12a
1241
(K12a
1241
)
A knot diagram
1
Linearized knot diagam
5 6 9 1 10 11 12 4 3 2 8 7
Solving Sequence
3,6 2,10
11 7 5 1 9 4 8 12
c
2
c
10
c
6
c
5
c
1
c
9
c
3
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.62020 × 10
506
u
97
+ 3.30268 × 10
507
u
96
+ ··· + 1.26259 × 10
508
b − 1.88289 × 10
510
,
1.51364 × 10
508
u
97
+ 4.93052 × 10
508
u
96
+ ··· + 3.04411 × 10
511
a − 6.63987 × 10
513
,
u
98
+ 7u
97
+ ··· + 6163u + 2411i
I
u
2
= h−35958023u
20
− 5871878u
19
+ ··· + 82788619b + 51534009,
28948786u
20
− 9908114u
19
+ ··· + 82788619a + 47650307, u
21
+ 3u
19
+ ··· + 4u
3
− 1i
* 2 irreducible components of dim
C
= 0, with total 119 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
= h5.62 × 10
506
u
97
+ 3.30 × 10
507
u
96
+ · · · + 1.26 × 10
508
b − 1.88 ×
10
510
, 1.51 × 10
508
u
97
+ 4.93 × 10
508
u
96
+ · · · + 3.04 × 10
511
a − 6.64 ×
10
513
, u
98
+ 7u
97
+ · · · + 6163u + 2411i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
−0.000497238u
97
− 0.00161969u
96
+ ··· + 444.575u + 218.122
−0.0445132u
97
− 0.261579u
96
+ ··· + 164.459u + 149.129
a
11
=
0.0435860u
97
+ 0.269441u
96
+ ··· + 269.846u + 64.5064
−0.0606907u
97
− 0.356223u
96
+ ··· + 289.418u + 239.593
a
7
=
0.230430u
97
+ 1.78272u
96
+ ··· + 3320.78u + 1062.60
−0.0866751u
97
− 0.662088u
96
+ ··· − 1338.01u − 353.286
a
5
=
0.299926u
97
+ 2.27131u
96
+ ··· + 3812.28u + 1215.95
−0.144750u
97
− 1.03754u
96
+ ··· − 1552.10u − 316.827
a
1
=
−0.142659u
97
− 1.24303u
96
+ ··· − 3628.12u − 1358.82
0.0981813u
97
+ 0.780441u
96
+ ··· + 1918.65u + 630.422
a
9
=
0.0440160u
97
+ 0.259960u
96
+ ··· + 280.116u + 68.9932
−0.0445132u
97
− 0.261579u
96
+ ··· + 164.459u + 149.129
a
4
=
0.163505u
97
+ 0.986985u
96
+ ··· − 1062.50u − 885.931
−0.0320956u
97
− 0.211873u
96
+ ··· + 194.491u + 143.704
a
8
=
−0.0452535u
97
− 0.318641u
96
+ ··· − 510.276u − 346.848
0.0816803u
97
+ 0.517141u
96
+ ··· + 179.363u − 83.0401
a
12
=
0.0571524u
97
+ 0.334182u
96
+ ··· + 137.694u − 213.754
−0.0435898u
97
− 0.259607u
96
+ ··· + 177.399u + 261.550
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.161576u
97
− 1.15515u
96
+ ··· − 1184.37u − 255.285
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
98
− 2u
97
+ ··· + 454u + 52
c
2
u
98
− 7u
97
+ ··· − 6163u + 2411
c
3
, c
8
, c
9
u
98
+ u
97
+ ··· − 625u + 77
c
5
u
98
+ 3u
97
+ ··· + 18901u + 4059
c
6
u
98
− 30u
96
+ ··· + 455u + 97
c
7
, c
11
, c
12
u
98
+ 42u
96
+ ··· + 17u + 1
c
10
u
98
+ 5u
97
+ ··· + 7783u + 1015
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
98
− 86y
97
+ ··· + 334372y + 2704
c
2
y
98
+ 29y
97
+ ··· + 216614209y + 5812921
c
3
, c
8
, c
9
y
98
+ 107y
97
+ ··· + 162543y + 5929
c
5
y
98
+ 33y
97
+ ··· + 550117295y + 16475481
c
6
y
98
− 60y
97
+ ··· + 4415607y + 9409
c
7
, c
11
, c
12
y
98
+ 84y
97
+ ··· + 511y + 1
c
10
y
98
− 23y
97
+ ··· − 47629779y + 1030225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253022 + 0.971744I
a = 1.228300 − 0.565343I
b = 0.22606 + 1.48582I
−4.47832 + 4.71335I 0
u = 0.253022 − 0.971744I
a = 1.228300 + 0.565343I
b = 0.22606 − 1.48582I
−4.47832 − 4.71335I 0
u = −0.361168 + 0.912422I
a = −0.938996 − 0.090557I
b = −1.102380 − 0.355055I
−1.31097 + 1.94718I 0
u = −0.361168 − 0.912422I
a = −0.938996 + 0.090557I
b = −1.102380 + 0.355055I
−1.31097 − 1.94718I 0
u = −0.953890 + 0.418609I
a = −0.897666 + 0.239337I
b = −0.676448 + 0.223462I
6.31069 − 0.36260I 0
u = −0.953890 − 0.418609I
a = −0.897666 − 0.239337I
b = −0.676448 − 0.223462I
6.31069 + 0.36260I 0
u = −0.086926 + 1.046640I
a = −0.855169 − 0.016414I
b = −0.41197 + 1.62733I
−7.82875 − 7.69575I 0
u = −0.086926 − 1.046640I
a = −0.855169 + 0.016414I
b = −0.41197 − 1.62733I
−7.82875 + 7.69575I 0
u = 0.732080 + 0.574872I
a = 1.35164 + 0.54134I
b = 0.527080 + 0.217054I
4.60166 + 4.95582I 0
u = 0.732080 − 0.574872I
a = 1.35164 − 0.54134I
b = 0.527080 − 0.217054I
4.60166 − 4.95582I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151039 + 0.912026I
a = 0.965108 − 0.073747I
b = 0.34093 − 1.67994I
−12.49310 − 3.58757I 0
u = −0.151039 − 0.912026I
a = 0.965108 + 0.073747I
b = 0.34093 + 1.67994I
−12.49310 + 3.58757I 0
u = 0.719249 + 0.578215I
a = 0.510756 + 0.568805I
b = 0.319764 − 0.549263I
3.90783 + 4.05242I 0
u = 0.719249 − 0.578215I
a = 0.510756 − 0.568805I
b = 0.319764 + 0.549263I
3.90783 − 4.05242I 0
u = 0.011715 + 0.911513I
a = 0.751748 + 0.335932I
b = 0.598604 − 0.265419I
1.37687 − 1.50928I 0
u = 0.011715 − 0.911513I
a = 0.751748 − 0.335932I
b = 0.598604 + 0.265419I
1.37687 + 1.50928I 0
u = −0.411815 + 0.812519I
a = 1.030430 + 0.031946I
b = 1.076620 + 0.516415I
−5.12526 − 1.90924I 0
u = −0.411815 − 0.812519I
a = 1.030430 − 0.031946I
b = 1.076620 − 0.516415I
−5.12526 + 1.90924I 0
u = −0.555460 + 0.700572I
a = −2.65690 + 0.21983I
b = −0.02164 + 1.53493I
−9.53244 − 4.05758I 0
u = −0.555460 − 0.700572I
a = −2.65690 − 0.21983I
b = −0.02164 − 1.53493I
−9.53244 + 4.05758I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.477299 + 0.724656I
a = −1.101160 + 0.068783I
b = −1.080780 − 0.663592I
−1.04793 − 5.79172I 0
u = −0.477299 − 0.724656I
a = −1.101160 − 0.068783I
b = −1.080780 + 0.663592I
−1.04793 + 5.79172I 0
u = 0.234186 + 0.806850I
a = −1.68852 + 0.70590I
b = −0.096508 − 0.608610I
−2.46525 + 3.67993I 0
u = 0.234186 − 0.806850I
a = −1.68852 − 0.70590I
b = −0.096508 + 0.608610I
−2.46525 − 3.67993I 0
u = 0.293389 + 1.155010I
a = −1.051790 + 0.520303I
b = −0.091467 − 0.999276I
−2.63731 + 3.64297I 0
u = 0.293389 − 1.155010I
a = −1.051790 − 0.520303I
b = −0.091467 + 0.999276I
−2.63731 − 3.64297I 0
u = −0.511481 + 0.622118I
a = 0.941842 + 0.089696I
b = 0.476021 − 0.247877I
0.762154 − 1.099890I 0
u = −0.511481 − 0.622118I
a = 0.941842 − 0.089696I
b = 0.476021 + 0.247877I
0.762154 + 1.099890I 0
u = 0.140471 + 0.791468I
a = −1.43894 + 0.87695I
b = −0.10479 − 1.50633I
−7.69184 + 0.59503I 0
u = 0.140471 − 0.791468I
a = −1.43894 − 0.87695I
b = −0.10479 + 1.50633I
−7.69184 − 0.59503I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968387 + 0.758823I
a = −0.452375 + 0.502174I
b = −0.07400 + 1.60154I
−9.10905 − 0.25018I 0
u = −0.968387 − 0.758823I
a = −0.452375 − 0.502174I
b = −0.07400 − 1.60154I
−9.10905 + 0.25018I 0
u = −0.582839 + 0.494454I
a = 0.59706 + 1.83322I
b = 0.513909 − 0.332393I
0.10343 − 5.42157I 0. + 9.49655I
u = −0.582839 − 0.494454I
a = 0.59706 − 1.83322I
b = 0.513909 + 0.332393I
0.10343 + 5.42157I 0. − 9.49655I
u = 0.642839 + 1.056130I
a = −1.109050 + 0.101431I
b = −0.664693 − 0.827070I
−3.13702 + 3.92759I 0
u = 0.642839 − 1.056130I
a = −1.109050 − 0.101431I
b = −0.664693 + 0.827070I
−3.13702 − 3.92759I 0
u = −0.181205 + 1.275240I
a = 0.589758 + 0.246208I
b = 0.183271 − 0.218860I
1.51179 − 1.16300I 0
u = −0.181205 − 1.275240I
a = 0.589758 − 0.246208I
b = 0.183271 + 0.218860I
1.51179 + 1.16300I 0
u = −0.240973 + 0.664061I
a = −1.207900 + 0.353763I
b = −0.23164 + 1.74547I
−9.48090 + 0.46429I −9.33722 − 0.88532I
u = −0.240973 − 0.664061I
a = −1.207900 − 0.353763I
b = −0.23164 − 1.74547I
−9.48090 − 0.46429I −9.33722 + 0.88532I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676028 + 1.106150I
a = 1.013210 − 0.107878I
b = 0.176915 + 1.347300I
−4.23006 + 3.45286I 0
u = 0.676028 − 1.106150I
a = 1.013210 + 0.107878I
b = 0.176915 − 1.347300I
−4.23006 − 3.45286I 0
u = 0.386745 + 0.579689I
a = −0.643360 − 0.550780I
b = −0.363776 + 0.467216I
−1.20735 + 1.03467I −4.78917 + 0.I
u = 0.386745 − 0.579689I
a = −0.643360 + 0.550780I
b = −0.363776 − 0.467216I
−1.20735 − 1.03467I −4.78917 + 0.I
u = 0.787509 + 1.051300I
a = 1.034020 + 0.011995I
b = 0.842973 + 0.733535I
−5.98704 + 8.16987I 0
u = 0.787509 − 1.051300I
a = 1.034020 − 0.011995I
b = 0.842973 − 0.733535I
−5.98704 − 8.16987I 0
u = −1.070030 + 0.777663I
a = 1.23144 − 0.75638I
b = 0.12152 − 1.46773I
−1.04050 − 7.00303I 0
u = −1.070030 − 0.777663I
a = 1.23144 + 0.75638I
b = 0.12152 + 1.46773I
−1.04050 + 7.00303I 0
u = 0.012621 + 0.673624I
a = 1.43960 − 1.30487I
b = 0.00251 + 1.51873I
−3.19203 − 3.60931I −3.60074 + 2.59640I
u = 0.012621 − 0.673624I
a = 1.43960 + 1.30487I
b = 0.00251 − 1.51873I
−3.19203 + 3.60931I −3.60074 − 2.59640I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.669031 + 0.057218I
a = −0.882681 + 0.590887I
b = −0.355258 − 0.829069I
4.45227 + 3.37263I 2.57498 − 4.45245I
u = 0.669031 − 0.057218I
a = −0.882681 − 0.590887I
b = −0.355258 + 0.829069I
4.45227 − 3.37263I 2.57498 + 4.45245I
u = 0.070567 + 0.663650I
a = −0.965466 − 0.774419I
b = −0.401206 − 0.489636I
−1.70244 − 1.41603I −3.82463 − 4.35155I
u = 0.070567 − 0.663650I
a = −0.965466 + 0.774419I
b = −0.401206 + 0.489636I
−1.70244 + 1.41603I −3.82463 + 4.35155I
u = −0.274034 + 0.597207I
a = 0.58410 − 2.43839I
b = −0.306884 + 0.424273I
−4.73792 − 0.91594I −14.1775 + 7.1751I
u = −0.274034 − 0.597207I
a = 0.58410 + 2.43839I
b = −0.306884 − 0.424273I
−4.73792 + 0.91594I −14.1775 − 7.1751I
u = −0.782678 + 1.100260I
a = −0.674478 − 0.011090I
b = −0.426595 + 0.459532I
−1.08514 − 3.89925I 0
u = −0.782678 − 1.100260I
a = −0.674478 + 0.011090I
b = −0.426595 − 0.459532I
−1.08514 + 3.89925I 0
u = 0.872848 + 1.035340I
a = −0.992791 − 0.070139I
b = −0.933028 − 0.664235I
−1.25539 + 12.36790I 0
u = 0.872848 − 1.035340I
a = −0.992791 + 0.070139I
b = −0.933028 + 0.664235I
−1.25539 − 12.36790I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179029 + 0.608657I
a = 3.54093 + 2.48800I
b = −0.06719 − 1.51489I
−11.28210 + 2.12682I −19.6517 − 0.8079I
u = −0.179029 − 0.608657I
a = 3.54093 − 2.48800I
b = −0.06719 + 1.51489I
−11.28210 − 2.12682I −19.6517 + 0.8079I
u = 0.089926 + 0.598124I
a = −0.84393 − 3.85606I
b = 0.14492 + 1.47331I
−5.84333 + 7.70252I −9.7981 − 11.2309I
u = 0.089926 − 0.598124I
a = −0.84393 + 3.85606I
b = 0.14492 − 1.47331I
−5.84333 − 7.70252I −9.7981 + 11.2309I
u = 1.271310 + 0.611048I
a = 0.001508 − 0.596122I
b = 0.359510 − 0.682661I
−1.01263 + 2.26697I 0
u = 1.271310 − 0.611048I
a = 0.001508 + 0.596122I
b = 0.359510 + 0.682661I
−1.01263 − 2.26697I 0
u = 1.090940 + 0.897595I
a = 0.118660 + 0.563108I
b = −0.330387 + 0.507102I
−4.98910 − 1.42208I 0
u = 1.090940 − 0.897595I
a = 0.118660 − 0.563108I
b = −0.330387 − 0.507102I
−4.98910 + 1.42208I 0
u = 1.15829 + 0.86848I
a = −0.794019 − 0.292135I
b = −0.259473 − 1.347090I
1.36352 + 3.73435I 0
u = 1.15829 − 0.86848I
a = −0.794019 + 0.292135I
b = −0.259473 + 1.347090I
1.36352 − 3.73435I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509418 + 0.015335I
a = 0.685640 − 0.008444I
b = 0.110118 − 0.780072I
−0.661179 − 1.248990I −2.42504 + 5.87685I
u = 0.509418 − 0.015335I
a = 0.685640 + 0.008444I
b = 0.110118 + 0.780072I
−0.661179 + 1.248990I −2.42504 − 5.87685I
u = −1.02084 + 1.09369I
a = 0.652315 − 0.066750I
b = 0.521275 − 0.555138I
3.74698 − 7.24813I 0
u = −1.02084 − 1.09369I
a = 0.652315 + 0.066750I
b = 0.521275 + 0.555138I
3.74698 + 7.24813I 0
u = −0.88831 + 1.22196I
a = −1.164150 + 0.057315I
b = −0.20453 + 1.60891I
−11.15240 − 7.16359I 0
u = −0.88831 − 1.22196I
a = −1.164150 − 0.057315I
b = −0.20453 − 1.60891I
−11.15240 + 7.16359I 0
u = 0.98697 + 1.19362I
a = −0.193337 − 0.484475I
b = 0.352727 − 0.338516I
−1.04985 − 5.14578I 0
u = 0.98697 − 1.19362I
a = −0.193337 + 0.484475I
b = 0.352727 + 0.338516I
−1.04985 + 5.14578I 0
u = −0.76861 + 1.42402I
a = 0.487964 − 0.188076I
b = 0.13072 − 1.43122I
−2.88616 − 0.46954I 0
u = −0.76861 − 1.42402I
a = 0.487964 + 0.188076I
b = 0.13072 + 1.43122I
−2.88616 + 0.46954I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.96362 + 1.33021I
a = 1.024180 − 0.042463I
b = 0.26543 − 1.61976I
−13.7565 − 12.2933I 0
u = −0.96362 − 1.33021I
a = 1.024180 + 0.042463I
b = 0.26543 + 1.61976I
−13.7565 + 12.2933I 0
u = −0.211165 + 0.255277I
a = 2.83520 − 0.04950I
b = 0.551289 + 0.974623I
2.41153 − 1.09819I −0.23981 + 2.82127I
u = −0.211165 − 0.255277I
a = 2.83520 + 0.04950I
b = 0.551289 − 0.974623I
2.41153 + 1.09819I −0.23981 − 2.82127I
u = −1.03724 + 1.37921I
a = −0.946320 + 0.059889I
b = −0.31087 + 1.60890I
−8.6855 − 16.9635I 0
u = −1.03724 − 1.37921I
a = −0.946320 − 0.059889I
b = −0.31087 − 1.60890I
−8.6855 + 16.9635I 0
u = 0.79524 + 1.66544I
a = 0.652174 − 0.180397I
b = 0.04078 + 1.48538I
−4.40204 + 1.83496I 0
u = 0.79524 − 1.66544I
a = 0.652174 + 0.180397I
b = 0.04078 − 1.48538I
−4.40204 − 1.83496I 0
u = 1.00328 + 1.64054I
a = −0.628453 + 0.097365I
b = −0.11468 − 1.52643I
−7.75971 + 5.78094I 0
u = 1.00328 − 1.64054I
a = −0.628453 − 0.097365I
b = −0.11468 + 1.52643I
−7.75971 − 5.78094I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16084 + 1.63108I
a = 0.598586 − 0.046585I
b = 0.16721 + 1.55416I
−3.32821 + 9.79518I 0
u = 1.16084 − 1.63108I
a = 0.598586 + 0.046585I
b = 0.16721 − 1.55416I
−3.32821 − 9.79518I 0
u = −1.89459 + 0.85168I
a = −0.175177 + 0.324024I
b = 0.05072 + 1.60993I
−8.94260 − 0.96211I 0
u = −1.89459 − 0.85168I
a = −0.175177 − 0.324024I
b = 0.05072 − 1.60993I
−8.94260 + 0.96211I 0
u = −1.77035 + 1.31272I
a = 0.239271 − 0.254991I
b = −0.08249 − 1.54381I
−11.94420 + 2.84627I 0
u = −1.77035 − 1.31272I
a = 0.239271 + 0.254991I
b = −0.08249 + 1.54381I
−11.94420 − 2.84627I 0
u = −1.72554 + 1.57449I
a = −0.254697 + 0.210266I
b = 0.11181 + 1.49815I
−7.26258 + 6.81165I 0
u = −1.72554 − 1.57449I
a = −0.254697 − 0.210266I
b = 0.11181 − 1.49815I
−7.26258 − 6.81165I 0
14
II.
I
u
2
= h−3.60 × 10
7
u
20
− 5.87 × 10
6
u
19
+ · · · + 8.28 × 10
7
b + 5.15 × 10
7
, 2.89 ×
10
7
u
20
−9.91×10
6
u
19
+· · ·+8.28×10
7
a+4.77×10
7
, u
21
+3u
19
+· · ·+4u
3
−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
−0.349671u
20
+ 0.119680u
19
+ ··· − 0.328416u − 0.575566
0.434335u
20
+ 0.0709261u
19
+ ··· + 0.538125u − 0.622477
a
11
=
−0.425572u
20
− 0.583010u
19
+ ··· − 1.21621u + 0.166591
0.840659u
20
+ 0.126118u
19
+ ··· + 0.462224u − 1.32517
a
7
=
−1.07577u
20
+ 0.626412u
19
+ ··· − 0.347425u − 1.24751
−0.0441834u
20
− 0.193456u
19
+ ··· − 0.554242u + 1.16960
a
5
=
−0.221566u
20
+ 0.0501958u
19
+ ··· − 1.68495u + 0.104535
0.191143u
20
− 0.380578u
19
+ ··· − 0.0806184u + 0.859053
a
1
=
−1.08062u
20
+ 0.859053u
19
+ ··· + 1.12989u + 2.18515
0.456808u
20
− 0.473624u
19
+ ··· − 1.88948u − 0.521525
a
9
=
−0.784006u
20
+ 0.0487535u
19
+ ··· − 0.866541u + 0.0469111
0.434335u
20
+ 0.0709261u
19
+ ··· + 0.538125u − 0.622477
a
4
=
1.23963u
20
− 0.0745222u
19
+ ··· + 1.32610u − 0.271762
−0.380578u
20
+ 0.265665u
19
+ ··· − 0.140947u + 0.191143
a
8
=
−0.684952u
20
+ 0.104535u
19
+ ··· − 0.833063u − 0.210797
−0.287508u
20
+ 0.447015u
19
+ ··· − 0.272806u + 0.314656
a
12
=
0.185703u
20
+ 0.0640186u
19
+ ··· − 0.305374u + 0.258156
0.0746521u
20
− 0.109910u
19
+ ··· − 0.342353u − 0.510214
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
367253532
82788619
u
20
+
83600533
82788619
u
19
+ ··· +
462458306
82788619
u −
448782682
82788619
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 3u
20
+ ··· − 3u − 1
c
2
u
21
+ 3u
19
+ ··· + 4u
3
− 1
c
3
u
21
+ 12u
19
+ ··· − 3u
2
− 1
c
4
u
21
− 3u
20
+ ··· − 3u + 1
c
5
u
21
+ 3u
19
+ ··· − 3u
2
− 1
c
6
u
21
− u
20
+ ··· + 3u
2
− 1
c
7
u
21
+ u
20
+ ··· − 2u − 1
c
8
, c
9
u
21
+ 12u
19
+ ··· + 3u
2
+ 1
c
10
u
21
+ 2u
20
+ ··· − 4u
3
+ 1
c
11
, c
12
u
21
− u
20
+ ··· − 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 21y
20
+ ··· + 15y −1
c
2
y
21
+ 6y
20
+ ··· + 4y
2
− 1
c
3
, c
8
, c
9
y
21
+ 24y
20
+ ··· − 6y −1
c
5
y
21
+ 6y
20
+ ··· − 6y −1
c
6
y
21
− 7y
20
+ ··· + 6y −1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 6y −1
c
10
y
21
− 6y
20
+ ··· − 8y
2
− 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407597 + 0.870717I
a = 0.680319 + 1.087480I
b = −0.18046 − 1.47117I
−5.51707 + 6.87921I −4.74851 − 2.86739I
u = −0.407597 − 0.870717I
a = 0.680319 − 1.087480I
b = −0.18046 + 1.47117I
−5.51707 − 6.87921I −4.74851 + 2.86739I
u = 0.094729 + 1.047450I
a = 0.561172 + 0.309540I
b = 0.480951 + 0.574674I
1.329940 − 0.100531I −4.48837 − 1.47261I
u = 0.094729 − 1.047450I
a = 0.561172 − 0.309540I
b = 0.480951 − 0.574674I
1.329940 + 0.100531I −4.48837 + 1.47261I
u = −0.580685 + 0.636837I
a = 0.947436 − 0.573177I
b = 0.195506 + 0.576897I
3.38035 − 4.48387I −6.73945 + 6.02054I
u = −0.580685 − 0.636837I
a = 0.947436 + 0.573177I
b = 0.195506 − 0.576897I
3.38035 + 4.48387I −6.73945 − 6.02054I
u = −0.673019 + 0.436808I
a = −1.65014 + 0.46045I
b = 0.09381 + 1.54272I
−10.54320 + 2.25396I −7.32485 − 1.89994I
u = −0.673019 − 0.436808I
a = −1.65014 − 0.46045I
b = 0.09381 − 1.54272I
−10.54320 − 2.25396I −7.32485 + 1.89994I
u = −0.172176 + 0.734347I
a = −1.150890 − 0.189980I
b = −0.327687 − 0.508652I
−1.96242 − 1.97147I −10.38839 + 7.19935I
u = −0.172176 − 0.734347I
a = −1.150890 + 0.189980I
b = −0.327687 + 0.508652I
−1.96242 + 1.97147I −10.38839 − 7.19935I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599944 + 0.405600I
a = 0.457584 − 0.789305I
b = −0.609912 − 0.214868I
−0.67685 − 4.01014I −3.90329 + 2.87470I
u = 0.599944 − 0.405600I
a = 0.457584 + 0.789305I
b = −0.609912 + 0.214868I
−0.67685 + 4.01014I −3.90329 − 2.87470I
u = −1.255920 + 0.286813I
a = 0.281896 − 0.479640I
b = −0.06568 − 1.67537I
−8.29699 − 1.29880I −1.40444 + 6.09499I
u = −1.255920 − 0.286813I
a = 0.281896 + 0.479640I
b = −0.06568 + 1.67537I
−8.29699 + 1.29880I −1.40444 − 6.09499I
u = 0.635071 + 1.167840I
a = −1.037320 + 0.119056I
b = −0.148982 − 1.265150I
−4.77902 + 3.72263I −12.7993 − 6.1964I
u = 0.635071 − 1.167840I
a = −1.037320 − 0.119056I
b = −0.148982 + 1.265150I
−4.77902 − 3.72263I −12.7993 + 6.1964I
u = 0.994776 + 0.915498I
a = 1.050060 + 0.469010I
b = 0.095962 + 1.246490I
0.84337 + 5.57019I −2.71521 − 5.54678I
u = 0.994776 − 0.915498I
a = 1.050060 − 0.469010I
b = 0.095962 − 1.246490I
0.84337 − 5.57019I −2.71521 + 5.54678I
u = 0.503863
a = −1.63350
b = 0.532145
−4.47496 −8.88530
u = 0.51294 + 1.50845I
a = 0.676633 − 0.200309I
b = 0.200421 + 1.238650I
−1.14943 + 2.54928I −2.54552 − 2.42691I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.51294 − 1.50845I
a = 0.676633 + 0.200309I
b = 0.200421 − 1.238650I
−1.14943 − 2.54928I −2.54552 + 2.42691I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
98
− 2u
97
+ ··· + 454u + 52)
c
2
(u
21
+ 3u
19
+ ··· + 4u
3
− 1)(u
98
− 7u
97
+ ··· − 6163u + 2411)
c
3
(u
21
+ 12u
19
+ ··· − 3u
2
− 1)(u
98
+ u
97
+ ··· − 625u + 77)
c
4
(u
21
− 3u
20
+ ··· − 3u + 1)(u
98
− 2u
97
+ ··· + 454u + 52)
c
5
(u
21
+ 3u
19
+ ··· − 3u
2
− 1)(u
98
+ 3u
97
+ ··· + 18901u + 4059)
c
6
(u
21
− u
20
+ ··· + 3u
2
− 1)(u
98
− 30u
96
+ ··· + 455u + 97)
c
7
(u
21
+ u
20
+ ··· − 2u − 1)(u
98
+ 42u
96
+ ··· + 17u + 1)
c
8
, c
9
(u
21
+ 12u
19
+ ··· + 3u
2
+ 1)(u
98
+ u
97
+ ··· − 625u + 77)
c
10
(u
21
+ 2u
20
+ ··· − 4u
3
+ 1)(u
98
+ 5u
97
+ ··· + 7783u + 1015)
c
11
, c
12
(u
21
− u
20
+ ··· − 2u + 1)(u
98
+ 42u
96
+ ··· + 17u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
21
− 21y
20
+ ··· + 15y −1)(y
98
− 86y
97
+ ··· + 334372y + 2704)
c
2
(y
21
+ 6y
20
+ ··· + 4y
2
− 1)
· (y
98
+ 29y
97
+ ··· + 216614209y + 5812921)
c
3
, c
8
, c
9
(y
21
+ 24y
20
+ ··· − 6y −1)(y
98
+ 107y
97
+ ··· + 162543y + 5929)
c
5
(y
21
+ 6y
20
+ ··· − 6y −1)
· (y
98
+ 33y
97
+ ··· + 550117295y + 16475481)
c
6
(y
21
− 7y
20
+ ··· + 6y −1)(y
98
− 60y
97
+ ··· + 4415607y + 9409)
c
7
, c
11
, c
12
(y
21
+ 21y
20
+ ··· + 6y −1)(y
98
+ 84y
97
+ ··· + 511y + 1)
c
10
(y
21
− 6y
20
+ ··· − 8y
2
− 1)
· (y
98
− 23y
97
+ ··· − 47629779y + 1030225)
22
