
c
7
, c
8
(u − 1)
6
c
12
(u + 1)
6
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
3
c
4
, c
5
, c
9
c
10
, c
11
y
6
c
7
, c
8
, c
12
(y −1)
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 0
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 0
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 0
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 0
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 0
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
7
)(u
107
+ 54u
106
+ ··· − 8u − 1)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)
3
(u
107
− 2u
106
+ ··· + 2u − 1)
c
3
((u
2
− u + 1)
3
)(u
2
+ u + 1)
4
(u
107
+ 2u
106
+ ··· − 188610u − 36209)
c
4
u
6
(u
4
− 2u
2
+ 2)
2
(u
107
+ u
106
+ ··· + 3876u + 3764)
c
5
, c
10
u
6
(u
4
+ 2u
2
+ 2)
2
(u
107
− u
106
+ ··· + 4u + 4)
c
6
((u
2
− u + 1)
3
)(u
2
+ u + 1)
4
(u
107
− 2u
106
+ ··· + 2u − 1)
c
7
, c
8
((u − 1)
6
)(u + 1)
8
(u
107
+ 3u
106
+ ··· − 111u + 13)
c
9
u
6
(u
2
+ 2u + 2)
4
(u
107
− 51u
106
+ ··· − 80u + 16)
c
11
u
6
(u
4
− 2u
2
+ 2)
2
(u
107
− 5u
106
+ ··· − 692004u + 563884)
c
12
((u − 1)
8
)(u + 1)
6
(u
107
+ 3u
106
+ ··· − 111u + 13)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
7
)(y
107
+ 6y
106
+ ··· + 40y −1)
c
2
, c
6
((y
2
+ y + 1)
7
)(y
107
+ 54y
106
+ ··· − 8y −1)
c
3
((y
2
+ y + 1)
7
)(y
107
− 42y
106
+ ··· + 2.26449 × 10
9
y −1.31109 × 10
9
)
c
4
y
6
(y
2
− 2y + 2)
4
(y
107
− 21y
106
+ ··· + 4.24757 × 10
8
y −1.41677 × 10
7
)
c
5
, c
10
y
6
(y
2
+ 2y + 2)
4
(y
107
+ 51y
106
+ ··· − 80y −16)
c
7
, c
8
, c
12
((y −1)
14
)(y
107
− 103y
106
+ ··· − 9207y −169)
c
9
y
6
(y
2
+ 4)
4
(y
107
+ 15y
106
+ ··· − 2304y −256)
c
11
y
6
(y
2
− 2y + 2)
4
· (y
107
+ 39y
106
+ ··· − 10755598905296y −317965165456)
25
