12a
0892
(K12a
0892
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 11 10 5 12 2 3 9 8
Solving Sequence
6,10 3,7
4 11 2 1 5 9 12 8
c
6
c
3
c
10
c
2
c
1
c
5
c
9
c
11
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.09914 × 10
1018
u
144
− 2.88524 × 10
1018
u
143
+ ··· + 3.72547 × 10
1017
b − 1.57837 × 10
1020
,
− 5.40470 × 10
1019
u
144
− 6.78220 × 10
1019
u
143
+ ··· + 1.15490 × 10
1019
a − 6.04250 × 10
1021
,
u
145
+ u
144
+ ··· + 238u − 31i
I
u
2
= h3.61659 × 10
28
u
31
+ 7.73832 × 10
28
u
30
+ ··· + 3.44067 × 10
28
b − 8.89248 × 10
28
,
5.39323 × 10
28
u
31
+ 9.21403 × 10
28
u
30
+ ··· + 3.44067 × 10
28
a + 1.58031 × 10
28
, u
32
+ 2u
31
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 177 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−2.10 × 10
1018
u
144
− 2.89 × 10
1018
u
143
+ · · · + 3.73 × 10
1017
b −
1.58 × 10
1020
, −5.40 × 10
1019
u
144
− 6.78 × 10
1019
u
143
+ · · · + 1.15 ×
10
1019
a − 6.04 × 10
1021
, u
145
+ u
144
+ · · · + 238u − 31i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
4.67981u
144
+ 5.87256u
143
+ ··· − 2318.63u + 523.207
5.63455u
144
+ 7.74462u
143
+ ··· − 2112.83u + 423.668
a
7
=
1
u
2
a
4
=
−0.771919u
144
− 1.57602u
143
+ ··· − 344.597u + 136.514
4.76589u
144
+ 6.61597u
143
+ ··· − 1806.59u + 361.766
a
11
=
2.79017u
144
+ 2.81371u
143
+ ··· − 749.380u + 174.315
−4.73297u
144
− 6.56048u
143
+ ··· + 2011.61u − 424.449
a
2
=
−0.954736u
144
− 1.87207u
143
+ ··· − 205.798u + 99.5386
5.63455u
144
+ 7.74462u
143
+ ··· − 2112.83u + 423.668
a
1
=
−1.31802u
144
− 2.68164u
143
+ ··· + 272.155u − 87.1026
3.05808u
144
+ 3.78139u
143
+ ··· − 1380.60u + 310.975
a
5
=
3.84388u
144
+ 6.25083u
143
+ ··· − 1397.32u + 245.504
3.38549u
144
+ 4.43042u
143
+ ··· − 1403.13u + 273.429
a
9
=
6.45647u
144
+ 8.13085u
143
+ ··· − 2347.32u + 522.309
1.06667u
144
+ 1.24334u
143
+ ··· − 411.667u + 76.4553
a
12
=
7.52566u
144
+ 9.42017u
143
+ ··· − 3397.01u + 725.029
−7.30654u
144
− 9.43795u
143
+ ··· + 3301.93u − 734.941
a
8
=
1.58406u
144
+ 3.01115u
143
+ ··· + 35.0302u − 71.9586
−2.19792u
144
− 2.14369u
143
+ ··· + 1374.66u − 309.390
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.57129u
144
+ 6.71330u
143
+ ··· − 3177.35u + 441.593
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
145
+ 6u
144
+ ··· + 241016u + 53041
c
2
u
145
− 8u
144
+ ··· + 31u + 1
c
3
u
145
− 25u
143
+ ··· − 366697u + 53551
c
5
u
145
− 2u
144
+ ··· − 584109u + 262673
c
6
u
145
− u
144
+ ··· + 238u + 31
c
7
u
145
+ 4u
144
+ ··· + 220494628u + 11977767
c
8
, c
11
, c
12
u
145
+ 6u
144
+ ··· − 13u + 1
c
9
u
145
− 10u
143
+ ··· − 2690u + 1025
c
10
u
145
+ 4u
144
+ ··· − 193u + 27
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
145
+ 114y
144
+ ··· − 109382835062y −2813347681
c
2
y
145
+ 8y
144
+ ··· + 245y −1
c
3
y
145
− 50y
144
+ ··· + 55811088111y −2867709601
c
5
y
145
+ 48y
144
+ ··· − 7065213404445y −68997104929
c
6
y
145
− 17y
144
+ ··· + 83242y −961
c
7
y
145
+ 38y
144
+ ··· − 9969062284337030y −143466902306289
c
8
, c
11
, c
12
y
145
+ 148y
144
+ ··· − 23y −1
c
9
y
145
− 20y
144
+ ··· − 85056950y −1050625
c
10
y
145
+ 32y
144
+ ··· − 44723y −729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.175233 + 0.993312I
a = −1.50509 + 0.99291I
b = 0.984730 + 0.148375I
9.85859 + 8.66525I 0
u = −0.175233 − 0.993312I
a = −1.50509 − 0.99291I
b = 0.984730 − 0.148375I
9.85859 − 8.66525I 0
u = −0.270642 + 0.973406I
a = 0.37280 − 1.37338I
b = −0.197005 + 0.309824I
8.44939 + 3.42419I 0
u = −0.270642 − 0.973406I
a = 0.37280 + 1.37338I
b = −0.197005 − 0.309824I
8.44939 − 3.42419I 0
u = −0.457505 + 0.873801I
a = 0.001931 − 1.056370I
b = −1.10167 − 1.39405I
10.5547 + 10.4208I 0
u = −0.457505 − 0.873801I
a = 0.001931 + 1.056370I
b = −1.10167 + 1.39405I
10.5547 − 10.4208I 0
u = 0.853690 + 0.554488I
a = 0.24679 − 1.57189I
b = 1.20444 − 1.27727I
6.99182 − 4.73153I 0
u = 0.853690 − 0.554488I
a = 0.24679 + 1.57189I
b = 1.20444 + 1.27727I
6.99182 + 4.73153I 0
u = −0.779856 + 0.578252I
a = 0.08031 + 1.59012I
b = 0.95266 + 1.16365I
1.26897 + 4.48898I 0
u = −0.779856 − 0.578252I
a = 0.08031 − 1.59012I
b = 0.95266 − 1.16365I
1.26897 − 4.48898I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966669
a = 0.511382
b = −0.230935
−1.29626 0
u = −0.842836 + 0.473333I
a = 0.114165 + 0.731850I
b = 1.34113 + 1.21796I
3.56283 + 6.56801I 0
u = −0.842836 − 0.473333I
a = 0.114165 − 0.731850I
b = 1.34113 − 1.21796I
3.56283 − 6.56801I 0
u = 0.328978 + 0.898582I
a = 0.249788 + 1.287120I
b = −0.0809638 − 0.0060685I
2.99294 − 2.90031I 0
u = 0.328978 − 0.898582I
a = 0.249788 − 1.287120I
b = −0.0809638 + 0.0060685I
2.99294 + 2.90031I 0
u = 0.985932 + 0.403210I
a = 0.773146 − 0.957633I
b = 1.131940 − 0.532852I
7.33618 − 2.02582I 0
u = 0.985932 − 0.403210I
a = 0.773146 + 0.957633I
b = 1.131940 + 0.532852I
7.33618 + 2.02582I 0
u = −0.927787 + 0.062557I
a = 0.364733 + 0.697991I
b = 0.529992 + 1.300080I
0.88219 + 1.22730I 0
u = −0.927787 − 0.062557I
a = 0.364733 − 0.697991I
b = 0.529992 − 1.300080I
0.88219 − 1.22730I 0
u = 0.794588 + 0.464628I
a = 0.851818 + 0.312631I
b = −0.096564 + 0.431521I
−1.38971 − 0.42921I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794588 − 0.464628I
a = 0.851818 − 0.312631I
b = −0.096564 − 0.431521I
−1.38971 + 0.42921I 0
u = 0.809274 + 0.438011I
a = −0.245927 − 0.502995I
b = −0.894106 − 0.707102I
−2.09607 − 0.26844I 0
u = 0.809274 − 0.438011I
a = −0.245927 + 0.502995I
b = −0.894106 + 0.707102I
−2.09607 + 0.26844I 0
u = 0.834733 + 0.378244I
a = 0.120339 − 0.828214I
b = 1.04293 − 1.22525I
−1.62770 − 3.91436I 0
u = 0.834733 − 0.378244I
a = 0.120339 + 0.828214I
b = 1.04293 + 1.22525I
−1.62770 + 3.91436I 0
u = 0.432543 + 0.996527I
a = 0.027076 + 1.027480I
b = −0.76676 + 1.24530I
4.17885 − 5.54834I 0
u = 0.432543 − 0.996527I
a = 0.027076 − 1.027480I
b = −0.76676 − 1.24530I
4.17885 + 5.54834I 0
u = −1.066270 + 0.247929I
a = −0.206778 + 0.289540I
b = −1.200350 + 0.617183I
3.12685 − 0.12674I 0
u = −1.066270 − 0.247929I
a = −0.206778 − 0.289540I
b = −1.200350 − 0.617183I
3.12685 + 0.12674I 0
u = −0.162959 + 1.082590I
a = 0.198535 − 0.111941I
b = 0.648377 − 0.887697I
2.09440 − 1.76971I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162959 − 1.082590I
a = 0.198535 + 0.111941I
b = 0.648377 + 0.887697I
2.09440 + 1.76971I 0
u = −0.967028 + 0.516281I
a = 1.004840 + 0.297297I
b = 0.219267 − 0.422014I
3.49440 − 1.89700I 0
u = −0.967028 − 0.516281I
a = 1.004840 − 0.297297I
b = 0.219267 + 0.422014I
3.49440 + 1.89700I 0
u = 1.101490 + 0.040866I
a = 0.48056 − 1.45999I
b = 0.024912 − 0.558133I
−0.861624 + 0.409948I 0
u = 1.101490 − 0.040866I
a = 0.48056 + 1.45999I
b = 0.024912 + 0.558133I
−0.861624 − 0.409948I 0
u = −0.722310 + 0.843040I
a = 0.34411 − 1.42106I
b = −0.763936 − 0.462647I
5.23556 + 5.23001I 0
u = −0.722310 − 0.843040I
a = 0.34411 + 1.42106I
b = −0.763936 + 0.462647I
5.23556 − 5.23001I 0
u = 0.355968 + 0.798221I
a = −1.17073 − 1.66706I
b = 0.807566 − 0.466961I
2.77202 − 6.23642I 0
u = 0.355968 − 0.798221I
a = −1.17073 + 1.66706I
b = 0.807566 + 0.466961I
2.77202 + 6.23642I 0
u = −0.711648 + 0.877783I
a = 0.045504 − 1.080010I
b = −0.077228 − 1.046060I
6.84476 + 0.58245I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711648 − 0.877783I
a = 0.045504 + 1.080010I
b = −0.077228 + 1.046060I
6.84476 − 0.58245I 0
u = −0.509051 + 1.017630I
a = 0.064952 − 0.952618I
b = −0.772460 − 0.661107I
5.89302 + 0.19949I 0
u = −0.509051 − 1.017630I
a = 0.064952 + 0.952618I
b = −0.772460 + 0.661107I
5.89302 − 0.19949I 0
u = 0.750068 + 0.374115I
a = 0.27446 − 1.75411I
b = 0.48114 − 1.55804I
5.33434 − 5.39101I 0
u = 0.750068 − 0.374115I
a = 0.27446 + 1.75411I
b = 0.48114 + 1.55804I
5.33434 + 5.39101I 0
u = 0.559310 + 1.043510I
a = −0.022095 + 0.894625I
b = −1.110140 + 0.547552I
13.46280 + 2.57020I 0
u = 0.559310 − 1.043510I
a = −0.022095 − 0.894625I
b = −1.110140 − 0.547552I
13.46280 − 2.57020I 0
u = 0.677087 + 0.322793I
a = 0.092962 + 0.965597I
b = 1.28360 + 1.51766I
6.87184 − 10.70990I 0
u = 0.677087 − 0.322793I
a = 0.092962 − 0.965597I
b = 1.28360 − 1.51766I
6.87184 + 10.70990I 0
u = −0.568846 + 1.113300I
a = 0.162339 + 0.183610I
b = 1.100390 + 0.403905I
10.38580 + 4.15509I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568846 − 1.113300I
a = 0.162339 − 0.183610I
b = 1.100390 − 0.403905I
10.38580 − 4.15509I 0
u = −0.659678 + 1.064510I
a = 0.590704 − 0.199088I
b = −0.466431 − 0.492976I
3.38993 + 3.85851I 0
u = −0.659678 − 1.064510I
a = 0.590704 + 0.199088I
b = −0.466431 + 0.492976I
3.38993 − 3.85851I 0
u = −0.856740 + 0.927176I
a = −0.831698 + 0.861803I
b = 0.289995 + 0.586627I
6.56094 + 5.30740I 0
u = −0.856740 − 0.927176I
a = −0.831698 − 0.861803I
b = 0.289995 − 0.586627I
6.56094 − 5.30740I 0
u = 0.637639 + 0.329081I
a = −0.47670 + 2.53347I
b = −0.312601 + 0.534758I
−2.41986 − 3.05864I 0
u = 0.637639 − 0.329081I
a = −0.47670 − 2.53347I
b = −0.312601 − 0.534758I
−2.41986 + 3.05864I 0
u = −1.136110 + 0.646165I
a = −0.294255 + 0.471721I
b = −0.702647 + 1.194120I
2.22638 − 0.12544I 0
u = −1.136110 − 0.646165I
a = −0.294255 − 0.471721I
b = −0.702647 − 1.194120I
2.22638 + 0.12544I 0
u = −1.170270 + 0.605888I
a = 0.285001 + 0.717823I
b = 0.774449 + 0.730807I
0.46547 + 2.09210I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.170270 − 0.605888I
a = 0.285001 − 0.717823I
b = 0.774449 − 0.730807I
0.46547 − 2.09210I 0
u = −0.104328 + 0.661044I
a = −0.03414 − 1.78053I
b = 0.620897 + 0.232105I
8.37051 + 1.60856I 0
u = −0.104328 − 0.661044I
a = −0.03414 + 1.78053I
b = 0.620897 − 0.232105I
8.37051 − 1.60856I 0
u = 0.661436 + 0.014358I
a = 0.173534 − 1.294400I
b = −0.95347 − 1.62284I
1.32185 − 4.06716I 0
u = 0.661436 − 0.014358I
a = 0.173534 + 1.294400I
b = −0.95347 + 1.62284I
1.32185 + 4.06716I 0
u = −0.578994 + 0.298296I
a = −0.71154 + 1.53149I
b = 0.929249 + 0.898528I
0.07179 + 3.70060I 0
u = −0.578994 − 0.298296I
a = −0.71154 − 1.53149I
b = 0.929249 − 0.898528I
0.07179 − 3.70060I 0
u = −0.550613 + 0.347580I
a = 0.038949 − 0.919566I
b = 1.45706 − 1.12848I
0.68944 + 6.98932I 0
u = −0.550613 − 0.347580I
a = 0.038949 + 0.919566I
b = 1.45706 + 1.12848I
0.68944 − 6.98932I 0
u = −0.613680 + 0.203109I
a = 2.84986 − 1.48270I
b = −0.155422 − 0.487057I
0.30339 + 6.35289I 0. − 25.1026I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613680 − 0.203109I
a = 2.84986 + 1.48270I
b = −0.155422 + 0.487057I
0.30339 − 6.35289I 0. + 25.1026I
u = 0.591375 + 0.256999I
a = −0.55267 − 2.24509I
b = 0.980139 − 1.004110I
5.89423 − 4.66757I 0
u = 0.591375 − 0.256999I
a = −0.55267 + 2.24509I
b = 0.980139 + 1.004110I
5.89423 + 4.66757I 0
u = 1.072280 + 0.838787I
a = −0.073824 − 0.857507I
b = 0.98899 − 1.14772I
−1.91092 − 4.53651I 0
u = 1.072280 − 0.838787I
a = −0.073824 + 0.857507I
b = 0.98899 + 1.14772I
−1.91092 + 4.53651I 0
u = −0.625242 + 0.104972I
a = 0.810423 + 0.997280I
b = 0.556069 + 0.687308I
0.68161 + 1.58841I 0
u = −0.625242 − 0.104972I
a = 0.810423 − 0.997280I
b = 0.556069 − 0.687308I
0.68161 − 1.58841I 0
u = 0.562625 + 0.271590I
a = 0.98707 − 1.67557I
b = 0.995209 − 0.465961I
7.40415 − 1.90436I 0
u = 0.562625 − 0.271590I
a = 0.98707 + 1.67557I
b = 0.995209 + 0.465961I
7.40415 + 1.90436I 0
u = 0.369904 + 0.468983I
a = −0.603481 + 0.212699I
b = 1.183390 − 0.469764I
1.58948 − 2.62456I 0. + 3.62743I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369904 − 0.468983I
a = −0.603481 − 0.212699I
b = 1.183390 + 0.469764I
1.58948 + 2.62456I 0. − 3.62743I
u = 0.371064 + 0.461167I
a = −0.268667 + 0.858423I
b = 1.251690 + 0.170593I
1.70497 − 2.66262I 0. + 6.62401I
u = 0.371064 − 0.461167I
a = −0.268667 − 0.858423I
b = 1.251690 − 0.170593I
1.70497 + 2.66262I 0. − 6.62401I
u = 1.083310 + 0.908174I
a = 0.016723 + 1.094320I
b = −0.831442 + 1.025920I
−3.19557 − 5.94519I 0
u = 1.083310 − 0.908174I
a = 0.016723 − 1.094320I
b = −0.831442 − 1.025920I
−3.19557 + 5.94519I 0
u = 0.497529 + 0.282324I
a = 3.82000 + 0.64029I
b = −0.313502 + 0.520244I
7.70025 − 10.38410I −6.0000 + 16.0066I
u = 0.497529 − 0.282324I
a = 3.82000 − 0.64029I
b = −0.313502 − 0.520244I
7.70025 + 10.38410I −6.0000 − 16.0066I
u = −0.486754 + 0.297305I
a = 0.88123 + 2.29211I
b = 0.006286 + 0.981261I
0.46950 + 3.52931I −11.59746 − 5.64649I
u = −0.486754 − 0.297305I
a = 0.88123 − 2.29211I
b = 0.006286 − 0.981261I
0.46950 − 3.52931I −11.59746 + 5.64649I
u = −1.00830 + 1.01817I
a = −0.266712 + 0.840438I
b = 1.23990 + 1.10914I
2.55761 + 7.40596I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00830 − 1.01817I
a = −0.266712 − 0.840438I
b = 1.23990 − 1.10914I
2.55761 − 7.40596I 0
u = −1.18863 + 0.80119I
a = −0.047559 + 0.688065I
b = 0.486127 + 1.210110I
1.08652 + 2.07918I 0
u = −1.18863 − 0.80119I
a = −0.047559 − 0.688065I
b = 0.486127 − 1.210110I
1.08652 − 2.07918I 0
u = −0.556768 + 0.038672I
a = 0.031722 + 1.231130I
b = −1.22823 + 1.28194I
−3.65244 + 1.72670I −21.4514 − 5.0713I
u = −0.556768 − 0.038672I
a = 0.031722 − 1.231130I
b = −1.22823 − 1.28194I
−3.65244 − 1.72670I −21.4514 + 5.0713I
u = 1.08513 + 0.95150I
a = −0.170686 − 0.386102I
b = −0.233957 − 0.718289I
−2.26919 − 0.66351I 0
u = 1.08513 − 0.95150I
a = −0.170686 + 0.386102I
b = −0.233957 + 0.718289I
−2.26919 + 0.66351I 0
u = 0.529427 + 0.121719I
a = −2.50547 − 2.05101I
b = 0.294527 − 0.823997I
1.89483 − 4.47916I −13.3702 + 6.6534I
u = 0.529427 − 0.121719I
a = −2.50547 + 2.05101I
b = 0.294527 + 0.823997I
1.89483 + 4.47916I −13.3702 − 6.6534I
u = −1.13569 + 0.91956I
a = −0.041880 − 1.052690I
b = −1.00525 − 1.11497I
−4.11430 + 10.02680I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13569 − 0.91956I
a = −0.041880 + 1.052690I
b = −1.00525 + 1.11497I
−4.11430 − 10.02680I 0
u = −0.514987 + 0.053999I
a = −2.24549 − 2.98451I
b = 0.017963 − 0.599980I
−3.51088 − 1.35231I −23.2910 + 3.3744I
u = −0.514987 − 0.053999I
a = −2.24549 + 2.98451I
b = 0.017963 + 0.599980I
−3.51088 + 1.35231I −23.2910 − 3.3744I
u = −1.46228 + 0.26379I
a = −0.482951 − 0.780205I
b = −0.420296 − 0.640012I
6.42247 + 5.98655I 0
u = −1.46228 − 0.26379I
a = −0.482951 + 0.780205I
b = −0.420296 + 0.640012I
6.42247 − 5.98655I 0
u = 1.17057 + 0.91668I
a = −0.101247 + 1.044950I
b = −1.14666 + 1.12493I
1.95287 − 13.11790I 0
u = 1.17057 − 0.91668I
a = −0.101247 − 1.044950I
b = −1.14666 − 1.12493I
1.95287 + 13.11790I 0
u = 1.06134 + 1.15983I
a = 0.290866 + 0.840933I
b = −1.08775 + 1.01185I
−1.48980 − 7.19259I 0
u = 1.06134 − 1.15983I
a = 0.290866 − 0.840933I
b = −1.08775 − 1.01185I
−1.48980 + 7.19259I 0
u = −1.00710 + 1.21075I
a = 0.396548 − 0.871295I
b = −1.23418 − 1.02046I
3.78215 + 7.83286I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00710 − 1.21075I
a = 0.396548 + 0.871295I
b = −1.23418 + 1.02046I
3.78215 − 7.83286I 0
u = −1.14288 + 1.10201I
a = −0.025648 + 0.997008I
b = 1.00226 + 1.13946I
−0.1104 + 15.3505I 0
u = −1.14288 − 1.10201I
a = −0.025648 − 0.997008I
b = 1.00226 − 1.13946I
−0.1104 − 15.3505I 0
u = 1.15081 + 1.09791I
a = −0.030003 − 1.020660I
b = 1.12279 − 1.13424I
6.9949 − 19.7067I 0
u = 1.15081 − 1.09791I
a = −0.030003 + 1.020660I
b = 1.12279 + 1.13424I
6.9949 + 19.7067I 0
u = 1.14125 + 1.12989I
a = −0.011180 − 0.972430I
b = 0.827355 − 1.078260I
−0.20472 − 9.22747I 0
u = 1.14125 − 1.12989I
a = −0.011180 + 0.972430I
b = 0.827355 + 1.078260I
−0.20472 + 9.22747I 0
u = −1.22379 + 1.09810I
a = 0.017653 + 0.917259I
b = 0.673357 + 0.716516I
8.13394 + 4.05463I 0
u = −1.22379 − 1.09810I
a = 0.017653 − 0.917259I
b = 0.673357 − 0.716516I
8.13394 − 4.05463I 0
u = 0.307554 + 0.154586I
a = 3.39026 − 1.13438I
b = −0.720259 − 0.623857I
1.56557 + 0.67995I −2.42170 − 4.86730I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307554 − 0.154586I
a = 3.39026 + 1.13438I
b = −0.720259 + 0.623857I
1.56557 − 0.67995I −2.42170 + 4.86730I
u = 0.329955 + 0.025626I
a = −0.06445 − 1.65101I
b = −1.90495 − 0.84217I
−1.047060 + 0.869818I −20.8494 + 1.2292I
u = 0.329955 − 0.025626I
a = −0.06445 + 1.65101I
b = −1.90495 + 0.84217I
−1.047060 − 0.869818I −20.8494 − 1.2292I
u = −1.17816 + 1.18635I
a = 0.217123 − 0.632934I
b = −0.851518 − 1.095940I
2.26413 + 6.60189I 0
u = −1.17816 − 1.18635I
a = 0.217123 + 0.632934I
b = −0.851518 + 1.095940I
2.26413 − 6.60189I 0
u = 0.99162 + 1.34973I
a = 0.127144 + 0.282380I
b = −0.090432 + 0.845531I
−0.51554 − 3.03375I 0
u = 0.99162 − 1.34973I
a = 0.127144 − 0.282380I
b = −0.090432 − 0.845531I
−0.51554 + 3.03375I 0
u = −0.242721 + 0.189733I
a = 4.85248 + 0.35743I
b = −0.957873 + 0.192495I
8.92002 − 4.00313I 2.19779 + 2.09749I
u = −0.242721 − 0.189733I
a = 4.85248 − 0.35743I
b = −0.957873 − 0.192495I
8.92002 + 4.00313I 2.19779 − 2.09749I
u = 1.43136 + 0.97804I
a = −0.327669 + 0.522569I
b = −0.923323 + 0.372366I
10.6141 − 9.7736I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43136 − 0.97804I
a = −0.327669 − 0.522569I
b = −0.923323 − 0.372366I
10.6141 + 9.7736I 0
u = 1.61882 + 0.64012I
a = 0.182021 + 0.559726I
b = −0.103544 + 0.592485I
−1.035610 + 0.080466I 0
u = 1.61882 − 0.64012I
a = 0.182021 − 0.559726I
b = −0.103544 − 0.592485I
−1.035610 − 0.080466I 0
u = 0.69404 + 1.61334I
a = −0.258376 + 0.114266I
b = −0.422112 − 0.451167I
3.67587 + 5.14877I 0
u = 0.69404 − 1.61334I
a = −0.258376 − 0.114266I
b = −0.422112 + 0.451167I
3.67587 − 5.14877I 0
u = −1.35889 + 1.18561I
a = −0.075214 − 0.465586I
b = −0.654863 − 0.638412I
2.49668 + 7.42652I 0
u = −1.35889 − 1.18561I
a = −0.075214 + 0.465586I
b = −0.654863 + 0.638412I
2.49668 − 7.42652I 0
u = 1.22410 + 1.34142I
a = −0.220476 − 0.354537I
b = 0.122506 − 0.422165I
−1.94572 − 1.90721I 0
u = 1.22410 − 1.34142I
a = −0.220476 + 0.354537I
b = 0.122506 + 0.422165I
−1.94572 + 1.90721I 0
u = −0.92489 + 1.69832I
a = −0.243371 + 0.050641I
b = −0.188996 + 0.408334I
−2.61907 − 2.06320I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.92489 − 1.69832I
a = −0.243371 − 0.050641I
b = −0.188996 − 0.408334I
−2.61907 + 2.06320I 0
u = 1.42436 + 1.38893I
a = 0.312943 + 0.128735I
b = 0.371339 + 0.634069I
7.17709 + 10.75390I 0
u = 1.42436 − 1.38893I
a = 0.312943 − 0.128735I
b = 0.371339 − 0.634069I
7.17709 − 10.75390I 0
u = −1.58503 + 1.22762I
a = 0.265276 − 0.229194I
b = 0.141739 − 0.592882I
−0.16117 − 6.34878I 0
u = −1.58503 − 1.22762I
a = 0.265276 + 0.229194I
b = 0.141739 + 0.592882I
−0.16117 + 6.34878I 0
19
II.
I
u
2
= h3.62 × 10
28
u
31
+ 7.74 × 10
28
u
30
+ · · · + 3.44 × 10
28
b − 8.89 × 10
28
, 5.39 ×
10
28
u
31
+9.21×10
28
u
30
+· · ·+3.44×10
28
a+1.58×10
28
, u
32
+2u
31
+· · ·−u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−1.56749u
31
− 2.67798u
30
+ ··· + 0.447580u − 0.459304
−1.05113u
31
− 2.24907u
30
+ ··· − 0.696011u + 2.58452
a
7
=
1
u
2
a
4
=
−1.35112u
31
− 1.73786u
30
+ ··· + 3.16810u − 3.50084
−1.25788u
31
− 2.75976u
30
+ ··· − 0.405026u + 2.07716
a
11
=
−0.483239u
31
− 0.524494u
30
+ ··· + 1.98152u − 2.12181
−0.133827u
31
− 1.23298u
30
+ ··· − 0.184214u − 0.00969783
a
2
=
−0.516364u
31
− 0.428901u
30
+ ··· + 1.14359u − 3.04382
−1.05113u
31
− 2.24907u
30
+ ··· − 0.696011u + 2.58452
a
1
=
2.03773u
31
+ 4.53441u
30
+ ··· + 1.01245u − 1.50697
−0.385017u
31
− 1.14000u
30
+ ··· − 5.07614u + 1.05225
a
5
=
2.35656u
31
+ 2.86776u
30
+ ··· + 0.424283u + 1.40474
0.525047u
31
+ 0.282613u
30
+ ··· − 1.74040u + 0.495953
a
9
=
−0.776499u
31
+ 0.270111u
30
+ ··· + 6.08595u − 0.702777
0.427087u
31
+ 0.438374u
30
+ ··· − 1.92022u − 1.40934
a
12
=
0.405957u
31
+ 1.84513u
30
+ ··· + 3.17463u − 5.72185
−1.01188u
31
− 3.80125u
30
+ ··· − 0.818655u + 0.867011
a
8
=
−0.205937u
31
− 2.29513u
30
+ ··· + 1.79936u + 0.753290
1.71145u
31
+ 3.03215u
30
+ ··· − 0.877205u + 1.65118
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9.04209u
31
+ 16.4503u
30
+ ··· − 6.34383u − 16.7797
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 7u
31
+ ··· − 11u + 1
c
2
u
32
+ u
31
+ ··· + 2u + 1
c
3
u
32
+ u
31
+ ··· − 8u + 1
c
4
u
32
+ 7u
31
+ ··· + 11u + 1
c
5
u
32
− u
31
+ ··· − 8u + 1
c
6
u
32
+ 2u
31
+ ··· − u + 1
c
7
u
32
+ 5u
31
+ ··· + 111u + 17
c
8
u
32
− 7u
31
+ ··· + 2u + 1
c
9
u
32
− u
31
+ ··· − 7u + 1
c
10
u
32
− u
31
+ ··· + 2u + 1
c
11
, c
12
u
32
+ 7u
31
+ ··· − 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
32
+ 31y
31
+ ··· + 15y + 1
c
2
y
32
+ y
31
+ ··· + 20y + 1
c
3
y
32
− 17y
31
+ ··· + 14y + 1
c
5
y
32
+ 21y
31
+ ··· − 10y + 1
c
6
y
32
− 8y
31
+ ··· − 9y + 1
c
7
y
32
− 13y
31
+ ··· − 13y + 289
c
8
, c
11
, c
12
y
32
+ 33y
31
+ ··· − 24y + 1
c
9
y
32
+ y
31
+ ··· − 13y + 1
c
10
y
32
+ 21y
31
+ ··· + 36y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022426 + 0.961456I
a = −0.645889 + 0.132990I
b = −0.241809 − 0.427079I
−2.48524 − 1.51052I −12.43093 + 2.19531I
u = 0.022426 − 0.961456I
a = −0.645889 − 0.132990I
b = −0.241809 + 0.427079I
−2.48524 + 1.51052I −12.43093 − 2.19531I
u = −0.736928 + 0.592892I
a = −0.707619 + 0.840043I
b = 0.520185 + 1.022860I
3.07571 + 4.72411I −4.27650 − 6.25172I
u = −0.736928 − 0.592892I
a = −0.707619 − 0.840043I
b = 0.520185 − 1.022860I
3.07571 − 4.72411I −4.27650 + 6.25172I
u = 0.716295 + 0.581208I
a = −0.04103 − 1.62674I
b = 0.84715 − 1.16868I
1.06653 − 4.54772I −17.0622 + 16.0080I
u = 0.716295 − 0.581208I
a = −0.04103 + 1.62674I
b = 0.84715 + 1.16868I
1.06653 + 4.54772I −17.0622 − 16.0080I
u = −0.318229 + 1.088270I
a = −0.688768 + 0.080851I
b = 0.258467 + 0.629324I
3.13261 + 4.42693I −7.57575 − 6.49141I
u = −0.318229 − 1.088270I
a = −0.688768 − 0.080851I
b = 0.258467 − 0.629324I
3.13261 − 4.42693I −7.57575 + 6.49141I
u = −1.005940 + 0.563864I
a = 0.489242 + 1.237170I
b = 0.758960 + 0.827442I
6.47740 + 3.02424I −2.60662 − 4.16406I
u = −1.005940 − 0.563864I
a = 0.489242 − 1.237170I
b = 0.758960 − 0.827442I
6.47740 − 3.02424I −2.60662 + 4.16406I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685996 + 0.496224I
a = −0.20418 + 2.01980I
b = 0.94573 + 1.24163I
6.41698 + 5.33981I 0.48064 − 11.37051I
u = −0.685996 − 0.496224I
a = −0.20418 − 2.01980I
b = 0.94573 − 1.24163I
6.41698 − 5.33981I 0.48064 + 11.37051I
u = −1.123360 + 0.371214I
a = −0.240380 + 0.510345I
b = −0.60112 + 1.32586I
0.333435 − 0.316469I −11.06515 − 1.48103I
u = −1.123360 − 0.371214I
a = −0.240380 − 0.510345I
b = −0.60112 − 1.32586I
0.333435 + 0.316469I −11.06515 + 1.48103I
u = −0.659831 + 0.130237I
a = −0.436980 − 1.235320I
b = 0.556162 + 0.248693I
0.93477 − 5.87209I −4.32645 + 5.96982I
u = −0.659831 − 0.130237I
a = −0.436980 + 1.235320I
b = 0.556162 − 0.248693I
0.93477 + 5.87209I −4.32645 − 5.96982I
u = 0.598600 + 0.305377I
a = −0.50271 + 1.42441I
b = 0.164249 − 0.615739I
7.94608 + 9.61613I −1.35542 − 4.59648I
u = 0.598600 − 0.305377I
a = −0.50271 − 1.42441I
b = 0.164249 + 0.615739I
7.94608 − 9.61613I −1.35542 + 4.59648I
u = −1.101510 + 0.819862I
a = 0.138085 − 1.156940I
b = −0.564029 − 0.500089I
7.53790 + 5.62370I 2.35992 − 7.85868I
u = −1.101510 − 0.819862I
a = 0.138085 + 1.156940I
b = −0.564029 + 0.500089I
7.53790 − 5.62370I 2.35992 + 7.85868I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.370800 + 0.128159I
a = −0.115526 + 1.063450I
b = 0.052016 + 0.540405I
−0.598809 + 0.612645I 3.65302 − 13.18789I
u = 1.370800 − 0.128159I
a = −0.115526 − 1.063450I
b = 0.052016 − 0.540405I
−0.598809 − 0.612645I 3.65302 + 13.18789I
u = 0.313801 + 0.476983I
a = −0.510320 − 0.524271I
b = −1.54381 + 0.10949I
−0.712793 − 1.100790I −2.86026 + 9.24500I
u = 0.313801 − 0.476983I
a = −0.510320 + 0.524271I
b = −1.54381 − 0.10949I
−0.712793 + 1.100790I −2.86026 − 9.24500I
u = 1.23232 + 0.78418I
a = −0.116491 − 0.506159I
b = −0.008606 − 0.651179I
−1.99902 − 1.33246I −11.56431 + 2.50661I
u = 1.23232 − 0.78418I
a = −0.116491 + 0.506159I
b = −0.008606 + 0.651179I
−1.99902 + 1.33246I −11.56431 − 2.50661I
u = 0.412137 + 0.285133I
a = −0.439508 − 1.085520I
b = 1.59813 − 0.97300I
1.04794 − 2.73578I −11.9118 + 8.0050I
u = 0.412137 − 0.285133I
a = −0.439508 + 1.085520I
b = 1.59813 + 0.97300I
1.04794 + 2.73578I −11.9118 − 8.0050I
u = 1.07246 + 1.12234I
a = 0.229962 + 0.874367I
b = −0.978345 + 1.011560I
−1.39853 − 6.77157I −6.00000 + 0.I
u = 1.07246 − 1.12234I
a = 0.229962 − 0.874367I
b = −0.978345 − 1.011560I
−1.39853 + 6.77157I −6.00000 + 0.I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10705 + 1.21197I
a = 0.292118 − 0.754427I
b = −1.26333 − 1.10870I
2.12371 + 8.22607I 0. − 11.82419I
u = −1.10705 − 1.21197I
a = 0.292118 + 0.754427I
b = −1.26333 + 1.10870I
2.12371 − 8.22607I 0. + 11.82419I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
32
− 7u
31
+ ··· − 11u + 1)(u
145
+ 6u
144
+ ··· + 241016u + 53041)
c
2
(u
32
+ u
31
+ ··· + 2u + 1)(u
145
− 8u
144
+ ··· + 31u + 1)
c
3
(u
32
+ u
31
+ ··· − 8u + 1)(u
145
− 25u
143
+ ··· − 366697u + 53551)
c
4
(u
32
+ 7u
31
+ ··· + 11u + 1)(u
145
+ 6u
144
+ ··· + 241016u + 53041)
c
5
(u
32
− u
31
+ ··· − 8u + 1)(u
145
− 2u
144
+ ··· − 584109u + 262673)
c
6
(u
32
+ 2u
31
+ ··· − u + 1)(u
145
− u
144
+ ··· + 238u + 31)
c
7
(u
32
+ 5u
31
+ ··· + 111u + 17)
· (u
145
+ 4u
144
+ ··· + 220494628u + 11977767)
c
8
(u
32
− 7u
31
+ ··· + 2u + 1)(u
145
+ 6u
144
+ ··· − 13u + 1)
c
9
(u
32
− u
31
+ ··· − 7u + 1)(u
145
− 10u
143
+ ··· − 2690u + 1025)
c
10
(u
32
− u
31
+ ··· + 2u + 1)(u
145
+ 4u
144
+ ··· − 193u + 27)
c
11
, c
12
(u
32
+ 7u
31
+ ··· − 2u + 1)(u
145
+ 6u
144
+ ··· − 13u + 1)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
32
+ 31y
31
+ ··· + 15y + 1)
· (y
145
+ 114y
144
+ ··· − 109382835062y −2813347681)
c
2
(y
32
+ y
31
+ ··· + 20y + 1)(y
145
+ 8y
144
+ ··· + 245y −1)
c
3
(y
32
− 17y
31
+ ··· + 14y + 1)
· (y
145
− 50y
144
+ ··· + 55811088111y −2867709601)
c
5
(y
32
+ 21y
31
+ ··· − 10y + 1)
· (y
145
+ 48y
144
+ ··· − 7065213404445y −68997104929)
c
6
(y
32
− 8y
31
+ ··· − 9y + 1)(y
145
− 17y
144
+ ··· + 83242y −961)
c
7
(y
32
− 13y
31
+ ··· − 13y + 289)
· (y
145
+ 38y
144
+ ··· − 9969062284337030y −143466902306289)
c
8
, c
11
, c
12
(y
32
+ 33y
31
+ ··· − 24y + 1)(y
145
+ 148y
144
+ ··· − 23y −1)
c
9
(y
32
+ y
31
+ ··· − 13y + 1)
· (y
145
− 20y
144
+ ··· − 85056950y −1050625)
c
10
(y
32
+ 21y
31
+ ··· + 36y + 1)(y
145
+ 32y
144
+ ··· − 44723y −729)
28
