11a
281
(K11a
281
)
A knot diagram
1
Linearized knot diagam
6 8 1 10 2 4 11 3 7 5 9
Solving Sequence
4,10
5
7,11
6 9 1 2 3 8
c
4
c
10
c
6
c
9
c
11
c
1
c
3
c
8
c
2
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−41702317014899u
28
− 43018944579853u
27
+ ··· + 142344490041062b − 32762826071390,
− 214382018217017u
28
− 235461945222166u
27
+ ··· + 284688980082124a + 218463983805488,
u
29
− 12u
27
+ ··· + 4u + 4i
I
u
2
= h1.20003 × 10
196
u
67
+ 5.15521 × 10
196
u
66
+ ··· + 5.31191 × 10
195
b − 8.00012 × 10
197
,
2.93592 × 10
198
u
67
+ 1.24026 × 10
199
u
66
+ ··· + 1.06610 × 10
199
a − 1.22115 × 10
200
,
3u
68
+ 16u
67
+ ··· − 121u − 223i
I
u
3
= h4170u
11
+ 9821u
10
+ ··· + 1318b − 848, 60429u
11
+ 266417u
10
+ ··· + 23724a − 45544,
3u
12
+ 5u
11
− 3u
10
− 15u
9
− 10u
8
+ 16u
7
+ 45u
6
+ 35u
5
− 15u
4
− 36u
3
− 10u
2
+ 8u + 4i
I
u
4
= h−u
3
+ b + u, u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− u
2
+ a − 2u − 3, u
8
− 4u
6
+ 5u
4
+ u
3
− u
2
− 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 117 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−4.17 × 10
13
u
28
− 4.30 × 10
13
u
27
+ · · · + 1.42 × 10
14
b − 3.28 ×
10
13
, −2.14 × 10
14
u
28
− 2.35 × 10
14
u
27
+ · · · + 2.85 × 10
14
a + 2.18 ×
10
14
, u
29
− 12u
27
+ · · · + 4u + 4i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
0.753039u
28
+ 0.827085u
27
+ ··· − 5.75342u − 0.767378
0.292968u
28
+ 0.302217u
27
+ ··· + 0.399336u + 0.230166
a
11
=
−u
−u
3
+ u
a
6
=
1.04601u
28
+ 1.12930u
27
+ ··· − 5.35408u − 0.537212
0.292968u
28
+ 0.302217u
27
+ ··· + 0.399336u + 0.230166
a
9
=
0.198212u
28
− 0.192154u
27
+ ··· − 3.96388u + 2.24602
0.345416u
28
+ 0.736164u
27
+ ··· − 1.81377u − 2.24478
a
1
=
−0.725032u
28
+ 0.125199u
27
+ ··· + 5.96387u − 2.97699
0.292968u
28
+ 0.302217u
27
+ ··· + 0.399336u + 0.230166
a
2
=
0.509247u
28
+ 0.788403u
27
+ ··· − 2.80042u − 4.75011
1.07963u
28
+ 0.955979u
27
+ ··· − 4.36333u − 2.25401
a
3
=
0.597496u
28
+ 0.850646u
27
+ ··· − 1.53897u + 0.554680
−0.183225u
28
+ 0.412070u
27
+ ··· − 0.178498u − 0.775938
a
8
=
1.04886u
28
+ 1.10674u
27
+ ··· − 5.79918u − 0.143960
0.757487u
28
+ 0.896403u
27
+ ··· − 1.85681u − 1.51189
a
8
=
1.04886u
28
+ 1.10674u
27
+ ··· − 5.79918u − 0.143960
0.757487u
28
+ 0.896403u
27
+ ··· − 1.85681u − 1.51189
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
234334445013910
71172245020531
u
28
+
29393885069647
71172245020531
u
27
+ ··· −
1325794999050934
71172245020531
u +
786361770134424
71172245020531
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
29
− 8u
28
+ ··· − 26u + 4
c
2
, c
4
, c
8
c
10
u
29
− 12u
27
+ ··· + 4u − 4
c
3
, c
6
u
29
− 2u
28
+ ··· + 15u + 1
c
7
u
29
− 17u
28
+ ··· + 520u − 92
c
9
, c
11
u
29
+ u
28
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
29
+ 16y
28
+ ··· − 356y −16
c
2
, c
4
, c
8
c
10
y
29
− 24y
28
+ ··· + 32y −16
c
3
, c
6
y
29
− 24y
28
+ ··· + 155y −1
c
7
y
29
+ 3y
28
+ ··· − 62088y −8464
c
9
, c
11
y
29
+ 15y
28
+ ··· − 53y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092989 + 1.030980I
a = −1.045850 + 0.532791I
b = 1.200380 − 0.719634I
−2.34877 + 6.13504I −3.24652 − 5.83976I
u = 0.092989 − 1.030980I
a = −1.045850 − 0.532791I
b = 1.200380 + 0.719634I
−2.34877 − 6.13504I −3.24652 + 5.83976I
u = −1.093210 + 0.089149I
a = 0.222968 + 0.946010I
b = 1.37085 − 0.79374I
−6.04162 + 3.07394I −9.12279 − 3.57971I
u = −1.093210 − 0.089149I
a = 0.222968 − 0.946010I
b = 1.37085 + 0.79374I
−6.04162 − 3.07394I −9.12279 + 3.57971I
u = −1.051540 + 0.405368I
a = −0.268647 + 0.851561I
b = 1.232730 − 0.569718I
−5.87192 + 3.62470I −10.59188 − 4.43960I
u = −1.051540 − 0.405368I
a = −0.268647 − 0.851561I
b = 1.232730 + 0.569718I
−5.87192 − 3.62470I −10.59188 + 4.43960I
u = 1.124770 + 0.122076I
a = 0.765930 + 0.269870I
b = 0.400225 − 0.035987I
−2.35736 − 0.14468I −4.20415 + 0.31069I
u = 1.124770 − 0.122076I
a = 0.765930 − 0.269870I
b = 0.400225 + 0.035987I
−2.35736 + 0.14468I −4.20415 − 0.31069I
u = 1.162300 + 0.163964I
a = −0.690487 − 0.803933I
b = −1.375730 + 0.311121I
−8.57749 − 2.95224I −10.14138 + 0.50640I
u = 1.162300 − 0.163964I
a = −0.690487 + 0.803933I
b = −1.375730 − 0.311121I
−8.57749 + 2.95224I −10.14138 − 0.50640I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.132500 + 0.443307I
a = −0.367552 + 0.368736I
b = −0.251678 − 0.659845I
−4.32469 + 5.13774I −3.70899 − 4.15997I
u = −1.132500 − 0.443307I
a = −0.367552 − 0.368736I
b = −0.251678 + 0.659845I
−4.32469 − 5.13774I −3.70899 + 4.15997I
u = −0.191379 + 0.745473I
a = 1.203770 + 0.611915I
b = −0.670826 − 0.350125I
1.16747 − 2.08448I 2.66828 + 2.72024I
u = −0.191379 − 0.745473I
a = 1.203770 − 0.611915I
b = −0.670826 + 0.350125I
1.16747 + 2.08448I 2.66828 − 2.72024I
u = −0.054807 + 0.621332I
a = −1.108420 + 0.565655I
b = 0.996625 + 0.524906I
−1.67478 − 1.54885I −1.065400 + 0.655405I
u = −0.054807 − 0.621332I
a = −1.108420 − 0.565655I
b = 0.996625 − 0.524906I
−1.67478 + 1.54885I −1.065400 − 0.655405I
u = 1.370480 + 0.176714I
a = −0.187638 + 0.535925I
b = −1.71821 − 1.20659I
−10.72490 − 6.90472I −14.4851 + 7.2562I
u = 1.370480 − 0.176714I
a = −0.187638 − 0.535925I
b = −1.71821 + 1.20659I
−10.72490 + 6.90472I −14.4851 − 7.2562I
u = 1.341530 + 0.446549I
a = 0.322309 − 1.193140I
b = 1.162950 + 0.674420I
−6.19793 − 11.41400I −6.14943 + 7.59206I
u = 1.341530 − 0.446549I
a = 0.322309 + 1.193140I
b = 1.162950 − 0.674420I
−6.19793 + 11.41400I −6.14943 − 7.59206I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25402 + 0.72255I
a = 0.517215 + 0.703731I
b = −1.169770 + 0.395148I
−9.23241 − 4.90891I −10.64744 + 3.17644I
u = 1.25402 − 0.72255I
a = 0.517215 − 0.703731I
b = −1.169770 − 0.395148I
−9.23241 + 4.90891I −10.64744 − 3.17644I
u = −1.45508 + 0.18906I
a = −0.598691 − 1.023850I
b = −0.960588 + 0.037736I
−12.41910 + 4.43110I −10.98771 − 3.17812I
u = −1.45508 − 0.18906I
a = −0.598691 + 1.023850I
b = −0.960588 − 0.037736I
−12.41910 − 4.43110I −10.98771 + 3.17812I
u = 0.252564 + 0.409637I
a = 0.395939 + 0.235648I
b = 0.288573 + 0.480574I
−0.394622 − 1.222500I −4.75766 + 5.17356I
u = 0.252564 − 0.409637I
a = 0.395939 − 0.235648I
b = 0.288573 − 0.480574I
−0.394622 + 1.222500I −4.75766 − 5.17356I
u = −1.40162 + 0.60645I
a = −0.220729 − 1.079620I
b = −1.54790 + 0.88008I
−10.4386 + 18.3111I −6.86769 − 9.17372I
u = −1.40162 − 0.60645I
a = −0.220729 + 1.079620I
b = −1.54790 − 0.88008I
−10.4386 − 18.3111I −6.86769 + 9.17372I
u = −0.437045
a = 3.11977
b = 0.0847605
2.60472 20.6160
7
II. I
u
2
= h1.20 × 10
196
u
67
+ 5.16 × 10
196
u
66
+ · · · + 5.31 × 10
195
b − 8.00 ×
10
197
, 2.94 × 10
198
u
67
+ 1.24 × 10
199
u
66
+ · · · + 1.07 × 10
199
a − 1.22 ×
10
200
, 3u
68
+ 16u
67
+ · · · − 121u − 223i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−0.275389u
67
− 1.16336u
66
+ ··· − 15.1864u + 11.4543
−2.25913u
67
− 9.70500u
66
+ ··· − 59.6219u + 150.607
a
11
=
−u
−u
3
+ u
a
6
=
−2.53452u
67
− 10.8684u
66
+ ··· − 74.8083u + 162.061
−2.25913u
67
− 9.70500u
66
+ ··· − 59.6219u + 150.607
a
9
=
0.292498u
67
+ 1.10114u
66
+ ··· + 11.7933u − 17.6526
2.03825u
67
+ 8.49090u
66
+ ··· + 44.8246u − 129.281
a
1
=
1.72493u
67
+ 7.51771u
66
+ ··· + 66.3490u − 101.298
1.82144u
67
+ 7.63740u
66
+ ··· + 41.5956u − 124.562
a
2
=
1.95206u
67
+ 8.24471u
66
+ ··· + 46.3401u − 129.732
2.03002u
67
+ 8.39951u
66
+ ··· + 32.1084u − 139.503
a
3
=
−3.39243u
67
− 14.3105u
66
+ ··· − 62.0909u + 236.473
−4.18269u
67
− 17.6453u
66
+ ··· − 96.2259u + 279.330
a
8
=
−2.78880u
67
− 11.9828u
66
+ ··· − 88.0824u + 178.897
−2.53305u
67
− 10.9013u
66
+ ··· − 69.2773u + 175.348
a
8
=
−2.78880u
67
− 11.9828u
66
+ ··· − 88.0824u + 178.897
−2.53305u
67
− 10.9013u
66
+ ··· − 69.2773u + 175.348
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.63264u
67
+ 19.8135u
66
+ ··· + 132.810u − 264.318
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
9(3u
34
+ 5u
33
+ ··· − 313u − 43)
2
c
2
, c
4
, c
8
c
10
3(3u
68
− 16u
67
+ ··· + 121u − 223)
c
3
, c
6
u
68
− 6u
67
+ ··· − 210229u + 37581
c
7
(u
34
+ 7u
33
+ ··· − 1316u − 99)
2
c
9
, c
11
9(9u
68
+ 148u
67
+ ··· − 31630u − 5631)
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
81(9y
34
+ 167y
33
+ ··· + 5317y + 1849)
2
c
2
, c
4
, c
8
c
10
9(9y
68
− 436y
67
+ ··· − 726903y + 49729)
c
3
, c
6
y
68
− 8y
67
+ ··· − 8820260035y + 1412331561
c
7
(y
34
+ 9y
33
+ ··· − 255568y + 9801)
2
c
9
, c
11
81(81y
68
− 4570y
67
+ ··· + 2.22957 × 10
8
y + 3.17082 × 10
7
)
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01495
a = 8.12625
b = 0.418373
−3.31997 128.500
u = 0.084125 + 0.978412I
a = 0.645453 − 0.352487I
b = −0.078035 + 0.585559I
−0.688971 − 0.534639I −3.37867 + 0.I
u = 0.084125 − 0.978412I
a = 0.645453 + 0.352487I
b = −0.078035 − 0.585559I
−0.688971 + 0.534639I −3.37867 + 0.I
u = 1.022130 + 0.065391I
a = −1.237250 + 0.294836I
b = −1.28088 − 0.75605I
−1.35617 − 1.08274I 0
u = 1.022130 − 0.065391I
a = −1.237250 − 0.294836I
b = −1.28088 + 0.75605I
−1.35617 + 1.08274I 0
u = −0.956268 + 0.146033I
a = −0.857284 − 0.438631I
b = −1.65712 − 0.30481I
−2.95554 + 5.40447I −6.87590 − 8.44285I
u = −0.956268 − 0.146033I
a = −0.857284 + 0.438631I
b = −1.65712 + 0.30481I
−2.95554 − 5.40447I −6.87590 + 8.44285I
u = 0.974936 + 0.357597I
a = 0.340244 − 0.677467I
b = −0.00964 + 2.48814I
−5.95387 − 8.42267I 0
u = 0.974936 − 0.357597I
a = 0.340244 + 0.677467I
b = −0.00964 − 2.48814I
−5.95387 + 8.42267I 0
u = −0.984857 + 0.337672I
a = 0.414598 + 1.058750I
b = 0.340621 − 1.066560I
0.66865 + 3.44265I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984857 − 0.337672I
a = 0.414598 − 1.058750I
b = 0.340621 + 1.066560I
0.66865 − 3.44265I 0
u = 0.403789 + 0.854293I
a = −0.767026 − 1.077830I
b = 1.29616 + 0.77938I
−6.90938 − 1.20549I −8.29824 + 1.65199I
u = 0.403789 − 0.854293I
a = −0.767026 + 1.077830I
b = 1.29616 − 0.77938I
−6.90938 + 1.20549I −8.29824 − 1.65199I
u = −1.123670 + 0.068782I
a = −0.237943 − 0.619176I
b = 0.73333 + 1.28865I
−4.32234 + 4.89818I 0
u = −1.123670 − 0.068782I
a = −0.237943 + 0.619176I
b = 0.73333 − 1.28865I
−4.32234 − 4.89818I 0
u = 0.869999 + 0.009395I
a = −0.486635 − 0.507707I
b = 0.48264 + 1.35416I
−0.688971 − 0.534639I −3.37867 − 1.20172I
u = 0.869999 − 0.009395I
a = −0.486635 + 0.507707I
b = 0.48264 − 1.35416I
−0.688971 + 0.534639I −3.37867 + 1.20172I
u = −1.134910 + 0.070979I
a = −0.365689 − 0.974919I
b = −1.155790 + 0.161103I
−6.25593 − 1.69778I 0
u = −1.134910 − 0.070979I
a = −0.365689 + 0.974919I
b = −1.155790 − 0.161103I
−6.25593 + 1.69778I 0
u = −0.759375 + 0.404771I
a = 1.139510 + 0.580807I
b = 0.78804 − 2.03645I
−0.21933 + 1.79666I −9.10855 − 5.99711I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759375 − 0.404771I
a = 1.139510 − 0.580807I
b = 0.78804 + 2.03645I
−0.21933 − 1.79666I −9.10855 + 5.99711I
u = −0.114864 + 0.846300I
a = 0.833754 − 0.974386I
b = −0.900503 + 0.322826I
−1.72873 + 6.64102I −1.14066 − 7.30703I
u = −0.114864 − 0.846300I
a = 0.833754 + 0.974386I
b = −0.900503 − 0.322826I
−1.72873 − 6.64102I −1.14066 + 7.30703I
u = −1.146880 + 0.244106I
a = −1.79438 + 0.35430I
b = −0.853864 + 0.511152I
−8.00578 + 8.92199I 0
u = −1.146880 − 0.244106I
a = −1.79438 − 0.35430I
b = −0.853864 − 0.511152I
−8.00578 − 8.92199I 0
u = 1.120340 + 0.384558I
a = 0.111110 − 0.624242I
b = 1.185950 + 0.419986I
−2.56983 − 1.25654I 0
u = 1.120340 − 0.384558I
a = 0.111110 + 0.624242I
b = 1.185950 − 0.419986I
−2.56983 + 1.25654I 0
u = 0.569693 + 0.554078I
a = 1.44018 − 0.40603I
b = 0.87062 + 1.29644I
−4.83370 + 4.73328I −5.56628 − 2.61380I
u = 0.569693 − 0.554078I
a = 1.44018 + 0.40603I
b = 0.87062 − 1.29644I
−4.83370 − 4.73328I −5.56628 + 2.61380I
u = 0.265017 + 0.737170I
a = 0.091708 − 1.018770I
b = −0.146604 + 0.691144I
0.66865 − 3.44265I 2.41460 + 6.50572I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265017 − 0.737170I
a = 0.091708 + 1.018770I
b = −0.146604 − 0.691144I
0.66865 + 3.44265I 2.41460 − 6.50572I
u = −0.563838 + 1.100000I
a = 0.588855 + 0.266692I
b = 0.151018 − 0.642744I
−1.35617 + 1.08274I 0
u = −0.563838 − 1.100000I
a = 0.588855 − 0.266692I
b = 0.151018 + 0.642744I
−1.35617 − 1.08274I 0
u = −1.156150 + 0.472820I
a = 0.121369 + 1.326300I
b = 1.010250 − 0.803688I
−1.72873 + 6.64102I 0
u = −1.156150 − 0.472820I
a = 0.121369 − 1.326300I
b = 1.010250 + 0.803688I
−1.72873 − 6.64102I 0
u = −1.030570 + 0.768387I
a = −0.201547 + 0.870543I
b = 0.613952 − 1.108430I
−2.95554 + 5.40447I 0
u = −1.030570 − 0.768387I
a = −0.201547 − 0.870543I
b = 0.613952 + 1.108430I
−2.95554 − 5.40447I 0
u = −0.068549 + 1.287830I
a = −0.810185 − 0.460608I
b = 1.134510 + 0.753190I
−6.18575 − 11.73780I 0
u = −0.068549 − 1.287830I
a = −0.810185 + 0.460608I
b = 1.134510 − 0.753190I
−6.18575 + 11.73780I 0
u = −1.309510 + 0.340214I
a = −0.621421 − 1.131870I
b = −1.57219 + 0.91801I
−11.97080 + 5.03934I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.309510 − 0.340214I
a = −0.621421 + 1.131870I
b = −1.57219 − 0.91801I
−11.97080 − 5.03934I 0
u = −1.287910 + 0.440347I
a = 0.166868 − 0.867618I
b = −1.118380 − 0.115176I
−6.90938 − 1.20549I 0
u = −1.287910 − 0.440347I
a = 0.166868 + 0.867618I
b = −1.118380 + 0.115176I
−6.90938 + 1.20549I 0
u = 1.264220 + 0.532124I
a = 0.076859 − 0.873804I
b = 0.89361 + 1.16318I
−4.32234 − 4.89818I 0
u = 1.264220 − 0.532124I
a = 0.076859 + 0.873804I
b = 0.89361 − 1.16318I
−4.32234 + 4.89818I 0
u = −0.386755 + 0.494676I
a = 1.23844 + 1.06478I
b = −0.060694 − 0.503994I
2.28288 7.45974 + 0.I
u = −0.386755 − 0.494676I
a = 1.23844 − 1.06478I
b = −0.060694 + 0.503994I
2.28288 7.45974 + 0.I
u = 0.120184 + 1.398900I
a = −0.509998 − 0.015882I
b = 0.627531 + 0.109078I
−0.21933 − 1.79666I 0
u = 0.120184 − 1.398900I
a = −0.509998 + 0.015882I
b = 0.627531 − 0.109078I
−0.21933 + 1.79666I 0
u = 1.31493 + 0.53742I
a = −0.289141 + 1.212710I
b = −1.59502 − 0.85850I
−6.18575 − 11.73780I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31493 − 0.53742I
a = −0.289141 − 1.212710I
b = −1.59502 + 0.85850I
−6.18575 + 11.73780I 0
u = −1.32529 + 0.51349I
a = −0.222146 − 0.710598I
b = −1.33116 + 0.54804I
−5.28119 + 6.47716I 0
u = −1.32529 − 0.51349I
a = −0.222146 + 0.710598I
b = −1.33116 − 0.54804I
−5.28119 − 6.47716I 0
u = 0.515511 + 0.032987I
a = 0.64753 + 1.88164I
b = 1.43175 − 0.53223I
−6.25593 + 1.69778I −10.84288 − 2.54059I
u = 0.515511 − 0.032987I
a = 0.64753 − 1.88164I
b = 1.43175 + 0.53223I
−6.25593 − 1.69778I −10.84288 + 2.54059I
u = 1.41121 + 0.51529I
a = −0.079859 + 0.876591I
b = −0.861201 − 0.444000I
−4.83370 − 4.73328I 0
u = 1.41121 − 0.51529I
a = −0.079859 − 0.876591I
b = −0.861201 + 0.444000I
−4.83370 + 4.73328I 0
u = 0.283530 + 0.362246I
a = 2.28902 + 0.53866I
b = −0.593632 − 0.143324I
−2.56983 − 1.25654I −2.66105 + 0.95348I
u = 0.283530 − 0.362246I
a = 2.28902 − 0.53866I
b = −0.593632 + 0.143324I
−2.56983 + 1.25654I −2.66105 − 0.95348I
u = −1.51877 + 0.51486I
a = −0.062077 − 0.706185I
b = −0.862019 + 0.734114I
−5.95387 + 8.42267I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51877 − 0.51486I
a = −0.062077 + 0.706185I
b = −0.862019 − 0.734114I
−5.95387 − 8.42267I 0
u = −0.242253 + 0.308533I
a = 0.44630 − 2.65251I
b = 0.93673 + 1.17077I
−5.28119 − 6.47716I −3.81235 + 1.99791I
u = −0.242253 − 0.308533I
a = 0.44630 + 2.65251I
b = 0.93673 − 1.17077I
−5.28119 + 6.47716I −3.81235 − 1.99791I
u = 1.49349 + 0.67322I
a = −0.225108 + 0.704263I
b = −1.264860 − 0.403964I
−8.00578 − 8.92199I 0
u = 1.49349 − 0.67322I
a = −0.225108 − 0.704263I
b = −1.264860 + 0.403964I
−8.00578 + 8.92199I 0
u = 1.65262 + 0.39491I
a = 0.077126 + 0.559808I
b = −0.864364 + 0.178088I
−11.97080 + 5.03934I 0
u = 1.65262 − 0.39491I
a = 0.077126 − 0.559808I
b = −0.864364 − 0.178088I
−11.97080 − 5.03934I 0
u = −2.85887
a = 0.148014
b = 1.00010
−3.31997 0
17
III. I
u
3
= h4170u
11
+ 9821u
10
+ · · · + 1318b − 848, 60429u
11
+ 266417u
10
+
· · · + 23724a − 45544, 3u
12
+ 5u
11
+ · · · + 8u + 4i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−2.54717u
11
− 11.2299u
10
+ ··· + 29.6340u + 1.91974
−3.16388u
11
− 7.45144u
10
+ ··· + 16.9590u + 0.643399
a
11
=
−u
−u
3
+ u
a
6
=
−5.71105u
11
− 18.6813u
10
+ ··· + 46.5931u + 2.56314
−3.16388u
11
− 7.45144u
10
+ ··· + 16.9590u + 0.643399
a
9
=
−2.28746u
11
+ 5.09169u
10
+ ··· − 52.3658u − 25.1053
24.7413u
11
+ 29.8174u
10
+ ··· − 9.18968u + 17.4972
a
1
=
−9.64285u
11
− 18.4134u
10
+ ··· + 36.7907u + 4.46412
−10.9256u
11
− 14.9294u
10
+ ··· + 21.2686u + 3.55994
a
2
=
−12.9909u
11
− 37.2805u
10
+ ··· + 102.002u + 20.0754
−12.9856u
11
− 29.9302u
10
+ ··· + 60.8786u + 3.42489
a
3
=
−9.09543u
11
− 25.3812u
10
+ ··· + 93.8650u + 34.7039
3.10470u
11
− 9.30880u
10
+ ··· + 67.2762u + 27.0334
a
8
=
−3.07069u
11
− 16.1858u
10
+ ··· + 47.2532u + 3.75282
−0.291351u
11
− 1.85812u
10
+ ··· + 10.9272u + 4.25493
a
8
=
−3.07069u
11
− 16.1858u
10
+ ··· + 47.2532u + 3.75282
−0.291351u
11
− 1.85812u
10
+ ··· + 10.9272u + 4.25493
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
507188
53379
u
11
−
3141961
160137
u
10
+ ··· −
5552344
53379
u −
19591552
160137
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(3u
6
− 2u
5
+ 7u
4
− u
3
+ 5u
2
+ 1)
2
c
2
, c
10
3(3u
12
− 5u
11
+ ··· − 8u + 4)
c
3
, c
6
u
12
+ 5u
11
+ ··· − 5u + 3
c
4
, c
8
3(3u
12
+ 5u
11
+ ··· + 8u + 4)
c
5
9(3u
6
+ 2u
5
+ 7u
4
+ u
3
+ 5u
2
+ 1)
2
c
7
(u
6
− 3u
5
+ 5u
4
− 7u
3
+ 9u
2
− 10u + 9)
2
c
9
, c
11
9(9u
12
− 11u
11
+ ··· − 2u + 3)
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
81(9y
6
+ 38y
5
+ 75y
4
+ 75y
3
+ 39y
2
+ 10y + 1)
2
c
2
, c
4
, c
8
c
10
9(9y
12
− 43y
11
+ ··· − 144y + 16)
c
3
, c
6
y
12
+ 3y
11
+ ··· + 323y + 9
c
7
(y
6
+ y
5
+ y
4
− y
3
+ 31y
2
+ 62y + 81)
2
c
9
, c
11
81(81y
12
+ 95y
11
+ ··· + 20y + 9)
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.794683 + 0.322780I
a = 0.964563 + 0.565969I
b = 0.98698 − 1.80455I
0.26321 + 1.57785I 5.58560 − 0.74731I
u = −0.794683 − 0.322780I
a = 0.964563 − 0.565969I
b = 0.98698 + 1.80455I
0.26321 − 1.57785I 5.58560 + 0.74731I
u = −0.744705 + 0.252741I
a = −1.000590 + 0.254282I
b = 0.42147 − 1.53855I
−6.15131 + 7.24013I −9.06270 − 5.78437I
u = −0.744705 − 0.252741I
a = −1.000590 − 0.254282I
b = 0.42147 + 1.53855I
−6.15131 − 7.24013I −9.06270 + 5.78437I
u = −0.272046 + 1.252650I
a = 0.447545 + 0.053587I
b = −0.069213 − 0.195664I
0.26321 + 1.57785I 5.58560 − 0.74731I
u = −0.272046 − 1.252650I
a = 0.447545 − 0.053587I
b = −0.069213 + 0.195664I
0.26321 − 1.57785I 5.58560 + 0.74731I
u = −1.106930 + 0.691135I
a = −0.164599 + 0.949619I
b = 0.754119 − 0.959663I
−2.33657 + 4.85586I 0.31456 − 2.62742I
u = −1.106930 − 0.691135I
a = −0.164599 − 0.949619I
b = 0.754119 + 0.959663I
−2.33657 − 4.85586I 0.31456 + 2.62742I
u = 0.669060 + 0.005462I
a = 1.186220 − 0.719007I
b = 1.57189 − 0.45536I
−2.33657 − 4.85586I 0.31456 + 2.62742I
u = 0.669060 − 0.005462I
a = 1.186220 + 0.719007I
b = 1.57189 + 0.45536I
−2.33657 + 4.85586I 0.31456 − 2.62742I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41598 + 0.57815I
a = −0.044254 + 0.717304I
b = −1.165250 − 0.513557I
−6.15131 − 7.24013I −9.06270 + 5.78437I
u = 1.41598 − 0.57815I
a = −0.044254 − 0.717304I
b = −1.165250 + 0.513557I
−6.15131 + 7.24013I −9.06270 − 5.78437I
22
IV. I
u
4
= h−u
3
+ b + u, u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− u
2
+ a − 2u − 3, u
8
−
4u
6
+ 5u
4
+ u
3
− u
2
− 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 5u
3
+ u
2
+ 2u + 3
u
3
− u
a
11
=
−u
−u
3
+ u
a
6
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 4u
3
+ u
2
+ u + 3
u
3
− u
a
9
=
−2u
7
+ 7u
5
− u
4
− 7u
3
+ 3
0
a
1
=
2u
7
− 2u
6
− 8u
5
+ 6u
4
+ 9u
3
− 3u
2
− 3u − 5
−u
3
+ u
a
2
=
u
7
− 4u
5
+ u
4
+ 4u
3
− u
2
− 2
u
6
− 2u
4
− u
3
+ 2u + 1
a
3
=
−u
6
− u
5
+ 2u
4
+ 2u
3
− u
2
− u − 1
−u
6
+ 2u
4
− u
2
a
8
=
−u
7
+ u
6
+ 5u
5
− 3u
4
− 6u
3
+ u
2
+ u + 3
u
7
− 2u
5
+ u
3
a
8
=
−u
7
+ u
6
+ 5u
5
− 3u
4
− 6u
3
+ u
2
+ u + 3
u
7
− 2u
5
+ u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
7
− 7u
6
− 34u
5
+ 28u
4
+ 44u
3
− 23u
2
− 14u − 22
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 3u
7
+ 6u
6
+ 9u
5
+ 8u
4
+ 7u
3
+ 4u
2
+ 2u + 1
c
2
, c
10
u
8
− 4u
6
+ 5u
4
− u
3
− u
2
+ 2u − 1
c
3
, c
6
u
8
+ u
6
+ u
4
+ 4u
3
+ 5u
2
+ 4u + 1
c
4
, c
8
u
8
− 4u
6
+ 5u
4
+ u
3
− u
2
− 2u − 1
c
5
u
8
− 3u
7
+ 6u
6
− 9u
5
+ 8u
4
− 7u
3
+ 4u
2
− 2u + 1
c
7
u
8
+ 4u
7
+ 10u
6
+ 15u
5
+ 23u
4
+ 31u
3
+ 21u
2
+ 5u − 1
c
9
, c
11
u
8
+ u
7
− 2u
6
− 3u
5
− u
4
+ 2u
3
+ 2u
2
− 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
+ 3y
7
− 2y
6
− 19y
5
− 24y
4
− 9y
3
+ 4y
2
+ 4y + 1
c
2
, c
4
, c
8
c
10
y
8
− 8y
7
+ 26y
6
− 42y
5
+ 31y
4
− 3y
3
− 5y
2
− 2y + 1
c
3
, c
6
y
8
+ 2y
7
+ 3y
6
+ 12y
5
+ 13y
4
− 4y
3
− 5y
2
− 6y + 1
c
7
y
8
+ 4y
7
+ 26y
6
+ 29y
5
− 23y
4
− 165y
3
+ 85y
2
− 67y + 1
c
9
, c
11
y
8
− 5y
7
+ 8y
6
− 5y
5
+ 3y
4
− 4y
3
+ 6y
2
− 4y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29302
a = 1.15106
b = 0.868767
−3.51228 −12.4280
u = 1.244870 + 0.382035I
a = 0.076911 − 0.739194I
b = 0.139250 + 1.338340I
−5.40373 − 6.46685I −9.03927 + 7.27263I
u = 1.244870 − 0.382035I
a = 0.076911 + 0.739194I
b = 0.139250 − 1.338340I
−5.40373 + 6.46685I −9.03927 − 7.27263I
u = −0.213724 + 0.605076I
a = 0.588443 + 0.997522I
b = 0.438706 − 0.743690I
0.792434 + 1.108790I 2.96197 − 2.81670I
u = −0.213724 − 0.605076I
a = 0.588443 − 0.997522I
b = 0.438706 + 0.743690I
0.792434 − 1.108790I 2.96197 + 2.81670I
u = −1.399610 + 0.181081I
a = −0.542533 − 0.395115I
b = −1.20440 + 0.87714I
−9.65027 + 6.44768I −7.33532 − 4.67890I
u = −1.399610 − 0.181081I
a = −0.542533 + 0.395115I
b = −1.20440 − 0.87714I
−9.65027 − 6.44768I −7.33532 + 4.67890I
u = −0.556101
a = 2.60330
b = 0.384128
2.42660 −24.7470
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
81(3u
6
− 2u
5
+ 7u
4
− u
3
+ 5u
2
+ 1)
2
· (u
8
+ 3u
7
+ 6u
6
+ 9u
5
+ 8u
4
+ 7u
3
+ 4u
2
+ 2u + 1)
· (u
29
− 8u
28
+ ··· − 26u + 4)(3u
34
+ 5u
33
+ ··· − 313u − 43)
2
c
2
, c
10
9(u
8
− 4u
6
+ ··· + 2u − 1)(3u
12
− 5u
11
+ ··· − 8u + 4)
· (u
29
− 12u
27
+ ··· + 4u − 4)(3u
68
− 16u
67
+ ··· + 121u − 223)
c
3
, c
6
(u
8
+ u
6
+ u
4
+ 4u
3
+ 5u
2
+ 4u + 1)(u
12
+ 5u
11
+ ··· − 5u + 3)
· (u
29
− 2u
28
+ ··· + 15u + 1)(u
68
− 6u
67
+ ··· − 210229u + 37581)
c
4
, c
8
9(u
8
− 4u
6
+ ··· − 2u − 1)(3u
12
+ 5u
11
+ ··· + 8u + 4)
· (u
29
− 12u
27
+ ··· + 4u − 4)(3u
68
− 16u
67
+ ··· + 121u − 223)
c
5
81(3u
6
+ 2u
5
+ 7u
4
+ u
3
+ 5u
2
+ 1)
2
· (u
8
− 3u
7
+ 6u
6
− 9u
5
+ 8u
4
− 7u
3
+ 4u
2
− 2u + 1)
· (u
29
− 8u
28
+ ··· − 26u + 4)(3u
34
+ 5u
33
+ ··· − 313u − 43)
2
c
7
(u
6
− 3u
5
+ 5u
4
− 7u
3
+ 9u
2
− 10u + 9)
2
· (u
8
+ 4u
7
+ 10u
6
+ 15u
5
+ 23u
4
+ 31u
3
+ 21u
2
+ 5u − 1)
· (u
29
− 17u
28
+ ··· + 520u − 92)(u
34
+ 7u
33
+ ··· − 1316u − 99)
2
c
9
, c
11
81(u
8
+ u
7
− 2u
6
− 3u
5
− u
4
+ 2u
3
+ 2u
2
− 1)
· (9u
12
− 11u
11
+ ··· − 2u + 3)(u
29
+ u
28
+ ··· + u − 1)
· (9u
68
+ 148u
67
+ ··· − 31630u − 5631)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
6561(9y
6
+ 38y
5
+ 75y
4
+ 75y
3
+ 39y
2
+ 10y + 1)
2
· (y
8
+ 3y
7
− 2y
6
− 19y
5
− 24y
4
− 9y
3
+ 4y
2
+ 4y + 1)
· (y
29
+ 16y
28
+ ··· − 356y −16)
· (9y
34
+ 167y
33
+ ··· + 5317y + 1849)
2
c
2
, c
4
, c
8
c
10
81(y
8
− 8y
7
+ 26y
6
− 42y
5
+ 31y
4
− 3y
3
− 5y
2
− 2y + 1)
· (9y
12
− 43y
11
+ ··· − 144y + 16)(y
29
− 24y
28
+ ··· + 32y −16)
· (9y
68
− 436y
67
+ ··· − 726903y + 49729)
c
3
, c
6
(y
8
+ 2y
7
+ 3y
6
+ 12y
5
+ 13y
4
− 4y
3
− 5y
2
− 6y + 1)
· (y
12
+ 3y
11
+ ··· + 323y + 9)(y
29
− 24y
28
+ ··· + 155y −1)
· (y
68
− 8y
67
+ ··· − 8820260035y + 1412331561)
c
7
(y
6
+ y
5
+ y
4
− y
3
+ 31y
2
+ 62y + 81)
2
· (y
8
+ 4y
7
+ 26y
6
+ 29y
5
− 23y
4
− 165y
3
+ 85y
2
− 67y + 1)
· (y
29
+ 3y
28
+ ··· − 62088y −8464)
· (y
34
+ 9y
33
+ ··· − 255568y + 9801)
2
c
9
, c
11
6561(y
8
− 5y
7
+ 8y
6
− 5y
5
+ 3y
4
− 4y
3
+ 6y
2
− 4y + 1)
· (81y
12
+ 95y
11
+ ··· + 20y + 9)(y
29
+ 15y
28
+ ··· − 53y −1)
· (81y
68
− 4570y
67
+ ··· + 222956684y + 31708161)
28
