12a
1077
(K12a
1077
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 12 11 3 1 2 8 6 5
Solving Sequence
5,12
6
1,9
4 2 8 11 7 10 3
c
5
c
12
c
4
c
1
c
8
c
11
c
6
c
10
c
3
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.32263 × 10
205
u
108
+ 2.10413 × 10
205
u
107
+ ··· + 1.51200 × 10
205
b + 2.12390 × 10
207
,
8.91650 × 10
206
u
108
− 2.53673 × 10
207
u
107
+ ··· + 7.40879 × 10
206
a + 2.25210 × 10
209
,
u
109
− u
108
+ ··· − 523u − 49i
I
u
2
= h−9u
23
− 12u
22
+ ··· + 19b + 21, −28u
23
− 31u
22
+ ··· + 19a + 135, u
24
+ 17u
22
+ ··· − 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 133 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−3.32 × 10
205
u
108
+ 2.10 × 10
205
u
107
+ · · · + 1.51 × 10
205
b + 2.12 ×
10
207
, 8.92 × 10
206
u
108
− 2.54 × 10
207
u
107
+ · · · + 7.41 × 10
206
a + 2.25 ×
10
209
, u
109
− u
108
+ · · · − 523u − 49i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−1.20350u
108
+ 3.42395u
107
+ ··· − 3004.64u − 303.976
2.19751u
108
− 1.39162u
107
+ ··· − 1752.63u − 140.470
a
4
=
−1.37215u
108
+ 3.93654u
107
+ ··· − 2223.85u − 232.662
0.727465u
108
+ 1.09516u
107
+ ··· − 2021.37u − 186.044
a
2
=
0.854596u
108
+ 2.89992u
107
+ ··· − 4341.93u − 409.928
3.39114u
108
− 2.27160u
107
+ ··· − 2131.50u − 172.223
a
8
=
0.0951266u
108
+ 2.08332u
107
+ ··· − 2431.47u − 234.663
3.49614u
108
− 2.73225u
107
+ ··· − 1179.46u − 71.1568
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−1.45883u
108
+ 1.21077u
107
+ ··· + 154.279u − 11.8482
−1.84653u
108
+ 2.51112u
107
+ ··· − 630.667u − 84.4362
a
3
=
1.36227u
108
+ 1.16042u
107
+ ··· − 3434.48u − 316.934
3.40469u
108
− 3.71429u
107
+ ··· − 821.383u − 43.9644
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.53824u
108
− 9.87015u
107
+ ··· + 4065.85u + 443.964
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
109
− 7u
108
+ ··· + 29u − 1
c
2
, c
7
u
109
+ u
108
+ ··· + 328u − 176
c
3
u
109
+ u
108
+ ··· + 3264u − 131
c
4
u
109
+ 3u
108
+ ··· + 39937u − 4076
c
5
, c
6
, c
11
c
12
u
109
− u
108
+ ··· − 523u − 49
c
8
u
109
+ 17u
107
+ ··· − 1024u − 512
c
9
u
109
− 3u
108
+ ··· − 983u − 1829
c
10
u
109
− u
108
+ ··· + 1782u − 113
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
109
+ 19y
108
+ ··· + 39y −1
c
2
, c
7
y
109
− 55y
108
+ ··· + 548288y −30976
c
3
y
109
+ 35y
108
+ ··· + 4271638y −17161
c
4
y
109
+ 39y
108
+ ··· + 366066273y −16613776
c
5
, c
6
, c
11
c
12
y
109
+ 137y
108
+ ··· − 74371y −2401
c
8
y
109
+ 34y
108
+ ··· − 1310720y −262144
c
9
y
109
− 9y
108
+ ··· + 149049445y −3345241
c
10
y
109
+ 3y
108
+ ··· + 2676742y −12769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460766 + 0.870808I
a = 0.73852 + 1.55368I
b = −0.758718 + 1.157840I
−2.62204 − 8.66245I 0
u = −0.460766 − 0.870808I
a = 0.73852 − 1.55368I
b = −0.758718 − 1.157840I
−2.62204 + 8.66245I 0
u = −0.593725 + 0.770210I
a = −0.332197 − 1.215910I
b = 0.789284 − 1.170020I
−2.71012 − 6.04112I 0
u = −0.593725 − 0.770210I
a = −0.332197 + 1.215910I
b = 0.789284 + 1.170020I
−2.71012 + 6.04112I 0
u = 0.152477 + 0.943526I
a = 0.42012 − 1.85220I
b = −0.401619 − 0.827359I
−2.14389 + 2.29297I 0
u = 0.152477 − 0.943526I
a = 0.42012 + 1.85220I
b = −0.401619 + 0.827359I
−2.14389 − 2.29297I 0
u = 0.112809 + 0.946326I
a = 0.00319 − 1.59483I
b = −1.13577 − 1.10507I
−1.54044 + 5.26091I 0
u = 0.112809 − 0.946326I
a = 0.00319 + 1.59483I
b = −1.13577 + 1.10507I
−1.54044 − 5.26091I 0
u = 0.639446 + 0.862678I
a = −0.756118 + 0.465562I
b = 0.084260 + 0.832973I
−1.32969 + 6.35271I 0
u = 0.639446 − 0.862678I
a = −0.756118 − 0.465562I
b = 0.084260 − 0.832973I
−1.32969 − 6.35271I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.418748 + 0.997230I
a = 0.24444 − 1.43084I
b = −0.712188 − 1.118230I
−3.00826 + 2.66354I 0
u = 0.418748 − 0.997230I
a = 0.24444 + 1.43084I
b = −0.712188 + 1.118230I
−3.00826 − 2.66354I 0
u = −0.218252 + 1.062430I
a = 0.223229 − 1.038330I
b = 0.159835 − 0.031348I
1.50379 + 0.03899I 0
u = −0.218252 − 1.062430I
a = 0.223229 + 1.038330I
b = 0.159835 + 0.031348I
1.50379 − 0.03899I 0
u = 0.587407 + 0.935708I
a = −0.42035 + 1.44738I
b = 0.88993 + 1.18924I
0.4966 + 14.5114I 0
u = 0.587407 − 0.935708I
a = −0.42035 − 1.44738I
b = 0.88993 − 1.18924I
0.4966 − 14.5114I 0
u = −0.727402 + 0.519252I
a = −0.715358 − 0.045331I
b = −0.483422 − 0.763862I
−1.49581 + 1.55709I 0
u = −0.727402 − 0.519252I
a = −0.715358 + 0.045331I
b = −0.483422 + 0.763862I
−1.49581 − 1.55709I 0
u = 0.109823 + 0.880396I
a = −0.355056 − 1.298960I
b = −0.417616 − 0.733453I
−1.94521 + 1.92752I 0
u = 0.109823 − 0.880396I
a = −0.355056 + 1.298960I
b = −0.417616 + 0.733453I
−1.94521 − 1.92752I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877879 + 0.036702I
a = 0.1174360 − 0.0630406I
b = −0.782835 − 0.914666I
3.44815 + 9.68868I 0
u = 0.877879 − 0.036702I
a = 0.1174360 + 0.0630406I
b = −0.782835 + 0.914666I
3.44815 − 9.68868I 0
u = −0.347938 + 0.806778I
a = −0.768867 − 0.818905I
b = 0.903265 − 0.424132I
2.63909 − 5.44235I 0
u = −0.347938 − 0.806778I
a = −0.768867 + 0.818905I
b = 0.903265 + 0.424132I
2.63909 + 5.44235I 0
u = 0.822787 + 0.178559I
a = −0.0403524 − 0.0243912I
b = 0.362533 + 0.754917I
0.76129 − 1.39793I 0
u = 0.822787 − 0.178559I
a = −0.0403524 + 0.0243912I
b = 0.362533 − 0.754917I
0.76129 + 1.39793I 0
u = −0.379688 + 0.747993I
a = 1.274130 + 0.220939I
b = −0.038809 + 0.777447I
−4.15829 − 0.71433I 0
u = −0.379688 − 0.747993I
a = 1.274130 − 0.220939I
b = −0.038809 − 0.777447I
−4.15829 + 0.71433I 0
u = −0.095987 + 0.802723I
a = −0.890588 − 0.950454I
b = −0.362411 − 0.980984I
−2.06588 + 2.06817I 0
u = −0.095987 − 0.802723I
a = −0.890588 + 0.950454I
b = −0.362411 + 0.980984I
−2.06588 − 2.06817I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171530 + 0.752934I
a = −1.79053 + 2.22766I
b = −0.146393 + 0.485362I
0.21939 − 6.24723I 0
u = −0.171530 − 0.752934I
a = −1.79053 − 2.22766I
b = −0.146393 − 0.485362I
0.21939 + 6.24723I 0
u = 0.494722 + 0.567515I
a = −1.136220 + 0.713311I
b = 0.754657 + 0.858140I
3.36852 + 4.41963I 0
u = 0.494722 − 0.567515I
a = −1.136220 − 0.713311I
b = 0.754657 − 0.858140I
3.36852 − 4.41963I 0
u = 0.757016 + 1.017730I
a = 0.687807 − 0.210831I
b = 0.453740 − 0.661393I
0.69815 − 4.29313I 0
u = 0.757016 − 1.017730I
a = 0.687807 + 0.210831I
b = 0.453740 + 0.661393I
0.69815 + 4.29313I 0
u = −0.377348 + 0.626015I
a = 1.142720 + 0.101264I
b = 1.55616 + 0.50379I
2.49834 − 6.59777I 0
u = −0.377348 − 0.626015I
a = 1.142720 − 0.101264I
b = 1.55616 − 0.50379I
2.49834 + 6.59777I 0
u = 0.647391 + 0.326742I
a = −0.065850 − 0.666232I
b = −0.532455 + 0.719738I
4.13259 − 0.53685I 0
u = 0.647391 − 0.326742I
a = −0.065850 + 0.666232I
b = −0.532455 − 0.719738I
4.13259 + 0.53685I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256537 + 0.646430I
a = −0.685536 − 0.318233I
b = −1.037580 + 0.250937I
−0.24868 + 2.24073I 0
u = 0.256537 − 0.646430I
a = −0.685536 + 0.318233I
b = −1.037580 − 0.250937I
−0.24868 − 2.24073I 0
u = −0.057770 + 0.665411I
a = 2.58890 + 1.23024I
b = −0.170394 + 0.644772I
−3.57204 − 0.28957I 0. − 5.29911I
u = −0.057770 − 0.665411I
a = 2.58890 − 1.23024I
b = −0.170394 − 0.644772I
−3.57204 + 0.28957I 0. + 5.29911I
u = −0.063893 + 0.642845I
a = −0.45053 − 2.08483I
b = 0.93471 − 1.35688I
−1.92964 − 2.95489I 2.57875 + 1.41426I
u = −0.063893 − 0.642845I
a = −0.45053 + 2.08483I
b = 0.93471 + 1.35688I
−1.92964 + 2.95489I 2.57875 − 1.41426I
u = −0.638909 + 0.024881I
a = −0.563125 + 0.175451I
b = 0.646567 − 0.970277I
0.07830 − 4.93794I 6.00000 + 6.09027I
u = −0.638909 − 0.024881I
a = −0.563125 − 0.175451I
b = 0.646567 + 0.970277I
0.07830 + 4.93794I 6.00000 − 6.09027I
u = 0.253510 + 1.343030I
a = 0.351524 − 0.178459I
b = 0.122627 − 0.594413I
−1.10669 + 2.74590I 0
u = 0.253510 − 1.343030I
a = 0.351524 + 0.178459I
b = 0.122627 + 0.594413I
−1.10669 − 2.74590I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140262 + 0.609607I
a = 0.07457 + 3.26477I
b = −0.137741 + 1.365270I
2.62926 − 2.52071I 6.81610 + 3.73768I
u = −0.140262 − 0.609607I
a = 0.07457 − 3.26477I
b = −0.137741 − 1.365270I
2.62926 + 2.52071I 6.81610 − 3.73768I
u = −0.106902 + 1.388570I
a = 0.13391 − 2.45500I
b = 0.08264 − 1.73255I
−1.97866 + 1.32972I 0
u = −0.106902 − 1.388570I
a = 0.13391 + 2.45500I
b = 0.08264 + 1.73255I
−1.97866 − 1.32972I 0
u = −0.505744 + 0.313859I
a = 0.22999 + 1.77910I
b = −0.926807 + 1.010130I
3.41210 + 3.48311I 11.92159 − 4.33364I
u = −0.505744 − 0.313859I
a = 0.22999 − 1.77910I
b = −0.926807 − 1.010130I
3.41210 − 3.48311I 11.92159 + 4.33364I
u = −0.511040 + 0.064240I
a = 1.24085 + 1.22763I
b = −0.631150 − 0.306840I
4.88085 + 2.47938I 16.1714 − 2.9846I
u = −0.511040 − 0.064240I
a = 1.24085 − 1.22763I
b = −0.631150 + 0.306840I
4.88085 − 2.47938I 16.1714 + 2.9846I
u = −0.415054 + 0.266709I
a = −1.066750 + 0.615432I
b = −0.527823 − 0.763713I
−1.50863 + 1.76364I −0.07333 − 1.83560I
u = −0.415054 − 0.266709I
a = −1.066750 − 0.615432I
b = −0.527823 + 0.763713I
−1.50863 − 1.76364I −0.07333 + 1.83560I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233047 + 0.425362I
a = −0.170005 + 0.247426I
b = 0.663430 + 1.008570I
3.02593 + 1.12920I 7.44217 + 4.49627I
u = −0.233047 − 0.425362I
a = −0.170005 − 0.247426I
b = 0.663430 − 1.008570I
3.02593 − 1.12920I 7.44217 − 4.49627I
u = 0.01686 + 1.51660I
a = −0.664703 − 0.915309I
b = −1.089160 − 0.899568I
−3.36859 + 0.58272I 0
u = 0.01686 − 1.51660I
a = −0.664703 + 0.915309I
b = −1.089160 + 0.899568I
−3.36859 − 0.58272I 0
u = 0.442362 + 0.136023I
a = −1.017570 + 0.579897I
b = 0.719527 + 0.546714I
1.232000 + 0.242137I 9.84419 − 1.89118I
u = 0.442362 − 0.136023I
a = −1.017570 − 0.579897I
b = 0.719527 − 0.546714I
1.232000 − 0.242137I 9.84419 + 1.89118I
u = 0.439589
a = −0.343474
b = 0.701822
0.902802 11.7930
u = 0.08629 + 1.57817I
a = 0.26015 − 1.55005I
b = −0.858718 − 0.987170I
−3.82764 + 6.26940I 0
u = 0.08629 − 1.57817I
a = 0.26015 + 1.55005I
b = −0.858718 + 0.987170I
−3.82764 − 6.26940I 0
u = −0.08842 + 1.60955I
a = −1.82188 − 0.26121I
b = −2.08409 − 0.31933I
−5.23634 − 8.20536I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08842 − 1.60955I
a = −1.82188 + 0.26121I
b = −2.08409 + 0.31933I
−5.23634 + 8.20536I 0
u = −0.03234 + 1.61311I
a = 0.04407 − 2.69479I
b = −0.04210 − 1.74247I
−5.18858 − 3.11447I 0
u = −0.03234 − 1.61311I
a = 0.04407 + 2.69479I
b = −0.04210 + 1.74247I
−5.18858 + 3.11447I 0
u = 0.03872 + 1.61588I
a = 1.217070 − 0.079614I
b = 1.52995 − 0.17696I
−8.11108 + 3.13142I 0
u = 0.03872 − 1.61588I
a = 1.217070 + 0.079614I
b = 1.52995 + 0.17696I
−8.11108 − 3.13142I 0
u = −0.01440 + 1.62505I
a = −0.48073 + 2.16907I
b = −1.11064 + 1.63615I
−9.94149 − 3.22393I 0
u = −0.01440 − 1.62505I
a = −0.48073 − 2.16907I
b = −1.11064 − 1.63615I
−9.94149 + 3.22393I 0
u = −0.00863 + 1.63161I
a = −0.90238 − 1.39932I
b = 0.416147 − 0.734773I
−11.70050 − 0.48970I 0
u = −0.00863 − 1.63161I
a = −0.90238 + 1.39932I
b = 0.416147 + 0.734773I
−11.70050 + 0.48970I 0
u = −0.12802 + 1.63733I
a = −0.514822 − 0.981847I
b = 0.365389 − 0.912694I
−12.37520 − 2.75357I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12802 − 1.63733I
a = −0.514822 + 0.981847I
b = 0.365389 + 0.912694I
−12.37520 + 2.75357I 0
u = 0.00804 + 1.64429I
a = 0.32220 + 1.59846I
b = −0.125109 + 1.071180I
−10.63920 + 2.06989I 0
u = 0.00804 − 1.64429I
a = 0.32220 − 1.59846I
b = −0.125109 − 1.071180I
−10.63920 − 2.06989I 0
u = −0.04565 + 1.64511I
a = 0.92794 − 1.54875I
b = −0.183795 − 0.597198I
−8.19749 − 7.06148I 0
u = −0.04565 − 1.64511I
a = 0.92794 + 1.54875I
b = −0.183795 + 0.597198I
−8.19749 + 7.06148I 0
u = −0.17098 + 1.64596I
a = −0.16647 + 2.08892I
b = −0.84380 + 1.55724I
−10.9647 − 8.9348I 0
u = −0.17098 − 1.64596I
a = −0.16647 − 2.08892I
b = −0.84380 − 1.55724I
−10.9647 + 8.9348I 0
u = −0.08812 + 1.65892I
a = 0.006826 + 0.918066I
b = −1.065520 + 0.482337I
−5.96098 − 7.06983I 0
u = −0.08812 − 1.65892I
a = 0.006826 − 0.918066I
b = −1.065520 − 0.482337I
−5.96098 + 7.06983I 0
u = −0.13141 + 1.66942I
a = −0.08075 − 1.99725I
b = 0.82905 − 1.32942I
−11.3994 − 10.9715I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13141 − 1.66942I
a = −0.08075 + 1.99725I
b = 0.82905 + 1.32942I
−11.3994 + 10.9715I 0
u = 0.18431 + 1.67503I
a = 0.433984 − 1.205970I
b = −0.355017 − 1.021980I
−10.00210 + 9.53915I 0
u = 0.18431 − 1.67503I
a = 0.433984 + 1.205970I
b = −0.355017 + 1.021980I
−10.00210 − 9.53915I 0
u = 0.02728 + 1.68819I
a = −0.22100 + 1.80736I
b = 0.394131 + 0.877863I
−11.42230 + 2.89917I 0
u = 0.02728 − 1.68819I
a = −0.22100 − 1.80736I
b = 0.394131 − 0.877863I
−11.42230 − 2.89917I 0
u = 0.03886 + 1.69770I
a = 0.60629 + 1.86428I
b = 1.27696 + 1.39142I
−10.91290 + 5.92179I 0
u = 0.03886 − 1.69770I
a = 0.60629 − 1.86428I
b = 1.27696 − 1.39142I
−10.91290 − 5.92179I 0
u = 0.17192 + 1.69091I
a = −0.08202 − 2.01203I
b = −0.93273 − 1.40567I
−8.5158 + 17.5207I 0
u = 0.17192 − 1.69091I
a = −0.08202 + 2.01203I
b = −0.93273 + 1.40567I
−8.5158 − 17.5207I 0
u = 0.02446 + 1.70070I
a = 0.22547 + 1.52311I
b = 0.457882 + 1.148320I
−11.24260 + 2.32048I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02446 − 1.70070I
a = 0.22547 − 1.52311I
b = 0.457882 − 1.148320I
−11.24260 − 2.32048I 0
u = 0.10914 + 1.69863I
a = 0.14913 + 1.95949I
b = 0.81566 + 1.40603I
−12.39230 + 4.74623I 0
u = 0.10914 − 1.69863I
a = 0.14913 − 1.95949I
b = 0.81566 − 1.40603I
−12.39230 − 4.74623I 0
u = −0.20784 + 1.70978I
a = 0.444581 + 1.049360I
b = −0.031378 + 0.789708I
−9.57753 − 2.41613I 0
u = −0.20784 − 1.70978I
a = 0.444581 − 1.049360I
b = −0.031378 − 0.789708I
−9.57753 + 2.41613I 0
u = −0.132257 + 0.153763I
a = −3.93927 + 4.00487I
b = 0.768548 + 0.604426I
2.01071 + 4.98034I 8.20165 − 5.61065I
u = −0.132257 − 0.153763I
a = −3.93927 − 4.00487I
b = 0.768548 − 0.604426I
2.01071 − 4.98034I 8.20165 + 5.61065I
u = 0.09474 + 1.80431I
a = −0.297448 + 0.880722I
b = 0.098000 + 0.621739I
−9.84597 − 0.49133I 0
u = 0.09474 − 1.80431I
a = −0.297448 − 0.880722I
b = 0.098000 − 0.621739I
−9.84597 + 0.49133I 0
15
II. I
u
2
= h−9u
23
− 12u
22
+ · · · + 19b + 21, −28u
23
− 31u
22
+ · · · + 19a +
135, u
24
+ 17u
22
+ · · · − 8u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
1.47368u
23
+ 1.63158u
22
+ ··· + 14.2632u − 7.10526
0.473684u
23
+ 0.631579u
22
+ ··· + 4.26316u − 1.10526
a
4
=
−2.26316u
23
+ 0.315789u
22
+ ··· − 29.3684u + 3.94737
−0.315789u
23
+ 0.578947u
22
+ ··· − 4.84211u − 0.263158
a
2
=
−0.789474u
23
− 0.0526316u
22
+ ··· − 4.10526u + 4.84211
−u
21
+ u
20
+ ··· − 9u + 2
a
8
=
1.47368u
23
+ 0.631579u
22
+ ··· + 21.2632u − 8.10526
0.473684u
23
− 0.368421u
22
+ ··· + 11.2632u − 2.10526
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
1.57895u
23
+ 0.105263u
22
+ ··· + 42.2105u − 11.6842
−0.526316u
23
− 0.368421u
22
+ ··· + 12.2632u − 2.10526
a
3
=
−1.05263u
23
+ 0.263158u
22
+ ··· − 10.4737u + 6.78947
−0.0526316u
23
+ 0.263158u
22
+ ··· − 7.47368u + 1.78947
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
59
19
u
23
−
28
19
u
22
+ ··· +
248
19
u +
182
19
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 4u
23
+ ··· + 4u
2
+ 1
c
2
u
24
− 5u
22
+ ··· + u + 1
c
3
u
24
+ 6u
22
+ ··· + u + 1
c
4
u
24
+ 6u
22
+ ··· − 2u + 1
c
5
, c
6
u
24
+ 17u
22
+ ··· − 8u + 1
c
7
u
24
− 5u
22
+ ··· − u + 1
c
8
u
24
+ u
23
+ ··· + 2u
2
+ 1
c
9
u
24
+ 2u
22
+ ··· − 2u + 1
c
10
u
24
− 8u
23
+ ··· − 79u + 11
c
11
, c
12
u
24
+ 17u
22
+ ··· + 8u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 8y
23
+ ··· + 8y + 1
c
2
, c
7
y
24
− 10y
23
+ ··· − 21y + 1
c
3
y
24
+ 12y
23
+ ··· + 17y + 1
c
4
y
24
+ 12y
23
+ ··· + 14y + 1
c
5
, c
6
, c
11
c
12
y
24
+ 34y
23
+ ··· − 18y + 1
c
8
y
24
+ 15y
23
+ ··· + 4y + 1
c
9
y
24
+ 4y
23
+ ··· + 34y + 1
c
10
y
24
+ 8y
23
+ ··· − 499y + 121
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478478 + 0.833064I
a = 1.115640 − 0.334631I
b = 0.551092 − 0.370175I
0.99760 − 3.52622I 6.24401 + 1.39201I
u = 0.478478 − 0.833064I
a = 1.115640 + 0.334631I
b = 0.551092 + 0.370175I
0.99760 + 3.52622I 6.24401 − 1.39201I
u = −0.262141 + 0.818317I
a = −0.07732 − 1.69834I
b = 1.01437 − 1.27308I
−2.16668 − 4.06335I 2.40315 + 7.26743I
u = −0.262141 − 0.818317I
a = −0.07732 + 1.69834I
b = 1.01437 + 1.27308I
−2.16668 + 4.06335I 2.40315 − 7.26743I
u = −0.548804 + 0.560408I
a = −0.891155 − 0.268928I
b = −0.580288 − 0.855599I
−1.02527 + 1.41995I 11.07258 + 1.55795I
u = −0.548804 − 0.560408I
a = −0.891155 + 0.268928I
b = −0.580288 + 0.855599I
−1.02527 − 1.41995I 11.07258 − 1.55795I
u = 0.284755 + 0.642296I
a = 0.599239 + 0.345710I
b = −0.936541 − 0.296163I
1.34642 + 6.11668I 4.54984 − 8.96982I
u = 0.284755 − 0.642296I
a = 0.599239 − 0.345710I
b = −0.936541 + 0.296163I
1.34642 − 6.11668I 4.54984 + 8.96982I
u = −0.199573 + 0.663075I
a = −2.28261 − 0.36973I
b = 0.140669 − 0.627994I
−3.43628 − 0.70377I 6.83683 + 10.77442I
u = −0.199573 − 0.663075I
a = −2.28261 + 0.36973I
b = 0.140669 + 0.627994I
−3.43628 + 0.70377I 6.83683 − 10.77442I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134486 + 1.349140I
a = 0.144806 − 0.146179I
b = 0.183622 + 0.415970I
−0.76849 + 3.11269I 9.83926 − 7.64985I
u = 0.134486 − 1.349140I
a = 0.144806 + 0.146179I
b = 0.183622 − 0.415970I
−0.76849 − 3.11269I 9.83926 + 7.64985I
u = 0.05132 + 1.42224I
a = 0.21771 − 2.62646I
b = 0.29704 − 1.93684I
−1.66761 − 1.03370I 14.0161 − 3.2121I
u = 0.05132 − 1.42224I
a = 0.21771 + 2.62646I
b = 0.29704 + 1.93684I
−1.66761 + 1.03370I 14.0161 + 3.2121I
u = 0.07622 + 1.63617I
a = 0.101929 + 0.405310I
b = 1.139880 + 0.348041I
−6.71868 + 7.43842I 1.50236 − 7.81320I
u = 0.07622 − 1.63617I
a = 0.101929 − 0.405310I
b = 1.139880 − 0.348041I
−6.71868 − 7.43842I 1.50236 + 7.81320I
u = −0.05868 + 1.65356I
a = 0.686776 + 1.157620I
b = −0.361633 + 0.703637I
−11.70920 − 1.71148I 0.362162 + 1.154218I
u = −0.05868 − 1.65356I
a = 0.686776 − 1.157620I
b = −0.361633 − 0.703637I
−11.70920 + 1.71148I 0.362162 − 1.154218I
u = −0.06218 + 1.68510I
a = −0.54264 + 1.99528I
b = −1.16124 + 1.49277I
−11.09620 − 5.27024I 2.04104 + 1.03200I
u = −0.06218 − 1.68510I
a = −0.54264 − 1.99528I
b = −1.16124 − 1.49277I
−11.09620 + 5.27024I 2.04104 − 1.03200I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07826 + 1.77851I
a = 0.054600 + 1.125900I
b = −0.138538 + 0.855802I
−10.04990 − 1.61550I 0.729320 + 1.178226I
u = −0.07826 − 1.77851I
a = 0.054600 − 1.125900I
b = −0.138538 − 0.855802I
−10.04990 + 1.61550I 0.729320 − 1.178226I
u = 0.184379 + 0.083037I
a = −4.12697 + 3.23979I
b = −0.148424 + 1.017250I
3.52599 − 1.84531I 12.90330 + 1.32554I
u = 0.184379 − 0.083037I
a = −4.12697 − 3.23979I
b = −0.148424 − 1.017250I
3.52599 + 1.84531I 12.90330 − 1.32554I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 4u
23
+ ··· + 4u
2
+ 1)(u
109
− 7u
108
+ ··· + 29u − 1)
c
2
(u
24
− 5u
22
+ ··· + u + 1)(u
109
+ u
108
+ ··· + 328u − 176)
c
3
(u
24
+ 6u
22
+ ··· + u + 1)(u
109
+ u
108
+ ··· + 3264u − 131)
c
4
(u
24
+ 6u
22
+ ··· − 2u + 1)(u
109
+ 3u
108
+ ··· + 39937u − 4076)
c
5
, c
6
(u
24
+ 17u
22
+ ··· − 8u + 1)(u
109
− u
108
+ ··· − 523u − 49)
c
7
(u
24
− 5u
22
+ ··· − u + 1)(u
109
+ u
108
+ ··· + 328u − 176)
c
8
(u
24
+ u
23
+ ··· + 2u
2
+ 1)(u
109
+ 17u
107
+ ··· − 1024u − 512)
c
9
(u
24
+ 2u
22
+ ··· − 2u + 1)(u
109
− 3u
108
+ ··· − 983u − 1829)
c
10
(u
24
− 8u
23
+ ··· − 79u + 11)(u
109
− u
108
+ ··· + 1782u − 113)
c
11
, c
12
(u
24
+ 17u
22
+ ··· + 8u + 1)(u
109
− u
108
+ ··· − 523u − 49)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 8y
23
+ ··· + 8y + 1)(y
109
+ 19y
108
+ ··· + 39y −1)
c
2
, c
7
(y
24
− 10y
23
+ ··· − 21y + 1)(y
109
− 55y
108
+ ··· + 548288y −30976)
c
3
(y
24
+ 12y
23
+ ··· + 17y + 1)
· (y
109
+ 35y
108
+ ··· + 4271638y −17161)
c
4
(y
24
+ 12y
23
+ ··· + 14y + 1)
· (y
109
+ 39y
108
+ ··· + 366066273y −16613776)
c
5
, c
6
, c
11
c
12
(y
24
+ 34y
23
+ ··· − 18y + 1)(y
109
+ 137y
108
+ ··· − 74371y −2401)
c
8
(y
24
+ 15y
23
+ ··· + 4y + 1)
· (y
109
+ 34y
108
+ ··· − 1310720y −262144)
c
9
(y
24
+ 4y
23
+ ··· + 34y + 1)
· (y
109
− 9y
108
+ ··· + 149049445y −3345241)
c
10
(y
24
+ 8y
23
+ ··· − 499y + 121)
· (y
109
+ 3y
108
+ ··· + 2676742y −12769)
23
